diff --git a/.gitignore b/.gitignore index 72364f99f..6321dc27f 100644 --- a/.gitignore +++ b/.gitignore @@ -87,3 +87,16 @@ ENV/ # Rope project settings .ropeproject + + +# Emacs +*~ + + +# Temporary data files +notebooks/recipeitems-latest.json +notebooks/FremontBridge.csv +notebooks/gistemp250.nc +notebooks/marathon-data.csv +notebooks/my_figure.png +notebooks/hello.png \ No newline at end of file diff --git a/.gitmodules b/.gitmodules new file mode 100644 index 000000000..279a902c3 --- /dev/null +++ b/.gitmodules @@ -0,0 +1,6 @@ +[submodule "website/plugins/ipynb"] + path = website/plugins/ipynb + url = git://github.com/danielfrg/pelican-ipynb.git +[submodule "website/plugins/pelican-plugins"] + path = website/plugins/pelican-plugins + url = git://github.com/getpelican/pelican-plugins.git diff --git a/LICENSE b/LICENSE-CODE similarity index 100% rename from LICENSE rename to LICENSE-CODE diff --git a/LICENSE-TEXT b/LICENSE-TEXT new file mode 100644 index 000000000..30b08e74d --- /dev/null +++ b/LICENSE-TEXT @@ -0,0 +1,308 @@ +Creative Commons Legal Code + +Attribution-NonCommercial-NoDerivs 3.0 Unported + + CREATIVE COMMONS CORPORATION IS NOT A LAW FIRM AND DOES NOT PROVIDE + LEGAL SERVICES. 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For the avoidance of doubt, + this trademark restriction does not form part of this License. + + Creative Commons may be contacted at https://creativecommons.org/. diff --git a/README.md b/README.md index 9548d1294..165a2b39d 100644 --- a/README.md +++ b/README.md @@ -1,31 +1,58 @@ -# Python Data Science Handbook Supplemental Materials +# Python Data Science Handbook -Supplemental materials for my OReilly project, the -[Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) +[![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/jakevdp/PythonDataScienceHandbook/master?filepath=notebooks%2FIndex.ipynb) +[![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/Index.ipynb) -![cover image](cover-early-release.jpg) +This repository contains the entire [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do), in the form of (free!) Jupyter notebooks. -See also the free companion project, [A Whirlwind Tour of Python](https://github.com/jakevdp/WhirlwindTourOfPython). +![cover image](notebooks/figures/PDSH-cover.png) +## How to Use this Book -## Code Listings +- Read the book in its entirety online at https://jakevdp.github.io/PythonDataScienceHandbook/ -All the code from the book can be found in [code_listings](code_listings). -The code is in IPython notebooks, organized by book chapter and section. +- Run the code using the Jupyter notebooks available in this repository's [notebooks](notebooks) directory. +- Launch executable versions of these notebooks using [Google Colab](http://colab.research.google.com): [![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/Index.ipynb) -## Figure Appendix +- Launch a live notebook server with these notebooks using [binder](https://beta.mybinder.org/): [![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/jakevdp/PythonDataScienceHandbook/master?filepath=notebooks%2FIndex.ipynb) -Nearly every figure used in the book was generated using Matplotlib. -Most figures are generated by the code within the text; those few that are not -can be found in the online-only [Figure Appendix](figure_appendix/06.00-Figure-Code.ipynb) +- Buy the printed book through [O'Reilly Media](http://shop.oreilly.com/product/0636920034919.do) +## About -## Full Notebooks +The book was written and tested with Python 3.5, though other Python versions (including Python 2.7) should work in nearly all cases. -I am still negotiating with OReilly the open publication of the full manuscript in the form of Jupyter notebooks. Stay tuned! +The book introduces the core libraries essential for working with data in Python: particularly [IPython](http://ipython.org), [NumPy](http://numpy.org), [Pandas](http://pandas.pydata.org), [Matplotlib](http://matplotlib.org), [Scikit-Learn](http://scikit-learn.org), and related packages. +Familiarity with Python as a language is assumed; if you need a quick introduction to the language itself, see the free companion project, +[A Whirlwind Tour of Python](https://github.com/jakevdp/WhirlwindTourOfPython): it's a fast-paced introduction to the Python language aimed at researchers and scientists. + +See [Index.ipynb](http://nbviewer.jupyter.org/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/Index.ipynb) for an index of the notebooks available to accompany the text. + +## Software + +The code in the book was tested with Python 3.5, though most (but not all) will also work correctly with Python 2.7 and other older Python versions. + +The packages I used to run the code in the book are listed in [requirements.txt](requirements.txt) (Note that some of these exact version numbers may not be available on your platform: you may have to tweak them for your own use). +To install the requirements using [conda](http://conda.pydata.org), run the following at the command-line: + +``` +$ conda install --file requirements.txt +``` + +To create a stand-alone environment named ``PDSH`` with Python 3.5 and all the required package versions, run the following: + +``` +$ conda create -n PDSH python=3.5 --file requirements.txt +``` + +You can read more about using conda environments in the [Managing Environments](http://conda.pydata.org/docs/using/envs.html) section of the conda documentation. ## License -The code here is released under the [MIT license](LICENSE). Read more at the [Open Source Initiative](https://opensource.org/licenses/MIT). \ No newline at end of file +### Code +The code in this repository, including all code samples in the notebooks listed above, is released under the [MIT license](LICENSE-CODE). Read more at the [Open Source Initiative](https://opensource.org/licenses/MIT). + +### Text +The text content of the book is released under the [CC-BY-NC-ND license](LICENSE-TEXT). Read more at [Creative Commons](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode). diff --git a/code_listings/01.07-Timing-and-Profiling.ipynb b/code_listings/01.07-Timing-and-Profiling.ipynb deleted file mode 100644 index fe5771d59..000000000 --- a/code_listings/01.07-Timing-and-Profiling.ipynb +++ /dev/null @@ -1,298 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Profiling and Timing Code" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "100000 loops, best of 3: 1.54 µs per loop\n" - ] - } - ], - "source": [ - "%timeit sum(range(100))" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1 loops, best of 3: 407 ms per loop\n" - ] - } - ], - "source": [ - "%%timeit\n", - "total = 0\n", - "for i in range(1000):\n", - " for j in range(1000):\n", - " total += i * (-1) ** j" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "100 loops, best of 3: 1.9 ms per loop\n" - ] - } - ], - "source": [ - "import random\n", - "L = [random.random() for i in range(100000)]\n", - "%timeit L.sort()" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "sorting an unsorted list:\n", - "CPU times: user 40.6 ms, sys: 896 µs, total: 41.5 ms\n", - "Wall time: 41.5 ms\n" - ] - } - ], - "source": [ - "import random\n", - "L = [random.random() for i in range(100000)]\n", - "print(\"sorting an unsorted list:\")\n", - "%time L.sort()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "sorting an already sorted list:\n", - "CPU times: user 8.18 ms, sys: 10 µs, total: 8.19 ms\n", - "Wall time: 8.24 ms\n" - ] - } - ], - "source": [ - "print(\"sorting an already sorted list:\")\n", - "%time L.sort()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 504 ms, sys: 979 µs, total: 505 ms\n", - "Wall time: 505 ms\n" - ] - } - ], - "source": [ - "%%time\n", - "total = 0\n", - "for i in range(1000):\n", - " for j in range(1000):\n", - " total += i * (-1) ** j" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "def sum_of_lists(N):\n", - " total = 0\n", - " for i in range(5):\n", - " L = [j ^ (j >> i) for j in range(N)]\n", - " total += sum(L)\n", - " return total" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " " - ] - } - ], - "source": [ - "%prun sum_of_lists(1000000)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%load_ext line_profiler" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%lprun -f sum_of_lists sum_of_lists(5000)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%load_ext memory_profiler" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "peak memory: 100.08 MiB, increment: 61.36 MiB\n" - ] - } - ], - "source": [ - "%memit sum_of_lists(1000000)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Overwriting mprun_demo.py\n" - ] - } - ], - "source": [ - "%%file mprun_demo.py\n", - "def sum_of_lists(N):\n", - " total = 0\n", - " for i in range(5):\n", - " L = [j ^ (j >> i) for j in range(N)]\n", - " total += sum(L)\n", - " del L # remove reference to L\n", - " return total" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n" - ] - } - ], - "source": [ - "from mprun_demo import sum_of_lists\n", - "%mprun -f sum_of_lists sum_of_lists(1000000)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.1" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/code_listings/02.00-Introduction-to-NumPy.ipynb b/code_listings/02.00-Introduction-to-NumPy.ipynb deleted file mode 100644 index 911e4c02d..000000000 --- a/code_listings/02.00-Introduction-to-NumPy.ipynb +++ /dev/null @@ -1,66 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Introduction to NumPy" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "'1.11.1'" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import numpy\n", - "numpy.__version__" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.1" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/code_listings/02.01-Understanding-Data-Types.ipynb b/code_listings/02.01-Understanding-Data-Types.ipynb deleted file mode 100644 index 96d1f9847..000000000 --- a/code_listings/02.01-Understanding-Data-Types.ipynb +++ /dev/null @@ -1,521 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Understanding Data Types in Python" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "L = list(range(10))\n", - "L" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "int" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "type(L[0])" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "L2 = [str(c) for c in L]\n", - "L2" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "str" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "type(L2[0])" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[bool, str, float, int]" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "L3 = [True, \"2\", 3.0, 4]\n", - "[type(item) for item in L3]" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import array\n", - "L = list(range(10))\n", - "A = array.array('i', L)\n", - "A" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([1, 4, 2, 5, 3])" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# integer array:\n", - "np.array([1, 4, 2, 5, 3])" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 3.14, 4. , 2. , 3. ])" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.array([3.14, 4, 2, 3])" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 1., 2., 3., 4.], dtype=float32)" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.array([1, 2, 3, 4], dtype='float32')" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[2, 3, 4],\n", - " [4, 5, 6],\n", - " [6, 7, 8]])" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# nested lists result in multi-dimensional arrays\n", - "np.array([range(i, i + 3) for i in [2, 4, 6]])" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create a length-10 integer array filled with zeros\n", - "np.zeros(10, dtype=int)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 1., 1., 1., 1., 1.],\n", - " [ 1., 1., 1., 1., 1.],\n", - " [ 1., 1., 1., 1., 1.]])" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create a (3 x 5) floating-point array filled with ones\n", - "np.ones((3, 5), dtype=float)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 3.14, 3.14, 3.14, 3.14, 3.14],\n", - " [ 3.14, 3.14, 3.14, 3.14, 3.14],\n", - " [ 3.14, 3.14, 3.14, 3.14, 3.14]])" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create a (3 x 5) array filled with 3.14\n", - "np.full((3, 5), 3.14)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create an array filled with a linear sequence\n", - "# Starting at 0, ending at 20, stepping by 2\n", - "# (this is similar to the built-in range() function)\n", - "np.arange(0, 20, 2)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0. , 0.25, 0.5 , 0.75, 1. ])" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create an array of 5 values evenly spaced between 0 and 1\n", - "np.linspace(0, 1, 5)" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 0.99844933, 0.52183819, 0.22421193],\n", - " [ 0.08007488, 0.45429293, 0.20941444],\n", - " [ 0.14360941, 0.96910973, 0.946117 ]])" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create a (3 x 3) array of uniformly-distributed\n", - "# random values between 0 and 1\n", - "np.random.random((3, 3))" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 1.51772646, 0.39614948, -0.10634696],\n", - " [ 0.25671348, 0.00732722, 0.37783601],\n", - " [ 0.68446945, 0.15926039, -0.70744073]])" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create a (3 x 3) array of normally-distributed random values\n", - "# with mean 0 and standard deviation 1\n", - "np.random.normal(0, 1, (3, 3))" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[2, 3, 4],\n", - " [5, 7, 8],\n", - " [0, 5, 0]])" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create a (3 x 3) array of random integers in the interval\n", - "# [0, 10)\n", - "np.random.randint(0, 10, (3, 3))" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 1., 0., 0.],\n", - " [ 0., 1., 0.],\n", - " [ 0., 0., 1.]])" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create a (3 x 3) identity matrix\n", - "np.eye(3)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 1., 1., 1.])" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create an uninitialized array of 3 integers\n", - "# The values will be whatever happens to already exist at that memory location\n", - "np.empty(3)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.1" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/code_listings/02.03-Computation-on-arrays-ufuncs.ipynb b/code_listings/02.03-Computation-on-arrays-ufuncs.ipynb deleted file mode 100644 index 755a6f0eb..000000000 --- a/code_listings/02.03-Computation-on-arrays-ufuncs.ipynb +++ /dev/null @@ -1,716 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Computation on NumPy Arrays: Universal Functions" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0.16666667, 1. , 0.25 , 0.25 , 0.125 ])" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import numpy as np\n", - "np.random.seed(0)\n", - "\n", - "def compute_reciporicals(values):\n", - " output = np.empty(len(values))\n", - " for i in range(len(values)):\n", - " output[i] = 1.0 / values[i]\n", - " return output\n", - " \n", - "values = np.random.randint(1, 10, size=5)\n", - "compute_reciporicals(values)" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1 loop, best of 3: 2.91 s per loop\n" - ] - } - ], - "source": [ - "big_array = np.random.randint(1, 100, size=1000000)\n", - "%timeit compute_reciporicals(big_array)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 0.16666667 1. 0.25 0.25 0.125 ]\n", - "[ 0.16666667 1. 0.25 0.25 0.125 ]\n" - ] - } - ], - "source": [ - "print(compute_reciporicals(values))\n", - "print(1.0 / values)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "100 loops, best of 3: 4.6 ms per loop\n" - ] - } - ], - "source": [ - "%timeit (1.0 / big_array)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0. , 0.5 , 0.66666667, 0.75 , 0.8 ])" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.arange(5) / np.arange(1, 6)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 1, 2, 4],\n", - " [ 8, 16, 32],\n", - " [ 64, 128, 256]])" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x = np.arange(9).reshape((3, 3))\n", - "2 ** x" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "x = [0 1 2 3]\n", - "x + 5 = [5 6 7 8]\n", - "x - 5 = [-5 -4 -3 -2]\n", - "x * 2 = [0 2 4 6]\n", - "x / 2 = [ 0. 0.5 1. 1.5]\n", - "x // 2 = [0 0 1 1]\n" - ] - } - ], - "source": [ - "x = np.arange(4)\n", - "print(\"x =\", x)\n", - "print(\"x + 5 =\", x + 5)\n", - "print(\"x - 5 =\", x - 5)\n", - "print(\"x * 2 =\", x * 2)\n", - "print(\"x / 2 =\", x / 2)\n", - "print(\"x // 2 =\", x // 2) # floor division" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-x = [ 0 -1 -2 -3]\n", - "x ** 2 = [0 1 4 9]\n", - "x % 2 = [0 1 0 1]\n" - ] - } - ], - "source": [ - "print(\"-x = \", -x)\n", - "print(\"x ** 2 = \", x ** 2)\n", - "print(\"x % 2 = \", x % 2)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([-1. , -2.25, -4. , -6.25])" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "-(0.5*x + 1) ** 2" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([2, 3, 4, 5])" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.add(x, 2)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([2, 1, 0, 1, 2])" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x = np.array([-2, -1, 0, 1, 2])\n", - "abs(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([2, 1, 0, 1, 2])" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.absolute(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([2, 1, 0, 1, 2])" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.abs(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 5., 5., 2., 1.])" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x = np.array([3 - 4j, 4 - 3j, 2 + 0j, 0 + 1j])\n", - "np.abs(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "theta = np.linspace(0, np.pi, 3)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "theta = [ 0. 1.57079633 3.14159265]\n", - "sin(theta) = [ 0.00000000e+00 1.00000000e+00 1.22464680e-16]\n", - "cos(theta) = [ 1.00000000e+00 6.12323400e-17 -1.00000000e+00]\n", - "tan(theta) = [ 0.00000000e+00 1.63312394e+16 -1.22464680e-16]\n" - ] - } - ], - "source": [ - "print(\"theta = \", theta)\n", - "print(\"sin(theta) = \", np.sin(theta))\n", - "print(\"cos(theta) = \", np.cos(theta))\n", - "print(\"tan(theta) = \", np.tan(theta))" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "x = [-1, 0, 1]\n", - "arcsin(x) = [-1.57079633 0. 1.57079633]\n", - "arccos(x) = [ 3.14159265 1.57079633 0. ]\n", - "arctan(x) = [-0.78539816 0. 0.78539816]\n" - ] - } - ], - "source": [ - "x = [-1, 0, 1]\n", - "print(\"x = \", x)\n", - "print(\"arcsin(x) = \", np.arcsin(x))\n", - "print(\"arccos(x) = \", np.arccos(x))\n", - "print(\"arctan(x) = \", np.arctan(x))" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "x = [1, 2, 3]\n", - "e^x = [ 2.71828183 7.3890561 20.08553692]\n", - "2^x = [ 2. 4. 8.]\n", - "3^x = [ 3 9 27]\n" - ] - } - ], - "source": [ - "x = [1, 2, 3]\n", - "print(\"x =\", x)\n", - "print(\"e^x =\", np.exp(x))\n", - "print(\"2^x =\", np.exp2(x))\n", - "print(\"3^x =\", np.power(3, x))" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "x = [1, 2, 4, 10]\n", - "ln(x) = [ 0. 0.69314718 1.38629436 2.30258509]\n", - "log2(x) = [ 0. 1. 2. 3.32192809]\n", - "log10(x) = [ 0. 0.30103 0.60205999 1. ]\n" - ] - } - ], - "source": [ - "x = [1, 2, 4, 10]\n", - "print(\"x =\", x)\n", - "print(\"ln(x) =\", np.log(x))\n", - "print(\"log2(x) =\", np.log2(x))\n", - "print(\"log10(x) =\", np.log10(x))" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "exp(x) - 1 = [ 0. 0.0010005 0.01005017 0.10517092]\n", - "log(1 + x) = [ 0. 0.0009995 0.00995033 0.09531018]\n" - ] - } - ], - "source": [ - "x = [0, 0.001, 0.01, 0.1]\n", - "print(\"exp(x) - 1 =\", np.expm1(x))\n", - "print(\"log(1 + x) =\", np.log1p(x))" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from scipy import special" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "gamma(x) = [ 1.00000000e+00 2.40000000e+01 3.62880000e+05]\n", - "ln|gamma(x)| = [ 0. 3.17805383 12.80182748]\n", - "beta(x, 2) = [ 0.5 0.03333333 0.00909091]\n" - ] - } - ], - "source": [ - "# Gamma functions (generalized factorials) & related functions\n", - "x = [1, 5, 10]\n", - "print(\"gamma(x) =\", special.gamma(x))\n", - "print(\"ln|gamma(x)| =\", special.gammaln(x))\n", - "print(\"beta(x, 2) =\", special.beta(x, 2))" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "erf(x) = [ 0. 0.32862676 0.67780119 0.84270079]\n", - "erfc(x) = [ 1. 0.67137324 0.32219881 0.15729921]\n", - "erfinv(x) = [ 0. 0.27246271 0.73286908 inf]\n" - ] - } - ], - "source": [ - "# Error function (Integral of Gaussian)\n", - "# its complement, and its inverse\n", - "x = np.array([0, 0.3, 0.7, 1.0])\n", - "print(\"erf(x) =\", special.erf(x))\n", - "print(\"erfc(x) =\", special.erfc(x))\n", - "print(\"erfinv(x) =\", special.erfinv(x))" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 0. 10. 20. 30. 40.]\n" - ] - } - ], - "source": [ - "x = np.arange(5)\n", - "y = np.empty(5)\n", - "np.multiply(x, 10, out=y)\n", - "print(y)" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 1. 0. 2. 0. 4. 0. 8. 0. 16. 0.]\n" - ] - } - ], - "source": [ - "y = np.zeros(10)\n", - "np.power(2, x, out=y[::2])\n", - "print(y)" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "15" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x = np.arange(1, 6)\n", - "np.add.reduce(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "120" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.multiply.reduce(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 1, 3, 6, 10, 15])" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.add.accumulate(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 1, 2, 6, 24, 120])" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.multiply.accumulate(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": false, - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 1, 2, 3, 4, 5],\n", - " [ 2, 4, 6, 8, 10],\n", - " [ 3, 6, 9, 12, 15],\n", - " [ 4, 8, 12, 16, 20],\n", - " [ 5, 10, 15, 20, 25]])" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x = np.arange(1, 6)\n", - "np.multiply.outer(x, x)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.1" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/code_listings/02.09-Structured-Data-NumPy.ipynb b/code_listings/02.09-Structured-Data-NumPy.ipynb deleted file mode 100644 index cda2448bc..000000000 --- a/code_listings/02.09-Structured-Data-NumPy.ipynb +++ /dev/null @@ -1,378 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Structured Data: NumPy's Structured Arrays" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "name = ['Alice', 'Bob', 'Cathy', 'Doug']\n", - "age = [25, 45, 37, 19]\n", - "weight = [55.0, 85.5, 68.0, 61.5]" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "x = np.zeros(4, dtype=int)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[('name', '\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
OpenHighLowCloseVolume
Date
2004-08-1949.9651.9847.9350.12NaN
2004-08-2050.6954.4950.2054.10NaN
2004-08-2355.3256.6854.4754.65NaN
2004-08-2455.5655.7451.7352.38NaN
2004-08-2552.4353.9551.8952.95NaN
\n", - "" - ], - "text/plain": [ - " Open High Low Close Volume\n", - "Date \n", - "2004-08-19 49.96 51.98 47.93 50.12 NaN\n", - "2004-08-20 50.69 54.49 50.20 54.10 NaN\n", - "2004-08-23 55.32 56.68 54.47 54.65 NaN\n", - "2004-08-24 55.56 55.74 51.73 52.38 NaN\n", - "2004-08-25 52.43 53.95 51.89 52.95 NaN" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from pandas_datareader import data\n", - "\n", - "goog = data.DataReader('GOOG', start='2004', end='2016',\n", - " data_source='google')\n", - "goog.head()" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "goog = goog['Close']" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "import seaborn; seaborn.set()" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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eLa1T7JqZiwG5d2NAJiKKoM9/OIl7/v6tZD9xsHLHDIBcJi0c8cjP88XHDMi9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\n+soPSIxXh1XWz3XRV1t7h8cKZqtVwKp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I/tXpWsrUde30BQghxCjkraqi5l9/QfXPfhoZh021mZg+KXVQ97EnGQf92vtr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\nGIC8tCg8LjellY2cOWNh/2E3ZquDcalRfLTd+7rxGdEYw7V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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "goog.plot(alpha=0.5, style='-')\n", - "goog.resample('BA').mean().plot(style=':')\n", - "goog.asfreq('BA').plot(style='--');\n", - "plt.legend(['input', 'resample', 'asfreq'],\n", - " loc='upper left');" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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51bR+3HpVH6rrjLzw/kEOnSxXJIuDC7UelQqGSqEWQgjh5FQqFTOSYnjg5sHY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\nN2/Ojh07ND+//jJHbm4uzZs3p7q6WvNzq6M5rG/xwIEDjB0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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(2, sharex=True)\n", - "data = goog.iloc[:10]\n", - "\n", - "data.asfreq('D').plot(ax=ax[0], marker='o')\n", - "\n", - "data.asfreq('D', method='bfill').plot(ax=ax[1], style='-o')\n", - "data.asfreq('D', method='ffill').plot(ax=ax[1], style='--o')\n", - "ax[1].legend([\"back-fill\", \"forward-fill\"]);" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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hjDqejLeHI22aepT7/GuTJl/P5PfN57+d9Vhv2jf3LLavr68b8YlXmLy4+Hy5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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(3, sharey=True)\n", - "\n", - "# apply a frequency to the data\n", - "goog = goog.asfreq('D', method='pad')\n", - "\n", - "goog.plot(ax=ax[0])\n", - "goog.shift(900).plot(ax=ax[1])\n", - "goog.tshift(900).plot(ax=ax[2])\n", - "\n", - "# legends and annotations\n", - "local_max = pd.to_datetime('2007-11-05')\n", - "offset = pd.Timedelta(900, 'D')\n", - "\n", - "ax[0].legend(['input'], loc=2)\n", - "ax[0].get_xticklabels()[4].set(weight='heavy', color='red')\n", - "ax[0].axvline(local_max, alpha=0.3, color='red')\n", - "\n", - "ax[1].legend(['shift(900)'], loc=2)\n", - "ax[1].get_xticklabels()[4].set(weight='heavy', color='red')\n", - "ax[1].axvline(local_max + offset, alpha=0.3, color='red')\n", - "\n", - "ax[2].legend(['tshift(900)'], loc=2)\n", - "ax[2].get_xticklabels()[1].set(weight='heavy', color='red')\n", - "ax[2].axvline(local_max + offset, alpha=0.3, color='red');" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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TN8ADznlo7vBi8YV6WdsUOrwfYu3cMRHDejrLm2a0c14UPXSDcw8KKnYSeMfO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\n3AkrUPtYNzSZQnoN8GpH8aR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YZW6ttfXABazdVYovfj0hfTDbNqtkgBJaohgMzF4SiX4O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\ns8WKLX+cR/+C9qIXklwJca4XpW+t/AP3XGvf80A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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ROI = 100 * (goog.tshift(-365) / goog - 1)\n", - "ROI.plot()\n", - "plt.ylabel('% Return on Investment');" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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oI9alHq/MJKtypznncf+w9cmNdc6sOW2AeZXZu0sBnLukErs1N9/ZYprcOtYg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\nX4vfgTqYSFNT4+Jwoier9nFKOB4hkoj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xs3ZDctpMWdnjUHx7vXfpu+kLe9jTvY9/ffE7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\n2X5Po0JhvhUZVn0MzpDEWnhCkBEp9B0ghERHwg2OVje48bn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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rolling = goog.rolling(365, center=True)\n", - "\n", - "data = pd.DataFrame({'input': goog,\n", - " 'one-year rolling_mean': rolling.mean(),\n", - " 'one-year rolling_std': rolling.std()})\n", - "ax = data.plot(style=['-', '--', ':'])\n", - "ax.lines[0].set_alpha(0.3)" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# !curl -o FremontBridge.csv https://data.seattle.gov/api/views/65db-xm6k/rows.csv?accessType=DOWNLOAD" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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Fremont Bridge West SidewalkFremont Bridge East Sidewalk
Date
2012-10-03 00:00:004.09.0
2012-10-03 01:00:004.06.0
2012-10-03 02:00:001.01.0
2012-10-03 03:00:002.03.0
2012-10-03 04:00:006.01.0
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" - ], - "text/plain": [ - " Fremont Bridge West Sidewalk \\\n", - "Date \n", - "2012-10-03 00:00:00 4.0 \n", - "2012-10-03 01:00:00 4.0 \n", - "2012-10-03 02:00:00 1.0 \n", - "2012-10-03 03:00:00 2.0 \n", - "2012-10-03 04:00:00 6.0 \n", - "\n", - " Fremont Bridge East Sidewalk \n", - "Date \n", - "2012-10-03 00:00:00 9.0 \n", - "2012-10-03 01:00:00 6.0 \n", - "2012-10-03 02:00:00 1.0 \n", - "2012-10-03 03:00:00 3.0 \n", - "2012-10-03 04:00:00 1.0 " - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "data = pd.read_csv('FremontBridge.csv', index_col='Date', parse_dates=True)\n", - "data.head()" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "data.columns = ['West', 'East']\n", - "data['Total'] = data.eval('West + East')" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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WestEastTotal
count33544.00000033544.00000033544.000000
mean61.72656853.541706115.268275
std83.21081376.380678144.773983
min0.0000000.0000000.000000
25%8.0000007.00000016.000000
50%33.00000028.00000064.000000
75%80.00000066.000000151.000000
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" - ], - "text/plain": [ - " West East Total\n", - "count 33544.000000 33544.000000 33544.000000\n", - "mean 61.726568 53.541706 115.268275\n", - "std 83.210813 76.380678 144.773983\n", - "min 0.000000 0.000000 0.000000\n", - "25% 8.000000 7.000000 16.000000\n", - "50% 33.000000 28.000000 64.000000\n", - "75% 80.000000 66.000000 151.000000\n", - "max 825.000000 717.000000 1186.000000" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "data.dropna().describe()" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import seaborn; seaborn.set()" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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RLPJEROQUgl6Pgl07oc3PEzuKaAxarVO3xyJPREROUXL8GPI2b0Tat1+LHUU0Rfv2OnV7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\nTExEx44dnR23RvmFcuTm3v6PpKH40mW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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "data.plot()\n", - "plt.ylabel('Hourly Bicycle Count');" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Dh9+XVZks6Bvs5yCRzvNr8bhlTATdj6WbYYb6i7bz5fH47dEy0c4n6ClMYRbP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RzMKSqkADq9IR766ycsmpnHVWcr819EivLIzt+TZ83h2tlrmT+GkdDJl7gfJKwJREVV7EYfC5+P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\nC90y8e/atYsJEyYAMHToUPbv3+/nFgkhhBDdQ7dM/FVVVYSEhHi/12q1u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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "weekly = data.resample('W').sum()\n", - "weekly.plot(style=[':', '--', '-'])\n", - "plt.ylabel('Weekly bicycle count');" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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a/VsoknogIjUVgPNgNd5ohP7CeYf7rq99EfKkJBivXgEAaL87jbDelCHUFVqn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LptitMfPHzDPH574e1cMHLRgB+7NxQ2llBpqwZAaWrkykUjmZIVS3W9DUmSaLK5utlD7xHtnbuu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\nDUluqmooWtYjlzb5+fnccsstX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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "daily = data.resample('D').sum()\n", - "daily.rolling(30, center=True).sum().plot(style=[':', '--', '-'])\n", - "plt.ylabel('mean hourly count');" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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gspmOSL9qDoAUwuhB3vpg9/bF1irHisZoJHXGTPxNjTjKdsY6nIQWcDk5+fJL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\nfOGZjjLlj8QwYAD27Vvxt7TEOpxucR4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2J91lpdQ+8zTOzk6CN29h5k9/wYx77p+uNJkA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1qqqybt06TCaT5j+ImFxCHg+e/Y2Yp1VgGOeIixbM0ypw72vA29KMVeNjHsXk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\nw7dHf0CiMZNalD7S6+dV6PRE3XQrxgmTKHnnLaq++xbLL7uJuvnWdle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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "by_time = data.groupby(data.index.time).mean()\n", - "hourly_ticks = 4 * 60 * 60 * np.arange(6)\n", - "by_time.plot(xticks=hourly_ticks, style=[':', '--', '-']);" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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RVVWFZcuWYdWqVVi6dCmef/55X30iIvp+mkGDoZ84CU1nTqNu88Zwh0M9WLtJ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\nY+bVuBFXw+VxobyhEudbpqH1vcT97z/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QYQAbxq0DWkf+Npcdq8OKw+X02l6v1vHXoRPv\nu04JbSGEEOI+KIqCVhWIVhXYbpsQXR/mRs2478/y79vohBBCiB5EQlsIIYTwExLaQgghhJ+Q0BZC\nCCH8hIS2EEII4ScktIUQQgg/IaEthBBC+AkJbSGEEMJPSGgLIYQQfkJCWwghhPATEtpCCCGEn+jU\ns8cdDgeZmZnU1dVht9tJS0sjMjKStWvXEhAQQFRUFNnZbV9iLoQQQojO61Ro79+/n5CQEN5++22u\nX7/OrFmzMBqNZGRkEBcXR3Z2Nt9++y1Tpkx50PUKIYQQPVanpsenTp3KsmXLAHA6nahUKk6ePElc\nXBwAEydO5OjRow+uSiGEEEJ0LrT1ej1BQUE0NjaybNkyli9fjtvt9qw3GAw0NDQ8sCKFEEIIcR/v\n07506RJLly5l4cKFTJ8+na1bt3rWNTU10bt37w5tJzQ0uLMl9CjSTx0nfdUx0k8dJ33VMdJPXa9T\nI+2rV6/yyiuvsGrVKubMmQNAdHQ0FRUVABw+fJjY2NgHV6UQQgghUNy3z2t30KZNmzh48CDh4eG4\n3W4URSErK4uNGzdit9uJiIhg48aNKIrSFTULIYQQPVKnQlsIIYQQ3U8eriKEEEL4CQltIYQQwk9I\naAshhBB+QkJbCCGE8BNdFtrl5eUYjUYOHDhwx/KZM2eybt26rvpYv5Kfn4/JZGLq1KlMmjQJs9lM\nenq6r8t6KL344ov8+uuvANjtduLi4ti5c6dnvclk4tSpU3fdhs1mY/LkyV1ap6/8+btkMpmIj49n\nxYoVvi7Nr9TV1REbG4vZbMZkMmE2myksLLyjzYoVK3A4HD6q0Pc++ugjXnrpJUwmE4sWLaKqqqrd\ntqWlpTidzm6s7uFwL310rzr9cJWOCA8P58CBA0ybNg2AmpoarFZrV36kX1mzZg0Ae/fupba2loyM\nDB9X9PAaP348x44d44knnqCyspKEhAR+/PFHXn75ZWw2G5cuXcJoNN51G7f+PPFR5O27VF5ezu7d\nu31cmf+Jiopi165d7a5/9913u7Gah8uZM2f4/vvvKSkpAeDUqVOsXbuWsrIyr+0//PBDZs+ejUql\n6s4yfepe++heden0uNFo5Pfff6exsRFofdHI888/D8BXX31FYmIiKSkpZGZm4nA42Lt3L+np6aSl\npTF9+vQHtpP+pLy8/I7wnjBhAgCXL19m8eLFmM1mUlNTqa+vx2az8dprr2EymUhKSuLIkSO+KrvL\njRs3jsrKSqD14T1JSUk0NDTQ2NjI8ePHGTt2LBUVFSQnJ2MymcjKysLpdHLjxg1ef/11TCYTubm5\nPt6L7ldbW0tqaiovvPACBQUFQOusRG1tLQAlJSUUFBRQV1fHzJkzMZvNfPLJJ3z22WfMmzePBQsW\nsGnTJl/uQrf781/BlpeXM2/ePBYuXMi+ffuYPHkyNpvNR9X5Vq9evbh8+TJ79uyhvr4eo9HIF198\nQUVFBYsWLcJsNpOYmMj58+fZs2cPV69e7XGDEW99VFpa2u5xt2DBApYvX87cuXPJycn5v9vv0pE2\nwLPPPss333zDnDlzOHHiBKmpqVRVVVFQUEBZWRl6vZ68vDx2797teZ75jh07OH/+PGlpacyePbur\nS3zoeBsN5ufnYzabSUhI4OjRo2zdupW0tDSuXbvGjh07sFgsnDt3rvuL7SaPP/44Z8+eBaCiooKM\njAzi4+M5cuQI1dXVTJgwgTfeeIPPP/+cvn378v777/Pll1/S0NDAqFGjSE9P58SJE/z8888+3pPu\nZbfbKSwsxOFwMGnSJJYuXdpuW4vFQllZGSqViqSkJLKzsxk9ejQlJSW4XC4CAnrGLTCnT5/GbDZ7\nZmaSkpKw2WyUlpYC8MEHH/i4Qt8ZOHAg27dvp7i4mG3btqHX60lPT8disfDOO+8QGhpKUVERhw4d\nYsmSJWzfvp333nvP12V3q/b6qL1ZvnPnzvHpp5+i1WqZMmUKFouFfv36tbv9Lg1tRVGYMWMG2dnZ\nhIWFMXbsWNxuN263m8jISPR6PQBxcXH89NNPxMTEEB0dDcDgwYN77NWsNzU1NRQVFfHxxx/jdrvR\naDRERkYyf/58MjIycDgcmM1mX5fZZRRFwWg0cvjwYUJDQ9FoNCQkJPDDDz9QXV1NSkoKb775Junp\n6bjdbmw2G+PGjcNisfD0008DEBMTg1rd5depD5WoqCjUajVqtdrrFOXto8qwsDBPm82bN7Nz504u\nXrzImDFj2ow+H2V/nh4vLy9n5MiRPqzo4XHhwgUMBgObN28GoKqqildffZU1a9awYcMGDAYD9fX1\nPPnkkwCe831P0l4fDRgwwNPm9j4ZPny4JwsHDBhAS0vLXbff5ZfOYWFhNDc3U1xc7JkaVxSF06dP\n09zcDLQeFCNGjPCsu6Wn/WcDaLVa/vjjD6D1pphr164BEBERwcqVK9m1axe5ubk899xz1NTU0NTU\nRFFREXl5eWzYsMGXpXe5+Ph4ioqKmDhxIgCxsbFUVVXhcrkICQlh8ODBFBYWUlxczJIlS3jqqaeI\njIzk+PHjAJw8ebLH3UDk7epeq9Vy5coVoLVPvLUtLS0lNzeX4uJiqqqqPH3YE3g779w+y9ATz0u3\nVFdX89Zbb2G324HWwOnduzdbtmwhLy+PLVu23BFOAQEBPa6/2uujPn36eM7ttx93t+tIX3XLsGPa\ntGns37+f4cOHc+HCBUJCQjy/n6lUKoYNG8bKlSv5+uuv7/h3j+pNQ3czevRogoODmT9/PuHh4Qwd\nOhSAVatWkZOTg81mo6WlhaysLEaMGEFBQQEHDx7E7XZ73nH+qBo/fjzr16/3vFFOo9Hw2GOPER0d\njaIoZGZmkpqaisvlIjg4mPz8fMaMGcPq1atJSUlh5MiRBAYG+ngvfM9kMpGTk8OQIUMYOHCgZ/nt\nx9uoUaNITk7GYDAwaNAgYmJifFGqT/y/805PPC/d8swzz3D27FkSExMxGAy4XC5Wr15NZWUlycnJ\nBAUF0b9/f084xcXFsXjx4rve2Peoaa+PNBoNubm5dz3uOvLdkmePCyGEEH6iZ9xZIoQQQjwCJLSF\nEEIIPyGhLYQQQvgJCW0hhBDCT0hoCyGEEH5CQlsIIYTwExLaQgghhJ/4LyhICZKHn6ZMAAAAAElF\nTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "by_weekday = data.groupby(data.index.dayofweek).mean()\n", - "by_weekday.index = ['Mon', 'Tues', 'Wed', 'Thurs', 'Fri', 'Sat', 'Sun']\n", - "by_weekday.plot(style=[':', '--', '-']);" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "weekend = np.where(data.index.weekday < 5, 'Weekday', 'Weekend')\n", - "by_time = data.groupby([weekend, data.index.time]).mean()" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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CAk6n1iGJViTJjAiLMyUz5na5APgKCzSJSUQW34lpZo3pMVOXrJsRQojmK/3k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\nLXJzM2pvb3wvnIt1x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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "fig, ax = plt.subplots(1, 2, figsize=(14, 5))\n", - "by_time.ix['Weekday'].plot(ax=ax[0], title='Weekdays',\n", - " xticks=hourly_ticks, style=[':', '--', '-'])\n", - "by_time.ix['Weekend'].plot(ax=ax[1], title='Weekends',\n", - " xticks=hourly_ticks, style=[':', '--', '-']);" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.1" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/code_listings/04.09-Text-and-Annotation.ipynb b/code_listings/04.09-Text-and-Annotation.ipynb deleted file mode 100644 index ae652bc27..000000000 --- a/code_listings/04.09-Text-and-Annotation.ipynb +++ /dev/null @@ -1,471 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Text and Annotation" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.style.use('seaborn-whitegrid')\n", - "import numpy as np\n", - "import pandas as pd" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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dateDecimaldatedriveInfosizeInMbsizeInGbcostdollarsPerGbpredictedDollarsPerGblogCostPerGbpredictedLogCostPerGb
01980.001980 JanuaryMorrow Designs260.02650001930001974730.745.296.30
11980.501980 JulyNorth Star180.01841992330001480897.965.376.17
21981.671981 SeptemberApple50.0053500700000756656.415.855.88
\n", - "
" - ], - "text/plain": [ - " dateDecimal date driveInfo sizeInMb sizeInGb cost \\\n", - "0 1980.00 1980 January Morrow Designs 26 0.026 5000 \n", - "1 1980.50 1980 July North Star 18 0.018 4199 \n", - "2 1981.67 1981 September Apple 5 0.005 3500 \n", - "\n", - " dollarsPerGb predictedDollarsPerGb logCostPerGb predictedLogCostPerGb \n", - "0 193000 1974730.74 5.29 6.30 \n", - "1 233000 1480897.96 5.37 6.17 \n", - "2 700000 756656.41 5.85 5.88 " - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "data = pd.read_csv('memory-price.tsv', sep='\\t')\n", - "data.head(3)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Morm5GYfDQVRUFKGhoezduxe/34mq+lGUrh+Q2tttREfDr3/9v4SEZJGa2vGP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\nO15RFPfPSUlJFBUVMXz48CuOq6iouH4zcR2YzeY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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots()\n", - "ax.set_yscale('log')\n", - "ax.grid(True)\n", - "\n", - "color = np.log10(data['sizeInGb']) // 3\n", - "color[np.isnan(color)] = -1 # missing data\n", - "\n", - "ax.scatter(data['dateDecimal'], data['dollarsPerGb'],\n", - " c=color, alpha=0.5, s=50, cmap='jet')\n", - "ax.yaxis.set_major_formatter(plt.FormatStrFormatter('$%.2f'));" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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ajRcajY6amrqWOVhBENxOFDXBrSIjIy84UsmFlJbWEhUVQ2npSTQaXyTJysmT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\nxwej0fiTdjfccAMajeYnz7fUTgghhGu59eFHi8VCeno6+/b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- "text/plain": [ - "" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ax.set_xlabel('year')\n", - "ax.set_ylabel('cost per GB (USD)')\n", - "ax.set_title('Hard Drive costs per GB')\n", - "fig" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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i1+tRq9Xk5uYSEhJCeno6ycnJKBQKFi1axJQpU8jPz0eSJDw9PenZsyfbtm1j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\nGDBqjJi0JmTlcjRnNHRt0w2DwYDZbAbAZDKRmprKb5t/I2l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- "text/plain": [ - "" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ax.text(1990, 1E5, 'Megabyte Drives', color='blue')\n", - "ax.text(2001, 40, 'Gigabyte Drives', color='green')\n", - "ax.text(2008, 0.03, 'Terabyte Drives', color='red', ha='right')\n", - "fig" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(facecolor='lightgray')\n", - "ax.axis([0, 10, 0, 10])\n", - "\n", - "# transform=ax.transData is the default, but we'll specify it anyway\n", - "ax.text(1, 5, \". Data: (1, 5)\", transform=ax.transData)\n", - "ax.text(0.5, 0.1, \". Axes: (0.5, 0.1)\", transform=ax.transAxes)\n", - "ax.text(0.2, 0.2, \". Figure: (0.2, 0.2)\", transform=fig.transFigure);" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "\n", - "import warnings\n", - "warnings.simplefilter('ignore')\n", - "\n", - "fig, ax = plt.subplots()\n", - "\n", - "x = np.linspace(0, 20, 1000)\n", - "ax.plot(x, np.cos(x))\n", - "ax.axis('equal')\n", - "\n", - "ax.annotate('local maximum', xy=(6.28, 1), xytext=(10, 4),\n", - " arrowprops=dict(facecolor='black', shrink=0.05))\n", - "\n", - "ax.annotate('local minimum', xy=(5 * np.pi, -1), xytext=(2, -6),\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " connectionstyle=\"angle3,angleA=0,angleB=-90\"));" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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///wTDMNg7dq1GDlyJBuwAEB8fDwA5YrYeXt7AwAePXpU7b67d+/Cz88P//d/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\nEsgDXrTW5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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Adapted from http://matplotlib.org/examples/pylab_examples/annotation_demo2.html\n", - "from matplotlib.patches import Ellipse\n", - "\n", - "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 4))\n", - "\n", - "# plot a line on the first axes\n", - "t = np.arange(0.0, 5.0, 0.01)\n", - "s = np.cos(2*np.pi*t)\n", - "line, = ax1.plot(t, s, lw=3, color='purple')\n", - "ax1.axis([-1, 5, -4, 3])\n", - "\n", - "# add an ellipse to the second axes\n", - "el = Ellipse((2, -1), 0.5, 0.5)\n", - "ax2.add_patch(el)\n", - "ax2.axis([-1, 5, -5, 3])\n", - "\n", - "# Now for some annotations\n", - "ax1.annotate('arrowstyle', xy=(0, 1), xycoords='data',\n", - " xytext=(-50, 30), textcoords='offset points',\n", - " arrowprops=dict(arrowstyle=\"->\"))\n", - "\n", - "ax1.annotate('arc3', xy=(0.5, -1), xycoords='data',\n", - " xytext=(-30, -30), textcoords='offset points',\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " connectionstyle=\"arc3,rad=.2\"))\n", - "\n", - "ax1.annotate('arc #1', xy=(1., 1), xycoords='data',\n", - " xytext=(-40, 30), textcoords='offset points',\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " connectionstyle=\"arc,angleA=0,armA=30,rad=10\"))\n", - "\n", - "ax1.annotate('arc #2', xy=(1.5, -1), xycoords='data',\n", - " xytext=(-40, -30), textcoords='offset points',\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " connectionstyle=\"arc,angleA=0,armA=20,angleB=-90,armB=15,rad=7\"))\n", - "\n", - "ax1.annotate('angle3', xy=(2.5, -1), xycoords='data',\n", - " xytext=(-50, -30), textcoords='offset points',\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " connectionstyle=\"angle3,angleA=0,angleB=-90\"))\n", - "\n", - "ax1.annotate('angle #1', xy=(2., 1), xycoords='data',\n", - " xytext=(-50, 30), textcoords='offset points',\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " connectionstyle=\"angle,angleA=0,angleB=90,rad=10\"))\n", - "\n", - "ax1.annotate('angle #2', xy=(3., 1), xycoords='data',\n", - " xytext=(-50, 30), textcoords='offset points',\n", - " bbox=dict(boxstyle=\"round\", fc=\"0.8\"),\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " connectionstyle=\"angle,angleA=0,angleB=90,rad=10\"))\n", - "\n", - "ax1.annotate('angle #3', xy=(4., 1), xycoords='data',\n", - " xytext=(-50, 30), textcoords='offset points',\n", - " bbox=dict(boxstyle=\"round\", fc=\"0.8\"),\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " shrinkA=0, shrinkB=10,\n", - " connectionstyle=\"angle,angleA=0,angleB=90,rad=10\"))\n", - "\n", - "ax1.annotate('angle #4', xy=(3.5, -1), xycoords='data',\n", - " xytext=(-70, -60), textcoords='offset points',\n", - " size=20,\n", - " bbox=dict(boxstyle=\"round4,pad=.5\", fc=\"0.8\"),\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " connectionstyle=\"angle,angleA=0,angleB=-90,rad=10\"))\n", - "\n", - "ax1.annotate('', xy=(4., 1.), xycoords='data',\n", - " xytext=(4.5, -1), textcoords='data',\n", - " arrowprops=dict(arrowstyle=\"<->\",\n", - " connectionstyle=\"bar\",\n", - " ec=\"k\",\n", - " shrinkA=5, shrinkB=5))\n", - "\n", - "ax2.annotate('$->$', xy=(2., -1), xycoords='data',\n", - " xytext=(-150, -90), textcoords='offset points',\n", - " bbox=dict(boxstyle=\"round\", fc=\"0.8\"),\n", - " arrowprops=dict(arrowstyle=\"->\",\n", - " patchB=el,\n", - " connectionstyle=\"angle,angleA=90,angleB=0,rad=10\"))\n", - "\n", - "ax2.annotate('fancy', xy=(2., -1), xycoords='data',\n", - " xytext=(-100, 60), textcoords='offset points',\n", - " size=20,\n", - " arrowprops=dict(arrowstyle=\"fancy\",\n", - " fc=\"0.6\", ec=\"none\",\n", - " patchB=el,\n", - " connectionstyle=\"angle3,angleA=0,angleB=-90\"))\n", - "\n", - "ax2.annotate('simple', xy=(2., -1), xycoords='data',\n", - " xytext=(100, 60), textcoords='offset points',\n", - " size=20,\n", - " arrowprops=dict(arrowstyle=\"simple\",\n", - " fc=\"0.6\", ec=\"none\",\n", - " patchB=el,\n", - " connectionstyle=\"arc3,rad=0.3\"))\n", - "\n", - "ax2.annotate('wedge #1', xy=(2., -1), xycoords='data',\n", - " xytext=(-100, -100), textcoords='offset points',\n", - " size=20,\n", - " arrowprops=dict(arrowstyle=\"wedge,tail_width=0.7\",\n", - " fc=\"0.6\", ec=\"none\",\n", - " patchB=el,\n", - " connectionstyle=\"arc3,rad=-0.3\"))\n", - "\n", - "ax2.annotate('wedge #2', xy=(2., -1), xycoords='data',\n", - " xytext=(35, 0), textcoords='offset points',\n", - " size=20, va=\"center\",\n", - " bbox=dict(boxstyle=\"round\", fc=(1.0, 0.7, 0.7), ec=\"none\"),\n", - " arrowprops=dict(arrowstyle=\"wedge,tail_width=1.\",\n", - " fc=(1.0, 0.7, 0.7), ec=\"none\",\n", - " patchA=None,\n", - " patchB=el,\n", - " relpos=(0.2, 0.5)));" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.1" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/code_listings/04.10-Customizing-Ticks.ipynb b/code_listings/04.10-Customizing-Ticks.ipynb deleted file mode 100644 index da19f55f2..000000000 --- a/code_listings/04.10-Customizing-Ticks.ipynb +++ /dev/null @@ -1,313 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Customizing Ticks" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.style.use('seaborn-whitegrid')\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ax = plt.axes(xscale='log', yscale='log')" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n" - ] - } - ], - "source": [ - "print(ax.xaxis.get_major_locator())\n", - "print(ax.xaxis.get_minor_locator())" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n" - ] - } - ], - "source": [ - "print(ax.xaxis.get_major_formatter())\n", - "print(ax.xaxis.get_minor_formatter())" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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gtnJdlyVjK1fSv0VduEZGgJ/8BLj55uB/l1k5FkWc0w0T3SJGCwKTuW6Q0x0f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\nAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ax = plt.axes()\n", - "ax.plot(np.random.rand(50))\n", - "\n", - "ax.yaxis.set_major_locator(plt.NullLocator())\n", - "ax.xaxis.set_major_formatter(plt.NullFormatter())" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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h7a9/g9uv36KYlnzw2z/iR7/9I77xV79JNask7bUGkDJifiZOKY/t2dRxcj7w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1iecPT9g/P8A5C8+8rM3mDpvNXcryBHcqx25CXhhUq5p0lhoSFxzbEe2+RQug2TSsOxSS4adh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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(5, 5, figsize=(5, 5))\n", - "fig.subplots_adjust(hspace=0, wspace=0)\n", - "\n", - "# Get some face data from scikit-learn\n", - "from sklearn.datasets import fetch_olivetti_faces\n", - "faces = fetch_olivetti_faces().images\n", - "\n", - "for i in range(5):\n", - " for j in range(5):\n", - " ax[i, j].xaxis.set_major_locator(plt.NullLocator())\n", - " ax[i, j].yaxis.set_major_locator(plt.NullLocator())\n", - " ax[i, j].imshow(faces[10 * i + j], cmap=\"bone\")" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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g1zQNADL7nQaDQZw4cQJHjhyBaZoIBoNYv369rSKIiCh/LA32DRs2IBqNAgBaWloyx30+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\nk+iedmvt7OxEe3s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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(4, 4, sharex=True, sharey=True)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# For every axis, set the x & y major locator\n", - "for axi in ax.flat:\n", - " axi.xaxis.set_major_locator(plt.MaxNLocator(3))\n", - " axi.yaxis.set_major_locator(plt.MaxNLocator(3))\n", - "fig" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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2eBvMpHy2TUJGAjw2eODWi1vCBaUjEgm/RxcSomo7fZovbc/QIrVUasIuKuKf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\n5a+//sKlS5cQGRmJiIgIjYsq/o1iY2M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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot a sine and cosine curve\n", - "fig, ax = plt.subplots()\n", - "x = np.linspace(0, 3 * np.pi, 1000)\n", - "ax.plot(x, np.sin(x), lw=3, label='Sine')\n", - "ax.plot(x, np.cos(x), lw=3, label='Cosine')\n", - "\n", - "# Set up grid, legend, and limits\n", - "ax.grid(True)\n", - "ax.legend(frameon=False)\n", - "ax.axis('equal')\n", - "ax.set_xlim(0, 3 * np.pi);" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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nxp5IzU4VJigdsrAAIiP5xWmFtWuBUaOovsybjtw/gt6beiMzj39jq2JVBScD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\nuRMSiQQ5OTmIi4tDdHQ0rK2thQi9RHK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- "text/plain": [ - "" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))\n", - "ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))\n", - "fig" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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0em/ujfTcdHGCEpC5ORAWxi8wK61fD4wZQ/VcXnXk/hH03dIX2QX8m1k1y2o4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\nblW1+TTwwbmx51QzggyZ8kM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- "text/plain": [ - "" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "def format_func(value, tick_number):\n", - " # find number of multiples of pi/2\n", - " N = int(np.round(2 * value / np.pi))\n", - " if N == 0:\n", - " return \"0\"\n", - " elif N == 1:\n", - " return r\"$\\pi/2$\"\n", - " elif N == 2:\n", - " return r\"$\\pi$\"\n", - " elif N % 2 > 0:\n", - " return r\"${0}\\pi/2$\".format(N)\n", - " else:\n", - " return r\"${0}\\pi$\".format(N // 2)\n", - "\n", - "ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))\n", - "fig" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.1" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} diff --git a/code_listings/remove_empty_notebooks.py b/code_listings/remove_empty_notebooks.py deleted file mode 100644 index 7c8f5d58a..000000000 --- a/code_listings/remove_empty_notebooks.py +++ /dev/null @@ -1,18 +0,0 @@ -import os -import io -import glob - -import nbformat - - -def count_cells(filename): - with io.open(filename, 'r', encoding='utf8') as f: - nb = nbformat.read(f, as_version=4) - return len(nb.cells) - - - -for filename in glob.glob('0[0-6].[0-9][0-9]-*.ipynb'): - if count_cells(filename) < 2: - print("removing", filename) - os.remove(filename) diff --git a/cover-early-release.jpg b/cover-early-release.jpg deleted file mode 100644 index b6353c787..000000000 Binary files a/cover-early-release.jpg and /dev/null differ diff --git a/environment.yml b/environment.yml new file mode 100644 index 000000000..247ddfccb --- /dev/null +++ b/environment.yml @@ -0,0 +1,7 @@ +name: data-science-handbook +channels: + - conda-forge +dependencies: + - python=3.5 + - pip: + - -r requirements.txt \ No newline at end of file diff --git a/notebooks/00.00-Preface.ipynb b/notebooks/00.00-Preface.ipynb new file mode 100644 index 000000000..8be26e3a7 --- /dev/null +++ b/notebooks/00.00-Preface.ipynb @@ -0,0 +1,163 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Preface" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## What Is Data Science?\n", + "\n", + "This is a book about doing data science with Python, which immediately begs the question: what is *data science*?\n", + "It's a surprisingly hard definition to nail down, especially given how ubiquitous the term has become.\n", + "Vocal critics have variously dismissed it as a superfluous label (after all, what science doesn't involve data?) or a simple buzzword that only exists to salt resumes and catch the eye of overzealous tech recruiters.\n", + "\n", + "In my mind, these critiques miss something important.\n", + "Data science, despite its hype-laden veneer, is perhaps the best label we have for the cross-disciplinary set of skills that are becoming increasingly important in many applications across industry and academia.\n", + "This *cross-disciplinary* piece is key: in my mind, the best existing definition of data science is illustrated by Drew Conway's Data Science Venn Diagram, first published on his blog in September 2010 (see the following figure)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Data Science Venn Diagram](images/Data_Science_VD.png)\n", + "\n", + "(source: [Drew Conway](http://drewconway.com/zia/2013/3/26/the-data-science-venn-diagram), used by permission)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While some of the intersection labels are a bit tongue-in-cheek, this diagram captures the essence of what I think people mean when they say \"data science\": it is fundamentally an interdisciplinary subject.\n", + "Data science comprises three distinct and overlapping areas: the skills of a *statistician* who knows how to model and summarize datasets (which are growing ever larger); the skills of a *computer scientist* who can design and use algorithms to efficiently store, process, and visualize this data; and the *domain expertise*—what we might think of as \"classical\" training in a subject—necessary both to formulate the right questions and to put their answers in context.\n", + "\n", + "With this in mind, I would encourage you to think of data science not as a new domain of knowledge to learn, but a new set of skills that you can apply within your current area of expertise.\n", + "Whether you are reporting election results, forecasting stock returns, optimizing online ad clicks, identifying microorganisms in microscope photos, seeking new classes of astronomical objects, or working with data in any other field, the goal of this book is to give you the ability to ask and answer new questions about your chosen subject area." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Who Is This Book For?\n", + "\n", + "In my teaching both at the University of Washington and at various tech-focused conferences and meetups, one of the most common questions I have heard is this: \"How should I learn Python?\"\n", + "The people asking are generally technically minded students, developers, or researchers, often with an already strong background in writing code and using computational and numerical tools.\n", + "Most of these folks don't want to learn Python per se, but want to learn the language with the aim of using it as a tool for data-intensive and computational science.\n", + "While a large patchwork of videos, blog posts, and tutorials for this audience is available online, I've long been frustrated by the lack of a single good answer to this question; that is what inspired this book.\n", + "\n", + "The book is not meant to be an introduction to Python or to programming in general; I assume the reader has familiarity with the Python language, including defining functions, assigning variables, calling methods of objects, controlling the flow of a program, and other basic tasks.\n", + "Instead, it is meant to help Python users learn to use Python's data science stack—libraries such as those mentioned in the following section, and related tools—to effectively store, manipulate, and gain insight from data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Why Python?\n", + "\n", + "Python has emerged over the last couple of decades as a first-class tool for scientific computing tasks, including the analysis and visualization of large datasets.\n", + "This may have come as a surprise to early proponents of the Python language: the language itself was not specifically designed with data analysis or scientific computing in mind.\n", + "The usefulness of Python for data science stems primarily from the large and active ecosystem of third-party packages: *NumPy* for manipulation of homogeneous array-based data, *Pandas* for manipulation of heterogeneous and labeled data, *SciPy* for common scientific computing tasks, *Matplotlib* for publication-quality visualizations, *IPython* for interactive execution and sharing of code, *Scikit-Learn* for machine learning, and many more tools that will be mentioned in the following pages.\n", + "\n", + "If you are looking for a guide to the Python language itself, I would suggest the sister project to this book, [https://www.oreilly.com/library/view/a-whirlwind-tour/9781492037859](_A Whirlwind Tour of the Python Language_).\n", + "This short report provides a tour of the essential features of the Python language, aimed at data scientists who already are familiar with one or more other programming languages." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Outline of the Book\n", + "\n", + "Each numbered part of this book focuses on a particular package or tool that contributes a fundamental piece of the Python data science story, and is broken into short self-contained chapters that each discuss a single concept:\n", + "\n", + "- *Part I, Jupyter: Beyond Normal Python*, introduces IPython and Jupyter. These packages provide the computational environment in which many Python-using data scientists work.\n", + "- *Part II, Introduction to NumPy*, focuses on the NumPy library, which provides the `ndarray` for efficient storage and manipulation of dense data arrays in Python.\n", + "- *Part III, Data Manipulation with Pandas*, introduces the Pandas library, which provides the `DataFrame` for efficient storage and manipulation of labeled/columnar data in Python.\n", + "- *Part IV, Visualization with Matplotlib*, concentrates on Matplotlib, a library that provides capabilities for a flexible range of data visualizations in Python.\n", + "- *Part V, Machine Learning*, focuses on the Scikit-Learn library, which provides efficient and clean Python implementations of the most important and established machine learning algorithms.\n", + "\n", + "The PyData world is certainly much larger than these six packages, and is growing every day.\n", + "With this in mind, I make every attempt throughout this book to provide references to other interesting efforts, projects, and packages that are pushing the boundaries of what can be done in Python.\n", + "Nevertheless, the packages I concentrate on are currently fundamental to much of the work being done in the Python data science space, and I expect they will remain important even as the ecosystem continues growing around them." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using Code Examples\n", + "\n", + "Supplemental material (code examples, figures, etc.) is available for download at http://github.com/jakevdp/PythonDataScienceHandbook/. This book is here to help you get your job done. In general, if example code is offered with this book, you may use it in your programs and documentation. You do not need to contact us for permission unless you’re reproducing a significant portion of the code. For example, writing a program that uses several chunks of code from this book does not require permission. Selling or distributing a CD-ROM of examples from O’Reilly books does require permission. Answering a question by citing this book and quoting example code does not require permission. Incorporating a significant amount of example code from this book into your product’s documentation does require permission.\n", + "\n", + "We appreciate, but do not require, attribution. An attribution usually includes the title, author, publisher, and ISBN. For example: \"*Python Data Science Handbook*, 2nd edition, by Jake VanderPlas (O’Reilly). Copyright 2023 Jake VanderPlas, 978-1-098-12122-8.\"\n", + "\n", + "If you feel your use of code examples falls outside fair use or the permission given above, feel free to contact us at permissions@oreilly.com." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installation Considerations\n", + "\n", + "Installing Python and the suite of libraries that enable scientific computing is straightforward. This section will outline some of the things to keep in mind when setting up your computer.\n", + "\n", + "Though there are various ways to install Python, the one I would suggest for use in data science is the Anaconda distribution, which works similarly whether you use Windows, Linux, or macOS.\n", + "The Anaconda distribution comes in two flavors:\n", + "\n", + "- [Miniconda](http://conda.pydata.org/miniconda.html) gives you the Python interpreter itself, along with a command-line tool called *conda* which operates as a cross-platform package manager geared toward Python packages, similar in spirit to the apt or yum tools that Linux users might be familiar with.\n", + "\n", + "- [Anaconda](https://www.continuum.io/downloads) includes both Python and conda, and additionally bundles a suite of other preinstalled packages geared toward scientific computing. Because of the size of this bundle, expect the installation to consume several gigabytes of disk space.\n", + "\n", + "Any of the packages included with Anaconda can also be installed manually on top of Miniconda; for this reason I suggest starting with Miniconda.\n", + "\n", + "To get started, download and install the Miniconda package—make sure to choose a version with Python 3—and then install the core packages used in this book:\n", + "\n", + "```\n", + "[~]$ conda install numpy pandas scikit-learn matplotlib seaborn jupyter\n", + "```\n", + "\n", + "Throughout the text, we will also make use of other more specialized tools in Python's scientific ecosystem; installation is usually as easy as typing **`conda install packagename`**.\n", + "If you ever come across packages that are not available in the default conda channel, be sure to check out [*conda-forge*](https://conda-forge.org/), a broad, community-driven repository of conda packages.\n", + "\n", + "For more information on conda, including information about creating and using conda environments (which I would *highly* recommend), refer to [conda's online documentation](http://conda.pydata.org/docs/)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.00-IPython-Beyond-Normal-Python.ipynb b/notebooks/01.00-IPython-Beyond-Normal-Python.ipynb new file mode 100644 index 000000000..ed5be0334 --- /dev/null +++ b/notebooks/01.00-IPython-Beyond-Normal-Python.ipynb @@ -0,0 +1,54 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Jupyter: Beyond Normal Python" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are many options for development environments for Python, and I'm often asked which one I use in my own work.\n", + "My answer sometimes surprises people: my preferred environment is [IPython](http://ipython.org/) plus a text editor (in my case, Emacs or VSCode depending on my mood).\n", + "Jupyter got its start as the IPython shell, which was created in 2001 by Fernando Perez as an enhanced Python interpreter and has since grown into a project aiming to provide, in Perez's words, \"Tools for the entire life cycle of research computing.\"\n", + "If Python is the engine of our data science task, you might think of Jupyter as the interactive control panel.\n", + "\n", + "As well as being a useful interactive interface to Python, Jupyter also provides a number of useful syntactic additions to the language; we'll cover the most useful of these additions here.\n", + "Perhaps the most familiar interface provided by the Jupyter project is the Jupyter Notebook, a browser-based environment that is useful for development, collaboration, sharing, and even publication of data science results.\n", + "As an example of the usefulness of the notebook format, look no further than the page you are reading: the entire manuscript for this book was composed as a set of Jupyter notebooks.\n", + "\n", + "This part of the book will start by stepping through some of the Jupyter and IPython features that are useful to the practice of data science, focusing especially on the syntax they offer beyond the standard features of Python.\n", + "Next, we will go into a bit more depth on some of the more useful *magic commands* that can speed up common tasks in creating and using data science code.\n", + "Finally, we will touch on some of the features of the notebook that make it useful for understanding data and sharing results." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.01-Help-And-Documentation.ipynb b/notebooks/01.01-Help-And-Documentation.ipynb new file mode 100644 index 000000000..a37fc4c3a --- /dev/null +++ b/notebooks/01.01-Help-And-Documentation.ipynb @@ -0,0 +1,400 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Getting Started in IPython and Jupyter\n", + "\n", + "In writing Python code for data science, I generally go between three modes of working: I use the IPython shell for trying out short sequences of commands, the Jupyter Notebook for longer interactive analysis and for sharing content with others, and interactive development environments (IDEs) like Emacs or VSCode for creating reusable Python packages.\n", + "This chapter focuses on the first two modes: the IPython shell and the Jupyter Notebook.\n", + "Use of an IDE for software development is an important third tool in the data scientist's repertoire, but we will not directly address that here." + ] + }, + { + "cell_type": "markdown", + "id": "7b582097", + "metadata": {}, + "source": [ + "## Launching the IPython Shell\n", + "\n", + "The text in this part, like most of this book, is not designed to be absorbed passively.\n", + "I recommend that as you read through it, you follow along and experiment with the tools and syntax we cover: the muscle memory you build through doing this will be far more useful than the simple act of reading about it.\n", + "Start by launching the IPython interpreter by typing **`ipython`** on the command line; alternatively, if you've installed a distribution like Anaconda or EPD, there may be a launcher specific to your system (we'll discuss this more fully in [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)).\n", + "\n", + "Once you do this, you should see a prompt like the following:\n", + "\n", + "```ipython\n", + "Python 3.9.2 (v3.9.2:1a79785e3e, Feb 19 2021, 09:06:10) \n", + "Type 'copyright', 'credits' or 'license' for more information\n", + "IPython 7.21.0 -- An enhanced Interactive Python. Type '?' for help.\n", + "\n", + "In [1]:\n", + "```\n", + "With that, you're ready to follow along." + ] + }, + { + "cell_type": "markdown", + "id": "d1d2d0fb", + "metadata": {}, + "source": [ + "## Launching the Jupyter Notebook\n", + "\n", + "The Jupyter Notebook is a browser-based graphical interface to the IPython shell, and builds on it a rich set of dynamic display capabilities.\n", + "As well as executing Python/IPython statements, notebooks allow the user to include formatted text, static and dynamic visualizations, mathematical equations, JavaScript widgets, and much more.\n", + "Furthermore, these documents can be saved in a way that lets other people open them and execute the code on their own systems.\n", + "\n", + "Though you'll view and edit Jupyter notebooks through your web browser window, they must connect to a running Python process in order to execute code.\n", + "You can start this process (known as a \"kernel\") by running the following command in your system shell:\n", + "\n", + "```\n", + "$ jupyter lab\n", + "```\n", + "\n", + "This command will launch a local web server that will be visible to your browser.\n", + "It immediately spits out a log showing what it is doing; that log will look something like this:\n", + "\n", + "```\n", + "$ jupyter lab\n", + "[ServerApp] Serving notebooks from local directory: /Users/jakevdp/PythonDataScienceHandbook\n", + "[ServerApp] Jupyter Server 1.4.1 is running at:\n", + "[ServerApp] http://localhost:8888/lab?token=dd852649\n", + "[ServerApp] Use Control-C to stop this server and shut down all kernels (twice to skip confirmation).\n", + "```\n", + "\n", + "Upon issuing the command, your default browser should automatically open and navigate to the listed local URL;\n", + "the exact address will depend on your system.\n", + "If the browser does not open automatically, you can open a window and manually open this address (*http://localhost:8888/lab/* in this example)." + ] + }, + { + "cell_type": "markdown", + "id": "92286db8", + "metadata": {}, + "source": [ + "## Help and Documentation in IPython" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you read no other section in this chapter, read this one: I find the tools discussed here to be the most transformative contributions of IPython to my daily workflow.\n", + "\n", + "When a technologically minded person is asked to help a friend, family member, or colleague with a computer problem, most of the time it's less a matter of knowing the answer than of knowing how to quickly find an unknown answer.\n", + "In data science it's the same: searchable web resources such as online documentation, mailing list threads, and Stack Overflow answers contain a wealth of information, even (especially?) about topics you've found yourself searching on before.\n", + "Being an effective practitioner of data science is less about memorizing the tool or command you should use for every possible situation, and more about learning to effectively find the information you don't know, whether through a web search engine or another means.\n", + "\n", + "One of the most useful functions of IPython/Jupyter is to shorten the gap between the user and the type of documentation and search that will help them do their work effectively.\n", + "While web searches still play a role in answering complicated questions, an amazing amount of information can be found through IPython alone.\n", + "Some examples of the questions IPython can help answer in a few keystrokes include:\n", + "\n", + "- How do I call this function? What arguments and options does it have?\n", + "- What does the source code of this Python object look like?\n", + "- What is in this package I imported? \n", + "- What attributes or methods does this object have?\n", + "\n", + "Here we'll discuss the tools provided in the IPython shell and Jupyter Notebook to quickly access this information, namely the `?` character to explore documentation, the `??` characters to explore source code, and the Tab key for autocompletion." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Accessing Documentation with ?\n", + "\n", + "The Python language and its data science ecosystem are built with the user in mind, and one big part of that is access to documentation.\n", + "Every Python object contains a reference to a string, known as a *docstring*, which in most cases will contain a concise summary of the object and how to use it.\n", + "Python has a built-in `help` function that can access this information and prints the results.\n", + "For example, to see the documentation of the built-in `len` function, you can do the following:\n", + "\n", + "```ipython\n", + "In [1]: help(len)\n", + "Help on built-in function len in module builtins:\n", + "\n", + "len(obj, /)\n", + " Return the number of items in a container.\n", + "```\n", + "\n", + "Depending on your interpreter, this information may be displayed as inline text or in a separate pop-up window." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because finding help on an object is so common and useful, IPython and Jupyter introduce the `?` character as a shorthand for accessing this documentation and other relevant information:\n", + "\n", + "```ipython\n", + "In [2]: len?\n", + "Signature: len(obj, /)\n", + "Docstring: Return the number of items in a container.\n", + "Type: builtin_function_or_method\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notation works for just about anything, including object methods:\n", + "\n", + "```ipython\n", + "In [3]: L = [1, 2, 3]\n", + "In [4]: L.insert?\n", + "Signature: L.insert(index, object, /)\n", + "Docstring: Insert object before index.\n", + "Type: builtin_function_or_method\n", + "```\n", + "\n", + "or even objects themselves, with the documentation from their type:\n", + "\n", + "```ipython\n", + "In [5]: L?\n", + "Type: list\n", + "String form: [1, 2, 3]\n", + "Length: 3\n", + "Docstring: \n", + "Built-in mutable sequence.\n", + "\n", + "If no argument is given, the constructor creates a new empty list.\n", + "The argument must be an iterable if specified.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Importantly, this will even work for functions or other objects you create yourself!\n", + "Here we'll define a small function with a docstring:\n", + "\n", + "```ipython\n", + "In [6]: def square(a):\n", + " ....: \"\"\"Return the square of a.\"\"\"\n", + " ....: return a ** 2\n", + " ....:\n", + "```\n", + "\n", + "Note that to create a docstring for our function, we simply placed a string literal in the first line.\n", + "Because docstrings are usually multiple lines, by convention we used Python's triple-quote notation for multiline strings." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll use the `?` to find this docstring:\n", + "\n", + "```ipython\n", + "In [7]: square?\n", + "Signature: square(a)\n", + "Docstring: Return the square of a.\n", + "File: \n", + "Type: function\n", + "```\n", + "\n", + "This quick access to documentation via docstrings is one reason you should get in the habit of always adding such inline documentation to the code you write!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Accessing Source Code with ??\n", + "\n", + "Because the Python language is so easily readable, another level of insight can usually be gained by reading the source code of the object you're curious about.\n", + "IPython and Jupyter provide a shortcut to the source code with the double question mark (`??`):\n", + "\n", + "```ipython\n", + "In [8]: square??\n", + "Signature: square(a)\n", + "Source: \n", + "def square(a):\n", + " \"\"\"Return the square of a.\"\"\"\n", + " return a ** 2\n", + "File: \n", + "Type: function\n", + "```\n", + "\n", + "For simple functions like this, the double question mark can give quick insight into the under-the-hood details." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you play with this much, you'll notice that sometimes the `??` suffix doesn't display any source code: this is generally because the object in question is not implemented in Python, but in C or some other compiled extension language.\n", + "If this is the case, the `??` suffix gives the same output as the `?` suffix.\n", + "You'll find this particularly with many of Python's built-in objects and types, including the `len` function from earlier:\n", + "\n", + "```ipython\n", + "In [9]: len??\n", + "Signature: len(obj, /)\n", + "Docstring: Return the number of items in a container.\n", + "Type: builtin_function_or_method\n", + "```\n", + "\n", + "Using `?` and/or `??` is a powerful and quick way of finding information about what any Python function or module does." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exploring Modules with Tab Completion\n", + "\n", + "Another useful interface is the use of the Tab key for autocompletion and exploration of the contents of objects, modules, and namespaces.\n", + "In the examples that follow, I'll use `` to indicate when the Tab key should be pressed." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Tab completion of object contents\n", + "\n", + "Every Python object has various attributes and methods associated with it.\n", + "Like the `help` function mentioned earlier, Python has a built-in `dir` function that returns a list of these, but the tab-completion interface is much easier to use in practice.\n", + "To see a list of all available attributes of an object, you can type the name of the object followed by a period (\"`.`\") character and the Tab key:\n", + "\n", + "```ipython\n", + "In [10]: L.\n", + " append() count insert reverse \n", + " clear extend pop sort \n", + " copy index remove \n", + "```\n", + "\n", + "To narrow down the list, you can type the first character or several characters of the name, and the Tab key will find the matching attributes and methods:\n", + "\n", + "```ipython\n", + "In [10]: L.c\n", + " clear() count()\n", + " copy() \n", + "\n", + "In [10]: L.co\n", + " copy() count()\n", + "```\n", + "\n", + "If there is only a single option, pressing the Tab key will complete the line for you.\n", + "For example, the following will instantly be replaced with `L.count`:\n", + "\n", + "```ipython\n", + "In [10]: L.cou\n", + "\n", + "```\n", + "\n", + "Though Python has no strictly enforced distinction between public/external attributes and private/internal attributes, by convention a preceding underscore is used to denote the latter.\n", + "For clarity, these private methods and special methods are omitted from the list by default, but it's possible to list them by explicitly typing the underscore:\n", + "\n", + "```ipython\n", + "In [10]: L._\n", + " __add__ __delattr__ __eq__ \n", + " __class__ __delitem__ __format__()\n", + " __class_getitem__() __dir__() __ge__ >\n", + " __contains__ __doc__ __getattribute__ \n", + "```\n", + "\n", + "For brevity, I've only shown the first few columns of the output.\n", + "Most of these are Python's special double-underscore methods (often nicknamed \"dunder\" methods)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Tab completion when importing\n", + "\n", + "Tab completion is also useful when importing objects from packages.\n", + "Here we'll use it to find all possible imports in the `itertools` package that start with `co`:\n", + "\n", + "```ipython\n", + "In [10]: from itertools import co\n", + " combinations() compress()\n", + " combinations_with_replacement() count()\n", + "```\n", + "\n", + "Similarly, you can use tab-completion to see which imports are available on your system (this will change depending on which third-party scripts and modules are visible to your Python session):\n", + "\n", + "```ipython\n", + "In [10]: import \n", + " abc anyio \n", + " activate_this appdirs \n", + " aifc appnope >\n", + " antigravity argon2 \n", + "\n", + "In [10]: import h\n", + " hashlib html \n", + " heapq http \n", + " hmac \n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Beyond tab completion: Wildcard matching\n", + "\n", + "Tab completion is useful if you know the first few characters of the name of the object or attribute you're looking for, but is little help if you'd like to match characters in the middle or at the end of the name.\n", + "For this use case, IPython and Jupyter provide a means of wildcard matching for names using the `*` character.\n", + "\n", + "For example, we can use this to list every object in the namespace whose name ends with `Warning`:\n", + "\n", + "```ipython\n", + "In [10]: *Warning?\n", + "BytesWarning RuntimeWarning\n", + "DeprecationWarning SyntaxWarning\n", + "FutureWarning UnicodeWarning\n", + "ImportWarning UserWarning\n", + "PendingDeprecationWarning Warning\n", + "ResourceWarning\n", + "```\n", + "\n", + "Notice that the `*` character matches any string, including the empty string.\n", + "\n", + "Similarly, suppose we are looking for a string method that contains the word `find` somewhere in its name.\n", + "We can search for it this way:\n", + "\n", + "```ipython\n", + "In [11]: str.*find*?\n", + "str.find\n", + "str.rfind\n", + "```\n", + "\n", + "I find this type of flexible wildcard search can be useful for finding a particular command when getting to know a new package or reacquainting myself with a familiar one." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.02-Shell-Keyboard-Shortcuts.ipynb b/notebooks/01.02-Shell-Keyboard-Shortcuts.ipynb new file mode 100644 index 000000000..988dcea67 --- /dev/null +++ b/notebooks/01.02-Shell-Keyboard-Shortcuts.ipynb @@ -0,0 +1,176 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Keyboard Shortcuts in the IPython Shell" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you spend any amount of time on a computer, you've probably found a use for keyboard shortcuts in your workflow.\n", + "Most familiar perhaps are Cmd-c and Cmd-v (or Ctrl-c and Ctrl-v), used for copying and pasting in a wide variety of programs and systems.\n", + "Power users tend to go even further: popular text editors like Emacs, Vim, and others provide users an incredible range of operations through intricate combinations of keystrokes.\n", + "\n", + "The IPython shell doesn't go this far, but does provide a number of keyboard shortcuts for fast navigation while typing commands.\n", + "While some of these shortcuts do work in the browser-based notebooks, this section is primarily about shortcuts in the IPython shell.\n", + "\n", + "Once you get accustomed to these, they can be very useful for quickly performing certain commands without moving your hands from the \"home\" keyboard position.\n", + "If you're an Emacs user or if you have experience with Linux-style shells, the following will be very familiar.\n", + "I'll group these shortcuts into a few categories: *navigation shortcuts*, *text entry shortcuts*, *command history shortcuts*, and *miscellaneous shortcuts*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Navigation Shortcuts\n", + "\n", + "While the use of the left and right arrow keys to move backward and forward in the line is quite obvious, there are other options that don't require moving your hands from the \"home\" keyboard position:\n", + "\n", + "| Keystroke | Action |\n", + "|---------------------------------|--------------------------------------------|\n", + "| Ctrl-a | Move cursor to beginning of line |\n", + "| Ctrl-e | Move cursor to end of the line |\n", + "| Ctrl-b or the left arrow key | Move cursor back one character |\n", + "| Ctrl-f or the right arrow key | Move cursor forward one character |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Text Entry Shortcuts\n", + "\n", + "While everyone is familiar with using the Backspace key to delete the previous character, reaching for the key often requires some minor finger gymnastics, and it only deletes a single character at a time.\n", + "In IPython there are several shortcuts for removing some portion of the text you're typing; the most immediately useful of these are the commands to delete entire lines of text.\n", + "You'll know these have become second-nature if you find yourself using a combination of Ctrl-b and Ctrl-d instead of reaching for Backspace to delete the previous character!\n", + "\n", + "| Keystroke | Action |\n", + "|-----------------------------|--------------------------------------------------|\n", + "| Backspace key | Delete previous character in line |\n", + "| Ctrl-d | Delete next character in line |\n", + "| Ctrl-k | Cut text from cursor to end of line |\n", + "| Ctrl-u | Cut text from beginning of line to cursor |\n", + "| Ctrl-y | Yank (i.e., paste) text that was previously cut |\n", + "| Ctrl-t | Transpose (i.e., switch) previous two characters |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Command History Shortcuts\n", + "\n", + "Perhaps the most impactful shortcuts discussed here are the ones IPython provides for navigating the command history.\n", + "This command history goes beyond your current IPython session: your entire command history is stored in a SQLite database in your IPython profile directory.\n", + "The most straightforward way to access previous commands is by using the up and down arrow keys to step through the history, but other options exist as well:\n", + "\n", + "| Keystroke | Action |\n", + "|-----------------------------------|--------------------------------------------|\n", + "| Ctrl-p (or the up arrow key) | Access previous command in history |\n", + "| Ctrl-n (or the down arrow key) | Access next command in history |\n", + "| Ctrl-r | Reverse-search through command history |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The reverse-search option can be particularly useful.\n", + "Recall that earlier we defined a function called `square`.\n", + "Let's reverse-search our Python history from a new IPython shell and find this definition again.\n", + "When you press Ctrl-r in the IPython terminal, you'll see the following prompt:\n", + "\n", + "```ipython\n", + "In [1]:\n", + "(reverse-i-search)`': \n", + "```\n", + "\n", + "If you start typing characters at this prompt, IPython will autofill the most recent command, if any, that matches those characters:\n", + "\n", + "```ipython\n", + "In [1]: \n", + "(reverse-i-search)`sqa': square??\n", + "```\n", + "\n", + "At any point, you can add more characters to refine the search, or press Ctrl-r again to search further for another command that matches the query. If you followed along earlier, pressing Ctrl-r twice more gives:\n", + "\n", + "```ipython\n", + "In [1]: \n", + "(reverse-i-search)`sqa': def square(a):\n", + " \"\"\"Return the square of a\"\"\"\n", + " return a ** 2\n", + "```\n", + "\n", + "Once you have found the command you're looking for, press Return and the search will end.\n", + "You can then use the retrieved command and carry on with your session:\n", + "\n", + "```ipython\n", + "In [1]: def square(a):\n", + " \"\"\"Return the square of a\"\"\"\n", + " return a ** 2\n", + "\n", + "In [2]: square(2)\n", + "Out[2]: 4\n", + "```\n", + "\n", + "Note that you can use Ctrl-p/Ctrl-n or the up/down arrow keys to search through your history in a similar way, but only by matching characters at the beginning of the line.\n", + "That is, if you type **`def`** and then press Ctrl-p, it will find the most recent command (if any) in your history that begins with the characters `def`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Miscellaneous Shortcuts\n", + "\n", + "Finally, there are a few miscellaneous shortcuts that don't fit into any of the preceding categories, but are nevertheless useful to know:\n", + "\n", + "| Keystroke | Action |\n", + "|-----------------------------|--------------------------------------------|\n", + "| Ctrl-l | Clear terminal screen |\n", + "| Ctrl-c | Interrupt current Python command |\n", + "| Ctrl-d | Exit IPython session |\n", + "\n", + "The Ctrl-c shortcut in particular can be useful when you inadvertently start a very long-running job." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While some of the shortcuts discussed here may seem a bit obscure at first, they quickly become automatic with practice.\n", + "Once you develop that muscle memory, I suspect you will even find yourself wishing they were available in other contexts." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.03-Magic-Commands.ipynb b/notebooks/01.03-Magic-Commands.ipynb new file mode 100644 index 000000000..a30e95404 --- /dev/null +++ b/notebooks/01.03-Magic-Commands.ipynb @@ -0,0 +1,155 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# IPython Magic Commands" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The previous chapter showed how IPython lets you use and explore Python efficiently and interactively.\n", + "Here we'll begin discussing some of the enhancements that IPython adds on top of the normal Python syntax.\n", + "These are known in IPython as *magic commands*, and are prefixed by the `%` character.\n", + "These magic commands are designed to succinctly solve various common problems in standard data analysis.\n", + "Magic commands come in two flavors: *line magics*, which are denoted by a single `%` prefix and operate on a single line of input, and *cell magics*, which are denoted by a double `%%` prefix and operate on multiple lines of input.\n", + "I'll demonstrate and discuss a few brief examples here, and come back to a more focused discussion of several useful magic commands later." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running External Code: %run\n", + "As you begin developing more extensive code, you will likely find yourself working in IPython for interactive exploration, as well as a text editor to store code that you want to reuse.\n", + "Rather than running this code in a new window, it can be convenient to run it within your IPython session.\n", + "This can be done with the `%run` magic command.\n", + "\n", + "For example, imagine you've created a *myscript.py* file with the following contents:\n", + "\n", + "```python\n", + "# file: myscript.py\n", + "\n", + "def square(x):\n", + " \"\"\"square a number\"\"\"\n", + " return x ** 2\n", + "\n", + "for N in range(1, 4):\n", + " print(f\"{N} squared is {square(N)}\")\n", + "```\n", + "\n", + "You can execute this from your IPython session as follows:\n", + "\n", + "```ipython\n", + "In [6]: %run myscript.py\n", + "1 squared is 1\n", + "2 squared is 4\n", + "3 squared is 9\n", + "```\n", + "\n", + "Note also that after you've run this script, any functions defined within it are available for use in your IPython session:\n", + "\n", + "```ipython\n", + "In [7]: square(5)\n", + "Out[7]: 25\n", + "```\n", + "\n", + "There are several options to fine-tune how your code is run; you can see the documentation in the normal way, by typing **`%run?`** in the IPython interpreter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Timing Code Execution: %timeit\n", + "Another example of a useful magic function is `%timeit`, which will automatically determine the execution time of the single-line Python statement that follows it.\n", + "For example, we may want to check the performance of a list comprehension:\n", + "\n", + "```ipython\n", + "In [8]: %timeit L = [n ** 2 for n in range(1000)]\n", + "430 µs ± 3.21 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n", + "```\n", + "\n", + "The benefit of `%timeit` is that for short commands it will automatically perform multiple runs in order to attain more robust results.\n", + "For multiline statements, adding a second `%` sign will turn this into a cell magic that can handle multiple lines of input.\n", + "For example, here's the equivalent construction with a `for` loop:\n", + "\n", + "```ipython\n", + "In [9]: %%timeit\n", + " ...: L = []\n", + " ...: for n in range(1000):\n", + " ...: L.append(n ** 2)\n", + " ...: \n", + "484 µs ± 5.67 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n", + "```\n", + "\n", + "We can immediately see that list comprehensions are about 10% faster than the equivalent `for` loop construction in this case.\n", + "We'll explore `%timeit` and other approaches to timing and profiling code in [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Help on Magic Functions: ?, %magic, and %lsmagic\n", + "\n", + "Like normal Python functions, IPython magic functions have docstrings, and this useful\n", + "documentation can be accessed in the standard manner.\n", + "So, for example, to read the documentation of the `%timeit` magic function, simply type this:\n", + "\n", + "```ipython\n", + "In [10]: %timeit?\n", + "```\n", + "\n", + "Documentation for other functions can be accessed similarly.\n", + "To access a general description of available magic functions, including some examples, you can type this:\n", + "\n", + "```ipython\n", + "In [11]: %magic\n", + "```\n", + "\n", + "For a quick and simple list of all available magic functions, type this:\n", + "\n", + "```ipython\n", + "In [12]: %lsmagic\n", + "```\n", + "\n", + "Finally, I'll mention that it is quite straightforward to define your own magic functions if you wish.\n", + "I won't discuss it here, but if you are interested, see the references listed in [More IPython Resources](01.08-More-IPython-Resources.ipynb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.04-Input-Output-History.ipynb b/notebooks/01.04-Input-Output-History.ipynb new file mode 100644 index 000000000..3e315c0c5 --- /dev/null +++ b/notebooks/01.04-Input-Output-History.ipynb @@ -0,0 +1,194 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Input and Output History" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Previously you saw that the IPython shell allows you to access previous commands with the up and down arrow keys, or equivalently the Ctrl-p/Ctrl-n shortcuts.\n", + "Additionally, in both the shell and notebooks, IPython exposes several ways to obtain the output of previous commands, as well as string versions of the commands themselves.\n", + "We'll explore those here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## IPython's In and Out Objects\n", + "\n", + "By now I imagine you're becoming familiar with the `In [1]:`/`Out[1]:` style of prompts used by IPython.\n", + "But it turns out that these are not just pretty decoration: they give a clue as to how you can access previous inputs and outputs in your current session.\n", + "Suppose we start a session that looks like this:\n", + "\n", + "```ipython\n", + "In [1]: import math\n", + "\n", + "In [2]: math.sin(2)\n", + "Out[2]: 0.9092974268256817\n", + "\n", + "In [3]: math.cos(2)\n", + "Out[3]: -0.4161468365471424\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We've imported the built-in `math` package, then computed the sine and the cosine of the number 2.\n", + "These inputs and outputs are displayed in the shell with `In`/`Out` labels, but there's more—IPython actually creates some Python variables called `In` and `Out` that are automatically updated to reflect this history:\n", + "\n", + "```ipython\n", + "In [4]: In\n", + "Out[4]: ['', 'import math', 'math.sin(2)', 'math.cos(2)', 'In']\n", + "\n", + "In [5]: Out\n", + "Out[5]:\n", + "{2: 0.9092974268256817,\n", + " 3: -0.4161468365471424,\n", + " 4: ['', 'import math', 'math.sin(2)', 'math.cos(2)', 'In', 'Out']}\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `In` object is a list, which keeps track of the commands in order (the first item in the list is a placeholder so that `In [1]` can refer to the first command):\n", + "\n", + "```ipython\n", + "In [6]: print(In[1])\n", + "import math\n", + "```\n", + "\n", + "The `Out` object is not a list but a dictionary mapping input numbers to their outputs (if any):\n", + "\n", + "```ipython\n", + "In [7]: print(Out[2])\n", + "0.9092974268256817\n", + "```\n", + "\n", + "Note that not all operations have outputs: for example, `import` statements and `print` statements don't affect the output.\n", + "The latter may be surprising, but makes sense if you consider that `print` is a function that returns `None`; for brevity, any command that returns `None` is not added to `Out`.\n", + "\n", + "Where this can be useful is if you want to interact with past results.\n", + "For example, let's check the sum of `sin(2) ** 2` and `cos(2) ** 2` using the previously computed results:\n", + "\n", + "```ipython\n", + "In [8]: Out[2] ** 2 + Out[3] ** 2\n", + "Out[8]: 1.0\n", + "```\n", + "\n", + "The result is `1.0`, as we'd expect from the well-known trigonometric identity.\n", + "In this case, using these previous results probably is not necessary, but it can become quite handy if you execute a very expensive computation and forget to assign the result to a variable." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Underscore Shortcuts and Previous Outputs\n", + "\n", + "The standard Python shell contains just one simple shortcut for accessing previous output: the variable `_` (i.e., a single underscore) is kept updated with the previous output. This works in IPython as well:\n", + "\n", + "```ipython\n", + "In [9]: print(_)\n", + "1.0\n", + "```\n", + "\n", + "But IPython takes this a bit further—you can use a double underscore to access the second-to-last output, and a triple underscore to access the third-to-last output (skipping any commands with no output):\n", + "\n", + "```ipython\n", + "In [10]: print(__)\n", + "-0.4161468365471424\n", + "\n", + "In [11]: print(___)\n", + "0.9092974268256817\n", + "```\n", + "\n", + "IPython stops there: more than three underscores starts to get a bit hard to count, and at that point it's easier to refer to the output by line number.\n", + "\n", + "There is one more shortcut I should mention, however—a shorthand for `Out[X]` is `_X` (i.e., a single underscore followed by the line number):\n", + "\n", + "```ipython\n", + "In [12]: Out[2]\n", + "Out[12]: 0.9092974268256817\n", + "\n", + "In [13]: _2\n", + "Out[13]: 0.9092974268256817\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Suppressing Output\n", + "Sometimes you might wish to suppress the output of a statement (this is perhaps most common with the plotting commands that we'll explore in [Introduction to Matplotlib](04.00-Introduction-To-Matplotlib.ipynb)).\n", + "Or maybe the command you're executing produces a result that you'd prefer not to store in your output history, perhaps so that it can be deallocated when other references are removed.\n", + "The easiest way to suppress the output of a command is to add a semicolon to the end of the line:\n", + "\n", + "```ipython\n", + "In [14]: math.sin(2) + math.cos(2);\n", + "```\n", + "\n", + "The result is computed silently, and the output is neither displayed on the screen nor stored in the `Out` dictionary:\n", + "\n", + "```ipython\n", + "In [15]: 14 in Out\n", + "Out[15]: False\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Related Magic Commands\n", + "For accessing a batch of previous inputs at once, the `%history` magic command is very helpful.\n", + "Here is how you can print the first four inputs:\n", + "\n", + "```ipython\n", + "In [16]: %history -n 1-3\n", + " 1: import math\n", + " 2: math.sin(2)\n", + " 3: math.cos(2)\n", + "```\n", + "\n", + "As usual, you can type `%history?` for more information and a description of options available (see [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb) for details on the `?` functionality).\n", + "Other useful magic commands are `%rerun`, which will re-execute some portion of the command history, and `%save`, which saves some set of the command history to a file)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.05-IPython-And-Shell-Commands.ipynb b/notebooks/01.05-IPython-And-Shell-Commands.ipynb new file mode 100644 index 000000000..598d01517 --- /dev/null +++ b/notebooks/01.05-IPython-And-Shell-Commands.ipynb @@ -0,0 +1,225 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# IPython and Shell Commands" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When working interactively with the standard Python interpreter, one of the frustrations is the need to switch between multiple windows to access Python tools and system command-line tools.\n", + "IPython bridges this gap, and gives you a syntax for executing shell commands directly from within the IPython terminal.\n", + "The magic happens with the exclamation point: anything appearing after `!` on a line will be executed not by the Python kernel, but by the system command line.\n", + "\n", + "The following discussion assumes you're on a Unix-like system, such as Linux or macOS.\n", + "Some of the examples that follow will fail on Windows, which uses a different type of shell by default, though if you use the *Windows Subsystem for Linux* the examples here should run correctly.\n", + "If you're unfamiliar with shell commands, I'd suggest reviewing the [Unix shell tutorial](http://swcarpentry.github.io/shell-novice/) put together by the always excellent Software Carpentry Foundation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quick Introduction to the Shell\n", + "\n", + "A full introduction to using the shell/terminal/command line is well beyond the scope of this chapter, but for the uninitiated I will offer a quick introduction here.\n", + "The shell is a way to interact textually with your computer.\n", + "Ever since the mid-1980s, when Microsoft and Apple introduced the first versions of their now ubiquitous graphical operating systems, most computer users have interacted with their operating systems through the familiar menu selections and drag-and-drop movements.\n", + "But operating systems existed long before these graphical user interfaces, and were primarily controlled through sequences of text input: at the prompt, the user would type a command, and the computer would do what the user told it to.\n", + "Those early prompt systems were the precursors of the shells and terminals that most data scientists still use today.\n", + "\n", + "Someone unfamiliar with the shell might ask why you would bother with this, when many of the same results can be accomplished by simply clicking on icons and menus.\n", + "A shell user might reply with another question: why hunt for icons and menu items when you can accomplish things much more easily by typing?\n", + "While it might sound like a typical tech preference impasse, when moving beyond basic tasks it quickly becomes clear that the shell offers much more control of advanced tasks—though admittedly the learning curve can be intimidating.\n", + "\n", + "As an example, here is a sample of a Linux/macOS shell session where a user explores, creates, and modifies directories and files on their system (`osx:~ $` is the prompt, and everything after the `$` is the typed command; text that is preceded by a `#` is meant just as description, rather than something you would actually type in):\n", + "\n", + "```bash\n", + "osx:~ $ echo \"hello world\" # echo is like Python's print function\n", + "hello world\n", + "\n", + "osx:~ $ pwd # pwd = print working directory\n", + "/home/jake # This is the \"path\" that we're sitting in\n", + "\n", + "osx:~ $ ls # ls = list working directory contents\n", + "notebooks projects \n", + "\n", + "osx:~ $ cd projects/ # cd = change directory\n", + "\n", + "osx:projects $ pwd\n", + "/home/jake/projects\n", + "\n", + "osx:projects $ ls\n", + "datasci_book mpld3 myproject.txt\n", + "\n", + "osx:projects $ mkdir myproject # mkdir = make new directory\n", + "\n", + "osx:projects $ cd myproject/\n", + "\n", + "osx:myproject $ mv ../myproject.txt ./ # mv = move file. Here we're moving the\n", + " # file myproject.txt from one directory\n", + " # up (../) to the current directory (./).\n", + "osx:myproject $ ls\n", + "myproject.txt\n", + "```\n", + "\n", + "Notice that all of this is just a compact way to do familiar operations (navigating a directory structure, creating a directory, moving a file, etc.) by typing commands rather than clicking icons and menus.\n", + "With just a few commands (`pwd`, `ls`, `cd`, `mkdir`, and `cp`) you can do many of the most common file operations, but it's when you go beyond these basics that the shell approach becomes really powerful." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Shell Commands in IPython\n", + "\n", + "Any standard shell command can be used directly in IPython by prefixing it with the `!` character.\n", + "For example, the `ls`, `pwd`, and `echo` commands can be run as follows:\n", + "\n", + "```ipython\n", + "In [1]: !ls\n", + "myproject.txt\n", + "\n", + "In [2]: !pwd\n", + "/home/jake/projects/myproject\n", + "\n", + "In [3]: !echo \"printing from the shell\"\n", + "printing from the shell\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Passing Values to and from the Shell\n", + "\n", + "Shell commands not only can be called from IPython, but can also be made to interact with the IPython namespace.\n", + "For example, you can save the output of any shell command to a Python list using the assignment operator, `=`:\n", + "\n", + "```ipython\n", + "In [4]: contents = !ls\n", + "\n", + "In [5]: print(contents)\n", + "['myproject.txt']\n", + "\n", + "In [6]: directory = !pwd\n", + "\n", + "In [7]: print(directory)\n", + "['/Users/jakevdp/notebooks/tmp/myproject']\n", + "```\n", + "\n", + "These results are not returned as lists, but as a special shell return type defined in IPython:\n", + "\n", + "```ipython\n", + "In [8]: type(directory)\n", + "IPython.utils.text.SList\n", + "```\n", + "\n", + "This looks and acts a lot like a Python list but has additional functionality, such as\n", + "the `grep` and `fields` methods and the `s`, `n`, and `p` properties that allow you to search, filter, and display the results in convenient ways.\n", + "For more information on these, you can use IPython's built-in help features." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Communication in the other direction—passing Python variables into the shell—is possible using the `{varname}` syntax:\n", + "\n", + "```ipython\n", + "In [9]: message = \"hello from Python\"\n", + "\n", + "In [10]: !echo {message}\n", + "hello from Python\n", + "```\n", + "\n", + "The curly braces contain the variable name, which is replaced by the variable's contents in the shell command." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Shell-Related Magic Commands\n", + "\n", + "If you play with IPython's shell commands for a while, you might notice that you cannot use `!cd` to navigate the filesystem:\n", + "\n", + "```ipython\n", + "In [11]: !pwd\n", + "/home/jake/projects/myproject\n", + "\n", + "In [12]: !cd ..\n", + "\n", + "In [13]: !pwd\n", + "/home/jake/projects/myproject\n", + "```\n", + "\n", + "The reason is that shell commands in the notebook are executed in a temporary subshell that does not maintain state from command to command.\n", + "If you'd like to change the working directory in a more enduring way, you can use the `%cd` magic command:\n", + "\n", + "```ipython\n", + "In [14]: %cd ..\n", + "/home/jake/projects\n", + "```\n", + "\n", + "In fact, by default you can even use this without the `%` sign:\n", + "\n", + "```ipython\n", + "In [15]: cd myproject\n", + "/home/jake/projects/myproject\n", + "```\n", + "\n", + "This is known as an *automagic* function, and the ability to execute such commands without an explicit `%` can be toggled with the `%automagic` magic function.\n", + "\n", + "Besides `%cd`, other available shell-like magic functions are `%cat`, `%cp`, `%env`, `%ls`, `%man`, `%mkdir`, `%more`, `%mv`, `%pwd`, `%rm`, and `%rmdir`, any of which can be used without the `%` sign if `automagic` is on.\n", + "This makes it so that you can almost treat the IPython prompt as if it's a normal shell:\n", + "\n", + "```ipython\n", + "In [16]: mkdir tmp\n", + "\n", + "In [17]: ls\n", + "myproject.txt tmp/\n", + "\n", + "In [18]: cp myproject.txt tmp/\n", + "\n", + "In [19]: ls tmp\n", + "myproject.txt\n", + "\n", + "In [20]: rm -r tmp\n", + "```\n", + "\n", + "This access to the shell from within the same terminal window as your Python session lets you more naturally combine Python and the shell in your workflows with fewer context switches." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.06-Errors-and-Debugging.ipynb b/notebooks/01.06-Errors-and-Debugging.ipynb new file mode 100644 index 000000000..8b3110d37 --- /dev/null +++ b/notebooks/01.06-Errors-and-Debugging.ipynb @@ -0,0 +1,424 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Errors and Debugging" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Code development and data analysis always require a bit of trial and error, and IPython contains tools to streamline this process.\n", + "This section will briefly cover some options for controlling Python's exception reporting, followed by exploring tools for debugging errors in code." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Controlling Exceptions: %xmode\n", + "\n", + "Most of the time when a Python script fails, it will raise an exception.\n", + "When the interpreter hits one of these exceptions, information about the cause of the error can be found in the *traceback*, which can be accessed from within Python.\n", + "With the `%xmode` magic function, IPython allows you to control the amount of information printed when the exception is raised.\n", + "Consider the following code:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def func1(a, b):\n", + " return a / b\n", + "\n", + "def func2(x):\n", + " a = x\n", + " b = x - 1\n", + " return func1(a, b)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "ZeroDivisionError", + "evalue": "division by zero", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mZeroDivisionError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfunc2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mfunc2\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mfunc1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mfunc1\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mfunc1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mfunc2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero" + ] + } + ], + "source": [ + "func2(1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `func2` results in an error, and reading the printed trace lets us see exactly what happened.\n", + "In the default mode, this trace includes several lines showing the context of each step that led to the error.\n", + "Using the `%xmode` magic function (short for *exception mode*), we can change what information is printed.\n", + "\n", + "`%xmode` takes a single argument, the mode, and there are three possibilities: `Plain`, `Context`, and `Verbose`.\n", + "The default is `Context`, which gives output like that just shown.\n", + "`Plain` is more compact and gives less information:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exception reporting mode: Plain\n" + ] + } + ], + "source": [ + "%xmode Plain" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "ZeroDivisionError", + "evalue": "division by zero", + "output_type": "error", + "traceback": [ + "Traceback \u001b[0;36m(most recent call last)\u001b[0m:\n", + " File \u001b[1;32m\"\"\u001b[0m, line \u001b[1;32m1\u001b[0m, in \u001b[1;35m\u001b[0m\n func2(1)\n", + " File \u001b[1;32m\"\"\u001b[0m, line \u001b[1;32m7\u001b[0m, in \u001b[1;35mfunc2\u001b[0m\n return func1(a, b)\n", + "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m2\u001b[0;36m, in \u001b[0;35mfunc1\u001b[0;36m\u001b[0m\n\u001b[0;31m return a / b\u001b[0m\n", + "\u001b[0;31mZeroDivisionError\u001b[0m\u001b[0;31m:\u001b[0m division by zero\n" + ] + } + ], + "source": [ + "func2(1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `Verbose` mode adds some extra information, including the arguments to any functions that are called:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exception reporting mode: Verbose\n" + ] + } + ], + "source": [ + "%xmode Verbose" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "ZeroDivisionError", + "evalue": "division by zero", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mZeroDivisionError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfunc2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m \u001b[0;36mglobal\u001b[0m \u001b[0;36mfunc2\u001b[0m \u001b[0;34m= \u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mfunc2\u001b[0;34m(x=1)\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mfunc1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m \u001b[0;36mglobal\u001b[0m \u001b[0;36mfunc1\u001b[0m \u001b[0;34m= \u001b[0m\u001b[0;34m\n \u001b[0m\u001b[0;36ma\u001b[0m \u001b[0;34m= 1\u001b[0m\u001b[0;34m\n \u001b[0m\u001b[0;36mb\u001b[0m \u001b[0;34m= 0\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mfunc1\u001b[0;34m(a=1, b=0)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mfunc1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m \u001b[0;36ma\u001b[0m \u001b[0;34m= 1\u001b[0m\u001b[0;34m\n \u001b[0m\u001b[0;36mb\u001b[0m \u001b[0;34m= 0\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mfunc2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero" + ] + } + ], + "source": [ + "func2(1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This extra information can help you narrow in on why the exception is being raised.\n", + "So why not use the `Verbose` mode all the time?\n", + "As code gets complicated, this kind of traceback can get extremely long.\n", + "Depending on the context, sometimes the brevity of `Plain` or `Context` mode is easier to work with." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Debugging: When Reading Tracebacks Is Not Enough\n", + "\n", + "The standard Python tool for interactive debugging is `pdb`, the Python debugger.\n", + "This debugger lets the user step through the code line by line in order to see what might be causing a more difficult error.\n", + "The IPython-enhanced version of this is `ipdb`, the IPython debugger.\n", + "\n", + "There are many ways to launch and use both these debuggers; we won't cover them fully here.\n", + "Refer to the online documentation of these two utilities to learn more.\n", + "\n", + "In IPython, perhaps the most convenient interface to debugging is the `%debug` magic command.\n", + "If you call it after hitting an exception, it will automatically open an interactive debugging prompt at the point of the exception.\n", + "The `ipdb` prompt lets you explore the current state of the stack, explore the available variables, and even run Python commands!\n", + "\n", + "Let's look at the most recent exception, then do some basic tasks. We'll print the values of `a` and `b`, then type `quit` to quit the debugging session:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "> (2)func1()\n", + " 1 def func1(a, b):\n", + "----> 2 return a / b\n", + " 3 \n", + "\n", + "ipdb> print(a)\n", + "1\n", + "ipdb> print(b)\n", + "0\n", + "ipdb> quit\n" + ] + } + ], + "source": [ + "%debug" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The interactive debugger allows much more than this, though—we can even step up and down through the stack and explore the values of variables there:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "> (2)func1()\n", + " 1 def func1(a, b):\n", + "----> 2 return a / b\n", + " 3 \n", + "\n", + "ipdb> up\n", + "> (7)func2()\n", + " 5 a = x\n", + " 6 b = x - 1\n", + "----> 7 return func1(a, b)\n", + "\n", + "ipdb> print(x)\n", + "1\n", + "ipdb> up\n", + "> (1)()\n", + "----> 1 func2(1)\n", + "\n", + "ipdb> down\n", + "> (7)func2()\n", + " 5 a = x\n", + " 6 b = x - 1\n", + "----> 7 return func1(a, b)\n", + "\n", + "ipdb> quit\n" + ] + } + ], + "source": [ + "%debug" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This allows us to quickly find out not only what caused the error, but what function calls led up to the error.\n", + "\n", + "If you'd like the debugger to launch automatically whenever an exception is raised, you can use the `%pdb` magic function to turn on this automatic behavior:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exception reporting mode: Plain\n", + "Automatic pdb calling has been turned ON\n" + ] + }, + { + "ename": "ZeroDivisionError", + "evalue": "division by zero", + "output_type": "error", + "traceback": [ + "Traceback \u001b[0;36m(most recent call last)\u001b[0m:\n", + " File \u001b[1;32m\"\"\u001b[0m, line \u001b[1;32m3\u001b[0m, in \u001b[1;35m\u001b[0m\n func2(1)\n", + " File \u001b[1;32m\"\"\u001b[0m, line \u001b[1;32m7\u001b[0m, in \u001b[1;35mfunc2\u001b[0m\n return func1(a, b)\n", + "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m2\u001b[0;36m, in \u001b[0;35mfunc1\u001b[0;36m\u001b[0m\n\u001b[0;31m return a / b\u001b[0m\n", + "\u001b[0;31mZeroDivisionError\u001b[0m\u001b[0;31m:\u001b[0m division by zero\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "> (2)func1()\n", + " 1 def func1(a, b):\n", + "----> 2 return a / b\n", + " 3 \n", + "\n", + "ipdb> print(b)\n", + "0\n", + "ipdb> quit\n" + ] + } + ], + "source": [ + "%xmode Plain\n", + "%pdb on\n", + "func2(1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, if you have a script that you'd like to run from the beginning in interactive mode, you can run it with the command `%run -d`, and use the `next` command to step through the lines of code interactively." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Partial list of debugging commands\n", + "\n", + "There are many more available commands for interactive debugging than I've shown here. The following table contains a description of some of the more common and useful ones:\n", + "\n", + "| Command | Description |\n", + "|---------------|-------------------------------------------------------------|\n", + "| `l(ist)` | Show the current location in the file |\n", + "| `h(elp)` | Show a list of commands, or find help on a specific command |\n", + "| `q(uit)` | Quit the debugger and the program |\n", + "| `c(ontinue)` | Quit the debugger, continue in the program |\n", + "| `n(ext)` | Go to the next step of the program |\n", + "| `` | Repeat the previous command |\n", + "| `p(rint)` | Print variables |\n", + "| `s(tep)` | Step into a subroutine |\n", + "| `r(eturn)` | Return out of a subroutine |\n", + "\n", + "For more information, use the `help` command in the debugger, or take a look at `ipdb`'s [online documentation](https://github.com/gotcha/ipdb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.07-Timing-and-Profiling.ipynb b/notebooks/01.07-Timing-and-Profiling.ipynb new file mode 100644 index 000000000..203ca1d58 --- /dev/null +++ b/notebooks/01.07-Timing-and-Profiling.ipynb @@ -0,0 +1,530 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Profiling and Timing Code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the process of developing code and creating data processing pipelines, there are often trade-offs you can make between various implementations.\n", + "Early in developing your algorithm, it can be counterproductive to worry about such things. As Donald Knuth famously quipped, \"We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil.\"\n", + "\n", + "But once you have your code working, it can be useful to dig into its efficiency a bit.\n", + "Sometimes it's useful to check the execution time of a given command or set of commands; other times it's useful to examine a multiline process and determine where the bottleneck lies in some complicated series of operations.\n", + "IPython provides access to a wide array of functionality for this kind of timing and profiling of code.\n", + "Here we'll discuss the following IPython magic commands:\n", + "\n", + "- `%time`: Time the execution of a single statement\n", + "- `%timeit`: Time repeated execution of a single statement for more accuracy\n", + "- `%prun`: Run code with the profiler\n", + "- `%lprun`: Run code with the line-by-line profiler\n", + "- `%memit`: Measure the memory use of a single statement\n", + "- `%mprun`: Run code with the line-by-line memory profiler\n", + "\n", + "The last four commands are not bundled with IPython; to use them you'll need to get the `line_profiler` and `memory_profiler` extensions, which we will discuss in the following sections." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Timing Code Snippets: %timeit and %time\n", + "\n", + "We saw the `%timeit` line magic and `%%timeit` cell magic in the introduction to magic functions in [IPython Magic Commands](01.03-Magic-Commands.ipynb); these can be used to time the repeated execution of snippets of code:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.53 µs ± 47.8 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n" + ] + } + ], + "source": [ + "%timeit sum(range(100))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that because this operation is so fast, `%timeit` automatically does a large number of repetitions.\n", + "For slower commands, `%timeit` will automatically adjust and perform fewer repetitions:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "536 ms ± 15.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "total = 0\n", + "for i in range(1000):\n", + " for j in range(1000):\n", + " total += i * (-1) ** j" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes repeating an operation is not the best option.\n", + "For example, if we have a list that we'd like to sort, we might be misled by a repeated operation; sorting a pre-sorted list is much faster than sorting an unsorted list, so the repetition will skew the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.71 ms ± 334 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" + ] + } + ], + "source": [ + "import random\n", + "L = [random.random() for i in range(100000)]\n", + "%timeit L.sort()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this, the `%time` magic function may be a better choice. It also is a good choice for longer-running commands, when short, system-related delays are unlikely to affect the result.\n", + "Let's time the sorting of an unsorted and a presorted list:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sorting an unsorted list:\n", + "CPU times: user 31.3 ms, sys: 686 µs, total: 32 ms\n", + "Wall time: 33.3 ms\n" + ] + } + ], + "source": [ + "import random\n", + "L = [random.random() for i in range(100000)]\n", + "print(\"sorting an unsorted list:\")\n", + "%time L.sort()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sorting an already sorted list:\n", + "CPU times: user 5.19 ms, sys: 268 µs, total: 5.46 ms\n", + "Wall time: 14.1 ms\n" + ] + } + ], + "source": [ + "print(\"sorting an already sorted list:\")\n", + "%time L.sort()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice how much faster the presorted list is to sort, but notice also how much longer the timing takes with `%time` versus `%timeit`, even for the presorted list!\n", + "This is a result of the fact that `%timeit` does some clever things under the hood to prevent system calls from interfering with the timing.\n", + "For example, it prevents cleanup of unused Python objects (known as *garbage collection*) that might otherwise affect the timing.\n", + "For this reason, `%timeit` results are usually noticeably faster than `%time` results.\n", + "\n", + "For `%time`, as with `%timeit`, using the `%%` cell magic syntax allows timing of multiline scripts:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 655 ms, sys: 5.68 ms, total: 661 ms\n", + "Wall time: 710 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "total = 0\n", + "for i in range(1000):\n", + " for j in range(1000):\n", + " total += i * (-1) ** j" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on `%time` and `%timeit`, as well as their available options, use the IPython help functionality (e.g., type `%time?` at the IPython prompt)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Profiling Full Scripts: %prun\n", + "\n", + "A program is made up of many single statements, and sometimes timing these statements in context is more important than timing them on their own.\n", + "Python contains a built-in code profiler (which you can read about in the Python documentation), but IPython offers a much more convenient way to use this profiler, in the form of the magic function `%prun`.\n", + "\n", + "By way of example, we'll define a simple function that does some calculations:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def sum_of_lists(N):\n", + " total = 0\n", + " for i in range(5):\n", + " L = [j ^ (j >> i) for j in range(N)]\n", + " total += sum(L)\n", + " return total" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can call `%prun` with a function call to see the profiled results:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " " + ] + }, + { + "data": { + "text/plain": [ + " 14 function calls in 0.932 seconds\n", + "\n", + " Ordered by: internal time\n", + "\n", + " ncalls tottime percall cumtime percall filename:lineno(function)\n", + " 5 0.808 0.162 0.808 0.162 :4()\n", + " 5 0.066 0.013 0.066 0.013 {built-in method builtins.sum}\n", + " 1 0.044 0.044 0.918 0.918 :1(sum_of_lists)\n", + " 1 0.014 0.014 0.932 0.932 :1()\n", + " 1 0.000 0.000 0.932 0.932 {built-in method builtins.exec}\n", + " 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%prun sum_of_lists(1000000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a table that indicates, in order of total time on each function call, where the execution is spending the most time. In this case, the bulk of the execution time is in the list comprehension inside `sum_of_lists`.\n", + "From here, we could start thinking about what changes we might make to improve the performance of the algorithm.\n", + "\n", + "For more information on `%prun`, as well as its available options, use the IPython help functionality (i.e., type `%prun?` at the IPython prompt)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Line-by-Line Profiling with %lprun\n", + "\n", + "The function-by-function profiling of `%prun` is useful, but sometimes it's more convenient to have a line-by-line profile report.\n", + "This is not built into Python or IPython, but there is a `line_profiler` package available for installation that can do this.\n", + "Start by using Python's packaging tool, `pip`, to install the `line_profiler` package:\n", + "\n", + "```\n", + "$ pip install line_profiler\n", + "```\n", + "\n", + "Next, you can use IPython to load the `line_profiler` IPython extension, offered as part of this package:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext line_profiler" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the `%lprun` command will do a line-by-line profiling of any function. In this case, we need to tell it explicitly which functions we're interested in profiling:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Timer unit: 1e-06 s\n", + "\n", + "Total time: 0.014803 s\n", + "File: \n", + "Function: sum_of_lists at line 1\n", + "\n", + "Line # Hits Time Per Hit % Time Line Contents\n", + "==============================================================\n", + " 1 def sum_of_lists(N):\n", + " 2 1 6.0 6.0 0.0 total = 0\n", + " 3 6 13.0 2.2 0.1 for i in range(5):\n", + " 4 5 14242.0 2848.4 96.2 L = [j ^ (j >> i) for j in range(N)]\n", + " 5 5 541.0 108.2 3.7 total += sum(L)\n", + " 6 1 1.0 1.0 0.0 return total" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%lprun -f sum_of_lists sum_of_lists(5000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The information at the top gives us the key to reading the results: the time is reported in microseconds, and we can see where the program is spending the most time.\n", + "At this point, we may be able to use this information to modify aspects of the script and make it perform better for our desired use case.\n", + "\n", + "For more information on `%lprun`, as well as its available options, use the IPython help functionality (i.e., type `%lprun?` at the IPython prompt)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Profiling Memory Use: %memit and %mprun\n", + "\n", + "Another aspect of profiling is the amount of memory an operation uses.\n", + "This can be evaluated with another IPython extension, the `memory_profiler`.\n", + "As with the `line_profiler`, we start by `pip`-installing the extension:\n", + "\n", + "```\n", + "$ pip install memory_profiler\n", + "```\n", + "\n", + "Then we can use IPython to load it:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext memory_profiler" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The memory profiler extension contains two useful magic functions: `%memit` (which offers a memory-measuring equivalent of `%timeit`) and `%mprun` (which offers a memory-measuring equivalent of `%lprun`).\n", + "The `%memit` magic function can be used rather simply:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "peak memory: 141.70 MiB, increment: 75.65 MiB\n" + ] + } + ], + "source": [ + "%memit sum_of_lists(1000000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that this function uses about 140 MB of memory.\n", + "\n", + "For a line-by-line description of memory use, we can use the `%mprun` magic function.\n", + "Unfortunately, this works only for functions defined in separate modules rather than the notebook itself, so we'll start by using the `%%file` cell magic to create a simple module called `mprun_demo.py`, which contains our `sum_of_lists` function, with one addition that will make our memory profiling results more clear:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting mprun_demo.py\n" + ] + } + ], + "source": [ + "%%file mprun_demo.py\n", + "def sum_of_lists(N):\n", + " total = 0\n", + " for i in range(5):\n", + " L = [j ^ (j >> i) for j in range(N)]\n", + " total += sum(L)\n", + " del L # remove reference to L\n", + " return total" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now import the new version of this function and run the memory line profiler:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + }, + { + "data": { + "text/plain": [ + "Filename: /Users/jakevdp/github/jakevdp/PythonDataScienceHandbook/notebooks_v2/mprun_demo.py\n", + "\n", + "Line # Mem usage Increment Occurences Line Contents\n", + "============================================================\n", + " 1 66.7 MiB 66.7 MiB 1 def sum_of_lists(N):\n", + " 2 66.7 MiB 0.0 MiB 1 total = 0\n", + " 3 75.1 MiB 8.4 MiB 6 for i in range(5):\n", + " 4 105.9 MiB 30.8 MiB 5000015 L = [j ^ (j >> i) for j in range(N)]\n", + " 5 109.8 MiB 3.8 MiB 5 total += sum(L)\n", + " 6 75.1 MiB -34.6 MiB 5 del L # remove reference to L\n", + " 7 66.9 MiB -8.2 MiB 1 return total" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mprun_demo import sum_of_lists\n", + "%mprun -f sum_of_lists sum_of_lists(1000000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, the `Increment` column tells us how much each line affects the total memory budget: observe that when we create and delete the list `L`, we are adding about 30 MB of memory usage.\n", + "This is on top of the background memory usage from the Python interpreter itself.\n", + "\n", + "For more information on `%memit` and `%mprun`, as well as their available options, use the IPython help functionality (e.g., type `%memit?` at the IPython prompt)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/01.08-More-IPython-Resources.ipynb b/notebooks/01.08-More-IPython-Resources.ipynb new file mode 100644 index 000000000..63819e7c0 --- /dev/null +++ b/notebooks/01.08-More-IPython-Resources.ipynb @@ -0,0 +1,70 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# More IPython Resources" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this set of chapters, we've just scratched the surface of using IPython to enable data science tasks.\n", + "Much more information is available both in print and on the web, and here I'll list some other resources that you may find helpful." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Web Resources\n", + "\n", + "- [The IPython website](http://ipython.org): The IPython website provides links to documentation, examples, tutorials, and a variety of other resources.\n", + "- [The nbviewer website](http://nbviewer.jupyter.org/): This site shows static renderings of any Jupyter notebook available on the internet. The front page features some example notebooks that you can browse to see what other folks are using IPython for!\n", + "- [A curated collection of Jupyter notebooks](https://github.com/jupyter/jupyter/wiki): This ever-growing list of notebooks, powered by nbviewer, shows the depth and breadth of numerical analysis you can do with IPython. It includes everything from short examples and tutorials to full-blown courses and books composed in the notebook format!\n", + "- Video tutorials: Searching the internet, you will find many video tutorials on IPython. I'd especially recommend seeking tutorials from the PyCon, SciPy, and PyData conferences by Fernando Perez and Brian Granger, two of the primary creators and maintainers of IPython and Jupyter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Books\n", + "\n", + "- [*Python for Data Analysis* (O'Reilly)](http://shop.oreilly.com/product/0636920023784.do): Wes McKinney's book includes a chapter that covers using IPython as a data scientist. Although much of the material overlaps what we've discussed here, another perspective is always helpful.\n", + "- [*Learning IPython for Interactive Computing and Data Visualization* (Packt)](https://www.packtpub.com/big-data-and-business-intelligence/learning-ipython-interactive-computing-and-data-visualization): This short book by Cyrille Rossant offers a good introduction to using IPython for data analysis.\n", + "- [*IPython Interactive Computing and Visualization Cookbook* (Packt)](https://www.packtpub.com/big-data-and-business-intelligence/ipython-interactive-computing-and-visualization-cookbook): Also by Cyrille Rossant, this book is a longer and more advanced treatment of using IPython for data science. Despite its name, it's not just about IPython; it also goes into some depth on a broad range of data science topics.\n", + "\n", + "Finally, a reminder that you can find help on your own: IPython's `?`-based help functionality (discussed in [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)) can be useful if you use it well and use it often.\n", + "As you go through the examples here and elsewhere, this can be used to familiarize yourself with all the tools that IPython has to offer." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.00-Introduction-to-NumPy.ipynb b/notebooks/02.00-Introduction-to-NumPy.ipynb new file mode 100644 index 000000000..62257da1c --- /dev/null +++ b/notebooks/02.00-Introduction-to-NumPy.ipynb @@ -0,0 +1,139 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction to NumPy\n", + "\n", + "This part of the book, along with [Part 3](03.00-Introduction-to-Pandas.ipynb), outlines techniques for effectively loading, storing, and manipulating in-memory data in Python.\n", + "The topic is very broad: datasets can come from a wide range of sources and in a wide range of formats, including collections of documents, collections of images, collections of sound clips, collections of numerical measurements, or nearly anything else.\n", + "Despite this apparent heterogeneity, many datasets can be represented fundamentally as arrays of numbers.\n", + "\n", + "For example, images—particularly digital images—can be thought of as simply two-dimensional arrays of numbers representing pixel brightness across the area.\n", + "Sound clips can be thought of as one-dimensional arrays of intensity versus time.\n", + "Text can be converted in various ways into numerical representations, such as binary digits representing the frequency of certain words or pairs of words.\n", + "No matter what the data is, the first step in making it analyzable will be to transform it into arrays of numbers.\n", + "(We will discuss some specific examples of this process in [Feature Engineering](05.04-Feature-Engineering.ipynb).)\n", + "\n", + "For this reason, efficient storage and manipulation of numerical arrays is absolutely fundamental to the process of doing data science.\n", + "We'll now take a look at the specialized tools that Python has for handling such numerical arrays: the NumPy package and the Pandas package (discussed in [Part 3](03.00-Introduction-to-Pandas.ipynb)).\n", + "\n", + "This part of the book will cover NumPy in detail. NumPy (short for *Numerical Python*) provides an efficient interface to store and operate on dense data buffers.\n", + "In some ways, NumPy arrays are like Python's built-in `list` type, but NumPy arrays provide much more efficient storage and data operations as the arrays grow larger in size.\n", + "NumPy arrays form the core of nearly the entire ecosystem of data science tools in Python, so time spent learning to use NumPy effectively will be valuable no matter what aspect of data science interests you.\n", + "\n", + "If you followed the advice outlined in the Preface and installed the Anaconda stack, you already have NumPy installed and ready to go.\n", + "If you're more the do-it-yourself type, you can go to http://www.numpy.org/ and follow the installation instructions found there.\n", + "Once you do, you can import NumPy and double-check the version:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.21.2'" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy\n", + "numpy.__version__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the pieces of the package discussed here, I'd recommend NumPy version 1.8 or later.\n", + "By convention, you'll find that most people in the SciPy/PyData world will import NumPy using `np` as an alias:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Throughout this chapter, and indeed the rest of the book, you'll find that this is the way we will import and use NumPy." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reminder About Built-in Documentation\n", + "\n", + "As you read through this part of the book, don't forget that IPython gives you the ability to quickly explore the contents of a package (by using the tab completion feature), as well as the documentation of various functions (using the `?` character). For a refresher on these, refer back to [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb).\n", + "\n", + "For example, to display all the contents of the NumPy namespace, you can type this:\n", + "\n", + "```ipython\n", + "In [3]: np.\n", + "```\n", + "\n", + "And to display NumPy's built-in documentation, you can use this:\n", + "\n", + "```ipython\n", + "In [4]: np?\n", + "```\n", + "\n", + "More detailed documentation, along with tutorials and other resources, can be found at http://www.numpy.org." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.01-Understanding-Data-Types.ipynb b/notebooks/02.01-Understanding-Data-Types.ipynb new file mode 100644 index 000000000..2649cc369 --- /dev/null +++ b/notebooks/02.01-Understanding-Data-Types.ipynb @@ -0,0 +1,864 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Understanding Data Types in Python" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Effective data-driven science and computation requires understanding how data is stored and manipulated.\n", + "This chapter outlines and contrasts how arrays of data are handled in the Python language itself, and how NumPy improves on this.\n", + "Understanding this difference is fundamental to understanding much of the material throughout the rest of the book.\n", + "\n", + "Users of Python are often drawn in by its ease of use, one piece of which is dynamic typing.\n", + "While a statically typed language like C or Java requires each variable to be explicitly declared, a dynamically typed language like Python skips this specification. For example, in C you might specify a particular operation as follows:\n", + "\n", + "```C\n", + "/* C code */\n", + "int result = 0;\n", + "for(int i=0; i<100; i++){\n", + " result += i;\n", + "}\n", + "```\n", + "\n", + "While in Python the equivalent operation could be written this way:\n", + "\n", + "```python\n", + "# Python code\n", + "result = 0\n", + "for i in range(100):\n", + " result += i\n", + "```\n", + "\n", + "Notice one main difference: in C, the data types of each variable are explicitly declared, while in Python the types are dynamically inferred. This means, for example, that we can assign any kind of data to any variable:\n", + "\n", + "```python\n", + "# Python code\n", + "x = 4\n", + "x = \"four\"\n", + "```\n", + "\n", + "Here we've switched the contents of `x` from an integer to a string. The same thing in C would lead (depending on compiler settings) to a compilation error or other unintended consequences:\n", + "\n", + "```C\n", + "/* C code */\n", + "int x = 4;\n", + "x = \"four\"; // FAILS\n", + "```\n", + "\n", + "This sort of flexibility is one element that makes Python and other dynamically typed languages convenient and easy to use.\n", + "Understanding *how* this works is an important piece of learning to analyze data efficiently and effectively with Python.\n", + "But what this type flexibility also points to is the fact that Python variables are more than just their values; they also contain extra information about the *type* of the value. We'll explore this more in the sections that follow." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A Python Integer Is More Than Just an Integer\n", + "\n", + "The standard Python implementation is written in C.\n", + "This means that every Python object is simply a cleverly disguised C structure, which contains not only its value, but other information as well. For example, when we define an integer in Python, such as `x = 10000`, `x` is not just a \"raw\" integer. It's actually a pointer to a compound C structure, which contains several values.\n", + "Looking through the Python 3.10 source code, we find that the integer (long) type definition effectively looks like this (once the C macros are expanded):\n", + "\n", + "```C\n", + "struct _longobject {\n", + " long ob_refcnt;\n", + " PyTypeObject *ob_type;\n", + " size_t ob_size;\n", + " long ob_digit[1];\n", + "};\n", + "```\n", + "\n", + "A single integer in Python 3.10 actually contains four pieces:\n", + "\n", + "- `ob_refcnt`, a reference count that helps Python silently handle memory allocation and deallocation\n", + "- `ob_type`, which encodes the type of the variable\n", + "- `ob_size`, which specifies the size of the following data members\n", + "- `ob_digit`, which contains the actual integer value that we expect the Python variable to represent\n", + "\n", + "This means that there is some overhead involved in storing an integer in Python as compared to a compiled language like C, as illustrated in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Integer Memory Layout](images/cint_vs_pyint.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, `PyObject_HEAD` is the part of the structure containing the reference count, type code, and other pieces mentioned before.\n", + "\n", + "Notice the difference here: a C integer is essentially a label for a position in memory whose bytes encode an integer value.\n", + "A Python integer is a pointer to a position in memory containing all the Python object information, including the bytes that contain the integer value.\n", + "This extra information in the Python integer structure is what allows Python to be coded so freely and dynamically.\n", + "All this additional information in Python types comes at a cost, however, which becomes especially apparent in structures that combine many of these objects." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A Python List Is More Than Just a List\n", + "\n", + "Let's consider now what happens when we use a Python data structure that holds many Python objects.\n", + "The standard mutable multielement container in Python is the list.\n", + "We can create a list of integers as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L = list(range(10))\n", + "L" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "int" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(L[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or, similarly, a list of strings:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L2 = [str(c) for c in L]\n", + "L2" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "str" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(L2[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of Python's dynamic typing, we can even create heterogeneous lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[bool, str, float, int]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L3 = [True, \"2\", 3.0, 4]\n", + "[type(item) for item in L3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this flexibility comes at a cost: to allow these flexible types, each item in the list must contain its own type, reference count, and other information. That is, each item is a complete Python object.\n", + "In the special case that all variables are of the same type, much of this information is redundant, so it can be much more efficient to store the data in a fixed-type array.\n", + "The difference between a dynamic-type list and a fixed-type (NumPy-style) array is illustrated in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Array Memory Layout](images/array_vs_list.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At the implementation level, the array essentially contains a single pointer to one contiguous block of data.\n", + "The Python list, on the other hand, contains a pointer to a block of pointers, each of which in turn points to a full Python object like the Python integer we saw earlier.\n", + "Again, the advantage of the list is flexibility: because each list element is a full structure containing both data and type information, the list can be filled with data of any desired type.\n", + "Fixed-type NumPy-style arrays lack this flexibility, but are much more efficient for storing and manipulating data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fixed-Type Arrays in Python\n", + "\n", + "Python offers several different options for storing data in efficient, fixed-type data buffers.\n", + "The built-in `array` module (available since Python 3.3) can be used to create dense arrays of a uniform type:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import array\n", + "L = list(range(10))\n", + "A = array.array('i', L)\n", + "A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, `'i'` is a type code indicating the contents are integers.\n", + "\n", + "Much more useful, however, is the `ndarray` object of the NumPy package.\n", + "While Python's `array` object provides efficient storage of array-based data, NumPy adds to this efficient *operations* on that data.\n", + "We will explore these operations in later chapters; next, I'll show you a few different ways of creating a NumPy array." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Creating Arrays from Python Lists\n", + "\n", + "We'll start with the standard NumPy import, under the alias `np`:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can use `np.array` to create arrays from Python lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 4, 2, 5, 3])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Integer array\n", + "np.array([1, 4, 2, 5, 3])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember that unlike Python lists, NumPy arrays can only contain data of the same type.\n", + "If the types do not match, NumPy will upcast them according to its type promotion rules; here, integers are upcast to floating point:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3.14, 4. , 2. , 3. ])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.array([3.14, 4, 2, 3])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we want to explicitly set the data type of the resulting array, we can use the `dtype` keyword:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1., 2., 3., 4.], dtype=float32)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.array([1, 2, 3, 4], dtype=np.float32)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, unlike Python lists, which are always one-dimensional sequences, NumPy arrays can be multidimensional. Here's one way of initializing a multidimensional array using a list of lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[2, 3, 4],\n", + " [4, 5, 6],\n", + " [6, 7, 8]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Nested lists result in multidimensional arrays\n", + "np.array([range(i, i + 3) for i in [2, 4, 6]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The inner lists are treated as rows of the resulting two-dimensional array." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Creating Arrays from Scratch\n", + "\n", + "Especially for larger arrays, it is more efficient to create arrays from scratch using routines built into NumPy.\n", + "Here are several examples:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a length-10 integer array filled with 0s\n", + "np.zeros(10, dtype=int)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 1., 1., 1., 1.],\n", + " [1., 1., 1., 1., 1.],\n", + " [1., 1., 1., 1., 1.]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x5 floating-point array filled with 1s\n", + "np.ones((3, 5), dtype=float)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[3.14, 3.14, 3.14, 3.14, 3.14],\n", + " [3.14, 3.14, 3.14, 3.14, 3.14],\n", + " [3.14, 3.14, 3.14, 3.14, 3.14]])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x5 array filled with 3.14\n", + "np.full((3, 5), 3.14)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create an array filled with a linear sequence\n", + "# starting at 0, ending at 20, stepping by 2\n", + "# (this is similar to the built-in range function)\n", + "np.arange(0, 20, 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0.25, 0.5 , 0.75, 1. ])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create an array of five values evenly spaced between 0 and 1\n", + "np.linspace(0, 1, 5)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.09610171, 0.88193001, 0.70548015],\n", + " [0.35885395, 0.91670468, 0.8721031 ],\n", + " [0.73237865, 0.09708562, 0.52506779]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x3 array of uniformly distributed\n", + "# pseudorandom values between 0 and 1\n", + "np.random.random((3, 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-0.46652655, -0.59158776, -1.05392451],\n", + " [-1.72634268, 0.03194069, -0.51048869],\n", + " [ 1.41240208, 1.77734462, -0.43820037]])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x3 array of normally distributed pseudorandom\n", + "# values with mean 0 and standard deviation 1\n", + "np.random.normal(0, 1, (3, 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4, 3, 8],\n", + " [6, 5, 0],\n", + " [1, 1, 4]])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x3 array of pseudorandom integers in the interval [0, 10)\n", + "np.random.randint(0, 10, (3, 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 0., 0.],\n", + " [0., 1., 0.],\n", + " [0., 0., 1.]])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x3 identity matrix\n", + "np.eye(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1., 1., 1.])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create an uninitialized array of three integers; the values will be\n", + "# whatever happens to already exist at that memory location\n", + "np.empty(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## NumPy Standard Data Types\n", + "\n", + "NumPy arrays contain values of a single type, so it is important to have detailed knowledge of those types and their limitations.\n", + "Because NumPy is built in C, the types will be familiar to users of C, Fortran, and other related languages.\n", + "\n", + "The standard NumPy data types are listed in the following table.\n", + "Note that when constructing an array, they can be specified using a string:\n", + "\n", + "```python\n", + "np.zeros(10, dtype='int16')\n", + "```\n", + "\n", + "Or using the associated NumPy object:\n", + "\n", + "```python\n", + "np.zeros(10, dtype=np.int16)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Data type\t | Description |\n", + "|-------------|-------------|\n", + "| `bool_` | Boolean (True or False) stored as a byte |\n", + "| `int_` | Default integer type (same as C `long`; normally either `int64` or `int32`)| \n", + "| `intc` | Identical to C `int` (normally `int32` or `int64`)| \n", + "| `intp` | Integer used for indexing (same as C `ssize_t`; normally either `int32` or `int64`)| \n", + "| `int8` | Byte (–128 to 127)| \n", + "| `int16` | Integer (–32768 to 32767)|\n", + "| `int32` | Integer (–2147483648 to 2147483647)|\n", + "| `int64` | Integer (–9223372036854775808 to 9223372036854775807)| \n", + "| `uint8` | Unsigned integer (0 to 255)| \n", + "| `uint16` | Unsigned integer (0 to 65535)| \n", + "| `uint32` | Unsigned integer (0 to 4294967295)| \n", + "| `uint64` | Unsigned integer (0 to 18446744073709551615)| \n", + "| `float_` | Shorthand for `float64`| \n", + "| `float16` | Half-precision float: sign bit, 5 bits exponent, 10 bits mantissa| \n", + "| `float32` | Single-precision float: sign bit, 8 bits exponent, 23 bits mantissa| \n", + "| `float64` | Double-precision float: sign bit, 11 bits exponent, 52 bits mantissa| \n", + "| `complex_` | Shorthand for `complex128`| \n", + "| `complex64` | Complex number, represented by two 32-bit floats| \n", + "| `complex128`| Complex number, represented by two 64-bit floats| " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "More advanced type specification is possible, such as specifying big- or little-endian numbers; for more information, refer to the [NumPy documentation](http://numpy.org/).\n", + "NumPy also supports compound data types, which will be covered in [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.02-The-Basics-Of-NumPy-Arrays.ipynb b/notebooks/02.02-The-Basics-Of-NumPy-Arrays.ipynb new file mode 100644 index 000000000..1a429455c --- /dev/null +++ b/notebooks/02.02-The-Basics-Of-NumPy-Arrays.ipynb @@ -0,0 +1,1641 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Basics of NumPy Arrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Data manipulation in Python is nearly synonymous with NumPy array manipulation: even newer tools like Pandas ([Part 3](03.00-Introduction-to-Pandas.ipynb)) are built around the NumPy array.\n", + "This chapter will present several examples of using NumPy array manipulation to access data and subarrays, and to split, reshape, and join the arrays.\n", + "While the types of operations shown here may seem a bit dry and pedantic, they comprise the building blocks of many other examples used throughout the book.\n", + "Get to know them well!\n", + "\n", + "We'll cover a few categories of basic array manipulations here:\n", + "\n", + "- *Attributes of arrays*: Determining the size, shape, memory consumption, and data types of arrays\n", + "- *Indexing of arrays*: Getting and setting the values of individual array elements\n", + "- *Slicing of arrays*: Getting and setting smaller subarrays within a larger array\n", + "- *Reshaping of arrays*: Changing the shape of a given array\n", + "- *Joining and splitting of arrays*: Combining multiple arrays into one, and splitting one array into many" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## NumPy Array Attributes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First let's discuss some useful array attributes.\n", + "We'll start by defining random arrays of one, two, and three dimensions.\n", + "We'll use NumPy's random number generator, which we will *seed* with a set value in order to ensure that the same random arrays are generated each time this code is run:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "rng = np.random.default_rng(seed=1701) # seed for reproducibility\n", + "\n", + "x1 = rng.integers(10, size=6) # one-dimensional array\n", + "x2 = rng.integers(10, size=(3, 4)) # two-dimensional array\n", + "x3 = rng.integers(10, size=(3, 4, 5)) # three-dimensional array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each array has attributes including `ndim` (the number of dimensions), `shape` (the size of each dimension), `size` (the total size of the array), and `dtype` (the type of each element):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x3 ndim: 3\n", + "x3 shape: (3, 4, 5)\n", + "x3 size: 60\n", + "dtype: int64\n" + ] + } + ], + "source": [ + "print(\"x3 ndim: \", x3.ndim)\n", + "print(\"x3 shape:\", x3.shape)\n", + "print(\"x3 size: \", x3.size)\n", + "print(\"dtype: \", x3.dtype)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more discussion of data types, see [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array Indexing: Accessing Single Elements" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are familiar with Python's standard list indexing, indexing in NumPy will feel quite familiar.\n", + "In a one-dimensional array, the $i^{th}$ value (counting from zero) can be accessed by specifying the desired index in square brackets, just as with Python lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([9, 4, 0, 3, 8, 6])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "9" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "8" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[4]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To index from the end of the array, you can use negative indices:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "6" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[-1]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "8" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[-2]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In a multidimensional array, items can be accessed using a comma-separated `(row, column)` tuple:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[3, 1, 3, 7],\n", + " [4, 0, 2, 3],\n", + " [0, 0, 6, 9]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[0, 0]" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[2, 0]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "9" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[2, -1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Values can also be modified using any of the preceding index notation:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[12, 1, 3, 7],\n", + " [ 4, 0, 2, 3],\n", + " [ 0, 0, 6, 9]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[0, 0] = 12\n", + "x2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind that, unlike Python lists, NumPy arrays have a fixed type.\n", + "This means, for example, that if you attempt to insert a floating-point value into an integer array, the value will be silently truncated. Don't be caught unaware by this behavior!" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3, 4, 0, 3, 8, 6])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[0] = 3.14159 # this will be truncated!\n", + "x1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array Slicing: Accessing Subarrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as we can use square brackets to access individual array elements, we can also use them to access subarrays with the *slice* notation, marked by the colon (`:`) character.\n", + "The NumPy slicing syntax follows that of the standard Python list; to access a slice of an array `x`, use this:\n", + "``` python\n", + "x[start:stop:step]\n", + "```\n", + "If any of these are unspecified, they default to the values `start=0`, `stop=`, `step=1`.\n", + "Let's look at some examples of accessing subarrays in one dimension and in multiple dimensions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### One-Dimensional Subarrays\n", + "\n", + "Here are some examples of accessing elements in one-dimensional subarrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3, 4, 0, 3, 8, 6])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3, 4, 0])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[:3] # first three elements" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3, 8, 6])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[3:] # elements after index 3" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([4, 0, 3])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[1:4] # middle subarray" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3, 0, 8])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[::2] # every second element" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([4, 3, 6])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[1::2] # every second element, starting at index 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A potentially confusing case is when the `step` value is negative.\n", + "In this case, the defaults for `start` and `stop` are swapped.\n", + "This becomes a convenient way to reverse an array:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([6, 8, 3, 0, 4, 3])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[::-1] # all elements, reversed" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([8, 0, 3])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1[4::-2] # every second element from index 4, reversed" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multidimensional Subarrays\n", + "\n", + "Multidimensional slices work in the same way, with multiple slices separated by commas.\n", + "For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[12, 1, 3, 7],\n", + " [ 4, 0, 2, 3],\n", + " [ 0, 0, 6, 9]])" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[12, 1, 3],\n", + " [ 4, 0, 2]])" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[:2, :3] # first two rows & three columns" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[12, 3],\n", + " [ 4, 2],\n", + " [ 0, 6]])" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[:3, ::2] # three rows, every second column" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 9, 6, 0, 0],\n", + " [ 3, 2, 0, 4],\n", + " [ 7, 3, 1, 12]])" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[::-1, ::-1] # all rows & columns, reversed" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Accessing array rows and columns\n", + "\n", + "One commonly needed routine is accessing single rows or columns of an array.\n", + "This can be done by combining indexing and slicing, using an empty slice marked by a single colon (`:`):" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([12, 4, 0])" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[:, 0] # first column of x2" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([12, 1, 3, 7])" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[0, :] # first row of x2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the case of row access, the empty slice can be omitted for a more compact syntax:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([12, 1, 3, 7])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2[0] # equivalent to x2[0, :]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Subarrays as No-Copy Views\n", + "\n", + "Unlike Python list slices, NumPy array slices are returned as *views* rather than *copies* of the array data.\n", + "Consider our two-dimensional array from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[12 1 3 7]\n", + " [ 4 0 2 3]\n", + " [ 0 0 6 9]]\n" + ] + } + ], + "source": [ + "print(x2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's extract a $2 \\times 2$ subarray from this:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[12 1]\n", + " [ 4 0]]\n" + ] + } + ], + "source": [ + "x2_sub = x2[:2, :2]\n", + "print(x2_sub)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now if we modify this subarray, we'll see that the original array is changed! Observe:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[99 1]\n", + " [ 4 0]]\n" + ] + } + ], + "source": [ + "x2_sub[0, 0] = 99\n", + "print(x2_sub)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[99 1 3 7]\n", + " [ 4 0 2 3]\n", + " [ 0 0 6 9]]\n" + ] + } + ], + "source": [ + "print(x2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some users may find this surprising, but it can be advantageous: for example, when working with large datasets, we can access and process pieces of these datasets without the need to copy the underlying data buffer." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Creating Copies of Arrays\n", + "\n", + "Despite the nice features of array views, it is sometimes useful to instead explicitly copy the data within an array or a subarray. This can be most easily done with the `copy` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[99 1]\n", + " [ 4 0]]\n" + ] + } + ], + "source": [ + "x2_sub_copy = x2[:2, :2].copy()\n", + "print(x2_sub_copy)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we now modify this subarray, the original array is not touched:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[42 1]\n", + " [ 4 0]]\n" + ] + } + ], + "source": [ + "x2_sub_copy[0, 0] = 42\n", + "print(x2_sub_copy)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[99 1 3 7]\n", + " [ 4 0 2 3]\n", + " [ 0 0 6 9]]\n" + ] + } + ], + "source": [ + "print(x2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reshaping of Arrays\n", + "\n", + "Another useful type of operation is reshaping of arrays, which can be done with the `reshape` method.\n", + "For example, if you want to put the numbers 1 through 9 in a $3 \\times 3$ grid, you can do the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 2 3]\n", + " [4 5 6]\n", + " [7 8 9]]\n" + ] + } + ], + "source": [ + "grid = np.arange(1, 10).reshape(3, 3)\n", + "print(grid)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that for this to work, the size of the initial array must match the size of the reshaped array, and in most cases the `reshape` method will return a no-copy view of the initial array." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A common reshaping operation is converting a one-dimensional array into a two-dimensional row or column matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 2, 3]])" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([1, 2, 3])\n", + "x.reshape((1, 3)) # row vector via reshape" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1],\n", + " [2],\n", + " [3]])" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x.reshape((3, 1)) # column vector via reshape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A convenient shorthand for this is to use `np.newaxis` in the slicing syntax:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 2, 3]])" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x[np.newaxis, :] # row vector via newaxis" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1],\n", + " [2],\n", + " [3]])" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x[:, np.newaxis] # column vector via newaxis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a pattern that we will utilize often throughout the remainder of the book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array Concatenation and Splitting\n", + "\n", + "All of the preceding routines worked on single arrays. NumPy also provides tools to combine multiple arrays into one, and to conversely split a single array into multiple arrays." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Concatenation of Arrays\n", + "\n", + "Concatenation, or joining of two arrays in NumPy, is primarily accomplished using the routines `np.concatenate`, `np.vstack`, and `np.hstack`.\n", + "`np.concatenate` takes a tuple or list of arrays as its first argument, as you can see here:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 2, 3, 3, 2, 1])" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([1, 2, 3])\n", + "y = np.array([3, 2, 1])\n", + "np.concatenate([x, y])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can also concatenate more than two arrays at once:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1 2 3 3 2 1 99 99 99]\n" + ] + } + ], + "source": [ + "z = np.array([99, 99, 99])\n", + "print(np.concatenate([x, y, z]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And it can be used for two-dimensional arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "grid = np.array([[1, 2, 3],\n", + " [4, 5, 6]])" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 2, 3],\n", + " [4, 5, 6],\n", + " [1, 2, 3],\n", + " [4, 5, 6]])" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# concatenate along the first axis\n", + "np.concatenate([grid, grid])" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 2, 3, 1, 2, 3],\n", + " [4, 5, 6, 4, 5, 6]])" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# concatenate along the second axis (zero-indexed)\n", + "np.concatenate([grid, grid], axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For working with arrays of mixed dimensions, it can be clearer to use the `np.vstack` (vertical stack) and `np.hstack` (horizontal stack) functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 2, 3],\n", + " [1, 2, 3],\n", + " [4, 5, 6]])" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# vertically stack the arrays\n", + "np.vstack([x, grid])" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1, 2, 3, 99],\n", + " [ 4, 5, 6, 99]])" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# horizontally stack the arrays\n", + "y = np.array([[99],\n", + " [99]])\n", + "np.hstack([grid, y])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, for higher-dimensional arrays, `np.dstack` will stack arrays along the third axis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Splitting of Arrays\n", + "\n", + "The opposite of concatenation is splitting, which is implemented by the functions `np.split`, `np.hsplit`, and `np.vsplit`. For each of these, we can pass a list of indices giving the split points:" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 2 3] [99 99] [3 2 1]\n" + ] + } + ], + "source": [ + "x = [1, 2, 3, 99, 99, 3, 2, 1]\n", + "x1, x2, x3 = np.split(x, [3, 5])\n", + "print(x1, x2, x3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that *N* split points leads to *N* + 1 subarrays.\n", + "The related functions `np.hsplit` and `np.vsplit` are similar:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11],\n", + " [12, 13, 14, 15]])" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grid = np.arange(16).reshape((4, 4))\n", + "grid" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 1 2 3]\n", + " [4 5 6 7]]\n", + "[[ 8 9 10 11]\n", + " [12 13 14 15]]\n" + ] + } + ], + "source": [ + "upper, lower = np.vsplit(grid, [2])\n", + "print(upper)\n", + "print(lower)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1]\n", + " [ 4 5]\n", + " [ 8 9]\n", + " [12 13]]\n", + "[[ 2 3]\n", + " [ 6 7]\n", + " [10 11]\n", + " [14 15]]\n" + ] + } + ], + "source": [ + "left, right = np.hsplit(grid, [2])\n", + "print(left)\n", + "print(right)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, for higher-dimensional arrays, `np.dsplit` will split arrays along the third axis." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.03-Computation-on-arrays-ufuncs.ipynb b/notebooks/02.03-Computation-on-arrays-ufuncs.ipynb new file mode 100644 index 000000000..72621ddc8 --- /dev/null +++ b/notebooks/02.03-Computation-on-arrays-ufuncs.ipynb @@ -0,0 +1,1170 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Computation on NumPy Arrays: Universal Functions" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Up until now, we have been discussing some of the basic nuts and bolts of NumPy. In the next few chapters, we will dive into the reasons that NumPy is so important in the Python data science world: namely, because it provides an easy and flexible interface to optimize computation with arrays of data.\n", + "\n", + "Computation on NumPy arrays can be very fast, or it can be very slow.\n", + "The key to making it fast is to use vectorized operations, generally implemented through NumPy's *universal functions* (ufuncs).\n", + "This chapter motivates the need for NumPy's ufuncs, which can be used to make repeated calculations on array elements much more efficient.\n", + "It then introduces many of the most common and useful arithmetic ufuncs available in the NumPy package." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Slowness of Loops\n", + "\n", + "Python's default implementation (known as CPython) does some operations very slowly.\n", + "This is partly due to the dynamic, interpreted nature of the language; types are flexible, so sequences of operations cannot be compiled down to efficient machine code as in languages like C and Fortran.\n", + "Recently there have been various attempts to address this weakness: well-known examples are the [PyPy project](http://pypy.org/), a just-in-time compiled implementation of Python; the [Cython project](http://cython.org), which converts Python code to compilable C code; and the [Numba project](http://numba.pydata.org/), which converts snippets of Python code to fast LLVM bytecode.\n", + "Each of these has its strengths and weaknesses, but it is safe to say that none of the three approaches has yet surpassed the reach and popularity of the standard CPython engine.\n", + "\n", + "The relative sluggishness of Python generally manifests itself in situations where many small operations are being repeated; for instance, looping over arrays to operate on each element.\n", + "For example, imagine we have an array of values and we'd like to compute the reciprocal of each.\n", + "A straightforward approach might look like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.11111111, 0.25 , 1. , 0.33333333, 0.125 ])" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "rng = np.random.default_rng(seed=1701)\n", + "\n", + "def compute_reciprocals(values):\n", + " output = np.empty(len(values))\n", + " for i in range(len(values)):\n", + " output[i] = 1.0 / values[i]\n", + " return output\n", + " \n", + "values = rng.integers(1, 10, size=5)\n", + "compute_reciprocals(values)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This implementation probably feels fairly natural to someone from, say, a C or Java background.\n", + "But if we measure the execution time of this code for a large input, we see that this operation is very slow—perhaps surprisingly so!\n", + "We'll benchmark this with IPython's `%timeit` magic (discussed in [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.61 s ± 192 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" + ] + } + ], + "source": [ + "big_array = rng.integers(1, 100, size=1000000)\n", + "%timeit compute_reciprocals(big_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It takes several seconds to compute these million operations and to store the result!\n", + "When even cell phones have processing speeds measured in gigaflops (i.e., billions of numerical operations per second), this seems almost absurdly slow.\n", + "It turns out that the bottleneck here is not the operations themselves, but the type checking and function dispatches that CPython must do at each cycle of the loop.\n", + "Each time the reciprocal is computed, Python first examines the object's type and does a dynamic lookup of the correct function to use for that type.\n", + "If we were working in compiled code instead, this type specification would be known before the code executed and the result could be computed much more efficiently." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introducing Ufuncs\n", + "\n", + "For many types of operations, NumPy provides a convenient interface into just this kind of statically typed, compiled routine. This is known as a *vectorized* operation.\n", + "For simple operations like the element-wise division here, vectorization is as simple as using Python arithmetic operators directly on the array object.\n", + "This vectorized approach is designed to push the loop into the compiled layer that underlies NumPy, leading to much faster execution.\n", + "\n", + "Compare the results of the following two operations:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.11111111 0.25 1. 0.33333333 0.125 ]\n", + "[0.11111111 0.25 1. 0.33333333 0.125 ]\n" + ] + } + ], + "source": [ + "print(compute_reciprocals(values))\n", + "print(1.0 / values)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the execution time for our big array, we see that it completes orders of magnitude faster than the Python loop:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.54 ms ± 383 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%timeit (1.0 / big_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vectorized operations in NumPy are implemented via ufuncs, whose main purpose is to quickly execute repeated operations on values in NumPy arrays.\n", + "Ufuncs are extremely flexible—before we saw an operation between a scalar and an array, but we can also operate between two arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0.5 , 0.66666667, 0.75 , 0.8 ])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.arange(5) / np.arange(1, 6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And ufunc operations are not limited to one-dimensional arrays. They can act on multidimensional arrays as well:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1, 2, 4],\n", + " [ 8, 16, 32],\n", + " [ 64, 128, 256]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.arange(9).reshape((3, 3))\n", + "2 ** x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Computations using vectorization through ufuncs are nearly always more efficient than their counterparts implemented using Python loops, especially as the arrays grow in size.\n", + "Any time you see such a loop in a NumPy script, you should consider whether it can be replaced with a vectorized expression." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exploring NumPy's Ufuncs\n", + "\n", + "Ufuncs exist in two flavors: *unary ufuncs*, which operate on a single input, and *binary ufuncs*, which operate on two inputs.\n", + "We'll see examples of both these types of functions here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Array Arithmetic\n", + "\n", + "NumPy's ufuncs feel very natural to use because they make use of Python's native arithmetic operators.\n", + "The standard addition, subtraction, multiplication, and division can all be used:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [0 1 2 3]\n", + "x + 5 = [5 6 7 8]\n", + "x - 5 = [-5 -4 -3 -2]\n", + "x * 2 = [0 2 4 6]\n", + "x / 2 = [0. 0.5 1. 1.5]\n", + "x // 2 = [0 0 1 1]\n" + ] + } + ], + "source": [ + "x = np.arange(4)\n", + "print(\"x =\", x)\n", + "print(\"x + 5 =\", x + 5)\n", + "print(\"x - 5 =\", x - 5)\n", + "print(\"x * 2 =\", x * 2)\n", + "print(\"x / 2 =\", x / 2)\n", + "print(\"x // 2 =\", x // 2) # floor division" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is also a unary ufunc for negation, a `**` operator for exponentiation, and a `%` operator for modulus:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-x = [ 0 -1 -2 -3]\n", + "x ** 2 = [0 1 4 9]\n", + "x % 2 = [0 1 0 1]\n" + ] + } + ], + "source": [ + "print(\"-x = \", -x)\n", + "print(\"x ** 2 = \", x ** 2)\n", + "print(\"x % 2 = \", x % 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, these can be strung together however you wish, and the standard order of operations is respected:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-1. , -2.25, -4. , -6.25])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "-(0.5*x + 1) ** 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these arithmetic operations are simply convenient wrappers around specific ufuncs built into NumPy. For example, the `+` operator is a wrapper for the `add` ufunc:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 3, 4, 5])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.add(x, 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following table lists the arithmetic operators implemented in NumPy:\n", + "\n", + "| Operator | Equivalent ufunc | Description |\n", + "|-------------|-------------------|-------------------------------------|\n", + "|`+` |`np.add` |Addition (e.g., `1 + 1 = 2`) |\n", + "|`-` |`np.subtract` |Subtraction (e.g., `3 - 2 = 1`) |\n", + "|`-` |`np.negative` |Unary negation (e.g., `-2`) |\n", + "|`*` |`np.multiply` |Multiplication (e.g., `2 * 3 = 6`) |\n", + "|`/` |`np.divide` |Division (e.g., `3 / 2 = 1.5`) |\n", + "|`//` |`np.floor_divide` |Floor division (e.g., `3 // 2 = 1`) |\n", + "|`**` |`np.power` |Exponentiation (e.g., `2 ** 3 = 8`) |\n", + "|`%` |`np.mod` |Modulus/remainder (e.g., `9 % 4 = 1`)|\n", + "\n", + "Additionally, there are Boolean/bitwise operators; we will explore these in [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Absolute Value\n", + "\n", + "Just as NumPy understands Python's built-in arithmetic operators, it also understands Python's built-in absolute value function:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 1, 0, 1, 2])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([-2, -1, 0, 1, 2])\n", + "abs(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The corresponding NumPy ufunc is `np.absolute`, which is also available under the alias `np.abs`:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 1, 0, 1, 2])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.absolute(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 1, 0, 1, 2])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.abs(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This ufunc can also handle complex data, in which case it returns the magnitude:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([5., 5., 2., 1.])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([3 - 4j, 4 - 3j, 2 + 0j, 0 + 1j])\n", + "np.abs(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Trigonometric Functions\n", + "\n", + "NumPy provides a large number of useful ufuncs, and some of the most useful for the data scientist are the trigonometric functions.\n", + "We'll start by defining an array of angles:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "theta = np.linspace(0, np.pi, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can compute some trigonometric functions on these values:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = [0. 1.57079633 3.14159265]\n", + "sin(theta) = [0.0000000e+00 1.0000000e+00 1.2246468e-16]\n", + "cos(theta) = [ 1.000000e+00 6.123234e-17 -1.000000e+00]\n", + "tan(theta) = [ 0.00000000e+00 1.63312394e+16 -1.22464680e-16]\n" + ] + } + ], + "source": [ + "print(\"theta = \", theta)\n", + "print(\"sin(theta) = \", np.sin(theta))\n", + "print(\"cos(theta) = \", np.cos(theta))\n", + "print(\"tan(theta) = \", np.tan(theta))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The values are computed to within machine precision, which is why values that should be zero do not always hit exactly zero.\n", + "Inverse trigonometric functions are also available:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [-1, 0, 1]\n", + "arcsin(x) = [-1.57079633 0. 1.57079633]\n", + "arccos(x) = [3.14159265 1.57079633 0. ]\n", + "arctan(x) = [-0.78539816 0. 0.78539816]\n" + ] + } + ], + "source": [ + "x = [-1, 0, 1]\n", + "print(\"x = \", x)\n", + "print(\"arcsin(x) = \", np.arcsin(x))\n", + "print(\"arccos(x) = \", np.arccos(x))\n", + "print(\"arctan(x) = \", np.arctan(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exponents and Logarithms\n", + "\n", + "Other common operations available in NumPy ufuncs are the exponentials:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [1, 2, 3]\n", + "e^x = [ 2.71828183 7.3890561 20.08553692]\n", + "2^x = [2. 4. 8.]\n", + "3^x = [ 3. 9. 27.]\n" + ] + } + ], + "source": [ + "x = [1, 2, 3]\n", + "print(\"x =\", x)\n", + "print(\"e^x =\", np.exp(x))\n", + "print(\"2^x =\", np.exp2(x))\n", + "print(\"3^x =\", np.power(3., x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The inverse of the exponentials, the logarithms, are also available.\n", + "The basic `np.log` gives the natural logarithm; if you prefer to compute the base-2 logarithm or the base-10 logarithm, these are available as well:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [1, 2, 4, 10]\n", + "ln(x) = [0. 0.69314718 1.38629436 2.30258509]\n", + "log2(x) = [0. 1. 2. 3.32192809]\n", + "log10(x) = [0. 0.30103 0.60205999 1. ]\n" + ] + } + ], + "source": [ + "x = [1, 2, 4, 10]\n", + "print(\"x =\", x)\n", + "print(\"ln(x) =\", np.log(x))\n", + "print(\"log2(x) =\", np.log2(x))\n", + "print(\"log10(x) =\", np.log10(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are also some specialized versions that are useful for maintaining precision with very small input:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exp(x) - 1 = [0. 0.0010005 0.01005017 0.10517092]\n", + "log(1 + x) = [0. 0.0009995 0.00995033 0.09531018]\n" + ] + } + ], + "source": [ + "x = [0, 0.001, 0.01, 0.1]\n", + "print(\"exp(x) - 1 =\", np.expm1(x))\n", + "print(\"log(1 + x) =\", np.log1p(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When `x` is very small, these functions give more precise values than if the raw `np.log` or `np.exp` were to be used." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Specialized Ufuncs\n", + "\n", + "NumPy has many more ufuncs available, including for hyperbolic trigonometry, bitwise arithmetic, comparison operations, conversions from radians to degrees, rounding and remainders, and much more.\n", + "A look through the NumPy documentation reveals a lot of interesting functionality.\n", + "\n", + "Another excellent source for more specialized ufuncs is the submodule `scipy.special`.\n", + "If you want to compute some obscure mathematical function on your data, chances are it is implemented in `scipy.special`.\n", + "There are far too many functions to list them all, but the following snippet shows a couple that might come up in a statistics context:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from scipy import special" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "gamma(x) = [1.0000e+00 2.4000e+01 3.6288e+05]\n", + "ln|gamma(x)| = [ 0. 3.17805383 12.80182748]\n", + "beta(x, 2) = [0.5 0.03333333 0.00909091]\n" + ] + } + ], + "source": [ + "# Gamma functions (generalized factorials) and related functions\n", + "x = [1, 5, 10]\n", + "print(\"gamma(x) =\", special.gamma(x))\n", + "print(\"ln|gamma(x)| =\", special.gammaln(x))\n", + "print(\"beta(x, 2) =\", special.beta(x, 2))" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "erf(x) = [0. 0.32862676 0.67780119 0.84270079]\n", + "erfc(x) = [1. 0.67137324 0.32219881 0.15729921]\n", + "erfinv(x) = [0. 0.27246271 0.73286908 inf]\n" + ] + } + ], + "source": [ + "# Error function (integral of Gaussian),\n", + "# its complement, and its inverse\n", + "x = np.array([0, 0.3, 0.7, 1.0])\n", + "print(\"erf(x) =\", special.erf(x))\n", + "print(\"erfc(x) =\", special.erfc(x))\n", + "print(\"erfinv(x) =\", special.erfinv(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are many, many more ufuncs available in both NumPy and `scipy.special`.\n", + "Because the documentation of these packages is available online, a web search along the lines of \"gamma function python\" will generally find the relevant information." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Advanced Ufunc Features\n", + "\n", + "Many NumPy users make use of ufuncs without ever learning their full set of features.\n", + "I'll outline a few specialized features of ufuncs here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Specifying Output\n", + "\n", + "For large calculations, it is sometimes useful to be able to specify the array where the result of the calculation will be stored.\n", + "For all ufuncs, this can be done using the `out` argument of the function:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0. 10. 20. 30. 40.]\n" + ] + } + ], + "source": [ + "x = np.arange(5)\n", + "y = np.empty(5)\n", + "np.multiply(x, 10, out=y)\n", + "print(y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can even be used with array views. For example, we can write the results of a computation to every other element of a specified array:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 0. 2. 0. 4. 0. 8. 0. 16. 0.]\n" + ] + } + ], + "source": [ + "y = np.zeros(10)\n", + "np.power(2, x, out=y[::2])\n", + "print(y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we had instead written `y[::2] = 2 ** x`, this would have resulted in the creation of a temporary array to hold the results of `2 ** x`, followed by a second operation copying those values into the `y` array.\n", + "This doesn't make much of a difference for such a small computation, but for very large arrays the memory savings from careful use of the `out` argument can be significant." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Aggregations\n", + "\n", + "For binary ufuncs, aggregations can be computed directly from the object.\n", + "For example, if we'd like to *reduce* an array with a particular operation, we can use the `reduce` method of any ufunc.\n", + "A reduce repeatedly applies a given operation to the elements of an array until only a single result remains.\n", + "\n", + "For example, calling `reduce` on the `add` ufunc returns the sum of all elements in the array:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "15" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.arange(1, 6)\n", + "np.add.reduce(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, calling `reduce` on the `multiply` ufunc results in the product of all array elements:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "120" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.multiply.reduce(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we'd like to store all the intermediate results of the computation, we can instead use `accumulate`:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1, 3, 6, 10, 15])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.add.accumulate(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1, 2, 6, 24, 120])" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.multiply.accumulate(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that for these particular cases, there are dedicated NumPy functions to compute the results (`np.sum`, `np.prod`, `np.cumsum`, `np.cumprod`), which we'll explore in [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Outer Products\n", + "\n", + "Finally, any ufunc can compute the output of all pairs of two different inputs using the `outer` method.\n", + "This allows you, in one line, to do things like create a multiplication table:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1, 2, 3, 4, 5],\n", + " [ 2, 4, 6, 8, 10],\n", + " [ 3, 6, 9, 12, 15],\n", + " [ 4, 8, 12, 16, 20],\n", + " [ 5, 10, 15, 20, 25]])" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.arange(1, 6)\n", + "np.multiply.outer(x, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `ufunc.at` and `ufunc.reduceat` methods are useful as well, and we will explore them in [Fancy Indexing](02.07-Fancy-Indexing.ipynb).\n", + "\n", + "We will also encounter the ability of ufuncs to operate between arrays of different shapes and sizes, a set of operations known as *broadcasting*.\n", + "This subject is important enough that we will devote a whole chapter to it (see [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ufuncs: Learning More" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "More information on universal functions (including the full list of available functions) can be found on the [NumPy](http://www.numpy.org) and [SciPy](http://www.scipy.org) documentation websites.\n", + "\n", + "Recall that you can also access information directly from within IPython by importing the packages and using IPython's tab completion and help (`?`) functionality, as described in [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.04-Computation-on-arrays-aggregates.ipynb b/notebooks/02.04-Computation-on-arrays-aggregates.ipynb new file mode 100644 index 000000000..7684d9381 --- /dev/null +++ b/notebooks/02.04-Computation-on-arrays-aggregates.ipynb @@ -0,0 +1,663 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Aggregations: min, max, and Everything in Between" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A first step in exploring any dataset is often to compute various summary statistics.\n", + "Perhaps the most common summary statistics are the mean and standard deviation, which allow you to summarize the \"typical\" values in a dataset, but other aggregations are useful as well (the sum, product, median, minimum and maximum, quantiles, etc.).\n", + "\n", + "NumPy has fast built-in aggregation functions for working on arrays; we'll discuss and try out some of them here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summing the Values in an Array\n", + "\n", + "As a quick example, consider computing the sum of all values in an array.\n", + "Python itself can do this using the built-in `sum` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "rng = np.random.default_rng()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "52.76825337322368" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L = rng.random(100)\n", + "sum(L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The syntax is quite similar to that of NumPy's `sum` function, and the result is the same in the simplest case:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "52.76825337322366" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.sum(L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "However, because it executes the operation in compiled code, NumPy's version of the operation is computed much more quickly:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "89.9 ms ± 233 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", + "521 µs ± 8.37 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" + ] + } + ], + "source": [ + "big_array = rng.random(1000000)\n", + "%timeit sum(big_array)\n", + "%timeit np.sum(big_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Be careful, though: the `sum` function and the `np.sum` function are not identical, which can sometimes lead to confusion!\n", + "In particular, their optional arguments have different meanings (`sum(x, 1)` initializes the sum at `1`, while `np.sum(x, 1)` sums along axis `1`), and `np.sum` is aware of multiple array dimensions, as we will see in the following section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Minimum and Maximum\n", + "\n", + "Similarly, Python has built-in `min` and `max` functions, used to find the minimum value and maximum value of any given array:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(2.0114398036064074e-07, 0.9999997912802653)" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "min(big_array), max(big_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "NumPy's corresponding functions have similar syntax, and again operate much more quickly:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(2.0114398036064074e-07, 0.9999997912802653)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.min(big_array), np.max(big_array)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "72 ms ± 177 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", + "564 µs ± 3.11 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" + ] + } + ], + "source": [ + "%timeit min(big_array)\n", + "%timeit np.min(big_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For `min`, `max`, `sum`, and several other NumPy aggregates, a shorter syntax is to use methods of the array object itself:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.0114398036064074e-07 0.9999997912802653 499854.0273321711\n" + ] + } + ], + "source": [ + "print(big_array.min(), big_array.max(), big_array.sum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whenever possible, make sure that you are using the NumPy version of these aggregates when operating on NumPy arrays!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multidimensional Aggregates\n", + "\n", + "One common type of aggregation operation is an aggregate along a row or column.\n", + "Say you have some data stored in a two-dimensional array:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 3 1 2]\n", + " [1 9 7 0]\n", + " [4 8 3 7]]\n" + ] + } + ], + "source": [ + "M = rng.integers(0, 10, (3, 4))\n", + "print(M)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "NumPy aggregations will apply across all elements of a multidimensional array:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "45" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M.sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aggregation functions take an additional argument specifying the *axis* along which the aggregate is computed. For example, we can find the minimum value within each column by specifying `axis=0`:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 3, 1, 0])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M.min(axis=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function returns four values, corresponding to the four columns of numbers.\n", + "\n", + "Similarly, we can find the maximum value within each row:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3, 9, 8])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M.max(axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The way the axis is specified here can be confusing to users coming from other languages.\n", + "The `axis` keyword specifies the dimension of the array that will be *collapsed*, rather than the dimension that will be returned.\n", + "So, specifying `axis=0` means that axis 0 will be collapsed: for two-dimensional arrays, values within each column will be aggregated." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Other Aggregation Functions\n", + "\n", + "NumPy provides several other aggregation functions with a similar API, and additionally most have a `NaN`-safe counterpart that computes the result while ignoring missing values, which are marked by the special IEEE floating-point `NaN` value (see [Handling Missing Data](03.04-Missing-Values.ipynb)).\n", + "\n", + "The following table provides a list of useful aggregation functions available in NumPy:\n", + "\n", + "|Function name | NaN-safe version| Description |\n", + "|-----------------|-------------------|-----------------------------------------------|\n", + "| `np.sum` | `np.nansum` | Compute sum of elements |\n", + "| `np.prod` | `np.nanprod` | Compute product of elements |\n", + "| `np.mean` | `np.nanmean` | Compute mean of elements |\n", + "| `np.std` | `np.nanstd` | Compute standard deviation |\n", + "| `np.var` | `np.nanvar` | Compute variance |\n", + "| `np.min` | `np.nanmin` | Find minimum value |\n", + "| `np.max` | `np.nanmax` | Find maximum value |\n", + "| `np.argmin` | `np.nanargmin` | Find index of minimum value |\n", + "| `np.argmax` | `np.nanargmax` | Find index of maximum value |\n", + "| `np.median` | `np.nanmedian` | Compute median of elements |\n", + "| `np.percentile` | `np.nanpercentile`| Compute rank-based statistics of elements |\n", + "| `np.any` | N/A | Evaluate whether any elements are true |\n", + "| `np.all` | N/A | Evaluate whether all elements are true |\n", + "\n", + "You will see these aggregates often throughout the rest of the book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: What Is the Average Height of US Presidents?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aggregates available in NumPy can act as summary statistics for a set of values.\n", + "As a small example, let's consider the heights of all US presidents.\n", + "This data is available in the file *president_heights.csv*, which is a comma-separated list of labels and values:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "order,name,height(cm)\n", + "1,George Washington,189\n", + "2,John Adams,170\n", + "3,Thomas Jefferson,189\n" + ] + } + ], + "source": [ + "!head -4 data/president_heights.csv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use the Pandas package, which we'll explore more fully in [Part 3](03.00-Introduction-to-Pandas.ipynb), to read the file and extract this information (note that the heights are measured in centimeters):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[189 170 189 163 183 171 185 168 173 183 173 173 175 178 183 193 178 173\n", + " 174 183 183 168 170 178 182 180 183 178 182 188 175 179 183 193 182 183\n", + " 177 185 188 188 182 185 191 182]\n" + ] + } + ], + "source": [ + "import pandas as pd\n", + "data = pd.read_csv('data/president_heights.csv')\n", + "heights = np.array(data['height(cm)'])\n", + "print(heights)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have this data array, we can compute a variety of summary statistics:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean height: 180.04545454545453\n", + "Standard deviation: 6.983599441335736\n", + "Minimum height: 163\n", + "Maximum height: 193\n" + ] + } + ], + "source": [ + "print(\"Mean height: \", heights.mean())\n", + "print(\"Standard deviation:\", heights.std())\n", + "print(\"Minimum height: \", heights.min())\n", + "print(\"Maximum height: \", heights.max())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that in each case, the aggregation operation reduced the entire array to a single summarizing value, which gives us information about the distribution of values.\n", + "We may also wish to compute quantiles:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "25th percentile: 174.75\n", + "Median: 182.0\n", + "75th percentile: 183.5\n" + ] + } + ], + "source": [ + "print(\"25th percentile: \", np.percentile(heights, 25))\n", + "print(\"Median: \", np.median(heights))\n", + "print(\"75th percentile: \", np.percentile(heights, 75))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that the median height of US presidents is 182 cm, or just shy of six feet.\n", + "\n", + "Of course, sometimes it's more useful to see a visual representation of this data, which we can accomplish using tools in Matplotlib (we'll discuss Matplotlib more fully in [Part 4](04.00-Introduction-To-Matplotlib.ipynb)). For example, this code generates the following chart:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(heights)\n", + "plt.title('Height Distribution of US Presidents')\n", + "plt.xlabel('height (cm)')\n", + "plt.ylabel('number');" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.05-Computation-on-arrays-broadcasting.ipynb b/notebooks/02.05-Computation-on-arrays-broadcasting.ipynb new file mode 100644 index 000000000..67bd7af9a --- /dev/null +++ b/notebooks/02.05-Computation-on-arrays-broadcasting.ipynb @@ -0,0 +1,845 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Computation on Arrays: Broadcasting" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We saw in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) how NumPy's universal functions can be used to *vectorize* operations and thereby remove slow Python loops.\n", + "This chapter discusses *broadcasting*: a set of rules by which NumPy lets you apply binary operations (e.g., addition, subtraction, multiplication, etc.) between arrays of different sizes and shapes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introducing Broadcasting\n", + "\n", + "Recall that for arrays of the same size, binary operations are performed on an element-by-element basis:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([5, 6, 7])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.array([0, 1, 2])\n", + "b = np.array([5, 5, 5])\n", + "a + b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Broadcasting allows these types of binary operations to be performed on arrays of different sizes—for example, we can just as easily add a scalar (think of it as a zero-dimensional array) to an array:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([5, 6, 7])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a + 5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can think of this as an operation that stretches or duplicates the value `5` into the array `[5, 5, 5]`, and adds the results.\n", + "\n", + "We can similarly extend this idea to arrays of higher dimension. Observe the result when we add a one-dimensional array to a two-dimensional array:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 1., 1.],\n", + " [1., 1., 1.],\n", + " [1., 1., 1.]])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M = np.ones((3, 3))\n", + "M" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 2., 3.],\n", + " [1., 2., 3.],\n", + " [1., 2., 3.]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M + a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the one-dimensional array `a` is stretched, or broadcasted, across the second dimension in order to match the shape of `M`.\n", + "\n", + "While these examples are relatively easy to understand, more complicated cases can involve broadcasting of both arrays. Consider the following example:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 1 2]\n", + "[[0]\n", + " [1]\n", + " [2]]\n" + ] + } + ], + "source": [ + "a = np.arange(3)\n", + "b = np.arange(3)[:, np.newaxis]\n", + "\n", + "print(a)\n", + "print(b)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 1, 2],\n", + " [1, 2, 3],\n", + " [2, 3, 4]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a + b" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as before we stretched or broadcasted one value to match the shape of the other, here we've stretched *both* `a` and `b` to match a common shape, and the result is a two-dimensional array!\n", + "The geometry of these examples is visualized in the following figure. (Code to produce this plot can be found in the online [appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Broadcasting), and is adapted from a source published in the [astroML](http://astroml.org) documentation. Used by permission.)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Broadcasting Visual](images/02.05-broadcasting.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The light boxes represent the broadcasted values. This way of thinking about broadcasting may raise questions about its efficiency in terms of memory use, but worry not: NumPy broadcasting does not actually copy the broadcasted values in memory. Still, this can be a useful mental model as we think about broadcasting." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Rules of Broadcasting\n", + "\n", + "Broadcasting in NumPy follows a strict set of rules to determine the interaction between the two arrays:\n", + "\n", + "- Rule 1: If the two arrays differ in their number of dimensions, the shape of the one with fewer dimensions is *padded* with ones on its leading (left) side.\n", + "- Rule 2: If the shape of the two arrays does not match in any dimension, the array with shape equal to 1 in that dimension is stretched to match the other shape.\n", + "- Rule 3: If in any dimension the sizes disagree and neither is equal to 1, an error is raised.\n", + "\n", + "To make these rules clear, let's consider a few examples in detail." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Broadcasting Example 1\n", + "\n", + "Suppose we want to add a two-dimensional array to a one-dimensional array:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "M = np.ones((2, 3))\n", + "a = np.arange(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's consider an operation on these two arrays, which have the following shapes:\n", + "\n", + "- `M.shape` is `(2, 3)`\n", + "- `a.shape` is `(3,)`\n", + "\n", + "We see by rule 1 that the array `a` has fewer dimensions, so we pad it on the left with ones:\n", + "\n", + "- `M.shape` remains `(2, 3)`\n", + "- `a.shape` becomes `(1, 3)`\n", + "\n", + "By rule 2, we now see that the first dimension disagrees, so we stretch this dimension to match:\n", + "\n", + "- `M.shape` remains `(2, 3)`\n", + "- `a.shape` becomes `(2, 3)`\n", + "\n", + "The shapes now match, and we see that the final shape will be `(2, 3)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 2., 3.],\n", + " [1., 2., 3.]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M + a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Broadcasting Example 2\n", + "\n", + "Now let's take a look at an example where both arrays need to be broadcast:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "a = np.arange(3).reshape((3, 1))\n", + "b = np.arange(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, we'll start by determining the shapes of the arrays:\n", + "\n", + "- `a.shape` is `(3, 1)`\n", + "- `b.shape` is `(3,)`\n", + "\n", + "Rule 1 says we must pad the shape of `b` with ones:\n", + "\n", + "- `a.shape` remains `(3, 1)`\n", + "- `b.shape` becomes `(1, 3)`\n", + "\n", + "And rule 2 tells us that we must upgrade each of these ``1``s to match the corresponding size of the other array:\n", + "\n", + "- `a.shape` becomes `(3, 3)`\n", + "- `b.shape` becomes `(3, 3)`\n", + "\n", + "Because the results match, these shapes are compatible. We can see this here:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 1, 2],\n", + " [1, 2, 3],\n", + " [2, 3, 4]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a + b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Broadcasting Example 3\n", + "\n", + "Next, let's take a look at an example in which the two arrays are not compatible:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "M = np.ones((3, 2))\n", + "a = np.arange(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is just a slightly different situation than in the first example: the matrix `M` is transposed.\n", + "How does this affect the calculation? The shapes of the arrays are as follows:\n", + "\n", + "- `M.shape` is `(3, 2)`\n", + "- `a.shape` is `(3,)`\n", + "\n", + "Again, rule 1 tells us that we must pad the shape of `a` with ones:\n", + "\n", + "- `M.shape` remains `(3, 2)`\n", + "- `a.shape` becomes `(1, 3)`\n", + "\n", + "By rule 2, the first dimension of `a` is then stretched to match that of `M`:\n", + "\n", + "- `M.shape` remains `(3, 2)`\n", + "- `a.shape` becomes `(3, 3)`\n", + "\n", + "Now we hit rule 3—the final shapes do not match, so these two arrays are incompatible, as we can observe by attempting this operation:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "ValueError", + "evalue": "operands could not be broadcast together with shapes (3,2) (3,) ", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mM\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,2) (3,) " + ] + } + ], + "source": [ + "M + a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note the potential confusion here: you could imagine making `a` and `M` compatible by, say, padding `a`'s shape with ones on the right rather than the left.\n", + "But this is not how the broadcasting rules work!\n", + "That sort of flexibility might be useful in some cases, but it would lead to potential areas of ambiguity.\n", + "If right-side padding is what you'd like, you can do this explicitly by reshaping the array (we'll use the `np.newaxis` keyword introduced in [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb) for this):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(3, 1)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[:, np.newaxis].shape" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 1.],\n", + " [2., 2.],\n", + " [3., 3.]])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M + a[:, np.newaxis]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Also notice that while we've been focusing on the `+` operator here, these broadcasting rules apply to *any* binary ufunc.\n", + "For example, here is the `logaddexp(a, b)` function, which computes `log(exp(a) + exp(b))` with more precision than the naive approach:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.31326169, 1.31326169],\n", + " [1.69314718, 1.69314718],\n", + " [2.31326169, 2.31326169]])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.logaddexp(M, a[:, np.newaxis])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on the many available universal functions, refer to [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Broadcasting in Practice" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Broadcasting operations form the core of many examples you'll see throughout this book.\n", + "We'll now take a look at some instances of where they can be useful." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Centering an Array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb), we saw that ufuncs allow a NumPy user to remove the need to explicitly write slow Python loops. Broadcasting extends this ability.\n", + "One commonly seen example in data science is subtracting the row-wise mean from an array of data.\n", + "Imagine we have an array of 10 observations, each of which consists of 3 values.\n", + "Using the standard convention (see [Data Representation in Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb#Data-Representation-in-Scikit-Learn)), we'll store this in a $10 \\times 3$ array:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "rng = np.random.default_rng(seed=1701)\n", + "X = rng.random((10, 3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compute the mean of each column using the `mean` aggregate across the first dimension:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.38503638, 0.36991443, 0.63896043])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Xmean = X.mean(0)\n", + "Xmean" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And now we can center the `X` array by subtracting the mean (this is a broadcasting operation):" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "X_centered = X - Xmean" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To double-check that we've done this correctly, we can check that the centered array has a mean near zero:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 4.99600361e-17, -4.44089210e-17, 0.00000000e+00])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X_centered.mean(0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To within machine precision, the mean is now zero." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting a Two-Dimensional Function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One place that broadcasting often comes in handy is in displaying images based on two-dimensional functions.\n", + "If we want to define a function $z = f(x, y)$, broadcasting can be used to compute the function across the grid:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# x and y have 50 steps from 0 to 5\n", + "x = np.linspace(0, 5, 50)\n", + "y = np.linspace(0, 5, 50)[:, np.newaxis]\n", + "\n", + "z = np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use Matplotlib to plot this two-dimensional array, shown in the following figure (these tools will be discussed in full in [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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ldPwLI0+adU5eXRHtf1z4MdGO6vakqSUNCkM/kv2nBes4WzgpswNUK/K4zXIg03BVHufJijSqXFc4arbZmZUGhSgTmBjU7TOnRPyDjY1mkwO1Ted/n2/90O5zibTdPQb0iY2I3gjgBDM/tth6zHw3M+9h5j35jLXoOI5zeXEuVjTJZ72R5IntFgBvIqI3ACgCGCaiTzHzr13arjmOc6lJa82DnmfFzHcx83Zm3oV2SMSDPqk5zvqnnbaIEn3WG5eNg26rKQcvqLGpku0hUTOnnF51xWxTtQpAPi+1rqbSqPJZ6+CazYTC3C8QCpvXDroFdb+MRKakOyoFGSh/uhioZJ9XO1LNaMEG/hdPy/3Eah+Nih3/p6syAeQ3ylIL26KqWAHAy3LynF6mAucB4A3jUnebvFa63z5ZtwH51JT9Y5Ka4NBR6bDb3kZelcKEuleO2/upNiYdl58d2yzaz1Vt4Pz1eamxjWV6J1FYUK97x5pW43x29sKxFwIO7MshrRrbkkaHmb+KdloRx3HWOe3sHul8FfXIA8cZUNohVT6xOY6TKvyJbWW0An5sSqJiFQS/0Oztxxay6ERK0NMFUspZ69+kfdtqGal35LNWoyr00NhCZEwleNkeDWhsYwW57GDJHrc5pMZFFW/R2hIAZOflOZUycpvmkPUdmyxL7eufKleL9pa8rdg+Ovy4aO/MWk3nJ1SCyrObpLvQbMP25fmm1raU5patQFOYkNc+EyvN7awdp+Jp5d93SvpoPr1BBskDwCuKPxLtzZEdlxwWd6GYiYtm2ZHZ0fO/h5JELIe0Rh74E5vjDCjnrKJpxCc2xxlg/FXUcZxU0ceaB5cd6ZyuHcfpCQNocibRpxdEdCsRPUdE+4novYHv305EJ4lob+fzzq7v7iCifZ3PHf04t8vGQRcqa+1CbLs2F8tMpPUkGXV7VK0CgCHltEuqw8WA8SCnjAdR0CW3R99U9aJqxgbBb1DGg6hsHYybZSmcN4fkjchRwMgyIx1/86dl/yv5QGUrZaQ4Ux4T7YdK0mEXADbmZCbbssqoCwDjKkj8J4cOiPbMFiuk/1VT3h8v8BWizZG9fypFeY/pal7mngSQ1X6+U3IMnj+7wWxzcET25fqAU/K4MtbkEjw4zTUuHLtfT1r9eBXt5Gr8MIDXoV0s+REiujdQlOVzzPxute042lXh96A91z7W2dYO2hLwJzbHGVS4/Sqa5NODmwHsZ+YDzFwH8FkAtyXsxS8AeICZJzqT2QMAbl32OXXwic1xBpRziSaTfABsJKJHuz53du3qSgDdPjuHO8s0v0xETxDRF4joXIHlpNsuCTceOM4As4RX2lPMvGcFh/p/AD7TKYz8bwF8AsBrVrC/RVmdiS2ksWk/U62xBRx0ayy722Dbfa116crwIQfdSl7qTboC1VDW6lo6uF4nuAwRkXxAzih9YzhjK8GP56XIUyrVzDrzFenQWi/LsYyH7DhlJ+U5Zs5KLc+qWsBwTjqnNtV+9xdlgDgAfDl3g2iXN9v+v7ookyZuiWTfXl3aZ7aZ3ip7+GX1B3qcbKLGVl5qmsWT6noELqHWh6N5uc3EnM09eKQutceJor2XR1RgfDlB0tFc1za0jESnmj4mmjwCYEdXe3tn2YVjMZ/uan4UF6q9HwHws2rbr660Q/4q6jgDCoPQbGUSfXrwCIDdRHQ1EeXRTm92b/cKRNQdKvImtOunAO3q8a8nojEiGgPw+s6yFeGvoo4zwPQjpIqZm0T0brQnpAjAPcz8FBG9H8CjzHwvgN8gojcBaAKYAPD2zrYTRPSHaE+OAPB+5pUXTfWJzXEGFe6f2wgz3wfgPrXs97t+vwvAXRfZ9h4A9/SlIx1WyY+tdzEXUokma7H1UZuLZTC0TjwJWL81rX2Vs1bjCfm29fq+kJG+bZE6oSTv+Dnjx2aPo/3AxktWe/nhsNS+6iNKi6zascxPyLGjGbnfzIStpD6k/M1G8jLQvJW3weqPF7aLdimgV+Y2yrG8sfCCaG8O6E0/VXlOtGtb5Dk/GPiDPZ6VhVm0RpibMZvAxJqr3TYa9k/odF2Oy2TL6nAtlgerKr+2bTnrxrVx6MI22QTJK3uR5mIu/sTmOAOMT2yO46QKBiHubRhYl/jE5jgDjOdjcxwnVXAfjQeXG2vooMuqLQe43rSC97w2HrA1HuRYCtHaeKBFfwCo5hZ30K2GDA6RdtC1+9XErA0Mi1eGB4DxSDrodgvI5zg8LB1CtfGgNmLHslCVCQXyU3IdnrHZfKMTUtCuqLeYVlYaMdrLpHD+7WiXWUcnFGiNyR2/JFBtfUskx+EnK/tFu7HFnvM31HU9lpfj1jhj/xyooZydy/Ia5gMifk1ZHGbZGlVi9UdRUoakHbnT0OyuXqh+9XDU+35LAvvE5jhOukhvPjaf2BxngPEnNsdxUgUzELd8Yls2yRx0ZbvetF2bVRpbLeCgW85IPUwHxZcCTrBlpZdllP4RdOrVQfBYetUqTSjZoK5ctaVoHWerFenAOjWmtMgNAY3trBy77FlZgYrmrFMsT0tdK2rJsR3OWNcBjsqifSYqmXX+ia4RbV1gZGHMXufd+WOivUFpbjeWZaUoAGhskuPwuEog+kLZVl9vLMj7MJOT51wdsvdGSMftxRDJa7YtULHs5aUL2X10Eobl4lZRx3FSBcNfRR3HSR1uPHAcJ4UEVKJUsEqV4O0i7bKlg+CbQT82qbXMtax/UCWQfLKbUELIIa2xKQGwEoU0NrlMB9+Hysy0eiQHDAW36AIvG/LWj21TRS47OyZ9xxbO2rSRubORakvtqzgd0NjmZSLM1pSscB4F/kqGaZPcB5XNOpOQy77JUnNbiK3G9uox2d9r8idEezTSVViAl5RkcL3WX0fyNtHnqXnb3242lazmqa9REv1VJyEdz9h7u1tXLJJNJrAc/FXUcZxU0baKeqyo4zgpw19FHcdJHWl9FU3nc6jjOD1hEJiTfXqRoBL8bxHR053ye18hop1d38VdFeLv1dsuh1UKgu/toKsrBDUbgQy6zd4ZdBuqOrwWiHMB50kb0C47k8R4kFcCcUS9b4ZWgurx2iixMWuNB5tLUsQ/OaKcYjfacZqfVdlj55TD7tyw2SZbk+PUOiUDtePTNuurNiiMsq1kRSz7O9mShoFHmzuhObtdGkT2jMsA/KsKNoi8SLL/u4pynaHICvITJdk37Ty8IWeNFFfl5X5D1cc0OkFC6P7Z0HXPZRPcO0nox5towkrw/wxgDzPPEdG/Q7tK1a92vptn5hv70JXz9HxiI6IiEX2HiB4noqeI6A/62QHHcdYIBrhFiT496FkJnpkfYuZz4RQPo11m75KR5FW0BuA1zPwKADcCuJWIfvJSdspxnNVhCa+i/agEf453APi7rnaxs8+HiejN/Tivnq+izMwAzr3/5DqflNpSHGewWIJVdKWV4AEARPRrAPYA+JmuxTuZ+QgRXQPgQSJ6kpl/sJLjJNLYOu/QjwF4EYAPM/O3A+vcCeBOAChGUu/Q1bSBQBC80thasX38nVfV4WfigllHB8brSvAhB92CisAvqCR+1chqJGUVhFxMkGhSa2qxuqtCqokN4rd63+aCdBI9VZVVkubGrbPnwoLUjqKafHjP1mxlpcrCqGhnarIv8cSk2aZ1WpaIzLTszTCidDdqyf5PNayD8XO1bXKdmlznpeMySB4Adg5J7auirquuCAYA41mpoen7ZyTgCHylqjA1Hrh/IhV8XlMJUnUbAOKubbgf9UDRN6toz0rwAEBErwXwPgA/w8znbx5mPtL5eYCIvgrgJgArmtgSWUWZOe6Ie9sB3ExELw2sczcz72HmPfmM/aNwHOcygwEwJfssTpJK8DcB+AiANzHzia7lY0RU6Py+EcAtALqNDstiSVZRZp4koocA3Argeys9uOM4a0s/HHQTVoL/HwAqAP6S2hbfHzHzmwC8GMBHiKiF9oPWB5U1dVn0nNiI6AoAjc6kNoS2Sfe/rfTAjuOsNYksnolIUAn+tRfZ7psAXtaXTnSR5IltK4BPdHS2DIDPM/Pf9LsjjuOsASk1Ayaxij6Btpi3fALPuxldpaop5b5WwEF3viENAzrbB2CddrXYGwWupHaC1dk9QoK9ztSbI12ByqKNBVogbgRusljtSfcVAMayMtvqlaUp0Z4PZKA9pLKnzDWkLpoJjH+mLkX9ckONbTMgeKsMILEyJgBApJxTh+Mt8rhNedx2/+Q5Ha9tFO3peWtwOL5BGrWuqZwS7a15OW4AMKaMBzpT7xVZeX4AsEUZFMYDN0NGOeDOsLyupwPGs+Pxhf432I7jkuH0hlR5rKjjDDKD+sTmOE6a8Sc2x3HSRn9CTi871q4SvA6C1/JMw/4nqanKVbNN66Crs+pqTSrkoKuX6aruWk8DAhl0jZZnhRXtoNtQA7PAVtfSQf0htAPx5oLUfZpV2xedYPCIso7Nxlajojir2jJQvtSyfyWRcsiNp60TrHbs1WdcbW2CJtOQellUU/dGIIj/6Xl5b0xulLri7hF7zj9WPi7am5SmNhoIcNeaWjWQDbfB8n6ZVuN0qDlqttlXv6A9zvNR8/2SOefHlkL8ic1xBhhPNOk4Tvrwic1xnNThr6LLJ1EleFMZ3upCNe171QwkUFS+bQsZ2c5EVgfSGpvW5UJ+bLpKkK7irv2UAKCh/LUW1LjMBipszbakjhjS3LTfnQ7cjobsOetq9xmVqeAwjZltZqA1KDX+NGq2KalxiI7a/reU7taalP5kmcD9U2kqv8G61NSihcBYLsj+H5rfINraTzLEiKrQviNr/clyaiwLZPerfRr1tT/UkH0DgKdmL2QCmm893rOvSQglqEgD/sTmOIMKE9CnkKrLDZ/YHGeQ8Sc2x3FSh09sjuOkDp/YVkAgayqZIHi1QtO++9frsru6ahUAzCsH3RorR1q2QeSRMQQoYwLZbbRDbjFBVapY3UWzykl2umUdRCdjWbFJGxMAa1DQ/Q9VtiqU5IDrCk25yDoyHyQpaM+ohKIcWZGco1HRLuXtLRcdk9esdVYaE3hWCvYAQCekaF9SYnwmtg66OnA+05DHPRWPmG2eVOp6NScdcrepbLkAsC06IdojCdK5NliudKpZNescnBk//3s97sOfrjvoOo6TRtwq6jhO+vCJzXGctOFPbCsgSZUqHQQfyKeIpkmOaDW2GaW7VbNSVymp6lIhdBB8KLmj1thyKv2LrkIEtAu0irbSxibjMjRTatlU3LtQjj5HXY0JAKrRvGiPqGSV5ax1Sh7KynHYl7tCtKdztv+tnLzFmkWrHZWHVHLQY1Jr5LM2cB4NeY50RganBzVPVf2KWN8/ViM8GUnd7cmCrI51ZcFqbLtyUv8bD+i6vdAJUwFZiUtXpF82fdoPEd0K4H+incPgo8z8QfV9AcAnAbwSwGkAv8rMBzvf3YV2rdEYwG8w8/0r7U+iKlWO46QQXsJnETplAz4M4BcBvATAW4noJWq1dwA4w8wvAvAhdOqmdNa7HcANaBeJ+j+d/a0In9gcZ5Dpw8QG4GYA+5n5ADPXAXwWwG1qndsAfKLz+xcA/Dy1y1XdBuCzzFxj5ucB7O/sb0X4xOY4Awy1kn0AbCSiR7s+d3bt5koAh7rahzvLEFqHmZsApgBsSLjtklmlRJMJguCV21Qm4MfWrMsn1IWm7b72besVFA8AlWjx+V1XYweAohIOc+rpORP4nxGr4i2zLPuifdYA4JQqZHKmYdfRAewjWamfFQIa4agqODKqgrt1GwBGlC5XUTrcM3lZ0R0AJovSnywu2mvWKMlzqpTlOoUTVlfMnFX9a8obiOasrpg/LfdbyqkCQjnbt7gor9GhyqhoP1vZara5riCTQG6JTpp1SqR9D+X3IV33kpDceHCKmfdcwp70FX9ic5wBhTj5pwdHAOzoam/vLAuuQ0RZACNoGxGSbLtkfGJznEGGKdlncR4BsJuIriaiPNrGgHvVOvcCuKPz+1sAPMjM3Fl+OxEViOhqALsBfGelp+V+bI4zyPTBj42Zm0T0bgD3o+3ucQ8zP0VE7wfwKDPfC+BjAP6ciPYDmEB78kNnvc8DeBpAE8C7mNnG8y0Rn9gcZ4Dpl4MuM98H4D617Pe7fl8A8K8usu0HAHygPz1ps4bGAxW03FRB8QHtlBvyzXmhYbs/05BB4rM52a5E1vFUB5HravGhylb6HT5kLDDHUe0FZTyYChgPTtalQ+tEPWA8UP2tq0DzgskwEDAWZGR7PGcD53UV9I056Tg7nrcGhyeK0qH18NC4WadRkQafRlVes/Kovc5DJ6VBITslryvV7TmTqqKVm5PrFKas+1TtjLyuM2ek8/CBDTbT7YGqrKq1O3fKrFPIymtWNokLrFPySOGCQSTqx4zE1oiXFvyJzXEGGQ+pchwndfjE5jhO2vAg+JUQeI/XslUSB11dHV4nngRsYPxsrBJPtgIOokpjiwMB7Jq8CrLWDrq66jsAqNyaJmlkKMBda2on5ytmnZYyx2snZa3BAUBJaY3VjHS+3UDSgRcANijH33GluWkNDgCuyEut6J+LO8w636/IYPqpqgymrw9b7WthVGpdQ6flOefPWo0tU5fXpJWV+plOfgoAWeXnG83IvpyetZrn0fqoaE8M2QSiW1juuJqR13BH7rTZZlflQnD9Y5E9P+cC/sTmOIOMP7E5jpMq3CrqOE4q8Se25ROsBB9rPzb5fSgGOFOXmkgz4Memq3lrvWkmtsVQaiqpX4t7+6RZPzaty9l96H+Oxo+taTW2MwtSwzkzZ9dpxFL3mVG+e83A+WQzUtTUySmHM4HklMq3aktG6nQbMi+Yba7IygSQW/OTZp1tpatE+/GK9H07OjJqtqmPynOsnZJjUJiw55ybXdx3Mi5YbVUPnX7CaQTuwcmGvEbTLXvNYqiEAqpa/I7slNnmhvKFEMr7+hAkT3DjgeM4aSSlE1vPRxMi2kFEDxHR00T0FBG9ZzU65jjOJaZ/2T0uO5I8sTUB/Edm/i4RVQE8RkQPMPPTl7hvjuNcagbVeMDMRwEc7fw+TUTPoJ3h0ic2x1nnrMensSQsSWMjol0AbgLw7cB3dwK4EwCKkapElCAI3jroBo6vHHTjWsBxU4m5s9phN2eNB7oiUJ2XXksiIpWNNUHmFX3c2abtW3dlIgCYmbXOns2G7O98Vv4brjft+WinXp0lOB8InNfVu3aoylYjGSu+VzPS0XdD5gdmnS3ZSdHeVpDtveXtZpt9w9Kp9+yYdFxeOG1v7fyUvEbK3zhIQxXeahWUASJjH3m08SnJ/VQg2d8tAQfcGwoXjAdD1LvaWiJSOrElTjRJRBUAXwTwm8x8Vn/PzHcz8x5m3pPP9C4R5zjOGtOnKlWXI4me2Igoh/ak9mlm/qtL2yXHcVaLgX0V7ZTI+hiAZ5j5jy99lxzHWTUGdWIDcAuAtwF4koj2dpb9p07GzGVjHXRVu2H1Gu2TGNftm7QOjJ8zDru2SpWpZKUqhOsg+eWig+sbrPTApq5MDszWVF/mbP9pXgXgq6E7u2AvczOWYxe3ZDt0znFZj7d0yNWaGwBUlfa4PXDHVTMnRFsH02/NTZpttpek7vZMdYtoHxobNdvMnZESSUYFtIfuuVZO3petYal9lYtW6yqr6l35QKJSjdZoS4Fqatu6HKRzfYqFWo2QKiIaB/A5ALsAHATwK8x8Rq1zI4A/BTCMdkX4DzDz5zrffRzAz6Bdsg8A3s7Mexc7ZhKr6DeABOkuHMdZX6yefvZeAF9h5g8S0Xs77d9T68wB+HVm3kdE29B2K7ufmSc73/8OM38h6QG9SpXjDCi0hM8K6a4C/wkAb9YrMPP3mXlf5/cXAJwAcIVeLyk+sTnOIJPcKrpYJfhebO74wwLAMQC2snYXRHQzgDyAbt+gDxDRE0T0ISKyflEKjxV1nAFmCVbRRSvBE9E/ANgS+Op93Q1mZqKLH5WItgL4cwB3MPM5BfAutCfEPIC70X6Nff9inV3DKlWyndEZdQMOulFdPhQ3A2Jvsy4F4YW6Mh4UrECvM37obB9a5AeWF4kSszYeqL7G9ji1mlxGc1bUz87oTLDy+9asfTCfq8llzyujy3zQyCLHbroinYWnC0eh2ZkVGjE2RHbktIHhGmWEqGYOmm1s1hCZDePZsv0be35YVpQ6NaMy9dbs+OvRHi5Jw8C2inHpxCZVvauUsZXRNDG3VNv+zXRXT6N+iWP9K7/32ot9R0THiWgrMx/tTFwnLrLeMIC/BfA+Zn64a9/nbqwaEf0ZgN/u1R9/FXWcQaWTaDLJZ4V0V4G/A8Bf6xU6FeS/BOCT2kjQmQzPuZ69GcD3eh3QJzbHGWRWJ/LggwBeR0T7ALy20wYR7SGij3bW+RUAPw3g7US0t/O5sfPdp4noSQBPAtgI4I96HdA1NscZYFYj8oCZTwP4+cDyRwG8s/P7pwB86iLbv2apx1y7KlUmCF476AZ0OaWpZWpWY9OB8Vpjm6lbg4oOPp9rSS0pFMSsNRCtkSQhVg/M9UAFrVgFsEfzgcyw02pclM9oyL84OyePVV+Q+z0c0JumF+Q4nR6T2X1PVIfNNtcPSSfeXXlbFX1LJAPli+qyVgOC667chGgXSXpvj0TWWXhTQWpfRyqjoj1ZtzHOTeW4PFqQkfM7S7IfALCzIM9xNJCNOFJOFPMsL9p0y57z6a6qZs1+vWwNcOSB4zgpZWBjRR3HSSmMwU006ThOOvFiLitkWVWqQn5sKgg+FLSsA+Mb2j8rUFVIB8ZPx9I/S1eTAoCV1wiyCQm1ngMArYZKjhjIL6hjz7NzSr8M/FeO83LssnNK75u1/n5Ts3LsnlBJL4+OWY3toPId212xLkxXF06K9jbl+xaqmJVTznpl5Su2LSf3EdpmJJJ62VRsNTadkHNEZae8KqAZXpuT5zgeuJkzJIXPOZWY9FCgmtqzta3nf19o2eMuC5/YHMdJG6GHjjTgE5vjDCrrNDtuEnxic5wBxjU2x3FSx2okmlwL1jAIvlcGXbsbvSxTt8aDjDIe9HLYBYDZhhRqdVD8XCtQ2UqJyq0+PNMzBzJfqXS4IYNJtCCPnZ+W7Sjg7KwP1ZyW45azsd1onJVjWZuSYvuxSWtwODUqK5Y9PzZu1tmhst/uGJLC/5WqahUAjGdlll3toBsiUn/FI8rqUopssLo2OIwqx98dudNmm23KwDCa6f1nNq3+Hg41Nph1npq/kDV4np/ruc9E+BOb4zipYp1WeU+CT2yOM8j4xOY4TppwB92VEvKV6RUE37TbaE0tIIkgVoHxrR4Ou0CgWrwKip8NaGwN5VzbUA6WObKR55G6izJJlFs1DKGCR5Fy2s3Ny/1m5+xxSI0vZ+W4xQXrLNyYlMsKZ+Q2tRE7tvUROQ7HR+1YHh8ZEe3nhjeJ9saKDJIHgM1DMqB9PC+1L10pCgCKSqTV+lkhIOxq7a6a0fqZdR7WiTOHyGqPNZZOu7MqmekLjTGzzb7pCyUAQklJl4PWutOCP7E5zqDifmyO46QRd/dwHCd9+BPbCgi8x1PcUu3Fg+IBm3wyWC1e6U2kipboYi8AMKd826ZN4smQH5vcTwNSr9GJBENEKmdMsHhPgqKOpjBOXe4nOxsIwl5QepL+zx3ZAxfy8pybJXn7NKoBja0qx782Yse/PqwCwkfkeB8Ylr5wAPDDqvTzKpWl1lUtWo2tmpfLhvNym7G8TU65rSCLxOjCLI3spNkmo66jrvIOwEwoWrMNBeSfmq+c/z2UMGE5pNV44DUPHGdQYbQNe0k+K4CIxonoASLa1/lpLSPt9eKuegf3di2/moi+TUT7iehzncIvi+ITm+MMMKtUpeq9AL7CzLsBfKXTDjHPzDd2Pm/qWv7fAHyImV8E4AyAd/Q6oE9sjjOgnPNjS/JZIbcB+ETn90+gXUIvWR/bJfdeA+BcSb5E2/vE5jiDStLX0Par6EYierTrc+cSjrS5q+jxMQCbL7JesbPvh4nozZ1lGwBMMp93/DsM4MpeB1wzq6j+L2CC4EMOurpKVSCbbKQddJWG3KxZ8dpUi2+qiucqoy4AzLJcp8GLV1oCZCVvwDqI5qOA921GOdKGdGh9LO3U27D7zcwr40Fdtqlpt4lIZd3NydunMGSlj7isxqlqkxBo40FtWDk/D4eMEiozsq5KX7H9p5JyyC3LG2i0Yo0HZ6qyEldLWXM2qGB8ALgiktltSyGv6mXQ6DIYcBKrUgKW8DR2ipn3XHQ/RP8AYEvgq/d1N5iZKWglAwDsZOYjRHQNgAc7tUSnLrLuori7h+MMMn2yijLzay/2HREdJ6KtzHy0U9Xd5odv7+NI5+cBIvoqgJsAfBHAKBFlO09t2wEc6dUffxV1nAFmlTS2ewHc0fn9DgB/bfpBNEZEhc7vGwHcAuBpZmYADwF4y2Lba3xic5xBhQHEnOyzMj4I4HVEtA/AazttENEeIvpoZ50XA3iUiB5HeyL7IDM/3fnu9wD8FhHtR1tz+1ivA65hEHwvB127jU6YqIO/AaClAuXjHg67gA2M10HxOvEkYJ12Gyy1Fl0pHrD/RXKqwnk+VM0oK8eJs4GkkeoqsnauzQT0GNU/qkmNjRcCGQaaAa/p7n1EgSr1BTlO2SE7lsWy1MeaVTW2w711uXqVVNve2o2KdiiW1/nYqNVSpzeovinHWF3pCgA2ZKTeWqVQAku5n6J6LKpENri+lLtwjbQT8HJZDQddZj4N4OcDyx8F8M7O798E8LKLbH8AwM1LOWbPJzYiuoeIThDR95ayY8dx1gGr4KC7FiR5Ff04gFsvcT8cx1kDVkljW3V6TmzM/HUAE6vQF8dxVhNewmed0TeNreOwdycAFCMVtJygEjw1pZakA97by1Q7oLHpZdqvTSeiBIBYBcbP1ntrbDr5pE5R2DJR5TauXCc+LAXKvEc56QPVCkTJxQV1jsqJrlWwvnuZnFxGWbuOhpXGxnXV3zjgr6W0JMrZW46UDpcvyQDwXNkGhBeH5bKm0svqgaSXtarylxtViTJnQoV+yqK9P7NRtMfyVmPTVeg3R4fMOuPqZtC+bluy1n3ryvLk+d+fCGWJWCIE+3eYFvo2sTHz3QDuBoCR/OZ0jpbjpAyvBO84TrpYp6+ZSfCJzXEGlvVp8UxCEnePzwD4FoDriOgwEfVMGeI4zvogrVbRnk9szPzWFR8liYNuj8rwQMhB1xoCWjW5jhbWQ9XjY+W0O28y6gaC4JWKryvDh9D/RXQFpErAeFAoSJF4rmjHpTkkj90oySNlKwHBXp+TzsIbumasVlLXkAPGA27UF20DAOalAE9zMhg9M22NN9G0DE7PVGQ7O2kNDnlVISs3J69zVA/9n5djN52XxoQDZVux/YdlaWDYnT9u1hlV4n9VOVHvyslAegC4vnxhPw/1wXgAILVPbP4q6jiDCrtV1HGcNJLOec0nNscZZNzdYwUEq033dNC1Dq4ZpYFEebvfuEe1+JAu11T7rTdUUHzTesXaIHi5jzjwrzCvEjWWVcWjcqC0fbkgNamZIatjNcuq/yognGLrfMuqL3lVCT4KOfUW5Dhk5mSgNs9bZ1WuKY1NO/UCtoqZamvHYABWl1N/oFFs759ef8StrL3OzZIKrp+W98bErNT2AOBEXTqoT7as3hfjrGhXM/LY27J2LF86dMHRdyjknb4cfGJzHCdVMGzZxZTgE5vjDCgE9ldRx3FSSCudj2xrN7HpRIe6MnyomEtT+7EFfN1yiyeazATyJ2rftkZDVSZPoLHpyvAtDiSNVG3txzYS0FWqBdnhk2W730ZFHltrkToQHQBaapya2vctUHQlO1dUbeVLpgvEACBVcT5TC2hDunCM9ocLPVVESgNUQfycIKg/ie+klrL0vaL1WMAmTVhgO5aaAsl1xjNWS702d7pr/T74saX4VdRTgzvOAEPMiT4rOkaCSvBE9HNdVeD3EtHCuRJ8RPRxInq+67sbex3TJzbHGWRWJ4Nuz0rwzPzQuSrwaBdIngPw912r/E5Xlfi9vQ7oE5vjDCwJJ7WVT2y3YWmV4N8C4O+Y2RZ6TYhPbI4zqCytStVqVII/x+0APqOWfYCIniCiD50r07cYa1elShsLejjsAkCmrpx4s9bZNsotXslKV5MPLWuqjLrzTSv+zrV0JXi5TWxy6gKRqt5dVsaDsaysbgQAYwX5T2uoZMX3WVUpvd5SGXRz9pwbZVXVfV47NgfGdkGeY7amgshr9jpHtdaibcBeV2NICjl462UqiJwDlbl0JuFmSbWLgW2U3YgjZXDIXBr1PUfW+FHqqnaV6VMs1BL0s9WoBI9OQeWXAbi/a/FdaE+IebST2f4egPcv1ll393CcQaZPfmz9qATf4VcAfImZz//X73raqxHRnwH47V798VdRxxlUGO0n3ySfldGzEnwXb4V6De1MhiAiQluf61kK1Cc2xxlYVs14kKQSPIhoF4AdAL6mtv80ET0J4EkAGwH8Ua8Drp3GppfpIPiAxsYNHSgf0IHUMh30Hqoer50wuSHn+4WmHaaFltSXtBNmC7aSd04FnhdUZaLRyBqBNhak7jZask68uiq6HpZ4yP7/yigNLdNUgfNWIjRjSc0EY6ucnRNVH1O+pxQqfqWeIpJkeVV5CtBUSUibZXs/1UdkO67Ie7BctCc9nJXXXjtih4hVEs+FgIP3NF+4D2PYvi6LVQipSlIJvtM+CODKwHqvWeoxXWNznEGFYYx4acEnNscZWNime08JPrE5ziDj2T0cx0kV56yiKWTtjAemSpWqeBQwHtgsuwFRXGX80GJ1KPGoqVylRPGFQAaH+VgaC+rcO5tEDnKdsupMNWMNA+M5aTzYOGSdeOsqQ+5MVo5To27734qVcK6cerkVEKdjbZXo0QZA8eIGh9AyndgiaDxoymtP6nbR7RD6kjVDFcCG5cEL4/IabavITLgAsDU/JdrVjDUkaWfteZb3wqlAxa+DjU3nf6/zafP9svAnNsdxUodPbI7jpApmm/suJfjE5jiDjD+x9RftYMkmKN7+J8koXUU77ALWaVc77AaD4LVDqFqnEajyVFMOug2ln8WBGyZSgdlF5bAbdNDNTYv25iGr6TSV52kpJx1CG61ABl1VuT6jPFyTuH/qM9T7BIBYHTsOaHdNNb5mm9j2P1b3Qktt0wpoeVo3VMOPTM7eT5WSzGC8bViO/+6qDXu8piCXbQikbc6oIPfplrwJDzaVZzCAJ+avOv/7fOuH5vtl4ROb4zjpoi9xoJclPrE5zqDCALuDruM4qcNDqlZA6HFXOxppv7aAH5t2cKJswI9N+bZpP7YoEI+sC/5ov6qQxlNryaFrcO+hzKhkKjmTeNI62Y1HM6J9RX7GrNNSGttszlbV0mTVWBZUeygQ0Z5TDmVZlWQxSlDyKA4klNHanB5b3QasH+FCjzYA1FQyA61NZgPObyMF6be2szQh2jeUjphtdmWlj9l4xp6z9mObVmNwqLHBbPPszIU8jjoJw7Jg9vJ7juOkEDceOI6TNtif2BzHSRd9SSJ5WeITm+MMKh4Ev0ISZNClphSmWXtPAkBGGwasEy9n9Tqq3QxkcNVB2ImMB9LBUgfBJwlUKZAc/pK2YsA67Y4HKllp8X04K/erRX4AKKkA/JGsPE4ocLusHE1Lqp0PRKvnAuekiZWIr52dQ4aZ2ZaswDYdF0V7Ki6ZbfQ6IaOEphLJc9yel8aDa/LWQXezslBVMkNmnQbLsZpTzsMnm1WzzdG54fO/11u9ky70ggFwSkOqEtU8IKJbieg5ItpPRKaKs+M46xDuJJpM8lln9PyXRUQRgA8DeB2AwwAeIaJ7mfnpS905x3EuLZzSV9EkT2w3A9jPzAeYuQ7gs2iXrHccZ72T0ic24h5WESJ6C4BbmfmdnfbbALyKmd+t1rsTwLmy9y9Fgtp/lwkbAZxa604sgfXU3/XUV2B99fc6ZrZC3BIgoi+jfc5JOMXMt67keKtJ34wHzHw32uXnQUSPMvOefu37UrKe+gqsr/6up74C66u/RPToSvexniaqpZLkVfQI2kVMz7G9s8xxHOeyJMnE9giA3UR0NRHlAdyOdsl6x3Gcy5Ker6LM3CSidwO4H0AE4B5mfqrHZnf3o3OrxHrqK7C++rue+gqsr/6up76uOj2NB47jOOuNRA66juM46wmf2BzHSR19ndjWU+gVEd1DRCeI6LL3tyOiHUT0EBE9TURPEdF71rpPi0FERSL6DhE93unvH6x1n3pBRBER/TMR/c1a96UXRHSQiJ4kor39cPtII33T2DqhV99HV+gVgLderqFXRPTTAGYAfJKZX7rW/VkMItoKYCszf5eIqgAeA/Dmy3hsCUCZmWeIKAfgGwDew8wPr3HXLgoR/RaAPQCGmfmNa92fxSCigwD2MPN6cSZedfr5xLauQq+Y+esAJnqueBnAzEeZ+bud36cBPAPgyrXt1cXhNudymOc6n8vWSkVE2wH8EoCPrnVfnP7Qz4ntSgCHutqHcRn/8a1XiGgXgJsAfHuNu7IonVe7vQBOAHiAmS/n/v4JgN8FEhRtuDxgAH9PRI91QhkdhRsP1hFEVAHwRQC/ycy2cvJlBDPHzHwj2pEqNxPRZfm6T0RvBHCCmR9b674sgZ9i5h8H8IsA3tWRVZwu+jmxeejVJaSjVX0RwKeZ+a/Wuj9JYeZJAA8BuFzjEm8B8KaObvVZAK8hok+tbZcWh5mPdH6eAPAltGUgp4t+TmweenWJ6IjxHwPwDDP/8Vr3pxdEdAURjXZ+H0LboPTsmnbqIjDzXcy8nZl3oX3PPsjMv7bG3booRFTuGJBARGUAr8f6yaSzavRtYmPmJoBzoVfPAPh8gtCrNYOIPgPgWwCuI6LDRPSOte7TItwC4G1oP03s7XzesNadWoStAB4ioifQ/of3ADNf9m4U64TNAL5BRI8D+A6Av2XmL69xny47PKTKcZzU4cYDx3FSh09sjuOkDp/YHMdJHT6xOY6TOnxicxwndfjE5jhO6vCJzXG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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(z, origin='lower', extent=[0, 5, 0, 5])\n", + "plt.colorbar();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a compelling visualization of the two-dimensional function." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.06-Boolean-Arrays-and-Masks.ipynb b/notebooks/02.06-Boolean-Arrays-and-Masks.ipynb new file mode 100644 index 000000000..06b256964 --- /dev/null +++ b/notebooks/02.06-Boolean-Arrays-and-Masks.ipynb @@ -0,0 +1,1369 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Comparisons, Masks, and Boolean Logic" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This chapter covers the use of Boolean masks to examine and manipulate values within NumPy arrays.\n", + "Masking comes up when you want to extract, modify, count, or otherwise manipulate values in an array based on some criterion: for example, you might wish to count all values greater than a certain value, or remove all outliers that are above some threshold.\n", + "In NumPy, Boolean masking is often the most efficient way to accomplish these types of tasks." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Counting Rainy Days\n", + "\n", + "Imagine you have a series of data that represents the amount of precipitation each day for a year in a given city.\n", + "For example, here we'll load the daily rainfall statistics for the city of Seattle in 2015, using Pandas (see [Part 3](03.00-Introduction-to-Pandas.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "365" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "from vega_datasets import data\n", + "\n", + "# Use DataFrame operations to extract rainfall as a NumPy array\n", + "rainfall_mm = np.array(\n", + " data.seattle_weather().set_index('date')['precipitation']['2015'])\n", + "len(rainfall_mm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The array contains 365 values, giving daily rainfall in millimeters from January 1 to December 31, 2015.\n", + "\n", + "As a first quick visualization, let's look at the histogram of rainy days in the following figure, which was generated using Matplotlib (we will explore this tool more fully in [Part 4](04.00-Introduction-To-Matplotlib.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(rainfall_mm, 40);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This histogram gives us a general idea of what the data looks like: despite the city's rainy reputation, the vast majority of days in Seattle saw near zero measured rainfall in 2015.\n", + "But this doesn't do a good job of conveying some information we'd like to see: for example, how many rainy days were there in the year? What was the average precipitation on those rainy days? How many days were there with more than 10 mm of rainfall?\n", + "\n", + "One approach to this would be to answer these questions by hand: we could loop through the data, incrementing a counter each time we see values in some desired range.\n", + "But for reasons discussed throughout this chapter, such an approach is very inefficient from the standpoint of both time writing code and time computing the result.\n", + "We saw in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) that NumPy's ufuncs can be used in place of loops to do fast element-wise arithmetic operations on arrays; in the same way, we can use other ufuncs to do element-wise *comparisons* over arrays, and we can then manipulate the results to answer the questions we have.\n", + "We'll leave the data aside for now, and discuss some general tools in NumPy to use *masking* to quickly answer these types of questions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison Operators as Ufuncs\n", + "\n", + "[Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) introduced ufuncs, and focused in particular on arithmetic operators. We saw that using `+`, `-`, `*`, `/`, and other operators on arrays leads to element-wise operations.\n", + "NumPy also implements comparison operators such as `<` (less than) and `>` (greater than) as element-wise ufuncs.\n", + "The result of these comparison operators is always an array with a Boolean data type.\n", + "All six of the standard comparison operations are available:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "x = np.array([1, 2, 3, 4, 5])" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ True, True, False, False, False])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x < 3 # less than" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, False, True, True])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x > 3 # greater than" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ True, True, True, False, False])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x <= 3 # less than or equal" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, True, True, True])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x >= 3 # greater than or equal" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ True, True, False, True, True])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x != 3 # not equal" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, True, False, False])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x == 3 # equal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is also possible to do an element-wise comparison of two arrays, and to include compound expressions:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, True, False, False, False])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(2 * x) == (x ** 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As in the case of arithmetic operators, the comparison operators are implemented as ufuncs in NumPy; for example, when you write `x < 3`, internally NumPy uses `np.less(x, 3)`.\n", + " A summary of the comparison operators and their equivalent ufuncs is shown here:\n", + "\n", + "| Operator | Equivalent ufunc | Operator | Equivalent ufunc |\n", + "|-------------|-------------------|------------|------------------|\n", + "|`==` |`np.equal` |`!=` |`np.not_equal` |\n", + "|`<` |`np.less` |`<=` |`np.less_equal` |\n", + "|`>` |`np.greater` |`>=` |`np.greater_equal`|" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as in the case of arithmetic ufuncs, these will work on arrays of any size and shape.\n", + "Here is a two-dimensional example:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[9, 4, 0, 3],\n", + " [8, 6, 3, 1],\n", + " [3, 7, 4, 0]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rng = np.random.default_rng(seed=1701)\n", + "x = rng.integers(10, size=(3, 4))\n", + "x" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[False, True, True, True],\n", + " [False, False, True, True],\n", + " [ True, False, True, True]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x < 6" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In each case, the result is a Boolean array, and NumPy provides a number of straightforward patterns for working with these Boolean results." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Working with Boolean Arrays\n", + "\n", + "Given a Boolean array, there are a host of useful operations you can do.\n", + "We'll work with `x`, the two-dimensional array we created earlier:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[9 4 0 3]\n", + " [8 6 3 1]\n", + " [3 7 4 0]]\n" + ] + } + ], + "source": [ + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Counting Entries\n", + "\n", + "To count the number of `True` entries in a Boolean array, `np.count_nonzero` is useful:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "8" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# how many values less than 6?\n", + "np.count_nonzero(x < 6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that there are eight array entries that are less than 6.\n", + "Another way to get at this information is to use `np.sum`; in this case, `False` is interpreted as `0`, and `True` is interpreted as `1`:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "8" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.sum(x < 6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The benefit of `np.sum` is that, like with other NumPy aggregation functions, this summation can be done along rows or columns as well:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3, 2, 3])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# how many values less than 6 in each row?\n", + "np.sum(x < 6, axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This counts the number of values less than 6 in each row of the matrix.\n", + "\n", + "If we're interested in quickly checking whether any or all the values are `True`, we can use (you guessed it) `np.any` or `np.all`:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# are there any values greater than 8?\n", + "np.any(x > 8)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# are there any values less than zero?\n", + "np.any(x < 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# are all values less than 10?\n", + "np.all(x < 10)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# are all values equal to 6?\n", + "np.all(x == 6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`np.all` and `np.any` can be used along particular axes as well. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, True])" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# are all values in each row less than 8?\n", + "np.all(x < 8, axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here all the elements in the third row are less than 8, while this is not the case for others.\n", + "\n", + "Finally, a quick warning: as mentioned in [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb), Python has built-in `sum`, `any`, and `all` functions. These have a different syntax than the NumPy versions, and in particular will fail or produce unintended results when used on multidimensional arrays. Be sure that you are using `np.sum`, `np.any`, and `np.all` for these examples!" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Boolean Operators\n", + "\n", + "We've already seen how we might count, say, all days with less than 20 mm of rain, or all days with more than 10 mm of rain.\n", + "But what if we want to know how many days there were with more than 10 mm and less than 20 mm of rain? We can accomplish this with Python's *bitwise logic operators*, `&`, `|`, `^`, and `~`.\n", + "Like with the standard arithmetic operators, NumPy overloads these as ufuncs that work element-wise on (usually Boolean) arrays.\n", + "\n", + "For example, we can address this sort of compound question as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.sum((rainfall_mm > 10) & (rainfall_mm < 20))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This tells us that there were 16 days with rainfall of between 10 and 20 millimeters.\n", + "\n", + "The parentheses here are important. Because of operator precedence rules, with the parentheses removed this expression would be evaluated as follows, which results in an error:\n", + "\n", + "``` python\n", + "rainfall_mm > (10 & rainfall_mm) < 20\n", + "```\n", + "\n", + "Let's demonstrate a more complicated expression. Using De Morgan's laws, we can compute the same result in a different manner:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.sum(~( (rainfall_mm <= 10) | (rainfall_mm >= 20) ))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Combining comparison operators and Boolean operators on arrays can lead to a wide range of efficient logical operations.\n", + "\n", + "The following table summarizes the bitwise Boolean operators and their equivalent ufuncs:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Operator | Equivalent ufunc | Operator | Equivalent ufunc |\n", + "|-------------|-------------------|-------------|-------------------|\n", + "|`&` |`np.bitwise_and` || |`np.bitwise_or` |\n", + "|`^` |`np.bitwise_xor` |`~` |`np.bitwise_not` |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using these tools, we can start to answer many of the questions we might have about our weather data.\n", + "Here are some examples of results we can compute when combining masking with aggregations:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number days without rain: 221\n", + "Number days with rain: 144\n", + "Days with more than 10 mm: 34\n", + "Rainy days with < 5 mm: 83\n" + ] + } + ], + "source": [ + "print(\"Number days without rain: \", np.sum(rainfall_mm == 0))\n", + "print(\"Number days with rain: \", np.sum(rainfall_mm != 0))\n", + "print(\"Days with more than 10 mm: \", np.sum(rainfall_mm > 10))\n", + "print(\"Rainy days with < 5 mm: \", np.sum((rainfall_mm > 0) &\n", + " (rainfall_mm < 5)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Boolean Arrays as Masks\n", + "\n", + "In the preceding section we looked at aggregates computed directly on Boolean arrays.\n", + "A more powerful pattern is to use Boolean arrays as masks, to select particular subsets of the data themselves. Let's return to our `x` array from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[9, 4, 0, 3],\n", + " [8, 6, 3, 1],\n", + " [3, 7, 4, 0]])" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose we want an array of all values in the array that are less than, say, 5. We can obtain a Boolean array for this condition easily, as we've already seen:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[False, True, True, True],\n", + " [False, False, True, True],\n", + " [ True, False, True, True]])" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x < 5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, to *select* these values from the array, we can simply index on this Boolean array; this is known as a *masking* operation:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([4, 0, 3, 3, 1, 3, 4, 0])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x[x < 5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is returned is a one-dimensional array filled with all the values that meet this condition; in other words, all the values in positions at which the mask array is `True`.\n", + "\n", + "We are then free to operate on these values as we wish.\n", + "For example, we can compute some relevant statistics on our Seattle rain data:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Median precip on rainy days in 2015 (mm): 3.8\n", + "Median precip on summer days in 2015 (mm): 0.0\n", + "Maximum precip on summer days in 2015 (mm): 32.5\n", + "Median precip on non-summer rainy days (mm): 4.1\n" + ] + } + ], + "source": [ + "# construct a mask of all rainy days\n", + "rainy = (rainfall_mm > 0)\n", + "\n", + "# construct a mask of all summer days (June 21st is the 172nd day)\n", + "days = np.arange(365)\n", + "summer = (days > 172) & (days < 262)\n", + "\n", + "print(\"Median precip on rainy days in 2015 (mm): \",\n", + " np.median(rainfall_mm[rainy]))\n", + "print(\"Median precip on summer days in 2015 (mm): \",\n", + " np.median(rainfall_mm[summer]))\n", + "print(\"Maximum precip on summer days in 2015 (mm): \",\n", + " np.max(rainfall_mm[summer]))\n", + "print(\"Median precip on non-summer rainy days (mm):\",\n", + " np.median(rainfall_mm[rainy & ~summer]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By combining Boolean operations, masking operations, and aggregates, we can very quickly answer these sorts of questions about our dataset." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using the Keywords and/or Versus the Operators &/|\n", + "\n", + "One common point of confusion is the difference between the keywords `and` and `or` on the one hand, and the operators `&` and `|` on the other.\n", + "When would you use one versus the other?\n", + "\n", + "The difference is this: `and` and `or` operate on the object as a whole, while `&` and `|` operate on the elements within the object.\n", + "\n", + "When you use `and` or `or`, it is equivalent to asking Python to treat the object as a single Boolean entity.\n", + "In Python, all nonzero integers will evaluate as `True`. Thus:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(True, False)" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bool(42), bool(0)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bool(42 and 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bool(42 or 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When you use `&` and `|` on integers, the expression operates on the bitwise representation of the element, applying the *and* or the *or* to the individual bits making up the number:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'0b101010'" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bin(42)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'0b111011'" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bin(59)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'0b101010'" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bin(42 & 59)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'0b111011'" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bin(42 | 59)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the corresponding bits of the binary representation are compared in order to yield the result.\n", + "\n", + "When you have an array of Boolean values in NumPy, this can be thought of as a string of bits where `1 = True` and `0 = False`, and `&` and `|` will operate similarly to in the preceding examples:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ True, True, True, False, True, True])" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.array([1, 0, 1, 0, 1, 0], dtype=bool)\n", + "B = np.array([1, 1, 1, 0, 1, 1], dtype=bool)\n", + "A | B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But if you use `or` on these arrays it will try to evaluate the truth or falsehood of the entire array object, which is not a well-defined value:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "ValueError", + "evalue": "The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/var/folders/xc/sptt9bk14s34rgxt7453p03r0000gp/T/ipykernel_93010/3447948156.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mA\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()" + ] + } + ], + "source": [ + "A or B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, when evaluating a Boolean expression on a given array, you should use `|` or `&` rather than `or` or `and`:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, False, False, False, True, True, True, False,\n", + " False])" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.arange(10)\n", + "(x > 4) & (x < 8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Trying to evaluate the truth or falsehood of the entire array will give the same `ValueError` we saw previously:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "ValueError", + "evalue": "The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/var/folders/xc/sptt9bk14s34rgxt7453p03r0000gp/T/ipykernel_93010/2869511139.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()" + ] + } + ], + "source": [ + "(x > 4) and (x < 8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, remember this: `and` and `or` perform a single Boolean evaluation on an entire object, while `&` and `|` perform multiple Boolean evaluations on the content (the individual bits or bytes) of an object.\n", + "For Boolean NumPy arrays, the latter is nearly always the desired operation." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.07-Fancy-Indexing.ipynb b/notebooks/02.07-Fancy-Indexing.ipynb new file mode 100644 index 000000000..7a1b6d56d --- /dev/null +++ b/notebooks/02.07-Fancy-Indexing.ipynb @@ -0,0 +1,980 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fancy Indexing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The previous chapters discussed how to access and modify portions of arrays using simple indices (e.g., `arr[0]`), slices (e.g., `arr[:5]`), and Boolean masks (e.g., `arr[arr > 0]`).\n", + "In this chapter, we'll look at another style of array indexing, known as *fancy* or *vectorized* indexing, in which we pass arrays of indices in place of single scalars.\n", + "This allows us to very quickly access and modify complicated subsets of an array's values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exploring Fancy Indexing\n", + "\n", + "Fancy indexing is conceptually simple: it means passing an array of indices to access multiple array elements at once.\n", + "For example, consider the following array:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[90 40 9 30 80 67 39 15 33 79]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "rng = np.random.default_rng(seed=1701)\n", + "\n", + "x = rng.integers(100, size=10)\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose we want to access three different elements. We could do it like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[30, 15, 9]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[x[3], x[7], x[2]]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, we can pass a single list or array of indices to obtain the same result:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([30, 15, 80])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ind = [3, 7, 4]\n", + "x[ind]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When using arrays of indices, the shape of the result reflects the shape of the *index arrays* rather than the shape of the *array being indexed*:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[30, 15],\n", + " [80, 67]])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ind = np.array([[3, 7],\n", + " [4, 5]])\n", + "x[ind]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Fancy indexing also works in multiple dimensions. Consider the following array:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X = np.arange(12).reshape((3, 4))\n", + "X" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Like with standard indexing, the first index refers to the row, and the second to the column:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 2, 5, 11])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "row = np.array([0, 1, 2])\n", + "col = np.array([2, 1, 3])\n", + "X[row, col]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the first value in the result is `X[0, 2]`, the second is `X[1, 1]`, and the third is `X[2, 3]`.\n", + "The pairing of indices in fancy indexing follows all the broadcasting rules that were mentioned in [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb).\n", + "So, for example, if we combine a column vector and a row vector within the indices, we get a two-dimensional result:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 2, 1, 3],\n", + " [ 6, 5, 7],\n", + " [10, 9, 11]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X[row[:, np.newaxis], col]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, each row value is matched with each column vector, exactly as we saw in broadcasting of arithmetic operations.\n", + "For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 0, 0],\n", + " [2, 1, 3],\n", + " [4, 2, 6]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "row[:, np.newaxis] * col" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is always important to remember with fancy indexing that the return value reflects the *broadcasted shape of the indices*, rather than the shape of the array being indexed." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Combined Indexing\n", + "\n", + "For even more powerful operations, fancy indexing can be combined with the other indexing schemes we've seen. For example, given the array `X`:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3]\n", + " [ 4 5 6 7]\n", + " [ 8 9 10 11]]\n" + ] + } + ], + "source": [ + "print(X)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can combine fancy and simple indices:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([10, 8, 9])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X[2, [2, 0, 1]]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also combine fancy indexing with slicing:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 6, 4, 5],\n", + " [10, 8, 9]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X[1:, [2, 0, 1]]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can combine fancy indexing with masking:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 2],\n", + " [ 4, 6],\n", + " [ 8, 10]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mask = np.array([True, False, True, False])\n", + "X[row[:, np.newaxis], mask]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these indexing options combined lead to a very flexible set of operations for efficiently accessing and modifying array values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Selecting Random Points\n", + "\n", + "One common use of fancy indexing is the selection of subsets of rows from a matrix.\n", + "For example, we might have an $N$ by $D$ matrix representing $N$ points in $D$ dimensions, such as the following points drawn from a two-dimensional normal distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(100, 2)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mean = [0, 0]\n", + "cov = [[1, 2],\n", + " [2, 5]]\n", + "X = rng.multivariate_normal(mean, cov, 100)\n", + "X.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the plotting tools we will discuss in [Introduction to Matplotlib](04.00-Introduction-To-Matplotlib.ipynb), we can visualize these points as a scatter plot (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "\n", + "plt.scatter(X[:, 0], X[:, 1]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's use fancy indexing to select 20 random points. We'll do this by first choosing 20 random indices with no repeats, and using these indices to select a portion of the original array:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([82, 84, 10, 55, 14, 33, 4, 16, 34, 92, 99, 64, 8, 76, 68, 18, 59,\n", + " 80, 87, 90])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "indices = np.random.choice(X.shape[0], 20, replace=False)\n", + "indices" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(20, 2)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "selection = X[indices] # fancy indexing here\n", + "selection.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now to see which points were selected, let's overplot large circles at the locations of the selected points (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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Jly9fZu/evSQmJuLi4kLz5s1p2bIlCoUi3/flN485a1521pxsnT4Trc7A7WQdTWpUKdd9GwuzYbAoW5ISEQ+U4sxPPnDgAM8++yyPP/44hw8f5tatW5w9e5aQkBCaNWvGqlWrcuxynqWgh5yeahXXE1LNc7L9PZzxdlfhaG9HgjaDA5GxpT6TJa9ZM/LAseKREbZ44BRlfvJ///tflixZwrx589i0aRMuLi7m14xGI3v37uWtt95i9+7dhIaGolJZBrOC5jH7uzux9uhV9AYjnmoV9nYKYu7qSM0wkqK7RbfGfuYgXxqV9vKr6mfN1ZLCOmSELUQeVq1axbJlyzh69CjDhg2zCNZwb/uvrl27cvDgQTIyMhgxYgQmk8ninPwecmY91NM4O+Dp4sDtZB0R0cmYAD93R9INRs5cT0JvMBZ6JktMTAzr169nxYoVrFmzhnPnzuV7fn6zZqy1WlJYT7FG2Hq9npkzZ3Ljxg0yMjIYO3YsTz31lLXbJkS50Wq1TJ8+ncOHDxMQEJDvuY6Ojqxfv54mTZrw66+/0qZNG/Nr+T3kzAqWgV5q0jONKJQKXB0NxKWko3FxQOPsgMFgZF9ELD5ujvnWGzlz5gzz5s1j9+7ddOrUCS8vL9LS0pg5cya1a9dm/PjxDBgwIEe+vaA8tTVWSwrrKVbA3rZtGxqNhsWLF5OYmEifPn0kYItK5ZtvvqFdu3YEBwdbHM/rAaKLiwvjx49n2bJlFgE7v7TCgchYvF0dqeXtwqmou9xNy8TD0Y5Mo5H4lAxU9kr+jklBqQQPZzvUjg65pkZWrlzJG2+8wZtvvsny5cvRaDTm1/R6Pdu3b2f+/Pn88MMPrFq1CgeHf788KtKsGVGwYqVEunfvzsSJE4F7Oz7bZdswVIjsynMZeEmsWrWKMWPGWBwr6AHiyy+/zM6dO7l79675PfmlFbKCpafakaY1PHBztOdOqh6NswOZJhNJaXpUdgrsFQou3U7F38M5R2pkw4YNzJ8/n3Xr1jFx4kSLYA3g4OBAv379OHLkCDExMYwbN84ibZN9AY/sIVnxKUz3J92KICUlhbFjx9K/f3969uxp8Vp4eHiOnF9loNPpcHJyKu9mlApr9+22Vs+xqFTUDkqcHRSk6U1o9UZa1XDBR+1Q8AWsqKh9a9euHZs3b8bHx8d87NerWnSZRlxU/45zUjOMONkreSJQDUCPHj345JNPqFOnToH3uP/ziUnW8+ftDFz++d0beScdgxH83BzwdFbi4WRPQx9HEtKM9GjgTnp6Op06dWLlypXUqVOnwP5ptVr69OnD4sWLadq0qUU7zsdlkKgzoHGyI8hbVeZ/Pvl50P6fS01NpXnz5rmeX+xZItHR0YwfP57BgwfnCNZZ7v85WRlERERUyn6B9ft29Vw0QYEGi5/byTo9qSo7goP9rXafwihq3xQKBQ0bNsTX19d87GTSVWq4OqLMlgc2mkzEpaQTHBwIgIuLC4GBgYW6VzAQVO/fFMuj1VX0aOHExt+iUCoApwyquKjwdnXEZDKRpNNTxacK1f75/NasWUPLli157rnnLPqX37zvyZMns2vXLgYNGmTRjicL/cmUvQft/7nw8PA8zy9WwI6Li2P48OHMmTOH1q1bF+cS4gFgywsvqlatyqVLlywCdkH53vT0dG7evGnxnrzcH1Q7NvA1B9XoJB1pGQb0BhOnohJJ02diMoK9UmExre6LL77g9ddfz3Hd/DbfHTZsGHXq1OHu3bt4eHiU+HMSZatYOewVK1aQlJTEsmXLCAkJISQkBJ1OZ+22CRtnywsvBg0axKpVqyyOFZTv/e6773jssccKDNgF5cKz7uNgp6CWlzOXbmv57Vo8GZkGizoeFy5cyPHTuaDiVp6envj7+3Pjxg0rfEqirBVrhD179mxmz55t7baISsaWF16MGDGChg0bsnDhQry87rU36wHi6euJxKWk46lWmZeOm0wmli5dyvTp0wu8doGLaf65z8HIWM7eSKKWlwvdGlXF0d6O09fv4uvuhL/GmczMTOztLf8XLsyvGnt7e/R6fYk+H1E+ZKWjKDX5BbiKzs/Pj1GjRvHCCy+wc+dOnJ3vtTm3eckmk4lZs2ZhMpnyfJ6TXUFBNS0tDVNqAvaZWjrU98bDxfLcrMDu6+vL1atXqVq1qvm1gtI2er2+0GkbUfHISkdRqvw1znRv7M/gloF0b+xvE8E6y8KFC6lWrRqdO3fmzJkzuZ4THR3NK6+8wo4dO9i2bVuOEW9ucksVJWl1RB7fT7du3fD09KR58+YMfbo1o3u0YM2ni4mLiQYsS8H279+f1atXW1ynoLTNtm3baNSoEf7+ZfvQV1iHBGwh8mBnZ8eaNWvo168fPXr0oG3btixdupT169fzxRdfMGDAABo1aoS9vT2HDh0q9Kj1/qB66fIVJg/uzs51KwgJCSEhIYHo6Gi++/Uv3vxkHYnxdxjdpyPb1q+2GC2PHDmSDRs2kJCQYL52fvO+TSYTn3zyCePGjSuVz0uUPkmJiAovv2lqpU2pVDJ16lQmTpzI9u3b+fHHH83lVZ988klWrlyJu7t7ka6ZPVV0/vI15r3yPGPHvcrbs2ZYnNckQENsUj2GTZvPcy+P4Y1XBhGfnMbit/8DQLVq1QgJCWHw4MEsXLjQ4vq5fT6LFi0iPj6efv36FeOTEBWBBGxRoRU0Ta2s2Nvb07dvX/r27WuV62UF1e6vD2P8K6OYc1+wzjonK7CnVfHjvZUbmT6kJzFD++L/z8KX//73v/Tv359XXnmFtWvXEhQUlOM6CQkJvPPOO3z//fccOHAgR0VBYTskYItyo9fr2bZtG+fOnUOn0+Hp6UnPnj1p2LCh+ZyCZlRYU1mP5CMjIzl58iTff/99IdsRyPUJE/j0009ZuXIlcO+LJCwsjIkTJ/LEE0/QrFkzBgwYgI+PD1qtlj179vDdd9/x7LPPcvToUby9vUutP6L0ScAWZU6r1fL++++zcuVK6tevz5NPPombmxvXrl2jQ4cONGrUiClTppCSksL6XYewM+lxdfOgZfvO1G/UpFQW35THSH7FihWMGDECR8d/Z4EU1I6s6YaLFy821w2xs7Nj/PjxfPDBB4SFhbF7927u3r2Li4sLjz76KJGRkRYzSYTtkoAtytSdO3d4+umnqV27Nnv27KFRo0YWr8+fP59hw4bRq1cv6tatS+tufVHYq0hLSmDepBFU8fKhZ8gYOj1d8PS5orD2SL4wo/WjR4/y4YcfFqkdfn5+NGrUiLNnz9KuXTuL9zo5OZkXsonKSWaJiDKTkZFB7969adeuHRs2bMgRrOPj4+nWrRsqlYqffvqJjIwMWjzckE4vjGDg+P+wetcx+g1/ja8/epc96z6xatusuZt6QSsZs6SkpODm5pZvO+K1Gfwdk8Tuc9Hmaodubm4kJycXuV3C9knAFmUmLCwMe3t7Fi9enKOQfmZmJn379qV169Zs2LCBp556is2bN/Pu3Nl0CPLEWWVHQlom7Tp3Y++Bn9m1bQuffvqp1dpmzWX0BS0Pz+Lu7k5iouWx7O2I12ZwKiqRJF0mfu7O5sAfG3enyDNTROUgAVuUmWXLljFp0iSUyn//2mXVy566eCWxiVqmzXnHHMybNWtGvXr1OH7wR4vFNw8HBbJ161beeustUlNTrdI2a9aFLuxovWPHjmzevDnPdlyOS0ahMGEyKajjo8bNyYG0hFtcuHCRRx99tMjtErZPArYoE+fPn+fy5cs8++yz5mPZUwc/bw2lx8Bh7Pvrtjl1EJ2YRqse/Xn3/5bn2Pygfv36tG7dmvXr11ulfdkXnFyITeavW0lo0zM5fT2xyJsuFHa0Pnr0aNauXYtWq821HdF3dbg5OtC0hgee6nsPJg9+v54nuvVGrVYXs6fClknAFmUiKiqKBg0aWCzdzkodpCXEcuV8BJ2f7mVOHWQFc2ffQG7dvMG+iFg+2nee09f+XdU3evRovv76a6u10V/jTJMADa6ODjT0c6eur2ue+ee8RCemkaBN50BkLEcu3CYuJT3P0XpgYCCdOnVi5syZOdrRvbE/3Rv708DPzRysr1z4ix++DeX5l4Zbpb/C9kjAFmXCZDLlugGs2tGeuNhb+FWviYNKZU4dnL6eSKbRSFSCDqPJhK+bI3ZKWH/imjl4BgcHF7pM6G2tvlBblR2MjOVyXAq/X0vgVFQCeoOp0DuWZ33JODnY80TdexX+jlyIQ6c35Dk9cOXKlezfv59p06ZhNBotXsueHvn7zzPMGDWQQRNm80y7xwrVZ1H5SMAWZaJ69eqcP38eg8FgPpZf6iBem0FsUjopMVFovKuiUCjQOKswGE2FCp7ZRSemcSwqlbQMA0qFguOX7vDergjWH79iEbijE9P49eIdFApwd3IgPdPIqahE0jONhZotkv1ho7erE23q+dCpoS9V1Ko8pwZqNBp+/vlnTp48SVBQEIsXLyY6Ohqj0UgVJwWOsX/wwfTRzBjRnzEz5vHW5FdsqoCWsC4J2KJMNGzYED8/P3788UfzsawRpLOHN7duXCM+WWtOHXiqVdzRZnByTxjNn+oNgC7TgLeryhw8IyIiCAgIKPDep68nonZQojeYOHP9LkqlAm+1I3/HpFikO05fT8TbVYUCJQqFAmcHe5xVSiJvJRVqtkhxpwZ6enqyZ88e1q9fzx9//EFwcDAODg54eHiwcO5shrzQm+gbUbwzZZQE6wecLJwRZWbcuHF89NFHPP300ygUimy1MhypXqcBv//yIxNHDTUHpbC9R7lxKZJhbbqSps8kLcNIgK+rOXh+/vnnDBkypMD7xmszcHZQcOVOCs4qJc4O9uY9ErPSHf4aZ+K1GTTwc+PM9SQAnByUmIxwR5tRqNkiBdWizo9CoaBFixa0aNECgOt3Ujh7M4mEVD2eahXJmXa4FngVUdnJCFuUmUGDBhEXF8e8efMwmUzAvw/Y5r0xlZ83r6Gq+70HbMr0JPYtnUG7geOITzeislMQ5OuKnVJBkwANf//9N0ePHrXYTDYvnmoVaXoTybpMnOztANDpjbg5OliMgD3VKhzt7WhawwNHeyVJOj0mTLSu41moka21pgZGJ6axPzIOnd6It6sjF8+fZ+a7S3hz3rssX76c33//vUjXE5WHBGxRZpycnNixYwdhYWGMHj2aq1evml/r3bs3jo6OTJo0iR07dtC6dWtGDB3C6oUzeSq4KjU81fhrnOjyUFXsMpLp3bs38+bNw8XFpcD7NgnQoNUbsVcq/hmpG0jTG6jl7WIxAv53L0UlTWtqaFazCrW9XenQ4F4djqw543k9uLTW1MCsXPif//uZN0YNYPao57gWeZo/L17j1KlT9O3bl1atWhEaGmr+4hMPBkmJiDLl7+/P4cOHmTt3Ls2aNaNNmza0a9cOJycnmjVrxqeffsq6det4++23ee211+6955/RrcFg4IcffmDy5MmEhIRYFOK/evUqmzdvJjY2FgcHB+rVq8dzzz2HWq3GX+NMqxou3DC48evFO3i7qngkwB0HO6XFHpP5bWlW2OJQWf8em5SOv4ezeS/LohSSupOSzg9ff8z+Hd8xdMIM2nV9FnsHFXEp6QxuGWj+HObMmcPevXv54osvrPbnIyo2CdiizGk0GpYsWcKCBQvYtGkTf/zxB2lpaXh6erJ3715++ukn3nvvPbZu3UrHjh1xdnYmNjaWjRs3Uq1aNd5//31zEf7jx4/z5tvzOHb0KI937E5AjZr4qI2EhYWZA/usWbPwUTvwZHAgHRr4mosyOavscuwxmVfx/6IUhyppIamD363m8J4f+PibnVTx8gEgWac3/xKws7OjZ8+edOrUiV69ejFp0iTZReYBIQFblBu1Ws2wYcNyHG/Xrh1vvvkmW7du5cyZMyQkJFClShW2bNlCs2bNzOdt3LiR8a9OoOfwSXw2ewleGnfzzuxTZ1Ql424sH3zwAa1bt2bZsmUEBwfnGZALUtDGudmr8/1x8y4PV/fADYdcz81PXFwcmz7/iLdX78RercFoMuW527xarWbz5s0EBwfTpUsXgoODi9wvYVskYIsKSaVS0b9/f/r375/r6/v37+e1115j/mcb8KtVP9fRbPfGgSxdupRPPvmEUaNGcfz4cfz8/IrVnvxmgNyfLlHZKTlxJYGWtT3NqxQLO1tk9erV9O3bh4GdmlmkZup4qzl9PZEDkbEW5Vo9PDwYPXo0GzZsoFevXsXqm7Ad8tBR2ByTycS0adNYsWIFHtXr5jn3OTIykkmTJvHWW28RFRVFQEAAPj4+vP7661y8eLFI98xvBsj91fmC/T0wmSAiOqnIs0W+/PJLXnnlFa5FnmH94v8wuVcLejevxRONazFjRH8iju4hWauzmD8+atQoduzYQUZG0UvBCtsiAVvYnBMnTpCQkEDv3r1zlCP9/Vo8u89E8dHc6bR78klcXFwIDw8nLCwMf39/Dh06hFKppFWrVkycONFi5WV+8tuN/P4FM55qFS1qe5KeacxxbkEuXbrE66+/zuDBg3n44Yf57bff2HQkgmVbDvHsCy/x/bpVjO/TlhuRp8wrPqtXr45KpeLOnTtF/zCFTSl2SsRoNPL2228TGRmJSqViwYIFBAYGWrNtQuTq66+/ZtSoUSiVSpoEaNjzZwyJqXr+jklGgZFdS2fjYEpnQeh+ej5WB3+NM2lpaVSrVo2oqCjef/99Zs2aRb9+/Rg+fDhfffVVjjonuckr/51busTRXsmT9X3o3ti/0P26desWGRkZdO7cmbfeestchvbQzav4+/lSvUcfOvbow/8O7WPR6yN5df4ndG88ELj3IDIzMzO/y4tKoNgj7L1795KRkcHGjRuZOnUqCxcutGa7RAWn0+k4fPgwO3bsYP/+/cTExJTZvaOionjooYeAf0e+t5LSyDSaOPvTRkhNYOHyNfh4eljUHQkODiYqKgoADw8Ptm/fTkRERImnxVlrwczgwYNxc3Nj0KBBFjXD76+50qLdU0x551M+fXMCd+7cISkpieTkZLy8vHK7rKhEij3CDg8PN+8p17RpU86dO2e1RomK68qVKyxfvpzVq1cTGBiIj48PqampnD59mm7dujF+/Pgcew0WR357It5f+c9f40ygl5pHaziwbso3zFq8ApXKEXuTyWJmxv2jaBcXFxYtWsSECRMYOXJkoUbZuclv/nZhnTx5kgsXLjBq1ChWrVrF4sWLza9l/YoAzPO6az3Sks5duvLVV1/h7OxMu3btCrWISNi2YgfslJQUXF3/rW6Q9ZMse73jiIiIkrWuAtLpdJWyX1Bw337++WdmzpxJ7969WbNmjUUKLCkpiW3btjFw4EB69OjB5MmTix0Ab2v1HItKRe2gxNlBwcXbJs6cv0qrGi74qB1wcXHhl19+ISgoyPyetAQt23YdxtFZjUsVb6KuR5GaYcTJXskvv93lj+gUDh4LR1OvGb/8dgYf9b30RdWqVUlLS2Pt2rU8/vjjxWpvlkA7CHQHSCUxOpHE6MK/97333qNv37507dqVQYMGMWDAANRqNbe1es7HZRB1Nx1thgm1SkEND0eCvFU816cn06dPx8HBgRkzZjywfy9tWVH7VuyA7erqarFThtFotAjWQKWcFxoREVEp+wX59+3AgQPMmTOHH374gVatWuV6TsuWLZk8eTI9evQgNDSUd955p1D3vX80nWBIp7qXA+lJdzCmG/Dz8kHp7E6qyo7gYH9ee+01hg0bxvvvv29OHWj809gS+iWtn+pBQEANtOmZ2OkyaRLgwenrd7l+7Q+S42/zROdnuZKhIKjevw8B+/fvz7Vr1wpVSKq0/Pbbb+zatYsGDRrw3HPPMX/+fJZ+sZYTCfF4+tpTo4a9eT521gNMY7PGjBw5kiZNmtC2bdsH8u+lrcutb+Hh4XmeX+wcdrNmzfjll18AOHXqFPXr1y/upUQFl5mZycsvv0xoaGiewTqLt7c3O3fu5KuvvuLUqVMFXjv7NmFeahW//+8Yb08Zy6geLXlrwlDmTx7Fy0+35p0JL/HTrh1kZmbyxBNP4OzszO7du83X8dc44+NkRKPRWMzMiE7S4eZkz+EdG3nmhZeo4uaSY0MCDw8PkpKSivvxWMXdu3fx9PQEMG8u3KfXs9yNvpLrZr7Xrl0jJCQEo9HIwoULi/1rRtiWYo+wu3TpwpEjRxg4cCAmk4l3333Xmu0S5ej+EW/0mUMEBATQpUuXfM/LyjP7+PgwduxYli9fzmeffZbvvbLmMDsqjSx+YxIRZ37nka796Tv+TTo3rQtARrqOn3Z+zw9rl3N861d8//33LFq0iGHDhnHw4EEaNGgAgJ93FdRqGNzy31TN1pM32Pf9ek7+dpwOQ6cTr81A4+Jgkdu+e/cubm5u1vr4ikWtVpOSkoKPjw8qlYrvvvuOQeP/w9tjBlCzThBtuzyDm0cVUrXJHD6wh8vnwhkyZAh+fn74+fnJDJEHRLFH2Eqlknnz5rFhwwY2btxI3bp1rdkuUU6yj3i9XR1JyzDwf0uXM/jlkQWel30xx8iRI9m0aRMpKSn53i9em4GTvYL3po0jLVXL51v28/KoccRl2HPkwm0ORsZyIiqZuq26s+/gIdq2bUvnzp154oknWLhwIe3btyc0NJQrMYk413iIr9Z/a66kd+bvK3z90TvsCV1O/+kfYK/24FRUIjcS0syrDk0mE9u3b6dNmzal84EW0uOPP27xi8He3p4RE6ayfMdRerwQwqXIPzl6YDfnToXTpmNXrl27xpgxY9BqtTKd9gEiS9OFhdwKF928ch63Wo0LPC/ruL/G2Tzyu3btmnkKXm481Sq2bVhLfFwsi1d/i0rlSGx8Ki7mhSgmQAFKBUqlkoULF3L79m1mzpzJJ598QmBgIG++PY/xr02iXbdexN64ytJ3ZnEnLo6zx3+mefvuDHlvLfYqFU72duj0BiJjkuje+N4S9UOHDmE0GunYsaN1P8giGjduHJMnT2bMmDHm9Ma92SHpPNbpGdo/3dsih61WO7NixQpGjBiBSlXwkndROchKR2Eht22uMjPS0Rpy30A3u/u3w3JyckKn0+V7v0eqe7Bj42qeHzUJewcVyTo9kTFJ1PZ2wdnB3rxVl1plx+nriSgUCubNm0doaCjJycl06NCBWZ+EMv/zMLy8vKlZJ4gTB3+k8aOPMWbZTmYv/Ih2TYJwUCru7TDj6EBNTxfzYpoZM2bw2muvlUoOuKD62dl16tQJg8HAunXrzMfyW135119/sXbtWl555RWrt1tUXDLCFsC9WT6//PILYT/s487tWFQO9vgHBNK932BcPapgTIm3OL+g7bCMRiO3bt0yP0iD3HPeVyJO4YCBlm3bm+cwa5wdiE3KwEVlj7uTAzq9kfMxKej095aRBwQE0KlTJ0JDQxkzZsy9rb0aNiQ4OJhBoyfy5oTh/PrzQRoEtOHoxTiC/d0J9nWiRoAvyTo9Krt79bOHDh1KYGAgPfuHsPtcdK5zvu+X3/zw+88rTP3sLAqFgo0bN/LUU0/h5OTECy+8AOS+ujIiIoLu3bvzwQcfSDrkASMjbME333xDUFAQH3/8MU+1e4JOzw3lqb4v4uHpxZvjh5CSnMS+Tass3lPQ6r59+/bh6+trDih55bz3Hz5G965d6PFIdQa3DKR7Y39MgFIJziq7eyNslR1KJdxN05vv37VrV/NWWdlXAt7VZdJx7Luo3DzYN3cQu9YsZW/4XySm6YmIiGDJnCk81zKI2rVrc+zYMb7fto0XBr3IyRPH8VKrcuTisysob5/d/QWhss/wyEvjxo358ccfmTJlCj179mTXrl0YjUbz62fPnmXs2LG0bduW+fPnM3To0ML88YpKREbYD7iFCxfy+eefs27dOjQaDQ899NC/o8jWneg/YgLhuzbw9qwZbNu2zVzCs6DVfcuWLWPcuHHmVENeOe9LN+PwVqst2qRxVpGUlkma/t4ejLpMA0bjveNZ1Gq1eR1A9pWAl25rsVfZ02PcPLwyYvjpu7V8Nbkvmfp0TAYDKpUjgwcPYsaMGTRs2JCwI3/yw3cb+OTtKdSsXY+Zi1fg5qQq8sYEWf/MGnlfup1CPV/LmSeFqYndtGlTIiMjWb9+PbNmzWLQoEF4eXmh1Wqxt7dn9OjRnD17lmrVqhX0RysqIQnYD7CNGzfy2Wef8euvv+Lv729ecXX/z/Bnmk7j15/30b9/f37//XeLOh65/bxft24dJ0+eZO3ateZjeW0AgKOauNuWpU5r+6hxcrDjdorOvLN5gMYFf42T+Zy4uDg8PDzM7cj68riVlIa/hxO1vd3wVPvyyMOLUJoy+evPP/jlx+0EBARY5Kv19moGjRjHgJdH89G86cwcM5j3Vm4gXpuzil9efbgQm0xsUrpF+uNafCpODnbU9Pz3y6iwNbFdXFwYMWIEw4cP586dOyQmJuLi4oKvr2+OxWniwSIpkQeUyWRi7ty5fPnll/j7F1xRbsuWLfj5+dGzZ08SEhJyPSczM5OlS5cybdo0du7caVG64P4CRnAvgLXt0Int27eTlvZvWqFJgAY7pYIgXzfaBfkQ5Otm3i09y6ZNm+jWrZv5v7N2X+/e2J/6Vd3NgfHAzi1EnDnJ6+98TI0aNXI8XMxql72DA5PnfkgVL29Wffx+roE1rz7cTdPnSH80qOrO3zEpJSoIpVAo8Pb2pl69elSrVk2CtZAR9oPq559/RqFQ0KFDB4vjeT1Uc3Z25sCBAzRs2JBatWrx/PPPM3DgQLy9vUlNTWXfvn18/vnn1KlTh8OHD+eYl5+Vtrh++TzH9+4gNjYGg0lBm0cf4uGHHyYsLMy8NLygdMvJkye5fv06zzzzTI5+3V8o6du1K+kzYjIP19Dk2kcFJuK0egI0984f9OobTB/Skw/fW5Djc0nQpnP0UjxeahUN/NxxtL+3ia/GWZVjxkz1Ks7o9AbzDI/iFIQS4n4SsB9QmzZtYujQoRYjzttaPSfymdlQu3ZtunfvztNPP83du3dZsGCB+ef6o48+yq5du3j44Ydzvd/fp//HZ7PnEPHXXzzRrS8NGj2Mv5uKy3//yYkTJzh27Bh169Y1L2DJK92SlpbG+PHjmTRpUq4jzuzB/sRv4dy9E8vrIweRHHuvrGr22RtKBUTeSuFafCoxd9OornGhdp06tGzRgl9+3Eadfx7qZX/PE3W9iLyVzJELcTxR18t8r9xmzNT2URepHrYQBZGA/QDIbdR8+/btHKPr83EZePrmfKh2MDKGKmpH4rUZmNRe3E5M4c3/zGDGjBmFun9oaChTpkxhyZIlPP/88zkWenzwwQcMHDiQ9u3bs3HjRp577rlcr3Pnzh2ef/556taty6RJk/K8X1awv/jzFfr2epYAL1ciYu+9lvXgUG8wcuZ6Es4OdgR6uWAy3RthNwnQ8Fzf3vz666/mWRjZHza64YB3PSeSdXqcVXbmL5X7y5/mtmmuECUlOexKLq+paJkmJXq93uLcRJ0hx0/79EwDRy/Fm9+fnqHnwh2dxVS2/BaI7N+/n6lTp3LgwAEGDx6c66o8Dw8Pdu3axciRI3nhhRfo3r07P/30E7du3eL27dscP36cUaNGUa9ePR577DG++uoriwL/eUlJSclRIyRrwc+VuFScHexwVtnh7GBPptFknnbn7u5OcnJyjvdkl32RUH4LXISwJhlhV3J5TUVz8anOiRMnePHFF83napzscvy0j7yVjJdahZuTAyaTicsRZ2jV6WnztLeCFojMmjWLTz/9NN/l6VlWrFiBk5MTZ8+eZfbs2Vy9ehWDwYCfnx+DBw/mr7/+omrVqoXuu7u7OxcuXLA4lvXgMDldj/s//dRlGnBzsjdPu0tISMDd3T3He/JaJAR5p3CEsCYJ2JVcXlPRWnR7jnkjevHOO++g/mcedJC3iiu6TPM52vRM4lIyaFPPG4DIsydJTkqkVdv25tFlfnOToy9FcPPmTfr06WNx//xWC06ePJnmzZtz9epVc7uK68knn2T+/PkWu4lnPZS0VypIyzCgUEJahpEGVd3NQXjVli2MHDkyx3uyfy6S8hDlQVIilVxeU9Ea1KtDmzZtWLFihfm4j9ohx0/75tVdOPxDGB/Nnc78yaPw9Pbll30/4uFkB+SfLggNDWXYsGHY2dmZXytotWBgYCAtWrRg586dJe57o0aNqF+/Plu3bjUfy0pf1K/qSpw2HaPRRC0vZyKi73IgMpZz5/7g7LlzFnl0SXmIikICdiWX3xLyDz74gMWLF7N582bz+Vnzmfs87MPerz5kSr+2HPppJ9euXkahVNDkiY6EfbGUV559giVLlqBxts/1C8FTreLmzZsW23hBwUu2oxPTcKjiz/aj5wosmFQYkyZNYvbs2SQmJlr0cVDLWrzxdDD1q7px9sa9zQtaBLoT+tF82vZ8kTuplgtnsj6XrOXzEqxFeZCAXcnlNzqsX78+O3fuZMKECbz22mtcuXIFgMTERDp27MiNGzdYvuxTfN2d0GmTeeuLrQwZO5lDR35l2/dbCQsL44v5U7mrTc/1C0GpVGIymSzak9+IPGv0rTcYcXPKv65HYfXp04c+ffowcuRIoqMtN1n01zhTRa2iU0NfmldXs+KtiahUDgwe/Vq+NT+EKC8SsB8A+Y0OmzdvzokTJ3B1dSUkJIR27doRHBxMQkICZ86c4e2336bXM0/zw497qV2jGvHajHsPHOsEs2/fPu7G3+bYxo9z/UKoWbMm586ds2hLXikaT7XKPPq+eelvqlYLKFTBpMJYtGgRnTt3Jjj4IXq8EMK7a3ay8/R1bsRr+ev8RTYuf5+Qbi1wUbvy1kdf4q52sigTK0RFIQ8dBdWqVePdd99lwIABbN++nStXrjB79mzq1q3LE088wa27ujxngnz77bfUrVuXOTNnUK2xZanPl19+mQ4dOjB37lwcHe89+MzvAd6ByFhSY69x7dJ5Hm/XyXxOQQWTCqJQKHguZAR1n3qRY7vD+HjmWG7fugmAq7uGdt378OFXW6hZ5176JlmnL1TNDyHKmgRsG1PYeszFoVKpOHHiBHPmzLHYQfxgZCyX41LMc5VrebmaR77dG/szcOBAVq5cyVtvvWVxvYYNG9KoUSNCQ0MZPnw4kP+yc0+1iq+//pzuzw1GpboX4AtbMKkg5+MyqBFQjYdefZ3hr76O0WgkKTUdvUmB3nCvX0aTSWaAiApNUiI2pCj1mIsjJSWF/fv3M3jwYIt7/nrxDgoFuDs5kJ5p5FRUIumZRnPaYOTIkYSGhuZ6zUWLFjFjxgyOHDliPpZXiub0T2GcPPoLXfsPK3bBpLzcvyhIqVTirnbCBDIDRNgMGWHbkIL2USypO3fu4OPjYzH/+fT1RLxdVShQmrfrgkwibyXR8p9RaL169XI80Mvy2GOPsW7dOvr06cOMGTMYMWIEVapUsTjn8uXL/Pe//2Xnzp1s2baDZEdvqxdMym1RUNboXRa9CFshAduG5LUIJi4l3SqpEqVSabHDSdY9G/i5ceb6valvTg5KTEa4o80wj3wNBkO+S8W7devGgQMHWLhwIXXq1OGZZ56hdu3aGAwGTp06xf/+9z9efvlljh07hq+vb5HaXFi5LQqS1IewNRKwbUheS6QVUKT9A/Pi5eVFfHw8d+7cwcvLy3zPtAwDTWt4cCUulei7qSRo9Xi4OJhnb1w4d45atWrle+3GjRuzbt06YmNj2bJlC7du3cLJyYmXXnqJb7/9FhcXF4vzrZ2r91E7EFQv75KtQtgCCdg2JK8ZFg52WCVV4uLiQt++fVm9ejWvv/66xT3dnOyp6eVMTLKOKmpHWtT2NOfQt378qfmhYkF8fX0L3Om7qBvYFpakPoStk4eONiSvRTAmFPlWkyuKsWPHsmzZMlJTU3Pc8+yNu7g72dOqjhfero64OTmQFh/Nnh938/LLL1ulj1C8DWyFeBAUa4SdnJzMtGnTSElJQa/X85///IdHH33U2m0TuchtlFiYanKF1bJlS9q2bcugQYPYtGkTjo6O5ntm5dCV/2x6kHDnNu9NHkafEa+h0WhK1K/s8svVC/EgK9YIe/Xq1bRq1Yp169bx3nvvMW/ePGu3SxRBfvVCikqhUPDFF1/g4OBAx44d2bdvn3l5edYXgz4jg4O7tjLxxWdp2fFpBg8fY9X+5LcaUogHWbFG2EOHDjUXojcYDOZVbKJ8FLQHYlGpVCo2bdrEypUrmTRpEnq9/t6Gt/aOnL14g5OH9xJYN4hhU96mQYsONK1RpcBrFoWUMxUidwUG7LCwML7++muLY++++y6PPPIIt2/fZtq0acycObPUGigKx9oP1JRKJa+88gqjR4/myJEjnDhxAq1WS6cn/Bg4/BVcqwZafaVlFmt/AQlRWShM95dTK6TIyEimTJnC9OnTad++fY7Xw8PDc0zVqgx0Oh1OTk7l3YxSUdy+3dbqOR+XQaLOgMbJjiBvFT5qh4LfWIYq858bVO7+PWh9S01NpXnz5rmeX6yUyIULF5g4cSL/93//R8OGDfM8Lzg4uDiXr5Cy5gX/cfUajer5lcrIsrxFREQU+c8sOjGNE3/G4OlrT41/0hdXdJkE1atYy7uL0zdbUpn796D1LTw8PM/zixWwP/zwQzIyMnjnnXcAcHV1Zfny5cW5lE3IPi+4irPSPP9Yak6U/nJ5IcS/ihWwK3Nwzk32oJT4z7zgrOMPelCSKXhClB1ZOFMI+e2S8qCTKXhClB0J2IUgQSlv1pwDLoTInwTsQsgelEwSlCzIjuJClB0p/lQI2ecFX0ozUk1lJ/OCs5GiSkKUDQnYhZQVlALtEgkO9i/z+5fm1mBCCNsgKREbUNpbgwkhbIOMsG2ANeY6ywhdCNsnI2wbUNJphTJCF6JykIBtA0o6rVA2BBCicpCAbQNKOtdZFv4IUTlIwLYBJZ3rLAt/hKgc5KGjjSjJXGfZEECIyqHCB+yrV6+yYcMGbt68iVKppFatWgwePBgfH5/ybprNkA0BhKgcKmxKJDw8nF69etGsWTOuXbtGrVq1CAgI4OTJk9SvX5+XXnqJCxculHczbYa/xpnujf0Z3DKQ7o39JVgLYYMq5Ah7x44dDB8+nPnz57Nhw4YcO9fEx8ezYsUK2rZty44dO3jsscfKqaUlI3OjhRBFUeEC9okTJxg+fDg7duygRYsWuZ7j6enJzJkzadSoET179uTo0aPUqlWrbBtaQtk3RfB2dUSbnsmeP2NoEuBBdJJOgrgQIocKlxKZPXs2ixYtyjNYZ9e7d29GjBjB+++/XwYts67c5kYbjCbWn4iSBS5CiFxVqID9999/c/LkSQYPHmxxPDoxjd3novnm+FV2n4u2CGDjxo1j/fr1JCUllXVzSyS3udGxyWkYjCZZ4CKEyFWFCtihoaEMGTIER8d/t5wqaFl1tWrV6NChA1u2bCmvZhdLbnOj41Iy8LpvbrQscBFCZKlQOewbN27QsmVLi2OFKXzUoEEDbt68WbaNLQGTyYT2yhlWffMdGanJuLg4U71OA5wbPomvv7vFubLARQiRpUIFbLgXzLIrzCav97+nIluzZg2LFi0C4Nm+z6Ozr09CUgpnjv3MuU8W0rJLb4a8Og1fby+LBS4yo0QIUaECdo0aNfjzzz8tjmWlDrJG1pBz1BkREUH//v3LrJ3FYTKZmD59Ojt37mTZsmW0b98ehUKRLRAPw5B8m61fLuXNkc8z/aO11K5Z3bwaMbcZJbktT5fALkTlVaFy2CEhIaxbt460tH8fKhZU+CgqKorDhw/Tp0+f8ml0IS1ZsoSffvqJI0eO0KFDB3Owzp6fd/X0o9f4t+nTtw9fvjWWjkGe+GucC11tr6zKqOb3EFgIUXoqVMCuU6cOLVu2ZM2aNeZjBRU+Wrp0KS+99BKurq7l1ewCpaSksGDBArZu3UqVKlXMx3MLxO7ODnQNmYCbmxvffvstUPhqe2VRRlVqawtRfipUSgRgwYIFdO3alUaNGtG2bVsg78JHGzdu5JtvvuHYsWNl3cwiCQ0NpX379tSuXdvi+OXbWpJ0GaSkG3BzsqeWlysaFwfiUtJ57bXXeP/993nxxRcLlRaCwuX7S8oau98IIYqnRCPsixcv0rx5c9LTrRcQHn30Ub755hv69u3LkiVLuHv3bo5zbt26xaxZs5gyZQo7d+4kICDAavcvDaGhoYwcOdLiWHRiGlfjU0nSZeLu5EB6ppFTUYncSEjDU63i2Wef5dKlS1y6dKnQ9bDLooyq1NYWovwUO2CnpKSwaNEiVCrrTznr0qUL+/fv5/jx49SqVYthw4axYMEC5s2bR//+/QkODiYuLo6jR4/SpEkTq9/f2m7evElQUJDFsdPXE6lf1RWTSYFOb8TJ3g6FwkRkTBJNAjTY29tTu3ZtoqOjC10Pu6QbHRSG1NYWovwUKyViMpl48803mTJlCuPGjbN2mwB4+OGH2bBhA7du3SIsLIzo6GiUSiVdunTh888/R6PRlMp9S4NSqcx1umJAFRdcHe25EpdKkk6Pm6MD7s725kBsMplQKu99pxamHnZZlFGV2tpClJ8CA3ZYWBhff/21xbFq1arRo0cPGjZsWGoNy+Ln58eECRNK/T6lqWbNmpw7d44GDRqYj2WNVD3Vjniq7+Wdk3V6nFV2AKSnp3PhwgVq1KhRpHuVZKODwl5famsLUT4UpmKsOunSpQt+fn4AnDp1ikceeYTQ0FCLc8LDw3OURa0MdDodTk5ORXrP9u3b+f777/niiy/Mx25r9RyLSkXtoMTZQUGa3oRWb6RVDRd81A65vqe0FadvtqIy9w0qd/8etL6lpqbSvHnz3N9gKqGOHTuadDpdjuO//fZbSS9dIf35559Ffo9OpzP5+vqaTp06ZXH8ZkKqadfZm6bQY1dMu87eNN1MSDWZTCaTXq83PfbYY6YtW7ZYo8mFVpy+2YrK3DeTqXL370HrW36xs8JN68uNra/ec3R05IMPPqBPnz78/PPP1KxZE8g9fWEwGBg7diyenp707NmzPJorhKigSrxwZv/+/RbV9aytsizUCAkJYdKkSbRp04Z169ah0+lynHPixAl69erFhQsXCAsLw87OrhxaKoSoqCr8CLsyLdSYOHEijRo1YvHixUyZMoV+/frh6+tLWloaBw8eJC4ujrFjxzJx4sRS/RIUQtimCh+wy2L1Xlnq3LkznTt35vz58/zwww8kJCTg7e3N3Llz6datm4yqhRB5qvABu7DLsm2Nq08ADZ7qb5GXl2AthMhPhSr+lJuyWL1X1ipLXl4IUbYqfMAu7LJsW1IWVfWEEJVPhU+JQOmv3itrlS0vL4QoGxV+hF0ZSQElIURxSMAuB5UxLy+EKH0SsMtBZczLCyFKn03ksCujypaXF0KUPhlhCyGEjZCALYQQNkICthBC2AgJ2EIIYSMkYAshhI14oGeJ2PrGCEKIB4tNB+ySBNysAkxuTvZ4uzqiTc9kz58xMh9aCFFh2WxKpKQV76QAkxDC1thswC5pwI3XZqB2tPyBoXa0J16bUQqtFUKIkqtQKZGipDhKWvGusm6MIISovCrMCLuoKY6SVryTAkxCCFtTYQJ2UVMcJQ24UoBJCGFrKkxKpKgpjqyAe/p6InEp6XiqVbSq41WkgCsFmIQQtqTCBOzi5JQl4AohHiQVJiUiOWUhhMhfsQK2wWBgwYIFDBw4kH79+nHgwIESN0RyykIIkb9ipUS+//57MjMz2bBhAzExMezatcsqjZEUhxBC5K1YAfvw4cMEBQUxevRoTCYTb775prXbJYQQ4j4FBuywsDC+/vpri2NVqlTB0dGRzz77jBMnTvDGG28QGhpaao0UQggBCpPJZCrqmyZPnkz37t3p1q0bAG3atOHIkSMW54SHh+Pi4mKdVlYgOp0OJyen8m5GqZC+2a7K3L8HrW+pqak0b9481/OLlRJp3rw5P//8M926deOvv/7C398/1/OCg4OLc/kKLSIiolL2C6Rvtqwy9+9B61t4eHie5xdrlkj//v0xmUz079+fN998k7lz5xbnMkIIIYqgWCmRwsjvW0IIIUTe8kqJlFrAFkIIYV0VZqWjEEKI/EnAFkIIGyEBu4iSk5MZM2YML730EgMGDODkyZPl3SSr27NnD1OnTi3vZliF0Whkzpw5DBgwgJCQEK5evVreTbK606dPExISUt7NsCq9Xs+0adMYPHgwzz//PPv27SvvJlmVwWDgjTfeYODAgQwaNIi///67UO+rMNX6bMXq1atp1aoVQ4cO5dKlS0ydOpUtW7aUd7OsZsGCBRw+fLjSTKPau3cvGRkZbNy4kVOnTrFw4UKWL19e3s2ympUrV7Jt2zacnStXSYdt27ah0WhYvHgxiYmJ9OnTh6eeeqq8m2U1WfWXNmzYwPHjx1myZEmh/l5KwC6ioUOHolLdK/lqMBhwdHQs4B22pVmzZnTu3JmNGzeWd1OsIjw8nHbt2gHQtGlTzp07V84tsq6aNWuydOlSpk+fXt5NsarsC/NMJhN2dnbl3CLr6ty5Mx06dADg5s2buLu7F+p9ErDzkduy/HfffZdHHnmE27dvM23aNGbOnFlOrSuZvPrWo0cPjh8/Xk6tsr6UlBRcXV3N/21nZ0dmZib29pXjr363bt24fv16eTfD6tRqNXDvz++1115j0qRJ5dugUmBvb8+MGTPYs2cPH3/8ceHeU8ptsmkvvPACL7zwQo7jkZGRTJkyhenTp9OiRYtyaFnJ5dW3ysbV1RWtVmv+b6PRWGmCdWUXHR3N+PHjGTx4MD179izv5pSKRYsW8frrr9O/f3927txZYDkPeehYRBcuXGDixIl8+OGHtG/fvrybIwrQrFkzfvnlFwBOnTpF/fr1y7lFojDi4uIYPnw406ZN4/nnny/v5ljd1q1b+eyzzwBwdnZGoVCgVBYcjmWoUUQffvghGRkZvPPOO8C9EVxleohV2XTp0oUjR44wcOBATCYT7777bnk3SRTCihUrSEpKYtmyZSxbtgy494C1shSB6tq1K2+88QYvvvgimZmZzJw5s1B9k5WOQghhIyQlIoQQNkICthBC2AgJ2EIIYSMkYAshhI2QgC2EEDZCArYQQtgICdhCCGEjJGALIYSN+H9gFra5Dx1ZjgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(X[:, 0], X[:, 1], alpha=0.3)\n", + "plt.scatter(selection[:, 0], selection[:, 1],\n", + " facecolor='none', edgecolor='black', s=200);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This sort of strategy is often used to quickly partition datasets, as is often needed in train/test splitting for validation of statistical models (see [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb)), and in sampling approaches to answering statistical questions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Modifying Values with Fancy Indexing\n", + "\n", + "Just as fancy indexing can be used to access parts of an array, it can also be used to modify parts of an array.\n", + "For example, imagine we have an array of indices and we'd like to set the corresponding items in an array to some value:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0 99 99 3 99 5 6 7 99 9]\n" + ] + } + ], + "source": [ + "x = np.arange(10)\n", + "i = np.array([2, 1, 8, 4])\n", + "x[i] = 99\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use any assignment-type operator for this. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0 89 89 3 89 5 6 7 89 9]\n" + ] + } + ], + "source": [ + "x[i] -= 10\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice, though, that repeated indices with these operations can cause some potentially unexpected results. Consider the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[6. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n" + ] + } + ], + "source": [ + "x = np.zeros(10)\n", + "x[[0, 0]] = [4, 6]\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Where did the 4 go? This operation first assigns `x[0] = 4`, followed by `x[0] = 6`.\n", + "The result, of course, is that `x[0]` contains the value 6.\n", + "\n", + "Fair enough, but consider this operation:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([6., 0., 1., 1., 1., 0., 0., 0., 0., 0.])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "i = [2, 3, 3, 4, 4, 4]\n", + "x[i] += 1\n", + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You might expect that `x[3]` would contain the value 2 and `x[4]` would contain the value 3, as this is how many times each index is repeated. Why is this not the case?\n", + "Conceptually, this is because `x[i] += 1` is meant as a shorthand of `x[i] = x[i] + 1`. `x[i] + 1` is evaluated, and then the result is assigned to the indices in `x`.\n", + "With this in mind, it is not the augmentation that happens multiple times, but the assignment, which leads to the rather nonintuitive results.\n", + "\n", + "So what if you want the other behavior where the operation is repeated? For this, you can use the `at` method of ufuncs and do the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0. 0. 1. 2. 3. 0. 0. 0. 0. 0.]\n" + ] + } + ], + "source": [ + "x = np.zeros(10)\n", + "np.add.at(x, i, 1)\n", + "print(x)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `at` method does an in-place application of the given operator at the specified indices (here, `i`) with the specified value (here, 1).\n", + "Another method that is similar in spirit is the `reduceat` method of ufuncs, which you can read about in the [NumPy documentation](https://numpy.org/doc/stable/reference/ufuncs.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Binning Data\n", + "\n", + "You could use these ideas to efficiently do custom binned computations on data.\n", + "For example, imagine we have 100 values and would like to quickly find where they fall within an array of bins.\n", + "We could compute this using `ufunc.at` like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "rng = np.random.default_rng(seed=1701)\n", + "x = rng.normal(size=100)\n", + "\n", + "# compute a histogram by hand\n", + "bins = np.linspace(-5, 5, 20)\n", + "counts = np.zeros_like(bins)\n", + "\n", + "# find the appropriate bin for each x\n", + "i = np.searchsorted(bins, x)\n", + "\n", + "# add 1 to each of these bins\n", + "np.add.at(counts, i, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The counts now reflect the number of points within each bin—in other words, a histogram (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot the results\n", + "plt.plot(bins, counts, drawstyle='steps');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course, it would be inconvenient to have to do this each time you want to plot a histogram.\n", + "This is why Matplotlib provides the `plt.hist` routine, which does the same in a single line:\n", + "\n", + "```python\n", + "plt.hist(x, bins, histtype='step');\n", + "```\n", + "\n", + "This function will create a nearly identical plot to the one just shown.\n", + "To compute the binning, Matplotlib uses the `np.histogram` function, which does a very similar computation to what we did before. Let's compare the two here:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NumPy histogram (100 points):\n", + "33.8 µs ± 311 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n", + "Custom histogram (100 points):\n", + "17.6 µs ± 113 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n" + ] + } + ], + "source": [ + "print(f\"NumPy histogram ({len(x)} points):\")\n", + "%timeit counts, edges = np.histogram(x, bins)\n", + "\n", + "print(f\"Custom histogram ({len(x)} points):\")\n", + "%timeit np.add.at(counts, np.searchsorted(bins, x), 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our own one-line algorithm is twice as fast as the optimized algorithm in NumPy! How can this be? If you dig into the `np.histogram` source code (you can do this in IPython by typing `np.histogram??`), you'll see that it's quite a bit more involved than the simple search-and-count that we've done; this is because NumPy's algorithm is more flexible, and particularly is designed for better performance when the number of data points becomes large:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NumPy histogram (1000000 points):\n", + "84.4 ms ± 2.82 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", + "Custom histogram (1000000 points):\n", + "128 ms ± 2.04 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "x = rng.normal(size=1000000)\n", + "print(f\"NumPy histogram ({len(x)} points):\")\n", + "%timeit counts, edges = np.histogram(x, bins)\n", + "\n", + "print(f\"Custom histogram ({len(x)} points):\")\n", + "%timeit np.add.at(counts, np.searchsorted(bins, x), 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What this comparison shows is that algorithmic efficiency is almost never a simple question. An algorithm efficient for large datasets will not always be the best choice for small datasets, and vice versa (see [Big-O Notation](02.08-Sorting.ipynb#Big-O-Notation)).\n", + "But the advantage of coding this algorithm yourself is that with an understanding of these basic methods, the sky is the limit: you're no longer constrained to built-in routines, but can create your own approaches to exploring the data.\n", + "Key to efficiently using Python in data-intensive applications is not only knowing about general convenience routines like `np.histogram` and when they're appropriate, but also knowing how to make use of lower-level functionality when you need more pointed behavior." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.08-Sorting.ipynb b/notebooks/02.08-Sorting.ipynb new file mode 100644 index 000000000..07744e596 --- /dev/null +++ b/notebooks/02.08-Sorting.ipynb @@ -0,0 +1,772 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sorting Arrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Up to this point we have been concerned mainly with tools to access and operate on array data with NumPy.\n", + "This chapter covers algorithms related to sorting values in NumPy arrays.\n", + "These algorithms are a favorite topic in introductory computer science courses: if you've ever taken one, you probably have had dreams (or, depending on your temperament, nightmares) about *insertion sorts*, *selection sorts*, *merge sorts*, *quick sorts*, *bubble sorts*, and many, many more.\n", + "All are means of accomplishing a similar task: sorting the values in a list or array.\n", + "\n", + "Python has a couple of built-in functions and methods for sorting lists and other iterable objects. The `sorted` function accepts a list and returns a sorted version of it:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 1, 2, 3, 4, 5, 6, 9]" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L = [3, 1, 4, 1, 5, 9, 2, 6]\n", + "sorted(L) # returns a sorted copy" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By contrast, the `sort` method of lists will sort the list in-place:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1, 1, 2, 3, 4, 5, 6, 9]\n" + ] + } + ], + "source": [ + "L.sort() # acts in-place and returns None\n", + "print(L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Python's sorting methods are quite flexible, and can handle any iterable object. For example, here we sort a string:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['h', 'n', 'o', 'p', 't', 'y']" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sorted('python')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These built-in sorting methods are convenient, but as previously discussed, the dynamism of Python values means they are less performant than routines designed specifically for uniform arrays of numbers.\n", + "This is where NumPy's sorting routines come in." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fast Sorting in NumPy: np.sort and np.argsort\n", + "\n", + "The `np.sort` function is analogous to Python's built-in `sorted` function, and will efficiently return a sorted copy of an array:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 2, 3, 4, 5])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "x = np.array([2, 1, 4, 3, 5])\n", + "np.sort(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly to the `sort` method of Python lists, you can also sort an array in-place using the array `sort` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 2 3 4 5]\n" + ] + } + ], + "source": [ + "x.sort()\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A related function is `argsort`, which instead returns the *indices* of the sorted elements:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 0 3 2 4]\n" + ] + } + ], + "source": [ + "x = np.array([2, 1, 4, 3, 5])\n", + "i = np.argsort(x)\n", + "print(i)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first element of this result gives the index of the smallest element, the second value gives the index of the second smallest, and so on.\n", + "These indices can then be used (via fancy indexing) to construct the sorted array if desired:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 2, 3, 4, 5])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x[i]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You'll see an application of `argsort` later in this chapter.\n", + "\n", + "### Sorting Along Rows or Columns" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A useful feature of NumPy's sorting algorithms is the ability to sort along specific rows or columns of a multidimensional array using the `axis` argument. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 7 6 4 4 8]\n", + " [0 6 2 0 5 9]\n", + " [7 7 7 7 5 1]\n", + " [8 4 5 3 1 9]]\n" + ] + } + ], + "source": [ + "rng = np.random.default_rng(seed=42)\n", + "X = rng.integers(0, 10, (4, 6))\n", + "print(X)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 4, 2, 0, 1, 1],\n", + " [0, 6, 5, 3, 4, 8],\n", + " [7, 7, 6, 4, 5, 9],\n", + " [8, 7, 7, 7, 5, 9]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# sort each column of X\n", + "np.sort(X, axis=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 4, 4, 6, 7, 8],\n", + " [0, 0, 2, 5, 6, 9],\n", + " [1, 5, 7, 7, 7, 7],\n", + " [1, 3, 4, 5, 8, 9]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# sort each row of X\n", + "np.sort(X, axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind that this treats each row or column as an independent array, and any relationships between the row or column values will be lost!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Partial Sorts: Partitioning\n", + "\n", + "Sometimes we're not interested in sorting the entire array, but simply want to find the *k* smallest values in the array. NumPy enables this with the `np.partition` function. `np.partition` takes an array and a number *K*; the result is a new array with the smallest *K* values to the left of the partition and the remaining values to the right:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 1, 3, 4, 6, 5, 7])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([7, 2, 3, 1, 6, 5, 4])\n", + "np.partition(x, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the first three values in the resulting array are the three smallest in the array, and the remaining array positions contain the remaining values.\n", + "Within the two partitions, the elements have arbitrary order.\n", + "\n", + "Similarly to sorting, we can partition along an arbitrary axis of a multidimensional array:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 4, 4, 7, 6, 8],\n", + " [0, 0, 2, 6, 5, 9],\n", + " [1, 5, 7, 7, 7, 7],\n", + " [1, 3, 4, 5, 8, 9]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.partition(X, 2, axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is an array where the first two slots in each row contain the smallest values from that row, with the remaining values filling the remaining slots.\n", + "\n", + "Finally, just as there is an `np.argsort` function that computes indices of the sort, there is an `np.argpartition` function that computes indices of the partition.\n", + "We'll see both of these in action in the following section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: k-Nearest Neighbors\n", + "\n", + "Let's quickly see how we might use the `argsort` function along multiple axes to find the nearest neighbors of each point in a set.\n", + "We'll start by creating a random set of 10 points on a two-dimensional plane.\n", + "Using the standard convention, we'll arrange these in a $10\\times 2$ array:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "X = rng.random((10, 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get an idea of how these points look, let's generate a quick scatter plot (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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yWsyoc89PUiJS2+HTl7D6DQ/aj55HICRCxleXlK5+w4PDpy9pHTHlKJZ4d3c3wuEwOjo60NDQgJaWlui28+fP489//jPa29uxb98+/OMf/8CpU6dUDUz6kTXLjtYaF9KtFghm05htgtmEdKsFrTUuHp1NEbykVJ8US9zr9cLtdgMAlixZgpMnT0a3zZkzBzt37oTFYoHJZIIoirDZbOqlJd1ZkTsbXRvcqC5wwmETYDIBDpuA6gInuja4eaPPFMJLSvVJcU48EAjA4XBEH1ssFoiiCEEQYLVaMXPmTMiyjF/96ld48MEHMX/+xL86+3y+xKW+QyMjI5q+/0SmWqa1uRaszXWOeW7o0mfwJeC366n2vVKL2pne9cY+/wF8eUS+3/sZ1uZakpZrMqZSJsUSdzgcCAa/+vVIkiQIwlcvC4VC+NnPfga73Y7Nmzffdj95eXl3HC5RfD6fpu8/EWaKnx5zpWKm4dGB+MaJ8pgcqfi9moxbM3m93rhepzid4nK50NPTAwDo7+9HTk5OdJssy6ivr0dubi6amppgsVhutxsiMjheUqpPit/toqIiHDlyBFVVVZBlGc3Nzdi9ezecTickScLRo0cRDofh8XgAABs3bkR+fr7qwYkouXhJqT4plrjZbEZTU9OY57Kzs6Nf/+tf/0p8KiLSnfXuBdjvvQBRitx2DC8pTT7esUlEceElpfrEEieiuPGSUv3hGQgiuiNZs+zYUrIIW0oWaR2FwCNxIiJDY4kTERkYS5yIyMBY4kREBsYSJyIyMJY4EZGBscSJiAyMJU5EZGAscSIiA2OJExEZGEuciMjAWOJERAbGEiciMjCWOBGRgbHEiYgMjCVORGRg/FAISgn+wSB2eAbQ2XcRwZAIu01ASX4m1rsX8OPEyNBY4jTlHT59CfVtvRiNSNFPag+ERLQfPY/93gtorXHxY8XIsDidQlOafzCI+rZeDI9GogV+kyjJGB6NoL6tF/7BoEYJie4OS5ymtB2eAYxGpJhjRiMSdnrOJSkRUWJxOoVUp+V8dGffxXFH4LcSJRkH+i7wg3/JkFjipCqt56ODITG+ceH4xhHpDadTSDV6mI+22+I7TrGn8XiGjIklTqrRw3x0SX4mBLMp5hjBbEJp/jzVMhCpiSVOqrmT+Wi1rHcvgNUS+8fcajGjzj1ftQxEamKJk2r0MB+dNcuO1hoX0q2WcUfkgtmEdKsFrTUu3vBDhsUSJ9XoZT56Re5sdG1wo7rACYdNgMkEOGwCqguc6Nrg5o0+ZGg8m0OqKcnPRPvR8zGnVJI1H501y44tJYt4GSFNOTwSJ9VwPppIfSxxUg3no4nUxxInVXE+mkhdnBMn1XE+mkg9ikfikiShsbERlZWVqK2thd/vH7N93759WLNmDSoqKnD48GHVghIR0XiKR+Ld3d0Ih8Po6OhAf38/Wlpa8Nvf/hYAcPnyZezduxf79+9HKBTC2rVrsWzZMqSlpakenIiI4jgS93q9cLvdAIAlS5bg5MmT0W2ffPIJ8vPzkZaWhoyMDDidTpw6dUq9tERENIbikXggEIDD4Yg+tlgsEEURgiAgEAggIyMjus1utyMQCEy4H6/Xm4C4k6f1+0+EmeKnx1zMFD895poqmRRL3OFwIBj8apU5SZIgCMKE24LB4JhSv2np0qV3HIyIiJQpTqe4XC709PQAAPr7+5GTkxPdtnjxYni9XoRCIdy4cQNnz54ds52IiNRlkmU55jJzkiTh5ZdfxpkzZyDLMpqbm9HT0wOn04nCwkLs27cPHR0dkGUZzz77LFatWpWs7EREKU+xxImISL+mzM0+N39jOH36NNLS0vDKK68gKysrun3Pnj147733AACPPPIInn/+eV3k+uMf/4h3330XJpMJP/zhD/HYY49pnunmmB/96EcoLCxEdXW15pleeeUV9Pb2wm7/8hb91tbWCc+/JDPThx9+iG3btkGWZSxcuBCbN2+GyRT7AyjUzuXz+dDc3Bwd29/fj23btmH58uWaZQKAXbt24dChQzCZTHjuuedQVFSkap54Mm3fvh3vvfceHA4H6urqsGLFCtUz3XTixAm8/vrr2Lt375jnP/jgA2zbtg2CIKCsrAwVFRXKO5OniL/+9a/yT3/6U1mWZbmvr09+7rnnots+++wzubS0VBZFUZYkSa6srJR9Pp/muQYHB+Xi4mI5HA7LN27ckJcvXy5LkqRpppt+/etfy+Xl5fJbb72lep54MlVVVcmDg4NJyRJPphs3bsjFxcXRTNu3b09avnj+/mRZlv/yl7/IGzdu1DzTF198IT/yyCNyKBSSr127Jn/ve9/TPNOpU6fkJ554Qh4ZGZFHRkbkkpISeWhoKCm5tm/fLj/++ONyeXn5mOfD4bD86KOPyteuXZNDoZC8Zs0a+fLly4r7mzJrp8S6nn3OnDnYuXMnLBYLTCYTRFGEzWbTPNfMmTPR2dkJq9WK//3vf7DZbEk5kouVCQC6urpgMpmiY5IhViZJkuD3+9HY2Iiqqiq88847mmfq6+tDTk4OXn31Vaxduxb33nsvZs6cqXmum4aGhrB161b8/Oc/1zxTeno6MjMzMTw8jOHh4aT8jCtlOnv2LAoKCmCz2WCz2ZCVlYXTp08nJZfT6cTWrVvHPX/27Fk4nU7MmDEDaWlpWLp0KY4dO6a4vylT4re7nh0ArFYrZs6cCVmW8eqrr+LBBx/E/PnJWf40Vi4AEAQBbW1tqKysxPe//33NM505cwaHDh3CT37yk6RkiSfT0NAQampq8Nprr2Hnzp146623knJTWaxMV69exccff4wXX3wRO3bswO9//3ucO6feZ4XGm+umd955B6tXr07afyxKmebOnYvi4mKUlpbi6aef1jxTbm4ujh8/jkAggKtXr6Kvrw/Dw8NJybVq1aroZdq35o33vpuvmzIlHut6dgAIhUJ48cUXEQwGsXnzZt3kAoCamhp4PB4cO3YM//znPzXN1NnZic8//xzPPPMMDhw4gD179kQvMdUqU3p6Op5++mmkp6fD4XDgu9/9blJKPFame+65Bw899BDuu+8+2O12PPzww/D5fKpnUsp108GDB1FeXp6UPEqZenp6cOnSJbz//vv4+9//ju7ubnzyySeaZsrOzsZTTz2Furo6bNmyBd/5znfwjW98Q/VMscR7382tpkyJx7qeXZZl1NfXIzc3F01NTbBYLLrINTAwgOeffx6yLMNqtSItLQ1ms/p/JbEybdq0CW+//Tb27t2L0tJS/OAHP1D9pJhSpn//+9+orq5GJBLB6Ogoent7sXDhQk0zLVy4EGfOnMGVK1cgiiJOnDiBBx54QPVMSrkA4MaNGwiHw5g7d25S8ihlmjFjBqZNm4a0tDTYbDZkZGTg+vXrmma6cuUKgsEg2tvb8Ytf/AL//e9/8a1vfUv1TLFkZ2fD7/fj2rVrCIfDOH78OPLz8xVfN2WuTikqKsKRI0dQVVUVvZ599+7dcDqdkCQJR48eRTgchsfjAQBs3Lgxrm+QmrkKCwvx7W9/G5WVldE56IKCAs0zaUEp05NPPomKigpYrVY8+eSTSfkHp5SpoaEBdXV1AIDVq1cn7UY3pVznzp3DvHnqf+TdnWT66KOPUFFRAbPZDJfLhWXLlmmaaeXKlRgYGEBZWRmsVis2bdqU1IO7rzt48CCGhoZQWVmJl156CevWrYMsyygrK8P999+v+HpeJ05EZGBTZjqFiCgVscSJiAyMJU5EZGAscSIiA2OJExEZGEuciMjAWOJERAb2/wAdJtaghhbgJwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "plt.scatter(X[:, 0], X[:, 1], s=100);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll compute the distance between each pair of points.\n", + "Recall that the squared distance between two points is the sum of the squared differences in each dimension;\n", + "using the efficient broadcasting ([Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb)) and aggregation ([Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb)) routines provided by NumPy we can compute the matrix of square distances in a single line of code:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "dist_sq = np.sum((X[:, np.newaxis] - X[np.newaxis, :]) ** 2, axis=-1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This operation has a lot packed into it, and it might be a bit confusing if you're unfamiliar with NumPy's broadcasting rules. When you come across code like this, it can be useful to break it down into its component steps:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(10, 10, 2)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# for each pair of points, compute differences in their coordinates\n", + "differences = X[:, np.newaxis] - X[np.newaxis, :]\n", + "differences.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(10, 10, 2)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# square the coordinate differences\n", + "sq_differences = differences ** 2\n", + "sq_differences.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(10, 10)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# sum the coordinate differences to get the squared distance\n", + "dist_sq = sq_differences.sum(-1)\n", + "dist_sq.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As a quick check of our logic, we should see that the diagonal of this matrix (i.e., the set of distances between each point and itself) is all zeros:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dist_sq.diagonal()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the pairwise square distances converted, we can now use `np.argsort` to sort along each row. The leftmost columns will then give the indices of the nearest neighbors:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 9 3 5 4 8 1 6 2 7]\n", + " [1 7 2 6 4 8 3 0 9 5]\n", + " [2 7 1 6 4 3 8 0 9 5]\n", + " [3 0 4 5 9 6 1 2 8 7]\n", + " [4 6 3 1 2 7 0 5 9 8]\n", + " [5 9 3 0 4 6 8 1 2 7]\n", + " [6 4 2 1 7 3 0 5 9 8]\n", + " [7 2 1 6 4 3 8 0 9 5]\n", + " [8 0 1 9 3 4 7 2 6 5]\n", + " [9 0 5 3 4 8 6 1 2 7]]\n" + ] + } + ], + "source": [ + "nearest = np.argsort(dist_sq, axis=1)\n", + "print(nearest)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the first column gives the numbers 0 through 9 in order: this is due to the fact that each point's closest neighbor is itself, as we would expect.\n", + "\n", + "By using a full sort here, we've actually done more work than we need to in this case. If we're simply interested in the nearest $k$ neighbors, all we need to do is partition each row so that the smallest $k + 1$ squared distances come first, with larger distances filling the remaining positions of the array. We can do this with the `np.argpartition` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "K = 2\n", + "nearest_partition = np.argpartition(dist_sq, K + 1, axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to visualize this network of neighbors, let's quickly plot the points along with lines representing the connections from each point to its two nearest neighbors (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(X[:, 0], X[:, 1], s=100)\n", + "\n", + "# draw lines from each point to its two nearest neighbors\n", + "K = 2\n", + "\n", + "for i in range(X.shape[0]):\n", + " for j in nearest_partition[i, :K+1]:\n", + " # plot a line from X[i] to X[j]\n", + " # use some zip magic to make it happen:\n", + " plt.plot(*zip(X[j], X[i]), color='black')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each point in the plot has lines drawn to its two nearest neighbors.\n", + "At first glance, it might seem strange that some of the points have more than two lines coming out of them: this is due to the fact that if point A is one of the two nearest neighbors of point B, this does not necessarily imply that point B is one of the two nearest neighbors of point A.\n", + "\n", + "Although the broadcasting and row-wise sorting of this approach might seem less straightforward than writing a loop, it turns out to be a very efficient way of operating on this data in Python.\n", + "You might be tempted to do the same type of operation by manually looping through the data and sorting each set of neighbors individually, but this would almost certainly lead to a slower algorithm than the vectorized version we used. The beauty of this approach is that it's written in a way that's agnostic to the size of the input data: we could just as easily compute the neighbors among 100 or 1,000,000 points in any number of dimensions, and the code would look the same.\n", + "\n", + "Finally, I'll note that when doing very large nearest neighbor searches, there are tree-based and/or approximate algorithms that can scale as $\\mathcal{O}[N\\log N]$ or better rather than the $\\mathcal{O}[N^2]$ of the brute-force algorithm. One example of this is the KD-Tree, [implemented in Scikit-Learn](http://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KDTree.html)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/02.09-Structured-Data-NumPy.ipynb b/notebooks/02.09-Structured-Data-NumPy.ipynb new file mode 100644 index 000000000..b9942b336 --- /dev/null +++ b/notebooks/02.09-Structured-Data-NumPy.ipynb @@ -0,0 +1,614 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Structured Data: NumPy's Structured Arrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While often our data can be well represented by a homogeneous array of values, sometimes this is not the case. This chapter demonstrates the use of NumPy's *structured arrays* and *record arrays*, which provide efficient storage for compound, heterogeneous data. While the patterns shown here are useful for simple operations, scenarios like this often lend themselves to the use of Pandas ``DataFrame``s, which we'll explore in [Part 3](03.00-Introduction-to-Pandas.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Imagine that we have several categories of data on a number of people (say, name, age, and weight), and we'd like to store these values for use in a Python program.\n", + "It would be possible to store these in three separate arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "name = ['Alice', 'Bob', 'Cathy', 'Doug']\n", + "age = [25, 45, 37, 19]\n", + "weight = [55.0, 85.5, 68.0, 61.5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this is a bit clumsy. There's nothing here that tells us that the three arrays are related; NumPy's structured arrays allow us to do this more naturally by using a single structure to store all of this data.\n", + "\n", + "Recall that previously we created a simple array using an expression like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "x = np.zeros(4, dtype=int)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can similarly create a structured array using a compound data type specification:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[('name', '`, means \"little endian\" or \"big endian,\" respectively, and specifies the ordering convention for significant bits.\n", + "The next character specifies the type of data: characters, bytes, ints, floating points, and so on (see the table below).\n", + "The last character or characters represent the size of the object in bytes.\n", + "\n", + "| Character | Description | Example |\n", + "| --------- | ----------- | ------- | \n", + "| `'b'` | Byte | `np.dtype('b')` |\n", + "| `'i'` | Signed integer | `np.dtype('i4') == np.int32` |\n", + "| `'u'` | Unsigned integer | `np.dtype('u1') == np.uint8` |\n", + "| `'f'` | Floating point | `np.dtype('f8') == np.int64` |\n", + "| `'c'` | Complex floating point| `np.dtype('c16') == np.complex128`|\n", + "| `'S'`, `'a'` | String | `np.dtype('S5')` |\n", + "| `'U'` | Unicode string | `np.dtype('U') == np.str_` |\n", + "| `'V'` | Raw data (void) | `np.dtype('V') == np.void` |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More Advanced Compound Types\n", + "\n", + "It is possible to define even more advanced compound types.\n", + "For example, you can create a type where each element contains an array or matrix of values.\n", + "Here, we'll create a data type with a `mat` component consisting of a $3\\times 3$ floating-point matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0, [[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]])\n", + "[[0. 0. 0.]\n", + " [0. 0. 0.]\n", + " [0. 0. 0.]]\n" + ] + } + ], + "source": [ + "tp = np.dtype([('id', 'i8'), ('mat', 'f8', (3, 3))])\n", + "X = np.zeros(1, dtype=tp)\n", + "print(X[0])\n", + "print(X['mat'][0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now each element in the `X` array consists of an `id` and a $3\\times 3$ matrix.\n", + "Why would you use this rather than a simple multidimensional array, or perhaps a Python dictionary?\n", + "One reason is that this NumPy `dtype` directly maps onto a C structure definition, so the buffer containing the array content can be accessed directly within an appropriately written C program.\n", + "If you find yourself writing a Python interface to a legacy C or Fortran library that manipulates structured data, structured arrays can provide a powerful interface." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Record Arrays: Structured Arrays with a Twist\n", + "\n", + "NumPy also provides record arrays (instances of the `np.recarray` class), which are almost identical to the structured arrays just described, but with one additional feature: fields can be accessed as attributes rather than as dictionary keys.\n", + "Recall that we previously accessed the ages in our sample dataset by writing:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([25, 45, 37, 19], dtype=int32)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['age']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we view our data as a record array instead, we can access this with slightly fewer keystrokes:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([25, 45, 37, 19], dtype=int32)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data_rec = data.view(np.recarray)\n", + "data_rec.age" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The downside is that for record arrays, there is some extra overhead involved in accessing the fields, even when using the same syntax:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "121 ns ± 1.4 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n", + "2.41 µs ± 15.7 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n", + "3.98 µs ± 20.5 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n" + ] + } + ], + "source": [ + "%timeit data['age']\n", + "%timeit data_rec['age']\n", + "%timeit data_rec.age" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whether the more convenient notation is worth the (slight) overhead will depend on your own application." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## On to Pandas\n", + "\n", + "This chapter on structured and record arrays is purposely located at the end of this part of the book, because it leads so well into the next package we will cover: Pandas.\n", + "Structured arrays can come in handy in certain situations, like when you're using NumPy arrays to map onto binary data formats in C, Fortran, or another language.\n", + "But for day-to-day use of structured data, the Pandas package is a much better choice; we'll explore it in depth in the chapters that follow." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.00-Introduction-to-Pandas.ipynb b/notebooks/03.00-Introduction-to-Pandas.ipynb new file mode 100644 index 000000000..759ad4730 --- /dev/null +++ b/notebooks/03.00-Introduction-to-Pandas.ipynb @@ -0,0 +1,141 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Data Manipulation with Pandas" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In [Part 2](02.00-Introduction-to-NumPy.ipynb), we dove into detail on NumPy and its `ndarray` object, which enables efficient storage and manipulation of dense typed arrays in Python.\n", + "Here we'll build on this knowledge by looking in depth at the data structures provided by the Pandas library.\n", + "Pandas is a newer package built on top of NumPy that provides an efficient implementation of a `DataFrame`.\n", + "``DataFrame``s are essentially multidimensional arrays with attached row and column labels, often with heterogeneous types and/or missing data.\n", + "As well as offering a convenient storage interface for labeled data, Pandas implements a number of powerful data operations familiar to users of both database frameworks and spreadsheet programs.\n", + "\n", + "As we've seen, NumPy's `ndarray` data structure provides essential features for the type of clean, well-organized data typically seen in numerical computing tasks.\n", + "While it serves this purpose very well, its limitations become clear when we need more flexibility (e.g., attaching labels to data, working with missing data, etc.) and when attempting operations that do not map well to element-wise broadcasting (e.g., groupings, pivots, etc.), each of which is an important piece of analyzing the less structured data available in many forms in the world around us.\n", + "Pandas, and in particular its `Series` and `DataFrame` objects, builds on the NumPy array structure and provides efficient access to these sorts of \"data munging\" tasks that occupy much of a data scientist's time.\n", + "\n", + "In this part of the book, we will focus on the mechanics of using `Series`, `DataFrame`, and related structures effectively.\n", + "We will use examples drawn from real datasets where appropriate, but these examples are not necessarily the focus." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing and Using Pandas\n", + "\n", + "Installation of Pandas on your system requires NumPy to be installed, and if you're building the library from source, you will need the appropriate tools to compile the C and Cython sources on which Pandas is built.\n", + "Details on the installation process can be found in the [Pandas documentation](http://pandas.pydata.org/).\n", + "If you followed the advice outlined in the [Preface](00.00-Preface.ipynb) and used the Anaconda stack, you already have Pandas installed.\n", + "\n", + "Once Pandas is installed, you can import it and check the version; here is the version used by this book:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.3.5'" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas\n", + "pandas.__version__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as we generally import NumPy under the alias `np`, we will import Pandas under the alias `pd`:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This import convention will be used throughout the remainder of this book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reminder About Built-in Documentation\n", + "\n", + "As you read through this part of the book, don't forget that IPython gives you the ability to quickly explore the contents of a package (by using the tab completion feature) as well as the documentation of various functions (using the `?` character). Refer back to [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb) if you need a refresher on this.\n", + "\n", + "For example, to display all the contents of the Pandas namespace, you can type:\n", + "\n", + "```ipython\n", + "In [3]: pd.\n", + "```\n", + "\n", + "And to display the built-in Pandas documentation, you can use this:\n", + "\n", + "```ipython\n", + "In [4]: pd?\n", + "```\n", + "\n", + "More detailed documentation, along with tutorials and other resources, can be found at http://pandas.pydata.org/." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.01-Introducing-Pandas-Objects.ipynb b/notebooks/03.01-Introducing-Pandas-Objects.ipynb new file mode 100644 index 000000000..46252a7ed --- /dev/null +++ b/notebooks/03.01-Introducing-Pandas-Objects.ipynb @@ -0,0 +1,1718 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introducing Pandas Objects" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At a very basic level, Pandas objects can be thought of as enhanced versions of NumPy structured arrays in which the rows and columns are identified with labels rather than simple integer indices.\n", + "As we will see during the course of this chapter, Pandas provides a host of useful tools, methods, and functionality on top of the basic data structures, but nearly everything that follows will require an understanding of what these structures are.\n", + "Thus, before we go any further, let's take a look at these three fundamental Pandas data structures: the `Series`, `DataFrame`, and `Index`.\n", + "\n", + "We will start our code sessions with the standard NumPy and Pandas imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Pandas Series Object\n", + "\n", + "A Pandas `Series` is a one-dimensional array of indexed data.\n", + "It can be created from a list or array as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 0.25\n", + "1 0.50\n", + "2 0.75\n", + "3 1.00\n", + "dtype: float64" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.Series([0.25, 0.5, 0.75, 1.0])\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `Series` combines a sequence of values with an explicit sequence of indices, which we can access with the `values` and `index` attributes.\n", + "The `values` are simply a familiar NumPy array:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.25, 0.5 , 0.75, 1. ])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.values" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `index` is an array-like object of type `pd.Index`, which we'll discuss in more detail momentarily:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "RangeIndex(start=0, stop=4, step=1)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.index" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Like with a NumPy array, data can be accessed by the associated index via the familiar Python square-bracket notation:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1 0.50\n", + "2 0.75\n", + "dtype: float64" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data[1:3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we will see, though, the Pandas `Series` is much more general and flexible than the one-dimensional NumPy array that it emulates." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Series as Generalized NumPy Array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From what we've seen so far, the `Series` object may appear to be basically interchangeable with a one-dimensional NumPy array.\n", + "The essential difference is that while the NumPy array has an *implicitly defined* integer index used to access the values, the Pandas `Series` has an *explicitly defined* index associated with the values.\n", + "\n", + "This explicit index definition gives the `Series` object additional capabilities. For example, the index need not be an integer, but can consist of values of any desired type.\n", + "So, if we wish, we can use strings as an index:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 0.25\n", + "b 0.50\n", + "c 0.75\n", + "d 1.00\n", + "dtype: float64" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.Series([0.25, 0.5, 0.75, 1.0],\n", + " index=['a', 'b', 'c', 'd'])\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the item access works as expected:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['b']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can even use noncontiguous or nonsequential indices:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2 0.25\n", + "5 0.50\n", + "3 0.75\n", + "7 1.00\n", + "dtype: float64" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.Series([0.25, 0.5, 0.75, 1.0],\n", + " index=[2, 5, 3, 7])\n", + "data" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data[5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Series as Specialized Dictionary\n", + "\n", + "In this way, you can think of a Pandas `Series` a bit like a specialization of a Python dictionary.\n", + "A dictionary is a structure that maps arbitrary keys to a set of arbitrary values, and a `Series` is a structure that maps typed keys to a set of typed values.\n", + "This typing is important: just as the type-specific compiled code behind a NumPy array makes it more efficient than a Python list for certain operations, the type information of a Pandas `Series` makes it more efficient than Python dictionaries for certain operations.\n", + "\n", + "The `Series`-as-dictionary analogy can be made even more clear by constructing a `Series` object directly from a Python dictionary, here the five most populous US states according to the 2020 census:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "California 39538223\n", + "Texas 29145505\n", + "Florida 21538187\n", + "New York 20201249\n", + "Pennsylvania 13002700\n", + "dtype: int64" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "population_dict = {'California': 39538223, 'Texas': 29145505,\n", + " 'Florida': 21538187, 'New York': 20201249,\n", + " 'Pennsylvania': 13002700}\n", + "population = pd.Series(population_dict)\n", + "population" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From here, typical dictionary-style item access can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "39538223" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "population['California']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Unlike a dictionary, though, the `Series` also supports array-style operations such as slicing:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "California 39538223\n", + "Texas 29145505\n", + "Florida 21538187\n", + "dtype: int64" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "population['California':'Florida']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll discuss some of the quirks of Pandas indexing and slicing in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constructing Series Objects\n", + "\n", + "We've already seen a few ways of constructing a Pandas `Series` from scratch. All of them are some version of the following:\n", + "\n", + "```python\n", + "pd.Series(data, index=index)\n", + "```\n", + "\n", + "where `index` is an optional argument, and `data` can be one of many entities.\n", + "\n", + "For example, `data` can be a list or NumPy array, in which case `index` defaults to an integer sequence:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 2\n", + "1 4\n", + "2 6\n", + "dtype: int64" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.Series([2, 4, 6])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or `data` can be a scalar, which is repeated to fill the specified index:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "100 5\n", + "200 5\n", + "300 5\n", + "dtype: int64" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.Series(5, index=[100, 200, 300])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or it can be a dictionary, in which case `index` defaults to the dictionary keys:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2 a\n", + "1 b\n", + "3 c\n", + "dtype: object" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.Series({2:'a', 1:'b', 3:'c'})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In each case, the index can be explicitly set to control the order or the subset of keys used:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1 b\n", + "2 a\n", + "dtype: object" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.Series({2:'a', 1:'b', 3:'c'}, index=[1, 2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Pandas DataFrame Object\n", + "\n", + "The next fundamental structure in Pandas is the `DataFrame`.\n", + "Like the `Series` object discussed in the previous section, the `DataFrame` can be thought of either as a generalization of a NumPy array, or as a specialization of a Python dictionary.\n", + "We'll now take a look at each of these perspectives." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### DataFrame as Generalized NumPy Array\n", + "If a `Series` is an analog of a one-dimensional array with explicit indices, a `DataFrame` is an analog of a two-dimensional array with explicit row and column indices.\n", + "Just as you might think of a two-dimensional array as an ordered sequence of aligned one-dimensional columns, you can think of a `DataFrame` as a sequence of aligned `Series` objects.\n", + "Here, by \"aligned\" we mean that they share the same index.\n", + "\n", + "To demonstrate this, let's first construct a new `Series` listing the area of each of the five states discussed in the previous section (in square kilometers):" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "California 423967\n", + "Texas 695662\n", + "Florida 170312\n", + "New York 141297\n", + "Pennsylvania 119280\n", + "dtype: int64" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "area_dict = {'California': 423967, 'Texas': 695662, 'Florida': 170312, \n", + " 'New York': 141297, 'Pennsylvania': 119280}\n", + "area = pd.Series(area_dict)\n", + "area" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have this along with the `population` Series from before, we can use a dictionary to construct a single two-dimensional object containing this information:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " foo bar\n", + "a 0.471098 0.317396\n", + "b 0.614766 0.305971\n", + "c 0.533596 0.512377" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.DataFrame(np.random.rand(3, 2),\n", + " columns=['foo', 'bar'],\n", + " index=['a', 'b', 'c'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### From a NumPy structured array\n", + "\n", + "We covered structured arrays in [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb).\n", + "A Pandas `DataFrame` operates much like a structured array, and can be created directly from one:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([(0, 0.), (0, 0.), (0, 0.)], dtype=[('A', '\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
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"outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Int64Index([2, 3, 5, 7, 11], dtype='int64')" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ind = pd.Index([2, 3, 5, 7, 11])\n", + "ind" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Index as Immutable Array\n", + "\n", + "The `Index` in many ways operates like an array.\n", + "For example, we can use standard Python indexing notation to retrieve values or slices:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ind[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Int64Index([2, 5, 11], dtype='int64')" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ind[::2]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Index` objects also have many of the attributes familiar from NumPy arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5 (5,) 1 int64\n" + ] + } + ], + "source": [ + "print(ind.size, ind.shape, ind.ndim, ind.dtype)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One difference between `Index` objects and NumPy arrays is that the indices are immutable—that is, they cannot be modified via the normal means:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "TypeError", + "evalue": "Index does not support mutable operations", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/var/folders/xc/sptt9bk14s34rgxt7453p03r0000gp/T/ipykernel_83282/393126374.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mind\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m~/.local/share/virtualenvs/python-data-science-handbook-2e-u_kwqDTB/lib/python3.9/site-packages/pandas/core/indexes/base.py\u001b[0m in \u001b[0;36m__setitem__\u001b[0;34m(self, key, value)\u001b[0m\n\u001b[1;32m 4583\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mfinal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4584\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__setitem__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4585\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Index does not support mutable operations\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4586\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4587\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__getitem__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: Index does not support mutable operations" + ] + } + ], + "source": [ + "ind[1] = 0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This immutability makes it safer to share indices between multiple ``DataFrame``s and arrays, without the potential for side effects from inadvertent index modification." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Index as Ordered Set\n", + "\n", + "Pandas objects are designed to facilitate operations such as joins across datasets, which depend on many aspects of set arithmetic.\n", + "The `Index` object follows many of the conventions used by Python's built-in `set` data structure, so that unions, intersections, differences, and other combinations can be computed in a familiar way:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "indA = pd.Index([1, 3, 5, 7, 9])\n", + "indB = pd.Index([2, 3, 5, 7, 11])" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Int64Index([3, 5, 7], dtype='int64')" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "indA.intersection(indB)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Int64Index([1, 2, 3, 5, 7, 9, 11], dtype='int64')" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "indA.union(indB)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Int64Index([1, 2, 9, 11], dtype='int64')" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "indA.symmetric_difference(indB)" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.02-Data-Indexing-and-Selection.ipynb b/notebooks/03.02-Data-Indexing-and-Selection.ipynb new file mode 100644 index 000000000..2eaf614c1 --- /dev/null +++ b/notebooks/03.02-Data-Indexing-and-Selection.ipynb @@ -0,0 +1,1703 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Data Indexing and Selection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In [Part 2](02.00-Introduction-to-NumPy.ipynb), we looked in detail at methods and tools to access, set, and modify values in NumPy arrays.\n", + "These included indexing (e.g., `arr[2, 1]`), slicing (e.g., `arr[:, 1:5]`), masking (e.g., `arr[arr > 0]`), fancy indexing (e.g., `arr[0, [1, 5]]`), and combinations thereof (e.g., `arr[:, [1, 5]]`).\n", + "Here we'll look at similar means of accessing and modifying values in Pandas `Series` and `DataFrame` objects.\n", + "If you have used the NumPy patterns, the corresponding patterns in Pandas will feel very familiar, though there are a few quirks to be aware of.\n", + "\n", + "We'll start with the simple case of the one-dimensional `Series` object, and then move on to the more complicated two-dimensional `DataFrame` object." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Data Selection in Series\n", + "\n", + "As you saw in the previous chapter, a `Series` object acts in many ways like a one-dimensional NumPy array, and in many ways like a standard Python dictionary.\n", + "If you keep these two overlapping analogies in mind, it will help you understand the patterns of data indexing and selection in these arrays." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Series as Dictionary\n", + "\n", + "Like a dictionary, the `Series` object provides a mapping from a collection of keys to a collection of values:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 0.25\n", + "b 0.50\n", + "c 0.75\n", + "d 1.00\n", + "dtype: float64" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "data = pd.Series([0.25, 0.5, 0.75, 1.0],\n", + " index=['a', 'b', 'c', 'd'])\n", + "data" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['b']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also use dictionary-like Python expressions and methods to examine the keys/indices and values:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "'a' in data" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Index(['a', 'b', 'c', 'd'], dtype='object')" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.keys()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('a', 0.25), ('b', 0.5), ('c', 0.75), ('d', 1.0)]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(data.items())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Series` objects can also be modified with a dictionary-like syntax.\n", + "Just as you can extend a dictionary by assigning to a new key, you can extend a `Series` by assigning to a new index value:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 0.25\n", + "b 0.50\n", + "c 0.75\n", + "d 1.00\n", + "e 1.25\n", + "dtype: float64" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['e'] = 1.25\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This easy mutability of the objects is a convenient feature: under the hood, Pandas is making decisions about memory layout and data copying that might need to take place, and the user generally does not need to worry about these issues." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Series as One-Dimensional Array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A `Series` builds on this dictionary-like interface and provides array-style item selection via the same basic mechanisms as NumPy arrays—that is, slices, masking, and fancy indexing.\n", + "Examples of these are as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 0.25\n", + "b 0.50\n", + "c 0.75\n", + "dtype: float64" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# slicing by explicit index\n", + "data['a':'c']" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 0.25\n", + "b 0.50\n", + "dtype: float64" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# slicing by implicit integer index\n", + "data[0:2]" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "b 0.50\n", + "c 0.75\n", + "dtype: float64" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# masking\n", + "data[(data > 0.3) & (data < 0.8)]" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 0.25\n", + "e 1.25\n", + "dtype: float64" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# fancy indexing\n", + "data[['a', 'e']]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of these, slicing may be the source of the most confusion.\n", + "Notice that when slicing with an explicit index (e.g., `data['a':'c']`), the final index is *included* in the slice, while when slicing with an implicit index (e.g., `data[0:2]`), the final index is *excluded* from the slice." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Indexers: loc and iloc\n", + "\n", + "If your `Series` has an explicit integer index, an indexing operation such as `data[1]` will use the explicit indices, while a slicing operation like `data[1:3]` will use the implicit Python-style indices:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1 a\n", + "3 b\n", + "5 c\n", + "dtype: object" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.Series(['a', 'b', 'c'], index=[1, 3, 5])\n", + "data" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'a'" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# explicit index when indexing\n", + "data[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3 b\n", + "5 c\n", + "dtype: object" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# implicit index when slicing\n", + "data[1:3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of this potential confusion in the case of integer indexes, Pandas provides some special *indexer* attributes that explicitly expose certain indexing schemes.\n", + "These are not functional methods, but attributes that expose a particular slicing interface to the data in the `Series`.\n", + "\n", + "First, the `loc` attribute allows indexing and slicing that always references the explicit index:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'a'" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.loc[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1 a\n", + "3 b\n", + "dtype: object" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.loc[1:3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `iloc` attribute allows indexing and slicing that always references the implicit Python-style index:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'b'" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.iloc[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3 b\n", + "5 c\n", + "dtype: object" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.iloc[1:3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One guiding principle of Python code is that \"explicit is better than implicit.\"\n", + "The explicit nature of `loc` and `iloc` makes them helpful in maintaining clean and readable code; especially in the case of integer indexes, using them consistently can prevent subtle bugs due to the mixed indexing/slicing convention." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Data Selection in DataFrames\n", + "\n", + "Recall that a `DataFrame` acts in many ways like a two-dimensional or structured array, and in other ways like a dictionary of `Series` structures sharing the same index.\n", + "These analogies can be helpful to keep in mind as we explore data selection within this structure." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### DataFrame as Dictionary\n", + "\n", + "The first analogy we will consider is the `DataFrame` as a dictionary of related `Series` objects.\n", + "Let's return to our example of areas and populations of states:" + ] + }, + { + "cell_type": "code", + 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" + ], + "text/plain": [ + " area pop density\n", + "California 423967 39538223 93.257784\n", + "Texas 695662 29145505 41.896072\n", + "Florida 170312 21538187 126.463121\n", + "New York 141297 20201249 142.970120\n", + "Pennsylvania 119280 13002700 109.009893" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['density'] = data['pop'] / data['area']\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This shows a preview of the straightforward syntax of element-by-element arithmetic between `Series` objects; we'll dig into this further in [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### DataFrame as Two-Dimensional Array\n", + "\n", + "As mentioned previously, we can also view the `DataFrame` as an enhanced two-dimensional array.\n", + "We can examine the raw underlying data array using the `values` attribute:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4.23967000e+05, 3.95382230e+07, 9.32577842e+01],\n", + " [6.95662000e+05, 2.91455050e+07, 4.18960717e+01],\n", + " [1.70312000e+05, 2.15381870e+07, 1.26463121e+02],\n", + " [1.41297000e+05, 2.02012490e+07, 1.42970120e+02],\n", + " [1.19280000e+05, 1.30027000e+07, 1.09009893e+02]])" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.values" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this picture in mind, many familiar array-like operations can be done on the `DataFrame` itself.\n", + "For example, we can transpose the full `DataFrame` to swap rows and columns:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " area pop\n", + "California 423967 39538223\n", + "Texas 695662 29145505\n", + "Florida 170312 21538187" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.loc[:'Florida', :'pop']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any of the familiar NumPy-style data access patterns can be used within these indexers.\n", + "For example, in the `loc` indexer we can combine masking and fancy indexing as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " pop density\n", + "Florida 21538187 126.463121\n", + "New York 20201249 142.970120" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.loc[data.density > 120, ['pop', 'density']]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any of these indexing conventions may also be used to set or modify values; this is done in the standard way that you might be accustomed to from working with NumPy:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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areapopdensity
California4239673953822390.000000
Texas6956622914550541.896072
Florida17031221538187126.463121
New York14129720201249142.970120
Pennsylvania11928013002700109.009893
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" + ], + "text/plain": [ + " area pop density\n", + "California 423967 39538223 90.000000\n", + "Texas 695662 29145505 41.896072\n", + "Florida 170312 21538187 126.463121\n", + "New York 141297 20201249 142.970120\n", + "Pennsylvania 119280 13002700 109.009893" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.iloc[0, 2] = 90\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To build up your fluency in Pandas data manipulation, I suggest spending some time with a simple `DataFrame` and exploring the types of indexing, slicing, masking, and fancy indexing that are allowed by these various indexing approaches." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Additional Indexing Conventions\n", + "\n", + "There are a couple of extra indexing conventions that might seem at odds with the preceding discussion, but nevertheless can be useful in practice.\n", + "First, while *indexing* refers to columns, *slicing* refers to rows:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " area pop density\n", + "Texas 695662 29145505 41.896072\n", + "Florida 170312 21538187 126.463121" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data[1:3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, direct masking operations are interpreted row-wise rather than column-wise:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " area pop density\n", + "Florida 170312 21538187 126.463121\n", + "New York 141297 20201249 142.970120" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data[data.density > 120]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These two conventions are syntactically similar to those on a NumPy array, and while they may not precisely fit the mold of the Pandas conventions, they are included due to their practical utility." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.03-Operations-in-Pandas.ipynb b/notebooks/03.03-Operations-in-Pandas.ipynb new file mode 100644 index 000000000..67059ea3d --- /dev/null +++ b/notebooks/03.03-Operations-in-Pandas.ipynb @@ -0,0 +1,1181 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Operating on Data in Pandas" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One of the strengths of NumPy is that it allows us to perform quick element-wise operations, both with basic arithmetic (addition, subtraction, multiplication, etc.) and with more complicated operations (trigonometric functions, exponential and logarithmic functions, etc.).\n", + "Pandas inherits much of this functionality from NumPy, and the ufuncs introduced in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) are key to this.\n", + "\n", + "Pandas includes a couple of useful twists, however: for unary operations like negation and trigonometric functions, these ufuncs will *preserve index and column labels* in the output, and for binary operations such as addition and multiplication, Pandas will automatically *align indices* when passing the objects to the ufunc.\n", + "This means that keeping the context of data and combining data from different sources—both potentially error-prone tasks with raw NumPy arrays—become essentially foolproof with Pandas.\n", + "We will additionally see that there are well-defined operations between one-dimensional `Series` structures and two-dimensional `DataFrame` structures." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ufuncs: Index Preservation\n", + "\n", + "Because Pandas is designed to work with NumPy, any NumPy ufunc will work on Pandas `Series` and `DataFrame` objects.\n", + "Let's start by defining a simple `Series` and `DataFrame` on which to demonstrate this:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 0\n", + "1 7\n", + "2 6\n", + "3 4\n", + "dtype: int64" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rng = np.random.default_rng(42)\n", + "ser = pd.Series(rng.integers(0, 10, 4))\n", + "ser" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " A B C D\n", + "0 4 8 0 6\n", + "1 2 0 5 9\n", + "2 7 7 7 7" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.DataFrame(rng.integers(0, 10, (3, 4)),\n", + " columns=['A', 'B', 'C', 'D'])\n", + "df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we apply a NumPy ufunc on either of these objects, the result will be another Pandas object *with the indices preserved:*" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 1.000000\n", + "1 1096.633158\n", + "2 403.428793\n", + "3 54.598150\n", + "dtype: float64" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.exp(ser)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is true also for more involved sequences of operations:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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01.224647e-16-2.449294e-160.000000-1.000000
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" + ], + "text/plain": [ + " A B C D\n", + "0 1.224647e-16 -2.449294e-16 0.000000 -1.000000\n", + "1 1.000000e+00 0.000000e+00 -0.707107 0.707107\n", + "2 -7.071068e-01 -7.071068e-01 -0.707107 -0.707107" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.sin(df * np.pi / 4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any of the ufuncs discussed in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) can be used in a similar manner." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ufuncs: Index Alignment\n", + "\n", + "For binary operations on two `Series` or `DataFrame` objects, Pandas will align indices in the process of performing the operation.\n", + "This is very convenient when working with incomplete data, as we'll see in some of the examples that follow." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Index Alignment in Series\n", + "\n", + "As an example, suppose we are combining two different data sources and wish to find only the top three US states by *area* and the top three US states by *population*:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "area = pd.Series({'Alaska': 1723337, 'Texas': 695662,\n", + " 'California': 423967}, name='area')\n", + "population = pd.Series({'California': 39538223, 'Texas': 29145505,\n", + " 'Florida': 21538187}, name='population')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what happens when we divide these to compute the population density:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Alaska NaN\n", + "California 93.257784\n", + "Florida NaN\n", + "Texas 41.896072\n", + "dtype: float64" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "population / area" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting array contains the *union* of indices of the two input arrays, which could be determined directly from these indices:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Index(['Alaska', 'California', 'Florida', 'Texas'], dtype='object')" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "area.index.union(population.index)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any item for which one or the other does not have an entry is marked with `NaN`, or \"Not a Number,\" which is how Pandas marks missing data (see further discussion of missing data in [Handling Missing Data](03.04-Missing-Values.ipynb)).\n", + "This index matching is implemented this way for any of Python's built-in arithmetic expressions; any missing values are marked by `NaN`:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 NaN\n", + "1 5.0\n", + "2 9.0\n", + "3 NaN\n", + "dtype: float64" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = pd.Series([2, 4, 6], index=[0, 1, 2])\n", + "B = pd.Series([1, 3, 5], index=[1, 2, 3])\n", + "A + B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If using `NaN` values is not the desired behavior, the fill value can be modified using appropriate object methods in place of the operators.\n", + "For example, calling ``A.add(B)`` is equivalent to calling ``A + B``, but allows optional explicit specification of the fill value for any elements in ``A`` or ``B`` that might be missing:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 2.0\n", + "1 5.0\n", + "2 9.0\n", + "3 5.0\n", + "dtype: float64" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.add(B, fill_value=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Index Alignment in DataFrames\n", + "\n", + "A similar type of alignment takes place for *both* columns and indices when performing operations on `DataFrame` objects:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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Use of a separate mask array requires allocation of an additional Boolean array, which adds overhead in both storage and computation. A sentinel value reduces the range of valid values that can be represented, and may require extra (often nonoptimized) logic in CPU and GPU arithmetic, because common special values like `NaN` are not available for all data types.\n", + "\n", + "As in most cases where no universally optimal choice exists, different languages and systems use different conventions.\n", + "For example, the R language uses reserved bit patterns within each data type as sentinel values indicating missing data, while the SciDB system uses an extra byte attached to every cell to indicate an NA state." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Missing Data in Pandas\n", + "\n", + "The way in which Pandas handles missing values is constrained by its reliance on the NumPy package, which does not have a built-in notion of NA values for non-floating-point data types.\n", + "\n", + "Perhaps Pandas could have followed R's lead in specifying bit patterns for each individual data type to indicate nullness, but this approach turns out to be rather unwieldy.\n", + "While R has just 4 main data types, NumPy supports *far* more than this: for example, while R has a single integer type, NumPy supports 14 basic integer types once you account for available bit widths, signedness, and endianness of the encoding.\n", + "Reserving a specific bit pattern in all available NumPy types would lead to an unwieldy amount of overhead in special-casing various operations for various types, likely even requiring a new fork of the NumPy package. Further, for the smaller data types (such as 8-bit integers), sacrificing a bit to use as a mask would significantly reduce the range of values it can represent.\n", + "\n", + "Because of these constraints and trade-offs, Pandas has two \"modes\" of storing and manipulating null values:\n", + "\n", + "- The default mode is to use a sentinel-based missing data scheme, with sentinel values `NaN` or `None` depending on the type of the data.\n", + "- Alternatively, you can opt in to using the nullable data types (dtypes) Pandas provides (discussed later in this chapter), which results in the creation an accompanying mask array to track missing entries. These missing entries are then presented to the user as the special `pd.NA` value.\n", + "\n", + "In either case, the data operations and manipulations provided by the Pandas API will handle and propagate those missing entries in a predictable manner. But to develop some intuition into *why* these choices are made, let's dive quickly into the trade-offs inherent in `None`, `NaN`, and `NA`. As usual, we'll start by importing NumPy and Pandas:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### None as a Sentinel Value\n", + "\n", + "For some data types, Pandas uses `None` as a sentinel value. `None` is a Python object, which means that any array containing `None` must have `dtype=object`—that is, it must be a sequence of Python objects.\n", + "\n", + "For example, observe what happens if you pass `None` to a NumPy array:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, None, 2, 3], dtype=object)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vals1 = np.array([1, None, 2, 3])\n", + "vals1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This `dtype=object` means that the best common type representation NumPy could infer for the contents of the array is that they are Python objects.\n", + "The downside of using `None` in this way is that operations on the data will be done at the Python level, with much more overhead than the typically fast operations seen for arrays with native types:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.73 ms ± 288 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%timeit np.arange(1E6, dtype=int).sum()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "92.1 ms ± 3.42 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "%timeit np.arange(1E6, dtype=object).sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Further, because Python does not support arithmetic operations with `None`, aggregations like `sum` or `min` will generally lead to an error:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "TypeError", + "evalue": "unsupported operand type(s) for +: 'int' and 'NoneType'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/var/folders/xc/sptt9bk14s34rgxt7453p03r0000gp/T/ipykernel_91333/1181914653.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mvals1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m~/.local/share/virtualenvs/python-data-science-handbook-2e-u_kwqDTB/lib/python3.9/site-packages/numpy/core/_methods.py\u001b[0m in \u001b[0;36m_sum\u001b[0;34m(a, axis, dtype, out, keepdims, initial, where)\u001b[0m\n\u001b[1;32m 46\u001b[0m def _sum(a, axis=None, dtype=None, out=None, keepdims=False,\n\u001b[1;32m 47\u001b[0m initial=_NoValue, where=True):\n\u001b[0;32m---> 48\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mumr_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minitial\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwhere\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 49\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 50\u001b[0m def _prod(a, axis=None, dtype=None, out=None, keepdims=False,\n", + "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for +: 'int' and 'NoneType'" + ] + } + ], + "source": [ + "vals1.sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this reason, Pandas does not use `None` as a sentinel in its numerical arrays." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### NaN: Missing Numerical Data\n", + "\n", + "The other missing data sentinel, `NaN` is different; it is a special floating-point value recognized by all systems that use the standard IEEE floating-point representation:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., nan, 3., 4.])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vals2 = np.array([1, np.nan, 3, 4]) \n", + "vals2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that NumPy chose a native floating-point type for this array: this means that unlike the object array from before, this array supports fast operations pushed into compiled code.\n", + "Keep in mind that `NaN` is a bit like a data virus—it infects any other object it touches.\n", + "Regardless of the operation, the result of arithmetic with `NaN` will be another `NaN`:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "nan" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1 + np.nan" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "nan" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "0 * np.nan" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This means that aggregates over the values are well defined (i.e., they don't result in an error) but not always useful:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(nan, nan, nan)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vals2.sum(), vals2.min(), vals2.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That said, NumPy does provide ``NaN``-aware versions of aggregations that will ignore these missing values:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(8.0, 1.0, 4.0)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.nansum(vals2), np.nanmin(vals2), np.nanmax(vals2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The main downside of `NaN` is that it is specifically a floating-point value; there is no equivalent `NaN` value for integers, strings, or other types." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### NaN and None in Pandas\n", + "\n", + "`NaN` and `None` both have their place, and Pandas is built to handle the two of them nearly interchangeably, converting between them where appropriate:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 1.0\n", + "1 NaN\n", + "2 2.0\n", + "3 NaN\n", + "dtype: float64" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.Series([1, np.nan, 2, None])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For types that don't have an available sentinel value, Pandas automatically typecasts when NA values are present.\n", + "For example, if we set a value in an integer array to ``np.nan``, it will automatically be upcast to a floating-point type to accommodate the NA:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 0\n", + "1 1\n", + "dtype: int64" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = pd.Series(range(2), dtype=int)\n", + "x" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 NaN\n", + "1 1.0\n", + "dtype: float64" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x[0] = None\n", + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that in addition to casting the integer array to floating point, Pandas automatically converts the ``None`` to a ``NaN`` value.\n", + "\n", + "While this type of magic may feel a bit hackish compared to the more unified approach to NA values in domain-specific languages like R, the Pandas sentinel/casting approach works quite well in practice and in my experience only rarely causes issues.\n", + "\n", + "The following table lists the upcasting conventions in Pandas when NA values are introduced:\n", + "\n", + "|Typeclass | Conversion when storing NAs | NA sentinel value |\n", + "|--------------|-----------------------------|------------------------|\n", + "| ``floating`` | No change | ``np.nan`` |\n", + "| ``object`` | No change | ``None`` or ``np.nan`` |\n", + "| ``integer`` | Cast to ``float64`` | ``np.nan`` |\n", + "| ``boolean`` | Cast to ``object`` | ``None`` or ``np.nan`` |\n", + "\n", + "Keep in mind that in Pandas, string data is always stored with an ``object`` dtype." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pandas Nullable Dtypes" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In early versions of Pandas, `NaN` and `None` as sentinel values were the only missing data representations available. The primary difficulty this introduced was with regard to the implicit type casting: for example, there was no way to represent a true integer array with missing data.\n", + "\n", + "To address this difficulty, Pandas later added *nullable dtypes*, which are distinguished from regular dtypes by capitalization of their names (e.g., `pd.Int32` versus `np.int32`). For backward compatibility, these nullable dtypes are only used if specifically requested.\n", + "\n", + "For example, here is a `Series` of integers with missing data, created from a list containing all three available markers of missing data:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0 1\n", + "1 \n", + "2 2\n", + "3 \n", + "4 \n", + "dtype: Int32" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.Series([1, np.nan, 2, None, pd.NA], dtype='Int32')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This representation can be used interchangeably with the others in all the operations explored through the rest of this chapter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Operating on Null Values\n", + "\n", + "As we have seen, Pandas treats `None`, `NaN`, and `NA` as essentially interchangeable for indicating missing or null values.\n", + "To facilitate this convention, Pandas provides several methods for detecting, removing, and replacing null values in Pandas data structures.\n", + "They are:\n", + "\n", + "- ``isnull``: Generates a Boolean mask indicating missing values\n", + "- ``notnull``: Opposite of ``isnull``\n", + "- ``dropna``: Returns a filtered version of the data\n", + "- ``fillna``: Returns a copy of the data with missing values filled or imputed\n", + "\n", + "We will conclude this chapter with a brief exploration and demonstration of these routines." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Detecting Null Values\n", + "Pandas data structures have two useful methods for detecting null data: `isnull` and `notnull`.\n", + "Either one will return a Boolean mask over the data. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "data = pd.Series([1, np.nan, 'hello', None])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 False\n", + "1 True\n", + "2 False\n", + "3 True\n", + "dtype: bool" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.isnull()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As mentioned in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb), Boolean masks can be used directly as a `Series` or `DataFrame` index:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 1\n", + "2 hello\n", + "dtype: object" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data[data.notnull()]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `isnull()` and `notnull()` methods produce similar Boolean results for ``DataFrame`` objects." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dropping Null Values\n", + "\n", + "In addition to these masking methods, there are the convenience methods `dropna`\n", + "(which removes NA values) and `fillna` (which fills in NA values). For a `Series`,\n", + "the result is straightforward:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 1\n", + "2 hello\n", + "dtype: object" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.dropna()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a ``DataFrame``, there are more options.\n", + "Consider the following ``DataFrame``:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " 0 1 2 3\n", + "1 2.0 3.0 5 NaN" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.dropna(axis='rows', thresh=3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, the first and last rows have been dropped because they each contain only two non-null values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Filling Null Values\n", + "\n", + "Sometimes rather than dropping NA values, you'd like to replace them with a valid value.\n", + "This value might be a single number like zero, or it might be some sort of imputation or interpolation from the good values.\n", + "You could do this in-place using the `isnull` method as a mask, but because it is such a common operation Pandas provides the `fillna` method, which returns a copy of the array with the null values replaced.\n", + "\n", + "Consider the following `Series`:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 1\n", + "b \n", + "c 2\n", + "d \n", + "e 3\n", + "dtype: Int32" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.Series([1, np.nan, 2, None, 3], index=list('abcde'), dtype='Int32')\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can fill NA entries with a single value, such as zero:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 1\n", + "b 0\n", + "c 2\n", + "d 0\n", + "e 3\n", + "dtype: Int32" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.fillna(0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can specify a forward fill to propagate the previous value forward:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 1\n", + "b 1\n", + "c 2\n", + "d 2\n", + "e 3\n", + "dtype: Int32" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# forward fill\n", + "data.fillna(method='ffill')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or we can specify a backward fill to propagate the next values backward:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "a 1\n", + "b 2\n", + "c 2\n", + "d 3\n", + "e 3\n", + "dtype: Int32" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# back fill\n", + "data.fillna(method='bfill')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the case of a `DataFrame`, the options are similar, but we can also specify an `axis` along which the fills should take place:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " 0 1 2 3\n", + "0 1.0 1.0 2.0 2.0\n", + "1 2.0 3.0 5.0 5.0\n", + "2 NaN 4.0 6.0 6.0" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.fillna(method='ffill', axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that if a previous value is not available during a forward fill, the NA value remains." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.05-Hierarchical-Indexing.ipynb b/notebooks/03.05-Hierarchical-Indexing.ipynb new file mode 100644 index 000000000..cdf373927 --- /dev/null +++ b/notebooks/03.05-Hierarchical-Indexing.ipynb @@ -0,0 +1,2752 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Hierarchical Indexing" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Up to this point we've been focused primarily on one-dimensional and two-dimensional data, stored in Pandas `Series` and `DataFrame` objects, respectively.\n", + "Often it is useful to go beyond this and store higher-dimensional data—that is, data indexed by more than one or two keys.\n", + "Early Pandas versions provided `Panel` and `Panel4D` objects that could be thought of as 3D or 4D analogs to the 2D `DataFrame`, but they were somewhat clunky to use in practice. A far more common pattern for handling higher-dimensional data is to make use of *hierarchical indexing* (also known as *multi-indexing*) to incorporate multiple index *levels* within a single index.\n", + "In this way, higher-dimensional data can be compactly represented within the familiar one-dimensional `Series` and two-dimensional `DataFrame` objects.\n", + "(If you're interested in true *N*-dimensional arrays with Pandas-style flexible indices, you can look into the excellent [Xarray package](https://xarray.pydata.org/).)\n", + "\n", + "In this chapter, we'll explore the direct creation of `MultiIndex` objects; considerations when indexing, slicing, and computing statistics across multiply indexed data; and useful routines for converting between simple and hierarchically indexed representations of data.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## A Multiply Indexed Series\n", + "\n", + "Let's start by considering how we might represent two-dimensional data within a one-dimensional `Series`.\n", + "For concreteness, we will consider a series of data where each point has a character and numerical key." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The Bad Way\n", + "\n", + "Suppose you would like to track data about states from two different years.\n", + "Using the Pandas tools we've already covered, you might be tempted to simply use Python tuples as keys:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(California, 2010) 37253956\n", + "(California, 2020) 39538223\n", + "(New York, 2010) 19378102\n", + "(New York, 2020) 20201249\n", + "(Texas, 2010) 25145561\n", + "(Texas, 2020) 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "index = [('California', 2010), ('California', 2020),\n", + " ('New York', 2010), ('New York', 2020),\n", + " ('Texas', 2010), ('Texas', 2020)]\n", + "populations = [37253956, 39538223,\n", + " 19378102, 20201249,\n", + " 25145561, 29145505]\n", + "pop = pd.Series(populations, index=index)\n", + "pop" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this indexing scheme, you can straightforwardly index or slice the series based on this tuple index:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(California, 2020) 39538223\n", + "(New York, 2010) 19378102\n", + "(New York, 2020) 20201249\n", + "(Texas, 2010) 25145561\n", + "dtype: int64" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop[('California', 2020):('Texas', 2010)]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But the convenience ends there. For example, if you need to select all values from 2010, you'll need to do some messy (and potentially slow) munging to make it happen:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(California, 2010) 37253956\n", + "(New York, 2010) 19378102\n", + "(Texas, 2010) 25145561\n", + "dtype: int64" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop[[i for i in pop.index if i[1] == 2010]]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This produces the desired result, but is not as clean (or as efficient for large datasets) as the slicing syntax we've grown to love in Pandas." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The Better Way: The Pandas MultiIndex\n", + "Fortunately, Pandas provides a better way.\n", + "Our tuple-based indexing is essentially a rudimentary multi-index, and the Pandas `MultiIndex` type gives us the types of operations we wish to have.\n", + "We can create a multi-index from the tuples as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "index = pd.MultiIndex.from_tuples(index)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The `MultiIndex` represents multiple *levels* of indexing—in this case, the state names and the years—as well as multiple *labels* for each data point which encode these levels.\n", + "\n", + "If we reindex our series with this `MultiIndex`, we see the hierarchical representation of the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "California 2010 37253956\n", + " 2020 39538223\n", + "New York 2010 19378102\n", + " 2020 20201249\n", + "Texas 2010 25145561\n", + " 2020 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop = pop.reindex(index)\n", + "pop" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here the first two columns of the Series representation show the multiple index values, while the third column shows the data.\n", + "Notice that some entries are missing in the first column: in this multi-index representation, any blank entry indicates the same value as the line above it." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now to access all data for which the second index is 2020, we can use the Pandas slicing notation:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "California 39538223\n", + "New York 20201249\n", + "Texas 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop[:, 2020]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result is a singly indexed Series with just the keys we're interested in.\n", + "This syntax is much more convenient (and the operation is much more efficient!) than the home-spun tuple-based multi-indexing solution that we started with.\n", + "We'll now further discuss this sort of indexing operation on hierarchically indexed data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### MultiIndex as Extra Dimension\n", + "\n", + "You might notice something else here: we could easily have stored the same data using a simple `DataFrame` with index and column labels.\n", + "In fact, Pandas is built with this equivalence in mind. The `unstack` method will quickly convert a multiply indexed `Series` into a conventionally indexed `DataFrame`:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " 2010 2020\n", + "California 37253956 39538223\n", + "New York 19378102 20201249\n", + "Texas 25145561 29145505" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop_df = pop.unstack()\n", + "pop_df" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Naturally, the ``stack`` method provides the opposite operation:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "California 2010 37253956\n", + " 2020 39538223\n", + "New York 2010 19378102\n", + " 2020 20201249\n", + "Texas 2010 25145561\n", + " 2020 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop_df.stack()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Seeing this, you might wonder why would we would bother with hierarchical indexing at all.\n", + "The reason is simple: just as we were able to use multi-indexing to manipulate two-dimensional data within a one-dimensional `Series`, we can also use it to manipulate data of three or more dimensions in a `Series` or `DataFrame`.\n", + "Each extra level in a multi-index represents an extra dimension of data; taking advantage of this property gives us much more flexibility in the types of data we can represent. Concretely, we might want to add another column of demographic data for each state at each year (say, population under 18); with a `MultiIndex` this is as easy as adding another column to the ``DataFrame``:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " total under18\n", + "California 2010 37253956 9284094\n", + " 2020 39538223 8898092\n", + "New York 2010 19378102 4318033\n", + " 2020 20201249 4181528\n", + "Texas 2010 25145561 6879014\n", + " 2020 29145505 7432474" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop_df = pd.DataFrame({'total': pop,\n", + " 'under18': [9284094, 8898092,\n", + " 4318033, 4181528,\n", + " 6879014, 7432474]})\n", + "pop_df" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In addition, all the ufuncs and other functionality discussed in [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb) work with hierarchical indices as well.\n", + "Here we compute the fraction of people under 18 by year, given the above data:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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20102020
California0.2492110.225050
New York0.2228310.206994
Texas0.2735680.255013
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" + ], + "text/plain": [ + " 2010 2020\n", + "California 0.249211 0.225050\n", + "New York 0.222831 0.206994\n", + "Texas 0.273568 0.255013" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f_u18 = pop_df['under18'] / pop_df['total']\n", + "f_u18.unstack()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This allows us to easily and quickly manipulate and explore even high-dimensional data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Methods of MultiIndex Creation\n", + "\n", + "The most straightforward way to construct a multiply indexed `Series` or `DataFrame` is to simply pass a list of two or more index arrays to the constructor. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " data1 data2\n", + "a 1 0.748464 0.561409\n", + " 2 0.379199 0.622461\n", + "b 1 0.701679 0.687932\n", + " 2 0.436200 0.950664" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.DataFrame(np.random.rand(4, 2),\n", + " index=[['a', 'a', 'b', 'b'], [1, 2, 1, 2]],\n", + " columns=['data1', 'data2'])\n", + "df" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The work of creating the ``MultiIndex`` is done in the background.\n", + "\n", + "Similarly, if you pass a dictionary with appropriate tuples as keys, Pandas will automatically recognize this and use a ``MultiIndex`` by default:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "California 2010 37253956\n", + " 2020 39538223\n", + "New York 2010 19378102\n", + " 2020 20201249\n", + "Texas 2010 25145561\n", + " 2020 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = {('California', 2010): 37253956,\n", + " ('California', 2020): 39538223,\n", + " ('New York', 2010): 19378102,\n", + " ('New York', 2020): 20201249,\n", + " ('Texas', 2010): 25145561,\n", + " ('Texas', 2020): 29145505}\n", + "pd.Series(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Nevertheless, it is sometimes useful to explicitly create a `MultiIndex`; we'll look at a couple of methods for doing this next." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Explicit MultiIndex Constructors\n", + "\n", + "For more flexibility in how the index is constructed, you can instead use the constructor methods available in the `pd.MultiIndex` class.\n", + "For example, as we did before, you can construct a `MultiIndex` from a simple list of arrays giving the index values within each level:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "MultiIndex([('a', 1),\n", + " ('a', 2),\n", + " ('b', 1),\n", + " ('b', 2)],\n", + " )" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.MultiIndex.from_arrays([['a', 'a', 'b', 'b'], [1, 2, 1, 2]])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Or you can construct it from a list of tuples giving the multiple index values of each point:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "MultiIndex([('a', 1),\n", + " ('a', 2),\n", + " ('b', 1),\n", + " ('b', 2)],\n", + " )" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.MultiIndex.from_tuples([('a', 1), ('a', 2), ('b', 1), ('b', 2)])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "You can even construct it from a Cartesian product of single indices:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "MultiIndex([('a', 1),\n", + " ('a', 2),\n", + " ('b', 1),\n", + " ('b', 2)],\n", + " )" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.MultiIndex.from_product([['a', 'b'], [1, 2]])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Similarly, you can construct a `MultiIndex` directly using its internal encoding by passing `levels` (a list of lists containing available index values for each level) and `codes` (a list of lists that reference these labels):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "MultiIndex([('a', 1),\n", + " ('a', 2),\n", + " ('b', 1),\n", + " ('b', 2)],\n", + " )" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.MultiIndex(levels=[['a', 'b'], [1, 2]],\n", + " codes=[[0, 0, 1, 1], [0, 1, 0, 1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Any of these objects can be passed as the `index` argument when creating a `Series` or `DataFrame`, or be passed to the `reindex` method of an existing `Series` or `DataFrame`." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### MultiIndex Level Names\n", + "\n", + "Sometimes it is convenient to name the levels of the `MultiIndex`.\n", + "This can be accomplished by passing the `names` argument to any of the previously discussed `MultiIndex` constructors, or by setting the `names` attribute of the index after the fact:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state year\n", + "California 2010 37253956\n", + " 2020 39538223\n", + "New York 2010 19378102\n", + " 2020 20201249\n", + "Texas 2010 25145561\n", + " 2020 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop.index.names = ['state', 'year']\n", + "pop" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With more involved datasets, this can be a useful way to keep track of the meaning of various index values." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### MultiIndex for Columns\n", + "\n", + "In a `DataFrame`, the rows and columns are completely symmetric, and just as the rows can have multiple levels of indices, the columns can have multiple levels as well.\n", + "Consider the following, which is a mock-up of some (somewhat realistic) medical data:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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subjectBobGuidoSue
typeHRTempHRTempHRTemp
yearvisit
2013130.038.056.038.345.035.8
247.037.127.036.037.036.4
2014151.035.924.036.732.036.2
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\n", + "
" + ], + "text/plain": [ + "subject Bob Guido Sue \n", + "type HR Temp HR Temp HR Temp\n", + "year visit \n", + "2013 1 30.0 38.0 56.0 38.3 45.0 35.8\n", + " 2 47.0 37.1 27.0 36.0 37.0 36.4\n", + "2014 1 51.0 35.9 24.0 36.7 32.0 36.2\n", + " 2 49.0 36.3 48.0 39.2 31.0 35.7" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# hierarchical indices and columns\n", + "index = pd.MultiIndex.from_product([[2013, 2014], [1, 2]],\n", + " names=['year', 'visit'])\n", + "columns = pd.MultiIndex.from_product([['Bob', 'Guido', 'Sue'], ['HR', 'Temp']],\n", + " names=['subject', 'type'])\n", + "\n", + "# mock some data\n", + "data = np.round(np.random.randn(4, 6), 1)\n", + "data[:, ::2] *= 10\n", + "data += 37\n", + "\n", + "# create the DataFrame\n", + "health_data = pd.DataFrame(data, index=index, columns=columns)\n", + "health_data" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This is fundamentally four-dimensional data, where the dimensions are the subject, the measurement type, the year, and the visit number.\n", + "With this in place we can, for example, index the top-level column by the person's name and get a full `DataFrame` containing just that person's information:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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typeHRTemp
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227.036.0
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" + ], + "text/plain": [ + "type HR Temp\n", + "year visit \n", + "2013 1 56.0 38.3\n", + " 2 27.0 36.0\n", + "2014 1 24.0 36.7\n", + " 2 48.0 39.2" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "health_data['Guido']" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Indexing and Slicing a MultiIndex\n", + "\n", + "Indexing and slicing on a `MultiIndex` is designed to be intuitive, and it helps if you think about the indices as added dimensions.\n", + "We'll first look at indexing multiply indexed `Series`, and then multiply indexed `DataFrame` objects." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Multiply Indexed Series\n", + "\n", + "Consider the multiply indexed `Series` of state populations we saw earlier:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state year\n", + "California 2010 37253956\n", + " 2020 39538223\n", + "New York 2010 19378102\n", + " 2020 20201249\n", + "Texas 2010 25145561\n", + " 2020 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can access single elements by indexing with multiple terms:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "37253956" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop['California', 2010]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The `MultiIndex` also supports *partial indexing*, or indexing just one of the levels in the index.\n", + "The result is another `Series`, with the lower-level indices maintained:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "year\n", + "2010 37253956\n", + "2020 39538223\n", + "dtype: int64" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop['California']" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Partial slicing is available as well, as long as the `MultiIndex` is sorted (see the discussion in [Sorted and Unsorted Indices](#Sorted-and-unsorted-indices)):" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state year\n", + "California 2010 37253956\n", + " 2020 39538223\n", + "New York 2010 19378102\n", + " 2020 20201249\n", + "dtype: int64" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop.loc['California':'New York']" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With sorted indices, partial indexing can be performed on lower levels by passing an empty slice in the first index:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state\n", + "California 37253956\n", + "New York 19378102\n", + "Texas 25145561\n", + "dtype: int64" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop[:, 2010]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Other types of indexing and selection (discussed in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb)) work as well; for example, selection based on Boolean masks:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state year\n", + "California 2010 37253956\n", + " 2020 39538223\n", + "Texas 2010 25145561\n", + " 2020 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop[pop > 22000000]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Selection based on fancy indexing also works:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state year\n", + "California 2010 37253956\n", + " 2020 39538223\n", + "Texas 2010 25145561\n", + " 2020 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop[['California', 'Texas']]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Multiply Indexed DataFrames\n", + "\n", + "A multiply indexed `DataFrame` behaves in a similar manner.\n", + "Consider our toy medical `DataFrame` from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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subjectBobGuidoSue
typeHRTempHRTempHRTemp
yearvisit
2013130.038.056.038.345.035.8
247.037.127.036.037.036.4
2014151.035.924.036.732.036.2
249.036.348.039.231.035.7
\n", + "
" + ], + "text/plain": [ + "subject Bob Guido Sue \n", + "type HR Temp HR Temp HR Temp\n", + "year visit \n", + "2013 1 30.0 38.0 56.0 38.3 45.0 35.8\n", + " 2 47.0 37.1 27.0 36.0 37.0 36.4\n", + "2014 1 51.0 35.9 24.0 36.7 32.0 36.2\n", + " 2 49.0 36.3 48.0 39.2 31.0 35.7" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "health_data" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Remember that columns are primary in a `DataFrame`, and the syntax used for multiply indexed `Series` applies to the columns.\n", + "For example, we can recover Guido's heart rate data with a simple operation:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "year visit\n", + "2013 1 56.0\n", + " 2 27.0\n", + "2014 1 24.0\n", + " 2 48.0\n", + "Name: (Guido, HR), dtype: float64" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "health_data['Guido', 'HR']" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Also, as with the single-index case, we can use the `loc`, `iloc`, and `ix` indexers introduced in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb). For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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subjectBob
typeHRTemp
yearvisit
2013130.038.0
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" + ], + "text/plain": [ + "subject Bob \n", + "type HR Temp\n", + "year visit \n", + "2013 1 30.0 38.0\n", + " 2 47.0 37.1" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "health_data.iloc[:2, :2]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "These indexers provide an array-like view of the underlying two-dimensional data, but each individual index in `loc` or `iloc` can be passed a tuple of multiple indices. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "year visit\n", + "2013 1 30.0\n", + " 2 47.0\n", + "2014 1 51.0\n", + " 2 49.0\n", + "Name: (Bob, HR), dtype: float64" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "health_data.loc[:, ('Bob', 'HR')]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Working with slices within these index tuples is not especially convenient; trying to create a slice within a tuple will lead to a syntax error:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (3311942670.py, line 1)", + "output_type": "error", + "traceback": [ + "\u001b[0;36m File \u001b[0;32m\"/var/folders/xc/sptt9bk14s34rgxt7453p03r0000gp/T/ipykernel_86488/3311942670.py\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m health_data.loc[(:, 1), (:, 'HR')]\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" + ] + } + ], + "source": [ + "health_data.loc[(:, 1), (:, 'HR')]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "You could get around this by building the desired slice explicitly using Python's built-in `slice` function, but a better way in this context is to use an `IndexSlice` object, which Pandas provides for precisely this situation.\n", + "For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "subject Bob Guido Sue\n", + "type HR HR HR\n", + "year visit \n", + "2013 1 30.0 56.0 45.0\n", + "2014 1 51.0 24.0 32.0" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "idx = pd.IndexSlice\n", + "health_data.loc[idx[:, 1], idx[:, 'HR']]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As you can see, there are many ways to interact with data in multiply indexed `Series` and ``DataFrame``s, and as with many tools in this book the best way to become familiar with them is to try them out!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Rearranging Multi-Indexes\n", + "\n", + "One of the keys to working with multiply indexed data is knowing how to effectively transform the data.\n", + "There are a number of operations that will preserve all the information in the dataset, but rearrange it for the purposes of various computations.\n", + "We saw a brief example of this in the `stack` and `unstack` methods, but there are many more ways to finely control the rearrangement of data between hierarchical indices and columns, and we'll explore them here." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Sorted and Unsorted Indices\n", + "\n", + "Earlier I briefly mentioned a caveat, but I should emphasize it more here.\n", + "*Many of the `MultiIndex` slicing operations will fail if the index is not sorted.*\n", + "Let's take a closer look.\n", + "\n", + "We'll start by creating some simple multiply indexed data where the indices are *not lexographically sorted*:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "char int\n", + "a 1 0.280341\n", + " 2 0.097290\n", + "c 1 0.206217\n", + " 2 0.431771\n", + "b 1 0.100183\n", + " 2 0.015851\n", + "dtype: float64" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "index = pd.MultiIndex.from_product([['a', 'c', 'b'], [1, 2]])\n", + "data = pd.Series(np.random.rand(6), index=index)\n", + "data.index.names = ['char', 'int']\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "If we try to take a partial slice of this index, it will result in an error:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "KeyError 'Key length (1) was greater than MultiIndex lexsort depth (0)'\n" + ] + } + ], + "source": [ + "try:\n", + " data['a':'b']\n", + "except KeyError as e:\n", + " print(\"KeyError\", e)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Although it is not entirely clear from the error message, this is the result of the `MultiIndex` not being sorted.\n", + "For various reasons, partial slices and other similar operations require the levels in the `MultiIndex` to be in sorted (i.e., lexographical) order.\n", + "Pandas provides a number of convenience routines to perform this type of sorting, such as the `sort_index` and `sortlevel` methods of the `DataFrame`.\n", + "We'll use the simplest, `sort_index`, here:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "char int\n", + "a 1 0.280341\n", + " 2 0.097290\n", + "b 1 0.100183\n", + " 2 0.015851\n", + "c 1 0.206217\n", + " 2 0.431771\n", + "dtype: float64" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = data.sort_index()\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With the index sorted in this way, partial slicing will work as expected:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "char int\n", + "a 1 0.280341\n", + " 2 0.097290\n", + "b 1 0.100183\n", + " 2 0.015851\n", + "dtype: float64" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['a':'b']" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Stacking and Unstacking Indices\n", + "\n", + "As we saw briefly before, it is possible to convert a dataset from a stacked multi-index to a simple two-dimensional representation, optionally specifying the level to use:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "year 2010 2020\n", + "state \n", + "California 37253956 39538223\n", + "New York 19378102 20201249\n", + "Texas 25145561 29145505" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop.unstack(level=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The opposite of `unstack` is `stack`, which here can be used to recover the original series:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state year\n", + "California 2010 37253956\n", + " 2020 39538223\n", + "New York 2010 19378102\n", + " 2020 20201249\n", + "Texas 2010 25145561\n", + " 2020 29145505\n", + "dtype: int64" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop.unstack().stack()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Index Setting and Resetting\n", + "\n", + "Another way to rearrange hierarchical data is to turn the index labels into columns; this can be accomplished with the `reset_index` method.\n", + "Calling this on the population dictionary will result in a `DataFrame` with `state` and `year` columns holding the information that was formerly in the index.\n", + "For clarity, we can optionally specify the name of the data for the column representation:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " state year population\n", + "0 California 2010 37253956\n", + "1 California 2020 39538223\n", + "2 New York 2010 19378102\n", + "3 New York 2020 20201249\n", + "4 Texas 2010 25145561\n", + "5 Texas 2020 29145505" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop_flat = pop.reset_index(name='population')\n", + "pop_flat" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "A common pattern is to build a `MultiIndex` from the column values.\n", + "This can be done with the `set_index` method of the `DataFrame`, which returns a multiply indexed `DataFrame`:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " population\n", + "state year \n", + "California 2010 37253956\n", + " 2020 39538223\n", + "New York 2010 19378102\n", + " 2020 20201249\n", + "Texas 2010 25145561\n", + " 2020 29145505" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop_flat.set_index(['state', 'year'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In practice, this type of reindexing is one of the more useful patterns when exploring real-world datasets." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.06-Concat-And-Append.ipynb b/notebooks/03.06-Concat-And-Append.ipynb new file mode 100644 index 000000000..116ef2d4b --- /dev/null +++ b/notebooks/03.06-Concat-And-Append.ipynb @@ -0,0 +1,1908 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Combining Datasets: concat and append" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some of the most interesting studies of data come from combining different data sources.\n", + "These operations can involve anything from very straightforward concatenation of two different datasets to more complicated database-style joins and merges that correctly handle any overlaps between the datasets.\n", + "`Series` and ``DataFrame``s are built with this type of operation in mind, and Pandas includes functions and methods that make this sort of data wrangling fast and straightforward.\n", + "\n", + "Here we'll take a look at simple concatenation of `Series` and ``DataFrame``s with the `pd.concat` function; later we'll dive into more sophisticated in-memory merges and joins implemented in Pandas.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For convenience, we'll define this function, which creates a `DataFrame` of a particular form that will be useful in the following examples:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
ABC
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1A1B1C1
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" + ], + "text/plain": [ + " A B C\n", + "0 A0 B0 C0\n", + "1 A1 B1 C1\n", + "2 A2 B2 C2" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def make_df(cols, ind):\n", + " \"\"\"Quickly make a DataFrame\"\"\"\n", + " data = {c: [str(c) + str(i) for i in ind]\n", + " for c in cols}\n", + " return pd.DataFrame(data, ind)\n", + "\n", + "# example DataFrame\n", + "make_df('ABC', range(3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, we'll create a quick class that allows us to display multiple ``DataFrame``s side by side. The code makes use of the special `_repr_html_` method, which IPython/Jupyter uses to implement its rich object display:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "class display(object):\n", + " \"\"\"Display HTML representation of multiple objects\"\"\"\n", + " template = \"\"\"
\n", + "

{0}

{1}\n", + "
\"\"\"\n", + " def __init__(self, *args):\n", + " self.args = args\n", + " \n", + " def _repr_html_(self):\n", + " return '\\n'.join(self.template.format(a, eval(a)._repr_html_())\n", + " for a in self.args)\n", + " \n", + " def __repr__(self):\n", + " return '\\n\\n'.join(a + '\\n' + repr(eval(a))\n", + " for a in self.args)\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The use of this will become clearer as we continue our discussion in the following section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Recall: Concatenation of NumPy Arrays\n", + "\n", + "Concatenation of `Series` and `DataFrame` objects behaves similarly to concatenation of NumPy arrays, which can be done via the `np.concatenate` function, as discussed in [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb).\n", + "Recall that with it, you can combine the contents of two or more arrays into a single array:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 2, 3, 4, 5, 6, 7, 8, 9])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = [1, 2, 3]\n", + "y = [4, 5, 6]\n", + "z = [7, 8, 9]\n", + "np.concatenate([x, y, z])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first argument is a list or tuple of arrays to concatenate.\n", + "Additionally, in the case of multidimensional arrays, it takes an `axis` keyword that allows you to specify the axis along which the result will be concatenated:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 2, 1, 2],\n", + " [3, 4, 3, 4]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = [[1, 2],\n", + " [3, 4]]\n", + "np.concatenate([x, x], axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simple Concatenation with pd.concat" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `pd.concat` function provides a similar syntax to `np.concatenate` but contains a number of options that we'll discuss momentarily:\n", + "\n", + "```python\n", + "# Signature in Pandas v1.3.5\n", + "pd.concat(objs, axis=0, join='outer', ignore_index=False, keys=None,\n", + " levels=None, names=None, verify_integrity=False,\n", + " sort=False, copy=True)\n", + "```\n", + "\n", + "`pd.concat` can be used for a simple concatenation of `Series` or `DataFrame` objects, just as `np.concatenate` can be used for simple concatenations of arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1 A\n", + "2 B\n", + "3 C\n", + "4 D\n", + "5 E\n", + "6 F\n", + "dtype: object" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ser1 = pd.Series(['A', 'B', 'C'], index=[1, 2, 3])\n", + "ser2 = pd.Series(['D', 'E', 'F'], index=[4, 5, 6])\n", + "pd.concat([ser1, ser2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It also works to concatenate higher-dimensional objects, such as ``DataFrame``s:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df1

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AB
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df2

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pd.concat([df1, df2])

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" + ], + "text/plain": [ + "df1\n", + " A B\n", + "1 A1 B1\n", + "2 A2 B2\n", + "\n", + "df2\n", + " A B\n", + "3 A3 B3\n", + "4 A4 B4\n", + "\n", + "pd.concat([df1, df2])\n", + " A B\n", + "1 A1 B1\n", + "2 A2 B2\n", + "3 A3 B3\n", + "4 A4 B4" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df1 = make_df('AB', [1, 2])\n", + "df2 = make_df('AB', [3, 4])\n", + "display('df1', 'df2', 'pd.concat([df1, df2])')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It's default behavior is to concatenate row-wise within the `DataFrame` (i.e., `axis=0`).\n", + "Like `np.concatenate`, `pd.concat` allows specification of an axis along which concatenation will take place.\n", + "Consider the following example:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df3

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AB
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df4

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CD
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pd.concat([df3, df4], axis='columns')

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" + ], + "text/plain": [ + "df3\n", + " A B\n", + "0 A0 B0\n", + "1 A1 B1\n", + "\n", + "df4\n", + " C D\n", + "0 C0 D0\n", + "1 C1 D1\n", + "\n", + "pd.concat([df3, df4], axis='columns')\n", + " A B C D\n", + "0 A0 B0 C0 D0\n", + "1 A1 B1 C1 D1" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df3 = make_df('AB', [0, 1])\n", + "df4 = make_df('CD', [0, 1])\n", + "display('df3', 'df4', \"pd.concat([df3, df4], axis='columns')\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We could have equivalently specified ``axis=1``; here we've used the more intuitive ``axis='columns'``. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Duplicate Indices\n", + "\n", + "One important difference between `np.concatenate` and `pd.concat` is that Pandas concatenation *preserves indices*, even if the result will have duplicate indices!\n", + "Consider this short example:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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x

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AB
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y

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pd.concat([x, y])

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" + ], + "text/plain": [ + "x\n", + " A B\n", + "0 A0 B0\n", + "1 A1 B1\n", + "\n", + "y\n", + " A B\n", + "0 A2 B2\n", + "1 A3 B3\n", + "\n", + "pd.concat([x, y])\n", + " A B\n", + "0 A0 B0\n", + "1 A1 B1\n", + "0 A2 B2\n", + "1 A3 B3" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = make_df('AB', [0, 1])\n", + "y = make_df('AB', [2, 3])\n", + "y.index = x.index # make indices match\n", + "display('x', 'y', 'pd.concat([x, y])')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the repeated indices in the result.\n", + "While this is valid within ``DataFrame``s, the outcome is often undesirable.\n", + "`pd.concat` gives us a few ways to handle it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Treating repeated indices as an error\n", + "\n", + "If you'd like to simply verify that the indices in the result of `pd.concat` do not overlap, you can include the `verify_integrity` flag.\n", + "With this set to `True`, the concatenation will raise an exception if there are duplicate indices.\n", + "Here is an example, where for clarity we'll catch and print the error message:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ValueError: Indexes have overlapping values: Int64Index([0, 1], dtype='int64')\n" + ] + } + ], + "source": [ + "try:\n", + " pd.concat([x, y], verify_integrity=True)\n", + "except ValueError as e:\n", + " print(\"ValueError:\", e)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Ignoring the index\n", + "\n", + "Sometimes the index itself does not matter, and you would prefer it to simply be ignored.\n", + "This option can be specified using the `ignore_index` flag.\n", + "With this set to `True`, the concatenation will create a new integer index for the resulting `DataFrame`:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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x

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AB
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y

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pd.concat([x, y], ignore_index=True)

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" + ], + "text/plain": [ + "x\n", + " A B\n", + "0 A0 B0\n", + "1 A1 B1\n", + "\n", + "y\n", + " A B\n", + "0 A2 B2\n", + "1 A3 B3\n", + "\n", + "pd.concat([x, y], ignore_index=True)\n", + " A B\n", + "0 A0 B0\n", + "1 A1 B1\n", + "2 A2 B2\n", + "3 A3 B3" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('x', 'y', 'pd.concat([x, y], ignore_index=True)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Adding MultiIndex keys\n", + "\n", + "Another option is to use the `keys` option to specify a label for the data sources; the result will be a hierarchically indexed series containing the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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x

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AB
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y

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AB
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pd.concat([x, y], keys=['x', 'y'])

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AB
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" + ], + "text/plain": [ + "x\n", + " A B\n", + "0 A0 B0\n", + "1 A1 B1\n", + "\n", + "y\n", + " A B\n", + "0 A2 B2\n", + "1 A3 B3\n", + "\n", + "pd.concat([x, y], keys=['x', 'y'])\n", + " A B\n", + "x 0 A0 B0\n", + " 1 A1 B1\n", + "y 0 A2 B2\n", + " 1 A3 B3" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('x', 'y', \"pd.concat([x, y], keys=['x', 'y'])\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use the tools discussed in [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb) to transform this multiply indexed `DataFrame` into the representation we're interested in." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Concatenation with Joins\n", + "\n", + "In the short examples we just looked at, we were mainly concatenating ``DataFrame``s with shared column names.\n", + "In practice, data from different sources might have different sets of column names, and `pd.concat` offers several options in this case.\n", + "Consider the concatenation of the following two ``DataFrame``s, which have some (but not all!) columns in common:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df5

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ABC
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df6

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BCD
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\n", + "

pd.concat([df5, df6])

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ABCD
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3NaNB3C3D3
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" + ], + "text/plain": [ + "df5\n", + " A B C\n", + "1 A1 B1 C1\n", + "2 A2 B2 C2\n", + "\n", + "df6\n", + " B C D\n", + "3 B3 C3 D3\n", + "4 B4 C4 D4\n", + "\n", + "pd.concat([df5, df6])\n", + " A B C D\n", + "1 A1 B1 C1 NaN\n", + "2 A2 B2 C2 NaN\n", + "3 NaN B3 C3 D3\n", + "4 NaN B4 C4 D4" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df5 = make_df('ABC', [1, 2])\n", + "df6 = make_df('BCD', [3, 4])\n", + "display('df5', 'df6', 'pd.concat([df5, df6])')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The default behavior is to fill entries for which no data is available with NA values.\n", + "To change this, we can adjust the `join` parameter of the `concat` function.\n", + "By default, the join is a union of the input columns (`join='outer'`), but we can change this to an intersection of the columns using `join='inner'`:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df5

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ABC
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2A2B2C2
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df6

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BCD
3B3C3D3
4B4C4D4
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\n", + "
\n", + "

pd.concat([df5, df6], join='inner')

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BC
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2B2C2
3B3C3
4B4C4
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" + ], + "text/plain": [ + "df5\n", + " A B C\n", + "1 A1 B1 C1\n", + "2 A2 B2 C2\n", + "\n", + "df6\n", + " B C D\n", + "3 B3 C3 D3\n", + "4 B4 C4 D4\n", + "\n", + "pd.concat([df5, df6], join='inner')\n", + " B C\n", + "1 B1 C1\n", + "2 B2 C2\n", + "3 B3 C3\n", + "4 B4 C4" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('df5', 'df6',\n", + " \"pd.concat([df5, df6], join='inner')\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another useful pattern is to use the `reindex` method before concatenation for finer control over which columns are dropped:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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ABC
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" + ], + "text/plain": [ + " A B C\n", + "1 A1 B1 C1\n", + "2 A2 B2 C2\n", + "3 NaN B3 C3\n", + "4 NaN B4 C4" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.concat([df5, df6.reindex(df5.columns, axis=1)])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The append Method\n", + "\n", + "Because direct array concatenation is so common, `Series` and `DataFrame` objects have an `append` method that can accomplish the same thing in fewer keystrokes.\n", + "For example, in place of `pd.concat([df1, df2])`, you can use `df1.append(df2)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df1

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AB
1A1B1
2A2B2
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df2

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AB
3A3B3
4A4B4
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\n", + "
\n", + "
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df1.append(df2)

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AB
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" + ], + "text/plain": [ + "df1\n", + " A B\n", + "1 A1 B1\n", + "2 A2 B2\n", + "\n", + "df2\n", + " A B\n", + "3 A3 B3\n", + "4 A4 B4\n", + "\n", + "df1.append(df2)\n", + " A B\n", + "1 A1 B1\n", + "2 A2 B2\n", + "3 A3 B3\n", + "4 A4 B4" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('df1', 'df2', 'df1.append(df2)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind that unlike the `append` and `extend` methods of Python lists, the `append` method in Pandas does not modify the original object; instead it creates a new object with the combined data.\n", + "It also is not a very efficient method, because it involves creation of a new index *and* data buffer.\n", + "Thus, if you plan to do multiple `append` operations, it is generally better to build a list of `DataFrame` objects and pass them all at once to the `concat` function.\n", + "\n", + "In the next chapter, we'll look at a more powerful approach to combining data from multiple sources: the database-style merges/joins implemented in `pd.merge`.\n", + "For more information on `concat`, `append`, and related functionality, see the [\"Merge, Join, Concatenate and Compare\" section](http://pandas.pydata.org/pandas-docs/stable/merging.html) of the Pandas documentation." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.07-Merge-and-Join.ipynb b/notebooks/03.07-Merge-and-Join.ipynb new file mode 100644 index 000000000..b3d2059f0 --- /dev/null +++ b/notebooks/03.07-Merge-and-Join.ipynb @@ -0,0 +1,4089 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Combining Datasets: merge and join" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One important feature offered by Pandas is its high-performance, in-memory join and merge operations, which you may be familiar with if you have ever worked with databases.\n", + "The main interface for this is the `pd.merge` function, and we'll see a few examples of how this can work in practice.\n", + "\n", + "For convenience, we will again define the `display` function from the previous chapter after the usual imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "\n", + "class display(object):\n", + " \"\"\"Display HTML representation of multiple objects\"\"\"\n", + " template = \"\"\"
\n", + "

{0}

{1}\n", + "
\"\"\"\n", + " def __init__(self, *args):\n", + " self.args = args\n", + " \n", + " def _repr_html_(self):\n", + " return '\\n'.join(self.template.format(a, eval(a)._repr_html_())\n", + " for a in self.args)\n", + " \n", + " def __repr__(self):\n", + " return '\\n\\n'.join(a + '\\n' + repr(eval(a))\n", + " for a in self.args)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Relational Algebra\n", + "\n", + "The behavior implemented in `pd.merge` is a subset of what is known as *relational algebra*, which is a formal set of rules for manipulating relational data that forms the conceptual foundation of operations available in most databases.\n", + "The strength of the relational algebra approach is that it proposes several fundamental operations, which become the building blocks of more complicated operations on any dataset.\n", + "With this lexicon of fundamental operations implemented efficiently in a database or other program, a wide range of fairly complicated composite operations can be performed.\n", + "\n", + "Pandas implements several of these fundamental building blocks in the `pd.merge` function and the related `join` method of `Series` and `DataFrame` objects.\n", + "As you will see, these let you efficiently link data from different sources." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Categories of Joins\n", + "\n", + "The `pd.merge` function implements a number of types of joins: *one-to-one*, *many-to-one*, and *many-to-many*.\n", + "All three types of joins are accessed via an identical call to the `pd.merge` interface; the type of join performed depends on the form of the input data.\n", + "We'll start with some simple examples of the three types of merges, and discuss detailed options a bit later." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### One-to-One Joins\n", + "\n", + "Perhaps the simplest type of merge is the one-to-one join, which is in many ways similar to the column-wise concatenation you saw in [Combining Datasets: Concat & Append](03.06-Concat-And-Append.ipynb).\n", + "As a concrete example, consider the following two `DataFrame` objects, which contain information on several employees in a company:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "

df1

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
employeegroup
0BobAccounting
1JakeEngineering
2LisaEngineering
3SueHR
\n", + "
\n", + "
\n", + "
\n", + "

df2

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
employeehire_date
0Lisa2004
1Bob2008
2Jake2012
3Sue2014
\n", + "
\n", + "
" + ], + "text/plain": [ + "df1\n", + " employee group\n", + "0 Bob Accounting\n", + "1 Jake Engineering\n", + "2 Lisa Engineering\n", + "3 Sue HR\n", + "\n", + "df2\n", + " employee hire_date\n", + "0 Lisa 2004\n", + "1 Bob 2008\n", + "2 Jake 2012\n", + "3 Sue 2014" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df1 = pd.DataFrame({'employee': ['Bob', 'Jake', 'Lisa', 'Sue'],\n", + " 'group': ['Accounting', 'Engineering',\n", + " 'Engineering', 'HR']})\n", + "df2 = pd.DataFrame({'employee': ['Lisa', 'Bob', 'Jake', 'Sue'],\n", + " 'hire_date': [2004, 2008, 2012, 2014]})\n", + "display('df1', 'df2')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To combine this information into a single `DataFrame`, we can use the `pd.merge` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
employeegrouphire_date
0BobAccounting2008
1JakeEngineering2012
2LisaEngineering2004
3SueHR2014
\n", + "
" + ], + "text/plain": [ + " employee group hire_date\n", + "0 Bob Accounting 2008\n", + "1 Jake Engineering 2012\n", + "2 Lisa Engineering 2004\n", + "3 Sue HR 2014" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df3 = pd.merge(df1, df2)\n", + "df3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `pd.merge` function recognizes that each `DataFrame` has an `employee` column, and automatically joins using this column as a key.\n", + "The result of the merge is a new `DataFrame` that combines the information from the two inputs.\n", + "Notice that the order of entries in each column is not necessarily maintained: in this case, the order of the `employee` column differs between `df1` and `df2`, and the `pd.merge` function correctly accounts for this.\n", + "Additionally, keep in mind that the merge in general discards the index, except in the special case of merges by index (see the `left_index` and `right_index` keywords, discussed momentarily)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Many-to-One Joins" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Many-to-one joins are joins in which one of the two key columns contains duplicate entries.\n", + "For the many-to-one case, the resulting `DataFrame` will preserve those duplicate entries as appropriate.\n", + "Consider the following example of a many-to-one join:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "

df3

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employeegrouphire_date
0BobAccounting2008
1JakeEngineering2012
2LisaEngineering2004
3SueHR2014
\n", + "
\n", + "
\n", + "
\n", + "

df4

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
groupsupervisor
0AccountingCarly
1EngineeringGuido
2HRSteve
\n", + "
\n", + "
\n", + "
\n", + "

pd.merge(df3, df4)

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
employeegrouphire_datesupervisor
0BobAccounting2008Carly
1JakeEngineering2012Guido
2LisaEngineering2004Guido
3SueHR2014Steve
\n", + "
\n", + "
" + ], + "text/plain": [ + "df3\n", + " employee group hire_date\n", + "0 Bob Accounting 2008\n", + "1 Jake Engineering 2012\n", + "2 Lisa Engineering 2004\n", + "3 Sue HR 2014\n", + "\n", + "df4\n", + " group supervisor\n", + "0 Accounting Carly\n", + "1 Engineering Guido\n", + "2 HR Steve\n", + "\n", + "pd.merge(df3, df4)\n", + " employee group hire_date supervisor\n", + "0 Bob Accounting 2008 Carly\n", + "1 Jake Engineering 2012 Guido\n", + "2 Lisa Engineering 2004 Guido\n", + "3 Sue HR 2014 Steve" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df4 = pd.DataFrame({'group': ['Accounting', 'Engineering', 'HR'],\n", + " 'supervisor': ['Carly', 'Guido', 'Steve']})\n", + "display('df3', 'df4', 'pd.merge(df3, df4)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting `DataFrame` has an additional column with the \"supervisor\" information, where the information is repeated in one or more locations as required by the inputs." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Many-to-Many Joins" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Many-to-many joins may be a bit confusing conceptually, but are nevertheless well defined.\n", + "If the key column in both the left and right arrays contains duplicates, then the result is a many-to-many merge.\n", + "This will be perhaps most clear with a concrete example.\n", + "Consider the following, where we have a `DataFrame` showing one or more skills associated with a particular group.\n", + "By performing a many-to-many join, we can recover the skills associated with any individual person:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "

df1

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employeegroup
0BobAccounting
1JakeEngineering
2LisaEngineering
3SueHR
\n", + "
\n", + "
\n", + "
\n", + "

df5

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
groupskills
0Accountingmath
1Accountingspreadsheets
2Engineeringsoftware
3Engineeringmath
4HRspreadsheets
5HRorganization
\n", + "
\n", + "
\n", + "
\n", + "

pd.merge(df1, df5)

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
employeegroupskills
0BobAccountingmath
1BobAccountingspreadsheets
2JakeEngineeringsoftware
3JakeEngineeringmath
4LisaEngineeringsoftware
5LisaEngineeringmath
6SueHRspreadsheets
7SueHRorganization
\n", + "
\n", + "
" + ], + "text/plain": [ + "df1\n", + " employee group\n", + "0 Bob Accounting\n", + "1 Jake Engineering\n", + "2 Lisa Engineering\n", + "3 Sue HR\n", + "\n", + "df5\n", + " group skills\n", + "0 Accounting math\n", + "1 Accounting spreadsheets\n", + "2 Engineering software\n", + "3 Engineering math\n", + "4 HR spreadsheets\n", + "5 HR organization\n", + "\n", + "pd.merge(df1, df5)\n", + " employee group skills\n", + "0 Bob Accounting math\n", + "1 Bob Accounting spreadsheets\n", + "2 Jake Engineering software\n", + "3 Jake Engineering math\n", + "4 Lisa Engineering software\n", + "5 Lisa Engineering math\n", + "6 Sue HR spreadsheets\n", + "7 Sue HR organization" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df5 = pd.DataFrame({'group': ['Accounting', 'Accounting',\n", + " 'Engineering', 'Engineering', 'HR', 'HR'],\n", + " 'skills': ['math', 'spreadsheets', 'software', 'math',\n", + " 'spreadsheets', 'organization']})\n", + "display('df1', 'df5', \"pd.merge(df1, df5)\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These three types of joins can be used with other Pandas tools to implement a wide array of functionality.\n", + "But in practice, datasets are rarely as clean as the one we're working with here.\n", + "In the following section we'll consider some of the options provided by `pd.merge` that enable you to tune how the join operations work." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Specification of the Merge Key" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We've already seen the default behavior of `pd.merge`: it looks for one or more matching column names between the two inputs, and uses this as the key.\n", + "However, often the column names will not match so nicely, and `pd.merge` provides a variety of options for handling this." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The on Keyword\n", + "\n", + "Most simply, you can explicitly specify the name of the key column using the `on` keyword, which takes a column name or a list of column names:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "

df1

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
employeegroup
0BobAccounting
1JakeEngineering
2LisaEngineering
3SueHR
\n", + "
\n", + "
\n", + "
\n", + "

df2

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
employeehire_date
0Lisa2004
1Bob2008
2Jake2012
3Sue2014
\n", + "
\n", + "
\n", + "
\n", + "

pd.merge(df1, df2, on='employee')

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employeegrouphire_date
0BobAccounting2008
1JakeEngineering2012
2LisaEngineering2004
3SueHR2014
\n", + "
\n", + "
" + ], + "text/plain": [ + "df1\n", + " employee group\n", + "0 Bob Accounting\n", + "1 Jake Engineering\n", + "2 Lisa Engineering\n", + "3 Sue HR\n", + "\n", + "df2\n", + " employee hire_date\n", + "0 Lisa 2004\n", + "1 Bob 2008\n", + "2 Jake 2012\n", + "3 Sue 2014\n", + "\n", + "pd.merge(df1, df2, on='employee')\n", + " employee group hire_date\n", + "0 Bob Accounting 2008\n", + "1 Jake Engineering 2012\n", + "2 Lisa Engineering 2004\n", + "3 Sue HR 2014" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('df1', 'df2', \"pd.merge(df1, df2, on='employee')\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This option works only if both the left and right ``DataFrame``s have the specified column name." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The left_on and right_on Keywords\n", + "\n", + "At times you may wish to merge two datasets with different column names; for example, we may have a dataset in which the employee name is labeled as \"name\" rather than \"employee\".\n", + "In this case, we can use the `left_on` and `right_on` keywords to specify the two column names:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "

df1

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
employeegroup
0BobAccounting
1JakeEngineering
2LisaEngineering
3SueHR
\n", + "
\n", + "
\n", + "
\n", + "

df3

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
namesalary
0Bob70000
1Jake80000
2Lisa120000
3Sue90000
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\n", + "
\n", + "
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pd.merge(df1, df3, left_on=\"employee\", right_on=\"name\")

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employeegroupnamesalary
0BobAccountingBob70000
1JakeEngineeringJake80000
2LisaEngineeringLisa120000
3SueHRSue90000
\n", + "
\n", + "
" + ], + "text/plain": [ + "df1\n", + " employee group\n", + "0 Bob Accounting\n", + "1 Jake Engineering\n", + "2 Lisa Engineering\n", + "3 Sue HR\n", + "\n", + "df3\n", + " name salary\n", + "0 Bob 70000\n", + "1 Jake 80000\n", + "2 Lisa 120000\n", + "3 Sue 90000\n", + "\n", + "pd.merge(df1, df3, left_on=\"employee\", right_on=\"name\")\n", + " employee group name salary\n", + "0 Bob Accounting Bob 70000\n", + "1 Jake Engineering Jake 80000\n", + "2 Lisa Engineering Lisa 120000\n", + "3 Sue HR Sue 90000" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df3 = pd.DataFrame({'name': ['Bob', 'Jake', 'Lisa', 'Sue'],\n", + " 'salary': [70000, 80000, 120000, 90000]})\n", + "display('df1', 'df3', 'pd.merge(df1, df3, left_on=\"employee\", right_on=\"name\")')" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result has a redundant column that we can drop if desired—for example, by using the `DataFrame.drop()` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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employeegroupsalary
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1JakeEngineering80000
2LisaEngineering120000
3SueHR90000
\n", + "
" + ], + "text/plain": [ + " employee group salary\n", + "0 Bob Accounting 70000\n", + "1 Jake Engineering 80000\n", + "2 Lisa Engineering 120000\n", + "3 Sue HR 90000" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.merge(df1, df3, left_on=\"employee\", right_on=\"name\").drop('name', axis=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The left_index and right_index Keywords\n", + "\n", + "Sometimes, rather than merging on a column, you would instead like to merge on an index.\n", + "For example, your data might look like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "

df1a

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group
employee
BobAccounting
JakeEngineering
LisaEngineering
SueHR
\n", + "
\n", + "
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df2a

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hire_date
employee
Lisa2004
Bob2008
Jake2012
Sue2014
\n", + "
\n", + "
" + ], + "text/plain": [ + "df1a\n", + " group\n", + "employee \n", + "Bob Accounting\n", + "Jake Engineering\n", + "Lisa Engineering\n", + "Sue HR\n", + "\n", + "df2a\n", + " hire_date\n", + "employee \n", + "Lisa 2004\n", + "Bob 2008\n", + "Jake 2012\n", + "Sue 2014" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df1a = df1.set_index('employee')\n", + "df2a = df2.set_index('employee')\n", + "display('df1a', 'df2a')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can use the index as the key for merging by specifying the `left_index` and/or `right_index` flags in `pd.merge()`:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df1a

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group
employee
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JakeEngineering
LisaEngineering
SueHR
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df2a

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hire_date
employee
Lisa2004
Bob2008
Jake2012
Sue2014
\n", + "
\n", + "
\n", + "
\n", + "

pd.merge(df1a, df2a, left_index=True, right_index=True)

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grouphire_date
employee
BobAccounting2008
JakeEngineering2012
LisaEngineering2004
SueHR2014
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" + ], + "text/plain": [ + "df1a\n", + " group\n", + "employee \n", + "Bob Accounting\n", + "Jake Engineering\n", + "Lisa Engineering\n", + "Sue HR\n", + "\n", + "df2a\n", + " hire_date\n", + "employee \n", + "Lisa 2004\n", + "Bob 2008\n", + "Jake 2012\n", + "Sue 2014\n", + "\n", + "pd.merge(df1a, df2a, left_index=True, right_index=True)\n", + " group hire_date\n", + "employee \n", + "Bob Accounting 2008\n", + "Jake Engineering 2012\n", + "Lisa Engineering 2004\n", + "Sue HR 2014" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('df1a', 'df2a',\n", + " \"pd.merge(df1a, df2a, left_index=True, right_index=True)\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For convenience, Pandas includes the `DataFrame.join()` method, which performs an index-based merge without extra keywords:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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grouphire_date
employee
BobAccounting2008
JakeEngineering2012
LisaEngineering2004
SueHR2014
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" + ], + "text/plain": [ + " group hire_date\n", + "employee \n", + "Bob Accounting 2008\n", + "Jake Engineering 2012\n", + "Lisa Engineering 2004\n", + "Sue HR 2014" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df1a.join(df2a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you'd like to mix indices and columns, you can combine `left_index` with `right_on` or `left_on` with `right_index` to get the desired behavior:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "

df1a

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group
employee
BobAccounting
JakeEngineering
LisaEngineering
SueHR
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df3

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namesalary
0Bob70000
1Jake80000
2Lisa120000
3Sue90000
\n", + "
\n", + "
\n", + "
\n", + "

pd.merge(df1a, df3, left_index=True, right_on='name')

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groupnamesalary
0AccountingBob70000
1EngineeringJake80000
2EngineeringLisa120000
3HRSue90000
\n", + "
\n", + "
" + ], + "text/plain": [ + "df1a\n", + " group\n", + "employee \n", + "Bob Accounting\n", + "Jake Engineering\n", + "Lisa Engineering\n", + "Sue HR\n", + "\n", + "df3\n", + " name salary\n", + "0 Bob 70000\n", + "1 Jake 80000\n", + "2 Lisa 120000\n", + "3 Sue 90000\n", + "\n", + "pd.merge(df1a, df3, left_index=True, right_on='name')\n", + " group name salary\n", + "0 Accounting Bob 70000\n", + "1 Engineering Jake 80000\n", + "2 Engineering Lisa 120000\n", + "3 HR Sue 90000" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('df1a', 'df3', \"pd.merge(df1a, df3, left_index=True, right_on='name')\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these options also work with multiple indices and/or multiple columns; the interface for this behavior is very intuitive.\n", + "For more information on this, see the [\"Merge, Join, and Concatenate\" section](http://pandas.pydata.org/pandas-docs/stable/merging.html) of the Pandas documentation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Specifying Set Arithmetic for Joins" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In all the preceding examples we have glossed over one important consideration in performing a join: the type of set arithmetic used in the join.\n", + "This comes up when a value appears in one key column but not the other. Consider this example:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df6

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namefood
0Peterfish
1Paulbeans
2Marybread
\n", + "
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\n", + "
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df7

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
namedrink
0Marywine
1Josephbeer
\n", + "
\n", + "
\n", + "
\n", + "

pd.merge(df6, df7)

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namefooddrink
0Marybreadwine
\n", + "
\n", + "
" + ], + "text/plain": [ + "df6\n", + " name food\n", + "0 Peter fish\n", + "1 Paul beans\n", + "2 Mary bread\n", + "\n", + "df7\n", + " name drink\n", + "0 Mary wine\n", + "1 Joseph beer\n", + "\n", + "pd.merge(df6, df7)\n", + " name food drink\n", + "0 Mary bread wine" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df6 = pd.DataFrame({'name': ['Peter', 'Paul', 'Mary'],\n", + " 'food': ['fish', 'beans', 'bread']},\n", + " columns=['name', 'food'])\n", + "df7 = pd.DataFrame({'name': ['Mary', 'Joseph'],\n", + " 'drink': ['wine', 'beer']},\n", + " columns=['name', 'drink'])\n", + "display('df6', 'df7', 'pd.merge(df6, df7)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we have merged two datasets that have only a single \"name\" entry in common: Mary.\n", + "By default, the result contains the *intersection* of the two sets of inputs; this is what is known as an *inner join*.\n", + "We can specify this explicitly using the `how` keyword, which defaults to `\"inner\"`:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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namefooddrink
0Marybreadwine
\n", + "
" + ], + "text/plain": [ + " name food drink\n", + "0 Mary bread wine" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.merge(df6, df7, how='inner')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Other options for the `how` keyword are `'outer'`, `'left'`, and `'right'`.\n", + "An *outer join* returns a join over the union of the input columns, and fills in all missing values with NAs:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df6

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namefood
0Peterfish
1Paulbeans
2Marybread
\n", + "
\n", + "
\n", + "
\n", + "

df7

\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
namedrink
0Marywine
1Josephbeer
\n", + "
\n", + "
\n", + "
\n", + "

pd.merge(df6, df7, how='outer')

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namefooddrink
0PeterfishNaN
1PaulbeansNaN
2Marybreadwine
3JosephNaNbeer
\n", + "
\n", + "
" + ], + "text/plain": [ + "df6\n", + " name food\n", + "0 Peter fish\n", + "1 Paul beans\n", + "2 Mary bread\n", + "\n", + "df7\n", + " name drink\n", + "0 Mary wine\n", + "1 Joseph beer\n", + "\n", + "pd.merge(df6, df7, how='outer')\n", + " name food drink\n", + "0 Peter fish NaN\n", + "1 Paul beans NaN\n", + "2 Mary bread wine\n", + "3 Joseph NaN beer" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('df6', 'df7', \"pd.merge(df6, df7, how='outer')\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *left join* and *right join* return joins over the left entries and right entries, respectively.\n", + "For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df6

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namefood
0Peterfish
1Paulbeans
2Marybread
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\n", + "
\n", + "
\n", + "

df7

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namedrink
0Marywine
1Josephbeer
\n", + "
\n", + "
\n", + "
\n", + "

pd.merge(df6, df7, how='left')

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namefooddrink
0PeterfishNaN
1PaulbeansNaN
2Marybreadwine
\n", + "
\n", + "
" + ], + "text/plain": [ + "df6\n", + " name food\n", + "0 Peter fish\n", + "1 Paul beans\n", + "2 Mary bread\n", + "\n", + "df7\n", + " name drink\n", + "0 Mary wine\n", + "1 Joseph beer\n", + "\n", + "pd.merge(df6, df7, how='left')\n", + " name food drink\n", + "0 Peter fish NaN\n", + "1 Paul beans NaN\n", + "2 Mary bread wine" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "display('df6', 'df7', \"pd.merge(df6, df7, how='left')\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output rows now correspond to the entries in the left input. Using\n", + "`how='right'` works in a similar manner.\n", + "\n", + "All of these options can be applied straightforwardly to any of the preceding join types." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Overlapping Column Names: The suffixes Keyword" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Last, you may end up in a case where your two input ``DataFrame``s have conflicting column names.\n", + "Consider this example:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df8

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namerank
0Bob1
1Jake2
2Lisa3
3Sue4
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df9

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namerank
0Bob3
1Jake1
2Lisa4
3Sue2
\n", + "
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pd.merge(df8, df9, on=\"name\")

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namerank_xrank_y
0Bob13
1Jake21
2Lisa34
3Sue42
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\n", + "
" + ], + "text/plain": [ + "df8\n", + " name rank\n", + "0 Bob 1\n", + "1 Jake 2\n", + "2 Lisa 3\n", + "3 Sue 4\n", + "\n", + "df9\n", + " name rank\n", + "0 Bob 3\n", + "1 Jake 1\n", + "2 Lisa 4\n", + "3 Sue 2\n", + "\n", + "pd.merge(df8, df9, on=\"name\")\n", + " name rank_x rank_y\n", + "0 Bob 1 3\n", + "1 Jake 2 1\n", + "2 Lisa 3 4\n", + "3 Sue 4 2" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df8 = pd.DataFrame({'name': ['Bob', 'Jake', 'Lisa', 'Sue'],\n", + " 'rank': [1, 2, 3, 4]})\n", + "df9 = pd.DataFrame({'name': ['Bob', 'Jake', 'Lisa', 'Sue'],\n", + " 'rank': [3, 1, 4, 2]})\n", + "display('df8', 'df9', 'pd.merge(df8, df9, on=\"name\")')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because the output would have two conflicting column names, the `merge` function automatically appends the suffixes ``_x`` and ``_y`` to make the output columns unique.\n", + "If these defaults are inappropriate, it is possible to specify a custom suffix using the ``suffixes`` keyword:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
namerank_Lrank_R
0Bob13
1Jake21
2Lisa34
3Sue42
\n", + "
" + ], + "text/plain": [ + " name rank_L rank_R\n", + "0 Bob 1 3\n", + "1 Jake 2 1\n", + "2 Lisa 3 4\n", + "3 Sue 4 2" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.merge(df8, df9, on=\"name\", suffixes=[\"_L\", \"_R\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These suffixes work in any of the possible join patterns, and also work if there are multiple overlapping columns." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on these patterns, see [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb), where we dive a bit deeper into relational algebra.\n", + "Also see the [\"Merge, Join, Concatenate and Compare\" section](http://pandas.pydata.org/pandas-docs/stable/merging.html) of the Pandas documentation for further discussion of these topics." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: US States Data\n", + "\n", + "Merge and join operations come up most often when combining data from different sources.\n", + "Here we will consider an example of some data about US states and their populations.\n", + "The data files can be found at [http://github.com/jakevdp/data-USstates](http://github.com/jakevdp/data-USstates):" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# Following are commands to download the data\n", + "# repo = \"https://raw.githubusercontent.com/jakevdp/data-USstates/master\"\n", + "# !cd data && curl -O {repo}/state-population.csv\n", + "# !cd data && curl -O {repo}/state-areas.csv\n", + "# !cd data && curl -O {repo}/state-abbrevs.csv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's take a look at the three datasets, using the Pandas ``read_csv`` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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pop.head()

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state/regionagesyearpopulation
0ALunder1820121117489.0
1ALtotal20124817528.0
2ALunder1820101130966.0
3ALtotal20104785570.0
4ALunder1820111125763.0
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areas.head()

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statearea (sq. mi)
0Alabama52423
1Alaska656425
2Arizona114006
3Arkansas53182
4California163707
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abbrevs.head()

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stateabbreviation
0AlabamaAL
1AlaskaAK
2ArizonaAZ
3ArkansasAR
4CaliforniaCA
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" + ], + "text/plain": [ + "pop.head()\n", + " state/region ages year population\n", + "0 AL under18 2012 1117489.0\n", + "1 AL total 2012 4817528.0\n", + "2 AL under18 2010 1130966.0\n", + "3 AL total 2010 4785570.0\n", + "4 AL under18 2011 1125763.0\n", + "\n", + "areas.head()\n", + " state area (sq. mi)\n", + "0 Alabama 52423\n", + "1 Alaska 656425\n", + "2 Arizona 114006\n", + "3 Arkansas 53182\n", + "4 California 163707\n", + "\n", + "abbrevs.head()\n", + " state abbreviation\n", + "0 Alabama AL\n", + "1 Alaska AK\n", + "2 Arizona AZ\n", + "3 Arkansas AR\n", + "4 California CA" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pop = pd.read_csv('data/state-population.csv')\n", + "areas = pd.read_csv('data/state-areas.csv')\n", + "abbrevs = pd.read_csv('data/state-abbrevs.csv')\n", + "\n", + "display('pop.head()', 'areas.head()', 'abbrevs.head()')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Given this information, say we want to compute a relatively straightforward result: rank US states and territories by their 2010 population density.\n", + "We clearly have the data here to find this result, but we'll have to combine the datasets to do so.\n", + "\n", + "We'll start with a many-to-one merge that will give us the full state names within the population `DataFrame`.\n", + "We want to merge based on the `state/region` column of `pop` and the `abbreviation` column of `abbrevs`.\n", + "We'll use `how='outer'` to make sure no data is thrown away due to mismatched labels:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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state/regionagesyearpopulationstate
0ALunder1820121117489.0Alabama
1ALtotal20124817528.0Alabama
2ALunder1820101130966.0Alabama
3ALtotal20104785570.0Alabama
4ALunder1820111125763.0Alabama
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" + ], + "text/plain": [ + " state/region ages year population state\n", + "0 AL under18 2012 1117489.0 Alabama\n", + "1 AL total 2012 4817528.0 Alabama\n", + "2 AL under18 2010 1130966.0 Alabama\n", + "3 AL total 2010 4785570.0 Alabama\n", + "4 AL under18 2011 1125763.0 Alabama" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "merged = pd.merge(pop, abbrevs, how='outer',\n", + " left_on='state/region', right_on='abbreviation')\n", + "merged = merged.drop('abbreviation', axis=1) # drop duplicate info\n", + "merged.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's double-check whether there were any mismatches here, which we can do by looking for rows with nulls:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state/region False\n", + "ages False\n", + "year False\n", + "population True\n", + "state True\n", + "dtype: bool" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "merged.isnull().any()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some of the ``population`` values are null; let's figure out which these are!" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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state/regionagesyearpopulationstate
2448PRunder181990NaNNaN
2449PRtotal1990NaNNaN
2450PRtotal1991NaNNaN
2451PRunder181991NaNNaN
2452PRtotal1993NaNNaN
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" + ], + "text/plain": [ + " state/region ages year population state\n", + "2448 PR under18 1990 NaN NaN\n", + "2449 PR total 1990 NaN NaN\n", + "2450 PR total 1991 NaN NaN\n", + "2451 PR under18 1991 NaN NaN\n", + "2452 PR total 1993 NaN NaN" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "merged[merged['population'].isnull()].head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It appears that all the null population values are from Puerto Rico prior to the year 2000; this is likely due to this data not being available in the original source.\n", + "\n", + "More importantly, we see that some of the new `state` entries are also null, which means that there was no corresponding entry in the `abbrevs` key!\n", + "Let's figure out which regions lack this match:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['PR', 'USA'], dtype=object)" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "merged.loc[merged['state'].isnull(), 'state/region'].unique()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can quickly infer the issue: our population data includes entries for Puerto Rico (PR) and the United States as a whole (USA), while these entries do not appear in the state abbreviation key.\n", + "We can fix these quickly by filling in appropriate entries:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state/region False\n", + "ages False\n", + "year False\n", + "population True\n", + "state False\n", + "dtype: bool" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "merged.loc[merged['state/region'] == 'PR', 'state'] = 'Puerto Rico'\n", + "merged.loc[merged['state/region'] == 'USA', 'state'] = 'United States'\n", + "merged.isnull().any()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "No more nulls in the `state` column: we're all set!\n", + "\n", + "Now we can merge the result with the area data using a similar procedure.\n", + "Examining our results, we will want to join on the `state` column in both:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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state/regionagesyearpopulationstatearea (sq. mi)
0ALunder1820121117489.0Alabama52423.0
1ALtotal20124817528.0Alabama52423.0
2ALunder1820101130966.0Alabama52423.0
3ALtotal20104785570.0Alabama52423.0
4ALunder1820111125763.0Alabama52423.0
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" + ], + "text/plain": [ + " state/region ages year population state area (sq. mi)\n", + "0 AL under18 2012 1117489.0 Alabama 52423.0\n", + "1 AL total 2012 4817528.0 Alabama 52423.0\n", + "2 AL under18 2010 1130966.0 Alabama 52423.0\n", + "3 AL total 2010 4785570.0 Alabama 52423.0\n", + "4 AL under18 2011 1125763.0 Alabama 52423.0" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final = pd.merge(merged, areas, on='state', how='left')\n", + "final.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, let's check for nulls to see if there were any mismatches:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state/region False\n", + "ages False\n", + "year False\n", + "population True\n", + "state False\n", + "area (sq. mi) True\n", + "dtype: bool" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final.isnull().any()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are nulls in the ``area`` column; we can take a look to see which regions were ignored here:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['United States'], dtype=object)" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final['state'][final['area (sq. mi)'].isnull()].unique()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that our ``areas`` ``DataFrame`` does not contain the area of the United States as a whole.\n", + "We could insert the appropriate value (using the sum of all state areas, for instance), but in this case we'll just drop the null values because the population density of the entire United States is not relevant to our current discussion:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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4ALunder1820111125763.0Alabama52423.0
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" + ], + "text/plain": [ + " state/region ages year population state area (sq. mi)\n", + "0 AL under18 2012 1117489.0 Alabama 52423.0\n", + "1 AL total 2012 4817528.0 Alabama 52423.0\n", + "2 AL under18 2010 1130966.0 Alabama 52423.0\n", + "3 AL total 2010 4785570.0 Alabama 52423.0\n", + "4 AL under18 2011 1125763.0 Alabama 52423.0" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final.dropna(inplace=True)\n", + "final.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have all the data we need. To answer the question of interest, let's first select the portion of the data corresponding with the year 2010, and the total population.\n", + "We'll use the `query` function to do this quickly (this requires the NumExpr package to be installed; see [High-Performance Pandas: `eval()` and `query()`](03.12-Performance-Eval-and-Query.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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state/regionagesyearpopulationstatearea (sq. mi)
3ALtotal20104785570.0Alabama52423.0
91AKtotal2010713868.0Alaska656425.0
101AZtotal20106408790.0Arizona114006.0
189ARtotal20102922280.0Arkansas53182.0
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" + ], + "text/plain": [ + " state/region ages year population state area (sq. mi)\n", + "3 AL total 2010 4785570.0 Alabama 52423.0\n", + "91 AK total 2010 713868.0 Alaska 656425.0\n", + "101 AZ total 2010 6408790.0 Arizona 114006.0\n", + "189 AR total 2010 2922280.0 Arkansas 53182.0\n", + "197 CA total 2010 37333601.0 California 163707.0" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data2010 = final.query(\"year == 2010 & ages == 'total'\")\n", + "data2010.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's compute the population density and display it in order.\n", + "We'll start by re-indexing our data on the state, and then compute the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "data2010.set_index('state', inplace=True)\n", + "density = data2010['population'] / data2010['area (sq. mi)']" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state\n", + "District of Columbia 8898.897059\n", + "Puerto Rico 1058.665149\n", + "New Jersey 1009.253268\n", + "Rhode Island 681.339159\n", + "Connecticut 645.600649\n", + "dtype: float64" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "density.sort_values(ascending=False, inplace=True)\n", + "density.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a ranking of US states, plus Washington, DC, and Puerto Rico, in order of their 2010 population density, in residents per square mile.\n", + "We can see that by far the densest region in this dataset is Washington, DC (i.e., the District of Columbia); among states, the densest is New Jersey.\n", + "\n", + "We can also check the end of the list:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "state\n", + "South Dakota 10.583512\n", + "North Dakota 9.537565\n", + "Montana 6.736171\n", + "Wyoming 5.768079\n", + "Alaska 1.087509\n", + "dtype: float64" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "density.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that the least dense state, by far, is Alaska, averaging slightly over one resident per square mile.\n", + "\n", + "This type of data merging is a common task when trying to answer questions using real-world data sources.\n", + "I hope that this example has given you an idea of some of the ways you can combine the tools we've covered in order to gain insight from your data!" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.08-Aggregation-and-Grouping.ipynb b/notebooks/03.08-Aggregation-and-Grouping.ipynb new file mode 100644 index 000000000..02c1cb588 --- /dev/null +++ b/notebooks/03.08-Aggregation-and-Grouping.ipynb @@ -0,0 +1,2596 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Aggregation and Grouping" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A fundamental piece of many data analysis tasks is efficient summarization: computing aggregations like `sum`, `mean`, `median`, `min`, and `max`, in which a single number summarizes aspects of a potentially large dataset.\n", + "In this chapter, we'll explore aggregations in Pandas, from simple operations akin to what we've seen on NumPy arrays to more sophisticated operations based on the concept of a `groupby`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For convenience, we'll use the same `display` magic function that we used in the previous chapters:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "class display(object):\n", + " \"\"\"Display HTML representation of multiple objects\"\"\"\n", + " template = \"\"\"
\n", + "

{0}

{1}\n", + "
\"\"\"\n", + " def __init__(self, *args):\n", + " self.args = args\n", + " \n", + " def _repr_html_(self):\n", + " return '\\n'.join(self.template.format(a, eval(a)._repr_html_())\n", + " for a in self.args)\n", + " \n", + " def __repr__(self):\n", + " return '\\n\\n'.join(a + '\\n' + repr(eval(a))\n", + " for a in self.args)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Planets Data\n", + "\n", + "Here we will use the Planets dataset, available via the [Seaborn package](http://seaborn.pydata.org/) (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)).\n", + "It gives information on planets that astronomers have discovered around other stars (known as *extrasolar planets*, or *exoplanets* for short). It can be downloaded with a simple Seaborn command:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1035, 6)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import seaborn as sns\n", + "planets = sns.load_dataset('planets')\n", + "planets.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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methodnumberorbital_periodmassdistanceyear
0Radial Velocity1269.3007.1077.402006
1Radial Velocity1874.7742.2156.952008
2Radial Velocity1763.0002.6019.842011
3Radial Velocity1326.03019.40110.622007
4Radial Velocity1516.22010.50119.472009
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" + ], + "text/plain": [ + " method number orbital_period mass distance year\n", + "0 Radial Velocity 1 269.300 7.10 77.40 2006\n", + "1 Radial Velocity 1 874.774 2.21 56.95 2008\n", + "2 Radial Velocity 1 763.000 2.60 19.84 2011\n", + "3 Radial Velocity 1 326.030 19.40 110.62 2007\n", + "4 Radial Velocity 1 516.220 10.50 119.47 2009" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "planets.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This has some details on the 1,000+ extrasolar planets discovered up to 2014." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simple Aggregation in Pandas" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In [\"Aggregations: Min, Max, and Everything In Between\"](02.04-Computation-on-arrays-aggregates.ipynb), we explored some of the data aggregations available for NumPy arrays.\n", + "As with a one-dimensional NumPy array, for a Pandas ``Series`` the aggregates return a single value:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 0.374540\n", + "1 0.950714\n", + "2 0.731994\n", + "3 0.598658\n", + "4 0.156019\n", + "dtype: float64" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rng = np.random.RandomState(42)\n", + "ser = pd.Series(rng.rand(5))\n", + "ser" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2.811925491708157" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ser.sum()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5623850983416314" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ser.mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a `DataFrame`, by default the aggregates return results within each column:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " A B\n", + "0 0.155995 0.020584\n", + "1 0.058084 0.969910\n", + "2 0.866176 0.832443\n", + "3 0.601115 0.212339\n", + "4 0.708073 0.181825" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.DataFrame({'A': rng.rand(5),\n", + " 'B': rng.rand(5)})\n", + "df" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "A 0.477888\n", + "B 0.443420\n", + "dtype: float64" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By specifying the `axis` argument, you can instead aggregate within each row:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 0.088290\n", + "1 0.513997\n", + "2 0.849309\n", + "3 0.406727\n", + "4 0.444949\n", + "dtype: float64" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.mean(axis='columns')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pandas `Series` and `DataFrame` objects include all of the common aggregates mentioned in [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb); in addition, there is a convenience method, `describe`, that computes several common aggregates for each column and returns the result.\n", + "Let's use this on the Planets data, for now dropping rows with missing values:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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numberorbital_periodmassdistanceyear
count498.00000498.000000498.000000498.000000498.000000
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std1.175721469.1282593.63627446.5960414.167284
min1.000001.3283000.0036001.3500001989.000000
25%1.0000038.2722500.21250024.4975002005.000000
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75%2.00000999.6000002.86750059.3325002011.000000
max6.0000017337.50000025.000000354.0000002014.000000
\n", + "
" + ], + "text/plain": [ + " number orbital_period mass distance year\n", + "count 498.00000 498.000000 498.000000 498.000000 498.000000\n", + "mean 1.73494 835.778671 2.509320 52.068213 2007.377510\n", + "std 1.17572 1469.128259 3.636274 46.596041 4.167284\n", + "min 1.00000 1.328300 0.003600 1.350000 1989.000000\n", + "25% 1.00000 38.272250 0.212500 24.497500 2005.000000\n", + "50% 1.00000 357.000000 1.245000 39.940000 2009.000000\n", + "75% 2.00000 999.600000 2.867500 59.332500 2011.000000\n", + "max 6.00000 17337.500000 25.000000 354.000000 2014.000000" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "planets.dropna().describe()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This method helps us understand the overall properties of a dataset.\n", + "For example, we see in the `year` column that although exoplanets were discovered as far back as 1989, half of all planets in the dataset were not discovered until 2010 or after.\n", + "This is largely thanks to the *Kepler* mission, which aimed to find eclipsing planets around other stars using a specially designed space telescope." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following table summarizes some other built-in Pandas aggregations:\n", + "\n", + "| Aggregation | Returns |\n", + "|--------------------------|---------------------------------|\n", + "| ``count`` | Total number of items |\n", + "| ``first``, ``last`` | First and last item |\n", + "| ``mean``, ``median`` | Mean and median |\n", + "| ``min``, ``max`` | Minimum and maximum |\n", + "| ``std``, ``var`` | Standard deviation and variance |\n", + "| ``mad`` | Mean absolute deviation |\n", + "| ``prod`` | Product of all items |\n", + "| ``sum`` | Sum of all items |\n", + "\n", + "These are all methods of `DataFrame` and `Series` objects." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To go deeper into the data, however, simple aggregates are often not enough.\n", + "The next level of data summarization is the `groupby` operation, which allows you to quickly and efficiently compute aggregates on subsets of data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## groupby: Split, Apply, Combine\n", + "\n", + "Simple aggregations can give you a flavor of your dataset, but often we would prefer to aggregate conditionally on some label or index: this is implemented in the so-called `groupby` operation.\n", + "The name \"group by\" comes from a command in the SQL database language, but it is perhaps more illuminative to think of it in the terms first coined by Hadley Wickham of Rstats fame: *split, apply, combine*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Split, Apply, Combine\n", + "\n", + "A canonical example of this split-apply-combine operation, where the \"apply\" is a summation aggregation, is illustrated in this figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](images/03.08-split-apply-combine.png)\n", + "\n", + "([figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Split-Apply-Combine))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This illustrates what the `groupby` operation accomplishes:\n", + "\n", + "- The *split* step involves breaking up and grouping a `DataFrame` depending on the value of the specified key.\n", + "- The *apply* step involves computing some function, usually an aggregate, transformation, or filtering, within the individual groups.\n", + "- The *combine* step merges the results of these operations into an output array.\n", + "\n", + "While this could certainly be done manually using some combination of the masking, aggregation, and merging commands covered earlier, an important realization is that *the intermediate splits do not need to be explicitly instantiated*. Rather, the `groupby` can (often) do this in a single pass over the data, updating the sum, mean, count, min, or other aggregate for each group along the way.\n", + "The power of the `groupby` is that it abstracts away these steps: the user need not think about *how* the computation is done under the hood, but rather can think about the *operation as a whole*.\n", + "\n", + "As a concrete example, let's take a look at using Pandas for the computation shown in the following figure.\n", + "We'll start by creating the input `DataFrame`:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " key data\n", + "0 A 0\n", + "1 B 1\n", + "2 C 2\n", + "3 A 3\n", + "4 B 4\n", + "5 C 5" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.DataFrame({'key': ['A', 'B', 'C', 'A', 'B', 'C'],\n", + " 'data': range(6)}, columns=['key', 'data'])\n", + "df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most basic split-apply-combine operation can be computed with the `groupby` method of the `DataFrame`, passing the name of the desired key column:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.groupby('key')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that what is returned is a `DataFrameGroupBy` object, not a set of `DataFrame` objects.\n", + "This object is where the magic is: you can think of it as a special view of the `DataFrame`, which is poised to dig into the groups but does no actual computation until the aggregation is applied.\n", + "This \"lazy evaluation\" approach means that common aggregates can be implemented efficiently in a way that is almost transparent to the user.\n", + "\n", + "To produce a result, we can apply an aggregate to this `DataFrameGroupBy` object, which will perform the appropriate apply/combine steps to produce the desired result:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " data\n", + "key \n", + "A 3\n", + "B 5\n", + "C 7" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.groupby('key').sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `sum` method is just one possibility here; you can apply most Pandas or NumPy aggregation functions, as well as most `DataFrame` operations, as you will see in the following discussion." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The GroupBy Object\n", + "\n", + "The `GroupBy` object is a flexible abstraction: in many ways, it can be treated as simply a collection of ``DataFrame``s, though it is doing more sophisticated things under the hood. Let's see some examples using the Planets data.\n", + "\n", + "Perhaps the most important operations made available by a `GroupBy` are *aggregate*, *filter*, *transform*, and *apply*.\n", + "We'll discuss each of these more fully in the next section, but before that let's take a look at some of the other functionality that can be used with the basic `GroupBy` operation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Column indexing\n", + "\n", + "The `GroupBy` object supports column indexing in the same way as the `DataFrame`, and returns a modified `GroupBy` object.\n", + "For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "planets.groupby('method')" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "planets.groupby('method')['orbital_period']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we've selected a particular `Series` group from the original `DataFrame` group by reference to its column name.\n", + "As with the `GroupBy` object, no computation is done until we call some aggregate on the object:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "method\n", + "Astrometry 631.180000\n", + "Eclipse Timing Variations 4343.500000\n", + "Imaging 27500.000000\n", + "Microlensing 3300.000000\n", + "Orbital Brightness Modulation 0.342887\n", + "Pulsar Timing 66.541900\n", + "Pulsation Timing Variations 1170.000000\n", + "Radial Velocity 360.200000\n", + "Transit 5.714932\n", + "Transit Timing Variations 57.011000\n", + "Name: orbital_period, dtype: float64" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "planets.groupby('method')['orbital_period'].median()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives an idea of the general scale of orbital periods (in days) that each method is sensitive to." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Iteration over groups\n", + "\n", + "The `GroupBy` object supports direct iteration over the groups, returning each group as a `Series` or `DataFrame`:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Astrometry shape=(2, 6)\n", + "Eclipse Timing Variations shape=(9, 6)\n", + "Imaging shape=(38, 6)\n", + "Microlensing shape=(23, 6)\n", + "Orbital Brightness Modulation shape=(3, 6)\n", + "Pulsar Timing shape=(5, 6)\n", + "Pulsation Timing Variations shape=(1, 6)\n", + "Radial Velocity shape=(553, 6)\n", + "Transit shape=(397, 6)\n", + "Transit Timing Variations shape=(4, 6)\n" + ] + } + ], + "source": [ + "for (method, group) in planets.groupby('method'):\n", + " print(\"{0:30s} shape={1}\".format(method, group.shape))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can be useful for manual inspection of groups for the sake of debugging, but it is often much faster to use the built-in `apply` functionality, which we will discuss momentarily." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Dispatch methods\n", + "\n", + "Through some Python class magic, any method not explicitly implemented by the `GroupBy` object will be passed through and called on the groups, whether they are `DataFrame` or `Series` objects.\n", + "For example, using the `describe` method is equivalent to calling `describe` on the `DataFrame` representing each group:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + " method \n", + "count Astrometry 2.0\n", + " Eclipse Timing Variations 9.0\n", + " Imaging 38.0\n", + " Microlensing 23.0\n", + " Orbital Brightness Modulation 3.0\n", + " ... \n", + "max Pulsar Timing 2011.0\n", + " Pulsation Timing Variations 2007.0\n", + " Radial Velocity 2014.0\n", + " Transit 2014.0\n", + " Transit Timing Variations 2014.0\n", + "Length: 80, dtype: float64" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "planets.groupby('method')['year'].describe().unstack()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at this table helps us to better understand the data: for example, the vast majority of planets until 2014 were discovered by the Radial Velocity and Transit methods, though the latter method became common more recently.\n", + "The newest methods seem to be Transit Timing Variation and Orbital Brightness Modulation, which were not used to discover a new planet until 2011.\n", + "\n", + "Notice that these dispatch methods are applied *to each individual group*, and the results are then combined within `GroupBy` and returned.\n", + "Again, any valid `DataFrame`/`Series` method can be called in a similar manner on the corresponding `GroupBy` object." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Aggregate, Filter, Transform, Apply\n", + "\n", + "The preceding discussion focused on aggregation for the combine operation, but there are more options available.\n", + "In particular, `GroupBy` objects have `aggregate`, `filter`, `transform`, and `apply` methods that efficiently implement a variety of useful operations before combining the grouped data.\n", + "\n", + "For the purpose of the following subsections, we'll use this ``DataFrame``:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " data1 data2\n", + "0 7 17\n", + "1 4 3\n", + "2 4 7" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L = [0, 1, 0, 1, 2, 0]\n", + "df.groupby(L).sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course, this means there's another, more verbose way of accomplishing the `df.groupby('key')` from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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data1data2
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A38
B57
C712
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" + ], + "text/plain": [ + " data1 data2\n", + "key \n", + "A 3 8\n", + "B 5 7\n", + "C 7 12" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.groupby(df['key']).sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### A dictionary or series mapping index to group\n", + "\n", + "Another method is to provide a dictionary that maps index values to the group keys:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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df2

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data1data2
key
A05
B10
C23
A33
B47
C59
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df2.groupby(mapping).sum()

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data1data2
key
consonant1219
vowel38
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" + ], + "text/plain": [ + "df2\n", + " data1 data2\n", + "key \n", + "A 0 5\n", + "B 1 0\n", + "C 2 3\n", + "A 3 3\n", + "B 4 7\n", + "C 5 9\n", + "\n", + "df2.groupby(mapping).sum()\n", + " data1 data2\n", + "key \n", + "consonant 12 19\n", + "vowel 3 8" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df2 = df.set_index('key')\n", + "mapping = {'A': 'vowel', 'B': 'consonant', 'C': 'consonant'}\n", + "display('df2', 'df2.groupby(mapping).sum()')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Any Python function\n", + "\n", + "Similar to mapping, you can pass any Python function that will input the index value and output the group:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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data1data2
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a1.54.0
b2.53.5
c3.56.0
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" + ], + "text/plain": [ + " data1 data2\n", + "key \n", + "a 1.5 4.0\n", + "b 2.5 3.5\n", + "c 3.5 6.0" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df2.groupby(str.lower).mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### A list of valid keys\n", + "\n", + "Further, any of the preceding key choices can be combined to group on a multi-index:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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data1data2
keykey
avowel1.54.0
bconsonant2.53.5
cconsonant3.56.0
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" + ], + "text/plain": [ + " data1 data2\n", + "key key \n", + "a vowel 1.5 4.0\n", + "b consonant 2.5 3.5\n", + "c consonant 3.5 6.0" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df2.groupby([str.lower, mapping]).mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Grouping Example\n", + "\n", + "As an example of this, in a few lines of Python code we can put all these together and count discovered planets by method and by decade:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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decade1980s1990s2000s2010s
method
Astrometry0.00.00.02.0
Eclipse Timing Variations0.00.05.010.0
Imaging0.00.029.021.0
Microlensing0.00.012.015.0
Orbital Brightness Modulation0.00.00.05.0
Pulsar Timing0.09.01.01.0
Pulsation Timing Variations0.00.01.00.0
Radial Velocity1.052.0475.0424.0
Transit0.00.064.0712.0
Transit Timing Variations0.00.00.09.0
\n", + "
" + ], + "text/plain": [ + "decade 1980s 1990s 2000s 2010s\n", + "method \n", + "Astrometry 0.0 0.0 0.0 2.0\n", + "Eclipse Timing Variations 0.0 0.0 5.0 10.0\n", + "Imaging 0.0 0.0 29.0 21.0\n", + "Microlensing 0.0 0.0 12.0 15.0\n", + "Orbital Brightness Modulation 0.0 0.0 0.0 5.0\n", + "Pulsar Timing 0.0 9.0 1.0 1.0\n", + "Pulsation Timing Variations 0.0 0.0 1.0 0.0\n", + "Radial Velocity 1.0 52.0 475.0 424.0\n", + "Transit 0.0 0.0 64.0 712.0\n", + "Transit Timing Variations 0.0 0.0 0.0 9.0" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "decade = 10 * (planets['year'] // 10)\n", + "decade = decade.astype(str) + 's'\n", + "decade.name = 'decade'\n", + "planets.groupby(['method', decade])['number'].sum().unstack().fillna(0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This shows the power of combining many of the operations we've discussed up to this point when looking at realistic datasets: we quickly gain a coarse understanding of when and how extrasolar planets were detected in the years after the first discovery.\n", + "\n", + "I would suggest digging into these few lines of code and evaluating the individual steps to make sure you understand exactly what they are doing to the result.\n", + "It's certainly a somewhat complicated example, but understanding these pieces will give you the means to similarly explore your own data." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.09-Pivot-Tables.ipynb b/notebooks/03.09-Pivot-Tables.ipynb new file mode 100644 index 000000000..ed06e806d --- /dev/null +++ b/notebooks/03.09-Pivot-Tables.ipynb @@ -0,0 +1,1659 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Pivot Tables" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have seen how the `groupby` abstraction lets us explore relationships within a dataset.\n", + "A *pivot table* is a similar operation that is commonly seen in spreadsheets and other programs that operate on tabular data.\n", + "The pivot table takes simple column-wise data as input, and groups the entries into a two-dimensional table that provides a multidimensional summarization of the data.\n", + "The difference between pivot tables and `groupby` can sometimes cause confusion; it helps me to think of pivot tables as essentially a *multidimensional* version of `groupby` aggregation.\n", + "That is, you split-apply-combine, but both the split and the combine happen across not a one-dimensional index, but across a two-dimensional grid." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "## Motivating Pivot Tables\n", + "\n", + "For the examples in this section, we'll use the database of passengers on the *Titanic*, available through the Seaborn library (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "titanic = sns.load_dataset('titanic')" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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survivedpclasssexagesibspparchfareembarkedclasswhoadult_maledeckembark_townalivealone
003male22.0107.2500SThirdmanTrueNaNSouthamptonnoFalse
111female38.01071.2833CFirstwomanFalseCCherbourgyesFalse
213female26.0007.9250SThirdwomanFalseNaNSouthamptonyesTrue
311female35.01053.1000SFirstwomanFalseCSouthamptonyesFalse
403male35.0008.0500SThirdmanTrueNaNSouthamptonnoTrue
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" + ], + "text/plain": [ + " survived pclass sex age sibsp parch fare embarked class \\\n", + "0 0 3 male 22.0 1 0 7.2500 S Third \n", + "1 1 1 female 38.0 1 0 71.2833 C First \n", + "2 1 3 female 26.0 0 0 7.9250 S Third \n", + "3 1 1 female 35.0 1 0 53.1000 S First \n", + "4 0 3 male 35.0 0 0 8.0500 S Third \n", + "\n", + " who adult_male deck embark_town alive alone \n", + "0 man True NaN Southampton no False \n", + "1 woman False C Cherbourg yes False \n", + "2 woman False NaN Southampton yes True \n", + "3 woman False C Southampton yes False \n", + "4 man True NaN Southampton no True " + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "titanic.head()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As the output shows, this contains a number of data points on each passenger on that ill-fated voyage, including sex, age, class, fare paid, and much more." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pivot Tables by Hand\n", + "\n", + "To start learning more about this data, we might begin by grouping according to sex, survival status, or some combination thereof.\n", + "If you read the previous chapter, you might be tempted to apply a `groupby` operation—for example, let's look at survival rate by sex:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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male0.188908
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" + ], + "text/plain": [ + " survived\n", + "sex \n", + "female 0.742038\n", + "male 0.188908" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "titanic.groupby('sex')[['survived']].mean()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us some initial insight: overall, three of every four females on board survived, while only one in five males survived!\n", + "\n", + "This is useful, but we might like to go one step deeper and look at survival rates by both sex and, say, class.\n", + "Using the vocabulary of `groupby`, we might proceed using a process like this:\n", + "we first *group by* class and sex, then *select* survival, *apply* a mean aggregate, *combine* the resulting groups, and finally *unstack* the hierarchical index to reveal the hidden multidimensionality. In code:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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male0.3688520.1574070.135447
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" + ], + "text/plain": [ + "class First Second Third\n", + "sex \n", + "female 0.968085 0.921053 0.500000\n", + "male 0.368852 0.157407 0.135447" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "titanic.groupby(['sex', 'class'])['survived'].aggregate('mean').unstack()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us a better idea of how both sex and class affected survival, but the code is starting to look a bit garbled.\n", + "While each step of this pipeline makes sense in light of the tools we've previously discussed, the long string of code is not particularly easy to read or use.\n", + "This two-dimensional `groupby` is common enough that Pandas includes a convenience routine, `pivot_table`, which succinctly handles this type of multidimensional aggregation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pivot Table Syntax\n", + "\n", + "Here is the equivalent to the preceding operation using the `DataFrame.pivot_table` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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classFirstSecondThird
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female0.9680850.9210530.500000
male0.3688520.1574070.135447
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" + ], + "text/plain": [ + "class First Second Third\n", + "sex \n", + "female 0.968085 0.921053 0.500000\n", + "male 0.368852 0.157407 0.135447" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "titanic.pivot_table('survived', index='sex', columns='class', aggfunc='mean')" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is eminently more readable than the manual `groupby` approach, and produces the same result.\n", + "As you might expect of an early 20th-century transatlantic cruise, the survival gradient favors both higher classes and people recorded as females in the\n", + "data. First-class females survived with near certainty (hi, Rose!), while only one in eight or so third-class males survived (sorry, Jack!)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multilevel Pivot Tables\n", + "\n", + "Just as in a `groupby`, the grouping in pivot tables can be specified with multiple levels and via a number of options.\n", + "For example, we might be interested in looking at age as a third dimension.\n", + "We'll bin the age using the `pd.cut` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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classFirstSecondThird
sexage
female(0, 18]0.9090911.0000000.511628
(18, 80]0.9729730.9000000.423729
male(0, 18]0.8000000.6000000.215686
(18, 80]0.3750000.0714290.133663
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" + ], + "text/plain": [ + "class First Second Third\n", + "sex age \n", + "female (0, 18] 0.909091 1.000000 0.511628\n", + " (18, 80] 0.972973 0.900000 0.423729\n", + "male (0, 18] 0.800000 0.600000 0.215686\n", + " (18, 80] 0.375000 0.071429 0.133663" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "age = pd.cut(titanic['age'], [0, 18, 80])\n", + "titanic.pivot_table('survived', ['sex', age], 'class')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can apply the same strategy when working with the columns as well; let's add info on the fare paid, using `pd.qcut` to automatically compute quantiles:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "fare (-0.001, 14.454] (14.454, 512.329] \\\n", + "class First Second Third First \n", + "sex age \n", + "female (0, 18] NaN 1.000000 0.714286 0.909091 \n", + " (18, 80] NaN 0.880000 0.444444 0.972973 \n", + "male (0, 18] NaN 0.000000 0.260870 0.800000 \n", + " (18, 80] 0.0 0.098039 0.125000 0.391304 \n", + "\n", + "fare \n", + "class Second Third \n", + "sex age \n", + "female (0, 18] 1.000000 0.318182 \n", + " (18, 80] 0.914286 0.391304 \n", + "male (0, 18] 0.818182 0.178571 \n", + " (18, 80] 0.030303 0.192308 " + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fare = pd.qcut(titanic['fare'], 2)\n", + "titanic.pivot_table('survived', ['sex', age], [fare, 'class'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a four-dimensional aggregation with hierarchical indices (see [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb)), shown in a grid demonstrating the relationship between the values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Additional Pivot Table Options\n", + "\n", + "The full call signature of the `DataFrame.pivot_table` method is as follows:\n", + "\n", + "```python\n", + "# call signature as of Pandas 1.3.5\n", + "DataFrame.pivot_table(data, values=None, index=None, columns=None,\n", + " aggfunc='mean', fill_value=None, margins=False,\n", + " dropna=True, margins_name='All', observed=False,\n", + " sort=True)\n", + "```\n", + "\n", + "We've already seen examples of the first three arguments; here we'll take a quick look at some of the remaining ones.\n", + "Two of the options, `fill_value` and `dropna`, have to do with missing data and are fairly straightforward; I will not show examples of them here.\n", + "\n", + "The `aggfunc` keyword controls what type of aggregation is applied, which is a mean by default.\n", + "As with `groupby`, the aggregation specification can be a string representing one of several common choices (`'sum'`, `'mean'`, `'count'`, `'min'`, `'max'`, etc.) or a function that implements an aggregation (e.g., `np.sum()`, `min()`, `sum()`, etc.).\n", + "Additionally, it can be specified as a dictionary mapping a column to any of the desired options:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " fare survived \n", + "class First Second Third First Second Third\n", + "sex \n", + "female 106.125798 21.970121 16.118810 91 70 72\n", + "male 67.226127 19.741782 12.661633 45 17 47" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "titanic.pivot_table(index='sex', columns='class',\n", + " aggfunc={'survived':sum, 'fare':'mean'})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice also here that we've omitted the `values` keyword; when specifying a mapping for `aggfunc`, this is determined automatically." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At times it's useful to compute totals along each grouping.\n", + "This can be done via the ``margins`` keyword:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "class First Second Third All\n", + "sex \n", + "female 0.968085 0.921053 0.500000 0.742038\n", + "male 0.368852 0.157407 0.135447 0.188908\n", + "All 0.629630 0.472826 0.242363 0.383838" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "titanic.pivot_table('survived', index='sex', columns='class', margins=True)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, this automatically gives us information about the class-agnostic survival rate by sex, the sex-agnostic survival rate by class, and the overall survival rate of 38%.\n", + "The margin label can be specified with the `margins_name` keyword; it defaults to `\"All\"`." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Birthrate Data\n", + "\n", + "As another example, let's take a look at the freely available data on births in the United States, provided by the Centers for Disease Control (CDC).\n", + "This data can be found at https://raw.githubusercontent.com/jakevdp/data-CDCbirths/master/births.csv\n", + "(this dataset has been analyzed rather extensively by Andrew Gelman and his group; see, for example, the [blog post on signal processing using Gaussian processes](http://andrewgelman.com/2012/06/14/cool-ass-signal-processing-using-gaussian-processes/)):\n", + "\n", + "[^1]: The CDC dataset used in this section uses the sex assigned at birth, which it calls \"gender,\" and limits the data to male and female. While gender is a spectrum independent of biology, I will be using the same terminology while discussing this dataset for consistency and clarity." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# shell command to download the data:\n", + "# !cd data && curl -O \\\n", + "# https://raw.githubusercontent.com/jakevdp/data-CDCbirths/master/births.csv" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "births = pd.read_csv('data/births.csv')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Taking a look at the data, we see that it's relatively simple—it contains the number of births grouped by date and gender:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " year month day gender births\n", + "0 1969 1 1.0 F 4046\n", + "1 1969 1 1.0 M 4440\n", + "2 1969 1 2.0 F 4454\n", + "3 1969 1 2.0 M 4548\n", + "4 1969 1 3.0 F 4548" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "births.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can start to understand this data a bit more by using a pivot table.\n", + "Let's add a `decade` column, and take a look at male and female births as a function of decade:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "gender F M\n", + "decade \n", + "1960 1753634 1846572\n", + "1970 16263075 17121550\n", + "1980 18310351 19243452\n", + "1990 19479454 20420553\n", + "2000 18229309 19106428" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "births['decade'] = 10 * (births['year'] // 10)\n", + "births.pivot_table('births', index='decade', columns='gender', aggfunc='sum')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that male births outnumber female births in every decade.\n", + "To see this trend a bit more clearly, we can use the built-in plotting tools in Pandas to visualize the total number of births by year, as shown in the following figure (see [Introduction to Matplotlib](04.00-Introduction-To-Matplotlib.ipynb) for a discussion of plotting with Matplotlib):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "births.pivot_table(\n", + " 'births', index='year', columns='gender', aggfunc='sum').plot()\n", + "plt.ylabel('total births per year');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With a simple pivot table and the `plot` method, we can immediately see the annual trend in births by gender. By eye, it appears that over the past 50 years male births have outnumbered female births by around 5%." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Though this doesn't necessarily relate to the pivot table, there are a few more interesting features we can pull out of this dataset using the Pandas tools covered up to this point.\n", + "We must start by cleaning the data a bit, removing outliers caused by mistyped dates (e.g., June 31st) or missing values (e.g., June 99th).\n", + "One easy way to remove these all at once is to cut outliers; we'll do this via a robust sigma-clipping operation:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "quartiles = np.percentile(births['births'], [25, 50, 75])\n", + "mu = quartiles[1]\n", + "sig = 0.74 * (quartiles[2] - quartiles[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This final line is a robust estimate of the sample standard deviation, where the 0.74 comes from the interquartile range of a Gaussian distribution (you can learn more about sigma-clipping operations in a book I coauthored with Željko Ivezić, Andrew J. Connolly, and Alexander Gray: [*Statistics, Data Mining, and Machine Learning in Astronomy*](https://press.princeton.edu/books/hardcover/9780691198309/statistics-data-mining-and-machine-learning-in-astronomy) (Princeton University Press)).\n", + "\n", + "With this, we can use the `query` method (discussed further in [High-Performance Pandas: `eval()` and `query()`](03.12-Performance-Eval-and-Query.ipynb)) to filter out rows with births outside these values:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "births = births.query('(births > @mu - 5 * @sig) & (births < @mu + 5 * @sig)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we set the `day` column to integers; previously it had been a string column because some columns in the dataset contained the value `'null'`:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# set 'day' column to integer; it originally was a string due to nulls\n", + "births['day'] = births['day'].astype(int)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can combine the day, month, and year to create a date index (see [Working with Time Series](03.11-Working-with-Time-Series.ipynb)).\n", + "This allows us to quickly compute the weekday corresponding to each row:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# create a datetime index from the year, month, day\n", + "births.index = pd.to_datetime(10000 * births.year +\n", + " 100 * births.month +\n", + " births.day, format='%Y%m%d')\n", + "\n", + "births['dayofweek'] = births.index.dayofweek" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using this, we can plot births by weekday for several decades (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "\n", + "births.pivot_table('births', index='dayofweek',\n", + " columns='decade', aggfunc='mean').plot()\n", + "plt.gca().set(xticks=range(7),\n", + " xticklabels=['Mon', 'Tues', 'Wed', 'Thurs', 'Fri', 'Sat', 'Sun'])\n", + "plt.ylabel('mean births by day');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Apparently births are slightly less common on weekends than on weekdays! Note that the 1990s and 2000s are missing because starting in 1989, the CDC data contains only the month of birth.\n", + "\n", + "Another interesting view is to plot the mean number of births by the day of the year.\n", + "Let's first group the data by month and day separately:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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births
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" + ], + "text/plain": [ + " births\n", + "1 1 4009.225\n", + " 2 4247.400\n", + " 3 4500.900\n", + " 4 4571.350\n", + " 5 4603.625" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "births_by_date = births.pivot_table('births', \n", + " [births.index.month, births.index.day])\n", + "births_by_date.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a multi-index over months and days.\n", + "To make this visualizable, let's turn these months and days into dates by associating them with a dummy year variable (making sure to choose a leap year so February 29th is correctly handled!):" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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births
2012-01-014009.225
2012-01-024247.400
2012-01-034500.900
2012-01-044571.350
2012-01-054603.625
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" + ], + "text/plain": [ + " births\n", + "2012-01-01 4009.225\n", + "2012-01-02 4247.400\n", + "2012-01-03 4500.900\n", + "2012-01-04 4571.350\n", + "2012-01-05 4603.625" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from datetime import datetime\n", + "births_by_date.index = [datetime(2012, month, day)\n", + " for (month, day) in births_by_date.index]\n", + "births_by_date.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Focusing on the month and day only, we now have a time series reflecting the average number of births by date of the year.\n", + "From this, we can use the `plot` method to plot the data. It reveals some interesting trends, as you can see in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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fODqRKIOWv904Ha1axcZezu9QRTNWh4tF0zMYP8LIBwcqz2A1/jWYbcRF6nv8+ujkKGparL4PMueifKInUzNjAdhzqnHAzkEIaP/AHaHXYJZMsRBCDE/1nhrU+EgDo5OjsDlcvQaFAGarg7f3uIPhTwqrg/55n3qOXRdEQLjlWC1Gg5ZbLxjJnFEJbDxag6Kcfguv9kxx5/KIk/WtmG1OLhqXRJhO3etmO2+pxYQ0d0/9cL2Giekx7DoReELbzhP1gHuT2VcmjmBHSX1QpRp9UWe2ER8gKB6VFAXAZk8JyUCWT0xIi0arhj0nGwfsHIQAdz1xktHAuBFG2iQoFkKI4anO7N7oFB+pY3SyO2Aqqu69rvjdveWYrA4uzUvmYHkzVUFcAm+x2H0bzT442HtQvOdkI1MyY1GrVcwbk0hpQ1ufu0PYnS4URaG62eLbVd41U+zdZDchLYas+AhKevlQcKiiCaNBS0Zce5eO80bG8WVpY8Aep7tKGsiICyclOozrZ2SgU6v580dH+rSe3tSbbSQECoo9j/EXRbXoNKqAx55tYToNOXEGvjwl457FwNp+vJ7zcxOI1GtplfIJIYQYnrz9cr2ZYoCjQQTFL28/ydiUKH5+xTgAPgsiW7y5uA6HS+HSvBQKK1s4GSDAbbM5Kaxs8V1inzcmCYCNRcGVULy9p4xrntxE/j3r+O3bB3xZ4tzEyG41xYfKm9GoVYxJiSIrPqJTpry62cJ7+yo6ZagPlTeTlxaNStVetzsjOx6bw8WBsia/56MoCjtLGpiZ7W5FlhEXwTcvyOb13aVBlZIEq7fyicy4cPQaNdUtVpKNYd1qj8+18YkG9pc2BV2yI0R/qzfbqGy2MCk9hnC9RjbaCSHEcNUeFOuJDtMxIjqMo9WBN87Vm23sK23i2mkZjEsxkh4bHlQJxfrDNUQZtPz6a+OBwNni/WXuQGlaViwAIxMiSI8NZ2MQwzUOljfxi9f3YrW7mJoZy5odp3zlGhePT6bGZMXudAHgcLr4tLCaMclRhOk0ZMVHcrK+FUVR+OBgJVf8eQM/fHk3+0rdwa7TpVBY2UJ+anSnn+ntu7uzhxKKSk+m2tszGOBHF48hOkzHI+8X9rqmYLhcCg2tgTPFWo3aN9gjJdrQ43HnyvgkA2abk4Pl/j9MCHG2FVa6P5SOTzUSKUGxEEIMX/VmG1q1iugwd0v60clRFPeSKa4zucsQ0uPCUalUXDw+iS+KagOWDiiKwueHq7lwdAK5SVHkpUYHDIq9l9S9mWKVSsWFoxPYfqIeV4CsotXh5Kev7iU2Qs+a783hrzdOQ6NS8erOU+QkRjI6OQpFgWpPKcU/Nx3nUEWzr2dwVnw4rTYna3ac4vurd/n6Ge/w1AOX1JlptTnJT+scFCdGGchNjGRHD0Fx1zpkgJgIHd9fkMuGIzUU90MrvMY2Oy6FgDXFgO+KwEDWE3udlxGBXqPmrT1lA30qYpgqrHAnAcaPiCZcr5WgWAghhqt6z+V2bynAaE8f20Ab2urM7R0rAC4Zn0Krzcm2Y/U93qegooXyJgsLPB0eLs1LZvfJBpot/nsP7znZSFZ8RKchFLNzEmhstXM4QAu4v31SxOGqFh67bjJxkXpSY8K5fqZ76MeEtGhft4XKpjaKa0ys/OgIl+encNXkVACyEyIBuOc/Bxg/wsg7d1xIZny4LwPsrT/umikGmJEdx66Ser+/u0PlzahUML7L/a6fnoFaBW/tPvOgsGPWPxDvZrvBEBQbDRouy0/hP1+WY3O4Bvp0xDBUUNFMYpSeJKOBCL1GWrIJIcRwVddlY9aYlCjMNqffXr5eDZ7gKy7Cfb/zRyUQplP7Okv48/zm44Tp1FwxIQWAObkJuBT35jN/vjzV6MsSe83KiQdgWw99jotrTPzfhmIWTUvnYk8vYIDbF4xCr1UzMzuOVE9QXNFkYdWm42jVKh68dqLvQ0FWgru0QFHgicVTMGg1nJcdz05PsHuovBmtp/64q1k58TS02n2dHTo6WN7MyIRIogydh8QmR4dx4ehE3tpTFjADHoxgg2Jvpngg27F1dP3MDOrNNj4t7P++zUL0prCyhfEj3B9WI/QaWu3OgEkBCYqFECJE1Xdp4TV+hBFoLxfwe5/WzsFXmE7DBaMS+bSw2u+bSVWzhbf3lHPDjExf5nd6VhxatcpvdrmyyUJFk8VXT+yVGe+uK97uObcDZU1YPNlFRVG4752DhOk03P21vG7327TiYm6ek01qdLjvZ2w9VsfsnPhOI58z4sJJNhr42eXjmJAWA8DMkfHUmmycqGtlw9EaxqYYMWg13c776ilppMeG88C7h3A4O2c9D1U0+80uAyyank5ZY1vA33kw6n2dRAIHxWNT3I9xZlzEGf28/jJ/TBIp0QZe21k60KcihhmH08WRqhbyUt1/E+F6DYoC1gBXLSQoFkKIENXQJSielhlHZnw4r2w/GfA+AHGR7aOEF45P5mR9K8U13afBPffFCRwuF9+Zl+O7LVyvYXJGDNuPd8+q7ittBGByRmy3r83OiWf78Xp2nqjnqr9t4u1D7g1anx+pYePRWn5++TiSjN03kCUbw9Bq1ESHawnXadhf1sSxGjNzchM6HWfQath69yXcftEo323neTbRPbaukANlzXzzgmy/v5cwnYbfXZXH4aoWXtxa4ru92WLnZH1rtzpkrysmjCBCrznjutp6s7sUpbegOC81mpe/M9uXtR9oGrWKb0xLZ/2Rmh7LaYQ4G07UtWJ1uHyZ4ki9+0qO2dpzCYUExUIIEaK6lk+o1SqWnpfF1mP1PW7+qjPbiDJoO2VLveUKXS+BWx1OXtpawlcnpfrqdb1m5yawr7SpW1/Qg576W2/2pvN93FnbO17ZA8D+KneZx/rDNUToNSybnRVwvSqVitSYMD70jFie3SUo9v4OOhqVFEVshI73D1SSFR/BoukZPX7/KyaMYO7oRP708VFfh4sCzya7noLiCL2Wr0wcwX/3VQR8M+5NsJligAtGJ6LVDJ639wtHJeJ0Kew7JV0oxLnjbYc4vkOmGAi42W7w/NUIIYToN3ani6Y2e7e+tjfMzECrVvHKNv/ZYncvXF2n29Jjwxk/wtitrvh4rZkWq4MrJozo9n1m5cTjcCndJpodLG8mNzGSCL22231m57iD2IomC7mJkRTUWHC6FLYdr2dGdhy6IAK9ETFhtNmdROo1TOwhUO1IrVb5+gvfsXB0wJ+hUqm4aXYWTW129nrGF7cPB+n5Zy2blYXJ6uDdveXYnS5++/Z+9pzs21ALfx9WhoqpWbGoVHRas6Io/P2zIt/vUYj+Vljp7lHurbOP8ATFbXYJioUQYlhpaO3cRcIr2RjG5RNSeH13qd82a/WtduIjumcjF45PZueJBpra2i+Be6fjjU7qvjFtZnYcalX3jXOHypuYmB7j95yzEyLIio/gonFJ/GjhaNrsCjtO1FNY2cyskfG9rNjNu8Fsxsj4oLOl18/I4NK8FK6dlt7rseePSkClco+OBXeQnxhl6FS73NWM7DjGpkTx8vaTPL2+mBe3ngxqFHZH/j6sDBXRYTpGJ0Wxu0NQ/O6+Ch7/4DA/XrMnYLs/IU7XkSoTOYmRvg+SEZIpFkKI4anjNLuurpmSTmOrnf2l3S9n9zQ1beH4ZBwuhY1H2wdsFFebUakgJzGy2/HGMB0T02N4adtJXth8AovdSb3ZRnmTpcesqkql4u0fXsjTN89gZrY7CH7682IUBc7LCS4o9nagmJMb3PEAX5mYyj+/OTOoIDo2Qs/EtBi+KKpFURS+PNXYY+mEl0qlYtmsLPaVNvHnT44C7b2Ug1Vntvl9LIeKaVmx7DnViKIomK0OHnrvECnRBkrqWnlh84mBPj0RgupM1k5DbMJ17qtTgUY9S1AshBBDTL3ZRmmTjermnlurBWrh5d1c5m8YRdeOFV7TsuKIjdB1KqEorjGRHhvuq9Xr6uFrJ5GbFMm97xz0jGN2B+Hezg/+xEfqCdNpyIwPJy5cw/rDNeg16m4t3HqSGuPuQOEtxTgbLhydyO6TDaw7UElRtYmvTuxePtLVtdMyMGjVxITrGJUUSXVLz4+dP/VmG/ERQzNTDO6OJI2tdk7UtfLXT45S1WzlHzfNYOH4ZP72SRG1pr59SBCiN41tdmLD21/LIg2eTLFVMsVCCBES7E4XX/nzBr77dimzHv6E9/ZV+D0uUFCc4JnQtquke5swd/DV/T4atYqLxiax/nANTk/P3eIak29YhD8T02NY+/3z+eb52by9p4xPCtwBdaD6Wy+VSkV+sjvrOyUzhjBdcLW0V09O4/dfn8C0IIPo0zF3dCIOl8KKN/aRFhPGdQE253nFROj4243TePaWmYxJNlLd3LcgsGHIZ4rdH8T+tek4z248xpKZmczIjuPXX8vDZHPwb8kWi37W1GonpsMHSV/5xJnWFF977bUsX76c5cuXc/fdd/Pll19yww03sHTpUp588kkAXC4X99xzD0uWLGH58uWUlLhb1vg7VgghxOnZXFxHdYuVJZNiATha7X8CXG/DHmaOjGNXSUOnoRJtNidtdqff8gmAhXkp1Jtt7C1txOVSOFZjDhgUgzu4/c68XFyKwr+3nCA9NpxYP0G3PxOS3EHgrCBLJ8AdfC4/f2S3LhP9aebIOPRaNc0WBz+4yD08JBiXTxjBjOw4kqMNfssnjtWYWPz0Fr77752dblcUxd1JJCq439tgNCY5CqNBy+qtJaTGhPObq9z9pkcnR7FgbBKv7jzVrf+zEKdLURRPprg9KA73bO4NNNWu179kq9WKoiisXr2a1atX88gjj3DvvffyxBNP8Morr7B3714OHTrExx9/jM1m49VXX+VnP/sZf/jDHwD8HiuEEOL0/HdvOUaDlmVTYomL0PV42bnO5J1M5/+S+8xs94S2Y7XtrdkaWgMH0gvGJKFRq/issJqKZgttdqdvZ3cgmfERfHVSKi6l59Zl/kxPi0CnUbGwwwS7wSBMp/EMBjGweGZmn++fbDTQ1GbH0iFj9WlhFV/760a2n6jn08LqTu3b2uxOrA6Xb8rgUKRWq5jiyd7/8YYpRIe1Py9vnJVFVbM14NREIfrCZHXgdCnEdswU6/pho11hYSFtbW3cdttt3HLLLezYsQObzUZWVhYqlYq5c+eyefNmdu3axbx58wCYOnUqBw4cwGQy+T1WCCFE39kcLj44WMll+SnoNWoSowzUttj8HtvQaiM2Qtfj5rGZnrrinR3qinvLLsdE6JiZHcd/91VwtMqdoR6V1H2TnT/fnZcLwKQeOk/4kx2nZ/99VzAjO/hM8bnyxOIpvHH7BUGXdXTk7VRR48kWN7XZ+eXr+xmZEMlj103G6XJv4PPyfsDp2klkqPnZ5WP5y9KpnD+qc733JeOTSYk2BBwqI0RfNLa6u+R0vCoVYeg9KO7eKLKLsLAwvv3tb3PDDTdw4sQJvvvd7xId3f5JPzIyklOnTmEymYiKas8YaDSabrd5j/WnoKCgt1MZ0iwWS8itMRTX1FUorzGU1+YVamvcdspMs8XBlHgnFouFCLWDk9UNftd4oqKWKG3Pr62KohATpubjvceZYnRPqvuyrBWA5poKCgr899G9KFPLoxvq+fO6AwC4GisoKOg9w2cA7r9kBHkJ1qAfE4vFwvGiI0EdO1AKqno/pitLo/v3vGP/YXKi4e5XtlBvtnLvRYmk6ptRAe/vOEK83d3pY/1xdzZfZa6loMD/0JXBqOvfXxgw1gAFBc3djl04Mpw1+2rYsHM/SZG9hiaDQqi9vnQ1lNdXVOf+wGmqq/L9zSiKgloFJ8urmBPtv4Vir8+8nJwcsrOzUalU5OTkYDQaaWxs9H3dbDYTHR2NxWLBbG4fAepyuYiKiup0m/dYf/Ly8vzeHioKCgpCbo2huKauQnmNobw2r1Bb47P7vyQmXMeNF0+j+OhhslLi2Vfa6HeNjk1NpMTpA65/dm4rh6tafMccsZYBlUzLH9NjWcSYsS5e3LeeLyvaiAnXMWfaBFSq4Op3+/pQhNrj5+WKaYJPKolIGEFpYxX/O9LCt+fmcPXcfADGr6/nhFnjW/ufduwk2WjguvlTz2qtdH/ry+P3vSQzr+xbT7E1ivkzc3q/wyAQqs9Pr6G8vrqjtUAZE8fmktdhT0Kk/hQR0bGA/+4vvZZPvP7667764KqqKtra2oiIiODkyZMoisKmTZuYOXMm06dPZ8OGDYB7c93YsWOJiopCp9N1O1YIIUTf7SttYlZOvG9jV1KUgdoe+t2arQ6MYYHzHheMSqCkrpXjte7khbd8ItBleq1Gza0XjgTcpRPBBsSinbd8oqrZyu7yNgB+dPFo39dnZsex52QDDqeLFoud9Udq+Nqk1CEVEPdVTmIko5Oj+OiQO/X+8P8KuOVf2wf4rMRQ5d0fEdtlT0W4XkPbmZRPXH/99dx9993ceOONqFQqHn74YdRqNT//+c9xOp3MnTuXKVOmMGnSJL744guWLl2Koig8/PDDANx///3djhVCCNE3LpfCyfrWTpvOEo16zDYnbTZnt17BJquDjLiIgN/zkrwU7nv3EJ8UVPGdebnUm22oVRAdHrgf7tJZWfzt0yLyUoPfNCfaJUTq0ahVVLdYOFZvJT02vFPHj5kj41i9tYTCyhaOVrdgc7i4ekrqAJ7xuXFZfgrPbDhGcY2J5zefQK1yX/KWD16h7ZH3CzhRa+avN07rNMb8cGULY1OiTuvxb/RM3ozt8loWodecWU2xXq/niSee6Hb72rVrO/1brVbzwAMPdDtu6tSp3Y4VQgjRN1UtFmwOF1nx7YFuYpS7ZVmtyUpmfOcAuNXm9DWr70lmfATjUox83CEojo1wB2yBRBm0/PeOub0Gz8I/tVpFYpSe6mYrxxps5Kd33kh4nmek9f/2V7CvtIm0mDCmZcYNxKmeU5flp/DU+mJ++NJubA53e7bGVnuPLQLF0Gd3unh560larA5++fo+/rxkKiqVinUHKvjBi7v5922zmD82qc/ft8mTKe76GhWh13om2vkvlJDhHUIIMQSU1Lk3Z2UntAe/SZ6guMZPWzaz1UGEvvcNS5fkJbPjRANNrXYaWm09tnDrKjM+ghgJik9bsjGMk/WtlDXbye+ScU+LDScjLpx/rC9mU1EtV09JC+nSCa+pGbEkGQ0UVrZgNLifu+VNbQN8VuJs2nmigRarg7mjE/nPl+Ws/OgITpfCHz90b7A9VNF9U2YwGlvthOs03brD9JYplqBYCCGGgJI6d91vdnx7CzRfprhLXbGiKJiDyBSDu4TC6VJYf6SaerONhCE8NW0oSTYa2H2yAZeC3zKU52+dxdM3z+D5W8/jzkvHDsAZnntqtYpL89zlQT9a6K6xrmjs2zhsMbSsP1yNTqPi6eUzWDIzk799WsSPXt5NUbUJlQqKqk+v20pjm71bPTG4a4rPqHxCCCHEwCupa0WrVpEW295KKNHovqxca+rcq9jqcOF0KUFliqdmxpIQqef/Pj9GrcnKtKzYfj1v4V9ytAG70z1N0N/Y69HJUUENRgk1/++i0UxIi+Gy/BQeeb+QiubuQbHN4eKTgiouzU9B10MfbjE0fFpYzeycBKIMWh68diLlTW28f6CS/NRoosO1FNecZlDcavc7OTNCrwk4Yl2eTUIIMQSU1LeSHhfeaRiHN6vbdaqdNxMSZeg9KNaoVaz4yniqWyxUt1hJjQnvx7MWPUnydKCI0KnIiJPfuVdmfAQ3z8kmMcqAVq2iorF7+cSHhyq5/aXd/OK1vZ3GlIuh5VR9K0erTVw0zl0zrNOo+ftN07luegYPXTuRMclGiqpNKErfH+OmNlu3TXbgrik2BxjzLJliIYQYAk7WtXbaZAeg16qJCe8+6tk7IjhCH9y0tcXnZXLdjAwOlTeTlRC4Y4XoH8lG9wea3DiDdFfwQ6NWkRIdRkVT90zxXs+0v7e/LCcmXMf9X594js9O9If1R9zDaS7u0FEnOkzHE4vdXcr2lTbRYnFQ02IluYdhGz1pbLX7vdIS0UtLNskUCyHEEFBSZ+60yc4rMUrfPSj2ZEIig8gUe2nUKiZlxMjmuXPEFxTHS2eFnqTFhlHuJ1O8v6yJKZmx3DQ7ixe2lFDnZ6OpGPwOlTcRH6knN9H/qHhvUHs6dcU91RTLRjshhBjiGlttNFscjEzo/uaRZDRQ09I1U+x+0e9LUCzOrREx7syXBMU9GxET3i1T7HIpHChrZlJ6NJfmpwBwrNbs7+5ikKtsspAaE9bjlZJRSZ6guI91xYqi0NhqIya8+99WuF5Lm12CYiGEGJS2HqvjP1+WYXe6ejzG246ta/kEuDtQdN1o1+rNFAdZPiHOvYlpMTx87SQW5Ay/zXTBSosJo7LJ0qlu+ESdGZPVweT0WEYlun93x05zM5YYWBWeoLgnKdEGogzaPmeKW21O7E6lx0xxIBIUCyHEAFEUhZ+t3ctP1nzJRY+vZ/vxer/HnfC2Y/OTKU70M+q5vaZYMsWDlVqtYtnsLMK08jbck9SYMGxOFzUmK1f/bROrNh1nf1kTABPTY0iPC0evUUumeIiqaraQEqBWWKVSMSo5qs8dKHqaZgcSFAshxKB1tNpEWWMbS8/LRFEU/vB+gd/jTgbIFCcZDbRYHVg6XBJsL5+QTLEYulJj3V053thdyv6yJv7y8RE2F9Vh0KoZkxKFRq0iOyGCYzUSFA81FruThlY7I3rZQDc6KarPmeJGzzQ7/5niwIkCCYpFv3C6lNNqmyLEcPZpYTUAP7l0DN+8YCS7TzZ2uxRstjp4a08ZOYmRhPvJciRGeXsVt2eLW09jo50Qg02apz3gvzadwKBV02xxsHbXKfJSo339iXMSIzkumeIhx9srOCVA+QS4N9tVNVtpttiD/t5Nre5j/dUUS6ZYnHVtNiczHvyIt78sG+hTEWJI+bSwmrzUaFJjwrl2WjpqFby5u/Pf0T3/OcjxOjMPXzvJ7/fwTbXrUFds8maKpXxCDGGpnkE1tSYr10xJ47L8FBQFJmfE+I7JTYqipM6MI0BNfiiqbrEM6URUhWd8d6CaYoB8z2CbA6VNQX9vb/lEXKT/iXaBSFA8xNkcLpav2sbukw399j0tdmefGqKXNrTS2GrnvX0V/XYOQgwlDqeLFzaf4Kq/bWTJ/20J6j5NbXZ2lTSwcLy7cX1ydBjzxiTx1p4yXC4Fl0vhLx8f5Y3dpdyxcAznj0rw+32MYe4XfpOlvSF9q82BWgVhOnmJF0NXQqQevafm+pqpafzkkjFo1CrOGxnvOyY3KRK7U6HMT+u2jtYfrubmf27D5hj6wfPeU41c8Min/OH9woE+ldNW6ZlU2Fv5xNTMWAB2lQQf4zS2emuK/WSKdRIUh7TqFgsbj9aypbiuX76fxe7k8j9t4LEPDgd9n3JPy5wtxXUh8YIjRF+t2XGKe985SGWTlW3H64PaDb/xaA1Ol8LCDo3rr5uRQVljG3e8sodb/rWdP318hK9PTePHC0f3+H28QUPH7hVmq5NIvVaGQoghTaVSkRoTRmKUgfNzE5iYHsOWuxdy1eRU3zHeHreB6ord9fqFbCqqZW9p41k9Z7vTPWL9bHG5FO75zwEcLoVnNx7r14TYuVTlCYp7K5+ICdcxNiWKXX1YZ2NbzzXFWQkRhAcIjCUoHuKa29zZoa59Sk/XaztPcbK+lc3FtUHfxzuG02xzsmeI/oEKcSaOVLVgDNPy1v+7AIDPDtf0ep/PD9cQG6Fjamac77bL81O4eFwSO0vq+fJUI/ddnc+fl0ztNNq5K73na1ZHx6DYQYRsshMh4DvzcvnNleN9fwPJxs59bXM9vWwDdSjYcLSWwsoWgH5LIPmjKAo3/3Mb/++lXUHfx+508cr2kxRVtwR1/Ks7T7G3tIkHvzGREdFh/PL1fVgdPffdHawqmixE6jUYg9j3MD0rjj0nG4O+gt3UZkevURPmJ/hNjQnn0ANX9HhfKTgb4rzF53VmWy9H9s7mcPHU+mIACiqasTqcGLS9v7GWN1lQqUCtUrHxaC2zc/1f5hUiVJU2tJERF0FmfASjk6NYf7iab8/NCXifrcfrmJOTgEbd/gYfptPw3K2zAPcbbDCZXr3WfUynTLHNIfXEIiQsn5Md8OvxkXpiI3QBN9v93+fFpEQbiA3Xs7m4lh9fMqa/TxOAz4/UsO14PRq1igazjbjIwINZCiubuevVvRRUNPPViSN46uYZAY9XFIU/f3yEWSPjuWl2Fumx4dz6/A5e2HyC780f1W/rUBSFDUdribSdvSu/Vc0WUgIM7uhoenYca3ac4litidHJxl6Pt9pdAUvHAv1MyRQPcc2egvKufUpPxxu7SylvsrD0vEzsToXCiuA+uVY0tpEUZWBaZiwbj/aeITtddqeLQ+XNZ+37C9HR0aoWHvlfQVDZiVP1rWTGuXfKXzwuiW3H6n29gh1OF394v5BT9a2+40sbWjlV38ac3Hi/3w8Cv3B3pNe4P7h2LF1qtTklUyyGjZzEyB7LJw6VN7O5uI7bLsxh3phEdp9s7NS+sL8oisJfPjmK0aDF6VL48FBlr/f52dq91LRYmJIZy9Zjdb2+1pQ1tlHVbOXqqWmoVCouHp/MReOSePLTIl8bsv6wubiOb/5rO8tfL2HlR0fOyoa+yiZLr/XEXjOy3VfTgq0rtjqcGHqpHe6JBMVDTJvNyf99XswHB91/cC2ezTV1Zv9BcXWzxVe705vXdp4iPzWaH3nqF/cFWXtV0WQhNTaceWOS2FfWREM/ZK39eW9fBVf+bWOfG3kLcTpWbTrO/2045rvs2hNFUShtaCPT00P44nHJ2JwuNnsu0x4ob+bpz4t5e097V4mtx9xDOub0sHmuL3SeTLHN2bl8QjLFYriYmBbDtuN1rPzoSLfJkB8XVKFSwQ0zM7lgdAI2h4vdvQRXFruTpz8v5mt/2cjyVduCOoeNR2vZc7KRX31tPJnx4by3P3BQXGuycrC8mVsvzGH5nGwaWu0crgr8WnPAM7hkcnp7941ffXU8JquDJz8tCuo8g/HlqUYAJiSH8ddPjnK0j32Cg1HZZPGNOu9NbmIksRG6PgTFLl9ZWV8Fda+6ujoWLFhAcXExBQUFLF68mBtvvJG7774bl8v9BFy7di2LFi1i8eLFfPbZZwDU19dz2223sWzZMu68807a2gLvDj0bVm06zl7PAzzUbS6q5ZIn1vPI+4W+Mgdv+UTXMa/g7h1847NbuePlPb1+b6dLoaCihdm58aTHhpMQqWdfkC1QypvaSIsJY/7YRBQFPjtc3YdVBe94rRlFwRdsCHG2KIriex7vOOF/ypxXndlGm91JhidTPHNkPFEGra8HsbfOvuMb3tZjdcRF6BgbxKXA3nhf/LuVT0iPYjFM/PIr4/jGtHT++slR7vnPwU5f23i0hknpMcRH6jlvZDwatYotxwK/h6z86Ah/eL+QOrOVjUdre+1sAfD2l2XER+q5fkYGX5uUyuai2oDZW29t84WjE32dZbb2cl77SpvQaVSMT21/3Rg/IprrZ2TwwpYT/XYl9VB5M5nx4Xx7hvu8DpYH3w4tGC6XQnWLNehMsUqlYnpWXJ+CYsNpdt7p9V52u5177rmHsDD3yT/55JP88Ic/5JVXXsFms7F+/XpqampYvXo1a9asYdWqVaxcuRKbzcY//vEPrrrqKl5++WXy8/N59dVXT+skT1ebzcmD7x3ihS0nzunPPRt2ldRz2ws7iDBomZwR4/tj8260a2i1devT+L/9FRTXmNlb2thrD8fjtSba7E4mpMWgUqmYnBETVFCsKAoVjRZSY8KZkhFLemw4/z1LrdkqPV0uenvhEEPLjhP1nQZP9Lc2W98vlR6qaKbK01x+ey9BsbcsIjPOnSnWa9XMHZ3I+sPVKIrC7pONgHszntfWY3XMzklArT7z7hA6T/eJTuUTVmevTeqFCBXGMB0rF0/la5NGsOFIewlfs8XO7pONzBuT6DtuUnpMwMSKxe7k1R2nuHJSKqu/PRuATUGUBR6rMZOXasSg1XDlpFQcLoUPD1b1ePzm4lqMYVompceQHhtOVnxEr5sA95c1MTbF2G2vzy+/Mp64CD0/emW3r2zrTBwsb2JiWgyZMToMWjUHy/q3bLHWbMXhUoLOFAPkpRo5XmsOqpzNdjYzxY8++ihLly4lOdndNigvL4/GxkYURcFsNqPVatm3bx/Tpk1Dr9djNBrJysqisLCQXbt2MW/ePADmz5/P5s2bT+skT9exWhOKQp9HBA42x2vN3PrcDlJjwlnzvTlMzYylwdOHz5spVhSo7/Cp1OVSePLTItQq96emol5KDg56PmFO8DTKnpwRy9HqFt9krJ40tdlpsztJiw1DrVZx1eRUNhyp6df6Jq8KTxnItmN1Q7ppuWhnc7i46dlt/P2z/rv011Fdq4OpD3zIC5tP9Ol+6z3dIy4YlcDOE/UBn2+lDe4sUkZ8uO+2i8cnUdFk4XBViy9TfKzGjM3h4lR9K6UNgeuJ+8L74m/rkimOkkyxGGamZ8VR1tjm+5C9pbgOp0th/pgk3zEXjEpg76nGHoPHd/eW09Rm5+Y52YxJjiIl2sCGo713YzpRZ2Zkgrs9nDfQ/big56B4U1Et5+e2b7SdkxvPtuP1PQZ9iqKwr7Sp0+ASr8QoA39eOpXjtWYeePdQr+caSLPFzom6ViakRaNRqxg/wuiLDwLZeqyOCx75hP8EMcTLm+BKCTJTDO41uhR3ArA37kzx6SUFAr5qvvnmm8THxzNv3jyeeeYZAEaOHMkDDzzAU089hdFoZPbs2axbtw6jsT2dHxkZiclkwmQy+W6PjIykpaXnepmCgoLTWkAgG465A8HDlc0cPHQIdZAbV+rbHMSGaYI+PhgWi+W01/jy3gaaLQ7+8rVUak4dw9HaRHObnQMHD3Gqsv2Pdee+QnLi3dOttpw0c7iqhSWTYnl1fyMf7ihEGd3zpdoN++vQqVU46kspaFQRTysuBd7bvI+JKeF+72OxWPhij/sP0GWqo6DAysRo9yfA5z7aw1fGRp/WentSUt2IWuUuFflo2z4yYwLv7O0PZ/K4DXaDYW0lDTZsThe7iyspKOj/LQ7bS5qxOlw8/L9DZOuaSYnq3rfSn/d2lzEmwcC0RBWbi618tmM/qUb/9919uBGA1upTFDS415Cudr/hPv3BXkob2hiToOdonY1Pt+/nSJ37DTtZ1XxGv3/v4+fyBOzlFdUUFHg+LLfZsJiaBvzxPVOD4Tl6toXyGs/12qId7g+o7205wKyMCN7ZXku4VkV4axUFBe5ypnRdKw6Xwpsb9zIzPaLb9/jn+jIyY3TEWKsoLKxmUpKODYerOHDwUKdOMdC+vhark8ZWOxFOk2+9k5K0fH60mv0HD6Htcr/KFjun6tu4anSE7/jsMCtNbXbe27yX0QmGbudV0WKnqc1OoqbN7+80Drh0VBTv7C3lWxOCe53zZ3+l+3cY7WzGYlGTFuFi44kGDh06FHDz73/21FPeZOEna77kne1FfO+8BKLD2gPT4norGdHuzPPOk+5NkZb6SgoKgiyJaHLHc9v3FTIyLvB7f2NzCy7X6cWVAYPiN954A5VKxZYtWygoKGDFihUUFhby1ltvMWbMGF566SX+8Ic/MHfuXMzm9p2fZrMZo9FIVFQUZrOZsLAwzGYz0dE9B0l5eXl9PvnevH/qMFCN1aEQPWKkbyNMIF+eauSW1Zv5w6JJ3DAzs9/OpaCg4LTX2Lx3D+mxFi6eNRmAMfXHUfY2kjZyNOrdbYD7w0Z0cgZ5nstEf9+zm2Sjgd8vOZ//Hv6QeiUy4M+v/GIr41OjmTQhH4CEDAv3flJJizaOvDz/raUKCgoIC4sHypg5YTR5WXGMVxRWbm1kZ43CXV/v+ed52781tNpIjjbw3Xm5vln2Pal/9STzxyax/nAN1cRyeV7gVj394Uwet8FuMKzt+P4KoJQyk+usnMsTmz4nOsy9G/xf+y28cOukXrs6NJhtFNYe40cLx3DlpFT+vm0D9Zp4FuZl+D3eWrif+EgT0ydP6HR7/qZG/nfU/UL+zXlj+e3bB7BHJlFwrIJko4GvzJl8RuUTHR8/rfoEMfHx5OWNR1EULI5jZKYmk5c37rS//2AwGJ6jZ1sor/Fcry0z18GKDytoVEWTlzeG/e9+xoVjkpk8Md93zMhRTu779ANKbREs73JuB8ubOFx7jPuuzic/3/2+d5Ulmo+Lv8QVk8bEjNhOx3vX574aVMLs/Fzy8lIA+LojlnVHd9MWMYLzRsZxvNbs66m8d/tJ4BTXzZ3gazEWm9bG45s+pUqJ5uq8XBRFwepw+XrtHttXAZzi8hnjyfOTLQaYWKblo6IjjB47rtf3055srjsOVPCVOROoKz3OhfnxvH/kAMZeYqjWvXtIi7Fw/cxM/vFZEbsrrTx+/RQuzU+hssnCT1Z/ym+vzOPWC3PY0XgCqOL8KeNJDjJb3Kivgw3VRCenkzc6MeCxms/qiTFoAz73du3y30s64G/tpZde4sUXX2T16tXk5eXx6KOPkpGRQVSU+4FNTk6mubmZyZMns2vXLqxWKy0tLRQXFzN27FimT5/O559/DsCGDRuYMSNwD77+Vlxjxvv+dzSIxthOl8Lv3j6A06XwQYBaoHOtuMbE6OQo37/jItyfkhpabTRb7MR7eiF2rMvcXdLArJx49Fo1+WnR7C/ruT5YURQOljf7SicAkqIMGMO0nKjrufcjuDtPAKTFuLPJKpW7hGJLcR31AbpQbDtex58+PsJrO0/x2LrDrN5SEvDnmKwOWiwOZuckMCI6TOqKQ8TRKnfQWGuyUdfPdcWKorC3so15Y5L4xRXj2HCkJqhNmrtKGnApMG9MImOSo4gJ17HjeM91xafqW32b7DpaOD4Zm8OFTqPi61PT0KhV7C9r4vMjNVyan9Iv9cReeq3aV1NssbtQFIiQ7hNimIkyaBmdFMW+0kYKKpo5Wd/K/LGdA6hwvYZpmXF+N9v9b38FGrWKr09N9912oScA2xighML7PjnSM10P4ILRiWjUKjYcqeGtPWUsfOJzPvGUU7y3v4K0mDBGJbW/r6fGhJMZH87OE+7M6Vt7ypj54MdUNLkzt/vKGtFr1Iwd0X6frrwT3LytWk/HwfImko0Gko3uYDXfExf0VkJxoq6VnKRIfnrZWP7747kkGQ389u0DKIrC5uJanC7F10u6rLENvUZNYlT3jHhPkozd45yenNWa4q4efPBB7rrrLm6++WZefvll7rrrLpKSkli+fDnLli3jm9/8JnfddRcGg4Hbb7+d9957j6VLl7Jnzx5uvvnm0zrJ01VUbWKmp7+d9803kJe3n2R/WRO5iZF8UVQb9JSYyiYLP1u7l6bW038i9sTlUiiuNnf64/E2BG/0BMU5nj9E75OlvLGN8iaLr7ffxPQYDpU39zh6srzJQmOrvVNQrFKpyEmM5ERdq9/7eFU0taFVq0gytj+5549NwqXAzgAblLx/HJ/+/CLmj03iTx8fCfhkr/S8MKTFhjEnN54txXV9muLzyP8K+NnavUEfL86NjrXuR4L4G+2LE3Wt1JidnD8qgaWzsjAatLy5u3O928vbTnZqlQZQ4tk4NyopCrVaxczsOL7wvKj7U9bQ5ttk19HF4911jPlpMRjDdOQkRrJ25ylabU4uy0/pjyX66DTtQbHJUysZJX2KxTA0KSOGfWVNPPfFccJ0aq6ZktbtmPNHJXCgrImmLsHjhwermJ0T32noRpLRwIS0aNYdqOxxb8HxGjNqFWR1yKTGhOuYmhnLxwVVPLbuMAD/t+EYR6ta2Hi0lmWzs7pdtTovO56dJe49DP/bX4nJ6uCFzSW4XAobj9QyPrX7JruOvEFx4xkExYe6JMjyRkSjVsGhXjpQnKwzkxXvjkXGj4jmO3NzqWy2UFDRwhdF7g8gZZ79F2UNbaR69iEFyxtA++u01dVZ7T7htXr1akaNGsXMmTNZs2YNL774Is899xwZGe5LiosXL+aNN97gzTff5Ior3CP0EhMTWbVqFWvWrOGpp54iIqL38oX+4nC6OF5rZnpWHMlGQ69vuBa7kyc+PMwFoxL4zZV5tNmdbA+QHerokfcLeGN3KRuC2KHqcLpYd6CS9/dXUFDRe/F6RbOFNruTUcntn0DjPE/8BrOdFouDjLhwdBqV78ninYXuC4rTYmizOznWw2a7g54scn5a50sy2QmRnAgwJQigotFCSnRYp1qrSekx6DXqgO1TjtWYidBrSDYauOeqfNpsTh5bV9jzz/FkpEdEh3HdjAzqzLZes8teTpfCqztP8c7esn7ZmSv6T1G1ibxU9wtwMFdz+sI7qvyCUQmE6TR8bVIq6w5U+LpRKIrCyo+O8M9Nxzrd72SdGaNB6/s7u3Z6OqUNbfxvf/euKi6Xu0dxx012XlMz49ytCj0lTeNSjDS22onUa7igH/oTd6TXqrE53W/Y3s2xkikWw9Hk9BhqWqy8ubuM66ZnEBvRvf70/FEJuBQ6vccfqzFxtNrE5X4+sC6dlcX+siZ2nPD/nna8rpX0uHD02s4h1fwxSRRWtlDZbOHKyalsP17Pr97cj0Gr5sZZWd2+z8yR8dSabBytNrGluBaVCl7eVsK/t5zgUEVzr9P9osPdr1ldg/1gWexOjlabmNAhFgjXa8hNigqYKW5qs9PQamdkQnuMd5EnKfDZ4Wq2eF6Lva3tyhvbSI/1v1epJ9FhOrRq1eDLFA8VpxrasDldjEqOYmyKsde54h8eqqKx1c7/u2g0F4xKRK9V81lh70HuvtJG/vNlOdDeWDuQR9cV8oMXd3H7S7u58q8bewxUvYo9nTM6ZYo7lk+02YkO05EQafBdft5V0kCYTu0LNiZ56o/8tVgrqjbx8vaTqFTulicdjUyIoLShtVOrp67Km9pI7dJWJUynYWJ6NDsDBMXHa83kJEaiUqkYnRzF4vMyeXtPeY87b31lGp4hIXNHJ/LkZ0W+7huB7C1tpLHVjt2pBP1BR5x9TpfCsRoTc0cnYAzTdmpZ1h82F9eREKHxXUn5+rQ0zDYnH3kuYVY0Wag1WTleY+6UATpZ30pmfIQvi/O1iamMSY7iL58c7ZYtrjFZsTldZPjJFGvUKj766QJ+4hkpOzbF/fe1YFxSUOPT+0LfIVNstrqD/kjJFIthaHJmLAAOl8KtF/rfDzMtKxaDVs397x5k1kMf89B7h3wlk5dPGNHt+OunZxAXoePZjce6fQ3gRG1754mOvKUbV0xI4dHrJmMM07KrpIFrp6WT4Kd0YFaOO5H19PpizDYnty8YRbPFwX3vHmJGdhzXTfe/r8Er1hsUn+ZV6+O1ZpwuhXEjOscCEzwlmD1lyk96rihndwiKk41hTEqP4eVtJylvshBl0PqC4rLGNtL6GBSr1SoSovRBTe+1Opyn/RobskGxN5gcnRzF6OQojlabAva3e23nKdJjw7lgVALheg3n5yawvpchFIqi8NB7BSRE6hmdHMWBXi4vrD9czbMbj3PjrEzeuP18NGoVq7cGznYW+QmKvZdI3DXFDqLDtSQa9b5PULtLGpiSEesrtM9NjCRcp+Fnr+1l7G/f59NC9x//xqM1XLryczYX1fGji0d3yyxlJ0TiUuixcfnROiuHK1tI9fPknpEdx/7Sph5LHE7UmTvVX01Ii8bmdFHdwxPe28IlOdr9QvKrr46nsdXO054hJoF8frgGlcqdTQtUFybOrdKGVqwOF6M9H1z7u3xi27F6powI9wW3c3ISSI0J85VLeIf6mG3OTs+7k/WtnS6DqtUqfnLpGIqqTbzXJVvsna7or6YYINKgRev5OxznqQXs79IJcD+3vcM7vJliGd4hhqP81Gi0ahUXjUvqtBenI4NWw6LpGei1asakRPHsxuP85ZMjTEqP8Rushes13Dwnm48Lqnylf16KonDCk+TpampmLPdenc8DX59IlEHLTbOzUanoMVgflRRFXISOt78sQ6tWcftFo5iRHYdaBQ98fUKv5QberHhj2+m1RPW+nnX9vc0dnUh1i9U36a6rknr378RbPuF18fhkX/xw9ZRUWiwO6s02qlusfc4Ug7uEoi6Iibk2h6tb1j5YIRsUF3V4cMemGGm1OSlv8h/clTW2samolutnZPiedBePS+JYrZmSABvNth2vZ9vxen58yRjOGxnPgbLmHj9JWRwufv7aXsaPMHLv1ROYkR3P1yal8vrO0oCX9ItrTMSE60iMar8EFGXQolWrKGtow+lS2jPFZhttNicHy5t9pRMAWo2av980jbsuHYtaBZuOuut7Pj9cg0GrZvPdC/nZ5d13qXsvhfjbbPfC5hP85L9laNRqvnVB90s6M7LjsTldfrPn3l6tuR1eRLyZttIG/zXMFU0WEqP0vk9/E9NjuGpyKv/eUuKroezJ50dqmJoZy+yceDYGUeLSkdOlcNXfNrLuwNkZSDKcFVV3/hs9UtUSdP/p8sa2gMda7E5qTe4WQF5qtYprpqbx+ZEa6kxWvuwwxtz7ZuByKZxqaOuU8QB3tjg3KZJXtp3sdPuqjceJDtMyPSuO3lw8Ppn7r5nAlZO61zieKb2fmmIpnxDDUZhOw7PfnMlD104KeNwjiybx6c8u4sVvz2b5nGwsdpff0gmvW84fiVatYs2Ozq8BdWYbLVaH36BYpVJx64U5vn68d102hnd+OLdbJrbj8TOy43EpMD07DmOYjseun8yzt8zsVNLQk5gzzBQXVZtQqei2lismjkCvUfPO3nK/9yvxkykG92ZjgNSYMN+GxV0lDSgKpx0UB1M+YXW4MEhQ3FlRtYlko4HoMB1jUtyfenrabPfGrlIUBa6f0X5pYlaOu+Zvb4Cpbqs2HScuQseS8zKZmB5NU5vd18i/qxMNNmpNNu68dKyvxcot54+kxerg7QDNrotrTIxKiuxUkK9SqYiN0HPSsyHIGKZzP1larOwrbcThUjoFxQALx6fwk0vHMM4TfIB77OyYlKged4B6M7n+6opf31VKbryeT3++gBnZ3YcQeH/+Tj81WCfr3T2QczoFxe4/kJ5+f5VNbd2m33xnXi4mq4PXd57yex+AerONvaWNLBjrLrk4Wm3yZZ2DUdfq5EBZM58fkQxzf/MFxUlGxqZE0dhqpyaIF7yKpjbmP/ZZjy/QgK/zSWx450to105Lx+lS+O++CvaeaiTFc+XBm/2parFgc7i6tR5Sq1XMzkngYHn7JcSdJ+r5pLCa7y8Y5XszCsSg1fDNC0aedgYjEJ1W5Rve0WqT8gkxvF08LjnooEulUnH/NRN4ZvkMvjs/t8fjkowGxqYYKahoL/Nqs7t8748j/QTFXRm0Gl85Y0/OG+l+71ww1l2TOyopikvygru6FB3m/iB8uhvtimvMZMSF+2KU9u+r46JxSby3rwKbw8V97xxk3YFK39dL6swkRhm6XZ2anB5DWkwYF3V4PHZ4NuCn93B1LRBvnNMbyRR3oSgKX55q9AXD3lq+Q342tpmtDlZvLeHC0Qmd3ghHJUeiVaso7GEz3IlaMx8XVHHT7GzCdBompbuf6D21PitpdL9Jj+/wCXF6ViwT06MDbhgrruncecIrLkLn2yUfHa4lMUpPrdnG21+WodOoesxcjU0xctgTFB+pavH9bvxJiNQTZdD6PgV2VNHUxthE94cOf5KMBkYmRLDteD0VTW2dJuN5X0Q6BsXeP5hAmeIR0Z3/iKZmxjI1M5YXtrh359aZrN1qPjcerUFR3C8wcz0bnjYVBQ5wWyx230S+mlb3eR+vHdpTEQejomoTSUYDMRE63/MwmMlJB8qacbgC14d7swlxYZ1f3MePiGb8CCNv7C7lQFkzl+ePIEyn5liN+znprY3L8tOPMz/VSLPFQXmTBUVReOyDwyRGGbj1wpFBrfds0mvayye8V54iJVMsRFDUahWXTxjRLRjsamyKkaOe988vTzWy6OUTLPvnNgBy/NQUn45L8lJIjw3nqxO71zb3RqtRYzRoaTzNTHFxtclvvAFw9ZQ0qlus3LxqG89vPsGqDhuUS+pau2WJwf17feeOudxzVb7vPX6b53W7rzXFgDvOMdkCXiV0uhQcLkVqijtaf6SGomoT3/D0GowJ15EVH+H3Uv7TnxdT02LtVj5g0GoYlRRFYaX/zT/Pbz6BVq3ilvPdpQNjU4xo1aoeN9uVNNoxaNWdAm+VSsU3pqZTWNnit263qc1OTYuVUX7qouIi9JTWeybPeDLFNoeLV3ec4qbZ2Z1aynQ0boSRmhYrJ2rNVDVbGRcgKFapVGQnRHQrn3BfmraRFBH4TXfmyHg+Lazm/Ec+Zer9H/Gt57az91SjLyvXMSgO02lIjDL4MsWrt5zgiw7Ba0WTpduGPoBbLxzJ8Voz1z29mRkPfszqLSc6fX3tzlMkGQ1Mzoglb0Q0iVF6Pj8SuITi56/t5Tsv7ASgxuwOMLxBk+g/h6taGO15AZ6UEUN8pJ5fvLaXzwqr+flre7nmyU1+x4x7r3T42zjq5Q2Ku2aKwZ0t3lfahMnqYFpWLDmJUb4Nr94Pmv5e4L0bVwvKmzlabWL78Xpuv2jUoChT0GnUWB1dgmKpKRaiX41JiaKiyUKzxe7rbvONqWksmZkZ1HCwYIxOjuKLXy30Dfroq5gI3Wn1KXa5FI7VmnyvyV1dkpdMhF7D9uP1jIgOY8/JRl+p1sl6/0ExuLO74Xr3+7teo/Z1u/L3ft6bxCgDNqeLlgAlk94ysmGRKQ623vCp9cWkxYR1asA9KSOmWxa3rLGNZzYc45opaX4zq3mpRr9t0worm3ll+0munpzmm8YSptMwNsUYMFM8Ojmq25jI+Z5LJJv81Lp6P5H6++QWG6HzXS6NDteR4Kk5Dtdp+NHC0X7PAdqz5v/dV97p3z0ZmRDZLVPsLT9Iigr8pnvXZWO59+p8Hr52EsvPz+ZAWRM/WbOHo9UtxEXourXKyYgLp7ShDbvTxYPvFfCnj44A7o1DTW32buUTAF+dmEp6bDjHaszERej47HD773HniXq+KKrj+/Nz0ahVqNUqLs1L4bPCaix2/xsAXS6FzcV1FFS468O9QXF1i7XX2mW708Xv3j7gmW4kAqk329hf1sSsHHfpTXSYjrXfPx+DVsOtz+/g7T1l7Ctt4q093UuLvEFxYWVzjxs5a1s85RNh3YPia6am+Yb6TMmMJTcp0vdB7VR9K2qV/yzGeG9QXNHMZs8HtkA1iOdSx412Zk/5RIReyieE6E9jPNPniqpN7C9tYkSUlseun8Kj10/u9t4+UGIjdKdVPlHW2IbF7vKbhAP3HoUfXjyab10wkj/eMMVzta4Oi91JRZOF7PjAmXK1WkVabBgOl0JilKHXrLw/id4BHgFKKLzvCcOipvjbL+zkN2/tD3jMrpIGth+v5zvzcjt9UpiUHkNpQxsNHXYuejsXrPjqeL/fa3xqNBVNFt+ldHBfWr/9xd1Eh+v41dc6329iejQHy/1vtitptPkNQMckR5ESbWCDn64IG4+6+xROz4rt9rW4DgGlMUzrG57xnXm5AafEeAv8393r3jg2toeCf6+RiRGcqm/F4Wxvy1buyWr3lilOjw3n1gtzWDY7i99dlc+j103mRF0rb+8p97spwR0Ut3K4sgWrw8WeU400tdl9Qbi/T5Z6rZr//WQeW+++hK9NSmXniXrfuf710yISIvUsm93eD/Krk1IxWR1s6qELxdFqEy0WB2abkzqzzRcUg7tBeyDPfXGc1VtLeHVHzzXOXdmdLlZv7X2zYKjxlrVc7NmIAe4MyZv/7wLuunQsn/38IiakRfPC5hPd/p4OV7Z4gkCFgooWjlS1sPLDw52OqzX3nClOjQnn/NwEosO05CREkpsY6W7h6HBxsr6VtNhwvyNSowxasuIjKKhs5oviOjLjw/stO3SmOm60a7U50KhVp/2mIITwb6xvf1IL+0qbGJsY/ES2cyUmXNcpZgmWd7NxT+UTAD+8eDT3XTOBmSPjMGjVbDpa57uS3FOmuCNvsiE9tu9ZYghugMewyRSfqm/l08LqXutB//rJUWIjdCydldnpdn81v58fqWH+2KQeC/K99b8dSygeePcQJ+tbefLGab4xiL6fkRFLvdnGqfrOpRBNbXbqWp2+GueOVCoV88Yk8UVR94lZHxdUMSMrzm8/w9jI9lre6DAds3MSuP+aCfxgwSi/a/FKNhqICddxuKqFKIOWtF4uYWQnROJwKTz9eTFrtp9EURRfqUdSZN8uzy4cn8z0rFhsThc5id1/FxlxEZQ1tvnavjhdCpuLan1t1MaPiO52H3C/CITrNczOTcDs6b7x5alGNhyp4bvzcztd3r5gVAIx4Tr+d6ACh9PFZ4XVvgwbwM6S9jrVkjoztWaHL7g4FqCuuKyxjT99dBRoH54SjFWbjvO7tw+wtg+B9GC08sPD3PKv7UEf/1lhNQmReiand950khIdxk8uHUNmfATfumAkR6pMbOkwmtnhdHGsxswVnl6i+0obefT9Qv76aVGntmq1LTYi9RrCenhhfGTRJP75zfNQq1XkJkXidCmcrDf3WBvnlZdq5EBZM1uP1XHhqMQejzvXOo55NludROg13aZlCSHOTGZcBGE6NVuP1VPW2MaYhMEXFMeG609reEexJ+kzKqn32ugwnYZZOfFsKqrhr58cRa9Vd9vc74831jqdTXbQMSgOlCl2vw6GfKb4P54ODSV1rT22MNtSXMfnR2q4fUH3Or+JaZ2D4lP1rZysb+XCAJOlvDWE3s12bTYn7+4rZ+l5mczO7X4/70jpHV3GG3sHh4xN9p+VnTcmkcZWe6d65PLGNg6WN3NpD5dnu2aK9Vo137xgJOG9XDJVqVS+OuKxKVG9vnHmeQLRP354hF+9uZ/iGpNvkEZiH4NilUrFL7/izq53nNDnlREXjt2p8ElBFTHhOoxhWj4/UsOLW0uYnBHjm8HekzmeS/Hbjtfx9PpiYsJ13NxlApBOo+ay/BQ+PlTFna9+ya3P7+Bfm477vr7rRANaz2WwkrpWqs0OZmTHoVIFrit+6L1DACyemcHRalNQQ0XKG9v46yfuQPqzXnpid+Rwus7qEJLGVhufFlb1ONa4K0VxTwzccKSGQ0FslHO6FDYcrWXB2KSAfTevnpJGfKSef31xwnfbibpWbE4XF41NIjFKz3/3VfCp53fn7cYC7hfNRGPPb1jZCZG+0o1czwe0YzVmTnXpUdxVXmo0J+tbabE4OL+fp9KdiY7lE202p5ROCHEWqNXuYVPezguDMlMcoTvNoNhEbISO+B72I3V14ehEjlSZ+N/+Sn5yyZigrpp5g+G0mDMLiuuCCYpPozwDhkhQrCgKb39Z7ov8/U2+UhSFP6wrJDUmjG9eMLLb12MiOm+2842AHd1ztifZaCA+Uu/LFH9RVIvF7uIrPewKHZdixBim7ZRtdJ+vO8PYU/3uXM85dOyh+4ln6talPbRi8Y6gNWjVfa7NGesZItBTr8SOJmXE8OnPFvDit2cD7p3/5Y1tnqL5vmei5uQm8Nyt53HTrO69jb1t2TYV1TI5I4YLRyXy1p4yjlabuHl24PGWAMnRYeQkRvLm7jI+OFTJzXOyiPKz2eirE0fQbHHw330VJEYZ+NcXx31Ztl0nG5g3JhGVyh0U15gdjEyMJCMunGO1ZqwOZ7dex80WOx8erGL5+dlcPSUNRWkfDBHIQ+8V4HQpXDk5la3H6oIuoXjuixMs/r8t7Co5O4Hxc1+c4Lbnd3LtP74IakrjwfJmqprdL1Jv7Sn13a4oCkeqWroNzdlX2ki92cZFHUon/AnTtTfM99b2e//2x40wMik9hu3H6/FWTXSsfa81WUkI8sU9x5MZ+dunRdSZbQFf3L0flIFBFRTrOpRPtNmdhJ/mG4IQIrAxyUba7E5UKhgVPwiD4nB3UBzsHiyv4mr3JrtgrzB545a81Gi+F6CVXUdpZ5gpjovQoVJBTYDyCW9NcUiPeT5U0UxRtYlveYJdfx0hPimoZu+pRu68dEyPQeKk9PbNdpuL60gyGhjTQ1E5uDOb40cYKfD8vI8OVWE0aJmd4//NUK1WMTM7rtt89CNVLRi0qh6nXiVEGZiUHsP/9lf6nsgfFVSTkxjZ46UM7yY1Yw8t0QJpzxT3HhQD5CZFMTs3Hr1WzaGKZsqbLKSdZk0QuHtIxkR0P2/vAA+7U2FyRgwLxiVhdbgwhmm5akpqUN97dk48hZUt6NRqvx+OAOaOSWR2Tjy/vTKPJxZPoarZyttfllHTYqWkrpXzRyWQFhPOkaoWmq0u0mLCfB0K/vLxUZav2t5pbPimo7U4XAqX5acwJTMWlQr2nGwMeJ6tNgfv7a/gmxeMZPmcbOxOxe9my65sDherPJnt9/dX9nL06SmpM2MM01LZZOHGZ7b6ash74p38OCM7jre/LMfhGdpy47NbufxPG7jv3YOdjv/scA1qFcwf03v5wbcvzMEYpuUvH7sz6ocrW1Cp3PXHkzNiAfcIVbWqc6a4zmQLWFvfUXSYjoXjk2lqszM1M5aLx/UcrOd7guIxyVHdyqcGkl6rxuZ0v3ZY7M7T2sQihOidtwwyNzGSSP3gC6Fiw3XYnYqvX3mw3DMRgu94kZ8azY8vGcPfbpzqdw+GP5me93jve31faTVq4iP0wZVP6EI4KH53bwVatYrvzc8lQq/hsJ+geHNxHeE6TcDZ4JMy3JvtalqsbC6u44JRCb1+Kho/IprDlc20WOx8UljFgnFJAQu4z8uJp6ja5BseAO6hIVkxuoCXim+ek8WhimY+P1JDZZOFrcV1XJaf0uP5ecsnosP73nZpWpa7HGBaEFO4vHQaNeNSjBwsb6K8se20L38E0vFDw+SMWOaPTUKlguumZwTd9mp2rvuS+HUz0nsMWgxaDa9+/3y+My+X+WMSyUuN5qn1xfzrC3ewOSM7jmxPj2Vwb8zKTYykuMbE85tPAO2DJwA+LawmJlzHtMxY97CY5Khe64rLG90lKHmpRmZkxxEdpuXTwt5LKN7bX05ls4Uko4F1Byv7nA0IRmlDG/mp0bz2g/NxKgq/eH1vwBHpnxZWMzkjhu/Oy6GmxcrtL+3mmic3caTKxMXjkvj3lpJONdPrD1czLSuuW/cRf2IidNx2YQ7rDlZysLyJo9UtZMdHEKbTcP6oBNQq+N78UaTGhHOqD+UTXf3rW+ex4ZcX8/YPL+yUDe4qIy6cEdFhLMwLnOU+19wb7dxvgm0SFAtx1njLIKd4PpQPNrGehFNfOlA0trqHi/kra+yJWq3ip5eNZXQPZaH+zM6J5/HrJ3PRuKSg79NVbwM8vFfMDKGcKd52vI5pWbEkRBkYN8JIYWX3usWj1S2MTo5CG+AXceEo92XxRU99QU2LlQuCuPx5+YQU7E6Fa578glqTjct6acF03kh3ULazQ13x4aoWsmIDBwDXTssgLSaMJz8t4s5X96DVqLhxVlaPx3vLJ3oanhHIxPQYdv7mUqZmxvbpfhPS3N01yhvbSD2DTHFPvL2Kwf2Ckx4bzprvzuHnV3QfQd2TheNTuGpyKj+8uOe2dB2pVO4/7FP1rTy1vphIvYaJ6TFkJ0T4PtikxoYxKikSi93la+V2zNPCy+VSWH+4mvljk3zPvelZcew52RgwYK3wjBxPjXF3OlgwLplPC2sCBp+KovDMhuOMSY7iZ5eNpbShrddhFy6Xwv4A/Xz9KW1oIyMuguyESH57ZT5fFNXx0jb/A2bqzTb2nGrk4nHJXDw+mZhwHR8dqmLxzEzW/+Iinr1lJnNHJ/Lbtw9QUmempsXKvtImLu7Di+Jtc93Z4ltWbWfjkVrfFY45uQns/t1lzMiOIys+wpcpdjhd1LcGnynuC5VKxbo75/Gzy4J/Tp4L3m4c4M4US/mEEGfH+FSjJ6kUO9Cn4tfpjHpu32R3er2Rg6VWq7hhZmbQmWV/Eo3DPFNsc7g4WN7sC+DGjzBSWNnSLeAoqjYFLIUAd6b4hVtnYba6A5sLgtg9Pic3gb8uncbJ+la0ahUXBbi0CjA5Iwa9Vu3bbFfR5M5Mj+6l9kivVfP9BaPYWdLA1mP13H/NBL9ty7xifZnivgfFgN+OFr2ZkBZNY6udVpvztOaWByMjLpxko8HXk3h2boLfuuCexITreHLZ9D5dnrksP4Vdv7uM//14Hv/98TwMWg1Z8Z2n7XkbqV83PYMko8E3le9AeRO1JhsLx7cHedOyYmlqs/sCZ38qPJli7+9x4fgkak3WgEHuwfJmCiqauW1uDpflu0sGPjwYuITig4OVXP3kpm6Z63f2lrOnvPv0QJvDRVWLxZe1v3FWJrNy4nn682N+N96tP1yNorg7ixi0Gp5ZPoNXvjuHP1w3megwHVqNmicWT8GpKLy8/aRvcEpvf0cdxYTrWPXN85iTm4BarWJeh7IL799Bx6C4vtWGorinH50NsRH6szKq+UzoNO1jni12F2Gn+YYghAgsIy6CN26/gCXn9Zy0Gkgx4e7XvcY2G+sOVLB2xymO1ZjYcaKed/aW+30dD6Yd22ARG6EPmAX3tWTTnF5iYNCPPCqsbMbmcDE1032pf/yIaF7ZforqFispnsEZLRY7FU0WRvtpedbV/LFJvP+TeRypagm6x+iVk1OJDtdS0WTxfQrriUGrYUpGDNs9dcVfempLxyf1HoQuOS+T5744zsyR8Vw/o+cyEGi/RGIMO3cPYX5ae/us1JhwoPcZ5H1164UjfR9azqWYcF2nx3Zkh7ZcI2LCSIkO47YLc/jBglxK6lt9wx4+LaxGpYL5Y9qDYu/Vgk1Ha3t8kSlvakOlwvccvtCzaeGL4lomZcT4vY+3Vd3c0YkkRBmYlRPP+wcq+enlPWctvaPN399f4RtQ02yx88vX9xJjULP0YqVTWU9FUxuK0l7KolKp+Ob5I/nhy7vZVOTuGOGlKAovbD5BdkKEr+Whv64sKdFhXDI+mTd2lTI9K45ko4EJvXQS6WpWTryvW4Q/WQkR1LRYabU5qPNswnBnigPXQ4cKvUaD06XgdCnujXbSfUKIs8bfsK/Bwvs+Vt5o4e439/muIHmF6zTdrngXV5vQa9SDpu96ILHhuoBZcN/wjlDNFHt38U/JdL/pejsmdJw0563vHBNkbUtKdBjzxvStpmXemCQWz8zs/UDg/NwE9pc20tjqvrSs16jJDWKXaphOw4d3LeCPN0zptdZZp1ETG6HzlVGcC3mey0bAGW20C+TrU9M7DdsYKFmeoDg2TINBqyFMp+Geq/NJjg4jN7F9AtrGo7VMzojtlHnPTYpi/Agj7+wt7/H7VzRa3B08PBnHZGMYY1OifKOtWyz2bm1n9p5qJCFS7wtYLxmfwtFqE9XNlh5/jvdv44ODVb6rK+/tq8Bid1FlcnTr++0ds90x035pfjLxkXpe3XGy07Gbi+vYW9rE9+ePClgvD3DjrCxqTTY+PFTFReOS+r2HrvfF/FR9m+/S2tkonxisdFr379PudMlGOyGGMW/CbN2BCuxOhUcWTeKRRZN4ZvkMdBqV3/0uxTUmchIjB81UvkC8E/t6Kk9szxSHaFC851QjiVF632VmfwM1jvqC4sGR+l+Yl4JLgfWHa/jyZCP5adFBty/ry2XZf9w0ne/PDzysoz9F6LW+kg5/Y3BDSXaCe51Jkd2Di5zESGpNNqqaLewrbWRObvcM5jVT09hV0tBp81dH5U1t3QanXDg6kR0n6rHYnfzgxV0se3Zbp6/vLW30dLdwP5eme/pi7wnQ/u1otQmdRsXJ+lbf38xrO0+RmxRJtEHNmi6BbmmD+3w7bno0aDVcOy2djw5Vdarl+sf6IpKMBhZNT6c388cm+dYbqLvD6fL2Fj5Z3+o7x4SzVD4xGHnfAKwOCYqFGM68QfHnR2qI0GtYND2dG2dlcfmEEeSnxbDHb1Bs7tMmu4EUG67H6VJ6bGEa8jXFe081MrVDIBAboSfZaKC4w+7/omoTeu3gSf1PTo8hMcrABwcr2VfWeNYK8i8YlXjO1zwhLQatWhXyWbgog5bEKL3fqX3eDwZv7i7D7lSY46dF39WT0wB6zBZXNFk8JSjtLhyViMXubrn2RVEdh6tafEGqyergaLWp047nCWnR6DSqHtu/2Z0uTtSauXZaOiqVu764qNrE7pONLD0vk0tHGfnwYBU1HXbylja0oVbhq+n2WnJeJnanwrMbjgHuF9wviur4ztycoAIwjVrFTXOyiTJouTCIVmx91SkobulYPjE8eHu4250u2myy0U6I4Spcp0GnUWF3KlwwKgGDtv21YFpmLPtKm3B0mOJqdTg5Wd86JOqJAV8718YeSijOSaa4rq6OBQsWUFxcTF1dHbfffjs33XQTS5cu5eRJd6Zp7dq1LFq0iMWLF/PZZ58BUF9fz2233cayZcu48847aWvrW31fU5ud4hpzt9YnOR0uX4N7DvmopKhBk/pXq1UsHJ/EBwcrsdhdfWp9Ntj9YEEuD107cdD8rs+mR6+bzI2Tuz92uZ7e0a/uOIlaBTNHdj8mMz6CGdlx/OfLMk7Vt/q6VoC7FtdfB4/ZufFo1CpWfnTEF+Rs8oy43l/ahKK0lxGBu9ymp0/+4O437HApnD8qgZnZcazZfoqfrNmDRq3iG9PS+cpYIw6X0mngRmlDm68jRkdjU4wsmZnJ/204xn3vHOQHq3cxLsXYbWJgILcvGMWmFRefVseU3sRF6IgyaDlV30qt2Ypeoyb6HNbbDzTv42VzuLA4XBIUCzFMqVQq32a7jntAwL0JvNXm5HCHAWglda04XQqjB8mV9t7Eertr9LDZrr2m+CxNtLPb7dxzzz2EhbnfwB9//HGuvvpqXnrpJe68806OHTtGTU0Nq1evZs2aNaxatYqVK1dis9n4xz/+wVVXXcXLL79Mfn4+r776ap9OzttKamqXTGtuUmSnnf1Hg+g8ca4tHO8uoQD3p7NQMSEtZtDuuu1vl+SlMNrPbPvM+AjUKvfI4QlpMT0OUPnG1DSOVJmY99hnzHvsM98QjOY2B602Z7dez8YwHVMyYnC6FH6wYBQp0QY2emp+95Y2At17Y3b85N+1ndtRzyTF0UlGlp6XRZvdiUuBu786nmRjGJkxevJTo/n4UHt/5NKG1h6nDT107UQuzUvh+c0nSI0JY/V3ZhHZh84garUqqN7Ep0OlUpEZH0FJnZnaFhuJUfp+r1sezLxlV2arA6dLke4TQgxj3hKKBWM7l6p5Nwh2vLroveo+VDLF3veQAcsUP/rooyxdupTkZPcvd/fu3VRVVfGtb32Ld999l1mzZrFv3z6mTZuGXq/HaDSSlZVFYWEhu3btYt68eQDMnz+fzZs39+nkNhXVolbB5PTYTrfnJEZSb7bR2Gqj1eagtKFt0AXF88YkoteoSYzS9zjJTgxNBq3GtxEtUEeEpbOyePaWmTyyaBKtVgd3vfolTpdCubdHsZ/NipfmpxATruNbF4xk7ugkNhfV4nIp7D3VSHZCBHFdRhdPy4qlze5kf1kT1z61meWrttFqc9daeTfZjUqO5LoZGey993Le/8k8vjOvfSTnJXnJ7Cypp7HVXXLg7lHs//mq1ah5ctk0fvO1PF7+7pxBNdENIDs+gp0nGthcXHtaLQeHMm+muNnifqOQmmIhhq/4CD05iZG+DeNeGXHhJEbpOwfFnnZsgVrADibtw0n8j3q2OlyoVO42lacjYJrnzTffJD4+nnnz5vHMM88AUFZWRnR0NM8//zxPPvkkzz77LCNHjsRobO/8EBkZiclkwmQy+W6PjIykpaX7JDqvgoKCTv+2OV28vPUkczIjKC8pomNlps7izhJ/tvMgak82KNze1O17DLSFuZEYtCoKCwuxWCyD7vzOVCiuqaue1pgcrnASSNe1BvwdZKggwwjfPy+elV/U8ODrWxkZ5w5sbQ1VFBR0HqwxP0lh1jfSqTxZTG6klTda7axdv4ftxTVMTAnr9rNi7O4g6I4Xd1DabEcF3PiPz7lv4Qh2FdWQHKmlpPhoj2vLDQOXAi9/tpe52ZFUNVsIc5oDrmluEjSUH6eh5+YaA+LSLDWV9Tr2V7aRn6CloKAgpJ+jHddWXenpm33EPZWxqa6GgoL+b5l4roXy4+cVymsM5bXB4F3fTRPCUej+fgEwOk7LtqIq39d2F1WTFKnh5LHu7xODcX31re6kT+GxU4zSdR9MVVFVh07tjrtOR8Cg+I033kClUrFlyxYKCgpYsWIFarWahQsXArBw4UL+9Kc/MXHiRMzm9nIGs9mM0WgkKioKs9lMWFgYZrOZ6Oiee5Pm5eV1+vdrO0/RbHXxo8snkTe688YcfaIJPq1CiUqiyeoAyrj8vPxun4oG2tMd1lRQUNBtjUNdKK6pq57WOKnIxa7yEyyaNzmokoDx4xUONu7i1QO13LFwDFDJBVPzum1o6ygxw8rjGz/mNx9X4lIUbpw7jry81M7fV1FI/KCa0mYr105LZ8HYJH669kv+vqeVyjY1+RlxPT5GBQUFfH3KeB78vJbDLVquSh2JSznO1NFZ5OUF135wMMnLg+sXQKvNgU6jRqdRh/RztOPaKlXVQBWxSSOASkZmppOXF7jX+VAQyo+fVyivMZTXBoN3fYHOaF6ljsc/OExa9mhiInRUf1zL+DT/7xODcX0WuxNeO0l4TAJ5ed0n10YdPUiYztzree/atcvv7QHLJ1566SVefPFFVq9eTV5eHo8++igXX3wxn3/+OQA7duxg9OjRTJ48mV27dmG1WmlpaaG4uJixY8cyffp037EbNmxgxowZQS1aURSe33yCsSlRnO9nFHNmXAQatYrjtWa2FNeRHhtOZryUKIhz5zvzcnn65hlB18iqVCruWDiGVpuTf248hlatIskY+BJ/ktHAhaMTyEs18tb/u5CvTEztdoxKpWJ2TjwJkXp+d1U+35iWzr1XT+DjgmoKK1sY3UudmNozpXH94Ro+KawCGPLlPhF67RmNER2KvDXFzZ7NJzK8Qwjhz0TPoKVDFc04XQpHq0yMSwluxsNgEKbTEK7T+Er+urI6XOi1p//61+ft2StWrOC3v/0ta9asISoqiieeeIKYmBiWL1/OsmXLUBSFu+66C4PBwO23386KFStYu3YtcXFxPPHEE0H9jH2lTRwsb+bBb0z0u1lGr1WTGRdOUbWJrcfqWDg+ZVhtqhEDLz02vM+jriemxzArJ57tx+tJjw0PqoPHi9+e3etz++FrJ2FxOIn31Bvfcn42h6taeHnbScYEMeVx4fhk3thdyv3vHmJMclSPE/XE4OUNir07sqX7hBDCnzzfrIdmUqINWB0u31C0oSI2QtfjRjurw+nr3nQ6gg6KV69e7fv/5557rtvXFy9ezOLFizvdlpiYyKpVq/p8UjtO1ANwxYQRPR6TkxjJhiM1mG1Ov9lkIQaj2y7MYfvxelIDlE10FMyHvZgIHTG0d8BQqVTcf80EJqfHcKWnX3IgC8cns2RmJrNy4vn61DS0wyzLGgraN9q56+1Ot3G9ECK0JRkNxEfqKaxo8b0PDbWgOCbcPdXOH5vDdW6C4nPpYHkzI6LDAl5ezk2K4rPDNQASFIsh47L8FEYlRZ71FyGdRs3SWcG1zgvXa3j0+sln9XzE2eVtP9QsmWIhRAAqlYq8VCMFlc2kxYajUsGY5KEVFMdG6GjqMVPs6tNk4K4GZVB8oKyJiek9b8qD9vYh2QkRfb6MLcRA0ahVvPOjucOu5lWcXXqt+4qCtyWb1BQLIXoyfkQ0L24tIS0mnOz4iCH3ehEbrudYrcnv1840Uzzo3plbbQ6Ka0xMSAtc15jrCYrPz5UssRhaIg3aM/okK0RXeo37Tc1bUxx2BhtNhBChLS81GqvDxYajNYwdQpvsvHqvKT79179B985cUNGCS2nfIdmTvNRoosO0fGViz3XHQggxHOi8meI2d03xUMv8CCHOnfGe8r1Wm3PI1RODex9NY5sdRVG6fc0WauUTB8vdzZh7K5+Ii9Sz997LpeuEEGLY08tEOyFEkEYnR6FRq3C6lCEZFMeG67E5XFjsrm4JAKvDRVxECJVPHChrIiFSz4jo3nfnS0AshBDd+xSHSfcJIUQPwnQaRiW5S1CHUo9ir0Cjns80UzzoXjkPlDUzIT1GAl4hhAhSx5ZsalV75lgIIfwZPyIanUbFSM/+rKEkNtwTFPupK7aGUks2q8PJkaoWLhqXNNCnIoQQQ4Y3CHa6FCL1GkkqCCEC+uHFo7k0P2VIdkKK8WSKm/z0Kg6pmuLyRgsOl8Lo5N6ncAkhhHBTq1Vo1SocLkXqiYUQvRo3wjgk64nBXVMMPWWKQ6j7hMkzjSk6TNfLkUIIITryZkckKBZChLJYX6bYf01xyPQpbrG6o/6osEGVwBZCiEHPexlU2rEJIUKZb6NdDzXFIbPRzpspjjJIUCyEEH3RnikeVC/rQgjRr8J1GvQaNY1daoqdLgWHSwmh8gmrOyg2SqZYCCH6xLvZLlzKJ4QQIUylUrkHeLR2Lp+wOVwAIZQptkqmWAghTofUFAshhosogxaz1dnpNm9QHDo1xd7yCckUCyFEn3gzxRIUCyFCXZhOQ5u9c1Bsdbj/HVKZYp1GdUb1IEIIMRzptO7exFI+IYQIdRF6DW22rkFxiGWKTRaHlE4IIcRpkJpiIcRwEe43UxxiNcVmq0NKJ4QQ4jToNNJ9QggxPITp/GWK3f8Ome4TLVYHUQYZ3CGEEH3l22gnfYqFECEuQt89U3zONtrV1dWxYMECiouLfbe9++67LFmyxPfvtWvXsmjRIhYvXsxnn30GQH19PbfddhvLli3jzjvvpK2tLeDPMVkcGKV8Qggh+sz7RiDlE0KIUBfuN1N8DoJiu93OPffcQ1hYmO+2Q4cO8frrr6MoCgA1NTWsXr2aNWvWsGrVKlauXInNZuMf//gHV111FS+//DL5+fm8+uqrAX+WSconhBDitOik+4QQYpgID5ApPqs1xY8++ihLly4lOTkZgIaGBlauXMmvf/1r3zH79u1j2rRp6PV6jEYjWVlZFBYWsmvXLubNmwfA/Pnz2bx5c8CfZbI6iJRMsRBC9JleMsVCiGEiPGD3idN/DQwYgb755pvEx8czb948nnnmGVwuF7/5zW+4++67MRgMvuNMJhNGo9H378jISEwmU6fbIyMjaWlp6fFnFRQU0Giy4GhTU1BQcNoLGqwsFkvIrSsU19RVKK8xlNfmFcpr7Lq21pZmABpqqygoCFyqNlSE8uPnFcprDOW1gaxvIJkaG7A5XRw4eAiN2t2O8niJCYDSkyfQtuhP6/sGDIrfeOMNVCoVW7ZsoaCggKuvvpqMjAzuu+8+rFYrRUVFPPTQQ8yZMwez2ey7n9lsxmg0EhUVhdlsJiwsDLPZTHR0dI8/Ky8vjzbnCTJHJJGXl3daixnMCgoKQm5dobimrkJ5jaG8Nq9QXmPXtSUVOqDYRE5WBnl56QN4Zv0nlB8/r1BeYyivDWR9Aymr5hh82cDI0WN9rXwL2kqBasaPHU1OYmTA++/atcvv7QGD4pdeesn3/8uXL+e+++5j1KhRAJSWlvLTn/6U3/zmN9TU1PDnP/8Zq9WKzWajuLiYsWPHMn36dD7//HMWLVrEhg0bmDFjRo8/y+F0YbG7pE+xEEKcBulTLIQYLsI9XXZabe3zLfqj+0S/RKBJSUksX76cZcuWoSgKd911FwaDgdtvv50VK1awdu1a4uLieOKJJ3r8Ht4Z1hIUCyFE3/lqiqUlmxAixHk//FtsLt9tdqf7/72bjk9H0BHo6tWrO/07IyODtWvX+v69ePFiFi9e3OmYxMREVq1aFdT3b7HaAaT7hBBCnAa9dJ8QQgwT3g//HTtQhNREO5PVAUimWAghTodOyieEEMNEx/IJL7vT3SZYfwaZ4sETFFskKBZCiNPlm2gnQbEQIsR5P/x3zBSfkz7F50qLN1Ms5RNCCNFnOo27LVGYbtC8rAshxFnhqynuEBTbnS7UKnwt2k7HoHn19GaKZcyzEEL0XWZ8BEaDlriI0+vPKYQQQ0V7+USHTLHTdUZZYuin7hP9wSSZYiGEOG2X56ew83eXntE0JyGEGAp85RO2zuUTZ9J5AgZRptgsG+2EEOK0qVQqCYiFEMOCN1PcsXzC5nSdUY9iGERBcYunfCJSL0GxEEIIIYTwz5sp7lg+YQ+lTLHJ6iBSr0F9BgXSQgghhBAitPntPtEPNcWDJyi2OKSeWAghhBBCBKRWqzBo1Z2CYrszxDLFUk8shBBCCCF6E67XdNtodyaDO2AQBcUtVgdRYbqBPg0hhBBCCDHIRei6BMVOJZTKJ+xEGWTntBBCCCGECCxMr+ky0c4ZOpliKZ8QQgghhBDBCO+SKbaHUqbYbHUSZZDyCSGEEEIIEVhEt0yxyzfu/nQNmqC4xWLHKN0nhBBCCCFEL8J0mm7dJ0ImUyzlE0IIIYQQIhhdyydCasyzS0EyxUIIIYQQolfdyidCKVMMyPAOIYQQQgjRq5DuUwxglD7FQgghhBCiFwNWU1xXV8eCBQsoLi6moKCAZcuWsXz5cr797W9TW1sLwNq1a1m0aBGLFy/ms88+A6C+vp7bbruNZcuWceedd9LW1hbw50j5hBBCCCGE6E2En0zxWa8pttvt3HPPPYSFhQHw0EMP8bvf/Y7Vq1dz2WWX8eyzz1JTU8Pq1atZs2YNq1atYuXKldhsNv7xj39w1VVX8fLLL5Ofn8+rr74a8GdFS1AshBBCCCF6Ea7T4HAp2J0uoH/6FPcahT766KMsXbqUZ555BoCVK1eSnJwMgNPpxGAwsG/fPqZNm4Zer0ev15OVlUVhYSG7du3i+9//PgDz589n5cqVfOtb3+rxZ1WXnaKgteqMFjRYWSwWCgoKBvo0+lUorqmrUF5jKK/NK5TXGMpr85I1Dm2hvDaQ9Q205vpGAPYeKCBCp8LmdNHUUHdG5xwwKH7zzTeJj49n3rx5vqDYGxDv3r2bF198kZdeeomNGzdiNBp994uMjMRkMmEymXy3R0ZG0tLSEvBkpuSPJS02/LQXM5gVFBSQl5c30KfRr0JxTV2F8hpDeW1eobzGUF6bl6xxaAvltYGsb6DtaT4JO+vJzBlFbIQOOE76iBTy8kb3et9du3b5vT1gUPzGG2+gUqnYsmULBQUFrFixgqeeeoodO3bw1FNP8cwzzxAfH09UVBRms9l3P7PZjNFo9N0eFhaG2WwmOjo64ElKTbEQQgghhOhNuN5dKtFmcxLpmXNxphPtAkahL730ku//ly9fzn333cfmzZt59dVXWb16NbGxsQBMnjyZP//5z1itVmw2G8XFxYwdO5bp06fz+eefs2jRIjZs2MCMGTN6/FkqFUTqJSgWQgghhBCBhes0ALTZndgc7rriM23J1qco1OVy8dBDD5Gamsodd9wBwHnnncePf/xjli9fzrJly1AUhbvuuguDwcDtt9/OihUrWLt2LXFxcTzxxBM9fu8ovRa1+swifCGEEEIIEfrCPYnUVpvTt9lOd7Y32nmtXr0agO3bt/v9+uLFi1m8eHGn2xITE1m1alVQ319KJ4QQQgghRDC8mWJLP2aKB83wDhncIYQQQgghguErn7A5sXkyxSEz5lkyxUIIIYQQIhjhendQ3BqKmeIoCYqFEEIIIUQQvEGxpWNNcagExVI+IYQQQgghguG3+4SUTwghhBBCiOEkwpMpNtscvpriEMoUS1AshBBCCCF6Z9CqUaug1RqKmWKDBMVCCCGEEKJ3KpWKSIMWs82B3akA7kD5TAyeoFhqioUQQgghRJAi9VrMVocvUyzlE0IIIYQQYtiJNGgwd+g+ETrlE5IpFkIIIYQQQYo0dM0Uq87o+w2ioFgyxUIIIYQQIjiReq17o12oZYqjZKOdEEIIIYQIUqRBg6lDpjhkJtpFS/mEEEIIIYQIUoReS6vNEYo1xZIpFkIIIYQQwYk0aDF16FMcMt0noiQoFkIIIYQQQYrUa3yZYpUKtOoQ2Wh3ptG9EEIIIYQYPiINWlptTqwOFzqNGpUqRIJiIYQQQgghghVp0ADQ2GrH0A/JVQmKhRBCCCHEkBPp6VzW0GpDd4ab7CDIoLiuro4FCxZQXFxMSUkJN954I8uWLePee+/F5XIXNz/55JNcf/31LF26lH379gH0eKwQQgghhBBnIlLvDoobW+1n3I4NggiK7XY799xzD2FhYQA88sgj3Hnnnbz88ssoisInn3zCwYMH2b59O6+99horV67k/vvv7/FYIYQQQgghzlTnTPGZ1RNDEEHxo48+ytKlS0lOTgbg4MGDzJo1C4D58+ezefNmdu3axdy5c1GpVKSlpeF0Oqmvr/d7rBBCCCGEEGcqUu+uKW7op0xxwD5ob775JvHx8cybN49nnnkGAEVRfLv7IiMjaWlpwWQyERsb236Sntv9HduTgoKCM13LoGaxWEJujaG4pq5CeY2hvDavUF5jKK/NS9Y4tIXy2kDWNxhU11gAaDBbMeqUMz7fgEHxG2+8gUqlYsuWLRQUFLBixQrq6+t9XzebzURHRxMVFYXZbO50u9FoRK1Wdzu2J3l5eWeyjkGvoKAg5NYYimvqKpTXGMpr8wrlNYby2rxkjUNbKK8NZH2DgS6hBf5XjlOB6MjwoM93165dfm8PmGt+6aWXePHFF1m9ejV5eXk8+uijzJ8/n23btgGwYcMGZs6cyfTp09m0aRMul4vy8nJcLhfx8fHk5+d3O1YIIYQQQogzFaFvz+32x7yLPo+RW7FiBb/73e9YuXIlubm5XHHFFWg0GmbOnMmSJUtwuVzcc889PR4rhBBCCCHEmfJutAPQ90NLtqCD4tWrV/v+/8UXX+z29TvuuIM77rij0205OTl+jxVCCCGEEOJMeDfaQf9kimV4hxBCCCGEGHK0GjUGT4a4PzLFEhQLIYQQQoghyVtCcU6GdwghhBBCCDEYRRrcJRSSKRZCCCGEEMOWd9SzTnMOJtoJIYQQQggxGEXoJVMshBBCCCGGufaaYk0vR/ZOgmIhhBBCCDEk+contFI+IYQQQgghhilvptgg3SeEEEIIIcRw5e0+IcM7hBBCCCHEsOWrKZaNdkIIIYQQYrjyjnqWTLEQQgghhBi2JFMshBBCCCGGPW/3CRnzLIQQQgghhq0IGfMshBBCCCGGO2/5hNQUCyGEEEKIYctXPiGZYiGEEEIIMVxNSIvmG1PTmJYVe8bfS3vmpyOEEEIIIcS5F2nQ8uel0/rle0mmWAghhBBCDHu9ZoqdTie//e1vOX78OCqVivvvvx+n08m9996LRqNh5MiRPPTQQ6jVatauXcuaNWvQarXcfvvtXHzxxdTX1/Pzn/8ci8VCcnIyjzzyCOHh4edibUIIIYQQQgSl10zxZ599BsCaNWu48847+dOf/sSTTz7JD3/4Q1555RVsNhvr16+npqaG1atXs2bNGlatWsXKlSux2Wz84x//4KqrruLll18mPz+fV1999awvSgghhBBCiL7oNSi+9NJL+f3vfw9AeXk50dHR5OXl0djYiKIomM1mtFot+/btY9q0aej1eoxGI1lZWRQWFrJr1y7mzZsHwPz589m8efPZXZEQQgghhBB9FNRGO61Wy4oVK/joo4/461//SmNjIw888ABPPfUURqOR2bNns27dOoxGo+8+kZGRmEwmTCaT7/bIyEhaWlr8/oyCgoJ+WM7gZbFYQm6NobimrkJ5jaG8Nq9QXmMor81L1ji0hfLaQNYXioLuPvHoo4/y85//nMWLF9PW1sZLL73EmDFjeOmll/jDH/7A3LlzMZvNvuPNZjNGo5GoqCjMZjNhYWGYzWaio6P9fv+8vLwzX80gVlBQEHJrDMU1dRXKawzltXmF8hpDeW1essahLZTXBrK+oWzXrl1+b++1fOLtt9/m//7v/wAIDw9HpVIRExNDVFQUAMnJyTQ3NzN58mR27dqF1WqlpaWF4uJixo4dy/Tp0/n8888B2LBhAzNmzOivNQkhhBBCCNEves0UX3755dx9993cdNNNOBwOfv3rXxMbG8tdd92FVqtFp9Px+9//nqSkJJYvX86yZctQFIW77roLg8HA7bffzooVK1i7di1xcXE88cQT52JdQgghhBBCBE2lKIoy0CfRUxpbCCGEEEKI/uavcmFQBMVCCCGEEEIMJJloJ4QQQgghhj0JioUQQgghxLB3zoPi5cuXU1xcfK5/7FlXWlrK9OnTWb58ue+/J5980u+xQ+V3sG3bNsaNG8d7773X6farr76aX/3qVwN0VmfPs88+y9y5c7FarQN9KmdsuD12MHT+rs5EoDUuXLhwyD53Q+lvr6tnnnmGb33rW9x8880sX76cAwcODPQp9atTp05xxx13sHz5cpYuXcp9992HyWTye2x5eTmffvrpOT7D07dt2zZmzJhBRUWF77Y//vGPvPnmmwN4Vv1j27ZtnH/++Sxfvpybb76ZpUuX8r///W+gT2vABd2nWPRu9OjRrF69eqBPo1/l5uby3nvvceWVVwJw+PBh2traBviszo533nmHr33ta7z33nssWrRooE/njA2nx04MbaH2t+dVVFTEp59+yiuvvIJKpaKgoIAVK1bwzjvvDPSp9QuLxcL/+3//jwcffJApU6YA8NZbb/Gzn/3M18q1o61bt3Ls2DEWLlx4rk/1tOn1eu6++26ee+45VCrVQJ9Ov5ozZw5/+tOfAPdsieXLl5OTkxOyvYmDMSDlEw0NDfzgBz/g1ltv5aqrruLjjz8G3Fms3//+975P1D1NvxtKnnjiCW688UaWLFnC+++/77v9r3/9K7fccgvf+c53qK+vH8AzDGz8+PGUl5f7Hot33nmHq6++GoAXX3yRW265hRtuuIHvfe972Gw23nzzTW666SZuvPFGtmzZMpCn3ifbtm0jKyuLpUuX8tJLLwHurNw999zj+yRdU1PDtm3buOGGG1i2bBlvv/32wJ50L/r62P3sZz9j/fr1ABQXF/O9731voE79tD355JO88sorgHsNy5cvB0LrtaWnNQ5VPf3teTPir7zyCn/7298A+Pvf/861117Lt7/9bZYtW8a2bdsG7LyDYTQaKS8v5/XXX6eqqoq8vDxef/11Dh8+7LuieMcdd9DS0sK2bdu49dZb+fa3v80111zj+10MZuvXr+e8887zBcQA1157LQ0NDZw4cYKbb76ZJUuW8M1vfpPa2lqeeeYZ/vvf//LJJ58M4Fn3zZw5c4iJien2ePzrX//iuuuuY8mSJTz++OMALFq0iNLSUgDWrVvHgw8+eM7P93RFRkayZMkS1q1b5zdu2bt3L0uWLOGGG27gRz/6ERaLZYDP+OwYkKC4sLCQW2+9leeee44HHnjA92Qzm81ceeWVvPjiiyQnJ7Nhw4aBOL3TVlRU1Kl84p133qG0tJRXXnmFf//73zz99NM0NzcD7v7P//73v7n44ov9fqIeTC6//HI+/PBDFEVh3759TJs2DZfLRWNjI88//zyvvfYaTqeT/fv3AxAdHc0rr7zC+eefP8BnHrzXXnuNG264gdzcXPR6PXv37gVg+vTprF69mq9+9au+x8lqtfLyyy/zjW98YwDPODh9eexuuOEG3nrrLQBef/11rr/++gE++/4z1F9bQllPf3tdFRYWsnHjRl5//XX+/ve/U1NTc47PtO9SUlJ46qmn2L17N0uWLOErX/kKn332Gb/73e+49957Wb16NfPnz+ef//wnAFVVVTz11FOsXbuW559/nrq6ugFeQWCnTp0iKyur2+0ZGRlcd911fO973+PVV1/llltuobCwkO9973tcddVVXHLJJQNwtqfvvvvu4/nnn6ekpARwv568//77rFmzhjVr1lBSUsJnn33G9ddf70uWvPnmmyxevHgAz7rvEhISWLdund+45Z577uHhhx/mtddeY8GCBSFbqnZOyifMZjN6vR6dTgfAzJkzeeaZZ3j99ddRqVQ4HA7fsfn5+QCkpqYOufqyruUTzz77LAcPHvRlchwOB2VlZYD7dwB0mvg3WF199dXcd999ZGZm+s5brVaj0+n46U9/SkREBJWVlb7HMScnZyBPt8+amprYsGED9fX1rF69GpPJxIsvvgi4swTgfpy8tXBDaX19eexmz57Ngw8+SH19PV988QU//elPB/jse9f1tSXQ5c2h+trSlzUONYH+9ry8XUOLi4uZNGkSGo0GjUbDxIkTB+KU+6SkpISoqCgeeeQRAPbv3893v/tdrFYr999/PwB2u52RI0cCMG3aNPR6PQBjxozh5MmTJCQkDMi5ByMlJYV9+/Z1u72kpASr1cq0adMAfEHwUK3FjYuL49e//jUrVqxg+vTpWK1WpkyZ0immOXr0KDfeeCPLli3jhhtuwGQyMXbs2AE+874pLy/n6quv5p133ukWt9TW1jJq1CgAbrjhhoE8zbPqnGSKf/WrX7Fr1y5cLhd1dXU8/PDDfP3rX+fxxx9n9uzZdGyVHEov+Lm5ucyePZvVq1fzwgsv8NWvfpXMzEwAX1Z1586djBkzZiBPs1eZmZm0trayevVqrrnmGgBMJhMff/wxf/7zn/nd736Hy+XyPY5q9dBqavLOO+9w3XXX8a9//YtVq1axdu1avvjiC+rr632bYnbv3s3o0aOBobW+vjx2KpWKa665hgcffJALL7zQ94I/mHV9bRk7dqwvg3jw4MFOxw7V15a+rHGo6elvT61W+9Z46NAhwJ102L9/Py6XC5vN5rt9MDt8+DAPPPAANpsNcH+gjo6OJjs7m0cffZTVq1fzi1/8gosuugiAgoICnE4nbW1tFBUVkZ2dPYBn37tLLrmEzZs3dwqMX3vtNeLi4liwYIHvfe6dd95h9erVqNVqXC7XQJ3uGVm4cCE5OTm89dZbGAwG9u3bh8PhQFEUduzYQU5ODkajkYkTJ/LII48Mudp4k8nEa6+9htFo9Bu3JCcnc+LECcC9efSjjz4a2BM+S85JpvjWW2/11dZcccUVjBo1iscee4xnnnmGESNG0NDQcC5O45xbuHAh27dvZ9myZbS2tnLppZcSFRUFwMcff8wLL7xAZGQkjz766ACfae++9rWv8Z///IecnBxOnTqFRqMhPDycpUuXApCUlER1dfUAn+Xpee2113jsscd8/w4PD+fyyy/n9ddf56233uL5558nPDycxx57jCNHjgzgmZ6evjx2ixYt4qKLLuI///nPQJ5y0Lq+tlx55ZXceeed7NixgwkTJgzw2fWPUF5jT397I0aM4P777yctLY3k5GQAxo0bx4IFC1i8eDFxcXHodDq02sG9V/zyyy+nuLiY66+/noiICBRF4Ze//CUjRoxgxYoVOBwOVCoVDz30ENXV1TgcDr773e/S2NjI7bffTnx8/EAvIaDIyEiefvppHn74YRobG3E6nYwbN46VK1fS0NDAPffcw1NPPUVYWBiPP/445eXlPPXUU0yYMMG3AXgo+c1vfsPWrVuJjIzkq1/9KjfeeCMul4sZM2Zw6aWXAu4s6ne+8x0efvjhAT7b3m3dupXly5ejVqtxOp3ccccdXHbZZfzhD3/oFrfcf//9/PrXv0atVpOUlMS3vvWtgT79s0Im2gnRg+XLl3Pffff5LhkNB1VVVfzyl7/khRdeGOhTEaKTuro61q1bx0033YTNZuPKK6/khRdeIC0tbaBPrV9s27aNNWvW+LoBCCHOvcH9MVsIcc58+OGH/O1vf+O+++4b6FMRopu4uDgOHDjAddddh0ql4oYbbgiZgFgIMThIplgIIYQQQgx7Q2fHkBBCCCGEEGfJWSufsNvt/PrXv6asrAybzcbtt9/O6NGj+dWvfoVKpWLMmDHce++9vp38JSUl/OhHP+Ldd98F3K1Bfv3rX+N0OlEUhQceeIDc3NyzdbpCCCGEEGIYO2tB8TvvvENsbCyPP/44jY2NfOMb32D8+PHceeedzJ49m3vuuYdPPvmEyy67jLfffpt///vfnSa7/eUvf+Hmm2/m0ksvZePGjaxcuZInn3zybJ2uEEIIIYQYxs5a+cRXvvIVfvKTnwDu5usajYaDBw8ya9YsAObPn8/mzZsBiImJ6dawfcWKFSxYsAAAp9OJwWA4W6cqhBBCCCGGubMWFEdGRhIVFYXJZOLHP/4xd955p29AgPfrLS0tAFx88cVERER0un98fDw6nY5jx47x6KOP8sMf/vBsnaoQQgghhBjmzupGu4qKCm655Ra+/vWvc/XVV3eaBGY2m4mOjg54/61bt/LDH/6Qxx57TOqJhRBCCCHEWXPWguLa2lpuu+02fvGLX3D99dcDkJ+fz7Zt2wDYsGEDM2fO7PH+W7du5aGHHuKf//wnkyZNOlunKYQQQgghxNnrU/zggw/y/vvvd8rw/uY3v+HBBx/EbreTm5vLgw8+iEaj8X39wgsv5IsvvgDgmmuuwWazkZSUBLhnxj/wwANn41SFEEIIIcQwJ8M7hBBCCCHEsCfDO4QQQgghxLAnQbEQQgghhBj2JCgWQgghhBDDngTFQgghhBBi2JOgWAghhBBCDHsSFAshhBBCiGFPgmIhhBBCCDHs/X/pWcvlr+9FFwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the results\n", + "fig, ax = plt.subplots(figsize=(12, 4))\n", + "births_by_date.plot(ax=ax);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In particular, the striking feature of this graph is the dip in birthrate on US holidays (e.g., Independence Day, Labor Day, Thanksgiving, Christmas, New Year's Day), although this likely reflects trends in scheduled/induced births rather than some deep psychosomatic effect on natural births.\n", + "For more discussion of this trend, see the analysis and links in [Andrew Gelman's blog post](http://andrewgelman.com/2012/06/14/cool-ass-signal-processing-using-gaussian-processes/) on the subject.\n", + "We'll return to this figure in [Example:-Effect-of-Holidays-on-US-Births](04.09-Text-and-Annotation.ipynb), where we will use Matplotlib's tools to annotate this plot.\n", + "\n", + "Looking at this short example, you can see that many of the Python and Pandas tools we've seen to this point can be combined and used to gain insight from a variety of datasets.\n", + "We will see some more sophisticated applications of these data manipulations in future chapters!" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.10-Working-With-Strings.ipynb b/notebooks/03.10-Working-With-Strings.ipynb new file mode 100644 index 000000000..5f0a844e1 --- /dev/null +++ b/notebooks/03.10-Working-With-Strings.ipynb @@ -0,0 +1,1377 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Vectorized String Operations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One strength of Python is its relative ease in handling and manipulating string data.\n", + "Pandas builds on this and provides a comprehensive set of *vectorized string operations* that are an important part of the type of munging required when working with (read: cleaning up) real-world data.\n", + "In this chapter, we'll walk through some of the Pandas string operations, and then take a look at using them to partially clean up a very messy dataset of recipes collected from the internet." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introducing Pandas String Operations\n", + "\n", + "We saw in previous chapters how tools like NumPy and Pandas generalize arithmetic operations so that we can easily and quickly perform the same operation on many array elements. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 4, 6, 10, 14, 22, 26])" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "x = np.array([2, 3, 5, 7, 11, 13])\n", + "x * 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This *vectorization* of operations simplifies the syntax of operating on arrays of data: we no longer have to worry about the size or shape of the array, but just about what operation we want done.\n", + "For arrays of strings, NumPy does not provide such simple access, and thus you're stuck using a more verbose loop syntax:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['Peter', 'Paul', 'Mary', 'Guido']" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = ['peter', 'Paul', 'MARY', 'gUIDO']\n", + "[s.capitalize() for s in data]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is perhaps sufficient to work with some data, but it will break if there are any missing values, so this approach requires putting in extra checks:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['Peter', 'Paul', None, 'Mary', 'Guido']" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = ['peter', 'Paul', None, 'MARY', 'gUIDO']\n", + "[s if s is None else s.capitalize() for s in data]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This kind of manual approach is not only verbose and inconvenient, it can be error-prone.\n", + "\n", + "Pandas includes features to address both this need for vectorized string operations and the need for correctly handling missing data via the `str` attribute of Pandas `Series` and `Index` objects containing strings.\n", + "So, for example, if we create a Pandas `Series` with this data we can directly call the `str.capitalize` method, which has missing value handling built in:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 Peter\n", + "1 Paul\n", + "2 None\n", + "3 Mary\n", + "4 Guido\n", + "dtype: object" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "names = pd.Series(data)\n", + "names.str.capitalize()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tables of Pandas String Methods\n", + "\n", + "If you have a good understanding of string manipulation in Python, most of the Pandas string syntax is intuitive enough that it's probably sufficient to just list the available methods. We'll start with that here, before diving deeper into a few of the subtleties.\n", + "The examples in this section use the following `Series` object:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "monte = pd.Series(['Graham Chapman', 'John Cleese', 'Terry Gilliam',\n", + " 'Eric Idle', 'Terry Jones', 'Michael Palin'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Methods Similar to Python String Methods\n", + "\n", + "Nearly all of Python's built-in string methods are mirrored by a Pandas vectorized string method. Here is a list of Pandas `str` methods that mirror Python string methods:\n", + "\n", + "| | | | |\n", + "|-----------|----------------|----------------|----------------|\n", + "|`len()` | `lower()` | `translate()` | `islower()` | \n", + "|`ljust()` | `upper()` | `startswith()` | `isupper()` | \n", + "|`rjust()` | `find()` | `endswith()` | `isnumeric()` | \n", + "|`center()` | `rfind()` | `isalnum()` | `isdecimal()` | \n", + "|`zfill()` | `index()` | `isalpha()` | `split()` | \n", + "|`strip()` | `rindex()` | `isdigit()` | `rsplit()` | \n", + "|`rstrip()` | `capitalize()` | `isspace()` | `partition()` | \n", + "|`lstrip()` | `swapcase()` | `istitle()` | `rpartition()` |\n", + "\n", + "Notice that these have various return values. Some, like `lower`, return a series of strings:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 graham chapman\n", + "1 john cleese\n", + "2 terry gilliam\n", + "3 eric idle\n", + "4 terry jones\n", + "5 michael palin\n", + "dtype: object" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "monte.str.lower()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But some others return numbers:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 14\n", + "1 11\n", + "2 13\n", + "3 9\n", + "4 11\n", + "5 13\n", + "dtype: int64" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "monte.str.len()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or Boolean values:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 False\n", + "1 False\n", + "2 True\n", + "3 False\n", + "4 True\n", + "5 False\n", + "dtype: bool" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "monte.str.startswith('T')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Still others return lists or other compound values for each element:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 [Graham, Chapman]\n", + "1 [John, Cleese]\n", + "2 [Terry, Gilliam]\n", + "3 [Eric, Idle]\n", + "4 [Terry, Jones]\n", + "5 [Michael, Palin]\n", + "dtype: object" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "monte.str.split()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll see further manipulations of this kind of series-of-lists object as we continue our discussion." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Methods Using Regular Expressions\n", + "\n", + "In addition, there are several methods that accept regular expressions (regexps) to examine the content of each string element, and follow some of the API conventions of Python's built-in `re` module:\n", + "\n", + "| Method | Description |\n", + "|-----------|-------------|\n", + "| `match` | Calls `re.match` on each element, returning a Boolean. |\n", + "| `extract` | Calls `re.match` on each element, returning matched groups as strings.|\n", + "| `findall` | Calls `re.findall` on each element |\n", + "| `replace` | Replaces occurrences of pattern with some other string|\n", + "| `contains`| Calls `re.search` on each element, returning a boolean |\n", + "| `count` | Counts occurrences of pattern|\n", + "| `split` | Equivalent to `str.split`, but accepts regexps |\n", + "| `rsplit` | Equivalent to `str.rsplit`, but accepts regexps |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With these, we can do a wide range of operations.\n", + "For example, we can extract the first name from each element by asking for a contiguous group of characters at the beginning of each element:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 Graham\n", + "1 John\n", + "2 Terry\n", + "3 Eric\n", + "4 Terry\n", + "5 Michael\n", + "dtype: object" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "monte.str.extract('([A-Za-z]+)', expand=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or we can do something more complicated, like finding all names that start and end with a consonant, making use of the start-of-string (`^`) and end-of-string (`$`) regular expression characters:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 [Graham Chapman]\n", + "1 []\n", + "2 [Terry Gilliam]\n", + "3 []\n", + "4 [Terry Jones]\n", + "5 [Michael Palin]\n", + "dtype: object" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "monte.str.findall(r'^[^AEIOU].*[^aeiou]$')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ability to concisely apply regular expressions across `Series` or `DataFrame` entries opens up many possibilities for analysis and cleaning of data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Miscellaneous Methods\n", + "Finally, there are some miscellaneous methods that enable other convenient operations:\n", + "\n", + "| Method | Description |\n", + "|--------|-------------|\n", + "| `get` | Indexes each element |\n", + "| `slice` | Slices each element|\n", + "| `slice_replace` | Replaces slice in each element with the passed value|\n", + "| `cat` | Concatenates strings|\n", + "| `repeat` | Repeats values |\n", + "| `normalize` | Returns Unicode form of strings |\n", + "| `pad` | Adds whitespace to left, right, or both sides of strings|\n", + "| `wrap` | Splits long strings into lines with length less than a given width|\n", + "| `join` | Joins strings in each element of the `Series` with the passed separator|\n", + "| `get_dummies` | Extracts dummy variables as a `DataFrame` |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Vectorized item access and slicing\n", + "\n", + "The `get` and `slice` operations, in particular, enable vectorized element access from each array.\n", + "For example, we can get a slice of the first three characters of each array using `str.slice(0, 3)`.\n", + "Note that this behavior is also available through Python's normal indexing syntax; for example, `df.str.slice(0, 3)` is equivalent to `df.str[0:3]`:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 Gra\n", + "1 Joh\n", + "2 Ter\n", + "3 Eri\n", + "4 Ter\n", + "5 Mic\n", + "dtype: object" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "monte.str[0:3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Indexing via `df.str.get(i)` and `df.str[i]` are likewise similar.\n", + "\n", + "These indexing methods also let you access elements of arrays returned by `split`.\n", + "For example, to extract the last name of each entry, we can combine `split` with `str` indexing:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 Chapman\n", + "1 Cleese\n", + "2 Gilliam\n", + "3 Idle\n", + "4 Jones\n", + "5 Palin\n", + "dtype: object" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "monte.str.split().str[-1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Indicator variables\n", + "\n", + "Another method that requires a bit of extra explanation is the `get_dummies` method.\n", + "This is useful when your data has a column containing some sort of coded indicator.\n", + "For example, we might have a dataset that contains information in the form of codes, such as A = \"born in America,\" B = \"born in the United Kingdom,\" C = \"likes cheese,\" D = \"likes spam\":" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " name info\n", + "0 Graham Chapman B|C|D\n", + "1 John Cleese B|D\n", + "2 Terry Gilliam A|C\n", + "3 Eric Idle B|D\n", + "4 Terry Jones B|C\n", + "5 Michael Palin B|C|D" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "full_monte = pd.DataFrame({'name': monte,\n", + " 'info': ['B|C|D', 'B|D', 'A|C',\n", + " 'B|D', 'B|C', 'B|C|D']})\n", + "full_monte" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `get_dummies` routine lets us split out these indicator variables into a `DataFrame`:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " A B C D\n", + "0 0 1 1 1\n", + "1 0 1 0 1\n", + "2 1 0 1 0\n", + "3 0 1 0 1\n", + "4 0 1 1 0\n", + "5 0 1 1 1" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "full_monte['info'].str.get_dummies('|')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With these operations as building blocks, you can construct an endless range of string processing procedures when cleaning your data.\n", + "\n", + "We won't dive further into these methods here, but I encourage you to read through [\"Working with Text Data\"](https://pandas.pydata.org/pandas-docs/stable/user_guide/text.html) in the Pandas online documentation, or to refer to the resources listed in [Further Resources](03.13-Further-Resources.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Recipe Database\n", + "\n", + "These vectorized string operations become most useful in the process of cleaning up messy, real-world data.\n", + "Here I'll walk through an example of that, using an open recipe database compiled from various sources on the web.\n", + "Our goal will be to parse the recipe data into ingredient lists, so we can quickly find a recipe based on some ingredients we have on hand. The scripts used to compile this can be found at https://github.com/fictivekin/openrecipes, and the link to the most recent version of the database is found there as well.\n", + "\n", + "This database is about 30 MB, and can be downloaded and unzipped with these commands:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# repo = \"https://raw.githubusercontent.com/jakevdp/open-recipe-data/master\"\n", + "# !cd data && curl -O {repo}/recipeitems.json.gz\n", + "# !gunzip data/recipeitems.json.gz" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The database is in JSON format, so we will use `pd.read_json` to read it (`lines=True` is required for this dataset because each line of the file is a JSON entry):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(173278, 17)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "recipes = pd.read_json('data/recipeitems.json', lines=True)\n", + "recipes.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see there are nearly 175,000 recipes, and 17 columns.\n", + "Let's take a look at one row to see what we have:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "_id {'$oid': '5160756b96cc62079cc2db15'}\n", + "name Drop Biscuits and Sausage Gravy\n", + "ingredients Biscuits\\n3 cups All-purpose Flour\\n2 Tablespo...\n", + "url http://thepioneerwoman.com/cooking/2013/03/dro...\n", + "image http://static.thepioneerwoman.com/cooking/file...\n", + "ts {'$date': 1365276011104}\n", + "cookTime PT30M\n", + "source thepioneerwoman\n", + "recipeYield 12\n", + "datePublished 2013-03-11\n", + "prepTime PT10M\n", + "description Late Saturday afternoon, after Marlboro Man ha...\n", + "totalTime NaN\n", + "creator NaN\n", + "recipeCategory NaN\n", + "dateModified NaN\n", + "recipeInstructions NaN\n", + "Name: 0, dtype: object" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "recipes.iloc[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is a lot of information there, but much of it is in a very messy form, as is typical of data scraped from the web.\n", + "In particular, the ingredient list is in string format; we're going to have to carefully extract the information we're interested in.\n", + "Let's start by taking a closer look at the ingredients:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "count 173278.000000\n", + "mean 244.617926\n", + "std 146.705285\n", + "min 0.000000\n", + "25% 147.000000\n", + "50% 221.000000\n", + "75% 314.000000\n", + "max 9067.000000\n", + "Name: ingredients, dtype: float64" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "recipes.ingredients.str.len().describe()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ingredient lists average 250 characters long, with a minimum of 0 and a maximum of nearly 10,000 characters!\n", + "\n", + "Just out of curiosity, let's see which recipe has the longest ingredient list:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Carrot Pineapple Spice & Brownie Layer Cake with Whipped Cream & Cream Cheese Frosting and Marzipan Carrots'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "recipes.name[np.argmax(recipes.ingredients.str.len())]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can do other aggregate explorations; for example, we can see how many of the recipes are for breakfast foods (using regular expression syntax to match both lowercase and capital letters):" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3524" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "recipes.description.str.contains('[Bb]reakfast').sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or how many of the recipes list cinnamon as an ingredient:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "10526" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "recipes.ingredients.str.contains('[Cc]innamon').sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We could even look to see whether any recipes misspell the ingredient as \"cinamon\":" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "11" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "recipes.ingredients.str.contains('[Cc]inamon').sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is the type of data exploration that is possible with Pandas string tools.\n", + "It is data munging like this that Python really excels at." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### A Simple Recipe Recommender\n", + "\n", + "Let's go a bit further, and start working on a simple recipe recommendation system: given a list of ingredients, we want to find any recipes that use all those ingredients.\n", + "While conceptually straightforward, the task is complicated by the heterogeneity of the data: there is no easy operation, for example, to extract a clean list of ingredients from each row.\n", + "So, we will cheat a bit: we'll start with a list of common ingredients, and simply search to see whether they are in each recipe's ingredient list.\n", + "For simplicity, let's just stick with herbs and spices for the time being:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "spice_list = ['salt', 'pepper', 'oregano', 'sage', 'parsley',\n", + " 'rosemary', 'tarragon', 'thyme', 'paprika', 'cumin']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then build a Boolean `DataFrame` consisting of `True` and `False` values, indicating whether each ingredient appears in the list:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n", + "
" + ], + "text/plain": [ + " salt pepper oregano sage parsley rosemary tarragon thyme paprika \\\n", + "0 False False False True False False False False False \n", + "1 False False False False False False False False False \n", + "2 True True False False False False False False False \n", + "3 False False False False False False False False False \n", + "4 False False False False False False False False False \n", + "\n", + " cumin \n", + "0 False \n", + "1 False \n", + "2 True \n", + "3 False \n", + "4 False " + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import re\n", + "spice_df = pd.DataFrame({\n", + " spice: recipes.ingredients.str.contains(spice, re.IGNORECASE)\n", + " for spice in spice_list})\n", + "spice_df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, as an example, let's say we'd like to find a recipe that uses parsley, paprika, and tarragon.\n", + "We can compute this very quickly using the `query` method of ``DataFrame``s, discussed further in [High-Performance Pandas: `eval()` and `query()`](03.12-Performance-Eval-and-Query.ipynb):" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "selection = spice_df.query('parsley & paprika & tarragon')\n", + "len(selection)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find only 10 recipes with this combination. Let's use the index returned by this selection to discover the names of those recipes:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2069 All cremat with a Little Gem, dandelion and wa...\n", + "74964 Lobster with Thermidor butter\n", + "93768 Burton's Southern Fried Chicken with White Gravy\n", + "113926 Mijo's Slow Cooker Shredded Beef\n", + "137686 Asparagus Soup with Poached Eggs\n", + "140530 Fried Oyster Po’boys\n", + "158475 Lamb shank tagine with herb tabbouleh\n", + "158486 Southern fried chicken in buttermilk\n", + "163175 Fried Chicken Sliders with Pickles + Slaw\n", + "165243 Bar Tartine Cauliflower Salad\n", + "Name: name, dtype: object" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "recipes.name[selection.index]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have narrowed down our recipe selection from 175,000 to 10, we are in a position to make a more informed decision about what we'd like to cook for dinner." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Going Further with Recipes\n", + "\n", + "Hopefully this example has given you a bit of a flavor (heh) of the types of data cleaning operations that are efficiently enabled by Pandas string methods.\n", + "Of course, building a robust recipe recommendation system would require a *lot* more work!\n", + "Extracting full ingredient lists from each recipe would be an important piece of the task; unfortunately, the wide variety of formats used makes this a relatively time-consuming process.\n", + "This points to the truism that in data science, cleaning and munging of real-world data often comprises the majority of the work—and Pandas provides the tools that can help you do this efficiently." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.11-Working-with-Time-Series.ipynb b/notebooks/03.11-Working-with-Time-Series.ipynb new file mode 100644 index 000000000..65ceb9f81 --- /dev/null +++ b/notebooks/03.11-Working-with-Time-Series.ipynb @@ -0,0 +1,2049 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Working with Time Series" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pandas was originally developed in the context of financial modeling, so as you might expect, it contains an extensive set of tools for working with dates, times, and time-indexed data.\n", + "Date and time data comes in a few flavors, which we will discuss here:\n", + "\n", + "- *Timestamps* reference particular moments in time (e.g., July 4th, 2021 at 7:00 a.m.).\n", + "- *Time intervals* and *periods* reference a length of time between a particular beginning and end point; for example, the month of June 2021. Periods usually reference a special case of time intervals in which each interval is of uniform length and does not overlap (e.g., 24-hour-long periods comprising days).\n", + "- *Time deltas* or *durations* reference an exact length of time (e.g., a duration of 22.56 seconds).\n", + "\n", + "This chapter will introduce how to work with each of these types of date/time data in Pandas.\n", + "This is by no means a complete guide to the time series tools available in Python or Pandas, but instead is intended as a broad overview of how you as a user should approach working with time series.\n", + "We will start with a brief discussion of tools for dealing with dates and times in Python, before moving more specifically to a discussion of the tools provided by Pandas.\n", + "After listing some resources that go into more depth, we will review some short examples of working with time series data in Pandas." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Dates and Times in Python\n", + "\n", + "The Python world has a number of available representations of dates, times, deltas, and time spans.\n", + "While the time series tools provided by Pandas tend to be the most useful for data science applications, it is helpful to see their relationship to other tools used in Python." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Native Python Dates and Times: datetime and dateutil\n", + "\n", + "Python's basic objects for working with dates and times reside in the built-in `datetime` module.\n", + "Along with the third-party `dateutil` module, you can use this to quickly perform a host of useful functionalities on dates and times.\n", + "For example, you can manually build a date using the `datetime` type:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "datetime.datetime(2021, 7, 4, 0, 0)" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from datetime import datetime\n", + "datetime(year=2021, month=7, day=4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or, using the `dateutil` module, you can parse dates from a variety of string formats:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "datetime.datetime(2021, 7, 4, 0, 0)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from dateutil import parser\n", + "date = parser.parse(\"4th of July, 2021\")\n", + "date" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once you have a `datetime` object, you can do things like printing the day of the week:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Sunday'" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "date.strftime('%A')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we've used one of the standard string format codes for printing dates (`'%A'`), which you can read about in the [`strftime` section](https://docs.python.org/3/library/datetime.html#strftime-and-strptime-behavior) of Python's [`datetime` documentation](https://docs.python.org/3/library/datetime.html).\n", + "Documentation of other useful date utilities can be found in [``dateutil``'s online documentation](http://labix.org/python-dateutil).\n", + "A related package to be aware of is [`pytz`](http://pytz.sourceforge.net/), which contains tools for working with the most migraine-inducing element of time series data: time zones.\n", + "\n", + "The power of `datetime` and `dateutil` lies in their flexibility and easy syntax: you can use these objects and their built-in methods to easily perform nearly any operation you might be interested in.\n", + "Where they break down is when you wish to work with large arrays of dates and times:\n", + "just as lists of Python numerical variables are suboptimal compared to NumPy-style typed numerical arrays, lists of Python `datetime` objects are suboptimal compared to typed arrays of encoded dates." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Typed Arrays of Times: NumPy's datetime64\n", + "\n", + "NumPy's `datetime64` dtype encodes dates as 64-bit integers, and thus allows arrays of dates to be represented compactly and operated on in an efficient manner.\n", + "The `datetime64` requires a specific input format:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array('2021-07-04', dtype='datetime64[D]')" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "date = np.array('2021-07-04', dtype=np.datetime64)\n", + "date" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once we have dates in this form, we can quickly do vectorized operations on it:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['2021-07-04', '2021-07-05', '2021-07-06', '2021-07-07',\n", + " '2021-07-08', '2021-07-09', '2021-07-10', '2021-07-11',\n", + " '2021-07-12', '2021-07-13', '2021-07-14', '2021-07-15'],\n", + " dtype='datetime64[D]')" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "date + np.arange(12)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of the uniform type in NumPy `datetime64` arrays, this kind of operation can be accomplished much more quickly than if we were working directly with Python's `datetime` objects, especially as arrays get large\n", + "(we introduced this type of vectorization in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb)).\n", + "\n", + "One detail of the `datetime64` and related `timedelta64` objects is that they are built on a *fundamental time unit*.\n", + "Because the `datetime64` object is limited to 64-bit precision, the range of encodable times is $2^{64}$ times this fundamental unit.\n", + "In other words, `datetime64` imposes a trade-off between *time resolution* and *maximum time span*.\n", + "\n", + "For example, if you want a time resolution of 1 nanosecond, you only have enough information to encode a range of $2^{64}$ nanoseconds, or just under 600 years.\n", + "NumPy will infer the desired unit from the input; for example, here is a day-based `datetime`:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.datetime64('2021-07-04')" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.datetime64('2021-07-04')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a minute-based datetime:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.datetime64('2021-07-04T12:00')" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.datetime64('2021-07-04 12:00')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can force any desired fundamental unit using one of many format codes; for example, here we'll force a nanosecond-based time:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.datetime64('2021-07-04T12:59:59.500000000')" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.datetime64('2021-07-04 12:59:59.50', 'ns')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following table, drawn from the NumPy `datetime64` documentation, lists the available format codes along with the relative and absolute time spans that they can encode:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "|Code | Meaning | Time span (relative) | Time span (absolute) |\n", + "|------|-------------|----------------------|------------------------|\n", + "| `Y` | Year | ± 9.2e18 years | [9.2e18 BC, 9.2e18 AD] |\n", + "| `M` | Month | ± 7.6e17 years | [7.6e17 BC, 7.6e17 AD] |\n", + "| `W` | Week | ± 1.7e17 years | [1.7e17 BC, 1.7e17 AD] |\n", + "| `D` | Day | ± 2.5e16 years | [2.5e16 BC, 2.5e16 AD] |\n", + "| `h` | Hour | ± 1.0e15 years | [1.0e15 BC, 1.0e15 AD] |\n", + "| `m` | Minute | ± 1.7e13 years | [1.7e13 BC, 1.7e13 AD] |\n", + "| `s` | Second | ± 2.9e12 years | [ 2.9e9 BC, 2.9e9 AD] |\n", + "| `ms` | Millisecond | ± 2.9e9 years | [ 2.9e6 BC, 2.9e6 AD] |\n", + "| `us` | Microsecond | ± 2.9e6 years | [290301 BC, 294241 AD] |\n", + "| `ns` | Nanosecond | ± 292 years | [ 1678 AD, 2262 AD] |\n", + "| `ps` | Picosecond | ± 106 days | [ 1969 AD, 1970 AD] |\n", + "| `fs` | Femtosecond | ± 2.6 hours | [ 1969 AD, 1970 AD] |\n", + "| `as` | Attosecond | ± 9.2 seconds | [ 1969 AD, 1970 AD] |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the types of data we see in the real world, a useful default is `datetime64[ns]`, as it can encode a useful range of modern dates with a suitably fine precision.\n", + "\n", + "Finally, note that while the `datetime64` data type addresses some of the deficiencies of the built-in Python `datetime` type, it lacks many of the convenient methods and functions provided by `datetime` and especially `dateutil`.\n", + "More information can be found in [NumPy's `datetime64` documentation](http://docs.scipy.org/doc/numpy/reference/arrays.datetime.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dates and Times in Pandas: The Best of Both Worlds\n", + "\n", + "Pandas builds upon all the tools just discussed to provide a `Timestamp` object, which combines the ease of use of `datetime` and `dateutil` with the efficient storage and vectorized interface of `numpy.datetime64`.\n", + "From a group of these `Timestamp` objects, Pandas can construct a `DatetimeIndex` that can be used to index data in a `Series` or `DataFrame`.\n", + "\n", + "For example, we can use Pandas tools to repeat the demonstration from earlier.\n", + "We can parse a flexibly formatted string date and use format codes to output the day of the week, as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Timestamp('2021-07-04 00:00:00')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "date = pd.to_datetime(\"4th of July, 2021\")\n", + "date" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Sunday'" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "date.strftime('%A')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Additionally, we can do NumPy-style vectorized operations directly on this same object:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2021-07-04', '2021-07-05', '2021-07-06', '2021-07-07',\n", + " '2021-07-08', '2021-07-09', '2021-07-10', '2021-07-11',\n", + " '2021-07-12', '2021-07-13', '2021-07-14', '2021-07-15'],\n", + " dtype='datetime64[ns]', freq=None)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "date + pd.to_timedelta(np.arange(12), 'D')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the next section, we will take a closer look at manipulating time series data with the tools provided by Pandas." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pandas Time Series: Indexing by Time\n", + "\n", + "The Pandas time series tools really become useful when you begin to index data by timestamps.\n", + "For example, we can construct a `Series` object that has time-indexed data:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2020-07-04 0\n", + "2020-08-04 1\n", + "2021-07-04 2\n", + "2021-08-04 3\n", + "dtype: int64" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "index = pd.DatetimeIndex(['2020-07-04', '2020-08-04',\n", + " '2021-07-04', '2021-08-04'])\n", + "data = pd.Series([0, 1, 2, 3], index=index)\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And now that we have this data in a `Series`, we can make use of any of the `Series` indexing patterns we discussed in previous chapters, passing values that can be coerced into dates:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2020-07-04 0\n", + "2020-08-04 1\n", + "2021-07-04 2\n", + "dtype: int64" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['2020-07-04':'2021-07-04']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are additional special date-only indexing operations, such as passing a year to obtain a slice of all data from that year:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2021-07-04 2\n", + "2021-08-04 3\n", + "dtype: int64" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['2021']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Later, we will see additional examples of the convenience of dates-as-indices.\n", + "But first, let's take a closer look at the available time series data structures." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pandas Time Series Data Structures\n", + "\n", + "This section will introduce the fundamental Pandas data structures for working with time series data:\n", + "\n", + "- For *timestamps*, Pandas provides the `Timestamp` type. As mentioned before, this is essentially a replacement for Python's native `datetime`, but it's based on the more efficient `numpy.datetime64` data type. The associated `Index` structure is `DatetimeIndex`.\n", + "- For *time periods*, Pandas provides the `Period` type. This encodes a fixed-frequency interval based on `numpy.datetime64`. The associated index structure is `PeriodIndex`.\n", + "- For *time deltas* or *durations*, Pandas provides the `Timedelta` type. `Timedelta` is a more efficient replacement for Python's native `datetime.timedelta` type, and is based on `numpy.timedelta64`. The associated index structure is `TimedeltaIndex`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most fundamental of these date/time objects are the `Timestamp` and `DatetimeIndex` objects.\n", + "While these class objects can be invoked directly, it is more common to use the `pd.to_datetime` function, which can parse a wide variety of formats.\n", + "Passing a single date to `pd.to_datetime` yields a `Timestamp`; passing a series of dates by default yields a `DatetimeIndex`, as you can see here:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2021-07-03', '2021-07-04', '2021-07-06', '2021-07-07',\n", + " '2021-07-08'],\n", + " dtype='datetime64[ns]', freq=None)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dates = pd.to_datetime([datetime(2021, 7, 3), '4th of July, 2021',\n", + " '2021-Jul-6', '07-07-2021', '20210708'])\n", + "dates" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any `DatetimeIndex` can be converted to a `PeriodIndex` with the `to_period` function, with the addition of a frequency code; here we'll use `'D'` to indicate daily frequency:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "PeriodIndex(['2021-07-03', '2021-07-04', '2021-07-06', '2021-07-07',\n", + " '2021-07-08'],\n", + " dtype='period[D]')" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dates.to_period('D')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A `TimedeltaIndex` is created, for example, when a date is subtracted from another:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "TimedeltaIndex(['0 days', '1 days', '3 days', '4 days', '5 days'], dtype='timedelta64[ns]', freq=None)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dates - dates[0]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Regular Sequences: pd.date_range\n", + "\n", + "To make creation of regular date sequences more convenient, Pandas offers a few functions for this purpose: `pd.date_range` for timestamps, `pd.period_range` for periods, and `pd.timedelta_range` for time deltas.\n", + "We've seen that Python's `range` and NumPy's `np.arange` take a start point, end point, and optional step size and return a sequence.\n", + "Similarly, `pd.date_range` accepts a start date, an end date, and an optional frequency code to create a regular sequence of dates:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-03', '2015-07-04', '2015-07-05', '2015-07-06',\n", + " '2015-07-07', '2015-07-08', '2015-07-09', '2015-07-10'],\n", + " dtype='datetime64[ns]', freq='D')" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.date_range('2015-07-03', '2015-07-10')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, the date range can be specified not with a start and end point, but with a start point and a number of periods:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-03', '2015-07-04', '2015-07-05', '2015-07-06',\n", + " '2015-07-07', '2015-07-08', '2015-07-09', '2015-07-10'],\n", + " dtype='datetime64[ns]', freq='D')" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.date_range('2015-07-03', periods=8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The spacing can be modified by altering the `freq` argument, which defaults to `D`.\n", + "For example, here we construct a range of hourly timestamps:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-03 00:00:00', '2015-07-03 01:00:00',\n", + " '2015-07-03 02:00:00', '2015-07-03 03:00:00',\n", + " '2015-07-03 04:00:00', '2015-07-03 05:00:00',\n", + " '2015-07-03 06:00:00', '2015-07-03 07:00:00'],\n", + " dtype='datetime64[ns]', freq='H')" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.date_range('2015-07-03', periods=8, freq='H')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To create regular sequences of `Period` or `Timedelta` values, the similar `pd.period_range` and `pd.timedelta_range` functions are useful.\n", + "Here are some monthly periods:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "PeriodIndex(['2015-07', '2015-08', '2015-09', '2015-10', '2015-11', '2015-12',\n", + " '2016-01', '2016-02'],\n", + " dtype='period[M]')" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.period_range('2015-07', periods=8, freq='M')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And a sequence of durations increasing by an hour:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "TimedeltaIndex(['0 days 00:00:00', '0 days 01:00:00', '0 days 02:00:00',\n", + " '0 days 03:00:00', '0 days 04:00:00', '0 days 05:00:00'],\n", + " dtype='timedelta64[ns]', freq='H')" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.timedelta_range(0, periods=6, freq='H')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these require an understanding of Pandas frequency codes, which are summarized in the next section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Frequencies and Offsets\n", + "\n", + "Fundamental to these Pandas time series tools is the concept of a *frequency* or *date offset*. The following table summarizes the main codes available; as with the `D` (day) and `H` (hour) codes demonstrated in the previous sections, we can use these to specify any desired frequency spacing:" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Code | Description | Code | Description |\n", + "|------|-------------------|------|----------------------|\n", + "| `D` | Calendar day | `B` | Business day |\n", + "| `W` | Weekly | | |\n", + "| `M` | Month end | `BM` | Business month end |\n", + "| `Q` | Quarter end | `BQ` | Business quarter end |\n", + "| `A` | Year end | `BA` | Business year end |\n", + "| `H` | Hours | `BH` | Business hours |\n", + "| `T` | Minutes | | |\n", + "| `S` | Seconds | | |\n", + "| `L` | Milliseconds | | |\n", + "| `U` | Microseconds | | |\n", + "| `N` | Nanoseconds | | |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The monthly, quarterly, and annual frequencies are all marked at the end of the specified period.\n", + "Adding an `S` suffix to any of these causes them to instead be marked at the beginning:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Code | Description | Code | Description |\n", + "|-------|-------------------|-------|------------------------|\n", + "| `MS` | Month start |`BMS` | Business month start |\n", + "| `QS` | Quarter start |`BQS` | Business quarter start |\n", + "| `AS` | Year start |`BAS` | Business year start |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Additionally, you can change the month used to mark any quarterly or annual code by adding a three-letter month code as a suffix:\n", + "\n", + "- `Q-JAN`, `BQ-FEB`, `QS-MAR`, `BQS-APR`, etc.\n", + "- `A-JAN`, `BA-FEB`, `AS-MAR`, `BAS-APR`, etc.\n", + "\n", + "In the same way, the split point of the weekly frequency can be modified by adding a three-letter weekday code:\n", + "\n", + "- `W-SUN`, `W-MON`, `W-TUE`, `W-WED`, etc.\n", + "\n", + "On top of this, codes can be combined with numbers to specify other frequencies.\n", + "For example, for a frequency of 2 hours and 30 minutes, we can combine the hour (`H`) and minute (`T`) codes as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "TimedeltaIndex(['0 days 00:00:00', '0 days 02:30:00', '0 days 05:00:00',\n", + " '0 days 07:30:00', '0 days 10:00:00', '0 days 12:30:00'],\n", + " dtype='timedelta64[ns]', freq='150T')" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.timedelta_range(0, periods=6, freq=\"2H30T\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these short codes refer to specific instances of Pandas time series offsets, which can be found in the `pd.tseries.offsets` module.\n", + "For example, we can create a business day offset directly as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-01', '2015-07-02', '2015-07-03', '2015-07-06',\n", + " '2015-07-07', '2015-07-08'],\n", + " dtype='datetime64[ns]', freq='B')" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from pandas.tseries.offsets import BDay\n", + "pd.date_range('2015-07-01', periods=6, freq=BDay())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more discussion of the use of frequencies and offsets, see the [`DateOffset` section](https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#dateoffset-objects) of the Pandas documentation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Resampling, Shifting, and Windowing\n", + "\n", + "The ability to use dates and times as indices to intuitively organize and access data is an important aspect of the Pandas time series tools.\n", + "The benefits of indexed data in general (automatic alignment during operations, intuitive data slicing and access, etc.) still apply, and Pandas provides several additional time series–specific operations.\n", + "\n", + "We will take a look at a few of those here, using some stock price data as an example.\n", + "Because Pandas was developed largely in a finance context, it includes some very specific tools for financial data.\n", + "For example, the accompanying `pandas-datareader` package (installable via `pip install pandas-datareader`) knows how to import data from various online sources.\n", + "Here we will load part of the S&P 500 price history:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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HighLowOpenCloseVolumeAdj Close
Date
2018-01-022695.8898932682.3601072683.7299802695.81005933672500002695.810059
2018-01-032714.3701172697.7700202697.8500982713.06005935386600002713.060059
2018-01-042729.2900392719.0700682719.3100592723.98999036952600002723.989990
2018-01-052743.4499512727.9199222731.3300782743.14990232366200002743.149902
2018-01-082748.5100102737.6000982742.6699222747.70996132426500002747.709961
\n", + "
" + ], + "text/plain": [ + " High Low Open Close Volume \\\n", + "Date \n", + "2018-01-02 2695.889893 2682.360107 2683.729980 2695.810059 3367250000 \n", + "2018-01-03 2714.370117 2697.770020 2697.850098 2713.060059 3538660000 \n", + "2018-01-04 2729.290039 2719.070068 2719.310059 2723.989990 3695260000 \n", + "2018-01-05 2743.449951 2727.919922 2731.330078 2743.149902 3236620000 \n", + "2018-01-08 2748.510010 2737.600098 2742.669922 2747.709961 3242650000 \n", + "\n", + " Adj Close \n", + "Date \n", + "2018-01-02 2695.810059 \n", + "2018-01-03 2713.060059 \n", + "2018-01-04 2723.989990 \n", + "2018-01-05 2743.149902 \n", + "2018-01-08 2747.709961 " + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from pandas_datareader import data\n", + "\n", + "sp500 = data.DataReader('^GSPC', start='2018', end='2022',\n", + " data_source='yahoo')\n", + "sp500.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For simplicity, we'll use just the closing price:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "sp500 = sp500['Close']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can visualize this using the ``plot`` method, after the normal Matplotlib setup boilerplate (see [Part 4](04.00-Introduction-To-Matplotlib.ipynb)); the result is shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "sp500.plot();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Resampling and Converting Frequencies\n", + "\n", + "One common need when dealing with time series data is resampling at a higher or lower frequency.\n", + "This can be done using the `resample` method, or the much simpler `asfreq` method.\n", + "The primary difference between the two is that `resample` is fundamentally a *data aggregation*, while `asfreq` is fundamentally a *data selection*.\n", + "\n", + "Let's compare what the two return when we downsample the S&P 500 closing price data.\n", + "Here we will resample the data at the end of business year; the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sp500.plot(alpha=0.5, style='-')\n", + "sp500.resample('BA').mean().plot(style=':')\n", + "sp500.asfreq('BA').plot(style='--');\n", + "plt.legend(['input', 'resample', 'asfreq'],\n", + " loc='upper left');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the difference: at each point, `resample` reports the *average of the previous year*, while `asfreq` reports the *value at the end of the year*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For upsampling, `resample` and `asfreq` are largely equivalent, though `resample` has many more options available.\n", + "In this case, the default for both methods is to leave the upsampled points empty; that is, filled with NA values.\n", + "Like the `pd.fillna` function discussed in [Handling Missing Data](03.04-Missing-Values.ipynb), `asfreq` accepts a `method` argument to specify how values are imputed.\n", + "Here, we will resample the business day data at a daily frequency (i.e., including weekends); the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(2, sharex=True)\n", + "data = sp500.iloc[:20]\n", + "\n", + "data.asfreq('D').plot(ax=ax[0], marker='o')\n", + "\n", + "data.asfreq('D', method='bfill').plot(ax=ax[1], style='-o')\n", + "data.asfreq('D', method='ffill').plot(ax=ax[1], style='--o')\n", + "ax[1].legend([\"back-fill\", \"forward-fill\"]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because the S&P 500 data only exists for business days, the top panel has gaps representing NA values.\n", + "The bottom panel shows the differences between two strategies for filling the gaps: forward filling and backward filling." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Time Shifts\n", + "\n", + "Another common time series–specific operation is shifting of data in time.\n", + "For this, Pandas provides the `shift` method, which can be used to shift data by a given number of entries.\n", + "With time series data sampled at a regular frequency, this can give us a way to explore trends over time.\n", + "\n", + "For example, here we resample the data to daily values, and shift by 364 to compute the 1-year return on investment for the S&P 500 over time (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sp500 = sp500.asfreq('D', method='pad')\n", + "\n", + "ROI = 100 * (sp500.shift(-365) - sp500) / sp500\n", + "ROI.plot()\n", + "plt.ylabel('% Return on Investment after 1 year');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The worst one-year return was around March 2019, with the coronavirus-related market crash exactly a year later. As you might expect, the best one-year return was to be found in March 2020, for those with enough foresight or luck to buy low." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Rolling Windows\n", + "\n", + "Calculating rolling statistics is a third type of time series–specific operation implemented by Pandas.\n", + "This can be accomplished via the `rolling` attribute of `Series` and `DataFrame` objects, which returns a view similar to what we saw with the `groupby` operation (see [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb)).\n", + "This rolling view makes available a number of aggregation operations by default.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "For example, we can look at the one-year centered rolling mean and standard deviation of the stock prices (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rolling = sp500.rolling(365, center=True)\n", + "\n", + "data = pd.DataFrame({'input': sp500,\n", + " 'one-year rolling_mean': rolling.mean(),\n", + " 'one-year rolling_median': rolling.median()})\n", + "ax = data.plot(style=['-', '--', ':'])\n", + "ax.lines[0].set_alpha(0.3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with `groupby` operations, the `aggregate` and `apply` methods can be used for custom rolling computations." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Where to Learn More\n", + "\n", + "This chapter has provided only a brief summary of some of the most essential features of time series tools provided by Pandas; for a more complete discussion, you can refer to the [\"Time Series/Date Functionality\" section](http://pandas.pydata.org/pandas-docs/stable/timeseries.html) of the Pandas online documentation.\n", + "\n", + "Another excellent resource is the book [*Python for Data Analysis*](https://learning.oreilly.com/library/view/python-for-data/9781098104023/) by Wes McKinney (O'Reilly).\n", + "It is an invaluable resource on the use of Pandas.\n", + "In particular, this book emphasizes time series tools in the context of business and finance, and focuses much more on particular details of business calendars, time zones, and related topics.\n", + "\n", + "As always, you can also use the IPython help functionality to explore and try out further options available to the functions and methods discussed here. I find this often is the best way to learn a new Python tool." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Visualizing Seattle Bicycle Counts\n", + "\n", + "As a more involved example of working with time series data, let's take a look at bicycle counts on Seattle's [Fremont Bridge](http://www.openstreetmap.org/#map=17/47.64813/-122.34965).\n", + "This data comes from an automated bicycle counter installed in late 2012, which has inductive sensors on the east and west sidewalks of the bridge.\n", + "The hourly bicycle counts can be downloaded from [http://data.seattle.gov](http://data.seattle.gov); the Fremont Bridge Bicycle Counter dataset is available under the Transportation category.\n", + "\n", + "The CSV used for this book can be downloaded as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# url = ('https://raw.githubusercontent.com/jakevdp/'\n", + "# 'bicycle-data/main/FremontBridge.csv')\n", + "# !curl -O {url}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once this dataset is downloaded, we can use Pandas to read the CSV output into a `DataFrame`.\n", + "We will specify that we want the `Date` column as an index, and we want these dates to be automatically parsed:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Fremont Bridge Total Fremont Bridge East Sidewalk \\\n", + "Date \n", + "2019-11-01 00:00:00 12.0 7.0 \n", + "2019-11-01 01:00:00 7.0 0.0 \n", + "2019-11-01 02:00:00 1.0 0.0 \n", + "2019-11-01 03:00:00 6.0 6.0 \n", + "2019-11-01 04:00:00 6.0 5.0 \n", + "\n", + " Fremont Bridge West Sidewalk \n", + "Date \n", + "2019-11-01 00:00:00 5.0 \n", + "2019-11-01 01:00:00 7.0 \n", + "2019-11-01 02:00:00 1.0 \n", + "2019-11-01 03:00:00 0.0 \n", + "2019-11-01 04:00:00 1.0 " + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv('FremontBridge.csv', index_col='Date', parse_dates=True)\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For convenience, we'll shorten the column names:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "data.columns = ['Total', 'East', 'West']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's take a look at the summary statistics for this data:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Total East West\n", + "count 147255.000000 147255.000000 147255.000000\n", + "mean 110.341462 50.077763 60.263699\n", + "std 140.422051 64.634038 87.252147\n", + "min 0.000000 0.000000 0.000000\n", + "25% 14.000000 6.000000 7.000000\n", + "50% 60.000000 28.000000 30.000000\n", + "75% 145.000000 68.000000 74.000000\n", + "max 1097.000000 698.000000 850.000000" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.dropna().describe()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Visualizing the Data\n", + "\n", + "We can gain some insight into the dataset by visualizing it.\n", + "Let's start by plotting the raw data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "data.plot()\n", + "plt.ylabel('Hourly Bicycle Count');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ~150,000 hourly samples are far too dense for us to make much sense of.\n", + "We can gain more insight by resampling the data to a coarser grid.\n", + "Let's resample by week (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "weekly = data.resample('W').sum()\n", + "weekly.plot(style=['-', ':', '--'])\n", + "plt.ylabel('Weekly bicycle count');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This reveals some trends: as you might expect, people bicycle more in the summer than in the winter, and even within a particular season the bicycle use varies from week to week (likely dependent on weather; see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), where we explore this further). Further, the effect of the COVID-19 pandemic on commuting patterns is quite clear, starting in early 2020.\n", + "\n", + "Another option that comes in handy for aggregating the data is to use a rolling mean, utilizing the `pd.rolling_mean` function.\n", + "Here we'll examine the 30-day rolling mean of our data, making sure to center the window (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "daily = data.resample('D').sum()\n", + "daily.rolling(30, center=True).sum().plot(style=['-', ':', '--'])\n", + "plt.ylabel('mean hourly count');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The jaggedness of the result is due to the hard cutoff of the window.\n", + "We can get a smoother version of a rolling mean using a window function—for example, a Gaussian window, as shown in the following figure.\n", + "The following code specifies both the width of the window (here, 50 days) and the width of the Gaussian window (here, 10 days):" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "daily.rolling(50, center=True,\n", + " win_type='gaussian').sum(std=10).plot(style=['-', ':', '--']);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Digging into the Data\n", + "\n", + "While these smoothed data views are useful to get an idea of the general trend in the data, they hide much of the structure.\n", + "For example, we might want to look at the average traffic as a function of the time of day.\n", + "We can do this using the `groupby` functionality discussed in [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb) (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "by_time = data.groupby(data.index.time).mean()\n", + "hourly_ticks = 4 * 60 * 60 * np.arange(6)\n", + "by_time.plot(xticks=hourly_ticks, style=['-', ':', '--']);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The hourly traffic is a strongly bimodal sequence, with peaks around 8:00 a.m. and 5:00 p.m.\n", + "This is likely evidence of a strong component of commuter traffic crossing the bridge.\n", + "There is a directional component as well: according to the data, the east sidewalk is used more during the a.m. commute, and the west sidewalk is used more during the p.m. commute.\n", + "\n", + "We also might be curious about how things change based on the day of the week. Again, we can do this with a simple `groupby` (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "by_weekday = data.groupby(data.index.dayofweek).mean()\n", + "by_weekday.index = ['Mon', 'Tues', 'Wed', 'Thurs', 'Fri', 'Sat', 'Sun']\n", + "by_weekday.plot(style=['-', ':', '--']);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This shows a strong distinction between weekday and weekend totals, with around twice as many average riders crossing the bridge on Monday through Friday than on Saturday and Sunday.\n", + "\n", + "With this in mind, let's do a compound `groupby` and look at the hourly trends on weekdays versus weekends.\n", + "We'll start by grouping by flags marking the weekend and the time of day:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "weekend = np.where(data.index.weekday < 5, 'Weekday', 'Weekend')\n", + "by_time = data.groupby([weekend, data.index.time]).mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll use some of the Matplotlib tools that will be described in [Multiple Subplots](04.08-Multiple-Subplots.ipynb) to plot two panels side by side, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "fig, ax = plt.subplots(1, 2, figsize=(14, 5))\n", + "by_time.loc['Weekday'].plot(ax=ax[0], title='Weekdays',\n", + " xticks=hourly_ticks, style=['-', ':', '--'])\n", + "by_time.loc['Weekend'].plot(ax=ax[1], title='Weekends',\n", + " xticks=hourly_ticks, style=['-', ':', '--']);" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result shows a bimodal commuting pattern during the work week, and a unimodal recreational pattern during the weekends.\n", + "It might be interesting to dig through this data in more detail and examine the effects of weather, temperature, time of year, and other factors on people's commuting patterns; for further discussion, see my blog post [\"Is Seattle Really Seeing an Uptick in Cycling?\"](https://jakevdp.github.io/blog/2014/06/10/is-seattle-really-seeing-an-uptick-in-cycling/), which uses a subset of this data.\n", + "We will also revisit this dataset in the context of modeling in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.12-Performance-Eval-and-Query.ipynb b/notebooks/03.12-Performance-Eval-and-Query.ipynb new file mode 100644 index 000000000..94f175f3b --- /dev/null +++ b/notebooks/03.12-Performance-Eval-and-Query.ipynb @@ -0,0 +1,1243 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# High-Performance Pandas: eval and query" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we've already seen in previous chapters, the power of the PyData stack is built upon the ability of NumPy and Pandas to push basic operations into lower-level compiled code via an intuitive higher-level syntax: examples are vectorized/broadcasted operations in NumPy, and grouping-type operations in Pandas.\n", + "While these abstractions are efficient and effective for many common use cases, they often rely on the creation of temporary intermediate objects, which can cause undue overhead in computational time and memory use.\n", + "\n", + "To address this, Pandas includes some methods that allow you to directly access C-speed operations without costly allocation of intermediate arrays: `eval` and `query`, which rely on the [NumExpr package](https://github.com/pydata/numexpr).\n", + "In this chapter I will walk you through their use and give some rules of thumb about when you might think about using them." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivating query and eval: Compound Expressions\n", + "\n", + "We've seen previously that NumPy and Pandas support fast vectorized operations; for example, when adding the elements of two arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.21 ms ± 142 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "rng = np.random.default_rng(42)\n", + "x = rng.random(1000000)\n", + "y = rng.random(1000000)\n", + "%timeit x + y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As discussed in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb), this is much faster than doing the addition via a Python loop or comprehension:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "263 ms ± 43.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" + ] + } + ], + "source": [ + "%timeit np.fromiter((xi + yi for xi, yi in zip(x, y)),\n", + " dtype=x.dtype, count=len(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this abstraction can become less efficient when computing compound expressions.\n", + "For example, consider the following expression:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "mask = (x > 0.5) & (y < 0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because NumPy evaluates each subexpression, this is roughly equivalent to the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "tmp1 = (x > 0.5)\n", + "tmp2 = (y < 0.5)\n", + "mask = tmp1 & tmp2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In other words, *every intermediate step is explicitly allocated in memory*. If the `x` and `y` arrays are very large, this can lead to significant memory and computational overhead.\n", + "The NumExpr library gives you the ability to compute this type of compound expression element by element, without the need to allocate full intermediate arrays.\n", + "The [NumExpr documentation](https://github.com/pydata/numexpr) has more details, but for the time being it is sufficient to say that the library accepts a *string* giving the NumPy-style expression you'd like to compute:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numexpr\n", + "mask_numexpr = numexpr.evaluate('(x > 0.5) & (y < 0.5)')\n", + "np.all(mask == mask_numexpr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The benefit here is that NumExpr evaluates the expression in a way that avoids temporary arrays where possible, and thus can be much more efficient than NumPy, especially for long sequences of computations on large arrays.\n", + "The Pandas `eval` and `query` tools that we will discuss here are conceptually similar, and are essentially Pandas-specific wrappers of NumExpr functionality." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pandas.eval for Efficient Operations\n", + "\n", + "The `eval` function in Pandas uses string expressions to efficiently compute operations on `DataFrame` objects.\n", + "For example, consider the following data:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "nrows, ncols = 100000, 100\n", + "df1, df2, df3, df4 = (pd.DataFrame(rng.random((nrows, ncols)))\n", + " for i in range(4))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To compute the sum of all four ``DataFrame``s using the typical Pandas approach, we can just write the sum:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "73.2 ms ± 6.72 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "%timeit df1 + df2 + df3 + df4" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The same result can be computed via ``pd.eval`` by constructing the expression as a string:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "34 ms ± 4.2 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "%timeit pd.eval('df1 + df2 + df3 + df4')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `eval` version of this expression is about 50% faster (and uses much less memory), while giving the same result:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.allclose(df1 + df2 + df3 + df4,\n", + " pd.eval('df1 + df2 + df3 + df4'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`pd.eval` supports a wide range of operations.\n", + "To demonstrate these, we'll use the following integer data:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "df1, df2, df3, df4, df5 = (pd.DataFrame(rng.integers(0, 1000, (100, 3)))\n", + " for i in range(5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Arithmetic operators\n", + "`pd.eval` supports all arithmetic operators. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result1 = -df1 * df2 / (df3 + df4) - df5\n", + "result2 = pd.eval('-df1 * df2 / (df3 + df4) - df5')\n", + "np.allclose(result1, result2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Comparison operators\n", + "`pd.eval` supports all comparison operators, including chained expressions:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result1 = (df1 < df2) & (df2 <= df3) & (df3 != df4)\n", + "result2 = pd.eval('df1 < df2 <= df3 != df4')\n", + "np.allclose(result1, result2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Bitwise operators\n", + "`pd.eval` supports the `&` and `|` bitwise operators:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result1 = (df1 < 0.5) & (df2 < 0.5) | (df3 < df4)\n", + "result2 = pd.eval('(df1 < 0.5) & (df2 < 0.5) | (df3 < df4)')\n", + "np.allclose(result1, result2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, it supports the use of the literal `and` and `or` in Boolean expressions:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result3 = pd.eval('(df1 < 0.5) and (df2 < 0.5) or (df3 < df4)')\n", + "np.allclose(result1, result3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Object attributes and indices\n", + "\n", + "`pd.eval` supports access to object attributes via the `obj.attr` syntax and indexes via the `obj[index]` syntax:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result1 = df2.T[0] + df3.iloc[1]\n", + "result2 = pd.eval('df2.T[0] + df3.iloc[1]')\n", + "np.allclose(result1, result2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Other operations\n", + "\n", + "Other operations, such as function calls, conditional statements, loops, and other more involved constructs are currently *not* implemented in `pd.eval`.\n", + "If you'd like to execute these more complicated types of expressions, you can use the NumExpr library itself." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## DataFrame.eval for Column-Wise Operations\n", + "\n", + "Just as Pandas has a top-level `pd.eval` function, `DataFrame` objects have an `eval` method that works in similar ways.\n", + "The benefit of the `eval` method is that columns can be referred to by name.\n", + "We'll use this labeled array as an example:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n", + "
" + ], + "text/plain": [ + " A B C D\n", + "0 0.850888 0.966709 0.958690 -0.120812\n", + "1 0.820126 0.385686 0.061402 7.075399\n", + "2 0.059729 0.831768 0.652259 -1.183638\n", + "3 0.244774 0.140322 0.041711 2.504142\n", + "4 0.818205 0.753384 0.578851 0.111982" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.eval('D = (A - B) / C', inplace=True)\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Local Variables in DataFrame.eval\n", + "\n", + "The `DataFrame.eval` method supports an additional syntax that lets it work with local Python variables.\n", + "Consider the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "column_mean = df.mean(1)\n", + "result1 = df['A'] + column_mean\n", + "result2 = df.eval('A + @column_mean')\n", + "np.allclose(result1, result2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `@` character here marks a *variable name* rather than a *column name*, and lets you efficiently evaluate expressions involving the two \"namespaces\": the namespace of columns, and the namespace of Python objects.\n", + "Notice that this `@` character is only supported by the `DataFrame.eval` *method*, not by the `pandas.eval` *function*, because the `pandas.eval` function only has access to the one (Python) namespace." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The DataFrame.query Method\n", + "\n", + "The `DataFrame` has another method based on evaluated strings, called `query`.\n", + "Consider the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result1 = df[(df.A < 0.5) & (df.B < 0.5)]\n", + "result2 = pd.eval('df[(df.A < 0.5) & (df.B < 0.5)]')\n", + "np.allclose(result1, result2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the example used in our discussion of `DataFrame.eval`, this is an expression involving columns of the `DataFrame`.\n", + "However, it cannot be expressed using the `DataFrame.eval` syntax!\n", + "Instead, for this type of filtering operation, you can use the `query` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result2 = df.query('A < 0.5 and B < 0.5')\n", + "np.allclose(result1, result2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition to being a more efficient computation, compared to the masking expression this is much easier to read and understand.\n", + "Note that the `query` method also accepts the `@` flag to mark local variables:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Cmean = df['C'].mean()\n", + "result1 = df[(df.A < Cmean) & (df.B < Cmean)]\n", + "result2 = df.query('A < @Cmean and B < @Cmean')\n", + "np.allclose(result1, result2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Performance: When to Use These Functions\n", + "\n", + "When considering whether to use `eval` and `query`, there are two considerations: *computation time* and *memory use*.\n", + "Memory use is the most predictable aspect. As already mentioned, every compound expression involving NumPy arrays or Pandas ``DataFrame``s will result in implicit creation of temporary arrays. For example, this:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "x = df[(df.A < 0.5) & (df.B < 0.5)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "is roughly equivalent to this:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "tmp1 = df.A < 0.5\n", + "tmp2 = df.B < 0.5\n", + "tmp3 = tmp1 & tmp2\n", + "x = df[tmp3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If the size of the temporary ``DataFrame``s is significant compared to your available system memory (typically several gigabytes), then it's a good idea to use an `eval` or `query` expression.\n", + "You can check the approximate size of your array in bytes using this:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "32000" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.values.nbytes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On the performance side, `eval` can be faster even when you are not maxing out your system memory.\n", + "The issue is how your temporary objects compare to the size of the L1 or L2 CPU cache on your system (typically a few megabytes); if they are much bigger, then `eval` can avoid some potentially slow movement of values between the different memory caches.\n", + "In practice, I find that the difference in computation time between the traditional methods and the `eval`/`query` method is usually not significant—if anything, the traditional method is faster for smaller arrays!\n", + "The benefit of `eval`/`query` is mainly in the saved memory, and the sometimes cleaner syntax they offer.\n", + "\n", + "We've covered most of the details of `eval` and `query` here; for more information on these, you can refer to the Pandas documentation.\n", + "In particular, different parsers and engines can be specified for running these queries; for details on this, see the discussion within the [\"Enhancing Performance\" section](https://pandas.pydata.org/pandas-docs/dev/user_guide/enhancingperf.html) of the documentation." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/03.13-Further-Resources.ipynb b/notebooks/03.13-Further-Resources.ipynb new file mode 100644 index 000000000..0c3a8c88e --- /dev/null +++ b/notebooks/03.13-Further-Resources.ipynb @@ -0,0 +1,58 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Further Resources" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In this part of the book, we've covered many of the basics of using Pandas effectively for data analysis.\n", + "Still, much has been omitted from our discussion.\n", + "To learn more about Pandas, I recommend the following resources:\n", + "\n", + "- [Pandas online documentation](http://pandas.pydata.org/): This is the go-to source for complete documentation of the package. While the examples in the documentation tend to be based on small generated datasets, the description of the options is complete and generally very useful for understanding the use of various functions.\n", + "\n", + "- [*Python for Data Analysis*](https://learning.oreilly.com/library/view/python-for-data/9781098104023/): Written by Wes McKinney (the original creator of Pandas), this book contains much more detail on the Pandas package than we had room for in this chapter. In particular, McKinney takes a deep dive into tools for time series, which were his bread and butter as a financial consultant. The book also has many entertaining examples of applying Pandas to gain insight from real-world datasets.\n", + "\n", + "- [*Effective Pandas*](https://leanpub.com/effective-pandas): This short e-book by Pandas developer Tom Augspurger provides a succinct outline of using the full power of the Pandas library in an effective and idiomatic way.\n", + "\n", + "- [Pandas on PyVideo](http://pyvideo.org/search?q=pandas): From PyCon to SciPy to PyData, many conferences have featured tutorials by Pandas developers and power users. The PyCon tutorials in particular tend to be given by very well-vetted presenters.\n", + "\n", + "Using these resources, combined with the walkthrough given in these chapters, my hope is that you'll be poised to use Pandas to tackle any data analysis problem you come across!" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.00-Introduction-To-Matplotlib.ipynb b/notebooks/04.00-Introduction-To-Matplotlib.ipynb new file mode 100644 index 000000000..19bf8a7bc --- /dev/null +++ b/notebooks/04.00-Introduction-To-Matplotlib.ipynb @@ -0,0 +1,525 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Visualization with Matplotlib" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll now take an in-depth look at the Matplotlib package for visualization in Python.\n", + "Matplotlib is a multiplatform data visualization library built on NumPy arrays and designed to work with the broader SciPy stack.\n", + "It was conceived by John Hunter in 2002, originally as a patch to IPython for enabling interactive MATLAB-style plotting via `gnuplot` from the IPython command line.\n", + "IPython's creator, Fernando Perez, was at the time scrambling to finish his PhD, and let John know he wouldn’t have time to review the patch for several months.\n", + "John took this as a cue to set out on his own, and the Matplotlib package was born, with version 0.1 released in 2003.\n", + "It received an early boost when it was adopted as the plotting package of choice of the Space Telescope Science Institute (the folks behind the Hubble Telescope), which financially supported Matplotlib’s development and greatly expanded its capabilities.\n", + "\n", + "One of Matplotlib’s most important features is its ability to play well with many operating systems and graphics backends.\n", + "Matplotlib supports dozens of backends and output types, which means you can count on it to work regardless of which operating system you are using or which output format you desire.\n", + "This cross-platform, everything-to-everyone approach has been one of the great strengths of Matplotlib.\n", + "It has led to a large user base, which in turn has led to an active developer base and Matplotlib’s powerful tools and ubiquity within the scientific Python world.\n", + "\n", + "In recent years, however, the interface and style of Matplotlib have begun to show their age.\n", + "Newer tools like `ggplot` and `ggvis` in the R language, along with web visualization toolkits based on D3js and HTML5 canvas, often make Matplotlib feel clunky and old-fashioned.\n", + "Still, I'm of the opinion that we cannot ignore Matplotlib's strength as a well-tested, cross-platform graphics engine.\n", + "Recent Matplotlib versions make it relatively easy to set new global plotting styles (see [Customizing Matplotlib: Configurations and Style Sheets](04.11-Settings-and-Stylesheets.ipynb)), and people have been developing new packages that build on its powerful internals to drive Matplotlib via cleaner, more modern APIs—for example, Seaborn (discussed in [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)), [`ggpy`](http://yhat.github.io/ggpy/), [HoloViews](http://holoviews.org/), and even Pandas itself can be used as wrappers around Matplotlib's API.\n", + "Even with wrappers like these, it is still often useful to dive into Matplotlib's syntax to adjust the final plot output.\n", + "For this reason, I believe that Matplotlib itself will remain a vital piece of the data visualization stack, even if new tools mean the community gradually moves away from using the Matplotlib API directly." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# General Matplotlib Tips\n", + "\n", + "Before we dive into the details of creating visualizations with Matplotlib, there are a few useful things you should know about using the package." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Importing Matplotlib\n", + "\n", + "Just as we use the `np` shorthand for NumPy and the `pd` shorthand for Pandas, we will use some standard shorthands for Matplotlib imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import matplotlib as mpl\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `plt` interface is what we will use most often, as you shall see throughout this part of the book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Setting Styles\n", + "\n", + "We will use the `plt.style` directive to choose appropriate aesthetic styles for our figures.\n", + "Here we will set the `classic` style, which ensures that the plots we create use the classic Matplotlib style:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "plt.style.use('classic')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Throughout this chapter, we will adjust this style as needed.\n", + "For more information on stylesheets, see [Customizing Matplotlib: Configurations and Style Sheets](04.11-Settings-and-Stylesheets.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## show or No show? How to Display Your Plots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A visualization you can't see won't be of much use, but just how you view your Matplotlib plots depends on the context.\n", + "The best use of Matplotlib differs depending on how you are using it; roughly, the three applicable contexts are using Matplotlib in a script, in an IPython terminal, or in a Jupyter notebook." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting from a Script\n", + "\n", + "If you are using Matplotlib from within a script, the function `plt.show` is your friend.\n", + "`plt.show` starts an event loop, looks for all currently active `Figure` objects, and opens one or more interactive windows that display your figure or figures.\n", + "\n", + "So, for example, you may have a file called *myplot.py* containing the following:\n", + "\n", + "```python\n", + "# file: myplot.py \n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "x = np.linspace(0, 10, 100)\n", + "\n", + "plt.plot(x, np.sin(x))\n", + "plt.plot(x, np.cos(x))\n", + "\n", + "plt.show()\n", + "```\n", + "\n", + "You can then run this script from the command-line prompt, which will result in a window opening with your figure displayed:\n", + "\n", + "```\n", + "$ python myplot.py\n", + "```\n", + "\n", + "The `plt.show` command does a lot under the hood, as it must interact with your system's interactive graphical backend.\n", + "The details of this operation can vary greatly from system to system and even installation to installation, but Matplotlib does its best to hide all these details from you.\n", + "\n", + "One thing to be aware of: the `plt.show` command should be used *only once* per Python session, and is most often seen at the very end of the script.\n", + "Multiple `show` commands can lead to unpredictable backend-dependent behavior, and should mostly be avoided." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting from an IPython Shell\n", + "\n", + "Matplotlib also works seamlessly within an IPython shell (see [IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb)).\n", + "IPython is built to work well with Matplotlib if you specify Matplotlib mode.\n", + "To enable this mode, you can use the `%matplotlib` magic command after starting `ipython`:\n", + "\n", + "```ipython\n", + "In [1]: %matplotlib\n", + "Using matplotlib backend: TkAgg\n", + "\n", + "In [2]: import matplotlib.pyplot as plt\n", + "```\n", + "\n", + "At this point, any `plt` plot command will cause a figure window to open, and further commands can be run to update the plot.\n", + "Some changes (such as modifying properties of lines that are already drawn) will not draw automatically: to force an update, use `plt.draw`.\n", + "Using `plt.show` in IPython's Matplotlib mode is not required." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting from a Jupyter Notebook\n", + "\n", + "The Jupyter notebook is a browser-based interactive data analysis tool that can combine narrative, code, graphics, HTML elements, and much more into a single executable document (see [IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb)).\n", + "\n", + "Plotting interactively within a Jupyter notebook can be done with the `%matplotlib` command, and works in a similar way to the IPython shell.\n", + "You also have the option of embedding graphics directly in the notebook, with two possible options:\n", + "\n", + "- `%matplotlib inline` will lead to *static* images of your plot embedded in the notebook.\n", + "- `%matplotlib notebook` will lead to *interactive* plots embedded within the notebook.\n", + "\n", + "For this book, we will generally stick with the default, with figures rendered as static images (see the following figure for the result of this basic plotting example):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "x = np.linspace(0, 10, 100)\n", + "\n", + "fig = plt.figure()\n", + "plt.plot(x, np.sin(x), '-')\n", + "plt.plot(x, np.cos(x), '--');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Saving Figures to File\n", + "\n", + "One nice feature of Matplotlib is the ability to save figures in a wide variety of formats.\n", + "Saving a figure can be done using the `savefig` command.\n", + "For example, to save the previous figure as a PNG file, we can run this:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "fig.savefig('my_figure.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have a file called *my_figure.png* in the current working directory:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-rw-r--r-- 1 jakevdp staff 26K Feb 1 06:15 my_figure.png\n" + ] + } + ], + "source": [ + "!ls -lh my_figure.png" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To confirm that it contains what we think it contains, let's use the IPython `Image` object to display the contents of this file (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import Image\n", + "Image('my_figure.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In `savefig`, the file format is inferred from the extension of the given filename.\n", + "Depending on what backends you have installed, many different file formats are available.\n", + "The list of supported file types can be found for your system by using the following method of the figure canvas object:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'eps': 'Encapsulated Postscript',\n", + " 'jpg': 'Joint Photographic Experts Group',\n", + " 'jpeg': 'Joint Photographic Experts Group',\n", + " 'pdf': 'Portable Document Format',\n", + " 'pgf': 'PGF code for LaTeX',\n", + " 'png': 'Portable Network Graphics',\n", + " 'ps': 'Postscript',\n", + " 'raw': 'Raw RGBA bitmap',\n", + " 'rgba': 'Raw RGBA bitmap',\n", + " 'svg': 'Scalable Vector Graphics',\n", + " 'svgz': 'Scalable Vector Graphics',\n", + " 'tif': 'Tagged Image File Format',\n", + " 'tiff': 'Tagged Image File Format'}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fig.canvas.get_supported_filetypes()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that when saving your figure, it is not necessary to use `plt.show` or related commands discussed earlier." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Two Interfaces for the Price of One\n", + "\n", + "A potentially confusing feature of Matplotlib is its dual interfaces: a convenient MATLAB-style state-based interface, and a more powerful object-oriented interface. I'll quickly highlight the differences between the two here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### MATLAB-style Interface\n", + "\n", + "Matplotlib was originally conceived as a Python alternative for MATLAB users, and much of its syntax reflects that fact.\n", + "The MATLAB-style tools are contained in the `pyplot` (`plt`) interface.\n", + "For example, the following code will probably look quite familiar to MATLAB users (the following figure shows the result):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure() # create a plot figure\n", + "\n", + "# create the first of two panels and set current axis\n", + "plt.subplot(2, 1, 1) # (rows, columns, panel number)\n", + "plt.plot(x, np.sin(x))\n", + "\n", + "# create the second panel and set current axis\n", + "plt.subplot(2, 1, 2)\n", + "plt.plot(x, np.cos(x));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is important to recognize that this interface is *stateful*: it keeps track of the \"current\" figure and axes, which are where all `plt` commands are applied.\n", + "You can get a reference to these using the `plt.gcf` (get current figure) and `plt.gca` (get current axes) routines.\n", + "\n", + "While this stateful interface is fast and convenient for simple plots, it is easy to run into problems.\n", + "For example, once the second panel is created, how can we go back and add something to the first?\n", + "This is possible within the MATLAB-style interface, but a bit clunky.\n", + "Fortunately, there is a better way." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Object-oriented interface\n", + "\n", + "The object-oriented interface is available for these more complicated situations, and for when you want more control over your figure.\n", + "Rather than depending on some notion of an \"active\" figure or axes, in the object-oriented interface the plotting functions are *methods* of explicit `Figure` and `Axes` objects.\n", + "To re-create the previous plot using this style of plotting, as shown in the following figure, you might do the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# First create a grid of plots\n", + "# ax will be an array of two Axes objects\n", + "fig, ax = plt.subplots(2)\n", + "\n", + "# Call plot() method on the appropriate object\n", + "ax[0].plot(x, np.sin(x))\n", + "ax[1].plot(x, np.cos(x));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For simpler plots, the choice of which style to use is largely a matter of preference, but the object-oriented approach can become a necessity as plots become more complicated.\n", + "Throughout the following chapters, we will switch between the MATLAB-style and object-oriented interfaces, depending on what is most convenient.\n", + "In most cases, the difference is as small as switching `plt.plot` to `ax.plot`, but there are a few gotchas that I will highlight as they come up in the following chapters." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.01-Simple-Line-Plots.ipynb b/notebooks/04.01-Simple-Line-Plots.ipynb new file mode 100644 index 000000000..bbcb7d87a --- /dev/null +++ b/notebooks/04.01-Simple-Line-Plots.ipynb @@ -0,0 +1,629 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simple Line Plots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Perhaps the simplest of all plots is the visualization of a single function $y = f(x)$.\n", + "Here we will take a first look at creating a simple plot of this type.\n", + "As in all the following chapters, we'll start by setting up the notebook for plotting and importing the packages we will use:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For all Matplotlib plots, we start by creating a figure and axes.\n", + "In their simplest form, this can be done as follows (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = plt.axes()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In Matplotlib, the *figure* (an instance of the class `plt.Figure`) can be thought of as a single container that contains all the objects representing axes, graphics, text, and labels.\n", + "The *axes* (an instance of the class `plt.Axes`) is what we see above: a bounding box with ticks, grids, and labels, which will eventually contain the plot elements that make up our visualization.\n", + "Throughout this part of the book, I'll commonly use the variable name `fig` to refer to a figure instance and `ax` to refer to an axes instance or group of axes instances.\n", + "\n", + "Once we have created an axes, we can use the `ax.plot` method to plot some data. Let's start with a simple sinusoid, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = plt.axes()\n", + "\n", + "x = np.linspace(0, 10, 1000)\n", + "ax.plot(x, np.sin(x));" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the semicolon at the end of the last line is intentional: it suppresses the textual representation of the plot from the output.\n", + "\n", + "Alternatively, we can use the PyLab interface and let the figure and axes be created for us in the background\n", + "(see [Two Interfaces for the Price of One](04.00-Introduction-To-Matplotlib.ipynb#Two-Interfaces-for-the-Price-of-One) for a discussion of these two interfaces); as the following figure shows, the result is the same:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we want to create a single figure with multiple lines (see the following figure), we can simply call the `plot` function multiple times:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x))\n", + "plt.plot(x, np.cos(x));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's all there is to plotting simple functions in Matplotlib!\n", + "We'll now dive into some more details about how to control the appearance of the axes and lines." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adjusting the Plot: Line Colors and Styles" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first adjustment you might wish to make to a plot is to control the line colors and styles.\n", + "The `plt.plot` function takes additional arguments that can be used to specify these.\n", + "To adjust the color, you can use the `color` keyword, which accepts a string argument representing virtually any imaginable color.\n", + "The color can be specified in a variety of ways; see the following figure for the output of the following examples:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x - 0), color='blue') # specify color by name\n", + "plt.plot(x, np.sin(x - 1), color='g') # short color code (rgbcmyk)\n", + "plt.plot(x, np.sin(x - 2), color='0.75') # grayscale between 0 and 1\n", + "plt.plot(x, np.sin(x - 3), color='#FFDD44') # hex code (RRGGBB, 00 to FF)\n", + "plt.plot(x, np.sin(x - 4), color=(1.0,0.2,0.3)) # RGB tuple, values 0 to 1\n", + "plt.plot(x, np.sin(x - 5), color='chartreuse'); # HTML color names supported" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If no color is specified, Matplotlib will automatically cycle through a set of default colors for multiple lines.\n", + "\n", + "Similarly, the line style can be adjusted using the `linestyle` keyword (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, x + 0, linestyle='solid')\n", + "plt.plot(x, x + 1, linestyle='dashed')\n", + "plt.plot(x, x + 2, linestyle='dashdot')\n", + "plt.plot(x, x + 3, linestyle='dotted');\n", + "\n", + "# For short, you can use the following codes:\n", + "plt.plot(x, x + 4, linestyle='-') # solid\n", + "plt.plot(x, x + 5, linestyle='--') # dashed\n", + "plt.plot(x, x + 6, linestyle='-.') # dashdot\n", + "plt.plot(x, x + 7, linestyle=':'); # dotted" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Though it may be less clear to someone reading your code, you can save some keystrokes by combining these `linestyle` and `color` codes into a single non-keyword argument to the `plt.plot` function; the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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2x+cpKZxo355GVaqw1goP0JQM6V5NehEdEW2XIW0hYS2ErZ08CZs2weuv6/Ok33vPKvOk8/LyWLVqFdOmTePixYv4+voSGRnJsGHDlNe2hPQnRe2OmIYNqWmFwUq3CumYiBja1Ve78W5ZkLAWwtY2b4YpU2DAAGjYEB56SGm5kiF93333sWrVKiIiIpTWtbien0+HAwfwcHTkjYAAXrJBu6M8hbSFhLUQ1paaCqNH6+Hco4f+1OHAgVCnjtKytwrpt99+mwcffFD5G4cJmZlsTk4mJiCAWi4u/F/z5nT08lIe0hl5GSzeu5i5u+aW25C2kLAWwlqKZsJTtSokJOh7HQJUqaL/UGjdunWMGzeOixcvcv/991s1pMemprL16lWqOznxgq8vdV1d6VVD5UipihXSFhLWQljDlCnw3//qt+I5O8OhQ1Z5LNzBwQFnZ2euX79Ow4YNrRbSSUYjI0+e5NPkZDwNBt4MDOSl+vWV7xReMqR7B/cmulN0uQ5pCwlrIVQ5eRL8/fU3DVu2hMxMDJara8VBnZSUxH333ceUKVMYOnQoL730Eq+88orykM4qKKCqkxOeTk4cy87mzcBAHsrKol3Dhkrr3iqkYyJiaFtP/bwSa5ENc4VQ4eefoWlTWL1aP+7bF+bMUTr432g0snv3bkAfvtarVy+Cg4MBcHR0VBrU+zMy6PPzz9z700+YNQ0vJyd+ueceJjZsSFUHdTGTkZfBtB+mEbggkInfTeQ+v/vY9499fPrUpxUqqEGurIUoO7/8oj/Q0rOnPrcjNlYPacWMRiNvvfUW06dPJz09naSkJLy9vYmPj1dee39GBlPOn2dzcjLVnZx4zc8Pk6bhajDgoPAvh4y8DBbtWcTcXXNJNaZWyCvpkiSshSgro0fDsWNw+rTe5njlFaXlbg7pS5cu0bFjRyZPnoyXlZ52/DolhYcOH6a6k5NVe9I3h3Sf4D5ER0RX6JC2kLAWorTOndM3op01C2rU0Od2WGGe9K1C+p133qFz587Ke9L7MzK4lJ/PIzVr8oC3N/ODghhSt65NQjomIoY29doorWtPJKyFuFOWedJZWfoj4Y8/Dt27Q+PGistqxMXF/S6k3333XR544AGrhLSl3RHq7s7DNWrg5ODAKw0aKK0rIf0bCWshbpemwbBh+lClefP0vvSVK/rVtEJmsxkHBwcMBgOfffYZgYGBVgvpI1lZjD97ls3Jyfg4OTE1MJBR9esrrysh/UcS1kL8lWvXoHZt/Wq6WjX9oRYLxUG9fft2nnvuOb777jsCAwN5//338fDwUB6WhZqGo8HAVZOJnenpxSFtjXbHwj0Lid0VKyFdgoS1EP/LunUwdCgcPaqPLF2wQHlJo9HI9evX8fPzo3HjxgQFBZGdnQ1A1Zv/olBgX0YGU86dI9jdndigIDp7e3O+QweqWjmkHw55mOhO0RLSN5GwFqKkEyfAwUHf07BLF/0uD29v5WWNRiMrV65k+vTpBAcHs3XrVurXr8/XX3+tvLYlpD9LScHHyYnO1asDYDAYlAZ1ujGdRXsXSUjfBglrIW5mNMJ99+khvXGjPlxp5kzFJX8L6cuXLxMeHs6kSZOU1rzZnAsXGHvmDD5OTkwrandUU3wlLSF95ySshThxAj78ECZM0Pc33LjRKvOkS4Z0p06dWLt2LZGRkcp70nszMvB2ciLY3Z1eNWpg0jSrhfTCPQuJ3R1LmjGNh0MeJiYihrt971ZatyIo1XfGZDIxbtw4Ll26hIODA2+88QaNFd+2JIQyX3wBU6fCM8/oszy6dFFaLi8vjxUrVvwupNetW0dkZKTSuqCHtGVnlufq1GF1aCihHh6EKt6IVkL67yvVQ/vbtm2joKCADRs2MHLkSObPn1/GyxJCoZQUePpp+Pxz/fiFF/QHXKy0lZXRaGTSpEkEBQWxdetWtm3bpjyo92Vk0OvwYe45cIDdGRlMCwxkUZMmSmuCHtJLjy4lYEEA0d9HE9EwgoTnE/h4wMcS1HeoVFfWgYGBFBYWYjabycrKwknxP52EKBNGo97mqFZNH7R04YL+cSvMk96wYQNvv/02sbGxeHl5cfjwYfz8/JTWvNkH168Xh7Qt2h2PhDxCdES0BPTfYNA0TbvTL7py5Qr//Oc/ycnJITU1lfj4eO6++/ffhISEBNxLOWHMaDTi5uZWqq8tr+Sc1aq5aBGeX33FmY8+0h8HLyy0yjxpTdNwc3Nj8+bNvP/++8ycORNfX1+ldQEOm0zEZWXxtLs74a6uZJrNOAAeCifgAWTmZ7L25Fre+eUdMkwZdK7XmWFBw2hdt7XSuvbm7/zZzsnJoU2bW7zRqpXCtGnTtDlz5miapmmXL1/WunbtqhmNxt/9N/v37y/NS2uapmnHjh0r9deWV3LOCiQmaprlz+VHH2nav/+tadnZamtqmpabm6stXLhQ8/X11aZPn65pmqaZzWbNbDYrP+c96elaz0OHNLZu1Wr88IO27tdfldazSMtN06Z8P0XznuGtMRntkfWPaAcuH9A0Tf5s36k/y85S/VvI09MT56KdiL28vCgoKKCwsLBUf4sIocThw9CqFcTF6XscPvKI/kOh3NxcVqxYwYwZM7hy5QoRERHcf//9AMrv7gAYfvw4b/36KzWcnJjRqBEj69VT/jBLujGdBXsWMG/3PNKMafRt2pfoTtG09q1cV9LWUKrv5ODBg5kwYQIDBw7EZDIxZsyYUrc8hCgzx4/r86R794YWLWDhQnjsMeVlS4Z0ZGQk7733ntXu7mhVtSouDg7c7+VFE3d3q4R0mjGNhXsWSkhbUam+ox4eHiywwmO3QtyRV1+FxER9x3BHRxg1Smk5W4b07vR0ppw/z5aUFFaGhDDM15chVuiFS0jbjtzGIcqvs2f1jWjnztXnSS9ebJV50hY7d+7klVdesVlIW9odT9aqpbyuhLTtSViL8scyTzo7GzZtgqeegm7doFEj5aWXLFlCRkYG48ePp3Pnzuzbt4+2ba2zS4mmaYw4eZIko9FqPek0YxoLdus96fS8dAlpG5KwFuWHpsFzz0H16vr0u+bN4fLl348sVcBkMhW/ob5v3z6uXbvGuHHjMBgMyoN6d3o6s5OSWBkSQnVnZzaEhVHfxcXqIf1o00eJjoimVd1WSuuKPydhLezfr79C3br61XSNGvrwfwuFQZ2bm8vy5cuZOXMmmzdv5u677yY+Pt4q94bf3O6o6ezM0exsOnp7E6L4jXwJafslYS3s29q1v82TbtJE36FFMUtIz5gxg19//ZUHHngAh6KHSVQHdZ7ZTN8jR4pDemajRvzTBu0OCWn7I2Et7M+xY+DkBMHB0LUrjB2rX1Erlpuby7Jly5g5c2ZxSG/YsIGIiAjltc/m5hJYpQquDg7UsXJIz989n/m750tI2zkJa2FfjEYID9dDesMGfZ701KlKS9oypHelpzPl3Dm+TUvjRPv2NKpShdWhocrrSkiXPxLWwvYSE/V50lFR+qClDz6wyjxpi+nTp/PGG2/YJKS/TE2lprMz0wIDqV30JqZKJUO6X2g/ojtF07JuS+W1xd8jYS1s78sv9d1Ynn1WH1PaubPScnl5eSxdupRWrVoRGRnJqFGjePDBB60S0gDX8vOJOHgQLycnZjVqxAgbtDskpMsfCWthfcnJMHIkVSMjITRUnyf9zDNQs6bSspqmYTAYMBgMxMbG8thjjxEZGUnt2rWpXbu20tq70tP5LDmZp4HaLi582qIF93t6SkiL2yZhLawnN1efG+3pCceP42TpzSqeJ23pSa9bt44dO3bg6upKQkICtazw5N+u9HQmnzvHV0Xtjm5Ftx128/FRWjc1N1UP6T3zycjLkJCuACSshXVMnAj/93/60H9nZzhwgLQTJ1A5zSInJ6f4jcOrV6/SuXNnrl+/ToMGDZQH9XmjkedPnCgOaUu7I+nkSaV1S4b0Y6GPER0RzV11rPcegFBDwlqoc/QoBAWBqyvcc4/+sfx8/Spa4RD8W4X0+++/T6dOnZTVtEgvKMDLyYnqTk6cNxqt1pOWkK74JKyFGpZ50kuWwIgR8PDD+g+FbBnSlnbHpbw8Drdrh6eTE8fat8dB8RxrCenKQ8JalJ2jR+H0aT2UW7TQg/qJJ6xWvm/fvnz99dc2CemvUlOp5ezMv/38KNA0XAwGpUEtIV35SFiLsjN2rL4BQO/eeptjxAil5XJycli+fDmDBw/G29ubSZMmERUVZZWQBvgyJYXuhw9Ty9mZ2Y0aMaJ+fTwUj2dNzU1l3u55LNizQEK6kpGwFqV3+jRMngzz5+uPgy9Zot/poXhTVouTJ08yZswYvLy8GDJkCOHh4cpr/pieztX8fPrVqsWD3t7ENWnCs3XrWj2k+4f1Z1KnSRLSlYiEtbhzZrMeyEYjfPqp/jBL164QGKi0bE5ODvHx8Vy8eJHY2FhatmzJ0aNHCQsLU1oX9JCecu4cX6em0tzDg0dr1sTJwYER9esrrZuSm8L83fN/F9LRnaJpUaeF0rrC/khYi9unafrDKzVq6PsbNmumz5NWPLbTEtIzZ87k2rVrPPTQQxQUFODk5KQ8qA9mZvLvM2f4uqgnbWl3qN4AV0JalCRhLf7a5ctQr54+T7puXfD2/u1zCoM6Ozub+Ph4Zs2axbVr1+jSpQsxMTF07NhRWU2LArMZJwcHUgsKOJiVZbWedEpuCvN26e2OzPxMCWlRTMJa/G/vvgvDhul3egQH6/sdKmbLkP6x6O6O5h4ezAsKItLbm/MdOlBFQlrYmIS1+KOffwYXFwgJ0fc2HD8erPBoNoDRaKRp06ZcvHjRJiH9TWoqtZ2d6Vs0p8RgMCgN6pIh/XjY40zqNElCWvxBqcN62bJlfPfdd5hMJp566ikef/zxslyXsBWjESIjfz9P+j//UVoyOzubzz77jCeeeAI3Nzdef/11WrVqZZWQBph+/jwTzp6ltrMzcxs35sV69XC38pW0hLT4K6UK6z179vDTTz+xfv16cnNzWbVqVVmvS1jTkSP6POmYGH2e9IcfWnWe9IoVKxgzZgxhYWE0b96cUaNGKa+5Iy2Nms7ONC26s8PVwcEqIZ2Wl8ak7yZJSIs7Vqqw3rFjB8HBwYwcOZKsrCz+/e9/l/W6hDV9+63eix46FPz89CtrhbKzs1m6dCnOzs6Ehobyj3/8g3bt2tG8eXOldUEP6clFO7MMqVuXVU2b0tTDg6YeHkrrpuSmELsrlvm75pNdkM3jYY8THRFN89rqz1lUDAZN07Q7/aKoqCguX75cfM/riBEj2LJly+9uZ0pISMC9lHcKGI1Gq+wgbU+sec6OqanUnTKF9L59yYqMxGA0YjAaMd98l4cCOTk5bNiwgVWrVpGSkkK/fv148803lda0OJCfz+LsbHbn51PDwYFh7u486e5OFcW34KXlpfHOL++w9uRacgpy6FKvC6NajKKJVxOlde2J/P98Z3JycmjTps0fPl6qK2tvb28aNWqEi4sLjRo1wtXVlZSUFGqU2NQ0tJR7ySUmJpb6a8srq5xzTo5+q53JBNev4+nsrA//V8xyJT1r1iyuX79O165diYmJwcfHx2rf59WnT3MmK8tqPenknGTm7Z7Hwj0LycrP4vFmervDMdlR/mxXAn/nnBMSEm758VI9F9ymTRt++OEHNE3j6tWr5Obm4q34qkz8TePHQ9u2UFioz5Pevx+GD1daMjs7m9mzZxMYGMjYsWNp1aoVO3bs4KuvvuL+++9XWvuHtDS6HDzIF8nJAExs2JCzHTrwqp+f0qBOzkkm6rsoAhcEMu2HafRo0oPDIw6zsf9GaXmIv6VUV9YPPPAA+/bto3///miaRnR0NI6Kr1REKRw+rN9+5+oK99+vh7QV5kkDHD16lAceeIDr16/z0EMPERMTw3333ae0JughbdktvI6zM5mFhQB4Kp4n/WdX0hLQoqyU+k+wvKlo5w4d0udJx8Xp0+9699Z/KJSdnU1iYiJt27YlJCSE3r17M3z4cKuENMCziYmsuXqVOs7OxDZuzAtWanfE7opl4d6FZOdnS0gLZeShmIrk8GE4cwb69tVvvYuPt+o86cGDB7N9+3YuXLiAq6urVW7p3JGWRntPT1wcHOhSvTqtq1a1SUg/0ewJJnWaRLPazZTWFZWXhHVFMm4c/PKLPvzfwUHfNVyh7Oxs4uLiGDBgAH5+fkycOJExY8bg6uqqtC7A9qJb8LampfFWSAhDfX15tm5d5XUlpIWtSFiXZydP6g+yLFqkT8KLiwMvL+X9aEtIz5o1ixs3buDm5sZLL71Eq1atlNaF34d0HWdn5jVuzIDatZXXlZAWtiZhXR5Z5kmbTLBlCxw8CA8+CAEBSsuWDOlu3boRExPDvffeq7SuhaZpvHLqFFfy8pjXuDHPW6HdcSPnBrG7Ylm0d5GEtLApCevyRNNg4ECoWVO/mg4Lg0uX9Ls7FLJlSG9PS2N2UhLvNm1KdWdnPggLo56rq4S0qHQkrMuDpCT9MXCDARo0gOrVf/uc4qDevHkzQ4YMsUlIW9oddV1cOJ6Tw71eXgQp3uigZEg/2fxJJnWaRFgt9bvRCPG/SFjbu9Wr9YdXjh3T50nPnq28ZFZWFpmZmfj6+tK4cWPatm1LdHS0VULaWFhIz59/Lg7peUW34KmeJy0hLeydhLU9OnhQn37XtCn07AmTJoEV3kQDKCwspFWrVrRu3ZoPPviA0NBQvvjiC+V1f8nJIdjdHTdHRxq5ufGwhLQQvyNhbW9yc6FzZ33o//r1ekjHxCgtmZWVxfr16xk+fDiOjo5MmTKFxo0bK61psa3oicPtaWkcb9+eIHd3VjZtqrzujZwbzN05l0V7F5FjypGQFnZPwtoeHD5Mzfh4/da7KlXgo4+sMk86KyuLJUuWMHv2bJKTkwkNDaVjx448/fTTymtvS0vj9ZQU9ly9Sl0XF+YGBVHfCvdnlwzpAc0HENUpSkJa2D0Ja3uwdSs+a9fqw5b8/KBTJ6XlSoZ09+7diYmJoUOHDkrrWlzNz6froUN4GQzMDwrieV9fq7Q7Sob0pE6TCK1VuabBifJLwtoWbtyAf/xDH/bfpw+88AKnOnQgxM9PadmSId2jRw9iYmK45557lNYF+D41lS9SUpjZuDF1XFzYctddVL9yhdYNGiitKyEtKgoJa2vKyoKqVcHbW78d78YN/eNubpg9PZWWXr58ORMmTLBJSE8+d45t6en4urjwmp8ftV1c6Fy9Oom//qqsroS0qGgkrK3l9dfhk0/0/Q6dnGDfPv2+aYUyMzNxc3PD2dmZvLw82rdvb7WQPpOby9Djx4tDekFQEP+wQrvjevZ15u6ay+K9iyWkRYUiYa3SwYP6TiyurhAeDh4e+iPijo7Kg/rcuXO0bduWGTNmMHz4cEaNGsVLL72ktCZAismEj7MzNZ2dSS4osFlIP9XiKaLCoySkRYUhYa3KwYPQurVV50lnZmaSkJBAZGQkDRs25LnnnqN169YAv9sfUwVLu+O6ycThdu3wdHLicNu2yutKSIvKQsK6LP30E5w9C/36QcuWsGIFPP648rKZmZksWbKEOXPmYDQauXTpEl5eXsydO1d57ZI96fH+/pg1DUeDQWlQS0iLykbCuixNnKiPLe3bV5+Kp3iPw5tDOjk5mZ49exITE4OXl5fSuhafJyfT6+ef8XVxYWFRu8PNCu2OOTvnsGTfkuKQntRpEk1rqn+QRghbkrD+O375RX8UfMkSfRLe0qX6nR6K50n/WUi3b99eaV1N0/g+LY0bJhOP167NQ9WrszIkhKdr17ZaSC/et5hcU66EtKh0JKxLo7BQf5OwoAC++UbfTqtzZ2jYUGlZTdOYOXNmcUj36tWL6Ohoq4X05HPn2J6eTquqVelfqxZODg4M8/VVWvvmkDYWGHmq+VNEdYqSkBaVjoT1ndA0fU/DOnVg8eLf5km7uSktazKZcHZ2xmAwsGPHDjp06EBMTAzt2rVTWhdgf0YGr50+zfainrSl3WGNNw4lpIX4jYT17Th/Xr9qNhggMFDfQstCcVB/8803PPPMM/z44480btyYDz/8UPkeh5qmYdI0XBwcyCos5GRurtV70hLSQvze32quJicnExERwenTp8tqPfZn1Spo3BhOnNCPZ83SH3BRKDMzkzNnzgDQrFkzOnToQEFBAYDSoNY0ja2pqUQePMjYou9pZPXqnO3QgZcaNFAa1Neyr/Hvr/9NwIIA5uyaw6NNH+XoP4+ytt9aCWoh+BtX1iaTiejoaNwUX1naxIED+vS70FD93ujJk8EKO2dnZmayePFi5syZQ/Pmzdm2bRu+vr589NFHSuuW7EnXd3HhmTp1ij/vqvAN02vZ14rv7jAWGBnYYiBR4VGE1AxRVlOI8qjUYT1z5kwGDBjA8uXLy3I9tpebC126QPfu8N57+jzpqCilJTMyMli2bBlr1qwhJSWFXr16EaN4hvXNpp4/z6Rz56jv4sLiJk0YVreu8nbHtexrzDk0hw3/t0FCWojbUKqw3rRpEz4+PoSHh1eMsP7pJ/jwQ3jzTf2K+pNPoEUL5WUzMjJYvHgxc+fO/V1Iq37jUNM0vktLw9fFhTAPDx6vXZvqzs7WC2m5khbijhk0TdPu9IuefvppDEVPqCUmJhIQEMDSpUupVatW8X+TkJCAeyk3NzUajVZtr1Rfs4ZaS5Zw5qOPKLBCuyMnJ4c1a9awevVq0tPTiYiIYPjw4bRp00ZpXU3T2J2fz5LsbA6YTPRzc+NNKz1Ak2xM5u0Tb7P+1HryzHn08u/FkMZDKl0/2tp/tu2BnPOdycnJuXUWaH/TM888o506deoPH9+/f3+pX/PYsWN/Z0l/7do1TevdW9M+/lg/zs3VtPR0tTU1TTObzZqmaVp6errm4+Oj9erVS9u7d6+maerPeWtKitbxwAGNrVu1+j/+qC2+eFHLLShQWlPTNO1q1lXtX1/+S3Of6q45THHQntn0jHb8+nFN06zwfbZDcs6Vw9855z/Lzsp1615mJlSrBtWrw9WrkJqqf9zNTfkteKtWrWL16tV8//33eHp6cvz48d/9S0QFregfTQaDgS9TUzmbm2vVnvTsH2cTtz8OY4GRp1s8TVSnKIJrBCutK0RF9bfDes2aNWWxDvX+9S/49FM4elSfJ71nj/IxpRkZGTg6OuLh4YGHhwdeXl6kpaXh4+OjNKi1op705HPnGO/vT88aNZjg709Mw4YS0kKUU2qHWNhaQgLk5em/7twZnn1Wf0QclAZ1RkYGU6dOJSAggAULFgDw5JNP8umnn+Lj46OsrqZpfJuaSqeDB+ly6BBnc3Mxms0AVHNyUn6f9NivxhIwP4DY3bE8FvoYiSMTeffRdyWohSgDFbcN8tNP0Lbtb/Oke/bUfyiUkZHBokWLmDt3LqmpqfTp04fu3bsrrXmzp44dY+P169R3cWFJkyYMtUK742rWVWbvnE3cvjjyCvPkSloIRSpWWO/frz8a/thj0KoVvPUW9O+vvGxGRgYLFy4kNja2OKRjYmKscnfH92lp3O/lhYuDA31q1qSTtzfDfH2VPsgCEtJCWFvFCuuYGH2e9KOP6mNKhw5VWs6WIW3pSe9IT2dVSAhDfH15+qanDlUpGdLP3PUME8MnSkgLoVj5Duvjx/WnC+PjrTpP2iIhIYFJkybZLKQbuLoS16QJA20U0lHhUTSp0UR5bSFEeQ1ryzxpsxm2bdN3DI+MBH9/5aVnzJiB0Whk8uTJREZGcvToUcLCwpTXtRh7+jTXTSbimjRhqA3aHRLSQthG+QprTdP70b6++u4sYWFw8aK+e7hCOTk5xU9jnjx5kuzsbDRNw2AwKA1qTdP4JjWVOUlJrA8Lw8fZmQ+bNaOeq6vykP4161dm/zibpfuXSkgLYQfKR1ifPavPkTYYICREb3lYKAzq9PR0Fi5cyLx58/jqq69o27Yty5Ytw8lJ7W+bJaQnnzvHzowMGri6cjI3l3ucnQmsUkVp7ZIhPeiuQUwMnyghLYSN2X9Yv/UWPP88HDumB/X06cpLWkI6NjaWtLQ0HnnkETw8PACUB3VuYSFdDx3ix6KQtla7Q0JaCPtml2Htdviw3vIIC4M+ffRpePXqKa97q5COjo7m7rvvVlpX0zROFhQQClRxdKRF1ao8XaeOhLQQopj9hXVODv7PP68P/V+3Tp8nPX680pK2DGlLu2NPRgbHc3IIcndnabD62+BuDun8wvziW/AkpIWwT/YX1u7uJC1dSkCfPlYrOXv2bKZOnWqTkN6ZkYGfqysTq1XDzwpjJH/N+pVZP85i6f6lmApN+huHnaII8glSXlsIUXr2F9ZAbuvW+nQ8Va+fm8ucOXO499576dKlC6NHj6Zfv37KQ9rian4+vX/+mTouLixt0oQhvr6cOXFCacujZEgPaqm3OySkhSgf7DKsVTGbzTg4OODo6MiqVavIzc2lS5cu1KxZk5o332FSxjRN4+vUVLakpBAbFERdV1e+admS9p6eVulJS0gLUf5VirBOS0tj4cKFbNy4kYSEBNzc3Dh06BCenp5K61pCevK5c+wqandM8PenposL4d7eSmtLSAtRsVTosLaE9Lx584rfOExNTcXX11d5UJ/OzWVQYmJxSMcHBzO4bl3lV9JXMq8w68dZxCfES0gLUYFUyLBOS0tjwYIFzJs3j/T0dPr27Ut0dDStW7dWWlfTNK6bTNR2caG2szNGs1lCWghRJipUWNsypL8qanekFRRwpF07qjk5kdCmDQbFu9GUDOlnWz7LxPCJNPZprLSuEMK6KlRY9+vXj61bt9okpHdnZODv6srEhg31vQ+Ldn9XRUJaiMqlXId1WloaixYtYuTIkfj4+DBt2jRcXV2Vh7TFZ8nJ9DlyBH9XV5YVtTtcrNzukJAWonIo12F94cIFYmJiaNSoEU8//TQdOnRQWk/TNL5MSSG1oICn6tShu48P7zZtypO1a1slpGf+OJNlCcskpIWohMpVWKelpTF//nyuXr3K0qVLueuuuzhz5gwBAQFK61pCevK5c+zJzKRttWoMqF0bJwcHBtWtq7R2yZB+ruVzTAifICEtRCVTLsLaEtLz588nPT2dxx57jMLCQhwdHZUH9e70dEafOsWezMzftTus8cZhyZCe2Gkijao3UlpXCGGfShXWJpOJCRMmcOnSJfLz8xkxYgQPPvhgWa/tDyH96KOPEh0dTatWrcq81s00TSPPbMbN0RGj2cyV/Hyr9qQlpIUQJZUqrD/55BO8vb2ZPXs2aWlp9O3bt0zDOiMjg8mTJxeHdL9+/YiOjqZly5ZlVuNWbm53tPf0ZGGTJkRWr86pe+7BWXFIX8+9zrItyySkhRC3VKqw7t69O926dQP0gHN0dCyzBeXk5NCrVy+Sk5NtEtJ7MjNp6OpKm5sGSakM6suZl5m5Yybx++Mp1AolpIUQt2TQNE0r7RdnZWUxYsQInnjiCfqUGGmakJBQvG/hnVq/fj2tW7emadOmpV3aHVmclUVcdjb1HBx40cODh6tUwUVxT/pa7jVWHl/J+6ffp1ArpI9fH0Y0H4FfVT+lde2J0WjEzQpjYe2JnHPl8HfOOScnhzZt2vzxE1opXb58WXv00Ue1Dz744Jaf379/f2lfWjt27Fipv/Z2mM1m7fMbN7SjWVmapmnaiexsbcWlS1peYaHSupqmaZcyLmkvf/6y5vqGq+Y4xVEb9vEw7XTKaeXnbI/knCsHOec782fZWao2yI0bNxg6dCjR0dHce++9pfrbwxY0TWNLUbtjb2Ym//D1ZXlICMHu7gSX8l8Bt8vS7liWsIwCcwGDWw1mQviE4nZH4q+JSusLIcq3UoV1fHw8GRkZxMXFERcXB8CKFSvs+p86X6WkEHX2LPuKetIrgoN5VvE90vD7kLb0pG8OaSGEuB2lCuuoqCiioqLKei1lTitqxxsMBr5PS+Nafn5xSKu+Be9SxiVm/jiT5QnLJaSFEH9buXgo5k5pmsYXRe2OmIAAetWowcSGDZkcEGD1kB7cUm93BFYPVFpXCFGxVaiwvjmk92VmEuDmRmHR1bVHGd5eeCsS0kIIlSpUWPc/epRNN24Q4OZms3aHhLQQQoVyHdZa0cMsD1SvjquDA/1r1aKHj4/VQnrGjhmsOLBCQloIoVy5DOuS7Y5VISEM8fXlqTp1lNe2hPTyA8sxa2YJaSGEVZSrsL5VT3plSAjP2CCkh7QawoTwCQR4ByivLYQQ5SqsASadPUtKQQErQ0J4tk4d5QOWJKSFEPbArsNa0zQ+S05m7sWL/LdZM2o4O/N/zZvj6+IiIS2EqFTsMqw1TWPzjRtMPneOhKwsAt3cOJubSw1nZ/wVPyV5MeNi8RuHEtJCCHthd2GdU1jIkykpHLl2jUA3N94KCWGQFdodJUN6aKuhjA8fLyEthLALdhfW7o6O3OXszJjGjSWkhRCiiN2FNUCUpyehvr5Ka0hICyHKE7sMa5UkpIUQ5VGlCeuk9CRm7JjByp9WFof0hPAJNPRuaOulCSHEX6rwYX1zSGuaxtDWQxnfcbyEtBCiXKmwYS0hLYSoSCpcWEtICyEqogoT1knpSUzfMZ23fnpLQloIUeGU+7C2hPTKAysBJKSFEBVSuQ3rkiE9rPUwxoePx9/L38YrE0KIslfuwlpCWghRGZWbsJaQFkJUZqUKa7PZzOTJkzlx4gQuLi68+eabNGyopkd8If0C03/Q3zgECWkhROVUqrD+5ptvyM/PZ+PGjRw8eJAZM2awdOnSMl1YyZAefvdwxnUcJyEthKiUShXWCQkJhIeHA9CqVSuOHDlSZgtKzklmSsIUNv13EyAhLYQQUMqwzsrKomrVqsXHjo6OFBQU4OT0+5dLTEy849d+58Q7fHjmQ/o36s/wpsOp51GP7MvZJF6+89cqT4xGY6l+v8ozOefKQc65bJQqrKtWrUp2dnbxsdls/kNQA4SGht7xa78Z8iaPN36cNi3alGZp5VZiYmKpfr/KMznnykHO+c4kJCTc8uOlmux/9913s337dgAOHjxIcHBwqRZ1K04OTrg7uZfZ6wkhREVQqivrrl278uOPPzJgwAA0TWPatGllvS4hhBA3KVVYOzg48J///Kes1yKEEOJPqN3gUAghRJmQsBZCiHJAwloIIcoBCWshhCgHJKyFEKIcMGiapql44T+7sVsIIcT/1qbNHx8KVBbWQgghyo60QYQQohyQsBZCiHLArsLabDYTHR3Nk08+yaBBgzh//rytl6ScyWRi7NixDBw4kP79+/Ptt9/aeklWkZycTEREBKdPn7b1Uqxi2bJlPPnkk/Tr148PPvjA1stRzmQy8dprrzFgwAAGDhxY4b/Phw4dYtCgQQCcP3+ep556ioEDBxITE4PZbC6TGnYV1jdvavDaa68xY8YMWy9JuU8++QRvb2/ee+89Vq5cyRtvvGHrJSlnMpmIjo7Gzc3N1kuxij179vDTTz+xfv161qxZw6+//mrrJSm3bds2CgoK2LBhAyNHjmT+/Pm2XpIyK1asICoqiry8PACmT5/O6NGjee+999A0rcwuwOwqrFVuamCvunfvziuvvAKApmk4OjraeEXqzZw5kwEDBlC7dm1bL8UqduzYQXBwMCNHjuTFF18kMjLS1ktSLjAwkMLCQsxmM1lZWbccoVxR+Pv7s2jRouLjo0eP0r59ewA6derEzp07y6SOXf0O3u6mBhWJh4cHoJ/7yy+/zOjRo227IMU2bdqEj48P4eHhLF++3NbLsYrU1FQuX75MfHw8Fy9eZMSIEWzZsgWDwWDrpSnj7u7OpUuX6NGjB6mpqcTHx9t6Scp069aNixcvFh9rmlb8vfXw8CAzM7NM6tjVlfXtbmpQ0Vy5coVnn32WRx55hD59+th6OUp9+OGH7Ny5k0GDBpGYmMjrr7/O9evXbb0spby9venYsSMuLi40atQIV1dXUlJSbL0spVavXk3Hjh358ssv+fjjjxk3blxxm6Cic3D4LVazs7Px9PQsm9ctk1cpIyo3NbBXN27cYOjQoYwdO5b+/fvbejnKrVu3jrVr17JmzRpCQ0OZOXMmtWrVsvWylGrTpg0//PADmqZx9epVcnNz8fb2tvWylPL09KRatWoAeHl5UVBQQGFhoY1XZR1hYWHs2bMHgO3bt9O2bdsyeV27umytjJsaxMfHk5GRQVxcHHFxcYD+hkVlefOtMnjggQfYt28f/fv3R9M0oqOjK/x7E4MHD2bChAkMHDgQk8nEmDFjcHevHDtAvf7660yaNInY2FgaNWpEt27dyuR15QlGIYQoB+yqDSKEEOLWJKyFEKIckLAWQohyQMJaCCHKAQlrIYQoBySshRCiHJCwFkKIckDCWgghyoH/B67ttdHTd7FoAAAAAElFTkSuQmCC", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, x + 0, '-g') # solid green\n", + "plt.plot(x, x + 1, '--c') # dashed cyan\n", + "plt.plot(x, x + 2, '-.k') # dashdot black\n", + "plt.plot(x, x + 3, ':r'); # dotted red" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These single-character color codes reflect the standard abbreviations in the RGB (Red/Green/Blue) and CMYK (Cyan/Magenta/Yellow/blacK) color systems, commonly used for digital color graphics.\n", + "\n", + "There are many other keyword arguments that can be used to fine-tune the appearance of the plot; for details, read through the docstring of the `plt.plot` function using IPython's help tools (see [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adjusting the Plot: Axes Limits\n", + "\n", + "Matplotlib does a decent job of choosing default axes limits for your plot, but sometimes it's nice to have finer control.\n", + "The most basic way to adjust the limits is to use the `plt.xlim` and `plt.ylim` functions (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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dBodlQlunCnsk1XhktD98XC1zilFDPZkQjPp2BQ7QfOms89nJCvi42OOR0X5MRzGJlHFiuDrw8WlWOdNRLILeZ/cOHz4MpVKJzMxMnDt3Du+++y4+/vjjnuUXL17Eli1b4OnpaZSgTNmZew2dSg1WTmLf3vktCWHeCPd1wadZ5VgU7c+a46y27nJDB05cacLLM8Mg4LPzy7jQno/0CYHY+EsZyhtlCPYWMh2JUXoXukQiweTJkwEAY8aMQVFRUc8yrVYLqVSKtWvXoqmpCUuWLMGSJUvueo/iYvPdhUShUAx4fWqtDluOX8NoXwdw2mpQ3FZjonSG02f7bjdvmAPeP9mIL4/kI9bfyYjJjMPQ7bN0pti+f2c3QsDjINajm/H/dqb8/CZ6q/EJB/jn9wV4avwgk6zjXizpd1PvQpfJZBAK//d/Qx6PB7VaDT6fj87OTixduhTLly+HRqPBsmXLMHLkSISHh9/xHhEREfonH6Di4uIBr29/YS2aOivwXuJYRERY9gklfbbvdiGhWnxReBRHqzRIf8h8n0t/Gbp9ls7Y29cs68bRikosjhFh/NiRRntffZn683vkqgYHi+rx19TxZp8wz9y/mxKJpM9len8PEwqFkMvlPT9rtVrw+Tf//+Do6Ihly5bB0dERQqEQ48ePR0lJib6rYoROp8NnJ8oRPMgZU4f7MB3H5AR8Ln4fL8ax0kZUNMnv/wJi0b7KuQalWouVk4KYjmIWyycORadSgz15tj0dgN6FHh0djaysLADAuXPnEBb2v/khKisrkZqaCo1GA5VKhfz8fIwYMcLwtGYkkd5AYXUblk8ayrqrA/qSFi+GHY+D7XSbOqvWrdYg44wUCWHeGObjwnQcsxgV4IaYQA9sz66ERmu7A430LvQZM2ZAIBAgJSUF77zzDv74xz9i69atOHLkCEJCQrBgwQIkJSUhPT0dCxYsQGhoqDFzm9xnJyvg5miHxdH+TEcxGx8XBzwc5YevJdWQdauZjkP09H1hHRo7ull9Ir83j00MwrWWTvxSaru3qdP7GDqXy8Vbb711x2MhISE9/3788cfx+OOP65+MQXVtXfjpYj2emBIMJwE7hvn316MTg7CvoAbfSKrxKItGxdoKnU6HbdmVCPURYnKo+U8QMmn2SF8MdrXHtuxKTLfwc16mws5rmQy0M+cadACWxgcyHcXsxojcMUbkju3ZldDa8FdXa1VY3YYLNW1YNjHI5i4/teNxkT4+ECeuNOFKg3WOezEUFfpvqDRa7MytwtThPhB5Wt7le+aw/IEglDfJkXWF5siwNhmnpXAW8PC7sbZzqPB2qePEEPC52H66kukojKBC/42fLzagsaMb6eNtb+/8ljkjh8Db5eZXV2I9bsiVOHC+Fr+L9oeQJTOCDpSX8Oao2G8kNWi3wQnnqNB/I+NMJUSejphiZTfQNSYBn4u0cWIcv9yIqpZOpuOQfvpaUg2lWoulNrwzAgDLJgSiS6XBtwWWOxDQVKjQb3OloQNnyluQNi4QPBu5VLEvKeNE4ADYefYa01FIP2i1OnyZI8W4IE+E+7oyHYdRUQHuGOXvhq/OXLO5udKp0G/z5RkpBDwukmIDmI7CuCFujpgeMRi786poFkYrcOJqE6TNnfj9eOu/m5Yx/D5ejNKGDkiktjULIxX6r+TdauzNr8G8qCHwEtozHccipMWL0SRT4tClBqajkPv48owUg4QCzB7py3QUizB/tB9c7Pn4Kse2vmFSof/qu3O16OhW2/zxx9tNCfVGgIcjvsqR3v/JhDE1rV04UtyA5DgR7PnWffNyY3G25+N30f744UIdbsiVTMcxGyp03ByM8cXpSkQOcUW02J3pOBaDx+UgdZwY2WXNKG+UMR2H9GHnr3uhqePocMvt0uLFUKq1+CbfduZ3oUIHkH+tFSX1HUifEGhzgzHuJzE2AHwuh06OWiiVRotduVWYFu6DAA/bHDfRl3BfV8QGeuCrHNs5OUqFDmDX2WtwFvBYe1cXQ/i4OGDmiMH4WlINhUrDdBzyG0eKr6NJ1o20eNo7783vx4tR0STH6bJmpqOYhc0XeodChe/P1+GRMX5wttHBGPeTNi4QNzpVOFhUz3QU8huZudfg6+qAKaG2O27iXuaMHAJ3JzubOTlq84V+oLAOXSoNkuNoD6cvE0O8EOTlhB028kdhLWpbu3D8cuPNw2I8m/9T7pWDHQ+JMQH46WI9rncomI5jcjb/W5CZew3hvi4YHeDGdBSLxf315OjZyhZcttFJjyzR15JqaHVAUqyI6SgWLXWcGGqtDnvz2T9y1KYL/VJtOwqr25AcJ6KTofexJCYAdjwOdp2tYjoKwc2RoZm5VZg0bJDNTiLXX8HeQowL8kRmbhXrT47adKHvzquCgM+12ZnpBsJLaI+Zkb7YV1CNbjWdHGXaqbIm1LR2ITmO9s77IzlOhIomOc5WtDAdxaRsttAVKg325ldj9ghfuDsJmI5jFZLiRLjRqaKRoxZgV24V3J3sMHOEbd7IYaDmjhoCF3s+MvPY/Q3TZgv9p4v1aFeokUJ7OP02adgg+Ls7IjOX3X8Ulq5FrsTPF+uxaGwAjQztJ0cBD4+M8cOPF+rQ1sXeaXVtttAzc6sg9nTC+GAvpqNYDR6XgyUxATh5tQnVN2haXabsza+GSqOjwy0DlBInhkKlxf7CWqajmIxNFrq0WY7ssmYkx4nAtfFpcgcq8deZKPfk2c5wakui0908GTpW7I7hvi5Mx7EqI/1dETnEFZm57L381iYLfXdeFbicm1dukIEJ8HDCpGGD8LWkGhq656jZ5V9rxZXrMjpUqAcOh4PkOBGKatpRVNPGdByTsLlCV2u02JNXjWnhPhjs6sB0HKuUHCdCTWsXTl5tYjqKzcnMvTlNxcNRNE2FPhaO8YeAz8Vulp4ctblC/6W0Edc7umlkqAFmRA6Gh5MddtPJUbPqUKhwoLAO80fTNBX6cnOyw9yRvthXUMPKuYlsrtB35VbBx8UeU4fT3Bf6sufz8LuxAfj5Uj2aZd1Mx7EZ35+/NU0FHW4xRFKcCB0KNSvnJrKpQm9oV+BY6XUsiaG5LwyVHCeCSqPDPhu8ES9TduVWYfhgF4wRuTMdxaqNH+qFQC8n7GLhyVGbarVbJ/Jo7gvDDfe9WSy2MJzaEhTXtaOwqpWmqTACLpeDpFgRzpS3oLJJznQco7KZQtfqdNidV4XxwZ4IGuTMdBxWSI4T4cp1GQqqWpmOwnqZuVUQ8GiaCmNZEhMALgesOzlqM4V+oV4BaXMnUuhkqNHMH+0HJwGPTo6amEKlwb6CGswa6QsPZ5qmwhgGuzpgWrgP9kiqodZomY5jNHoXularxdq1a5GcnIz09HRIpXfeSHj37t1YtGgRkpKScOzYMYODGurglQ64OvDpruhGJLTnY96oIThQWAt5t5rpOKz108V6tHWp6NpzI0uKFaGxoxtHS64zHcVo9C70w4cPQ6lUIjMzEy+99BLefffdnmWNjY3IyMjArl278Nlnn+GDDz6AUsncnbdbO5U4JZXjd2P94WBHc18YU3KcCHKlBj+cr2M6CmvtOlsFkacjJtA0FUY1LdwH3i72rDrsonehSyQSTJ48GQAwZswYFBUV9Sw7f/48xo4dC4FAABcXF4jFYpSUlBieVk8S6Q2otTq69twEYgI9EOLtzMorBiyBtFmO0+XNSI6laSqMjc/jYklMAI6VNqKhnR13M9J7dIJMJoNQKOz5mcfjQa1Wg8/nQyaTwcXlf/NMODs7QyaT3fUexcXF+q5+QLw1Ovxzljc4bTUobmPnZXYKhcJs/z1/60GxPT6TtODg6UIEupvmGC+T22cOfW3f9vwWcDnAaFfr3n5L/fxiPFTQaHX4+GA+kkd56PUelrRtehe6UCiEXP6/S360Wi34fH6vy+Ry+R0Ff0tERIS+qx8wu+Jis67P3IoZ3L7Vom5sLziCvGY7zJ5gmgxMbp859LZ9ao0Wx/YdRUKYNybHjmIomXFY6ucXAWB8oRzHpAqsXRKu17cgc2+bRCLpc5neh1yio6ORlZUFADh37hzCwsJ6lkVFRUEikaC7uxsdHR0oKyu7Yzlhl0FCe8yIHIy9BTV0NyMjyrrSiIZ2mqbC1FLixJA2d+JMRTPTUQym9x76jBkzcOrUKaSkpECn02H9+vXYunUrxGIxpk+fjvT0dKSlpUGn0+GFF16Avb29MXMTC5McJ8J/i+px+NJ1zIsawnQcVsjMrcIgoQDTI3yYjsJqs0f6wvU7PjJzqzAxZBDTcQyid6FzuVy89dZbdzwWEhLS8++kpCQkJSXpn4xYlcmh3vBzc8Cu3GtU6EbQ2NGNI8XXsWLSUNjRNBUm5WDHw8Kx/tiVW4X/16m06ltS0m8KMQoel4PEWBFOXm1CVQvdzchQe/OroaZpKswmOU4EpVqLb618biIqdGI0PXczktDdjAyh0+mQmVeF2EAPDPMR3v8FxGAj/Nwwyt8Nu6x8biIqdGI0AR5OmBzqjT15VXQ3IwPkSW+gvFGOJBoZalbJcSKU1HfgghXfzYgKnRhVSpwIdW0KZF1pZDqK1crMreqZVoGYzyNj/OBgx8UuK56biAqdGNVDEYPh6SxA5lnr/aNgUodChR/O12H+6CF0VyIzc3Www7xRfth/rhadSuucm4gKnRiVgM/F4mh/HC5uQGMH3c1ooA4U3rwrEZ0MZUbKOBFk3WqrnZuICp0YXXKcCGqtDnvz6eToQGXm0V2JmBQb6IFgb2dkWulhFyp0YnTDfFwQG+hBdzMaoJL6m3clSqK7EjGGw+EgOVaEPOkNXL3ewXScAaNCJyaRHCdCeZMcuZU3mI5iNTJzq2DH49BdiRi2KDoAfC4Hu/Os7xsmFToxiXlRQyC059O0uv2k/PWG2zNH+MKT7krEKG8XezwUMRjfSKqhVFvX3Yyo0IlJOAn4eGSMH368UIe2LhXTcSzemSo5WjtVSKaToRYheZwIzXIljhQ3MB1lQKjQicmkxImgUGmxv7CW6SgW78fSdgR4OOKBYdY9ORRbTAn1xhA3B6u7Jp0KnZjMKH83RAxxRSYddrmn8kYZCusVSB0nBo/uSmQRbs1NlHWlETWtXUzH6TcqdGIyHA4HKXEiFNW0o8iKh1Ob2s6z18Dj/G8uHGIZEmN+nZvIiu45SoVOTGrhGH8I+Fyrva7X1BQqDfZIqjFB7AwfFwem45DbiDydMGnYIOzJq7aauYmo0IlJuTnZYe5IX3xbUAN5t3UOpzalg0X1aO1UYe5wV6ajkF6kxIlR09qFE1YyNxEVOjG5peMD0dGtppOjvfgqR4ogLyeM9qW9c0s0I3IwBgkF+PKMdZwHokInJhcT6IFwXxdknJbSyNHbXG7oQG7lDaTFi8GlkaEWScDnIiVOjKMlDai+Yfk3bqFCJybH4XCQPiEQl+rakX+tlek4FmNHzjUIeFwsiaFrzy1ZavzNm3TvPGv5e+lU6MQsFo7xh9Cejy/PSJmOYhG6lBp8k1+NOaNoZKil83d3xLTwwcjMrbL4kaNU6MQsnO35WBTtjx/O16FZRtPqHjhfiw6FGmnjxExHIf2QPiEQTTIlDl6sZzrKPVGhE7NZOj4QSo2W7jkK4KucaxjmI8S4oZ5MRyH9MHnYIAR6OeHL05b9DZMKnZhN2GAXxA/1xFc5Uqu5rtcUzlW1orCqFb+PF9M0uVaCy+Xg9/FinK1sQUl9O9Nx+kSFTswqfUIgqlq6kHXZOq7rNYXt2ZVwFvCwJIZGhlqTxBgRBHyuRZ8HokInZjUz0hfeLvbIsOA/ClO63qHA9+drkRgrgouDHdNxyAB4OAswP8oP+/JrILPQQXJU6MSsBHwuUuNEOFZ6HVUtln9dr7HtzKmCSqPDsgmBTEchekifEAi5UmOxt1ekQidml/rrQJovTlcyHcWslGotvsyRIiHMG8HeQqbjED2MDnDD6AA3bD1VCa0FngeiQidmN8TNEXNHDcGus1UW+9XVFP5bVIfGjm489kAQ01GInjgcDlZMGoqKJjmOlV5nOs5d9Cp0hUKBP/zhD0hLS8MTTzyBlpaWu56zevVqpKSkID09HY8//rjBQQm7rJw0FB3dauy2oVkYt2VXYuggZySEejMdhRhg7qghGOLmgM9OVjAd5S56FfrOnTsRFhaGHTt2YOHChdi4ceNdz5FKpdi5cycyMjKwZcsWg4MSdhkjckdsoAe2ZlfYxCWMhVWtKLjWimUTAsGlm1hYNTseF8smBCG7rBmXai3rEka9Cl0ikWDy5MkAgClTpuD06dN3LG9qakJ7eztWrVqF1NRUHDt2zPCkhHUenzwUVS1dOHTJskffGcPnpyroUkUWSRsnhqMdD5+fsqy9dP79nrBnzx5s3779jse8vLzg4uICAHB2dkZHR8cdy1UqFVasWIFly5ahra0NqampiIqKgpeX1x3PKy4uNjR/vykUCrOuz9yscfsCODr4CvnY8PMlBPJa7/lca9y+WxpkKhworMXCCDdUV1zt9TnWvH39wcbtmx7sjG8LqjHXfzBgIdt230JPTExEYmLiHY8988wzkMvlAAC5XA5X1zsn5x80aBBSUlLA5/Ph5eWFiIgIVFRU3FXoERERhubvt+LiYrOuz9ysdfv+74Yj3vr+EpTCIRgtcu/zeda6fQCw+8BFcDkcvPxIDPzcHXt9jjVvX3+wcfteHCTD9+8fx2FpN9ZPjDXbeiUSSZ/L9DrkEh0djePHjwMAsrKyEBMTc8fy7OxsPPfccwBuFv6VK1cQHBysz6oIyyXFieBiz7fIE0zG0NqpRGZuFR4Z7ddnmRPrFOwtxPRwH/xQ2m4xlzDqVeipqam4cuUKUlNTkZmZiWeeeQYA8Le//Q3nz59HQkICgoKCkJSUhJUrV+LFF1+EpydNQkTuJrTnI2WcCD9cqGPlQKMvz0jRqdTgiSm0Q8NGr84OxwSRMyxlSp77HnLpjaOjIz788MO7Hn/11Vd7/v2nP/1J/1TEpqycFIzt2VJ8klWGdQtHMR3HaBQqDbZlSzElzBsRQ+ieoWw03NcFz030tphJ1mhgEWGcr5sDFscEYHdeNa63K5iOYzT7CmrQJOvGKto7J2ZChU4swqqEYKg1WmxhybF0lUaLj38pwyh/N0wI8br/CwgxAip0YhECvZzxyGg/fHlGihtyJdNxDPbduVpca+nEs9NDLebrOGE/KnRiMZ6aOgydSg22ZlcyHcUgao0WHx29gsghrngowofpOMSGUKETixE22AUzIwdj26kKtCtUTMfR24Hztahspr1zYn5U6MSiPDs9FO0KNbacsM5j6RqtDhuOXkW4783/ORFiTlToxKKM9HfD3FG++OxEOZpl3UzHGbADhbUob5TjuemhNAkXMTsqdGJxXpwRhi6VBh//UsZ0lAFRqrV4/1ApIoa4YtYIX6bjEBtEhU4szjAfFyyKDsAXZ6Soa+tiOk6/7ciRoqqlC2vmhNPeOWEEFTqxSM9ND4VOp8OHR3qfndDSyLrV2HD0KiaGeGFK6CCm4xAbRYVOLJLI0wlp48TYnVeF0vqO+7+AYZuzytEsV+K12eF0ZQthDBU6sVjPPxQGoT0fb39/CTqdZcxm15u6ti5sPlGOeaPuPQUwIaZGhU4sloezAM8/FIqTV5uQU2W5MzGu/7EEGq0Oa+aEMx2F2DgqdGLRlo4PxDAfITbnNaNbrWE6zl1OlzXjQGEtViWEQOTpxHQcYuOo0IlFs+Nx8ebDkajtUGNzVjnTce6g1mjxl/0X4e/uiNUPhjAdhxAqdGL5EsK8MSnQGR8evYqyRhnTcXpsy65EaUMH3nw4Eg52PKbjEEKFTqzD6ngvOPC5+OPeCxZxu6+KJjn+8XMppof7YNYIGuJPLAMVOrEKno58vDEvEmcrWrAz9xqjWbRaHV77+jzseFz89Xej6DJFYjGo0InVSIwNwMQQL6z/oRiVTXLGcmw/XYmzlS148+FI+Lo5MJaDkN+iQidWg8Ph4O+Jo8HjcvDcrgIo1VqzZ7hY24Z3/luCqcO9kRgTYPb1E3IvVOjEqvi7O+K9xVEorG7D+4dKzbpuWbcaz+wogIeTHf6ROJoOtRCLQ4VOrM6cUUOQFi/GJ8fLcbCozizr1Ol0eH3vBUib5fgwZSy8hPZmWS8hA0GFTqzS2ocjMUbkjhcyC1FU02by9X109Cr2F9bipZnDER9MN30mlokKnVglBzsePl0WAw8nOzzxRR7q2xQmW9f+wlq8f+gyFo31x1M0gIhYMCp0YrV8XByw+dFYtHepkLblDK53GL/UD11qwEu7z2FckCfeWUyXKBLLRoVOrNoIPzdsWzEO9W0KpG3OwfV245X6oUsNeOorCSL93LDlsVjY82k0KLFsVOjE6sUFeeLzx+JQ29qFhf85hUu17Qa/5/bsSjyZkYdIPzd8sWIcXB3sjJCUENOiQiesMD7YC7ufnACtDkjclI1vJNV6zaEu61bjlT2F+PP+i5gW7oMdj8fDzZHKnFgHgwr90KFDeOmll3pdtnv3bixatAhJSUk4duyYIashpF9G+rvh26cfQKSfK17aU4gnvshDeT8n89LpdDhYVIc5/87CN/nVeHpqCD5Jj4WzPd/EqQkxHr1/W9etW4eTJ08iIiLirmWNjY3IyMjAN998g+7ubqSlpeGBBx6AQCAwKCwh9+Pr5oBd/zcBW06U499HrmDGP7Mwb9QQJMWKEDfU467j4M2ybvx8qQE7cq7hQk0bQn2EyHxyAuKCPBnaAkL0p3ehR0dH46GHHkJmZuZdy86fP4+xY8dCIBBAIBBALBajpKQEUVFRBoUlpD94XA6eTAjBougAfPxLGb6WVGF/YS0EfC5CfYTwdBZApdGivk2Byuabd0IKGyzEu4tGYUlMAPg8OhJJrNN9C33Pnj3Yvn37HY+tX78ec+fORU5OTq+vkclkcHFx6fnZ2dkZMtndX32Li4sHmldvCoXCrOszN9q+3iUO42DB0ADk1XThYoMC19qUuH6jG3wuB/5CHqYGemLMEEeEegnA4chx5bJ5pxO4hT4/62VJ23bfQk9MTERiYuKA3lQoFEIu/99seHK5/I6Cv6W3wzWmUlxcbNb1mRtt372NHmnEMCZAn5/1Mve2SSSSPpeZ5LtlVFQUJBIJuru70dHRgbKyMoSFhZliVYQQQn5l1FP4W7duhVgsxvTp05Geno60tDTodDq88MILsLenyYwIIcSUDCr0+Ph4xMfH9/y8fPnynn8nJSUhKSnJkLcnhBAyAHQ6nxBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIIKnRBCWIJvyIsPHTqEgwcP4v33379r2bp165Cfnw9nZ2cAwMaNG+Hi4mLI6gghhNyD3oW+bt06nDx5EhEREb0uv3jxIrZs2QJPT0+9wxFCCOk/jk6n0+nzwh9//BGenp7IzMzEP//5zzuWabVaTJo0CdHR0WhqasKSJUuwZMmSO54jkUj0T00IITYsJiam18fvu4e+Z88ebN++/Y7H1q9fj7lz5yInJ6fX13R2dmLp0qVYvnw5NBoNli1bhpEjRyI8PPy+gQghhOjnvoWemJiIxMTEAb2po6Mjli1bBkdHRwDA+PHjUVJSckehE0IIMS6TXOVSWVmJ1NRUaDQaqFQq5OfnY8SIEaZYFSGEkF8ZdJXLb23duhVisRjTp0/HggULkJSUBDs7OyxYsAChoaHGXBUhhJDf0PukqLXQarX4y1/+gtLSUggEAqxbtw6BgYFMxzIalUqF119/HTU1NVAqlVi9ejWmT5/OdCyjam5uxqJFi/D5558jJCSE6ThG9cknn+Do0aNQqVRITU0d8OFNS6ZSqbBmzRrU1NSAy+Xi7bffZs3nV1hYiH/84x/IyMiAVCrFmjVrwOFwEBoaij//+c/gcpkZ4sP6gUWHDx+GUqlEZmYmXnrpJbz77rtMRzKq/fv3w93dHTt27MCWLVvw9ttvMx3JqFQqFdauXQsHBwemoxhdTk4OCgoKsHPnTmRkZKC+vp7pSEZ1/PhxqNVq7Nq1C08//TT+9a9/MR3JKDZv3ow33ngD3d3dAIB33nkHzz//PHbs2AGdTocjR44wlo31hS6RSDB58mQAwJgxY1BUVMRwIuOaPXs2nnvuOQCATqcDj8djOJFxvffee0hJSYGPjw/TUYzu5MmTCAsLw9NPP41Vq1bhwQcfZDqSUQ0dOhQajQZarRYymQx8vlGP8DJGLBZjw4YNPT9fvHgR48aNAwBMmTIF2dnZTEUz7jF0SySTySAUCnt+5vF4UKvVrPnlujUSVyaT4dlnn8Xzzz/PbCAj2rt3Lzw9PTF58mR8+umnTMcxuhs3bqC2thabNm1CdXU1Vq9ejYMHD4LD4TAdzSicnJxQU1ODOXPm4MaNG9i0aRPTkYxi1qxZqK6u7vlZp9P1fGbOzs7o6OhgKhr799CFQiHkcnnPz1qtljVlfktdXR2WLVuGBQsWYP78+UzHMZpvvvkG2dnZSE9PR3FxMV577TU0NjYyHcto3N3dMWnSJAgEAgQHB8Pe3h4tLS1MxzKabdu2YdKkSfjpp5/w3XffYc2aNT2HKdjk9uPlcrkcrq6uzGVhbM1mEh0djaysLADAuXPnEBYWxnAi42pqasKKFSvwyiuv3DUa19p99dVX+PLLL5GRkYGIiAi899578Pb2ZjqW0cTExODEiRPQ6XRoaGhAV1cX3N3dmY5lNK6urj3zN7m5uUGtVkOj0TCcyvgiIyN7BllmZWUhNjaWsSzs2lXtxYwZM3Dq1CmkpKRAp9Nh/fr1TEcyqk2bNqG9vR0bN27Exo0bAdw8acPGk4hsM3XqVOTm5mLJkiXQ6XRYu3Ytq86BPPbYY3j99deRlpYGlUqFF154AU5OTkzHMrrXXnsNb775Jj744AMEBwdj1qxZjGVh/WWLhBBiK1h/yIUQQmwFFTohhLAEFTohhLAEFTohhLAEFTohhLAEFTohhLAEFTohhLDE/wcUc+ywwVVXnAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x))\n", + "\n", + "plt.xlim(-1, 11)\n", + "plt.ylim(-1.5, 1.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If for some reason you'd like either axis to be displayed in reverse, you can simply reverse the order of the arguments (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x))\n", + "\n", + "plt.xlim(10, 0)\n", + "plt.ylim(1.2, -1.2);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A useful related method is `plt.axis` (note here the potential confusion between *axes* with an *e*, and *axis* with an *i*), which allows more qualitative specifications of axis limits. For example, you can automatically tighten the bounds around the current content, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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nWA/weTxsPWt/32QpyT/Et2dKEejmhKcifNgOpdtGR/rCWybGNjv8oJPHl3GuDAaGQeoQ27/B8XN1xOi+PvjufLndFe2jJP8A12qVOHG1HilDgjlR+0Uk4GPmoCD8UliDyiZa8Jvcn05vwPazZUjs7Y0QT9vtpvy9lKEhqFdpcMjOFvymJP8A287egJDPw8xBtjds8n5mDw6BgQF2nCtnOxRixY4U1qDqthp/5kA35R2Jvb0R6OZkd99kKcnfh1qrx055OZKjfeHj4sh2OCYT7OGMhN5eyDh3gx7Akvv69swN+Ls6YlRf2++mvEPA52HW4GD8erXOrh7AUpK/j315lbjVosWfh7K/QLeppQ4Jwc0mNTKv0ANYcq+yhhZkXanF7MEhNjW7+1HMHBQMPg/Yfq6M7VAshlvvoAntPF+OEA9nPBFmvTXjjTUmyhdeUjG2nrGfDzp5dN/Jy8HjATMGBbEdisn5uTpiVF9f7DxfZjcPYCnJd6G8sQUni+sxPT4IfA48cP2juw9gq1F9W812OMSKGAwMdl0ox5O9vBDA0cU2UocGo06pwRGFfTyApSTfhTsLYE+NC3zIK23X9PggGBjYdeEmcq8zJQ0ob2zF9Hju3cXf8VSED3xdxNh1wT4GH1CS/wOGYfCdvBzDwz0R5M6NoWNdCfOWIi7EDbsulINh6AEsabdTXgaZWIix0bY7w/VhBHwepgwMxLHLtahTtrEdjtlRkv+Dc9cbcaOhhdN3MndMjQvClWol8m/eZjsUYgWUbTrsy63CxP4BcBTZ9gzXh5k6MAg6A4Pd2TfZDsXsKMn/wXfyMkgcBDZdq+NRTYoNgIOAj+/k9vG1lTzY3txKtGr1dnGD08dPhphAF3x/kfuffUryv9Oi0eHnnEo8E+sPZwejS+3bDFdnEcZE+WD3pZvQ6u1jpAG5v+/k5QjzkiAuxI3tUCxiWlwQ8ipu43JVM9uhmBUl+d/Zn1cFlUaP6fHcmeH6MNPigtCg0uDY5Vq2QyEsKq1X4WxJA6bFB9lsSeHH9Wz/AAj5PHzP8QewRt+uGgwGvP/++7h8+TIcHBywYsUK9Ohxd+LQihUrcOHCBUgk7cuFrV+/HlqtFv/4xz+gVqvh4+ODVatWdSzsbQ2+k7ePjbfFxRGMlRjhDU+JA76/UI6kKF+2wyEs+f5CBXg8bo8o+yNPqRgj+/jgh4sVWDK2D+cmft1hdKsOHz4MjUaDjIwMLF68GKtXr+60Pz8/Hxs3bkR6ejrS09Mhk8mwfv16TJw4EVu3bkVUVBQyMjK63QBTqWpS49S1evxpYKDd3MkA7WPmJw8IxBFFDW61aNgOh7CAYRjsvnQTT4R5wt/Vem66LGFaXCBqmttwgsOrRhmd5OVyORISEgAAAwYMQF5eXsc+g8GA0tJSLFu2DLNnz8Z33313zzGJiYk4efJkd2I3qZ9yboJh2leRsTdT4wKh0RuwJ6eS7VAIC3IrmlBSp8Kz/e3vsz8q0geuTiLs4vDgA6O7a5RKJaRSacfPAoEAOp0OQqEQLS0tmDNnDubPnw+9Xo+5c+ciJiYGSqUSMpkMACCRSNDc3PUDD4VCYVRMarXa6GMzTlegl4cDNHVlUNQZdQpWdKfNd/AZBiGuImScvIpBri0misx8TNFmW2PONn99rh5CPhDmcNuq/l0t9T6PCHbEgfxKXMxxgKOI3S4bc7TZ6CQvlUqhUt2t5GYwGCAUtp/OyckJc+fO7ehvHzZsGAoLCzuOcXR0hEqlgouLS5fnjoyMNComhUJh1LEldSoU1V/D2xP6IjIy3Khrs8XYNv/R9EoRPjp0BW4BPa3+K7up2mxLzNVmvYHBiR+OYGQfXwwZEGPy83eHpd7nuWIf7L1yGuWMOyZFsvttpjttlsvlXW43+tdWXFwcsrKyAADZ2dmIiIjo2Hf9+nWkpKRAr9dDq9XiwoULiI6ORlxcHDIzMwEAWVlZiI+PN/byJrXn0k3weMAkO/y6esedtv9MXTZ25WxJA6pvt2GyHXZT3jG4pwd8XcTYfYmbE6OMvpNPSkrCiRMnMHv2bDAMg5UrV2Lz5s0ICQnB6NGjMXnyZMycORMikQiTJ09G7969sXDhQixduhQ7duyAu7s71q5da8q2GIVhGPyYXYHBPT2s/g7WnEK9JOgX6Irdl27i+YQwtsMhFrL7UgWcHQQYE2m/I6sEfB6e6ReAb06XoqlVC1cnEdshmZTRSZ7P52P58uWdtoWH3+3qeP755/H888932u/l5YVNmzYZe0mzKKi8jeJaFeaPCGU7FNZN6u+PlXsLcb1OhZ5eErbDIWam0RmwN7cKyVG+cHLgdhmDh5nU3x9fnSjBwfwqzODQSnAATYbC7uybEPJ5mNDPn+1QWDcxtv0r+x6Ofm0lnWVdqUVTqxaTB9jP2Pj7GRDshmAPJ06OMLPrJG8wMNhz6SYSenvBQ+LAdjisC3BzwuCe7tiTQ0neHvx46SbcnUV4srcX26GwjsfjYVJsAE5crUM9xypT2nWSl99oxM0mtV2Ojb+fZ/sH4Eq1EoVVVJmSy1o0OhwuqMaEfv4QcXSm5+Oa1D8AegODvXlVbIdiUnb97v506SbEQj6SorhfcfJRje/nDwGfR102HPdLYQ1atfqOLjoC9PWTobePlHOffbtN8gYDg315VXi6jw+kYu5XnHxUXlIxhod7Ys+lSlpMhMP25VbBSyrGkFAPtkOxGjweD5P6B+Dc9QZUNrWyHY7J2G2Sl99oRE1zG8b3o7v4P5oUG4AbDS3IrWhiOxRiBq0aPX4prMG4GF8IOLiGcXdM6h8AhuHWfBG7TfJ7cyvhIORjVF8ftkOxOsnRvhDyedjHsb5J0u7Y5faumgkxNKLsj0K9JIj0d+HUZ98uk7zBwGB/XhUSe3tD5sitiQ+m4ObsgCfCPbEvl7psuGhvXhU8JA7UVXMfE2L8IC9tRFWTmu1QTMIuk3x2+S1UNqkxgbpq7mt8jD+u17dAUcntVXPsjVqrxy+KaoyN9uVs/fTuutOFeyCfG3fzdvku78uthEjAwxhaJOO+kqN9wecB+/O40zdJgMwrtVBp9DT57wF6+bSPstnHkc++3SV5hmGwN7cKCb294UJdNfflJRVjaKgn58YM27t9uZVwcxZhWJgn26FYtfH9/HG2pAF1HJgYZXdJPqe8CRW3WjE+hrpqHmZ8Pz9crVGiqJq6bLigTafHYUUNkqN8aQLUQ4yP8YOBAQ7mV7MdSrfZ3Tu9N68SQj6P1jN9BGOj/cDjgVMjDezZr0V1ULbpMJ66ah6qr58MoV4STnTZ2FWSZxgG+3KrMLyXF9ycqVbNw/i6OGJQD3fszbX9DzoBfs6thIujECPCqVbNw/B4PIyL8cPJ4no0qmx77WO7SvL5N2/jRkMLJlBXzSMbF+OPwqpmlNSpHv5iYrU0OgMOFVQjKcoPDkK7+m9vtAkx/tAbGBxS2HaXjV292/vyKiHg85AcTUn+UY377RciF7622rMTxXVoVuto2PBjiAl0QZC7E/bbeHel3ST5O6NqngjzpLLCjyHQzQn9g92wL9e2P+j2bl9uJWRiIZUVfgw8Hg/jY/xwvKgWt9VatsMxmlFJ3mAwYNmyZZg1axbS0tJQWlraaf/XX3+NGTNmYMaMGfj0008BtCfZhIQEpKWlIS0tzeJL/12pVqKkTtVxZ0oe3YQYP+RWNKGsoYXtUIgRdPr2rpqn+/pALLTvFaAe17gYf2j1DH5R1LAditGMKr94+PBhaDQaZGRkIDs7G6tXr8aGDRsAAGVlZdi9ezd27twJPp+PlJQUjBkzBk5OToiOjsZnn31m0gY8qkMF7XeiyTSq5rGNj/HHqn2F2J9XhRcSaf1XWyMvbURjixZjqZvysQ0MdoOfiyP25lZiykDbXEHLqDt5uVyOhIQEAMCAAQOQl5fXsc/Pzw8bN26EQCAAj8eDTqeDWCxGfn4+qqurkZaWhhdeeAHXrl0zTQse0cGCagwMcYOPi6NFr8sFIZ7O6Osnw6EC234AZa8OFlTDQcDHU3282Q7F5vD5PCRH+yKrqBatGj3b4RjFqDt5pVIJqVTa8bNAIIBOp4NQKIRIJIKHhwcYhsGHH36IqKgohIaGoq6uDn/9618xfvx4nD9/HkuWLMGuXbu6PL9CoTCqMWq1ustja1U65JQ3YX6ch9Hntlb3a7OpxfkKsD2nAacu5MHNid2v/JZqszUxts0Mw+Dn7DL09xOj7FqRGSIzH2t5n/tK26DWGrD96EUMCzHvAvfmaLNRSV4qlUKlujukzmAwQCi8e6q2tja8/fbbkEgkeO+99wAAMTExEAjak8OgQYNQU1MDhmHA491bzzoyMtKYsKBQKLo89typ6wCAOU/3Q7i39J79tux+bTa1VJcmbL30K8r0rngikt3V7C3VZmtibJsLq26jSlmCV5MiERkZYobIzMda3udeEQasPn4IBbdFmG/meLrTZrlc3uV2o7pr4uLikJWVBQDIzs5GRERExz6GYfD3v/8dffr0wfLlyzsS+6effootW7YAAAoLC+Hv799lgjeHg/nVCPOWcC7BW1J0gAsC3ZxwsIBG2diSg/nV4PGAMVG0boKxRAI+Rkf64rCiGjq9ge1wHptRd/JJSUk4ceIEZs+eDYZhsHLlSmzevBkhISEwGAw4e/YsNBoNjh8/DgB444038Ne//hVLlixBZmYmBAIBVq1aZdKG3E9Tixanr9Xj+QR6YNgdPF573+S3Z25A1aaDhJZMtAkHC6owMNgNPjJ6FtUdyVG++OFiBc6XNtpccTej/qfy+XwsX76807bw8PCOv+fm5nZ53BdffGHM5brl6OUa6AwMkqNpVE13JUf5YfOJ68i6Ukv1T2xAxa1W5FXcxlvj+7Idis1LjPCGg5CPg/nVNpfkOT8Z6mBBFbxlYgwIcmM7FJs3uKc73JxFOEijbGzC4d/eJxo23H0SsRAJvbxwsKDK5lZL43SSV2v1yLxci6QoX/BpweJuEwr4GN3XF0cU1dDaYN+kvTlYUIVwbwnC6FmUSSRH+6K8sdXmVkvjdJI/VVwPlUZPdzImlBzti9tqHc6WNLAdCnmA9mdRDVSnyYRGR/qCx4PNDT7gdJI/WFAFqViIJ8Jtqw/NmiX29oajiI+DHFn/kqt+uVwNvYGhGxwT8pKKMaiHu80tJMLZJK83MDhUUI2RfbypXocJOTkIkNDbGwcLqm2ub9KeHCqoho9MjP70LMqkkqP8UFB526bqOHE2yWeXNaJOqaGvq2YwNtoPlU1q5FY0sR0K6YJaq8cxehZlFndWlLOlEh+cTfIH86shEvAwkup1mNzovj7g87ix/iUXnSyuQ4tGTzc4ZtDTS4I+vjKb6pfnZJJnGAYH8qswLMwTLo4itsPhHHeJA4aEetjUB92eHMyvhlQsxLAwD7ZD4aTkaF+cLWmwmWUBOZnkr9Yocb2+he5kzCg5yq+jRj+xHnoDg8MKehZlTslRfjAwwGEbWRaQk0n+zmSdpEgaWWAud/sm6W7emtCzKPOLCXSBv6ujzUwK5GyS7x/sBj9XqtdhLsEezojyd6F+eStDz6LMj8fjITnKF8dtpMY855J8VZMal8pu0fhgC0iO9oX8RiNqm9vYDoWg/VnUwYJqPBHuRc+izCw52g9qrQFZRbVsh/JQnEvyh37rJxtLBcnMLjnKDwwDHLGRvkmuK65tf0aSRDc4Zjck1AMujkIcsIFJgZxL8gfzqxDmRbXjLSHSX4Ygdyeb6ZvkugP59CzKUu7UmP+lsMbqa8xzKskrNXqcKq5HUrSvxRYksWftfZN++PVqHZRtOrbDsXv0LMqykqN8catFi3PXG9kO5YE4leTPl7e2146PopEFlpIc7QuNzoCsK9bfN8ll9CzK8u7UmLf22a9GJ3mDwYBly5Zh1qxZSEtLQ2lpaaf9O3bswNSpUzFz5kwcPXoUANDQ0IAFCxYgNTUVixYtQmtra/ei/4NTZSp4ScUYGOxm0vOS+xvUwx3uziKr/6BzHT2LsjyJWIgnbaDGvNFJ/vDhw9BoNMjIyMDixYuxevXqjn21tbVIT0/H9u3bsWnTJnz00UfQaDRYv349Jk6ciK1btyIqKgoZGRkmaQQAtOn0OFfRgqQoH6rXYUFCAR+jqMY86w4VVCOUnkVZXHKU9deYNzrJy+VyJCQkAAAGDBiAvLy8jn05OTkYOHAgHBwcIJPJEBISgsLCwk7HJCYm4uTJk90M/65TxfVo1VJXDRuoxjy7bqu1OFVch+QoehZlabZQY97oJK9UKiGV3r1rEAgE0Ol0HftkMlnHPolEAqVS2Wm7RCJBc7PpfvvlljdBIuJT7XgWUI15dh27XAutntYxZoO3TIz4EOuuMW/UQt4AIJVKoVLdrVtiMBggFAq73KdSqSCTyTq2Ozo6QqVSwcXFpctzKxSKx47nCS8DwpO8UHL1ymMfa8vUarVR/16mNtDPEXtzyjGrN9/sd5PW0mZLelCbvztVDXdHAcTKKig4NGfBVt7n/l48bJLfxrFzOfCVdm8SmjnabHSSj4uLw9GjRzFhwgRkZ2cjIiKiY19sbCw+/vhjtLW1QaPRoLi4GBEREYiLi0NmZiamTp2KrKwsxMfHd3nuyMhIo2JSKBRGH2urrKXNU1VSLPkuBwbXQMQEupr1WtbSZku6X5vbdHpc2H4Dk/oHICY6ioXIzMdW3uc53ipskh9DiUaGkZGh3TpXd9osl8u73G50kk9KSsKJEycwe/ZsMAyDlStXYvPmzQgJCcHo0aORlpaG1NRUMAyD119/HWKxGAsXLsTSpUuxY8cOuLu7Y+3atcZenliZ0ZG+v9WYrzJ7kid3nb7WAGWbjma5sijUS4LePlIczK/G/BHdS/LmYHSS5/P5WL58eadt4eHhHX+fOXMmZs6c2Wm/l5cXNm3aZOwliRXzkDhgUE8PHCyoxhvJfdgOx24czK+Cs4MAw8O92A7FriVH++KzzGu41aKBm7MD2+F0wqnJUIRdyVG+KKxqRmk91Zi3BMPv1jF2FFHteDYlRflBb2DwS2EN26Hcg5I8MZk7w1dpYpRl5FQ0oaa5jYYNW4HYQFf4uoitcpQNJXliMiGezujrJ6OCZRZyML8KAj4PT/fxYTsUu8fn85AU5YvMK7VQa62rxjwleWJSydF+OH+9AfVKqjFvbgcLqjEszAOuzlQ73hokR/mhVavHr0V1bIfSCSV5YlLJUb4wMMARK+yb5JLiWiWu1iipq8aKDAvzhEwstLrZr5TkiUlFB7gg0M3JKvsmueTOcw8aOmk9HIR8jOzrgyOKGugN1lOwjJI8MSker71v8nhRLVo0VGPeXNrnI7ggwM2J7VDI7yRH+aJepcGFG9ZTY56SPDG55ChftOkMOG5lfZNcUdOsxsWyW9RVY4VG9vGGSMCzqjpOlOSJyQ0O9YCrk4i6bMzkiKIGDAMqSGaFZI4iDA/3wsGCaqupMU9JnpicSMDH6L4+OFJYbfXrX9qig/lVCPFwRh9f2cNfTCwuOdoXpfUtKKpRsh0KAEryxEySo21j/Utbo2zT4cTVeqodb8XG/LaQurV02VCSJ2aR0Lt9/UtrG05m6zIv10KjN9CoGivm6+KIAcFuVjMpkJI8MQuJWIiEXl44ZEV9k1xwqKAKHhIHxPdwZzsU8gDJ0b7IKW9CZZNp17E2BiV5YjbJ0da//qUt0eoNOFJYg9F9fSAU0H9da3Zn5NNhK7ibp08KMRtbWP/Slpy51oBmtQ7J0TR00tr18pEizEtiFV02lOSJ2XhJxRjUw7rXv7QlBwuq4Cji48leVDveFiRF++JUcT2aWrWsxkFJnphVcpQfCipvo6yhhe1QbBrDtNeOT+ztDScHqh1vC5Kj/KAzMDh2md06TkYlebVajVdeeQWpqal44YUX0NDQcM9r1qxZg1mzZmHatGnYsWMHAODWrVsYOnQo0tLSkJaWhi1btnQvemL17owCOcyhBabZcLVBg8omNXXV2JCBwW7wkrJfY96oJL9t2zZERERg69atmDJlCtavX99p/+nTp3Hjxg1kZGRg27Zt+PLLL9HU1ISCggJMnDgR6enpSE9Px1/+8heTNIJYr55eEkT4Sln/oNu6UzdU4POA0X2pdrytuFNj/tjlGrTp2Ksxb1SSl8vlSEhIAAAkJibi1KlTnfYPHDgQK1eu7PhZr9dDKBQiLy8P+fn5mDNnDl599VXU1FA5WnuQHOWHs9cb0KjSsB2KzTp1Q4XBPT3gLrGu9UPJgyVH+UKl0eNkcT1rMTx0Ie+dO3fe063i6ekJmax9SrVEIkFzc+chcmKxGGKxGFqtFm+99RZmzZoFiUSCsLAwxMTEYPjw4di9ezdWrFiBdevW3XNNhUJhVGPUarXRx9oqW2hzb+c26A0MvjmajTHh3Z+KbwttNqXyJg2u39JiXATPrtrNhffZQ2+Ak5CHHScK4Wd4eKI3R5sfmuRnzJiBGTNmdNr28ssvQ6VqX6xZpVLBxcXlnuOamprw6quvYsiQIXjxxRcBAMOGDYOTU3tp1KSkpC4TPABERkY+Xit+o1AojD7WVtlCm/syDFYdr0deIx+vmCBWW2izKf1y9CoA4C+j+8Pf1X5KC3PlfR4V2Yaz1xvQp09f8PkPLkXRnTbL5fIutxvVXRMXF4fMzEwAQFZWFuLj4zvtV6vVmDdvHqZNm4aXXnqpY/u7776LAwcOAABOnTqF6OhoYy5PbAyPx0NytC+yrtRZ3fqXtmBfXiX6eIntKsFzSXK0L2qb25BdfouV6xuV5FNSUlBUVISUlBRkZGTg5ZdfBgB8+OGHyMnJwfbt21FWVoadO3d2jKQpKyvD4sWLsW3bNqSlpWH79u145513TNoYYr2Sonytcv1La1fW0IK8itt4soeE7VCIkUb28YGQz2Nt8MFDu2u64uTk1GVXy5tvvgkAiI2Nxbx587o8Nj093ZhLEhs3NNQTMkchDuRXYQwV13pk+/PaZwuPoCRvs1ydRHgi3BP78yqxdFwfi1cPpclQxCIchO015g8pqqGlGvOPbF9eJaIDXOAvE7EdCumG8TH+uF7fwkodJ0ryxGIm9PPHrRYtTl9jbziZLalsasWFG7cwPoYmQNm65Ghf8HnA3txKi1+bkjyxmMQIb0gcBKx80G3Rgd+6asbF+LMcCekuL6kYw8I8sTe30uKltynJE4txFAkwOtIXB/JpWcBHsS+vCr19pOjlI2U7FGIC4/v541qdCperLdtlQ0meWNSEfv5oUGlw+tq99Y7IXXXKNpy73kBdNRwyLtqvvcsmx7LfZCnJE4sa2ccbzg4C7M2jLpsHOZhfDQPTfvdHuMFbJsaQUA/szbPs+gqU5IlFOYoEGNXXBwfyqqjL5gH25VWip6cz+vp1vwwEsR4T+vnjao0SVyzYZUNJnljcM/38Ua/S4GwJddl05VaLBqeK6zEuxt/iY6qJeY2L8QPPwqNsKMkTixvZxwdOIuqyuZ9DBdXQGRjqj+cgH5kjBvf0oCRPuM3Job3LZn9eNfQGyw4nswU/5VQiyN0JsUGubIdCzGBCjB+uVCtxtcYyXTaU5AkrJvTzR52yjbps/qBBpcGvV+swqX8AddVw1J2H6XtzLfMAlpI8YcXTfb3hKOLTxKg/2JdXCb2BwaTYALZDIWbi6+KIQT3cLfbZpyRPWOHsIMSovj7Yl1dFXTa/s+fSTYR7SxDpT6NquGxCP38UVjWjuFZp9mtRkiesmRgbgDplG85QLRsAQPVtNc6UNFBXjR2Y0M8fPF77L3VzoyRPWDOqrw+kYiF+zDb/B90W/JxTCYZp/+VHuM3P1RFDQz2wO/um2WvZUJInrHEUCTA22g978ypZXc3eWuzJuYkofxeqVWMnJg8IxLU6FfIqbpv1OpTkCaueHRCAZrUOxy7Xsh0Kq8oaWnDxxi1M7E9lDOzF+Bg/iAQ8/JhdYdbrGLUylFqtxpIlS1BfXw+JRII1a9bAw8Oj02sWLlyIxsZGiEQiiMVibNy4EaWlpXjrrbfA4/HQu3dvvPfee+Dz6feMPRsR7glPiQN2Z9/E2Gj7nfzz828jLWhUjf1wc3bAUxE+2JNzE/+cEAnBQxb5NpZRGXbbtm2IiIjA1q1bMWXKFKxfv/6e15SWlmLbtm1IT0/Hxo0bAQCrVq3CokWLsHXrVjAMgyNHjnQvemLzhAI+Jsb647CiGs1qLdvhsGbPpZsYEOyGYA9ntkMhFjR5QACqb7fhTIn5Bh8YleTlcjkSEhIAAImJiTh16lSn/XV1dbh9+zb+9re/ISUlBUePHgUA5OfnY8iQIR3HnTx5sjuxE454dkAg2nQG1hY6ZtvVmmbk37yNSf3pLt7ejIn0hcRBgN1mHHzw0O6anTt3YsuWLZ22eXp6QiZrH8crkUjQ3Nx5eq5Wq8WCBQswd+5cNDU1ISUlBbGxsWAYpmNoWFfH3aFQKIxqjFqtNvpYW8WFNjsxDHylQmw9cQVRzg+f6s2FNv/e1xcawOcBfZ2V920X19r8KOylzcOCnPDTpQqk9BHCoG0zeZsfmuRnzJiBGTNmdNr28ssvQ6VSAQBUKhVcXFw67ffy8sLs2bMhFArh6emJyMhIlJSUdOp/7+q4OyIjIx+7IUD7Lwdjj7VVXGnz9DI+Psu8Bq+gMHjLxA98LVfaDAAGA4Pj//0FiRHeGBHX776v41KbH5W9tDmN74kjm8+hiueBEMdGo9ssl8u73G5Ud01cXBwyMzMBAFlZWYiPj++0/+TJk3jttdcAtCfzoqIihIWFISoqCmfOnOk4btCgQcZcnnDQ5AGB0BsY/JxjX2PmT5fU42aTGlPjgtgOhbBkRC+vjsEH5mBUkk9JSUFRURFSUlKQkZGBl19+GQDw4YcfIicnB0899RR69uyJmTNn4rnnnsMbb7wBDw8PLF26FJ988glmzZoFrVaLsWPHmrQxxHZF+MoQ6e+CHy6adziZtfn+QgVkYiGSo3zZDoWwRCTg45nfBh+oNKZfSMeoIZROTk5Yt27dPdvffPPNjr+/88479+wPDQ3FN998Y8wliR2YFheIFT8rcKW6GRG+3K/d0qLRYV9uJSbGBsBRJGA7HMKiWYOD8cOFCjS26kx+bhqkTqzGnwYGQsjnYef5MrZDsYiD+dVQafSYGhfIdiiEZdEBrriwLAlBrg4mPzcleWI1PKVijOrrgx8u3oTWDtZ/3XWhHIFuThjc0+PhLyacJxKYJx1TkidWZcagYNQp25DJ8TIH1bfVOHG1DlPjAsE300xHQgBK8sTKjOzjDS+pA3bKud1l88PFChiY9i4qQsyJkjyxKiIBH1MGBOKIogb1yja2wzELhmGQca4Mg3u6I8ybKk4S86IkT6zOjEHB0BkYztaZP32tASV1KsweHMJ2KMQOUJInVqePnwyxQa7YKS83+4IKbNh+7gZcHIV4JpbKChPzoyRPrNKMQcFQVN7GpfImtkMxqUaVBvtyq/CngYE0Np5YBCV5YpWmDAiAs4MA35wuZTsUk/r+YgU0egNmD6GuGmIZlOSJVZI5ijBlYCD2XLqJWy0atsMxCYZhsP3sDfQPdkOkf9fF+QgxNUryxGrNGdoDbToDvpOXsx2KSVy40YiiGiVShwSzHQqxI5TkidWKCnBBfA93fHvmBgwG238A+83pG5CKhZhIS/wRC6IkT6zanGEhKKlT4WSx+ZZHs4SaZjV+yrmJ6fFBkIiNqgtIiFEoyROrNj7GH+7OIpt/APvt6RvQGRjMG96T7VCInaEkT6yao0iAmYOCcUhRjYpbrWyHY5Q2nR7fnrmBp/v4oKeXhO1wiJ2hJE+s3tzf7n6/PlHCbiBG2ptbiTplG93FE1ZQkidWL9DNCRP6+WP72TI0q7Vsh/NYGIbB5hPXEe4tQUJvL7bDIXbIqCdAarUaS5YsQX19PSQSCdasWQMPj7s1sbOysvDll18CaP+Qy+Vy/PTTT2hra8OLL76Inj17AmhfRnDChAndbwXhvBcSQrHn0k1knCvDCBvKlfLSRuSUN+GDydHg8aikMLE8o5L8tm3bEBERgVdeeQU///wz1q9fj3fffbdjf2JiIhITEwEAGzduRFxcHMLDw7Fz507Mnz8fCxYsME30xG7EBrlhaKgHvvq1BEOftZ2aLxuOFcPdWYRp8bRQN2GHUd01crkcCQkJANoT+qlTp7p8XVVVFX788ceOhb7z8vJw7Ngx/PnPf8bbb78NpVJpZNjEHr2QEIabTWr8el3FdiiPpLDqNo4U1mDe8FA4O9CwScKOh37ydu7ciS1btnTa5unpCZmsfaFliUSC5ubmLo/dvHkz5s2bBweH9nULY2NjMWPGDMTExGDDhg34z3/+g6VLl95znEKheOyGAO3dSMYea6vsqc3+YBDkIsLO3EY8FVpg9d0fHx6vgaOQhye82rr9HtnT+3wHtdlEGCO89NJLzKVLlxiGYZjbt28zzzzzzD2v0ev1THJyMtPa2tqxrampqePvRUVFzNy5c+857vz588aExDAMwxQUFBh9rK2ytzbvOHeD6bH0J+ZQfhXboTzQjXoVE/bPn5kP9uSb5Hz29j4zDLX5cd0vdxrVXRMXF4fMzEwA7Q9Z4+Pj73nNlStXEBoaCkdHx45tzz33HHJycgAAp06dQnR0tDGXJ3bsTwMD4ScV4uMjV6y61vznWcXg84DnE8LYDoXYOaOSfEpKCoqKipCSkoKMjIyOPvcPP/ywI4mXlJQgOLhzIab3338fK1euRFpaGi5cuIC///3v3Qyf2BuhgI/ZsW7Iq7iNXwpr2A6nS2UNLcg4V4YZg4Lh5+r48AMIMSOjngY5OTlh3bp192x/8803O/4+fvx4jB8/vtP+6OhobN++3ZhLEtJhdLgMuwpV+PeRIozq62N1ffP/PlIEHo+HV0b1YjsUQmgyFLE9Qj4PLz/dCznlTThUUM12OJ1crWnG9xfKkTasB/xdndgOhxBK8sQ2TY0LQri3BKv3F0KrN7AdTof/O1QER5EAC0eGsx0KIQAoyRMbJRLw8c/xkbhWq8L2szfYDgcAkF12Cz/nVmLBiFB4ScVsh0MIAEryxIaNjvTBE2Ge+L/DRbjNck0bg4HB+7vz4SUV48WnaEQNsR6U5InN4vF4eOeZSDSoNPjP0ausxvLDxQpkl93C0nF9IHMUsRoLIb9HSZ7YtJhAV8yID8Km4yW4XNX1zGtzU7bpsGZ/IfoHu2FaHNWoIdaFkjyxeW9PiISLkwhv/5DLylqwa/YVolbZhvcnRYHPt67hnIRQkic2z13igHcmREJe2oitFn4Ie/paPdJPl2L+8FAMDHG36LUJeRSU5AknTI0LxIhenli1V4HrdZapUtmq0WPprhyEeDjjH2MjLHJNQh4XJXnCCTweD/87vT8EfB5e237RImPnP/i5AKX1LVg9rR+VEiZWi5I84YwANyesnhaLS+VN+OjQFbNe68fsCmw9cwN/eyocw8NtaKkqYncoyRNOmdDPH7MHB2PDsWLsy600yzWuVDfj7e9zMaiHOxYnUzcNsW6U5AnnvP9sNAaGuOH1HdnIq2gy6blrbqsxf/M5SMRCfJI6ECIB/Rci1o0+oYRzHEUCfJE2CJ4SMeZtPoerNaZZZrKpRYv5X59DY4sGX80bTAXIiE2gJE84yVsmxpYFQwAAKV+e7naib1BpkLrxNIqqlfhPahxiAl1NESYhZkdJnnBWLx8ptr0wFAzDYNqGk/i1qM6o81yrVWLm56dwtUaJL+bG4+m+PiaOlBDz6VaSP3ToEBYvXtzlvh07dmDq1KmYOXMmjh49CgBoaGjAggULkJqaikWLFqG1tbU7lyfkoXr7yvD9whHwdRHjL5vPYt2RokceXskwDH64WI7Jn55Ag0qDLQuGYGQfSvDEthid5FesWIG1a9fCYLj3P0xtbS3S09Oxfft2bNq0CR999BE0Gg3Wr1+PiRMnYuvWrYiKikJGRka3gifkUYR4OmPXwuF4pp8/Pjp0Bc+sO46fcyqhv08JBIZhcOZaPf688Qxez7iEXr5S7H55BIaFeVo4ckK6z+gZHHFxcRgzZkyXiTonJwcDBw6Eg4MDHBwcEBISgsLCQsjlcrz44osAgMTERHz00UeYN2+e0cET8qhkjiKsSxmISf0DsGqfAi9tvQAvqQOe7uODSH8XuDqJ0KLVo7hGiWOXa3C9vgVeUgcsnxyNPw/tAQHVpCE26qFJfufOndiyZUunbStXrsSECRNw5syZLo9RKpWQyWQdP0skEiiVyk7bJRIJmpu7rhqoUCgeuQG/p1arjT7WVlGbH08QD1g3zgeny1qQWaLE/ryb2Ckv79gvFvIQ7eOIZ5/wwqgwKcTCVly5XGiq0I1G77N9MEebH5rkZ8yYgRkzZjzWSaVSKVSqu/VDVCoVZDJZx3ZHR0eoVCq4uLh0eXxkZORjXe8OhUJh9LG2itpsnJho4Hm0d83UKTVo1eghEvLgK3O0ykqS9D7bh+60WS6Xd7ndLKNrYmNjIZfL0dbWhubmZhQXFyMiIgJxcXHIzMwEAGRlZSE+Pt4clyfkkfF4PHjLxAjxdIa/q5NVJnhCusOkVZU2b96MkJAQjB49GmlpaUhNTQXDMHj99dchFouxcOFCLF26FDt27IC7uzvWrl1ryssTQgj5g24l+aFDh2Lo0KEdP8+fP7/j7zNnzsTMmTM7vd7LywubNm3qziUJIYQ8BpoMRQghHEZJnhBCOIySPCGEcBgleUII4TBK8oQQwmE8hmG6LuDBkvsN6CeEEPJgXc09srokTwghxHSou4YQQjiMkjwhhHAYJ5K8wWDAsmXLMGvWLKSlpaG0tJTtkMxOq9ViyZIlSE1NxfTp03HkyBG2Q7KI+vp6PPXUUyguLmY7FIv4/PPPMWvWLEydOhU7d+5kOxyz02q1WLx4MWbPno3U1FTOv8+XLl1CWloaAKC0tBQpKSlITU3Fe++91+VaHcbgRJI/fPgwNBoNMjIysHjxYqxevZrtkMxu9+7dcHNzw9atW7Fx40Z88MEHbIdkdlqtFsuWLYOjoyPboVjEmTNncPHiRWzbtg3p6emoqqpiOySzy8zMhE6nw/bt2/HSSy/h448/Zjsks/nyyy/x7rvvoq2tDQCwatUqLFq0CFu3bgXDMCa7ceNEkpfL5UhISAAADBgwAHl5eSxHZH7jxo3Da6+9BqC9XK5AIGA5IvNbs2YNZs+eDR8f+1iC79dff0VERAReeukl/O1vf8PIkSPZDsnsQkNDodfrYTAYoFQqIRSatIaiVQkJCcEnn3zS8XN+fj6GDGlffD4xMREnT540yXU48S+oVCohlUo7fhYIBNDpdJz+gEgkEgDtbX/11VexaNEidgMys++//x4eHh5ISEjAF198wXY4FtHY2IibN2/is88+Q3l5ORYuXIj9+/eDx+NuOWRnZ2dUVFRg/PjxaGxsxGeffcZ2SGYzduxYlJffXbCGYZiO9/ZBiyo9Lk7cyf9xkRKDwcDpBH9HZWUl5s6di8mTJ2PSpElsh2NWu3btwsmTJ5GWlgaFQoGlS5eitraW7bDMys3NDU8++SQcHBwQFhYGsViMhoYGtsMyq6+//hpPPvkkDhw4gB9//BFvvfVWR3cG1/H5d9PxgxZVeuzzmuQsLIuLi0NWVhYAIDs7GxERESxHZH51dXVYsGABlixZgunTp7Mdjtl9++23+Oabb5Ceno7IyEisWbMG3t7ebIdlVvHx8Th+/DgYhkF1dTVaW1vh5ubGdlhm5eLi0rFEqKurK3Q6HfR6PctRWUZUVFTHkqpZWVkYNGiQSc7LidvdpKQknDhxArNnzwbDMFi5ciXbIZndZ599htu3b2P9+vVYv349gPYHOfbyUNIePP300zh37hymT58OhmGwbNkyzj97mTdvHt5++22kpqZCq9Xi9ddfh7OzM9thWcTSpUvxr3/9Cx999BHCwsIwduxYk5yXZrwSQgiHcaK7hhBCSNcoyRNCCIdRkieEEA6jJE8IIRxGSZ4QQjiMkjwhhHAYJXlCCOEwSvKEEMJh/x9XQdMfuDnYiAAAAABJRU5ErkJggg==", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x))\n", + "plt.axis('tight');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or you can specify that you want an equal axis ratio, such that one unit in `x` is visually equivalent to one unit in `y`, as seen in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x))\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Other axis options include `'on'`, `'off'`, `'square'`, `'image'`, and more. For more information on these, refer to the `plt.axis` docstring." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Labeling Plots\n", + "\n", + "As the last piece of this chapter, we'll briefly look at the labeling of plots: titles, axis labels, and simple legends.\n", + "Titles and axis labels are the simplest such labels—there are methods that can be used to quickly set them (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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M9UQvH0d8dqyA5lEiOrf2eAEcbPiYPrgL26E8pJOTLaYN6Izdl0pQWCllOxyjYNDEoNFosHTpUiQkJCApKQlFRX8MS8/Ly0NSUlLLv549eyI9PR337t1D//79W7Zv3rzZkCHrzM7filFR34R3hhnnYjkcDgfzRgThzr1G/JhBTw1Ed3Lv3seR3HK88kwAHHQ0nbauvTk0EFY8Lr46Wch2KEbBoOsxHD16FAqFAqmpqcjIyMCqVauwfv16AEBwcDC2bNkCADh48CA8PDwQExODs2fPYuzYsfjnP/9pyFB1SqHSYP3JQkR1djbKp4UHhnR3R7CXA9anFWJipI9Op/4mluuLEwUQCYzzaeEBN3sBpvT1xbYLtzEvNgjeepzM0hQY9IlBIpEgOjoaANC7d29kZ2c/9JqGhgZ8/vnneP/99wEA2dnZyMnJwbRp0/DOO++gosL05lPffakEd+vkeGd4N6NqW/grDoeDt4YG4kaljHooEZ24Vl6PA1llmDG4CxxtjfNp4YFZMc2jsL9Np3ENBn1ikEqlsLf/Y2FvHo8HlUoFPv+PMHbt2oVRo0bBxcUFABAQEICwsDAMGjQI+/btw/Lly1tdBzovr2Ojd+VyeYePbQsNw+DzI8Xo5iqAu6oSeXnsDyR7XJm78Bh4O1hhzaFs+PNrjTqRtYe+32djZAxl/uRMBQR8Dga7Kw0Sy9OWeai/EMkXijDSh4GTLTujsttLH++zQRODvb09ZDJZy88ajUYrKQDA/v37tb74BwwYAFvb5se62NjYVpMC0FwV1RF5eXkdPrYtjuSW4279TXye2BMhIZ30dp32eFKZ5zaKsGhXJir57ng2SH9z5BuSvt9nY8R2mSvq5Ui7eQuJ/fzQPyLMINd82jIvdvXF0f+l4UylFf4+srsOI9OfpymzRCJpdbtBq5IiIyORnp4OAMjIyEBQkPYc7PX19VAoFPDy+qOP/wcffIBffvkFAHDu3DmEhoYaLmAd2HDqBrydbDE6zJPtUNpsQm9vuIsE+O40zbxKOm7LuSIoNRrMGOzPdiht1tXDHrHBYmy7UGTRcygZNDHExsbC2toaU6ZMwcqVK/GPf/wDmzZtwrFjxwAAN2/ehLe3t9YxCxYsQHJyMpKSkpCSktLS9mAKskrqcOFmDaYP6gI+z3R6BlvzuUga0Blp1ypxvYK675H2a1SosfV8EWKDxUYzyrmtZgz2R22DEj9cttzeeQatSuJyuVi2bJnWtsDAwJb/h4eHY926dVr7fX19W3ormZqNp29AaM1DQj9ftkNpt6n9/fDF8ev4/uxNLJ/Qk+1wiInZfakEtQ1KvBpt+Gm1n9aAABf08BRh05lbSOjrazbtbO1hOrexJqasTo6fMkuR0NfPaPtuP46bvQDP9+6E3ZI7qGtQsh0OMSEaDYPvTt9EuI8j+nZxZjucduNwOJg52B9Xy+txrrCa7XBYQYlBT7aeL4KGYTDDiPtuP8mMwf5oVKqR+ttttkMhJuT09SrcqJLhlWf8TfZue3zvTnARWuO7M7fYDoUVlBj0QKnWIOViMYb18ICvix3b4XRYSCcHDAhwweazRVBraEpu0jZbzxfBVWiNUSbU4eKvbKx4mNrPD8fyy1FULXvyAWaGEoMeHMktR5W0CVP7+7EdylObPqgL7txrxMmrpjewkBheaV0jjuVXIL6PL2urs+nKtAGdweVwsP1Xy3tipsSgB9suFMHbyRbPBnmwHcpTGx4shrtIgGQL/HCQ9ku9WAwNw2BqP9O/KfJ0tMHwHh7Y9VuJxU0sSYlBx25USnHmejUS+/maxVxDVjwuJvfxwfH8CpTWNbIdDjFiKrUGKb8WI6abO/xcTbcK9c8S+/uhWqbAkdxytkMxKEoMOpb8623wuRxM7mN6XVQfZUpfP2gYYMfFErZDIUbsWH4Fyu7L8ZIZVKE+ENPNHd5Othb3xEyJQYfkSjV2SkoQFyqGh4MN2+HojK+LHaK7uSH14m1qhCaPtO3CbXg52mBYD9OvQn2Ax+Ugoa8vTl+vsqhGaEoMOnQwuxT3GpR4qX9ntkPRuan9/HC3To60a9QITR5WXNOA9GuVmNLXz6RG+bfF5D6+4HKAlIvFbIdiMOb1DrJs528l8HOxw8AA411zoaNGhIjhZi/A9guW8+EgbbdLUgIOB4jv48N2KDrn6WiDYT3E2PlbscU0QlNi0JGS2gacLazGi1E+4JpBo/Nf/dEIXY7y+3K2wyFGRKNhsPtSCZ7p6oZOZrrAzdT+vqiSKnAszzIaoSkx6MieS80Tbk2M9H7CK03Xi1E+0DCw6MnFyMMu3KxBSW0jXowyv6eFB54N8oDYQYDdlyyjAwYlBh1gGAa7JCUYFOgKH2fz6KbXmgB3e0T6OWH3pRIwDDVCk2Y7JcUQCfgYGWq6I52fhMflYEKEN05erUSVtIntcPSOEoMOXLxVi9s1DWZ9x/TAxEgfXCuXIufufbZDIUZA2qTCwawyjO3VCTZWpj3S+UkmRvhApWGwL+Mu26HoHSUGHdglKYbQmmfSc8O01bjwTrDmcbFLYhmP1OTxDmSVolGptoibou6eIoR5O2DPZfP/26fE8JQaFCr8nFmK58K9YGdt0OUtWOFoZ4URIR7Yd+UulGrL6KFBHm2XpAQBbkJE+jmxHYpBTIr0Qfad+7haVs92KHpFieEpHcoug0yhxotR5jPS+UkmRfqgRqbAyauVbIdCWFRULcOvN2swKcrHZKfXbq/xvTqBz+Vgj5k3Qhv0Flej0eDDDz/E1atXYW1tjeXLl6Nz5z8Ggy1fvhyXLl2CUNi8FOC6deugVCrx97//HXK5HB4eHli5ciVsbY2nS9wuSfPYBVNckKSjYoLc4Sq0xp5LJYgNEbMdDmHJnkt3wOGYd0+8v3K1F2BIdw/svXwHC0d2N7vBfA8YtFRHjx6FQqFAamoqFixYgFWrVmntz8nJwYYNG7BlyxZs2bIFIpEI69atw9ixY7F9+3aEhIQgNTXVkCE/VlmdHOduVOOFCG+LuWMCmsc0PN/bG8fyKnCvQcF2OIQFDMNg35W7GBjgCi9H47lRM4RJkd6oqG/CGTNe3c2giUEikSA6OhoA0Lt3b2RnZ7fs02g0KCoqwtKlSzFlyhTs2rXroWNiYmJw9uxZQ4b8WD9l3gXDNK/2ZGkmRnpDodZgf2Yp26EQFmTdqcPNKhnG97K8v/1hwR5wtLXCbjPugGHQqiSpVAp7e/uWn3k8HlQqFfh8PhoaGjBt2jTMmDEDarUaL7/8MsLCwiCVSiESiQAAQqEQ9fWtN/rk5eV1KCa5XN7hY1PP30FXF2soqoqRV9WhU7Diacr8AJdh4OdohdSz19HHsUFHkemPLspsavRZ5u8vVoPPBQKs7xvV79VQ7/NgXxv8klOKy5nWsLFitzpJH2U2aGKwt7eHTPbHDIUajQZ8fnMItra2ePnll1vaDwYMGID8/PyWY2xsbCCTyeDg4NDquYODgzsUU15eXoeOvVklQ0H1Dbw3pgeCgwM7dG22dLTMf/ViqRU+OXINTp26GH11gq7KbEr0VWa1hsGZvccwpLsY/XqH6fz8T8NQ7/PLAg8cuHYeJYwzxgWz+9T0NGWWSCStbjdoqouMjER6ejoAICMjA0FBQS37bt26hcTERKjVaiiVSly6dAmhoaGIjIxEWloaACA9PR1RUVGGDPmR9l+5Cw4HGGeBj9IPPCj7z1SdZFF+vVmD8vtNeN4Cq1Af6NvFBWIHAfZdMc/BbgZ9YoiNjcWZM2cwZcoUMAyDFStWYNOmTfDz88Pw4cPx/PPPY/LkybCyssLzzz+Pbt26Yfbs2Vi8eDF27NgBZ2dnrFmzxpAht4phGPyYcQd9u7gY/Z2yPvm7CdHT2xH7rtzFq9EBbIdDDGTflTuws+ZhRLDl9kjjcTl4rmcnbD1fhLpGJRxtrdgOSacMmhi4XC6WLVumtS0w8I9qmFdffRWvvvqq1n43Nzds3LjRIPG1VW7pfRRWyjBjsD/bobBuXC8vrDiQj1tVMnRxE7IdDtEzhUqDA1lliAsRw9bavKfAeJJxvbzw3ZmbOJxThngzWrERoAFuHbIv4y74XA7G9PRiOxTWjQ1vrk7Yb6aP1ERb+rVK1DUq8Xxvyxm78Ci9fZ3g62Jrlj3zKDG0k0bDYP+Vu4ju5gYXoTXb4bCuk5Mt+nZxxv5MSgyW4Mcrd+FsZ4VnurmxHQrrOBwOxoV3wpnrVag2sxlXKTG0k+R2Le7WyS1y7MKjjO/VCdfKpcgvoxlXzVmDQoWjueUY09MLVmY64re9xvXqBLWGwYHsMrZD0Sl6d9vppyt3IeBzERti/jOpttXonl7gcTlUnWTmjudXoFGpbqk+JEAPTxG6edib3d8+JYZ20GgYHMwuw9DuHrAXmP9Mqm3lZi/AoEBX7L9SSgv4mLGDWWVwsxegn78L26EYDQ6Hg3G9OuHirRqU1jWyHY7OUGJoB8ntWlTUN2F0T3pa+Ktx4Z1wu6YBWXfq2A6F6EGjQo3j+RUYFSYGzwzXNH8a43p1AsOY13geSgztcCCrFNZ8Lob18GA7FKMTFyoGn8vBQTOrayXNTl5trkYaE0Y98f7K302IYC8Hs/rbp8TQRhoNg0PZZYjp5g6RjXkNZtEFJztrDAx0xcEsqk4yRweyy+AitKZqpEcYE+YJSVEtyurkbIeiE5QY2iij5B5K6+QYQ9VIjzQ6zAu3qhuQV2req1tZGrlSjeN55RgZKjbb9Qee1oPq5V9yzOOpgd7lNjqYVQorHgcjaGGaR4oLFYPLAQ5lm09dKwHSrlVCplDTgM7H6OrR3DvpoJn87VNiaAOGYXAgqwzR3dzhQNVIj+RmL0B/f1ez69Nt6Q5mlcLJzgoDAlzZDsWoje7phV9v1qDKDAa7UWJog8ySOty514jRYVSN9CSje3rieoUUBeVUnWQOmlRqHM2rQFyImAa1PcHoME9oGOBwTjnboTw1eqfb4EB2KfhcDq1v3AYjQz3B4cCsemhYstMFVZA2qTCaqpGeqIenCP5uQrOoTqLE8AQMw+BgVhkGdXWDkx3NjfQkYgcb9OnsjANZpv/hIMDPWaVwsOFjcCDNjfQkHA4Ho8I8cbawGrUy014LnRLDE+TcvY/bNQ0YQ9VIbTYqzAv5ZfW4WSV78ouJ0VKoNDiSW47YEE9Y8+mroi3GhHlBrWFwJM+0q5Po3X6Cg9ml4HE5iAulxNBWo35PoubwSG3JzhRWoV6uoi7a7RDm7QAfZ1scMvGqVEoMj/GgN9LAAFeaYrsdvJ1s0cvXCQezTPvDYekOZpVCJODTFNvtwOFwMDrME6cKKnFfrmQ7nA4zWGLQaDRYunQpEhISkJSUhKKiIq3933//PeLj4xEfH48vvvgCQPMXc3R0NJKSkpCUlGTwZT2vlUtxs0rWcgdM2m5MmCey7tShuKaB7VBIB6jUzdVIQ3t4QMC37JXa2mtUmBeUagbH8yrYDqXDDDZF6NGjR6FQKJCamoqMjAysWrUK69evBwAUFxdj37592LlzJ7hcLhITEzFixAjY2toiNDQUX331laHC1HIkt/mON456I7Xb6DAvrDyYj0PZZZgVQ+tBmxpJUS1qG5QYSVWo7Rbh6wRPBxscyCrFhAjTXOnOYE8MEokE0dHRAIDevXsjOzu7ZZ+npyc2bNgAHo8HDocDlUoFgUCAnJwclJeXIykpCbNmzcKNGzcMFS4A4HBuOSL8nODhYGPQ65oDP1c79PAU4UiuaTfCWarDueWw5nHxbHd3tkMxOVwuB3GhYqQXVKJRoWY7nA4x2BODVCqFvb19y888Hg8qlQp8Ph9WVlZwcXEBwzD4+OOPERISAn9/f1RVVeG1117D6NGj8dtvv2HhwoXYvXt3q+fPy8vrUFxyubzVYytlKmSW1GFGpEuHz22sHlVmXYsU85CSWYNzl7LhZMtudYShymxMOlpmhmHwc0YxenkKUHyjQA+R6Y+xvM897JsgV2qQcuIyBvgJ9XotfZTZYInB3t4eMtkf3Rc1Gg34/D8u39TUhPfeew9CoRD/+te/AABhYWHg8Zq/UPr06YOKigowDAMO5+H54IODgzsUV15eXqvHXjx3CwAwbWhPBLrbP7TflD2qzLo21aEO26+cRrHaEQODffV+vccxVJmNSUfLnF92H2XSm3gnNhjBwX56iEx/jOV97hqkwapTR5B73woz9BzP05RZIpG0ut1gVUmRkZFIT08HAGRkZCAoKKhlH8MwePPNN9G9e3csW7asJRl88cUX2Lx5MwAgPz8fXl5erSYFfTicU44Ad6HZJQVDCu3kAG8nWxzOpd5JpuRwTjk4HGBECK070lFWPC6GB4txNK8cKrWG7XDazWBPDLGxsThz5gymTJkChmGwYsUKbNq0CX5+ftBoNPj111+hUChw6tQpAMD8+fPx2muvYeHChUhLSwOPx8PKlSsNEmtdgxLnb1Tj1WhqNH0aHE5zXeu2C7cha1JBSMuhmoTDuWWI8HWCh4ja1p5GXIgYey/fwW9FtSY3AaHBPqlcLhfLli3T2hYYGNjy/6ysrFaP++abb/QaV2tOXK2ASsMgLpR6Iz2tuBBPbDpzC+nXKmm+HRNw514jsu/cx5LRPdgOxeTFBLnDms/F4Zxyk0sMNMCtFYdzy+AuEqC3jxPboZi8vl2c4WRnhcPUO8kkHP39faIu2k9PKOAjuqsbDueWmdyqhpQY/kKuVCPtaiViQ8Tg0qLnT43P42J4DzGO5ZVDaYJ1rZbmcG4ZAt2FCKC2NZ2ICxWjpLbR5FY1pMTwF+cKqyFTqOmOSYfiQsW4L1fh15s1bIdCHqO5ba2G5gXToeHBYnA4MLkOGJQY/uJwbhnsBXwMDDStOkFjFtPNHTZWXBw2k/VwzdXxq+VQaxi6KdIhN3sB+nR2NrnFeygx/Ilaw+BIbjmGdHen+WF0yNaah+hu7jicW25yda2W5EhuOTxEAvSitjWdigvxRG7pfZOaN4wSw59kFNeiSqqgR2k9GBnqidI6ObLu1LEdCmmFXKnGSWpb04sHKz+a0vQwlBj+5HBOOax4HAyh+WF0bngPD3A55rEerjk6W1iFBoWabor0oIubEN3FIpNqZ6DE8DuGYfBLThkGBLjCwcaK7XDMjrPQGv38XUzqw2FJDueUw17Ax4AAF7ZDMUtxoWL8erPGZJb8pMTwu+sVUtyqbqA7Jj2KC/FsWeOCGA+1hsHRPGpb06e4EE9oGOCoiSz52abEUFdXhxMnTmDv3r1IS0vTmgzPXDwYgBUbTD0y9OWPulZ6ajAm1Lamf2HeDvBytDGZgZ6PnRKjpqYG//3vf3Hjxg34+/vDw8MDV65cwbp16xAUFIS5c+fCzc08lv07nFuOXr5O8HSk+WH0xdfFDiFeDjicU47XYgKffAAxCGpb0z8Oh4O4EDFSfytGo0INW2vjfjJ7bGL44osvMGvWLPj7+z+0r7CwEF9++WXLFNmmrKxOjivF97BwZHe2QzF7caFifHasAJX1TXAXCdgOx+IxDIPDueUYGOhGbWt6Fhfqic3nipBeUGn0K+M9tipp6dKl8Pf3h0ajPZWBVCpFYGCgWSQFADjye73fSJo0T+/iQjzBMMAxE6lrNXeFlc1tPrE0qE3v+vm7wMGGj19MYKBnm9oYXn75ZVRUNC9sfeXKFUyZMkWvQRna4ZwyBLjR2guGEOwlgo+zrcnUtZq7X3Kobc1QHqzRcDy/wujXaGjTtNtvvfUWXnvtNfTt2xfZ2dn47LPP9B2XwUgVapwrrMYr0f4GWwTIkjXXtXpi64UiSJtUsKc1GlhFbWuG9WCNhou3ao162p02PTF069YNrq6uOHv2LMLDw+HnZ1rL/T3ObyWNzWsvhBh3nZ85iQsVQ6HSIP1aJduhWLQHbWs0N5LhPFijwdhHQbcpMbz00ktITEzEzz//DLFYjISEhA5dTKPRYOnSpUhISEBSUhKKioq09u/YsQMTJ07E5MmTceLECQDNPaNmzpyJqVOnYt68eWhsbOzQtR/lXLEMbvYCRPg66fS85NH6dHaGs52V0X84zB21rRmeUMDHMyawRkObEsPmzZsxYsQIAMDMmTMfWomtrY4ePQqFQoHU1FQsWLAAq1atatlXWVmJLVu2ICUlBRs3bsQnn3wChUKBdevWYezYsdi+fTtCQkKQmpraoWu3pkmlxsU7DYgN8aD5YQyIz+NiGK3RwLojueXwp7Y1g4sLMf41Gp7YK+natWvw9NSuZgkLC0NeXh6WLl3arotJJBJER0cDAHr37o3s7OyWfZmZmYiIiIC1tTVEIhH8/PyQn5+vdUxMTAzOnj3brms+zrnCajQqqRqJDbRGA7vuy5U4V1iFuBAxta0ZmCms0fDYlr/58+fj008/RXZ2Nvz9/eHm5oa6ujrk5+cjPDwc8+bNa9fFpFIp7O3/uDvh8XhQqVTg8/mQSqUQiUQt+4RCIaRSqdZ2oVCI+nrdZdmskjoIrbhG3Qhkrv68RsPgruYxSNKUnLxaCaWa1jVng7tIgCi/5jUa5o0IYjucVj02MTg5OeHDDz+EVCrFlStXUFtbC1dXV3zwwQews7Nr98Xs7e21ptPQaDTg8/mt7pPJZBCJRC3bbWxsIJPJ4ODg0Oq58/Ly2h3PQDcNAmPdcPP6tXYfa8rkcnmHfl+6FuFpgwOZJUjoxtX7XauxlNmQHlfmXefK4WzDg0BahjwzGlNiKu9zLzcONkru4+TFTIjtn25goT7K3Ka+gkKhECKRCNbW1gCAnJwc9O3bt90Xi4yMxIkTJzBmzBhkZGQgKOiPbBkeHo5PP/0UTU1NUCgUKCwsRFBQECIjI5GWloaJEyciPT0dUVFRrZ47ODi43fEAzQmlo8eaKmMp80SZPRbuyoTG0Rth3o56vZaxlNmQHlXmJpUal1JuY1yvTggLDWEhMv0xlfd5mrsMGyUncVMhwpDgh2eWaI+nKbNEIml1e5sSw5w5c1BTUwMvLy8AzX3RO5IYYmNjcebMGUyZMgUMw2DFihXYtGkT/Pz8MHz4cCQlJWHq1KlgGAbvvvsuBAIBZs+ejcWLF2PHjh1wdnbGmjVr2n1dYpyGB4t/X6OhTO+Jgfzh/I0aSJtUNNqZRf5uQnTzsMfhnHLMGPx0iUEf2pQYqqurkZKS8tQX43K5D/VoCgz8YzK1yZMnY/LkyVr73dzcsHHjxqe+NjE+LkJr9OnigsO55ZgfR/NUGcrhnDLYWfMwKJDadtgUFyrGV2k3cK9BASc7a7bD0dKm7qr+/v4oLzefekhiPOJCxMgvq0dRtflN5W6MNH9a19zGyrhn+DR3sSGeUGsYHM+vYDuUh7QpMUgkEgwdOhTPPPNMyz9CdOFBV2Ea7GYYmXfqUFHfRF20jUC4tyPEDgKjXO62TVVJhw8f1nccxEL5udqhh6cIh3PL8Wp0ANvhmL3DOWXgcTkY2t2D7VAsHpfLQWyIGLsldyBXqo3qCe6xiWHdunV48803MX/+/Ie6E1IjMNGVuFBPfHG8ANXSJrja0xoN+nQ4txwDAlzgaEdrLxiDuBBPbD1/G6cLqjDCiDoDPLYqadiwYQCAZ599FpGRkejbty8yMjLQs2dPgwRHLENciBgaBjhmhHWt5qSwUorrFVKqRjIiAwJcIRLwjW4U9GMTQ48ePQAAO3fuRGBgIM6ePYv58+fj2LFjBgmOWIbQTg7wdrI1yrpWc/KgHYe6qRoPaz4XQ3p44FheBdQa45lUr02Nzw/GLdy/fx/PPfccuNw2HUZIm3A4zXWtpwoq0aBQsR2O2WoeL+KATk62bIdC/iQuRIxqmQKXbteyHUqLNn3Dq1Qq/Oc//0GfPn1w/vx5KJVKfcdFLExciBhNKg1OFVSxHYpZqqiX43LxPapGMkJDurvDisfBYSNa8rNNiWHlypXw9fXFa6+9hpqaGqxevVrfcREL09ffBY62VlSdpCfH8irAMKBJ84yQyMYKgwLdcDi33GjWaGhTd9UuXbqgS5cuAIAxY8boMx5ioax4XAzv4YFj+eVQqTXg86i6UpcO55TBz8UO3cWiJ7+YGFxcqBjv781GQYUUQUbwHtGnjxiNuFAx7jUocfGW8dS1mgNpkwpnrlfT2gtGbERw85OcsVQnUWIgRiO6W/N6uMbWdc/UpV2thEKtod5IRkzsYIPevk44bCQzAFBiIEZDKOAjuqsbjhhRXas5OJJbBhehNaI6O7MdCnmMuFAxMkvqUFqn23XtO4ISAzEqcaHGvx6uKVGqNTiWX4HhPTyo3cbIPegxdtQInhroL4UYFVNYD9eUXLhRg3q5CnGh1E3V2HX1sEeAm9AoqpMoMRCj4mYvQJ/OztRtVUcO55bBxoqLZ2hdbZMQGyrGucJq1DWyO1aMEgMxOnEhnsgtvY/imga2QzFpDNO89kJMN3fYWhvPzJ3k0eJCPKHSMDh5ld15wwyWGORyOd5++21MnToVs2bNQk1NzUOvWb16NRISEjBp0iTs2LEDAHDv3j30798fSUlJSEpKwubNmw0VMmHJg94zR81okXo2XK9RoLROTtVIJiTC1wlu9uyv0WCwxJCcnIygoCBs374dEyZMwLp167T2nz9/Hrdv30ZqaiqSk5Px7bffoq6uDrm5uRg7diy2bNmCLVu24G9/+5uhQiYs6eImRJDYnvUPh6k7d1sGLgcY3oPWXjAVD9ZoOHm1Ak0qNXtxGOpCEokE0dHRAICYmBicO3dOa39ERARWrFjR8rNarQafz0d2djZycnIwbdo0vPPOO6iooKmZLUFciCd+vVWDWpmC7VBM1rnbMvTt4gJnoXGtJ0weLy5EDJlCjbOF1azF0KYpMdpr586dD1X5uLq6QiRqHuotFApRX6/dHVEgEEAgEECpVGLJkiVISEiAUChEQEAAwsLCMGjQIOzbtw/Lly/H2rVrH7pmXl5eh2KVy+UdPtZUmUKZu9k1Qa1hsPVEBkYEPv0UAaZQZl0qqVPg1j0lRgVxLKrc5vA+u6g1sOVzsONMPjw1T04O+iizXhJDfHw84uPjtbbNmTMHMlnzgu8ymQwODg4PHVdXV4d33nkH/fr1w+uvvw4AGDBgAGxtm6cJjo2NbTUpAEBwcHCHYs3Ly+vwsabKFMrcg2Gw8lQ1smu5eFsHsZpCmXXp+InrAIC/De8FL0fLmWbbXN7nYcFN+PVWDbp37wEu9/HTmDxNmSUSSavbDVaVFBkZibS0NABAeno6oqKitPbL5XJMnz4dkyZNwltvvdWy/YMPPsAvv/wCADh37hxCQ0MNFTJhEYfDQVyoGOnXqiBXslfXaqoOZpeiu5vAopKCOYkLFaOyvgkZJfdYub7BEkNiYiIKCgqQmJiI1NRUzJkzBwDw8ccfIzMzEykpKSguLsbOnTtbeiAVFxdjwYIFSE5ORlJSElJSUvD+++8bKmTCstgQMRqVapymNRrapbimAdl37uOZzkK2QyEdNKS7B/hcDmsdMPRSldQaW1vbVquBFi1aBAAIDw/H9OnTWz12y5Yt+gyNGKn+/q4Q2fDxS06ZUS2UbuwOZTePGh9MicFkOdpaYWCgKw5ll2LxqO4GnxWXBrgRo2XNb16j4UheOZRqDdvhmIyD2aUI7eQAL5EV26GQpzA6zAu3qhtYmTeMEgMxamN6euFegxLnb7DXdc+UlNY14tLtexgdRoPaTF1cqBhcDnAgq9Tg16bEQIxaTJA7hNY8Vj4cpuiX36uRRoV5sRwJeVpu9gIMCHDFgaxSg09DT4mBGDUbKx6GB4vxS07zkp/k8Q5ml6Gbhz26etizHQrRgdE9vXCjSoar5YatTqLEQIzemJ5eqJEpcP7Gw/NrkT9USZtw8VYNVSOZkVGhns3VSZmGfWKmxECM3pDu7rCz5uFANlUnPc7hnHJomOa7TGIe3EUC9PN3wYFsw65PQomBGD0bKx6G9fDAL9llVJ30GAezS9HF1Q49PJ9+ChFiPMb09ML1CimuGbA6iRIDMQnP9fRCtUyBX29SdVJr7jUocK6wGqPCvAze553o16gwT3AM3DuJEgMxCUO6e8DWiqqTHuVIbjlUGobaF8yQh8gGfbu4UGIg5K9srZurkw5ll0OtMWzXPVPwU2YpfJxtEe7jyHYoRA/GhHniWrkU1ysMU51EiYGYjDE9vVAlbaLqpL+okSlw+noVxvXqRNVIZupBh4IDWYZphKbEQEzG0B7usLHi0mC3vziYXQq1hsG48E5sh0L0ROxggz6dnQ32t0+JgZgMO2s+hvXwwMHsMqpO+pP9V+4i0F2IYC/qjWTOxvT0Qn5ZPQorpXq/FiUGYlLGhndClbQJF2juJABA+X05LtysoWokCzCmpxc4nOYbAX2jxEBMyrAeHrAX8PFjhv4/HKbg58xSMExzwiTmzdPRBv39XbAv467e506ixEBMio0VDyNDPXEguxRNKlrZbX/mXYR4OdDcSBbi+d7euFElQ/ad+3q9DiUGYnLG9+6EerkKJ69Wsh0Kq4prGnD59j2M7UVTYFiK0WGesOJx8GPGHb1ex2AruMnlcixcuBDV1dUQCoVYvXo1XFxctF4ze/Zs1NbWwsrKCgKBABs2bEBRURGWLFkCDoeDbt264V//+he4XMpnlmxwoCtchdbYl3EXI0Mtd0DXz7/3UKHeSJbDyc4azwZ5YH/mXfxjTDB4XP20KxnsGzY5ORlBQUHYvn07JkyYgHXr1j30mqKiIiQnJ2PLli3YsGEDAGDlypWYN28etm/fDoZhcOzYMUOFTIwUn8fF2HAvHM0rR71cyXY4rNl/5S56+zrB18WO7VCIAT3fuxPK7zfhwk39dcAwWGKQSCSIjo4GAMTExODcuXNa+6uqqnD//n288cYbSExMxIkTJwAAOTk56NevX8txZ8+eNVTIxIiN7+2NJpWGtcXS2Xa9oh45d+9jXC96WrA0I4LFEFrzsE+PHTD0UpW0c+dObN68WWubq6srRKLmftZCoRD19dpDu5VKJWbOnImXX34ZdXV1SExMRHh4OBiGaemG19pxD+Tl5XUoVrlc3uFjTZU5lNmWYSC252P7mWsIsXvyNAHmUOY/+/5SDbgcoIed9JHlMrcyt4WllHmAjy1+unIHid350CibdF5mvSSG+Ph4xMfHa22bM2cOZDIZAEAmk8HBwUFrv5ubG6ZMmQI+nw9XV1cEBwfj5s2bWu0JrR33QHBwcIdizcvL6/CxpspcyvxiMRdfpd2Am08A3EWCx77WXMoMABoNg1M/HEdMkDsGR/Z85OvMqcxtZSllTuK64timiyjjuMDPprbDZZZIJK1uN1hVUmRkJNLS0gAA6enpiIqK0tp/9uxZzJ07F0BzAigoKEBAQABCQkJw4cKFluP69OljqJCJkXu+tzfUGgY/Z1rWmIbzN6txt06OiZE+bIdCWDK4q1tLBwx9MFhiSExMREFBARITE5Gamoo5c+YAAD7++GNkZmbi2WefRZcuXTB58mS88sormD9/PlxcXLB48WJ8/vnnSEhIgFKpxMiRIw0VMjFyQWIRgr0csPeyfrvuGZs9l+5AJOAjLkTMdiiEJVY8Lp77vQOGTKH7xasM1l3V1tYWa9eufWj7okWLWv7//vvvP7Tf398fW7du1WtsxHRNivTG8p/zcK28HkFi858rqEGhwsGsUowN7wQbKx7b4RAWJfT1xd5Ld1DbqNL5uWlAADFpL0R4g8/lYOdvxWyHYhCHc8ohU6gxMdKb7VAIy0I7OeLS0lj4OFrr/NyUGIhJc7UXYFgPD+y9fBdKC1gPevelEng72aJvF5cnv5iYPSuefr7CKTEQkxffxxdV0iakmfkUGeX35ThzvQoTI73B1dOIV0IASgzEDAzp7g43e2vslJh3ddLey3egYZqrzwjRJ0oMxORZ8biY0Nsbx/IqUC1tYjscvWAYBqkXi9G3izMC3GkmVaJflBiIWYjv4wuVhjHbdRrO36jBzSoZpvT1YzsUYgEoMRCz0N1ThHAfR+yUlOh9ERM2pFy8DQcbPp4Lpym2if5RYiBmI76PL/JK7+NKSR3boehUrUyBg1lleCHCm8YuEIOgxEDMxoTenWBnzcPW80Vsh6JTey7fgUKtwZR+VI1EDIMSAzEbIhsrTIjwxv4rd3GvQcF2ODrBMAxSfr2NXr5OCPZqfQJJQnSNEgMxK9P6d0aTSoNdkhK2Q9GJS7drUVAhxdR+vmyHQiwIJQZiVkI6OSCqszO2XbgNjcb0G6G3nr8NewEfY2n5TmJAlBiI2Zk2wA83q2Q4W6i/pQ8NoaJejp8y7+LFKB8IBQab75IQSgzE/IwO84KznZXJN0JvO38bKg2D6YO6sB0KsTCUGIjZsbHiYXIfXxzJK8ede41sh9MhTSo1tl24jaHdPdDFTch2OMTCUGIgZunl3++yvz9zk91AOuhAVimqpE30tEBYQYmBmCVvJ1uM6emFlF+LUS9Xsh1OuzAMg01nbiHQXYjobm5sh0MskMFatORyORYuXIjq6moIhUKsXr0aLi5/zCmfnp6Ob7/9FkDzB0MikeCnn35CU1MTXn/9dXTp0gVA8xKhY8aMMVTYxITNivbH/it3kXqxGINN6PtVUlSLzJI6fPR8KDgcml6bGJ7BEkNycjKCgoLw9ttv4+eff8a6devwwQcftOyPiYlBTEwMAGDDhg2IjIxEYGAgdu7ciRkzZmDmzJmGCpWYiXAfJ/T3d8F3p2+i/3jTmWNo/clCONtZYVKUD9uhEAtlsKokiUSC6OhoAM1J4Ny5c62+rqysDD/++CPmzJkDAMjOzsbJkyfx0ksv4b333oNUKjVUyMQMzIoOwN06OU7fkrEdSpvkl93HsfwKTB/kDztr6qJK2KGXv7ydO3di8+bNWttcXV0hEjUv1i4UClFfX9/qsZs2bcL06dNhbd28jml4eDji4+MRFhaG9evX48svv8TixYsfOi4vL69Dscrl8g4fa6osqcxeYODjYIWdWbV41j/X6KtmPj5VARs+BwPdmp76PbKk9/kBKrNu6CUxxMfHIz4+XmvbnDlzIJM137XJZDI4ODw874tGo8HJkyfx7rvvtmyLjY1teW1sbCw++uijVq8ZHBzcoVjz8vI6fKypsrQyz20QYeGuTNyFK0YEi9kO55GKaxqQfusmZgzqgn69Q576fJb2PgNU5vaSSCStbjdYVVJkZCTS0tIANDc0R0VFPfSaa9euwd/fHzY2Ni3bXnnlFWRmZgIAzp07h9DQUMMETMzGCxHe8LTn49Nj14x6rYav0wvB5QCvRgewHQqxcAZLDImJiSgoKEBiYiJSU1Nb2hA+/vjjli/+mzdvwtdXe7KwDz/8ECtWrEBSUhIuXbqEN99801AhEzPB53ExJdwJ2Xfu43h+BdvhtKq4pgGpF4sR38cXno42Tz6AED0yWOuWra0t1q5d+9D2RYsWtfx/9OjRGD16tNb+0NBQpKSk6D0+Yt6GB4qwO1+Gz44VYFgPD6Nra/jsWAE4HA7eHtaV7VAIoQFuxDLwuRzMGdoVmSV1OJJbznY4Wq5X1GPPpRIkDegML0dbtsMhhBIDsRwTI30Q6C7EqkP5UKo1bIfT4n9HCmBjxcPsIYFsh0IIAEoMxIJY8bj4x+hg3KiUIeXX22yHAwDIKL6Hn7NKMXOwP9zsBWyHQwgASgzEwgwP9sDAAFf872gB7rM8h5JGw+DDfTlwsxfg9WepJxIxHpQYiEXhcDh4/7lg1MgU+PLEdVZj2Xv5DjKK72HxqO4Q2VixGgshf0aJgVicMG9HxEf5YOOpm7ha1voIfH2TNqmw+lA+evk6YVIkzYlEjAslBmKR3hsTDAdbK7y3N4uVtaFXH8xHpbQJH44LAZdrXF1nCaHEQCySs9Aa748JhqSoFtsN3BB9/kY1tpwvwoxB/ojwczbotQlpC0oMxGJNjPTG4K6uWHkgD7eqDDP7aqNCjcW7M+HnYoe/jwwyyDUJaS9KDMRicTgc/OfFXuBxOZibctkgYxs++jkXRdUNWDWpJ02rTYwWJQZi0To52WLVpHBcKanDJ0eu6fVaP2bcwfYLt/HGs4EYFGhCS8oRi0OJgVi8MT29MKWvL9afLMTBrFK9XONaeT3e25OFPp2dsSCOqpCIcaPEQAiAD8eHIsLPCe/uyED2nTqdnrvivhwzNl2EUMDH51MjYMWjjx0xbvQXSggAGysevknqA1ehANM3XcT1Ct0sIVvXoMSM7y+itkGB76b3pUnyiEmgxEDI79xFAmye2Q8AkPjt+adODjUyBaZuOI+Ccim+nBqJMG9HXYRJiN5RYiDkT7p62CN5Vn8wDINJ68/idEFVh85zo1KKyV+fw/UKKb55OQpDe3joOFJC9MfgieHIkSNYsGBBq/t27NiBiRMnYvLkyThx4gQAoKamBjNnzsTUqVMxb948NDY2GjJcYoG6iUXYM3swxA4C/G3Tr1h7rKDNXVkZhsHeyyV4/oszqJEpsHlmPwzpTkmBmBaDJobly5djzZo10Gge/pBVVlZiy5YtSElJwcaNG/HJJ59AoVBg3bp1GDt2LLZv346QkBCkpqYaMmRiofxc7bB79iA819MLnxy5hufWnsLPmaVQP2L6DIZhcOFGNV7acAHvpl5BV7E99s0ZjAEBrgaOnJCnZ9ARNpGRkRgxYkSrX+6ZmZmIiIiAtbU1rK2t4efnh/z8fEgkErz++usAgJiYGHzyySeYPn26IcMmFkpkY4W1iREY16sTVh7Mw1vbL8HN3hpDu3sg2MsBjrZWaFCqUVghxcmrFbhV3QA3e2ssez4UL/XvDB7NgURMlF4Sw86dO7F582atbStWrMCYMWNw4cKFVo+RSqUQiUQtPwuFQkilUq3tQqEQ9fWtz4aZl5fXoVjlcnmHjzVVVOb28eEAa0d54HxxA9JuSnEo+y52Skpa9gv4HIR62GD8QDcMC7CHgN+Ia1fzdRV6h9H7bBn0UWa9JIb4+HjEx8e36xh7e3vIZH/MVyOTySASiVq229jYQCaTwcHBodXjg4ODOxRrXl5eh481VVTmjgkLBV5Fc7VRlVSBRoUaVnwOxCIbo5whld5ny/A0ZZZIJK1uN5peSeHh4ZBIJGhqakJ9fT0KCwsRFBSEyMhIpKWlAQDS09MRFRXFcqTE0nE4HLiLBPBztYOXo61RJgVCngbrs3ht2rQJfn5+GD58OJKSkjB16lQwDIN3330XAoEAs2fPxuLFi7Fjxw44OztjzZo1bIdMCCFmzeCJoX///ujfv3/LzzNmzGj5/+TJkzF58mSt17u5uWHjxo0Gi48QQiyd0VQlEUIIMQ6UGAghhGihxEAIIUQLJQZCCCFaKDEQQgjRwmEYpvXJX0zIowZpEEIIebzWxoaZRWIghBCiO1SVRAghRAslBkIIIVosNjFoNBosXboUCQkJSEpKQlFREdsh6Z1SqcTChQsxdepUvPjiizh27BjbIRlEdXU1nn32WRQWFrIdikF8/fXXSEhIwMSJE7Fz5062w9E7pVKJBQsWYMqUKZg6darZv89XrlxBUlISAKCoqAiJiYmYOnUq/vWvf7W61k1HWGxiOHr0KBQKBVJTU7FgwQKsWrWK7ZD0bt++fXBycsL27duxYcMGfPTRR2yHpHdKpRJLly6FjY0N26EYxIULF3D58mUkJydjy5YtKCsrYzskvUtLS4NKpUJKSgreeustfPrpp2yHpDfffvstPvjgAzQ1NQEAVq5ciXnz5mH79u1gGEZnN3sWmxgkEgmio6MBAL1790Z2djbLEenfqFGjMHfuXADNU0fzeDyWI9K/1atXY8qUKfDwsIzlNU+fPo2goCC89dZbeOONNzBkyBC2Q9I7f39/qNVqaDQaSKVS8Pmszw2qN35+fvj8889bfs7JyUG/fv0ANC9kdvbsWZ1cx3x/g08glUphb2/f8jOPx4NKpTLrPyqhUAiguezvvPMO5s2bx25AerZnzx64uLggOjoa33zzDdvhGERtbS3u3r2Lr776CiUlJZg9ezYOHToEDsd8pwa3s7PDnTt3MHr0aNTW1uKrr75iOyS9GTlyJEpK/lgkimGYlvf2cQuZtZfFPjH8dWEgjUZj1knhgdLSUrz88st4/vnnMW7cOLbD0avdu3fj7NmzSEpKQl5eHhYvXozKykq2w9IrJycnPPPMM7C2tkZAQAAEAgFqamrYDkuvvv/+ezzzzDP45Zdf8OOPP2LJkiUtVS3mjsv94yv8cQuZtfu8OjmLCYqMjER6ejoAICMjA0FBQSxHpH9VVVWYOXMmFi5ciBdffJHtcPRu27Zt2Lp1K7Zs2YLg4GCsXr0a7u7ubIelV1FRUTh16hQYhkF5eTkaGxvh5OTEdlh65eDg0LL8r6OjI1QqFdRqNctRGUZISEjLcsnp6eno06ePTs5r/rfIjxAbG4szZ85gypQpYBgGK1asYDskvfvqq69w//59rFu3DuvWrQPQ3JhlKQ2zlmDo0KG4ePEiXnzxRTAMg6VLl5p9W9L06dPx3nvvYerUqVAqlXj33XdhZ2fHdlgGsXjxYvzzn//EJ598goCAAIwcOVIn56WRz4QQQrRYbFUSIYSQ1lFiIIQQooUSAyGEEC2UGAghhGihxEAIIUQLJQZCCCFaKDEQQgjRQomBED3Ytm0b5s+fD6B5ENK2bdtYjoiQtqMBboToyZtvvgkHBwcoFAp88sknbIdDSJtRYiBETzIyMpCQkIA9e/YgNDSU7XAIaTNKDITogUKhwLRp0zBp0iTs3r0bW7duhbW1NdthEdIm1MZAiB7897//xZAhQ5CQkIDo6GisWbOG7ZAIaTN6YiCEEKKFnhgIIYRoocRACCFECyUGQgghWigxEEII0UKJgRBCiBZKDIQQQrRQYiCEEKKFEgMhhBAt/x/mRQhKVuiJbwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x))\n", + "plt.title(\"A Sine Curve\")\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"sin(x)\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The position, size, and style of these labels can be adjusted using optional arguments to the functions, described in the docstrings." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When multiple lines are being shown within a single axes, it can be useful to create a plot legend that labels each line type.\n", + "Again, Matplotlib has a built-in way of quickly creating such a legend; it is done via the (you guessed it) `plt.legend` method.\n", + "Though there are several valid ways of using this, I find it easiest to specify the label of each line using the `label` keyword of the `plot` function (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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xzmrEjhEqOj7aZDVkNAnsNHjyjTpypFJBQc9/bkxCjPpi6xfKZrSNchrnpEbuHKnuxd9L1/aN8bDNqampatvZbaqafzXFKFSV2VVUyOWQDK8nI2SFwN60SamICO32zZtKhYW9+PkZ0eaVK5VydVXq7NkXPy8lNUXNCZuj3Ca6KcMog/Jb7afO3U3jns4rSEubT948qTqv6KwYhSo4qaBadmyZ2b7dmpMEthESEpTy8lLqk0+e/fjaU2tVkclFFKNQvdb0Ujdibphku8b4d5tTU1NVwJ8ByuMHD2UYZVB91/ZVUXFRFqrOPPQe2JGRSuXMqVTv3q/+moxq870n9jnGjlVq//6nH//z+p+q5tyailGoOvPqqD+v/2m2Woxp8+9//668ZnkpRqEaLGigIm5HmKEy8zFXYGfpk4JtbSEk5PH53CdOwMyZcOdBJD4rfWgb2BYXWxf2vreXue/MJZ9TPssW/ASDwYBveV9ODTzFZzU+Y97heZSfUZ7t57ZburRsTSnYt0+7nSsXbN8O//d/Fi3pmVxdtX+jo2HOHO2gJGhnLo3dM5bKsysTcSeC+e/MJ7hnMOXzZ66LHKoVrkZInxBmtJrB4euHqTCzAtMOTiNVpVq6NMsy+mMgHZ8SL2OuvZDPPlMqp1uC8vimgrIZbaPGBI9RicmJZtlWWr2szSGXQ1TpaaUVo1Afrv9QxSTEZFBl5qPHPezAQKVAqS1bjHu9JdocHa1UbKxSZ+6cURW+8VX09VI+v/io2w9uZ8j209vmy/cuqxZLWihGoRoubKguRl00UWXmI3vY6ZSUkoSh6WDu+ZXE1S2eA71+o03OEbo5/7Nqoar88f4ffFr9U2aEzqDanGqE38oeF51kBgkJ2r/t24O/PzRqZNl60sLFBX6JWEyFmRU4sdwXt1/3ML/1Ut2cQlfItRAbfDfg38afg1cOUnFmRdZHrLd0WRaRLQL72v1rNFrUiEm//0D/xq34o98fnN9fhYoVYds2S1f36hxyOPBjsx/Z0m0LNx/c5G3/t1l6bKmly8rypk+HKlW0i2By5IA+fcDa2tJVvZqE5AT6r++P3xo/qhSsQtj6imxa54id3eOLc/TAYDDQp3IfjvQ7whu53qDNsjYM3T6U5NSMv+rTkrJ8YO+5uIfKsysTdi2MgPYBTG81HcccjrRuDT/99PjqST1pUrwJh/sdppJHJbqu6soH6z8gMSXR0mVlWaVLQ7lykKqz7tNL9y5RZ34dZobNZEitIWz3245n0UJUrao9Pm+eNj7PS0aYyFSKuxXnQO8D9PPqx8T9E2m4sCHXY65buqwMk6UD+/8O/h8NFzbE1c6VkD4h+Jb3ffSYoyN89JG2pxQVBS1bwvHjlqs1rQq5FmJXj118UfMLZoXNosniJtyOvW3psrKMs2dh5UrtdsOGsGzZ01ceZnZ7Lu6h8qzKnL5zmtVdVvNt42+xsXr6wua33oJ69aBAAQsVaSR7G3tmtp7JkneXEHYtjKr+VTly/Yily8oQWTKwk1OT+WjTRwzcNJCWJVtyqO8hyuUr99znX7qknUESFZVxNZqCjZUNE5tMZGn7pYRcDqGqf1VO3Dxh6bKyhKFDYeBArRtEbxYdXUTjRY3J45iHQ30P0a50u2c+r3p1mD9fG5vk3j2YMUPrJtGLrp5d2ffePhSKWvNqsTp8taVLMrssF9j3E+7zTuA7TD04lc+qf8bqLqtxtXN94Ws8PSEiAmrX1pZPncqAQk3Ip7wPe97bQ1xyHDXm1mBDxAZLl6RbD7s9/P3hwAHtm5hepKpURuwcQY81Pajzeh1+6/0bb7q/+UqvnTtX+8Z5Qmef95U8KnGo7yHK5ytP+6D2jN87HqWnT500ylKBfeneJWrNq8WWM1uY2Womk5pNejR86cvY/TOeTWio1q83d64ZCzWDqoWqcqjvIUq4laBtYFv8w/wtXZLujB8P774LKSnaOdZFi1q6olcXlxSH9y/ejNs7jj6V+rC562ZyO+R+5dd/+ql2zUK5f76I6inzCjgXYFePXfiU8+HLnV/Sd13fLHswMssE9ombJ6gxtwYX711kY9eN9KvSz6j1VKoEY8ZAp04mLjADFHYtzN739tKseDPeX/8+o4NHZ+m9DVPLmVO74CQl5eXPzUzuxd+j2ZJm/HLyF75v8j2z28xO8+mqBgNUrqzdDg6GatW0IY31wiGHAwHtAxhRZwRzD8+lQ1AHYpN02J/1ElkisH+//Dt15tdBKcXe9/bStHhTo9dlba31X7q6arOCfP211r+nF062Tvzq/Ss9KvTg691fM2DjAFJSdZZAGSghAf76S7s9YAAsWmS+8aXN4XrMdeotqMfvl39nWYdlfF7z86fGpTZGUpIW4HY6G+XXYDAwpuEYprWYxrrT62i6uCl34+5auiyT0n1gbzmzhUaLGuHm4Ma+XvvwzO9psnUfOqR9Td640WSrzBA5rHMw/535DKk1hBmhM+j8S2fik+MtXVamNHAg1Kr1+IBzZpqG62XOR56n9rza/HX3L9b5rKNLuS4mWW/jxvD77+DmpvXpP/xA04sBVQcQ1CmIQ1cPUWd+HS5H6+i8xZfQdWAvP76cNsvaUNKtJPt67aNY7mImXX+NGtoBSB8fbVlPvQsGg4FvG3/L5GaTWRW+ipYBLYlJjLF0WZnOkCHa7C25clm6krQ5duMYtebVIjI+kh1+O2hWoplJ1//wg2vMGK2r5OJFk67e7DqW7cjmrpu5HH2ZmnNr8tcdnX3qPIduA3tW6Cx8VvpQrXA1dvfcTQFn85xMWry49u/p01q/nt72Nj6p/gmL311M8MVgmi1pxr14HfXvmElMDCxerN0uUQL8/CxbT1r99vdv1F1QFyuDFXvf2/vUbEam1rcvjB4NRYqYbRNm06BoA4J7BhOXHEe9BfU4eeukpUtKN10G9pTfp/DBhg9oWbIlW7ptIZd9LrNvMzYW4uL0tZf9UDfPbizvuJyDVw7SaFEj7sTesXRJFjVtGvTsCSd1+Pe79+Jemi5pSl7HvOzvtZ+yec07D2jBgtoZJAaDtpe9dq1ZN2dyFQtUJLhnMAD1FtTT/QU2ugvsSQcm8emWT2lfpj2ruqzCMUfGnChbqRIcPapN9gtw61aGbNZkOpbtyJouazh+8zgNFjbgRswNS5dkMYMHw969oLc5j3ed30XzgOYUdi1McM9gXs/1eoZuf8QI6NVLG7JVT8rmLcue9/bgmMORBgsbEHI5xNIlGU1XgT1x30Q+3/Y5ncp2IrBDILbWGXs4/+Gs7P7+2qSqEREZuvl0a/VmKzb4buBs5FnqLaiXpQ7GvMzdu9pEzVFR2plANWtauqK02X5uO62WtqJorqLs7rEbDxePDK9h5kxtAmzXF1+HlimVcCvBnp57cHNwo/Hixuy5uMfSJRlFN4E9bs84hu4Yinc5b5Z2WGrRYVGbNNH6PYuZ9hhnhmhUrBFbum3h6v2r1J1flwtRFyxdUoY4ehRWrND+1ZstZ7ZoB9fdS7Krxy7yO+e3SB1OTlChgnZ74UKYNcsiZRjt9Vyvs6fnHgq7Fqb5kua6nAxEF4H9ze5vGLFrBN08u7H43cX/GcQmo73xBkyZoo3BEB0Nhw9btJw0q12kNjv8dhAZH0m9BfU4e/espUsym4eXmjdoABcuaIMd6cmGiA20DWxL6Tyl2em3k7xOeS1dEkppM9isWqW/EQwLuRYiuGcwJd1L0nppazaf2WzpktIkUwe2UoqRu0YyKngUPSv2ZME7Cywe1v82YIB23qqeLq4BeLvQ2+z028mDxAfUW1CPiDs66995BdeugZfX4zHP3dwsW09a/XrqV95d/i7l85Vnh9+OTDPhgMEAQUGwZo3WTai30M7nlI+dfjspm7cs7wS+w7rT6yxd0iszOrBTU1MZOXIkXbp0oXv37lw08YmaSim+3PklY/aMoU+lPsxtO/eVxwXJSN9+q10dlzOnpStJu0oeldjVYxeJKYlZ5rSnJ9naakOi2ttbupK0W3lyJR1XdKSyR2W2+23HzSFzfdrY2YGDA8THQ+vW2pk3euLu6M4Ovx1UyF+B9kHtWRW+ytIlvRKjA3v79u0kJiayfPlyBg0axLfffmuyopRSDNk+hAn7JtDPqx+z2szCypA5vwwUKgStWmm3d++GXbssWk6alc9fnt09dwNQf0F9jt04ZtmCTODGDW2vz90d9uyBOnUsXVHaBJ0IossvXahaqCpbu2/NkNNWjWVlpX0gOjhYupK0y+2Qm23dt/F2wbfpvKIzy48vt3RJL2V0CoaFhVHnn7+EihUrctxEo/8rpfju6Hd8f+B7Brw9gBmtZmTasH6SUtpVc198ob+viGXzliW4ZzC21rY0WNiAw9d01in/hLt34e23tVP3QF+XmgMsO7YMn5U+1HytJpu7bn7p0MCWZmurTfTQu7e2fFtnc2jktM/Jlm5bqPlaTXxX+bLkzyWWLumFjE7CmJgYnJ+YgsPa2prk5PQPaRh2LYyFEQv5uNrHTG0xNd0D2WQUgwHWrdN+rDL/58t/vOn+JsE9g3GydaLhooYcunLI0iUZJXdu6N8funWzdCVpF/BnAN1Wd6NOkTps7LoRFzsXS5f0Sh7+iUZEaNcp+OtsZF8XOxc2dd1Evdfr4bfaj/mH51u6pOcyKCPH35wwYQIVKlSgZcuWANStW5c9ex6f2xgWFoajEaO/K6U4fOMwlfJX0k1Y/5tS8N13+ahR4wF1677aLKfx8fHYZ4LO1isPrvDe7veISoxidp3ZVMxT0WzbMmWbz561xd5eUahQkknWZy7Pa/PaC2sZfmg4VfJUYXqd6Tja6GjmhH8kJcF33+WnR4+7FC78+PeQWd7bLxOXHMdH+z9i/439jPIaRefinY1eV3raHBsbi5eX17MfVEbavHmzGjJkiFJKqcOHD6vevXs/9XhoaKixq1YnT540+rWZQXS0UpUrKzVs2Ku/JjO1+VLUJVXy55LKebyzCr4QbLbtmKrNyclKlSqlVM2aSqWmmmSVZvOsNi84vEAZRhlUw4UN1YPEBxaoyjz27NH+zUzv7ZeJS4pTrQJaKUahpoZMNXo96Wnzi7LT6C/vTZo0wdbWFm9vbyZMmMCwYcOMXVWW4+KiHewaN05bNkFPUYZ6Ledr7O65m8KuhWkR0IKd53dauqQXsraGJUu0+Qn19qVswZEFvPfrezQq1oh1PusybKgFc1u9GurWhfXrLV1J2tjb2LOqyyralW7H/zb9jx9/+9HSJT3F6MC2srJi9OjRBAYGsnz5coo/HNZOANpVYQYDXL2qXR22WmfzgxZ0KcjuHrspmqsorZa2YuvZrZYu6T8OHtROqQSoUuXxOC96Me/wPHr92ovGxRqz1nttlglrgLZtYc4c+KfHVFdsrW0J6hhEp7KdGLR1EN/uM90ZcOmlw8Nj+uLsDK+9BgXMM/qrWeV3zs+uHrso5V6KNsvaZLrJfSdN0sZrjtfh3Az+Yf70XtubpsWb8qv3rzjk0OF5cS9gba2dOWJlBVFRVkydqq+RLnNY52Bph6X4lvdl2I5hjA4ebemSAAlss3N1hc2btckQAP7+27L1pFVep7zs7LGT8vnK8+7yd1lzao2lS3pkwQJt/kEdHM96yuyw2by//n2al2jOGu81WS6s/23lylwMHqy/wdJsrGxY1G7Ro+n2vtr5lcXnSJXAzkBbt2oTImzZYulK0sbNwY3tftup7FGZTis6seLECovVsnkztGunzcXo4KCN16wnAX8F0G99P1qWbMnqLquxt9HZp40RevW6S2ioNsKl3lhbWTPvnXn0qdSHsXvHMnT7UIuGtgR2BqpVSxsMvnZtS1eSdrnsc7G1+1aqF66O90pvlh5bapE6rl+Hy5fhwaudLZmpTNg7gXGHx9G2VFtWdV6VLcIatGM55cpptzdtgo8/1tfFZVYGK2a1mcWHVT7kuwPf8emWTy0W2hLYGcjJCSZO1P5NSND2FvXE1c6VTV03Uff1unRb1Y2FRxZm2LYfTpLbs+fjCWL1QinFsO3DGL5zOK2KtOKXTr9gZ6OzKclN5MAB2LdPfx+4VgYrprWcxsfVPuankJ8YsHEAqSrjP3UksC1k0iTtCPqJE5auJG2cbZ3Z4LuBRsUa8d6v7+EfZv7L2pYv1+ZefDill03mGrDxhVJVKh9t+ohv93/L+5Xf59uq31p0LHdLGz1am+3HxUU73TUhwdIVvTqDwcDkZpMZXHMwM0Jn0G9dvwwPbR299bOWzz8HT0946y1LV5J2jjkcWeezjvbL2/P++vdJTElkQNUBZtte9eraaWJvvGG2TZhFcmoyfdf1ZcGRBQyqMYjvm3zPqVOnLF2WRRkM8PAC6H79tIPwGzfq50PYYDAwsfFEbK1tGbd3HEmpSRk6kqjsYVuIra02LCXAn3/C+PH5dXWBjb2NPau7rKZtqbYM3DSQyb9NNun6U1Ph11+1U8Fefx3mzXv8h64HcUlxdFrRiQVHFvBN/W/4vsn3uh1qwVzq1NF+9BLWDxkMBsY2HMvo+qNZeHQhfmv8SE7NmD9enf1XZU3btsG2bS7cugUeGT9Vn9HsbOxY0WkFvit9+WzrZ9yOvc3YhmNNEkzLlmkDOG3dqk3Jpie3Y2/Tdllbfr/8Oz83/5n/VfufpUvKlHr2fHw7IkI76+e11yxWTpp9Ve8rcljnYNiOYdyNu0tQxyCzD9glgZ0JDBoEtWqdw8OjFErB/fv6mejU1tqWwI6B9F/fn/H7xnPh3gXmtZ2X7oNqPj7awdnGjU1UaAY5H3me5gHNuRh1kRWdVtChbAdLl5TppaZCp07apAghIfoaXmBo7aG4O7jTf0N/6i6oywbfDRR0Md+5ptIlkknkzKkdvPjhB6hcWRuEXy9srGyY3WY24xqOY+mxpTRb0ozIuMg0r+fvv7U/3Lt3tSvk2rXT1x/vH9f+oMbcGtx6cIvtftslrF+RlZU2xMD06fr6fT/U16sv63zWcebuGarPqc6Jm+Y7k0ACO5OpXRuaN4d8+SxdSdoYDAaG1xlOQPsAfrv8GzXn1eR85Pk0rePyZW3WnvBw89RoTitOrKD2vNrY2dixv9d+ahfR4cn2FlShgjYeDMDPP8NPP+nrUvYWJVuwp+ceklOTqTWvFqeizHNwWQI7k6lRQ5sfz2CAW7dgqWWuTzGab3lftnbbyvWY61Txr8K2s9te+pqz/0zaXqOGNrN5rVrmrdGUUlUqX+38is6/dKaSRyUO9jlImbxlLF2WbimlnfYXHKyvwAZtjtTf+/xO9cLVuRFnnq/IEtiZ2A8/aAPo6G38kXpv1ONQ30MUdClI84DmfL//++deGbZ8OZQuDb/9pi07OWVgoel0P+E+7Ze3Z+zesfSu1JudfjvJ75zf0mXpmsGgvSeWLtW6Sm7dgmvXLF3VqyuSswibu22mnkc9s6xfAjsTGzdO29t4eOQ8Jsay9aRFCbcS/Nb7NzqU6cAX27/Ae6U3MYn/bUDLljBsGDxvgo3M6tiNY1SdU5X1Eev5ufnP+Lfxz7ZXL5raw4l9Afr0gZo19XWBjTlJYGdiNjaP+/U2b4aiRbVztvXC2daZ5R2XM7HxRH45+Qtes70IuxrGrl3g7a1d6ebiol39Zmtr6WpfjVIK/zB/qs6pSlR8FNu6b+N/1f4n51ibyfjx2jdNu38+C/XWTWJqEtg6Ubw4NGoEJUtaupK0MRgMfFHrC3b47eBB4gNqzK3BzB0bOHpUcfeuvs4qjYyLxHeVL++vf586RepwpN8RGhRtYOmysrS33oIO/5xss3mz9jdw86Zla7IkCWydKFkSAgO1iwuSkrTzlENDLV3Vq8sZWZ8pJcJpW6otQTlaU+DzFiQ6XrB0Wa9s3el1vDX9LVacWMG4huPY3G2z9FdnsHv3tMkq9HKNgjlIYOvQxYuwf792GpweKAUDBsDoES4s77CCOW3mEHpzP223tOWHAz9k2GW9xrgde5vuq7vTNrAteZ3ycqjvIYbXGY6VQf50MlqXLtr73t4eEhPhww8fn2GUXci7TodKlNDOVW7XTltetkw7sp6Z+veU0iZgjYnRjvwHBGjnWFtbG+hduTcnPzxJjfw1GLxtMG/7v82Bvw9YuuSnJKcmMzVkKiWnliTweCBf1/uaQ30PUcmjkqVLy9YeHir4809t4mU9nrOfHhLYOvXw9DeltIGRZs/OXFeJRURAmzYwY4a2XLTo02NYv5bzNabVmsbKziu5+eAmtebVov3y9py+fdoyBf9DKcWGiA1UnFmRjzZ/RJWCVTjS7wij6o/C1lonR0azgSpV4Pz5xwOoLVig/Vh6p+XKFW38G3ORwNY5g0E7GPPwApuoKO3y7odjR2ekP/54PIt5qVKwdi188snzn28wGGhfpj0RAyMY02AM289t563pb/Her++Z9fLeZ3kY1FXnVKX1stbEJcexustqtnbbylv5dDgGbjbg7v74dmCg9vNwp8VSwT18OPTooR1nMgcJ7CzA2hry/3P869gxrevh4Rvm4YEac3lySNhp02Do0MfnzLZpAzleYax+J1snRtQdwZmPzjCw6kCCTgRRbkY5Wi9tzZYzW0hJTTFP8UB0QjT/d/D/tO0ta82d2DvMbTuXUwNO0a50OzldTyc2bdK6BkEbi6ZMGe0+czt/XjtF9dw5bXnMGO0isFd53xsjXYG9bds2Bg0aZKpahAnUqaMdjKxQQVseNUobT9ocFx5s3aoNB/vwwM+4cdqevZ2R14/kc8rHlOZTuPTJJUbXH83BKwdpHtCcIlOKMHT7UEIuh5gkvOOS4lgVvgqflT4UnFSQgZsG4mDjwIJ3FnB64Gl6VeqVrWeF0SODAXLn1m7fuQOFCmk/AH/9pe19m2LHRSk4fhxO/9NzZ2sLO3Zo9wEUKWLeiTaMPhF27Nix7Nu3jzJlZNyEzObJwGzXTus/fnhfx47awFLTp2vLUVGQM+fz+7+VgpQU7SKeq1fhgw+0o/PNm2uXlDdu/Hgv21Rjebs7uvNVva/4otYXrI9Yz4KjC/jhwA9M3D8Rdwd3mhRvQtWCVfEq6EW5fOXIbZ/7uXvCKakpXLp3iVO3TxFyJYTgi8H8fvl34pPjcXdwx6ecD329+lK1UFXTFC8srmRJLUQfWrpUuzjr7l3tDJODB7WdmnfffbXjPocOaTs8tWtrQ8HWqwctWmgHPQsV0v4uzLVH/W9GB3blypVp3Lgxy5cvN2U9wsTq1dN+Hipe/PGeCGjTlDVvrh20BGjaVOvK+N//tKDOlUvr5vjyS63P8MIFrZsFtL2Jh19DzcHOxo4OZTvQoWwH7sTeYevZrWw8s5Gd53cSeDzw0fMcczjymutruNq5Ymtti7WVNffi7xEZH8mNmBskpGhfL6wMVlQsUJEPvD6g1ZutqP9GfWys9HXxjki7r77SppjLmVNbnjRJ67Zo315b/vhjrUtj3TptefBgLYQDArTlzz7T/t27V+t+DArSulweyqiwBjCol8zXvmLFChYufHp27PHjx+Pp6UlISAiBgYFMnvzf6aHCwsJwNHJOp/j4eOwfDiaQTViizUpBQEBuihRJpG5dbRrrAQMKU6dODN7eUQBMmZKXypVjHz1uSulp8624W5yMPMmF+xe4Hneda7HXiEuOIyk1iRSVgnMOZ1xzuOJm70Yxl2IUdS1KSdeSuNiad0aQl5H3tuXFxRm4ccOGN97QDvQsWODGjRs2DBmiXUI5dWoeYmKsGTZMG3EvIsIOZ+cUChZ89esF0tPm2NhYvJ4zuM5LA/tFXhbYz9voy4SHh2e7rhZpc/Ygbc4e0tPmF2WnnCUihBA6IYEthBA6ka4jLtWqVaNatWqmqkUIIcQLyB62EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohAS2EELohI0xL7p//z6DBw8mJiaGpKQkhg4dSqVKlUxdmxBCiCcYFdjz58+nevXq9OzZk3PnzjFo0CBWr15t6tqEEEI8wajA7tmzJ7a2tgCkpKRgZ2dn0qKEEEL8l0EppV70hBUrVrBw4cKn7hs/fjyenp7cunWLvn37Mnz4cKpWrfrUc8LCwnB0dDSqqPj4eOzt7Y16rV5Jm7MHaXP2kJ42x8bG4uXl9ewHlZFOnTqlWrZsqXbv3v3Mx0NDQ41dtTp58qTRr9UraXP2IG3OHtLT5hdlp1FdImfOnOHjjz9mypQplC5d2qhPESGEEGljVGBPmjSJxMRExo0bB4CzszMzZswwaWFCCCGeZlRgSzgLIUTGkwtnhBBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJySwhRBCJ2yMeVFsbCyDBg0iOjqaHDlyMHHiRPLnz2/q2oQQQjzBqD3soKAg3nrrLQICAmjbti3+/v6mrksIIcS/GLWH3bNnT1JSUgC4evUqrq6uJi1KCCHEfxmUUupFT1ixYgULFy586r7x48fj6emJn58fERERzJ8/nzJlyjz1nLCwMBwdHY0qKj4+Hnt7e6Neq1fS5uxB2pw9pKfNsbGxeHl5PfOxlwb2y5w9e5Z+/fqxffv2p+4PCwt77kZfJjw8/D8fAFmdtDl7kDZnD+lp84uy06g+7FmzZrFmzRoAnJycsLa2NqowIYQQr86oPuwOHTowZMgQVq5cSUpKCuPHjzd1XUIIIf7FqMDOkycPc+fONXUtQgghXkAunBFCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ2QwBZCCJ1I93jYzxMWFmaO1QohRJZntgkMhBBCZAzpEhFCCJ2QwBZCCJ3IVIGdmprKyJEj6dKlC927d+fixYuWLsnskpKSGDx4ML6+vnTs2JEdO3ZYuqQMcefOHerVq8fZs2ctXUqGmTVrFl26dKF9+/asWLHC0uWYVVJSEoMGDcLb2xtfX98s/3s+evQo3bt3B+DixYv4+Pjg6+vL119/TWpqqsm2k6kCe/v27SQmJrJ8+XIGDRrEt99+a+mSzG7t2rXkypWLpUuXMmfOHMaMGWPpkswuKSmJkSNHZquZtENCQjh8+DDLli1j8eLFXL9+3dIlmVVwcDDJyckEBgYyYMAApkyZYumSzMbf358RI0aQkJAAwIQJE/jkk09YunQpSimT7oRlqsAOCwujTp06AFSsWJHjx49buCLza968OR9//DEASqlsMaHxxIkT8fb2Jl++fJYuJcPs27ePN998kwEDBvDBBx9Qv359S5dkVkWLFiUlJYXU1FRiYmKwsTFqNkJdKFKkCFOnTn20fOLECapWrQpA3bp1OXDggMm2lan+F2NiYnB2dn60bG1tTXJycpb+ZTs5OQFa2z/66CM++eQTyxZkZqtWrcLNzY06deowe/ZsS5eTYSIjI7l69SozZ87k8uXL9O/fn82bN2MwGCxdmlk4Ojpy5coVWrRoQWRkJDNnzrR0SWbTrFkzLl++/GhZKfXo9+rk5MT9+/dNtq1MtYft7OzMgwcPHi2npqZm6bB+6Nq1a/j5+fHOO+/Qpk0bS5djVitXruTAgQN0796d8PBwhgwZwq1btyxdltnlypWL2rVrY2trS7FixbCzs+Pu3buWLstsFixYQO3atdmyZQu//vorQ4cOfdRlkNVZWT2O1QcPHuDq6mq6dZtsTSZQuXJl9uzZA8CRI0d48803LVyR+d2+fZtevXoxePBgOnbsaOlyzC4gIIAlS5awePFiypQpw8SJE8mbN6+lyzI7Ly8v9u7di1KKGzduEBcXR65cuSxdltm4urri4uICQM6cOUlOTiYlJcXCVWWMsmXLEhISAsCePXuoUqWKydadqXZfmzRpwv79+/H29kYpxfjx4y1dktnNnDmT6Ohopk+fzvTp0wHtIEZ2OiCXHTRo0IBDhw7RsWNHlFKMHDkySx+v6NmzJ8OHD8fX15ekpCQ+/fRTHB0dLV1WhhgyZAhfffUVP/74I8WKFaNZs2YmW7dc6SiEEDqRqbpEhBBCPJ8EthBC6IQEthBC6IQEthBC6IQEthBC6IQEthBC6IQEthBC6IQEthBC6MT/A29OFa4uNkbgAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, np.sin(x), '-g', label='sin(x)')\n", + "plt.plot(x, np.cos(x), ':b', label='cos(x)')\n", + "plt.axis('equal')\n", + "\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, the `plt.legend` function keeps track of the line style and color, and matches these with the correct label.\n", + "More information on specifying and formatting plot legends can be found in the `plt.legend` docstring; additionally, we will cover some more advanced legend options in [Customizing Plot Legends](04.06-Customizing-Legends.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Matplotlib Gotchas\n", + "\n", + "While most `plt` functions translate directly to `ax` methods (`plt.plot` → `ax.plot`, `plt.legend` → `ax.legend`, etc.), this is not the case for all commands.\n", + "In particular, functions to set limits, labels, and titles are slightly modified.\n", + "For transitioning between MATLAB-style functions and object-oriented methods, make the following changes:\n", + "\n", + "- `plt.xlabel` → `ax.set_xlabel`\n", + "- `plt.ylabel` → `ax.set_ylabel`\n", + "- `plt.xlim` → `ax.set_xlim`\n", + "- `plt.ylim` → `ax.set_ylim`\n", + "- `plt.title` → `ax.set_title`\n", + "\n", + "In the object-oriented interface to plotting, rather than calling these functions individually, it is often more convenient to use the `ax.set` method to set all these properties at once (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes()\n", + "ax.plot(x, np.sin(x))\n", + "ax.set(xlim=(0, 10), ylim=(-2, 2),\n", + " xlabel='x', ylabel='sin(x)',\n", + " title='A Simple Plot');" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.02-Simple-Scatter-Plots.ipynb b/notebooks/04.02-Simple-Scatter-Plots.ipynb new file mode 100644 index 000000000..7a1b94424 --- /dev/null +++ b/notebooks/04.02-Simple-Scatter-Plots.ipynb @@ -0,0 +1,353 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simple Scatter Plots" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another commonly used plot type is the simple scatter plot, a close cousin of the line plot.\n", + "Instead of points being joined by line segments, here the points are represented individually with a dot, circle, or other shape.\n", + "We’ll start by setting up the notebook for plotting and importing the packages we will use:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Scatter Plots with plt.plot\n", + "\n", + "In the previous chapter we looked at using `plt.plot`/`ax.plot` to produce line plots.\n", + "It turns out that this same function can produce scatter plots as well (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 10, 30)\n", + "y = np.sin(x)\n", + "\n", + "plt.plot(x, y, 'o', color='black');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The third argument in the function call is a character that represents the type of symbol used for the plotting. Just as you can specify options such as `'-'` or `'--'` to control the line style, the marker style has its own set of short string codes. The full list of available symbols can be seen in the documentation of `plt.plot`, or in Matplotlib's [online documentation](https://matplotlib.org/stable/api/_as_gen/matplotlib.markers.MarkerStyle.html). Most of the possibilities are fairly intuitive, and a number of the more common ones are demonstrated here (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.default_rng(0)\n", + "for marker in ['o', '.', ',', 'x', '+', 'v', '^', '<', '>', 's', 'd']:\n", + " plt.plot(rng.random(2), rng.random(2), marker, color='black',\n", + " label=\"marker='{0}'\".format(marker))\n", + "plt.legend(numpoints=1, fontsize=13)\n", + "plt.xlim(0, 1.8);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For even more possibilities, these character codes can be used together with line and color codes to plot points along with a line connecting them (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, y, '-ok');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Additional keyword arguments to `plt.plot` specify a wide range of properties of the lines and markers, as you can see in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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UO++8g1dffRX79u3Dvn37BHNazoMHD/Do0SP28cQmV1JlO+3S3t7u9D82kZZg3quQmZmJyMhI9vHY2Bi++uoryZ656/GUS0VFBQwGA06cOIGbN2/ivffe41RUNDY2Qq1WC24e7ptvvuE8XrJkCaZPn87TaAJj3rx5SExMxP3799lrtbW1eOmll3gcFQmkYCkEsBUSEoLc3FxcuXKFvTbxz1I7c9fjDF2j0bCF+jk5OZx5aYvFgo6ODhw9ehTFxcX4wx/+4P1IfcBgMODWrVuca66Wcomdo8VRs9nM02hIoC1cuBBy+dT/3aVQCGDLtibdek2KZ+56nKEPDw9zWmwqFAqYTCaEhITg6dOn2Lt3L773ve/BbDZj//79yMrKsisZam5u9njgo6Ojbv/9b7/9ltMqNDw8HGaz2atxBJIn92wVEhKCkJAQtsJlZGQEFy5cEHTTIm/uV6z8dc+PHz/mbKyRyWR45ZVXHG4cun37ts9f3xl//5zv37/v0pm7//7v/47Vq1cjMTHRb2Ox8tc9exzQo6OjOf0RLBYLezp4REQE9u/fz24ZXrduHW7fvm0X0K3zep5obm52++9fu3aN8zg3N1dU1R6e3PNEnZ2duHHjBvu4p6dH0DXp3t6vGPnrnv/3f/+X83jJkiWC+XTqr3v25Mzdq1evBuTMXW/ueWJ3TFseT7nk5uayc3E3b95EWloa+7Vvv/0Wu3fvhtlshtFoRG1tLe+BU6fTobOzk3MtNzeXp9Hww/Z+29ra2H4XRLpMJpNdqa6U5skdCdYzdz3O0Ddt2oSrV6+iuLgYDMPg3XffxccffwylUomCggJs27YNO3fuRGhoKLZt22bX0jLQbBdDlUpl0G2Bj4+PR0JCAh48eMBe++abb9i1EH9mJIQ/LS0tnOAUERHBScCkKFjP3PU4oMvlcvzsZz/jXFu8eDH75zfeeANvvPGG5yPzIbPZbFeuJZSPm4GWm5vLCeg3btxAU1MTZDIZduzYgfnz5/M4OuIPtu/9rKwsdnpUqoK1j01QbCxqbW3lzPdPmzZNMhsn3JWVlcXJxPV6Pfr6+qDT6aBWq1FdXQ2GYXgcIfGl4eFhtLa2cq7l5OTwM5gAk+KBNlORdEC37gaz3RmZlZWFsLAwnkbFr2nTpnEONwCkW8JFgFu3bnF+Qc+ZMwfx8fE8jihwgrGPjWQ/d1lPNbdYLHa7IoNtMXQirVbLZmzOSrhKSkqwbds2u+BPxINhGE63QUC8UwmeCrY+NpIL6AzDoLq6GpWVlQ4b2s+bNy9oMpSJPCnhKisrC0gJF/GPhw8f2rW5sO3rI3XW5nTWPjaTZd5S6WMjqSmXoaEhlJaW4vz587BYLOxUwkQZGRlBlaEAwVvCFexsF0MXL17s8GcuZcHWx0YyGbpWq8Xp06eh1+snnUrQ6/WoqanB/Pnzg2oqIVhLuIKZ2Wy2a3MRLIuhtoKpj43oM3R3TzXX6/WiP9XcXRM7Stp2xXRG7CVcway1tRVPnz5lH4eHhwdVEjORq2fuSqGPjagz9GA91dwTwXoUWbCynV5YtmyZ5GvPJ+PozN2hoSH88pe/5FQAffe73xV94iLqDD1YTzX3RDCWcAUjo9GIgYEBtLS0cK4H63TLZGJiYrBo0SLONdspKjESdUCnqQT3WP9TO1scspJCCVew6e7uhkqlglqt5lR4zZo1KyAdBMUmKyuL87ihoUH0m+pEHdCB4NwN5qlgPopMyhiGQVVVFdRqNXQ6HWdXNDD+izyYEhdXZWRkQKFQsI/7+/s5h8CIkegDOk0luC7YSriCgSuluikpKTyNTtjCw8PtmpSJfdpFEqskwbYbzBvBVMIlda6W6paWltKu30lkZWVxDppobGxEYWGhS6c7CZE4R22DphJc52oJ1/Tp00VfwiVVVKrrO2lpaZxPoSMjI7h79y6PI/KOJDJ061RCfX096urqkJ+f7/B5NJXguIQLAD766CPOCejPPPMMzbsKEJXq+lZISAgyMjI4PW8aGho4rcDFRBIBHaCpBG9lZWVxAnpDQwPWrl3L44iII7Tr1/eys7M5Ab2pqQkvv/yyKPsXSWLKBRifSph4aPVkpLAbzB9sjwjs6uqi4+kEiEp1fS85ORlRUVHsY4PBYNdDXiwkk6FbO8lVVVWx15YuXYri4mIeRyUecXFxSEpKwr1799hrjY2NeO6553gcFXGEdv36llwuR1ZWFmpqathrt27dEuU6m2QydIZh0NjYyLnG98HUYuNoowURHirV9b3s7GzO49bWVoyOjvI0Gs9JJqB3dXVhcHCQfRwSEkJlWm7KzMzkfBzv6elBb28vjyMik6Fdv76VkJCAGTNmsI/NZjOnnFEsJBPQbbPJpUuXBu0xc56Kjo62W1+gLF2YqFTXt2QymV2WLsZNRpII6BaLxe6jJ023eMZ22qWxsVH0/S2kiHb9+p5tQL979y4eP34sqtp9SSyKdnR0YHh4mH0cFhaG1NRUHkckXhkZGfjjH//INnfq6+vDw4cPg/LYPqGjUl3fmj17NuLj49Hd3c1eO3bsGCIiIrBjxw7Mnz+fx9G5RhIZuu1iaHp6uihrSIUgIiLC7pchTbsIU3JysksbhKhU13W2n1BHRkag0+mgVqtRXV0t+E+ros/QzWaz3XSL7Q+FuCcrK4vTT7uxsREvvfQS1S8LjEwmw/z58zlb1Tdu3IgNGzbwOCpxs/3Ft2rVKjAMA41Gg/Lycty5c8fucHUhEX1Av3v3LucA4/DwcOou56WlS5ciJCQEJpMJADA4OIh79+5BqVTyPDIy0fDwMLthyIrWjjxnbXYGYNJmZ+3t7SgpKRFsszPRT7nYTgfY9jgm7gsLC7N7s9K0i/A0NzdzpgDmzZuH2bNn8zgicZJSszNRB3STyYTbt29zrtF0i2/YZnpNTU2cU3AI/2gjnff0ej1UKhU0Gg0UCgU2b96MvXv3OpxSsTY727x5MxQKBTQaDVQqFWeGgG+iDuh37tzhnFIUFRVFiz8+smTJEru2onfu3BFcRhKshoaG7Hq5UEB3n9TOJRZ1QLfNUDIzM0XbmF5oQkJCkJ6ezrl26tQpqFQqTldGwg/bQoD4+Hja1u8BqTU7E230M5lM0Gq1nGs03eJbtv+eY2NjoirhkjKabvEdKZ1LLNqA3t3dzfn4P336dCQlJfE4IumZPXs25xOP9bxKs9mM8vJylJaWYmhoiMcRBidr1dFEFNA9J6VmZ6IM6Eaj0WG5lpA++oidVquFSqWCxWJBZGQkiouLUVRUhK1bt2LXrl2IiIhgS7hsPykR/7LNzhMTExEXF8fPYCRCKs3ORFeH3t3djZMnT6Kvr49znTIU3zAajTh37hw0Gg2A8RPjbTdSpKenIzExEV988QXa29tRVlaGvLw8FBYW0g7dAKDpFt/LzMzEl19+yTY7myzzFnqzM9Fk6AzDoKqqCmq12i6Yx8XFISEhgaeRSYfUSrikqL+/Hw8ePOBco4DuPak0OxNFhj40NMRmgwB3O67V8PCwYLfjigWdVyl8ttm5UqnE9OnTeRqNtEih2ZngM3StVouSkhK0t7dPOpc7MDBAc7k+ILUSLimi6Rb/SU5ORmxs7JTPE/J+F48zdIvFgp/+9KfQarUICwvDO++8g4ULF7Jf/+yzz1BWVoaQkBAcOnQI+fn5bn1/msvlB51XKVzWVsYTCXEeV6xkMhkOHz5sd/306dPsQigApKWlCTZx8ThDr6iogMFgwIkTJ3DkyBG899577Nd6e3tx/PhxlJWV4T//8z/xi1/8AgaDweXvTXO5/JFSCZeUGI1G1NfXc64lJycjOjqapxEFD9tPQc3NzTCbzTyNxjmPA7pGo8Hzzz8PYHzuaWLzpvr6eqxcuRJhYWGIiYmBUqm067nijNS244qNVEq4pKK7uxsqlQpXr17lXKfplsBYtGgRp+/86Ogou54nNB4H9OHhYU52oFAo2HartguUUVFRnBOFpkJzufyi8yqFYWJll06ns8sKrVUZxL8UCoXdv7XtWoZQeDyHHh0djZGREfaxxWJBSEiIw6+NjIw4nC5xdqq29ZeFJ3O50dHRojyxeyqjo6MBu6+EhAR0dHSgrq5u0vUPawafkJDgl4wlkPcrFNZ71uv1+Prrr9HT0wPAvrIrLCwMWq3WpROLhE4MP2fb+NXU1ITU1FSPW3X76549Dui5ubm4ePEiXn75Zdy8eRNpaWns15YvX45f/epXGBsbg8FgQFtbG+frVlNlGA0NDejs7ERTU9OUJXQT53JXr17t2U0JXHNzc8CysvDwcPz3f/+3SyVcGzZswKJFi3w+hkDer1A0NzdDLpejoqICer1+0oMW9Ho9KioqBHvQgjvE8HNeunQprl+/jqdPnwIYn9YNDQ31+N/em3ueWK5ty+OAvmnTJly9ehXFxcVgGAbvvvsuPv74YyiVShQUFGDfvn3Ys2cPGIbBW2+95VERfk5ODjo7O1FXVzdlQKe5XN+ylnANDg46fV5ERIRgS7jExmg0QqPRoK2tDQBVdgmJXC5HZmYmbty4wV5ramoS3C9TjwO6XC7Hz372M861xYsXs3/euXMndu7c6fnIIJ3tuGI0WQnXV199hQsXLrCP586dS+sVPqDX63Hs2DHodDooFAoUFBRg3bp1Dv9trZVd165dQ2VlJTQaDTo6OnDgwAFJTMEI1bJlyzgB/fbt2zCZTOxUsxAIemORVLbjSoltZUVHRwd1XPQBquwSPqVSySkEMRgMuHPnDo8jsiecXy2TkMJ2XCmZOXMm4uPj0d3dzV5rbGzEunXreByV+Fkruy5fvoyOjo4ppxitqLIrcKzTLl9//TV7rbGx0e4gGD4JOkMHXN+OGxsbS3O5AWKbpQu1hEtspHTQglTZvve1Wq2gjmUUfIY+2VyuGFbGpWrZsmWoqKhgH3d1dWFgYIB6cntp5syZmD17NnQ6nduVXbRLNzCSkpIQExPDTjMajUa0trYKZu1O8Bk6EZ64uDgsWLCAc42ydN+wfsqkXbrCJJPJ7IK3kN77FNCJR2jaxT+SkpJol67A2Z6129LS4lavKn+igE48YhvQu7u7nQYg4prQ0FCq7BK4xMREzrqeyWRCS0sLjyP6P4KfQyfCFBMTg4ULF3J67TQ2NrIN24jnqLJL2KzTLtXV1ey1xsZGdpMRnxu8KEMnHqNpF/9ITk52KShQZRd/bN/7LS0t+Oijj6BSqex61gcSZejEY9advAzDAAB6enrQ29uLOXPm8DwycTOZTHY15fv37/dLvxzimYSEBMTFxWFgYADAeHNC61nHarXa6U5ff6IMnXgsKirKLshQlu4920W26OhozmlghH8ymQypqamca6tWrUJeXh7MZjPKy8tRWloa8F3UFNCJVxxNu1gzduKZiYfFAOP/xnI5/VcVEq1Wi1u3bgHApGcdt7e3B/ysY3qXEK9kZGRwgo1Op8OjR494HJG4GQwGtLa2cq7ZlskR/hiNRpw9exZlZWUYGxtDSkoKDh48yOm6mJ6ejkOHDiElJQV6vR5lZWU4e/ZsQHaUUkAnXomIiOB02QTsM0ziuvv373NOJpoxYwYSExN5HBGxEsNZxxTQidccTbsYDAZB9bgQi87OTs7jrKwsarolEGLoiEkBnXht6dKlnKO4+vv7UVJSwnsJl9gMDw/bTVfRdItwiOGsYwroxGvh4eF2K/4DAwPQ6XRQq9Worq6mhVIXNDU1cf6d5s6di7lz5/I4ImJL6B0xKaATn0hJSeE8FkIJl9jYrj1Qdi48M2fOhFKphNFoZAO1M4HuiEkBnXhNq9Xiz3/+MwBhlXCJycDAAO7du8e5RgFdmHJycgAIsyMmBXTisYklXHq9XnAlXGJim50vWLAAM2bM4Gk0xJnMzEzBdsSkgE48IoYSLjGh6RbxEPJZx9TLhXjEtoRrqtN1rCVc4eHhOHPmDB1qPEFvby96enrYxzKZzK4UlAiLUDtiUoZOPCKGEi6xsG4ht1q0aBHndHkiPEI965gydOIx6yn1TU1N2LJly5QfK+lQY3sMw9B0iwg5OuvYbDbj3/7t3zhTiYWFhQFNXChDJx4TegmX0BmNRnR2dqK/v5+9JpfL6fBzkVIoFHa/jOvr6wM6BgroxCtCLuESsu7ubqhUKpw4cYJzPT4+ntYWRMz2vd3S0oKnT58G7PUpoBOvCLmES4gYhkFVVRXUajV0Op1dpY9SqeRpZMQXEhISMGvWLPaxxWIJaLM6CujEK0Iu4RKaoaEhlJaW4vz587BYLOxuWiuZTIa4uDj+Bki8NrFYwCqQ0y60KEq8JtQSLiHRarU4ffo09Ho9IiMj8Z3vfIfdgJWamoozZ85Ar9ejsrISsbGxnM1ZRFyWL1+OCxcusI/v378PnU6H2bNn+/21KUMnXnO1hCsqKiroDjV2dzetwWCg3bQi56hU0ZU1Jl+gDJ14zVEJFwCcOnWKU2OdkpISVLXner0ex44dg06ng0KhcHpwsHU37bVr11BZWQmNRoOOjg4cOHAAERERPIyeeGPFihXsngtgfNrlxRdfpPa5RLysFTBWzc3NGB0d5WcwPBDDgQjEPzIyMhAS8n/58pMnTzgB3l8ooBO/WbRoEWcqxmQyBdXxdLSbNnhNLBawCsTiKAV04jeOVvyttejBQugHIhD/sf35NTU1wWAw+PU1KaATv7Kddrl//z56e3v5GQwPaDdt8LLtyWMwGHD79m2/viYFdOJXM2bMsFvx/+abb/gZDE9oN21wksvlWL58Oeeav6ddKKATv7NtrVtfXw+z2czTaAKPdtMGL9tfzO3t7ejr64PJZPLL61FAJ36XkZHB2R06MjKCO3fu8DiiwKLdtMFr7ty5mD9/PvuYYRgcO3YMFRUVePjwoc9fz6M69NHRUbz99tvo6+tDVFQU3n//fbv5vkOHDqG/vx+hoaGYNm0a1Gq1TwZMxCc0NBTLli1DbW0te+3mzZtBtRuSdtMGr+XLl3OCt7VZl1qtdro3wRMeZeiffvop0tLS8Mknn2D79u344IMP7J7T0dGBTz/9FMePH6dgTuymXVpaWjAyMsLTaAJPqVS69J82MjIy6HbTSt2iRYs4j609fMxmM8rLy1FaWoqhoSGfvJZHGbpGo8Ebb7wBAHjhhRfsArpOp8OTJ09w8OBBPHnyBH/1V3+F/Px870dLRCsxMRGzZ8+GTqcDMN6Frr6+HuvXr+d5ZIHR3t4OhmHYxwqFAkeOHLHbBdrc3Ey15xJi7eEDYNIePu3t7SgpKcG2bdu8/tQ6ZUD//PPP8bvf/Y5zbdasWexhwFFRUXa/XYxGIw4cOID9+/djcHAQu3fvxvLlyzltJYHxN6+nRkdHvfr7YiT2e05ISGADOgDU1NQgNjZ20gAm9vud6MqVK5zHCxYscLhzUEr37Cop3rPJZEJdXR3a2toAjLe92L59O+cQ9fT0dCQmJuKLL75Ae3s7ysrKsHjxYqxYsYKzy9QdU/6t119/Ha+//jrn2g9/+EP24/LIyAimT5/O+frs2bNRXFyMkJAQzJo1CxkZGbh7965dQPfmZJbm5uagO9lF7PeclJSEW7dusZnq4OAgoqOjER8fj9DQULvni/1+rQYHB9Hd3c25VlBQgKSkJLvnSuWe3SG1e/amh09bWxsGBwed9vDRaDSTvrZHc+i5ubm4dOkSAODy5cucns4AUFVVhTfffBPAeMBvbW1FSkqKJy9FJCQ6OhpLlizhXPv000+hUqn8suIvFLW1tZzplnnz5mHBggU8joj4E589fDwK6Lt370Zrayt2796NEydO4Ic//CEA4F/+5V9QX1+PDRs2IDk5GTt37sT3v/99/O3f/i3teiMA7HeOjo6OQqfTQa1Wo7q6mhP4pMBsNnOqe4DxRTGaJ5cuPnv4eDRRExERgV//+td21//u7/6O/fM//MM/eDQgIm3x8fGQy+WwWCwAxoMbwzDQaDQoLy/HnTt37OYaxUyr1WJ4eJh9HBYWhuzsbB5HRAJhxYoVuHz5MpqamrBly5Yp9xX4qocP9UMnAWNd8bdYLC6t+EuB7XxndnY2bRoKAtYePp2dnWhqarIr27Xlqx4+FNCJ3xmNRpw7d44Nbu6s+KempjpcMBWDvr4+tLe3c66tWrWKp9GQQMvJyUFnZyfq6uqmDOi+6uFDW/+JX+n1eqhUKmg0GigUCmzevBl79+51OKViXfHfvHkzFAoF2traoFKpoNfreRi592yz8wULFnC2gRNp46OHDwV04lfBeGqP0WiEXq+36/1uWw1GpI2PHj405UL8yrrif/nyZXR0dEz50dNKrKf2dHd349SpUxgbG+N8sggPD8eyZct4HBnhQ6B7+FCGTvwuGE7tYRgGVVVVUKvV0Ol0drunc3JyRLsWQDyXnJzMOYZxMrGxsT7p4UMZOvE7T1f858yZI4r9C0NDQ+xiLsAtxbRKT0/na3iERzKZDIcPH7a77q/dsZShk4Dw5NQeMXQd1Gq1KCkpQXt7OyIjI1FcXIyioiJs3boVu3btYrdvnzhxAlqtlufREqmjgE4CwpMVfyFvjzcajTh79izKysqg1+uRkpKCgwcPcrrlpaen49ChQ0hJSYFer0dZWRnOnj3LLhIT4msU0ElAuLvin5GRIdg5Z29KMTUajahLMYmw0Rw6CRh3VvyFPHduW4o51ZqAtRQzPDwcZ86cEWUpJhEHytBJwLi64g+ML4wKtVEXn82XCHGGMnQSMJOt+ANAb28v5+SrR48e4cGDB17vnPMXvpovEeIMZehEEObMmWO38aaxsVGwWbq1FNNoNLKB2hlfNV8ixBkK6EQwXnjhBc7jgYEBQZf6eVKKSdk58ScK6EQw5s6dazfFcunSJcFm6Xw0XyLEGQroRFBss/SHDx+ipaWFp9E4N23aNKSmpgIIXPMlQpyhRVEiKPPmzUNGRgbnFPhLly4hLS0NJpMJAARVn27tTROo5kuEOEMBnQjOhg0bOAG9u7sbNTU1bG+UHTt2CKKveFdXl90BFpPxVfMlQpyhgE4Ex1GWfu7cOfbParUaBQUFWLduHW/13AzDcMYEjK8B/PVf/zXkcprJJPygdx4RJNu5dGC8i2FeXh7MZjPKy8tRWlpq16Y2UBoaGtDV1cW5VlhYSMGc8IoydCJIg4ODkMvlLh8oPbEplr8ZjUZUVFRwri1duhQpKSkBGwMhjlBAJ4Li6YHSeXl5KCws9NuCqbV3S2hoKKqqqvDkyRP2a3K5HJs2bfLL6xLiDgroRDD0ej2OHTsGnU4HhULhdJ7c2sXw2rVrqKyshEajQUdHBw4cOMD2IPcV67FywPi0ytWrVzlfX7t2LWbNmuXT1yTEExTQiWAIrYshwzCorq5GZWUlLBYLAOCTTz7hbHSKjIx0ON9PCB9oBYcIhpC6GA4NDaG0tBTnz5+HxWJhF2Rtd63m5+dTK1wiGJShE0ERQhdDrVaL06dPQ6/XT7ogq9frIZPJEBUV5ZPXJMQXKEMngsJnF0N3j5VjGAafffYZHStHBIMCOhEcProY0rFyRAoooBPBcbeLoVwuZ88rBcYzbXczZtsF2fXr1zudj7cuyBYVFbGvSXPphG8U0InguHugtMViQW1tLYDxEkOVSgWVSoWHDx+6/JpCWpAlxFO0KEoEyZ0DpQHg/Pnz6OnpQUNDA1ti6ErPl4kbhoSwIEuINyhDJ4KUnJyMyMhIt/5OfX09p8Rwqp4vttk8HStHxI4ydCJIMpkMW7du5cyN22pra8Pvf/97tjbc1Z4vjjYMWbP5uXPnorOzE3V1dVNubKJj5YjQUEAnomQ0GtHc3MwGc1d7vmRnZ2N4eBh3794FMN7BkWEYaDQalJeXs3/XuiA7WeZNx8oRIaKATkTH054vFRUVuHXrFoDJs/mJpYd1dXXIz893OAY6Vo4IEQV0Ijru9nwxmUzo6+tjp1dcyeYBOlaOiI9Xi6Lnz5/HkSNHHH7ts88+w6uvvoqdO3fi4sWL3rwMIRzulBh6smHI1Va4dKwcERqPM/R33nkHV65ccbho1dvbi+PHj+PkyZMYGxvDnj178OyzzyIsLMyrwRJi5WqJoScdHJ955hlERETgzJkziI2NxZtvvkk15kQUPM7Qc3Nz8dOf/tTh1+rr67Fy5UqEhYUhJiYGSqUSt2/f9vSlCLHjaokhbRgiwWTKDP3zzz/H7373O861d999Fy+//DJqamoc/p3h4WHOR9qoqCgMDw/bPW/iIcDuGh0d9ervi1Gw3fNU9+tqiaE3G4aio6MD+m8ebD9jgO7Zl6YM6K+//jpef/11t75pdHQ0RkZG2McjIyMO5yyd1RhPpbm52au/L0bBds9T3W9KSgrq6uqmLDG0smbzU027TNwwtHr1ao/G7qlg+xkDdM/ush7P6IhfdoouX74cGo0GY2NjGBoaQltbG9LS0vzxUiSIudvzZarnWdGGISJWPi1b/Pjjj6FUKlFQUIB9+/Zhz549YBgGb731FtXqEr9wp+dLSEgIbRgikuZVQF+7di3Wrl3LPv7e977H/nnnzp3YuXOnN9+ekCklJycjNjYWg4ODTp8XGxuLhQsXor6+njYMEcmijUVE1GQyGQ4fPuzSc+/evetyNk/TLUSMqNsiCRrWbH4qtGGIiBVl6CRouJPNEyJGlKETQohEUEAnhBCJoIBOCCESQQGdEEIkggI6IYRIBAV0QgiRCArohBAiERTQCSFEIiigE0KIRFBAJ4QQiZAxDMPw8cLOmrQTQgiZXF5ensPrvAV0QgghvkVTLoQQIhEU0AkhRCJEFdAtFguOHj2KXbt2Yd++fejo6OB7SH5nNBrx9ttvY8+ePXjttddQWVnJ95ACpq+vDxs2bEBbWxvfQwmIjz76CLt27cKrr76Kzz//nO/h+J3RaMSRI0dQXFyMPXv2SP7nXFdXh3379gEAOjo6sHv3buzZswf//M//DIvF4pPXEFVAr6iogMFgwIkTJ3DkyBG89957fA/J786cOYO4uDh88sknUKvV+H//7//xPaSAMBqNOHr0KMLDw/keSkDU1NTgm2++waefforjx4/j4cOHfA/J7y5dugSTyYSysjL84Ac/wK9+9Su+h+Q3v/3tb/GP//iPGBsbAwD8/Oc/x+HDh/HJJ5+AYRifJWqiCugajQbPP/88gPHDgRsaGngekf/9xV/8Bd58800AAMMwUCgUPI8oMN5//30UFxdj7ty5fA8lIK5cuYK0tDT84Ac/wMGDB7Fx40a+h+R3ixYtgtlshsViwfDwMEJCpHvejlKpxG9+8xv2cWNjI9asWQMAeOGFF1BVVeWT1xHVv+Dw8DCio6PZxwqFAiaTSdJvhKioKADj9/6jH/0oKE7cOXXqFGbOnInnn38eKpWK7+EERH9/Px48eIAPP/wQXV1dOHToEP70pz9BJpPxPTS/iYyMxP3797Flyxb09/fjww8/5HtIflNYWIiuri72McMw7M82KioKQ0NDPnkdUWXo0dHRGBkZYR9bLBZJB3Or7u5u7N+/H9u2bcMrr7zC93D87uTJk6iqqsK+ffvQ3NyMH//4x+jt7eV7WH4VFxeH5557DmFhYUhJScG0adPw+PFjvoflV//1X/+F5557DufOncPp06fxk5/8hJ2SkDq5/P9C78jICKZPn+6b7+uT7xIgubm57GntN2/eRFpaGs8j8j+dTocDBw7g7bffxmuvvcb3cALi97//PUpLS3H8+HFkZGTg/fffx5w5c/gell/l5eXhq6++AsMw6OnpgV6vR1xcHN/D8qvp06cjJiYGwPjB3CaTCWazmedRBUZmZiZqamoAAJcvX8aqVat88n1Fld5u2rQJV69eRXFxMRiGwbvvvsv3kPzuww8/xJMnT/DBBx/ggw8+ADC+wBIsi4XBIj8/H9evX8drr70GhmFw9OhRya+X/OVf/iX+/u//Hnv27IHRaMRbb72FyMhIvocVED/+8Y/xT//0T/jFL36BlJQUFBYW+uT70k5RQgiRCFFNuRBCCJkcBXRCCJEICuiEECIRFNAJIUQiKKATQohEUEAnhBCJoIBOCCESQQGdEEIk4v8DwlouNzIDz/kAAAAASUVORK5CYII=", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, y, '-p', color='gray',\n", + " markersize=15, linewidth=4,\n", + " markerfacecolor='white',\n", + " markeredgecolor='gray',\n", + " markeredgewidth=2)\n", + "plt.ylim(-1.2, 1.2);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These kinds of options make `plt.plot` the primary workhorse for two-dimensional plots in Matplotlib.\n", + "For a full description of the options available, refer to the [`plt.plot` documentation](https://matplotlib.org/3.5.0/api/_as_gen/matplotlib.pyplot.plot.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Scatter Plots with plt.scatter\n", + "\n", + "A second, more powerful method of creating scatter plots is the `plt.scatter` function, which can be used very similarly to the `plt.plot` function (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x, y, marker='o');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The primary difference of `plt.scatter` from `plt.plot` is that it can be used to create scatter plots where the properties of each individual point (size, face color, edge color, etc.) can be individually controlled or mapped to data.\n", + "\n", + "Let's show this by creating a random scatter plot with points of many colors and sizes.\n", + "In order to better see the overlapping results, we'll also use the `alpha` keyword to adjust the transparency level (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.default_rng(0)\n", + "x = rng.normal(size=100)\n", + "y = rng.normal(size=100)\n", + "colors = rng.random(100)\n", + "sizes = 1000 * rng.random(100)\n", + "\n", + "plt.scatter(x, y, c=colors, s=sizes, alpha=0.3)\n", + "plt.colorbar(); # show color scale" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the color argument is automatically mapped to a color scale (shown here by the `colorbar` command), and that the size argument is given in pixels.\n", + "In this way, the color and size of points can be used to convey information in the visualization, in order to visualize multidimensional data.\n", + "\n", + "For example, we might use the Iris dataset from Scikit-Learn, where each sample is one of three types of flowers that has had the size of its petals and sepals carefully measured (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import load_iris\n", + "iris = load_iris()\n", + "features = iris.data.T\n", + "\n", + "plt.scatter(features[0], features[1], alpha=0.4,\n", + " s=100*features[3], c=iris.target, cmap='viridis')\n", + "plt.xlabel(iris.feature_names[0])\n", + "plt.ylabel(iris.feature_names[1]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A full-color version of this plot is available in the [online version](http://github.com/jakevdp/PythonDataScienceHandbook) of the book.\n", + "\n", + "We can see that this scatter plot has given us the ability to simultaneously explore four different dimensions of the data:\n", + "the (*x*, *y*) location of each point corresponds to the sepal length and width, the size of the point is related to the petal width, and the color is related to the particular species of flower.\n", + "Multicolor and multifeature scatter plots like this can be useful for both exploration and presentation of data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## plot Versus scatter: A Note on Efficiency\n", + "\n", + "Aside from the different features available in `plt.plot` and `plt.scatter`, why might you choose to use one over the other? While it doesn't matter as much for small amounts of data, as datasets get larger than a few thousand points, `plt.plot` can be noticeably more efficient than `plt.scatter`.\n", + "The reason is that `plt.scatter` has the capability to render a different size and/or color for each point, so the renderer must do the extra work of constructing each point individually.\n", + "With `plt.plot`, on the other hand, the markers for each point are guaranteed to be identical, so the work of determining the appearance of the points is done only once for the entire set of data.\n", + "For large datasets, this difference can lead to vastly different performance, and for this reason, `plt.plot` should be preferred over `plt.scatter` for large datasets." + ] + } + ], + "metadata": { + "jupytext": { + "encoding": "# -*- coding: utf-8 -*-", + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.03-Errorbars.ipynb b/notebooks/04.03-Errorbars.ipynb new file mode 100644 index 000000000..8c92f56fc --- /dev/null +++ b/notebooks/04.03-Errorbars.ipynb @@ -0,0 +1,239 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Visualizing Uncertainties" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For any scientific measurement, accurate accounting of uncertainties is nearly as important, if not more so, as accurate reporting of the number itself.\n", + "For example, imagine that I am using some astrophysical observations to estimate the Hubble Constant, the local measurement of the expansion rate of the Universe.\n", + "I know that the current literature suggests a value of around 70 (km/s)/Mpc, and I measure a value of 74 (km/s)/Mpc with my method. Are the values consistent? The only correct answer, given this information, is this: there is no way to know.\n", + "\n", + "Suppose I augment this information with reported uncertainties: the current literature suggests a value of 70 ± 2.5 (km/s)/Mpc, and my method has measured a value of 74 ± 5 (km/s)/Mpc. Now are the values consistent? That is a question that can be quantitatively answered.\n", + "\n", + "In visualization of data and results, showing these errors effectively can make a plot convey much more complete information." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Basic Errorbars\n", + "\n", + "One standard way to visualize uncertainties is using an errorbar. A basic errorbar can be created with a single Matplotlib function call, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 10, 50)\n", + "dy = 0.8\n", + "y = np.sin(x) + dy * np.random.randn(50)\n", + "\n", + "plt.errorbar(x, y, yerr=dy, fmt='.k');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the `fmt` is a format code controlling the appearance of lines and points, and it has the same syntax as the shorthand used in `plt.plot`, outlined in the previous chapter and earlier in this chapter.\n", + "\n", + "In addition to these basic options, the `errorbar` function has many options to fine-tune the outputs.\n", + "Using these additional options you can easily customize the aesthetics of your errorbar plot.\n", + "I often find it helpful, especially in crowded plots, to make the errorbars lighter than the points themselves (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.errorbar(x, y, yerr=dy, fmt='o', color='black',\n", + " ecolor='lightgray', elinewidth=3, capsize=0);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition to these options, you can also specify horizontal errorbars, one-sided errorbars, and many other variants.\n", + "For more information on the options available, refer to the docstring of `plt.errorbar`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Continuous Errors\n", + "\n", + "In some situations it is desirable to show errorbars on continuous quantities.\n", + "Though Matplotlib does not have a built-in convenience routine for this type of application, it's relatively easy to combine primitives like `plt.plot` and `plt.fill_between` for a useful result.\n", + "\n", + "Here we'll perform a simple *Gaussian process regression*, using the Scikit-Learn API (see [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) for details).\n", + "This is a method of fitting a very flexible nonparametric function to data with a continuous measure of the uncertainty.\n", + "We won't delve into the details of Gaussian process regression at this point, but will focus instead on how you might visualize such a continuous error measurement:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.gaussian_process import GaussianProcessRegressor\n", + "\n", + "# define the model and draw some data\n", + "model = lambda x: x * np.sin(x)\n", + "xdata = np.array([1, 3, 5, 6, 8])\n", + "ydata = model(xdata)\n", + "\n", + "# Compute the Gaussian process fit\n", + "gp = GaussianProcessRegressor()\n", + "gp.fit(xdata[:, np.newaxis], ydata)\n", + "\n", + "xfit = np.linspace(0, 10, 1000)\n", + "yfit, dyfit = gp.predict(xfit[:, np.newaxis], return_std=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have `xfit`, `yfit`, and `dyfit`, which sample the continuous fit to our data.\n", + "We could pass these to the `plt.errorbar` function as in the previous section, but we don't really want to plot 1,000 points with 1,000 errorbars.\n", + "Instead, we can use the `plt.fill_between` function with a light color to visualize this continuous error (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Visualize the result\n", + "plt.plot(xdata, ydata, 'or')\n", + "plt.plot(xfit, yfit, '-', color='gray')\n", + "plt.fill_between(xfit, yfit - dyfit, yfit + dyfit,\n", + " color='gray', alpha=0.2)\n", + "plt.xlim(0, 10);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Take a look at the `fill_between` call signature: we pass an x value, then the lower *y*-bound, then the upper *y*-bound, and the result is that the area between these regions is filled.\n", + "\n", + "The resulting figure gives an intuitive view into what the Gaussian process regression algorithm is doing: in regions near a measured data point, the model is strongly constrained, and this is reflected in the small model uncertainties.\n", + "In regions far from a measured data point, the model is not strongly constrained, and the model uncertainties increase.\n", + "\n", + "For more information on the options available in `plt.fill_between` (and the closely related `plt.fill` function), see the function docstring or the Matplotlib documentation.\n", + "\n", + "Finally, if this seems a bit too low-level for your taste, refer to [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb), where we discuss the Seaborn package, which has a more streamlined API for visualizing this type of continuous errorbar." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.04-Density-and-Contour-Plots.ipynb b/notebooks/04.04-Density-and-Contour-Plots.ipynb new file mode 100644 index 000000000..ec5e37d1e --- /dev/null +++ b/notebooks/04.04-Density-and-Contour-Plots.ipynb @@ -0,0 +1,321 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Density and Contour Plots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes it is useful to display three-dimensional data in two dimensions using contours or color-coded regions.\n", + "There are three Matplotlib functions that can be helpful for this task: `plt.contour` for contour plots, `plt.contourf` for filled contour plots, and `plt.imshow` for showing images.\n", + "This chapter looks at several examples of using these. We'll start by setting up the notebook for plotting and importing the functions we will use: " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-white')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Visualizing a Three-Dimensional Function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our first example demonstrates a contour plot using a function $z = f(x, y)$, using the following particular choice for $f$ (we've seen this before in [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb), when we used it as a motivating example for array broadcasting):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def f(x, y):\n", + " return np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A contour plot can be created with the `plt.contour` function.\n", + "It takes three arguments: a grid of *x* values, a grid of *y* values, and a grid of *z* values.\n", + "The *x* and *y* values represent positions on the plot, and the *z* values will be represented by the contour levels.\n", + "Perhaps the most straightforward way to prepare such data is to use the `np.meshgrid` function, which builds two-dimensional grids from one-dimensional arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "x = np.linspace(0, 5, 50)\n", + "y = np.linspace(0, 5, 40)\n", + "\n", + "X, Y = np.meshgrid(x, y)\n", + "Z = f(X, Y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's look at this with a standard line-only contour plot (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.contour(X, Y, Z, colors='black');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that when a single color is used, negative values are represented by dashed lines and positive values by solid lines.\n", + "Alternatively, the lines can be color-coded by specifying a colormap with the `cmap` argument.\n", + "Here we'll also specify that we want more lines to be drawn, at 20 equally spaced intervals within the data range, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.contour(X, Y, Z, 20, cmap='RdGy');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we chose the `RdGy` (short for *Red–Gray*) colormap, which is a good choice for divergent data: (i.e., data with positive and negative variation around zero).\n", + "Matplotlib has a wide range of colormaps available, which you can easily browse in IPython by doing a tab completion on the `plt.cm` module:\n", + "```\n", + "plt.cm.\n", + "```\n", + "\n", + "Our plot is looking nicer, but the spaces between the lines may be a bit distracting.\n", + "We can change this by switching to a filled contour plot using the `plt.contourf` function, which uses largely the same syntax as `plt.contour`.\n", + "\n", + "Additionally, we'll add a `plt.colorbar` command, which creates an additional axis with labeled color information for the plot (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.contourf(X, Y, Z, 20, cmap='RdGy')\n", + "plt.colorbar();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The colorbar makes it clear that the black regions are \"peaks,\" while the red regions are \"valleys.\"\n", + "\n", + "One potential issue with this plot is that it is a bit splotchy: the color steps are discrete rather than continuous, which is not always what is desired.\n", + "This could be remedied by setting the number of contours to a very high number, but this results in a rather inefficient plot: Matplotlib must render a new polygon for each step in the level.\n", + "A better way to generate a smooth representation is to use the `plt.imshow` function, which offers the `interpolation` argument to generate a smooth two-dimensional representation of the data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(Z, extent=[0, 5, 0, 5], origin='lower', cmap='RdGy',\n", + " interpolation='gaussian', aspect='equal')\n", + "plt.colorbar();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a few potential gotchas with `plt.imshow`, however:\n", + "\n", + "- It doesn't accept an *x* and *y* grid, so you must manually specify the *extent* [*xmin*, *xmax*, *ymin*, *ymax*] of the image on the plot.\n", + "- By default it follows the standard image array definition where the origin is in the upper left, not in the lower left as in most contour plots. This must be changed when showing gridded data.\n", + "- It will automatically adjust the axis aspect ratio to match the input data; this can be changed with the `aspect` argument." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, it can sometimes be useful to combine contour plots and image plots.\n", + "For example, here we'll use a partially transparent background image (with transparency set via the `alpha` parameter) and overplot contours with labels on the contours themselves, using the `plt.clabel` function (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "contours = plt.contour(X, Y, Z, 3, colors='black')\n", + "plt.clabel(contours, inline=True, fontsize=8)\n", + "\n", + "plt.imshow(Z, extent=[0, 5, 0, 5], origin='lower',\n", + " cmap='RdGy', alpha=0.5)\n", + "plt.colorbar();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The combination of these three functions—`plt.contour`, `plt.contourf`, and `plt.imshow`—gives nearly limitless possibilities for displaying this sort of three-dimensional data within a two-dimensional plot.\n", + "For more information on the options available in these functions, refer to their docstrings.\n", + "If you are interested in three-dimensional visualizations of this type of data, see [Three-dimensional Plotting in Matplotlib](04.12-Three-Dimensional-Plotting.ipynb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "encoding": "# -*- coding: utf-8 -*-", + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.05-Histograms-and-Binnings.ipynb b/notebooks/04.05-Histograms-and-Binnings.ipynb new file mode 100644 index 000000000..c3c611c40 --- /dev/null +++ b/notebooks/04.05-Histograms-and-Binnings.ipynb @@ -0,0 +1,404 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Histograms, Binnings, and Density" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A simple histogram can be a great first step in understanding a dataset.\n", + "Earlier, we saw a preview of Matplotlib's histogram function (discussed in [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb)), which creates a basic histogram in one line, once the normal boilerplate imports are done (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-white')\n", + "\n", + "rng = np.random.default_rng(1701)\n", + "data = rng.normal(size=1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(data);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `hist` function has many options to tune both the calculation and the display; \n", + "here's an example of a more customized histogram, shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(data, bins=30, density=True, alpha=0.5,\n", + " histtype='stepfilled', color='steelblue',\n", + " edgecolor='none');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `plt.hist` docstring has more information on other available customization options.\n", + "I find this combination of `histtype='stepfilled'` along with some transparency `alpha` to be helpful when comparing histograms of several distributions (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x1 = rng.normal(0, 0.8, 1000)\n", + "x2 = rng.normal(-2, 1, 1000)\n", + "x3 = rng.normal(3, 2, 1000)\n", + "\n", + "kwargs = dict(histtype='stepfilled', alpha=0.3, density=True, bins=40)\n", + "\n", + "plt.hist(x1, **kwargs)\n", + "plt.hist(x2, **kwargs)\n", + "plt.hist(x3, **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are interested in computing, but not displaying, the histogram (that is, counting the number of points in a given bin), you can use the `np.histogram` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 23 241 491 224 21]\n" + ] + } + ], + "source": [ + "counts, bin_edges = np.histogram(data, bins=5)\n", + "print(counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Two-Dimensional Histograms and Binnings\n", + "\n", + "Just as we create histograms in one dimension by dividing the number line into bins, we can also create histograms in two dimensions by dividing points among two-dimensional bins.\n", + "We'll take a brief look at several ways to do this here.\n", + "We'll start by defining some data—an `x` and `y` array drawn from a multivariate Gaussian distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "mean = [0, 0]\n", + "cov = [[1, 1], [1, 2]]\n", + "x, y = rng.multivariate_normal(mean, cov, 10000).T" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### plt.hist2d: Two-dimensional histogram\n", + "\n", + "One straightforward way to plot a two-dimensional histogram is to use Matplotlib's `plt.hist2d` function (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist2d(x, y, bins=30)\n", + "cb = plt.colorbar()\n", + "cb.set_label('counts in bin')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just like `plt.hist`, `plt.hist2d` has a number of extra options to fine-tune the plot and the binning, which are nicely outlined in the function docstring.\n", + "Further, just as `plt.hist` has a counterpart in `np.histogram`, `plt.hist2d` has a counterpart in `np.histogram2d`:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(30, 30)\n" + ] + } + ], + "source": [ + "counts, xedges, yedges = np.histogram2d(x, y, bins=30)\n", + "print(counts.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the generalization of this histogram binning when there are more than two dimensions, see the `np.histogramdd` function." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### plt.hexbin: Hexagonal binnings\n", + "\n", + "The two-dimensional histogram creates a tesselation of squares across the axes.\n", + "Another natural shape for such a tesselation is the regular hexagon.\n", + "For this purpose, Matplotlib provides the `plt.hexbin` routine, which represents a two-dimensional dataset binned within a grid of hexagons (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hexbin(x, y, gridsize=30)\n", + "cb = plt.colorbar(label='count in bin')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`plt.hexbin` has a number of additional options, including the ability to specify weights for each point and to change the output in each bin to any NumPy aggregate (mean of weights, standard deviation of weights, etc.)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Kernel density estimation\n", + "\n", + "Another common method for estimating and representing densities in multiple dimensions is *kernel density estimation* (KDE).\n", + "This will be discussed more fully in [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb), but for now I'll simply mention that KDE can be thought of as a way to \"smear out\" the points in space and add up the result to obtain a smooth function.\n", + "One extremely quick and simple KDE implementation exists in the `scipy.stats` package.\n", + "Here is a quick example of using KDE (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from scipy.stats import gaussian_kde\n", + "\n", + "# fit an array of size [Ndim, Nsamples]\n", + "data = np.vstack([x, y])\n", + "kde = gaussian_kde(data)\n", + "\n", + "# evaluate on a regular grid\n", + "xgrid = np.linspace(-3.5, 3.5, 40)\n", + "ygrid = np.linspace(-6, 6, 40)\n", + "Xgrid, Ygrid = np.meshgrid(xgrid, ygrid)\n", + "Z = kde.evaluate(np.vstack([Xgrid.ravel(), Ygrid.ravel()]))\n", + "\n", + "# Plot the result as an image\n", + "plt.imshow(Z.reshape(Xgrid.shape),\n", + " origin='lower', aspect='auto',\n", + " extent=[-3.5, 3.5, -6, 6])\n", + "cb = plt.colorbar()\n", + "cb.set_label(\"density\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "KDE has a smoothing length that effectively slides the knob between detail and smoothness (one example of the ubiquitous bias–variance trade-off).\n", + "The literature on choosing an appropriate smoothing length is vast; `gaussian_kde` uses a rule of thumb to attempt to find a nearly optimal smoothing length for the input data.\n", + "\n", + "Other KDE implementations are available within the SciPy ecosystem, each with its own strengths and weaknesses; see, for example, `sklearn.neighbors.KernelDensity` and `statsmodels.nonparametric.KDEMultivariate`.\n", + "For visualizations based on KDE, using Matplotlib tends to be overly verbose.\n", + "The Seaborn library, discussed in [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb), provides a much more compact API for creating KDE-based visualizations." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "encoding": "# -*- coding: utf-8 -*-", + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.06-Customizing-Legends.ipynb b/notebooks/04.06-Customizing-Legends.ipynb new file mode 100644 index 000000000..4f0ddad24 --- /dev/null +++ b/notebooks/04.06-Customizing-Legends.ipynb @@ -0,0 +1,452 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Customizing Plot Legends" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot legends give meaning to a visualization, assigning meaning to the various plot elements.\n", + "We previously saw how to create a simple legend; here we'll take a look at customizing the placement and aesthetics of the legend in Matplotlib.\n", + "\n", + "The simplest legend can be created with the `plt.legend` command, which automatically creates a legend for any labeled plot elements (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 10, 1000)\n", + "fig, ax = plt.subplots()\n", + "ax.plot(x, np.sin(x), '-b', label='Sine')\n", + "ax.plot(x, np.cos(x), '--r', label='Cosine')\n", + "ax.axis('equal')\n", + "leg = ax.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But there are many ways we might want to customize such a legend.\n", + "For example, we can specify the location and turn on the frame (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.legend(loc='upper left', frameon=True)\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use the ``ncol`` command to specify the number of columns in the legend, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.legend(loc='lower center', ncol=2)\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can use a rounded box (`fancybox`) or add a shadow, change the transparency (alpha value) of the frame, or change the padding around the text (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.legend(frameon=True, fancybox=True, framealpha=1,\n", + " shadow=True, borderpad=1)\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on available legend options, see the `plt.legend` docstring." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choosing Elements for the Legend\n", + "\n", + "As we have already seen, by default the legend includes all labeled elements from the plot.\n", + "If this is not what is desired, we can fine-tune which elements and labels appear in the legend by using the objects returned by `plot` commands.\n", + "`plt.plot` is able to create multiple lines at once, and returns a list of created line instances.\n", + "Passing any of these to `plt.legend` will tell it which to identify, along with the labels we'd like to specify (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "y = np.sin(x[:, np.newaxis] + np.pi * np.arange(0, 2, 0.5))\n", + "lines = plt.plot(x, y)\n", + "\n", + "# lines is a list of plt.Line2D instances\n", + "plt.legend(lines[:2], ['first', 'second'], frameon=True);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I generally find in practice that it is clearer to use the first method, applying labels to the plot elements you'd like to show on the legend (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, y[:, 0], label='first')\n", + "plt.plot(x, y[:, 1], label='second')\n", + "plt.plot(x, y[:, 2:])\n", + "plt.legend(frameon=True);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the legend ignores all elements without a `label` attribute set." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Legend for Size of Points\n", + "\n", + "Sometimes the legend defaults are not sufficient for the given visualization.\n", + "For example, perhaps you're using the size of points to mark certain features of the data, and want to create a legend reflecting this.\n", + "Here is an example where we'll use the size of points to indicate populations of California cities.\n", + "We'd like a legend that specifies the scale of the sizes of the points, and we'll accomplish this by plotting some labeled data with no entries (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# Uncomment to download the data\n", + "# url = ('https://raw.githubusercontent.com/jakevdp/PythonDataScienceHandbook/'\n", + "# 'master/notebooks/data/california_cities.csv')\n", + "# !cd data && curl -O {url}" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import pandas as pd\n", + "cities = pd.read_csv('data/california_cities.csv')\n", + "\n", + "# Extract the data we're interested in\n", + "lat, lon = cities['latd'], cities['longd']\n", + "population, area = cities['population_total'], cities['area_total_km2']\n", + "\n", + "# Scatter the points, using size and color but no label\n", + "plt.scatter(lon, lat, label=None,\n", + " c=np.log10(population), cmap='viridis',\n", + " s=area, linewidth=0, alpha=0.5)\n", + "plt.axis('equal')\n", + "plt.xlabel('longitude')\n", + "plt.ylabel('latitude')\n", + "plt.colorbar(label='log$_{10}$(population)')\n", + "plt.clim(3, 7)\n", + "\n", + "# Here we create a legend:\n", + "# we'll plot empty lists with the desired size and label\n", + "for area in [100, 300, 500]:\n", + " plt.scatter([], [], c='k', alpha=0.3, s=area,\n", + " label=str(area) + ' km$^2$')\n", + "plt.legend(scatterpoints=1, frameon=False, labelspacing=1, title='City Area')\n", + "\n", + "plt.title('California Cities: Area and Population');" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The legend will always reference some object that is on the plot, so if we'd like to display a particular shape we need to plot it.\n", + "In this case, the objects we want (gray circles) are not on the plot, so we fake them by plotting empty lists.\n", + "Recall that the legend only lists plot elements that have a label specified.\n", + "\n", + "By plotting empty lists, we create labeled plot objects that are picked up by the legend, and now our legend tells us some useful information.\n", + "This strategy can be useful for creating more sophisticated visualizations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multiple Legends\n", + "\n", + "Sometimes when designing a plot you'd like to add multiple legends to the same axes.\n", + "Unfortunately, Matplotlib does not make this easy: via the standard `legend` interface, it is only possible to create a single legend for the entire plot.\n", + "If you try to create a second legend using `plt.legend` or `ax.legend`, it will simply override the first one.\n", + "We can work around this by creating a new legend artist from scratch (`Artist` is the base class Matplotlib uses for visual attributes), and then using the lower-level `ax.add_artist` method to manually add the second artist to the plot (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "lines = []\n", + "styles = ['-', '--', '-.', ':']\n", + "x = np.linspace(0, 10, 1000)\n", + "\n", + "for i in range(4):\n", + " lines += ax.plot(x, np.sin(x - i * np.pi / 2),\n", + " styles[i], color='black')\n", + "ax.axis('equal')\n", + "\n", + "# Specify the lines and labels of the first legend\n", + "ax.legend(lines[:2], ['line A', 'line B'], loc='upper right')\n", + "\n", + "# Create the second legend and add the artist manually\n", + "from matplotlib.legend import Legend\n", + "leg = Legend(ax, lines[2:], ['line C', 'line D'], loc='lower right')\n", + "ax.add_artist(leg);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a peek into the low-level artist objects that comprise any Matplotlib plot.\n", + "If you examine the source code of `ax.legend` (recall that you can do this with within the Jupyter notebook using `ax.legend??`) you'll see that the function simply consists of some logic to create a suitable `Legend` artist, which is then saved in the `legend_` attribute and added to the figure when the plot is drawn." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.07-Customizing-Colorbars.ipynb b/notebooks/04.07-Customizing-Colorbars.ipynb new file mode 100644 index 000000000..5de7df641 --- /dev/null +++ b/notebooks/04.07-Customizing-Colorbars.ipynb @@ -0,0 +1,558 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Customizing Colorbars" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot legends identify discrete labels of discrete points.\n", + "For continuous labels based on the color of points, lines, or regions, a labeled colorbar can be a great tool.\n", + "In Matplotlib, a colorbar is drawn as a separate axes that can provide a key for the meaning of colors in a plot.\n", + "Because the book is printed in black and white, this chapter has an accompanying [online supplement](https://github.com/jakevdp/PythonDataScienceHandbook) where you can view the figures in full color.\n", + "We'll start by setting up the notebook for plotting and importing the functions we will use:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-white')" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we have seen several times already, the simplest colorbar can be created with the `plt.colorbar` function (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 10, 1000)\n", + "I = np.sin(x) * np.cos(x[:, np.newaxis])\n", + "\n", + "plt.imshow(I)\n", + "plt.colorbar();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll now discuss a few ideas for customizing these colorbars and using them effectively in various situations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Customizing Colorbars\n", + "\n", + "The colormap can be specified using the `cmap` argument to the plotting function that is creating the visualization (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(I, cmap='Blues');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The names of available colormaps are in the `plt.cm` namespace; using IPython's tab completion feature will give you a full list of built-in possibilities:\n", + "\n", + "```\n", + "plt.cm.\n", + "```\n", + "But being *able* to choose a colormap is just the first step: more important is how to *decide* among the possibilities!\n", + "The choice turns out to be much more subtle than you might initially expect." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Choosing the Colormap\n", + "\n", + "A full treatment of color choice within visualizations is beyond the scope of this book, but for entertaining reading on this subject and others, see the article [\"Ten Simple Rules for Better Figures\"](http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003833) by Nicholas Rougier, Michael Droettboom, and Philip Bourne.\n", + "Matplotlib's online documentation also has an [interesting discussion](https://matplotlib.org/stable/tutorials/colors/colormaps.html) of colormap choice.\n", + "\n", + "Broadly, you should be aware of three different categories of colormaps:\n", + "\n", + "- *Sequential colormaps*: These are made up of one continuous sequence of colors (e.g., `binary` or `viridis`).\n", + "- *Divergent colormaps*: These usually contain two distinct colors, which show positive and negative deviations from a mean (e.g., `RdBu` or `PuOr`).\n", + "- *Qualitative colormaps*: These mix colors with no particular sequence (e.g., `rainbow` or `jet`).\n", + "\n", + "The `jet` colormap, which was the default in Matplotlib prior to version 2.0, is an example of a qualitative colormap.\n", + "Its status as the default was quite unfortunate, because qualitative maps are often a poor choice for representing quantitative data.\n", + "Among the problems is the fact that qualitative maps usually do not display any uniform progression in brightness as the scale increases.\n", + "\n", + "We can see this by converting the `jet` colorbar into black and white (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from matplotlib.colors import LinearSegmentedColormap\n", + "\n", + "def grayscale_cmap(cmap):\n", + " \"\"\"Return a grayscale version of the given colormap\"\"\"\n", + " cmap = plt.cm.get_cmap(cmap)\n", + " colors = cmap(np.arange(cmap.N))\n", + " \n", + " # Convert RGBA to perceived grayscale luminance\n", + " # cf. http://alienryderflex.com/hsp.html\n", + " RGB_weight = [0.299, 0.587, 0.114]\n", + " luminance = np.sqrt(np.dot(colors[:, :3] ** 2, RGB_weight))\n", + " colors[:, :3] = luminance[:, np.newaxis]\n", + " \n", + " return LinearSegmentedColormap.from_list(\n", + " cmap.name + \"_gray\", colors, cmap.N)\n", + " \n", + "\n", + "def view_colormap(cmap):\n", + " \"\"\"Plot a colormap with its grayscale equivalent\"\"\"\n", + " cmap = plt.cm.get_cmap(cmap)\n", + " colors = cmap(np.arange(cmap.N))\n", + " \n", + " cmap = grayscale_cmap(cmap)\n", + " grayscale = cmap(np.arange(cmap.N))\n", + " \n", + " fig, ax = plt.subplots(2, figsize=(6, 2),\n", + " subplot_kw=dict(xticks=[], yticks=[]))\n", + " ax[0].imshow([colors], extent=[0, 10, 0, 1])\n", + " ax[1].imshow([grayscale], extent=[0, 10, 0, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "view_colormap('jet')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the bright stripes in the grayscale image.\n", + "Even in full color, this uneven brightness means that the eye will be drawn to certain portions of the color range, which will potentially emphasize unimportant parts of the dataset.\n", + "It's better to use a colormap such as `viridis` (the default as of Matplotlib 2.0), which is specifically constructed to have an even brightness variation across the range; thus, it not only plays well with our color perception, but also will translate well to grayscale printing (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "view_colormap('viridis')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For other situations, such as showing positive and negative deviations from some mean, dual-color colorbars such as `RdBu` (*Red–Blue*) are helpful. However, as you can see in the following figure, it's important to note that the positive/negative information will be lost upon translation to grayscale!" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "view_colormap('RdBu')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll see examples of using some of these colormaps as we continue.\n", + "\n", + "There are a large number of colormaps available in Matplotlib; to see a list of them, you can use IPython to explore the `plt.cm` submodule. For a more principled approach to colors in Python, you can refer to the tools and documentation within the Seaborn library (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Color Limits and Extensions\n", + "\n", + "Matplotlib allows for a large range of colorbar customization.\n", + "The colorbar itself is simply an instance of `plt.Axes`, so all of the axes and tick formatting tricks we've seen so far are applicable.\n", + "The colorbar has some interesting flexibility: for example, we can narrow the color limits and indicate the out-of-bounds values with a triangular arrow at the top and bottom by setting the `extend` property.\n", + "This might come in handy, for example, if displaying an image that is subject to noise (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# make noise in 1% of the image pixels\n", + "speckles = (np.random.random(I.shape) < 0.01)\n", + "I[speckles] = np.random.normal(0, 3, np.count_nonzero(speckles))\n", + "\n", + "plt.figure(figsize=(10, 3.5))\n", + "\n", + "plt.subplot(1, 2, 1)\n", + "plt.imshow(I, cmap='RdBu')\n", + "plt.colorbar()\n", + "\n", + "plt.subplot(1, 2, 2)\n", + "plt.imshow(I, cmap='RdBu')\n", + "plt.colorbar(extend='both')\n", + "plt.clim(-1, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that in the left panel, the default color limits respond to the noisy pixels, and the range of the noise completely washes out the pattern we are interested in.\n", + "In the right panel, we manually set the color limits and add extensions to indicate values that are above or below those limits.\n", + "The result is a much more useful visualization of our data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Discrete Colorbars\n", + "\n", + "Colormaps are by default continuous, but sometimes you'd like to represent discrete values.\n", + "The easiest way to do this is to use the `plt.cm.get_cmap` function and pass the name of a suitable colormap along with the number of desired bins (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(I, cmap=plt.cm.get_cmap('Blues', 6))\n", + "plt.colorbar(extend='both')\n", + "plt.clim(-1, 1);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The discrete version of a colormap can be used just like any other colormap." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Handwritten Digits\n", + "\n", + "As an example of where this can be applied, let's look at an interesting visualization of some handwritten digits from the digits dataset, included in Scikit-Learn; it consists of nearly 2,000 $8 \\times 8$ thumbnails showing various handwritten digits.\n", + "\n", + "For now, let's start by downloading the digits dataset and visualizing several of the example images with `plt.imshow` (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# load images of the digits 0 through 5 and visualize several of them\n", + "from sklearn.datasets import load_digits\n", + "digits = load_digits(n_class=6)\n", + "\n", + "fig, ax = plt.subplots(8, 8, figsize=(6, 6))\n", + "for i, axi in enumerate(ax.flat):\n", + " axi.imshow(digits.images[i], cmap='binary')\n", + " axi.set(xticks=[], yticks=[])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because each digit is defined by the hue of its 64 pixels, we can consider each digit to be a point lying in 64-dimensional space: each dimension represents the brightness of one pixel.\n", + "Visualizing such high-dimensional data can be difficult, but one way to approach this task is to use a *dimensionality reduction* technique such as manifold learning to reduce the dimensionality of the data while maintaining the relationships of interest.\n", + "Dimensionality reduction is an example of unsupervised machine learning, and we will discuss it in more detail in [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb).\n", + "\n", + "Deferring the discussion of these details, let's take a look at a two-dimensional manifold learning projection of the digits data (see [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) for details):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# project the digits into 2 dimensions using Isomap\n", + "from sklearn.manifold import Isomap\n", + "iso = Isomap(n_components=2, n_neighbors=15)\n", + "projection = iso.fit_transform(digits.data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use our discrete colormap to view the results, setting the `ticks` and `clim` to improve the aesthetics of the resulting colorbar (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the results\n", + "plt.scatter(projection[:, 0], projection[:, 1], lw=0.1,\n", + " c=digits.target, cmap=plt.cm.get_cmap('plasma', 6))\n", + "plt.colorbar(ticks=range(6), label='digit value')\n", + "plt.clim(-0.5, 5.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The projection also gives us some insights on the relationships within the dataset: for example, the ranges of 2 and 3 nearly overlap in this projection, indicating that some handwritten 2s and 3s are difficult to distinguish, and may be more likely to be confused by an automated classification algorithm.\n", + "Other values, like 0 and 1, are more distantly separated, and may be less likely to be confused.\n", + "\n", + "We'll return to manifold learning and digit classification in [Part 5](05.00-Machine-Learning.ipynb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.08-Multiple-Subplots.ipynb b/notebooks/04.08-Multiple-Subplots.ipynb new file mode 100644 index 000000000..149372e18 --- /dev/null +++ b/notebooks/04.08-Multiple-Subplots.ipynb @@ -0,0 +1,447 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Multiple Subplots" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes it is helpful to compare different views of data side by side.\n", + "To this end, Matplotlib has the concept of *subplots*: groups of smaller axes that can exist together within a single figure.\n", + "These subplots might be insets, grids of plots, or other more complicated layouts.\n", + "In this chapter we'll explore four routines for creating subplots in Matplotlib. We'll start by importing the packages we will use:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-white')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## plt.axes: Subplots by Hand\n", + "\n", + "The most basic method of creating an axes is to use the `plt.axes` function.\n", + "As we've seen previously, by default this creates a standard axes object that fills the entire figure.\n", + "`plt.axes` also takes an optional argument that is a list of four numbers in the figure coordinate system (`[left, bottom, width, height]`), which ranges from 0 at the bottom left of the figure to 1 at the top right of the figure.\n", + "\n", + "For example, we might create an inset axes at the top-right corner of another axes by setting the *x* and *y* position to 0.65 (that is, starting at 65% of the width and 65% of the height of the figure) and the *x* and *y* extents to 0.2 (that is, the size of the axes is 20% of the width and 20% of the height of the figure). The following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ax1 = plt.axes() # standard axes\n", + "ax2 = plt.axes([0.65, 0.65, 0.2, 0.2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The equivalent of this command within the object-oriented interface is `fig.add_axes`. Let's use this to create two vertically stacked axes, as seen in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax1 = fig.add_axes([0.1, 0.5, 0.8, 0.4],\n", + " xticklabels=[], ylim=(-1.2, 1.2))\n", + "ax2 = fig.add_axes([0.1, 0.1, 0.8, 0.4],\n", + " ylim=(-1.2, 1.2))\n", + "\n", + "x = np.linspace(0, 10)\n", + "ax1.plot(np.sin(x))\n", + "ax2.plot(np.cos(x));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have two axes (the top with no tick labels) that are just touching: the bottom of the upper panel (at position 0.5) matches the top of the lower panel (at position 0.1 + 0.4)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## plt.subplot: Simple Grids of Subplots\n", + "\n", + "Aligned columns or rows of subplots are a common enough need that Matplotlib has several convenience routines that make them easy to create.\n", + "The lowest level of these is `plt.subplot`, which creates a single subplot within a grid.\n", + "As you can see, this command takes three integer arguments—the number of rows, the number of columns, and the index of the plot to be created in this scheme, which runs from the upper left to the bottom right (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in range(1, 7):\n", + " plt.subplot(2, 3, i)\n", + " plt.text(0.5, 0.5, str((2, 3, i)),\n", + " fontsize=18, ha='center')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The command `plt.subplots_adjust` can be used to adjust the spacing between these plots.\n", + "The following code uses the equivalent object-oriented command, `fig.add_subplot`; the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "fig.subplots_adjust(hspace=0.4, wspace=0.4)\n", + "for i in range(1, 7):\n", + " ax = fig.add_subplot(2, 3, i)\n", + " ax.text(0.5, 0.5, str((2, 3, i)),\n", + " fontsize=18, ha='center')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we've used the `hspace` and `wspace` arguments of `plt.subplots_adjust`, which specify the spacing along the height and width of the figure, in units of the subplot size (in this case, the space is 40% of the subplot width and height)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## plt.subplots: The Whole Grid in One Go\n", + "\n", + "The approach just described quickly becomes tedious when creating a large grid of subplots, especially if you'd like to hide the x- and y-axis labels on the inner plots.\n", + "For this purpose, `plt.subplots` is the easier tool to use (note the `s` at the end of `subplots`). Rather than creating a single subplot, this function creates a full grid of subplots in a single line, returning them in a NumPy array.\n", + "The arguments are the number of rows and number of columns, along with optional keywords `sharex` and `sharey`, which allow you to specify the relationships between different axes.\n", + "\n", + "Let's create a $2 \\times 3$ grid of subplots, where all axes in the same row share their y-axis scale, and all axes in the same column share their x-axis scale (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(2, 3, sharex='col', sharey='row')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By specifying `sharex` and `sharey`, we've automatically removed inner labels on the grid to make the plot cleaner.\n", + "The resulting grid of axes instances is returned within a NumPy array, allowing for convenient specification of the desired axes using standard array indexing notation (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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FT0T0FJk9s4+KisKpU6cQHx8PQRCQnZ2NgoIC+Pr6wmg04uzZszAYDDh58iQA4MMPP0R6ejpWrVqFEydOQCaTIScnx+EHQkREj2e27F1cXJCZmWky5u/vL/75559/7vJ5u3fvtnFqRERkL/xSFRGRBLDsiYgkgGVPRCQBLHsiIglg2RMRSQDLnohIAlj2REQSwLInIpIAlj0RkQSw7ImIJIBlT0QkASx7IiIJYNkTEUkAy56ISAJY9kREEsCyJyKSAJY9EZEEmL1TldFoxObNm3HlyhXI5XJkZWXBz89PXF5UVIQvvvgCrq6uWLJkCaZMmYKGhgZ89NFHuH//PgYPHoycnBwoFAqHHggRET2e2TP7kpISGAwGqNVqrFy5Erm5ueKy+vp6FBYW4osvvsB//vMfbN++HQaDAfn5+YiOjsahQ4cwbtw4qNVqhx4EERE9mdkz+/LycoSHhwMAgoODUVlZKS67ePEixo8fD7lcDrlcDl9fX2i1WpSXl2Px4sUAgIiICGzfvh0pKSni89ra2gAAN27csOexkBU6MujIxBbMtedgrn2TLbmaLXudTgelUik+lslkaG1thaurK3Q6HTw8PMRl7u7u0Ol0JuPu7u5oamoy2WZ9fT0AYN68eRZPmByjvr7e5O05a7cBMNeehLn2TdbkarbslUol9Hq9+NhoNMLV1bXLZXq9Hh4eHuK4m5sb9Ho9PD09TbYZGBiIgwcPwtvbGzKZzKIJk321tbWhvr4egYGBNm+LufYczLVvsiVXs2UfEhKC77//HjNnzoRGo4FKpRKXBQUF4V//+hdaWlpgMBhQXV0NlUqFkJAQnDhxArNmzUJZWRlCQ0NNtunm5oYJEyZYPFlyDFvP/Dow156FufZN1ubaTxAE4UkrdFyN88svv0AQBGRnZ6OsrAy+vr6YNm0aioqKoFarIQgCFi9ejOnTp+PWrVvIyMiAXq/HM888g23btmHgwIFWTZCIiGxntuyJiKj345eqiIgkgGVPRCQBLHsiIglg2RMRSQDLnohIAlj2REQSwLInIpIAlj0RkQSw7ImIJIBlT0QkASx7IiIJYNkTEUlAt8r+p59+QlJSUqfx0tJSxMbGIi4uDkVFRQCA+/fv4/3338fcuXORlpaGhoYG+86YiIgsZvZXL/fs2YOvvvoKCoVCLHQAePDgAWbOnIkjR45AoVAgISEB//73v3Hs2DHodDq8//77KC4uxoULF7BhwwaTbd6/fx+VlZW8GUIP8PDNENzc3GzaFnPtOZhr32RLrmZvXuLr64u8vDysXr3aZLy6uhq+vr4YNGgQACA0NBTnzp1DeXk5Fi1aBKD9/rP5+fmdtllZWclbnPUwBw8etPkGFcy152GufZM1uZot++nTp+P69eudxq29/ywAeHt7ixP28fGxaMJkXzdu3MC8efPETGzBXHsO5to32ZKr2bJ/HHP3n+0Ye/T+swDEl4I+Pj4YMWKEtVMgO7LHy3Pm2vMw177JmlytvhrH398fNTU1aGxshMFgwPnz5zF+/Hjx/rMAurz/LBEROZ/FZ/bHjh1Dc3Mz4uLisGbNGixcuBCCICA2NhZDhgxBQkICMjIykJCQgP79+2Pbtm2OmDcREVmgW2U/YsQI8Uqct956SxyfOnUqpk6darKuQqHAjh077DhFIiKyFb9URUQkASx7IiIJYNkTEUkAy56ISAJY9kREEsCyJyKSAJY9EZEEsOyJiCSAZU9EJAEseyIiCWDZExFJAMueiEgCWPZERBLAsicikgCWPRGRBLDsiYgkgGVPRCQBZu9UZTQasXnzZly5cgVyuRxZWVnw8/MDAFy+fBnZ2dniuhqNBp999hmCgoIwffp0qFQqAEBkZCTmz5/voEMgIiJzzJZ9SUkJDAYD1Go1NBoNcnNzsXPnTgDA2LFjUVhYCAD4+uuvMXjwYEREROD06dOIjo7Gxo0bHTt7IiLqFrNv45SXlyM8PBwAEBwcjMrKyk7rNDc3Iy8vD+vXrwcAVFZWoqqqComJiVi+fDnq6ursPG0iIrKE2bLX6XRQKpXiY5lMhtbWVpN1jhw5ghkzZsDLywsAMHr0aCxfvhwHDhxAZGQksrKy7DxtIiKyhNmyVyqV0Ov14mOj0QhXV9N3f44dO4bZs2eLjydPnoxJkyYBAKKionDp0iV7zZeIiKxgtuxDQkJQVlYGoP0D2I4PXTs0NTXBYDBg6NCh4tiGDRtw/PhxAMCZM2cQEBBgzzkTEZGFzH5AGxUVhVOnTiE+Ph6CICA7OxsFBQXw9fXFtGnTcPXqVQwfPtzkOStXrsS6devw+eefQ6FQ8G0cIqKnzGzZu7i4IDMz02TM399f/HNQUBDy8/NNlo8cOVK8SoeIiJ4+fqmKiEgCWPZERBLAsicikgCWPRGRBLDsiYgkgGVPRCQBkiz7mzdvYtKkSaitre1y+caNG5GUlGTTPmpra7Fs2TKEhYUhLCwMq1evRkNDg8k669evR05Ojk37ob85I9fubI+52p8zsj158iTmzp2Ll156CePHj0dKSgo0Go3JOr05W0mW/ZYtW/Dmm29i5MiRnZYdPnwYRUVFNm3/zp07mD9/PjQaDRYtWoTU1FSUlpYiNTUVBoNBXG/p0qVQq9XQarU27Y/aOTrX7m6Pudqfo7M9e/Ys0tLS0NTUhBUrVmDp0qW4du0aEhMTcfHiRXG93pyt2S9V9TXnzp3Dd999h5KSEpPxtrY27Ny5E59++qnN+9i3bx9u3LiBY8eOiV9Ae+mll5Camoovv/wSc+bMAQAMGzYMb775JnJycrB//36b9ytlzsi1u9tjrvbljGyzs7MxdOhQFBUVQaFQAADefvttzJw5E5988gkKCgoA9O5sJXdmv2/fPoSGhpr8lk9LSwveeecd5OXlISYmBkOGDLFpH8XFxQgLCzP5pvHLL7+MUaNGobi42GTd2bNn44cffuiVZwo9iTNytWR7zNV+HJ3t3bt3odVqMWPGDLHoAeC5557DxIkTceHCBZP1e2u2kir7P//8E99//z0iIyNNxltaWqDT6fDJJ59g69atnX7V0xJ3795FbW1tlz/+FhAQgKqqKpOx4OBg+Pj44ODBg1bvU+qckaul22Ou9uGMbJVKJb755hukpKR0Wnbnzh3IZDKTsd6araTexjl58iTa2trw+uuvm4wrlUp8++23NpcB0P5BEoAuzzS8vb3R1NSEpqYmeHh4iOMTJ04Uf1mULOeMXK3ZHnO1nTOylclkeP755zuNa7VaVFRU4NVXX+20rDdmK6kz+/LycgwcOLDThzwuLi52K4SO3/5/+OVghwEDBgBov7PXw1QqFW7cuPHYKw3oyZyRqzXbY662c1a2j9Lr9cjIyAAApKend1reG7OVVNnX1tZi+PDh6Nevn8P2IQiC2XUe3X/HX+Tr1687ZE59nTNytQZztd3TyPbevXtYsmQJtFot0tPTERYW1mmd3pitpMq+sbHR5BaLjjBw4EAA7e8pPqpj7NE5dDy+c+eOQ+fWVzkjV2swV9s5O9u//voLCxYswI8//ojY2FisWLGiy/V6Y7aSKnsXFxcYjUaH7mPYsGEAgPr6+k7L6urq4OnpKf6D0KFjTo9+EETd44xcrcFcbefMbG/fvo3k5GRUVFQgLi4OW7Zseewrit6Yrdk3vYxGIzZv3owrV65ALpcjKysLfn5+4vKsrCxUVFTA3d0dAJCfn48HDx7go48+wv379zF48GDk5OR0+R62sz377LP4888/HboPT09PjBgxotNVNwBw6dIlBAYGdhpvbGwU50eWc0au1mCutnNWtjqdDgsXLsTly5eRkpKCtWvXPnH93pit2TP7kpISGAwGqNVqrFy5Erm5uSbLq6qqsHfvXhQWFqKwsBAeHh7Iz89HdHQ0Dh06hHHjxkGtVjvsACwxbNgw1NXVoa2tzaH7eeONN3DmzBlUV1eLY6dPn8bVq1cxc+bMTut3XMHT8aqALOOsXC3FXG3nrGwzMzNx+fJlJCcnmy16oHdma7bsy8vLER4eDqD9+tLKykpxmdFoRE1NDTZt2oT4+HgcOXKk03MiIiJw+vRpR8zdYpMnT8a9e/fw66+/WvX82tpaHD161Own8GlpaRg0aBBSUlJQUFCAXbt2Yfny5QgICEBMTEyn9TUaDfz8/HrVX5yexFm5Woq52s4Z2VZXV+Po0aPw9PTE2LFjcfTo0U7/Pao3Zmv2bRydTmfyAYlMJkNraytcXV3R3NyMxMREpKamoq2tDcnJyQgMDIROpxOvI3d3d0dTU5PjjsAC4eHhcHFxwfnz5zFmzBiLn3/u3DmsXbsWOTk5Xf5GRwcvLy8cOHAAOTk52LFjB9zc3BAZGYnVq1dDLpebrGs0GqHRaLo846fucVaulmCu9uGMbM+ePQug/cPZx53VP3yS1luzNVv2SqVSvHYcaD/QjutbFQoFkpOTxffjJ0+eDK1WKz7Hzc0Ner0enp6eDpq+Zby8vDB16lQUFxcjMTHxseuVlpZ2OT5r1ixotdpOhd2V0aNHY8+ePWbXO3PmDG7fvo13333X7LrUNWfm2p3tAczVXpyRbUJCAhISEro9p96ardm3cUJCQsRvimk0GqhUKnHZ77//joSEBLS1teHBgweoqKhAQEAAQkJCcOLECQBAWVkZQkNDHTR9yy1YsAAVFRW4du2axc+9desWSktLu/yQ1VpffvklXnnlFavOWuhvzLXvYrb2Ybbso6KiIJfLER8fj5ycHKxduxYFBQX47rvv4O/vj5iYGMyZMwdJSUmIiYnBCy+8gCVLlqC4uBjx8fG4cOHCE/9FdrbQ0FBMmTIFu3fvtvi5DQ0NyMjI6PKr1daora3F8ePH8cEHH9hle1LGXPsuZmsnwlNQW1srqFQqoba29mnsXvjjjz+EiRMnCjU1NU9l/x3WrFkjZGVlPdU52DML5tqOudofs21nSxaS+iG0DkOHDhU/lHmaeusdb3oq5tp3MVvbSeobtEREUsWyJyKSAJY9EZEEsOyJiCSAZU9EJAEseyIiCWDZExFJAMueiEgCWPZERBLAsicikgCWPRGRBLDsiYgkgGVPRCQBLHsiIglg2RMRSQDLnohIAszevMRoNGLz5s24cuUK5HI5srKy4OfnJy7ft28fiouLAQCvvfYali1bBkEQEBERId4KLDg4GCtXrnTMERARkVlmy76kpAQGgwFqtRoajQa5ubnYuXMngPb7MX711Vc4fPgwXFxckJCQgMjISCgUCgQEBGDXrl0OPwAiIjLP7Ns45eXlCA8PB9B+hl5ZWSku8/Hxwd69eyGTydCvXz+0trZiwIABqKqqws2bN5GUlIS0tDT89ttvjjsCIiIyy2zZ63Q6KJVK8bFMJkNraysAoH///vDy8oIgCNi6dSvGjRuHUaNGwdvbG+np6SgsLMTixYuxatUqxx0BERGZZfZtHKVSCb1eLz42Go1wdf37aS0tLVi3bh3c3d3x8ccfAwACAwMhk8kAABMmTEBdXR0EQUC/fv3sPX8iIuoGs2f2ISEhKCsrAwBoNBqoVCpxmSAIeO+99/Diiy8iMzNTLPhPP/0U+/fvBwBotVoMHTqURU9E9BSZPbOPiorCqVOnEB8fD0EQkJ2djYKCAvj6+sJoNOLs2bMwGAw4efIkAODDDz9Eeno6Vq1ahRMnTkAmkyEnJ8fhB0JERI9ntuxdXFyQmZlpMubv7y/++eeff+7yebt377ZxakREZC/8UhURkQSw7ImIJIBlT0QkASx7IiIJYNkTEUkAy56ISAJY9kREEsCyJyKSAJY9EZEEsOyJiCSAZU9EJAEseyIiCWDZExFJAMueiEgCWPZERBLAsicikgCWPRGRBJi9U5XRaMTmzZtx5coVyOVyZGVlwc/PT1xeVFSEL774Aq6urliyZAmmTJmChoYGfPTRR7h//z4GDx6MnJwcKBQKhx4IERE9ntmyLykpgcFggFqthkajQW5uLnbu3AkAqK+vR2FhIf73v/+hpaUFc+fOxSuvvIL8/HxER0dj1qxZ2L17N9RqNVJSUsRttrW1AQBu3LjhmKOibuvIoCMTWzDXnoO59k225Gq27MvLyxEeHg4ACA4ORmVlpbjs4sWLGD9+PORyOeRyOXx9faHValFeXo7FixcDACIiIrB9+3aTsq+vrwcAzJs3z+IJk2PU19ebvGKzdhsAc+1JmGvfZE2uZstep9NBqVSKj2UyGVpbW+Hq6gqdTgcPDw9xmbu7O3Q6ncm4u7s7mpqaTLYZGBiIgwcPwtvbGzKZzKIJk321tbWhvr4egYGBNm+LufYczLVvsiVXs2WvVCqh1+vFx0ajEa6url0u0+v18PDwEMfd3Nyg1+vh6elpsk03NzdMmDDB4smSY9h65teBufYszLVvsjZXs1fjhISEoKysDACg0WigUqnEZUFBQSgvL0dLSwuamppQXV0NlUqFkJAQnDhxAgBQVlaG0NBQqyZHRET20U8QBOFJK3RcjfPLL79AEARkZ2ejrKwMvr6+mDZtGoqKiqBWqyEIAhYvXozp06fj1q1byMjIgF6vxzPPPINt27Zh4MCBzjomIiJ6hNmyt5U1l272NOaOISsrCxUVFXB3dwcA5Ofnm3yW0ZP89NNP+Oc//4nCwkKT8dLSUnz22WdwdXVFbGws5syZ88TtMNeehbn+jbk+huBgx48fFzIyMgRBEIQLFy4I//jHP8RldXV1QnR0tNDS0iL89ddf4p97micdgyAIQnx8vHD79u2nMTWL7N69W4iOjhZmz55tMm4wGITIyEihsbFRaGlpEWbNmiXU19c/cVvMtedgrqaYa9cc/g3a7l666eHhIV662dM86RiMRiNqamqwadMmxMfH48iRI09rmmb5+voiLy+v03h1dTV8fX0xaNAgyOVyhIaG4ty5c0/cFnPtOZirKebaNbNX49jKmks3e5onHUNzczMSExORmpqKtrY2JCcnIzAwEGPGjHmKM+7a9OnTcf369U7j1uTAXHsO5mqKuXbN4Wf21ly62dM86RgUCgWSk5OhUCigVCoxefLkHnm28yTW5MBcez7m2o65tnN42Vtz6WZP86Rj+P3335GQkIC2tjY8ePAAFRUVCAgIeFpTtYq/vz9qamrQ2NgIg8GA8+fPY/z48U98DnPt+Zgrc32Yw9/GiYqKwqlTpxAfHy9eullQUCBeupmUlIS5c+dCEASsWLECAwYMcPSULGbuGGJiYjBnzhz0798fMTExeOGFF572lLvl2LFjaG5uRlxcHNasWYOFCxdCEATExsZiyJAhT3wuc+25mCtz7YrDL70kIqKnj79nT0QkASx7IiIJYNkTEUkAy56ISAJY9kREEsCyJyKSAJY9EZEE/D9adJdy0iZr/gAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# axes are in a two-dimensional array, indexed by [row, col]\n", + "for i in range(2):\n", + " for j in range(3):\n", + " ax[i, j].text(0.5, 0.5, str((i, j)),\n", + " fontsize=18, ha='center')\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In comparison to `plt.subplot`, `plt.subplots` is more consistent with Python's conventional zero-based indexing, whereas `plt.subplot` uses MATLAB-style one-based indexing." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## plt.GridSpec: More Complicated Arrangements\n", + "\n", + "To go beyond a regular grid to subplots that span multiple rows and columns, `plt.GridSpec` is the best tool.\n", + "`plt.GridSpec` does not create a plot by itself; it is rather a convenient interface that is recognized by the `plt.subplot` command.\n", + "For example, a `GridSpec` for a grid of two rows and three columns with some specified width and height space looks like this:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "grid = plt.GridSpec(2, 3, wspace=0.4, hspace=0.3)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From this we can specify subplot locations and extents using the familiar Python slicing syntax (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.subplot(grid[0, 0])\n", + "plt.subplot(grid[0, 1:])\n", + "plt.subplot(grid[1, :2])\n", + "plt.subplot(grid[1, 2]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This type of flexible grid alignment has a wide range of uses.\n", + "I most often use it when creating multiaxes histogram plots like the ones shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Create some normally distributed data\n", + "mean = [0, 0]\n", + "cov = [[1, 1], [1, 2]]\n", + "rng = np.random.default_rng(1701)\n", + "x, y = rng.multivariate_normal(mean, cov, 3000).T\n", + "\n", + "# Set up the axes with GridSpec\n", + "fig = plt.figure(figsize=(6, 6))\n", + "grid = plt.GridSpec(4, 4, hspace=0.2, wspace=0.2)\n", + "main_ax = fig.add_subplot(grid[:-1, 1:])\n", + "y_hist = fig.add_subplot(grid[:-1, 0], xticklabels=[], sharey=main_ax)\n", + "x_hist = fig.add_subplot(grid[-1, 1:], yticklabels=[], sharex=main_ax)\n", + "\n", + "# Scatter points on the main axes\n", + "main_ax.plot(x, y, 'ok', markersize=3, alpha=0.2)\n", + "\n", + "# Histogram on the attached axes\n", + "x_hist.hist(x, 40, histtype='stepfilled',\n", + " orientation='vertical', color='gray')\n", + "x_hist.invert_yaxis()\n", + "\n", + "y_hist.hist(y, 40, histtype='stepfilled',\n", + " orientation='horizontal', color='gray')\n", + "y_hist.invert_xaxis()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This type of distribution plotted alongside its margins is common enough that it has its own plotting API in the Seaborn package; see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb) for more details." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "encoding": "# -*- coding: utf-8 -*-", + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.09-Text-and-Annotation.ipynb b/notebooks/04.09-Text-and-Annotation.ipynb new file mode 100644 index 000000000..edd9be619 --- /dev/null +++ b/notebooks/04.09-Text-and-Annotation.ipynb @@ -0,0 +1,449 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Text and Annotation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Creating a good visualization involves guiding the reader so that the figure tells a story.\n", + "In some cases, this story can be told in an entirely visual manner, without the need for added text, but in others, small textual cues and labels are necessary.\n", + "Perhaps the most basic types of annotations you will use are axes labels and titles, but the options go beyond this.\n", + "Let's take a look at some data and how we might visualize and annotate it to help convey interesting information. We'll start by setting up the notebook for plotting and importing the functions we will use:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np\n", + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Effect of Holidays on US Births\n", + "\n", + "Let's return to some data we worked with earlier, in [Example: Birthrate Data](03.09-Pivot-Tables.ipynb#Example:-Birthrate-Data), where we generated a plot of average births over the course of the calendar year. We'll start with the same cleaning procedure we used there, and plot the results (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# shell command to download the data:\n", + "# !cd data && curl -O \\\n", + "# https://raw.githubusercontent.com/jakevdp/data-CDCbirths/master/births.csv" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from datetime import datetime\n", + "\n", + "births = pd.read_csv('data/births.csv')\n", + "\n", + "quartiles = np.percentile(births['births'], [25, 50, 75])\n", + "mu, sig = quartiles[1], 0.74 * (quartiles[2] - quartiles[0])\n", + "births = births.query('(births > @mu - 5 * @sig) & (births < @mu + 5 * @sig)')\n", + "\n", + "births['day'] = births['day'].astype(int)\n", + "\n", + "births.index = pd.to_datetime(10000 * births.year +\n", + " 100 * births.month +\n", + " births.day, format='%Y%m%d')\n", + "births_by_date = births.pivot_table('births',\n", + " [births.index.month, births.index.day])\n", + "births_by_date.index = [datetime(2012, month, day)\n", + " for (month, day) in births_by_date.index]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(12, 4))\n", + "births_by_date.plot(ax=ax);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we're visualizing data like this, it is often useful to annotate certain features of the plot to draw the reader's attention.\n", + "This can be done manually with the `plt.text`/`ax.text` functions, which will place text at a particular *x*/*y* value (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(12, 4))\n", + "births_by_date.plot(ax=ax)\n", + "\n", + "# Add labels to the plot\n", + "style = dict(size=10, color='gray')\n", + "\n", + "ax.text('2012-1-1', 3950, \"New Year's Day\", **style)\n", + "ax.text('2012-7-4', 4250, \"Independence Day\", ha='center', **style)\n", + "ax.text('2012-9-4', 4850, \"Labor Day\", ha='center', **style)\n", + "ax.text('2012-10-31', 4600, \"Halloween\", ha='right', **style)\n", + "ax.text('2012-11-25', 4450, \"Thanksgiving\", ha='center', **style)\n", + "ax.text('2012-12-25', 3850, \"Christmas \", ha='right', **style)\n", + "\n", + "# Label the axes\n", + "ax.set(title='USA births by day of year (1969-1988)',\n", + " ylabel='average daily births')\n", + "\n", + "# Format the x-axis with centered month labels\n", + "ax.xaxis.set_major_locator(mpl.dates.MonthLocator())\n", + "ax.xaxis.set_minor_locator(mpl.dates.MonthLocator(bymonthday=15))\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.xaxis.set_minor_formatter(mpl.dates.DateFormatter('%h'));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `ax.text` method takes an *x* position, a *y* position, a string, and then optional keywords specifying the color, size, style, alignment, and other properties of the text.\n", + "Here we used `ha='right'` and `ha='center'`, where `ha` is short for *horizontal alignment*.\n", + "See the docstrings of `plt.text` and `mpl.text.Text` for more information on the available options." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Transforms and Text Position\n", + "\n", + "In the previous example, we anchored our text annotations to data locations. Sometimes it's preferable to anchor the text to a fixed position on the axes or figure, independent of the data. In Matplotlib, this is done by modifying the *transform*.\n", + "\n", + "Matplotlib makes use of a few different coordinate systems: a data point at $(x, y) = (1, 1)$ corresponds to a certain location on the axes or figure, which in turn corresponds to a particular pixel on the screen.\n", + "Mathematically, transforming between such coordinate systems is relatively straightforward, and Matplotlib has a well-developed set of tools that it uses internally to perform these transforms (these tools can be explored in the `matplotlib.transforms` submodule).\n", + "\n", + "A typical user rarely needs to worry about the details of the transforms, but it is helpful knowledge to have when considering the placement of text on a figure. There are three predefined transforms that can be useful in this situation:\n", + "\n", + "- `ax.transData`: Transform associated with data coordinates\n", + "- `ax.transAxes`: Transform associated with the axes (in units of axes dimensions)\n", + "- `fig.transFigure`: Transform associated with the figure (in units of figure dimensions)\n", + "\n", + "Let's look at an example of drawing text at various locations using these transforms (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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7TY0aNVJwcLC6dOmiffv2ebQpLS3V+PHj9dRTT3lc3717d+3YsUMOh8PrMcTNV+dm4lcTFxenWbNmKTw8XJMmTVJFRYXatGmjTz75RH/+85/10EMPaceOHapfv74WLFigtm3bqmXLllqwYIGCgoI0aNAgRUZGavHixQoMDFRUVJQSExNVWlqqefPmuV42X5Kenq4+ffpIuvgl8GPGjJEk9ezZ87IQj4mJ8fjC/MrKStWrd+Vf3aFDhxQTE6Pg4GAFBwfrtttu09GjRz2+9z0tLc01M7Pb7a6vEH788cc1ZswY/fKXv7zO0TRTZmamBg4cqLZt2yo4OFiffvqp7r33Xi1YsEDjxo1T8+bNNXnyZN1666169dVXlZSUpDvuuEOZmZlas2aNYmJi1LhxY6WkpOjzzz9XWVmZJCklJeWy29q7d69uv/12SdK5c+c8Xhk2aNBAJSUlHq/G+vbtq2HDhslqteqVV17RX//618teYV3qq2HDhh59nTt3zqNNVFSUoqKitHv3bo/rAwMD1aRJEx07dkx33XVXjccP/lEnQ3z+/PlavXq1pIuzjxdffNH1s5UrV+rhhx/W8OHD9dFHH+mjjz66Zl82m02ZmZlyOp167LHHtHHjRjVt2lRLlizR+++/r0GDBmnKlCmXHbd3717Xy/XvPvAuPYC/q379+qpfv74uXLigKVOmaPDgwWrQoMEV66nOgzgiIkKS9OGHH2rPnj167bXXJEmNGjXSmTNnVFJS4tFHXVBcXKzdu3ersLBQaWlpOnfunNavX697771XrVq1UufOnXXw4EH17NlT0sUZ769//WtJF5cwbr/9dvXs2VNffPGFXnrpJddS1tWcOXNGd9xxhyTJarWqtLTU9bPS0lKP8Xc6nXrmmWdc1/Xq1UtHjhy5YohX1VdVIiIiVFRUVO328L86GeLx8fGuB+P3HT9+3DUT7dq16xXbOJ3ubUnbtGkj6eI6Y35+visQy8vL1b1796vWcObMGdds+LsPvNLSUt1yyy2XtS8uLtaECRN0//3364UXXrhqv9V9EK9du1YffPCB1qxZ47GZR7NmzVRUVFTnQnzbtm3q37+/EhISJF3cP/bhhx9WYWGhvvrqK3322We677779O6772r06NFq06aNkpOTFRkZqezsbBUUFGjPnj2KiIjQu+++qwMHDmjRokVKS0u74u01adLE9Xvq3Lmz5s+fr9GjR+t///ufHA6Hxyz83Llz6tevn/74xz8qLCxMe/bsUf/+/a/Yb7t27fTll1+qqKhIYWFh+uc//1mj7/4vLi5W06ZNq90e/lcnQ/xa7rzzTh04cEDR0dE6ePCg6/rg4GDl5+erVatWOnr0qNq1aydJCgi4+LZCeHi4fvSjH+ntt99Ww4YN9Ze//OWaG0U3adJEZ8+eldVqVefOnbVr1y517NhRu3fvVpcuXTzalpeXa9SoUXr22Wf15JNPXrP+jh07asmSJbLZbKqoqNDx48d15513erRZsWKFcnNztXbt2ss2pz179uxlb6rWNkVFRZoxY4ZSU1Nd12VmZnose4SGhqp3797auHGjduzYodTUVEVGRmrgwIG6//77NWvWLCUkJMhut8tisWjOnDlq3LixfvWrXyk9PV12u10vv/yypItr4q+99prHey4PPPCA68yRu+++W127dtXgwYPlcDg0c+ZMSdL27dtVVlamwYMHa+LEiRo5cqSCg4MVGxurXr16KS8vT1u2bNH06dNd/QYFBWnKlCkaPXq0nE6n+vfvrxYtWujzzz/X+vXrNWvWrKuOi8Ph0Ndff+16hQAzXNdu99dis9kuC6Ob6UoPVOni2SlPPPHEZTPx766JT548WTabTREREcrJydGHH36orKwsvfPOO2rZsqUaNmyoHj16qGXLlsrIyNDixYslSX//+9+1fPlyOZ1ONWjQQCkpKQoMDNSrr7562Zr44sWLddddd+nxxx/X+fPnlZCQoIKCAgUFBWnhwoVq3ry5UlJS9Nhjj2n//v1KTU31WBdPSkrSyZMndfToUY0dO9aj782bN2vTpk1yOp164YUX1KdPH3388cfKzs7WkCFD9NOf/lTt27f3WAsfNmyYzp49q7FjxyojI8Nnv4fvY0PcixwOhwYMGKCMjAwFBwd71UdZWZlWrVqliRMn+qSmXbt2KTc3Vy+99JJP+qsJ/i7csrOza7TVZa0NcW/t2rVL4eHh6tixo/7xj39o5cqV+t3vfnddfV7pD/Q///mPkpOTtXTpUq/7/eabb5SZmalx48ZdV32XbNiwQVar9bKzFnyJB6vb5s2bVVZWplGjRnl1fElJiSwWi6xW63XX4nQ6FR8fr8TExGu+grxR+Ltwq2mIs5zyPa1atdK0adMUGBgoh8Ph8VLVl1q2bKmf/OQnysnJ0T333ONVH06nU88995xP6ikvL9f+/fs1f/58n/SHqt1zzz3XFVy+fN/CYrFowYIFPusPNw8h/j3t2rXTpk2bbsptXVoz9dZ3P8BxvUJCQrRw4UKf9Qfg5qiTH/YBgNqCEAcAgxHiAGAwQhwADEaIA4DBCHEAMBghDgAGI8QBwGCEOAAYjBAHAIMR4gBgMEIcAAxGiAOAwQhxADAYIQ4ABvPq+8QdDodWr16tL774QkFBQXrxxRd16623+ro2AEAVvJqJ7927VxUVFZo7d65GjBhx2f6RAICbw6uZeF5enmJiYiRd3B3++PHjV2yXnZ3tfWW1DGPhxli4MRZujIV3vArx8+fPe2ymGhAQoMrKSgUGBrquq8lGnwAA73i1nBIaGqrz58+7LjscDo8ABwDcHF6F+F133aX9+/dLko4dO6bWrVv7tCgAQPVYcnJynDU96NLZKV9++aWcTqdefvlltWrV6kbUBwC4Bq9C/Go49dDNbrdr+fLlKigo0IULFzRgwADdd999/i7Lr4qLixUfH6+ZM2fW6Sf9LVu2aN++fbLb7erTp48eeeQRf5fkF3a7XcuWLVNBQYECAgI0bty4Ovl3cezYMa1fv16JiYk6deqUUlNTZbFYFBUVpeeff14BAddeMPHph3049dBt9+7datiwoWbPnq0ZM2ZozZo1/i7Jr+x2u1auXKng4GB/l+JXhw8f1tGjRzVnzhwlJibqm2++8XdJfrN//35VVlYqKSlJAwcO1MaNG/1d0k23detWrVixQhUVFZKktWvXaujQoZo9e7Ykad++fVX24dMQr+6ph3VBbGyshg4d6rpc1bNpbbdu3Tr17t1bTZo08XcpfnXw4EG1bt1aKSkpmjt3rrp06eLvkvwmMjJSDodDDodDZWVlqlfPq5PljNaiRQvFx8e7Lp84cUIdOnSQJMXExOjQoUNV9uHTZLnaqYd1UWhoqOssnvnz52vYsGH+Lslvdu7cqUaNGrme4OuykpISHT9+XK+//rpeeOEFvfXWW3I6fbaiaZSQkBDl5+drwoQJWrlypZ544gl/l3TTxcbGejx5OZ1OWSwWSRczpKysrMo+fBrinHro6fTp03rjjTfUq1cv9ejRw9/l+M3OnTv16aefaubMmTp58qSWLVumM2fO+Lssv7BarerUqZOCgoLUsmVLBQUF6ezZs/4uyy+2b9+uTp06KTU1VQsXLtSyZctcywp11aUAly6fFF+NT0OcUw/dioqKlJiYqBEjRujhhx/2dzl+NXv2bL355ptKTExUmzZtNH78eIWHh/u7LL+Ijo7WgQMH5HQ6VVhYKJvNJqvV6u+y/MJqtbpCymq1qrKyUg6Hw89V+VebNm10+PBhSdKBAwfUvn37Ko/x6SLUAw88oEOHDmnatGmuUw/rqvfee0+lpaXKyspSVlaWJGn69Ol8krWO69q1q44cOaKEhAQ5nU6NGTOmzr5a7devn5YvX64ZM2bIbrdr+PDhCgkJ8XdZfjVq1CitWLFCGzZsUKtWrdStW7cqj/HpKYYAgJurbp8yAQCGI8QBwGCEOAAYjBAHAIMR4gBgMEIcAAxGiAOAwf4fu/tv0B73ZfsAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(facecolor='lightgray')\n", + "ax.axis([0, 10, 0, 10])\n", + "\n", + "# transform=ax.transData is the default, but we'll specify it anyway\n", + "ax.text(1, 5, \". Data: (1, 5)\", transform=ax.transData)\n", + "ax.text(0.5, 0.1, \". Axes: (0.5, 0.1)\", transform=ax.transAxes)\n", + "ax.text(0.2, 0.2, \". Figure: (0.2, 0.2)\", transform=fig.transFigure);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matplotlib's default text alignment is such that the \".\" at the beginning of each string will approximately mark the specified coordinate location.\n", + "\n", + "The `transData` coordinates give the usual data coordinates associated with the x- and y-axis labels.\n", + "The `transAxes` coordinates give the location from the bottom-left corner of the axes (here the white box), as a fraction of the total axes size.\n", + "The `transFigure` coordinates are similar, but specify the position from the bottom-left corner of the figure (here the gray box) as a fraction of the total figure size.\n", + "\n", + "Notice now that if we change the axes limits, it is only the `transData` coordinates that will be affected, while the others remain stationary (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.set_xlim(0, 2)\n", + "ax.set_ylim(-6, 6)\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This behavior can be seen more clearly by changing the axes limits interactively: if you are executing this code in a notebook, you can make that happen by changing `%matplotlib inline` to `%matplotlib notebook` and using each plot's menu to interact with the plot." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Arrows and Annotation\n", + "\n", + "Along with tickmarks and text, another useful annotation mark is the simple arrow.\n", + "\n", + "While there is a `plt.arrow` function available, I wouldn't suggest using it: the arrows it creates are SVG objects that will be subject to the varying aspect ratio of your plots, making it tricky to get them right.\n", + "Instead, I'd suggest using the `plt.annotate` function, which creates some text and an arrow and allows the arrows to be very flexibly specified.\n", + "\n", + "Here is a demonstration of `annotate` with several of its options (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "x = np.linspace(0, 20, 1000)\n", + "ax.plot(x, np.cos(x))\n", + "ax.axis('equal')\n", + "\n", + "ax.annotate('local maximum', xy=(6.28, 1), xytext=(10, 4),\n", + " arrowprops=dict(facecolor='black', shrink=0.05))\n", + "\n", + "ax.annotate('local minimum', xy=(5 * np.pi, -1), xytext=(2, -6),\n", + " arrowprops=dict(arrowstyle=\"->\",\n", + " connectionstyle=\"angle3,angleA=0,angleB=-90\"));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The arrow style is controlled through the `arrowprops` dictionary, which has numerous options available.\n", + "These options are well documented in Matplotlib's online documentation, so rather than repeating them here it is probably more useful to show some examples.\n", + "Let's demonstrate several of the possible options using the birthrate plot from before (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(12, 4))\n", + "births_by_date.plot(ax=ax)\n", + "\n", + "# Add labels to the plot\n", + "ax.annotate(\"New Year's Day\", xy=('2012-1-1', 4100), xycoords='data',\n", + " xytext=(50, -30), textcoords='offset points',\n", + " arrowprops=dict(arrowstyle=\"->\",\n", + " connectionstyle=\"arc3,rad=-0.2\"))\n", + "\n", + "ax.annotate(\"Independence Day\", xy=('2012-7-4', 4250), xycoords='data',\n", + " bbox=dict(boxstyle=\"round\", fc=\"none\", ec=\"gray\"),\n", + " xytext=(10, -40), textcoords='offset points', ha='center',\n", + " arrowprops=dict(arrowstyle=\"->\"))\n", + "\n", + "ax.annotate('Labor Day Weekend', xy=('2012-9-4', 4850), xycoords='data',\n", + " ha='center', xytext=(0, -20), textcoords='offset points')\n", + "ax.annotate('', xy=('2012-9-1', 4850), xytext=('2012-9-7', 4850),\n", + " xycoords='data', textcoords='data',\n", + " arrowprops={'arrowstyle': '|-|,widthA=0.2,widthB=0.2', })\n", + "\n", + "ax.annotate('Halloween', xy=('2012-10-31', 4600), xycoords='data',\n", + " xytext=(-80, -40), textcoords='offset points',\n", + " arrowprops=dict(arrowstyle=\"fancy\",\n", + " fc=\"0.6\", ec=\"none\",\n", + " connectionstyle=\"angle3,angleA=0,angleB=-90\"))\n", + "\n", + "ax.annotate('Thanksgiving', xy=('2012-11-25', 4500), xycoords='data',\n", + " xytext=(-120, -60), textcoords='offset points',\n", + " bbox=dict(boxstyle=\"round4,pad=.5\", fc=\"0.9\"),\n", + " arrowprops=dict(arrowstyle=\"->\",\n", + " connectionstyle=\"angle,angleA=0,angleB=80,rad=20\"))\n", + "\n", + "\n", + "ax.annotate('Christmas', xy=('2012-12-25', 3850), xycoords='data',\n", + " xytext=(-30, 0), textcoords='offset points',\n", + " size=13, ha='right', va=\"center\",\n", + " bbox=dict(boxstyle=\"round\", alpha=0.1),\n", + " arrowprops=dict(arrowstyle=\"wedge,tail_width=0.5\", alpha=0.1));\n", + "\n", + "# Label the axes\n", + "ax.set(title='USA births by day of year (1969-1988)',\n", + " ylabel='average daily births')\n", + "\n", + "# Format the x-axis with centered month labels\n", + "ax.xaxis.set_major_locator(mpl.dates.MonthLocator())\n", + "ax.xaxis.set_minor_locator(mpl.dates.MonthLocator(bymonthday=15))\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.xaxis.set_minor_formatter(mpl.dates.DateFormatter('%h'));\n", + "\n", + "ax.set_ylim(3600, 5400);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The variety of options make `annotate` powerful and flexible: you can create nearly any arrow style you wish.\n", + "Unfortunately, it also means that these sorts of features often must be manually tweaked, a process that can be very time-consuming when producing publication-quality graphics!\n", + "Finally, I'll note that the preceding mix of styles is by no means best practice for presenting data, but rather is included as a demonstration of some of the available options.\n", + "\n", + "More discussion and examples of available arrow and annotation styles can be found in the Matplotlib [Annotations tutorial](https://matplotlib.org/stable/tutorials/text/annotations.html)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.10-Customizing-Ticks.ipynb b/notebooks/04.10-Customizing-Ticks.ipynb new file mode 100644 index 000000000..9c8c824c7 --- /dev/null +++ b/notebooks/04.10-Customizing-Ticks.ipynb @@ -0,0 +1,519 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Customizing Ticks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matplotlib's default tick locators and formatters are designed to be generally sufficient in many common situations, but are in no way optimal for every plot. This chapter will give several examples of adjusting the tick locations and formatting for the particular plot type you're interested in.\n", + "\n", + "Before we go into examples, however, let's talk a bit more about the object hierarchy of Matplotlib plots.\n", + "Matplotlib aims to have a Python object representing everything that appears on the plot: for example, recall that the `Figure` is the bounding box within which plot elements appear.\n", + "Each Matplotlib object can also act as a container of subobjects: for example, each `Figure` can contain one or more `Axes` objects, each of which in turn contains other objects representing plot contents.\n", + "\n", + "The tickmarks are no exception. Each axes has attributes `xaxis` and `yaxis`, which in turn have attributes that contain all the properties of the lines, ticks, and labels that make up the axes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Major and Minor Ticks\n", + "\n", + "Within each axes, there is the concept of a *major* tickmark, and a *minor* tickmark. As the names imply, major ticks are usually bigger or more pronounced, while minor ticks are usually smaller. By default, Matplotlib rarely makes use of minor ticks, but one place you can see them is within logarithmic plots (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.style.use('classic')\n", + "import numpy as np\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes(xscale='log', yscale='log')\n", + "ax.set(xlim=(1, 1E3), ylim=(1, 1E3))\n", + "ax.grid(True);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this chart each major tick shows a large tickmark, label, and gridline, while each minor tick shows a smaller tickmark with no label or gridline.\n", + "\n", + "These tick properties—locations and labels, that is—can be customized by setting the `formatter` and `locator` objects of each axis. Let's examine these for the x-axis of the just-shown plot:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n" + ] + } + ], + "source": [ + "print(ax.xaxis.get_major_locator())\n", + "print(ax.xaxis.get_minor_locator())" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n" + ] + } + ], + "source": [ + "print(ax.xaxis.get_major_formatter())\n", + "print(ax.xaxis.get_minor_formatter())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that both major and minor tick labels have their locations specified by a `LogLocator` (which makes sense for a logarithmic plot). Minor ticks, though, have their labels formatted by a `NullFormatter`: this says that no labels will be shown.\n", + "\n", + "We'll now look at a few examples of setting these locators and formatters for various plots." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hiding Ticks or Labels\n", + "\n", + "Perhaps the most common tick/label formatting operation is the act of hiding ticks or labels.\n", + "This can be done using `plt.NullLocator` and `plt.NullFormatter`, as shown here (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes()\n", + "rng = np.random.default_rng(1701)\n", + "ax.plot(rng.random(50))\n", + "ax.grid()\n", + "\n", + "ax.yaxis.set_major_locator(plt.NullLocator())\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We've removed the labels (but kept the ticks/gridlines) from the x-axis, and removed the ticks (and thus the labels and gridlines as well) from the y-axis.\n", + "Having no ticks at all can be useful in many situations—for example, when you want to show a grid of images.\n", + "For instance, consider the following figure, which includes images of different faces, an example often used in supervised machine learning problems (see, for example, [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(5, 5, figsize=(5, 5))\n", + "fig.subplots_adjust(hspace=0, wspace=0)\n", + "\n", + "# Get some face data from Scikit-Learn\n", + "from sklearn.datasets import fetch_olivetti_faces\n", + "faces = fetch_olivetti_faces().images\n", + "\n", + "for i in range(5):\n", + " for j in range(5):\n", + " ax[i, j].xaxis.set_major_locator(plt.NullLocator())\n", + " ax[i, j].yaxis.set_major_locator(plt.NullLocator())\n", + " ax[i, j].imshow(faces[10 * i + j], cmap='binary_r')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each image is shown in its own axes, and we've set the tick locators to null because the tick values (pixel numbers in this case) do not convey relevant information for this particular visualization." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reducing or Increasing the Number of Ticks\n", + "\n", + "One common problem with the default settings is that smaller subplots can end up with crowded labels.\n", + "We can see this in the plot grid shown here (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(4, 4, sharex=True, sharey=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Particularly for the x-axis ticks, the numbers nearly overlap, making them quite difficult to decipher.\n", + "One way to adjust this is with `plt.MaxNLocator`, which allows us to specify the maximum number of ticks that will be displayed.\n", + "Given this maximum number, Matplotlib will use internal logic to choose the particular tick locations (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# For every axis, set the x and y major locator\n", + "for axi in ax.flat:\n", + " axi.xaxis.set_major_locator(plt.MaxNLocator(3))\n", + " axi.yaxis.set_major_locator(plt.MaxNLocator(3))\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This makes things much cleaner. If you want even more control over the locations of regularly spaced ticks, you might also use `plt.MultipleLocator`, which we'll discuss in the following section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fancy Tick Formats\n", + "\n", + "Matplotlib's default tick formatting can leave a lot to be desired: it works well as a broad default, but sometimes you'd like to do something different.\n", + "Consider this plot of a sine and a cosine curve (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot a sine and cosine curve\n", + "fig, ax = plt.subplots()\n", + "x = np.linspace(0, 3 * np.pi, 1000)\n", + "ax.plot(x, np.sin(x), lw=3, label='Sine')\n", + "ax.plot(x, np.cos(x), lw=3, label='Cosine')\n", + "\n", + "# Set up grid, legend, and limits\n", + "ax.grid(True)\n", + "ax.legend(frameon=False)\n", + "ax.axis('equal')\n", + "ax.set_xlim(0, 3 * np.pi);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a couple of changes we might like to make here. First, it's more natural for this data to space the ticks and gridlines in multiples of $\\pi$. We can do this by setting a `MultipleLocator`, which locates ticks at a multiple of the number we provide. For good measure, we'll add both major and minor ticks in multiples of $\\pi/2$ and $\\pi/4$ (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))\n", + "ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But now these tick labels look a little bit silly: we can see that they are multiples of $\\pi$, but the decimal representation does not immediately convey this.\n", + "To fix this, we can change the tick formatter. There's no built-in formatter for what we want to do, so we'll instead use `plt.FuncFormatter`, which accepts a user-defined function giving fine-grained control over the tick outputs (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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QLSu1hFcxr1wfK6/4UtJScPLuSRyMOIit17Yi9FYoCNk/pw3LNcT/2v4PvWv3hrOTc4HjAmSi3bEDmDpVfi5y0rw50LmzLF+2aAEULZr74+UVX0ICcPw4sHs3EBIChOXSIbtLF/nZCwgArPD9ZZGCJHYQUaH8yafKn2tx12iKbgrV/KEmYTKy/QUuD6TQiNB8P15Wz54R/fILUZUqRPItZvrXoQPR0qVEDx6Y97j79u3L13Z6PdGJE0TjxhF5e2d/fiGIBg8munHD7NCsKr/x2SNbiu3M3TPUZVWXHN/3FedWpIl7JlJYTBjp9fp8P6Y58UU/jqaFxxdS88XNc2xDrR9q0dqwtWY9fya9nigkhKhp05w/ew0aEM2dSxQRYd7jmhPfzZtEU6cSVauWcxtee43o8GHznt/aMnKnWfnWpseKISLownX47uh32Hxlc7YjiR61emBux7moXrp6vh5v+3bg3/8GrlwxXV+qFPDOO8AHHwDV8/dQikhNBTZuBObNA44cMb2tSBFg1Cjgq6+AMmUKr01MHZEJkfi/ff+H5WeWZ3ufv171dYxrPg6dqndCEafC6+9wNvosFp1chOAzwUhKM62TNK/YHHM6zkGbl9vk77HOys/evn2m611dgf795WevefPCO1omAg4eBL79Fti0KXu5plcvYOZMoLby1V+zaeaIPSfX467TyE0jyXmKs8kRhOtUV5qwawI9Tnmc632vXCHq0iX7t3Pp0kQzZhAlJFjUNEUcOpRzG728iH76iSgtTe0WMmtISUuhqfunUrFpxUze12KyoL7r+tLJqJNqN5FinsTQ/3b/jzxmemQ7gu+zrg9FPorM9b737hGNHk3k5GT6vnZzI/rwQ6LbtwsxkFxcuUI0ahSRs7NpG11ciD7/nOjpU3XbhwIcsdtNYs90Pe46DVk/hMRkke1nasiVEJNtnz0jmjaNyNXVdId5eBBNn65sQlfq53xoKFG7dtkTfJMmRCdV/IzbUrlCaWrFdjDiINVZUCdbsuyyqguFxYQp9jxKxfcg8QF9suMTcp3qatJe9xnutODoAkpLNx596PVEv/1GVKaM6fvY2ZlozBiiqChFmkREysV39SrRgAHZP3uVKxNt2qTIUxSIQyT2TMcij1GLJS2yfSiGrB9CcYlxdPo0kb+/6Q4Sguhf/yKKiVG0KUSkbHLQ64k2b85+HqBIEaLJk+UXVmHjxK6cxymP6b0t72V77zb8qSHtublH8edTOr5/4v+ht/98O1v7WyxpQVfuX6Hbt4m6dcueIDt1IrpwQdGmEJHy8Z06RdS6dfb2Dxpk/rk3JRQksdt0jf1F9KTHynMr8cnOTxCbGGtYX4J8kLRmGfRX3jCsa9ZMdqtq1EjRJlhVUhLwzTey1peSYlzfqBGwfLm88ILZl6ORRzF4w2Bcf3DdsK6ka0lMaz8NY5uNtbjHSWHShevwbsi7uBpnvILITRSH2DkPyX+PBiDLwr6+wI8/At262V6Pk9zo9fIz9umnQFyccX3FisDSpUDHjoXXFtW6O+briaw4CNj9xPsY99c4/Hb+N9MbDv8bbqEzMX2KGz7+GHC2n8+MievXZV/30FDjOldXYM4cYOxY+/mwOLI0fRqmH5iOqQemIp3SDet71OqBBW8sgG8pXxVbV3DJacmYFToLMw7OQKo+1XjDlW7A5iX4YJgPZs4EPDzUa6Ml4uKA//wHWLHCdP2YMfLzl1c3TKU47EQbZYqXQV+nVSixeRPwOMtVPi2/RfUZrdB9+FWrJ/XMK8esoXp1eXn1nDlyeAJAjk/z0UdA377Ao0dWe2oDa8anNmvHdvfxXQQuD8Tk/ZMNSd3d1R3Ley3Hxv4brZ7UrRlf0SJF0d19MsptOQbcq2u8oVYISk9sgP6fHbB6UrdmfC+9JI/cN2yQY0Bl+vFHoHVr4OZNqz21Rew+saelyW/U3r2Bp6d6AAvPAVe7Gm6/EH8KjX9ujA2XNqjYSss5OwPjxwOnTsmBjTL9+acszZw8qV7bWO4ORBxAw0UNcfDWQcO6Ni+3wbn3z2Fog6FWuZqzMC1ZArRqBdw+7g/8fBw4Ms5w24NnMQhcHog5h+agsCoD1tKrl7y4qVcv47pTp+Rnb4MtphZzi/IF/YPCJ0+JZFeq9u1NT3C8/DJRaKie5h+en+3s/aQ9k0zO3NurpCTZs+D57mPLl6vdMpZJr9fT7L9nm3TPdZriRNP2T9PEezA5WXZjzPoedHcnWrmSaMf1HeT9jbfJZ+/NtW/So+RHajfbYno90Q8/yK6QWWP/9FPrdUmGI/WKOXlSJvGsL27PnqZnrU9FnaKq31XN1pUsPile0baoZd06+WHK+hr85z9Eqalqt8yxJT5LpP6/9zd533l/4027b+xWu2mKuHOHqEUL0/dd/fpE168bt7n96Ha2Xmu1fqhF1+KuqddwBR07JrtBZn0NunQhevhQ+edymMS+Zg1R0aLGF1QIeZlwenr2beMS46jjrx1N3mDVv69OV+5fUaw9ROp1B7x2jahuXdM3WKdOynfL4u6O+XP38V1qtrhZtm6Atx+pdyWOkvGdOEFUrpzp+23gQKInT7Jvm5KWQh9u+9DktSj9dWnS/aNTrD1E6r03HzzI3q2zTh35mVRSQRK7XdXYieSgXQMGyAkuAHm2fcsWYNKknAfpKl2sNLa9vQ0TWk8wrLv+4Dpa/tISByMOZr+DnaleHTh8GOjZ07huxw45cFJuY1Qz6zgXcw7NFjfDsTvHDOvea/we9g/fj0oelVRsmTI2bQLatTPOTeDsLIfDWLUq5zHOXZ1d8f0b32PVm6tQtIjsPvIg6QFe//V1LDu9rBBbbh1eXnJIkM8/N667dEl2rd67V7VmSeZ+ExT0DxYesaemZq/p1a4tLwfOr3Vh60wu3Xad6kqrzq2yqF22Ij2d6P/+z/T18fYmOnpU7ZY5hpArIVRyRkmTevoPR39Qu1mKmT9f/jLOfG95ehLtMeNaqqORR8lnto/J0ftnOz+jdH0OP7Pt0KpVplUEFxe5TgnQaikmIYGoc2fTpBUQULByw7HIY1R2dlmTN9jU/VMLNFqdLVq3zvQNVqyYvIqVWc/ik4vJaYqTySX2269tV7tZikhLk2O6ZP3sVa1KdOmS+Y8V8TCC6i+sb/LZG/DHAEpOTVa+4So4doyoQgXT12rWLHnC1RKaTOxRUXI4z6wv1pAhRCkpBXo4IpKXRL/y4ysmb7BRm0dZ1FvBlmrQf/9N9NJLxtfLyYlo4ULLHtOW4lNaQWPT6/U0bf80k/eR33w/Oh9zXtkGWqig8SUlEfXqZfrZa9FC9kYrqITkBOr2WzeT16zDig6UkFzwgZts6b1561b2c15jxljWY6Ygid2ma+w3bsiLAM5mmXfjiy/kBQOZsxYVhJ+nH/5+528EVgk0rFt8ajEG/DkAKWkpedzTPrRqJScwqJIx7ZleD7z/PjBxonyrMcul69Px0faPMGnfJMO6RuUb4cjII6hX1v7HekhIkJNPbNxoXNenj6wdZ71Qx1zubu7Y2H8jxjQdY1i3++ZuBCwPyHOGKHvh6yuvEH/tNeO6H3+Ur11uM0RZhbnfBAX9g5lH7OfOmZ59L1JEToChpJS0FBq8frDJ0UPQ8iCLjh5sSXS0HBUy69HDBx/k3HuI5V9yajL1+72fZt839+4RNW5s+r4ZP17Z941er6ep+6dm661244GNzTBTQMnJRP37Zy8fF2REWWilFHP4sByHPPMFKVpUzrxiDen6dBq3fZzJG6zpz00p9mmsdZ6wkD15QtS1q+kbbPBgdUaI1IKE5AQKWh5k8n7p/3t/zdSJb92SnRKerxNby88nfjY5P+Ez24fORp+13hMWovR0+YWY9bVs2pTo/n3zHkcTiX3nTqLixY0vhIcH0f795r0Q5sqpVlp7QW2z+h7bUp3vec+eyb7GWd9gPXrIGmp+2XJ8lspvbPFJ8dkuuvlw24c237Mjv/Fdvkzk62t8jwhBtGiRddtGRLTh0gYqOq2o4TX1muVFx+8cz/f9bf29+fXXpp+9evXMG4++IIndpmrsf/wBdO0KJCbKZW9vOZVWu3bWfV4hBCa2m4iFXRdCZAw1evn+ZbRb1g7hD8Ot++SFwMVFTtz93nvGdZs3y9f68WP12mVP4hLjELQiCEcijXMYTms/Dd91/g5OwqY+RgVy5gzQtq1xonUXF2DtWmD0aOs/d6/avbBz8E54uMnRwuKT4xG0Igh/3/rb+k9eCD77TA4ZnjksUFiYfK3Dw634pOZ+ExT0Dy84Yl+1ynT6LF9feQRR2NaGrSWXr1wMRw++83w1cxm0Xk/03/+aHj00b67O5AH2JPpxNNX7f/VMjtQXHF2gdrMUc+KEaemzeHGiHTtUaMedE1T669KG17j49OJWmXhELStXmk6/V6lS/rqNogBH7DYxHvuvvwLDh8veGwBQqxawa5c8w6yGrVe34q11byElXfaQKV+yPPYO24vaZWxgZlsFzJplerVco0by9S5dWr022ao7CXcQtCIIV+LkDOgCAou7L8bIRiNVbpkyjh+Xk0Y8fCiXPT2BbduAli3VaU/YvTB0WNEBMU9jAABuzm5Y3389utTook6DFLZ5M9Cvn3HiHB8fYM8eoG7d3O9jl+OxBwcDw4YZk3q9esCBA+oldQDoWrMrtgzcgmJFigEA7j65i9eCX0PYvbBc72NP45VPmCC7YGU6dQoICgLu38/9PvYUn7lyiy3iYQTaBbczJHUn4YQVvVfYXVLPLb6jR4EOHYxJ3ctLJhm1kjoA1CtbD/uH70dF94oAgJT0FPRa0wvrL63P9T729N7s0QPYutU4BENMDNC+PXD+vLLPo2piX7IEeOcdY9/q+vVlP9myZdVslfR6tdexbdA2lHCRe+De03sICA7A6bunVW6ZMj74QL7+mXW/M2eAwEAgNjbPuzmM6w+uo11wO9yMlzMpFHEqgrV91mJw/cEqt0wZhw8Dr78u+6sDckKJvXttY+rIWmVq4eCIg/Dz9AMApOpT0e/3flgTtkbdhikkKEiO5+TuLpdjY+VnL+v1OpZSrRSzaJHpyTx/f2D3bvkGsyWHbh/CG6veQEKK/AR4FvXEjsE70KxiM5VbpozgYNMv17p15VGbj4+qzVLVlftXELgiEFGPowDIwaz+6PsHutfqrnLLlBEaCrzxBvDkiVwuU0bu8/r11W3X8yITIhG0Isgwp6qTcMKvvX/F26++rXLLlHH4MNC5s/HLtXRpmQOzTqQD2NGcpz/+KOfqzGTrNd7jd46j48qOeJj8EADg4eaBvwb9hZa+Kv5mVdDKlablsNq15dFb+fLqtksNl+9fRvvl7RH9RA5hWLRIUWzsvxGdqndSuWXKOHBAXlH69Klc9vaW+9pWJ0aPeRKDwBWBuBh7EUBGOazXCgyqP0jllinj2DF5jiNzektPT5ncGzc2bmMXNfbvvzdN6k2bykBsNakDQNOKTbF36F68VEz+nEhISUDHlR0Ress4u7Q91fmeN3iwTO6Zwx5fvgwEBAB37hi3sef4XiQztkuxlxAQHGBI6iVcSmD7oO12n9Qz49Pp5JF6ZlL38ZHrbDWpA4BPSR/sG7YPdb3l2UU96TF041CsPLfSsI09vzebNZP5z9NTLj98KEs1x47lda8XUySxCyE6CyGuCCGuCyEm5Lbdt98C48YZl5s3l0fqXl5KtMK6GpZvCN1wHbyLy4Eynjx7gs4rO2N/+H6VW6aMgQOBNWtgmPT76lWZ3CMjVW1WobkYexEBywMMvTEyk3qAX4Cq7VLKnj3ySD3zGpHy5WVSf+UVVZuVL2VLlMW+YfsMY/DoSY+hG4bi17O/qtwyZTRpIvdPZh589Eie/zhyJO/75cXiUowQwhnAVQCvA4gEcBzAQCK6+Nx2BBifq1UrYPt2WH0Gc6VdjL2IwOWBhgRQrEgxhLwdYjKgmD1bvx7o319OEg4AVavKi8ReflnddlnThXsXELgi0DAIVUnXktg+aDvavNxG5ZYpY9cu2Rsjc3KaChXkPq1ZU912mSv2aSyCVgTh/D3ZhURAILhXMIY2GKpyy5Rx5ozspRQXJ5fd3YG//gJat1anFNMMwHUiuklEzwCsAdAzrzu0aSMbbG9JHQBe8X4FuuE6lC8pC9BJaUno+ltX7LyxU+WWKePNN+UVwC4ucvnmTTlSnVWvklNR2L0wtF/e3iSp/zXoL80k9R07gO7djUm9UiVg/377S+oA4F3CG3uG7kF9H3mWl0AYvnE4lp9ZrnLLlOHvL893lCkjlx8/BjoVsAqoRGKvCOB2luXIjHU5atdOHqlndvWxR7XL1Dbpa5ucloxuM7ph+7XtKrdMGT17yiP3zKGRw8OB5s11uHlT1WYpLuxeGAKXByL2guzjmZnUW7/cWuWWKWPbNrkvU1J0AOS1ITqdnE7RXmUm9wY+DQBkJPf5wzUx1R4geybt22fs8p3Zc8lchXry1MdnOFq3now5cyZj/vz5Jic9dDqdXS3fOX8HX1f/Gi+XkjWK1Dup6DGrB0KuhthE+yxdLllShylTdHBzk8v37p1BixY6wzyqarfP0uWl65ei9RetEZsok3qxyGKYWW2mIamr3T5Ll2fO1KFnT12WKxx1+PprHapVs432WbJcpngZTPGbgmqPqhluf+e7d/DZ4s9son2WLt+/r0OLFsPh5jYcwGQUhBI19pYAJhNRp4zlzwGAiGY+tx09fUooXtyip7M54Q/D0X55e8NgYS5OLljXdx161e6laruUsmMH0KuX8ad8xYryiKJGDVWbZZFzMecQuDwQcUmymOnu6o4dg3dopvvqpk1A375AaqpcrlJF7rPKldVtl9LiEuPw+q+v43S0vGhQa8M9XLggL1y6d0+FfuxCiCKQJ0+DANyBPHn6NhFdeG67XMeKsXe3Ht1C++XtTa5SXP3WavR5pY/KLVPG7t2mddry5WWiqFVL3XYVxNnoswhaEWRI6h5uHtgxeAdaVGqhcsuU4Wgnvx8kPUCHFR0MyR0AFndfjH81+peKrVJOVBRQsaIKJ0+JKA3AWAA7AFwCsO75pK51L5d6GbOqzUKN0vIwNk2fhgF/DMDasLUqt0wZHToA06frUEwOnYO7d2VXyEuXVG2W2c5En8mW1HcO3onk68kqt0wZv/8uB5jKTOo1asgTpTdv6lRtlzWVLlYak/0mo1F541gIo7aMws8nf1axVcqpUKFg91Okxk5E24ioJhFVI6LpSjymvfEu4Q3dcB1qvSQPY9MpHW+vfxurzq1SuWXKaNRInvTOHLwoOlom9wt28hV++u5pk6Reyq0Udg3ZheaVmqvcMmWsWSOvRUhPl8s1awI6newFo3Uebh7YPWQ3GpdvbFj3bsi7WHRikYqtUpdNDNurJdFPohG0IshwCbSAwLKeyzDMf5jKLVPGwYPyQpfMs/Xe3vLiildfVbddeclM6vHJ8QCMSb1pxaYqt0wZq1YBQ4fykBDxSfHouLIjTkSdMKz7rvN3+Kj5Ryq2ynJ2MaSA1pUrWc7kKjkCYcSmEVh6eqnKLVNG27byGoSsI9O1b6/syHRKOnbnGAJXBBqSumdRT+weulszSX3FCmDIEGNSf+UVeaTuaEkdALyKeckv7ArGfTvur3H45u9vVGyVOjixKyRr16XMS6Cz9rUduXmkXdf9ssbXujWwc6fxArO4OHn2/rSNjWh8MOIgOqzoYBi8zbOoJ3YP2Y0mFZqYbJc1NnuybJmcoCbzh/Crr8oTpc+PzGmv8eVX1vg8i3pi15BdaOXbyrDuv7v/i6/2fwVHqBhk4sRuJWWKl8HeYXtNTuq8G/Iufjz2Yx73sh8tWshL1UuVkssPHsjkfvKkuu3KtPvmbnRa2QmPnz0GALxU7CXsGboHjSs0fsE97cPPP5sOt9ygge3MZaC2UkVLYcfgHSbj/Hyp+xL/2/M/h0nuXGO3svikeHRa2QnHo44b1s3vNB/jWozL417248QJOWBR5iw8pUrJo/lmKg5XH3I1BH3W9TFMbehTwgd7hu5B3bJ5zD9mR2bPlhMkZ2rYUH7J2tpcBmpLTE1E77W9TYb7GNd8HL7t9C2EMKtkrSqusdugzLpf1n7SH+/4GHMPzVWxVcrJaWS6Dh1kNzs1/H7hd/Re29uQ1Ct5VMKBEQc0kdSJgEmTTJN6kya2OUGNLSjuUhybB2xG95rGCVK+O/od3t/6PvSkV7Fl1seJXSF51TEzfxq29jWOQfLJrk/wdejXhdAyZeQVX6NGsgyQmVwyBy/avLlw2pbp17O/YsCfA5Cmlx25q3hWwcERB1HzpbxHvLKHGrReL4e8np6lM/Frr8kv1RfNZWAP8Vkir/jcirjhj35/mFwsuOjkIozYNAKp6amF0Dp1cGIvJB5uHvhr8F9oV7mdYd2EPRM0U/fz9zftjZGSIkeKXLGicJ7/28PfYujGoYYjsVovmc6bac/S0mQ9/YcfjOu6drXPYa/V4OrsitVvrTaZr3bF2RXovbY3ElMTVWyZ9XCNvZA9ffYU3Vd3x77wfYZ1I/xH4OfuP6OIUxEVW6aMf/6RNffMwcIAOcHKxx9b5/mICBN2T8A3h4xd2l4t+yp2DdkFn5L2P3FrUhIwaBCwYYNxXb9+wK+/GkffZPmTrk/H+1vfx+JTiw3rWvm2wpaBW1C6mO1O4WY3c546usTURPT/o79hJEgA6FqjK9b1XYfiLvY/Slp0tCzFnDtnXDdpEvDVV4CS56xS01MxassoLD9rHI+7tW9rbBm4BV7F7GBarhd48EBOkPH338Z1//oX8NNPxpmumHmICJP2TsKM0BmGda94v4Idg3egkodtXqbLJ09VZE4ds7hLcWzovwHv+L9jWLf12lZ5yXtinBVaZzlz4itXTp48bZ1lWPNp02Q54dkzZdrz9NlT9FrbyySp96jVA7uG7DI7qdtiDTo8XL5+WZP6+PGym6O5Sd0W41OSOfEJITA9aDq+6/ydYd3F2Ito9UsrXIq1s8GP8sCJXSVFnIpgSY8lmNh2omHdkcgjaLOsDf6J/0fFlinD01N2e+zSxbguOFhOppzZNbKgYp7EIGhFELZd22ZYN7LhSPzZ708Ucylm2YPbgNOngZYt5aTimebNA+bMUfYXjyP7qPlHWP3Warg4yanCbifcRptlbXAg4oDKLVMGl2JswIJjC/DR9o9AGXPClileBhv6b9DE9GypqcC778qrJDO98gqwdSvg52f+452POY9uq7vh1qNbhnUT207E1PZT7apvcm7++kuOpZ45Fo+rq6yn9+unbru0ateNXei9tjeepj4FIOdT+Ln7zxjuP1zdhmXBpRg7NbbZWKztsxauzvJs2P3E+whaEYQVZwupS4kVubgAv/wiSzGZLl6UV64eO2beY229uhWtlrYyJHUn4YQFbyzAtMBpdp/UieRRedeuxqSe+auHk7r1vF7tdewbtg8+JeSJ9lR9KkZsGoEJuyfYdV93TuwKsbSO2bduX+wbtg/exb0BAM/Sn2HYxmH4fPfnNvEGsyQ+IYCJE4HffjP25IiJkf2w89Mdkogw/8h89FjTA0+eyazn7uqOkIEhGNNsTIHblUntGnRKijz/MH68cTAvX18gNFS+RpZSOz5rszS+phWb4tioY4ZJsgHg67+/Rp91ffD02VMLW6cOTuw2pJVvKxwfddwwMiQAzPp7Fnqs7oH4pHgVW6aMgQNNL6hJTgaGDQM++sg4jdvzElMTMXTjUPx7x78NX3CVS1XGoZGH8EaNNwqp5dYTHS1HxwwONq5r2VL+mqlr/xfL2o2XS72M0BGh6Fazm2Hdhssb0OKXFrgad1XFlhUM19ht0OOUxxj450BsvbbVsM7P0w9/9P1DE4NYXbsm51G9eNG4rm1bOQNQ1pEJr8Vdw1vr3sL5e+cN61pWaomNAzaibAn7H+1Kp5NfdtHRxnXDh8vujJmTiLPCla5Px2e7PsO8I/MM69xd3RHcKxhv1nlTlTZxjV0j3N3csWnAJnza6lPDuvCH4Wi9tDV+Pvmz3V+pWqMGcOQI8NZbxnUHD8rBrPbulcsbLm1Ak8VNTJL6yIYjsXfYXrtP6no9MGMGEBRkTOpOTrLGvnQpJ3U1OTs5Y26nuVjaYymKFikKAHj87DHeWvcWPt35qWG4ClvHiV0hStcxnZ2c8c3r32B9v/XwcJPXjaekp+DdkHcxaP2gQi/NKB2fu7s8Qp8509iF7+5dIKhzIhp98QHeXPcmElISAABuzm5Y0n0JlvRYYviwKakwa9DR0fIE6cSJxnq6t7fsDfPvf1unOyPX2M03ouEIHHrnEKp4VjGsm3N4DtosbYPrD64r/nxK48Ru43rX6Y0To06YnNhZHbYa9X+qjz0396jYMssJAUyYIJOatzeACieAdxvitPNCwzZVPKvg0MhDGNlopHoNVcgffwD16sl4M7VtC5w5I4dhYLalYfmGODn6pEnd/eido/D/yR9LTi2x6V/OXGO3E4mpifhw24dYesZ0ir2Pm3+M6UHT7XoogmfpzzBx+yzMPT4V5GT8qet0pTemNP4Fn3/sZdeX0MfHAx9+KOcmzerzz+UwC0Xsf4ggTdOTHrP/no1J+yaZlGJ61OqBhV0XooJ7Bas+P48V4wA2XNqA0SGjcT/xvmGdn6cffuzyI7rU6JLHPW1T6K1QjN4yGpfuZ7mcO6UksP174MxwAALNmsm+8PXq5fYotokIWLMG+M9/TE+Q+vrKC7aCgtRrGzPfqbunMGj9IFy+b7wk2MPNAzODZuLdxu/C2ck6Rx988lRFhVXH7F2nN86/fx5da3Q1rAt/GI6uv3VF39/74vaj21Z5XqXji30ai9FbRqPtsrYmSb2Vbyts7HwW9fUjAMj38rFj8sTq+PGWD0eQE2vsu8uX5YQjb79tmtSHDQPOny/cpM41dmU0Kt8IJ0efxNimYw3rElISMGbbGLRe2hono2xkXkhwYrdL5UqWw5aBW/BLj19Mhhv94+IfqLmgJj7f/blhAmdbk5iaiBkHZ6Da99VMhk8t6VoS8zvNx/7h+9GzXVWcOAFMnWq8oCktTfYaqVFDdgdMs9HOCTExsuxSv76xhw8gx6lfv172V8+cJ5bZn+IuxfFDlx+wb9g+kwlcjt45iiaLm2DIhiEmw12ohUsxdi72aSw+3fWpySiHAFC6WGn8r83/8G6Td1HStaRKrTNKTktG8JlgTD84HZEJkSa39ajVAwveWADfUr7Z7nfxohxrJjTUdH316rJnyaBBctgCtT18KL945s0Dnma5WNHJSV6ANWUKT4qhNclpyZh5cCZmhs5Eqt54hZ2bsxvGNB2D8a3GK1J/5xq7A9sfvh//2fkfnLp7ymS9V1EvjG02Fh82+xDeJbwLvV0Pkx9i8cnFmHdkHqKfRJvcVrtMbcx+fTa61uia51gvRLJr5GefARERprdVqSLXDx4MlFTh+ys8HPjuO2DJEuMYL5natJGzHvn7F367WOG5cv8KJuyZgI2XN5qsd3V2xdD6Q/Fp609fOD1jXgo9sQsh+gKYDKAOgGZEdCKPbTWd2HU6HQICAlRtg570WBu2FhP3TsQ/D02H/nV1dkWv2r0wsuFIdKjaAU7CvCqcOfEREY5EHsGik4uw7sI6JKUlmdzuU8IHUwKmYGSjkWbNGpWUJGdjmj07e63d3R0YOlRORNGggXn9wc3dd8+eydEpg4Plv+nppre/+qrsn9+li20Ms2sL701rspX4DkQcwCc7P8HxqOPZbgusEoh/NfwXetfpbfa1GGok9joA9AAWAfiEE3uA2s0AAKSkpWDZmWWYc2gObsTfyHZ7BfcK6FmrJ3rV7oUAvwDDqJJ5eVF8qempOBJ5BBsub8D6S+sR8Sgi2zYV3Cvgk5afYFTjURaVhx49AhYskGWPBw+y316zphz6tmdPedL1Rd0J87Pvnj4Fdu8GtmwBNm0C7t/Pvk3durIL48CBsgRjK2zpvWkNthSfnvTYenUrZobOxOHIw9lu93DzQNcaXdGrdi90rt7ZcPFhXlQrxQghdHDwxG6L0vXp+PPSn5h3eB6O3jma4zZFixRF0wpN0dq3NRqVb4SaL9VE9dLVUcK1RK6P+yz9Ga4/uI7L9y/jXMw5hN4KxeHIw7lODFzfpz7GNh2LoQ2Gwq2IctfLP34su0EuXAhczWWcJg8PoF07OUxw3bryz88v77p8QgJw86bs2XL0qPw7eTL32Z8CA4FPPgE6d7aNI3SmPiLCwVsHMfvQbGy7ti3HEVqdhBMa+DRAa9/WaFaxGWq+VBM1XqqRbf5VTuwsV+djzuOX079g5bmViEt68fR7nkU94VXUC6WKloKAgJ70SExNRGxibL563JRyK4U+r/TB6Maj0bRCU6uOl04E7NsHLF4sj6if5mOk1dKlgbJlZa+bIkVkL5tHj2SJ59GjF9+/UiXZdXHYMNlTh7HcRCZEIvhMMJaeXpqtRJoTd1d3eBXzgldRLxQtUhRHRx1VPrELIXYDKJfDTROJaFPGNjo4eGK3pZ+DeUnTpyH0Vig2Xd6EkGsh+R/34h8AVfLe5OVSL6NTtU54q85baF+lfb5KPEpLSpKX7G/YILsb3rmTn3vpAAS8cKtXXwW6dQO6dweaNbOfCaXt5b1ZUPYSHxHhbMxZbLq8CZuubMKZ6DOGWdPyNBlmJ/YXnrkiog7mPGBehg8fDr+M+dA8PT3h7+9v2CGZFxnY6/KZM2dsqj15LQf4BQDhQM9Xe6JW41o4dPsQ1m1dh1uPbuFBuQe4GX8TaTcyOopnJvPMDi1V5E/IMvfKoHKpymjdtjWaVmwK5whn+JT0sYn4evcGvLx0GDEC8PUNwIEDwLZtOvzzD3D3bgCiowEiXUZAARn/Gpfd3ICyZXWoUAHo0CEALVoAqak6eHnZxv7jZfte9i/nj9fwGp5UeQKXqi74+/bf0Ol0iEyIRHSZaCRdSwLOQPJEgXAphmWTrk9HfHI84pPi8SjlEQQEnIQT3Iq4oWyJsvAq6mW1y6cLQ1qaPPl5/76c4CM9XZ7sLFVKTkfn5WVbJz+Z49CTHgkpCYhPikd8cjyepT9DS9+Whd4rpjeAHwB4A3gI4AwRdcplW07sjDFmpkIfK4aINhBRJSJyIyKf3JK6I8j8qaVVWo5Py7EBHJ8j4h+cjDGmMTykAGOM2TAetpcxxhgndqVovc6n5fi0HBvA8TkiTuyMMaYxXGNnjDEbxjV2xhhjnNiVovU6n5bj03JsAMfniDixM8aYxnCNnTHGbBjX2BljjHFiV4rW63xajk/LsQEcnyPixM4YYxrDNXbGGLNhXGNnjDHGiV0pWq/zaTk+LccGcHyOiBM7Y4xpDNfYGWPMhnGNnTHGGCd2pWi9zqfl+LQcG8DxOSJO7IwxpjFcY2eMMRvGNXbGGGOc2JWi9TqfluPTcmwAx+eIOLEzxpjGcI2dMcZsGNfYGWOMWZbYhRCzhRCXhRDnhBAbhBCeCrXL7mi9zqfl+LQcG8DxOSJLj9h3AahHRPUBXAXwueVNYowxZgnFauxCiN4A+hDRoFxu5xo7Y4yZSe0a+zsAtiv4eIwxxgqgyIs2EELsBlAuh5smEtGmjG0mAkgDsCqvxxo+fDj8/PwAAJ6envD390dAQAAAY53MXpfnz5+vqXgcKb6sNVpbaA/H59jx6XQ6BAcHA4AhX5rL4lKMEGI4gHcBBBFRYh7baboUo9PpDDtJi7Qcn5ZjAzg+e1eQUoxFiV0I0RnAPACvEVHsC7bVdGJnjDFrUCOxXwfgBiAuY9URInovl205sTPGmJkK/eQpEVUnIl8i8s/4yzGpO4KsdT4t0nJ8Wo4N4PgcEV95yhhjGsNjxTDGmA1Tux87Y4wxG8CJXSFar/NpOT4txwZwfI6IEztjjGkM19gZY8yGcY2dMcYYJ3alaL3Op+X4tBwbwPE5Ik7sjDGmMVxjZ4wxG8Y1dsYYY5zYlaL1Op+W49NybADH54g4sTPGmMZwjZ0xxmwY19gZY4xxYleK1ut8Wo5Py7EBHJ8j4sTOGGMawzV2xhizYVxjZ4wxxoldKVqv82k5Pi3HBnB8jogTO2OMaQzX2BljzIZxjZ0xxhgndqVovc6n5fi0HBvA8TkiTuyMMaYxXGNnjDEbVug1diHEVCHEOSHEGSHETiFEBUsejzHGmOUsLcXMJqL6ROQPIATAF5Y3yT5pvc6n5fi0HBvA8TkiixI7ESVkWSwBgGstjDGmMotr7EKI6QCGAngEoD0RxeayHdfYGWPMTAWpsb8wsQshdgMol8NNE4loU5btPgdQlIi+zOVxOLEzxpiZCpLYi7xoAyLqkM/HWgVgG4AcEzsADB8+HH5+fgAAT09P+Pv7IyAgAICxTmavy/Pnz9dUPI4UX9YarS20h+Nz7Ph0Oh2Cg4MBwJAvzUZEBf4DUCPL/z8E8Ece25KWffvtt2o3waq0HJ+WYyPi+OxdRu40Kze/8Ij9BWYJIWoB0AOIAPCehY9ntx4+fKh2E6xKy/FpOTaA43NElvaKeYuI6pHs8tidiO4o1TBLZf15pkVajk/LsQEcn72zh/g0O6RAYb/44eHhhfp8Wo5Py7EBHJ/StB5fQRTqkAKF8kSMMaYxpHR3R8YYY/ZFs6UYxhhzVJzYGWNMY6ye2IUQnYUQV4QQ14UQE6z9fIwx5uisWmMXQjgDuArgdQCRAI4DGEhEF632pIwx5uCsfcTeDMB1IrpJRM8ArAHQ08rPqQohhIsQorba7WCWsff9KIRwFUKMFUJ8IoSYpnZ7Cps97z8hhJsQYqgQ4i0hxDIhRMmCPpalV56+SEUAt7MsRwJobuXnVEsAgAghhCuA0QCKAvAkokmqtsoCQohSABYA8IW8ujgJwBYi+knVhuWTEMINQH8ATwF0A/AhET15wd0CYN/7sQ+A1UQUJ4T4QwjRgoiOqN2oghJC1AdwHkA1AHeIKOkFdwmA/e6/pgA6EtFgIcTbAAIBbC7IA/HJU+XUIqKrMH6w5gCoLYRooXK7LNEGwDsAFgH4CUA3e0nqGTI/KH8C8ID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" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def format_func(value, tick_number):\n", + " # find number of multiples of pi/2\n", + " N = int(np.round(2 * value / np.pi))\n", + " if N == 0:\n", + " return \"0\"\n", + " elif N == 1:\n", + " return r\"$\\pi/2$\"\n", + " elif N == 2:\n", + " return r\"$\\pi$\"\n", + " elif N % 2 > 0:\n", + " return rf\"${N}\\pi/2$\"\n", + " else:\n", + " return rf\"${N // 2}\\pi$\"\n", + "\n", + "ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is much better! Notice that we've made use of Matplotlib's LaTeX support, specified by enclosing the string within dollar signs. This is very convenient for display of mathematical symbols and formulae: in this case, `\"$\\pi$\"` is rendered as the Greek character $\\pi$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary of Formatters and Locators\n", + "\n", + "We've seen a couple of the available formatters and locators; I'll conclude this chapter by briefly listing all of the built-in locator and formatter options. For more information on any of these, refer to the docstrings or to the Matplotlib online documentation.\n", + "Each of the following is available in the `plt` namespace:\n", + "\n", + "Locator class | Description\n", + "-------------------|-------------\n", + "`NullLocator` | No ticks\n", + "`FixedLocator` | Tick locations are fixed\n", + "`IndexLocator` | Locator for index plots (e.g., where `x = range(len(y)))`\n", + "`LinearLocator` | Evenly spaced ticks from min to max\n", + "`LogLocator` | Logarithmically spaced ticks from min to max\n", + "`MultipleLocator` | Ticks and range are a multiple of base\n", + "`MaxNLocator` | Finds up to a max number of ticks at nice locations\n", + "`AutoLocator` | (Default) `MaxNLocator` with simple defaults\n", + "`AutoMinorLocator` | Locator for minor ticks\n", + "\n", + "Formatter class | Description\n", + "--------------------|---------------\n", + "`NullFormatter` | No labels on the ticks\n", + "`IndexFormatter` | Set the strings from a list of labels\n", + "`FixedFormatter` | Set the strings manually for the labels\n", + "`FuncFormatter` | User-defined function sets the labels\n", + "`FormatStrFormatter`| Use a format string for each value\n", + "`ScalarFormatter` | Default formatter for scalar values\n", + "`LogFormatter` | Default formatter for log axes\n", + "\n", + "We'll see further examples of these throughout the remainder of the book." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "encoding": "# -*- coding: utf-8 -*-", + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.11-Settings-and-Stylesheets.ipynb b/notebooks/04.11-Settings-and-Stylesheets.ipynb new file mode 100644 index 000000000..b17fc8143 --- /dev/null +++ b/notebooks/04.11-Settings-and-Stylesheets.ipynb @@ -0,0 +1,622 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Customizing Matplotlib: Configurations and Stylesheets" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While many of the topics covered in previous chapters involve adjusting the style of plot elements one by one, Matplotlib also offers mechanisms to adjust the overall style of a chart all at once. In this chapter we'll walk through some of Matplotlib's runtime configuration (*rc*) options, and take a look at the *stylesheets* feature, which contains some nice sets of default configurations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot Customization by Hand\n", + "\n", + "Throughout this part of the book, you've seen how it is possible to tweak individual plot settings to end up with something that looks a little nicer than the default.\n", + "It's also possible to do these customizations for each individual plot.\n", + "For example, here is a fairly drab default histogram, shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.style.use('classic')\n", + "import numpy as np\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.random.randn(1000)\n", + "plt.hist(x);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can adjust this by hand to make it a much more visually pleasing plot, as you can see in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# use a gray background\n", + "fig = plt.figure(facecolor='white')\n", + "ax = plt.axes(facecolor='#E6E6E6')\n", + "ax.set_axisbelow(True)\n", + "\n", + "# draw solid white gridlines\n", + "plt.grid(color='w', linestyle='solid')\n", + "\n", + "# hide axis spines\n", + "for spine in ax.spines.values():\n", + " spine.set_visible(False)\n", + " \n", + "# hide top and right ticks\n", + "ax.xaxis.tick_bottom()\n", + "ax.yaxis.tick_left()\n", + "\n", + "# lighten ticks and labels\n", + "ax.tick_params(colors='gray', direction='out')\n", + "for tick in ax.get_xticklabels():\n", + " tick.set_color('gray')\n", + "for tick in ax.get_yticklabels():\n", + " tick.set_color('gray')\n", + " \n", + "# control face and edge color of histogram\n", + "ax.hist(x, edgecolor='#E6E6E6', color='#EE6666');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks better, and you may recognize the look as inspired by that of the R language's `ggplot` visualization package.\n", + "But this took a whole lot of effort!\n", + "We definitely do not want to have to do all that tweaking each time we create a plot.\n", + "Fortunately, there is a way to adjust these defaults once in a way that will work for all plots." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Changing the Defaults: rcParams\n", + "\n", + "Each time Matplotlib loads, it defines a runtime configuration containing the default styles for every plot element you create.\n", + "This configuration can be adjusted at any time using the `plt.rc` convenience routine.\n", + "Let's see how we can modify the rc parameters so that our default plot will look similar to what we did before.\n", + "\n", + "We can use the `plt.rc` function to change some of these settings:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from matplotlib import cycler\n", + "colors = cycler('color',\n", + " ['#EE6666', '#3388BB', '#9988DD',\n", + " '#EECC55', '#88BB44', '#FFBBBB'])\n", + "plt.rc('figure', facecolor='white')\n", + "plt.rc('axes', facecolor='#E6E6E6', edgecolor='none',\n", + " axisbelow=True, grid=True, prop_cycle=colors)\n", + "plt.rc('grid', color='w', linestyle='solid')\n", + "plt.rc('xtick', direction='out', color='gray')\n", + "plt.rc('ytick', direction='out', color='gray')\n", + "plt.rc('patch', edgecolor='#E6E6E6')\n", + "plt.rc('lines', linewidth=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With these settings defined, we can now create a plot and see our settings in action (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(x);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what simple line plots look like with these rc parameters (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in range(4):\n", + " plt.plot(np.random.rand(10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For charts viewed onscreen rather than printed, I find this much more aesthetically pleasing than the default styling.\n", + "If you disagree with my aesthetic sense, the good news is that you can adjust the rc parameters to suit your own tastes!\n", + "Optionally, these settings can be saved in a *.matplotlibrc* file, which you can read about in the [Matplotlib documentation](https://matplotlib.org/stable/tutorials/introductory/customizing.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Stylesheets\n", + "\n", + "A newer mechanism for adjusting overall chart styles is via Matplotlib's `style` module, which includes a number of default stylesheets, as well as the ability to create and package your own styles. These stylesheets are formatted similarly to the *.matplotlibrc* files mentioned earlier, but must be named with a *.mplstyle* extension.\n", + "\n", + "Even if you don't go as far as creating your own style, you may find what you're looking for in the built-in stylesheets.\n", + "`plt.style.available` contains a list of the available styles—here I'll list only the first five for brevity:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['Solarize_Light2', '_classic_test_patch', 'bmh', 'classic', 'dark_background']" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plt.style.available[:5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The standard way to switch to a stylesheet is to call `style.use`:\n", + "\n", + "``` python\n", + "plt.style.use('stylename')\n", + "```\n", + "\n", + "But keep in mind that this will change the style for the rest of the Python session!\n", + "Alternatively, you can use the style context manager, which sets a style temporarily:\n", + "\n", + "``` python\n", + "with plt.style.context('stylename'):\n", + " make_a_plot()\n", + "```\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To demonstrate these styles, let's create a function that will make two basic types of plot:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def hist_and_lines():\n", + " np.random.seed(0)\n", + " fig, ax = plt.subplots(1, 2, figsize=(11, 4))\n", + " ax[0].hist(np.random.randn(1000))\n", + " for i in range(3):\n", + " ax[1].plot(np.random.rand(10))\n", + " ax[1].legend(['a', 'b', 'c'], loc='lower left')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use this to explore how these plots look using the various built-in styles." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Default Style\n", + "\n", + "Matplotlib's `default` style was updated in the version 2.0 release; let's look at this first (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with plt.style.context('default'):\n", + " hist_and_lines()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### FiveThiryEight Style\n", + "\n", + "The `fivethirtyeight` style mimics the graphics found on the popular [FiveThirtyEight website](https://fivethirtyeight.com).\n", + "As you can see in the following figure, it is typified by bold colors, thick lines, and transparent axes:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with plt.style.context('fivethirtyeight'):\n", + " hist_and_lines()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ggplot Style\n", + "\n", + "The `ggplot` package in the R language is a popular visualization tool among data scientists.\n", + "Matplotlib's `ggplot` style mimics the default styles from that package (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with plt.style.context('ggplot'):\n", + " hist_and_lines()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Bayesian Methods for Hackers Style\n", + "\n", + "There is a neat short online book called [*Probabilistic Programming and Bayesian Methods for Hackers*](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/) by Cameron Davidson-Pilon that features figures created with Matplotlib, and uses a nice set of rc parameters to create a consistent and visually appealing style throughout the book.\n", + "This style is reproduced in the ``bmh`` stylesheet (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with plt.style.context('bmh'):\n", + " hist_and_lines()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dark Background Style\n", + "\n", + "For figures used within presentations, it is often useful to have a dark rather than light background.\n", + "The `dark_background` style provides this (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with plt.style.context('dark_background'):\n", + " hist_and_lines()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Grayscale Style\n", + "\n", + "Sometimes you might find yourself preparing figures for a print publication that does not accept color figures.\n", + "For this, the `grayscale` style (see the following figure) can be useful:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with plt.style.context('grayscale'):\n", + " hist_and_lines()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Seaborn Style\n", + "\n", + "Matplotlib also has several stylesheets inspired by the Seaborn library (discussed more fully in [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)).\n", + "I've found these settings to be very nice, and tend to use them as defaults in my own data exploration (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with plt.style.context('seaborn-whitegrid'):\n", + " hist_and_lines()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Take some time to explore the built-in options and find one that appeals to you!\n", + "Throughout this book, I will generally use one or more of these style conventions when creating plots." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "encoding": "# -*- coding: utf-8 -*-", + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.12-Three-Dimensional-Plotting.ipynb b/notebooks/04.12-Three-Dimensional-Plotting.ipynb new file mode 100644 index 000000000..bd580cde2 --- /dev/null +++ b/notebooks/04.12-Three-Dimensional-Plotting.ipynb @@ -0,0 +1,641 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Three-Dimensional Plotting in Matplotlib" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matplotlib was initially designed with only two-dimensional plotting in mind.\n", + "Around the time of the 1.0 release, some three-dimensional plotting utilities were built on top of Matplotlib's two-dimensional display, and the result is a convenient (if somewhat limited) set of tools for three-dimensional data visualization.\n", + "Three-dimensional plots are enabled by importing the `mplot3d` toolkit, included with the main Matplotlib installation:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from mpl_toolkits import mplot3d" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once this submodule is imported, a three-dimensional axes can be created by passing the keyword `projection='3d'` to any of the normal axes creation routines, as shown here (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = plt.axes(projection='3d')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this three-dimensional axes enabled, we can now plot a variety of three-dimensional plot types. \n", + "Three-dimensional plotting is one of the functionalities that benefits immensely from viewing figures interactively rather than statically, in the notebook; recall that to use interactive figures, you can use `%matplotlib notebook` rather than `%matplotlib inline` when running this code." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Three-Dimensional Points and Lines\n", + "\n", + "The most basic three-dimensional plot is a line or collection of scatter plots created from sets of (x, y, z) triples.\n", + "In analogy with the more common two-dimensional plots discussed earlier, these can be created using the `ax.plot3D` and `ax.scatter3D` functions.\n", + "The call signature for these is nearly identical to that of their two-dimensional counterparts, so you can refer to [Simple Line Plots](04.01-Simple-Line-Plots.ipynb) and [Simple Scatter Plots](04.02-Simple-Scatter-Plots.ipynb) for more information on controlling the output.\n", + "Here we'll plot a trigonometric spiral, along with some points drawn randomly near the line (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes(projection='3d')\n", + "\n", + "# Data for a three-dimensional line\n", + "zline = np.linspace(0, 15, 1000)\n", + "xline = np.sin(zline)\n", + "yline = np.cos(zline)\n", + "ax.plot3D(xline, yline, zline, 'gray')\n", + "\n", + "# Data for three-dimensional scattered points\n", + "zdata = 15 * np.random.random(100)\n", + "xdata = np.sin(zdata) + 0.1 * np.random.randn(100)\n", + "ydata = np.cos(zdata) + 0.1 * np.random.randn(100)\n", + "ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Greens');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that scatter points have their transparency adjusted to give a sense of depth on the page.\n", + "While the three-dimensional effect is sometimes difficult to see within a static image, an interactive view can lead to some nice intuition about the layout of the points." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Three-Dimensional Contour Plots\n", + "\n", + "Analogous to the contour plots we explored in [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb), `mplot3d` contains tools to create three-dimensional relief plots using the same inputs.\n", + "Like `ax.contour`, `ax.contour3D` requires all the input data to be in the form of two-dimensional regular grids, with the *z* data evaluated at each point.\n", + "Here we'll show a three-dimensional contour diagram of a three-dimensional sinusoidal function (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def f(x, y):\n", + " return np.sin(np.sqrt(x ** 2 + y ** 2))\n", + "\n", + "x = np.linspace(-6, 6, 30)\n", + "y = np.linspace(-6, 6, 30)\n", + "\n", + "X, Y = np.meshgrid(x, y)\n", + "Z = f(X, Y)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = plt.axes(projection='3d')\n", + "ax.contour3D(X, Y, Z, 40, cmap='binary')\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('z');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes the default viewing angle is not optimal, in which case we can use the `view_init` method to set the elevation and azimuthal angles. In the following example, visualized in the following figure, we'll use an elevation of 60 degrees (that is, 60 degrees above the x-y plane) and an azimuth of 35 degrees (that is, rotated 35 degrees counter-clockwise about the z-axis):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.view_init(60, 35)\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, note that this type of rotation can be accomplished interactively by clicking and dragging when using one of Matplotlib's interactive backends." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Wireframes and Surface Plots\n", + "\n", + "Two other types of three-dimensional plots that work on gridded data are wireframes and surface plots.\n", + "These take a grid of values and project it onto the specified three-dimensional surface, and can make the resulting three-dimensional forms quite easy to visualize.\n", + "Here's an example of using a wireframe (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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wb7abDi8maa90Y7daeN/RJs5MRLkaLqTmfpi4nYR8OZan7ITQhl4sF/psNvuyFvpXtJAX576TyeRNX2xrCXnPWAibJKjz2fnWqWEWFhbwer3Y7Bqjy2ysMCLJZpFoKdeKYKo8dvO8Nkm71sWkTFtbGwcOHODAgQPMJFRafVYW4lm++NhJhoeHGVqI064X0vzEvjp8TiuPjOa5HXA7C/lyFHfYFQt9Mpk0hT6ZTL7shP4VKeTLc9+3irdsreh6z2iYnfUedgVUzs1l2bpjF6DlvCUBFyYjZp84YA7JeWEkZL40FtauPZTM0T+XACAjw1w8x6t21FHutnEh7kHYXSwm8tjSS5w7d47F2Sle0+XnzLzC4Hzipt/zRvFyEvLlWE3ojbbavr4+gsGgKfSKoty2Qv+KE/LiiaG3mqpoNU2ezMpcmI7QaE/x1kNtZGSVk2MRVFXl4nSU5nIX6bxKz1jEfM9MJIPDKvHUQNA871hIJ6YAHr2yAMDYkhZg66wp403dNTw1uMR0Vqtzv2/fVrZu3YrVakXNaNH2v//+BaampkilCtV2LzVuJyFfbUzVRlDMmrO0pMVEXg699K8oIc/n86TT6RW5bwM3e6ddLuSKovDt5y8gK/DmI9t59a5m3HYLTw8EURSFyzMxjrSVa68NapVui/EsoWSO7bVlPDcUIqtr+LFwBq/DwpE2P49eWUBVVYYXNeFtr3Tz43tqySsq376g5cU7qty4XC4aGhqwlPmxCnhhOk88nWdgYICTJ09y5coV5ubmzCDeS4HbTchvVj+70SdfHLkv1vTve9/76Ovruymf9WLxiiCNWM6aeq220GLSwheLYnM9lUpx/vx5+pesSAKOdFRht0rc21nJUwOL7N8L0XSePY1+QskcTw8E+T+v7WBwQTOp7+uq5NxUjBOjYdocgvFwlo6qMt6ws4bffXiQK7NxRoJJJAEt5S7sVomddR5eGA5hlQRNgQKD62Q4TY1bMJ1QOLVk5b2H96IoCrFYjKWlJaamppBlmUAgQHl5OYFAwIz232zcDCG/WZuzIeTJrMxvf2eAZ68GcdokvE4bkoA72gJ87LVbsFmuvxEsX0vLCTSWlpZwuVw35bpfLF72mnw9uW/YWCUbrG9hGZp8YWGBM2fOsHXrVi4vKTSXu/DqbaMPbKtiPpahZ1b77F0NXl61tYrZaIbBhaTpN7+luwaXrWCya0Lu4sFtVVgEPNa3yEgwSVPAid2qfW1v21vHUjJHrc9RsjAnQmmavBJ7Gr38x6lpFD1t6Pf7aW9vN4N4FRUVhMNhent7OXPmDCMjI4TD4Ztqat4MIb9ZGlhRFK4sKbztM6c06witwrC53MloMMV/nJ7hV79ymXRufZmJa91XIpHA4/Gs+feXEi9bIV9emnq94NpGhHwjBTHhcJjR0VEOHTqEx+fn/FSU2WgGRU9v3d9VhRBwbjGPzSLoqvFw/1aNxunpgSCD8wkqymzU+53cs6WCpweDRDMyoZTMlqoyAm4bd7SX8+jlBUb0VJmBN+6q1q636HpyssJsJE2NS/Dew42MLaU4NhRiOSwWC5WVlXR2dnLo0CG6u7spKytjdnaWU6dOce7cOZOl9cVo0pulyV/sOVI5mT96bJg/Pp7AKmnZi7fvq+f/vqGTxXiWcreNX7q/lR9cXeLD/36BZPbagn69Z5JMJjeF/MXAiJ6fO3fumkMNirHRmvTrfYmZTIa+vj5UVeXQoUM4HA765+LIikomr5hmeEWZnf3NfiZjKttqvditEjVeB90NXn5wdYnBhYRZ0fbA1koW4lmeH9Pe216lCfTrd1QzGU4zupQyXwPwOKwINL/eaEyZjWaQVah2C167vUobztAzdd17ttvt1NTUsH37do4cOcLWrVsBGB0d5eTJk1y8eJHp6ekNB/FuB02uqCo//2/n+caFRV7f4eQj97WSU1RetbWCD//7BfrmEoSTOf7umTEAzk5GedOnThKMZ274M3O5HHa7/YbffzPxshPy4tx3NBpd9wK6WY0nAMFgkFOnTtHU1ITX6zWvoXeiEDE/PlyoSHtVVxVpWQuOGbi/q5Lz0zGuLiTpqtaE/L7OCiwCnp/QAmxb9ONfva0Si9BIJox8OMB8LIMKpPMKL4yEAZgIaUJY4xLYLBLvOFDPseEQI8FCj/p64HK5sNvtdHd3c+TIEdra2sjnC0G8vr6+dQXxbpYmfzFC/jdPj3JuKoZNEvzcPi/PDoUIuKx85ewMp8YjBFxWPnhXM0fbAgBIAhYTOX734cE1z3m7BBPXg5eNkK+W+94INmqur3asqqoMDQ0xNDTEwYMHKS8vL9H4ZyfC1PoctFS4OD5SEPKdeoNJ8bJ4oKsSgExeoUvX5H6XjYMtfvoXMzisgnq/w3zdoIFqq9CEPJ7J892LWmTdbZP49vlZHu9b4Ne/egWAvzqT5Y4/f45/eFbTTv/v2/1mP/tGIYTA4/HQ0tLC3r17OXToEHV1dSSTSS5evMipU6cYHBwkGAwiy6Vm7s3S5Dd6jq+fm+Vzz09Q7raxq86NJFl4ZjCI3SLxyGUtw/Hhu1u4oz3AybEwd7QF+B/3tiIBTw8u8czgSsad61l5t1NGAV4m0XUj971Wamw9eLHmejab5cKFC3g8Hg4dOqRFaZPJknOenYiwv9mPz2nj4Yuz5GUFq0Uioft3i0VCtr3Og89pJZrOs1XX5ACv3lbFybEILQGb2S8O0FLh4vJsnCcGgvzlkyNcnI5hsEclcwqPXFnkEZ2AAmBHhcDt8/P8sOaPn5uKcf9fHcdtt+CySbhtFt51sJ7XbK+mMbCx2WqSJBEIBAgEArS3t5PP54lEIiwtLTE8PIzFYqG8vJyKioqbEjS70XP0jIX5/YcHOdLq58xElJ21fk7NZIhlZOIZmdfvqOLRK4t0N3j50L+dR1Xh+GiY46Nh8xy//N+X+NrPH6SzpvAdGemza+F2EvTbXpMbI4lejIDDizPXQ6EQPT09NDc3s23btlXnjs9FM0yF0+xvDnBHeznxjMzlWY0Iok/naeubjZnHCyFM4WquKAjZA1s1DW+UtRqwWbTfv3hiinNTmoA79Sj7jtrCAvTYJaySYCmjshDLlJj3oBXrBBM5JsJp/r8nRnjD35/kwJ88y1v/oYexpY2Z9AasViuVlZV0dXVx+PBhuru7cbvdzMzMEA6HuXz5MhMTEzccxLsRgRleTPArX7lES4WLD97VQl5R2Vbl4PO9GrPtn79tBwvxLB1Vbj7+zT6yssrrd1Tx9+/aRcBlpaXcyZ5GLyqsoL2+npDn8/mbmqp9sbhthXy1kUSrfdHrXTQ3Yq6rqsro6Cj9/f0cOHCAmpqaFccZn987GQbgQLOfo+0aP/oJvUy1bzZGwCEIJnIM6QE5IQR2XXCvLhSEq9ytdZnFs9q1ZvIK/9EzaZrmkiiY/VuqXFgEXNHLXhv9DuJZBYdVYjwGgwtJM0qsfxStFS4e/cgRarx2jKxbTlYZCaZ486dPccefH+PY0IsjhbTb7dTW1rJ9+3Z8Ph+dnZ1YLBYziHfp0qUNBfE2qslVVeVjX79CLC3zqw+0cVV/5rPRLPMJmcaAk8OtfnonoywlsizoVFvvO9rEHz86RFZW+dt3dvP37+zGKgmeGQySyBR6AWRZvub1JBIJysrK1vz7S43bUsjXm/veSKprI9xtkiSRy+Xo7e0llUpx5MiRVQsbijeOs+MRHFaJ7XVeqjwOumrKOK4L+ZXZGO0+7R6OF9Wnx9L5Fa+N66Wr8/E8R//sOQ796XN84rFhjPmGigoeh4XuBg+XZrV0EEC9z8FMJIPNIkhkZXMjiKS0yS936xtPvc9BQ8DJa7ZVISvwvqON/NcH9pufn8jK/OJ/XuJnPn+WydiLz5erqmpW4hlBvJaWlhVBvPn5eXNKzWrn2IiQf/nsDAPz2sZ5R3s5F6Zj1HjtfOHMIgLNWvre5QUUVbNsOirdtFe6+L3vDjAZTvPQ7lo6qtwE3Dbe1F2DrMIXTkya579eUdXtlCOH20zIr0XLtBosFsuKQM9aMFhC1oN8Ps+FCxeor69nx44d65o7/vzwEk3lhUKVO9orOD0WYi6aZjaaoavcQmPAaQbk8orCeChNVZmd43pkHDCj4Cqar70aXrejms/81B4kARndMfc4LChoWvloqx9j63v3wQYA9jb7ABjVTXKfSwvHlLtt7Kz34rRK2C2Ch/Zo1krvVIzffiHDXz05vK5nthaWm9pCCLxe74ogXjwe58KFC5w6dYqrV6+WBPE2EnibCqf5iydGqHDbaCl34rJZOD8VRVW1Z6MCexq8fObYOAB/+JatDMwnSGZlBhe0isIP39Ninu83HmxHEvDvPdPma9cz1283TX7bBN5UVSUUCpHJZCgvL78plMgbPVZVVSYmJgiFQuzYsYO6urprHm8IeSYnMzAfx2GVzEV9R3s5/3pigu/pnGstPgm5rILH++ZRFJXJUJq8orKr3sNzQ0vEM3k8Dit/9v2VQmURUETRTt+c5uMb2t1tkxhcSNLgdzAdyTAeKpjBD19ewG4RTIa19tbZaJarCwmmQtrvU+E0/XNx0nkFiyQIJUq16T+/MMlP7KujpeLG5q1dz58uDuKBtsGGw+GSIJ7TqcUsrme2q6rK73x3ANB47Dury1iMZ5mOaBmZu5pdPD+RIp7Js5TIsavew1wsiwosxLKUOSwcbQuYLb8AAbedt3TXoqiq+fnXE/J4PL6pyZfDyH0btdXr3bU3qsmvJeT5fJ7z588TjUapq6tbVyGDcc6LMzFUFdI5hVFdEx9uK0cI+IHeiNLslTjaXk4kladvLsbAnBaUu7ezHFmF0+MRvnV+1vQPiyEv80guzcT51gVt0IKgoPENSqiZaBabpH2587EsNovguaEQdT4tJfevJyZ4fiREjcfO88Mh/vLJESQBsqLy7FDI9N9Bsyje94VzN8wCu9GgmdVqpaqqqiSIZ7fbicfjnDp1ivPnz68ZxPvymRlOjIb56KtamY6k6aop4zmd+76zyo3DIgg4LfzTc5oWf8vuGj57TGPRef8dTcQzMj+xr37FNf3hW7fxiYe2mxvM9XzyeDx+W2nyH6qQLx9JZLVa1y20cPM0eSwW4+TJk1RXV9Pd3Y3Val3XeQ1NfraICea0/rPfpZnBfbMxarwOfHZNuwM8c2WWH/RqGqcuN4vdInjk4gy/891C8YVu9eN3Wumu17TClqpCXOAf9BHI9+rMMh6HhXm9QssqCbaWS+xp8mGVBImswkI8y0HdZP/m+XmCiRztVW6mIxme15tcBJpQ//SRRqAQrAsmc/zyf1+87vO41nO6Udjtdnw+HzU1NRw5coSuri4kSVoRxOubWuLPHh/mcKuf/U1+FBU6q8v4V93M/sRD2xkIZvG7LMzEjImrKpF0niOtfi7NxKnx2rlbHyp5LVxPk99OJa3wQxRyI/dtsKYavbobEfKbocknJye5cOECe/bsoaFB81/XG9AzFu/ZiQitFS4CbhtnxgtVb3e0VxBM5Nimp7hqvA6aA3aeujxJ0uqj3ufgjv3ddNe6+N6VJfJK4TO7qzWtHEnnCer5dZfNwuEWjcgxnNLu+5fua+Un9tWRyMgsxjVTO6+odAUk9jb6yCsqlXrE/ruXtL50wzI4UZQPtlslM01nFIDIKrjs2hI5NhzmP09dvzz2VqDYTHe5XDQ2Nq4I4v3Wt66QySscrlY5M6Qz4loFA/MJ/E4rDX4HU7E809Ec9T5teOS/n9I2gIPNfk6OhdnToFFfr+d6Xk4++Q9FyA3zfHlwbSMRcHhxmlyWZS5cuMDS0hJHjhwp2Xk3cl5VVTk7EeFAS4ADzX5TkwMc0AXS77KhqipXrlxhW0BwNSIYDWs5WofDwZZa/wqTvHeu4BvPRDUhvzgT5wF9Rjlo6bQd9V7ec6jRDLQ5dEEtswl21mkLzeey4nVa+bk7m0o+Y1+j19TWO+s8ZPWLGF1K47JJCCCTLTyHTzw6RCi5egT8VmItk98I4o1mPfQvaZvefdvqGZiLYRXwL0/3IYDuOhfnp7TNV5ZVXHYL9T4HU5EMAkyu+p/cv9JUXw3rCbz9yGry69EybSQCDjeuyePxOCdPniQQCLB79+4VvdQbEfKFlEowkWV/s5+DLQFGg0mCul/td2oaNJ3Nk0wmcTgcvPlwF4mszNBCgg7d/D5bVPMO8O49msm4fFlLwGeeHTF/N/LsjQEnFW7tHmy6nT8Zk6n2aj54OJWjrcLF432LJed88+5anDYLbpvEdCRNMWwWgQpUee3me1Tgn46Nreu53ExcK+CWzsn88aNX8Tut2C2C7S01zGdtNAScnF1QUIHmMpUvP98PwP2tDkaDSeZiGdw2icaAk7FQGodV4oheu349rEfIvV7vmn9/qfGSCfl6ct8bNddvRJPPzMxw/vx5du3aRXNz84vmXr8a1j5/f3OAg60BAM5MhAHMINzwzBJOp5O2tjaOtlcAWjqno8pNLJ3j6mJppdnXLmnv97pWLqRwunC/6bzK5NQ0Q3MRlpJazj2ZlfE7rZyeV8xCmFhaZiSYZCmRw6+fs9Zr519emCCdV8jLCpPhQsdVS4WTaFp776EWP8UcCt88f3MntKwH1xLyzz0/wWQ4TXuVi5YKFxZJcHUhQSIr49NZcO/Y3kJvULNM7m7zoqgQz8hk8gqhRAaL0JqD1kMWAZvFMCuwkdz3ciG/nqBtlAhiYWGB2dlZDh8+jM/nuynnvRpW8DqtdFaXsaveh8MqcXpMm2PWMziNRcBUAiSrZrJXlNlp0MtZt1S6V02ZGWbzgUZ/yevGFRU/vTMTUf7xicvma4oKexu9xHPw3JCRk1fJ5BQ+9e5u89z3bqlgKpJBVlSyy2717vZyfv7uZgAevrSAw1rYbKLpvJkZeKmwlrk+tpTicy9M8KbuGsKpPG0VbiKpHHOxLMFEjrs7tQ3VahGEkjmafRLTac262lbtRlYhkVORVWiSwly6dImZmRnS6fSKzyrGZjFMEa43kmg5LBYLmVyeRy/P8f7Pn2bPHzzF73+3zyRgWO349Wj+ZDJJf38/VquVffv2YbPZrnn8RoT8/IJMtceOJAnsVondjT5OjYW4cOEC/fNJWircZGSVsWiBzdNIZTUFnGYqbDXU+QppvJ/YW2v+XPw0/vz5JR4fz7OttpDHVlIRyqwqxwYXzNfe1F1DncdGUpfocretJFUG8PZ9dQjgq72zbK8pw6avjvyy9Nn/+87aLZi3AqtpclVV+cSjV3FYJX71VW1MhtK0VrrMPv5Kt5UKlw2nVeLbF7RA3MFaK9/v1zY+ozPQeMY/85qDtLS0kM1m6evr4+TJk/T3969aifdy88lvWTGMYZ6fPHmSI0eOrCuNIoTgk6dSXAxeoNxtQ0Xl305OMrSQ4M/f3k2N7mMaWI8PPz8/z+DgIG1tbYTD4XUX2eTz1+ctDydzBNMq8XwaRVGRJMGe+jK+cGIKh6eO8ViQN+7yMxJMMhAqCLlNX7D/dWaa5fuXwyqRySvc1ezgP8/Mmq//WHcNj/ctEs2U3m84pV1n31zB5O+ZVzlYJfHCbOEevnF+jm+cL2wo//R86ZSVCpeV333TVibDaU6NhflfX+/DCDRnZBWrJMzo/+XZOJmcjMP20jRhrCbkXz83x/PDId62t5aMrJJXVNoqXHxHJ7b8wJ0tPDu8RHOFi8f7tGxBYxl8fTBDg9/BibEwAD6njQq3XY9fOPB6vbS2tqIoCpFIhFAoxMTEBKqqUl5eTnl5+XUbUF7xKbTluW9ZltedJ31hJMTFoELAZSOUzLGzTntQPaNhHvrUcZPJ1MC1ovGKotDX18fExASHDx/G7/e/6H7y5TAi6Zm8wkgwycLCAr7MArIKfTEbyazM/uYAbZVu+pcKo3RjerPDvxaVShrI5hWsEvzykXKzLh3g8nSMdH7ta6rzFrR+Jq/y/KxaovHtFoHfUfi6l38jS6k8/3lqmu56jxnpryrqQLVIomSx/INeUPJSYLm5Hs/k+aRebntvZ4UZ+2itcPF4vxZcfM/hBq7OJ1FV1dxIh0LaBnnvlgqmIxnqfHYG5hPsblgZJJMkifLycjo6Ojh48CD79u3D7/ezuLjI0tISV65cYXR0lGg0usKtvJFiGCHEG4QQ/UKIq0KIj6/y958VQiwIIXr1fx9a77lvqpAb0fPi3PdG3vuXjw9R6RT8+wcOcveWCnNmt6KqLCVz/MkjA6UXv4ZZnU6n6enpwW63c+DAAex2+4YbVNZzbM9oCKt+i4+dHmB0dJSffOAgQsBT/Vql2856LwdbAgwsychGZ1swid9pMU3nkucAtAQcjIayJXnzv35mlKysrhBOgAafndnYtQkhXr+zmjv0oJ/xOcXw2gV/8thVk1hyd4OHBb06ttJtJZNXUIs64NZDKXWzsFyT/90zo6YF01bhZjSoXehEOE0klafe7yCWkVlMZBlfStEYcBJwWTk+qwm50VHm08k29zWvHZ8xYFTibd26FZ/Px/bt23E6nUxNTXHy5EnOnz/P5OSkWY23kei6EMIC/D3wRmAn8FNCiJ2rHPpfqqru0/99dr3nv2lCrqqqSct0I33fj12Z5+J0lBq34C2fOs6xoSUEAkkUFuS/n5qkb7YQ9FnNJ19cXOT06dN0dXXR0dFhXsfN5ngDjZSgIyBw2wRXFtIcOnSIan8ZXTUeLkzHsEoacePB1gDxnMabPhPJkMzKJVp6OZxWid96qsAso5Wcaj+v9lino9dnfJmJZHhc33iMxW3AImnTWWrcgh/opI/3NDnM536wJQCAqha+i1ROWZH6u1Uo7kK7PBPjP05Nm6Obm8qdjASTBFxWvnRyCoukzZQz2kuzsorTJlHvcxLKaJvUSX2wxUQojQBeU1R7sB7IsozL5aKuro4dO3Zw5MgROjs7AfjEJz5Bb28vH/vYx/jiF79oWrTXwRHgqqqqw6qqZoH/BB7a0EVdAzdNyA3BXi24dj2BURSVP/iulsfsW1KQVehu8CKEahIjaOeBj3/9shkIKhZcVVUZHBxkZGSEQ4cOUVFRUfIZG8nBr2dDiGfyXJ6J0lGm0F1Xxki0UAF3sCXATCTFluoy7FaJQ7qQnJmIMLigNZcs9639zoKPd3k+hUs3Eayi0IhikeDpXzm66vUYT3xX/epm4tnJiHkeo8XVQFd1GVlZZVt9oaQzlZVpKdMWSD6dMIN0xQvmL54Y4aWAkZWRFZU/+N5Vyt02WspdVHvsuGwWxpZSVLjtXJmNoyjQUek2m3j2NHiYCqdJ5mQkAfV+B/PxLA6rRCqn0FHlxrnB2MJyy0IIgdvtpqmpiU9/+tM0Njbya7/2a8zNza2XPKIRKA6STOqvLcfbhRDnhRBfEUI0r/d6b6q5vlrucD0Cc3k2xkI8y/1dleyplnDbLfzF23fzkwcbVgR3rszG+JNHteiuockzmYw5tdRgTr2R6zCwHp/88V6tx3tXjZ0jW6oZXEiYwnOwJYCsQINfc2pbKlz4HYKzE1GGdHM4t6zErXjeeGvAgUXS6tfzaukx5WUO00UohnHYPXrttb3oqxBoloDLJkqONbBLjzQ/O7yE12HBIiAk27mv1Y4CzCThSOPKZ3pp5tqptJs9FOErZ2e4OBPjN17TwWw0Q3O59nxHg0lCqSw1Hhsq0FbpMvnr37a3jlROYSKUwiZh1ugbz+LBbZUbvp7rNd0oisKRI0f42Mc+djOHVnwbaFNVdQ/wfeAL633jLc+TryfNZczafv8dLZxbUGircPHQPxznP3umCSdzeOylgv6VM9Nk84rJs3bq1Cna29vp7Oy8KcMVrmWuK4rC5cuXOX51Aask2FZpZ1+jD1XFLJ1s0ymXrLr6E0KwvdLG2ckoVxcSuGyFx25oSKO5xO+0MhPLEs2oVLi1YJpXL+pQdLrn/DVk5/iodg3lRUEz4/BkbvU3ntRr2GVFS+vJqtbOemeDDYE26OGn79LM0eInmFdUvvd8L9PT06vmlm8Wz5mqqszHc/zp94fYWlPGm3bVMBFK01zuIp7Js5jIEUrmubdTE9jWChcXp2M4rRI+ffNUVM0lmY6kUSnU/htNQxvBte7pBje2KaBYMzfprxWfN6iqqmH7fxY4uN6T33Iht1qt101HPTcUZHuth7984ioAg/Nx3ry7jr991x5etbWS+DKi+1RO5itnppieniYajXLw4EGqqq7tV22kiu16AT2Xy8XVhI32Kjcuu8bSIkShPNUoa40XmcU7quzMRLNcmY2RK4qSGwo9pQvgwRY/WZ3cwMinO3SXJZTKl8w+N++t6OcL0zEcVkFqHSXmRoHXRLggoAaV1NWFJA6LoK3SRSIrs6fRa2rBYpwOOcjn8/T19dHT08PAwACLi4vk8/mbJuSyLPNH3x8lJ6scavGTymlddS3lLjPo5ndaqdEzDJFUllROYWe9hwHdctpWo9URFCcobBbBnsbrB902ihuISfUAXUKIdiGEHXg38K1l5ywurH8rcGW9J7+pQn4jparJrMyZ8TA1PgcXp2O8utXBox85zB89tJPX7azhH967n6//4hF21JX6mn/1+ADZvDbPyyAV2Oi1XevY5UIeCoU4ffo0nZ2dVNc3c3Eqynw0gxCCMruFruoyk3f9om7GDgcLo4N3VGsLcGg+fk1N/J5DDebPNbqQJ4o2uSf61+Zfq/bYUFQos1uIX2NfNawHWdGCfB7dti/X2WKskrb5/NnJpKnpvt+3SEu5c4Wp/4ORKC0tLezbt48DBw5QVVVljl7q7e0lk8msmmbaCJ4ez3ByXHumO+s9JgFGc7mTpwa0YOI7DtQzGU5T67XzX3p9wf1dlbygs9UatNcB/R7ddgt7G33mBroRrIeSeYPnywO/BDyKJrz/rarqJSHE7wsh3qof9lEhxCUhxDngo8DPrvf8P3RzvWcsRE5WOTUa4kCLnw8f9OFzlF7WznofX/75o2YrJEAko3I56b0lI2KXB/RGR0cZGBjg4MGDVFZWcmI0hIrWBhrPqaiqyr7mAOcmIyiKNqK4ymNnLpplRm/8aA/YcFqFSdcEmvYphgCOtAVwGkE3SVBZZiOVU7AIcNslThVp8uLGEcCsDFxK5lHUwt+XL2TjEqyS4FCr30ytWSWBRYDxSAdCCqf11tn/PjPDTHRlpHg2kjEXtcVioaKiwhy9tH27RrQwOTlZMoXlemWjJeePpvnSpRRd1Zombgw4zQESLeUuk+Dy5+5oYjSopcue1v3xbTVl9M8ncFglFnXrygiypbIyh1v9yz/uurgeFVU2m71uReVqUFX1YVVVt6qqukVV1T/SX/ttVVW/pf/8f1RV3aWq6l5VVR9QVXXdI1NfEnP9WkJ+7GoQSWj+3Sce2oltjXy21SL4x4dKA4qffGqE/AYaWtYLwyc32GISiQSHDx82LYZjQ0FTcEYiCoqisK/ZTzSdZySY5OJ0lG69wOKs3qxitUi0lpeSQRpZtIC+qRlDEo2g3EwkQ5lDe62p3ImiwvCitsAb/Q7zMwwEk0b+V1vIKtBR5eItu0tZZkHT4HlFpc7rIJrWbPtIOk9jwGlupp1+yWSX7ZtLmJmOqrLC5qSCWc+wHDabDafTyc6dO0umsKxm2q8Gjc5pEEWF123X/O2mgMsU8lAyy1Qkg9+ptdKOBpPkZNXcxITQYhj7Gr1cnNGi7YvxrJmWLZ4rt1683HrJ4TYw1x+5NI+iwq+/ppP2qrJVjzeYU8tteXY3FMoFI6k8j4/c+LyqtSCEIJfL0dPTQ2VlJbt27SrJHBwbWuJwWwBJwNWQrGnyJk0rPDOwwEIsy50dFbhskkkiIYSg3F2quUN6QUc4o21q7ZUuxpZS5iIdCSbNKr/7OytJ5xRTa9/XWcGvv7p9xbVXldlKIvWv3V7N21ehNAroRBJlDgvnp7QgVVZWaS538cG7tM10KqHwFz+xw3zPz9+tERxalmVRPv9CaYmsgWKfvHgKy2qm/ZkzZ1ZUkH3l7CzPD4d45zY7iayCzSKo8dqZCKXxOa38a880FkmwrbaMYCJHLCMzGkxS53Pgskk8pk9IubuzgnhGpsatleba9WDEfV0Vq173tfByq1uHl8hcX2unDiayzMcyNPidvO+OFvP4YiGPRCL09PRQX1/Pzp07+fcPHC45x/dGczctVWNgaWmJSCTCzp07aWoqJVqYDKUYDSa5r7OKrbUeBkNagKm90o3fZeW5q1qmYG+Tnz1NfjNQJoQgk1+52RXXxFgkYTK3CrSOr6gevHuoqEEF4G376tjd6FsRCPO7bCZxIWgsrrvqPSvLWPVofjCRJZ1XzCEMZXYLH9KFOZWHiaIW1PNTUQQab5yjKI/3g6uFwp1iXCvwtty07+7uxul0mqb9t5/r5Q8fGaTCbeX+RonpSIZGvxNJCMZDKap0fjqbJGirdJsstLGMTMBlpa3SzRO62T6rPw+j9iCdV6gss1Fm33h66+XG1Ao/ZJ+8sszOk792N//wnr0m7Y5xvKqqjI+Pc/nyZfbu3Wsyp9ptFircBU21mFI5c5Mqr4yCmqmpKbxeL37/Sp/NSPfd01nJ3iY/V0N58rKMJAn2Nvm5MhtDErC91suB5gB9c3ESGa2HvlhgDDQHCvnn3sko372oNZGUO7XnkdQ51P/p2IQZNALN33RYJZoCpYSTw4vJknLY54dDhFP5koDZlkqX2V46Fc4gCbhfb8tcSmaxWSRqPNoz/tunR8yU31ODS3rjENT7C8HOjKyuSvS4kei63W6nrq6OnTt3sm33fv72rFaN1upRSSWTDM2FqSnTGocmQmli6Tx+l5V0XimJsld57ETSefxOK+FUHqsk6NGbUUJFvfhH9N7/jeLl1ksOL4G5fj2fvCHgYltdwbe0WCxks1mTOfXIkSMrHto/vmdvye+fe279bCVraf1sNsuZM2dQVZUDBw6s+f7nhoLU+Rx0VLnZ1+QnmVPNBba3yc9SMkdHVRkuu4X9LX5kReX8VBRFhWBipUXTUla4Hp9D4tyU5t8upQuvl7ttnB6PmPXaoE1HASizFzY8i1hZ6PLCSJg/eexqyWt+t41ynTxiMpxmV73XnPVlWAHGYEXNhHdqVFB5Bacu8I3+0ozGc6tMXbmRFJqsqHz8m/0sxLNIQrC3ox63281CUqXCrnLqzFmmw2kW4lke7NQ24eZyJ+cmtfFH79hXy0wkQziVwyK0nPnQYhKbRRDNFsZNvWFn9Yauy8DLrZccfsjm+mrI5XIMDw9TVVVFd3f3qg90T3OgxPx8on/B7ES6FtbKf0ejUXMU8datW9c8LptXeLJ/AYdVK93dq/vhRuBpX5OWczXy2/ub/AgBZ8bDzCbkFQIIcMe2QvXinY2FFNXOInfxdTuqeOKjRznaWsjp/sbXrpDMyiRzhQ30QNPKpgi7Bb53aaHktSuzcTprtIW4GM9qI3v1Bzob1WrrfUVltoPzSfO6ZqMaL1oqW5qI/6djK/3yGxHyTz87xrHhEL90fxs5RaXR7ySV18qAd7XVUt/ZjQo4rYIaqxalzwQneWFY22QO6CXEw4tJHFaJMrsFRcXswMsbhBzNG4+sw/XN9duNjhlugxRaMaamtAKXuro6GhtXK90t4P6u0nLE3/za9SmDV+tEm5qa4tKlS+zdu5faWs3vXWthvjCyRE5WmYtmUBTNDy+zCTNyW+PRhNtwPXwuG13VZZydiNC3UJo2MnzaTJGZ++iQtlFZBFQVUT/ZMxHm5uYI6dFzh1UwupTig186x2xRWqtplQEIlWX20pZTqyCVU4jrnVgqcLQtQEKvpVdUbWxTcdbNZS9dJioFS8LAldkEy7FRIf9a7yz/+Nw4D+2uYb++YTYGnCymVPPnY7q79KbuWixerQBqV2cr8/E8lU7ByfNaZikrqyRzCkvJLIIC244KNPgdZuBxo9gMvK2C9XCpy7LMxYsXWVxcpKura115xr94R3fJ7+f04XXXQrGGNspTFxYWOHz48Lp23+9fnsdhlUjnFYYWE0iSYGulnYszepppXhP2SFG52f6WAGcnwjzeHyo5l6pqQbeBuYJwGCSMsgqjsYJobmupIZ1OM6ZbK5VO7bj+ubi5eIFV/eKZZR1qXoeVfU0+hhdT5pe/u8HLnN6qapHgmcEl5nV6Z4ukWSSgbT61elVZLKOU5N/zispcrDTmsJFBhY9eWeB39eknH3vtFqb1zasx4GRBF/KmgIv/Oq314L//aBPjoRS1Xjs/GNUsjbu7qhF+LXZTocc0JsMZVCCqZzAEcNc6uNXXwo+8kK+VQruWuZ5IJDh58iR+v589e/Zgs9nWpfk9DhvLi5X+/ulrz+0yOtGM8lS3283evXvX1UQgKyqP9y2YFWBGddvWKjtDwRSJTJ4z4xGskqB/Lm52ym0ttxDPyAxGS8+XlVUCLhsXdVNfEpoQ2S1ae+10vCCwimTHWVGPvk5R9Oe8t6r0ec9EMisonXxOa8lrWVnlp480kskrCP35Dc4nmItqwxLL7FZ+cHWJ6Ygm9G3lLpb00UmySsmEl+Utq/96fLLk9/Vq8kcuL/C/v36FijIb1R47fpeNKb2qrcHvYCGl6PeXZjiYwipp5bbjS2layl38W4/2uYdbA1zRx0Tvb1k9PaYC7R5l3RNVl2M9gbfbiakVfsjm+uzsLOfOnSthTt2Ief+a7aXBk3/vmSSdW/u9kiSZ5aldXV20tbWt25w8PR4mlMzxtn31+F1Wzk1qQr69yoGiwsXpKGcnwnRUuUnlFPrn4oyNjeHLar5icfm9Ea02ZpcBHGzxkcwp5GSV5oCzpMZ6cCHBiVHNEhDAXCxPY8DBXK40sj4wG8VtK72f9kpXCad7LJ3nTp162FD8j11ZYCaaweuwIisqi4ksc7ow1/udDC4ksOmbT/F1Ld9kn7laGnxbj5A/cnmBj3/jCnubfLRVus2Z7dPhDFVldpw2CwspFZ/TymeOjeOwSrRUuLRsRSiFwyaZTLNtlS4u6a5TwK0115hU1UXXur3Sbk5U7e/vZ2FhYd1xox/5YpjVsJq5bpjKMzMzK5hTNyLkv/Pm7aXnVeGzz42ueqyqqiSTScbGxjh48OCKfvPr4bHL89itEvd1VbG3yW8K+bZqbVGeHA0zMBfnjg7tvN89eYVYLMab7j9SkvIDzIVsk4TZ1bWtVtv9VWC7TsrosklYBPSMRcxpJy67hIrWHjoR0ha3W1/BiTwoyzLiC9GCxjIWev9cqf98fDTMTCRNhdtm1skbSQi33UJeUbEIUdLbD7C0bNDC1LIU4bWEPCcr/On3h/jNr19he52HT797N7ORNA1+La4xFUnTEHCgqioLSU3IL83E8bustJS7iKXzLCVzTEcy5v03+J0sJXPU+zVudRXMikFjc7JIgiO7OsyJqjU1NUSjUbMgZ2RkhEgksmYWZtNcX0fFWzKZ5OTJk7jd7lWZUzci5BVljhVFHv/03NgKdtF8Ps+5c+eQZdmk7dkIZEXlOxdm2V7rocxhZW+Tn8GFBHE9H9scsPPcUBBFhTtbfZQ7BUNhlV27dmGxWEoi1QDlegupwSwKBUEFzE1BUaGiTCNDOKYXnBjBPX9Rzvx1O6rN4xNFlFJWCRaK0nbGJOQL06V1BYMLGmONkRUwrtcuFVpL84omsC6bFrEGjUuuGDlFLSn4WUvIB+YT/NQ/n+VLJ6dQgQ/e1YzdKjEbzZgb4GQ4TWPAiaqqLOoDLLZUuYim8jSXF+rXRxaTtFa48DqtprVzV3s5/Xr3mTHxxbjS1opCabHB47ZlyxazIMftdjM9Pc3Jkye5cOECU1NTJab9y20OGrwEmryYkWV+fp6zZ8+yffv2NU3ljQ5Y2FVV+sDTeYVPPVNgLEkkEvT09FBdXU1l5cYJAgCevRoklMyZTQ77mvyoKlyYjiJJEjtrXPTrRTDKwhAHmv30L+XM+1tcNg54Xg9QxXWBtEmC8aWU6TtP6f5wNq+Yi3JJz5E3lztpCjiZCBWi9XubfGYHWTHySkGwi3G8b2W6K51XTDYVY7CC3SKYj2VorXBq3O15ZdXquWJ861yBEXa5kE+EUvz1UyO8+5/PsJDI8v6jWjVhR6Wb+VgGWdXy73lFy2A0+p3IisJ8SiWVU/jAnc2k8wrN5S7G9fsXaE0nbRUuvqEPfri/SytjrfXaiWdks+EH4N4tawfd7HY7tbW1JqVTR0cHiqKUmParTVMtxo+Eub5ccI0+7v7+fpM51ZhFvRo2KuS/dHjll/a558eQFZX5+Xl6e3vZtWsXjY2NGx7GYOC/T0/hsknMRNLEM3mzB7l3IoIQgh01LlI5hTq34K7DB7izs4aZSIZpPXgUL6J6clglUwsZqPHauTATNwNZY3qJpopWCFNWRJrRUeVmd4PXDNiBlpd/467rF3fsqHUjCUhK2iKs9VhLBFZZZgHFcyoXp2Nm4UteUdlZ713R31+MTz83xgsjIa4uJLg0m+D8XIb/PjPN+7/Yy499qofPPj9BrdfB13/+oGmN1PudhUBbwMl8LENeUWkMOBldTKKo2uZmMO00lzsZXtQ09au2VjKjWwBGn8CCnikwSnWlojX5lt2l5cFrQQhBWVkZzc3NJaZ9Op1maGioxLQvXlM3Yq6vg6nVIYT4L/3vJ4QQbRs5/y3X5Ol0mmQyic1mM5lTr4WNDj2s9a08Xzqn8DcPn2V8fLzE59+okKuqplGeHljk/q1VWsfVVBSfy8aW6jLTL69AE7jWmgBut9ssyDgzEV5Rr17utq3gWq/1OZgKp83c7Wwsi11fl9F0Ho+joKV31nnpbvCWbBwLsQzvOVxaV7B8wpLPaeFN3XUoKkxFtFJWIUklOfSP31teIvTVLoGiYpaFQmmlm2N5KB9YiOf48L9f4G2fOc1HvjHKbz+1yB987yrBeJZfeaANr8PC3R3lVJTZmQqnqSiz4bZbTCFvChQEvjHg5FM69fN7DjUwFTH6yF1mjf87D9QzG82QzSvkFc13f1qfymoUvqR0c0Yj1rwxLWuY9h6Ph+7u7hLTvqenhwsXLvCNb3yDZDK5oei6rtCux9T6QSCkqmon8EngTzd07Rs5eKMwmFMdDkcJc+o1L2iDQw8laWX9NsCXzoXZt790U7mR2WlfOzuNrKj8/D1tQKF1dG+Tj97JCBMTEyj6YzSKYLbVenDbLZwZD/P1M6Xc6sYQRHuRgBj5ZqcxSTSv4ndpfx8LJgmnCmmrrTVu03c2cHw0TOuyQpj9NaVf7Rt3VvP6nVrxSCiRRVFhNpplR12ZKdjVtQ2UOSxm04yxBRRHpv1FHW4ZeW2z9Q07q/nEG5p47RZNqL78oQO860ADsYxciKBH0uamMR3RatXr9A0PtGGGT+gTT+7vqmQilNbIGH12+ubiOK0SVR7t+x0OahVuXdVuzk5GkQQMB1PmzHWALZXOEq1+IzB88tVM++npafr6+njjG9/IRz7ykXWl6U6ePAnXZ2p9iAKn21eAB8UGqoxuibm+nDnVarWuu1Nso2WQkiTxG/etrI6LZxU+8+zoimM3IuQ5Wea/Tk2yr8lPd4OPLUXsL9urnISSOXLOAKNJbaHN6r621SKxV+9A+8/TpfzkRhlqna+gEbN5jRQinpbx6kGvCofQz5ktCXA1BFymEIAWgX9qIEgyK5dEv5+fKb3PV2+rps7npNpjM1Nqb91Ty6t1CwXgM8fGUFRMuuioHkq4p8iPfezMoLkJHG1buzT0/q4KjjRpAl5VZsdlt5qTU41ZcFPhtGmCT0Uy1Hjt2CwSU2FN4D/97BgOq5a6q/M5mAilqPM56BmLmPRO47rrMxpMIYRmKcUz2uiqpWSupGDn3o4bK2UtxmqBN8O0/5//839SUVHBCy+8wLvf/e51BXinpqbg+kytJpurziITAdYdYLrpQm4wpwImc+qN+sLrgcViYX/j6ibY3z49XMKztlHG1m/2zjITzaDoG9S+Jj/nJqPMzMzgTMwAMJG0cHo6SbXHztBCgqhe7Xag2U//XNwkXTBg+OPJXOG6lhI5umrKmI1lcOrDBZfVmSCEFmRy2y28MBIyg3QdlVpe/smBRbPizSLgQLXEL9zdbGppIzBX7N//8v2tplYFeGEkQjIro6gqNovA6IeJZBRTsI9NK6a74VfWZmtt9GuR8bm4XBIxB2jyO1FUVWsfLRJ48+dIGq/TypXZBF3VbqpcEjaLxKRO3vhPxzQT/u6OcsaCBW2ZzilE9Is2MhTFHXl3XGNTWi+uVwyjKAput5t77733pvDb3QzcdCEfHh6mvb2drq4u8ybXU9p6oxBCMDExsVIo0FJKn3yy0IG1ESGXVcGnnx2j3G1jIpTUiSF8hFM5Tg9M8NCrjuC2W7gwk+LKfIojbeWoKmbb64GWAIpKSdlpMRbjhYj7ZCTN1uoycrJqbiixjCaYdovGIWcMNrg8E6NnLIJX99P3t/ho8Dv42tkZU0N3N/g4t6jwlt21ppZ+fiTE+akoo0uaoGklqg6adMEqbmPNK1BVRHAxG81SrgtNsYleVr52sK/eZ9dYVhNa4Q5QoskXYtqEmEY9Lz5dJOSjwRTxTJ67O8qRFZVaj7YxTYTTlNktnJ7Qygfbq9yMBFNIArrrtWBXv15aHNY3W0PIJQE76l58autapbo3wmug92hck6mVIjZXIYQV8ANrk/0tw00X8p07d65gTt1oJ9p6kU6nmZycxGaz8ZMHGkr+ZuyhXzoxyYCeGtpIUO/piRwz0Qxv3V1HKJlneCGGI67511lfE06Hnd2NPs5OJ8gr8NDeOmwWQY+eq93X5L9mqql4FHZOVqnTF7uhiaYTCm6HlZyilsyA+/zxSfKKilunaa71OHjTrhp6xgt1s7vqPSgq/HNRmekXT07xW9/uL/DKCW2DNIpPKj2lcY2aMo2TzmGVCCWz5mZQjNFgiqqy1fsMRvvOMzo2znwiT41OFzUVTuO2Wwi4rGYQrSHgJCcrzOnkIaqqmgyrv/XGTqYiGeo8VuKZPKFkjvFQykyJtZS7uDQTQ1Fhe60mwEb6b3ZZzb7TAg7bi+dAvx4T60aZWg8fPgzXYWrVf3+//vNPAk+qG9hRbnl0HTaeFoPr74rBYJDTp09TW1tLeXk5H3vt1pK/F4vy//nGJfKysm5NHkvn+Xp/kj0NHn7yoLZ5fP0HvRza2oTXaaVXj6rva/IzHc1htwjuaK+gu8FnDkH0OK14ViFqNCArpawwJr+brnnSsiYUqlp4rdxl5dhwCJ/TalakqWhjiYshCdhTJfHo5UKL6VIix0gwxUN7aszPX4xnzQUZcBpMrdrvQoKuCq00NJ6R2Va7UgtOhdMmDfJyfG8hQN6pWTOWdJiTJ08yMBWk1mNFUZSSCPpcLIOiaj9/8eQUmbzC0bYAfqeNSFqmzmNlUs+LX11ImmOHWyo0vjebReDQqwONlPjy1dNVbll3s8yNQlXVDWtzvW/iekytnwMqhRBXgV8HVqTZroWXRMg3aq5fa1NQVZWRkRGuXr3KwYMH8fl8yLKM024tEZpiXJyO8YnvDawrcq+qKv/vW5cJZ1RqPHYCUhqXFYLCT2NDA3sbfWbwbW+TX5vYEbDhsFk43FrOhakoKT2PnFs2hXT51+9zFq75YZ11FAosrtUee8nGkJMVouk8+5q8RPRYQySVI72s4mUmkuE1rdYSKmcAj92CtWihnxwLmyZ0XlGRBJTpbaWDi2m2VNhI5zUffDVhno9nS4KAxfjauTn+/HktMn5Ht0bxFExrk1LPnDnD6T6tYMlnlU0BTmZlPvmE1mT05t21pg9f77EyEdZ8b6uksb/UeO0sJXJkZZUddR7GllIgNMvAIihh9gW4s/7mCPm1hDibza46vWcd57weU2taVdV3qKraqarqEVVVr92JtQy3vBgGNq7J19K4RnlqKpUy2VOLj+2oWhmAM67m33omeWwgfF1N/pUz03zv0jw1bonhhRijIyMcaCnn4py2yPY1+xmcjxPP5KnV56UbFNKHWgPkFZVz+iSVzCqjhkXRNTmskqk5r8wlzNd/9g6tEiyWzrO/2Wfmo40pqKqqCQTAeCjNN87Pme91WgVDi0l2Vmjjpij6rHhW5oWiRpfjIyGzcm4hrqXVDHM3kVU4OVUQ4M8eG1v1eRnHL//W2ypcjIY0v7jB70AIwVw8T1dDJYcPHyZv91PhsjA9PsqxXm1OwKefGTF9/5byAitrvc9Gn96v/mO7apiLZmmtcJmTVV+/o5q+uQSyAjaLtKIOAWB/tbjlmvx2rHaDl9Bc34hPvtqmEI/HOXnyJDU1NezcudP8woqP/a03dq04l/F9V3vs/MmTEzw1HF/zc58fCvIHD/dzqMXPoWqV0XCOHXv2cbC1nMH5ONFUjr1NfhRVK4o5qQuMoUkPtAQQAk6Nhklk8qsywbjtFvP1bF4pCcxJusAbWjOdVzjSGjA3zqPtAUCb4w6aQF+ejfPwpXlq9dy53SoxHkqRVygZx7SjzkNbhYuhIrKH54dDZo+60Q1XfM3TscJ3IKti1cWiLvvfwFQ4Zb42EkwRSeVJZAuR9tl4juaKMnbv3o1V7wFP5RSOVGvvEvEFrs5qm2W912Z2uP383S2Mh1K0lLv43iXN+rmjLcBiPIvNIpiLaf3juaIxz0Zq7sVGu6/XH387ssLAbeqTLz9+bm6Oc+fO0d3dTUNDaYCtWJPfuWXtUUk5WWvj/OTxEH/+2GAJwYKqqnz++TE++K9nyeQVmuxJdtW49BbSOAdaAqgqnJuKmpRPZyfCPHp5Hr/TwtVQjpys4HVa2V7r4dR4mG+dm1n1OuxFeVvD5DaaU2RdBZUVVbh5nVbTIhgLpqjx2s2OKqNqLJrOm/PSUlnNvJ5JqGall90iSGVlfu7OphKGlLlYln/rKS3WMRBY1lSTk9WS6kK/c+0mDdBq5r02LT7w9z8YM83t4pRZQ8CBoqo81qdRJ//BW7fjr6qhzG6hxu9mYDqIxwaTs4sMzifwO61UlNkJJXMIofUEWIQ2NgtgZ20Z8YyMTd8sjU3m8A2SNi7Hy7EDDW5Tc72YsXVgYIDJyUmOHDlS0pK61rmLtZcBr8NCOJWnym2ltkzis8fGOPInz/CR/zjHb37tIvf8+bP88aOD3Nnmp8oJIbWMA61aiefp8TC7G31IAs6Oh/HrJa0nRkL0TkY42uIjnVe5pNeSH2otp3cizH+fWZ4F0WBEyo0UH8CvPtBm/t3vtJhUTKClzIzFOh3N8BN768y/GY+63GU1o/JGkG4sJpsmvdMmMRJMmnO4i7+iRFY22V6KBTecltlXW+qHGywzVgF//ZO7VtzbMpYoyhwWGn1aF90jehBQazpRmY1qXW//91v9jIfS1Psd/NiuGiZ0LV1fX08cF00BJ49OaSZ4p0/lkWOnAbgyE8UmCZrLXeboKCMgt5za6aFVhkvcCF6OveTwEgbeNmqup9NpTp8+jRCCAwcOrEkJtdx/f/3OlV+oMaZPy1trpqtNEpwZD/OdC3MmU+l+f5o7O2u4MJvA47DQUenk7HgYj8PKtlqPOdBwX5PfjLC/64DW8HBiRAsyHWoNkMopXJ1fyXlW7ijMNTOsvlqvnQe3FXrbA24bczHNFw64LLxg8LDrgvnm3bVm2sro3+6qdrOoU1+16uNM+5b0Ge5C85uzskqvzgRbHDuySIX8cVO5qyS191v3V5t57GJYLBL7m1duuMU19gDBpMyOGid+p5Vvnte604obUI4NLfHdi/O4bBJ365RME6E0Tfo9TIZS+BwSjw9rVsBdO5pxVmkp5cuzSewWlSp7nsevaOc2LB65yCkXaN/JzcB6WGF+JDT5atioJjdG6bS0tJQU1ax17mIh/83XrfTLYzpp4VIqTyitcLitnGgmz6892ImsqPzEFgs2CWLOGo60V7KUyDETl9ld5+bsZARZUdnfHKDX/NlPWh9gv6fRR4uv0MtsLKjVimCa/IWNyvAW9jf7EVJBOGJpmSG9oONQS8AkZrAIrbyzKeA0zXljdLtKwSr4uTs1ITi3oH1Acf+0kcMvRl4p0C/bLILiRrTvXY2Tyq7cnI10pHVZOmP5PecUcNgsRNJ5Iqk8brsFn9NqklYMzCf5jQfbSeW0llpZUZkKa1VtOVlhJpphKprF2DtaK11MRQr94RlZ0FEXYDKSw22FF65qPno4lTP98YDbis1yc5b5y5GpFW5Dc31ycpLFxUXa2tqoqbm+mbU8LVbpWal5VChZkE6rVkEm0N43GoN9zQHOTEQ4qAvp5YUMu2pdJDIyA3Nx9rf4SWZlBufjZr11R3UZQgh2Vds4Mx4mm1eo8jhoKhqYUPw0Kpe3hgGHW8sZWypEsZeSOc6MaVbB2/fVmufIKyqKCn2zMZMUQ6IQmQetlPOte2qxWwQ6sSv7m/1sqdKaV87olWKOooGKoM0UA+idLC1T/dyZCEupld+brMI3emfMajK3bqcvT9kBzERzWCXNErFbBF85O8NvfkOLpv/Ggx0c1Dv2mstdzEY1Dd9S7mQmouXOp6J57mjRtGNbhYuRpSSSgEPNfvKKSiKnfb87GvzMJ1XKbFrnnLHdNHosJJPXp+teDzZ98mtgPXlyRVG4ePEiwWCQ1tbWdU+GXC3dVr9K+6nLVvhylpJaq+Xxi0PUeGyMJSwcbA1weSZGnU+j6728kKG7TtNwZ8bD7G8O6D9HeGFYE0JV0Ta1XVXa5NHzU5oQFeeiVQqCnl7GVQ5wT2e5eT70Y5fSmgDeu7UGh0WURK5PjoYIpXJIQisx9TktZttpe5ULm0Uq8Um315SZgwQuz2pC/CsPtNPgd5hC+p2LpbzsBu5tLa1yq/YUzvv/vjtYOE6nvFotm3BxJs6D26pwWiXCqTy/9/AgfpcNqyR475FGLb+NZnEYzSYaKYT2s9cu0ay7DM3lLi5NaxVuh/SJpEZffYXLiqyCe9noo7fu8DMwMEAikWBgYIBgMHjDJdYvR1YYuE1SaKlUip6eHrxeL3v27NlQ8cxqVsIH7mpdcVy2qK/72YFFmr0Ss3IZh9sqODUe5mBzwJx2cqDZz6W5NNVuCzVeB2cmwjQFnFR77JwaC/GVs9PU+RyaXy4E2ystCFHwy2djK8chAUTUgtAYQarI9Ag9I4UyZI/DQkZWqfHaSeVks1bcbbfQWuHizGScVLZAh1w8UGFHrYfpSJrFWKGks7XSbdJDGVH5126v0gYq6DCsbGMxGK27Y+HS72yhqN6+iGyFZ1eZnmIgLWupOiPS/66D9eyq89Bc7sQqaXPNBJoAmyOJK5w8dkXbeN6+y8tcPE+N1671nUcylNklcwTxmJ7nn9JTgIZrZuBdd21l165d+Hw+qqqqCIVCnDlzht7eXsbHx0kkEuuuUltPCu12Y2qF28AnDwaDnDlzhq1bt9La2rphxtbVNPl7jjStOM4QFgswF89xtLOWSzNx9jX7mYtmqPU7EEKLph9sCTAVzbGUzHGgxc+ZcY0BZn+znxeGlwglc7xpdy3BRJbBhSRlNsH2Wo/ply+vQDO0+fCiZjbuqveYhItBvFzVWU5q3YKYrpUr3HYuF7G/eOwWjrQF6BnTZqNn9KF9V+YKpmitx8Y//GCU4nVot4iS2ndJb8c8N7myg8w46i59XvlsXBMYo4XVaAIByKuFnni/69pEIMagBLddYnA+wVgoZfa/jy9p7aMaY05ap6QWPHxpASHgzV1lTEWztFW4ODEaRlZUDrYEGFtK4rRJZsXgoB7oTBe15QacVnN9FA9YPHz4MNu3b8dqtTI8PExPTw99fX3XZW1djyb/kfXJV9PMRnnq0NAQBw8epLy80LO8ESFf9fMslhX84wYMqz2VU0jlFJNUsX8uzrZaD2fGw6ZffnE2yYHmANORNLORNPubtUBYS4WL9x3VJn+eGNWYPY+2V3B2IsJ4sDSqblxGRZnN7At/7Y5q01T+2qkJDMX7mh0FaqJoPM6T50fM34OJLLvqvSZRo6LCew43MhfLmmQVF2YTfPviAm/dVagX+Nzz4/z2d/rN5+G0Svz/vjXAsF4EY/jlRq6+wm01799wsQ+0aKbxUjJXMpvcCLR5nZZVWWJA21R+SmetSWUVzk5EGQsmTWqm8aUULXrgbyKUojHg5PcfHiSbV2ivdGMRMBnJ0lrh5lPPjALw43tqGQmmyMsqrRUuBIXUYTEe2KptVqsJp9PppKGhgd27d3Po0CHq6uqIxWIlY5RjsViJll9P4O1HxlxfLnjLzfV8Pk9vby/pdJpDhw6taK6/kYaW5TCKVkquC8xpnqf1dNhiPIPHYeH0WJhDLQHOTkTYVuPBbhFcnEuVUDkZAaaDLQHq/E66asp4YVQrlT3aXk42r/DHjwyUfKbHKC0tWizGfGy/HU7NF+7z/m01prDNpwTDYcU0i2UVrk4tmsdWuG186O5WGvxOFH2BP9W3iBBwyKvFBiQBzw2HuTKX4Ijuw6bzCo9eWeAX7tGi8BZJe69hTgdcNvY2lqbH3tytmfsL8Sz1vpWBzbFgak2WGEWFq3pPvar/yykaRzrAmJ4XB61E12aReObqkl5YVEY0LRNJy7jtEmf0oYbdDV4G5xPkFRW/y4bTJmG3iBIXAuB9R7V7vJ6ZLUkSgUCAjo6OkjHK4+PjnDx5ksuXLzM7O0s2m73meX6kffJik9ooTzWoc1Z7aDdDyH/51R0rXjNSTQGXjWm9g6p3MsL+5oCpwZNZmeFgku01Li7OpdlRp1E5nR4L8/XeGa2IRRequ7dUcmY8QiavcLi1HEnAseFS/9QgPQwmC5vcs4Naqmdfk59QUfS6we8kqQtbOq9wfi5V6BGvL+PJoai5kO9pdpBKxPmpQ/VmwCunQpdf0N6l8dEbys1lk9hSXWa+9qE7Gnh1l2Y5GS6scQ6rRaLB7yhZGK/eVqVpS1llIZ4ryRgIrk0DBXB8JIzNIqhw28xNorXCTSSVI5LK01rhQlVVJpZSDC8mOdTiJ5rO017pZkovwDk3FcNm0SihHVaJRFYT/HAyRyavYLdKFDNEC4FZ/7CRcU1QGKO8a9cujhw5QlNTE+l0mpmZGcbGxhgeHl5B4AgvrhhGCFEhhPi+EGJQ/798jeNkIUSv/m95S+qqeEmE3NDss7OznD9/nt27d68oTy3GzRDyO9vXHp5gRN/TOUX3wf0MzCforNZ24dNjYfbUlzEUzJCVVfY0+nh6YJHeySi7Grw8P7yEqqrctaWCrKzSF8zjcVjYVuthWdxn1YjzC6OaP/yq7QXz3O+0ckpnGwWNVy2izxX3OCz89NEWpmN5029+664qxsbGqE6XVtZlJAe90wWXwW7RBhwWTzZ9694GBhe0INdyI3s8lGJ8KWV+jkXSRicZzS6zsSzlRYQSqnmc9v/yqSoAF2diyIrKq7oq2VKt+eJuu2RG1lsqXMzHsqTzChYJPninFlNpr3IzFdUeaO9klFqvNjLaiKgfbQswHkppfPOZ0vXicxTM6o0KeTGEEPh8Ptra2qitraWjowOPx8P09DSnTp3i4sWLTE9PE4lEXuyIpI8DT6iq2gU8wdrtpClVVffp/966xjEleEnMdUVRSKfTTE1Ncfjw4es+iI0yti6H0a22Vnm1EZyJpvMsxLI0lWsLbzqisZOcHg+zt9GLrML5qQh7m/xMhtNsqXLzU4ebWIhnuTIb43BrOTaL4MJCnnw+v2p1GLCiaMRAvGhHaK5w8UT/Aj6nVc+La69LQisFff3OanwOi6mdpbIAu3fvprp1m3kOrw2GFlM8cqEg+Pd1VnKo1U+waNrJdy4t8NSgFiQsTvGBtvF94Evnzd9lnbTC6He3CLhbT5mVLB7jula51Ugqj6LCg9sq8emVLT1jEVPIm8ud/I4+7PCnDjUS1QW2o9LNdDyv0V7ZJDJ5rQDpG3r13F0d5Siq1h6rUtpe+sai+eMvRsiLIcsydrudmpoaduzYweHDh2lrayOfz/Oxj32Mnp4ePvnJT/Lkk0/eCEnKQxTIGr8A/PiLvmAdt1yTZ7PZdZWnllzUBhlbodDnm0wmzWEKxYGsYkyFS1k00zkZqyQ4PaZF1s+Mh+muc2u162NhJvXUzhu7a3lgq7Z4nhkI4rZb2N/s5+Jijv7+fsaWBd0MrSYrhY6oYk33zy8U+PtqvHaOj4So9toJuG2mhnRYJWp9DhxWCy1FjKxPDyySz+f55slCDCAlC3wOCwOLhRTe1GKE/pnSSPrTA4scL+KJKy/Kq0tC6xMvXhgXpsK49Blru+o9HNb9++LdQVa1oN5alOx2i+BoeznBZA6rJPjy2Rkm9PTZl05OcWxY23Tee7iRkUWt4KWlwsXQUg4VeMeBehbiWpT9uaElJAE2XXBNptois+mjr2o3f76ZQl4ceBNC4PF4aGlp4TOf+QxNTU28+tWv5pvf/OaNKKlaVVWNrqZZYC2CeKcQ4pQQ4rgQ4sfXc+JbKuSRSISenh7a2to21Ex/ow0twWCQs2fPsmPHDhobG/m1B7esenxWVs2qL9AKTHY1eDk9HuZQa4CFeJZ4TqXFb+XxK/N89+IcFkmwGM9S6dFon54eWESWZe5qL2cyDkmrj6uLpQQKjX7NLTACTgC1RSytoWTBvx0LpsjJKi6rhSad+MC41lqf1q01FtIi4jZJ8GT/AqdPn+ZCUDvz9toyrVqswkWqyDkdWMqt6GsfWkiQyMps12vWq/UGFaskTEuh2M24MB0nkTECc1aa9Yq+5QHtijWooAC21bhxWCWGF5PkFZXRYIors3Hcdgtf7Z1le20ZXoeFWq+dkaAWZXdYJa6G8kgC7tSnyYZTObMM1uBXN8qFjAi7ALxF1NHXi4qvF9erXc9ms7ztbW/jr//6r1edL/Ca17zG5Gwv/ieEeKj4OJ3aaa1AR6uqqoeA9wB/JYRYfZEX4ZYJ+cTEBJcvX2b//v1UV1dvyATfqJALIRgfHzfZYowJLU3LuMhBy5ODFkQy8IPBIAdbApyfirC7QYssX5hJ0uyzcHk2zo46Dw9sreLJ/kVUVeW+zkrOTUZYjKW5a4tmuv7XhciKb0XkSyvcBBDVOdRdNgmntTDcYGhRy/sOLSaYiaTNgJusqDitFp4eCBJLy2a6aDKcQapoZiysne+PH9L4+C/ro3ttFoFFEsgq3LmlAkGB9cU499E67Xcj2m80dtR4bJQV+bRfOzfPkl76Oh/Pmab7cmSXbSbFi8vrtJHMyiWjj0+OhklkZX7qUANuu4VOvUx4JJikvdLN80NLJPOwo7bMfN+zg5oWP9Dsp3cyilUSTEYyJZ/VWlGarblZmvx6XWiqql7zcx5//HEuXry44p+qqt8E5oQQ9QD6//OrnUNV1Sn9/2HgaWD/9a77lgj51atXCYVCHDlyBLdbE7SNCO5GjlUUhWQySTQaNdliilFciglgnNXQQhVuG+FUjuaAi5ysksjJBFw2nhhY4tSMtrB+/p42XrujmvlYhgtTUe7ZUo4KvDASZme9F7/TyjODK6u+ItlSsXdbIZZRsFsEeUUlvUwo0jmFdF4hnCr15y5MRfiMPq1VBYxU9T8cn0NRtVbSbXUeGvwO877ysmoKbf9cArfdwu5GX0l8oLFCi43MLsXMcwMEE7mSCS0jwaQZIxgNJgmlC9ddPMxx+cy34rubCmsBPdD8a7dNIplT2FLl5n+/toOrC0k6q8uQFZWxpRRNASf/T/fT37anhuHFJFZJMBpKo6iaixHWhx9GUnmsRf74h+5uKb2OW2SuF2O9s9ivgWKyxvcD31x+gBCiXAjh0H+uAu4GLl/vxLdEyFtbW9m9e3fJA9kIO8x6H1Y6naanpwebzUZnZ+eqX6Qx+WTFZ+j/G1Mvv39F2zgfuzyP12nh2EiECqeEVdJmj9/XVYUk4Im+eXbVe6hw23h2aAlJCHbUe1eUUwKEllW3elwaZ5vXLsjJ6oq8rkBLpzutWuuJ0X7ZOxXj/FTBr36HTi5pjApq1vPMW4ror1QwA4GzOnd8c7nLJJcAGItpF7CwjKZNZ7NaQRwBWtDyc8+PF461WkxLwL1KL7+ByXDGrOxL5RTyegzljTurWIzniKbzdFa7mYmmyeQVhhaTzOtVQt0NPoYXk9itknn9g3qnnkElXdwB95ZlxJYvhZDDixb0PwFeK4QYBF6j/44Q4pAQ4rP6MTuAU0KIc8BTwJ+oqvrDEXK73b5qQczN5F4Ph8OcPn2azs5OvF7vmvXH7z3SvOI1m6R5cZIojDZ6XqdU+uLxCZOc8JcPebizo5LvX1nA55DY3+TnqYFFrBYL93ZW8tzVJWRFJZpe2XiyGhJZmb1NPlShLRTDdTa+BOOJxbMyW2vLVtBMG9Tod26pwu+ympHxtko36ZzMxeloyfHFhkIqpyAJQajISvjiyQJlsxGZ9tgtJPWv6YGWglkuKBBMGpsLaESSBle8p2gDWS7vsgq/+x1NM2+rLeMj92r9BTPRrFks01VTxsiipu1PjIbZWedBElq3X99cnGRWNgt1jGsYD5XuUFaJFQJ9s3zyawnxjXCuL3t/UFXVB1VV7VJV9TWqqi7pr59SVfVD+s/Pq6q6W1XVvfr/n1vPuV+SFBrc3AELU1NTXLlyhf3791NZWXnNDcRqkVaUuBqXZ5jNzTpJgc9pxSoJvvRzBwG4uJDlNdurmQil6JuN8eptVfTPJZgKp7ivq4JwKse3z89yeWZt3rjiRxHPyNzdUWH2iIM2Z1xB23ACRa2or22SuDq9SDEM+Xx+eMlkglHRNq2/fHyoRIBrvHbmljXKXJyOUtSMV/JcDC5zuWixvvf+bvPngFPiVSunUZGVVbNEd76ogWU1UTCO+7uf3M5iXLu27/ctmnXnndVlpsDXeOxUltmoc2tnmotlsUoCj9OKV2/iAc21KMaBVcgsbpYmh7WtzHQ6jcvlWvVvP2y8JMUwcHMGLCiKwpUrV1hYWODw4cOmv389PvXuhtIv3jDtjHz5nkYtJRRL58krKqFUju21ZZyczvKqrVrQ6smBIA/o9ElPDQS5q6MCScA/PjdW4pcaMJeCSsl87OVrJJ7W8sAfuLOlpHf77XdsMckjDH1qpN++cHySjqpCUPGRS/N8qae0KKY4T2zg0kycXNFe6HMIqvWhCjF9FJJR3iqArhqPyUnnczt41317VpxzLeRXUWyyqsVAavxuzugNMtF0nmPDS1SV2fA7LXz7gpYD/903bWV4MUmTVzJLkI+2BRgNJpFVbUNejerr11epdLyZQr4WblfqJ3iJhfzFDFgw8u12u529e/capPTrOvcfPLT9mp8TSRXYRmwWwRN9Czy4rYqrIZlEIsneJh9P9C/SVummo8rNU/2L+F02uqrLGFtKcXfdynOqRf/vqi8U//yLnht3WCUq3VoPdJXXzi8/0F6yaP/3d0Y4NqZpNZdDwiIVFcigUSMd1fPVxdub4bM+enlhzQkuW8u1zwmlVWLpvFmgUpwSkyRBJi+bEfP5WIad9aV12Ws1AS0/VzH2N/uxWCxc1VljvQ4Ll2cTbKly85nnxhhcSFLjsbOnwcNUJEOzR/B3z4wB8NOHGxlaSGrDHW2SxlCz7Bp2NdxaTb4WbldWGHgJzfUXw70ei8U4deoUra2tbNmyZcX5r6fJt9Wu/OKLMTivRZ8loaXWnuhb4AF92udXnu9nqztJ32ycS6OzPLC1kp6xMKFkjqWEZnK6vKuWGZswgnIV7sLAg0xeYas+lWQxluWfj42ZWtTrkOgZixDLaam2RFZhX2Oh4UZBs0ZOjkVYDqNVdTaWNTea5V/HaLTwrDJ5Bb/uJhRH3mVF5We/0Gv+nsopzMey5saxtdptsrpsJNT0hp01TIW14FqN185b9tQRTefJ5BX+/tkJhIAf21XNwJym6XOywqWZODaLoNbnIKeo2CRt+ktOKd1MqtfI098MIb+ez72pybkxMkdZlpmdneXChQvs2bNnTTqo9WwgvmuMLJqLZdhaU4aiFmrGE9k8LRUuBpIufvY1Wiryu+cmqMnNkVdUPvafJ1lI5HHbJb596dqz5wyu86WiJpW2Shc9Y2FA44T/66dHAc2SSGYVU0BTOY1ieWgxiddhpdxtw27RqCn36f6n3yn4y/vd3N2gtdi2lDt52946fuaI5kQb6/PX9tv42cM1vGVPwfRQgQmdEDK/TP0aOXcD/+urF83r6qguo7JsZcGH/VrqHQjGk5zTSTAPtwbMEtneqRhH2jTq6wOt5Ywsadd0bAYcFkF3nYez41pw9JA+TNK2TI2/bf8qJhU3R8gVRblm5Px2pX6C29hclySJoaEhs979Wg9wPTPO3nu4lEjCWKzGAzDaHffqBAf/fWaG12yr4vhIiEqPk601ZVwMWXjXa45SZoMXJrMcqrXw1i32VXuZDZTrtETLMR5MmeZ3pGi8ck5nhWnwO5CENn3kM+/dww/+1114nBbu66zksY/eicdhNRlhP/FQN2+4/yhHtzUjq1DjkHlzTZiHWmV8Tu0OPTZ496v28ptv3MUfvGWHmXraXqtpn8++dy9//Y5CoO3H92pVlcUR8wvTBaHvGQszFoyXPEvQLAznNVJp/3JslK+d0Kij7mjx8B+ntFiCVRLc26kJfHe9hxP9k9gkCKYVFGBPk59Hrmib6bZa7bvyu0o37g/euTKTAjcnur4eOuYfKSF/seZ6Pp8nGo0iy/K66t3Xc+5fvL991dcNGiUjSpuVNW36eN8iD26vIq+oPDMY5MFtVZyZiPD4C2cxCik//tZ9vPOubaue18CdHYVuuOKHXbwlZfIK3TV2Ag7B63dU88Sv3s3Xf+GITgzRxD1bKhEIFmJZan0OarwOfv6eZmIZGYvADAh21Wm+f21VOUePHqW2poYqhyaClS6JaDRKJqNpSJ9Te6ZX5xMcaQ1w15YKHtxeZaYUjefybz93gLs7tEac4rFLwUSOy0WsNN6i4GP+Gq2n80kYjWvn/tPvj/DckEaZlVdUnuxbpNZrZ250gKGwQk6BB7ZWkpNV2irdnJmIUma3cEUfWZUsKpS3CI1Sa7XN/mZo8vWQOG6a6+tMoSUSCXp6eigrK6O5uXldxQXr0eROm2XVm03p6vT0uNbzPDgf50hbgExe4cn+Rao8dh7vW+DuNi+KCn/TmyUja6biZ49N8C8nVp+UYuCp/nnTNTCu0CoJPnRXC/fpmuv9u938wQNVpGRBgz5hxEh/GeOPlhLaPO9arwNVVTmp54kVtbDYjUYTVdWeSTieZCqmCZwi2cjlcly4cIGTJ08iy/r8bhXesEtzgyQhTM39zOASW2vK6Krx0N3gK6mga6+wYwFcRd02sXThuzXM/tWmrKgUhjRsr/eZn1fvsXBhKkqdPYuswkg4i90icVSvWT8xGkJWVe7trODSTAybhNl7D4XgpizL5HI5crkcsiyjKMpLIuS3KysM3GYptMXFRXp7e9m1axder3dDte7rOfaA0T21CtJ5hVqvg1RO4YGtmmb84olJ7tlSwbNXgwTH+nFaJcbDWf7wLdv4xfvaeOTyvEk4uBZS+aKea6EVm7xhVzW//potVJbZ8DsE7znUQF1Lhx6M0oR6PqoLuf57sdB/79I8zw2HtAo5tCGNUAhCpXIyw8PDfPXMFHpfCUvJPG1tbRw6dIj9+/eXdIuFFmZZWFgo2YRnoxnevFsz2Xc3+kxeOYDdARkZ+Nb/PMK7D9ab71m+HUfSa2/q+5p8/PFDO4hnZOr9Dn72zlbyKlT6yvjzk0kUFe6ol+gdmsFtk8wJLA1+J/GMXFJbD/C/XtOBw+HAbrdjtRa43fL5PLlcDlVVX1T78st1sALcJj65wfc2PDzMoUOH8Pl8G2o3Xe+xv/yq1Rt2jGCRUbkV0k33nKwysRgllVP45EWLWWtus1r4wF3NNAUcq7KiWKUC+aGB6jIb//aOFpI5GRIh+vv7GZycp9broLm52SzhNIYdzuvFIkaH2Kwu9G67xB89MmiSKlolwT+/ME4mL5vHTAWjxJMpHhtXzIkqiaxMQo/yW6xWwroAWgSMJ22Ew2FeOHGSaFFBzet2aBp+d0MhBeiywjvv1pphLkzHmI0WIu5dNes3V3/jNVt4Sq/3v7MtQGRBq777wViSc7NaFdvH37KPkYiMQMXwFB7v0/LokWV88Ifb9B53ScJqtWK327HZbExNTVFWpjW+yLJMNpsll8ttWOCv55PfrtRPcBv45LIsc+HCBVKpFIcOHTJbUjfK2LqeY+8o8o+LYRTHzOq0vk8OLFKhm76npzS/czyU5v97+052N3j5w+8NkMjIJbTGxcgrrGg++YX72qhrbEJRYWtzDXNzc0SyAhdZ+vr6GJzUaucNTT63XJPrv/9nzxSxdJ6Pva7TbGGdj2X5eu8s03rfezClMCpXMB3JlOSNH7k8b57L6MKr8To4M52kq6uL2s7dJUG0E6d7uXr1KjY5hUfvJ2+pcNPdXIFVEpybjPDCSMh0Ez722i3XzJ0XY3eD15xKusUa4krMqT87lQq3jaaAk4aKMq4GMyRyKjvrfbhtEuMhbTMsvs66VXj2DcWRyWTYvXs3TqfTFHxD4Jeb9dfCpk++CpYL+mopNKPBpLy8vGQcMWy8a209O7OqqtR7Suuxi2Gc4cpsHEUpXKtFQk/ZSPzhW7cTS+f5xCODPDO4xFqwWwQWvSUSNDPT0LT5qFaxF81LbGuppbq6mrH5MADByWGmp6eZiaTwOa0mv/hcLINFEjzWt8iH72k1h0XIisqOWg+fPTZG79UJbJIgmJT5zHPjdFaXYbMIMwr98EVNqEZ1pla7RVDmsDARSjEVTpvlpQYyvka8Xi8DAwOoqvZ0HBaQUNhW6+GF4ZDOb6fd43NDS2Ym4T2H16b3Aq0o6NJ0FAGknJU8O6LlxQ80+1hK5thSXcblmSiyolLncxBN57FapFXppd7aLJuVkMagzKtXr5LNZtm5c6e5Fg0tb5j1NpvNXDuG0Ofz+VXX0np88tuRcx1+iOZ6KBTi9OnTbNu2jebmlamPmy3khk/266/tLLx2jeNjepuo06rNB6sqs/P7Dw9Q7XXwP+5r4+FL8ytaKw184Wf2kZVVZFUjQQRNyC8Na+miu/fvRLLZiaTy1PmcVFZWIsq0ANPBnZ1kMhmuTi7gtSqMjo4Sj8eZWEqhKCqNAQcfvqfV3DAAXtVVznQkw1jCQpVu3g8Hk3zo7hYm9dliAGcmImRlxSRb2FJdZgbMToyGGJhPlNT1907GSCQSOBwOcqq2VCZC2iDKWlua4cUEbpvE6/Qhk9/RS1IBPnS31oCylmb/u6dHyMoqKvB3x2ZMDf5enTP/2NASH/9GHwAfvqeF4cUk0XSe/Cpf80ffdg+1tbUsLS3R09PDc889Rzgcpr29fc3ArSRJWCwWbDabqeUtFkuJls9ms6aWf7lOT4GXUMiLI+ATExP09/ev4Fsvxs0011VVNb+sN+5ai1Wn0GLptArTp07nNU2ymMgSSmT5k0cH+dDdLdR6VhInVJXZ8DqsWPVa9b2NXnMjSS5OMhHUtFVTRVnBB9ej5wuxLH6XlcqAj/b2dnJWNy3VPmw2G4NXr/Ls4AIqUO60YJVgJlLovooszNBV5WIslKFBZ54JuGy8cZdWXbalyo3dIsjkFXpGwzx7VRPy+7sqmYtlqHBbOT4SYmA+jiS0enarReLkSJBUKkV1S5fp0oTSClt27eeuHc3kFegMSOTnhoDSZpGhBY1bXVah3mtfIexGbXt3vYeH9OKcH99bx6O6S2GzCMaXUlglwZkigsvlcNskJEmioqKCrVu3EggEKC8vp6amhitXrnDixAkGBwcJhULXVASSJGGz2bDb7atq+WxW+77WOsemua7/rqoqly9fJhQKrUrwUIwXO0XFgKqq5PN5k7VDkiTKXaub7AZjUFZWzSEGu+tcpj9stQi+dX6ORy7NMx9fmSmo8ztprXTxBb0+/aePNDMVSlFmE3gcVkRZBXaLRMBlW+Fzz8cypj8Omnle53fS2NjI8xE/ybxW5z0fy3DixAkuDE1hk8BlgZyrgo880KFft3ZdO+o8qKrmfzeVu+ioLkMS8J2Lc4wFUwRcNnOe9/Y6LydGQlya1lhV9zX5SGZlFpMygcYO/vP0TMmzujwTw+vSrnVnSw1vvO+IWUNu0Y977sqUWUd/h85Msxp+643b+IG+6bxxVy2ndYE2SnwtkuA7F1clSQHgPYeMqj6Vvr4+JEli165dtLa2cuDAAQ4ePIjf72dmZoYTJ05w/vx5pqenTaFdDYaWt9vtOJ1Ostkss7OzBAKBNX35F8nUekvxkmnyTCZDMpnE5XKtIJRYDS+WLsrQ3vl8HiFEib//gTsLzCHFJns8J0yes5112q5c7hAm66uiqNgsgv/9jSsl77NKgjK7hVAyR73PwVMD2qI90FRG3/gctV6N1GI+lqHW50AIwbyeEqvx2lFVlclwyiwTzSsKi/EsNR4Hx4aW+PtnRrEI6Khys5CQ2X/oMOGcRIUD6soElyeDNFm16rMhnUHFYZWYjqRR0UglOqvLsFskHr+iWQQ76jx06lzsNV4HC/EsC/EsNotgq6tQ5NI7GeXxfi19tVWPnl+eiTG8WBiYEM0oZvqus6aMLVUuLs7GWYxox1RaMqt2pYE+wDGZw2ERHB8NmdaA0Qzz6q2Vhe95lZ3iVx/sMJWH1WpdMeraarVSU1PDzp07ueOOO2hvbyeTyXDu3Dl6enoYHh4mGo2uWZueSCS4dOkSe/bsIRAImFreUCyGll9aWvrRNtej0SinTp3C4XBc008qxkZTaMUbguF/G/XGyz/vZ+9cOSsNtMiuEURa1DnF+pdkfuN1WwGo9lhLuOFAK/vMKyrdjV5mImmCiRw5RcVplRjtu0BUttFapdMsRTPU6eb5kC4kf/nEEPd/8nn65xKcGA3x4X87x788P2HSOn3sa5fpqHIjq1pkWwV6rowyE0nTVutnd1sNixkLwZR2XTlZpc4jMbwQZ3xJE9bGgJOOKjfpvGI2yOyq99Jc7sJuKZ0z3ukXHOnUfGybRXBiJMRYMIXHYTGzExdnYjw9uESZ3cLgfILvXiz44jarxP6WAINLeeaS2jVJ19jQ//LJYUAb0PAXj2tm/wNbK5kOpzUmHn2DsQhWlAeX2TUf+tKlSzgcDjo7O6+5toQQeL1e2tvbOXz4MHv37sXlcjE2Nsbx48e5fPky8/PzZoA4kUiYcwIMAV6u5e12O6dPn2ZoaOiWd7rdKG65uT4zM8OlS5fYt28fVqt13QwaN8oJdz0BN443SA2Xw6FTGc3Hc1R5NOKFezvLsQiYia000e06a9zBeheKCpemo1S6rVS7VLq7u5lP5KjX55nPRjVN/sjleT53TKNQGlrQykoB9jT4GA+l+KS+8P/puXGS2Tz/6zVafr9TH0zQNxUiJltoCLhor3QzF8sSEwV/0GmzMhnJ8PQZjRnImY/TvozcsLXShUUStFe5mYtlzJLVh/bUcXB7Gy6bhcoyO8eGllCBPY0+9usNMWcnIvTPxdla6+HKbIyv9c6YLtBUOM3eJm0CijZK2MJMTC7hwF+ttP3t++vMVttfur+VcCqPVRJm0c5qlbIfurOZixcv4na7ryvgq8Fut1NfX8/u3bs5evQo9fX1RCIRTp8+TU9PD6dOnaKzs/OaGvrMmTP85m/+JsePH6e6emUP/+2AWybkqqrS39/PzMwMhw8fpqys7JYxthpfbnGAbS0BB21U8htbV//bab0+GrQ2R4C3/eMpZFUzy33LKq0iumtnzWtaMyOroOTpqgug2rTqrAa/E0VVmYtm6JuN8+tfuYTTZqGl3MVjH72Ljz6gER2882AD3/vIUX7lAa3OPpmTySsqef06PFmtCyvnrmIhlqXO56RdJ4/4rp5z3tvoZSycRVEh46zGbhHY5BSp2RHtWenXbXCVd1aXMTgfR9Gf9Tvv7EQSgq01ZUhCMKPHDu7vqmS/Pl/O4MV7oKuSVE7RiCL1nvRQMkedHluwSoId1dqIZ5vVYnLaWVbReAPj86RyCtUeK//WM60/f02yl3ebGTjij+DxeOjoWEkUsVFIkkR5eTldXV3s3r2bbDZLY2Mjk5OTHD9+nP7+foLBYMn67e3t5Zd/+Zf56le/Smtr64u+hluFWybkV69eRZIk9u/fbxI8bIQd5kZIJooDbGsJeCQSobe3l19/4+osJ7FMHp+ulQyKJcPEzSuqOd3DgKxqfOOqW8sS7KkSRLLgysd44ngvANVuCxeno+QVlaGFBP/jvjbq/U5z6N+0Hilv8DuJpPNmZ9buBq1e/o++p3VtbanxUuu10z8XR0XrUGuv1DT48RGtzPXjr+8yhWNoIUlTuYutXV0cPbgPgDK79lwuX77M0NAQdS6F2WgWowK1f07z7bfWeginCtHyfU1+qr0OqvSe7Rqv3WyMsQjBdDht5uNnY5qpXe600OLOMxVXiGVk8jozzPJCIYALQe21hXier/XOArC3QXs+uaLhFAbcVigPBGhvX73x6EaRTCY5f/48e/bsobOzk/3793P48GEqKytZWFjgxIkTfOpTn+J3f/d3+eAHP8iXv/xltmy5LvX5DxW3TMi3bNmyIghyq2iZZVnGarVy7tw5ZmZm1oyczs7O0tfXx759+wgEAuaCXY6ZSCk32kO7a/iZo6sQnOnwO608fE4ry/zwq3eSV+CO7k5clVpByPz0BL/4pTMAfOTeJn7p/jZmImkaA6VCXuaw8MF/7WUxnsVpk/j1BzUNZcQHmpsbaat0m3PO631Oc3RvKqdQ63Owt8nPLn1owkw0TZPe8PLls1qE3GnTBDHuqtVmwSdKa++f1XPo22s9ZuOLJGCbfk6jFbfR76RJL5n1uzVSScPteHogiKJCXpZ53cGtJcQOxbRVxQraiAu8SWdabfDZGVsqpAmXW+tv2xWgra2Nm4lUKsX58+fZuXNnSaTcYrFQVVXF9u3bzeDd448/jt/v5/3vfz/Dw8M39TpuNm6ZkK8WPb/ZQl5snh84cICtW7eSy+U4d+4cp06dYmxsjFQqhaqqDA8PMzMzw8GDB03CvV96VakWWK4tDHqlb12Y579OTa95HSPBFEOhPF6nxRSi1goXi3ow7CsjkMxrZ2+3x3jy2ReIpvMEbNq1T4fTCOBDX+qlby7O9toyWspd1Hu0r6elXDN//883+mitdDOlbwp1fgcqKhZJaIKoM828Ry8oWUpkaSp3kc7J/NfpaWq8dmIZGZdN4vG+Bebn5/mxu/eZ91Hpknj0/AS9vb1USIVRUi5bgXbZaFHNygoXdJroZEamsszGa3doPunzQ9pGEcmqdNV49HNIuGyS2cpqtwiKOlfNvgEjJ95c6SaUXjt+8z/ua3vRDKnFSKVSnDt3jh07duDzrc0kNDg4yO/93u/xhS98gePHj/PII4+sWsx1O+ElDQduhB3meu2jqwXYysrKaGtr4/Dhw2aa7sqVKzzzzDMsLCzQ0dFRsvm882CpdrbqfzJSNQqCcp36OLtK5MfwFY3NIZ1T+PYFzdRsqXAxFkwigOlQmh/rrkUArz66l/oujZyhjDRPHzvO106P69NLragqRNMyNR4rk4OX8dgtJHIqbZUuTo6FGQsmSes55Dqfk88eGyevqKgqpmZ9464aMxrdFHDy7QtzhJI57tlSQSav0OC10jeforFzFw57ITd/x5YqRqIKdc3tVBURjyazMvNLYVRVNX300WCKx/sWsAitTv9IW4D9eglvMqfic1pRVBhbSiEJ8Lts7Gn0mUQXWVmliCvD1PbG+U/orbQenZarGB0Vdqanpjh+/DiXLl0qiYjfCNLptCngfv/anYojIyO8733v4wtf+AK7d+8GwO/3r2u+3w8TL6mQb7TAZa2dej0BNofDQU1NDYqi0NraSmtrq5kq6e/vZ2lpCUVRuKsjYL4nVxTJdVglesbCq57bYFVxWLTrM66yxuvgm+fnkAQcHw7y8KV5VOCv3tGNqmIOLjQW8kjaxe/1KMwmFCpdFn5lj04/HE1jz8bYt28f7VXaHO+9jX7edbCBE6NhQEsfLcaz/NNz49p8bzCr3Zy2wnBEj93CF09MsKPOYzbUVDu0G/3BcIRvnJs17+sNO2tQVDg/n2FOKZirKvC901d55tgLnBkLIQktTvH9Kwu06eZ3tcdBdGYUv0O7B8Msf+zKAoqqTXDdWuMhmMzhtknmxigJSjS62y5R77VT5bEh0D5nOfHOHz20i+7ubu644w4aGxuJRqOcPn2aM2fOMD4+TipVOtDyWkin0/T29rJ9+/ZrCvj4+Djvec97+NznPsf+/fvXff7bAS9ZxRvcnAELhoBfL8CWSCQ4c+YMbW1ttLe3U1dXx549ezh69CiVlZXMzc1x4sQJPrCj9BEYvqER0S7mSDeQy+vpOqHlmI0zfOKh7TSXO1FU+Pg3+wklc7jtEpdmYpwY1QJjf/rYVf7gYW3IwFfPzrAQz+GxW7hjSyVvftUduKyCnAI1HisXL16k0i6TlbWa9f/z+i626QUpLruFTzwygNUiuL9LKxhxFOWmjLbP712eZ2ghyfuONhEOajzu7Y21dFS5ebxvga+fm8GlC909W8rxOCwcG1riOxfmzGdhkwSzaoBMxRayikbwAJrW9dk0CRybWdCKUWoLm0NHlZsT+tCKeEbmX/VhDslcgcPOYSmkyep8DpJZhZyishjPlQyKNGCzCPY2BwBtjQUCATo7Ozl69Cg7duxACMGVK1c4fvz4dctZiwXcmJ+3Gqampnj3u9/Npz/9aQ4fPrzmcbcrXnJz/cUIuVHBBiunZBQjGAxy4cIFuru7qaqqKvmbJElUVVWxY8cO7rjjDnZ1tuEt6lQ0WE0M6/xVXZUrfPVETqXSbSORVcgrKq16lNznsCIVbToCjaXlUz8YZTaaYTaa4UsnJoim8tgsgqd/9U7K3TYSWZl6v5OxsTEqXdr7j3Z3sX//fqr0dFRsforhqwP8wes1fzuczPKDq0v80v1t5jRRI+UHmGnAnrEwVWU2ttgixNOaBZHOKTy4rYqesTDzsSwumwUVCKXy3NFezg8Gl3j2atCMlu9u9PLC8BKP9y1S7rbxY3sLbs5MJIvHBlcWMthsNmT9Gvpm4+yq9zIeSpl++BZdu7dXFnwBYwKroNBOazT+VLhX9ge8YRU+eQMul4vm5mYOHDjA4cOHS8pZL1y4wOzsLLmcdu5MJkNvby/btm27poDPzs7yrne9i7/+67/mrrvuWvO42xkvubl+I77TevPfAJOTkwwPD7N///7rlhkKIfD7/fzum3eu+JvxYJ4eDK7arXafrj3tFkGVPqBgbClljlgK6L78a3cUGGZ/5dUdvHpbNZIQtFa4qfE5aSnXTG1LOkI8HqehQgv6NPid2Gw2qss1E3JLRzvV1dVIqTCg9axXua2860Cd2ZkVLWJiiesEEXkFuislHDYLOadWsTYfz/Lg9moUFcpskhlF759LcPeWCuZiGWQVc8Nqq3QzMJ/gyf5FHtxWxWGditkmCWYTMnvry5hPQSijMrSgpeDSeYV4MoWias+otcLFYiKL225hOlKo/DNQrLVtOhttJrtyrRiFQdeDxWIpKWdtbW0lkUhw9uxZTp48yYkTJ2htbb2mgM/Pz/OOd7yDP//zP+f+++9f1+fejrjtzXUjuCbL8jUFXFVVBgYGWFpa4sCBAxuah/7G7toVddEG95hhAS8fTmgUhOxq8JnUTM8PL5FXVCwCyuyaFjrYXPDzmstddNaUkczJ1OuL3Nggaj1Wdu3aZVaeGVrUmL2dkVUqKyupbCos8nhW5rkTZ7gyMoUAxoMFNtWZSLoQEFQtdHV1MRpM4bZZGF5MmAw0gaK8df9cnHv0UcwVbps5LtipRyRTOYXX7qimqbyQvwb46bu1VN8LsxDNas/MKsHxMW0225F6K/e1uYmk8hxq8ZPJK4T151fjKSV8sAitCEYFEstk/HCrnxrv2k1Na0EIgc/nY8uWLezbtw9ZlqmrqzNdttUKXRYXF3nHO97BH/3RH/Hggw9u+DNvJ6w+aPpWfZjVSjKZvP6BOiRJIpfLmd1jawm4wS7j8XjYvXv3DU2W/OirO/jkE4V8p1H0klOg3i2YSZbqc6MnuyngoHcigt9l5bt6t9SRtnJO6pzqd3cWWmlbyl1mpLjMoVk1uYSWMmpvadY3Me3vS4ksLRVuUno3nNG48bXeAnFkTlZ5cslPWkrjtOW4PLnEyZMnqaioYGgxiQo4rIJTUymWEllGgppwjy6l+PJpLSU4p7e8Vnu0Ipsf00kdbfquVu2xsxDPYLdojTtH28v5zrlCOrEx4OTezkr8LiuPXVnAIgT7mv2cn4qaJJnBrI1uq95VlolS6bYQTMpUe+wr/GWLJJDXYHv9i59YaXFtBNlslrNnz7J161YqKzVLTJZlQqEQCwsLDAwMMDU1xdjYGN/85jf5nd/5Hd7whje8qM+8HXDbmuuqquJyubh48SJzc3Nrvi+d1kgMampqbqh+2cCH7mpZsx1yVhfw/U2+ZQUccGFcq+2W0CLBAnjDrmpkRcXvstHgd5laubnCSb0+TlhVFc6cOYPHowXIDPPaIEscDmoR4ploRpvLHUwytpQ055QDPLS3nm+en2V4KUW1x8lsUrB33z6SiqVkplleUfl67zSjwZRZBvuVszNsqykzYxDb6zz0z8X5jt5sEtSHF+5p9HFpJoail/UquSzfPjWMUd1b4bYhCcGR1nKGF5McavWzq95r3kdLuYOLswkm09rY5iXZSbU+YP1otcJiMk9Vke+9WqoSNH74qhvQ4uZ5dQHv7Ow0BRxWL3R55JFHSCaT/Nmf/RnHjh274c+8XXBbmutGgG3nzp10dnaSSqU4c+YMZ86cYXJy0uQOj0ajnD17lq6uLhoark03tJ7rfeeB+pLXqvX4kIomLE6bpSSdY5UkZhLa/RgTRZsDNrbrjSRGRZ3HbkUSWiGJ4efOLYbo7OzEquepJ3R+tlAyixAwrE/3nAqn8DqtDC8m+NUvX0JVC3n8vU0+6n0OZiMZGvwOUjmZqaUkj1/UymK315aRzqt0BKx84dgImbxCm09780I8y8/e2YJNErhsEt31XkaDSb51fpYt1W7yikqNx86+Jh/TkQx5RSWdV/j2s6e5EoJ2fRa6YdJ36u850BxgNlqoVKv0aIL59ECQ1koX56bjBJN6LX6FFkTz2zUXxyZhcsktx+++6drz7K6FbDZLb28vW7ZsKRHw5YjH4/zf//t/+ehHP8rly5f5+te/zvbtN/65twtuqzz58gCbJElmA4KRIpFlmfPnz/P888+b0dG12GU2it9+07aSMT8LqdI5Yi/o6SAD6bxCRo8OH9I7tGrcFiKT/QAIJU8qlUIIrdgjk5cZntXOIVtdVFRUsJTIYZEEQ3qp6kwki89pNX+fDKep8dgZXkzSPxenu8FHU7kTm0UwFkzyS69qR6XgHz/ec5Hn5jXN+NN65dvdW+tY1OWu068FtawSdPsyOG0SWVmho8qNompFLu/U56KXOawmEaQRm7iU8hPNaIMQjYh4PJM3LQeAZwaDWPQHNzAXp63SRSSd503dGivPQiJHY8DJ432ayzMWVZBVzTWK59QVi/L+zgr2NF17nt1ayOVy9Pb20tHRsSLTUoxEIsG73/1uPvzhD/Oud70LgKqqqmtuCi8X3FIhX43M8Vq0zNdrEXW5XLS0tFBdXY3dbqe1tZXR0VFOnjzJ8PAw8Xj8RZU6CiH4q7csG6ekn84461t315jR3236iCFJwP/UJ7RUBbxs69aKJXKKypUrV4gmNQl77sIwz14aA2A0lOE/eqa4PBvDZZMYnI+TyOYJp3LUeh0MLyZIZPOEkjnyioqiwrsPNpDIyrRVltFRVcbgQsKMUl+a1oJcc6KCvvkUFgEPbtc0pddpNTevrvZmVKCyzI6sqsQzMrICA+Mz5r0cadM2zWAia7a31rgETQEHJ8bjSEJzJzqqtP72Z68u0TsRxiIJHu9bIJ1TzOrBRFY2U2h3d1RQqVs3b99Xz2IiS0elc8UMtmIvXQDvbU8zNDR0TXKH1ZDL5Th79izt7e3XFPBUKsVP/dRP8dM//dP8zM/8zLrP/3LBbeGTrzdFpigKly9fJplMcuDAAZPiZ//+/bj+/+2deXRUVbb/P7eqUhkqlbkqCZmADBACJBAgEQUUUGwZEpAGn9raIq3d/VB8Dv1sXd3te68Vm1Zb9Nnor9VnizMEQQgiNoMic4AQCFMICZmrMieVpFLT/f1xU5cAIQNkYKjPWqxFILnnVKX2Ofvss/d3e3qSn58va3rV19f36AMhiiL5+fn4OUyMHnTp1ZtT823acB1qlQJBkK6cQNqlX2sTPLA5RHkXbrTAqMQk2mJb/GlLCZkF0iLXaLbxP9+epqbJiqnVTk5pI0u/PApIAbqSWjP5bSmgzudNGOxHUU0LkQGexOk15Bmb5P8z20TcVQq25dWhUghEBXrh6ylJGxdUNxMZIJ09Pj8gReJNrXZMKj9EpAKbIwZpkgHusPOIVPXWYLbx+d5CADRentwWE0hxbYssWfXLNoWdrw6WcqS0kSh/D85UNjE20lf2cIK17pTUSotcdkm9/Lt1puC2L0IBqfClPU/eMYSUcWPRaDRyxmJ7ZdbL4dzBhwwZ0mmdt9ls5oEHHmD+/PksWrTost93NdTV1TF//nyGDx9OfHw8e/bs6ZNxLseAu+vtM9g6M3Dnquzt7U18fPwFyTBubm6EhoaSmJgoJ0EUFxezd+9eTp48KaewXg6Hw0Fubi5Wq5XExERWPZJ8gVoKnNdR/8M3J2lqlVIt72iTJtJr1XIH0PL6VlkaqabZyuJVh893UHGTGhkO8pF2sweGSdvd2EGSR3CkVNqNj5Y1IAKvficZ27S4IJSCJMXUYrUT6e9JrF5DRUMrB/MNaNwgbZSOVpsDQ2MrPh4qOa00LlgKqDljAd8cNTImwpcmi53dZyVJ6bsT9GS16ct7enpwrkmJu1K6NvzyYBnuSoGiOjPxIVLpa7PVzugwH2aPDkapkOYlAnofD+nOXyH1TYvTa1AqpGCij4eKb3IMckWds3zWGWe7dajkPZS2E6iM0Xnx+KTBuLm5ERISIos7tFdmzc7OprS0VI7TgFRynJ2dTVRUVKcGbrFYePjhh7nnnnt4/PHHrzho2xVLly7l7rvv5uTJk3KOfH/Sr+76xUUnzjY2XaWoNjc3c/DgQSIiIoiKiur0l+FMghg5ciQpKSnodDr5PjQ3N/eSHcC5eGi1WoYPH44gCLgpFfzxnrgOn9++nryyzaCqTZYL9M++PWaQo/CHiyXDjQqQdNZqm62kDpUWhxZP6QN4S5hk9GP0ktGb2io3stuqvF6aFceQIA05bYtAZIAnsW36bMcrTMQF+/Dbdt1h6lusDA6UjHyYXiNF5qub0aiV2B0iD6dKR5ID5+rx93Jj4dhQSW5KpaCszkyusZWEEG9GBCqoaYWxg9wxWx3sO17Q9nzpfK1WKojVe0vtnbzdKKxuRiFIyjFThwUxZ3QIZe3Kdk+21aorFVIn1zBftZwvcKy8kWDv84UeaqXAV4vHXfL+O5VZhw0bRmpqKrGxsXKPtwMHDpCfn09WVhYRERGXbXUN0u990aJFTJkyhSeeeKLPDLy+vp4ff/yRRx99VHpdanWnCTh9Qb/u5BcruDgTXDpLUa2treXIkSOMGDGi019aRygUCgIDA+UU1rCwMGprazlw4AA5OTkUFRVx8OBBwsPDL1H2mD92EKlDLgzozR51fnxBkAxswmA/7CKy9LGIpC7jPGYODVDj7a5kTIQvJypMtFgdJEf64u2u5GSFCZVCYH5b26EKswof9wsXQoUgjTU8xFuuI4/090TdIgWtKs0Qo/eW+6GBtDs6jTwu2FsK+tlF+VrLapdc+zOVTSSEajG3udZeagV2UQqWhXm0EhIkvf5pCdKicLrhfEWYf0sJ+fn53DZYylV3VympaGhlWLA3VrvI5JgAuTbcx0NFQ9vCpRAkRVeQjhiVja3E6KREGYPpfJ3Ah79IlBtLdIaz8nDcuHEkJCRQUVGBQqGgoKCAkydPXpLkAtJO/6tf/Yrk5GSeeeaZPjNwkCrXdDodjzzyCGPGjGHx4sU0NTV1/YO9yIAoz3UVYHNSVlZGXl4eY8aM6bTGtzs4ixni4uJISUlBr9dTUFCAw+GgtLSUkpKSS8QmPvxFErp2GVnOtj5+nioEpLP4zJHBclWW83wM59/YgjorEf6eROs0stJKQqgPsToNpfVmhgR5oXFXonVXcra6hYZWByPD/RgS6ImHSkAUYcF7e/CmhQazDaUAJsM5fFQ2vNRKzFYHnm4KPthdJHdJBclzgPM15iDFC/RaNZ9nlRIXLHkV8SHerNpfgrtSQU2zZIgO4K4xsRwpbUSpEDhWbiJOr6GgxoxbW125WRuORqOhoa5O+l3Vm9F7u8nXhqX1ZnkXVyoEbo+V5uYQIXWwr7Sbt9iwiZeew/9+3yjGRvbsxsRms3H8+HGio6OZMGGC7MU51VxycnI4evQo5eXl/Pa3vyU+Pp4XXnihTw3cOa9Dhw7xm9/8hsOHD6PRaHj11Vf7dMyL6Vd3XRRFqSa5vFw28o5wtrmprKwkOTm5U332K6GqqorCwkLGjx/PxIkTGT58ODab7RKxCYANv00hrC2BxZkj3tyu/PHZjFz57/cmhcrR41d+FonOW43VLnKiwsTff5BcXQWwKdeIzSFS32LD2NDKLct/orHtnH9XvI6PHkpifJQfZpvIlNgA6iwKtpyRVn9vFZgaGxg0aJCcWLPleCV6rTvL0kfIO61TqTXC31OObt8W7c/DqREcLKpH25Z2G+LjzpbjlaQnhaAQkJNcWkUpG25shC//OllJZIAndofkDQRp1KzLMaIPDmafUcpht4uQqFexv7AWP3eBL/aX8MWBYtRKgdpmq3zUANh5tp7xkX4MbluIfjhzvt3UWz8fwe1xl4+Ed4TdbufIkSOEhYUREiI1anB6ce2TXHJycpgxYwY7d+5Eq9VSUVHRxZOvnvDwcMLDw0lJSQFg/vz5HDp0qM/HbU+/7eROFz0hIQGTyURWVpYs1+SsDILzKaqiKDJ69Ogu9dl7SklJCefOnWPs2LF4eUkurZeXV4diE/v376eqrIjPHkpgePB5NdT2WVkatRL3tiu1pZNCUYnSa7krabCsgfZQSjhTh0nnbwfw/346x9Ey6bytVilYfGuknDN+5/AgBEGQ88NHhfny4S+SaMtuxV2tZOjQoZSXlyNYpIWoorGV/5oZh7+XG1oPycv4+4/naLVJ11fOq//HJw1mXlIonm4KSuqknz1wrg4RkXuGqEgIUmF1SC71pqMGAjVuPHJLBKZWu6wTr1LAwnGDOFRcz7rscs7VtMg91EualbTa4d6kEAwmK5tyK0kNlVz8mmYbsUEeDAmUCnL2FtZxpp3nIwBfPTqW6fGX73DTEXa7nezsbGnRCw3t8HucgiIHDhxgzpw57N69Gz8/P6qrq3s01pUQEhJCREQEp05JuRNbt25lxIirS8/tKf1i5O27mGi1WmJjY0lJSSE6Oprm5mYOHTrE4cOHOXfuHFlZWQQGBl6iD9cbc8jLy6OmpoYxY8agVl/aCRMksYnw8PALrubKigp5MsGOXnN+wYnVeeHv5UZDq53WtoKK9buP0miT3tITFSbaPFsiAzxZPjcehSDlgh/7w+28NFMK7M0cqWfp1KGyqKNz/XDuvqIoEq/35HfjpPlWtziwqbWMGDECUS39zO1Rnqiq8jhy5AgWmx1BkGIE/9xbQmVjKxa7JISYGO6Dr6cbc0aHUNx2rbXjdBW3RHihtpq475ZoHKLkUu84XU16Yii3xQQQ4OVGflsGXmSAFwuSB6EUBP6xqwg/TxXVTRYUgvSa/T1VLJkWi4+HCrsI44fqZU/HAwuNzWZ8PS5cuL3cFOx+9lZGhl1etKEjnDt4aGjoZQ0cpOPh888/j1qt5rXXXiMsLIzFixczcuTIHo13pbz99ts88MADjB49muzsbF544YV+GddJnxv55bqYCIKAt7c30dHRpKSkEB4eTmFhIXa7nYqKCoqLiy+4FrkaHA6H7B10p3uLk/ZXc5NumcAHC2II9JReQ15lM14XlablNvvQbJEywfYW1FLSJn10pKSBsnozDlG6VrPYHHIQzNm40Pl1iZzeKnkExgYzhw8fJiQktO21iPzq0yPsOF1FfqW0E/5s7GBSU1MJCI2kxSolzowIVPLujwU8/3UuICXznGy75rt/fLh8rWe2icwYrGbUqFGymgxIHse9Y0JRKRTcFh0gt41qNNsI0qiZMMSPczUtDAv2psXq4K42fbcAjRtqpQK3NvfhH3vLUAgQFeDB0SoHVS0ies/znpC/p5KfnpmIr1fHi+7lcBp4cHBwpynNDoeDP/3pT1gsFt56660BaYCQlJREVlYWOTk5rFu3rtcyNLtLn77iTz/9lIMHD8p34JejsrKS/Px8xo0bx8SJE6VdShQ5evToJWfknmK1Wjl06BD+/v7ExcVdsXegVCqJjhjEzuem8My0IQhAaYMUqHPWV3x3QnL/YvUa9hbUklPWyCBfD/YU1HK8XHLP7Q6RQ8X1nDY24aYUZLe9oKoZD5WC7BLp7HqywoSnm4KDZw3ExMRwrklamAQBKZ31y6MISK710dJGBEHgbP35KPL0hDCsdpE9hfXyv+06bUQUxQtqudUKmDc5EYVCwYE2aSmQBDCcEXpvD+kFatVKKk0WDhbV49Oms36msonEMB+5R/nZqha+O26Uq+YaLJJn8MTtQ+R4QV6tNM+kQRren6Xj8EHJANqLOnRGewMPC7u8iq4oirz88stUV1ezcuXKPjNwu93OmDFjmDVrVp88/2rp01JTHx8f3nrrLU6dOsXUqVNJS0tj/Pjx8pstiiLFxcVUVlYyduxY2YV2pq9GRkbS2tqK0Wjk+PHj2O12dDodwcHB8nm6M5wa2tHR0b3a3eLRWwczNymUuSv3UtnsoC0oLe+Oecam8wkwgkBNs5U32spYFQJ8c6SCM5VNDPL14FxNCyW1zZw2NhHm50F2ST02u4Pcsgb81SIlJtD6+pFdUo6vh4p6sw13lSBnlEX4e5JVVAfA0VKp37enWkm5yYqHm1LWjB/k48bOUxUkelRxuvm8MovFISmx6LXu/HimGr1WjbHRQqPFRrPFhpdaxY7TkmxUi01Sel2bXc6Bc7WoFFIJ7OJbo3j9X/mMj/LjwLk6/rDhJErAmVEgAMu35KNWCvJ13eSYAN69P1F630QRk8mE0WikqKgIpVKJTqdDp9PJyrpOHA4HOTk56PX6Lg18+fLlFBUV8c9//rPXYzvtWbFiBfHx8TQ0NHT9zQNAn+7kc+fOZfXq1ezbt48pU6bw/vvvk5qaynPPPceOHTt47rnnMBqNXZ6RIyIiSE5OJikpCbVazalTp9i3bx/5+fmXzVevr6+Xs4t6u32Nw+GgvPAMf58ZzM8Szj9brZSCXM7ZKICANve+qKZFvnb75qiB4xUmatuu1L7IKqPBbGPkIB9MrXa255ZQ22IjeXAgrXaRPGMTh4sbGNSmoa5WKpjdVuwhAKcqTNS3WDlW1kC0TkNCqJbtp6ppsthRKQTUSoFbooM4XecgacxYfsiXPoz+bW/5P386Q3WjmSMlDdQ2WwnzdUcU4R+7isgzmCQlF607KoWCAC813+YaqWm24dvWBvabnHJUCoG/zhtBuK+aJosDB8jR/+EhGowmC2abFBtYljZcNnA436PMef01YsQIWavN+XtuaGiQd/CgoCDCwzvuZweSga9YsYLjx4/z0Ucfyc09+oKSkhIyMzNZvHhxn41xtfSLaISnpydz585l7ty5tLa2sm7dOh5//HH0ej0WiwWTycStt97apbStWq0mLCyMsLAwrFYrVVVV5Ofn09LSQmBgIMHBwWi1WiorKykoKCApKemSneBqcVbB+fv7M3jwYF6Ph6FBBXyZVUZVk+S+e7opaLFKH3SNG3iqoMUGL98ZytFqkS8OSVc3Oo0bDS02PmxrdaxqO8euyyoEYGp8MBtyq9h6qpKyejNl9VJNd8IgH/w0bigVAudqpGPMoaI6jpU1Mjk2EIvNwYFzddybFMLGY0ZabQ7qm6Uc+czdRzhktKNUwAcPJ3PvPw7ydU4Vbi21iIDdLvLGvOH820dH+PxAqXyOf3p6NCW1Lby1Q7oK1LorqW6yEuHvwYmKJu6IDcRsqqfFLL0HIlKKrwCcrJCCdjpvNf81a1iXV2ROrbaIiAisVivV1dUUFhZSVVWFVqvFy8sLh8PRofstiiIrV65k//79fPXVV30ul/zUU0+xfPlyGhsb+3Scq6FflWFA2plzc3N58803mT17Ntu3bycjI4PnnnuOCRMmkJ6ezpQpUy67sztxBsVCQ0Ox2+1UVVVx7tw5amtrEQSB+Pj4Xr9ft1gsHDlyhPDw8Auiuf8+ZQiP3BLJh7uLeHdnIS1WB+F+7pTUtXKi0iKrkRbXWwgWpGDZIK2Kz36RwHMbzrL7rGRgGYfLEYCcWgUCdkaFavF0U/CPn6TmiPPHhKJSCqzLrqC0roWJQ/3x83Rjw1EDH+4upqbZis5bzSdtqqjBPu602hykDPZj6ynJ5f6uSKTVLjJ9eBDDQ31IDPchu6SBPTUawMrPYjU0l+URH6gkt8rGj3nVaNRKZo7UY7E7+OfeIurNdposdgK83Ajxdqe8vpUfzlRztqKa6naxUgHpPK9RK1k0MZIHxof1OCbi5uaGXq/HYDAQHR2Nt7e3rOKi0WjQ6XQEBQXh5uaGKIp88MEH7Nixg4yMjC4/Q1fLxo0b0ev1JCcns2PHjj4d62oQuqjUuvK6zR5is9nYuXMnq1ev5ocffmDMmDGkp6czderUbhmrU+OttbWVkJAQKisraWhowN/fH71ej5+f31UFXpzn+9jY2E5rjM8YTbyx7SwHCmvliHRHhGpVzIt153B5C7vLHdw51JNIjchXeVYa2wQZBdoEKwRJKCLr91PIKqxj8adHAHjx7lgWJA9i0uu75LRRrbsSL7WSxlY7ob5SBdi3v0nmvg+ypPbGAtgd8PXj4xgWrGXH6Up++8UxQPISfnh6Iv5eanbnGVj8udQVdWqEkmduj6Da4cUjnx/HKQob4uNORUMrj6fo+eKwUW7+KAD3jQtjye2D8e9h1PxinDcjfn5+F6Qetz/HV1dX8/HHH9Pa2kpxcTFbtmzp9QW+I37/+9+zatUqVCoVZrOZhoYG5s2bxyeffNLTR/Vp2t01Y+Ttsdvt7N69mzVr1rBt2zZGjBhBeno6d955Z4cBN7vdzrFjx9BoNERHR8u7hcPhoLa2FoPBQH19Pb6+vuj1egICAnpk8A0NDeTm5pKQkNDt9Nomi4312RX8bdtZmix2FML5LiFO4+0M5/cHadyoarIyNNCLjf+egsXuIOUvO2m1OfjuiVQi/D157V9n+HC35PJ7uyv5avE43t1ZyIajBm4Z4sdjcVYaPXQ8sa4QkNJydz17G4IgYLE5SH71R+wOkUh/TzL/PQWlQqCgqomZf98PwOAAD56fHMyfvi/GbHFgdghS99a2eUb7Ksirkyw/WOvOe/ePIq6d/vqV4nA4OHbsGD4+Pl32PXvnnXf48ssv8fPzw2QysXXrVjQaTac/05vs2LGD1157jY0bN17Jj/epkfe7u94dlEolkyZNYtKkSTgcDg4cOMDq1at59dVXiYmJYc6cOdx9991otVoaGxs5efIkgwYNuiTa6kxtDAwMRBRF6urqMBgM5OXlodVq0ev1BAYGdhp5ra6uJi8vj8TExG5F9J1o1CrunxDOv40P40SFicxjBjIOl9NgtiEgCTm2tKXHatwEmm0iT0wZwprDJZTVW4n2FZgzTMvHx9pkoOrNnK1qYmiQBq27EpvdQVhbIE7VzgVuarWz52wtY8J9+SbHgLu1kaghI/jrjwb5e9xV5xe4PKMJR9vqU1TbwjMZuSy9YygPfnRY/p6y+laWfCO1YxoZ6k1uuXROVyCJauTVOVArBZalx3P3CH2vJDE5DVyr1XZp4KtXr2bjxo3s2LEDb29vTCZTvxr4tc41uZNfDofDQXZ2NmvWrOHbb78lMDCQgoICPv744x61rhFFkYaGBtnV8/LyQq/XExQUdEEktry8nJKSEhITE3vlfOcQRbafqiKrqJ7vco1UtKWKxuo0VDSYsTukWu3Zo4LZcNTA/9w9mA/2llBUb8MhSkY1f0wIGdkV2EVYPncE3+RU8FO+lPsd4e9BdJAXO/JqSI7QcrC4kUlDfPD0cGfLiUpujQ5gV9v3Th8exL+NC2PJl0dpsTpQKQQi/D0oqG5BrRSwOUT8vdxIGezPprbCHCdKhcB9owOYpDMzPHowe/Mq0Nga0fmfXzivJuAliiLHjh3D29u7y9bE69atY+XKlWzcuLHTNkfXODefu94ddu3axaOPPsrUqVPZv38/QUFBpKenM3PmzB7pcjnPdgaDgaqqKjw8PNDr9bS0tNDQ0MCoUaN6/QrGeRVUYvUkyyhwymCSk2IUAqQM9uNEhYl6sw1RhOemDeX1bWfRa5RUmC4U3dC6S91PQnzcOVPZzCtpw/npdCWbTlTL13kOEZZMGcyHe4oZFqyRa9xBuvbTeqhYmDyIv/94Tr4ZuBiFIDVkDPFx509Tg7E3VJKUlCS/N+3PyFVVVVJjiLa77p6cj0VRJDc3Fy8vL4YOHdrp92ZmZvK3v/2NzMzMPskiKy4u5qGHHsJgMCAIAo899hhLly7t9XFwGXnH7Nq1i6ioKMLDwxFFkVOnTrFmzRo2bNiAj48Pc+bMYfbs2eh0uh65jyaTSZaY8vHxQa/Xo9frey1S62ytPGjQoAvSMaubLHyyr4Si2mbyK6XkmO7g7F66ZFIE352soabJgsNupbZdlFupEIgO8iK/qpkHJ4Sz8WiFnJHWEZ5uCkJ9PZg9KpjhIVqGBWvQe6tRKBSUlZVRXl5OUlJSp8eclpYWjEYjlZWViKJIUFAQer2+UzdaFEWOHz+Oh4cH0dGdd0rZsmULy5YtY9OmTX0mtlheXk55eTljx46lsbGR5ORk1q1b1xcFJi4j7wlOrbaMjAzWr1+PWq1mzpw5pKWlERIS0qnBO8+BXl5eREdHX/BBVSgU6HQ69Hr9FUdunf23hgwZ0qUAhqnVxk9nalAI0Nhq41xNC0U1LcwaGczYSF/sDpHX/5VP5jEDHUmV+3u6MWd0MFUmC9+dqLxALFHqGCowcpCWFqudCVH+BHqr8VAp0HqomBwbeEFPNyclJSUYjUYSExN7lEFmsVioqqrCaDRiNpsJDAxEr9fj4+NzgZDI8ePHcXd3vyB42hHbt2/npZdeIjMzs8dCIldDWloaS5Ys4c477+ztR7uM/EoRRZGioiIyMjJYt24dDoeD2bNnk56eTnh4+AUfJGc9uV6v77CpvNlsxmg0YjRK+d/O9NruJts4r+Di4uIICAjo+ge6idVup7jWTEF5NTl5RRS0uBPt7WC83oG+zV1WeWhYta+E8VG+DAvR4u3e8+NHcXExVVVVV13+a7fbqa6uxmg00tjYiJ+fnyzRpVaru2yQsXPnTl544QUyMzPl2vH+oLCwkMmTJ8vR/l7GZeS9gVOsIiMjg6+//pqWlhZmzpxJWloaSqWSAwcOMHnyZIKDu65ntlgsssHbbDZ5h7+cK9rY2MixY8d6dAXXEyorKzl79ixJSUlyDzhngpDRaMRkMsn5Av7+/j2OfhcVFVFTU8Po0aN7tcjDecXpzG8ICAjoMADqZM+ePTz77LNs3Lix07z13sZkMjFlyhRefPFF5s2b1xdDuIy8LzAajXz99desWrWK06dPM3/+fH71q1/1uFLNarVSWVmJwWCgtbVVNnhvb28EQaCuro4TJ04wevToPrnWMRgMFBUVdXoD4HA4qKmpwWg0Ul9fL8caAgMDuzTac+fOUVdXx6hRo3q9iksURU6ePIlSqSQmJgaTyURlZaUcuNPr9eh0Otzd3cnKyuLJJ5/km2++ITIyslfn0RlWq5VZs2YxY8YMnn766b4axmXkfUVpaSkzZ87k7bffJi8vj4yMDCoqKpgxYwZz5869RPq5K2w2m7x7Njc34+npSVNTkyw+0duUlZVRVlZ2QZS7K0RRpL6+HoPBQE1NDRqN5rK7Z0FBAY2NjYwcObJPDPzUqVMIgtDhwtrc3ExlZSVbt25l5cqVmEwmPvzww37tMCqKIg8//DABAQG8+eabfTmUy8j7ClEUqa2tveCMXFdXx4YNG1i7di0FBQXceeedpKenk5iY2KMPemlpKYWFhXh7e9Pc3Cy7on5+fr2SLOIs0e1pEKw9F197qdVqefcsKSmhqamJhISEPjHw06dPI4oiw4YN6/T9OHbsGL/5zW+499572bdvH9OmTePJJ5/s1flcjp9++olJkyZd4MW88sor3HPPPb09lMvIB4rGxkYyMzPJyMjg1KlTTJs2jbS0NMaNG9fpB7+oqEgOUqlUKtldNhgMNDQ04OfnJ5+Pr8SACgsLqa+v73UXuqmpCaPRSHFxMaIoMnjwYIKDg3s1D9wpw+VwOLo08BMnTvDII4/wxRdf9LsuWj/jMvJrgZaWFjZv3syaNWvIyclhypQppKWlkZqaKu+koihy9uxZmpqaLuviOhwOOb22rq6uR+dj5/VgS0tLn+2wZ86cwWKxMHToUPno4RTr6Oqeu7vPt9lsciOLy3H69GkeeughPv30U0aNGnXFY14nXP9G/vbbb/POO++gVCqZOXMmy5cv743HDhhms5nvv/+eNWvWcPDgQSZOnMicOXPIzMxk4cKFjB8/vlsu+cXnY29vb/l8fLEL7nRx7XY78fHxva4X7txhbTbbJc+/+J7bmdii1Wq7PQ+ngVut1i7nX1BQwP33389HH33Uo3TlnrJ582aWLl2K3W5n8eLFPP/88302Vhdc30a+fft2Xn75ZTIzM3F3d8doNPZrAkNfY7FY+P7773nqqafw8vJi7NixzJ07l8mTJ/coS+7ifHpPT0/5fOyUiFYqlVelU9fZ2N09I9tsNvme22QydSvW4PRAWltbZdWXy1FUVMTChQt5//33GT9+/FW/tstht9uJi4vj+++/Jzw8nPHjx/P5558P1LHg+jbyBQsW8NhjjzF9+vSrfdQ1y4oVKxBFkSVLlvDjjz+yevVqdu7cKdfE33HHHT3O325qapLz6VtbW/Hx8WHEiBG9LoTgvMZSKBQ9XkAuvprz9fVFp9NdcvTIz8/HbDZ3aeClpaUsWLCAd955h4kTJ17V6+qKPXv28NJLL/Hdd98BsGzZMkCqER8Arm8jT0pKIi0tjc2bN+Ph4cFrr73Wpyv0QNCRGq3dbmfXrl1kZGSwbds2EhISSE9PZ/r06d0uWXU2mvDy8sLNzY3KykpUKtUF98dXO+8TJ06gUqmuWufeWcprNBrlq7ng4GAaGxsxm80kJCR0+vyKigrmz5/Pm2++yeTJk694Ht1lzZo1bN68mffffx+AVatWsW/fPv73f/+3z8fugGu/nnz69Okdtpx5+eWXsdls1NTUsHfvXg4cOMCCBQs4e/Zsn/eg6k86ei1KpZLJkyczefJkHA4H+/fvZ82aNSxbtoyYmBjS09OZMWMG3t6X9kKH85VqOp1OTrMdMmSInE+fk5ODIAhyAU1PI+A9yRXvDoIg4O/vj7+/P6Io0tjYyOnTp+XU1bKyMnQ6XYeeiNFo5Oc//zl//etf+8XAbzZ6xcj/9a9/Xfb/Vq5cybx58xAEgQkTJqBQKKiqqup1BdVrGYVCQWpqKqmpqXJN/OrVq3njjTeIjIxkzpw53HPPPXI9tLNSLSws7JLOIJ6enkRFRREVFSXLVefm5mK322WD78pTcJZzenp6MnTo0F5fcAVBoLq6GrVazZQpU+SFKTs7W5Zbdi5MVVVV/PznP+fll1/u10SXsLAwiouL5a9LSkr6NVW2P+lzd/3dd9+lrKyM//7v/+b06dNMmzaNoqKiK/pgvf766zz77LNUVlYSFNSzpnjXIk5xhNWrV7Np0yZ0Oh3Tp09n06ZNvPfee512BrkYi8Uip9dardYL0mvb46y08/b27rJe+0opLCykoaGhw2tEZ6HPmTNneP755xFFkSeeeIJf//rXfTKXy2Gz2YiLi2Pr1q2EhYUxfvx4PvvsMxISEvp1Hm1c32dyi8XCokWLyM7OlntRTZ06tcfPKS4uZvHixZw8eZKDBw/eEEbeHlEU2blzJ/fffz+RkZF4e3szZ84cZs2a1eOaeKdctcFguODKS6PRkJubi1ar7VJx5Urpbq57fX09CxYsIDExkeLiYnQ6nXw+7i82bdrEU089hd1uZ9GiRbz44ov9On47rm8j7y3mz5/PH/7wB9LS0sjKyrrhjBxg+fLlpKamMmnSpAtq4t3d3Zk9e3a3auIvxnnlVVFRQU1NDVqtlpiYGHx9fXvdTS8qKqK2trZLA29sbGT+/PksWbKEhQsXAh0HL28iXEa+fv16tm3bxooVKxg8ePANa+Qd0b4m/uuvvwZg1qxZHdbEXw6Hw8GRI0fw9/dHo9FgMBhobGy8qvLTi+luOWpTUxMLFixg0aJF/OIXv7iqMW8gbg4j7yxC/8orr7BlyxZ8fX1vOiNvT/ua+LVr12I2m5k1axZpaWkMGTKkQ0N1dnwJCgq6QAyjI7nq4ODgK8qndwpKdFXE09LSwoIFC3jggQdYtGhRj8a4Ep577jk2bNiAWq0mOjqa//u//8PPz6/Px70Cbg4jvxxHjx5l2rRpcsS4pKSEQYMGsX///n5VBrnWEEVRrolfu3YtdXV13HPPPaSlpclJLc5rOL1e32XvsNraWoxGI7W1tWi1WoKDgwkICOiywq2kpESuhuvMwM1mM/fffz/p6ek8/vjj/eKab9myhalTp6JSqfjP//xPAP7yl7/0+bhXwM1t5BdzNTv5dbSy95jq6mrWrVvH2rVrMRgMTJ06lZ07d/Lmm2/2qMDDmU/vTK91JrV0lE/fXc03i8XCgw8+yF133cUTTzwxIGfvr7/+mjVr1vDpp5/2+9jdwGXk7bkaI7+OVvarori4mBkzZqDT6WhoaJBr4nsq3+RManHWm3t4eMgGbzQaMRgMXRq41Wrll7/8JbfeeivPPPPMgAXXZs+ezcKFC3nwwQcHZPwucBl5X3CNr+xXxYYNG2hubmbhwoUX1MQ78xTS0tJITk7u8dnbKTBRVlaGzWYjOjqa4ODgy+bT22w2Hn30UcaMGcPvf//7PjHwzmI5aWlp8t+zsrJYu3bttRrBdxl5X3CNr+x9QnNzM99++y0ZGRkcO3ZMrolPSUnptrpMeXk5ZWVlxMXFydVoSqVSzrZrLyT561//mpiYGF566aUBM66PPvqI9957j61bt/aozVU/4zLynnCDrOx9Tvua+EOHDjFx4kTmzp3LxIkTL6sX5zTwixsrtJerrq2tZffu3RQXFxMVFcUrr7wyYO/x5s2befrpp/nhhx+u9TRql5H3JtfJyt6vWCwWtm3bRkZGBnv27CElJYX09HQmTZoku+IVFRWUlJR0KRppNBpZunQpR48eJSQkhMWLF/fLdVlHxMTE0NraKndYSU1N5d133x2QuXSBy8h7i6tZ2a8hFZE+xWazXVATP3bsWLlkdPny5Z0auMPhkN+Xt956i7q6OgoLCxk7dmx/Tf96xWXkvcWVruzXmIpIv2G321m2bBnvvfceQUFBDB8+nLS0tA5r4h0OB3/84x8xmUy8++67va4/d4Nz7deTXy+cOXPmin5u//79xMTEyFVb9913H+vXr7/hjdwpTOnsE75//35Wr17NsmXLiI2NJT09nbvuuguNRsOf//xnampq+OCDD/rVwG+0ysS+4KYy8iultLT0gpTQ8PBw9u3bN4Az6h9UKhUffvih/HX7mvjDhw+zevVqXn/9dSwWC3FxcaxZs+aq+qT1lOLiYrZs2dKvHVWuR1w+lYseo1AoSE5O5tVXX+XgwYMsW7aMVatW9auBA/zHf/wHy5cvv2lvSLqLayfvBjeTikhPUSgUzJkzp9/HXb9+PWFhYSQmJvb72NcbLiPvBuPHjycvL4+CggLCwsL44osv+Oyzz3r8nOLiYh566CEMBgOCIPDYY4+xdOnSPpjxjUF3KhNddANRFDv746KNzMxMMTY2Vhw6dKj45z//+YqeUVZWJh48eFAURVFsaGgQY2Njxdzc3N6c5k1BTk6OqNPpxKioKDEqKkpUKpViRESEWF5ePtBTu1K6ssOr+nNTXaFda6SlpbFkyRLuvPPOgZ7Kdc0NoDHQp0EFV+BtgCgsLOTw4cOkpKQM9FRc3OC4zuQDgMlk4t577+XNN9/Ex8dnoKdz3VNYWDjQU7imce3k/YzVauXee+/lgQceYN68eQM9HRc3AS4j70dEUeTRRx8lPj6ep59++qqfZ7fbGTNmDLNmzeqF2bm4UXEZeT+ya9cuVq1axbZt20hKSiIpKYlNmzZd8fNWrFhBfHx8L87w2uDtt99m+PDhJCQk8Lvf/W6gp3Pd4zqT9yO33XYbXdxmdJuSkhIyMzN58cUXeeONN3rlmdcC27dvZ/369Rw5ckRude3i6nDt5NcpTz31FMuXL7/hqr1WrlzJ888/LyvM3Ei97AeKG+sTcpOwceNG9Ho9ycnJAz2VXuf06dPs3LmTlJQUpkyZwoEDBwZ6Stc9Lnf9OmTXrl188803bNq0CbPZTENDAw8++CCffPLJQE+tW9zsra77m64y3lxc4wiCcDvwrCiKVxxiFwTBD3gfGImU5bhIFMU9vTG/K5jLZuAvoihub/s6H0gVRbFyIOZzI+By110ArAA2i6I4HEgETgzgXNYBdwAIghAHqIGqAZzPdY9rJ7/JEQTBF8gGhorXwIdBEAQ18CGQBFiQvJRtAzqp6xyXkd/kCIKQBPw/4DjSLn4QWCqKYtNAzstF7+Fy112ogLHASlEUxwBNwI0pRXuT4jJyFyVAiSiKTtG6NUhG7+IGwWXkNzmiKFYAxYIgDGv7p2lIrruLGwTXmdyF81z+PlIk+yzwiCiKtQM6KRe9hsvIXbi4wXG56y5c3OC4jNyFixscl5G7cHGD4zJyFy5ucFxG7sLFDY7LyF24uMFxGbkLFzc4LiN34eIG5/8DNdSpI5cfK+MAAAAASUVORK5CYII=", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = plt.axes(projection='3d')\n", + "ax.plot_wireframe(X, Y, Z)\n", + "ax.set_title('wireframe');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A surface plot is like a wireframe plot, but each face of the wireframe is a filled polygon.\n", + "Adding a colormap to the filled polygons can aid perception of the topology of the surface being visualized, as you can see in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes(projection='3d')\n", + "ax.plot_surface(X, Y, Z, rstride=1, cstride=1,\n", + " cmap='viridis', edgecolor='none')\n", + "ax.set_title('surface');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Though the grid of values for a surface plot needs to be two-dimensional, it need not be rectilinear.\n", + "Here is an example of creating a partial polar grid, which when used with the `surface3D` plot can give us a slice into the function we're visualizing (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "r = np.linspace(0, 6, 20)\n", + "theta = np.linspace(-0.9 * np.pi, 0.8 * np.pi, 40)\n", + "r, theta = np.meshgrid(r, theta)\n", + "\n", + "X = r * np.sin(theta)\n", + "Y = r * np.cos(theta)\n", + "Z = f(X, Y)\n", + "\n", + "ax = plt.axes(projection='3d')\n", + "ax.plot_surface(X, Y, Z, rstride=1, cstride=1,\n", + " cmap='viridis', edgecolor='none');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Surface Triangulations\n", + "\n", + "For some applications, the evenly sampled grids required by the preceding routines are too restrictive.\n", + "In these situations, triangulation-based plots can come in handy.\n", + "What if rather than an even draw from a Cartesian or a polar grid, we instead have a set of random draws?" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "theta = 2 * np.pi * np.random.random(1000)\n", + "r = 6 * np.random.random(1000)\n", + "x = np.ravel(r * np.sin(theta))\n", + "y = np.ravel(r * np.cos(theta))\n", + "z = f(x, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We could create a scatter plot of the points to get an idea of the surface we're sampling from, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes(projection='3d')\n", + "ax.scatter(x, y, z, c=z, cmap='viridis', linewidth=0.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This point cloud leaves a lot to be desired.\n", + "The function that will help us in this case is `ax.plot_trisurf`, which creates a surface by first finding a set of triangles formed between adjacent points (remember that `x`, `y`, and `z` here are one-dimensional arrays); the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes(projection='3d')\n", + "ax.plot_trisurf(x, y, z,\n", + " cmap='viridis', edgecolor='none');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is certainly not as clean as when it is plotted with a grid, but the flexibility of such a triangulation allows for some really interesting three-dimensional plots.\n", + "For example, it is actually possible to plot a three-dimensional Möbius strip using this, as we'll see next." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Visualizing a Möbius Strip\n", + "\n", + "A Möbius strip is similar to a strip of paper glued into a loop with a half-twist, resulting in an object with only a single side!\n", + "Here we will visualize such an object using Matplotlib's three-dimensional tools.\n", + "The key to creating the Möbius strip is to think about its parametrization: it's a two-dimensional strip, so we need two intrinsic dimensions. Let's call them $\\theta$, which ranges from $0$ to $2\\pi$ around the loop, and $w$, which ranges from –1 to 1 across the width of the strip:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "theta = np.linspace(0, 2 * np.pi, 30)\n", + "w = np.linspace(-0.25, 0.25, 8)\n", + "w, theta = np.meshgrid(w, theta)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now from this parametrization, we must determine the (*x*, *y*, *z*) positions of the embedded strip.\n", + "\n", + "Thinking about it, we might realize that there are two rotations happening: one is the position of the loop about its center (what we've called $\\theta$), while the other is the twisting of the strip about its axis (we'll call this $\\phi$). For a Möbius strip, we must have the strip make half a twist during a full loop, or $\\Delta\\phi = \\Delta\\theta/2$:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "phi = 0.5 * theta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we use our recollection of trigonometry to derive the three-dimensional embedding.\n", + "We'll define $r$, the distance of each point from the center, and use this to find the embedded $(x, y, z)$ coordinates:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# radius in x-y plane\n", + "r = 1 + w * np.cos(phi)\n", + "\n", + "x = np.ravel(r * np.cos(theta))\n", + "y = np.ravel(r * np.sin(theta))\n", + "z = np.ravel(w * np.sin(phi))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, to plot the object, we must make sure the triangulation is correct. The best way to do this is to define the triangulation *within the underlying parametrization*, and then let Matplotlib project this triangulation into the three-dimensional space of the Möbius strip.\n", + "This can be accomplished as follows (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# triangulate in the underlying parametrization\n", + "from matplotlib.tri import Triangulation\n", + "tri = Triangulation(np.ravel(w), np.ravel(theta))\n", + "\n", + "ax = plt.axes(projection='3d')\n", + "ax.plot_trisurf(x, y, z, triangles=tri.triangles,\n", + " cmap='Greys', linewidths=0.2);\n", + "\n", + "ax.set_xlim(-1, 1); ax.set_ylim(-1, 1); ax.set_zlim(-1, 1)\n", + "ax.axis('off');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Combining all of these techniques, it is possible to create and display a wide variety of three-dimensional objects and patterns in Matplotlib." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "encoding": "# -*- coding: utf-8 -*-", + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.14-Visualization-With-Seaborn.ipynb b/notebooks/04.14-Visualization-With-Seaborn.ipynb new file mode 100644 index 000000000..76f31337c --- /dev/null +++ b/notebooks/04.14-Visualization-With-Seaborn.ipynb @@ -0,0 +1,1782 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Visualization with Seaborn" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matplotlib has been at the core of scientific visualization in Python for decades, but even avid users will admit it often leaves much to be desired.\n", + "There are several complaints about Matplotlib that often come up:\n", + "\n", + "- A common early complaint, which is now outdated: prior to version 2.0, Matplotlib's color and style defaults were at times poor and looked dated.\n", + "- Matplotlib's API is relatively low-level. Doing sophisticated statistical visualization is possible, but often requires a *lot* of boilerplate code.\n", + "- Matplotlib predated Pandas by more than a decade, and thus is not designed for use with Pandas `DataFrame` objects. In order to visualize data from a `DataFrame`, you must extract each `Series` and often concatenate them together into the right format. It would be nicer to have a plotting library that can intelligently use the `DataFrame` labels in a plot.\n", + "\n", + "An answer to these problems is [Seaborn](http://seaborn.pydata.org/). Seaborn provides an API on top of Matplotlib that offers sane choices for plot style and color defaults, defines simple high-level functions for common statistical plot types, and integrates with the functionality provided by Pandas.\n", + "\n", + "To be fair, the Matplotlib team has adapted to the changing landscape: it added the `plt.style` tools discussed in [Customizing Matplotlib: Configurations and Style Sheets](04.11-Settings-and-Stylesheets.ipynb), and Matplotlib is starting to handle Pandas data more seamlessly.\n", + "But for all the reasons just discussed, Seaborn remains a useful add-on.\n", + "\n", + "By convention, Seaborn is often imported as `sns`:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "sns.set() # seaborn's method to set its chart style" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exploring Seaborn Plots\n", + "\n", + "The main idea of Seaborn is that it provides high-level commands to create a variety of plot types useful for statistical data exploration, and even some statistical model fitting.\n", + "\n", + "Let's take a look at a few of the datasets and plot types available in Seaborn. Note that all of the following *could* be done using raw Matplotlib commands (this is, in fact, what Seaborn does under the hood), but the Seaborn API is much more convenient." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Histograms, KDE, and Densities\n", + "\n", + "Often in statistical data visualization, all you want is to plot histograms and joint distributions of variables.\n", + "We have seen that this is relatively straightforward in Matplotlib (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "data = np.random.multivariate_normal([0, 0], [[5, 2], [2, 2]], size=2000)\n", + "data = pd.DataFrame(data, columns=['x', 'y'])\n", + "\n", + "for col in 'xy':\n", + " plt.hist(data[col], density=True, alpha=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Rather than just providing a histogram as a visual output, we can get a smooth estimate of the distribution using kernel density estimation (introduced in [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb)), which Seaborn does with ``sns.kdeplot`` (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.kdeplot(data=data, shade=True);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we pass `x` and `y` columns to `kdeplot`, we instead get a two-dimensional visualization of the joint density (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "
" + ], + "text/plain": [ + " sepal_length sepal_width petal_length petal_width species\n", + "0 5.1 3.5 1.4 0.2 setosa\n", + "1 4.9 3.0 1.4 0.2 setosa\n", + "2 4.7 3.2 1.3 0.2 setosa\n", + "3 4.6 3.1 1.5 0.2 setosa\n", + "4 5.0 3.6 1.4 0.2 setosa" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "iris = sns.load_dataset(\"iris\")\n", + "iris.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualizing the multidimensional relationships among the samples is as easy as calling ``sns.pairplot`` (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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total_billtipsexsmokerdaytimesize
016.991.01FemaleNoSunDinner2
110.341.66MaleNoSunDinner3
221.013.50MaleNoSunDinner3
323.683.31MaleNoSunDinner2
424.593.61FemaleNoSunDinner4
\n", + "
" + ], + "text/plain": [ + " total_bill tip sex smoker day time size\n", + "0 16.99 1.01 Female No Sun Dinner 2\n", + "1 10.34 1.66 Male No Sun Dinner 3\n", + "2 21.01 3.50 Male No Sun Dinner 3\n", + "3 23.68 3.31 Male No Sun Dinner 2\n", + "4 24.59 3.61 Female No Sun Dinner 4" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tips = sns.load_dataset('tips')\n", + "tips.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "tips['tip_pct'] = 100 * tips['tip'] / tips['total_bill']\n", + "\n", + "grid = sns.FacetGrid(tips, row=\"sex\", col=\"time\", margin_titles=True)\n", + "grid.map(plt.hist, \"tip_pct\", bins=np.linspace(0, 40, 15));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The faceted chart gives us some quick insights into the dataset: for example, we see that it contains far more data on male servers during the dinner hour than other categories, and typical tip amounts appear to range from approximately 10% to 20%, with some outliers on either end.\n", + "\n", + "### Categorical Plots\n", + "\n", + "Categorical plots can be useful for this kind of visualization as well. These allow you to view the distribution of a parameter within bins defined by any other parameter, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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pkpKSkowrvgnXvKZUWFiol19+WVVVVXI4HLLb7Tp16pSysrI8UR8AE8vPz9fHx06oU0j3Vre12+pXoT6ef6ZV7eouX2j1vnxZ3759tWfPHh06dEgHDx7UnDlzdP/99ys6Olq/+93vnO8rKSlxrvRdUFCg7t276/jx46qpqVFwcLBB1V/tmqH06KOP6rbbbtM//vEPTZgwQXv37tW3v/1tT9QGwAt0Cumurv3iPba/qlM5HtuXN3j11Vf14Ycfau3atRo5cqTOnTunEydO6MCBA/r888910003af/+/Xrssce0f/9+lZeXa/Xq1frjH/+o5557TmvXrtXSpUuN/jacrhlKly5d0pNPPqnVq1dr1KhRSktL05w5czxRG9ygradb2nOqReJ0C+AuU6ZM0eHDhzV+/Hh16dJFffr00erVq5WXl6dHHnlEDodDgYGBevbZZxUcHKxHH31UP/zhD3XLLbdo+fLlSkpK0ogRIzR69GijvxVJLQilhtFh/fr108mTJzVkyBDZ7XZ31wU3aevplraeapE43QK4U9euXRudpmuQmJioxMTEq57funWr8/ENN9ygd955x53ltdo1Q6lfv35avXq1kpOT9fjjj6uqqko1NTWeqA1uwukWAGZ1zVBasWKF3nnnHd16662aOnWq3n//fT311FOeqA3wO5xehb+7Zig999xz+tnPfiZJmj59uqZPn65Vq1bpO9/5jrtrA/xOfn6+Th7/RL26tW6ylS6O+lPqF0+faPU+SyttrW4DuIvLn/wNGzaooqJCu3fvVmVlpfP52tpa5ebmatmyZR4pEPA3vboFas6QcI/t78WjrI8G83AZSrfffrv++c9/KiAgoNFUOJ06ddIzzzzjidoAAH7GZSjFxMQoJiZGo0aN0pAhQ2Sz2eRwOBQUFOTJ+gDgKiUlJW26fsa1N/O75onrPn366MEHH9TBgwdVV1enu+66S7/5zW/Us2dPT9QHAFf5+uuvveLa25LHl+vsuQutbnctPf6nuzJXr7zm+4qLixUfH69p06Zp5cr/vP/48eOaMmWKMjIylJKS0mTbuLg4vfTSS4qKiuqwulvimv9Hn3rqKQ0dOlS//e1vVVdXpy1btmjFihV69tlnPVEfADTJG669nT13QVWhwzq8lrPnDrX4vd27d9e7776ruro6depUf7/h7t27FR7uuWPXGtdc5K+wsFAPP/ywQkNDFRYWpoULF6qoqMgTtQEA2um6667T4MGD9cEHHzife//99zVixAhJ0ssvv6ypU6dq4sSJSkpK0ueff96ofV1dnTIyMpScnKxJkybpj3/8o1vrvWZPyWazqbq6Wp07d5ZU3222WCxuLQowmlGzX5eUlKhbm/YKuJaYmKi//e1vGj58uI4ePapvfetbcjgcqqysVG5urrZs2aKQkBA9/fTTevXVV/XLX/7S2Xbbtm2SpB07dqimpkY//OEPddttt+m73/2uW2p1GUoNM8eOHz9es2fPdp533L59u8aNG+eWYgCzMGr2664hQerGWCJ0sNjYWP3ud7+T3W7Xm2++qcTERO3evVvdunXTunXr9Ne//lWFhYV69913NXjw4EZtDxw4oOPHj+vgwYOSpKqqKp04ccLzoTRt2jTt2LFD8+fPV69evfTuu+/KbrcrJSVF9957r1uKAczEmOmYLnlsf/Af3bp106BBg/Thhx/q4MGDevTRR7V7926VlJRo2rRpeuCBBzRq1Cj16NFDx48fb9S2rq5OP//5z50Lu5aXl6tr165uq9VlKDkcDufj1NRUpaamuq0IAIB7JSYmat26dbrtttsUGFj/0d+1a1f169dPs2fPVk1NjTZt2nTVAIjhw4dr27Ztio2NVU1NjaZPn64nn3xSw4Z1/AAOqZlQqq6u1rFjxxqF05VYUwkAvEdsbKwef/xx/fSnP3U+FxQUJLvdrvHjxys4OFhDhgzRyZMnG7WzWq06deqUkpOTZbPZlJKS4rZAkpoJpdOnT2vBggVNhpLFYlFODjM/A0BzevxP91YN327NdlsiKipKubm5kupH4R05csT5WmZmpiTpgQceaLJtQztJHp1WzmUoDRw4UK+//rrHCgEAX9OSG1zR2DXvUwIAwFNc9pTcNdwP+G+5ubnas2dPk69duHBBkhpNCnylMWPGKC4uzk2VAfA0l6HE0hQwg/Ly+qldXIUSAN/SutkMTYwVO71XXFycy95Ow/+XjIwMT5YEwCA+E0ptvQO/rXffS/V34AMAOo7PhJJk1B34AICO4lOhBABmsnJZur4qP9vh270hvIeWr7r2Ke3i4mIlJCTopptuavT8pk2b1Lt37w6tqbi4WGlpaY3ub2oLQgkA3OSr8rOa/s2mZ8Vpj1cLWx50kZGReuONNzq8BnchlADAz5w9e1bLly9XaWmpLBaLHn30UY0YMULPPPOMvvjiC504cULnzp3Tz372Mx08eFBHjhzRoEGDtH79etXV1WnFihU6efKkzp49q/79+2vjxo0t2n5LEEoA4MPKyso0efJk59dJSUn65JNPlJqaqvj4eJWVlWn69OnOGXw+/fRTbdu2TR999JFmzZqlv/zlL/rmN7+p8ePH68SJE7p48aKCgoK0detW2e12zZo1S/v37280H+rq1aub3H63btdeLYxQAgAf1tTpu2HDhik/P18bNmyQVL+Y6+nTpyVJ3/ve9xQYGKg+ffooIiJCAwcOlCT17NlTX331lYYNG6bu3bvrlVdeUX5+vgoLC1VVVdVo+3l5eU1u/7/XamoKoQQAfsZut2vz5s3Om9LPnDmjHj166O2331ZQ0H9WmWxY4uJKOTk52rBhg9LS0pSSkqLz589fNXG3q+23BHPfAYCfGT58uF599VVJ0meffaZJkybp66+/blHbAwcOKDExUampqerRo4c++OAD1dXVddj26SkBaLPz58+r7vIFj96zV3f5gmyBFskLlo2/IbxHq0bKtWa77bFs2TItX75cSUlJkqQ1a9a06HqPJE2dOlWPPfaYsrOzFRwcrKFDh6q4uLjDtu/WUNq4caPefPNNSVJMTIx+8YtfKC8vTxkZGaqurlZiYqIWLVrkzhIAwDAtuZfIna5cT+lKPXv21HPPPXfV8wsWLHDZdsuWLc7Hf/nLX5rcX8P7XW2/JdwWSnl5eXrvvfe0Y8cOWSwWPfjgg9q1a5fWrl2rLVu2qHfv3nrooYe0f/9+xcTEuKsMAG4UFham0vM1Hp9JJVCXJNV6bJ/wHLddU4qIiNCSJUsUHBysoKAg3XTTTSosLFS/fv3Ut29fBQYGKikpSdnZ2e4qAQDgZdzWU7r55pudjwsLC7V7927NnDlTERERzucjIyN15szVE6FWVFSooqKi0XOlpaXuKhUAYBJuH+hw8uRJPfTQQ1q8eLECAwNVUFDQ6HWLxXJVm82bN191hzAAwPe5NZQ+/PBDLVy4UEuXLtWECRN0+PBhnT37n5EoZWVlioyMvKrdrFmzlJyc3Oi50tJSzZgxw53lAgAM5rZQKikp0fz587V+/XpFR0dLkm6//XYVFBTo1KlTioqK0q5du5SamnpV29DQUIWGhrqrNACASbktlF544QVVV1crMzPT+ZzValVmZqYWLFig6upqxcTEKCEhwV0lAAC8jNtCadmyZVq2bFmTr+3cudNduwUAeDGmGQIAmAbTDLWDvaZS+fmXlJ6e3uq2+fn5ktSmtgMGDNDcuXNb3Q4AzI5QageH3aa6apsunj7R6rZdHHZJanXb0kpbq/cFAN6CUGqnXt0CNWdIuMf29+LRco/tC55ns9lUWm3z6P/n0kqbbOfPe2x/QHMIJaAJRs1+LYudX0r4NX7+ARPp1KmTenUJ8Hjv+/qwMI/tD2gOoQQ0gdmvAWMwJBwAYBqEEgDANDh9B8DrMErRdxFKfsaoUWXnzwd7bH8AvJfPhJIRH7ay21RZwxlQwNMCAwMV0cXBKEUf5DOhhJYxalRZGL/MAFrAZ0LJiA/biyf+rG6clQKADsO5JwCAafhMTwnmVlJS4vHZ1CVmVAe8DaEEj/j666918vgn6tWtdT9ybZ1NXWJGdcAbEUrwGGZUB3AtXFMCAJgGoQQAMA1O38EjmBYGQEsQSgC8Umll6//IqaypHzjTLbj1J4lKK226vtWt0FqEEjyCaWF8V1un97LbLkuSAgJDWr2/LmGh6j1gQKv3+eW/bzHo3bf1ba9X/S0GcC9CCUCbtedDuuEetAEDerayZc8233/WcL9bRkZGq9vCMwglAG3WnhuTCQg0hdF3AADTIJQAAKZBKAEATINrSoDJMNQZ/oxQag+HXaWVdm4I9VEMdQY8z6dCqS0fIm39AJEkOeokWVrfDqbHUGfAGD4TSm39EGn7B4iUn39JEUG13BDqgxjqDBjDZ0KprR8i7fkASU9Pb9M6PwCApjH6DgBgGoQSAMA0CCUAgGkQSgAA0yCUAACm4TOj79Bynr6fq+7yBSkkqNXtAPgfQqmd2jIljNT2aWHaOyWMEfdzST1VUlIi2WrbtG8A/oNQaof23PXf1mlh2jsljBH3czW0v3i6ok1tAfgPQqkduOsfADoWAx0AAKZBTwkew5IMAK6FUIJHtPU6GEsyAP6FUIJHGDXAAoB34ZoSAMA0CCUAgGm4PZQqKys1ceJEFRcXS5Ly8vKUlJSksWPHav369e7ePQDAi7g1lI4cOaL7779fhYWFkqTLly9r6dKl+sMf/qDdu3fr448/1v79+91ZAgDAi7g1lLZt26YnnnhCkZGRkqSjR4+qX79+6tu3rwIDA5WUlKTs7Gx3lgAA8CJuHX23evXqRl+XlZUpIiLC+XVkZKTOnDlzVbuKigpVVDSekqa0tNQ9RQIATMOjQ8IdDsdVz1kslque27x5szZu3OiJkgAAJuLRUOrZs6fOnj3r/LqsrMx5au9Ks2bNUnJycqPnSktLNWPGDLfXCMC75ebmas+ePU2+1jDbfcP9b00ZM2aM4uLi3FIbrs2joXT77beroKBAp06dUlRUlHbt2qXU1NSr3hcaGqrQ0FBPlgbAD4SHhxtdAq7Bo6HUuXNnZWZmasGCBaqurlZMTIwSEhI8WQIAHxcXF0dPx4t5JJRyc3Odj6Ojo7Vz505P7BYA4GWY0QEAYBqEEgDANJglHE6MWgJgNELJjdrzIW+2D3hGLQHwBELJIGb8kGfUEgCjEUpuxIc8ALQOAx0AAKZBTwlopeauFUred70QMBO/CCVGlcGTzHi9EPAWfhFKzeEDBK3FtULAffwilPgQATyP05xoC78IJQDmw1kKNIVQAuAWnKFAWzAkHABgGoQSAMA0CCUAgGkQSgAA0yCUAACmweg7GM6XlvgA0D6EEkyNe1kA/0IowXDczwKgAdeUAACmQSgBAEyDUAIAmAahBAAwDUIJAGAahBIAwDQIJQCAaRBKAADTIJQAAKZBKAEATINQAgCYBqEEADANQgkAYBrMEg54Cdadgj8glAAfwLpT8BWEEuAlWHcK/oBrSgAA0yCUAACmQSgBAEyDUAIAmAahBAAwDUIJAGAahBIAwDQIJQCAaRBKAADTIJQAAKbhNdMM1dXVSZJKS0sNrgQAXOvVq5cCA73mo9V0vObIffnll5KkGTNmGFwJALiWk5OjqKgoo8vwWhaHw+EwuoiWuHz5sj7++GNFRESoU6dORpcjqb7XNmPGDL3yyivq1auX0eWYFsepZThOLWP240RPqX285siFhITou9/9rtFlNKlXr178ZdQCHKeW4Ti1DMfJNzHQAQBgGoQSAMA0CCUAgGkQSu0QGhqqhx9+WKGhoUaXYmocp5bhOLUMx8m3ec3oOwCA76OnBAAwDUIJAGAaXnOfkic9+eST+uijj1RbW6uioiLddNNNkqSKigqlpKRowYIFBldobsXFxUpISHAetwabNm1S7969nV/PnTtXq1atUs+ePT1doqGys7P1v//7v7LZbHI4HJo8ebIefPBBl+/funWrrrvuOk2cONGDVRqrtccIvoNQasITTzwhqf7DNS0tTW+88YYk6ZlnnjGyLK8SGRnpPG6uPP/88x6qxjzOnDmjX//619q+fbvCwsJ06dIlzZw5U/3791d8fHyTbf7xj3/o7rvv9nClxmnLMYLv4PRdKx09elRWq1WxsbHOkNq+fbuWLFnifM/MmTN16NAhHTp0SPfee69SUlK0ePFio0o2jSVLlmjevHlKTExUbm6u4uLiVFxcbHRZHnX+/HnV1tbq8uXLkqTrrrtOmZmZGjhwoN58803dd999mjRpksaNG6cPPvhAeXl5ys3N1YYNG/Tuu+8aXL1nNHeMrvyZOXTokGbOnCmp/nduzZo1mjZtmsaMGaP9+/cbVj/ah55SK507d05ZWVmqrKxUXFyc5syZ0+z7CwsLtXfvXl1//fUeqtAcysrKNHnyZOfXSUlJkqTu3btr06ZNkqRVq1YZUpuRBg0apPj4eN1zzz0aPHiwhg0bpqSkJPXt21fLly/Xpk2bFB4ertdee00vvPCCNm3apLi4ON19990aOXKk0eV7hKtj1K9fv2bb1dbWauvWrcrNzdXTTz+tmJgYD1WMjkQotdLIkSMVHBys8PBwhYWF6auvvmr2/f379/e7QJKaPn23ZMkSDRkyxKCKzOPJJ5/UT37yE7333nt67733dN9992nt2rX6/e9/r9zcXBUUFOjw4cMKCPDfExmujlFzGkL75ptv1oULFzxQJdyBUGqlK2f/tVgscjgczv82qK2tdT4OCQnxaH1m5+/HY9++faqqqtL48eOVmpqq1NRUbdu2Ta+88orWrVunyZMn66677tK3vvUtvfLKK0aXawhXx+i1116TJOfvms1ma9Suc+fOkup/L+G9/PdPsQ4UFhamzz//XA6HQ6dPn9aJEyeMLgkmFRISonXr1jmvizgcDn322WcKDg5WQECA5s2bp+HDh+udd95xLmzZqVMn52N/4OoYDR48WGFhYfrss88k1a9bBN9DT6kDjBgxQn/+85+VkJCg/v3768477zS6JJjU8OHD9fDDD2vevHnOHvXIkSP1+9//XkuWLFFiYqJCQkJ011136YsvvpBU//P129/+Vtdff70SEhKMLN8jXB2j+fPn6zvf+Y6eeuopbdy4Ud///vcNrhTuwDRDAADT4PQdAMA0CCUAgGkQSgAA0yCUAACmQSgBAEyDIeHwScXFxRozZoxuueUWSZLdbldQUJDS0tI0ZcoUY4sD4BKhBJ8VEhLSaKqjf/3rX5o9e7a6dOmicePGGVgZAFc4fQe/ceONN2rhwoV64YUXVFBQoDlz5mjatGmKjY3Vj3/8Y1VXV2vnzp2yWq3ONl988YW+//3vq6amxsDKAf9BKMGvDBo0SJ9++qm2bdumKVOmaOvWrXrrrbdUXFysffv2KSEhQUVFRc6pbP70pz8pOTlZwcHBBlcO+AdCCX7FYrEoJCREP//5zxUeHq7nn39eK1asUFlZmaqqqhQcHKypU6dq27Ztqqur044dOzRt2jSjywb8BteU4Ff++c9/6pZbbtEjjzyiuro6JSYmavTo0SopKXHOPj1t2jRNnTpVd999t26++WZFRUUZXDXgP+gpwW8UFBToD3/4g37wgx/ovffe0/z58zV+/HhZLBYdOXLEORN3nz59NHToUP3qV7/S/fffb3DVgH+hpwSfdfnyZefqtwEBAercubMeeeQRjR49WosWLdL8+fN1ww03qEuXLrrrrrtUVFTkbJuSkqKnnnqK1UsBD2OWcOC/2O12rVy5Un369NGPfvQjo8sB/Aqn74ArVFZWatiwYTp9+rQeeOABo8sB/A49JQCAadBTAgCYBqEEADANQgkAYBqEEgDANAglAIBpEEoAANP4f1omo6LgpykvAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with sns.axes_style(style='ticks'):\n", + " g = sns.catplot(x=\"day\", y=\"total_bill\", hue=\"sex\", data=tips, kind=\"box\")\n", + " g.set_axis_labels(\"Day\", \"Total Bill\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Joint Distributions\n", + "\n", + "Similar to the pair plot we saw earlier, we can use `sns.jointplot` to show the joint distribution between different datasets, along with the associated marginal distributions (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with sns.axes_style('white'):\n", + " sns.jointplot(x=\"total_bill\", y=\"tip\", data=tips, kind='hex')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The joint plot can even do some automatic kernel density estimation and regression, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.jointplot(x=\"total_bill\", y=\"tip\", data=tips, kind='reg');" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Bar Plots\n", + "\n", + "Time series can be plotted using `sns.factorplot`. In the following example, we'll use the Planets dataset that we first saw in [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb); see the following figure for the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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methodnumberorbital_periodmassdistanceyear
0Radial Velocity1269.3007.1077.402006
1Radial Velocity1874.7742.2156.952008
2Radial Velocity1763.0002.6019.842011
3Radial Velocity1326.03019.40110.622007
4Radial Velocity1516.22010.50119.472009
\n", + "
" + ], + "text/plain": [ + " method number orbital_period mass distance year\n", + "0 Radial Velocity 1 269.300 7.10 77.40 2006\n", + "1 Radial Velocity 1 874.774 2.21 56.95 2008\n", + "2 Radial Velocity 1 763.000 2.60 19.84 2011\n", + "3 Radial Velocity 1 326.030 19.40 110.62 2007\n", + "4 Radial Velocity 1 516.220 10.50 119.47 2009" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "planets = sns.load_dataset('planets')\n", + "planets.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with sns.axes_style('white'):\n", + " g = sns.catplot(x=\"year\", data=planets, aspect=2,\n", + " kind=\"count\", color='steelblue')\n", + " g.set_xticklabels(step=5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can learn more by looking at the *method* of discovery of each of these planets (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with sns.axes_style('white'):\n", + " g = sns.catplot(x=\"year\", data=planets, aspect=4.0, kind='count',\n", + " hue='method', order=range(2001, 2015))\n", + " g.set_ylabels('Number of Planets Discovered')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on plotting with Seaborn, see the [Seaborn documentation](http://seaborn.pydata.org/), and particularly the [example gallery](https://seaborn.pydata.org/examples/index.html)." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Exploring Marathon Finishing Times\n", + "\n", + "Here we'll look at using Seaborn to help visualize and understand finishing results from a marathon.\n", + "I've scraped the data from sources on the web, aggregated it and removed any identifying information, and put it on GitHub, where it can be downloaded\n", + "(if you are interested in using Python for web scraping, I would recommend [*Web Scraping with Python*](http://shop.oreilly.com/product/0636920034391.do) by Ryan Mitchell, also from O'Reilly).\n", + "We will start by downloading the data and loading it into Pandas:[^2]\n", + "\n", + "[^2]: The marathon data used in this section divides runners into two genders: men and women. While gender is a\n", + "spectrum, the following discussion and visualizations use this binary because they depend on the data." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# url = ('https://raw.githubusercontent.com/jakevdp/'\n", + "# 'marathon-data/master/marathon-data.csv')\n", + "# !cd data && curl -O {url}" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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agegendersplitfinal
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" + ], + "text/plain": [ + " age gender split final\n", + "0 33 M 01:05:38 02:08:51\n", + "1 32 M 01:06:26 02:09:28\n", + "2 31 M 01:06:49 02:10:42\n", + "3 38 M 01:06:16 02:13:45\n", + "4 31 M 01:06:32 02:13:59" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv('data/marathon-data.csv')\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that Pandas loaded the time columns as Python strings (type `object`); we can see this by looking at the `dtypes` attribute of the `DataFrame`:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "age int64\n", + "gender object\n", + "split object\n", + "final object\n", + "dtype: object" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.dtypes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's fix this by providing a converter for the times:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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agegendersplitfinal
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" + ], + "text/plain": [ + " age gender split final\n", + "0 33 M 0 days 01:05:38 0 days 02:08:51\n", + "1 32 M 0 days 01:06:26 0 days 02:09:28\n", + "2 31 M 0 days 01:06:49 0 days 02:10:42\n", + "3 38 M 0 days 01:06:16 0 days 02:13:45\n", + "4 31 M 0 days 01:06:32 0 days 02:13:59" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import datetime\n", + "\n", + "def convert_time(s):\n", + " h, m, s = map(int, s.split(':'))\n", + " return datetime.timedelta(hours=h, minutes=m, seconds=s)\n", + "\n", + "data = pd.read_csv('data/marathon-data.csv',\n", + " converters={'split':convert_time, 'final':convert_time})\n", + "data.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "age int64\n", + "gender object\n", + "split timedelta64[ns]\n", + "final timedelta64[ns]\n", + "dtype: object" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.dtypes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That will make it easier to manipulate the temporal data. For the purpose of our Seaborn plotting utilities, let's next add columns that give the times in seconds:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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431M0 days 01:06:320 days 02:13:593992.08039.0
\n", + "
" + ], + "text/plain": [ + " age gender split final split_sec final_sec\n", + "0 33 M 0 days 01:05:38 0 days 02:08:51 3938.0 7731.0\n", + "1 32 M 0 days 01:06:26 0 days 02:09:28 3986.0 7768.0\n", + "2 31 M 0 days 01:06:49 0 days 02:10:42 4009.0 7842.0\n", + "3 38 M 0 days 01:06:16 0 days 02:13:45 3976.0 8025.0\n", + "4 31 M 0 days 01:06:32 0 days 02:13:59 3992.0 8039.0" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['split_sec'] = data['split'].view(int) / 1E9\n", + "data['final_sec'] = data['final'].view(int) / 1E9\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get an idea of what the data looks like, we can plot a `jointplot` over the data; the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with sns.axes_style('white'):\n", + " g = sns.jointplot(x='split_sec', y='final_sec', data=data, kind='hex')\n", + " g.ax_joint.plot(np.linspace(4000, 16000),\n", + " np.linspace(8000, 32000), ':k')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The dotted line shows where someone's time would lie if they ran the marathon at a perfectly steady pace. The fact that the distribution lies above this indicates (as you might expect) that most people slow down over the course of the marathon.\n", + "If you have run competitively, you'll know that those who do the opposite—run faster during the second half of the race—are said to have \"negative-split\" the race.\n", + "\n", + "Let's create another column in the data, the split fraction, which measures the degree to which each runner negative-splits or positive-splits the race:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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agegendersplitfinalsplit_secfinal_secsplit_frac
033M0 days 01:05:380 days 02:08:513938.07731.0-0.018756
132M0 days 01:06:260 days 02:09:283986.07768.0-0.026262
231M0 days 01:06:490 days 02:10:424009.07842.0-0.022443
338M0 days 01:06:160 days 02:13:453976.08025.00.009097
431M0 days 01:06:320 days 02:13:593992.08039.00.006842
\n", + "
" + ], + "text/plain": [ + " age gender split final split_sec final_sec \\\n", + "0 33 M 0 days 01:05:38 0 days 02:08:51 3938.0 7731.0 \n", + "1 32 M 0 days 01:06:26 0 days 02:09:28 3986.0 7768.0 \n", + "2 31 M 0 days 01:06:49 0 days 02:10:42 4009.0 7842.0 \n", + "3 38 M 0 days 01:06:16 0 days 02:13:45 3976.0 8025.0 \n", + "4 31 M 0 days 01:06:32 0 days 02:13:59 3992.0 8039.0 \n", + "\n", + " split_frac \n", + "0 -0.018756 \n", + "1 -0.026262 \n", + "2 -0.022443 \n", + "3 0.009097 \n", + "4 0.006842 " + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['split_frac'] = 1 - 2 * data['split_sec'] / data['final_sec']\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Where this split difference is less than zero, the person negative-split the race by that fraction.\n", + "Let's do a distribution plot of this split fraction (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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eAb2eQUvu4ZACEZFCGLhERAph4BIRKYSBS5ogCAJnBpDm8aIZyfLWW2thNveAzeb0+L4EQUDBznIEG3m6kraxh0uyBAUFISgoyOP7ae7Z2uodsNd7PtyJPIldBpJl8+ZNMJkCMWFCssf2wZ4t+Zou9XAzMzNbtaWnp3d7MaQdu3fvxI4dOzy+H/ZsyZd02HXIzc1FZWUlysrKcOHCBVe70+nE999/7/HiiIh8SYeBO3nyZBw/fhzHjh1zPVcMAHQ6He655x6PF0dE5Es6DNxhw4Zh2LBhGDNmDPr166dUTUREPqlLVyP++c9/IiMjA5cuXWqxUMf27ds9VhgRka/pUuC+/PLLSE5ORmRkJCefEwBg3boNfv8gQSJ3dSlw9Xo9Zs2a5elaiIh8Wpemhd155504duyYp2shDfnv/16Ht99+W+0yVMff+MgdXerhnj59GsnJybj11lsRGBjoaucYrv/65JOPYTCISE6eqnYpqgk2iijcexy/emAQFyGnLulS4C5YsMDTdRBpkr3BoXYJpCFdCty77rrL03UQEfm8LgXuqFGjIAgCJElyjVmZzWZ88sknHi2OiMiXdClwjx496nrtcDiwe/fuFm3kf4xGIwwGLipD5A63l2fU6/WYMGECPv30U0/UQxrxn//5Lt5//321yyDSlC51US5evOh6LUkSDh8+jMuXL3uqJiIin+T2GC4A9OnTB1lZWR4tjLzb2rX5CA42YNq0OWqXQqQZbo/hEgHA558fgMEgMnCJ3NClwG1qasK6devwySefwOl0YuzYsXjqqacgirxoQkTUVV26aPbaa6/hs88+w4wZMzBr1ix89dVXWLlypadrIz/FJ/SSr+pSF/Wvf/0r/vSnP0Gv1wMAHnjgAUyaNKnNR+8Q3Yzm55gBwKzxkSpXQ9S9uhS4kiS5whYADAZDi6/J/9xyyy0IDPTMOWCr5+2y5Ju6FLgRERF45ZVXMG3aNADA+++/z9t9/dxrr63merhEburSGG5ubi4uX76MJ554Ao8//jhqa2uRk5Pj6dqIiHxKh4F79epVvPjii/jss8+wYsUKlJaW4u6774ZOp4PJZFKqRvJCb775GpYvX652GUSa0mHgvvnmm7DZbC2e0Lt06VJcvnwZq1ev9nhx5L2+/voQysrK1C6DSFM6DNyPP/4Yr732Gvr06eNqCwsLw8qVK/HnP/9Z9k737NmDpKQkxMXF4T/+4z8AAKWlpUhISEBMTAxWrVrl2ra8vBzJycmIjY1FVlYWnE6n7P0SEampw8DV6/UwGo2t2k0mEwwGg6wdnj59Grm5ucjPz8f27dtx5MgR7Nu3D5mZmcjPz0dJSQkOHz6Mffv2AQAyMjKQk5ODXbt2QZIkFBYWytoveb8b599yKi75mg4DNyAgADabrVW7zWaT3dP86KOPMH78ePTr1w96vR6rVq1CUFAQBg4ciAEDBkAURSQkJMBqtaKiogINDQ2IiooCACQlJcFqtcraL3m35vm3m/f8HQAQYtRj26cnVK6KqHt1GLgTJ05EdnY26urqXG11dXXIzs5GTEyMrB2eOnUKjY2NmD17NiZNmoRNmzahqqoKZrPZtY3FYkFlZWWrdrPZjMrKSln7pe4VFtYP/fv379bPtNU7YK//6R/yOj6+hnxMh/NwZ8yYgdzcXIwdOxZ33nknmpqa8N133yEhIQFPP/20rB02Njbiyy+/xIYNGxAcHIz58+cjKCio1XbXr052Y7s7+vTx/GwKs7mHx/fhbd59t/uf2KvXixD1OugbJYh6HURR7LCts/c9/TkAoBdF9O3rnzN2/PG8v56c4+8wcAMCArB06VL85je/wZEjRxAQEIBhw4YhLCxMdpF9+/bF6NGjERoaCgB4+OGHYbVaodPpXNtUVVXBYrEgLCwMNTU1rvbq6mpYLBa39nf+vA1NTZ57oqo/T/7vjmO//h9Qh8MJp05w/d8pCh22dfa+pz8HRhEOpxM1NTa/e2qvP5/3QPvH31kId+nGh9tuuw0xMTF45JFHbipsAeDBBx/E/v37cfnyZTQ2NuKvf/0r4uLicOLECddww44dOxAdHY3w8HAEBga6ph8VFxcjOjr6pvZP3WPlylfw0ksv3dRnNI/bFuws52I15BcUX19x+PDhmDNnDlJSUuBwODB27FhMmTIFd9xxB9LT03HlyhWMGzcOcXFxAIC8vDxkZ2fDbrcjMjISqampSpdMbTh2rPymnmnWPCOB6yaQP1FlQdvJkydj8uTJLdpGjx6Nbdu2tdo2IiICRUVFSpVGCmju2QYbuZ4y+Ree8eRRbV38bO7Z+tmwJ5H7T+0l6ipBEPDBx/+44WYGAdtLW8+v5RAu+QP2cEmWgQNvR1BQ53cb2hscrsBt7uneOL+WNzmQv2DgkiwvvbS0S1ODggNFrC85AqDjJzjwJgfyBwxc8jhbvQMhRj3WlxzxyQtlN/bgidrDMVyS5eWXc7Bw4UK3vufGW3d9QXMPnnOJqSt8r7tBijh16uRNzcP1JZxLTF3FHi4RkUIYuERECmHgEhEphINwJMvgwUMQFKRXuwwiTWHgkiwLF2b6/RJ9RO7ikAIRkUIYuCRLZmYG0tPT233/xgdCEhGHFEimyspz7c7D5fKLRG1jD5c8whfvKiO6WQxcIiKFMHCJiBTCQTaSZfjwKAQHB6pdBpGmMHBJlmeffZ7zcIncxCEFom7CqXDUGQYuyfL88+mYO3eu2mV4jeYF1rkuLnWEQwoky8WLF7ke7g24Li51hj1cIiKFMHCJiBTCwCXqZhzDpfYwcEmWkSNHY+zYsWqX4XVCjHoU7j3O0KU28aoHyZKWNp/zcNthb+DFM2obe7hERAph4JIsTz89F9OmTVO7DCJN4ZACydLQ0ICmJp4+RO5gD5eISCEMXOp2vEJP1DYGLnUrQRCwvfSE2mUQeSUOwpEs0dEPwGQytvleHadFEbWJgUuyzJgxm/Nwidyk2pDC73//eyxatAgAUF5ejuTkZMTGxiIrKwtO57WHD549exZTp05FXFwc5s2bB7vdrla5REQ3TZXAPXDgAD788EPX1xkZGcjJycGuXbsgSRIKCwsBAEuWLEFKSgqsViuGDh2K/Px8NcqlNsyePR2TJ09WuwwiTVE8cC9evIhVq1bhqaeeAgBUVFSgoaEBUVFRAICkpCRYrVY4HA4cPHgQsbGxLdqJiLRK8cB96aWXsGDBAvTs2RMAUFVVBbPZ7HrfbDajsrIStbW1MJlMEEWxRTsRkVYpetHsgw8+QP/+/TF69Ghs2bIFACBJUqvtBEFot91dffqY3C/UTWZzD4/vw9s0P+2hrWMXRRF6vQhRr2vxWt8odWub2p9z47E2bxcgCOjb1/Pnndr88by/npzjVzRwS0pKUF1djcTERFy6dAl1dXUQBAE1NTWubaqrq2GxWBAaGgqbzYbGxkbodDpXu7vOn7ehqal1eHcXf71Sf/WqEwaD2OrYBUGA0+mEw+GEUyfAKQqu193dpvbnwCi2ONbm/wsBQE2Nrc1Og6/w1/O+WXvH31kIKxq469evd73esmULvvjiCyxfvhwTJ05EWVkZ7rvvPhQXFyM6Ohp6vR4jRoxASUkJEhISXO3kHWJi4mEyBapdBpGmeMU83Ly8PGRnZ8NutyMyMhKpqakAgNzcXCxatAhr1qxB//798frrr6tcKTX79a9T/L6XQ+Qu1QI3KSkJSUlJAICIiAgUFRW12iY8PBwbNmxQujTqgvr6etTXtzx9BEHgOgpEHfCKHi5pzzPPpMFgELFmzbVhIkEQULCzHMFGnlJE7eHiNdRtbPUO2OudapdB5LUYuERECmHgEhEphIFLRKQQXuEgWSZNegw9erS9Hi79dFekL9/8QO5j4JIsiYlJnIfbjuBAEetLjgAAZsYPYeiSCwOXZKmtrYVO5wCgV7sUr2Sr51MvqDWO4ZIsL7zwLNLS0tQug0hTGLhERAph4BIRKYSBS0SkEAYuEZFCOEuBZHn88Smch0vkJgYuyRIbO57zcIncxMAlWc6d+wFXr16GwdBT7VK8WnvP5yP/xDFckiUrayGee+45tcvwaiFGPQr3Huei7OTCwCXyIHsD7zijnzBwiYgUwsAlIlIIA5eISCGcpUCypKbOQs+eQWqXQaQpDFySZdy4hzgPl8hNDFyS5eTJ73HpUgh69QpTuxQizWDgkixLl+bCYBCxZs16tUsh0gxeNCMiUggDl4hIIQxcIiKFMHDppgmCwPUCiLqAF81Ilrlz56FXryAIgoCCneUINvJUIuoM/5aQLKNGjYHZ3AM1NTbY6h3gCoTta+79c5lG4pACyXL0aDkOHz6sdhleLzhQxPqSIyjYWc5hF2IPl+R59dVXYDCIePvtArVL8Xq2ei7RSNewh0tEpBAGLhGRQhi4REQKYeASKYTzlUmVi2ZvvfUWdu7cCQAYN24cFi5ciNLSUixfvhxXrlxBfHw8FixYAAAoLy9HdnY2bDYbRowYgSVLlkAUea1PbenpC3DLLcFql6EZIUY91pccAQDMjB/CKWJ+SvEebmlpKfbv348PP/wQxcXF+Pbbb7Fjxw5kZmYiPz8fJSUlOHz4MPbt2wcAyMjIQE5ODnbt2gVJklBYWKh0ydSGqKh78a//+q9ql6EptnoHZyz4OcUD12w2Y9GiRTAYDNDr9fjZz36GkydPYuDAgRgwYABEUURCQgKsVisqKirQ0NCAqKgoAEBSUhKsVqvSJVMbDh36Gw4ePKh2GUSaovjv5nfeeafr9cmTJ1FSUoLp06fDbDa72i0WCyorK1FVVdWi3Ww2o7Ky0q399eljuvmiO2E29/D4PrzNO++sBgAUFRVBrxch6nXQN0oQ9TqIouhqu/51W+/fTJvanwPA7c8GgL59PX9OKsEfz/vryTl+1QZDjx8/jt/85jd48cUXIYoiTpw40eJ9QRDaHOdy96LD+fM2NDV5brzMXx8zc/WqEwaDiPPn7XA4nHDqBNf/nWLbr7u7Te3PgVGE0+l067MBoKbGpvkxXH8975u1d/ydhbAqsxTKysowc+ZMPP/883jssccQFhaGmpoa1/tVVVWwWCyt2qurq2GxWNQomdqxvfRE5xsREQAVAveHH37A008/jby8PEyYMAEAMHz4cJw4cQKnTp1CY2MjduzYgejoaISHhyMwMBBlZWUAgOLiYkRHRytdMnWgroEXgYi6SvEhhXXr1uHKlStYsWKFq+2JJ57AihUrkJ6ejitXrmDcuHGIi4sDAOTl5SE7Oxt2ux2RkZFITU1VumQiom6heOBmZ2cjOzu7zfe2bdvWqi0iIgJFRUWeLovclJGRid69g/FJOXu47mrv+gT5Pt5pRrJERAzB0KFD1S5Dc0KMehTuPc47zvwUb9kiWT77rBS9egUB8O+pQXLYOe7ttxi4JMu7766BwSDioV9nqV0KkWZwSIGISCEMXCIihTBwiYgUwsAlIlIIL5qRLDk5S9C7dwh2f+W/99MTuYs9XJLl9tvvwKBBg9QuQ7P49Af/xB4uybJv3x707BkEwNzpttRScKDoevrDrPGRkCSJd575CfZwSZb33luPtWvXql2GZtnqHZAkYH3JERTsLGdv10+wh0ukIj5yx7+wh0tEpBAGLhGRQhi4REQK4RguybJs2UqEhoZga2mV2qUQaQYDl2Tp3//W/3v6LAO3O3BRcv/AIQVymyAIWLziXTybtVrtUnxC86LkAQEBnB7m49jDJVm+Ki2BTheAiKj71S7FJ0iS5LoZYmb8EPZ2fRQDl8hLcE6u7+OQAhGRQhi4REQKYeASESmEY7gkyyOPP48epkC1yyDSFAYuuaV5HVdjcE8EhxjVLscnNU8N40wF38PApS4TBAEFO8sRbBTx90N7EWTU477Rj6pdlk8JMepbrJXb1NSkckXUnTiGS26x1Ttgr3fi74c+xuGDf1G7HJ/UvFZu4d7jvBHCxzBwibyUvYHzcn0NA5eISCEMXCIvxodN+hYGLnUZ/+Irq/lhkwU7y7mwjY/gLAXqEkEQsL30hOvruKmZ6Ml5uB5nq3e0mLnAhW20jYFLnWr+tbbuuos4oj4QegPn4SqFC9v4BgYudej6ubfXO3JwF4yBIkaNm6hSZf6JC5VrG8dwqVPNc2+v9/23pTj29X6VKvJPNy5UzjFd7WEPl0hDmhcqDzaKEAQBv3pgECRJ4u3AGqGJHu727dsxfvx4PProo9i4caPa5fiF5h4Ue1Hep/k3DnuDA4IgICAgAAU7y1vMZrjx58afpXfw+h5uZWUlVq1ahS1btsBgMOCJJ57AyJEjMWjQILVL04zOxv2u/4vY3FvaceAkai7Wtxq7Je/RPG0s2Ci6ZjNsLz2Bmov1AK6txdD887xxlgPHgtXh9X+bSktLMWrUKNxyyy0AgNjYWFitVjzzzDNd+v6AAPf+VZfTC9DpvPcXBUEQ8Je/ncbD9w5o8y+YIAj4fwdOwmjQAQLw8L0DAACmID2uOhoRFChC1AUgKFBs8fq2W/shQBcAS+9gV1v9FWer7a5/3db7N9Om9ueEBBsQKAaoevwXLje0amv+ue38/BSMBh0CDTr0DDEA+Olc7eic6CpvPu+7Q2d/Nu5mCwAIkpf/M/fOO++grq4OCxYsAAB88MEH+Oabb7B06VKVKyMico/X/xPVXq+MiEhrvD5ww8LCUFNT4/q6qqoKFotFxYqIiOTx+sAdM2YMDhw4gAsXLqC+vh67d+9GdHS02mUREbnN6y+ahYWFYcGCBUhNTYXD4cDkyZNx9913q10WEZHbvP6iGRGRr/D6IQUiIl/BwCUiUggDl4hIIQxcIiKFMHDddPbsWUydOhVxcXGYN28e7HZ7q22qqqowe/ZsJCYm4rHHHsOBAwdUqLT7dLZ4UHl5OZKTkxEbG4usrCw4nc42PkW7Ojv+P//5z0hMTMSkSZMwf/58XLp0SYUqPaOrC0d9/PHHeOihhxSsTBmdHf/333+P6dOnY9KkSZg9e3bnP3uJ3JKWlibt2LFDkiRJeuutt6SVK1e22ub555+XNmzYIEmSJH333XfSmDFjJKfTqWid3eXcuXPSgw8+KNXW1kp2u11KSEiQjh8/3mKbCRMmSF999ZUkSZK0ePFiaePGjSpU6hmdHf+PP/4ojR07Vjp37pwkSZL0xhtvSEuXLlWr3G7VlZ+9JElSdXW1FBcXJz344IMqVOk5nR1/U1OTFBMTI+3bt0+SJEl69dVX28yD67GH6waHw4GDBw8iNjYWAJCUlASr1dpqu5iYGCQkJAAABg4ciCtXrqCurk7RWrvL9YsHBQcHuxYPalZRUYGGhgZERUUBaP/PRKs6O36Hw4Hf/e53CAsLAwAMHjwYP/zwg1rldqvOjr1ZdnZ2lxeT0pLOjv/bb79FcHCw60asp556ClOnTu3wMxm4bqitrYXJZIIoXrtfxGw2o7KystV2MTEx6NWrFwBg3bp1GDJkCHr06KFord2lqqoKZrPZ9bXFYmlxzDe+396fiVZ1dvy9e/fGI488AgBoaGjA2rVrXV9rXWfHDgDvvfceIiMjMXz4cKXL87jOjv+f//wn+vbtixdffBEJCQnIzc1FcHBwh5/p9XeaqWXnzp1Yvnx5i7bbb7+91XYdLaRTUFCAzZs34/333+/u8hQjdbJ4UGfva11Xj+/HH3/E/PnzERERgccee0yJ0jyus2P/+9//jt27d6OgoADnzp1TsjRFdHb8TqcTX3zxBd5//30MGzYMb7zxBlasWIEVK1a0+5kM3HbEx8cjPj6+RZvD4cDIkSPR2NgInU6H6urqdhfSWblyJfbt24eNGzeiX79+SpTsEWFhYfjyyy9dX9+4eNCNiwt19GeiRZ0df3Pb7NmzMWrUKGRmZipdosd0duxWqxXV1dVITk6Gw+FAVVUVUlJSsGnTJjXK7XadHb/ZbMbAgQMxbNgwAMDEiRPx7LPPdviZHFJwg16vx4gRI1BSUgIAKC4ubnMhnYKCAnz++ef44x//qOmwBTpfPCg8PByBgYEoKysD0P6fiVZ1dvyNjY146qmnEB8fj6ysLJ/q3Xd27M8++yx27dqFrVu3Yu3atbBYLD4TtkDnx3/PPffgwoULOHr0KABgz549+PnPf97xh3rqCp+vOnPmjDRt2jQpPj5eevLJJ6WLFy9KkiRJmzZtkt544w2pqalJGjFihPTAAw9IkyZNcv3XfBVbi7Zt2yZNmDBBiomJkdauXStJkiTNmTNH+uabbyRJkqTy8nIpOTlZiouLk/793/9dunLliprldruOjn/37t3S4MGDW/ysMzMzVa64+3T2s292+vRpn5ulIEmdH/+hQ4ek5ORkafz48dKTTz4p1dTUdPh5XLyGiEghHFIgIlIIA5eISCEMXCIihTBwiYgUwsAlIlIIA5f8wqJFi7Bu3ToAQGJiIi5fvowff/wRqampnX5vY2Mj5s2bh9jYWE3fNUjq451m5He2bt0KADhz5gz+93//t9PtKysrsX//fhw6dAg6nc7T5ZEPY+CSJtntdixevBinTp1CQEAAfv7zn2PChAnIy8tDWFgYTp8+DaPRiBUrVuBnP/tZi+8dPHgwDhw4gMWLF6OhoQGJiYnYsmVLm2Fqs9kwZ84cOJ1OJCUlYfXq1Rg/fjwefvhhHD16FHl5eTh27Bg2b94Mh8OBS5cuYe7cuUhJSQEAvPPOO/jwww8hiiIGDhyIFStWaHYhI7p5HFIgTfroo49gt9uxdetWFBUVAbjWYz1y5AiefPJJbN++HUlJScjIyGj3M5YvXw6j0YitW7e223M1mUxYu3ata7t/+Zd/gcPhwIMPPohdu3bhjjvuwAcffIC1a9eiuLgYq1atwquvvgoA+Mtf/oItW7Zg8+bN2LFjB2677TYOSfg59nBJk+677z6sWrUK06dPx5gxYzBjxgxcuHABERERGDFiBAAgOTkZL7/8Mmpra7t9/837CAkJwdtvv419+/bh5MmTOHr0qGvt4wMHDiAuLs61VOfixYu7vQ7SFvZwSZMGDBiAjz76CGlpabDZbJg1axZqa2tb9VQlSfLIuGvzuqfnzp3DL3/5S1RUVOC+++7Db3/7W9c2Op2uxWI2ly9fxpkzZ7q9FtIOBi5p0qZNm7B48WLcf//9yMjIwP3334+NGzfi6NGjrtWbNm/ejHvvvRc9e/Zs8zNEUURjY2Ob65521eHDhxEaGor58+fj3/7t37B3714A12Y2jBkzBh999BFsNhsAYPXq1SgoKJC9L9I+DimQJv3yl7/EF198gfHjxyMoKAi33norUlNTcfr0abzxxhuoqKhAaGgoVq5c2e5nmM1mREZGIj4+Hn/84x/Ru3dvt+sYO3YsioqKEBcXh6CgINx9990IDQ3FqVOnMG7cOPzjH//AlClTAACDBg3C0qVLZR8zaR9XCyOf8fnnn2Pp0qXYsWOH2qUQtYk9XCIAKSkpbT7yHgA2btwIk8mkcEXki9jDJSJSCC+aEREphIFLRKQQBi4RkUIYuERECmHgEhEphIFLRKSQ/w8SUlW3410NMQAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.displot(data['split_frac'], kde=False)\n", + "plt.axvline(0, color=\"k\", linestyle=\"--\");" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "251" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(data.split_frac < 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Out of nearly 40,000 participants, there were only 250 people who negative-split their marathon.\n", + "\n", + "Let's see whether there is any correlation between this split fraction and other variables. We'll do this using a `PairGrid`, which draws plots of all these correlations (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "g = sns.PairGrid(data, vars=['age', 'split_sec', 'final_sec', 'split_frac'],\n", + " hue='gender', palette='RdBu_r')\n", + "g.map(plt.scatter, alpha=0.8)\n", + "g.add_legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It looks like the split fraction does not correlate particularly with age, but does correlate with the final time: faster runners tend to have closer to even splits on their marathon time. Let's zoom in on the histogram of split fractions separated by gender, shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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PPPCAlE0QAgCobQrAzfsRtLmQqwE/jucwymVCVX0HrpraNXzD6YxgYX+OKiAkM/RkLMkLx4/XgvFqME3me8RmwyiXGZWn/Gdf0JnAaL0bojAU9CQvtNeeQELv6P+NWVZkNyAQTqAz3HUDmNOZaE16ojgZBf2Pf/xj7Ny5U+paCBmUWCIFVaAJvMWZ87Y5nkOJ04iTTV1z52lNeqJEGQX9/Pnz8dJLL2HBggVYt24d/H6/xGURkrlj9Z0YbwiAGXMf9ABQ7DDieENXuHM6M1iUHpgiypJR0N90003YsGEDXnrpJXi9Xtx222146KGHcODAAanrI6RfR2t9KFZ3ImXI/dANAJQ4TGhoDyElMECjA4QkxGRclloISSfjMXpRFFFXV4fa2lqkUik4nU489dRTeP7556Wsj5B+Han1wSr4IejtsrSv1apgN+nQ0BYCx3Hg9BYINPOGKEhG0yvXrFmDTZs2YfTo0VixYgVefPFFaDQaRCIRzJs3Dw899JDUdRKSViSWRKTTC9hVYGp9/wdIxO0w4mRzAGNLLOD0ZgghP6AzylYPIefKKOh9Ph/+8Ic/YPLkyT1eNxqN+I//+A9JCiMkE1X1fkwpSECQYcbNuYrsBhw6vcgZpzNBCHUAulJZayLkjIyGbgRBuCDkf/zjHwMArrnmmuxXRUiGjtT6MN4chaDP/raBA+Gw6uANRJFICuC0JqRCtKUgUY4+r+iffPJJtLa2Yt++ffD5zi7JmkqlUFNTI3lxhPTnaJ0fswsDELTyBr1KxcNh1aOxPYxROiNSQQp6ohx9Bv2tt96K6upqVFVVYcGCBd2vq1QqWreGyC4UTcLbGYPN7kPCOl7ucuCy6VHfFsJouwlC0AtpF0omJHN9Bv20adMwbdo0XH311XC73bmqiZCMVJ3qwKgiEzRRD6L6mXKXA5fdgGP1flxdbIbQ3iLtQlKEDECfn8Wf/OQnePHFF3H33Xen/f4777wjSVGEZOJIXQfKCw1QNXRC0FnlLgdOmx5tB6NgWjdSoQ4KeqIYfX4W77nnHgDAv/3bv+WkGEIGorKuAxVTDRDbzACvkrscaNQqmPQa+ONqWGgePVGQPmfdXHrppQCA2bNno6SkBLNnz4bf78fu3btxySWX5KRAQtIJhBPoCMZRrAnJPuPmXA6rDs0hQIyFaJNwohgZTa984okn8Ic//AEnTpzA008/jcbGRjz22GNS10ZIr47WdaDcbYEm6lXEsM0ZdrMOTb4oeJ2JNgknipFR0B86dAhPPfUUtm3bhltuuQXPPfccGhsbpa6NkF4drvVhtMsEdcQDQaekK3o9mr0RqAwWWpeeKEZGQc8YA8/z+Mc//oGrruraqi0ajUpaGCF9OVLrw5hiC9ThNkUFfYFFC18gBs5gpqAnipFR0JeXl+Oee+5BQ0MDZs+ejZ/+9KeYNGlSRg388pe/xMMPPzykIgk5V5s/ikRShNOqhzrSrqgxerVKBbNRizinh0g3ZIlCZDQD7LnnnsO2bdswc+ZMaDQazJo1C0uXLu33uF27dmHz5s24/vrrh1gmIWcdqfVhbLEFHBOhivkVNUYPAAVmLUIpDXRhejqWKENGV/RGoxGzZs1CIBDA4cOHMX369H6XQPD7/VizZg3uu+++rBRKyBn7q9sxxm2BKuaHqDECvLJmrFuNWvgSGogU9EQhMvoJef7557FhwwY4nWd38OE4Dh9++GGvxzzxxBN48MEH0dzcPPQqCTktJYioqvfj2uklUIdqZFuDvi92sw5tTTzGG339v5mQHMgo6N9//31s3bo142UQ3nzzTZSUlGDOnDnYtGnToApzOs2DOk5KLpdF7hIUKZf9sr/aA7fDiNJiG9THA+DNBTCbdTlrPxNlKh6fHAN4a4A+M72gfklPqn7JKOhLSkoGtNbNe++9B4/HgyVLlqCzsxORSAT//u//jkcffTTjc3i9IYgiy/j9UnO5LPB4gnKXoTi57pf/21ePUS4T/P4IrO2N4HgToiGFbdvHGIKCDomAjz4zadDPUnpD7Ree53q9QM4o6OfMmYPVq1fjhhtugF5/dhefqVOnpn3/f//3f3f/96ZNm7B79+4BhTwh6TDG8EW1BwtnjwEAqMNtSNjGyFxVGhwHo9UGJCJgYgqcwu4hkJEno0/gmeGXDz74oPu1/sboCcm2Bk8YyZSIYocBAKCOtCPqni5zVenZrQYk/QawSCc4s7P/AwiRUEZBv3379kE3sGzZMixbtmzQxxNyxp6jrbh4tB0cxwFMhDrWoaiHpc7lsOgQ8ethD3cAFPREZhlNrwyHw3j66afxve99D36/H0888QTC4bDUtRHSjTGG3ZVtuHiUHQCginVCVOsBlUbewnpRYNUjkNJBpKdjiQJkFPS/+MUvYLFY4PV6odPpEAqF8MQTT0hdGyHdTrWGkEgKKHEaAQCqSDsEnV3eovpgN+vQmVTTXHqiCBkF/dGjR/Hggw9CrVbDYDDghRdewNGjR6WujZBu2z9vwLTxzq5hG6BrMTO9sp6IPZdWq0Kc0yPi88hdCiGZBT3P93ybIAgXvEaIVKLxFPZWeTBt/Nmxbk24VbHj82cwnRlRX5vcZRCS2c3Yr3zlK3j++ecRi8Xw8ccfY8OGDbjyyiulro0QAMDOQ80od5thNpwdj1eHWhEvmCBjVf3j9BaIoZNyl0FIZlf0P/vZz2A0GmGxWLB27VpMnjwZ//qv/yp1bYQgnhDw7s46zJ7c84E9ddijyOUPzqUx2aCKd8pdBiH9X9Fv27YN69atQ1VVFfR6PSZNmoQZM2ZAp1PWY+ckP23dewqlhabum7AAADEFVVwZG4L3RWe1Qd8WAmOs+94CIXLoM+jfeustvPTSS1i5ciUmT54MjuNw8OBBPPvss4jH45g/f36u6iQj0KnWILbursftX7+ox+vqyOntAxWwIXhfrGYTkoyHGAtCZVD2P0okv/UZ9K+88grWr1+P0tLS7tcmTJiAyy67DI8++igFPZFMe2cUv/rfA5h3RRkcFn2P76nDbYoftgEAjUaFMDOAa2mBaxwFPZFPn0GfTCZ7hPwZ48aNQzyusIWkyLAiMoZGTxinWoNICiJ0GhUMWjUYYzjRHMCOLxpx1RQ3pox1XHBsV9Are8bNGXGVCcmWZrjGXSx3KWQE6zPoVarefzVmTDkrS5LhpdUXwX/9vyPwBeIoLTRBo+KRTAlIpEQAgNOqx7e+dhGcNn3a4zXBJqT0F/4DoESixoiIl6ZYEnnRsnokpzpDcTy38XPMmuTCsmvHD+ompSbUhLhD2VMru+nMiHe2y10FGeH6DPqqqirMmDHjgtcZY0gkEpIVRfKTyBhefucILh3nwKxJRYM8iQB1pB0pfUF2i5OI2mgB19oqdxlkhOsz6Ldt25arOsgIcPCEF75gDBVXDX4NeXXEA0FrUexiZufTmm0wNB6DKDLwPE2xJPLoM+jLyspyVQcZAbbtqcfMi11DCjxNqBkpw/BZ9pcz2FCgisDjj8LtMPZ/ACESoAVrSE40e8OoawticvnQhlzUwWYIBnt2isoBQWuGlYugkbbOIzKioCc58fH+Zkwb54RaNbSPnCbQMKyu6KHSIMVp0dZMM2+IfCjoSU58ebwdE8uGOPedMWgD9UiZBnkjVyZJjRn+lia5yyAjmKRB/+KLL2Lx4sWoqKjosWE4GVnaO6MIRBIoHuIYtSrmBxiDqLVkp7AcYXoLYn5al57IR7J59Lt378ann36Kt99+G6lUCosXL8Z1112H8ePHS9UkUaiDNT6ML7EOedaJprMOKbMbGGYLhPF6K7QJP+IJATqtstfnIflJsiv62bNn409/+hPUajW8Xi8EQYDRSLMORqL9x9sxtnjoV+Fafx1SRlcWKsotpjOjRB9DYzvts0zkIemTsRqNBv/5n/+JP/7xj1i4cCHcbnf/B53mdJolrGxwXK7hNWSQK331iygyVDd04sZrJ/TYOGQw9KFTSI26Ambz8Fgi+0ydvLUAbm0z/NEUfYZOo35IT6p+kXwJhJUrV+Kee+7BfffdhzfeeAPf/OY3MzrO6w1BFJWzno7LZYGHpshdoL9+aWwPw6BTIRVPwh9PDr4hIYkSfwOC5V8DCyl/QT2zWYfQ6TrVzAArC+LzEx7MmDA81uiREv0spTfUfuF5rtcLZMmGbk6cONG9gbjBYMD8+fNRVVUlVXNEoWqaOlHiNA35PDp/DQRDIZh6eFzNn0vQmmESg6hrpXAj8pAs6BsaGvD4448jkUggkUjgww8/xMyZM6VqjijUicZOFBcYhnweXXsVEtbh+aQ2UxvAsxTa2vwQadVXIgPJhm6uu+467N+/H0uXLoVKpcL8+fNRUVEhVXNEoU40BTDv8qEHtK69EuFRV2WhIhlwHESdDaX6KFp9kaz8hkPIQEg6Rr9y5UqsXLlSyiaIgsWTAto6oiga4hU9Hw9CHfUhZcr8Zr7SCDoLxloSqGsNUtCTnKMnY4lkTrUGUWQ3DHnZA33bQSTsYxS/R2xfRK0Fpfoo6pppnJ7kHgU9kUxDWwgu+9DH540tXyBuH94P2glaM1yqEE42B+QuhYxAFPREMqfaQnBYhzZLhk+EoOmsR8JWnqWq5CHorLAhgFNtIdqGk+QcBT2RTIMnBJdtaFf0+tYDXSE/TDYa6Y2os0IX74BOo0KbPyp3OWSEoaAnkmCMoak9DJc9/QbfmTI27kbceXGWqpKPoLVAFetAidOEk000fENyi4KeSKIjGIeK52HUD/5KXBVphzriQcI6OouVyYOp9QATMcrG4URTp9zlkBGGgp5IorE9POQbscbG3Yg7LhrWs226cRwEnQ3lpjhq6Iqe5BgFPZFEgycEp20IwzZMhKlxN2KFk7NXlMxEnRXF2hAaPGGkBFHucsgIQkFPJNHQFoJzCDNudO1VENV6CMbCLFYlL0FngT7egQKzDo0eWrKY5A4FPZFEszcCp3XwV/Sm+p15dTUPdE2xVEc8KHYaUUPz6UkOUdCTrGOMobUjAodlcFf0qmgHdB3H82K2zbkEna0r6B1GHG+gG7IkdyjoSdYFI13rzht0g1tKyVi/EzHnxWAqbTbLkp2gs0IV8aHUaaSZNySnKOhJ1rX4uoZtuEHs7cql4jA17ELMdakElclL1FqgSgRRaNHAH4ojEhvCRiyEDAAFPcm6Fl8EjkGOz5vq/4GkpRSCoSDLVSkAr4Kgs0Ab70CJw0Tj9CRnKOhJ1jW3h2E3D3zYhUvFYD65HZGS/N2gRtTZoIp4Uew04EQjDd+Q3KCgJ1nX5A3DYRn4Fb312LtI2MZAMDolqEoZzsy8KXGYUE03ZEmOUNCTrOsauhnYjBut7zgMLfsRHj1HoqqUQdDZoA63obTQhJPNQdpakOSEpEH/61//GhUVFaioqMDq1aulbIooREoQ0RGMw27OPOhVYQ8cX65HcNzXutaEyWOCvivozQYNdBoerb6I3CWREUCyoN+5cyc++eQTbN68GW+99RYOHz6Mbdu2SdUcUQhvZwwWozbjXaXUwWa49vwakbLZSNqG/+Jl/Unp7VBHPACA0kITjtM4PckByYLe5XLh4YcfhlarhUajwYQJE9DU1CRVc0QhWjsiKMjwQSlD8+dw7fk1wmVXIuaaInFlyiDqrFDFg4CQRAk9OEVyRLLNwS+66KLu/66trcV7772H1157TarmiEK0+qL9zrjhklHYD78BbWcdOi+6ESmTK0fVKQDHdw3fRNtRWmjF3/Y1yF0RGQEkC/ozqqur8c///M/4+c9/jrFjx2Z8nNNplq6oQXK5LHKXoEjn9ktnNImSQgvsdmPa93IhD/SfvAjRXobk7O9AP8x3juqLuZf7FJzJARsC0I8dhzc+OgGjWQ+TIX/7IR36WUpPqn6RNOj37duHlStX4tFHH0VFRcWAjvV6QxBF5cxIcLks8HiCcpehOOf3y8nGTkwZUwC//8KbjHwiDNenaxB2TUHMPR2IigDiOaw2d8xmHUKh9H83k9qMZFsDQuZJcDsM2H2wEZeOy98ppeejn6X0htovPM/1eoEs2Rh9c3MzfvjDH+KFF14YcMiT4autIwp7L2P0tiNvImEd3RXyI5igt0MdagYAlDpNqK6ncXoiLcmu6NetW4d4PI5Vq1Z1v/atb30Lt99+u1RNEpmlBBH+UBx204Vj9NqOGug6auC7lP7/p/QOmLzHAQBlhSYcPOmTuSKS7yQL+scffxyPP/64VKcnCuTxR2E1aaFKM7XSeuxdhMtmA3k8Jp8pwVAAdaQNYAxlLhPe3VWLlCBmPCWVkIGiTxbJmtaOaNo16NXBZqgjnq79XwmYWg/Ga6CK+aHXqmEz6VDfFpK7LJLHKOhJ1rT5IrClmWliOvUJYoWX5Mcm31kiGJxQh1sBAGUuWveGSIuCnmRNsy+CgvPn0IspGFs+HzEPRGWq64bs6aAvNOFoLY3TE+lQ0JOsafVd+FSsvr0KKYMTolZ5z0XIKWUogOb0zJtytwXHGjppgTMiGQp6kjWtHVEUnLc8saHlC8QLxstUkXIJ+gJogl1BbzZoYNKrUd9K4/REGhT0JCuSKQHBSAK2c6dWiinoPYeRoKC/QMrohDrcAjARADC6yIzKUx0yV0XyFQU9yYq2jihsZh14/uw+sbqOGqT0BTRskwZT68HUeqgiXgBdQX+YxumJRCjoSVakm1qp8xxB0pr/Sw8PVspYCE2wEQBQXmTG8YZOpARR5qpIPqKgJ1nR2hG5YLMRg+cwEvYxMlWkfCmDA5pAV9Ab9Ro4rDpatphIgoKeZEWLN9JjeWJVpB1cMoKUcQQtQTxAKUMhtMGzyxSPLbbiwAmvjBWRfEVBT7Ki+bwNwXXeKiRt5QDH9XHUyJYyFkITOLsZz7gSKw6caJexIpKvKOhJVrT4onBYzwa9vr0SCcsoGStSPlFnBScmwMcDAIAShxEdoQR8gZjMlZF8Q0FPhiwUTSKZEmE2nF4jj4nQ+Y4jaaWg7xPHIWkqhrazDkDXeuITSq3Yf5yu6kl2UdCTIWvxRlBo04M7PUyjCTRA1Jggak0yV6Z8KZMLWn9d99cTy2zYU9kmY0UkH1HQkyFr9obhsJ6dcaNrr0KCruYzkjK5oe042f312BILTrYEEYomZayK5BsKejJkTd4wCs6ZWqnzHUPSUipjRcNH0uyGJtjQ/YSsVq3CWLeFhm9IVlHQkyFrag+fvRErpqDtPEVBnyGm1kPUmKA+ve4N0DV8s/toq4xVkXxDQU+GrNkbgfN00Gs7T0HQF4Cp9f0cRc5IWsqg8x3v/nriKBuONXTS8A3JGsmDPhQK4cYbb0RDQ0P/bybDTjIldO0Te/phKZ23GklLicxVDS9Jayn03qrur3UaFcaXWLG3im7KkuyQNOj379+P22+/HbW1tVI2Q2RU3xqCw6Lv3idW56tG0lImc1XDS8JSBm1HDSAK3a9NLrdj16EWGasi+UTSoH/jjTfw5JNPoqioSMpmiIxONnXCZT87Pq/pPIWkma7oB4JpjBB0FmgCZ3/rHVdiRWN7GG3+qIyVkXwhadA/++yzmDVrlpRNEJnVNHWi0GYAAGg76yAYHGDqC/eNJX1LWkdB336k+2u1iseUMQX4eH9TH0cRkhm13AX0xulU3hrmLpdF7hIUp6axEzMnuWG3G6FpPAU4RsOcZoPwkWgg/cAXXwTdyZ1QzVre/drcy8rwyvtHcc8t07uHxvIF/SylJ1W/KDbovd4QRFE5e2i6XBZ4PEG5y1AUxhjqmgO49tIS+P0RFDYdQdR5MRKhuNylyc5s1iE0kH5QF8IZ9iHY3AjBUAAA0Ks4mPRqfPhpLa64OH9WAaWfpfSG2i88z/V6gZxflwkkpzrDCYgMXWvcdI/P0/z5QeF4JOxjoW871OPlyycW4oPdp2QqiuQLCnoyaPVtIZQWmsBx3Dnz52nYZrDi9nEwNO/r8dqk8gK0dkRR10JXwGTwchL027dvx6hRtPZJvqlrCcDtMAKg+fPZkLCVQxPxQBU5u/yBiucw46JCvPdpXR9HEtI3uqIng3asoROj3V03j2j+fBbwKsQcE2Fs2tPj5csmFuJIrQ9N7WGZCiPDHQU9GRTGGGqaAih3W7rG5wP1tL5NFsSdk2Fs+KzHw1M6jQpfmVyEzR/XyFgZGc4o6MmgtHZEoVHzsJl10HacRMrgBFNp+z+Q9CllckHUmqD3HO7x+uUXFeJYvR8nmwMyVUaGMwp6MignGjtRVti1sYjeW0m7SWVRzHUpzLV/7/GaVq3CNdNKsGHrMTCmnGnHZHigoCeDcqzej5IzN2I9FPTZFC8YD3XU17X+zTkuHedALJHCp4dpCWMyMBT0ZFCO1ftR5jIDsSDUUS+SJrfcJeUPXoVIyQxYq9/r8TLHcfj6zFF4bXs1wjFawphkjoKeDFibP4pwLAV3gQGqliNIWssAXiV3WXkl5pwEVdQLXXtVj9dLnCZcNMqGN7Yf7+VIQi5EQU8G7MDxdowvtYLjOKgbvkDCNkbukvIPr0J41BzYKjf1mIEDANdOK8X+E15U1nXIVBwZbijoyYB9Ud2OccUWQEhC1XoUcfs4uUvKSwn7ODCV/oIbszqtCl+fOQp/fO8o4gkh/cGEnIOCngxIPCHgRFMnxhZbofNVQzS7wDQGucvKTxyH4JivwnLyQ6hDPW/ATiyzwe0w4vWPqmUqjgwnFPRkQPZWtaG8yAydVgVj8+cQCifIXVJeE/U2hMtmw7H/fwAh0eN7N8wowxfH2nGwxitTdWS4oKAnA/LRF42YNt4JLhWDvu0QBPdkuUvKezHXVAg6CwoOvwGcM4der1Vj0ZXl+K93j6AjSEtDk95R0JOMNXpC8PijGF9qg6HlSySsowCtUe6y8h/HITjmOmgCjbAee7tH2Je7Lbh8YiF+s/kgkilRxiKJklHQk4xt3VOPaeOdUHGAue7/EC+kq/mcUWnReXEF9G2HYT/8Ro+ZOFdNcUOj5vFf7x6BSE/NkjQo6ElGmtrD+PyYB7MmubrWYREFmlaZY0ytR+fkpVCHW+H6bG33DVqO47D4yjFo8UXwP+9XUtiTC1DQk34xxvD69mrMvqQIeg0PS/X7iJTOBDhO7tJGHKbSIjBxEeL2cXB99iKslVvAJcLQqHks++p4nGoN4rebD9G0S9IDBT3p144vm9DaEcUVF7lgPvkRwPNI0Nx5+XAcYu7p6Jj6TagjHhR//Cws1e/BwKJY9tUJSKZEPP0/e1DTRCtdki4U9KRPxxs68b87TuCmuWNhDNTBcnI7gmPn0dW8AohaE0Jjr0fHJcuhCTbC/fGzcFW+iRsnd+1KtfbN/fj924fRSBuWjHhqKU/+zjvv4Le//S2SyST+6Z/+Cd/+9relbI5k2aGTXvx+y2EsvmoMSoQmOL74IwLjb4Cos8pdGjmHqLchNHYewmWzYfAcReEX6zBPpcVXJk/Hl5EYXtjogbPAjCunuDF9vBNFBQZw9A/1iCJZ0Le2tmLNmjXYtGkTtFotvvWtb+HKK6/ExIkTpWqSZEmbP4r3dtXiy+p23DLbhcmdH8F4dA+C4+YhaSuXuzzSC6YxIVI6C5GSmVCHW6Hzn8Q1kUO4zuRDhDnQctCOXbtN8IpW6BxFsBaVwFlUBLfTDJfdAItRA57+AchLkgX9zp07cdVVV8FutwMAFixYgA8++AA/+tGPMjqe55X3gVNiTf0RRBGJRAqCICAloutPiiGREhBLdP2JxFIIxRLwdUbR4WmHOtqOaQUx3HyxB7qmRiTs4xCZeQc4jRHn7yGl0WmhTQ2/fpGa7P1iGItk4VgkAUBMQh3zY1TMj/J4ECwWAuIHoPHtBO9NIQwDGgQzPCkzArwNEZUNCY0JotYMjc4Ak1EHm1kLq1ELm0kHs1EDo14NvVYNrZoDx3ED/g1hOP4s5cJQ+qWvYyUL+ra2Nrhcru6vi4qKcODAgYyPLygwSVHWkDidZrlLICQv0M9SelL1i2Q3Y9Ntd0bjgoQQknuSBb3b7UZ7e3v3121tbSgqKpKqOUIIIb2QLOjnzp2LXbt2wefzIRqNYuvWrfjqV78qVXOEEEJ6IdkYvdvtxoMPPog77rgDyWQSt956K6ZPny5Vc4QQQnrBsXSD6YQQQvIGPRlLCCF5joKeEELyHAU9IYTkOQp6QgjJcxT0vWhqasK3v/1tLFy4ED/4wQ8QDl+4AmBbWxvuuusuLFmyBLfccgt27dolQ6W58c4772Dx4sX4xje+gY0bN17w/aNHj2L58uVYsGABHnvsMaRSKRmqzL3++uVvf/sblixZgptvvhn3338/Ojs7Zagy9/rrlzP+/ve/42tf+1oOK5Nff31TU1OD7373u7j55ptx1113Zeczw0ha9957L3v33XcZY4z9+te/ZqtXr77gPT/96U/ZK6+8whhj7MSJE2zu3LkslUrltM5caGlpYfPmzWMdHR0sHA6zm266iVVXV/d4T0VFBfviiy8YY4w98sgjbOPGjTJUmlv99UswGGRXX301a2lpYYwxtnbtWvbMM8/IVW7OZPJ5YYwxj8fDFi5cyObNmydDlfLor29EUWTz589nO3bsYIwx9vzzz6fNnoGiK/o0kskk9uzZgwULFgAAli1bhg8++OCC982fPx833XQTAGDMmDGIx+OIRCI5rTUXzl2gzmg0di9Qd0ZjYyNisRguv/xyAL33V77pr1+SySSeeuopuN1uAMCkSZPQ3NwsV7k501+/nPH4449nvMhhvuivbw4fPgyj0dj9cOl9992XleXdKejT6OjogNlshlrd9TyZy+VCa2vrBe+bP38+bDYbAGDdunW45JJLYLFYclprLqRboO7c/jj/+731V77pr18KCgrw9a9/HQAQi8Xw8ssvd3+dz/rrFwD405/+hClTpuCyyy7LdXmy6q9vTp06hcLCQvz85z/HTTfdhCeffBJGo3HI7Uq68chw8P777+O5557r8drYsWMveF9fC7KtX78er7/+OjZs2JDt8hSB9bNAXX/fz1eZ/r2DwSDuv/9+TJ48GbfccksuSpNVf/1y7NgxbN26FevXr0dLS0suS5Ndf32TSqWwe/dubNiwAdOmTcPatWuxatUqrFq1akjtjvigX7RoERYtWtTjtWQyiSuvvBKCIEClUsHj8fS6INvq1auxY8cObNy4EcXFxbkoOefcbjf27t3b/fX5C9Sdv4BdX/2VT/rrlzOv3XXXXbjqqqvw6KOP5rpEWfTXLx988AE8Hg+WL1+OZDKJtrY2rFixAq+++qoc5eZUf33jcrkwZswYTJs2DQBw4403YuXKlUNul4Zu0tBoNJg1axbee+89AMBbb72VdkG29evX47PPPsOf//znvA15oP8F6srKyqDT6bBv3z4AvfdXvumvXwRBwH333YdFixbhscceGxG/5QD998vKlSvx17/+FVu2bMHLL7+MoqKiERHyQP99c8UVV8Dn86GyshIAsH37dkydOnXoDQ/5dm6eamhoYN/5znfYokWL2J133sn8fj9jjLFXX32VrV27lomiyGbNmsWuv/56dvPNN3f/OTPDIt+8/fbbrKKigs2fP5+9/PLLjDHG7r77bnbgwAHGGGNHjx5ly5cvZwsXLmT/8i//wuLxuJzl5kxf/bJ161Y2adKkHp+PRx99VOaKc6O/z8sZ9fX1I2rWDWP9982XX37Jli9fzhYvXszuvPNO1t7ePuQ2aVEzQgjJczR0QwgheY6CnhBC8hwFPSGE5DkKekIIyXMU9IQQkuco6MmI9/DDD2PdunUAgCVLliAQCCAYDOKOO+7o91hBEPCDH/wACxYsyNsno8nwN+KfjCXkXFu2bAEANDQ04ODBg/2+v7W1FZ988gm+/PJLqFQqqcsjZFAo6EneCYfDeOSRR1BXVwee5zF16lRUVFTghRdegNvtRn19PfR6PVatWoUJEyb0OHbSpEnYtWsXHnnkEcRiMSxZsgSbNm1KG+KhUAh33303UqkUli1bhl/96ldYvHgxbrjhBlRWVuKFF15AVVUVXn/9dSSTSXR2duKee+7BihUrAAC///3vsXnzZqjVaowZMwarVq3Ky0XxiPxo6IbknW3btiEcDmPLli34y1/+AqDrCv3IkSO488478c4772DZsmV46KGHej3Hc889B71ejy1btvR6pW42m/Hyyy93v6+8vBzJZBLz5s3DX//6V4wfPx5vvvkmXn75Zbz11ltYs2YNnn/+eQDAhx9+iE2bNuH111/Hu+++i1GjRtHQD5EMXdGTvDNz5kysWbMG3/3udzF37lx873vfg8/nw+TJkzFr1iwAwPLly/H000+jo6Mj6+2facNkMuF3v/sdduzYgdraWlRWVnbvV7Br1y4sXLiwe5nrRx55JOt1EHIGXdGTvDN69Ghs27YN9957L0KhEL7//e+jo6Pjgitzxpgk4+pn1g9vaWnB0qVL0djYiJkzZ+KBBx7ofo9KpeqxyFkgEEBDQ0PWayEEoKAneejVV1/FI488gmuuuQYPPfQQrrnmGmzcuBGVlZXdqwK+/vrrmDFjBqxWa9pzqNVqCIKQdv3wTB06dAgOhwP3338/rr32Wnz00UcAumbqzJ07F9u2bUMoFAIA/OpXv8L69esH3RYhfaGhG5J3li5dit27d2Px4sUwGAwoLS3FHXfcgfr6eqxduxaNjY1wOBxYvXp1r+dwuVyYMmUKFi1ahD//+c8oKCgYcB1XX301/vKXv2DhwoUwGAyYPn06HA4H6urqcN111+H48eO4/fbbAQATJ07EM888M+i/MyF9odUryYjw2Wef4ZlnnsG7774rdymE5Bxd0RPSjxUrViAcDqf93saNG2E2m3NcESEDQ1f0hBCS5+hmLCGE5DkKekIIyXMU9IQQkuco6AkhJM9R0BNCSJ6joCeEkDz3/wHgg6J61JcgAAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.kdeplot(data.split_frac[data.gender=='M'], label='men', shade=True)\n", + "sns.kdeplot(data.split_frac[data.gender=='W'], label='women', shade=True)\n", + "plt.xlabel('split_frac');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The interesting thing here is that there are many more men than women who are running close to an even split!\n", + "It almost looks like a bimodal distribution among the men and women. Let's see if we can suss out what's going on by looking at the distributions as a function of age.\n", + "\n", + "A nice way to compare distributions is to use a *violin plot*, shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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agegendersplitfinalsplit_secfinal_secsplit_fracage_dec
033M0 days 01:05:380 days 02:08:513938.07731.0-0.01875630
132M0 days 01:06:260 days 02:09:283986.07768.0-0.02626230
231M0 days 01:06:490 days 02:10:424009.07842.0-0.02244330
338M0 days 01:06:160 days 02:13:453976.08025.00.00909730
431M0 days 01:06:320 days 02:13:593992.08039.00.00684230
\n", + "
" + ], + "text/plain": [ + " age gender split final split_sec final_sec \\\n", + "0 33 M 0 days 01:05:38 0 days 02:08:51 3938.0 7731.0 \n", + "1 32 M 0 days 01:06:26 0 days 02:09:28 3986.0 7768.0 \n", + "2 31 M 0 days 01:06:49 0 days 02:10:42 4009.0 7842.0 \n", + "3 38 M 0 days 01:06:16 0 days 02:13:45 3976.0 8025.0 \n", + "4 31 M 0 days 01:06:32 0 days 02:13:59 3992.0 8039.0 \n", + "\n", + " split_frac age_dec \n", + "0 -0.018756 30 \n", + "1 -0.026262 30 \n", + "2 -0.022443 30 \n", + "3 0.009097 30 \n", + "4 0.006842 30 " + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['age_dec'] = data.age.map(lambda age: 10 * (age // 10))\n", + "data.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "men = (data.gender == 'M')\n", + "women = (data.gender == 'W')\n", + "\n", + "with sns.axes_style(style=None):\n", + " sns.violinplot(x=\"age_dec\", y=\"split_frac\", hue=\"gender\", data=data,\n", + " split=True, inner=\"quartile\",\n", + " palette=[\"lightblue\", \"lightpink\"]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see where the distributions among men and women differ: the split distributions of men in their 20s to 50s show a pronounced overdensity toward lower splits when compared to women of the same age (or of any age, for that matter).\n", + "\n", + "Also surprisingly, it appears that the 80-year-old women seem to outperform *everyone* in terms of their split time, although this is likely a small number effect, as there are only a handful of runners in that range:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "7" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(data.age > 80).sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Back to the men with negative splits: who are these runners? Does this split fraction correlate with finishing quickly? We can plot this very easily. We'll use `regplot`, which will automatically fit a linear regression model to the data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "g = sns.lmplot(x='final_sec', y='split_frac', col='gender', data=data,\n", + " markers=\".\", scatter_kws=dict(color='c'))\n", + "g.map(plt.axhline, y=0.0, color=\"k\", ls=\":\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Apparently, among both men and women, the people with fast splits tend to be faster runners who are finishing within ~15,000 seconds, or about 4 hours. People slower than that are much less likely to have a fast second split." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/04.15-Further-Resources.ipynb b/notebooks/04.15-Further-Resources.ipynb new file mode 100644 index 000000000..7bffc3a4a --- /dev/null +++ b/notebooks/04.15-Further-Resources.ipynb @@ -0,0 +1,63 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Further Resources\n", + "\n", + "A single part of a book can never hope to cover all the available features and plot types available in Matplotlib.\n", + "As with other packages we've seen, liberal use of IPython's tab completion and help functions (see [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)) can be very helpful when exploring Matplotlib's API.\n", + "In addition, Matplotlib’s [online documentation](http://matplotlib.org/) can be a helpful reference.\n", + "See in particular the [Matplotlib gallery](https://matplotlib.org/stable/gallery/), which shows thumbnails of hundreds of different plot types, each one linked to a page with the Python code snippet used to generate it.\n", + "This allows you to visually inspect and learn about a wide range of different plotting styles and visualization techniques.\n", + "\n", + "For a book-length treatment of Matplotlib, I would recommend *Interactive Applications Using Matplotlib* (Packt), written by Matplotlib core developer Ben Root." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Other Python Visualization Libraries\n", + "\n", + "Although Matplotlib is the most prominent Python visualization library, there are other more modern tools that are worth exploring as well.\n", + "I'll mention a few of them briefly here:\n", + "\n", + "- [Bokeh](http://bokeh.pydata.org) is a JavaScript visualization library with a Python frontend that creates highly interactive visualizations capable of handling very large and/or streaming datasets.\n", + "- [Plotly](http://plot.ly) is the eponymous open source product of the Plotly company, and is similar in spirit to Bokeh. It is actively developed and provides a wide range of interactive chart types.\n", + "- [HoloViews](https://holoviews.org/) is a more declarative, unified API for generating charts in a variety of backends, including Bokeh and Matplotlib.\n", + "- [Vega](https://vega.github.io/) and [Vega-Lite](https://vega.github.io/vega-lite) are declarative graphics representations, and are the product of years of research into how to think about data visualization and interaction. The reference rendering implementation is JavaScript, and the [Altair package](https://altair-viz.github.io/) provides a Python API to generate these charts.\n", + "\n", + "The visualization landscape in the Python world is constantly evolving, and I expect that this list may be out of date by the time this book is published.\n", + "Additionally, because Python is used in so many domains, you'll find many other visualization tools built for more specific use cases.\n", + "It can be hard to keep track of all of them, but a good resource for learning about this wide variety of visualization tools is https://pyviz.org/, an open, community-driven site containing tutorials and examples of many different visualization tools." + ] + } + ], + "metadata": { + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.00-Machine-Learning.ipynb b/notebooks/05.00-Machine-Learning.ipynb new file mode 100644 index 000000000..889866b91 --- /dev/null +++ b/notebooks/05.00-Machine-Learning.ipynb @@ -0,0 +1,54 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Machine Learning" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This final part is an introduction to the very broad topic of machine learning, mainly via Python's [Scikit-Learn](http://scikit-learn.org) package.\n", + "You can think of machine learning as a class of algorithms that allow a program to detect particular patterns in a dataset, and thus \"learn\" from the data to draw inferences from it.\n", + "This is not meant to be a comprehensive introduction to the field of machine learning; that is a large subject and necessitates a more technical approach than we take here.\n", + "Nor is it meant to be a comprehensive manual for the use of the Scikit-Learn package (for this, you can refer to the resources listed in [Further Machine Learning Resources](05.15-Learning-More.ipynb)).\n", + "Rather, the goals here are:\n", + "\n", + "- To introduce the fundamental vocabulary and concepts of machine learning\n", + "- To introduce the Scikit-Learn API and show some examples of its use\n", + "- To take a deeper dive into the details of several of the more important classical machine learning approaches, and develop an intuition into how they work and when and where they are applicable\n", + "\n", + "Much of this material is drawn from the Scikit-Learn tutorials and workshops I have given on several occasions at PyCon, SciPy, PyData, and other conferences.\n", + "Any clarity in the following pages is likely due to the many workshop participants and co-instructors who have given me valuable feedback on this material over the years!" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.01-What-Is-Machine-Learning.ipynb b/notebooks/05.01-What-Is-Machine-Learning.ipynb new file mode 100644 index 000000000..b5a952528 --- /dev/null +++ b/notebooks/05.01-What-Is-Machine-Learning.ipynb @@ -0,0 +1,463 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# What Is Machine Learning?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Before we take a look at the details of several machine learning methods, let's start by looking at what machine learning is, and what it isn't.\n", + "Machine learning is often categorized as a subfield of artificial intelligence, but I find that categorization can be misleading.\n", + "The study of machine learning certainly arose from research in this context, but in the data science application of machine learning methods, it's more helpful to think of machine learning as a means of *building models of data*.\n", + "\n", + "In this context, \"learning\" enters the fray when we give these models *tunable parameters* that can be adapted to observed data; in this way the program can be considered to be \"learning\" from the data.\n", + "Once these models have been fit to previously seen data, they can be used to predict and understand aspects of newly observed data.\n", + "I'll leave to the reader the more philosophical digression regarding the extent to which this type of mathematical, model-based \"learning\" is similar to the \"learning\" exhibited by the human brain.\n", + "\n", + "Understanding the problem setting in machine learning is essential to using these tools effectively, and so we will start with some broad categorizations of the types of approaches we'll discuss here." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Categories of Machine Learning\n", + "\n", + "Machine learning can be categorized into two main types: supervised learning and unsupervised learning.\n", + "\n", + "*Supervised learning* involves somehow modeling the relationship between measured features of data and some labels associated with the data; once this model is determined, it can be used to apply labels to new, unknown data.\n", + "This is sometimes further subdivided into classification tasks and regression tasks: in *classification*, the labels are discrete categories, while in *regression*, the labels are continuous quantities.\n", + "You will see examples of both types of supervised learning in the following section.\n", + "\n", + "*Unsupervised learning* involves modeling the features of a dataset without reference to any label.\n", + "These models include tasks such as *clustering* and *dimensionality reduction.*\n", + "Clustering algorithms identify distinct groups of data, while dimensionality reduction algorithms search for more succinct representations of the data.\n", + "You will also see examples of both types of unsupervised learning in the following section.\n", + "\n", + "In addition, there are so-called *semi-supervised learning* methods, which fall somewhere between supervised learning and unsupervised learning.\n", + "Semi-supervised learning methods are often useful when only incomplete labels are available." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Qualitative Examples of Machine Learning Applications\n", + "\n", + "To make these ideas more concrete, let's take a look at a few very simple examples of a machine learning task.\n", + "These examples are meant to give an intuitive, non-quantitative overview of the types of machine learning tasks we will be looking at in this part of the book.\n", + "In later chapters, we will go into more depth regarding the particular models and how they are used.\n", + "For a preview of these more technical aspects, you can find the Python source that generates the following figures in the online [appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Classification: Predicting Discrete Labels\n", + "\n", + "We will first take a look at a simple classification task, in which we are given a set of labeled points and want to use these to classify some unlabeled points.\n", + "\n", + "Imagine that we have the data shown in this figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-classification-1.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This data is two-dimensional: that is, we have two *features* for each point, represented by the (x,y) positions of the points on the plane.\n", + "In addition, we have one of two *class labels* for each point, here represented by the colors of the points.\n", + "From these features and labels, we would like to create a model that will let us decide whether a new point should be labeled \"blue\" or \"red.\"\n", + "\n", + "There are a number of possible models for such a classification task, but we will start with a very simple one. We will make the assumption that the two groups can be separated by drawing a straight line through the plane between them, such that points on each side of the line all fall in the same group.\n", + "Here the *model* is a quantitative version of the statement \"a straight line separates the classes,\" while the *model parameters* are the particular numbers describing the location and orientation of that line for our data.\n", + "The optimal values for these model parameters are learned from the data (this is the \"learning\" in machine learning), which is often called *training the model*.\n", + "\n", + "See the following figure shows a visual representation of what the trained model looks like for this data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-classification-2.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now that this model has been trained, it can be generalized to new, unlabeled data.\n", + "In other words, we can take a new set of data, draw this line through it, and assign labels to the new points based on this model (see the following figure).\n", + "This stage is usually called *prediction*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-classification-3.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This is the basic idea of a classification task in machine learning, where \"classification\" indicates that the data has discrete class labels.\n", + "At first glance this may seem trivial: it's easy to look at our data and draw such a discriminatory line to accomplish this classification.\n", + "A benefit of the machine learning approach, however, is that it can generalize to much larger datasets in many more dimensions.\n", + "\n", + "For example, this is similar to the task of automated spam detection for email. In this case, we might use the following features and labels:\n", + "\n", + "- *feature 1*, *feature 2*, etc. $\\to$ normalized counts of important words or phrases (\"Viagra\", \"Extended warranty\", etc.)\n", + "- *label* $\\to$ \"spam\" or \"not spam\"\n", + "\n", + "For the training set, these labels might be determined by individual inspection of a small representative sample of emails; for the remaining emails, the label would be determined using the model.\n", + "For a suitably trained classification algorithm with enough well-constructed features (typically thousands or millions of words or phrases), this type of approach can be very effective.\n", + "We will see an example of such text-based classification in [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb).\n", + "\n", + "Some important classification algorithms that we will discuss in more detail are Gaussian naive Bayes (see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)), support vector machines (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)), and random forest classification (see [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Regression: Predicting Continuous Labels\n", + "\n", + "In contrast with the discrete labels of a classification algorithm, we will next look at a simple regression task in which the labels are continuous quantities.\n", + "\n", + "Consider the data shown in the following figure, which consists of a set of points each with a continuous label." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-regression-1.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As with the classification example, we have two-dimensional data: that is, there are two features describing each data point.\n", + "The color of each point represents the continuous label for that point.\n", + "\n", + "There are a number of possible regression models we might use for this type of data, but here we will use a simple linear regression model to predict the points.\n", + "This simple model assumes that if we treat the label as a third spatial dimension, we can fit a plane to the data.\n", + "This is a higher-level generalization of the well-known problem of fitting a line to data with two coordinates.\n", + "\n", + "We can visualize this setup as shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-regression-2.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that the *feature 1–feature 2* plane here is the same as in the two-dimensional plot in Figure 37-4; in this case, however, we have represented the labels by both color and three-dimensional axis position.\n", + "From this view, it seems reasonable that fitting a plane through this three-dimensional data would allow us to predict the expected label for any set of input parameters.\n", + "Returning to the two-dimensional projection, when we fit such a plane we get the result shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-regression-3.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This plane of fit gives us what we need to predict labels for new points.\n", + "Visually, we find the results shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-regression-4.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As with the classification example, this task may seem trivial in a low number of dimensions.\n", + "But the power of these methods is that they can be straightforwardly applied and evaluated in the case of data with many, many features.\n", + "\n", + "For example, this is similar to the task of computing the distance to galaxies observed through a telescope—in this case, we might use the following features and labels:\n", + "\n", + "- *feature 1*, *feature 2*, etc. $\\to$ brightness of each galaxy at one of several wavelengths or colors\n", + "- *label* $\\to$ distance or redshift of the galaxy\n", + "\n", + "The distances for a small number of these galaxies might be determined through an independent set of (typically more expensive or complex) observations.\n", + "Distances to remaining galaxies could then be estimated using a suitable regression model, without the need to employ the more expensive observation across the entire set.\n", + "In astronomy circles, this is known as the \"photometric redshift\" problem.\n", + "\n", + "Some important regression algorithms that we will discuss are linear regression (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)), support vector machines (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)), and random forest regression (see [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Clustering: Inferring Labels on Unlabeled Data\n", + "\n", + "The classification and regression illustrations we just saw are examples of supervised learning algorithms, in which we are trying to build a model that will predict labels for new data.\n", + "Unsupervised learning involves models that describe data without reference to any known labels.\n", + "\n", + "One common case of unsupervised learning is \"clustering,\" in which data is automatically assigned to some number of discrete groups.\n", + "For example, we might have some two-dimensional data like that shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-clustering-1.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By eye, it is clear that each of these points is part of a distinct group.\n", + "Given this input, a clustering model will use the intrinsic structure of the data to determine which points are related.\n", + "Using the very fast and intuitive *k*-means algorithm (see [In Depth: K-Means Clustering](05.11-K-Means.ipynb)), we find the clusters shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-clustering-2.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "*k*-means fits a model consisting of *k* cluster centers; the optimal centers are assumed to be those that minimize the distance of each point from its assigned center.\n", + "Again, this might seem like a trivial exercise in two dimensions, but as our data becomes larger and more complex such clustering algorithms can continue to be employed to extract useful information from the dataset.\n", + "\n", + "We will discuss the *k*-means algorithm in more depth in [In Depth: K-Means Clustering](05.11-K-Means.ipynb).\n", + "Other important clustering algorithms include Gaussian mixture models (see [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb)) and spectral clustering (see [Scikit-Learn's clustering documentation](http://scikit-learn.org/stable/modules/clustering.html))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Dimensionality Reduction: Inferring Structure of Unlabeled Data\n", + "\n", + "Dimensionality reduction is another example of an unsupervised algorithm, in which labels or other information are inferred from the structure of the dataset itself.\n", + "Dimensionality reduction is a bit more abstract than the examples we looked at before, but generally it seeks to pull out some low-dimensional representation of data that in some way preserves relevant qualities of the full dataset.\n", + "Different dimensionality reduction routines measure these relevant qualities in different ways, as we will see in [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb).\n", + "\n", + "As an example of this, consider the data shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-dimesionality-1.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Visually, it is clear that there is some structure in this data: it is drawn from a one-dimensional line that is arranged in a spiral within this two-dimensional space.\n", + "In a sense, you could say that this data is \"intrinsically\" only one-dimensional, though this one-dimensional data is embedded in two-dimensional space.\n", + "A suitable dimensionality reduction model in this case would be sensitive to this nonlinear embedded structure and be able to detect this lower-dimensionality representation.\n", + "\n", + "The following figure shows a visualization of the results of the Isomap algorithm, a manifold learning algorithm that does exactly this." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.01-dimesionality-2.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that the colors (which represent the extracted one-dimensional latent variable) change uniformly along the spiral, which indicates that the algorithm did in fact detect the structure we saw by eye.\n", + "As with the previous examples, the power of dimensionality reduction algorithms becomes clearer in higher-dimensional cases.\n", + "For example, we might wish to visualize important relationships within a dataset that has 100 or 1,000 features.\n", + "Visualizing 1,000-dimensional data is a challenge, and one way we can make this more manageable is to use a dimensionality reduction technique to reduce the data to 2 or 3 dimensions.\n", + "\n", + "Some important dimensionality reduction algorithms that we will discuss are principal component analysis (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)) and various manifold learning algorithms, including Isomap and locally linear embedding (see [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Summary\n", + "\n", + "Here we have seen a few simple examples of some of the basic types of machine learning approaches.\n", + "Needless to say, there are a number of important practical details that we have glossed over, but this chapter was designed to give you a basic idea of what types of problems machine learning approaches can solve.\n", + "\n", + "In short, we saw the following:\n", + "\n", + "- *Supervised learning*: Models that can predict labels based on labeled training data\n", + "\n", + " - *Classification*: Models that predict labels as two or more discrete categories\n", + " - *Regression*: Models that predict continuous labels\n", + " \n", + "- *Unsupervised learning*: Models that identify structure in unlabeled data\n", + "\n", + " - *Clustering*: Models that detect and identify distinct groups in the data\n", + " - *Dimensionality reduction*: Models that detect and identify lower-dimensional structure in higher-dimensional data\n", + " \n", + "In the following sections we will go into much greater depth within these categories, and see some more interesting examples of where these concepts can be useful.\n", + "\n", + "All of the figures in the preceding discussion are generated based on actual machine learning computations; the code behind them can be found in [Appendix: Figure Code](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.02-Introducing-Scikit-Learn.ipynb b/notebooks/05.02-Introducing-Scikit-Learn.ipynb new file mode 100644 index 000000000..60b614cce --- /dev/null +++ b/notebooks/05.02-Introducing-Scikit-Learn.ipynb @@ -0,0 +1,1652 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introducing Scikit-Learn" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "There are several Python libraries that provide solid implementations of a range of machine learning algorithms.\n", + "One of the best known is [Scikit-Learn](http://scikit-learn.org), a package that provides efficient versions of a large number of common algorithms.\n", + "Scikit-Learn is characterized by a clean, uniform, and streamlined API, as well as by very useful and complete online documentation.\n", + "A benefit of this uniformity is that once you understand the basic use and syntax of Scikit-Learn for one type of model, switching to a new model or algorithm is straightforward.\n", + "\n", + "This chapter provides an overview of the Scikit-Learn API. A solid understanding of these API elements will form the foundation for understanding the deeper practical discussion of machine learning algorithms and approaches in the following chapters.\n", + "\n", + "We will start by covering data representation in Scikit-Learn, then delve into the Estimator API, and finally go through a more interesting example of using these tools for exploring a set of images of handwritten digits." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Data Representation in Scikit-Learn" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Machine learning is about creating models from data: for that reason, we'll start by discussing how data can be represented.\n", + "The best way to think about data within Scikit-Learn is in terms of *tables*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "A basic table is a two-dimensional grid of data, in which the rows represent individual elements of the dataset, and the columns represent quantities related to each of these elements.\n", + "For example, consider the [Iris dataset](https://en.wikipedia.org/wiki/Iris_flower_data_set), famously analyzed by Ronald Fisher in 1936.\n", + "We can download this dataset in the form of a Pandas `DataFrame` using the [Seaborn](http://seaborn.pydata.org/) library, and take a look at the first few items:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " sepal_length sepal_width petal_length petal_width species\n", + "0 5.1 3.5 1.4 0.2 setosa\n", + "1 4.9 3.0 1.4 0.2 setosa\n", + "2 4.7 3.2 1.3 0.2 setosa\n", + "3 4.6 3.1 1.5 0.2 setosa\n", + "4 5.0 3.6 1.4 0.2 setosa" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import seaborn as sns\n", + "iris = sns.load_dataset('iris')\n", + "iris.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here each row of the data refers to a single observed flower, and the number of rows is the total number of flowers in the dataset.\n", + "In general, we will refer to the rows of the matrix as *samples*, and the number of rows as `n_samples`.\n", + "\n", + "Likewise, each column of the data refers to a particular quantitative piece of information that describes each sample.\n", + "In general, we will refer to the columns of the matrix as *features*, and the number of columns as `n_features`." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The Features Matrix\n", + "\n", + "The table layout makes clear that the information can be thought of as a two-dimensional numerical array or matrix, which we will call the *features matrix*.\n", + "By convention, this matrix is often stored in a variable named `X`.\n", + "The features matrix is assumed to be two-dimensional, with shape `[n_samples, n_features]`, and is most often contained in a NumPy array or a Pandas `DataFrame`, though some Scikit-Learn models also accept SciPy sparse matrices.\n", + "\n", + "The samples (i.e., rows) always refer to the individual objects described by the dataset.\n", + "For example, a sample might represent a flower, a person, a document, an image, a sound file, a video, an astronomical object, or anything else you can describe with a set of quantitative measurements.\n", + "\n", + "The features (i.e., columns) always refer to the distinct observations that describe each sample in a quantitative manner.\n", + "Features are often real-valued, but may be Boolean or discrete-valued in some cases." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The Target Array\n", + "\n", + "In addition to the feature matrix `X`, we also generally work with a *label* or *target* array, which by convention we will usually call `y`.\n", + "The target array is usually one-dimensional, with length `n_samples`, and is generally contained in a NumPy array or Pandas `Series`.\n", + "The target array may have continuous numerical values, or discrete classes/labels.\n", + "While some Scikit-Learn estimators do handle multiple target values in the form of a two-dimensional, `[n_samples, n_targets]` target array, we will primarily be working with the common case of a one-dimensional target array.\n", + "\n", + "A common point of confusion is how the target array differs from the other feature columns. The distinguishing characteristic of the target array is that it is usually the quantity we want to *predict from the features*: in statistical terms, it is the dependent variable.\n", + "For example, given the preceding data we may wish to construct a model that can predict the species of flower based on the other measurements; in this case, the `species` column would be considered the target array.\n", + "\n", + "With this target array in mind, we can use Seaborn (discussed in [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)) to conveniently visualize the data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import seaborn as sns\n", + "sns.pairplot(iris, hue='species', height=1.5);" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For use in Scikit-Learn, we will extract the features matrix and target array from the `DataFrame`, which we can do using some of the Pandas `DataFrame` operations discussed in [Part 3](03.00-Introduction-to-Pandas.ipynb):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(150, 4)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X_iris = iris.drop('species', axis=1)\n", + "X_iris.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(150,)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y_iris = iris['species']\n", + "y_iris.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "To summarize, the expected layout of features and target values is visualized in the following figure." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.02-samples-features.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Features-and-Labels-Grid)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this data properly formatted, we can move on to consider Scikit-Learn's Estimator API." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## The Estimator API" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The Scikit-Learn API is designed with the following guiding principles in mind, as outlined in the [Scikit-Learn API paper](http://arxiv.org/abs/1309.0238):\n", + "\n", + "- *Consistency*: All objects share a common interface drawn from a limited set of methods, with consistent documentation.\n", + "\n", + "- *Inspection*: All specified parameter values are exposed as public attributes.\n", + "\n", + "- *Limited object hierarchy*: Only algorithms are represented by Python classes; datasets are represented\n", + " in standard formats (NumPy arrays, Pandas `DataFrame` objects, SciPy sparse matrices) and parameter\n", + " names use standard Python strings.\n", + "\n", + "- *Composition*: Many machine learning tasks can be expressed as sequences of more fundamental algorithms,\n", + " and Scikit-Learn makes use of this wherever possible.\n", + "\n", + "- *Sensible defaults*: When models require user-specified parameters, the library defines an appropriate default value.\n", + "\n", + "In practice, these principles make Scikit-Learn very easy to use, once the basic principles are understood.\n", + "Every machine learning algorithm in Scikit-Learn is implemented via the Estimator API, which provides a consistent interface for a wide range of machine learning applications." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Basics of the API\n", + "\n", + "Most commonly, the steps in using the Scikit-Learn Estimator API are as follows:\n", + "\n", + "1. Choose a class of model by importing the appropriate estimator class from Scikit-Learn.\n", + "2. Choose model hyperparameters by instantiating this class with desired values.\n", + "3. Arrange data into a features matrix and target vector, as outlined earlier in this chapter.\n", + "4. Fit the model to your data by calling the `fit` method of the model instance.\n", + "5. Apply the model to new data:\n", + " - For supervised learning, often we predict labels for unknown data using the `predict` method.\n", + " - For unsupervised learning, we often transform or infer properties of the data using the `transform` or `predict` method.\n", + "\n", + "We will now step through several simple examples of applying supervised and unsupervised learning methods." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Supervised Learning Example: Simple Linear Regression\n", + "\n", + "As an example of this process, let's consider a simple linear regression—that is, the common case of fitting a line to $(x, y)$ data.\n", + "We will use the following simple data for our regression example (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "rng = np.random.RandomState(42)\n", + "x = 10 * rng.rand(50)\n", + "y = 2 * x - 1 + rng.randn(50)\n", + "plt.scatter(x, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this data in place, we can use the recipe outlined earlier. Let's walk through the process: " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 1. Choose a class of model\n", + "\n", + "In Scikit-Learn, every class of model is represented by a Python class.\n", + "So, for example, if we would like to compute a simple `LinearRegression` model, we can import the linear regression class:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.linear_model import LinearRegression" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Note that other more general linear regression models exist as well; you can read more about them in the [`sklearn.linear_model` module documentation](http://Scikit-Learn.org/stable/modules/linear_model.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 2. Choose model hyperparameters\n", + "\n", + "An important point is that *a class of model is not the same as an instance of a model*.\n", + "\n", + "Once we have decided on our model class, there are still some options open to us.\n", + "Depending on the model class we are working with, we might need to answer one or more questions like the following:\n", + "\n", + "- Would we like to fit for the offset (i.e., *y*-intercept)?\n", + "- Would we like the model to be normalized?\n", + "- Would we like to preprocess our features to add model flexibility?\n", + "- What degree of regularization would we like to use in our model?\n", + "- How many model components would we like to use?\n", + "\n", + "These are examples of the important choices that must be made *once the model class is selected*.\n", + "These choices are often represented as *hyperparameters*, or parameters that must be set before the model is fit to data.\n", + "In Scikit-Learn, hyperparameters are chosen by passing values at model instantiation.\n", + "We will explore how you can quantitatively choose hyperparameters in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb).\n", + "\n", + "For our linear regression example, we can instantiate the `LinearRegression` class and specify that we would like to fit the intercept using the `fit_intercept` hyperparameter:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "LinearRegression()" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model = LinearRegression(fit_intercept=True)\n", + "model" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Keep in mind that when the model is instantiated, the only action is the storing of these hyperparameter values.\n", + "In particular, we have not yet applied the model to any data: the Scikit-Learn API makes very clear the distinction between *choice of model* and *application of model to data*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 3. Arrange data into a features matrix and target vector\n", + "\n", + "Previously we examined the Scikit-Learn data representation, which requires a two-dimensional features matrix and a one-dimensional target array.\n", + "Here our target variable `y` is already in the correct form (a length-`n_samples` array), but we need to massage the data `x` to make it a matrix of size `[n_samples, n_features]`.\n", + "In this case, this amounts to a simple reshaping of the one-dimensional array:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(50, 1)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X = x[:, np.newaxis]\n", + "X.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 4. Fit the model to the data\n", + "\n", + "Now it is time to apply our model to the data.\n", + "This can be done with the `fit` method of the model:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "LinearRegression()" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.fit(X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This `fit` command causes a number of model-dependent internal computations to take place, and the results of these computations are stored in model-specific attributes that the user can explore.\n", + "In Scikit-Learn, by convention all model parameters that were learned during the `fit` process have trailing underscores; for example in this linear model, we have the following:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1.9776566])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.coef_" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.9033107255311146" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.intercept_" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "These two parameters represent the slope and intercept of the simple linear fit to the data.\n", + "Comparing the results to the data definition, we see that they are close to the values used to generate the data: a slope of 2 and intercept of –1.\n", + "\n", + "One question that frequently comes up regards the uncertainty in such internal model parameters.\n", + "In general, Scikit-Learn does not provide tools to draw conclusions from internal model parameters themselves: interpreting model parameters is much more a *statistical modeling* question than a *machine learning* question.\n", + "Machine learning instead focuses on what the model *predicts*.\n", + "If you would like to dive into the meaning of fit parameters within the model, other tools are available, including the [`statsmodels` Python package](http://statsmodels.sourceforge.net/)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 5. Predict labels for unknown data\n", + "\n", + "Once the model is trained, the main task of supervised machine learning is to evaluate it based on what it says about new data that was not part of the training set.\n", + "In Scikit-Learn, this can be done using the `predict` method.\n", + "For the sake of this example, our \"new data\" will be a grid of *x* values, and we will ask what *y* values the model predicts:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "xfit = np.linspace(-1, 11)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As before, we need to coerce these *x* values into a `[n_samples, n_features]` features matrix, after which we can feed it to the model:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "Xfit = xfit[:, np.newaxis]\n", + "yfit = model.predict(Xfit)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, let's visualize the results by plotting first the raw data, and then this model fit (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x, y)\n", + "plt.plot(xfit, yfit);" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Typically the efficacy of the model is evaluated by comparing its results to some known baseline, as we will see in the next example." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Supervised Learning Example: Iris Classification\n", + "\n", + "Let's take a look at another example of this process, using the Iris dataset we discussed earlier.\n", + "Our question will be this: given a model trained on a portion of the Iris data, how well can we predict the remaining labels?\n", + "\n", + "For this task, we will use a simple generative model known as *Gaussian naive Bayes*, which proceeds by assuming each class is drawn from an axis-aligned Gaussian distribution (see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) for more details).\n", + "Because it is so fast and has no hyperparameters to choose, Gaussian naive Bayes is often a good model to use as a baseline classification, before exploring whether improvements can be found through more sophisticated models.\n", + "\n", + "We would like to evaluate the model on data it has not seen before, so we will split the data into a *training set* and a *testing set*.\n", + "This could be done by hand, but it is more convenient to use the `train_test_split` utility function:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.model_selection import train_test_split\n", + "Xtrain, Xtest, ytrain, ytest = train_test_split(X_iris, y_iris,\n", + " random_state=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With the data arranged, we can follow our recipe to predict the labels:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.naive_bayes import GaussianNB # 1. choose model class\n", + "model = GaussianNB() # 2. instantiate model\n", + "model.fit(Xtrain, ytrain) # 3. fit model to data\n", + "y_model = model.predict(Xtest) # 4. predict on new data" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we can use the ``accuracy_score`` utility to see the fraction of predicted labels that match their true values:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9736842105263158" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "accuracy_score(ytest, y_model)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With an accuracy topping 97%, we see that even this very naive classification algorithm is effective for this particular dataset!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Unsupervised Learning Example: Iris Dimensionality\n", + "\n", + "As an example of an unsupervised learning problem, let's take a look at reducing the dimensionality of the Iris data so as to more easily visualize it.\n", + "Recall that the Iris data is four-dimensional: there are four features recorded for each sample.\n", + "\n", + "The task of dimensionality reduction centers around determining whether there is a suitable lower-dimensional representation that retains the essential features of the data.\n", + "Often dimensionality reduction is used as an aid to visualizing data: after all, it is much easier to plot data in two dimensions than in four dimensions or more!\n", + "\n", + "Here we will use *principal component analysis* (PCA; see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), which is a fast linear dimensionality reduction technique.\n", + "We will ask the model to return two components—that is, a two-dimensional representation of the data.\n", + "\n", + "Following the sequence of steps outlined earlier, we have:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.decomposition import PCA # 1. Choose the model class\n", + "model = PCA(n_components=2) # 2. Instantiate the model\n", + "model.fit(X_iris) # 3. Fit to data\n", + "X_2D = model.transform(X_iris) # 4. Transform the data" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now let's plot the results. A quick way to do this is to insert the results into the original Iris `DataFrame`, and use Seaborn's `lmplot` to show the results (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "iris['PCA1'] = X_2D[:, 0]\n", + "iris['PCA2'] = X_2D[:, 1]\n", + "sns.lmplot(x=\"PCA1\", y=\"PCA2\", hue='species', data=iris, fit_reg=False);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that in the two-dimensional representation, the species are fairly well separated, even though the PCA algorithm had no knowledge of the species labels!\n", + "This suggests to us that a relatively straightforward classification will probably be effective on the dataset, as we saw before." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Unsupervised Learning Example: Iris Clustering\n", + "\n", + "Let's next look at applying clustering to the Iris data.\n", + "A clustering algorithm attempts to find distinct groups of data without reference to any labels.\n", + "Here we will use a powerful clustering method called a *Gaussian mixture model* (GMM), discussed in more detail in [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb).\n", + "A GMM attempts to model the data as a collection of Gaussian blobs.\n", + "\n", + "We can fit the Gaussian mixture model as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.mixture import GaussianMixture # 1. Choose the model class\n", + "model = GaussianMixture(n_components=3,\n", + " covariance_type='full') # 2. Instantiate the model\n", + "model.fit(X_iris) # 3. Fit to data\n", + "y_gmm = model.predict(X_iris) # 4. Determine labels" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As before, we will add the cluster label to the Iris ``DataFrame`` and use Seaborn to plot the results (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "iris['cluster'] = y_gmm\n", + "sns.lmplot(x=\"PCA1\", y=\"PCA2\", data=iris, hue='species',\n", + " col='cluster', fit_reg=False);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By splitting the data by cluster number, we see exactly how well the GMM algorithm has recovered the underlying labels: the *setosa* species is separated perfectly within cluster 0, while there remains a small amount of mixing between *versicolor* and *virginica*.\n", + "This means that even without an expert to tell us the species labels of the individual flowers, the measurements of these flowers are distinct enough that we could *automatically* identify the presence of these different groups of species with a simple clustering algorithm!\n", + "This sort of algorithm might further give experts in the field clues as to the relationships between the samples they are observing." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Application: Exploring Handwritten Digits" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "To demonstrate these principles on a more interesting problem, let's consider one piece of the optical character recognition problem: the identification of handwritten digits.\n", + "In the wild, this problem involves both locating and identifying characters in an image. Here we'll take a shortcut and use Scikit-Learn's set of preformatted digits, which is built into the library." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Loading and Visualizing the Digits Data\n", + "\n", + "We can use Scikit-Learn's data access interface to take a look at this data:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1797, 8, 8)" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import load_digits\n", + "digits = load_digits()\n", + "digits.images.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The images data is a three-dimensional array: 1,797 samples each consisting of an 8 × 8 grid of pixels.\n", + "Let's visualize the first hundred of these (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "fig, axes = plt.subplots(10, 10, figsize=(8, 8),\n", + " subplot_kw={'xticks':[], 'yticks':[]},\n", + " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", + "\n", + "for i, ax in enumerate(axes.flat):\n", + " ax.imshow(digits.images[i], cmap='binary', interpolation='nearest')\n", + " ax.text(0.05, 0.05, str(digits.target[i]),\n", + " transform=ax.transAxes, color='green')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In order to work with this data within Scikit-Learn, we need a two-dimensional, `[n_samples, n_features]` representation.\n", + "We can accomplish this by treating each pixel in the image as a feature: that is, by flattening out the pixel arrays so that we have a length-64 array of pixel values representing each digit.\n", + "Additionally, we need the target array, which gives the previously determined label for each digit.\n", + "These two quantities are built into the digits dataset under the `data` and `target` attributes, respectively:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1797, 64)" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X = digits.data\n", + "X.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1797,)" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y = digits.target\n", + "y.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see here that there are 1,797 samples and 64 features." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Unsupervised Learning Example: Dimensionality Reduction\n", + "\n", + "We'd like to visualize our points within the 64-dimensional parameter space, but it's difficult to effectively visualize points in such a high-dimensional space.\n", + "Instead, we'll reduce the number of dimensions, using an unsupervised method.\n", + "Here, we'll make use of a manifold learning algorithm called Isomap (see [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb)) and transform the data to two dimensions:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1797, 2)\n" + ] + } + ], + "source": [ + "from sklearn.manifold import Isomap\n", + "iso = Isomap(n_components=2)\n", + "iso.fit(digits.data)\n", + "data_projected = iso.transform(digits.data)\n", + "print(data_projected.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that the projected data is now two-dimensional.\n", + "Let's plot this data to see if we can learn anything from its structure (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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NFrJrHN+1bTNLjRYhEsfzyZoG2/p6KKSSvG/XNiqHj3FoZh4B9GbS3L1pmI/u3cnxpRUeOXMex/eZrzcoJBPUbYeWHRntC+mMmhJ51X4YRl62ohCEIQJoOg6KIhjMZjmzukbTdvCDkFBKMrpGIEM0RSWdMigkkxiqQimdwgsC1toWaUOnJ51ivLfER/fuvGHXPSbmWnI9jfl/BP4lUbbbvwT+LfB3r3bnbtL95wAOHjz4yoy5mGvI5lKBbb0lnpueW+/QowiBrmoIIWg6NistFSklQghK6RSKEPy9d97LXK3ObK1OQtPY0lNkz0A/Z1fXqFk2/dkMbddFEGmMW57Pjr4eXD/g68dPA9CXzXBmpYwbBBvSIv1Q0rQdhBAEQYipd8M0jovlCUqpFIGU9HbnAja6qhCEElUoWL5H23XRVZVGKFlstEgZOr94711s6y8RStjR10M+GeeZx9waXDdjLqVcvvBYCPGfgK92n84Dmy7ZdLQ7FnODEELw6+95gP/w+DPM1xoIAZqqkux28tFVla09Jbwg6nTfcV3mag2qlsU7t2257HiHZqI/Zy5hkkuY2J7P//vkM4z3lFAUhV39vXxy/24ePzfFWquDH4aX5bdLIq9cEZFAl6lrZIyoOjRp6CQNnZbjoCoKvekUpqbh+j6VjoUpIGXopNBZabVJGzqqiEIu09UaBzYNsaO/9zpe0ZiYN5/rZsyFEENSysXu0x8DjnUffwX4EyHE7wHDwA7gues1j5irI5dI8M8+9B7ajseT56cQEhRF6Za/FwCYqtSQ3ThIx/U4PLtwWUqflJK2464/X25GGuKW59OwXcaKBZ5uTbOjrwddVSl3Opiaih8GBKHcYNS7eSfreeOGpjKcy7Kjv5fFRnN9PKHr7B8e5MzKGvlkgtuHB3lhboGFWgPX95GhpJBMkktERUxnV8uxMY95TZxQZ8J+ay2MX6vUxD8F3kOkUTBHlILzHiHEASInawr4VQAp5fGuatgJopzLX5NSBlc4bMwN4J9/5D38wePP8tLcIqausqlQ4Mfu2MvnD720bsgBNEXh2ek56pbDgdEh7h/fhK6qTK5VcLyA+UadtuOy3GrTdlxSpkHLcXjy/BR9mTSztTr7hwcxFIWkHi2iSlUipcT2A5Tu3YGpqkiiuP7OgV5MVcNQVQ6MDLFvqJ8nJqbJmAZCCAZyGUxNY6nRYqnexPK8yOuXULMtTF3FDaImF+dWy4yVCldsOxcT81bkWmWz/MwVhv/La2z/r4B/dS3OHXNtSeg6v/n+d1LpWDRth8GugTyxOEwYSizPR1MEZ1bLWK5HtWNxeG6Bp85PM5LPsdbucHhugelKbV1+VlUEPZkU8/UGjheNjZUK1DoWa+0Oo8U8lXaHuu2gqwp1yyafSCAESMl6wVC51UFKyWy1xkf27OTBrZspJJPM1eq0XZdiKsk3T5zh/FoF2/MIpIw0WgTraY3PTs0ipYzCMZrGJ/ftZiifvdGXPSbmDRNXgMZgeVE15GS5QkLXOTA6xO3Dg5RSyfVt9g73s9JqYfs+J5dWsVwPRQg6rsdqq825tTKbCnnyyQS1joWhqpFcrSbwgpCFenN9cdXyPeZqDebrDZCS7X09aIpCTzpFxjRQFYXzaxUathOdw/foSaXQFIW1dhSW+e7ZCVaabRKGxkylhhcEzNbqVNoWbdclCKPiIwAZSnwZYns+/Zn0un6M4/s8cvY8P3vwjhty3WNiriWxMY/hWyfOMlurA+D4AY+dncRUNXYNXIwrFxMJVlttpio1Zrol9MVUgqYdxcf9IOzGxetYXiS6dSGEIQnw/ABEtNiqKype4GN7PooQTJarbOstsblUQFNVPD9gplpDUxRs38cPQtbanXUZ3dA0qHVsvCDgwPAQi40mq6025XYHQ1WjDJgw4II6iwIgBC3HZbynuOG9l9sdbM9fLyKKiXmrEn+C3+Y0bHvdkF/KyaWVdWPuBgHfOHmG/myGUjqFJhSmKlUsz0cSdRUKQokfBKjdfHBNUVAVgSIEdSsgRJLQIg0Wy4tK9C3PQ1MUvG6OeMf12Dc8gBcGpHSdesfuLnIGtDvRj4auKtQsa71g6fTqGmutSAfGC6L4eBBGKZRcKOFXBLqqbIj5XyCp6xhaHDePeesTG/O3OVewbwBcmiw4V63jdMWrNEVh92AvVcvqKiJ6hKGkkDQjFUQ/WPfYdUXF9n1Sht71yJXII/clQRiiKwq+lIRBQLVj4wYBuYSJoWnULBsvDNBVhY5zcTZR/0/wgqjoqGpZtBwP0Y2LR6GcKE4vpCCpRQVHAq6YU37/+KbLyv5jYt6KxMb8bU4+mWAwl2Wp0dwwvru/D4gMpOP7BGG4rvmdMgweGN9E23F5bmYeU1XRu3riihB8aPcOiqkkT0/OMFut03Ic2k4khxvKED+MPGYhRFSCrwgc3yOpq8xU6yQNnabtIGWks05XNAsisa4gDJHdps4yBD8MCGXk+V/oPKSralRFKgR+EFWRSmAon12X9d3R18tIIS7lj7k1iI15DB/du5PHzk4yWaliaip3jg6xd6ifyXKVR86cp+U4nF0tk08k1jM/cokEuwb6mK7WmatFcfJCIkE+mWCqUuUn79yPH4YsNprUuz05AUJ5sQHGhbBHGPhIBE3bJWUYUVGQrtP2PLTuD8UFDE3F8qJy/f5shlBKmp6LhmAwl410YkRU1aqrKodmFjA1lVzCZGdfD8Vkkt5Mmn1Db60c4pi3LkKIXcCfXzK0FfgXUsrfv5bniY15DBnT4OP7dq2LUkFUFPSNE2ciPRQh2N7bw3y9gaoItpSKbCkV+daps+t53KaqrjdLThsGT56f5vnpeeqdyJAH3fj1BSlaSbQwGV4S1zY0FdvzaTkOhVSCnDQpJJNoiqDcthAimmsgJfmESV8mTRBKLDfKJ88mTDQl0mG5b8soewb6KaWOdzNgNIbyWYQQVNrWDbrSMW9HpJSngQMAXYXYeeCvr/V5YmMes86lseOZSo3gkm49mqqwuVTgtqEBHto+zlPnp9EUhdF8jsV6A4gMc0KPRKwOzy1Qsyx6Mqko/h1cMOjddEEJF6y6rqnkEon1FnW25zNayPPg1jH8MKRu9WF5Pl4QZb+kdIPjSyvrsfFcMkFPKsmO/l7Mrp5603b5k0Mv88LMPKamUkwlKbc77B7oYzCXedOuaUzMK3g/MCGlnL7WB46NecxlWJ7HfL1BpWNRSCY2GPlEV6/lwlhC1zA1jY7rkTJ0hvLZKFtFSszutrmkScNyIAgQRDFvVUSZLgGShKqypZjHlxLb88knTe4f38TP3H0HCV3DC4L1Y0H0o/GtE2f4/uQsCHhfqYCpalQsC1VRUITA9jzW2m0ypkHLcalaNr3pFG4QsL2vZ8P7XW21WWw0KSYTjBbyUSZMTMzV0yuEuLQN3Oe6QoFX4qeBP70ek4iNecwGZio1vnb8NF4QMFetM1utsXugj6btUG5bZE1z3Uv/5okzTKxVSJsGjh9geZFey0ghh6oo6KqCHyoMZCNPuOO4SBHlpGuKgqaqaELQm0mxqVRACEHLdnjvzm18cPd2UoYOsMGQQ/RD8tHbdvG+XdvwgoCMebEISBGCP33hCG3XxfMDdFXF6Gq/jBULjPcUN/w4PXV+mhdnF9afjxULfGLfrrjBc8wPwpqU8uDrbSSEMIAfAX77ekwiNuYx60gpeeTsefxunHz3YB8LtQbT5RpCEWwq5mjYNn966AiKEJTbHWqWTdrQKaWTrLXauL7PUC6LrqqcXlljrJjH1DT2Dw9y96Yhzq1WeGZqdv2cKUOnkEyyuVRgKJfjwOgQm0uFq5qvqWkbDP2Fx4aqIiSstNrULBul+9psrc7dYxeFwSrtzgZDDjBTrXF2pczuwb4f/kLGxFyZjwIvXqooey2JjXkMEIUaDk3P8eLsAqVUklI6haGqbOkpcm61vB6aWGm2WGo0URWFtGlQSCYotzuR2BUCP5ScWSlz16Zh9gz0IYHbhvrZ1lti39AA79sZ6ZZPVaokdZ3edIodfb18fN+ua/Zebh8e5LtnJnB8Pyo6kqB04/+6etHjXmq0rrj/UrMZG/OY68HPcJ1CLBAb8xhgvtbgS0dO4IchDduh3O4w4nmMFvIAG5QFK50oEyQIQwxVoW47WJ5PUo9CIghouy5nV9fYO9jP/uFB3r9rGzOVGo+dm8TUNH7ungMsN1tU2h0GctnLSuzfKP3ZNMVkolvdqaEJhYxpdDsqXVzU7Umnrrh/6VXGY2J+WIQQaeCDdNVjrwexMY/h0Mz8elriSCHHVLnKUqPFUC5LQtd59/YtTFVqQFQBGoQhbTcqyXd9n47rkjF0vCDADQKCbnl+KOG2oQH++zMvMl9vkOsKXB2ZX+In7tzH7oHr4/26QcBIIc9qq4MXXFRXDqVkU/cHCmAgl2FHXw9nV8vrY72Z1A81L8+NWu0Zpv7GJh9zSyKlbAM9r7vhGyA25jG0HGf98UA2Q9rQKbct7hgZ4u6xYZK6zndPT3ButcxANsN8vUG6uzjZk0pFueGuixsE3abPPqVUEtvz+NbJM6w024RSMpLPMVrM4wYBh2bm+fCeHdfl/QzmsuQTCbb1lji3Wsbvhlj2DvZz56aNzTQ+vGdH1Oyi3qSYSrCzv3dDkdLr4Toez/zNIaZPzAEwtmeUB37kYGzUY950YmMeE+mJdy4W0mRMk9FCnvfsGOfMSpnnpmdp2A4DuQzv3LaFUMJSo4EXhKRNAzvwmel2IVIUgUAwV2+QsY0oc6Ubp15oNOnPZjA0lZp1/Qp3FCH4+L5dPHzqHBnTwPZ8DowO8ZErNG8WQrCtt8S23tIPda5D33qJqWMXF3Snj8+iGxoPfuqeH3r+MTE/DLExj+G+zZu6C5vRgqAiBO/atoWFepOHT51FEsXBD88t8M0TZ9G6aYd7BvuwPZ+pcpVcwsQPQjpeFG7wwxDHD+h4HhnFQBFR+zfL8zA0laHc9dVE6cuk+dmDd9B2XYxXSAJcSy415BeYPDYTG/OYN53YmL/NCaXk2OIybhASBCE126KQTPLV46dxPB9NjYpwou49Ubl+bz7HQqPJfL3BaCGPrirkkwk6rrceS9cVBU2JFh5zCZNOdzxlRBWi92weeVPeX7rbBPp6oekqvuu/Yiz+WsW8+cSfurc5z0zO8EI31/r06hpN22FTMc9wPsdcrY6hqfRl0uvGGCCbMNmbSmJ7PrcN9nPn6BD/47mXqIhO1JhCRD0784kkfhiQT0ax6G29Pdw5OsSm4s1TZRmEIXO1BoqAkUL+B5bD3XXPdl5+9PgrxrZdyynGxFwVsTF/GyO7XjlEGSDNbieflWab4XyO3kya6UqVoVwWRQjCbol+1OVesGegjw/s3g7Azv5evnrsFE+fn8HUNUYL+fVS+oe2b2HvYP9Nl/K31mrzlaOnaLtR44t8MsGn9u+5ou75q3H7Q3tRdZWJl6aQUrL9znFue/Da5czH3BjcUGW2VbjR0/iBiI3525ioS1CU6XFBKyWUkkBGY7mEyf7hQfLJBAO5LB3XZXO37F4Ad12SGTKYy/I/PXgPP3337TwzNcdivUExleSezaPr5fw3G4+cnVw35AB1y+ap89N87LarN8ZCCPa9Yzf73rH7ekwxJuaquSbGXAjxX4FPACtSyn3dsRKRhu8WYAr4tJSyKqL7638HfAzoAL8opXzxWswj5gdD6WZynF0toyoKvZk0K80WPamLHvSH9+xgZ38vUkpOLK1wbrWCoancPjx4xcYOGdPkA7tu/jBDEIaXNeQAmLtCC72YmLcC18oz/+/AfwD+6JKx3wK+K6X8XSHEb3Wf/1MifYId3X/3Af+x+3/Mm0TLcTm/VkEIuG/LJoJQMlmusKWnyLbeEvlkgoSuccfwIDv6oz6gQghuGxrgtlukqYPaXZxtOe6G8Vzi6kMsMTE3E9fEmEspHxdCbHnF8KeA93Qf/yHwKJEx/xTwRzJqM/OMEKIghBiSUi5ei7nEvDaz1RpfPXZ6vZDG1FQ+dftePrB7GwIwtLdP5O3ezaN878z59edCCO7dPHoDZxQT88NzPb+5A5cY6CXggks3AlyanDvXHdtgzIUQnwE+AzA2NnYdp/n24omJ6XVDDuD4AU+fn+bH7rjtsm1nqzVemF2g7biMlQrcu3kUx/fxg5Czq2VcP2D3YB99mfSb+RauGbcNDZBPJji9vIYiBHsH+xm4AY0rXMfjyGMnmD+7SDKTYO+DuxjdMfSmzyPmrc2b4oZJKaUQ4lX6wL/qPp8DPgdw8ODBH2jfmCsThCHlduey8dVW+7KxpUaTLx89td6nc6nZ4hsnzpA2dJ46P0MoJT2pJD2ZND93z4G3rEc7WsivC4rdKJ744jPMn418mfpqg+WpVT7w8+9maPzWCGnFvDlcTwX+ZSHEEED3/5Xu+Dyw6ZLtRrtjMdcZVVEopZLrz6WUNOsWihUS+MGGbY8uLK8bcoCpcpWZSo1D0/NYrofj+dQsm0q7w1+/fHy9oCjmB6NRaa4b8gtIKTnz/MQNmlHM9aAbTv6iEOKUEOKkEOKBa32O62nMvwL8QvfxLwBfvmT850XE/UA9jpe/ebxj62YUIXAdj9NH55g5vYRzosKX/sfTVFYvZne4lxh3KSU1yyYIQ5qXiHJdMOBr7Q7VTtwk+YfBc678I+g63hXHY96y/Dvgm1LK3cAdwMlrfYJrlZr4p0SLnb1CiDngd4DfBb4ghPhlYBr4dHfzrxOlJZ4jSk38pWsxh5irY0tPkZ+75wBf/Jvn2BSY9CXymELFajs8870TDI6WmDq7xHJgs5r26R2MqjVVRaAqGildp9nNAFGUqFrS1DSKl3j8MVdPabBAridLo3zxh9T3fEZ3xjHzWwUhRB54N/CLAFJKF3Bfa58fhmuVzfIzr/LS+6+wrQR+7VqcN+aHI59MkK1LRGhiNWxkUieRNDjy3HnWluooqkIWwWrDoaY0KQ7k2Nnfi0CwZDY5sbyCH4RkDAMBfGTPDhKxHskPhRCCh37qQZ78q2dZPL+8vgh6+LtHsdsOB96776aRPoh5VV6vofM4sAr8NyHEHcALwG90Nc6vGfE38G1Cud1hpdmiL5OmN5OmUWtz5ujc+uvF3gztpo1QLhqOrXqGlJvg/fccwJAK5+pVTi2vsamUp2E7lFJJ3r19C3dtenNEs25Viv15PvGrH+Qv/u1X0E0NVVXx3YCjj58kW8yw/c7xV93XsaKwl5k036zpxlzO6zV01oC7gH8opXxWCPHviOpu/vm1nERszN8GPHZ2kiMLS+vPx7N5XCcSxLqwxllZaWImdabOLiOEoKcvS7aQYmmqwud/72F8L2B4cw8PvHcPP3nnvhv0Tm5dqss17JaD+gqp3sljM1c05o7l8PSXDzF3OhJJG9szwgOfuiduinFzMgfMSSmf7T7/IpExv6bExvwWZ6He2GDIAQ5NzNKT1di2Z5i15QategfX8alX2iRSHkIIGtU2qbTJ6lKddDaqilyaq9CsW3z6Vx4inYkrJa8lryab+2rjz33jJWZPXUwCmz4xh57QefBHYh31mw0p5ZIQYlYIsUtKeZoo/HziWp/nemazxNwELNQ36o+sLdeZPb/CSydnWJqr0qx38LyA8kqDIIw0zQEQsDhbIZW5ePvuewFLs2Xmzq++mW/hbUGuJ8vQ1o155UIIdt2zjdW5MucOT1JbvagbM3Ni7pWHYPr45WMxNw3/EPi8EOIIcAD419f6BLFnfotTvETOtVZusTBdRghB1jRYnqng2B7FnixCESSSBqqqsOO2ERCCo8+fv2zxzWq7aPr16drzduehTz/A4e8dY/7MIolMgj0P7ODsi5NMHpnGsVyMhM4d77mNuz5wO6quXlYboJvx1/lmRUr5EvBacfU3TPzXv8UZ7y0xlM+yWG9SXYu89JxqcPt4H6cas/irTTL5JK2mTXm5gaIIcoU0m3f0MzTWQ6PSvuitA5qucOyFKZ577DQDwwXuftdO8sW3Zjn/zYaRMLjvY3dFibvA9IlZXvreUebPLRF4AYqqUF6oMr5/jN33bufIYyewWjZW0yKZTXLXB/bf2DcQc0OJwyy3OIoQ/Ojte3nvzq1sTmXZoWe5wyiiaSqDo0VyxRSdtkMybaBqCmEoqVVa6JrKj/ztB9m2Z4hcMYVhauSKKfqHCjRrHQI/YGGmzHe//OJlHmLMtWHm1DyzpxYIvOj6hkHI4vllTh+a4I733EYibTJzao7V+QqteptWrYNru5z4/mme+eoLTLw8RXiJDk/MrU3smb8N0BSFfUMDZO+7nSe+dXR9vNSXpd20qFc6aJpK70COYm+WQilDJp9i1/5RRrb0MHd+Fd3UqK42OXdiYcOxOy2HxdkKo+N9b/bbuuWxWs4GSYULNCstlqZWsNsOuw5uXx8/+cwZzrx4HsJonzOHJpg+Mcf7fuadb9qcY24csTF/G7F5xwC25XLixWmsjsOmrYO895N38rU/fQbH9shkE6wu1Zk8s0St0sLqONz/vr3sOziOlJJnn34ay1umtWaSTJtkclHVZxjGOmjXg20HNpPIJLBb9vpYtifD8LZBVmbWCPyAlZk1WrU2uqmj6iqGqTOw+eIP69zpBVZm1+jf1Hsj3kLMm0hszN9mDG0q0TuYR9UUjj43yQtPnMG2PVIpg+WFGgvTa5hJg1JfDsf2+MYXnuOOd/SjDjzPWjCLl18BNc30kV1ksyV27htleKznRr+tW5Itt23i7g/uZ+r4HHbbIZ1LMjDez9Y7NrM8tcrUsVlatQtFhBbNaoudd2297DiNcvMyYz51fJaXHjlGs9JiYHMf93z0Tor9N1Y9MuaNERvztwnNjs3XvvoCzaUmegCnXp4lk0+SzadIpgyOHprCtT2CIETVVFzHo7xcp1Zpkxx7Hq1apdWwyBZTqJpNcdsM1myOfQe3xNkt1wlVVfnoL7+fY0+eYnWuQqE/x7537iaZTpDKJwnlxnh4tpTBeYVAlxCC/rGNhnxpcpkv/Jsv06g00U2dZqVFo9zkx379Y6jatflbTp+c4+QzZ/Ecj7E9I+x75+7LCqJuZsJAod16c2ophBBHiVryXvYSkQLK7VdznNiYvw04tbTK57/zHEuLNQD8s3WC2Qb6kkaxJ0Ot0sL3AhRFgW4q4tSZZYQiCKWHmqnieQG+F4CE3oEcpV4FJzuM78cLbNeTZCbJPR+587Jx3/HZdscWqss1rJZNMpOk0J9jZWaNsy+ex3M8sqUsH/yFh0jnUwRBsG5Mv/QH32R5OqoVsJo2zUoLRVFYPL/M6M7hy871gzJ9YpbHvvD99efVpRqtapt3/Oi9b/jYtyifuBYHiY35LU7H9fjG0dPMz1UIuymGa65NRgWv5eDYLs2ahaII8j0ZCCX1SgszoWNbHoapUllyMJIBkqhwCAA/ipcXe978zjwx0D/WSyKdoGeotD7WrLVIJE0CP8CxXXzf54kvPsOZ5ycQQjB++xg7795KpfujfgEZStYWKtdsbqeeO3fZ2Pkj0xz88B2xhswVkFJOX3gshNgM7JBSfkcIkeQHsNFxauItziNPHufES9PUq20qq01qlRakVRwR4rreumft+yGtWgdNVzGTBq7jk84mKJSy1Ke7HriU6IaGROBXtjK8uYfhzXG8/Eag6RoPffoBUt1FaEVVSGWS1FYblOerBG7A7KkFXnrkGLWVGoEfcO7FSV78zlFKg/noBn7D8VSGtr12Z6MgCFg8v8zafPk1t3Pty7XYZSjx3biByWshhPgVIt2Wz3aHRoEvXe3+sWd+C1Ovtpk5vkipZ44t47O4dofyWoHJ8yNoGQOlGeDZXuRtC3Acn7XlOplski17B5FpjdZyi8bcEL5tMrrXZt9te/FqIwxs38HoeG8sz3oDGRof4Mf/0ceprzVJZRN8+w8f49iTpwCQSOyWjZSS8mKNXE8OgLWFCj3DPbi2x9LUKq7lki6k+PAvvfeKMW3XdvnOHz/OkcdPUFmssfWOzaQySXpHSrzvb7+LROpyT3tszwjVpdqGsd6REul8XFz2OvwacC/wLICU8qwQov9qd46N+S3M6kKNQmGBzT0zWDJAUQSF4jKbhixWDw9DGIIiQICiKCiKQDc0AkUyk3QxBwyCbJKgA5uze9k2uIkDOy+P38bcOBRFWc9C6R25GHIRRH9XVVNR1Is/uLqu8Z6ufnqhL4+qqew8uJUD742UMMMwZP7sIvW1Jj3DRX7/Vz/HuZcmsVo2QggmXp7iXT9+HwAvfe8Y93/i7svmtO+du2nXOky8PIUMJb0jJd75t+67npfhVsGRUroXHCQhhMaVF0avSGzMb2GyhRRafo5+NUHNc1istzFcyc5iGzspaNoSVVUwTJ0wCKO4eTFFIy1Idb00NaXjpKCpw947t9zYN3STEErJc8uznKysoiDY1zPAXf3DN/wu5c737+f7X3mepalVAi+gOFBAUQTZwsV1jR13b6VvtIcf/Ycfpb7WIJFOYCYNhBAEfsDD/+NxVrqLoyeeOcPp588RhiEylJG333Y4+sRJ3v0TD7B4fhmIWtxNHp2hXe8wvG2AwS39PPipe7j7Q7fjewHpXOqGXI+3II8JIf4ZkBRCfBD4+8DfXO3OsTG/hcmX0oShpF1tE3oBZsNHURT0ROStpTMJgjAKsaiqjpk0SPWkaUmb0d0DyLRGvRrF0Ud2DjMwUgSiL+/iTAXdUBncVIqyYN5GPLkwxQsrF+VnH1+YJJAh9w5ueo29rj+JlMmn/sFH+f7fHMJzvG52EqSzKRRVYdudW9j/rj2cOzzJCw+/zJHHT1BdrpMtphnbPcqeB3Yyd3qe6nKkzrg6txYdR1XWte/DMMRqO9htm6GtA1htm69/7jvMTyzRrrVRVIW7PngHH/y5d2MmTcy4m+APwm8BvwwcBX6VqMXmf77anWNjfovi2B5//tlHafgZkkOym4UiSKYMrEoJIU2EEtDTm0eGkkatg5nQ0YSgZ7RIaUsJRVPoGyoAMDYULXQuzJR5/BtH1rNaCqU07//UXSTTb48sBSklR8vLl40fKS/dcGMOsO2OLYzuHGJ1rkKmkKLQt7EQaHFyma9+9ts8943DVJdrhEGIqmvUVhucevYsUoCZMABwOi5hGBIGkVeOlAhVIZVNYCQM9j64k4f/6DGe/OtnKS9Uqa81CPyAZ7/2Ik9/6Vn+3u/9IgNjscwDgBBiCmgCAeBfqTORlDIUQvwhUcxcAqfllfQcXoXYmN8khDJkqn2WRXsWBYVNqa0oQmWyfRonsOlLDLIrezuGYlzV8f7m89/n+ItTQJZCY4Dc6DKq6tNYKFGf3EauAI1qh9HxPgZHijQbFkObSuzaN8pi2ufkytr6sUxN48DoEGEY8uz3Tl5MTwRqlTZHn5/k3vfsvrYX5CYmuIJ4lX8TCVqZSZPekRLHnz7N6swaO+7eyrY7tgDw9f/0XQ59+2Uqi1WCbiZTGHrMnV4g25MlmTYxB6PPmKarKIpC4AeEUkIo0TWVgc197LpvB9//ygs88qdPsDCxTKdpIbuyDq7tcfSJk3z2N/+Iv/d7vxBLCVzkvVLKtVd7UQjxceD/BSaI8o3GhRC/KqX8xtUcPDbmNwlnmseYbJ9Zfz5fnsYKOhiKiSZ05q1pDlefYXtmD5tT2xlJbX7VYzWqbSZOXggDCGpTo9SmRklnTYIQGpUahqnx4Z84yDs/tA9N1+gbyq/HfPdKyaZSkZlqjbShs394kGzCpFm3aF+iE3KBlYXqNb0WNzNCCHYWejlZXdkwvqt483ig9bUGf/g7f86JZ89i1SxCGXDbO/fw0//0R1maXKZdbxMGlzh8EjzXp11tI8MQSWTIG+UWYSgJZAgBCEVgpAwK/Xm+8Z++w9juEayWg91x1g05RGmInabN8vQqRx47wQd+7t2vOd92vQ1CxLF1+LdEBv8cgBBiG/A1IDbmbxVCGTLTOb9hbN6apuHVyOslWn4DgLSaZVVfou5VEUIwnBy74vEatQ6pbJLyysYuQ54Xsm33EDv2Rot1ruOzsljnwP3bNmwnhGDXQC+7Bi56VK2GxfTZZRrVDumsuaHsO1t4e6WcvWd0K4EMOVcvIxDsKvbxzuFX/3F9s3n2ay/y3DcP01xr4bkeIPj+l5+nulijd7iIQFymxihDSShDCv15nI5LbaWB3bYJPH9DPoXTdpg8NouZ0Kku19FMbb0Y7VI8x6O8WOWRP3uKTsPino8eYGh8Yx671bJ4/IvPsDwVLbiO7BjiXX/rPozE1d193kT0CiEOXfL8c1LKz71iGwl8Wwghgc9e4XWA5gVD3uU8UWjmqrjuxvxKsSIhRAn4c2ALMAV8Wkr59nHvXkEoQwJ5saDCCWxafoMoUhnihlEHdkMx17+EM52JVzXmpf4cxZ4MjWqbere5RKdlk/AMZiYuepTZfJKThwW33bUZKeWrNgOePb/CE988ShhKbNtlbnKVrXuGSCQNNF1l38Et1+hKvDVIaBofH9+NGwQIAbpyc2mOvPTIUVrVNr7vdxt2SzzHY22hgqop5PqyNKvtjTsJKPYXyBbTtGsdIKr2vdTmy1AiJbRrbfS+HBIwEq/SQFpC4Plki2lqK3W+9ydP8uO/8TGSmYsros989cV1Qw4wf3aRQ99++a3Yx3TtSjHwV/BOKeV8N2/8YSHEKSnl4wBCiB/vbnNICPF14AtExv8ngeevdhJvlmf+yljRbwHflVL+rhDit7rP/+mbNJcbjh96zFlTuIFDwehBIFCEihNY6IqBHVoYSoIg9C/zoEw1Ev/x5atX06XSJgceiHSu69UWp16apdCTIfBDzp9aRFEVevqztJs2q0t1FFXBcwNSaZNsIUXgh+RLaW67azPZQopDj59Zl7ntHyqQTJkoisJtd29h+55hsoW35+2xcZMKRwmhRIb3FdLEqqqQSJuomoae0PDs6DMkVIEiBH2beth2YJx23cJ1PIQiLjvGhezLoW0DkRbMtEkyk6TT6Gw8l65gJIx1Od7AC5g5tcCug9FdYBiGzJ3eqI0PMHNy/q1ozF8XKeV89/8VIcRfExUHPd59+ZOXbLoMPNR9vApcdT7QjQqzfAp4T/fxHwKP8jYx5rOdSR5d+TpVt4wAAumT0fP0G0OsuIuk1SymmqDX7EcTOnWviiYi72cgMbJ+nKHExswJKSWLsxXKy3XCUDI63ofd2cS3/vIQiqrgewGNWgfP9dcXvrL5JJ2mTathY5gaLz1zDtcJ2H3HJk69PM0T3zzKp37+wcvi5Nl8knQ2wZ0PbCfm5uPA+/bx4neO0HC7zoCUCFXFSBps2TfG2kIFRVXRzSjdUDPUqMhIEaRykWBXo9JENzQ86a3/kAtAMzS23LaJn/ntyJlsrDVJZhMcfeIknuMhpUTVVbLFDMPbB9fDcZ7rcfypU9RW6hx4320YpoGe0HEtd8PczeRbLsTyuggh0oAipWx2H38I+P9deF1K+UvX4jxvhjG/UqxoQEq52H19CbhMFEII8RngMwBjY1cOJ7zV6Pgtnlx9mOn2OXzpE8oAL/SoeTWcwGYouQkZSnSh0/TqgGA4sYnR5Dgtv0bR6EURCqPJccbTO9ePG4Yhj3/jCCcPzzBxcoF22yaVTpBMGeRKaeyOS63colnvIEOJoirYHQfP9Sn1ZvG9AMdysS0P3/N55Gsv41gumqYwdW6Jkc29bN6+8U9U7M2+yVcv5mq58/37eejTD/L8N19ktSuwlswm0Q2NxYllzFTUuFtVFaSUCCEY2tZPqT+PQJDryUaFRIpAM6KCMlWLPO0P/9J7+aV/+dPrce2Pf+YDHPrWyyTSCc4fmcZ3fYqDeYSikCtlmDgyRWWpxsr0Gv1jPRimwdc++zD/0//xt9lz/w5efuT4hrnvfWDnld7SW50B4K+7CQYa8CdSym++ciMhRIIoz/w2YF1/V0r5d6/mJG+GMb8sVnTpi1JK2TX0vGL8c8DnAA4ePPiWbmWz0JnhbOsEy/Y851on8MPo9rYdtPCljxs6eKHDsj2PH3oYaoKMlkMimbMm+cDAp9idu50QiSoUVKEhpaS61sRI6FRWGpw/tcSLT5+lstqMGjBLSKR08qUMtuVerOKToBsavQN5fD8gCEKSaZOluQrzU6vUq5HBV/Xulx1JGEgKPZn1xs2GqXPHfZc3QYi5OegdLvET//Mn2HlwK9/6b48ShpK+0RLF/jxr8xVSmRSD4/2szVcI/ABNVyn05Xnopx5kZPsQT3zxGYa2DvDSI8dYnS2jqAr9Yz3c/4mD/ORv/giBH/Did47wvT97koWzS6RySYa2DnDfx+4EIRjc0kemkOaJv3oWq2mzPLWG5zgsnFumZ7iIlJK//vdf59f/4FeiH4GXpxCKwo67xtdTKG8lpJTngTuuYtP/AZwCPkzkuf9t4OTVnue6G/NXiRUtCyGGpJSLQoghYOU1D/IW5qXaszy1+h0CGWAFHZzAwpMefujjE6nL+Xi0Ax+BEt3KKgYtv0FOL6AIjYZfR1MuLjSVVxp85fPfZ2FqDaFAsTfH4vQatUob14l+KKSUtFshnhcwNFqiXo2q8yL9FZVk2kQokEiarMxXefGpszSq7fUFr9AJ8ESkYe7aAatLdTaN97Nj3wjjOwdJpG692+Fbid6RHu77+N3MnV7cMK5oKp7jcc+H7+TokydYnYmMNQhmT87TaVjd53DX+2+nWWthNW0++svv47YHo1qC73z+cf7rP/tTaqv19Zh6Op/kfT/7Ln7t3/1dFEXh2JMn2bp/M7XVOmcOTRAGIV7os7ZQwfd89HN6lDV1cNt6HP2V2B2HqWMz+K7P2J5Rcj23/N3gdinlTwohPiWl/EMhxJ8AT1ztztfVmL9GrOgrwC8Av9v9/8vXcx43irKzyouVpwlkt8hGgic93NAlZGNH+yhzJUAgCGSAIhTswCKj6VjBxcwDKSVf/C+PM3Hy4uLR4mwFq+3iXSIxKoSIYvJ+iG5o9A0VKa/WyZTSCFMj3ZNGDWXkZT19llbDulzRJwq34nk+nuPTrLcZHuthbblOEIQMj/WgG3F2681KKpsk15OlUb6Y3dYzVECIiwuUfZt6SWZMdh3cxvSJOV54+AiaoZHMJPBcD6ftYqYjjXSAylKVL/yfX6G2Ut+Qktiqdnj4jx5nfP8Yn/jMh/C9ALvtMHlshsAP8FwfIQSe7VFdqrNp98X1H9/zefZrL3LsqVOYSYNtB8bpGS5w5NET63K6h793jHf++H2M77s1Qq6vwgXt4JoQYh9RCPqmUU28YqxICPE88AUhxC8D08Cnr/M8bghL9iwhFz/whmLihz6S164WdEObkAApQzJali2p7SzNVei0HIyExvS5jeXkZkKnXumgaer64qaiCAxTJ5k2yBfTpLIJ1FKSheU6WtuhutYi7HhYDQvfjcItVyIMQ4RQqaw2cGyPL/6XxzGT0V2CYeq89xN3rJf8x9xcCCF48FMHeeTPnsbpROmtg+MDfOwzH+DlR48zcXiK0kCB/s19LEwsUVmsoeqR574wsUQ6lyJTSCOE4PB3jzFzaoHZ0wssnFu8Ym653bL48v//m3ziMx/Cc33OvDBBZaEa5bB3hdxAJZQhY7tHgejz9YX/6yu88O2XCbyA6nKNR/7sKYoDecyUydbbN5NMJ5Ch5IVvv8zmvaO3shbQ54QQReCfEzm8GeBfXO3O19WYv1qsSEpZBt5/Pc/9ZhPIgGV7AS906TMHSWlpVKGR1fJ0/Miz9qSLEAJFqgS8WmqhIJQhoQxAAVMmOfbNNZrLUUWn5/o0a50NWihCCJL5BJgK7lJUYKRpKmZSZ8dtI7zjg/uYOL/M6qzP6GiJxdNLCC+gVetEPQpeQ+xPCIEQglq5zcSpRca29mMSGXPX8Xj20VN84mfuf6OXL+Y60T/Wx9/6xx9naWoVw9To2xRp0A9s7qNVaWO1bMJQrotrFQfy+F5AdaWO1bYxkgZGUuelR4/TO1Iik09ukHO4FClh7twik8emOfvCeTbtHqFZaXWleBUURUHVVPK9OUZ2DAKwcG6J08+dAwnNamv92Cszawxs6WfuzAI77ozWZzoNC7vtkMremupdUsoLolqPAT/wolR8j3wNsIMOz5QfWw+HCAS3F+5hNLWF6c45vNCl5lXwpYeCgn8FQy6ibHM0VLJ6gaHkJgbMYVaOO5yfnqYvEX34dUND1VXCMFz3UFpth2RvBml7mB0Xp+kgFcHQaJH+kSJryw0OvGMnq994mfMvztCpWfiuj9+99X1lLvGlKIogDCVCQG2txZ47Nt7m1sotXMd71YKjtxO273OuXsYPQ7YXSmT0m0N8TNM1RncMbRhTVZV7PnYn3/3jJ9aTx4UqUBSFMPDQdJXyaoNmpYWUEkWIbsei17irjCTU+epnHybfk6PYn2f/Q3tYmlqJPHkhMFMG+b4sTidKSWxUWnjddZ5XdiiSYUinbq1/1lO5JIlbUNBNCPE/v9brUsrfu5rjxMb8GjDROrUxro3kZOMl3tP/ce4pvZuJ1klafpOJxilWnaUrhlkECqaSwJQpxoLbKYgsuqrQWm3hd22t7wdUah16R4uIEHzHQ9VUtHwSS4SkkzqaoVKeKhO4Pr4vWZ6r0qx1aLVtjj92GsfyCLwohkm3OvC1CEOJoSoUe7MUei4v20+koirQtztrVpsvnjuG5UcG6Yn5ST65dQ9bcsUbPLMrM39ukUPffAmQdBoWhf48laUqy9OrrC1UWJurIGWIbugoqoJlOXheEIVLVIXwCkZdURVSuRSdeofSYJHAC5g7vYjZ7UakGRqariFDSbYUfZYGt/SRLWVwOg6qpqyHb/pHezCTJkJEmjBCEdzzkQNvWohFBAKt8aZ9rq/Jym5szK8Bde9yJQI3dLH8NiWjl2T+bpasOZ5e/c7Fhc9LbagATahYcxnmTiZZlGtkdJv8oED1PZJ+Btf1OTOxTODbSKmx455xdu8YZN/eUb728FEOPzsBRF3bPcsDKVmcLTPfbtBJC4w5Dd9z0QIZxcERCFXAa3jlEIVZzISOIgQ7942iqsqG+PqB+7bdyjHM16TpOpyorOAGAecb5XVDDuDLkEfnzvMLe+664U0rXolru3z3809Snq/g2A6arrI2XyFbTLM4uYzddlB1Fd+NFsgR0cfVc7zIuIrosyNDuf45VrSoyYlu6tz1wTsY2T7Ic984jNWyMUwdI6GTyiUJvADH9qitNrA7DqXBIh/4O+/ma599GMdyqK7UyZWy7HlgF0ZCZ2zPCENbBxjbM0rmFtUAklL+79fiOLExvwZktBxlZ4WmXyeQARktS0bLkVBTzHQmeHzlW1S9MmtulIEpJReNuYSgoyEMQaPuQArq9YCGV6N8LsPmvj6aCx4dY5KMPovj+wxt1ujvSTC9mOC++3ewd9cQLz47EWWvuNGPhZCSZkHQ7hF4XkAqqeJuMehdlphNH1/4mMkEvhdidxx878q3z4oQpLImRlJn711b2LFvhPMnF/H9gC07BukfLlz363szstJp8RfnjuEGUYjgheV5RjI5BtMXnayqY+EEAQnt5vmaBUHA9/7kSZ7+8nN0mha+5yMDiZQSzRgm35tDUSPZW8KomjPwAoQQqJpKImVit20kKrqu4nvBuucsgFxPhhPfP83h7xwhlU+R7S6+222H2kod1/ZIpKG23OAb//m7fPwzH+Dgh+6gd6TE7OkFUrkknh1Vko7vH7tMnCvm1bl5PmVvYQYSIzy99r11QayqW+ae0rsICXiu/AQVd42Kuxp55a9whCUQdFSsJZPAVtAKFsZgE1VRoW7jiRQ77xmmPfUyC+c1EmloN3wWT7xMaiTJt770Aq1yi2wA1ZaNqgiKPWla1Q7NvIL0A5ASzw9ACOw+lR5P0PYCwkCi6Sr5UobKavPy2LkAoUCzZuHaPoefPgvAgfu3ve1TEp9bnls35AAp3WCuVac/lUHpeuI5I4F5E+m3SCn53uef5LG/eJraSh2rZaOoCrqh4ToeteU66UKaVDYZldV3OwtJohBKOp9icLwPx/aozFcxUwa9IyXMlMnKzBr11TpLU6uszZVJ5ZL0DvegGRr9m3sJA0m73iGRTrD19jE0XaVZaXHsyVPMnJqnsRalT+Z6s7z/b7+LbDHz2m8m5jLe3t/Ia8SR2vPd0nyXhJpkMDHKkj3Hn538Y463XsCVNlJ3EYogpHtr2m3DJUNwWxq+rSCFBEXiN3WUnI9SalJvLNFJ2Fgt6LnESWk3oXPmKGIwhapq7NozTK3SolW3WFmsEQQhoeKBEIhuFERRFRL5FL2hgpk0yGQTVNeahKEkX0jhuH5XmzpaE1OUqNzbsTxSaZPZ86skUiaV1Sbv/eQBjLexQa/YG4WlNmXynKxGIZeEpqEIwbtHttxUIZb5c0ssnl9erwQO/ADP8XA6DmEoqa020AyNVC7Jpl0jCAGVpRqKqmAmTarLNZbOr+B7AYHvk8gYdJpWND65CkjCUKIoAseO1nMK/QU0XSNZTFAcLCClpLJcp123GNjSx4vfObJB8rax1uT5bxzmfT/7rht3oW4QQohxKeXk6429Gm/fb+M1Yqp9jvPt0/jSR1cMAhlQ88qsNMp0qgIv6RDiImWA6EYyZEhkzAMILAUZCFTTRwbRraoMFTqzCZIDNoreYWZFUgoUHN9DhpJkQpJKdEglq9y222J5dRfV2iYUIWg3LUp9OeZnK6CHSEWgphVS6Q6GYbKlUGDflh6mzi6jKIJcMc3qUo1W3cK2XZACoUhkSPSDEIJuKPh+wNpSHdtyOf6CYHWxxoH7t7Hv4PiNvPw3jKF0lnLXoPthSNVrkk0K0smQbZkiDwyOU0rcXGqSjbUobTWZTZLOJ2nX2wR+GIVYNBXHchEKjO4cpme4iJk02XPfDsZuG+V//di/plltYbejRhS6GakuKqpDZbFGKMP1zKgglAS+w8rMGlbTZtPuIX7mt3+Mf/OLf4DdsgncALfj0qq1GdkxSM9QacM8FyYub8v3NuEvgbteMfZF4O6r2Tk25j8koQxRhMJs5zwJJYETXFQWLDsrdNoSTwkIfEmghyh0Y+UKUWVlCH5Lx2tpyFAgpUAoPkpCorgCJRVAB+xGQG1eRWu56JoEQky9RSJhIGWKl573aNaPY3sOrVaUWZLvz+IlNTIrFhQDckkXww/Zsb/Npw+a/MV/bTF1pgZEi1nFviz1Srsb/4RLO6BJGWXRWB2XZt0i10phJgysjsPh75/DtjzazUh18fb7tpLOJHg7cN/gGKcqq6zZbc41l1nttOlNJZhrV9H1gHu58f1AX0lft33b4Hg/ixPLqN3SflVVUHUVTVcJQ0mhL8ff+Rc/uV5j8N0/eZylyRXsjrNeCeo5HlbbRtXVbkri5Smuvh/QbnSYOjrL8vQqxf48S20nUnIUUBosXtTUvYR0/ub6EbzeCCF2E4lr5S/RNgfIcYng1usRG/OrpOHVsIIOHb/FVOcsdmBRNHrp+C1KRh+doI0XegTSxwkdfMukLeqRNRRReEUoIELwmhrWUoqgoxJl5kqURFRpKRQfoUiMkouWDLFcheZJndlsgYKsIV2b6lKGZNpERce2AsyExEyssryQYtftm5iZWcPvuGgItufWCBWB0gzZUqtgrRznnnv6WVvaytxUgO8HNOsdij0mrq0TBBK7424I7UspsVoOuqmte3KLMxUMU+PlZ893K/vgO196kV/+Jx9hePOt1fPR8j1WrTYFM0nOMPHDkEfmJvDCgJVOi/O1GgPpJIoQLDTbtD2f24rz9CVyN3rqG+gb7WH3fTs49exZtt25hU7TilINNQVCCIOQZrnF3JmFDRlKj/zZU5FHfqHVnIQwiDJdfM9fr0PovrSOQKDpGoqm8tIjR+kf66U4kKfTtEmkDMyUSaaYpvWKRhn7373nOl+Jm45dwCeAAhu1zZvAr1ztQWJj/joEMuBw9RlWnUU6fotFe45+c5isnqPqrtH062TUHGOpbcxb05SdFaSUuMkqgeMBIQQK+AoIiTACqscKmMWonReADAVBR0Uf9PDqOkbBQc97hI6Ckg3I3l2jftbEWsyhSZ2U2WZpXkVBkM2r2HYAIqBvMM/c+VVarkfghxiah6EHCCTJpIuh2Whqjb7eFvfeW6de2US9ZqJrbXxXZdOYR7mcxbHF+hdXKKx3q4Go+0wYhFTXWlgdB0URZHJRRV6z3uFLf/QUf/+ffwoA1/V56fvnmD2/imlq7L5jjO23jXAz4oU+k60V2r7DpnQvvWaUlXJ4dYEn56fwZYgiBHf2DZPRTc7XKwghsAMPTRFUbYe0riGEoG47rFnt1zljxKJVZaFTJasn2JoZQHuVrkVSSmY7ZVbtBkUzzZZ0H4r4wVNC7/3oney4a5zFyRXMpMnLjx6nvFhBikgaWQiBY3lUlqqR5wxUFmooqsD35QZrLYQAKciVMtgdl069zaUbCEUQBAF22yaRThJ2CybylxSY3f+JKIIw8dIUANsObGF42+AP/L5udoQQKnAImJdSfuLS16SUXwa+LIR4QEr5/R/2HLExfx1mO+dZdSLluaZfJ5QhK84CaS2DIhQyao6i0cOqs4QddBAIjCCNqYdYlovb1NFSPoGnoOghqhCkBm0QELpKN0YNQgtQ9BCzx0bPeJGBr2moIiSR9GB4hdbZAj4iCs1IgRCSRgPSGYVQTVDrNPEHDWxP4LcUaCmEgUBVQ9Jpj3QmyoPutFQQAT/y4+dot3RUVeK6BidP9JPNtSivXLzNjW61o8XQXCGFEGK9DV0QBORfkXVQXmnQalhkckmefvg4c5NRWzCr7fDMIydRNYXxXRurEW80Hd/hb+ZeoO5FMfDnyxPc37uDsVQ/j81NIi/8kIUB35o5haaCikZWT2IoOqpQCGSIE4Qkus0YhhOlK57LCXxmm3WSms6MtcTR2sz6ay9VpjjYux07cBlMFCiZF6/td5aOMtm6KC46nCzy0ZE7UX8Ig14cKFAcKDC2Z4T/8xf/A9XlKOZtJk3yfTm2HdjC5NGZdWM+ON7H3LkFhCuiRfroZpNUNsnBD99OabDImRcmOPviJK1qe73wJ/CCqHDozCILE0t86u9/hGe/9iKNciTdvP/de9cN961owF/BbxDJ2V52uyaE+F+klP8G+FkhxM+88nUp5a9fzQliY/46lJ1L1XkjTzqUIXZgkdIiEaKd2f30m6MsLNWZrp3E99soOkhXw15JENoq6c0thC4RgUCgIpQQNRngNSIvRVUFXl0nOdhBqCBUidBC/LqGoQWIgoWjmaihwA+izjBhGC1QttomokdlNRsw0OMzaDRohC7NOYWV1RQjQ02yWY+xzU3CULCykqSnx6Knz+b0iSJSQjLlcuCuFY4fHaPYK6iWRVTZKSOvMJVJkEybhEFI4IcMbSrheT6tho1QWL8tz+RS6IaG1XaYv6S/4wXOHp9/Q8a86VkIIcho1y42f6Q2s27IL/B8ZQLHVS4x5CGnGwvYgYsiBKGUDCTy9CRTFK0Mda+NpghUobA118d9/ZcvDE81qnxt6jRu4OMEPjPWEvv6S2iKQiglz1cmONVYYDBZAODO0jj39GxjoVPlXHOJmtsmlJKCkWLBqjLVWmFb9oc3gmtzFUpDRQY29+E5Hrqps/ve7WiairgkzPLBn3+IiZemWFuoEChRi7ko42WYsd2j9IyUmHhpikJfDt/1sdvORSEuEakiPvWl59h1cBuf+gcfodO0SKQ2NgW/lRFCjAIfB/4VcKXS/Qua5Yeu8NpVExvz1yGpXqw6y+kFGl4NkNiBFXniQuF08yjz8zWWlut4ROmFgeKiJH1y2z1CS0NoEkXq4EgUFLyWQhCAWzOQvkB6CqV7In1yCYhQIFSQjiBUQkJHRXoKoYRUChxbI5AglcjgegWVvhEoFeYxhCC1F4pD0HlBZ20lzbvfM0ulbLK2msCxVYaGW7RbF//8YQim6TG+w6B/01bOnexEsrhSoukauqHSaUUl14mUgZHQMZI6c5NRa9dcIUXvYJ573r0TM6HTbtobmgFf4DW1PV6Dju/w3aVjLFpRte2mdA/vHdhHQv3hNGFsPzKoeTNB2bm8AXoQhkhxca6rTgM7iPREhjJpltsdVpwGt+XzbM2VCGSRoUyGkXSej2zeeVlKYiglD8+cXc9NtwOXhuMyW28xXsxRcVs0PAtVXDRwL1Wn2JEdYqq9wvHaLJ4MkFJyuunRa2QpGhk2p/teNTRz2XsKAhbPr5DOJyn2F3jpe8fI9+bI9WTxXR+rZXPksROk8ykkkkTKYNe929l5cDtDWwexWjZBECIE+K7PiWfOMHNmgbFdI/SNlmiUm6TzKcIgxLFcZCgRRPo+zXKLb//hozz06QdJ5265Bc5eIcSlhvhz3eY6F/h94H/hVcr2pZR/0/3/D9/IJGJj/jpsTm9nwZ7BC12Saopec4Ble56Kt0Lba5HU0phKgplaHUdtgaVBbxPUABEAloFhqKjJgMBW8LwALesSSIWgoePVdHxHIdHropghMhS4iwmMZKSaqOohaCBcQeknKgQrGt6ZJImmgaIlQVVI55Pot/Vh9J2huqLQsFQEkM4EfOjHAh798wRf+asd3Hv/HIbpoyiSdlOnUkmsL1ypqqDUqzI5ZdI3NkJhdXFdmTGTSzJ9bpnewTyqGqUpVlYaZPMpSn0ZqmstHNvj3R+9nQc+cBsA6WyC/uECKwu1Dddzy87LPclVq40bBAyls+sFN6/kydVT64YcYLZd5tm1szw0sPeq/5aBDFEQPDo/ydG1JQIZ0ptI05+7/AdBVRT2lYaYqNZY6jSxuoY8oamM5TMMZ1MstjoMZFJ8Ystudhb78MOAlH7lph0Vu0PLu9jvMqkakRqlE421/ajgLK1dFJKSUrJi15ntlNcNedlt4YU+Lc9mIFngawuH+eTIXa8bPz/zwgR//m++TG05auC95/4d61Wd2w5s5uQzZ6ksVaPFSAGnD03wl//3VxnbM8reB3Yyfvtm7I7D3NkF6iuNi+9rvkptqUbfaC8ju4ZAEXQaFhCFYoSqoOkaQhGszVdp1drkSrdck4k1KeXBK70ghPgEsCKlfEEI8Z7XOogQ4m+4XCypTuSxf1ZKaV++10ViY/46pLUMD/a8n5nOBHZgoQuTgl6i5lXWPc9VZxFVyeDZIY0Zg7CcITnSxix4hKYPQVR843k+Tl0jcAWKEeJ1NJyaiRASGfgEbQ2pS/ymQdZs4TcU/LKCPuChpECGKokxH2VTg9SyQUnbje0KRnYP0sblbDOk1UhEHwcpEa5Ksa/BB39qkK/8ecjXv76VTaMNOi2dIBA89L45dCNE16FYEij6Nga33Es6l2Hb7mGqa01K/VmGx3op9GRwHQ/d0GjWO6wtNZidXKXUl6V/OIqtnjs+z7s+vB+6juI7PrSPZx85yeJMGU3X2LlvlN13XEzZs32fr0yeZL4Vya9mDZMfGd9Df2pjHD6UITPttcv+NlPt1fU25q/FZGuF58rnqLsdLAeaHUjrUZhmzW7T8XXymSQN31rf557SNlKawY9vv41nlmaY71RACehNJxECkrrG9lKen9xy+3rIx+hWe3Y8l6bn0JtIo14IP+kmmlDwZdjdVmMoUcBTou9nUtVJqgamomEHLoai0eoaeC8M6DGzzHXK2L5HJ3AIpeRIdRrLd9ibG6Hitnl8+QSLdo2cluC+3p18cGg/mqJid5x1Qw5R1srxp07Tv7mXTCHNwsQSq3NlmtU2nuutL35bXsDE4UnK8xW23zVO/6YeTj5z5rLrGwaSynKNO9+/nzCUlAbyvPjdYwS+j6ZFhlw3dfo29VBdrt+Kxvy1eAfwI0KIjxGlGeaEEH8spfy5K2x7HugD/rT7/KeIMlp2Av8J+DuvdaLYmF8FKS3N7tztADyy8jWEFBe7BxGJaoW+ZOmERuCp+A1JeyFBfncdI+djZFyCdhKnCk5Tw14xaU9ncKsGajJAS/mEnkDTQ1QjJFm06e1rg6KyNKuhJUJCUxJ6oEnJpl02YT7HaLrJuHMfrSU9uvV9PodrNLGSLbKlFkXhcrhpsO3dNZRvgqGHrNopND/Eaug8+dgID757Gd3Q6Nj9VCsPsefOHdz1jh102g6JhI6qqbRbNgsza6ws1KiutahXW5SX6yhqtBiqqhe9wsXZMpu2Rs1R0pkE7/vknfhegNKVV72U7y/NrBtyiISrvjVzlr+z+84N2wkEuqLhBBslUhPK64dYqm6L7y4dJez+8p6rlWk4HvsKY2jd+XR8j0/27acVti/LZon2qTCYzGPRYsVu0vId9vcMcFfPtg2xeyklj81P8vLaIqGUpDSdD47tYDiT5VxriUxSMt+0SKtR9s/mTC/vHxvHxaHqtvjK3AtMtJZxAg878NiS7uPR5eOU3SZjqV4ansVUaxVfBqhCoeK0+L5zlnOtZWpem47nIonkal+qTXGoMsE/3PVR1s4sU1up80raDYvqUh3HcnAtF8/xLs8V9wJa9TbV5TplvxLliF+BwAtI5ZKkcyn+wb//Jb70H77JVz/7MHbLxkjojOwcYvuBcQp9N1e65vVGSvnbwG8DdD3zf/IqhhzgQSnlPZc8/xshxPNSynuEEMdfZZ91YmP+AxI1oZjHlz6B9FGFhqZolJcEpqHjiQBrOYnrSPScB6KDb0lkECIVSeNUEd/W8DsqgaOgGCFa1iPRa+OumugEiLpCZbYXWQhIbXJpBiq6KtFNj6EBFz+TojKvUl1tM2u+yE/c+zEq5Q6zExmyuXlKm6u0Fg2m53OoKYlZd8n0GtSmIHAUvFCg6iGtpsHzzwyxeXsPA8NJ+scG2H/PeHQ7P38IXZlmYHSIZPIO6pUOq4t1Oi2berVDu2mTSJuUVxqUerOU+rIk0+YVFRRfTSJ3unG52uSa1abpOmSNjc039hc2cah8fsO2+wqRl2/5LnboUtDTl8WqzzWX1w05ROGTQIbUvTY9lxjstG4ybOYvm8+pyioN10YVKtuSm2gGbdzQ4+7CTu4qbd6w7ZnaGodXL7bz6/geX548Tikb4oQeKKCZNiktwZ7cKPt7BikmkvhhwJ9MPUV/Io/X8Sk7TZKqSaobckkoBifqc0w3V3BCD0mkyuiELQAaXpRFFXSllQ2hYQmXc80lHl85wXiigN0v0Mshqn/x+ggh2H3vdpqVFvW1BtUrGHyA0A8JgxDjNfq+6mb0wy+UKHTz47/xMZLpBKvzZRQ1EuXaeXAb+d63lzH/AckIIcaklDMAQogxom5DAO6r7xYRG/MfgLPNEzS9Gi2/gRu6tP0muqIzZmxj1dFI+Flayy7tJQ+hB9RO5RBKiJKQqHqAW9dJ9Dk4VYlqRAJGXkcl4QmEq+DMJ2mXdXxbQwaACo6r0vfOFQwloC9vszBVZPY7OconC4SOixArfPuP/4h02iAlQowBQeO5XrxZFUVIpALPfDbB1t0K1Ukb35U4TRURgKpIFE3j3Bmb3q0at3/EYq28zON/+d8oFc4BcC5lMrT5BQql7fhukVNHZ0mmDbL5JJ12FAZot2x6B/MIRTA0duWUvCuR0U2qjrVhzFDUK6oM3lkcJ6EanGsuoSDYlR9mW2aAx1dOcqaxQCgleT3F+wb3bSjWafs2850KbuhTNKNYd9myEZe0V9qaK5E3Iw+77nY4VJ6g5nXoNbN0LolSCiHIadF3S+Hyu4LJ+uU/Tgv2Kpai4YY+TdchIKBjdHgos5W8GRnrstPkbHORFbuOFwa4oU8gJTWvw2CygCIEQbcsVyDWM2wuEHCpDCf4MsANA9zA569nnqMvkaP+bhN7vk1xQpBdFmiaxv537qbTsMj35egf62Pu7OLFwqBXcPeHDjC+fxOTR2boNK3LIrtbbtuEmTTYevvmda2Vj33mA0wemaZZbTM43s/I9ls+/fA1kVI+Cjz6Gpv8JvCkEGKCKHVuHPj73f7Jr7s4Ghvzq8QPPSbbp0moKXJ6kbn2FF7ooaKhKCpbc9s58czLVBt+1JzZF2CptOfSqAkfo+BBIBBqiGKEBB0VgQRHxSobpIYs1KxPaz6DV9dxGwZClSQGLTrLSZSxNmdfHMBZStBZTUY6LmqADBRcN8APbWQBFF/gzKnIQCJUUFUIbMH8ySTJYoJau0PgSmQo8AFvTdLuCA6dlpx57AXOn3mGfcVV9kmFlAixOg4nX5pByCz5ns0UShfj2Yap0WpYhIFEhhLX8SkvN666J+g9AyPMt+sbPOc7+4bRr5CdIYRgb36UvflR/DCg7DR5oXyeU/X59W3qXofvLB3lpzY/EEkttMscrkxxvD6LG/qAYFOqhwMDw4yZw9hBwHiuyL0DkYd/uDLJl+aeZ8mqAVA0MvQbBTqBvh4agcigbsldfI+hDPFlSFK/3MBbgUO90WSx1WSh1cILJYYmWGg12FHs56H+PUy2VzhZn8dUNJKaAd2m3lWnzYJVxQk8FEUhrSeoum3cVzQDfyUhklBK6p5FJ3Bo+TbOLgVbh3anQ8nU2fvJnQwf3Mapzx9B8xVUTSGZTqwvXl7yZukZLvK3/vHHKPTmKQ0U+Pd//z+xNLVCEIYkMgm2376ZA+/bz/537mH/uy5Wbxqmzq57tr/mXGMuIqX8uhBiB7C7O3T6kkXP33+9/WNjfpXYoUUgA0IZsmot0QzqhDLADR1O1F5mdnGCeieLMH2UsJsnrkjMHovObIZEn42WDbFWEtgrJm4lQeBE5fxhR6c5k8bI+EhFomV9vI6GUXBR9JDA1mhOZXBrOp6jIkOB0KLiDcX0CWyVMBTYDhhrBjIIu+EGifRBaCrWakhhu0Y1uCAOE/l3YSiwbZiY8TGPu9hNh4WCSkfmeYgqQoCmtlFw0A0NrathHYaRWlipL0epL8voeB8Ax1+c5j0fL1zVNd2cK/KT2/dzpLyEGwTsLPSyu9T3mvvMtNd4dPkEduBytrmEoaiMpXvXPe2mZ1F2WvQlcjxfPseCVSGrJWn6Fl4YUHVb7BkZ4GMjt284bt3t8OzaWVbsi6GGqtuioKfIp0ykG4VnFAEH+gfIdcNA31p4iYcXj9IObEp6noRf2hBHz+tpTtWrzDc7eKFEImk5IU/PrnKuvsZTK6fZkR1EFQpN38IKXKQMafkOCgq0JZbv0vEdOr57mVd+ZQSGomKqKm4YIEMPq9oheK6G8ASWrvDyd47RNFyGPthLz4sSRVHIFKM03CitMPr75vuyvPdn3kWhNwpBHXjvPv7g+d9l5tQC7Vqb3tESI9uH3jY549cDIcT7pJTfe4UuC8A2IQRSyr+6muPExvwqSakZEmqSulul7leihsuAKlTabhvbU1HSZvRl6971SgmECqW7KrhNHcX0casmfssARaKYAQIQmsStGoSBIGjqQFQVGroqgSXR0h5qOiDo6AReAI1IC0P6AoRENUNCV0EQklQ9bKF0JWEE0ldRWglMTUFUEmDbyLC7kCiif2EIgS0JfLA6KrYlKPsq5z2TsYJLOqvwjvt28/zTBkNjPZw7u0iqkIC6i2HqlIZyLHeaSAnp+g/WbHc4k2M4c3VxVC/0eWT5+PpCqCoU1pwmaS2xvmAphFjPPa+4bZqejaFq9KgX4+Nlp3XZsZftGl4YbLhLAGj5NjtKQ3xk6E6eXjnLZGeR0+0ppqcWKBop/mbuRdzu9VwNa5iiw92F+2n5Hpoa4jVbLLTb61ksfiDxAwWBoNIOaTkBnr/EaCaPLwMankVWS2AoAU7o0fQswm7IJZThaxpzBdBQ0RWV7dmhSDvGqUVyt4cb4IT4IkrRVEOF+cenGf/VTRQ/2cPeesDafIWw24kq8AKMpMHojmGEgImXp9h2xxYAkpkkuw5uu6q/WcxV8RDwPTbqslxAArExfyN0/DaT7TN0ghYFvYfx9A725w/yfOUJAhlFKRUp8IIAx/NIDLWpn812ZWwjL1E1Q4weFzXpofkCu2wQuBckb8NIClcK1ESAYgQEjgKIda8eQCgSLe9hFlzc5QRG1sOrmgS2ilSiOwDVDNCTITsPTpLWbHJmjtUzGTwrTeBqqMDOPcOcnVzETQBRqBuFSBIg1EFJSVJpl8DTWHw6Q153mNISrCo6D7xvM5v3vJfMmMefHX6RofdksdcsWs+vMFgocLy+it+N6bZClYPNOpuyGxcT257LiysLLHdauIGPqigkNZ2hdIaW5yGAvaX+y9ISL2XZrm/IaOlP5Ki5bRrd+DbAlnQfWT36QRlMFFCFwL/EQGe0RDeUcREpJVP1BkeWqyx2PBIGlNIaXiAp+x5rhsfZxjLHGzO0PJe0Fv1YfHHmKFWnxYVm9QldoWRkGMjp7DaLfGfxKLomUUODwLfxQonnR0VeqiZxfUkoBeW2hyk9PM0nqeqY3R8jv6uV3PQtFASKUJFCQYZ+N07+SgQIgaHplIw0Z2qLuIsdhKEiyx6CqGBNdN9z2PIIbJ+Tc+dJL7dIZZMkMwlWZhWMhEFpsMCe+3eiKArHnzq9bsxjri1Syt/p/v9Lb+Q4N8yYCyE+Avw7oqzk/yyl/N0bNZdX4gQ23y9f7By05iyz5ixxf8972Zu9i5dqz1Jx1nCDAN+G2sk89qqJoku8po6ih+gZn0S/RXpTm/Z0EjUZIv0A1fBRUz7Sjww3gNBCtJSPREP6EqPgYtkJpJCoyQDpKeg5j+LeKtZMBhGAUzGRocAsBGR6UqgFj9WwyJIN/Vs87txUo7kG7uIWensTzC+2cfs1tGQC35Pgh2imhh64aPkAfzNoikveU3ClQVZ4pNUsmcIY5dpOPE/hqZVpvIzAxMTMmRg5k6OPnifTXQwUJZ2ZHoffeeZh3ju6jXcOb2Y8X8ILA75w9ig1x2Kh3WCmUcNUNUYzeSbqFbYVSvQl07y8tsgnxnezLd9zxb9LSt3YmT2jJdiRHcRQdTJqChnoFJUSHc8lpRs82LeTo/UZJpvLeDJAEyqjyRKeH/IHJ79LytDYnh3ACFMcX1vDEAZpNUXFamG5Dk4Am1I5mnbI77/8GB3ZwtBUQhkgVZ9lu0KjAzKI9Fl0NYRsh5Zv8+jyCZbtOnk9RSGpsdyGIFDWRcuCIDLOoYh0kQ0SeIFDbyLF5kwfk81lFu0aduDhBl5XNlZEuuFdpc1LubCca6oaCoKz52doPryI3e6GXGsBSlYjUCXNbj59ppDB1gKc2Tb9+RQjO4ZYnFxGSonv+WzaNbzeUWr9ODHXHCHElUr815FS/t7VHOeGGPOugtgfAB8E5oDnhRBfkVKeuBHzeSWz1iRu6OAGDhV3jZAAJ7B5au27HG+8QEpJYykdGm6LzpKJs5oAJMmhDlrGw29pFPbXSI22IYy8JT1vkxn3SI50WHlsEGctKu5RjBDVDDB7nCgWDngtDdUMURIBaiIgt7NOouhj9lvoW+uolkIh47MpIzESD/Hi2TxzUyfRdQdPh1VLRdcFW7bPMHRfgSOPhJTDEKklMXIm2laN0AlIZwS3jyk45ZCKHbJ0SEE2LMbyFnt3FkjoOogynr1CZaXBQmtj2XuyN4nzjhw71BJSgxc6y7hum2SgMd2scvToEj+ydQ8ZzaTmRNIAi+3oGE7gc7q6iqYoLLQa9CXThFLy/cUZtmSLPLc8x6nqKqoQ7OsZ5M6+IUpmhrF074YCopKZ5UBuO0/MzxBIh5XWFM8tz/ET2/fRn8rwmW3v4w/OfJvJ1gq+DHh2dRrpLKMrOqoiOJyaYaFpU9AyFI0MPUZkcGcbdTJGgslajfl6i460CPUOWV3HxkZXVFxf4PuADBGKwAsE1bbkbGOJuU6FTuBQdpo0fYtiSqXWCfG7nQMVASoCGUJW0zAUA48EewujZLUE59d/gBQUoeBKD0VGaZ9XCrXIC69IScezCb5XR7Hl+l2iSKjIqkfYo0V5+5pGcHeKE4053usME2DTO1KiNFTASOhYLZtc78XQ1OjO4Wv3BXsLIELQL1d5uF5cuNC7gHuAr3SffxJ47moPcqM883uBc1LK8wBCiD8DPgXcFMbcCSzqbpWJ9im8MErvnGyfpaj14OPjBhYCBVpJnKUUuAZCd5G+QE1G6od6zgMpaE2nCT1BasRGeoLUkE3p7jJeQ8OrG4S+Eu2jStS2hwwUhAiRhkQxQkq3NUgUgqg0WkLSkPSkLPYnPbanx1gLEzzvLGNmakhCFE1HTwZYMkQftNh6QKe2FHJ2xSKUNqpIEfRoBLflyAwKPnGgzbN/0aR5xGYwBC9p02poTC1ZDPT7FMwESjhHOpug1Emy0N5YuNOXSqOlTZ5bnmW1K/talRJnMSCt6/z1ueOkdZ2UZqCrKl4Y6aH7MqTteRTMBF54MTuj5tg8sTC1IV/7sfnzSCm5e2CEDwzu50R9jrlOhYyeYF9+lC+dO00gL+qoOIHPU4vT/Ni223i2PIEbBhiqRsN1WLYbKKgMyEHKVocl24+aavsKpytlFEXS8Gw6bkDLdyHsauDIgGQ6JKEHSGSUPhgopFQDO/CREhKqTlpJEsiQvJ5i2a5Rdy3qbkhS1SkmDXw/0kf3pURXVXJ6gvtL42SMJAlNoTepsGLVSGg6m1O9uKEf6aRbVdzQRxMqMgQpw6gFYRcBqCiEMiSo+/gNL1pXAVQhCBPg95moe9JooYqyOUmmJ0dWSzJy2wgzCxNAJJg2vm+MZqWF2q1o7d/cx10f3LhgHHPtkFL+7wBCiMeBu6SUze7z/w342tUe50YZ8xFg9pLnc8B9l24ghPgM8BmAsbGxN29mQI8xwLw1vW7IQeKHLmtu1M4qJAQknqtFpfq+gtAF0heE3aIM6Qvs5SRrz/TTc/ca0lVQzJDQAz3jEtoq5ngb6Sv4toq9lGTf37Jor9lUz6YIg4D0eIv0oIMINHQZkFUl25I+SaFzb2Eza6GGlIuEBEhUhAhQVJ9AUcjmGxj9LSbazzD6wSF2Voc5Vpe00wZWr4KqQyuZ5JHZRUS4yNbbFM7WUpSUDmuTOVpVyBQjhcCDdxhkcjoPKGN8aeLEuuEUCH5y+36+fP4EbnDBIEd50HXXIqlrIKLS9fl2g635EqaiMt1u4IchmqJSc6wNYZWhdJbj5cvbhh0pL3H3wAiaonJ7cTO3F6OCHdv3qbuXhwBWOi0en5vki1OHWXEqJDUNL4z+br70aMvO+sJl2lCpdhwcGTVgcP0o9OGFIboSgK/ghyCdBL7pE6oBAkFSSSFRCaUkQOKEPmpgcbIxjxW41N0ObveHyg0CgkDidD3ztK6RMw36zQJ5M42hqNzW20cxqZFVE+vKkF4YUPc67MwNsWY3qXsdKm6bVbvBJYE6NEUhqRqoQsFJCaQCMpQoEqQvkUoIeY1gV4KEamKoGiESTVHZfdc2eklz+rlzeK7Prnu2cdcHb6dV66CqCrmet1X5/Y1kgI3FQW537Kq4aRdAu6pjnwM4ePDg1eRjXTNyeh5NXHppFDRFxwmiYpMLVYbJPg+/4eCUE4SuRugDoUDLuISWjrOQI6EmwTXwLRXDjIyg2efgVk3aU2kkAnsxye6HBKV0gr6MxtZxBTd0MVqjLFtzhNRJGD4p00YRJhlNQVU30/ZOYBpjbO6Zo+VquDaEBKCGDBSbkDRAhrRY4AM/WUJ7oYcn2wmSukJ/KctQpsFcu4Vph/SaFi3SJLQE/dstNJFmcBsk+5q0Nut89tiL7C318xPb93G+USGQkt3FXgZSWSbqFUIZcmRtGS8MsP0oSyeUkt5EioSmM5LJoQoFLwxQUMgbJqam0nRd0l1xqqxu8q7hLfzpmZcv+5v44ZVzq01VpWAmqb2i+KjlurywOk/YTQfs+B5BKNGEhicDAhmpFyIEI9k0ruvRCqJ4dCCjfYIwRNV8FE1D8UEzA0JCNDQUBXKGoN6OMmB0RcFQNJKJSCo3lBIvCLCCAE1XsCzwfAUZqIhu7FtBYVspy30Dm1hwV3i5NoFbDkjrGmtuk7RqsmTVmO6sIqXkvt4dJFWD7y4dwzcC2p6NqeooSuSRj6ZK+EHAoqzj7kwgnm8iFjyEE6LoCuHuFJHhjzzuQIbszA0xmCww+I4C+96xe8M1LPZfXhEbc135I+A5IcRfd5//KPDfr3bnG2XM52FDk8TR7thNQUJNMZAcjb7QMkQTKk2/gRPYGGqCQPpIGZI2kwzeniPYbFKeNlmasRFZC9SAoJqFmWFy+QC13Ye/aqPnKggVCATZHU2EEdCazFEYDdkyOsxwsgdXREapZPRST9foC7IsW5MoogEh6IpkU6rAgjdHIxSo/hoHN6uoWo3ZqkKAR3+pQjbjEkiNduBiKCp+osIH73+Q1MISoZT41GgFLZyUjtebotPUcFBY84sMGRX2vtOH/g5rts8TcztZcyeYqJW5Z3ATn96xf8P1Gs3meHZ5lpxhUnNtPBkiA8n2XIlEN/PjQN8Qg8kcVcfirv4RnCAKH5iqRkY3+cDYNjZni2iKwvZ8D2dqG4W1dhavnH8uhOBdQ5v5q4njqIqC0k1NlEqIEwYMmX2seVUkEj+MinsINXypoAvozyTZWxqmY6/gYWMHLqonQfokky6KGoJU0KWCVEBVNXRVwQ+g4TqEKqRJkjU1UoagHFToeG7krYdRZpOpS+g2Ok7oAlPREEDKUNmSzzOSS/GFI9PU7WjBXVUEg1mDFyrnmW6vIoRCXk9yoj7HcKJECh1/WaCXJYHukSiY6EMZcnqKea9CQtFQ7yrhPd8GU0HJ6Ki9Bqnz0LOvgNMb3T3dXdrGz21517X98sT80Egp/5UQ4hvAhT/KL0kpD1/t/jfKmD8P7BBCjBMZ8Z8GfvYGzeUyFKFwX+khvrn0RbzurXjBKBESFQ1pQsNQTNJalj5zgN39d3Bq8GXcfYIzzzpMnbTwyyn6CkUSmxo4noK/1o+ypYUf/H/t/WmwZNl134f+9j5TzuOd55qrurq6qwf0ADRAACRAgCAJkBRlkqJEyfSjwjbDzxH2B8n8YEUwFCH7yVRYlp4s2uKzJIukSYqTSJAgAIIAMTQa3V091zzduvO9OU9n2nu/DyfrVt2u6gHorh4K+Yu4cTN3nsy9z8mT6+yz9lr/FWNUUi1ISkGwnuXAvgWiVY+r7Tb33bNIYPr0VY9NP7m+TWYWiExIxR3jgcICveBrDEQax67Ri5ZxrTIPzOY5OLFBLYZB3MYWSYZpYKCvYjy1Q8n8a+JwDlt4CCw8I/CN4dhHtgjPelTOpOiYLPV9SzyXSrG+3mQzrBLEAi26+CpmLJ1lq9/dE0K4v1ihGwXYUpJzXBwhsaUkGIYr1vw+L9W2eFatcbFZ40CxQsG7kVizWCjtcbX84PwBtDFcbNWRQnC0PM4Hp2/vajvb2OavVi6hMbR9n4cmpvn00hF+98JLBIMeE26FQ+lFLgxWiLViwishtUtRVDhSHmOxnOJqv0bGdvGER1sNSLkCZUVYlsaQLFbYUgOaEM0gBAePtEgxiEKk9Akk9OIQX0VIIZKoleux/kAyIwZbCnJeMjN2LYkrHL65fsOQQ+JTf3pzB7wOCo0rbLqRTzcO2By06DV6KBWRkRKpoa76VJo2fS+gHnZJWS7jdY92JUdYirGlZDZdScS7agWmji9QcNJ8euaBW8I0R7y7GGOeBZ79Xt77rhhzY0wshPhl4AskoYm/YYx5Q1Wwd5J9uUP8zPwv8WLrGWITcSB7lL7u8ldbnyfUAdpoIh0S65hmVGNKH+a5c9co5AUPH59l/YJGKU3Gy5ApBPjTPYJIEA9shDBI22BnFaVZRXvZ49jEflQ3Ymd6jTV5HgBbWjjCQ6P4+PhnmMksst79E5CJDzNlTyKETahqjGeeYFJ4WO2/ZE1tIEWIJMYioGBJcqZN2oo5Woh4sTmNLRy0UezLxsyWmvBYzIHHm3z52ke43C5zpemz08/QDjvJ4itgS5tqKsXO4AIZp0TWnk+KUCNYyBV5sbZJrDVZ1yXneCzkixwrT/BibYOtXpda0KcRDHh2e42lfJlOFOJakk/OH9o97u0wObY/tv8YoUoWfm+X3g/QCnz+/Oo5tDF4lk3L+Pzx5TNc7bTIux5KGywpWEhP0+obqm7M/nyVnJXhUqvOX65cZrqRw49jDhbHSBfS1Hc6ZFyFcgxhfN0Qm2T1GYNSGm3ANz6xMSg0Whki3+A6icvFEhJXWkSxAgHSSCwkRkuwklgUiaDq5XhkfB9fX7+8u08GQyPs0VMBaZO49CKjiFSMFEmUuBWAkoJBRhF7EKeS4h0VA56VhElajoVr2TjS2l1nyFguTrlAG0M39vm9a09ytDDLE+NHbhEoG/H+413zmRtjPg98/t3q/81Q9qp8ZOKTe9oKTonznVe40H2FjJWjaJd56dka1y5co7+WwtZ5piZTHDtcoD8ImVyyuNK9xNp5FzPtgEjUFIUEK6WwKgPUdkhod6iXznAtuIKwE99t3imihWHcmqLoVpBCosxe8TRPVjEmphNepO5/h35cx5UaY2IsQrSwyAqNIxQWMfeXtziYb9IIPDwR0WjYXH0hR9QrkVsaZzprc6h0jnbY4U8vp2mFZYyxkQIiHXGlfYUg3mStK3Flkdn8Z5lM51jtdcjYDoM4YqvfY0W1cKRkLJ3lWqfFZr8zHK/FcrdFLwoRCLKOw//n2a/xi/c8zOVOnac2Vgi1Yn+xyt+/9xHKqTShUnxj/SoXWzVSls0D4zMcr05yqV3fzdjcGfS41KoDcK3TZC5fxLUsco5LpBWLuQrKGM7Waqx2l2kEfTDJtgJBbTDgB+aWmM4U6ek+2gqJVUysNVImRtYYUIrkuRH4cVLow+ikalRsJzOTZF0lCT+MY4ktXGwrSSrK2Imxvbc0z3g6zZP1V7jcaxEbxUCFdKOAvgqAJKlqoJIZe2w0NoKs7RFIhSMsIluhHYUtwVFJMWY5jGiRMymsgoNuJ1K6OTsFtqC9KHbrhhpjON1aYTpd4uBbKD834r3Be3YB9L3KbHoRT6YYqCQMr7YRsnE1QGtNbPexAo/1jRalQoZsxmNz2acdG8KuhT0sUhF3HZxCUrTZCM3YkqGTu0bsDHAcm9iEw0W7LgWnTDdu4w2FnnLufvzBjWiPgVoniLfx1TaRaqJNG0cki4VmmFziG0Nk5DB7X5F3Aip2h61ajmariBAWXi7i0jmb6ZMXQKRJWxpfueQcn26UBQQpS5GzDX2VJguEukVt8G1s+TjzuSIv1TZZ7bUJlcKRFpdadXpRRKAiPMsmMjG9OMn2DJRiJpvcYQziiH/xwreItcGWyQzx1NYq/+zU1/nbxx7gf3/x26x02uRdj32FMtuDHo608Kwbp+9m/0aKfqAU690OWdflF+95iKzr8VtnnuefPvs1Qq0YRBEasKUkZdkoo1juNvjysqbgecRRiJQuxsRIYWEBsYmSpB8tibUhCmyEEDhujJAaz5ZoI0HqoS6KQ1pqBpEmVBF5J8XBcpa8naHqlJhI54hEQCMMCERnWEVJkLE9YqPwXEXeSS7+gYqQRpC2XCZSRVbyAYO+j1QCRyfRNLlsUoptOl0i1DEag/xklerLhrF+icpchZnH5nnaujmILOFab2dkzO8gQogU8DXAI7G5v3c96/PtZGTMb4PvRzz34jLrGy1yOY/7js8zOZHohyil2dnu0espsgWL1k4SFeE4NuKmmpHdXoDn2dQGNZStsFQKfzWPXe5jYo2d0qiBTaFiMWF5xOkGs9NlmnJAJ46SBbthxMWkN4srE99m2bufSLVoh2cwaGLdw7FKDOI1jBGAQqIxQiDQCANt41E2GmUMaeFjhKAfW2z1Pfw4hzW8wx4vbRP6ZRwn0ZwpuTGRtpiwFVnbxpM+KSdF2btxSz6I15nOekxmcqx0W6z3LFzHQgqBIyWhjmn4A6Sj0CjCWONrhXNTQQuA9V6HnOPu0TF/sbbB/336FCvdNmCo+31Wui1mcwUCpfjl+x4n73h0oqTyTqQVW4MeO36PjO2SsR3+9MpZfnTfUf7kclIzVw8jVZJiTMnlLtAKrQ0b/TZbA4ElJR8bO8bVwSY7YQPXsmgMBggNBo1tKYxtiOPE/eQ4BmElPvXYaJQypF2XvJvlatREEGOMZLvvYzKGairN0611LCHYCTq4wiaXjfBDQdZNMV8sEokBAxUxky4TacWYm2fVr7MTtCkV8jjCRrY1hcDFH4NBStMK+3iWw5HCDO1oQE126D4Ws+wIGs4Ony7PQZtbyNjerY0j3k4C4OPGmK4QwiGRuf0zY8yTb2cnI2P+Kowx/MVXXqZWS2Z6zVaf9Y0WP/bp+4ljzV9+7TS9fsByf0CmaihPJNEaUgoWx2fYXB2gtcZ1bQ7un6R2YYNgABk3TRC69C45KF9S2D+gNKv5wL37+YD3IU5tPU2z0yC2XQrZIr4OsKXFdGqOx8c+tjs+ISwmsx9jLP042oQsd36HbngJS2aI1I2UtSSOQmLJDJ6xcEQLLWICQGm4HFq0LImQCqMTn3RKlMBOfMMaxZHSFn5tAk8kccyhtnliJrU7ewZwZZGUbfPw5BxfXb1MbDTSJLHlOdejG4ZEIsToEG2gONS6jnWcFK6+/jmWdUv9Tz+Okzhtk0SibA26GGPY7icXgj+7epafPnSCb29cY6ff53K7QTxMSvLjGDuTY7XX5murl+lEASnbxpESbQyBinczKbVJqvMkIYOQEhbr3T73lQ/wQm2dSTfLstqmHrbxdUAxk0SzRFpjSQulY6JYoZTAGJvQdtCWy0AKlE4SjOKohwF6asBm0MSVyU8vNopYKLTQFDIu1ZTFQqZMpHP04pBDhSkWs+N8c/ss2SiFr0ICE3N8epHqUo6Vfp162MXRSRKRr0JsYdEMe/TjgGbUpxMNGE8V+IuN51nMju9JsPIsh3uKc2/lJzPiDTBJeabrt47O8O9tD7ceGfNXsbXd2TXk11FKc/b8BqvrTfr9xNc7k1pkp7FJlFOUCzlSYQlppSgeLFAsZviRT9xLHCteWj7P8uo2uXyKzlqFTmOAWxlAN4O1XKFcfYDnN2u04zyt4jqRcBj4IeXxLAfSxym1D7Lc7bG0mCaXvTGDsmQKixQ59yCBqmPFaWwrTxx3AYMlPFyrgjY+FdHBQ+EbMVx8g2oqop3rkbNdwl6RDhkanXEOl7cIzQ5GBXxkTnBfdYdnt6a50lXM5ed5uVEnNhEfm7dJ2w6VdFLlSggoeakk29BoBIkxjrViJp9hQDJzFkJzpFrkanNAw++jjWEyk+dQqcrOoL/nuE+mc0n0zKDHSqe1p2TZWCrDSrdFP4745OIhIq241m1yqV0fZmMmi3+xVsOZvaAXJZEmjpVUWxIIXMvC0xbZ4V2Br2IE0I1Ccq5LyU1zud3E1xqXDNPZIp4bY9mGnUGfTn+A7wtikSghWlhERlOXfaIwILJ9hEyMNgwji3AIdXIxibRKQikNZIaRJQOVGOHJVBLn/Uz9EqGOkmghmUQBbQdtyl4WM7ww+TqkaGdAuqwP6kQqZstvERvNQCTnrCUk0+kyj44dZGPQIu+kOVFa2BUmG/E9MyaEePqm578+zJPZZShh8gxwEPiXxphvv92DGBnzVxFF8W3bW+0B7faAKFJs7XTwg4hspsBkMMnjHz/A7/3h02zVk3vYKI75J//sz1hZrZPLeYi8RXMnQCuHhbkUsxMHmUhNYUmHs6e6VMtZPApk+pM0S+cxgU0+mOHC+R75RocwbPKnX3iBE8dnefD+RaYmbyRzjKU/iDYBse4ms1yjQQhskUFKj1A1MKZD30hcNEok81EbjZMOURGoVB8dTbKwfwnbWyQOn8KWMTOZOaayk5xpa2aFYb0v0KbMSrfLjl/g04sP8+TGBtuDS5xv7rAvXybSmnONbQYqRoeGw6VxhO2j45i8J/Asi2OVKjZtmv0kIqUZ+izkS9w3Ns2p7aR+5lyuwI/vO8Zfr18ZGvreMPzRYl+xwuQwNLIfhxhjaAY++4qVYWq92Z3ld8OQtW6bSCssIehEYXKxMVD0PCbSOdp2gBQiib/XGltKqqkM/SiiHfo8MD5DL/Y5tbPKRjdgymSopNN8euYAX/7O8/ieRlvDAEQDxIJ+HBN2FJkxG2PrXWlkbRIXlkQS6ThJYIo1C5kxxr08nWjA5d4WjrAou1lio1gfNPCG9U5jbQhjTWwb2uGAephMPGxhJWsSKqBIhnY82C0jJxE0oh6xSTJXS26WT888QMnNvM2/nu9bdowxD7/eBsYYBZwUQpSAPxBC3GuMeentHMTImL+KqckinucQBHs1SA7sn2B1rcnZC5u7Br/dHmDJRAAjihVXlmu0Oz6dro8xBs+z6XR92BBMzWTp+iFWN0dpchJ7+OPs9QOq5SxKhvSzGzhRYqQ2NrpoS9PqW6ydNji2pNHssbnV5pGH93P8aCJ8ZAmX6ewPM5H+KMoEtINXaASniHSHdnAGV5aIdZdI92gCrk4iLRSAiClUJVYcUuEs0naIlAVC0tFjpO0ZzjeTULy1nibWfZQZYDBcaa/zu+f/H6rpIucbRZa7mrVem6KbYjqTJ9KJSGvN7+FYkkYUJVVrMg5BrOmHJJEbcQRxyF+vXaHgHuGffvhH6EUhE+mksn3BS/GtjWVOjk+z2m2zWCiTG2aMYgxX2w2+cPU8F5o1elFIYehDB5BCcLldx1cK17JwLAsRJuJTlhT4KuZqp4kElIC0ZSNEUrruaHmcmj9gOlugkspwdbvJuFfA1xFFJ8uB3DiXm9vMXMtRm9Sogo8ZZo9GKkL1LXRfoHsRXhpMVaCEACPo+BrLSpK5spaHNhrPslnIjtOPAq70t5FCsOW36EZ+EsGiYiyV4VK9gTaalO1yKJ0Y7X58I0bdHVYrytheooFOciGxhg6topOhEw14cuccn5o5eQd+QSNeD2NMUwjxFeBTwMiY30ls2+LjHznK15+8QKczwHYs7rtnjoP7Jnj2uatEUYzWhjCMsW0LKQUXLm3y0uk1giDC90PiWA2LQygikljjaJAh62UQ2mJ1vcmhYQX7wwcm6fUDVtprtGkjLUk+6yGEoNHs09oJ6dZLSCnoZUJio3nm5WV++KPHeeLRg5RLSXUYS3pYeIxlHqPo3cu5xj9H6T5COAyMjTagEUmUA9AziZ6ep7cxQEiIrVoYykhTIkOIYZGULVHGECoLTeIGMSYm0ltsDfr04hU8WzCRLnC5PU/XzVPx0kk/QrI96DGRzlJ2ivTiAVJ53Fda4rnVF+mEwU1H3vCdzRVawYD5fGm39WCpysFSFWNuVL4fRBHLnaQi0Lc3V5hIZ5nLlTjb3E6OaXmcUMVMpHOcb+3Qi3qkLBvPSlLpLZJknthoQqVxpMSzbDxpcag8xn3jU3xu3z20o4CvrFwiiGPCYcZq2nLJ22kkEl8ZZNohu+kShgK/EBIbQzwQmJbE6yhMQWKsENEGOy/RliHUgNDEWDhYHM5Nc39lEYnE82xW/Bpam119l+l0GaMlmx0fV9oYYzhemON8owFDVUV9k17OT8w+zNd3zrEvN85av8nqoI4lkkiZ2UxSo3V9WBpvxJ1HCDEORENDniZRi/2f3u5+Rsb8NkxNFvmpH3+Qbi8gnXKwhyWxFuYqFApplpdriX6H0Tz5dBshBN1ugG1Lokhx3bUbxwopBVIIYmUolVzanYB6o0chn+ahk4s88dhB/vX/76vUN0LIaYTSxCmHKFIopVGDpO8oVqy2O9TtpDr7nz59misbdf7Lv/WR3fFBoqZ3vvn/peZ/h1A1UdpHE2ISnUdiBPFwfBaaUPso5LDie4BgE0xM1kpR95+h4BY4Ui6wPZhgsw9gEGJAwe2wPUhCF8Ei73Ypeds0AodAJS4NMYxoiXWPVtjFloDS2MYmVDHasFvdx5YS17K41mntMebXEULw0bn9PDI5x78/cwrHsjhd38IYw2a/i4wF+7wyytZ87uBxAP7lC99ie9Bjs9dFCEEQR8kCrRBYJond1sM0f0cmcmU1v48xUAsGu5or2koSb1rBgF6caItvDrpkHIvevCD1jCYdS/qxh9IaOdC4mzG2b4gyyTqF3TfoSGErg0kJTEWgHRBG0FM+QkhirfAshzGvwEvNa/TjxP3jWg5OnCZQEb3YRyL41s75JJLGjalmHVK2gy2tpPiGk+IHp+7lyZ3zzKQrWHVBqGMO5qd3E7AKIz/5O8k08G+HfnMJ/I4x5k/e7k5Gxvw1EEKQzyWLTUEY4/sR1UqW7e0OfhjRag2I4sQHmcm4w9m4QV9foxPXq8cZtDRoGROGimzGpVrOUi1nqJSzhJGiWEhzxFmi4YZQ7CKlxPd7COVi6kWiOGKgYsKMIGXAsiVGCF5Z2+b8lW2OHZxC6QHN4EXq/jPUBt9GYBHrDpoQhr5TvfsoQWKI0UjARQ61IBWe2EFpQyfcopJ6mIfHx8nam/ynywUENjmnjS19yl6IhiTTVEDJjdkexOQcj7zr0Y8jNnpNNnsKxwLPAiE6PLv1DAeLVa51L+0m/QhI3Cqux4s7G1ztNMk5LifHpyl5NwxPpDX9ONqNPjHa0F0PaPcHNDM5HNfCXhD85fYlvOEiqMbQCwOc4SIlxqAAZa5H4kNsDBJBO/S50Kwl9XgExFpT9FLcNzbJV65dpppK7/rXG4OQA7OT9KpFKmt9ZqRh63KD1moHrYY1WvsGrzWsB7sM0b2AZdC+QWRBl2GgI/pxwIfGj/BC8yqtsI+vokSd0wjS0qZtAtrRAEdaBDpOpHER5GyLyCiEFkymS8xnqox5eabSJbK2x/nOBinLYctv7xpwKQQPVfbdmR/OiFswxrwAPHCn+xkZ8zfg6VNXeOXMGkppGq0+rc6Abi9IjLc2SZof4Lo2sdJYUiCHIWnSAcuGdAHsXIiQSehjtZLFsiRnzq0zP1sGIJN2ScfHGfR2CJ0OalAhH0/Ts9axpEIJkczUtaaSz+6W/tpsdjhiqlzr/gGhatAJLxCqJrHu7THkt8ND4AhASHyjkUYNY7CTfVJG0wxeQLsh94/dz/6iz5W2Qzto4MqrfOHaYS61y0TKIm3HSDJIIQhUzKAf0QlDBnHiO/cV9ASEynC2uc3xygx5JzH41zM1XcviTH2ba70bRZVfqW/xs4fvp5xKDJFrWbRDn/Veh04Y0NjuozvJou9mv0s2cvjNb5yiejDHbLbAWq+NJQR5x8OzbWbzRVa7bfpxhDW88kqRuJyU0WSkg2fZXGjVqPv9JDbfdnhiZpEPzSxQDwZYIsnkPNvYJlYw0FArgSMsghkHNmWSKgqkNmLsrEHWQfRAKKAP9hboMU3U8NnuBlTu83j8nsNsDVp8MzqXuH5IUXQzSXimDDEiUWH0VbJmk3VsSmmHvJNCIDiQm+DQUAVx22/zcmuFTb9F2c3yscl7GKgIIQSH89OMp95c3dUR7x9Gxvx1uHx1hxdfXgFgbaPJ+YtbtNsDlNJIKRGSpMq9MeRyHpm0myx4OhEmM8DNQDpjceieEhuXYjprPr1WzMZWEvUyNpajWEgTK41tJbPGjD9Oxh/nkaOTfPGvTpNJuaSnHGS/T0uFOLaFOyzlZduSpdkK3fAioWoAYFSGM5dKdAcFquU6xUKXbCa47f75ZEkJBShcIMTgK0GoBI6jEUKhdJ9edIWce4DFwg+wr+iy3F7n984bLKAbpuhGHrG2kEIylnapprLsDHqJ4qSEaHg9McPA8kstRT+6wIGiZqvvoUgWHMfTOV6ub+4R4QpUzHPba3xs/gBKa/7o0it8a/0avSgk4zjEfY2vIlKWg2tZZGyXy/UG3VrM0liZffkyQRyjjGEpX8azbVqBjyVEErpoNJZI1BaXCmUyts16r00j8OlFASCopjKc2loj47gsDF1AyV2Y4eX6Ft2h798SkrGJAuGjKcxXa5iLffA1/QdAhiBisK6CyYFJARFYdUh91fA7v/kV/uTPnmLf5+aRmUSoK+N4eNLGAFpBJhMRRRZxqJDSkE8LFrNjQ4Mf88mZk+zLjhPqmM+vndqtl1oPujTDHj85/ygV77VrrI54fzMy5kMuXNripdOr+H7E/FyFh08usnytBiRRK5tbbSxLYtsSpfRu6S+96x/XHD82gzFweXuZgRUMjZdgYtGmW4OVVwIsJL4foZQmjhXrG02iOEky0kpj2xZHD0/x8ANLXLyyg20lEgD78+O8vLlDo51UaS/k0tx/ZJbFqQp1/9Lufjx7JsO19Sk8r0E26+LvlJkca7zKoA9n3sQ0dQpPKGJluLKVotnOsrldJp0OuO/YJdJpn1DV8OMNbJFDGx8pH0STyAz4ysWYofsCi7o/oOzduJ0HibwpM1Zpw77yOkfLF7Gl4GDJ5lrnMMqMJfK1w1hrP45Z6bboRiFNf8Dx6iSnG9t8cfkChWGW6CCO8GyJsBzm88XdEmmebRGL5IuppDNkex6OkFhSsN5rU3Q9Kqk0jmVhTFKJB+Dx6QWWO02agU8r8Eni9SWdKGA6m2e522KWZEYrhCBlO7RvWsSVItEKdypp9v/d+6hYKRpn67z4Oy+h4hAVKOQyhI9ANE1y09SD6AjE0zCwezT+/CzWPof4sKAV9XClw2SqyGJ2HNhmYAe4blKk2rKSAhYVN8fhwgz7c8mi+nJ3Z0/ha0gSoy50N3jEO/hd/jJGvF8YGXPg6rUaf/3Nc7vPz53foNsNKBaSGWKrMxiKLGmMAc+zCaOkAIOQBiEEhUKKTNojm/PYaRYJdAc7Y6jOCxq9DibMk00J+oPEkFuWxLYstrY7zEyXmJ+t8MhD+3BdC9dJvpbZmRK1Wgffj5BIHliYphkF3HvvHNPVAvcfmEEIQcaZp+Y/Rd83bOxYCBz6g3RSXzI3IFY3qw5aMPSOGwJiFEIUOXN5itVNF62TV7v9NKcvLvDQvRcwKHrRFbYGXyWIt6kNtvFjj2YwjjIWUgImCbuzhEAZTdnL4Mcxnu3SDgdJuThgX6HLkXKP1FBwKlAxC/mzXOmM86P7HuEb61fpxyGv1LcIh+4EX8X87oWXCIfCVwIouh5F10NLQ3PQH6oVJka5XM1wYHyMx6YXWOm2mMoWqA/6nNpeQwjBRCbHtt+nFfjkHY8HJmY5VpngM0tH+NWn/pKa36cfJ4JmUgjyrkfO9ThRmURj+MLV8/SjkJTtcKBY4Vq3hTXUZpdCknEcXMvG9mzG75vgv/rAT/H0vzrFC09domf5BBmDfZN6v8qAOg5EICKDqEfIukRWEp+/Iy0eHTvAQqbKld42y71tenGAENCO+nxk8hiPVW8oT474/mRkzIGz5zduaVtbb3DPkWOcu7CJ1obN7Ra+H5HybFIpl14/wHMdKpUsM5MFpqdKCCG4dq3O0f2zRLJML7uBsnzcZp6FwhTd4jqZjKImbqSx205iaONY7cnwVErTbPa5ttogjhP/a6WS42//Z49zYN/eQg1pe4pq6gN0+08jsFCmj+tGSClRykbrmxOhbs4iTgqPRbrN+s48Wl9ftE1oNPPESmBZEKoGveAyvt4hZcNUVnCmHgJpJBZSWAiZ7FfRS3OiOsW5xnYS/dEV9KOIsXSGj86CEMsU3BDXzjOIMygN91bHuH98mqzj8n+ffW7XkJdTGSYzOUIVszXoUfJSbMQ3Zp1OxuLe49PQMcSxolBMUR3Pcrg8xkMTszw0MQuAH0f8k6e/xunGJmcbO4myoJQ40uLhyTl+aCGZsTZDn7FUhkhrBnGIJeRuJSRlDL9/8eVhcWoIVIeVbosDxequ6FfGcfih+YM8NDFDKwyYzRaYyRX49P92nEEv4P/8jT/n9698O1kgBXQBoiUweRJjHoAIDbqtccpQcXNUvHxyByElm36TbhxgCYElLLK2xwuNZc6010hbLveVFjhWnCVlufjqhsKmJSSHRmJadzUjYw5JaTEDG1stavUuxkC5lCGTcdm/NM6p55dptYY/4CAmCGMq5RyVcoYT9+zVtbiuC+3oDKXOfgCKxQz3f2SOs2c3cUli2VWsyGY9xquJD3Npobrnc64s79BuD1haqFJv9nAdm3IpSz53e1GkavoRitPHebr0u/g7GxRzDcDgBy6ZjA9DzcS95vpGfIvj+oRRevciA+A6icQrxES6Rz04hSXSSOnyyISiEYxxtStQRpC2LdK2Q851+dTMQaZMgYcmpqkJn54VDos2x4ylfp+M3SfQMdDGFnlgjsdnDgNJXPmP7TuKMQZXWmQcZ3c8c9kCvSik2RjQ7A9wMhaHJsf4L088yrc3VrjaaSTa6vkSeSfFF66eZzKT43h1gpTt4FqSnUE/WeIVAmMMGdvhXHOHj87tJxjGptf9AVOZHI3AT+4GjCJWime313cNeZIUZfBVzNagy2K+RCWV4dOLh/nhpcN7FB2vk856/MLf/2HOfr3FK186R6QV4X6gAEYBVuJPFwaMDVpHrPRrOMJCGc2FzgYr/UTm1xKScSfNi81rTKSKnCjNU486/P61p1iqjzOTKdMJBzSjPiU3yweqByi7I3/5m0Uog9e8fanC9yp3nTE3xtAfhHieg/0qZT6A/iDklTNrNJp9xsdyHDsyw/6lMU69cJWNzRtRFL1ewHMvrnD67Dqx1uRyKbpdPykHpjQYQ63eIwzj3QVJgJMn5mi1/d0MUsuSPPrwPmany/y9v/UEX/zKy2QzLtrA4nwFx7E5eniaQwf21m3d2Gpz7uImvV7ik7Vti0I+Ra3RY2L81kiEJIXd5fETHvWnWwiZ6KDkcz0KuR6JIZckhlzzap2fxblNXj67tKd1YXaT69pXhojYdNEmwCLNpZaFMTYfmnY418zgx22WClt8dCxi57KiIxZwrGScHzq+xIl907SCV1jvztMK24Qqwo8jhIhZLBxmMrO42+/R8jjfTF1NSrwNEQh+dPEov/nXp7B3oKQ9KnGGn7z3OLO5Ij95sEgvClFa858un+FbG1cBeKW+yZnGFj998AQpyyZtOQRxMuvPOElsdqBi+nFExnYop9I8MD6dFMnQmiudJp6VyN1ebTcIVRKdo4ZVlMRQhGw6V+C/OvHoa5a3u86zW2tUcmNMfrLHansD40fJynBMIr9kJeGWOAZNErZ4obPBb1z8CoGOCHWMJx3SlkMnGiTnYdjh+cZVtvw2QjAsJB2Tc1L8rX0fJmU5rzumEXcHd5UxX99o8o0nL9Dp+riuzcn7FnbT3iGJF//TL7xAt5tUc19ZrXN1ucaPfup+Up6DZSWLm/lcikolyx/+ySniWFGrdwnDGCkllgApJWGs2LcwRrM1YGI80eVOp12eePwwqZTD1Ws1lNIszlXIZJLZ9H33znHfvTdm8v1+gOvae5J+rlOrdXcNOSRumKvX6lTK2Vu2bYfnqA2epBct0zUXeOjERfrhAMsKhjNrEFhI4Q0LGYe3fMbUeAPHjlnbGEMbwdR4g8nxxvDVZEZvjMIIiTGac80i2vSZzy8ym4uo+1sU3Ri/rugNzqKsLfKpR5AyxzPnVji2MEmgdpDSo+Deg682SNsBjlVgLP3gnrFkHZfP7DvKV1Yu0Q59MrbDh2aWaNT6lEWaD0zdKB/7zLlrHJ0bJ5NyyToup+tbbA32CqWt9zq8Ut/Cs2z2Fcts9W8YN3dYEDrvuAgheHRynq+tXabopdjodQi14kCxiiUlM9k8m4MuiczK9eMqmM7kWcyXYM99ze250m5QdgpMeVW2Uw2MK1BaoYVCSxAWGCHAvvFpMZpW1McSyWL4dWVEz7IJtCIP9FVIZGIwiQjXMWbpRj4XOhvcW5p/vSGNuEu4a4x5EMZ8+atndnVTwjDmqacvUSllmJ4qAXDpyvauIb9OvdHj7IVNxqp5ioV0onEtJa+cWQNIQgaFwLLkbpKQJSXFQob9+8Y5cmiKSimL7VgsLVRxnSTd2vcjzpxb59TzyywuVPnAg0u7C5vXuW7kb0c8vKh0bhpvNuOSSe2t2RjEO2z2vpQsZ6rtxGAKG8+R6F1zYGGJDBYZoDPU64h59ey8Wu5QLXe4leuzeYExitgMGESSIOzS618knQ6xpSZQGjnokcLG0hEqfArp3I9PlUEYkbKSaAtLpsjKpRvHwZ65pcf9xQr7CmW6UZhU55GSL1w+e8t2Sht22j0WhselGez9fiOluNCqsdZt78bAe5ZNMPTJLxZK/ND8gV332EOTs1TTGc41dpLFT8ejG4esNdrkPY+UZSdx3iZZHM3ZDnnHQwrB1LDYxnWev7jGC5fX8cOIxckyTxzfR9Zxqfk9JGI3+kUIgcxZDPTei6xFcmepb/qektR9Q6AjsrZLPpUUcr5ZnyVZWI7wLIdevPd4jLh7uWuM+dp6c4/iYX8QUm/0+PxfvMiPfPIE01Ml+v29P5Y41ly5tsP2Toc41nT7AUsLVVQUEYYx1UoWz7Pp9gK0TtwrmYzHWCXH0cNTWFJy7PA01cpeX+Tps+s8c+rK7vNz5zcIw5iPffjom96ffC7FgX3jtDs+vh+RybiUS1m81N6vrBOdv6HLrRXaBAhh48gchiyx7mOJNLbMARFSO2gTkkS1KN6MrHK3l6bRypP2NBPVkNDPE2wLtlpZbG9AaaKB58XcU2hRzSlq7Ql6fTvRbClcoVyZIpdygUO0w7P045Xdzy559+LZY0AiRVD3n6YVvowxhoJ7mGr6MeSwzFkln+HyRn3P2ARQzt3IEJ3L3XBBRUrxzfVldgY9ZnIF9hXKjKezZGyXyUyOpUKZD88u3eLfXiqUWSqU2Vcs88+f+yZbwypGzcDHlpL5VIFWGOBZFuNDQbDHpxZ2QyYBzl7b4lunr+4+v7Rexw9j7j86yVe2XmCgfBxpE6mYrO0iBORFCs9yqQVt/KEWjBACrdUwFl4OJYYNRSfDZ2YfouLmeLp+EWOgFwdk7RRpy91VjZzL7F2LGXH3ctcYc8e54apod30uXd5O/MhS8Odfeol775ndFaW6zup6g243YG66nMR5b7bY2GwzN1tmvJpneqqIZUlyWY/V9RYCQ7GYJZ/1GBvL8dDJpVsMOcD5i5u3tF29ViMIYzz3zR3y+47PsbbepFhIUywkxuqeozO3zO4T2agEz67SjSwMClvmUWaAaxVxZRHbyoMRhLqBilZInLTXF0Ul5jWyRTe2S3z5rx9hEDg4tmJuqg5CYPoWqmfjdyyUH3Pk2FUeqVymrvNc3dxPGGVwrRQ77Yi//0B+OPO1mM39OP14mVDVSdnTpO0bERZ1/2lq/nd2nzeC59HETGY+CsC9S1OcX92m3b8xC7133zT5zI0ko/l8iZNj0zy3s87Zxg7bfo+c4xJEMS8tb7AvX2Futsh/ce8H3vA7mM7kd3V22mFAd1i39HoWqCUlAxVzuDRGNZ1BaY0lkwvP2ZXtWz5vrdamOrA5UCqx2e+Sdz1CArSIsbGYy1axhOB0a5Vr/RqRVmQtjy4+trBIWy7KaBxp8dHJ4/y9Ax9lub9DLeywLzfBdtBmpV+n6GTwLIf7you7wloj7n7uGmM+M1WiWMzQavXZ2GwNDbkkm/E4fW6Dl06vcvzoDLEyQ9cJtDs+M9MlUqnEhzo7XUJKyS/83Ad58juXOH02cbXksinuOZLhU584wXg1hx9EeK6DlLf3kerbTXaTOmVven8mJwr86Kfu48xwVr84X2X/0q2La3n3CI3gFI1mh0ZLgjuJld7EdUtYYhrXKjKW/hD96CqN4AVidb0ARGLIpXAQxiW+jR89iiTPv3yAge8Mn9ucuzyDbSkqpS7TqT5aKjynzwG7gZQRZ1Ym2T+1wyBQeFaRctZjZcdnaf4VYt0j6yyQdRbJOou39NcOz9zS1gnPMpH+CEJI0p7DT334Ps6v7tDpB8yNF5kfL93yno/NH2CpUGa736Pm96h1+jTWeqAMbcsnrsUszzVYmCi/7nfQjyMOlCpMZXM8vbnKmCdpBgMGw9DIdhiQcRz+avUSlhRUUhl+6uC95F3vtt5zYwwXu9tEWrNUKGPLGwv0oY53qw99cPwI3dinG/sczk+jtOLrO2dphX0ylsfJyhI/v+/D2NJif26Sj01pXm6uUHQyfHjiGEuZccZS+VE5uO8z7pgxF0L8I+D/BVyfovwPxpjPD1/7h8Avktzn/zfGmC+81f6kFHzqB49z6oVlLlzaolhIk/Icnnthmb4f4ToWSwtj5LIeBw9McHDfBK5nEwZ7i1F4XnJIHn14H9VKluWVOikviTi5PgtPv8pv/WoO7hvn6VO9PW3zcxU877uLKqhWcnzo0dfP2HOtIu21h7mw8mWko1DBSZQ/wYMPZRirlim4R5HYnPNP0YuuEpk2AtDXZ+bGQdHldot32/UiK+vjsLvYJ9Fa0o8kFTTGaFJWjCPB99PU4zI9P4eUUMhEuFYT6Zzk/PaTHOonx7nmP8VY+jEqqYdu6c/czuXzqibPsbl3aW+89CDeoBk8P7xYLFLyEi2X8UwWU4eoHsMwrjse1vv8+kuX+dmPlXZ95bdjLJ0l73hgIGXbLLcbif46u0vCBErRDAY0Ax8hBN/euMYPLRzkyPwEq7UbBTdjo1mx28hGxEa4k8R9l6qUvES464nxIzxVu7i7fcFJ81Pzj7KYSy7gf3Ppg6z267tFnW8e96H8NIfy06+5HyPeXYQQ88C/AyZJzuhfN8b8r293P3d6Zv7PjDH/9OYGIcQ9wM8Ax4EZ4EtCiMPDShxviUzG40OPHSKKNS+9vMKZCxv0B8mM0xjD1eUax45Ms7Xd4cOPH+bkiQWeevrSns+4Zxj9IoTg0IHJW0IG3wz33jNLFClOn1snjjVLC1Ue+8D+t7p7tyVWmtMvRYThB/e0L58pcvwTJwDQJqYbXQIMUjgoM0AgEwVE9yDt8BWG5SpehRiKbklEIkSDZcV4rkIpC2ErBCkwmvGqj7AdYk8S+xZpq8xAlNBGU8oFcJM7qDb4DgX3GLbcW+mm4B6h7j+zpy3nHhz2fXv8eJOVzh9ihuMfxOv48RYzuU8znsriSQsvtgiGiVrVdNJnux/ghzHpV11gLzRrfOnaeQaR4kCpwgdnFvjr1SukrSR1/3pw5/VrjDFJjkI3Cimn0qz1EgN+eG4cP4x3F0DDjKaaySIsQyvuMtA+l1p1HpiY5YHyPk5W9jGZLnGhs4FAcKQws0cMy5E2S8N0/RHvO2LgvzPGPCuEyAPPCCG+aIx55e3s5N1ws3wW+G1jTABcFkJcAB4BvvV2dfDwA0s8fepKUtR4uIhUyKcJo5hu12dqKim7dvzoDK5jcf7iFgAH949z+OBbz5ITQvDgyUUePLmYRMe8zuzvrRJFMWF4a6m7m8MapbCHhlNgiRRaxEgcLDIYE2CR2uNmabazbGxVMAaK+R7tTonrM/dMOuLksWvUG2UGfg7HSnPioKFaGhDrgP1LVzh97l584+LhIq0Bx/fvNcYGRaSaGBNjyTRSJAa1mvoAxiha4StgNHn3MOOZJ153/5vBC7uG/Drd6BKRavHj+4/x1OYK3WxACrUrzetZNtmUi/eq9YdnNlf5Z899nUgpEIILrR22+jP8vWMPMZ7KcrXTZLXTJBzGvxsSzZOs45K2k88q3yTXe9/+ae7bn8yYf+vs82z0k0ih/el5OqpLqCM+Nn4vh0vJOTedLjOdfn3Xz4j3H8aYdWB9+LgjhDgNzALvK2P+y0KIvwM8TXJlapDsxJM3bbMybHvbyGU9Hn/kAK5jkc95dLr+rkEVUnD86I3uvtfZ95vlThpySFw+5XKWRmOvW2d6urT7uDMIGPRmUKKO52iQSay4JiBQDWwrS6zadHspzl6c49raJJn0AMsyFHJ9SrmYXj9HOtPmvmMXmZ3sEIYF/H6JaqFEKtUn0hWMqTFWafKBB07RaR6l4DkcnR9HWHuPgdI+670vEpsuUtiUvPsZSz+GEBbjmQ8xnvnQm74IKj24bXtsBhS8Ij9/9CRfdM5z8ezObgr9bK7Ao0cX9qx5RFrx2+eeTww5gDHsDHpcaNVY6bU5Vp3gwzOL/MHFLiiFNjopXmElWiyVVAbXsnl06vYx3UUvtWvMpRAU7Ty2kCzkRtEmdwFvWND5OkKIJRJt8/dWQWchxJeA201lfwX4V8CvkkxgfhX4X4D//Lv47F8CfglgYWHhux7boQOTnL+wSS6XYqfWpdnqk0m7fO4zJ1mYf+/9gKJIceHSFvVGl0olx6H9E7dNJrodTzx2kC9/9fRu6GW1muPB+5NjtlZr8fmnzoB1nOL4RWynQzGXQ8p+UnxYJAZxfXOS0xdmWF6dII4tLCvH9EQNx1Hksx0+8/Fzw2IXCnDJpAz5dA9tmhgmcWSeUCUqkymvR2Vuh0pqHtvuY8nyDYleo4l1D2P6CNJgpan7z+BaFQru4d19erMXway7j158bU+bLbOkrIlE+z2V4b7paebyRfx2xEKuxCP756kW9kY2bfS6BOpWV1NzWHHoUGmMajrLUqHM1XaTQCs8KVnMlbh/bJr7x6bwLJv1Xoe865G297pvHp6Y5XKrnmiTD3lwYpaUPcrOvAt4w4LOAEKIHPAfgf/WGNN+o+2/W96SMTfG/NCb2U4I8X8A18skrQI3T1/mhm2v/uxfB34d4OGHH37zYSBDJsbyfPTDRzn1wjK2JXngvnkeeWj/bpjfewmlNH/+5ZfY2bmesLPJpcvbfPoTJ14zYuZmxqp5/sZnH2Zzq43tWEyM3UheefL0MrHSoKZpbv0UXuY8BPDw4X2sdj5PNzpHqCLOX1lKssrVdeEvi/WtKpVSDykiPGsCiUOoG8MCdOBaYwziVQK1hdYBygRc9yhHqkEreBnXqrCU+zv04sso3SMKTnGl/2coEwI2jj1HzjtBN7y4x5i/WYrucYJ4m3Z4FoPGkXmmsp8gUIrfvfASO4PhHYuBxxbn+cDM/G1lHrKOw1g6w2a/y82rrjnHY7FQwpaSnz9ykm+tLzOWyeLKpKBGUnVIc7q+vSs/8M31ZX7q4HEmMjfCVicyOX7uyElerG0wiGMOFCscLL33JhUj7gxCCIfEkP8HY8zv34k+7mQ0y/TQVwTwE9yoRP3HwG8KIX6NZAH0EPDUnRjD0kL1FgGr9yJXr9VuMuQJW9ttllfqb3r8liWZucm1cp16u7/7WEVj9FtjDFow9+BjdMOLRLpOu1uj3ckk8r5uSK+fotdLIyRo7RGFId2uIJuLhlEwYMsMrlUgUm0UPQxq6LvWCByEsAjUDmCwpEPBPYyJL7Lc/CJ5mhgh6BmXKF5mIIuUvRPf07ETQjKZ/TjV9GOJWqSsIITkm2tXdw15u+mzstzkxWiNF2fW+eA9S7dExFRSGR4Yn8GPY651W4QqpujZ/NyRHP3oDDnnAJV0hoV8cbd4MoBn2VzttKimb8z0fRXxjfWr/MSB43v6KKfSfGR2VK7t+w2R3Gb+G+C0MebX7lQ/d9Jn/j8LIU6STHOuAH8fwBjzshDid0ic/zHwX78dkSzvZ9qd2/t9X6v9u2GslGWjvvdCMVbMIoQg6yyx2jjPMy+MsbVTQimJEAbfT2Ow8WyJ52iqxZhXLhV45L4GyvQTbRKj6ZhLieYLKWL6CAQGicRF6QFKpYmjLJHusDP4Jt3ubxPGl/HQuEKTFSHbOkektil6x19jD94ctsxw4VqX5y48T8+PWHHapIsOGLhyqZ6IVwEt3+frL11mrJBlqrI3/f7TS0eYyRW40m5giTaz2efJOdts9mFHPMlc7rMcKo+RdVyagY8rLYgNz29vcEXXGS/myKZdgjhmud18S/sz4q7iQ8DfBl4UQjw3bNsN1X67uGPG3Bjzt1/ntX8M/OM71ff7jcnbqCACTE289TqNjx9b5E+/fZpwqInuWBYfPL4EQM7dz3deXKDVDinmImpNB2M04DJR8pibEKQzPcCm1gwI4p0kpFG4bGyXWF7PYIk0S9MeM5MZBvEaQoDWLi+em6VWm8Sxltk3+ds8eLSPaxpExhABJWFjC0NJakidJGW/tUXoq5sNvvrCWdJ2G2Oy9Nohq90Wk9n8riEXQpAapu5f3qijtObadpOM53J4bpyUa+9qoF9p/xahujEDH8QD/uTyX7DenWK502Q6WyDoRazstMjisNPus9XqIfOCWCRFoP/Fc9+i4CWJOwdLVR6ZnN+TKDTi+wNjzNd5Mypsb5G7JgP0/cz0VImjh6c5c259t+3YkZnbSt1+t0yW8/zsxx/g8noNY2D/dHU3tjojj7C+/UUwhrTjMF7U9P0iKijy+NFFfH2JWAti3SPj+Rgs0tYsq5vjvHzOQptErKvTyRGEkrnZBgbDxasHqNVKw/hwyZXNbYRwefRIBke4RCYgRJKVHrbIk8t9Fq3Nm1ofUFpzenmLa1tNsmmXE/umKefSrKw/xX2TX8OWEdpIyp19/OlWhTB146ZvJpvHsZI1gQtrOzx/KcnwjWPFV56/wE986F4WJspoExGqvRowf3Yh5szWFjknR8Z1WO+20S3NYW8MR0jOBDvsqB5xxzBZypFzPP567TJj6SwHS1VqG33aYcCnFr/7dYERI94MI2P+HuHxRw5w9PAU9UaPaiVHqZh54ze9SdKuwz2LtwYd2VYaSx2iO9ii2Q0IQgeBRymbxnEM3cEAbaDdExwcV/QHEl/0uLi8AIQIkSQeCWFxcUUyN2tjS4eNnRRSuDgyjxAWyvisbjuYwxlsexahaoQhNKJx+vrDnDvTod55klIuzWNHF1iaem09ka88d4ELa7Xd5xdWd/jc4/sZTz9Jq5dkZ0oUE6kz3GNOMlHaT67v4GFRcBMNFwE0uwMc22Kn1WN5q4E2hu1ml4/ct58ffOAQriwR6iYA59c037qokHj4drIGMVst4BMx5SSLnA+Kab7Su0xOSu4fm+Z8cweARnDDVXa2sc1HZ/eNIlhG3BFGxvw9RLmUvUUM7E5iW5IP3nOAf/+lJrG+fioYJso5PnC0yEpTstnsMDPZJZNOoXQGI306A4UUifqiI/NI4aKUIe8cRosOnu0RKhdLXi/s7IDo00Pg6j6dfhbZm6U/mOb3v1PEsq8wWc6zWe+wXmvzd3/4A3uUEK/T7A72GHKAMFa8eOllTkylaPWSBc9Gd8AgjMjZq/R3DnOoXKWcy7DRaDNVKTA3VuSvX7pMHKtdQw4wCCIurdeZH99mfuqDrPe+gEHxyhVNGBgGvsTQwnXsJJvUzdD3QzJeUiyiamcoFVK4loUafubNbhVtzJ6CGyNGvJ2MjPn3OY8cW+A7Z5dZ3Umq1MxPlFicrNBqZzlx0ENf2iSMDBhJ0DsMKIrZiIFfwR0a8tZgA9vKcvHKDOPVJkuz27xy0cFFkLKnUCZgauoFQhPRDsa4fDWHjB5hpT7BIGpQqzXYbnYTrfYd+L2vPc+h2XE2Gx1KuTQPHZpjrJilH9wqBgbQCyxKuTQLEyWubjboBxG2JSnkqrRCwwuX18mlPSr5DNe2m2w22rx4aR2lNUEU4wzj+bPpRHNnbafNsYVDLFo/S9M/x7Wrr9Da7BCjkI5BFTQXez7TEzku7NSwpODgzBj3lifQ5cRVVE1l6Ech05kbi6yz2QI5ZyR+NeLOMDLm3+ekHJv9M2Psnxnb0+5YKaayn+QV+VuEtDFIwt4x/N49jLmCyck0lzcv0x74NFoRM2OCS6twabXEiUNFPnhc0m08DlhkS09ycH4RWOBizbDeMDgyQiDpBxFhrHBti7TjY4mIr71wkZ4fknIdGt0Bqzst/uYP3M94KYfnWATRDT+4MYqxcooQm/FilkZnwFqtTT+0+Ob5LJp1wigpKpJPe5y6sIptSSbKOS5v1Km1+0yUcuTSHhOlxPDmh0VDXKvIxasTdHoXycQBfSsijjR+XZHzPKoyw/59FbqDkIlyjp/6yH382dWznK5vcaQ0xvHKJJ0oQBnNbK448pePuKOMjPn3OROlHGPFLDutG3IAUgiOLU6Sc3IcrvxdfuurX6PeNlgyzXRlwMcfmKY6+SSL+3p843mFkr1hIlHiIjp7RfJ3P/EhxrMPEesel1rf4rrkbrVgAIU2IaVcGqU0Rod8YPEM+yeSGqy9IEctzJKIzCWulLMr2zx0aI6PnzzEV567gB/FxLpHrniBayLg/EpMaVBn42rA8k6Z81vzWLakO+iQ9RwyKYfNRod6p08UK1KuvauPnk252JbFy1c2yKVdPnxiH0prrmzU+fpLl8hnPLyOjaUkBkPfj5hNFVBGE6iYfMaj1unx70+foh35eJZNNw754PQiJ8enUVqTcV5faXPEewsZa5zm+6tK08iYf58jhOAzjxzjqTPLrOy0yGc8Hjg4y0QpWdg7c61GxhmnbhKNeK0hX7xMrPukPUEUC5xhIQxLphFIHMZIy3uB66n140TxZSzjU8kXODhvs7qeyM96rs1ieYXp4g5hJEm5NsVMn5nqi5yrjeMHdRwrIAg86u0Ka7U2+6cqFHNpXtn4Al++OCC8DF5GUtssI2ML0anSC0KkGODaFpYFxVSLze1lLKAf59hqdtlqdJks5wmjGEtKxopZJko5vvrcRZ585SqR0lzbbtHq+qQdGy9rY4C2FTCwI853a9CFjO1QyqQYC/fqyXx74xonqpMjQz7iHWFkzEeQ9hx+4P4Dt7Rvt7qcXt7kymYDpTXGGOp2j+XtaywNtcrGS4Ju32CJNHnnAIIUYaR44dI6k+Uc/cBHhhtkUi/jOIasI/jY0UdRRz7Bs+c2afUG7C8+R2roS9bG4Dk2nlXj3NXv0PUNQkAxdY2vv/AyW50S2hganR71oMlAg5MyGC2QtkCJiImsQ8ZzCGPFTDVDOb1Cs+2Ttn3StiaV7bHVmsQAjW4fP1RYUjA/UUIpzUajS88PmB8vUcym6AchyhiyKQ+lNfmKR1vd8N/344jIMYyLvaGkymhq/mBkzEe8I4yM+YjXZOBHXNlsEClFu+czCCI26h0yOcFEJaIX+EyPS3aaLr2BjTEOF9Z2mKkWeP7SGmeubbF/bI28u81qfQFtFGkvy76JiANLDfIpl2I2zVipii1ClNIIIShlDVc3G2Rcj2NTTcYKmheuTfDSCsR6QNdXdP0QIcHJKgZDg+95klTeJlKajONg2xJPbqNVwLUdwXozxXghxBIxftgj1g4CQaQUUgiWNxusbrewbQvXljR7A3p+yNJkmVq7z7GFSR49tsAr0Rbn1neo7/QxxlCuZujYIX4ck7Jv/KRsIamm3ntaQCPuTkbGfMRrYgBLSmrtHv0g2m1fXsvzn75+jYOLifDb9KTFvvJn2K6VEcLCkpJ6u0/PD9lp7tC2AiDk0mYeSyjWam2euvxtun4y0+31J/jIwR1qgx5x3MIozWo9zdGJqxyZriOFw8Bv0+4FPLeySN/XxCqpWa8R2CmDlBAEmmKxwkyuwHajy3qtQxy0KaY7BJFL2rGIlEXWlaRdyU4nxpYSrZOQwVhphADHklQLWcIwZr3TZrPRYaKc4+SBGe7fP8Pliw0KxRSF4o3aozntUfRS9KIbM/bHpxdGs/IR7xgjYz7iNSlkPA7OVlmvJ0ZbCkEu5TII4OrKfmbKFkIGRMEkZVkl5SYx1VuNDpc3Guy0e3Q6LgcnYlr9NGFk4TmGazWHYq6LsCy0MnzjtObCyhhL1ZByNkOsbMrpHbKeT9btYVuGpTGf9sDlqcvzKH2jwFwcSpQSSAvSeQe6Nme3t+j7yUz53LpFKeMSxja2ZSgApYwmiATWsHCJJUFFmsgkF4goVgS1NgbwbIuU52DbFl989hzVQpaT4zNcaTf3lLk7UZ3ihxYOcqFZoxsFLORLe1QTR4y404yM+YjXxLEtDs6McX5lhyCKMdqw3e7SG0TUbEnGm+TQ7BSObbHV7HLv0hRnr23T7A7Yanbo+REd4dIPKoSxRBuDLSHWEs+L2Km1qGa3+IGDl8i6Pv0oy1Yrz71zK3h2n6wb4tiKlBMzkdfsH98h53UJohvZsQKwUXjScCDvo8nRDCN6w5BHEGx30riWwrYg7RrmJ2ap9SUb9Q7aaMI4mZFfr7etDWilk1qplqSQTtH3Q75z9hp9P+IXP/0InztwD6e21/DjmP3FCg9PzGJJydHKrUW3R4x4JxgZ8xG3MAgivvTsuaQgsUkyQjs9n6tbTWJl0EZjjODyRpIwc2R+gmo+i21ZWFLQGQRIKXFtizC26fgexigw4A+10DcaEYKAjx45j5QxxggWKtvcO/sCg8hFG+j6Do6lKKV9utLBsyNmSi1cS7HazCMA144Zy/XJp2JS0me9FWILB2NSMOxLG0kQCyIt6EUuO70yhhaT5TyxVskdRD+45Thcn3cPwghEMmP3o5gvnzrPz37sgVskbkeMeDcZSbiNuIW/funSjcryQjBVzrN/porWGte2KOczuLaF0oa1ehvHljx8ZI7uIODI3DiVfIZiNsX8eIlSNoslbSJloY2FMRDFkmbPsFjdQooYDBRSPvOVBralca0YWyhmyx2K6QEG+OrZfXz17H5ibWEAWxpKWZ8nDl/lk/ee4/jsGmO5NkEk8UOBQAMaicKSCsdSuJYm7STaM48cmaNSSJN2HVxpJVWXboMxhjCO8cMIbQyVXAqlkwXaESPeDEKI3xBCbAkhXnrjrb93RjPzEXvQ2nBlY6+hEkIQRoqpSoGdVhc/UtiWhW1JqrkMP/MDJ8mmvWSR9IJgopRlO8n/wbYttPGSaBNXEUYSbSzAYAlFUrnOMF9pkE8Fu37xjWaecq7PseltKtkBr6yOs9PNEkQWltTYMuZjRy5ycLJOPuXz3LUplBZMFDoEkcNYvsdYrsfz16ZZrpXQCLQxCDrUu30O5ss8csjj1MUB/cAj1ppW3991tQBYAoSUhLHaXS/YbvepFLK4zuinM+JN838B/wL4d3eyk9EZOWIPUgpc28KP4j3tlUKG4EpMzw9hmBijtOahw3MIIfh//uo5Tl1Yodbuk025pBybIFLsmyzzsh8SKU3Xl7vG0rZguT7Jg0sbHJrYxgCDyOY7l2dZqRexpaIfuDx1cY6cF7DWKtAPHGwJkUhm5UIY8imfQmrAA/MbrDTyLI01sKQh7UT0QpepYo//9NwRNlqF4fZd4mCZhfzX8OwAZ6FHwanwV/WFm6vF4TkWY4UshWwKKQSObSGloDsIiJVmaar8Dn0jI97vGGO+NizkfEcZGfMRt3Bi3zTfOXejSLLWhr4fEkQxsTLEOjH0addhbafFr/3Hr/Hs+RX8MCYYXgQOz1b58cfv4f4DM/zlqQv84TdeSiQDRFLz1HMdSoUq9V6RF1ckoZKEscXF7Qr7x5I7g/bAY6ebZSzXI4otLGkwRtMNUigt2WxniZTEdRSHS9scn93AtgxXd0rUehkGkQNSc2xmm61OHimg1Xf42LHnqbciwBBEirnSGkvjLi+vjiMFuLbFw4fnSXkOWhtmx4qs19oMwohsyuWRI/O7uugjRgBjQoinb3r+68Maxu8oI2M+4hYePDRLyrU5t7KNEElSzdXNBmnPYaqSY6PRIeU6TJRybDS6nF/bwZICP4yT4tHAaq3DpY06B2aq/M0fuJ9mb8BfPXeRVt/HsROVw+OzGzhC0AkyaG1QGqLYYqeboZQZUO9lyKdCShmf1sCn2U/h2REn51vYUnNycZ1YWQxCl8CLEQKkVFRzfXa66SRmXCpSdoxraQySjBuBGRDFAoPZlb9dqDY5sz6BANKey+xYieuO9LTnsH/mRi3WQ7OjiJURe9gxxjz8bg9iZMxH3IIQguNLUxwfFj3+D19+lmzKxbNteoMQ27JQSqONIe3ZRHGMlhJ1U5k1P4oxxnB6eYuj8xPMVPJ84MgclzfqrGy32W52KRy6xJXtPClnQNqJcGyNZ8c0emk8W2NJQyHtc2J+HSkMfmRzYKKGwJBLhSxUW1zeLlNIBSgt8CMbS2piLanmfLY7OZSxWK6VMUjAIoglOc9npuyz3c6w001+An7o4toWtpW4Uxxb8LkP3cfKTotXrm4mxwV4+PA8lcLbVzhkxIi3i5ExH/GGWJZECMHB2SovXApp9ZPM0NmxImP5DC9c3kDrvUUXsimHTj/g22eWubxeY63eYXasuOuLdyzJty9Msd1xyacy5FIBM6UO85UWKSdmqtQliBwWqg0WKx2yTkzai0g7MVJqjAGjBeOFHgZBrCVKSzq+i2NpypkB+8abbLbyPHJggwNTMRe3xpkotHAszUypSSHVQZsKm+0spzemsCxJJuUwXSnwNz5yPwsTZfZPVzmxb5pGp894MUs+k7rdIRox4l1nZMxHvCHHFyf5xstXSHsuDxyc5YXL64wVs8xWiwAcnRtnu9Vjs9kljhW5tMv+qSpXtxrMj5eItaHd99m+0KXW7tPzA7Qx7HTTWDKi2U8hBVyrC37s5AUK6ZgjUxsYI0i7ARutLBkv4tjMNkoLYiUJ4iSGvRc69EObQipESs1ON01rkMKWmmrOJ5cKcB2PE0tdPnpsk6culrDtNM1+jow7YKrYpRc4fPjQFc5sLhLoOX7w5AHmx0u7+1/OpW9b+WjEiDeDEOK3gI+S+NZXgP/RGPNv3u5+RsZ8xBtyYt80QgheubqJUpq/8eH76A1CGt0BY8UsP/boPVzdbvD8hVXW6x1Srk3Pj8imXSZKObQxaG3YaHTwg5gwVkNfdYp8ClJOgMEwW+pQzAQU0pJAlWj3LTJuH9syVDJtHEthS4HSEtdWaC2pd9P0IxfXVgSRx0Shhy0Na80cE4Ue1VyPek8QBDET+S6fON5jptJiEEokMblUyHw1TTes8VlRx0pPs3/fA3ukbEeMeCsYY372nejnLRlzIcRPA/8IOAY8Yox5+qbX/iHwi4AC/htjzBeG7Z8C/lfAAv5PY8w/eStjGHFnCaOYi+s1gijmYycPMF7MESvNs+dXiLWmF4S8srzB8aVpPnjPEpAk2vzlqQtc2bjGfPEpiqkNxh2fb56v8vzVKpESSAFKQy/IIISDlAOyKUXOC6lmB2RTHoemfLRWxCrGs0KUdhFCk3Fj/MhCSsMLK5N0gxRrzTwf2LdKyo6ZKHSZKbVIu0lForGcTyuY4d65GpKI2NjkPYUlAoSwsWQdRBqwwfoziKcx8gmEfOfqsY4Y8VZ5qzPzl4CfBP71zY1CiHuAnwGOAzPAl4QQ12tm/UvgE8AK8B0hxB8bY155i+MYcQfoDgL+6Jsv0xkkqe5PnVnmgYOzdAYBF9dqrO20WBuKcC28cpWjCxP85BMnsC2LI/PjWOHvkXWTMMOU7fOJ42vMVaf40ksOfhiA8SlnNY70GS9o/KgAOGx3HCyrx3Yny3jBIZMag+gylh2AHgAhttY0+2mC2Ob++Q0OTtaxhMZzFDkrxLMjEMlFI5cKcewdoljg2RG2UNhWDMQkSdACdCOJn9cWBM+A2sRkfg4hRjevI94fvKUz1RhzGrjdLelngd82xgTAZSHEBeCR4WsXjDGXhu/77eG2I2P+HuT5S+u7hrzW7rGy3eKZ8yvYlsVUOcd6vY0xhmZ3QK3dY3m7yXqtw8//0IPMVjWpSLBetwkjRSHjkXIdTqbbrLYPEfRfRAofhE0x1ebIdIedboaXVuf5gSMvU0wHGGHRGEwxnjkOKFBrIEIwNp5jMYjyzFfaHJ/dIp8K0AakMFRyfSSCSElsSyOFwZFbQ8MsAJ18HgYIwQylC4yVqG3pFkY5iPgSOKO6nSPeH9ypaccs8ORNz1eGbQDXXtX+6O0+QAjxS8AvASwsLNyBIY54I67XBfXDiCsbDQwGpTRRrDi/so0lJUGsGIQ3KtxvNDp8+dQFfvrD81TyGSr5JIyv3fO5sL5D0I/RqsbPP/4chYxAyAztfoDWgmq2yUShTTHtk3YiYt0nNAp0G5BgLQI2mB7ChNw7u8lceRPHisi6SZw5IjHXShtcW11PVsVzFLZ1vRC0JDHoDP8ndUmTN7ugV0CvYZz7ECNjPuJ9whsacyHEl4Cp27z0K8aYP3r7h5QwzKD6dYCHH374NWSQRtxJxktZ1uttGp3Brna3a9v0g5B6Z0CkNVprHNui4CZl31KuTb3TpzPIkLcmMSqJ0S5kU9yzMMXOmWl+5MTTzFQCbMsAA1K2i+tkWayuYowAWUCZPpZUlLwViAeAAeMAMnGJoLCkoZq7Ve0QwJJDSduhcWfPzaN+1dYeEAG5JFHIhCA80Gtvz4EcMeId4A2NuTHmh76Hz10F5m96Pjds43XaR7zHOLl/hqsbDbYaHSCxh7m0SxjHeK6NpTQ9Pyn3lvEc0q7DWCGLJUUiRGV/BhF8DdQVEGnS+Qc5sbTC2qaFryrkrBoAnhOSzhwmY/Vo9iKUNgwil0ImwpUxkAfTBeLE0O5a5qG/m1uv9ULsSsi8CXrDz+qBEiCc5C5A977nYzfi/Y2JFXqn/m4P47viTrlZ/hj4TSHEr5EsgB4CniL55R0SQuwjMeI/A/zcHRrDiLdIJuXyN37gPs4sb/EnT75CaqjFYlmS6UqBw3NjbDa7XFqrMVHOMz9WwrIkR+cnSLk2kIP0j+z5zMnyGo2GQycYxxhBxmnjWJJi4WGkspl0LhErjSXFcC1Ggz0J0Q7oJpgIuG7QHZKgqJi3RgzYIHIgLJCTwz5G+isj3j+81dDEnwD+N2Ac+FMhxHPGmB82xrwshPgdkoXNGPivjTFq+J5fBr5A8kv5DWPMy29pD0bcURzL4sS+aebGinzn3DXafR8hBTPVAinXYWmyQjWfYd90Fde22DdV4fji7bxyCZazxJH5s2y3evT9DI7nMF4qIVPHIaiBXsG2rtfRlJD+SYhOD10rJjG2JkXiFpFAGhiQGPfrhl1zqyvl9Ri+1wyALIn/3AV7tFYz4v3DW41m+QPgD17jtX8M/OPbtH8e+Pxb6XfEO085n+GTDx3h/v0z/NE3X94VqAI4Mj/Bjz9+o+qOMYYLqztc3WqQch2OL05SGmZQGusIlnueqfIlIJ8sOAL4f5E4ucU4sAOiCN6HEOkfw8gqhE+B6ZAY2bFkUVRWk/hwHYKUiTvHBEAOTA/okxhmTXKqaxJj/2q3zNAfI1Igs2DvA2sSYR94uw/jiBF3jFEQ7Yjvislyns88eoxTF1fpDULmJ0o8dGhuzzbfOn2VFy6t7z4/s7zF5z50nEqmgQi+hNHDUEB7P1j7IfhS8lxoMLXEIFtjSSji4I/AfRRSHwO1OQwjTIGdSYy7HAOZh/gKyH1AG/Q2qA0gC/Yx0FsQrwMNwCUx6DdHtgxDFo1MXCzWLMKaBPvgHTuOI0a83YyM+YjvmtmxIrNjxdu+NggjXr6ysactUornLlzj44e/hjH+sFVCfAlM/8aGageuv276QB6j1sFohDWNwSJZggHis2AtJVEnMFwg7YJzH+jqcKHUJlnctBODr9vccL9YJDNyAaRBlpOY8tSPIexZsI+MEoZGvK8Yna0j3lZ6gxClb40u6fQ2bjLkN2Fujhi5KcxQ3JCZFXQg/ROI8Nlkti5LmOuLljdvr2vDx+mh+8YkESm6BrpFYsgFSSjidfdLGqxxcE5C5j9Duvd/bzs+YsS7zMiYj3hbKefTZDwnqQd6EzNjr1FmzVpEyCYmXgFRANYTX7jMA8PsYmsOITzwHr/xPtNK3rP7ObPs+sKFA9Yk4EL0HIlb5XoETERixC0So54dvs1A8FWM3gTvEyOhrRHvO+S7PYARdxeWlHz0/oO49o2wvulKgZMHjyOs6T3bCmEjnPsh9TlE+kcQ6U9B+rO7vmohLHCfQMjbXAjcJxDihra4kEXI/3eI1McQ3gch/z8gsj8LskhitCWJ1b45ysUGKRLXjkpcQyY6A+rmJOURI946QohPCSHOCiEuCCH+wZ3oYzQzH/G2szBR4ud/8EHW6x3SXlJeDsDYP44Iv5MYS5EH92GENSzHdt2Au49gdAt0HeTEayoXCmsCk/2FRD8FA/Z+5M3GHcCqYtzHwf8CN1L25U1bxKD7IBToZYhzYO0DvQGMwhJHvD0IISzeAYHBkTEfcUdwHZvFyb0z6sRV8sQbvlfI4nBG/QbbCQ+cY6/5uomXk4VUWUkuDkaSuFksbhj1AEgB6WQbAPnjb9j3iBHfBY/wDggMjoz5iLuX+DyIbLK4aWJQV0mSgmwgGkbOuCAqQ389gMLIBUYe8xHfBWNCiKdvev7rQ22p68zyJgUG3wojYz7i7kUM/fbCBfcDEHlJnLp9NAlFVKtJeKNpJFE1Ipu4dsQojX/Ed8WOMebhd3sQI2M+4u7FPo6IXsYYlUS4OPclCUnuIwh7FqP7EH4DxBgwBoBw7x0Z8xFvN68nPPi2MTLmI+5ahDWOSf1YsuhqWmDNgftBhEwWZBP5AAuilwAF9pFkBj9ixNvLd3gHBAZHxnzEXY2wF15TMEsIAe7J5G/EiDuEMSZ+JwQGR8Z8xIgRI+4w74TA4ChpaMSIESPuAkbGfMSIESPuAkbGfMSIESPuAkbGfMSIESPuAkbGfMSIESPuAoQxt2pPv9cQQmwDV+/AR48BO3fgc79bRuPYy2gcexmN47sbw6IxZvytdCKE+HOuZ5K9MTvGmE+9lf7eDt4XxvxOIYR4+r2Qhjsax2gco3G8f8bwXmXkZhkxYsSIu4CRMR8xYsSIu4Dvd2P+62+8yTvCaBx7GY1jL6Nx3OC9MIb3JN/XPvMRI0aMuFv4fp+ZjxgxYsRdwciYjxgxYsRdwPeFMRdC/LQQ4mUhhBZCPHxT+5IQYiCEeG7497/f9NpDQogXh9W0/7kQ4i1XEnutcQxf+4fDvs4KIX74pvY7WtVbCPGPhBCrNx2DH3mjMd0p3okK5q/T95Xh9/3c9RJgQoiKEOKLQojzw//lN/qc76Hf3xBCbAkhXrqp7bb9ioR/Pjw+LwghHrzD43jHzw0hxLwQ4itCiFeGv5X/97D9HT8m7zuMMXf9H3AMOAL8FfDwTe1LwEuv8Z6ngMdIyrj/GfDpOziOe4DnAQ/YB1wk0T22ho/3A+5wm3ve5mPzj4D//jbttx3THfyO7vi+vkH/V4CxV7X9z8A/GD7+B8D/dAf6/Qjw4M3n4Wv1C/zI8FwUw3Pz23d4HO/4uQFMAw8OH+eBc8P+3vFj8n77+76YmRtjThtjzr7Z7YUQ00DBGPOkSc6Yfwd87g6O47PAbxtjAmPMZeACSUXv3arexpgQuF7V+53gtcZ0p3g39/W1+Czwb4eP/y1vwznwaowxXwPqb7LfzwL/ziQ8CZSG5+qdGsdrccfODWPMujHm2eHjDnCapCDyO35M3m98XxjzN2CfEOKUEOKrQogPD9tmSSpoX2dl2HanuF317tnXaX+7+eXhLepv3ORKeKf6vs473d+rMcBfCCGeEUL80rBt0hizPny8AUy+Q2N5rX7fjWP0rp0bQogl4AHg27y3jsl7krum0pAQ4kvA1G1e+hVjzB+9xtvWgQVjTE0I8RDwh0KI4+/COO4orzcm4F8Bv0pizH4V+F+A//ydG917hieMMatCiAngi0KIMze/aIwxQoh3PI733ep3yLt2bgghcsB/BP5bY0z75iWrd/mYvGe5a4y5MeaHvof3BEAwfPyMEOIicJik6OrcTZu+6Wra38s4eP3q3W+5qvebHZMQ4v8A/uRNjOlO8E73twdjzOrw/5YQ4g9I3AabQohpY8z68NZ96x0azmv1+44eI2PM5vXH7+S5IYRwSAz5fzDG/P6w+T1xTN7LfF+7WYQQ40IIa/h4P3AIuDS8nWsLIR4bRrH8HeBOzqr/GPgZIYQnkgreh0gWYHeregshXJKq3n/8dnb8Kv/iTwDXoxlea0x3iju+r6+FECIrhMhffwx8kuQ4/DHwC8PNfoE7ew7czGv1+8fA3xlGcDwGtG5yPbztvBvnxvD39m+A08aYX7vppffEMXlP826vwL4TfyQn4grJLHwT+MKw/aeAl4HngGeBH7vpPQ+TnLwXgX/BMFv2Toxj+NqvDPs6y02RMySr9eeGr/3KHTg2/x54EXiB5Icx/UZjuoPf0x3d19fpdz9JdMbzw/PhV4btVeDLwHngS0DlDvT9WyTuvmh4bvzia/VLErHxL4fH50Vuioi6Q+N4x88N4AkSt84Lw9/lc8Pz4h0/Ju+3v1E6/4gRI0bcBXxfu1lGjBgx4m5hZMxHjBgx4i5gZMxHjBgx4i5gZMxHjBgx4i5gZMxHjBgx4i5gZMxHjBgx4i5gZMxHjBgx4i7g/w/I6FN2eSnorgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(data_projected[:, 0], data_projected[:, 1], c=digits.target,\n", + " edgecolor='none', alpha=0.5,\n", + " cmap=plt.cm.get_cmap('viridis', 10))\n", + "plt.colorbar(label='digit label', ticks=range(10))\n", + "plt.clim(-0.5, 9.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This plot gives us some good intuition into how well various numbers are separated in the larger 64-dimensional space. For example, zeros and ones have very little overlap in the parameter space.\n", + "Intuitively, this makes sense: a zero is empty in the middle of the image, while a one will generally have ink in the middle.\n", + "On the other hand, there seems to be a more or less continuous spectrum between ones and fours: we can understand this by realizing that some people draw ones with \"hats\" on them, which causes them to look similar to fours.\n", + "\n", + "Overall, however, despite some mixing at the edges, the different groups appear to be fairly well localized in the parameter space: this suggests that even a very straightforward supervised classification algorithm should perform suitably on the full high-dimensional dataset.\n", + "Let's give it a try." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Classification on Digits\n", + "\n", + "Let's apply a classification algorithm to the digits data.\n", + "As we did with the Iris data previously, we will split the data into training and testing sets and fit a Gaussian naive Bayes model:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "Xtrain, Xtest, ytrain, ytest = train_test_split(X, y, random_state=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.naive_bayes import GaussianNB\n", + "model = GaussianNB()\n", + "model.fit(Xtrain, ytrain)\n", + "y_model = model.predict(Xtest)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now that we have the model's predictions, we can gauge its accuracy by comparing the true values of the test set to the predictions:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8333333333333334" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "accuracy_score(ytest, y_model)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With even this very simple model, we find about 83% accuracy for classification of the digits!\n", + "However, this single number doesn't tell us where we've gone wrong. One nice way to do this is to use the *confusion matrix*, which we can compute with Scikit-Learn and plot with Seaborn (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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uDQ6cOGtFt1j+3FZ0bRFIGOx546keBkBE8jppTFGU4CMrhWGGiEwGCohIf+AHwN4kdUVRcpzLDnAyxrwiIm2Ak0AVYLQx5nvrzhRFyTGyNPLRWwi0GCjKNcJlC4OInIILNwIj8DyVSDDG5LNpTFGUnCMrlxLRadsiIsBtQAObphRFyVmyNfLRePgvcIsdO9nHTenAwZyQHB4q/Ktbdf59x/W82bMGfetdB0Cn62N5984b+HrgTeTLHficu2Bug4w4feokL4waRr9et/FA7y5sWr/WEd1gT+DOyqVEt3QvQ4C6gJ2HwNkkLRl38ttTiY2N5c6e3WneoiUVKgYWetGpc1d69OrDs0+NcMipPa9O6SalGEbM3szZ5FRCQ4RXulRj5e4TbDpwiuV/HOMfnasF5NNJr1dKF2DSv/5B3QaNeGbMeJKSkjh39kzAmjb8Oq2ZlR5Dp3Q/twCn8FxO5DhuSgd2Q0Ly2WRPhk5YiBAWIhhj2HE4kYOnzgfs02mvV0I34fQp1q9ZRbtOXQEIDw8nKjrwW2tuSODOyj2G+/xWT4eI/McYc7cTWmlklIy7ft06J0/hGLa8OqkbIvBa9+spkT83czbEs/VgQsD+0uOGNkjPgX17yV+gIONfGs3ObVupFFeNgUOGkztPZEC6Nvw6rZlpYRCR1yHzYcnGmMcucezsi3cBLUSkgPfYzpkcpynROUiqgUGfbiBvRCjPtKtMmUJ5+ONo4F1nt5KSksL237bwyOMjiKtek0n/HMf0D6Zwz4BBOW3NOpfqMawMQLcksAl4B09xETz3JsZf6qBgSIm2hZsSkhPOp7Bu70nqlsrvaGFwUxsAFCkaS0xMLHHVPdOCGrdow4wPpgSs64YE7kzvMRhj3r/Uz2V06wKrgKeAE8aYecAZY8x8Y8x8v91ehJvSgYM9ITl/7jDyRoQCEBEq1C6Vjz3Hnb3HHOxtcDGFChehSGwse/7YBcCalcspXa58wLpuSODOylOJGDzTrqsBF6aOGWMyPasxJhX4p4h86v0zPivnyi5uSgcO9oTkgpHh/K1lBUJCBBFYuP0ov/xxnM41YrmjVgkKRoYzsUcNVuw+zqvzfs9Rr1dKF+CRoSMY99xIkpOSKFaiJMOeej5gTTckcGdl2vV3wHTgb8BDwD3AIWPMk1k+icitQCNjzKisHqPTru2h06512nUagUy7LmyMeRdI8l4K3A9kq49ijJmbnaKgKErOkpXufVpQ/n7vb/59QCF7lhRFyWmyUhhe9K4gNQx4HcgHDLXqSlGUHCUrhWG5MeYEcAJoYdmPoihBQFbuMSwWke9EpJ+IFLTuSFGUHOeyhcEYUxl4GqgOrBKROSLS17ozRVFyjGwtautdlHYC0McYE2rNFfq4EtzlFSD27g+s6Mb/5y7HNU+fTXZcEyDKganpVxK/H1eKSD4RuUdEvgaWAPuB+g77UxQliMhKeVsL/Bd43hiz1K4dRVGCgawUhvImO9cbiqK4nqzcfNSioCjXGLrataIoPmhhUBTFh6w8lagsIj+KyAbv65oi8rR9a1njWk+JtuUVnPUbIsLCMbcy/W+ewbNv9G/Iov+7lcVjO/KfwU3Jmyuwx3w22vbcuXM8cHdP7unVlT53dOadN99wRBeCPyU6Kz2Gt4GReCdTGWPWAb0COqtDpCXjTnzzHWbNnss3X81hx/btAet26tyV1yc5uzynm7yC834Hto9j694TF16P/HAljUfOpdGIOew5ksCAtlWCxmsaERERvPbmFN7/ZBbvf/QZy5csYoMD8fE2/DqtmZXCEGmM+eWifXZGh2QTTYm24xWc9VuiUCS31LqO//z81xf11JmkC9t5IkIDGs1mq21FhMhIz+LuycnJJCcnIxmPB8oWbkiJzkphOCwiFfAGw4pIdzyDnLKMiDQWkcdFpK0fHjMlo2Tc+Ph4J0/hGG7yCs76HXtXXUZ/vJrUix5w/fvBhmyb1J1KxfMz+dstQeH1YlJSUrindzc6tmlCvQYNqV6jZsCaNvw6rZmVwvAIMBmIE5G9wBBg4KUOEJFf0m33B94AooFnRSTTVVxEZICIrBSRlU6uJqTkHLfUvo5DJ8+y5vejPu89MnkpVR7+jN/2naBbw7JX3lwWCA0N5f2PP2fW1z+xacN6dm7fltOWrghZWVdiJ9BaRPICIcaYU1nQDU+3PQBoY4w5JCKvAMuAsZmcS1OigwSn/DaoXJT2dUrSptZ15A4PJTpPOG893IgBExcDkGoMny3dxeCO1Zk2f0eOer0U0dH5qFO3PsuWLKJ8gPmMrk6JTkNERovIaDxBLUPTvb6krogUFJHCeCZqHQIwxiTg4P0JTYm2h1N+n5v+K9Ue/Zyag2dx/+sLWbDxAAMmLqZ87IW1kulQpyTb9p24hMqV8Xoxx44d5dSpkwCcO3uWFcuXUqZsuYB1r4qUaCD9ckS5gY7A5ssckx9PfLwARkSKG2P2i0iUd58jaEq0Ha82/QKIwKSHbiY6Tzgiwobdx3h8iv8Btba8Hjl8iBefHUVqSiqpJpWWrW+hUdPmAeteFSnRPgeI5AK+NcY0z/bJRCKBWGPMZfPHddq1u7yCTruGq2fatT9/i0g8K01lG2NMIuDfogSKolwxsrLgzHr+WsMyFIgBAl91Q1GUoCUrPYaO6baTgXhjTFAMcFIUxQ6XLAwiEornfkLcFfKjKEoQcMnHlcaYFGCriJS+Qn4URQkCsnIpURDY6B3NeOHRpTGmszVXiqLkKFlZ1LZZRvudXM4+I2w9rrSFjUeLbloo1yYF6w1yXPPYCuemULuZQB5Xdrh4ZWsRGQdYLQyKouQcWZlE1SaDfe2dNqIoSvCQaY9BRAYCDwPlRWRdureigcW2jSmKknNc6lLiI+Br4P+A9FOlTxljfOfQKopy1ZBpYUi3wnXvK2dHUZRgQFOiFUXxwfWFIdjTdtNwS5qzbV0nNbfMfY4VM0ax7JMRLJo2HIBurWuzauZTJKx6jTrVAh+Xd622rasLgxvSdtNwS5qzTV0bmu0GvEqDXmNp3OcfAGzcsY9ew95m0Wr/0qBs+7WlmxMp0UGLG9J203BDmrNtXVte07P193i2/XHQEa1ruW2tFAYRuUlE8nm384jIcyLypYiMExHH/ne4IW3XNrb8uqFtjTF8OXEQi6cN5/5ujQLylhHXctva6jFMARK926/iiXob5903NbODNCVayQ6t7vsnN985ji6DJvJgzyY0qlMhpy1dNdjKoQpJl9lQ1xhTx7u9SETWZHZQMKREX6tpzldC12nNfYc8AbKHjp1m9k/rqFe9LIsduLeQxrXctrZ6DBtE5D7v9loRqQuedTDxLnXnBG5I27WNLb/B3raRuSOIisx1Ybt1wzg27tgXkL+LuVbbFuz1GB4AXvUufnsYWCoie4A93vccwQ1pu2m4Lc052Nu2aOFopk/o79ENDWX61yv5fslmOreoyYQn76BIwSg+f+0h1m3dS+dH/p3jfm3r5nhKdLbEPTcgy+EpQH8aY7J8N0SnXeu06zR02rU9nEyJzjLGmJNA4MsDK4pyRXH1OAZFUeyghUFRFB+0MCiK4oMWBkVRfNDCoCiKD1YfVwaC2x5Xugm3LZZrg4IdXraie+yrJ6zo2iKzx5XaY1AUxQctDIqi+KCFQVEUH7QwKIrigxYGRVF8cH1hCPZQTbfq2gqvdUMbhIQISyfezWfPdwPgh/G9WTbpHpZNuoedHw9kxt+7BJVfG5quLgxuCNV0q66N8Fq3tMGgrjeydfeRC69bD/uYBgPfp8HA91m+aR//XbQtqPza0HR1YXBDqKZbdW2E17qhDa4rEkW7+uWZ+s16n/eiIyNoVqs0Xy4JrDC44XtrKwz2MREpZUM7PW4I1XSrrg3c0AYvD2zJU+/MJzXVdxBYp5srMW/NH5xKPO+3V3DH99ZWj+EFYLmILBSRh0UkJisHaRiskpO0v6k8B48n8uu2jP9D9WgRx4yft1xhVzmDraCWncCNQGugJ/CciKwCPgY+N8acyuigqzkM1m26Ngj2NmhY/To6NqhIu3rlyRURRr7ICKY8eSv3j5tL4Xx5qFulOD3//t+g8WtT01aPwRhjUo0x3xlj+gElgIlAOzxFwxHcEKrpVl0bBHsbjJ6ykIp93iTu7re4e8yXzFuzm/vHzQWga5PKfL18B+eSUoLGr01NWz2G/5mYYYxJAmYDs0Uk0qmTuCFU0626NsJr3dYG6bmjeRyvTF/uiJYbvrdWZleKSGVjzG+BaOjsSnvo7EqdXZnGFZ1dGWhRUBQlZ3H1OAZFUeyghUFRFB+0MCiK4oMWBkVRfNDCoCiKD9dcGOyBE2dtyFIsf27HNd32WNFNfs86MFApI258+jsruhvHtbeiq2GwiqJkGS0MiqL4oIVBURQftDAoiuKDFgZFUXzQwqAoig+uLww20nZPnzrJC6OG0a/XbTzQuwub1q91RNdNac7gLr82vMYf2M/AB+6lZ7eO9OrWiU+mfeC3VkRYCJ8PbsicYY34+onGDL6lIgA3VyrMF0Nv5svHGzF90E2UKex/KoGmRHuxlTo86V//oG6DRrz7yRdM+s+nlC5bLmi92khzBnf5teU1NDSMwcOGM/3zObz7wSfMnP4RO3f4p3s+OZW+k36h4/jFdBq/mKZVYqhVugDP316dx6etpdOExcxevZ9H2lTwS19TotNhI2034fQp1q9ZRbtOXQEIDw8nKjpfUHoFO2nO4C6/trwWiYkhrmo1APLmzUvZ8uU5dPCg33qJ5z2DqsJChbBQwWAwxhCV25OXFJ07jPgT5/zSdroNrCQ4iUgE0AvYZ4z5QUTuBG4GNgNveROdAiajZNz169YFpHlg317yFyjI+JdGs3PbVirFVWPgkOHkzhNY8JQNrzZxk98r4XXf3r38tmUz1WvU9FsjROCLoY0oUySSDxfvZu3uE4ycsYF3H6jL2aRUTp9NpvtrS/3SdroNbPUYpgK3AoNF5APgDmA5UA94J7ODgiElOiUlhe2/baFj1zuY+P4McufOw/QPpuSIFyU4SExMYMTfBjP0iZFERUX5rZNqoNOExTR6/mduKJ2fysWiuL9pWfq9s5LGL/zMZyv+ZNRtcQ469x9bmY81jDE1RSQM2AuUMMakiMiHQKZ38oIhJbpI0VhiYmKJq+75zdC4RRtmOFAY3JTmDO7ya9NrclISI4YNoV2HjrRo1cYRzVNnk1m6/SjN4mKIK5GPtbtPADBnzX6m9q/nl6ZbUqJDvJcT0UAkkHZRmQsId+okNtJ2CxUuQpHYWPb8sQuANSuXU7pc+aD0ahM3+bXl1RjDi889Q9ly5bnzrnsD0iqUN4Jo772EXGEhNK5cmO3xp4nOE0bZIp7L1MaVi7Dj4Gm/9N2SEv0usAUIBZ4CPhWRnUAD4BOnTmIrHfiRoSMY99xIkpOSKFaiJMOeej5ovdpIc3abX1te165ZzddzZlOxUmX69vDcjB746BAaNWmWba2YfLl4uXdNQgVCRJi79gA/bz7EUzM2MPHeOqQaw4nEJEZM910aLyu4IiUaQERKABhj9olIATyLz+w2xvySleN12rW7pjGDu/zqtGsPmU27ttVjwBizL932cWCmrXMpiuIsrh7HoCiKHbQwKIrigxYGRVF80MKgKIoPWhgURfHhmkuJtvWYKnd4qOOaxxMdmVLiQ1QuOw+j3LSo7emzyVZ0T1j6N3v8i41WdL/oX1dTohVFyRpaGBRF8UELg6IoPmhhUBTFBy0MiqL4oIVBURQfrE2iulIsXriAcWNfIjUlla6330G//gMC0os/sJ+/Pz2So0cPIwhdbu9Brz53BaXX9KSkpDDg7p7EFC3K2H9ODFjvudGjWDh/HoUKFWbGrC8dcOjBVhvY0D137hyP9L+bpPPnSU5JoUWrtjzw0KCAdf/cvYuxzw6/8Hr/vr3c1W8gXXr0zZZOeKgwpmMc4aFCaIiwZOcxPl69j6LRETzRsjzRucLYcTiRf877neTU7D39d3VhSEvGnfz2VGJjY7mzZ3eat2hJhYoV/dZMSwaOq1qNhIQE7undnfoNGlK+gv+atrymZ+YnH1KmXHkSE/wL+riYTp270qNXH559aoQjemCvDWzpRkRE8NqbU4iMzEtyUhID+91Fg0ZNuL7GDQHplixdljemzrjg/e5ubWnYNPuhKkkphmfmbuVsciqhIoztXIVVf57gthqxzF4fz8KdxxjYuDStqxThm82HsqXt6ksJG+nATicD2/SaxsH4AyxbtICOt93uiB64K83Zlq6IEBmZF4Dk5GSSk5ORjOML/GbtquUUK1GS2GIl/Dr+bHIqAKEhnl4DBmqWiGbx78cA+Om3IzQoWyDbutZ6DCJSHugGlAJSgN+Aj4wxJ506h+10YCeSgdOw6fWNCeN46LHHSUxMcETPFrbawGbbpqSkcH/fO9i7ZzfdevR25LuQnvk/fkvz1v6HsIQIjO9ajeL5cvHVpoPsP3mOhHMppF05HEk4T6HIiOzr+u3oEojIY8CbQG48ydC58BSIZSLS/BLH5XhKdBpOJQPbZsnCeRQoWIgqVavntJWrktDQUN7/+HNmff0TmzasZ+f2bY5pJyUlsXzxfBq38D9kNtXA0M830e+jdVSOyUvJAs4kidnqMfQHanmToScAXxljmovIZOALoHZGBwVDSjTYSQa25XXD2l9ZsnAey5cs5Py5cyQkJPDiM0/y9AvjAtZ2GlttcCUSraOj81Gnbn2WLVlEeQfyJAFWLltEhcpxFCxUOGCthPMprN93irjYvOTNFUqIeIpG4bwRHE08n209m/cY0opOLiAKwBizmyBPiXYyGTg9tpKMBwwaysy5PzJ99neMHvMyderVD8qiAPbawJbusWNHOXXKc+V77uxZVixfShkHlitMY/4P39CsVTu/j8+XO4y8EZ7JexGhwg0l87Hn+FnW7ztFo3IFAWhZuTDLdx3PtratHsM7wAoRWQ40AcYBiEgMcNSpk9hIB3YyGdi2V5u4Kc3Zlu6Rw4d48dlRpKakkmpSadn6Fho1bR6wLsDZM2f4deUyHn3iab81CkaGM6RZOULEc6N08c6jrNx9gj3HzvC3lhXoU/c6dh5J5Puth7OtbTMlujpQFdhgjNmS3eN12rVOu7aJTrv2kNm0a5sp0RsBO38bRVGs4upxDIqi2EELg6IoPmhhUBTFBy0MiqL4oIVBURRfjDGu/wEGXOu6bvLqNl03eXVK92rpMTgXbOBeXTd5dZuum7w6onu1FAZFURxEC4OiKD5cLYXB1hxtN+m6yavbdN3k1RHdoF2iTlGUnONq6TEoiuIgWhgURfHB9YVBRNqJyFYR2S4ijkQai8gUETkoIhuc0PNqlhKRn0Vkk4hsFJHBDunmFpFfRGStV/c5J3S92qEi8quIzHFQc5eIrBeRNSKy0kHdAiIyU0S2iMhmEWnogGYVr8+0n5MiMsQBu4jIUO+/1wYR+VhEAs5kE5HBXr2NAfu0McDiSv0AocAOoDwQAawFqjmg2xSogydLwimvxYE63u1oPOG4TngVIMq7HQ4sBxo45Plx4CNgjoPtsAsoYuG78D7wgHc7Aihg4bt2ACjjgNZ1wO9AHu/rGcC9AWpeD2wAIvHEKfwAVPRXz+09hvrAdmPMTmPMeeAT4LZARY0xC3Awacqrud8Ys9q7fQrYjOcLEqiuMcakLSYR7v0J+I6yiJQEbsWTxhXUiEh+PMX8XQBjzHljzHGHT9MK2GGM+cMhvTAgj4iE4fnPvC9AvarAcmNMojEmGZiPJ6XdL9xeGK4D9qR7/ScO/GezjYiUxROIu9whvVARWQMcBL43xjih+y9gOJDqgFZ6DPCdiKwSEadG/pUDDgFTvZc+74hIXoe00+gFfOyEkDFmL/AKsBvYD5wwxnwXoOwGoImIFBaRSKADnmR2v3B7YXAdIhIFfAYMMQ6tsWGMSTHG1AJKAvVF5PpA9ESkI3DQGLPKCX8X0dgYUwdoDzwiIk0d0AzDc+k3yRhTG0gAHFtCS0QigM7Apw7pFcTTsy0HlADyikj21qe7CGPMZjzZqt8B3wBr8Kzn4hduLwx7+d+qWNK7LygRkXA8RWGaMeZzp/W93eefAf+jhz00AjqLyC48l2ctReTDADWBC78tMcYcBGbhuRwMlD+BP9P1lGbiKRRO0R5YbYyJd0ivNfC7MeaQMSYJ+By4OVBRY8y7xpgbjTFNgWN47mP5hdsLwwqgkoiU81b1XsDsHPaUISIieK6BNxtjJjioGyMiBbzbeYA2QLbDd9NjjBlpjClpjCmLp01/MsYE9BvN6y+viESnbQNt8XSBA8IYcwDYIyJVvLtaAZsC1U1Hbxy6jPCyG2ggIpHe70UrPPecAkJEinr/LI3n/sJH/mq5elFbY0yyiAwCvsVz13iK8YTQBoSIfAw0B4qIyJ/As8aYdwOUbQTcBaz33g8AGGWM+SpA3eLA+yISiqfQzzDGOPZ40WFigVme/wuE4Vmy8BuHtB8Fpnl/QewE7nNC1FvA2gAPOqEHYIxZLiIzgdVAMvArzgyP/kxECgNJwCOB3IDVIdGKovjg9ksJRVEsoIVBURQftDAoiuKDFgZFUXzQwqAoig9aGK5xRKR52uxJEel8qRmq3hmMD/txjr+LyN8C8emkjnJ5tDBcpXjHNWQLY8xsY8zYS3ykAJDtwqC4Dy0MLkNEynozB6Z5cwdmeifNpGUdjBOR1cAdItJWRJaKyGoR+dQ7TyMtw2KL93Pd0mnfKyJveLdjRWSWN+dhrYjcDIwFKnizCV72fu4JEVkhIuvSZ0GIyFMi8puILAKqcBEikl9E/hCREO/rvCKyR0TCRaS/V3OtiHyW9ve76Ph5IlLXu13EO3w7bULZy+k8OTYw6VpCC4M7qQJMNMZUBU7yv7/Fj3gnKf0APA209r5eCTzuDQR5G+gE3AgUy+QcrwHzjTE34Jl3sBHPxKQdxphaxpgnRKQtUAnPfIdawI0i0lREbsQzlLoWnll+9S4WN8acwDPRp5l3V0fg27S5A8aYet5zbwb6ZaNt+uGZrVjPe97+IlIuG8craGFwK3uMMYu92x8CjdO9N937ZwOgGrDYOwT7HqAMEIdnAs824xn2mtnkqJbAJLgwe/NEBp9p6/35Fc/w3jg8haIJMMubDXCSzOevTAd6erd7pfN+vYgsFJH1QB+geibHZ0Rb4G7v33k5UNjrSckGrp4rcQ1z8Tj29K8TvH8KnmyG3uk/KCK1HPQhwP8ZYyZfdI4hWTx+NjBGRArh6b385N3/HtDFGLNWRO7FM2/lYpL56xdb+lg0AR41xnybRQ9KBmiPwZ2Ulr8yDe8EFmXwmWVAIxGpCBeu4SvjmXlZVkQqeD/XO4NjAX4EBnqPDRVPStIpPLF0aXwL3J/u3sV13hl+C4AuIpLHO5uyU0Yn8CZPrQBexRMfl5YfEA3s905T75OJv114iglA94s8DfQei4hUFudDW656tDC4k614Qk42AwXxdvnTY4w5BNwLfCwi64ClQJwx5iyetQ3nem8+HszkHIOBFt7u/Co8+ZRH8FyabBCRl72pQx8BS72fmwlEeyPspuPJ4Pwaz3/+zJgO9OWvywiAZ/BcBiwm8ynkr+ApAL8CRdLtfwfPlOvV4gnznYz2jLONzq50GeKJhZtjjAkopUlRLoX2GBRF8UF7DIqi+KA9BkVRfNDCoCiKD1oYFEXxQQuDoig+aGFQFMWH/weGtiz7HJf4dQAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.metrics import confusion_matrix\n", + "\n", + "mat = confusion_matrix(ytest, y_model)\n", + "\n", + "sns.heatmap(mat, square=True, annot=True, cbar=False, cmap='Blues')\n", + "plt.xlabel('predicted value')\n", + "plt.ylabel('true value');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This shows us where the mislabeled points tend to be: for example, many of the twos here are misclassified as either ones or eights.\n", + "\n", + "Another way to gain intuition into the characteristics of the model is to plot the inputs again, with their predicted labels.\n", + "We'll use green for correct labels and red for incorrect labels; see the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(10, 10, figsize=(8, 8),\n", + " subplot_kw={'xticks':[], 'yticks':[]},\n", + " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", + "\n", + "test_images = Xtest.reshape(-1, 8, 8)\n", + "\n", + "for i, ax in enumerate(axes.flat):\n", + " ax.imshow(test_images[i], cmap='binary', interpolation='nearest')\n", + " ax.text(0.05, 0.05, str(y_model[i]),\n", + " transform=ax.transAxes,\n", + " color='green' if (ytest[i] == y_model[i]) else 'red')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Examining this subset of the data can give us some insight into where the algorithm might be not performing optimally.\n", + "To go beyond our 83% classification success rate, we might switch to a more sophisticated algorithm such as support vector machines (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)), random forests (see [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb)), or another classification approach." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Summary" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In this chapter we covered the essential features of the Scikit-Learn data representation and the Estimator API.\n", + "Regardless of the type of estimator used, the same import/instantiate/fit/predict pattern holds.\n", + "Armed with this information about the Estimator API, you can explore the Scikit-Learn documentation and begin trying out various models on your data.\n", + "\n", + "In the next chapter, we will explore perhaps the most important topic in machine learning: how to select and validate your model." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.03-Hyperparameters-and-Model-Validation.ipynb b/notebooks/05.03-Hyperparameters-and-Model-Validation.ipynb new file mode 100644 index 000000000..af5479981 --- /dev/null +++ b/notebooks/05.03-Hyperparameters-and-Model-Validation.ipynb @@ -0,0 +1,1187 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Hyperparameters and Model Validation" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In the previous chapter, we saw the basic recipe for applying a supervised machine learning model:\n", + "\n", + "1. Choose a class of model.\n", + "2. Choose model hyperparameters.\n", + "3. Fit the model to the training data.\n", + "4. Use the model to predict labels for new data.\n", + "\n", + "The first two pieces of this—the choice of model and choice of hyperparameters—are perhaps the most important part of using these tools and techniques effectively.\n", + "In order to make informed choices, we need a way to *validate* that our model and our hyperparameters are a good fit to the data.\n", + "While this may sound simple, there are some pitfalls that you must avoid to do this effectively." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Thinking About Model Validation\n", + "\n", + "In principle, model validation is very simple: after choosing a model and its hyperparameters, we can estimate how effective it is by applying it to some of the training data and comparing the predictions to the known values.\n", + "\n", + "This section will first show a naive approach to model validation and why it\n", + "fails, before exploring the use of holdout sets and cross-validation for more robust\n", + "model evaluation." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Model Validation the Wrong Way\n", + "\n", + "Let's start with the naive approach to validation using the Iris dataset, which we saw in the previous chapter.\n", + "We will start by loading the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.datasets import load_iris\n", + "iris = load_iris()\n", + "X = iris.data\n", + "y = iris.target" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next, we choose a model and hyperparameters. Here we'll use a *k*-nearest neighbors classifier with `n_neighbors=1`.\n", + "This is a very simple and intuitive model that says \"the label of an unknown point is the same as the label of its closest training point\":" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.neighbors import KNeighborsClassifier\n", + "model = KNeighborsClassifier(n_neighbors=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Then we train the model, and use it to predict labels for data whose labels we already know:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "model.fit(X, y)\n", + "y_model = model.predict(X)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we compute the fraction of correctly labeled points:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "accuracy_score(y, y_model)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see an accuracy score of 1.0, which indicates that 100% of points were correctly labeled by our model!\n", + "But is this truly measuring the expected accuracy? Have we really come upon a model that we expect to be correct 100% of the time?\n", + "\n", + "As you may have gathered, the answer is no.\n", + "In fact, this approach contains a fundamental flaw: *it trains and evaluates the model on the same data*.\n", + "Furthermore, this nearest neighbor model is an *instance-based* estimator that simply stores the training data, and predicts labels by comparing new data to these stored points: except in contrived cases, it will get 100% accuracy every time!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Model Validation the Right Way: Holdout Sets\n", + "\n", + "So what can be done?\n", + "A better sense of a model's performance can be found by using what's known as a *holdout set*: that is, we hold back some subset of the data from the training of the model, and then use this holdout set to check the model's performance.\n", + "This splitting can be done using the `train_test_split` utility in Scikit-Learn:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9066666666666666" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.model_selection import train_test_split\n", + "# split the data with 50% in each set\n", + "X1, X2, y1, y2 = train_test_split(X, y, random_state=0,\n", + " train_size=0.5)\n", + "\n", + "# fit the model on one set of data\n", + "model.fit(X1, y1)\n", + "\n", + "# evaluate the model on the second set of data\n", + "y2_model = model.predict(X2)\n", + "accuracy_score(y2, y2_model)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see here a more reasonable result: the one-nearest-neighbor classifier is about 90% accurate on this holdout set.\n", + "The holdout set is similar to unknown data, because the model has not \"seen\" it before." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Model Validation via Cross-Validation\n", + "\n", + "One disadvantage of using a holdout set for model validation is that we have lost a portion of our data to the model training.\n", + "In the preceding case, half the dataset does not contribute to the training of the model!\n", + "This is not optimal, especially if the initial set of training data is small.\n", + "\n", + "One way to address this is to use *cross-validation*; that is, to do a sequence of fits where each subset of the data is used both as a training set and as a validation set.\n", + "Visually, it might look something like the following figure:\n", + "\n", + "![](images/05.03-2-fold-CV.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#2-Fold-Cross-Validation)\n", + "\n", + "Here we do two validation trials, alternately using each half of the data as a holdout set.\n", + "Using the split data from earlier, we could implement it like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.96, 0.9066666666666666)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y2_model = model.fit(X1, y1).predict(X2)\n", + "y1_model = model.fit(X2, y2).predict(X1)\n", + "accuracy_score(y1, y1_model), accuracy_score(y2, y2_model)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "What comes out are two accuracy scores, which we could combine (by, say, taking the mean) to get a better measure of the global model performance.\n", + "This particular form of cross-validation is a *two-fold cross-validation*—that is, one in which we have split the data into two sets and used each in turn as a validation set.\n", + "\n", + "We could expand on this idea to use even more trials, and more folds in the data—for example, the following figure shows a visual depiction of five-fold cross-validation.\n", + "\n", + "![](images/05.03-5-fold-CV.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#5-Fold-Cross-Validation)\n", + "\n", + "Here we split the data into five groups, and use each of them in turn to evaluate the model fit on the other four-fifths of the data.\n", + "This would be rather tedious to do by hand, but we can use Scikit-Learn's `cross_val_score` convenience routine to do it succinctly:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.96666667, 0.96666667, 0.93333333, 0.93333333, 1. ])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.model_selection import cross_val_score\n", + "cross_val_score(model, X, y, cv=5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Repeating the validation across different subsets of the data gives us an even better idea of the performance of the algorithm.\n", + "\n", + "Scikit-Learn implements a number of cross-validation schemes that are useful in particular situations; these are implemented via iterators in the `model_selection` module.\n", + "For example, we might wish to go to the extreme case in which our number of folds is equal to the number of data points: that is, we train on all points but one in each trial.\n", + "This type of cross-validation is known as *leave-one-out* cross validation, and can be used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 0., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.model_selection import LeaveOneOut\n", + "scores = cross_val_score(model, X, y, cv=LeaveOneOut())\n", + "scores" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Because we have 150 samples, the leave-one-out cross-validation yields scores for 150 trials, and each score indicates either a successful (1.0) or an unsuccessful (0.0) prediction.\n", + "Taking the mean of these gives an estimate of the error rate:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.96" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scores.mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Other cross-validation schemes can be used similarly.\n", + "For a description of what is available in Scikit-Learn, use IPython to explore the ``sklearn.model_selection`` submodule, or take a look at Scikit-Learn's [cross-validation documentation](http://scikit-learn.org/stable/modules/cross_validation.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Selecting the Best Model\n", + "\n", + "Now that we've explored the basics of validation and cross-validation, we will go into a little more depth regarding model selection and selection of hyperparameters.\n", + "These issues are some of the most important aspects of the practice of machine learning, but I find that this information is often glossed over in introductory machine learning tutorials.\n", + "\n", + "Of core importance is the following question: *if our estimator is underperforming, how should we move forward?*\n", + "There are several possible answers:\n", + "\n", + "- Use a more complicated/more flexible model.\n", + "- Use a less complicated/less flexible model.\n", + "- Gather more training samples.\n", + "- Gather more data to add features to each sample.\n", + "\n", + "The answer to this question is often counterintuitive.\n", + "In particular, sometimes using a more complicated model will give worse results, and adding more training samples may not improve your results!\n", + "The ability to determine what steps will improve your model is what separates the successful machine learning practitioners from the unsuccessful." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The Bias-Variance Trade-off\n", + "\n", + "Fundamentally, finding \"the best model\" is about finding a sweet spot in the trade-off between *bias* and *variance*.\n", + "Consider the following figure, which presents two regression fits to the same dataset.\n", + "\n", + "![](images/05.03-bias-variance.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff)\n", + "\n", + "It is clear that neither of these models is a particularly good fit to the data, but they fail in different ways.\n", + "\n", + "The model on the left attempts to find a straight-line fit through the data.\n", + "Because in this case a straight line cannot accurately split the data, the straight-line model will never be able to describe this dataset well.\n", + "Such a model is said to *underfit* the data: that is, it does not have enough flexibility to suitably account for all the features in the data. Another way of saying this is that the model has high bias.\n", + "\n", + "The model on the right attempts to fit a high-order polynomial through the data.\n", + "Here the model fit has enough flexibility to nearly perfectly account for the fine features in the data, but even though it very accurately describes the training data, its precise form seems to be more reflective of the particular noise properties of the data than of the intrinsic properties of whatever process generated that data.\n", + "Such a model is said to *overfit* the data: that is, it has so much flexibility that the model ends up accounting for random errors as well as the underlying data distribution. Another way of saying this is that the model has high variance." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "To look at this in another light, consider what happens if we use these two models to predict the *y*-values for some new data.\n", + "In the plots in the following figure, the red/lighter points indicate data that is omitted from the training set.\n", + "\n", + "![](images/05.03-bias-variance-2.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff-Metrics)\n", + "\n", + "The score here is the $R^2$ score, or [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), which measures how well a model performs relative to a simple mean of the target values. $R^2=1$ indicates a perfect match, $R^2=0$ indicates the model does no better than simply taking the mean of the data, and negative values mean even worse models.\n", + "From the scores associated with these two models, we can make an observation that holds more generally:\n", + "\n", + "- For high-bias models, the performance of the model on the validation set is similar to the performance on the training set.\n", + "- For high-variance models, the performance of the model on the validation set is far worse than the performance on the training set." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "If we imagine that we have some ability to tune the model complexity, we would expect the training score and validation score to behave as illustrated in the following figure:\n", + "\n", + "![](images/05.03-validation-curve.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Validation-Curve)\n", + "\n", + "The diagram shown here is often called a *validation curve*, and we see the following features:\n", + "\n", + "- The training score is everywhere higher than the validation score. This is generally the case: the model will be a better fit to data it has seen than to data it has not seen.\n", + "- For very low model complexity (a high-bias model), the training data is underfit, which means that the model is a poor predictor both for the training data and for any previously unseen data.\n", + "- For very high model complexity (a high-variance model), the training data is overfit, which means that the model predicts the training data very well, but fails for any previously unseen data.\n", + "- For some intermediate value, the validation curve has a maximum. This level of complexity indicates a suitable trade-off between bias and variance.\n", + "\n", + "The means of tuning the model complexity varies from model to model; when we discuss individual models in depth in later chapters, we will see how each model allows for such tuning." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Validation Curves in Scikit-Learn\n", + "\n", + "Let's look at an example of using cross-validation to compute the validation curve for a class of models.\n", + "Here we will use a *polynomial regression* model: this is a generalized linear model in which the degree of the polynomial is a tunable parameter.\n", + "For example, a degree-1 polynomial fits a straight line to the data; for model parameters $a$ and $b$:\n", + "\n", + "$$\n", + "y = ax + b\n", + "$$\n", + "\n", + "A degree-3 polynomial fits a cubic curve to the data; for model parameters $a, b, c, d$:\n", + "\n", + "$$\n", + "y = ax^3 + bx^2 + cx + d\n", + "$$\n", + "\n", + "We can generalize this to any number of polynomial features.\n", + "In Scikit-Learn, we can implement this with a linear regression classifier combined with the polynomial preprocessor.\n", + "We will use a *pipeline* to string these operations together (we will discuss polynomial features and pipelines more fully in [Feature Engineering](05.04-Feature-Engineering.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.pipeline import make_pipeline\n", + "\n", + "def PolynomialRegression(degree=2, **kwargs):\n", + " return make_pipeline(PolynomialFeatures(degree),\n", + " LinearRegression(**kwargs))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now let's create some data to which we will fit our model:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "def make_data(N, err=1.0, rseed=1):\n", + " # randomly sample the data\n", + " rng = np.random.RandomState(rseed)\n", + " X = rng.rand(N, 1) ** 2\n", + " y = 10 - 1. / (X.ravel() + 0.1)\n", + " if err > 0:\n", + " y += err * rng.randn(N)\n", + " return X, y\n", + "\n", + "X, y = make_data(40)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can now visualize our data, along with polynomial fits of several degrees (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "\n", + "X_test = np.linspace(-0.1, 1.1, 500)[:, None]\n", + "\n", + "plt.scatter(X.ravel(), y, color='black')\n", + "axis = plt.axis()\n", + "for degree in [1, 3, 5]:\n", + " y_test = PolynomialRegression(degree).fit(X, y).predict(X_test)\n", + " plt.plot(X_test.ravel(), y_test, label='degree={0}'.format(degree))\n", + "plt.xlim(-0.1, 1.0)\n", + "plt.ylim(-2, 12)\n", + "plt.legend(loc='best');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The knob controlling model complexity in this case is the degree of the polynomial, which can be any nonnegative integer.\n", + "A useful question to answer is this: what degree of polynomial provides a suitable trade-off between bias (underfitting) and variance (overfitting)?\n", + "\n", + "We can make progress in this by visualizing the validation curve for this particular data and model; this can be done straightforwardly using the ``validation_curve`` convenience routine provided by Scikit-Learn.\n", + "Given a model, data, parameter name, and a range to explore, this function will automatically compute both the training score and the validation score across the range (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.model_selection import validation_curve\n", + "degree = np.arange(0, 21)\n", + "train_score, val_score = validation_curve(\n", + " PolynomialRegression(), X, y,\n", + " param_name='polynomialfeatures__degree',\n", + " param_range=degree, cv=7)\n", + "\n", + "plt.plot(degree, np.median(train_score, 1),\n", + " color='blue', label='training score')\n", + "plt.plot(degree, np.median(val_score, 1),\n", + " color='red', label='validation score')\n", + "plt.legend(loc='best')\n", + "plt.ylim(0, 1)\n", + "plt.xlabel('degree')\n", + "plt.ylabel('score');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This shows precisely the qualitative behavior we expect: the training score is everywhere higher than the validation score, the training score is monotonically improving with increased model complexity, and the validation score reaches a maximum before dropping off as the model becomes overfit.\n", + "\n", + "From the validation curve, we can determine that the optimal trade-off between bias and variance is found for a third-order polynomial. We can compute and display this fit over the original data as follows (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(X.ravel(), y)\n", + "lim = plt.axis()\n", + "y_test = PolynomialRegression(3).fit(X, y).predict(X_test)\n", + "plt.plot(X_test.ravel(), y_test);\n", + "plt.axis(lim);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that finding this optimal model did not actually require us to compute the training score, but examining the relationship between the training score and validation score can give us useful insight into the performance of the model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Learning Curves\n", + "\n", + "One important aspect of model complexity is that the optimal model will generally depend on the size of your training data.\n", + "For example, let's generate a new dataset with five times as many points (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X2, y2 = make_data(200)\n", + "plt.scatter(X2.ravel(), y2);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now let's duplicate the preceding code to plot the validation curve for this larger dataset; for reference, we'll overplot the previous results as well (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "degree = np.arange(21)\n", + "train_score2, val_score2 = validation_curve(\n", + " PolynomialRegression(), X2, y2,\n", + " param_name='polynomialfeatures__degree',\n", + " param_range=degree, cv=7)\n", + "\n", + "plt.plot(degree, np.median(train_score2, 1),\n", + " color='blue', label='training score')\n", + "plt.plot(degree, np.median(val_score2, 1),\n", + " color='red', label='validation score')\n", + "plt.plot(degree, np.median(train_score, 1),\n", + " color='blue', alpha=0.3, linestyle='dashed')\n", + "plt.plot(degree, np.median(val_score, 1),\n", + " color='red', alpha=0.3, linestyle='dashed')\n", + "plt.legend(loc='lower center')\n", + "plt.ylim(0, 1)\n", + "plt.xlabel('degree')\n", + "plt.ylabel('score');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The solid lines show the new results, while the fainter dashed lines show the results on the previous smaller dataset.\n", + "It is clear from the validation curve that the larger dataset can support a much more complicated model: the peak here is probably around a degree of 6, but even a degree-20 model is not seriously overfitting the data—the validation and training scores remain very close.\n", + "\n", + "So, the behavior of the validation curve has not one but two important inputs: the model complexity and the number of training points.\n", + "We can gain further insight by exploring the behavior of the model as a function of the number of training points, which we can do by using increasingly larger subsets of the data to fit our model.\n", + "A plot of the training/validation score with respect to the size of the training set is sometimes known as a *learning curve.*\n", + "\n", + "The general behavior we would expect from a learning curve is this:\n", + "\n", + "- A model of a given complexity will *overfit* a small dataset: this means the training score will be relatively high, while the validation score will be relatively low.\n", + "- A model of a given complexity will *underfit* a large dataset: this means that the training score will decrease, but the validation score will increase.\n", + "- A model will never, except by chance, give a better score to the validation set than the training set: this means the curves should keep getting closer together but never cross.\n", + "\n", + "With these features in mind, we would expect a learning curve to look qualitatively like that shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.03-learning-curve.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Learning-Curve)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The notable feature of the learning curve is the convergence to a particular score as the number of training samples grows.\n", + "In particular, once you have enough points that a particular model has converged, *adding more training data will not help you!*\n", + "The only way to increase model performance in this case is to use another (often more complex) model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Learning Curves in Scikit-Learn\n", + "\n", + "Scikit-Learn offers a convenient utility for computing such learning curves from your models; here we will compute a learning curve for our original dataset with a second-order polynomial model and a ninth-order polynomial (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.model_selection import learning_curve\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "\n", + "for i, degree in enumerate([2, 9]):\n", + " N, train_lc, val_lc = learning_curve(\n", + " PolynomialRegression(degree), X, y, cv=7,\n", + " train_sizes=np.linspace(0.3, 1, 25))\n", + "\n", + " ax[i].plot(N, np.mean(train_lc, 1),\n", + " color='blue', label='training score')\n", + " ax[i].plot(N, np.mean(val_lc, 1),\n", + " color='red', label='validation score')\n", + " ax[i].hlines(np.mean([train_lc[-1], val_lc[-1]]), N[0],\n", + " N[-1], color='gray', linestyle='dashed')\n", + "\n", + " ax[i].set_ylim(0, 1)\n", + " ax[i].set_xlim(N[0], N[-1])\n", + " ax[i].set_xlabel('training size')\n", + " ax[i].set_ylabel('score')\n", + " ax[i].set_title('degree = {0}'.format(degree), size=14)\n", + " ax[i].legend(loc='best')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This is a valuable diagnostic, because it gives us a visual depiction of how our model responds to increasing amounts of training data.\n", + "In particular, when the learning curve has already converged (i.e., when the training and validation curves are already close to each other) *adding more training data will not significantly improve the fit!*\n", + "This situation is seen in the left panel, with the learning curve for the degree-2 model.\n", + "\n", + "The only way to increase the converged score is to use a different (usually more complicated) model.\n", + "We see this in the right panel: by moving to a much more complicated model, we increase the score of convergence (indicated by the dashed line), but at the expense of higher model variance (indicated by the difference between the training and validation scores).\n", + "If we were to add even more data points, the learning curve for the more complicated model would eventually converge.\n", + "\n", + "Plotting a learning curve for your particular choice of model and dataset can help you to make this type of decision about how to move forward in improving your analysis." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Validation in Practice: Grid Search\n", + "\n", + "The preceding discussion is meant to give you some intuition into the trade-off between bias and variance, and its dependence on model complexity and training set size.\n", + "In practice, models generally have more than one knob to turn, meaning plots of validation and learning curves change from lines to multidimensional surfaces.\n", + "In these cases, such visualizations are difficult, and we would rather simply find the particular model that maximizes the validation score.\n", + "\n", + "Scikit-Learn provides some tools to make this kind of search more convenient: here we'll consider the use of grid search to find the optimal polynomial model.\n", + "We will explore a two-dimensional grid of model features, namely the polynomial degree and the flag telling us whether to fit the intercept.\n", + "This can be set up using Scikit-Learn's `GridSearchCV` meta-estimator:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.model_selection import GridSearchCV\n", + "\n", + "param_grid = {'polynomialfeatures__degree': np.arange(21),\n", + " 'linearregression__fit_intercept': [True, False]}\n", + "\n", + "grid = GridSearchCV(PolynomialRegression(), param_grid, cv=7)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that like a normal estimator, this has not yet been applied to any data.\n", + "Calling the ``fit`` method will fit the model at each grid point, keeping track of the scores along the way:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "grid.fit(X, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now that the model is fit, we can ask for the best parameters as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'linearregression__fit_intercept': False, 'polynomialfeatures__degree': 4}" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grid.best_params_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, if we wish, we can use the best model and show the fit to our data using code from before (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "model = grid.best_estimator_\n", + "\n", + "plt.scatter(X.ravel(), y)\n", + "lim = plt.axis()\n", + "y_test = model.fit(X, y).predict(X_test)\n", + "plt.plot(X_test.ravel(), y_test);\n", + "plt.axis(lim);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Other options in `GridSearchCV` include the ability to specify a custom scoring function, to parallelize the computations, to do randomized searches, and more.\n", + "For more information, see the examples in [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) and [Feature Engineering: Working with Images](05.14-Image-Features.ipynb), or refer to Scikit-Learn's [grid search documentation](http://Scikit-Learn.org/stable/modules/grid_search.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Summary\n", + "\n", + "In this chapter we began to explore the concept of model validation and hyperparameter optimization, focusing on intuitive aspects of the bias–variance trade-off and how it comes into play when fitting models to data.\n", + "In particular, we found that the use of a validation set or cross-validation approach is vital when tuning parameters in order to avoid overfitting for more complex/flexible models.\n", + "\n", + "In later chapters, we will discuss the details of particularly useful models, what tuning is available for these models, and how these free parameters affect model complexity.\n", + "Keep the lessons of this chapter in mind as you read on and learn about these machine learning approaches!" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.04-Feature-Engineering.ipynb b/notebooks/05.04-Feature-Engineering.ipynb new file mode 100644 index 000000000..507d74241 --- /dev/null +++ b/notebooks/05.04-Feature-Engineering.ipynb @@ -0,0 +1,952 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Feature Engineering" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The previous chapters outlined the fundamental ideas of machine learning, but all of the examples assumed that you have numerical data in a tidy, `[n_samples, n_features]` format.\n", + "In the real world, data rarely comes in such a form.\n", + "With this in mind, one of the more important steps in using machine learning in practice is *feature engineering*: that is, taking whatever information you have about your problem and turning it into numbers that you can use to build your feature matrix.\n", + "\n", + "In this chapter, we will cover a few common examples of feature engineering tasks: we'll look at features for representing categorical data, text, and images.\n", + "Additionally, we will discuss derived features for increasing model complexity and imputation of missing data.\n", + "This process is commonly referred to as vectorization, as it involves converting arbitrary data into well-behaved vectors." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Categorical Features\n", + "\n", + "One common type of nonnumerical data is *categorical* data.\n", + "For example, imagine you are exploring some data on housing prices, and along with numerical features like \"price\" and \"rooms,\" you also have \"neighborhood\" information.\n", + "For example, your data might look something like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "data = [\n", + " {'price': 850000, 'rooms': 4, 'neighborhood': 'Queen Anne'},\n", + " {'price': 700000, 'rooms': 3, 'neighborhood': 'Fremont'},\n", + " {'price': 650000, 'rooms': 3, 'neighborhood': 'Wallingford'},\n", + " {'price': 600000, 'rooms': 2, 'neighborhood': 'Fremont'}\n", + "]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "You might be tempted to encode this data with a straightforward numerical mapping:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "{'Queen Anne': 1, 'Fremont': 2, 'Wallingford': 3};" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But it turns out that this is not generally a useful approach in Scikit-Learn. The package's models make the fundamental assumption that numerical features reflect algebraic quantities, so such a mapping would imply, for example, that *Queen Anne < Fremont < Wallingford*, or even that *Wallingford–Queen Anne = Fremont*, which (niche demographic jokes aside) does not make much sense.\n", + "\n", + "In this case, one proven technique is to use *one-hot encoding*, which effectively creates extra columns indicating the presence or absence of a category with a value of 1 or 0, respectively.\n", + "When your data takes the form of a list of dictionaries, Scikit-Learn's ``DictVectorizer`` will do this for you:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 0, 850000, 4],\n", + " [ 1, 0, 0, 700000, 3],\n", + " [ 0, 0, 1, 650000, 3],\n", + " [ 1, 0, 0, 600000, 2]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.feature_extraction import DictVectorizer\n", + "vec = DictVectorizer(sparse=False, dtype=int)\n", + "vec.fit_transform(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that the `neighborhood` column has been expanded into three separate columns representing the three neighborhood labels, and that each row has a 1 in the column associated with its neighborhood.\n", + "With these categorical features thus encoded, you can proceed as normal with fitting a Scikit-Learn model.\n", + "\n", + "To see the meaning of each column, you can inspect the feature names:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['neighborhood=Fremont', 'neighborhood=Queen Anne',\n", + " 'neighborhood=Wallingford', 'price', 'rooms'], dtype=object)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vec.get_feature_names_out()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "There is one clear disadvantage of this approach: if your category has many possible values, this can *greatly* increase the size of your dataset.\n", + "However, because the encoded data contains mostly zeros, a sparse output can be a very efficient solution:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "<4x5 sparse matrix of type ''\n", + "\twith 12 stored elements in Compressed Sparse Row format>" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vec = DictVectorizer(sparse=True, dtype=int)\n", + "vec.fit_transform(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Nearly all of the Scikit-Learn estimators accept such sparse inputs when fitting and evaluating models. `sklearn.preprocessing.OneHotEncoder` and `sklearn.feature_extraction.FeatureHasher` are two additional tools that Scikit-Learn includes to support this type of encoding." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Text Features\n", + "\n", + "Another common need in feature engineering is to convert text to a set of representative numerical values.\n", + "For example, most automatic mining of social media data relies on some form of encoding the text as numbers.\n", + "One of the simplest methods of encoding this type of data is by *word counts*: you take each snippet of text, count the occurrences of each word within it, and put the results in a table.\n", + "\n", + "For example, consider the following set of three phrases:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "sample = ['problem of evil',\n", + " 'evil queen',\n", + " 'horizon problem']" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For a vectorization of this data based on word count, we could construct individual columns representing the words \"problem,\" \"of,\" \"evil,\" and so on.\n", + "While doing this by hand would be possible for this simple example, the tedium can be avoided by using Scikit-Learn's `CountVectorizer`:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "<3x5 sparse matrix of type ''\n", + "\twith 7 stored elements in Compressed Sparse Row format>" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.feature_extraction.text import CountVectorizer\n", + "\n", + "vec = CountVectorizer()\n", + "X = vec.fit_transform(sample)\n", + "X" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result is a sparse matrix recording the number of times each word appears; it is easier to inspect if we convert this to a `DataFrame` with labeled columns:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + 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" + ], + "text/plain": [ + " evil horizon of problem queen\n", + "0 1 0 1 1 0\n", + "1 1 0 0 0 1\n", + "2 0 1 0 1 0" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "pd.DataFrame(X.toarray(), columns=vec.get_feature_names_out())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "There are some issues with using a simple raw word count, however: it can lead to features that put too much weight on words that appear very frequently, and this can be suboptimal in some classification algorithms.\n", + "One approach to fix this is known as *term frequency–inverse document frequency* (*TF–IDF*), which weights the word counts by a measure of how often they appear in the documents.\n", + "The syntax for computing these features is similar to the previous example:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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evilhorizonofproblemqueen
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" + ], + "text/plain": [ + " evil horizon of problem queen\n", + "0 0.517856 0.000000 0.680919 0.517856 0.000000\n", + "1 0.605349 0.000000 0.000000 0.000000 0.795961\n", + "2 0.000000 0.795961 0.000000 0.605349 0.000000" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.feature_extraction.text import TfidfVectorizer\n", + "vec = TfidfVectorizer()\n", + "X = vec.fit_transform(sample)\n", + "pd.DataFrame(X.toarray(), columns=vec.get_feature_names_out())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For an example of using TF-IDF in a classification problem, see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Image Features\n", + "\n", + "Another common need is to suitably encode images for machine learning analysis.\n", + "The simplest approach is what we used for the digits data in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb): simply using the pixel values themselves.\n", + "But depending on the application, such an approach may not be optimal.\n", + "\n", + "A comprehensive summary of feature extraction techniques for images is well beyond the scope of this chapter, but you can find excellent implementations of many of the standard approaches in the [Scikit-Image project](http://scikit-image.org).\n", + "For one example of using Scikit-Learn and Scikit-Image together, see [Feature Engineering: Working with Images](05.14-Image-Features.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Derived Features\n", + "\n", + "Another useful type of feature is one that is mathematically derived from some input features.\n", + "We saw an example of this in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) when we constructed *polynomial features* from our input data.\n", + "We saw that we could convert a linear regression into a polynomial regression not by changing the model, but by transforming the input!\n", + "\n", + "For example, this data clearly cannot be well described by a straight line (see Figure 40-1):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "x = np.array([1, 2, 3, 4, 5])\n", + "y = np.array([4, 2, 1, 3, 7])\n", + "plt.scatter(x, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can still fit a line to the data using `LinearRegression` and get the optimal result, as shown in Figure 40-2:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "X = x[:, np.newaxis]\n", + "model = LinearRegression().fit(X, y)\n", + "yfit = model.predict(X)\n", + "plt.scatter(x, y)\n", + "plt.plot(x, yfit);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But it's clear that we need a more sophisticated model to describe the relationship between $x$ and $y$.\n", + "\n", + "One approach to this is to transform the data, adding extra columns of features to drive more flexibility in the model.\n", + "For example, we can add polynomial features to the data this way:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. 1. 1.]\n", + " [ 2. 4. 8.]\n", + " [ 3. 9. 27.]\n", + " [ 4. 16. 64.]\n", + " [ 5. 25. 125.]]\n" + ] + } + ], + "source": [ + "from sklearn.preprocessing import PolynomialFeatures\n", + "poly = PolynomialFeatures(degree=3, include_bias=False)\n", + "X2 = poly.fit_transform(X)\n", + "print(X2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The derived feature matrix has one column representing $x$, a second column representing $x^2$, and a third column representing $x^3$.\n", + "Computing a linear regression on this expanded input gives a much closer fit to our data, as you can see in Figure 40-3:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "model = LinearRegression().fit(X2, y)\n", + "yfit = model.predict(X2)\n", + "plt.scatter(x, y)\n", + "plt.plot(x, yfit);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This idea of improving a model not by changing the model, but by transforming the inputs, is fundamental to many of the more powerful machine learning methods.\n", + "We'll explore this idea further in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) in the context of *basis function regression*.\n", + "More generally, this is one motivational path to the powerful set of techniques known as *kernel methods*, which we will explore in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Imputation of Missing Data\n", + "\n", + "Another common need in feature engineering is handling of missing data.\n", + "We discussed the handling of missing data in `DataFrame` objects in [Handling Missing Data](03.04-Missing-Values.ipynb), and saw that `NaN` is often is used to mark missing values.\n", + "For example, we might have a dataset that looks like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from numpy import nan\n", + "X = np.array([[ nan, 0, 3 ],\n", + " [ 3, 7, 9 ],\n", + " [ 3, 5, 2 ],\n", + " [ 4, nan, 6 ],\n", + " [ 8, 8, 1 ]])\n", + "y = np.array([14, 16, -1, 8, -5])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "When applying a typical machine learning model to such data, we will need to first replace the missing values with some appropriate fill value.\n", + "This is known as *imputation* of missing values, and strategies range from simple (e.g., replacing missing values with the mean of the column) to sophisticated (e.g., using matrix completion or a robust model to handle such data).\n", + "\n", + "The sophisticated approaches tend to be very application-specific, and we won't dive into them here.\n", + "For a baseline imputation approach using the mean, median, or most frequent value, Scikit-Learn provides the `SimpleImputer` class:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4.5, 0. , 3. ],\n", + " [3. , 7. , 9. ],\n", + " [3. , 5. , 2. ],\n", + " [4. , 5. , 6. ],\n", + " [8. , 8. , 1. ]])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.impute import SimpleImputer\n", + "imp = SimpleImputer(strategy='mean')\n", + "X2 = imp.fit_transform(X)\n", + "X2" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that in the resulting data, the two missing values have been replaced with the mean of the remaining values in the column. This imputed data can then be fed directly into, for example, a `LinearRegression` estimator:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([13.14869292, 14.3784627 , -1.15539732, 10.96606197, -5.33782027])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model = LinearRegression().fit(X2, y)\n", + "model.predict(X2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Feature Pipelines\n", + "\n", + "With any of the preceding examples, it can quickly become tedious to do the transformations by hand, especially if you wish to string together multiple steps.\n", + "For example, we might want a processing pipeline that looks something like this:\n", + "\n", + "1. Impute missing values using the mean.\n", + "2. Transform features to quadratic.\n", + "3. Fit a linear regression model.\n", + "\n", + "To streamline this type of processing pipeline, Scikit-Learn provides a ``Pipeline`` object, which can be used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.pipeline import make_pipeline\n", + "\n", + "model = make_pipeline(SimpleImputer(strategy='mean'),\n", + " PolynomialFeatures(degree=2),\n", + " LinearRegression())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This pipeline looks and acts like a standard Scikit-Learn object, and will apply all the specified steps to any input data:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[14 16 -1 8 -5]\n", + "[14. 16. -1. 8. -5.]\n" + ] + } + ], + "source": [ + "model.fit(X, y) # X with missing values, from above\n", + "print(y)\n", + "print(model.predict(X))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "All the steps of the model are applied automatically.\n", + "Notice that for simplicity, in this demonstration we've applied the model to the data it was trained on; this is why it was able to perfectly predict the result (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for further discussion of this).\n", + "\n", + "For some examples of Scikit-Learn pipelines in action, see the following chapter on naive Bayes classification, as well as [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) and [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.05-Naive-Bayes.ipynb b/notebooks/05.05-Naive-Bayes.ipynb new file mode 100644 index 000000000..c7eb85078 --- /dev/null +++ b/notebooks/05.05-Naive-Bayes.ipynb @@ -0,0 +1,756 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: Naive Bayes Classification" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The previous four chapters have given a general overview of the concepts of machine learning.\n", + "In this chapter and the ones that follow, we will be taking a\n", + "closer look first at four algorithms for supervised learning,\n", + "and then at four algorithms for unsupervised learning.\n", + "We start here with our first supervised method, naive Bayes classification.\n", + "\n", + "Naive Bayes models are a group of extremely fast and simple classification algorithms that are often suitable for very high-dimensional datasets.\n", + "Because they are so fast and have so few tunable parameters, they end up being useful as a quick-and-dirty baseline for a classification problem.\n", + "This chapter will provide an intuitive explanation of how naive Bayes classifiers work, followed by a few examples of them in action on some datasets." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Bayesian Classification\n", + "\n", + "Naive Bayes classifiers are built on Bayesian classification methods.\n", + "These rely on Bayes's theorem, which is an equation describing the relationship of conditional probabilities of statistical quantities.\n", + "In Bayesian classification, we're interested in finding the probability of a label $L$ given some observed features, which we can write as $P(L~|~{\\rm features})$.\n", + "Bayes's theorem tells us how to express this in terms of quantities we can compute more directly:\n", + "\n", + "$$\n", + "P(L~|~{\\rm features}) = \\frac{P({\\rm features}~|~L)P(L)}{P({\\rm features})}\n", + "$$\n", + "\n", + "If we are trying to decide between two labels—let's call them $L_1$ and $L_2$—then one way to make this decision is to compute the ratio of the posterior probabilities for each label:\n", + "\n", + "$$\n", + "\\frac{P(L_1~|~{\\rm features})}{P(L_2~|~{\\rm features})} = \\frac{P({\\rm features}~|~L_1)}{P({\\rm features}~|~L_2)}\\frac{P(L_1)}{P(L_2)}\n", + "$$\n", + "\n", + "All we need now is some model by which we can compute $P({\\rm features}~|~L_i)$ for each label.\n", + "Such a model is called a *generative model* because it specifies the hypothetical random process that generates the data.\n", + "Specifying this generative model for each label is the main piece of the training of such a Bayesian classifier.\n", + "The general version of such a training step is a very difficult task, but we can make it simpler through the use of some simplifying assumptions about the form of this model.\n", + "\n", + "This is where the \"naive\" in \"naive Bayes\" comes in: if we make very naive assumptions about the generative model for each label, we can find a rough approximation of the generative model for each class, and then proceed with the Bayesian classification.\n", + "Different types of naive Bayes classifiers rest on different naive assumptions about the data, and we will examine a few of these in the following sections.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "plt.style.use('seaborn-whitegrid')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Gaussian Naive Bayes\n", + "\n", + "Perhaps the easiest naive Bayes classifier to understand is Gaussian naive Bayes.\n", + "With this classifier, the assumption is that *data from each label is drawn from a simple Gaussian distribution*.\n", + "Imagine that we have the following data, shown in Figure 41-1:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_blobs\n", + "X, y = make_blobs(100, 2, centers=2, random_state=2, cluster_std=1.5)\n", + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The simplest Gaussian model is to assume that the data is described by a Gaussian distribution with no covariance between dimensions.\n", + "This model can be fit by computing the mean and standard deviation of the points within each label, which is all we need to define such a distribution.\n", + "The result of this naive Gaussian assumption is shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![(run code in Appendix to generate image)](images/05.05-gaussian-NB.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Gaussian-Naive-Bayes)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The ellipses here represent the Gaussian generative model for each label, with larger probability toward the center of the ellipses.\n", + "With this generative model in place for each class, we have a simple recipe to compute the likelihood $P({\\rm features}~|~L_1)$ for any data point, and thus we can quickly compute the posterior ratio and determine which label is the most probable for a given point.\n", + "\n", + "This procedure is implemented in Scikit-Learn's `sklearn.naive_bayes.GaussianNB` estimator:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.naive_bayes import GaussianNB\n", + "model = GaussianNB()\n", + "model.fit(X, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Let's generate some new data and predict the label:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "rng = np.random.RandomState(0)\n", + "Xnew = [-6, -14] + [14, 18] * rng.rand(2000, 2)\n", + "ynew = model.predict(Xnew)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now we can plot this new data to get an idea of where the decision boundary is (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu')\n", + "lim = plt.axis()\n", + "plt.scatter(Xnew[:, 0], Xnew[:, 1], c=ynew, s=20, cmap='RdBu', alpha=0.1)\n", + "plt.axis(lim);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see a slightly curved boundary in the classifications—in general, the boundary produced by a Gaussian naive Bayes model will be quadratic.\n", + "\n", + "A nice aspect of this Bayesian formalism is that it naturally allows for probabilistic classification, which we can compute using the `predict_proba` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.89, 0.11],\n", + " [1. , 0. ],\n", + " [1. , 0. ],\n", + " [1. , 0. ],\n", + " [1. , 0. ],\n", + " [1. , 0. ],\n", + " [0. , 1. ],\n", + " [0.15, 0.85]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "yprob = model.predict_proba(Xnew)\n", + "yprob[-8:].round(2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The columns give the posterior probabilities of the first and second labels, respectively.\n", + "If you are looking for estimates of uncertainty in your classification, Bayesian approaches like this can be a good place to start.\n", + "\n", + "Of course, the final classification will only be as good as the model assumptions that lead to it, which is why Gaussian naive Bayes often does not produce very good results.\n", + "Still, in many cases—especially as the number of features becomes large—this assumption is not detrimental enough to prevent Gaussian naive Bayes from being a reliable method." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Multinomial Naive Bayes\n", + "\n", + "The Gaussian assumption just described is by no means the only simple assumption that could be used to specify the generative distribution for each label.\n", + "Another useful example is multinomial naive Bayes, where the features are assumed to be generated from a simple multinomial distribution.\n", + "The multinomial distribution describes the probability of observing counts among a number of categories, and thus multinomial naive Bayes is most appropriate for features that represent counts or count rates.\n", + "\n", + "The idea is precisely the same as before, except that instead of modeling the data distribution with the best-fit Gaussian, we model it with a best-fit multinomial distribution." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Example: Classifying Text\n", + "\n", + "One place where multinomial naive Bayes is often used is in text classification, where the features are related to word counts or frequencies within the documents to be classified.\n", + "We discussed the extraction of such features from text in [Feature Engineering](05.04-Feature-Engineering.ipynb); here we will use the sparse word count features from the 20 Newsgroups corpus made available through Scikit-Learn to show how we might classify these short documents into categories.\n", + "\n", + "Let's download the data and take a look at the target names:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['alt.atheism',\n", + " 'comp.graphics',\n", + " 'comp.os.ms-windows.misc',\n", + " 'comp.sys.ibm.pc.hardware',\n", + " 'comp.sys.mac.hardware',\n", + " 'comp.windows.x',\n", + " 'misc.forsale',\n", + " 'rec.autos',\n", + " 'rec.motorcycles',\n", + " 'rec.sport.baseball',\n", + " 'rec.sport.hockey',\n", + " 'sci.crypt',\n", + " 'sci.electronics',\n", + " 'sci.med',\n", + " 'sci.space',\n", + " 'soc.religion.christian',\n", + " 'talk.politics.guns',\n", + " 'talk.politics.mideast',\n", + " 'talk.politics.misc',\n", + " 'talk.religion.misc']" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import fetch_20newsgroups\n", + "\n", + "data = fetch_20newsgroups()\n", + "data.target_names" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For simplicity here, we will select just a few of these categories and download the training and testing sets:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "categories = ['talk.religion.misc', 'soc.religion.christian',\n", + " 'sci.space', 'comp.graphics']\n", + "train = fetch_20newsgroups(subset='train', categories=categories)\n", + "test = fetch_20newsgroups(subset='test', categories=categories)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here is a representative entry from the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Subject: Federal Hearing\n", + "Originator: dmcgee@uluhe\n", + "Organization: School of Ocean and Earth Science and Technology\n", + "Distribution: usa\n", + "Lines: 10\n", + "\n", + "\n", + "Fact or rumor....? Madalyn Murray O'Hare an atheist who eliminated the\n", + "use of the bible reading and prayer in public schools 15 years ago is now\n", + "going to appear before the FCC with a petition to stop the reading of the\n", + "Gospel on the airways of America. And she is also campaigning to remove\n", + "Christmas programs, songs, etc from the public schools. If it is true\n", + "then mail to Federal Communications Commission 1919 H Street Washington DC\n", + "20054 expressing your opposition to her request. Reference Petition number\n", + "\n", + "2493.\n", + "\n" + ] + } + ], + "source": [ + "print(train.data[5][48:])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In order to use this data for machine learning, we need to be able to convert the content of each string into a vector of numbers.\n", + "For this we will use the TF-IDF vectorizer (introduced in [Feature Engineering](05.04-Feature-Engineering.ipynb)), and create a pipeline that attaches it to a multinomial naive Bayes classifier:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.feature_extraction.text import TfidfVectorizer\n", + "from sklearn.naive_bayes import MultinomialNB\n", + "from sklearn.pipeline import make_pipeline\n", + "\n", + "model = make_pipeline(TfidfVectorizer(), MultinomialNB())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this pipeline, we can apply the model to the training data and predict labels for the test data:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "model.fit(train.data, train.target)\n", + "labels = model.predict(test.data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now that we have predicted the labels for the test data, we can evaluate them to learn about the performance of the estimator.\n", + "For example, let's take a look at the confusion matrix between the true and predicted labels for the test data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.metrics import confusion_matrix\n", + "mat = confusion_matrix(test.target, labels)\n", + "sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=False,\n", + " xticklabels=train.target_names, yticklabels=train.target_names,\n", + " cmap='Blues')\n", + "plt.xlabel('true label')\n", + "plt.ylabel('predicted label');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Evidently, even this very simple classifier can successfully separate space discussions from computer discussions, but it gets confused between discussions about religion and discussions about Christianity.\n", + "This is perhaps to be expected!\n", + "\n", + "The cool thing here is that we now have the tools to determine the category for *any* string, using the `predict` method of this pipeline.\n", + "Here's a utility function that will return the prediction for a single string:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def predict_category(s, train=train, model=model):\n", + " pred = model.predict([s])\n", + " return train.target_names[pred[0]]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Let's try it out:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'sci.space'" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "predict_category('sending a payload to the ISS')" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'soc.religion.christian'" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "predict_category('discussing the existence of God')" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'comp.graphics'" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "predict_category('determining the screen resolution')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Remember that this is nothing more sophisticated than a simple probability model for the (weighted) frequency of each word in the string; nevertheless, the result is striking.\n", + "Even a very naive algorithm, when used carefully and trained on a large set of high-dimensional data, can be surprisingly effective." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## When to Use Naive Bayes\n", + "\n", + "Because naive Bayes classifiers make such stringent assumptions about data, they will generally not perform as well as more complicated models.\n", + "That said, they have several advantages:\n", + "\n", + "- They are fast for both training and prediction.\n", + "- They provide straightforward probabilistic prediction.\n", + "- They are often easily interpretable.\n", + "- They have few (if any) tunable parameters.\n", + "\n", + "These advantages mean a naive Bayes classifier is often a good choice as an initial baseline classification.\n", + "If it performs suitably, then congratulations: you have a very fast, very interpretable classifier for your problem.\n", + "If it does not perform well, then you can begin exploring more sophisticated models, with some baseline knowledge of how well they should perform.\n", + "\n", + "Naive Bayes classifiers tend to perform especially well in the following situations:\n", + "\n", + "- When the naive assumptions actually match the data (very rare in practice)\n", + "- For very well-separated categories, when model complexity is less important\n", + "- For very high-dimensional data, when model complexity is less important\n", + "\n", + "The last two points seem distinct, but they actually are related: as the dimensionality of a dataset grows, it is much less likely for any two points to be found close together (after all, they must be close in *every single dimension* to be close overall).\n", + "This means that clusters in high dimensions tend to be more separated, on average, than clusters in low dimensions, assuming the new dimensions actually add information.\n", + "For this reason, simplistic classifiers like the ones discussed here tend to work as well or better than more complicated classifiers as the dimensionality grows: once you have enough data, even a simple model can be very powerful." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.06-Linear-Regression.ipynb b/notebooks/05.06-Linear-Regression.ipynb new file mode 100644 index 000000000..aef8483fd --- /dev/null +++ b/notebooks/05.06-Linear-Regression.ipynb @@ -0,0 +1,1464 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: Linear Regression" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Just as naive Bayes (discussed in [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)) is a good starting point for classification tasks, linear regression models are a good starting point for regression tasks.\n", + "Such models are popular because they can be fit quickly and are straightforward to interpret.\n", + "You are already familiar with the simplest form of linear regression model (i.e., fitting a straight line to two-dimensional data), but such models can be extended to model more complicated data behavior.\n", + "\n", + "In this chapter we will start with a quick walkthrough of the mathematics behind this well-known problem, before moving on to see how linear models can be generalized to account for more complicated patterns in data.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Simple Linear Regression\n", + "\n", + "We will start with the most familiar linear regression, a straight-line fit to data.\n", + "A straight-line fit is a model of the form:\n", + "$$\n", + "y = ax + b\n", + "$$\n", + "where $a$ is commonly known as the *slope*, and $b$ is commonly known as the *intercept*.\n", + "\n", + "Consider the following data, which is scattered about a line with a slope of 2 and an intercept of –5 (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.RandomState(1)\n", + "x = 10 * rng.rand(50)\n", + "y = 2 * x - 5 + rng.randn(50)\n", + "plt.scatter(x, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can use Scikit-Learn's `LinearRegression` estimator to fit this data and construct the best-fit line, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "model = LinearRegression(fit_intercept=True)\n", + "\n", + "model.fit(x[:, np.newaxis], y)\n", + "\n", + "xfit = np.linspace(0, 10, 1000)\n", + "yfit = model.predict(xfit[:, np.newaxis])\n", + "\n", + "plt.scatter(x, y)\n", + "plt.plot(xfit, yfit);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The slope and intercept of the data are contained in the model's fit parameters, which in Scikit-Learn are always marked by a trailing underscore.\n", + "Here the relevant parameters are `coef_` and `intercept_`:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Model slope: 2.0272088103606953\n", + "Model intercept: -4.998577085553204\n" + ] + } + ], + "source": [ + "print(\"Model slope: \", model.coef_[0])\n", + "print(\"Model intercept:\", model.intercept_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that the results are very close to the values used to generate the data, as we might hope." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The `LinearRegression` estimator is much more capable than this, however—in addition to simple straight-line fits, it can also handle multidimensional linear models of the form:\n", + "$$\n", + "y = a_0 + a_1 x_1 + a_2 x_2 + \\cdots\n", + "$$\n", + "where there are multiple $x$ values.\n", + "Geometrically, this is akin to fitting a plane to points in three dimensions, or fitting a hyperplane to points in higher dimensions.\n", + "\n", + "The multidimensional nature of such regressions makes them more difficult to visualize, but we can see one of these fits in action by building some example data, using NumPy's matrix multiplication operator:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.50000000000001\n", + "[ 1.5 -2. 1. ]\n" + ] + } + ], + "source": [ + "rng = np.random.RandomState(1)\n", + "X = 10 * rng.rand(100, 3)\n", + "y = 0.5 + np.dot(X, [1.5, -2., 1.])\n", + "\n", + "model.fit(X, y)\n", + "print(model.intercept_)\n", + "print(model.coef_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here the $y$ data is constructed from a linear combination of three random $x$ values, and the linear regression recovers the coefficients used to construct the data.\n", + "\n", + "In this way, we can use the single `LinearRegression` estimator to fit lines, planes, or hyperplanes to our data.\n", + "It still appears that this approach would be limited to strictly linear relationships between variables, but it turns out we can relax this as well." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Basis Function Regression\n", + "\n", + "One trick you can use to adapt linear regression to nonlinear relationships between variables is to transform the data according to *basis functions*.\n", + "We have seen one version of this before, in the `PolynomialRegression` pipeline used in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) and [Feature Engineering](05.04-Feature-Engineering.ipynb).\n", + "The idea is to take our multidimensional linear model:\n", + "$$\n", + "y = a_0 + a_1 x_1 + a_2 x_2 + a_3 x_3 + \\cdots\n", + "$$\n", + "and build the $x_1, x_2, x_3,$ and so on from our single-dimensional input $x$.\n", + "That is, we let $x_n = f_n(x)$, where $f_n()$ is some function that transforms our data.\n", + "\n", + "For example, if $f_n(x) = x^n$, our model becomes a polynomial regression:\n", + "$$\n", + "y = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \\cdots\n", + "$$\n", + "Notice that this is *still a linear model*—the linearity refers to the fact that the coefficients $a_n$ never multiply or divide each other.\n", + "What we have effectively done is taken our one-dimensional $x$ values and projected them into a higher dimension, so that a linear fit can fit more complicated relationships between $x$ and $y$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Polynomial Basis Functions\n", + "\n", + "This polynomial projection is useful enough that it is built into Scikit-Learn, using the `PolynomialFeatures` transformer:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 2., 4., 8.],\n", + " [ 3., 9., 27.],\n", + " [ 4., 16., 64.]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.preprocessing import PolynomialFeatures\n", + "x = np.array([2, 3, 4])\n", + "poly = PolynomialFeatures(3, include_bias=False)\n", + "poly.fit_transform(x[:, None])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see here that the transformer has converted our one-dimensional array into a three-dimensional array, where each column contains the exponentiated value.\n", + "This new, higher-dimensional data representation can then be plugged into a linear regression.\n", + "\n", + "As we saw in [Feature Engineering](05.04-Feature-Engineering.ipynb), the cleanest way to accomplish this is to use a pipeline.\n", + "Let's make a 7th-degree polynomial model in this way:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.pipeline import make_pipeline\n", + "poly_model = make_pipeline(PolynomialFeatures(7),\n", + " LinearRegression())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this transform in place, we can use the linear model to fit much more complicated relationships between $x$ and $y$. \n", + "For example, here is a sine wave with noise (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.RandomState(1)\n", + "x = 10 * rng.rand(50)\n", + "y = np.sin(x) + 0.1 * rng.randn(50)\n", + "\n", + "poly_model.fit(x[:, np.newaxis], y)\n", + "yfit = poly_model.predict(xfit[:, np.newaxis])\n", + "\n", + "plt.scatter(x, y)\n", + "plt.plot(xfit, yfit);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Our linear model, through the use of seventh-order polynomial basis functions, can provide an excellent fit to this nonlinear data!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Gaussian Basis Functions\n", + "\n", + "Of course, other basis functions are possible.\n", + "For example, one useful pattern is to fit a model that is not a sum of polynomial bases, but a sum of Gaussian bases.\n", + "The result might look something like the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.06-gaussian-basis.png)\n", + "\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The shaded regions in the plot are the scaled basis functions, and when added together they reproduce the smooth curve through the data.\n", + "These Gaussian basis functions are not built into Scikit-Learn, but we can write a custom transformer that will create them, as shown here and illustrated in the following figure (Scikit-Learn transformers are implemented as Python classes; reading Scikit-Learn's source is a good way to see how they can be created):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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ODvdS4P0VE/HZqilwkIrxu+2pWPCvX+Hq2Pt4L6hTArfGfgxcIBGL8MaScT0+X98snBW3vE/0ey+qMMxZhrkxvn2/WCCChznjnrgA7DxXRMu/7VxmWSO+vFiMx2aEY3Rg/37RzhjpjR+fmYnXH4yDTCJGg7bnhn8yiahLAhdKJRvQsmWnVw+9erjwC8VaeD1106g14OD1ciRPCoFMwvt/swbkf2ZF4NvLJfj8bCGemB3JdjiEJW8dyoKLXIrf3z6wa0AqESN5UiiSJ4WiWq3DRyfy8MmpfGg6z1X3MH0hlEo2APjLvaOxZs/lDjej+fgLpTe8zo4/pZdBZzQL5oIbiNggd0yL9MKnp/JhNPXdZ58IT3FtEw5cK8Py24YPahcyLxcHPDd/VLfHMJiZtjJLoUqKD8Jf7xuN1iVgge6OvP2F0hNeJ/of08sQ5OGEeDvdjOCRaWEoqdfikLKc7VAIC3aeKwTQsmp6IHpa7MTVahpbWDEtDC/cOxoAsEFgSR7gcaJv0htxIqcK80b7Wb2DHl/MjfFD8DAnbDuZz3YoxMb0RjN2ny/CnFF+CB7m3O/39bYKtKc5aSHNVfdm+dThCPJwwhs/ZwmuJThvE/2v2VXQG824y4pbmPGNRCzC8qnDcTavBsrSvnuBEOE4llWJKrUeKVNCBvS+3hY7CaWaxlJyqRjP3jkSV1X1OHCtjO1wrIq3if7g9XK4OUoxKdyT7VBYlTwpBI4yMT49nc92KMSGfrhaCncnGWaO9BnQ+3qbnhFSNY2lHogPQoSPAm/8nAWTgLYs5GXVjdnM4JfMCsyO9rW7apvOPJzlSBofhK/TVHi+hxtqRFi0BhMOXS/Hgjj/AV//fS12ElI1jSWkEjFW3xmFP+xMw8HrZZgfa90dtNjCyyyZVdGIKrUeM0fSJhwAsHJaGLSGljlbIny/ZlehUWfEPWMDB/xee5+e6Y+74wIQ6umM/xy7IZi5el4m+pM51QCA6SMo0QNATIAbpoR7YvuZAkH93CTdO3i9DG6OUkyLHPi+BDQ90zeJWITfzorA5aI6vPlzFufaMVuCl1M3p3KqEObl3GVptj17ZFoYntxxEUcyKjDPjm9QCx3DMDiWVYmZI30snra09+mZ/licEIzXf8zAu7/koHXsxJV2zJbg3YjeaDLjbF4NptFovoN5o/3g5+aAHWcL2A6FDKHM8kaUN+gwK4quf2vqvLbgp/QyiERA5x/It/bp5xPeJfrLxfVQ64yYTptkd9C6pP1YViWKaprYDocMkeM3Oy3OihpYtQ3pWU9rCxp76AHExwVkvEv0p3OrAAC3WTA/KXRLJ4VABGDX+UK2QyFD5FhWJaL9XBHgTtOW1tLT2gJJDwsx+biAzOI5erPZjJdeegmZmZmQy+V49dVXMXz48LbnX331VVy8eBEKhQIAsGXLFri6Dn73p/P5tYjyc4FnDx3n7FmghxPmjPLD7vPFeGZuFORS3v07TnqhM5pwIb8WD00Z3veLSb/1NEI3MQwcJGLobuklxdcKJYszwaFDh6DX67F7926sWbMGmzZt6vD8tWvX8OGHH2L79u3Yvn27VZK82czgYmEtEobb9yKp3jw0JRRVah0OXqf+N0JztbgeOqMZk+18kaC19TRCD/JwwqYH4yCTtIzs+dzszOJEn5qaipkzZwIAxo8fj/T09LbnzGYzCgoK8OKLL2Lp0qX48ssvBx8pgJxKNRq1RkwcPswqxxOiWVE+CPJwwufn6Kas0JzLrwEATAqj69+aeltb8MCEYLyW1LJX7j+Tx/MyyQODmLpRq9VwcXFp+1sikcBoNEIqlaKpqQkPP/wwHn30UZhMJqxYsQKxsbEYNWpUh2Molcp+f96RG43Yeralfv6179NRVlaCORHC2Ahcq9UO6Fz05c5wR3ySVo2DZy4j2J1fU1zWPhd81vlcHL1aihB3GSqKbqCCxbjYMJTXRbQj8PRUT3xysRaVGiN8FFKsnDAM0Y4NUCobMNLRDBe5GO/+fBVus/lZumxxondxcYFGo2n722w2QyptOZyTkxNWrFgBJ6eWn0RTp05FRkZGl0QfExPTr8/al6bCv88UoNnQMldW02zCv8/UIChQGPXASqWy3+eiP54K1mLH5SM4Vy3DvKnWO64tWPtc8Nmt58JkZpCxqxD3jgu0y/Mz1NdFTAzw1D09P78kX4TtZ/LhFxrJ+v3B1NTUAb/H4qmbCRMm4Pjx4wCAS5cuISoqqu25/Px8LFu2DCaTCQaDARcvXsSYMWMs/aheO+6RrnxdHXHXGD98mVoMraHr7vaEfzLKGtCoM2JyOE3bsCF5UggMJsb+VsbOmzcPJ0+exNKlS8EwDDZs2IBt27YhNDQUc+fOxf33348lS5ZAJpPh/vvvx8iRIy0O0p43RLDUQ1OG44erZfgpvUwQv3rs3fm81vl5uhHLhmh/V4wLdseeC0V4dHoY7/bAsDjRi8VivPzyyx0ei4xs37fy8ccfx+OPP255ZLfoq+Me6eq2CC+EeTljx9kCSvQCcLGwDv5ujgPaZIRY15JJIfjz1+m4qqrH2GAPtsMZEF4UWq9NjIZU3PFfUL7Ws9qKWCxCypRQnM+vRVZ5I9vhkEG6UlyHscHubIdh1+4bFwhHmZiXXWJ5keiT4oMwOsANErGIOu4NwKKEEMglYuw4Q6WWfFbfZEB+dRPG2eneyFzh5ijD3bEB+PZSCZr1/Lr3xYtEDwA1TXrMj/VH3qZ7cHLdHEry/eCpkGNBnD/2pql4d2GSdldUdQCAcTybLhCixRND0Kgz4qdrpWyHMiC8SPT1TQYU1zZjTKAb26HwzkNThqNRa8R3V0rYDoVY6EpxPQAgjqZuWDcl3BOhns7Yc76Y7VAGhBeJ/lpJy4UeG0gX+kBNChuGEb4u2HGWGp3x1eWiOoR7K+DuJGM7FLsnFouwZGIwTt+oRmE1f7rE8iTRNwAAjegtIBKJkDI5FJeL6pCuqmc7HGKBK8X1dCOWQx6YEAwA+JpHNfU8SfT18HdzhJeLA9uh8NKDE4Ihk4iw5L3TvN8Szd5UNGhR1qDlXTmfkJ3Pq4FcKsY/D2Vh2sbDvPgu8WIrwWslDYgNotG8pY5mVsBsBppMLTdk+bwlmr1JvzltGRdEI3ouaN2kRG9sacdSUq/lxXeJ8yP6Zr0JuZVqjKb5eYttPpAJU6fd7KmFBD8oS1vWQMQECKOBH9/xtR0L5xO9sqwBZobm5weDWkjw1/WSBoR4OsHVkW7EcgFfv0ucT/R0I3bwemoVQS0kuE9Z2oAYf7r2uYKv3yXuJ3pVPTycZQji+Inkst42ViDcpTWYkVetwWga5HBGd98lsQic/y5x/mbstZIGjAl04123OC5pvUm0+UAmVHXNEAH4y70xnL55RID8Oj0YBogJoETPFbd+l0rqmuEsl0BrNOOOaF+WI+sdZxP9vjQV/v5TBkrqtXBxkGJfmooS0yAkxbds0nK1uB73/ftEW2/t1gs20MMJaxOj6RxzyI1aPQBgNCV6Tmn9LgEtzeZ+8++T2H+1FClTQlmOrGecTPStJUytd7fVOiMvSpj4IC7YHWOD3bH1WC5qNXpob5aJUckl9+TV6OHqIEXwMJq25Kq4IHdE+ijwdVoxpxM9J+fo+VrCxBcpk0NRWq9tS/Kt6Bxzy41aHUYFuNK0JYeJRCIsnBCM8/m1KKrhbksETiZ6vpYw8cV94wJ7fI7OMTeYzQzyavU0bcMD949v+T5xeYUsJxM9X0uY+OLg9XL0NEakc8wNRbVNaDYwdCOWB4KHOWNymCe+vVwCptPCRK7gZKJfmxgNR2nH0Kgc0Dpa7390dznSOeaOrHI1gJa9Sgn33TcuANkVamRydDc3Tib6pPggrLmrPeHQjlLW0939DwCQiER0jjkkp6Il0Uf6urAcCemPBXEBkIhF+O4yN/d94GTVDQAEeDgCAL7/wwzEUkMnq+lpDt7MMJTkOSS7ohFeThK4UesDXvB2ccC0SC98d7kUf7wrmnM30Dk5ogeAdFUDZBIRRvrRiMaa6P4HP+RWqBHiIWc7DDIA940LRGFNEy4Xc2/fB84m+msl9Rjp6woHqaTvF5N+624JNwA8MTuChWhIdxiGQW6lBqHuNJrnk8Qx/pBLxJycvuFkomcYBtdvtj4g1pUUH4SNC+MQ5OEEEQBf15bNXNQ62jycK8oatFDrjAhxpxE9n7g7yTA72gffXymB2cyt6htOztGXN+hQrdHT3PwQuXUJNwAsee80dp4rxO9mRUAs5tbcoj1qvREb6kEjer65b1wgDl4vx/n8GkyJ8GI7nDacHNG37m1KI3rbeGhKKAprmvBrThXboRC0J/oQmrrhnTtjfOEkk+Bbjk3fcDLRXytpgEhEXftsZX6sP7wUcnx2poDtUAiA7Ao13J1k8HCk+1N84yyX4s7RfvgxvQwGk7nvN9gIRxN9PcK9FFA4cHJmSXAcpBIsmRSCw8rytvLLfWkqTN90hDYTZ0FOhRojfF04V6JH+ue+sQGo0ehxKrea7VDacDTRN9BmCzaWMjkUDICd5wrbVs+q6prBoL2zJSV728itUGMkLZTirdnRPnB1kOJ7Dk3fcC7R12j0UNU10673NpZaUAu5RIx3juTg/3Zfou6hLKnV6FGt0WMEJXrecpBKMDfGF4eU5TByZPqGc4n+6s0bsZTobad1BK+72ba4p0uTOlsOvZxKan0gBPNjA1DbZMC5vBq2QwHAwUTfVnFDid5meup/0xmtnh16rRU3I3wo0fPZ7CgfOMkk+DG9jO1QAHAw0V8trsdwL2e4O1Fpma30Z6ROnS1tI7tcDSeZBEH0jyqvOckluD3aBweulXFi8RT3Er2qnqZtbKynkbpEJIII1D3UlnIq1YjwUdDCNQGYH+uPikYd0orq2A6FW4m+lm7EsqKn/jcbFsYib9M9OLluDiV5G6GKG+GYM8oXcokYP6WXsh0KtxI93YhlR+f+N94u1GOFDRqdEaq6Zqq4EQhXRxmmj/DCT9fKWN95ipOJnm7E2l5SfBBOrpuDvE334Pyf70SUnwu2nylg/QK1JzcqNQBAiV5AFsQGoKimGddKGliNg1OJ/sf0UkjEIoz/28+0GpNFIpEID08djnRVAyd7awtVdkXLNnSU6IXjztF+kIhFOHCN3eobziT6ry8WI13VAJOZodWYHPBAfBCc5RLqf2NDORVqSMUiDPdSsB0KsRJPhRwJw4fhkLKC1Tg4k+g3/pjR5TFajckeV0cZkuKD8N3lEtQ16dkOxy7kVKgx3MsZMglnvpbECu6M8YWytIHVBYcWX1FmsxkvvvgikpOTsXz5chQUdBz57dmzBwsXLsSSJUtw9OjRPo9X0ajr9nFajcmeh6cMh85oxpepxWyHYhdyKtUY6evKdhjEyuaM8gMAHM5gb1RvcaI/dOgQ9Ho9du/ejTVr1mDTpk1tz1VWVmL79u3YtWsXPvroI7z55pvQ63sfFTrLu2/JSqsx2TM60A0TQj2w42whJxZ9CJneaEZBdRPNzwtQpI8CYV7OOKIsZy0GixN9amoqZs6cCQAYP3480tPT2567cuUK4uPjIZfL4erqitDQUGRkdJ2auZWLgxSd14jQakx23NqiOK9Kg7wqDadargpRQbUGJjNDiV6ARCIR5ozyw8ncajTpjazEYHHDd7VaDReX9otSIpHAaDRCKpVCrVbD1bX9J6hCoYBare5yDKVSCQCo0hhR0ajDrDAFMip1qNQY4aOQYuWEYYh2bIBSyW5p0lDTarVt54JtR2404u1TVdCZWkbwtU0GAMDf9qXh7XuDh/zzuXQubOnX/Jbvh0RT2Xa92+u56A7fz8UIhRZ6oxm7j17C1FDb32y3ONG7uLhAo9G0/W02myGVSrt9TqPRdEj8rWJiYgAAu88XAgD+lDQBo/ztrw+9UqlsOxdse/ybI21J/lbZ1XoMCwyHv7vjkH4+l86FLR0syQZQgbmTY+Esb/ke2eu56A7fz0XkSDM2HqtEplqORwf535Gamjrg91g8dTNhwgQcP34cAHDp0iVERUW1PTd27FikpqZCp9OhsbERubm5HZ7v7JfMSvi7OSLaj25Esa23m9+7bv6DTKwvp0KNIA+ntiRPhEUuFWNWlA+OZFSwcr/L4kQ/b948yOVyLF26FBs3bsT69euxbds2HD58GD4+Pli+fDlSUlKwcuVKrF69Gg4ODt0eR2sw4UR2FWZH+dDWaRzQ081vB6kYO88VcmofTCHJqVBjpB/NzwvZ3BhfVDTqkF5i+0WIFg8fxGIxXn755Q6PRUZGtv3vJUuWYMmSJb0eY/qmI7hrjB8adUbcMzbA0lCIFa1NjMb6vVc79Kd3kknw0JRQfHgiD4eV5ZgfS/9fWZPZzOBGlRrTIr3YDoUModujfSEWAYeVFRgb7GHTz2Z1ZYaqrhmfnMqHm6OULnKO6NzgrLVF8fq7YxDo7ojPztD0jbWp6pqhNZip4kbgPBVyjAvxwLGsSpt/NusTgq3TVVJaDcgZSfFB3bYlXjY5FG8czMKNSjUiaAckq6EeN/Zj1kgfvH0kG7UaPYYpbNcllhPZtUHLTm0pGZjkySGQikXYcZZG9dbUtn0gJXrBmx3tA4YB5rzxC8LX7bdZ80ZOJHraNo0ffF0dkTjGH1+mFkPbjz1mSf/kVKjh7SKHhzPtAyB0+TdbUdc2GWzavJH1RE+rX/nl4anDUd9swHeXS9gORTByKtQ0mrcTbxzM6vKYLZo3sproaS9S/pka4YlwbwU1OrMShmEo0duRntapDHXzRlYTPe1Fyj8ikQiLEoJxNq8GhdVNbIfDe5VqHRq0Roygm9t2oad1KkPdvJH1qRvCPw/EB0EkAr66SKP6wcopb70RS6vC7cHaxGg4yTp26rXF9DUlejJggR5OmB7pja8uFlP74kHKqaSKG3vSuk7FxaGlsj3A3dEm09eU6IlFFiUEo7i2GWfzatgOhddyKtRwcZDCz637FiFEeJLig7DloQkAgA0P2OYeJSV6YpHEMf5wcZDS9M0gtd6IpT5P9mVyuCccZWKbrZKlRE8s4iSX4J64APxwtRQaHS14sxRV3NgnR5kEU8K9cJwSPeG6RROD0aQ34cf0MrZD4aX6ZgMqGnWU6O3UrCgf3KjSoKhm6KvXKNETi00cPgzDvZzxZWoR26HwUlvrAyqttEuzo3wAwCbTN5ToicVEIhEeiA/C2bwalNVr2Q6Hd3JvJnrqQ2+fIn0UCPJwokRPuM9JJgHDAFM3HrZZgyahyK5ohINUjOBhzmyHQlggEokwO9oHp3KqoDcO7YY+lOiJxfalqfDWoey2v23VoEkosivUiPRxgURMFTf26vYoH2j0JlwoGNoyZUr0xGKbD2R22IkKsE2DJqHILqftA+3dtBHekIpFQz59Q4meWIytBk1CoNEZoaprxkiquLFrLg5STAwbhmOZlOgJR7HVoEkIciupxw1pcXu0LzLKGlHeMHQFDZToicW6a9DkIBXT/gL9kF1OFTekRWu/qCkbhq6ggfU9Ywl/tfbo2HwgE6qb0zUzRnpT6+l+yK5QQyYRYbgnVdzYs31pKrx9uGtBAwCrfo8o0ZNBuXUj8RUfn0NmWSMYhqHeLX3IqWhEhLcLpBL6UW3PNh/IhLZTaWVrQYM1Ez1dZcRqfjMuEMW1zbhUVMd2KJyXXaHGCJq2sXu2KmigRE+sZl6MH6RiEX6i3je90hpMKKxpooobYrOCBkr0xGrcnWWYNsIbP6aXgWFoQ5Ke5FaqwTDASKq4sXu22nGKEj2xqgWx/iisacL10ga2Q+GsHOpxQ25q3XEq6JYR/Op5I61e0ECJnljVXaP9IBaBpm96kVOhhkQsQpiXgu1QCAckxQfh5Lo5OLVuDgDAYOr513Cz3tTjc72hRE+sysvFAVPCvahHfS+yy9UI83KGXEpfP9Iu0MMJ40M8eh0kvXs0x6Jj05VGrG5BnD9yKtTIqWhkOxROyq5opPl50q0Fsf64qqrvcTMSS5ufUaInVpc4xh8A8ONVGtV3pjWYkF/dRPPzpFt3xwUAAL7uZnWs3mi2uHSZEj2xOj83RyQMH0bTN93IqVDDZGYwyt+N7VAIB4V4OmPmSG/sOlcIk7njXP3l4jpoDZb1radET4bEglh/XC9tQGH10O+HyScZZS3TWaMCaOqGdC9lcihK6rVdNg4/kV0FSxecU6InQ6Jt+ia9lOVIuCWjtAEOUjFV3JAe3TnaDz6uDvjg1xttjzEMg++vlGBSmKdFx6RET4ZEiKcz4oLcafqmk4yyRkT7u9KuUqRHMokYv789Eqdyq7HpRyWmbzqC8PU/ILdSY3ETPEr0ZMjMj/XHpaI62jj8FhllDYj2o2kb0ruUKaHwUsjx3rEbbZ1hAeC7yyUWHY8SPRky82Nbpm9+vk6jegCobNShSq3HqAC6EUt65yCVQCwSofPSqc6dLvuLEj0ZMpE+Lhjh60KrZG/KvHkjNsafRvSkb1VqndWORYmeDKn5Y/xxNq8GNRo926GwLqOspf9PNCV60g/W7GBJiZ4Mqfmx/jCZGRxSlrMdCuuUpY3wcXWAl4sD26EQHuips6UlLNphSqvVYu3ataiuroZCocDrr78OT8+OZT9PPvkkamtrIZPJ4ODggA8//NCiAAm/jQl0Q5CHE36+VoYlE0PYDodVGWUNGEWjedJPt27VWVLXjEAPp5b2xeaBT4ValOh37tyJqKgo/OEPf8D+/fuxZcsWvPDCCx1eU1BQgP3799OWcnZOJBIhcYw/PjtbALXOCBcH+9y90mAyI7tcjUemh7EdCuGRW7fqbJWaOvBEb9HUTWpqKmbOnAkAmDVrFk6fPt3h+aqqKjQ0NOCJJ57AsmXLcPToUUs+hgjE/Fh/6I1m/JJZwXYorMkqb4TeZMaYQKq4IbbX5/Dqiy++wCeffNLhMS8vL7i6tvwEVSgUaGzs2KXQYDDgsccew4oVK1BfX49ly5Zh7Nix8PLy6vA6pVI52PgFQavVCvpcOJsZeDhKsOdUFiJl9b2+Vqjn4mB2y41YZ20VlMr+bcoi1HNhCToXg9Nnol+8eDEWL17c4bGnn34aGo0GAKDRaODm1nGU4u3tjaVLl0IqlcLLywsxMTHIy8vrkuhjYmIGG78gKJVKwZ+LBZlGfHupBOEjouDYyw0loZ6LHZlX4eIgxdzJYyHu56pYoZ4LS9C5aJeamjrg91g0dTNhwgQcO3YMAHD8+HEkJCR0eP7UqVN45plnALT8Q5CdnY2IiAhLPooIROIYf2j0JpzKrWI7FFZcVTVgTKBbv5M8IdZkUaJftmwZsrOzsWzZMuzevRtPP/00AODvf/87rly5gtmzZyMsLAxLlizBqlWr8H//939dqnKIfZkW6Q1XB6ldLp4ymMxQljYgLsid7VCInbKoBMLJyQlvv/12l8efe+65tv/95z//2fKoiODIpWLMjfHFwevlMJrMkErsZwlHdrkaeqMZccGU6Ak77OfbRliXOMYftU0GnM+vZTsUm9iXpsL0TUdw99u/AgA1dyOsoURPbGZ2tA8cpGIcuCb86Zt9aSqs33u1Q+fBfx7Mwr5utogjZKhRoic24yyXYnaUD35KL4PZ3Lkvn7BsPpCJZoOpw2NaoxmbD2SyFBGxZ5ToiU3Nj/VHWYMWV1S919PzXcktI/n+PE7IUKJET2xq7ig/SMUiwVff9NR50JodCQnpL0r0xKbcnWW4LdILB66VgWGEO33TU+fBtYnRLEVE7BklemJziWP8kVelQXaFmu1QhkxSfBA2LoyDg7TlKxbk4YSNC+O6NKgixBYo0RObu2u0H0QiCH765jfjAuEklyB5YghOrptDSZ6whhI9sTlfN0dMCB0m+ER/o0qDuiYDEoYPYzsUYuco0RNWzB/jj+ulDSiqaWI7lCFzLq8GAJAQRomesIsSPWFF4hh/ABD04qmTuVXwc3NAhLeC7VCInaNET1gR6uWMmAA3/CjQ6RuzmcHp3GpMj/SmXdYI6yjRE9bcE+eP1IJaFNcKb/omo6wRNRo9po3wZjsUQijRE/bcP76lCuWbSyUsR2J9rX33p0V69fFKQoYeJXrCmhBPZ0wKG4a9F4sFt3jqeHYVIrwVtBKWcAIlesKqpPgg5FZqcK2kf/uo8oFaZ8SZ3GrMjfFlOxRCAFCiJyy7Ny4QErEIye+fRvi6/Vj5ZSHvW/n+mlUJvcmMO2P82A6FEAAW7jBFiLUczawAwzDQ6Fpa+lZojFi/9yoA8HYl6UFlOTycZbRQinAGjegJqzYfyETn1vTNBhNv+7YbTGYczajAnGhfu9oukXAbXYmEVULr2348qxK1TQYsiAtgOxRC2lCiJ6wSWt/2vRdV8FTIcXu0D9uhENKGEj1hlZD6ttc3G3BQWY7fjAuEjKZtCIfQzVjCqtYbrpsPZEJV1wyxCHg1KZaXN2K/vlgMvdGMBycEsx0KIR1QoiesS4oPQlJ8EI5klOOx/16ARMyP3jD70lTYfCATJXXNCHB3hN5kRnyoB+KC3dkOjZAO6Pcl4Yzbo3wR6i7D1mO5nF8puy9NhfV7r0JV1wwGQEm9FlVqPcYFe7AdGiFdUKInnCEWi7A4zgMZZY04klEBoCWhTt90BOHr9mP6piNWWUzFMAyUpQ345pIK288U4NvLJcipaIS5c51nLzYfyESzwdTl8Z8F3HaZ8BdN3RBOuT3cBbvS1Xj3aA4amg3409fpbQlVVdc8qMVUDVoDPj2Vjx1nC1Far+3yfJCHEx5MCMbDU0Ph6+rY67F6Kv/s7riEsI0SPeEUqViE398RiT9/nY786qYuo+bWxVQDSfQMw2DfJRVe25+BKrUOM0d6Y/W8KIwP8YC7kwy1TXpcKarH91dL8c6RbLx/PBcrp4XhiVmRGKaQd3vMQA8nqLpJ9mKRCPvSVLy8mUyEixI94ZzkiSH4+EQecis13T4/kMVUjVoD1u+9iu+vlGJ8iAe2PTKpy81SPzdHjPJ3w5JJIciv0uBfh7Px/vEb2HGmEI9ND8OqmRFwd5J1eM/axGg8/9UV6IzmDo+bGIb3LRyI8FCiJ5wjlYjxp7tjsOqTC90+391iqlsrYAI9nLA2MRqjAlzx5GcXUVjThOfmR+OJWZEQ91HRE+atwD+Tx+PJ2yPx1qEsvH0kB/89lY/ltw3H3XEBiPZzhUZvgtZgglQsgq6bY1jyq4OQoUSJnnDS3Bg/jAt2x+Xi+g6Pd7eYqrUC5ta5/Oe+vAIA8HCW4fPHp2BKxMA2AInyc8WWhxJwraQebx3Kxn9+ycW7R3M7vGZ8iAcuFdV1+36+tnAgwkSJnnDWhysn4fbNR9FsMLU1PnOUdS0U664CRm8yQyYR4fs/zICvW+83VnszJtAdH6yYiMpGHY5nVaKwpgmOMgkShg/DpLBhmPH60W7n6vnawoEIEyV6wlk+rg5YcVsY/nOsfSRd22ToMgfe0+jZYGIGleQ7x/JgQtcVr2sTozv8mgD428KBCBfV0RNO23W+sMtjndsYB7h3n8yDbDCqTooPwsaFcQjycILo5mduXBhH8/OEU2hETzhrX5oKtU2Gbp9T1TXjRHYVrqrqu/SzB2w7qm5t4UAIV1GiJ5zV1+YjD390FkDLTdE7Y3xxJKMCpfXatqobSr6EtKBETzirt8oVF7kEH6ychAgfBfysNA9PiFDRHD3hrN4qVzR6E26L9KIkT0g/UKInnLU2MRo9LW+i8kVC+o8SPeGspPggPDQ1tEuyp/JFQgZmUIn+4MGDWLNmTbfP7dmzBwsXLsSSJUtw9OjRwXwMsWOvJsXhn8njqXyRkEGw+Gbsq6++ihMnTiAmJqbLc5WVldi+fTu++uor6HQ6pKSkYPr06ZDLu+8ESEhvqHyRkMGxeEQ/YcIEvPTSS90+d+XKFcTHx0Mul8PV1RWhoaHIyMiw9KMIIYQMQp8j+i+++AKffPJJh8c2bNiAu+++G2fPnu32PWq1Gq6urm1/KxQKqNXqLq9TKpUDjVeQtFotnYub6Fy0o3PRjs7F4PSZ6BcvXozFixcP6KAuLi7QaNp7iWs0mg6Jv1V30z72SKlU0rm4ic5FOzoX7ehctEtNTR3we4ak6mbs2LFITU2FTqdDY2MjcnNzERUVNRQfRQghpA9WXRm7bds2hIaGYu7cuVi+fDlSUlLAMAxWr14NBwcHa34UIYSQfhIxDNNNS6ihZ8nPD0IIIUBCQsKAXs9aoieEEGIbtDKWEEIEjhI9IYQInM0Tvdlsxosvvojk5GQsX74cBQUFtg6BMwwGA9auXYuUlBQsWrQIhw8fZjsk1lVXV2P27NnIzc3t+8UC9t577yE5ORkLFy7EF198wXY4rDEYDFizZg2WLl2KlJQUu70uLl++jOXLlwMACgoKsGzZMqSkpOCvf/0rzGZzn++3eaI/dOgQ9Ho9du/ejTVr1mDTpk22DoEzvv32W3h4eODzzz/Hhx9+iFdeeYXtkFhlMBjw4osvwtHRvlsPnz17Fmlpadi5cye2b9+OsrIytkNizbFjx2A0GrFr1y489dRTeOutt9gOyeY++OADvPDCC9DpdACAjRs34tlnn8Xnn38OhmH6NUC0eaJPTU3FzJkzAQDjx49Henq6rUPgjPnz5+OZZ54BADAMA4lEwnJE7Hr99dexdOlS+Pr6sh0Kq06cOIGoqCg89dRTeOKJJ3D77bezHRJrwsPDYTKZYDaboVarIZXa315JoaGheOedd9r+vnbtGiZPngwAmDVrFk6dOtXnMWx+1tRqNVxcXNr+lkgkMBqNdvl/oEKhANByTv73f/8Xzz77LLsBsWjv3r3w9PTEzJkz8f7777MdDqtqa2tRUlKCrVu3ori4GE8++SR++ukniEQ9decXLmdnZ6hUKixYsAC1tbXYunUr2yHZXGJiIoqLi9v+Zhim7VpQKBRobGzs8xg2H9F3bo9gNpvtMsm3Ki0txYoVK3D//ffjvvvuYzsc1nz11Vc4deoUli9fDqVSieeffx6VlZVsh8UKDw8PzJgxA3K5HBEREXBwcEBNTQ3bYbHiv//9L2bMmIEDBw7gm2++wbp169qmMOyVWNyetjUaDdzc3Pp+z1AG1J0JEybg+PHjAIBLly7ZdWuEqqoqPPbYY1i7di0WLVrEdjis2rFjBz777DNs374dMTExeP311+Hj48N2WKxISEjAr7/+CoZhUF5ejubmZnh4eLAdFivc3Nza+mS5u7vDaDTCZDKxHBW7Ro8e3dZQ8vjx45g4cWKf77H5UHrevHk4efIkli5dCoZhsGHDBluHwBlbt25FQ0MDtmzZgi1btgBoufFi7zcj7d0dd9yB8+fPY9GiRWAYBi+++KLd3r955JFH8Kc//QkpKSkwGAxYvXo1nJ2d2Q6LVc8//zz+8pe/4M0330RERAQSExP7fA+tjCWEEIGjBVOEECJwlOgJIUTgKNETQojAUaInhBCBo0RPCCECR4meEEIEjhI9IYQIHCV6QggRuP8HalWaMre7sUcAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.base import BaseEstimator, TransformerMixin\n", + "\n", + "class GaussianFeatures(BaseEstimator, TransformerMixin):\n", + " \"\"\"Uniformly spaced Gaussian features for one-dimensional input\"\"\"\n", + " \n", + " def __init__(self, N, width_factor=2.0):\n", + " self.N = N\n", + " self.width_factor = width_factor\n", + " \n", + " @staticmethod\n", + " def _gauss_basis(x, y, width, axis=None):\n", + " arg = (x - y) / width\n", + " return np.exp(-0.5 * np.sum(arg ** 2, axis))\n", + " \n", + " def fit(self, X, y=None):\n", + " # create N centers spread along the data range\n", + " self.centers_ = np.linspace(X.min(), X.max(), self.N)\n", + " self.width_ = self.width_factor * (self.centers_[1] - self.centers_[0])\n", + " return self\n", + " \n", + " def transform(self, X):\n", + " return self._gauss_basis(X[:, :, np.newaxis], self.centers_,\n", + " self.width_, axis=1)\n", + " \n", + "gauss_model = make_pipeline(GaussianFeatures(20),\n", + " LinearRegression())\n", + "gauss_model.fit(x[:, np.newaxis], y)\n", + "yfit = gauss_model.predict(xfit[:, np.newaxis])\n", + "\n", + "plt.scatter(x, y)\n", + "plt.plot(xfit, yfit)\n", + "plt.xlim(0, 10);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "I've included this example just to make clear that there is nothing magic about polynomial basis functions: if you have some sort of intuition into the generating process of your data that makes you think one basis or another might be appropriate, you can use that instead." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Regularization\n", + "\n", + "The introduction of basis functions into our linear regression makes the model much more flexible, but it also can very quickly lead to overfitting (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for a discussion of this).\n", + "For example, the following figure shows what happens if we use a large number of Gaussian basis functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "model = make_pipeline(GaussianFeatures(30),\n", + " LinearRegression())\n", + "model.fit(x[:, np.newaxis], y)\n", + "\n", + "plt.scatter(x, y)\n", + "plt.plot(xfit, model.predict(xfit[:, np.newaxis]))\n", + "\n", + "plt.xlim(0, 10)\n", + "plt.ylim(-1.5, 1.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With the data projected to the 30-dimensional basis, the model has far too much flexibility and goes to extreme values between locations where it is constrained by data.\n", + "We can see the reason for this if we plot the coefficients of the Gaussian bases with respect to their locations, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def basis_plot(model, title=None):\n", + " fig, ax = plt.subplots(2, sharex=True)\n", + " model.fit(x[:, np.newaxis], y)\n", + " ax[0].scatter(x, y)\n", + " ax[0].plot(xfit, model.predict(xfit[:, np.newaxis]))\n", + " ax[0].set(xlabel='x', ylabel='y', ylim=(-1.5, 1.5))\n", + " \n", + " if title:\n", + " ax[0].set_title(title)\n", + "\n", + " ax[1].plot(model.steps[0][1].centers_,\n", + " model.steps[1][1].coef_)\n", + " ax[1].set(xlabel='basis location',\n", + " ylabel='coefficient',\n", + " xlim=(0, 10))\n", + " \n", + "model = make_pipeline(GaussianFeatures(30), LinearRegression())\n", + "basis_plot(model)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The lower panel of this figure shows the amplitude of the basis function at each location.\n", + "This is typical overfitting behavior when basis functions overlap: the coefficients of adjacent basis functions blow up and cancel each other out.\n", + "We know that such behavior is problematic, and it would be nice if we could limit such spikes explicitly in the model by penalizing large values of the model parameters.\n", + "Such a penalty is known as *regularization*, and comes in several forms." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Ridge Regression ($L_2$ Regularization)\n", + "\n", + "Perhaps the most common form of regularization is known as *ridge regression* or $L_2$ *regularization* (sometimes also called *Tikhonov regularization*).\n", + "This proceeds by penalizing the sum of squares (2-norms) of the model coefficients $\\theta_n$. In this case, the penalty on the model fit would be: \n", + "$$\n", + "P = \\alpha\\sum_{n=1}^N \\theta_n^2\n", + "$$\n", + "where $\\alpha$ is a free parameter that controls the strength of the penalty.\n", + "This type of penalized model is built into Scikit-Learn with the `Ridge` estimator (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.linear_model import Ridge\n", + "model = make_pipeline(GaussianFeatures(30), Ridge(alpha=0.1))\n", + "basis_plot(model, title='Ridge Regression')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The $\\alpha$ parameter is essentially a knob controlling the complexity of the resulting model.\n", + "In the limit $\\alpha \\to 0$, we recover the standard linear regression result; in the limit $\\alpha \\to \\infty$, all model responses will be suppressed.\n", + "One advantage of ridge regression in particular is that it can be computed very efficiently—at hardly more computational cost than the original linear regression model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Lasso Regression ($L_1$ Regularization)\n", + "\n", + "Another common type of regularization is known as *lasso regression* or *L~1~ regularization* involves penalizing the sum of absolute values (1-norms) of regression coefficients:\n", + "$$\n", + "P = \\alpha\\sum_{n=1}^N |\\theta_n|\n", + "$$\n", + "Though this is conceptually very similar to ridge regression, the results can differ surprisingly. For example, due to its construction, lasso regression tends to favor *sparse models* where possible: that is, it preferentially sets many model coefficients to exactly zero.\n", + "\n", + "We can see this behavior if we duplicate the previous example using L1-normalized coefficients (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.linear_model import Lasso\n", + "model = make_pipeline(GaussianFeatures(30), Lasso(alpha=0.001, max_iter=2000))\n", + "basis_plot(model, title='Lasso Regression')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With the lasso regression penalty, the majority of the coefficients are exactly zero, with the functional behavior being modeled by a small subset of the available basis functions.\n", + "As with ridge regularization, the $\\alpha$ parameter tunes the strength of the penalty and should be determined via, for example, cross-validation (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for a discussion of this)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: Predicting Bicycle Traffic" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As an example, let's take a look at whether we can predict the number of bicycle trips across Seattle's Fremont Bridge based on weather, season, and other factors.\n", + "We already saw this data in [Working With Time Series](03.11-Working-with-Time-Series.ipynb), but here we will join the bike data with another dataset and try to determine the extent to which weather and seasonal factors—temperature, precipitation, and daylight hours—affect the volume of bicycle traffic through this corridor.\n", + "Fortunately, the National Oceanic and Atmospheric Administration (NOAA) makes its daily [weather station data](http://www.ncdc.noaa.gov/cdo-web/search?datasetid=GHCND) available—I used station ID USW00024233—and we can easily use Pandas to join the two data sources.\n", + "We will perform a simple linear regression to relate weather and other information to bicycle counts, in order to estimate how a change in any one of these parameters affects the number of riders on a given day.\n", + "\n", + "In particular, this is an example of how the tools of Scikit-Learn can be used in a statistical modeling framework, in which the parameters of the model are assumed to have interpretable meaning.\n", + "As discussed previously, this is not a standard approach within machine learning, but such interpretation is possible for some models.\n", + "\n", + "Let's start by loading the two datasets, indexing by date:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "# url = 'https://raw.githubusercontent.com/jakevdp/bicycle-data/main'\n", + "# !curl -O {url}/FremontBridge.csv\n", + "# !curl -O {url}/SeattleWeather.csv" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "counts = pd.read_csv('FremontBridge.csv',\n", + " index_col='Date', parse_dates=True)\n", + "weather = pd.read_csv('SeattleWeather.csv',\n", + " index_col='DATE', parse_dates=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For simplicity, let's look at data prior to 2020 in order to avoid the effects of the COVID-19 pandemic, which significantly affected commuting patterns in Seattle:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "counts = counts[counts.index < \"2020-01-01\"]\n", + "weather = weather[weather.index < \"2020-01-01\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next we will compute the total daily bicycle traffic, and put this in its own `DataFrame`:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "daily = counts.resample('d').sum()\n", + "daily['Total'] = daily.sum(axis=1)\n", + "daily = daily[['Total']] # remove other columns" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We saw previously that the patterns of use generally vary from day to day. Let's account for this in our data by adding binary columns that indicate the day of the week:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "days = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']\n", + "for i in range(7):\n", + " daily[days[i]] = (daily.index.dayofweek == i).astype(float)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Similarly, we might expect riders to behave differently on holidays; let's add an indicator of this as well:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from pandas.tseries.holiday import USFederalHolidayCalendar\n", + "cal = USFederalHolidayCalendar()\n", + "holidays = cal.holidays('2012', '2020')\n", + "daily = daily.join(pd.Series(1, index=holidays, name='holiday'))\n", + "daily['holiday'].fillna(0, inplace=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We also might suspect that the hours of daylight would affect how many people ride. Let's use the standard astronomical calculation to add this information (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(8.0, 17.0)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def hours_of_daylight(date, axis=23.44, latitude=47.61):\n", + " \"\"\"Compute the hours of daylight for the given date\"\"\"\n", + " days = (date - pd.datetime(2000, 12, 21)).days\n", + " m = (1. - np.tan(np.radians(latitude))\n", + " * np.tan(np.radians(axis) * np.cos(days * 2 * np.pi / 365.25)))\n", + " return 24. * np.degrees(np.arccos(1 - np.clip(m, 0, 2))) / 180.\n", + "\n", + "daily['daylight_hrs'] = list(map(hours_of_daylight, daily.index))\n", + "daily[['daylight_hrs']].plot()\n", + "plt.ylim(8, 17)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can also add the average temperature and total precipitation to the data.\n", + "In addition to the inches of precipitation, let's add a flag that indicates whether a day is dry (has zero precipitation):" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "weather['Temp (F)'] = 0.5 * (weather['TMIN'] + weather['TMAX'])\n", + "weather['Rainfall (in)'] = weather['PRCP']\n", + "weather['dry day'] = (weather['PRCP'] == 0).astype(int)\n", + "\n", + "daily = daily.join(weather[['Rainfall (in)', 'Temp (F)', 'dry day']])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, let's add a counter that increases from day 1, and measures how many years have passed.\n", + "This will let us measure any observed annual increase or decrease in daily crossings:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "daily['annual'] = (daily.index - daily.index[0]).days / 365." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now our data is in order, and we can take a look at it:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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TotalMonTueWedThuFriSatSunholidaydaylight_hrsRainfall (in)Temp (F)dry dayannual
Date
2012-10-0314084.00.00.01.00.00.00.00.00.011.2773590.056.010.000000
2012-10-0413900.00.00.00.01.00.00.00.00.011.2191420.056.510.002740
2012-10-0512592.00.00.00.00.01.00.00.00.011.1610380.059.510.005479
2012-10-068024.00.00.00.00.00.01.00.00.011.1030560.060.510.008219
2012-10-078568.00.00.00.00.00.00.01.00.011.0452080.060.510.010959
\n", + "
" + ], + "text/plain": [ + " Total Mon Tue Wed Thu Fri Sat Sun holiday daylight_hrs \\\n", + "Date \n", + "2012-10-03 14084.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 11.277359 \n", + "2012-10-04 13900.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 11.219142 \n", + "2012-10-05 12592.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 11.161038 \n", + "2012-10-06 8024.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 11.103056 \n", + "2012-10-07 8568.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 11.045208 \n", + "\n", + " Rainfall (in) Temp (F) dry day annual \n", + "Date \n", + "2012-10-03 0.0 56.0 1 0.000000 \n", + "2012-10-04 0.0 56.5 1 0.002740 \n", + "2012-10-05 0.0 59.5 1 0.005479 \n", + "2012-10-06 0.0 60.5 1 0.008219 \n", + "2012-10-07 0.0 60.5 1 0.010959 " + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "daily.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this in place, we can choose the columns to use, and fit a linear regression model to our data.\n", + "We will set `fit_intercept=False`, because the daily flags essentially operate as their own day-specific intercepts:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# Drop any rows with null values\n", + "daily.dropna(axis=0, how='any', inplace=True)\n", + "\n", + "column_names = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun',\n", + " 'holiday', 'daylight_hrs', 'Rainfall (in)',\n", + " 'dry day', 'Temp (F)', 'annual']\n", + "X = daily[column_names]\n", + "y = daily['Total']\n", + "\n", + "model = LinearRegression(fit_intercept=False)\n", + "model.fit(X, y)\n", + "daily['predicted'] = model.predict(X)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we can compare the total and predicted bicycle traffic visually (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "daily[['Total', 'predicted']].plot(alpha=0.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "From the fact that the data and model predictions don't line up exactly, it is evident that we have missed some key features.\n", + "Either our features are not complete (i.e., people decide whether to ride to work based on more than just these features), or there are some nonlinear relationships that we have failed to take into account (e.g., perhaps people ride less at both high and low temperatures).\n", + "Nevertheless, our rough approximation is enough to give us some insights, and we can take a look at the coefficients of the linear model to estimate how much each feature contributes to the daily bicycle count:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Mon -3309.953439\n", + "Tue -2860.625060\n", + "Wed -2962.889892\n", + "Thu -3480.656444\n", + "Fri -4836.064503\n", + "Sat -10436.802843\n", + "Sun -10795.195718\n", + "holiday -5006.995232\n", + "daylight_hrs 409.146368\n", + "Rainfall (in) -2789.860745\n", + "dry day 2111.069565\n", + "Temp (F) 179.026296\n", + "annual 324.437749\n", + "dtype: float64" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "params = pd.Series(model.coef_, index=X.columns)\n", + "params" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "These numbers are difficult to interpret without some measure of their uncertainty.\n", + "We can compute these uncertainties quickly using bootstrap resamplings of the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.utils import resample\n", + "np.random.seed(1)\n", + "err = np.std([model.fit(*resample(X, y)).coef_\n", + " for i in range(1000)], 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With these errors estimated, let's again look at the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " effect uncertainty\n", + "Mon -3310.0 265.0\n", + "Tue -2861.0 274.0\n", + "Wed -2963.0 268.0\n", + "Thu -3481.0 268.0\n", + "Fri -4836.0 261.0\n", + "Sat -10437.0 259.0\n", + "Sun -10795.0 267.0\n", + "holiday -5007.0 401.0\n", + "daylight_hrs 409.0 26.0\n", + "Rainfall (in) -2790.0 186.0\n", + "dry day 2111.0 101.0\n", + "Temp (F) 179.0 7.0\n", + "annual 324.0 22.0\n" + ] + } + ], + "source": [ + "print(pd.DataFrame({'effect': params.round(0),\n", + " 'uncertainty': err.round(0)}))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The `effect` column here, roughly speaking, shows how the number of riders is affected by a change of the feature in question.\n", + "For example, there is a clear divide when it comes to the day of the week: there are thousands fewer riders on weekends than on weekdays.\n", + "We also see that for each additional hour of daylight, 409 ± 26 more people choose to ride; a temperature increase of one degree Fahrenheit encourages 179 ± 7 people to grab their bicycle; a dry day means an average of 2,111 ± 101 more riders,\n", + "and every inch of rainfall leads 2,790 ± 186 riders to choose another mode of transport.\n", + "Once all these effects are accounted for, we see a modest increase of 324 ± 22 new daily riders each year.\n", + "\n", + "Our simple model is almost certainly missing some relevant information. For example, as mentioned earlier, nonlinear effects (such as effects of precipitation *and* cold temperature) and nonlinear trends within each variable (such as disinclination to ride at very cold and very hot temperatures) cannot be accounted for in a simple linear model.\n", + "Additionally, we have thrown away some of the finer-grained information (such as the difference between a rainy morning and a rainy afternoon), and we have ignored correlations between days (such as the possible effect of a rainy Tuesday on Wednesday's numbers, or the effect of an unexpected sunny day after a streak of rainy days).\n", + "These are all potentially interesting effects, and you now have the tools to begin exploring them if you wish!" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.07-Support-Vector-Machines.ipynb b/notebooks/05.07-Support-Vector-Machines.ipynb new file mode 100644 index 000000000..e9f088f4a --- /dev/null +++ b/notebooks/05.07-Support-Vector-Machines.ipynb @@ -0,0 +1,1088 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: Support Vector Machines" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Support vector machines (SVMs) are a particularly powerful and flexible class of supervised algorithms for both classification and regression.\n", + "In this chapter, we will explore the intuition behind SVMs and their use in classification problems.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "from scipy import stats" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivating Support Vector Machines" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As part of our discussion of Bayesian classification (see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)), we learned about a simple kind of model that describes the distribution of each underlying class, and experimented with using it to probabilistically determine labels for new points.\n", + "That was an example of *generative classification*; here we will consider instead *discriminative classification*. That is, rather than modeling each class, we will simply find a line or curve (in two dimensions) or manifold (in multiple dimensions) that divides the classes from each other.\n", + "\n", + "As an example of this, consider the simple case of a classification task in which the two classes of points are well separated (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_blobs\n", + "X, y = make_blobs(n_samples=50, centers=2,\n", + " random_state=0, cluster_std=0.60)\n", + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A linear discriminative classifier would attempt to draw a straight line separating the two sets of data, and thereby create a model for classification.\n", + "For two-dimensional data like that shown here, this is a task we could do by hand.\n", + "But immediately we see a problem: there is more than one possible dividing line that can perfectly discriminate between the two classes!\n", + "\n", + "We can draw some of them as follows; the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xfit = np.linspace(-1, 3.5)\n", + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')\n", + "plt.plot([0.6], [2.1], 'x', color='red', markeredgewidth=2, markersize=10)\n", + "\n", + "for m, b in [(1, 0.65), (0.5, 1.6), (-0.2, 2.9)]:\n", + " plt.plot(xfit, m * xfit + b, '-k')\n", + "\n", + "plt.xlim(-1, 3.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are three *very* different separators which, nevertheless, perfectly discriminate between these samples.\n", + "Depending on which you choose, a new data point (e.g., the one marked by the \"X\" in this plot) will be assigned a different label!\n", + "Evidently our simple intuition of \"drawing a line between classes\" is not good enough, and we need to think a bit more deeply." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Support Vector Machines: Maximizing the Margin\n", + "\n", + "Support vector machines offer one way to improve on this.\n", + "The intuition is this: rather than simply drawing a zero-width line between the classes, we can draw around each line a *margin* of some width, up to the nearest point.\n", + "Here is an example of how this might look (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xfit = np.linspace(-1, 3.5)\n", + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')\n", + "\n", + "for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:\n", + " yfit = m * xfit + b\n", + " plt.plot(xfit, yfit, '-k')\n", + " plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none',\n", + " color='lightgray', alpha=0.5)\n", + "\n", + "plt.xlim(-1, 3.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The line that maximizes this margin is the one we will choose as the optimal model." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Fitting a Support Vector Machine\n", + "\n", + "Let's see the result of an actual fit to this data: we will use Scikit-Learn's support vector classifier (`SVC`) to train an SVM model on this data.\n", + "For the time being, we will use a linear kernel and set the ``C`` parameter to a very large number (we'll discuss the meaning of these in more depth momentarily):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "SVC(C=10000000000.0, kernel='linear')" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.svm import SVC # \"Support vector classifier\"\n", + "model = SVC(kernel='linear', C=1E10)\n", + "model.fit(X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To better visualize what's happening here, let's create a quick convenience function that will plot SVM decision boundaries for us (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def plot_svc_decision_function(model, ax=None, plot_support=True):\n", + " \"\"\"Plot the decision function for a 2D SVC\"\"\"\n", + " if ax is None:\n", + " ax = plt.gca()\n", + " xlim = ax.get_xlim()\n", + " ylim = ax.get_ylim()\n", + " \n", + " # create grid to evaluate model\n", + " x = np.linspace(xlim[0], xlim[1], 30)\n", + " y = np.linspace(ylim[0], ylim[1], 30)\n", + " Y, X = np.meshgrid(y, x)\n", + " xy = np.vstack([X.ravel(), Y.ravel()]).T\n", + " P = model.decision_function(xy).reshape(X.shape)\n", + " \n", + " # plot decision boundary and margins\n", + " ax.contour(X, Y, P, colors='k',\n", + " levels=[-1, 0, 1], alpha=0.5,\n", + " linestyles=['--', '-', '--'])\n", + " \n", + " # plot support vectors\n", + " if plot_support:\n", + " ax.scatter(model.support_vectors_[:, 0],\n", + " model.support_vectors_[:, 1],\n", + " s=300, linewidth=1, edgecolors='black',\n", + " facecolors='none');\n", + " ax.set_xlim(xlim)\n", + " ax.set_ylim(ylim)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')\n", + "plot_svc_decision_function(model);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is the dividing line that maximizes the margin between the two sets of points.\n", + "Notice that a few of the training points just touch the margin: they are circled in the following figure.\n", + "These points are the pivotal elements of this fit; they are known as the *support vectors*, and give the algorithm its name.\n", + "In Scikit-Learn, the identities of these points are stored in the `support_vectors_` attribute of the classifier:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.44359863, 3.11530945],\n", + " [2.33812285, 3.43116792],\n", + " [2.06156753, 1.96918596]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.support_vectors_" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A key to this classifier's success is that for the fit, only the positions of the support vectors matter; any points further from the margin that are on the correct side do not modify the fit.\n", + "Technically, this is because these points do not contribute to the loss function used to fit the model, so their position and number do not matter so long as they do not cross the margin.\n", + "\n", + "We can see this, for example, if we plot the model learned from the first 60 points and first 120 points of this dataset (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_svm(N=10, ax=None):\n", + " X, y = make_blobs(n_samples=200, centers=2,\n", + " random_state=0, cluster_std=0.60)\n", + " X = X[:N]\n", + " y = y[:N]\n", + " model = SVC(kernel='linear', C=1E10)\n", + " model.fit(X, y)\n", + " \n", + " ax = ax or plt.gca()\n", + " ax.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')\n", + " ax.set_xlim(-1, 4)\n", + " ax.set_ylim(-1, 6)\n", + " plot_svc_decision_function(model, ax)\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "for axi, N in zip(ax, [60, 120]):\n", + " plot_svm(N, axi)\n", + " axi.set_title('N = {0}'.format(N))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the left panel, we see the model and the support vectors for 60 training points.\n", + "In the right panel, we have doubled the number of training points, but the model has not changed: the three support vectors in the left panel are the same as the support vectors in the right panel.\n", + "This insensitivity to the exact behavior of distant points is one of the strengths of the SVM model." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are running this notebook live, you can use IPython's interactive widgets to view this feature of the SVM model interactively:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "ba29c3a8344b463a8848a4a7bfec4da8", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(IntSlider(value=10, description='N', max=200, min=10), Output()), _dom_classes=('widget-…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from ipywidgets import interact, fixed\n", + "interact(plot_svm, N=(10, 200), ax=fixed(None));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Beyond Linear Boundaries: Kernel SVM\n", + "\n", + "Where SVM can become quite powerful is when it is combined with *kernels*.\n", + "We have seen a version of kernels before, in the basis function regressions of [In Depth: Linear Regression](05.06-Linear-Regression.ipynb).\n", + "There we projected our data into a higher-dimensional space defined by polynomials and Gaussian basis functions, and thereby were able to fit for nonlinear relationships with a linear classifier.\n", + "\n", + "In SVM models, we can use a version of the same idea.\n", + "To motivate the need for kernels, let's look at some data that is not linearly separable (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_circles\n", + "X, y = make_circles(100, factor=.1, noise=.1)\n", + "\n", + "clf = SVC(kernel='linear').fit(X, y)\n", + "\n", + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')\n", + "plot_svc_decision_function(clf, plot_support=False);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is clear that no linear discrimination will *ever* be able to separate this data.\n", + "But we can draw a lesson from the basis function regressions in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), and think about how we might project the data into a higher dimension such that a linear separator *would* be sufficient.\n", + "For example, one simple projection we could use would be to compute a *radial basis function* (RBF) centered on the middle clump:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "r = np.exp(-(X ** 2).sum(1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can visualize this extra data dimension using a three-dimensional plot, as seen in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits import mplot3d\n", + "\n", + "ax = plt.subplot(projection='3d')\n", + "ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap='autumn')\n", + "ax.view_init(elev=20, azim=30)\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('r');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that with this additional dimension, the data becomes trivially linearly separable, by drawing a separating plane at, say, *r*=0.7.\n", + "\n", + "In this case we had to choose and carefully tune our projection: if we had not centered our radial basis function in the right location, we would not have seen such clean, linearly separable results.\n", + "In general, the need to make such a choice is a problem: we would like to somehow automatically find the best basis functions to use.\n", + "\n", + "One strategy to this end is to compute a basis function centered at *every* point in the dataset, and let the SVM algorithm sift through the results.\n", + "This type of basis function transformation is known as a *kernel transformation*, as it is based on a similarity relationship (or kernel) between each pair of points.\n", + "\n", + "A potential problem with this strategy—projecting $N$ points into $N$ dimensions—is that it might become very computationally intensive as $N$ grows large.\n", + "However, because of a neat little procedure known as the [*kernel trick*](https://en.wikipedia.org/wiki/Kernel_trick), a fit on kernel-transformed data can be done implicitly—that is, without ever building the full $N$-dimensional representation of the kernel projection.\n", + "This kernel trick is built into the SVM, and is one of the reasons the method is so powerful.\n", + "\n", + "In Scikit-Learn, we can apply kernelized SVM simply by changing our linear kernel to an RBF kernel, using the `kernel` model hyperparameter:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "SVC(C=1000000.0)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "clf = SVC(kernel='rbf', C=1E6)\n", + "clf.fit(X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's use our previously defined function to visualize the fit and identify the support vectors (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')\n", + "plot_svc_decision_function(clf)\n", + "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n", + " s=300, lw=1, facecolors='none');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using this kernelized support vector machine, we learn a suitable nonlinear decision boundary.\n", + "This kernel transformation strategy is used often in machine learning to turn fast linear methods into fast nonlinear methods, especially for models in which the kernel trick can be used." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Tuning the SVM: Softening Margins\n", + "\n", + "Our discussion thus far has centered around very clean datasets, in which a perfect decision boundary exists.\n", + "But what if your data has some amount of overlap?\n", + "For example, you may have data like this (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X, y = make_blobs(n_samples=100, centers=2,\n", + " random_state=0, cluster_std=1.2)\n", + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To handle this case, the SVM implementation has a bit of a fudge factor that \"softens\" the margin: that is, it allows some of the points to creep into the margin if that allows a better fit.\n", + "The hardness of the margin is controlled by a tuning parameter, most often known as `C`.\n", + "For a very large `C`, the margin is hard, and points cannot lie in it.\n", + "For a smaller `C`, the margin is softer and can grow to encompass some points.\n", + "\n", + "The plot shown in the following figure gives a visual picture of how a changing `C` affects the final fit via the softening of the margin:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X, y = make_blobs(n_samples=100, centers=2,\n", + " random_state=0, cluster_std=0.8)\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "\n", + "for axi, C in zip(ax, [10.0, 0.1]):\n", + " model = SVC(kernel='linear', C=C).fit(X, y)\n", + " axi.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')\n", + " plot_svc_decision_function(model, axi)\n", + " axi.scatter(model.support_vectors_[:, 0],\n", + " model.support_vectors_[:, 1],\n", + " s=300, lw=1, facecolors='none');\n", + " axi.set_title('C = {0:.1f}'.format(C), size=14)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The optimal value of `C` will depend on your dataset, and you should tune this parameter using cross-validation or a similar procedure (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Face Recognition\n", + "\n", + "As an example of support vector machines in action, let's take a look at the facial recognition problem.\n", + "We will use the Labeled Faces in the Wild dataset, which consists of several thousand collated photos of various public figures.\n", + "A fetcher for the dataset is built into Scikit-Learn:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['Ariel Sharon' 'Colin Powell' 'Donald Rumsfeld' 'George W Bush'\n", + " 'Gerhard Schroeder' 'Hugo Chavez' 'Junichiro Koizumi' 'Tony Blair']\n", + "(1348, 62, 47)\n" + ] + } + ], + "source": [ + "from sklearn.datasets import fetch_lfw_people\n", + "faces = fetch_lfw_people(min_faces_per_person=60)\n", + "print(faces.target_names)\n", + "print(faces.images.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot a few of these faces to see what we're working with (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(3, 5, figsize=(8, 6))\n", + "for i, axi in enumerate(ax.flat):\n", + " axi.imshow(faces.images[i], cmap='bone')\n", + " axi.set(xticks=[], yticks=[],\n", + " xlabel=faces.target_names[faces.target[i]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each image contains 62 × 47, or around 3,000, pixels.\n", + "We could proceed by simply using each pixel value as a feature, but often it is more effective to use some sort of preprocessor to extract more meaningful features; here we will use principal component analysis (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)) to extract 150 fundamental components to feed into our support vector machine classifier.\n", + "We can do this most straightforwardly by packaging the preprocessor and the classifier into a single pipeline:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.svm import SVC\n", + "from sklearn.decomposition import PCA\n", + "from sklearn.pipeline import make_pipeline\n", + "\n", + "pca = PCA(n_components=150, whiten=True,\n", + " svd_solver='randomized', random_state=42)\n", + "svc = SVC(kernel='rbf', class_weight='balanced')\n", + "model = make_pipeline(pca, svc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the sake of testing our classifier output, we will split the data into a training set and a testing set:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.model_selection import train_test_split\n", + "Xtrain, Xtest, ytrain, ytest = train_test_split(faces.data, faces.target,\n", + " random_state=42)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can use grid search cross-validation to explore combinations of parameters.\n", + "Here we will adjust ``C`` (which controls the margin hardness) and ``gamma`` (which controls the size of the radial basis function kernel), and determine the best model:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1min 19s, sys: 8.56 s, total: 1min 27s\n", + "Wall time: 36.2 s\n", + "{'svc__C': 10, 'svc__gamma': 0.001}\n" + ] + } + ], + "source": [ + "from sklearn.model_selection import GridSearchCV\n", + "param_grid = {'svc__C': [1, 5, 10, 50],\n", + " 'svc__gamma': [0.0001, 0.0005, 0.001, 0.005]}\n", + "grid = GridSearchCV(model, param_grid)\n", + "\n", + "%time grid.fit(Xtrain, ytrain)\n", + "print(grid.best_params_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The optimal values fall toward the middle of our grid; if they fell at the edges, we would want to expand the grid to make sure we have found the true optimum.\n", + "\n", + "Now with this cross-validated model we can predict the labels for the test data, which the model has not yet seen:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "model = grid.best_estimator_\n", + "yfit = model.predict(Xtest)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's take a look at a few of the test images along with their predicted values (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(4, 6)\n", + "for i, axi in enumerate(ax.flat):\n", + " axi.imshow(Xtest[i].reshape(62, 47), cmap='bone')\n", + " axi.set(xticks=[], yticks=[])\n", + " axi.set_ylabel(faces.target_names[yfit[i]].split()[-1],\n", + " color='black' if yfit[i] == ytest[i] else 'red')\n", + "fig.suptitle('Predicted Names; Incorrect Labels in Red', size=14);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Out of this small sample, our optimal estimator mislabeled only a single face (Bush’s\n", + "face in the bottom row was mislabeled as Blair).\n", + "We can get a better sense of our estimator's performance using the classification report, which lists recovery statistics label by label:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " precision recall f1-score support\n", + "\n", + " Ariel Sharon 0.65 0.73 0.69 15\n", + " Colin Powell 0.80 0.87 0.83 68\n", + " Donald Rumsfeld 0.74 0.84 0.79 31\n", + " George W Bush 0.92 0.83 0.88 126\n", + "Gerhard Schroeder 0.86 0.83 0.84 23\n", + " Hugo Chavez 0.93 0.70 0.80 20\n", + "Junichiro Koizumi 0.92 1.00 0.96 12\n", + " Tony Blair 0.85 0.95 0.90 42\n", + "\n", + " accuracy 0.85 337\n", + " macro avg 0.83 0.84 0.84 337\n", + " weighted avg 0.86 0.85 0.85 337\n", + "\n" + ] + } + ], + "source": [ + "from sklearn.metrics import classification_report\n", + "print(classification_report(ytest, yfit,\n", + " target_names=faces.target_names))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We might also display the confusion matrix between these classes (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.metrics import confusion_matrix\n", + "import seaborn as sns\n", + "mat = confusion_matrix(ytest, yfit)\n", + "sns.heatmap(mat.T, square=True, annot=True, fmt='d',\n", + " cbar=False, cmap='Blues',\n", + " xticklabels=faces.target_names,\n", + " yticklabels=faces.target_names)\n", + "plt.xlabel('true label')\n", + "plt.ylabel('predicted label');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This helps us get a sense of which labels are likely to be confused by the estimator.\n", + "\n", + "For a real-world facial recognition task, in which the photos do not come pre-cropped into nice grids, the only difference in the facial classification scheme is the feature selection: you would need to use a more sophisticated algorithm to find the faces, and extract features that are independent of the pixellation.\n", + "For this kind of application, one good option is to make use of [OpenCV](http://opencv.org), which, among other things, includes pretrained implementations of state-of-the-art feature extraction tools for images in general and faces in particular." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "This has been a brief intuitive introduction to the principles behind support vector machines.\n", + "These models are a powerful classification method, for a number of reasons:\n", + "\n", + "- Their dependence on relatively few support vectors means that they are compact and take up very little memory.\n", + "- Once the model is trained, the prediction phase is very fast.\n", + "- Because they are affected only by points near the margin, they work well with high-dimensional data—even data with more dimensions than samples, which is challenging for other algorithms.\n", + "- Their integration with kernel methods makes them very versatile, able to adapt to many types of data.\n", + "\n", + "However, SVMs have several disadvantages as well:\n", + "\n", + "- The scaling with the number of samples $N$ is $\\mathcal{O}[N^3]$ at worst, or $\\mathcal{O}[N^2]$ for efficient implementations. For large numbers of training samples, this computational cost can be prohibitive.\n", + "- The results are strongly dependent on a suitable choice for the softening parameter `C`. This must be carefully chosen via cross-validation, which can be expensive as datasets grow in size.\n", + "- The results do not have a direct probabilistic interpretation. This can be estimated via an internal cross-validation (see the `probability` parameter of `SVC`), but this extra estimation is costly.\n", + "\n", + "With those traits in mind, I generally only turn to SVMs once other simpler, faster, and less tuning-intensive methods have been shown to be insufficient for my needs.\n", + "Nevertheless, if you have the CPU cycles to commit to training and cross-validating an SVM on your data, the method can lead to excellent results." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.08-Random-Forests.ipynb b/notebooks/05.08-Random-Forests.ipynb new file mode 100644 index 000000000..913fada4a --- /dev/null +++ b/notebooks/05.08-Random-Forests.ipynb @@ -0,0 +1,779 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: Decision Trees and Random Forests" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Previously we have looked in depth at a simple generative classifier (naive Bayes; see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)) and a powerful discriminative classifier (support vector machines; see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n", + "Here we'll take a look at another powerful algorithm: a nonparametric algorithm called *random forests*.\n", + "Random forests are an example of an *ensemble* method, meaning one that relies on aggregating the results of a set of simpler estimators.\n", + "The somewhat surprising result with such ensemble methods is that the sum can be greater than the parts: that is, the predictive accuracy of a majority vote among a number of estimators can end up being better than that of any of the individual estimators doing the voting!\n", + "We will see examples of this in the following sections.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivating Random Forests: Decision Trees" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Random forests are an example of an ensemble learner built on decision trees.\n", + "For this reason, we'll start by discussing decision trees themselves.\n", + "\n", + "Decision trees are extremely intuitive ways to classify or label objects: you simply ask a series of questions designed to zero in on the classification.\n", + "For example, if you wanted to build a decision tree to classify animals you come across while on a hike, you might construct the one shown in the following figure." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](images/05.08-decision-tree.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Decision-Tree-Example)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The binary splitting makes this extremely efficient: in a well-constructed tree, each question will cut the number of options by approximately half, very quickly narrowing the options even among a large number of classes.\n", + "The trick, of course, comes in deciding which questions to ask at each step.\n", + "In machine learning implementations of decision trees, the questions generally take the form of axis-aligned splits in the data: that is, each node in the tree splits the data into two groups using a cutoff value within one of the features.\n", + "Let's now look at an example of this." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Creating a Decision Tree\n", + "\n", + "Consider the following two-dimensional data, which has one of four class labels (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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Pf5JS06yN8eabq3NIZVS9XikfesjaIHs8UlZUSHnQQZ0/I4QyrF2NYMf9HnhAyl12UfslP+/1Svnb3yrja3WD3H777tfK55Pyb3/r+/WvqpLyd79T8xJCynHj1EsIKf1+WXvsscqwW1FXJ2VDQ9+PP4qxDbY1I8lg9ykkMnXqVBKJBIZhEAgEcFgpuw0nhqHU1K64InV2g8+nBJMGgmuuUbFyt1tV52VmqrS1xx7rey51Y6N1TDoeV8UqPUnHxmLwf/9nHsMHFbp4+WWlS33zzbDlliqd8KCDVKqe1WJjIqFS5hYubE+Ni8dVLPypp1TYxiwXfo89VAz+sstUPrPHo2LJ996r0i37SmGhEvgKheCqq5Rka2Vl2wJzzhNPtGfxmJGbmzo0lA6NjSr7JVl4Y2MzgAgpey8UXVFRwR//+EdCoRD19fXccccdbL311p0+s2jRInxdf6wDQCQSwePx9Pi5gltuIf+++9CsFtIAw+lk9V13Ee6vwH0X9Pp6PN98g/T5CG21lbVUaQ9oTU0UX3EFWa+9hmZitA2PB6nr6Gn0LGyZMgX3ypWm2wy3m6rzzqM+KYgVj+MsK0N6vWS98AKFt92GZrJImPD5ENEomkXudKywkKqzz2b8FVcgIhEQAulwIF0uym66ieBOO/U4776gBQJsOGeOaY/LhNfLuksuofHXvx7Yg0ajFF9zDTnPP490OhHxONHJkym74Qai6VRnpoGIRsl65RWyn3sOEY3SvNdeNBx+OEZ/bzKk/7taHxnqaxMKhZg9e7b5xr647FdffbW84YYbpJRSlpeXy7322ktGIpG03fr+kNbjSTgspd/fc5hgv/1UbHck8vPPUhYUWMeB3W4pd91VytNOsw5ZJF+ZmVKefbb1NfF6pfz+e3Utbr1Vyrw8FeJwu1W4yOMx3y8vL3WcGqTccEMpXS7zsMjy5YNz7Z57TsqsLOs57bnnwB/zuOO6r5UIIWVurgrV9JdgUMqttuocsvJ61RrC6tX9Ht4OiVgz6kMiWVlZZLY2Rs3OziYej5MYSbrAy5alTvMSAv7yF5UhMdKEoJLMm6dU+qzCGNnZqkPL3/8OBQXWmRW6rqoIr7xSKeB1zdzwelUl5cqVKjxx+untXcpbWtq7yyR1NkClw+Xnq3LunlIIf/mle741qNDJzTen3rcvVFVBdXXqMNFA51eXlakQUNenOSnVe3fe2f9jXHutKszq+DQVDqtioVNO6f/4NqOCPj2rn3DCCVx00UXMnz+fWCzGOeecMyjhjz6TnZ26HHzatN63zRpKli1TP85URqe6WsWCv/hCiRNdcw3xBx/E0dysYss+nzKK22wDTzyhYsbr1nW+QQmhbgw77KD0VazCR7GYEsyaM0dJqc6YAYceqmLP8+apCtLeEo32vZt5U5Mq+V+0SOl8nHCCilWfcoq6bslKVjMyMgZe/Ouzz9QN0+yYkYhqbHzxxf07xt13m4+fSKgUyqYmtW5iM7YZDre+P6T9eDJ7tnn2hNcr5fXXD8rcBowFC6TMzu45pU7TpDz88Lbd2q5NWZmUH3wg5cqV6u+lS81DF06nlDvsoEImPR2rtNR8rs3N5iGPnl5CSHnUUe3jGIaUiUTP1+bLL6XMyWkPDbhcKnRjlZHS4ZVwOqXcYAMVXhhI/ve/1CGY/ffv/zFShZ58PinXrOnX8HZIxJpRHxIZFTz4oPI4Omon+3xKn+OMM4ZvXumw8cbWHmJHDEMV0XSlpES18Zo8Wf19883mTxyxmCo5TydEYKVB7ferxgOpQjJmeL0q/PLjj6oPpculxthlF/MyclDe5H77qfZnydBANKpCN1aVk5qm5uDx0HTggcobHuinwd12sw6tZWTAH/7Q/2PMmmW9ze0eOgkDm2Fl7BrsTTZRj8dnn62M9A47KMP1wQfqUX4k05tKv56SfKRUVYpWIaKkJnUqPB743e+st19wgTIYHSs9hVCG8ZZb1I0zWU2oaer9M89U+2y/varGjMfVjWPBAvjVr8ybIbz5pnVM3wq3W8XhAwEqrrpKVWUONC4XPPCAOq+O5fgZGUpTZSC0av7xD/MbTUaGErcaiam1NgPO2P5XHj9eLdb0tsS4qkrFBCdP7luZdH958MH0y7p1XcWekwYx2QJt8WJlSJ5/XsWdrejJu9Z1lZP9pz9ZfyYvT6nvXXWV6ibT0qI8/CuuULrShx2mYrALFqh/k1NOUTKuRxyh5tv1phMOK4O+eHHn91ev7n3TW8NQZfh9KZPvDYccom4y11yjvPiCAnXNjj9+YNQW99oLbr1VXZekNx+NqmOcf37/x7cZHQxHHKY/DGo8ackSKXfcUcVDMzJUHPnaawcm9a+hQZV/v/yylE1NUsbjUr7xhpR33aXKyzvGbw8+OP1YsNcr5T33SCmlXP70053ju/19aZqU55wzeNV/qeKyTqeqPOzIe+/1nK7Z9bXFFm27j4k4bTisvjcvvyxlff2ADTsmrs0gMZJi2GPbw+4NFRVKIKixUf3UkzHRyy5TqVN97d8npfI8r7663VuPRpX3K6XyGDVNpcm98Ybqf5iXp7yonsIdoLzRRx6B3/6WiSedpOK7/UHX1Wv//VU4o7S0f+OlIp3z68icOSo1MRQyfzJwONr1sIVQ55Gbq8IVRx7Z//mOBDyezo0ibNYrxm4Mu7fceKO5HnQkAjfcoBa7+tK9/L//VY/J4bAKszQ1qTGbmlRXk1BIhQVWr1bxzlgMfv/73i+MvfYawizfubdIqZrtPvfc4BprUNfUarFuxgxlbDsihLqpTZigyv4dDrXomZGhGhmfcoq68Tkc6iYYj6vON6efDjNnoldXD+752NgMMrbBTvLyy+YFHknefFPFZXsTQ5VSeejpLJRJqTIfXnxRZUoccUR7oUoqMjKUfOyqVYi+ttfqiGGoHor779+5SGMwuOoq816WXq/qPmPGtGlK8/uxx1Qx0K23qhzsY45RTwRXXqmeXjr+OwWDUFZGSX9zoW1shhnbYCfpKXMkkVCLd6+8kv6Y4bAKtaRLc7PqDC6E8szvvx923lllU5jNz+VSXvD8+bDhhsiByhRIJODdd1NnhgwEM2aoDjt77qnCF5qmFiP/97/UzQN0HQ44AC68UC3qdTT6N91k2ajC99lnfXtKsrEZIdgGO0k6YYhAoHs3lOpqlQFx440qU6Ijbnfv0q18vvZ8WiFU9eEFF3RvO5bkyCNVRkJrebnh96cutdd1dYyzzuq5JD8SUd5+ZWX68wf1pPDOO0od8MEH1U0oFZttpq5psnXb55+rJ5m+sm6d9dSEUEb+vPNUqmNvY+g2NsPNcKx09odBW7ENhaScNctaWB+UrvZf/9q+z7//rYSRfD5VcefzSbnbblIGAu2f+e1vexZn6pjx0XHl3zCkLCmxzqI466xOp7D05ZeVGFBmpqok9PlUxsusWVJusomUJ56oMmEMQ8opU3rW0dY01ZAgXcrLpZwxQ2VyOJ3qvz6flM8804d/kD6y006W52MkKyxb9bHlnDkq68LGzhJJwUjKErENdkcCASnPPTe1Qf32W/XZt94yT0tzu6U8+uj2MaurpZw6NT1j/dxznefz00+pU/S6lIv/8MMPUkajUj79tJRXXCHlvfcqwf7775dy+nRlgPPzVZOAxYuVGqBVc4Tky+PpPi8rttrKvFmEz6fUB4eC117rWUGw47mdc87QzGuEYxtsa2yD3Q+G5OJddln3H31GhpSnn97+mT32SG0IamvbPxsIqPzoVDnHJm3W5I8/pjbYJSWdPm56bf72t+5jeDzKE21sVOeU6qkCpJw4sedc9MWLrefqdEpp0pVo0LjxRnWOSQ8/1bllZEgZiw3d3EYotsG2ZiQZbDuGbcbf/64U7nbaCYqKlOLdf//bWQ40VZd1l0vJlSbJyFBjmsXIvV4VUzYTud9wQ2sFNqdT5Y3Pn6+ySs47D2dZWefPVFUpCdau2R6RCHzzjUp5u/lmSDYusKKmBlasSP2ZH3+0ruiLxVI3QR5ozjpLSZ7efrtaW0hVaRiL9Rxnt7EZKQzHXaI/jBhPYNttU3vYXRvJJhJSzp+vPD5dV3HUjAwp995byi7NHzrx1FPdhfE1TR0j2bsQpHS5ZMLrlfLNN9v3feCB1JWBSbU8w0it2Kfr7cp/Vnz0kfWxNE3KE07o23UeCCZMsD63rCxVdbqeM2J+VyMQ28MeC5x3nnmetMOhUvHGj+/8vqapisRPPlFa3BdfrHSMX3/dWgkPVKbI00/DppuqMRwO5VGD8pSlVP8fjap2aIcf3p5Pnki0bzejY1XgxInWn0skzPOlO7LVVtbH8niGVyHxggusn27OOGPwdUZsbAYI22D3lSOPVOGIjgptfr+qwnv4Yev9Zs1SBvsf/1BKdel0vNl/f5WfHQopI73hhtZFPoah8phBlTBbFdP4/Z3Lta3kSUGdY08hjWOOsT7WhRcqEajh4owzYN48DLdbhZIcDnVOe++tCptsbEYJtpZIXxEC7roLTj5ZKdQ1NsI++6hOLKk85v6QHLeiwlplzzBUbjiom8fvfqfyoTsWk7hcSomwYyPaoiLrTt+a1r1MvCPLlqknBTOj7/G0KwkOF5oG997LikMPZfr337fram+55fDOy8aml9gGu79ss416DSU776wqEc1aekkJHTvY33orTJmixKuam5XxOuYYtRjZUb/6tNPUQqRZOXpeXmrj9umn1gVCkYjS/7jggnTObFCJTpumKiRtbEYpdkhkNHLSSaYG0nA6Vcilo3HVNBWSqKpSr+ZmuOce1feyI0cfrW4EHePyTqcKnTz+eOrQTVZW6kyMwWgaYGOzHmIb7IFi7VoVGnniif5LnPZEYaEq/y4pUap1mZng9RKeNcta60TTlJG28oQdDrXvnXeqdMZNNlHhnq+/VumDqdhrL+sFxxQtsiKNUP0DRBpSD58O0oBoQP3XxmasYodE+ksioWQ9H35YeaRCqNzeq6+Gc84ZvONus40So/roI6X3sfnmrAZm9sebdThUuOSYY3q3n8cD992nhJgikfb4ekaG6te4556dPt7SDC+fCkueBd0JiShsfDAcdBd4cnp36EQU3rscvrgFYiFw+GDbP8Lul4PuMv/8jy9A9feQWQKbHtn7Y9q0IyVUfgXhWijaHPzFwz2jsY1tsPvL5Zcrqc+ujWAvvhg22AAOOmjwjq1pStQ/yZIlAzt+Q0O7iFNLi1pUTZ5XVw47TEmfXnstLFyoGg2ceabKROkQTpESHtpL/cgTLZBo1bT66QWo+wVOXgSiF899TxwKK96BeGs4P9oEn92kxj/m1c6RnKblLv69uzLs0WZw+uD1c+Dwx9QNoyekAcvfgtULwJ2ljH12imzIsU7Fl/Dk4RCsAs0B8QhschgcfC84Rnjb1NGKbbD7QzTa3vigK6GQMuaDabAHk/p6lYpXXt5+I3r4YXjmGdXIeKutuu+z1VYqJJSC1R9C1XfKWHckEYW6pcogTt87vSmWfQEr32031kniYVj9AZR/AaXbqfekAe//YRLhKqA1ehNr/Wd75mg4/cfUxjdUA/fvBo2rVOhFd8E7F8Nul8Iuf01vvkYClv1P3UwyimGTw8GT3eNuI5LmcnU9ol2KRJc8B4kYHPHksExrzGPHsPtDZWXqhgYD7fEOJf/8Z2djDepcAwE48cTun1+zBk49VaUHFhWpMNHq1d0+tuId0IKN+KkAOgecowFlsNPll1cgZtHwPRaGn15q/3v52xBr0tqMdUeMBCy6K/WxnjkGan9WcwR1g0lE4IMr1dipCNfB1w/CvyfA0/Pg3Uvh9bPgXyXwwzOp9x2pfH6LugZdiYfhpxehMUXfZ5u+Y3vY/SE3N7XBHs3ZEckwiBk//KBywZPVnMuXq5h6c3N78cx//wtPPQVffNGuk7J0KVs+fDK7sACJRgtZvMvlfMkpgEA4VJgiXYTW2vrSbJvoHA6pXwYyYZ7pkmhRXr8VTWXKYzdi3bfFQrDgOpi2R/dt0oA3LoAvblX7dlwQjbVmTz53PIzbAvJMokwjmRXvdH9KSuJwQ/nC9TtcNFj02cO+8847Oeqoozj00EN56qmnBnJOo4fMTFWFmGyu2xGvF/70p6Gf00BhluOdxOHovP3881XhUMdKx3hcvXfuuervigrYfnuyV7yPgyhOIvipYh/OY0f+BagFyE2PSn+KGx+sjIPpFD0w49ftf+dMAeEwz2TRXVAww/o4DStBT1ELVfeL+fvv/wMW3aEMm1X2ihGDz2+1Hnuk4s233ialvZA7WPTJYH/22WcsXryYxx57jIceeojK3nYlGUvccYdq09Uxf9nvhx12gLPP7v75Dz5Qi3elpaod1qOPptb7GC7mzrXOvfZ6VaUkqIyQl14yr7w0DHj1VfXfG2+EQADR5XMuQszlcry+MFv/AQpnpj/FcVvCRgeqzJCOOH2wwX4wvkP90LS9wOE1v85Ch21OsT5O9iRrbxIg10RoMd4Cn/yrPU5uhRGDdUMoZDhQbHMqOC1ajuoumNyPpkE21vTJYH/00UdstNFGnH766Zx66qnslqr/3linqEiFCG6+WVXRHXaYMsJvvtm5khBUjvN++6nKv/JylU1x8snw29+OPKN9+eXmJeU+n2qemxRMMozUYaFEQr2ef95a/0TTOOzCxex7U++neeijsNvf1SIeAjKKYM6lcHiXtU9Nhzl3r8abB85WHSuHBxxeOOS/ygO3InsiTNgRNJMHKacPdjYp4qxfrubTE0KHvOkqzm30or/zcLPRAbDhAV2MtqaeRH7zoMoa6Qkp1ZrF+1fApzephUyb1Agpe28pLr74YsrLy7njjjtYu3Ytp512Gq+//jqig0e2aNEifD31SOwDkUgET08Nc0cgWlMTG86di2YSFza8XlbfdRfhfgokDfS18S5cSMnFF+OoqkK2KgVWnXUWDUcf3elzUw4/HK+FPnhk441Z8dxzTD34YDxLl5p+JpGRwer//pfI5pv3a75Spi7IjEQiOKSXNa9n0fCjG9/4OJMPbMRT0LOljNTqvHPcZCJVDuIhHeEwEDrMOLGWzc6o6fb5cLWDV/aajhHtwSfSJZpDggG6R7Lh8XVscmoN2hALCPbluyMNWPtGJov/WUSkyonQJZpLIgRsfUklUw5usty3pUHnvRMmEVzrJB7W0FzKDG12ZhUzflffr3MZaIba5oRCIWZb2II+LTrm5OQwbdo0XC4X06ZNw+12U1dXR35+58DWzJm9eL5NkyVLlgzKuIPOQw+pWLeJwdYiEaZ88EHPjQR6YMCvzcyZak7LlqmCmBkzGO9wML7r526+WRXIdI17+3x4brlFzemUU5RKoUlsXPf5mHrYYYMuc6quzww237rju+lXemyxFJa+BqveB3eOxmbzIG96IVDY/cMzYfHWsPYzzFdFNfW+JgRGi7rLGDH45b5C9IZCDk0h+DgY9PW7U/00JJoBCTIuSLQuYyz+Rykzty9lym7m+z20DzSvaF/ITV6DJbeOY6sDxjFlbu/PYbAYapuzaNEiy219ConMnj2bDz/8ECkl69atIxwOk5OT09f5rR8EAtahAykHv5y9rwihCmU228y6rP1Xv1IZIZMnqzBKMsb9xBPtVY6nnKLi9l3DRD6fChWNAk1qTVcx872uhzl/U6GMVPz6AfDmgt7BOdNdKmyz6RHg9ILRRZE2FoIfnoJ7doArnHClB546Cup7aPgzHCSi8LFFnD4WgvcuM9+vcU3qrJuPrxvQaY4p+uRh77777nzxxRccfvjhSCm59NJL0UfBD25Y6ViR2BW/H/bdd+jmMhgccIDKmEm2RpsypXN8IjNTpfhdeSU88IAqLNpmG7jiitTXZgTS0gxrP1Ex7Yk7WWeq5G8Epy9RWSA/vwwuH2x9Emw2D14+zXpBMhGFss9a/4jDkqdh+ZtwypepY+1DTeMazJ8eWqlcbP5+wwoV645b5NDX/NjvqY1Z+pyH/ec//3kg5zH22XRTZZjef1+FF5LoulK7mzdv+OY2UAgBU6dab8/JgRtuUK9RiJTwwRXw0bUqBTHJfjfDFseb75NRpHRNdr+88/vpLMq1HdeAliblsf76/t7Oum80rVWVnD88rZ4CJu8Ke1wDJR2UhD05qqrRCqvUvh6zbkZZTvpQYlc6DiXPPgtHHKEaEWRlKdGknXZSetKDsEBr004iCqtfy+Tl0+Dtv/XNi/viNljwT1XN19LU/nrlNFj2Ru/G2vRIcPXQda0jMgE/Pt+7Y/SV5nK4cyv45mFV4JNoUdkc98+FVR+0f86Xr54wzLRfHF7Y5jTz8XOmQMm2IExuWk4f7HT+gJzGmMQ22EOJz6cqCMvLlTzq0qUqLztVP0WbXlP1PbxzCfzvXPjlVWhYDTdvBAsvHc+iO1SM9M6tleFOF2nA+5dbx2vfvaR3c5z6K5iwgzJsvZnDUPD+FUryVnZZcomF1M2pI4f8VxXRdDwPZwYUz4IdzrY+xhFPQs4kcGWqvzWnGmOnC2D6XgNxFmMTuzR9OMjLG91l6yMAKVUsVBqQO015ebKsnNfP0fjypWISMYFMwJd3q8/EIoCh1lmMuHp9dhNMngMb7NPz8YLV3YWOOlLZy+IXIWD+K6qs/fObIVQLmaXKUEZNsuGEBhsM0TLHD091XwxNUrcMmisgszVVKGcKnPEjLLobfnpeGd2tTlSLqmbytkn84+CMn5Tey6r3wZMLs44ZfSX6Q41tsG1GHUv/p/S0Q1Xqb3dmgv0KryT24yoWx28m3qFiJSnWZEYsqKoR0zHYLn9qD7c34Y0kugvmXKxCAM//Dn58zjq27cyA3f9hvq2lST1JRIMwZW7/jV5Xz7ojQuue3eHNg10uVK90MRJKo2XyrjDzN32bZyIG3z2ubsrRZthgf9jujPabyVjENtjrGYlEhIbAN7TEanA78snOnIVDH+YmuenQ3AwPP0zosTdp/jiPzMTvaWRHQBAL6Ty17hJUaWEa5YUdqF+e3udcGaq8fenr3Q2a7lZeZV957nj4+aVWffAui3FCh0m7wn7/Mdc7WXQXvH62MvTSUHPbYD847DHr7JWemL4v/PCk+Q0qoxCy+hHBk1Lpq7x7qQqxGAkYvxUcdA8UbZr+OIkoPLin0uROCmlVL1FCW79f0LuxRhN2DHs9Ihheyc+r/826ureob/qCdfVv8/PqfxMIWXRLHyksW6ZywS+4AN+Hz7FF4r8cx94cwCm055Vp9NZYI6CwFz/sA+8AX0GXeK1PhWSm7wWf3ghfPaBan6VL4xplrM1S3HS3igOf8C4UmxSBrnwP/neOWgSNNivDFY+om8prZ6Y/h67sfrm5TojDC/v8O3U1aU98dhO8cb7SF4+F1A1q7Wfw352gsbsaryWL7oaKRe3GGtRYLU3w3HF9n99IxzbY6wkJI8rqyscwZBQp1TOtlDGkjLF63RMkEhZJsSOBI4+Empq2ju4aEhdBZvEoG/NCn4d1emHnXmSnZk1QedVz/w7jtobSHWC3K5Qhe/zX8NZf4LUz4F/jVYZFOlQsso71Jlpg1YfW+35wlfkiaDwM3zyojFdfyN8Ifv8RTNxZLQbqLhVmOfwJmHlo38YEJYj13t9N5iyVfvnH16c/1he3WeSxS5UB1LCy7/McydghkfWEpsD3yBRVDvXN31KQs+0QzihNfvlFNYIwUQN0EWQH/s1P/DrlELpbGed4NEGiRVcGUsKe/4RJO3f+rJTKiFZ+rRbGpu/dOefam9s5XvvgnlD9XbuYfzKk8fIpynsfb9KYpyOe3NS6X4FKdQNAqPZbu/xV9aIEqPomxTm7lNEqnpX6+FYUz1JGu6VZnZs3r3+eNUDVt9bnasTgp5dVTns6RFLIjehOCNePrCKjgcI22OsJ0Xh9m2fdFSljfHh9HSsfhrkXw1Z/SP3jlFLSHPqZ+uYvMRJh/L4NyM2ajUO30NvsDxUVqpzdQp87i7IUO0ucPknR5hrHvgGfPb8WvXwy7izVniujqPOnA+vgkf1UZxlQC2y6E4563lwutGElrFlg0XklohY0e9IEmbhz6mvdvLY9lrzwTvj2MVXxmD1JKRQGq8z3i7eAz0TipLe4M/s/RhLdnXrh1pEiq6QrE3ZUi7SmHYTi6ilhLGKHRNYT3M58NGH+i4gFnTQvK6BptVrAeidFfrKUBmvWPc7aqmcIhH4m1LKG6oYP+WXNLUSi1QM/8Y037lwZ2gEDQQXmLqxGjCnTV3HM6xonfgKeLCjaNsQuf1Fd1ZPG2kioVLWmMmWsq75VcdFYUMWFw3Xw6P4qla0rNT9ZNzaQRs8619KAZ+ebG/zkL7OjgTNiyrN8s1XOdYezzWPNQlc53iMtW6JoU+vqR4cHtvxd+mPNuVg9NXXF6YNtz1CLxGMR22CvJ2RlbNK5JC2WwPfFKjI+Xo4WiLLm5c3U2yH45P9U3rEZjYFvCYRXdPLWpYxjGBHWrnt64CdeXKwaGZvIW8bxsoDuuWSaiJORn+DIz6cweVdrD3bxvSrccMcs+M801RzXLP/YiMOiO7u/nzXBXMAoSfZk620A3z+l0vFMNTUsPFFpqIpHKWGL38L0fTobbWeGuhn95qHUxx4OhKYKbbo2nNDd6lpu+8f0xxq/FRz+pCracWWCO1uJbG31e9jj6oGd90jCDomsJ2iakynjjmVl5cNkvrCY8Ze+AAmJFCCDGtXSyUdcBAh0pxIb2nx+93FqGz+3DK1E43W0xGpxO1P0j+q6TwA+vgG+vEd5taXbq3xjb74q4IgGYMpx9zG1/jeIjxcgEUTDOoIEL3EnFWzTaTzNCZsf42DPax14U9QmLb5XZVL01BEGlEFd+1n394s2VRki1T90f9R3ZsAO5yjDmuyyvvpD5bGP31ot4n3+n85ZDumSiKOkWXU48mnVX/Hr+1W8eYP9YPNjwN2HvPChYPrecMJ7qjJ0zcfKI97it7DrX8Gd1buxNjoAzq+ENZ+o61iyrSqXH8vYBns9wuspZeOlWyP+ehki3Nmt25WriZDDQk4HrBeHEoa1hRHoJBIhSNNgx0JKRrR+WbuXuex/sOJt2jL0jBh85veTO+1NTnjzOzzff8yyN7J45dUDCYXbrZLuVkbw5EXW+ccNP7l5+T+qQnLVByqbIh2ErmLGZhz1HNy7c3sYRehqLtueodTqnpmnFsBkojXjwg0yDlN2T53GJjTreG/J1u0PS0KoBsDFs+Dtv6o0v1dOUwuee1wNGx+U3jkOJaXbwrGvD8xYmmP9akdmG+z1DO3Sv0O4+zO4ixC7cRkLOY1ETLPUc/C6JxCLN2G22iNJ4HYWpD2XL+9RxrNrSKBrWCIagOof4fnrNmPeC5sx8ySIPgDvXQ6NK5U3u+XvYI+rOhtrKQ0aA99R1/Q5392xMd/csCNGTFp2T7dCd6sehmbkbQBnr1CLgSvfVeGILX+n0s6+uLmzB2/E2kMoy95UhtuKpOHvdlMRanH0zQtVDDtzvMr7vntbJdqUHL/6O3Wz2O8W2KoXsWGbkY1tsEcBLdEaqhs+IhRZha65yc3chpysrdBEHzTIv/rKcpOLILmeSmaeUdItgyJJQc4uNId+7hYWEcJBtn8Wei+qJhf/N72QBIARVSXpwWpVbbflCeplJDBtpyWlwerKxwlGVtL4Szbf3LADiUjvvu5Jo7nrRanT85w+2PpE9QJVDPP1/dZ6z5DaWIOqbtz2jyps09Kg8pSR6tW0RhWgfHk3/OEzlS0RrOoeT4+FlMc965jUuh42owfbYI9wguFVrKp8BClV4DIGVNa9QWPgWyaXHN97o52RYZkip5Fg56sy2foc69297nFMKDqMsurnWp1siSRBpm8m4wv279VUUhk0MxxuZawyOqSrWfU+bAouIRhZiZQxVjy+NUYsvfV13QUl26mskqyJyrMet2Xv5rnsDWXs+4MRU3nXM3+jmh18db+6aSVJtKjskhf/oDJHLMM7Esq+6J5vbjM6sQ32CEZKydqqZ7t5s1LGCEcraGz+htysHiozuvL738NNN3XrLSk1DX2v3Zl9bs+Jt1kZG+P3XUAovBLDaMHrmYDT0csVI1S7rc9XWKS1mZCIpq9jUde0sO26hcqzkYmeLajuAv94OPoFUi5YgtKteO8ytTirOdQC7a4XqZBIfwtMQIWKQMWqf3qhs7FuQ0LZp5CbolVZvAXqltoGe6xgp/WNYCLRSgzD3A2VMkZd08LeD/q3v8G0aZ0bJng8iLw8uOOOtIfRhI7fN50s/yZ9MtYAO56rwgnpSIBoLiW+lJFmMUjH65a35Vo0j/ldQehKac8/HrY/WxWl9GSsyxeqmPGSp5V3G6qGz2+B22ep0MQG+1nLk6ZLR8W9VJkkwgEb7q/ymM1ItMALJ8Bd21gX2diMHmyDPYIxjBZSWTNDpuizZEVWFixcCNddB7Nnw6xZ8Je/qPLvKVP6PNe+kFkCv/8YJmzfWj6eoQorpv5K/a21loS7/FA4QzW1TZcM71RAedVTjvgKTe++SCp0pYD3lyY4awX4i+Ge7eH6Qnj0QPNUPoCXTlZGtGMWh0xAcB08uJfysrc/s/Vm1AccXtipg8ZJSQrFAKcXdr5QlbinCsNUfKk6lacqg7cZ+dghkRGMxzUOiZU4sUaGd1rfBvb54PTT1WuYKZwJJ36ivL+WZpU+pztV9eH3T6j3pu4O0/Y0b0VlRX72DtQ3LcKQCdy5YeY89CAL/jCfRIsDI6ZjRB1IQ1XMGTF4YHdVOJOMBf/yqsr6OPQRmPHr9nGDVVD9vfVxq76Bty5UndXzN4IPrlTpe64M8Jeo8IRVUQyosMxOF8CG+7W/t/sV8NBe3ePUTp8SosoohJMXqhTJpjUWA0uo+xnWfgoTd7Q+vs3IxjbYIxhd95CbOZv65i+7xbE14aAge+z88jKKOmt75E1XMeG+4nRkMaXkt6xZ9zTh5gD+qbXs++5NfP9/v2Lpw9upD0mlEJeIwrpvuhhEqbIsXvg9bHhAuwBUvKXnBcUvboPdLoOt/6BeUrbHtX95FZ46AuLR9kyRZA755sfAZkepYpyOTNpZ6Vu/dJJaqBVCZcfM+ZsS7Af1tOLOBqwMNipMU7nYNtijGdtgj3DG5e+NEBp1TV8g0JEYOPVMSosOxeXMHe7pjWi87hIm5/2JO/arwuEP0/hTMbHGzmmHlV/Bwrus48RGXFXkTZmr/s4qVYp9zSmKbnSnqn4sbb0vdFyE3HB/+O17SsC/9idlqLc/S72farFyxiFqkbbiSxWXHj+7u5ZG7lSVf21FsnDnnUtUpxZpqEyUHc/r/LloQLXuCtepIpeSbXteSLVKr7QZWGyDPcIRQmNc/t4U5s6lJVqNrrlxOQsQA5GKMEJY9UUdH1yuU/6JH1eGxlYnCnY8d2CU4hwuQdMvxZaaH7oL6pda7y9EZ89baCrc8eyxmCrFgWpdZSZyJKUqyf7kX+150WtrYLOj08ss0XRlQJOs/gjevgjKPlcpj5PnKoPctWtNR969RBni5Gc+uwm+ug92f8wBM+GHp+H536qnCCOuzrdwE1WZ2HUx1oirnpSf/ls1JPAVqIXbXS60bnVm0z/sRcdRgq658Xkm4HYV9ttYSykJRlbTGPielmjNAM2w9yQSET5+8nUemutn+auZROp0mtYIPrrG4J7tUvdjTBfdpZrXmsW/hUNldIRqrfePRdo95SSbHqkWRq3ImWIu7/npv9UrHlHNBVqalCLga2eo3O3e8Mur8NDeSp8k2Wll6evqfM1CNg6vkiQNVXc26ImoKp1ffPU4qr6H536rQkHRZnWjigWV6uCTR3Qf8+l5qolCqPUrFKqBD69SIR+bwaFfBru2tpa5c+eybNkIbzFl00a4pYKfV9/I6opHKK9+iWVld7Ki/D7iiTSFNQaQVZVP8NHZO5IIu0C2fxUTLRoNqyQL088yTMl+/1FZFJqzfbVPdyuhoHFbpX6UL5zZ2bOs/Br+r7Q1g6TLfVN3KeW4Qx/pPo6RUMbMrLIzFlKeb7pIqTJVui5CGjFlgLc+CWYdp2LheRvCNqfDad8q7W6zdEOZgIoP/Xx8g7l3nojC2o/VQnCSii9h6WsQ73I+8bC6+ZT3IePUpmf6bLBjsRiXXnopHhPZS5uBRUpJLN5ENN6I7EdeVjwRYmX5A8QTTRgyiiFbkDJOKFLG6koTKzOItERrWPdtC9EuMeW2uYYFi+8dmGPlTFEGa4Nj6smerP7e8Vz1nqMHUf2q7+CHZ6Dqe1i9QGWTBKsgFqBTSEToMPtU+OP35mXswarW8nILyhfCf6bD/bu1y6daUbMEIg3m2xItsOx1+M2DcOYy+NPPcMAtyninCpUgofJL647puku13kry88vWlaqxCPz0Yopj2fSZPkea/vnPfzJv3jzuuuuugZyPTRcC4eVUVL9CLKEa9Dn0DMbn70dmxsa9HquucRGGqYhFgki0inBLBV730KjeR6LrMCIuhGZtLWNdDIKUsORZpdfdtEbFVnf5a/uCYCoyx8OWf65i5n2dlQSn7akqFq1i3DIBTx2uQgpSglXrS6dX5ZNnW1RiujOtjSGom0b9cvUqXwizjlVNf81IxpatMPOihYDiLVSWiBkZJTFyprpYZ9F2zEi0tyYDdS0s7ynSzvceLPrkYT/77LPk5eWx667rka7hAGIYMaKxehJG6sKXUGQ1qysfIxqvQ8o4UsaJxRtZU/U0zaEUK2VdkFJS2/g51Q3vgWVeN0RaTNqqDBIOPYPsGVUgzePxwmGwwb6d33vlNLUgtvZjZbCX/U91g/n81u77R1oqKa9+mVUVj1BV/x6xuHlAfPzW6VVPxsPWxhpUvL0qRX62yw9T90xPYyQWhG8eUjnTZhRuYr2opzlh41+bb9vzWvNiHqcPZp1XxfZnWRT7CMgs7aypstGB4LR4uHZ6YeODzbfZ9A8h+/CMfcwxxyCEQAjBkiVLmDJlCrfffjuFhe3f/EWLFuHzmf3r949IJDIiwjBS1CL1H0FrAOlFJDYCoxSRojJRkkDqX4O+ou0djFJEfDaC7nJqhvNt0CxWxIwstFhni2Z1bQz9B9CXgEjl4jkQ8e0RRqn1ZwYQiUS6XuLHu7Zmyc1zVRy7w1ZHRoK9n1uJf4Jyfeu+9/DucZNJRLr7GJrL4KD3luLOUedn6EtA/wEwQMjW+LhGpG4HVjywOcufyiUW0MjZJMJmZ9Tw/a0FVH/Rv55Susdgiz+vY4N5DZafCVU4ePPIqcSDWofzkJhWs2qSaYc1sM3llaZjLX8mm8VXjet8PYTE6TfY5/nl+Mab18aveT2TL68cR6JFHVPosMWf11Gy/zo8Hg/f/F8hvzycRyIqwBDoXgPdbfCrh1aRNb1zef9Hp09g3ScZneagewyKtguy6x1rLa/DaGOobU4oFGL27Nmm2/pksDty3HHHcdlllzF9emcFmkWLFlketD8sWbKEmTNnDvi4vaG++Wsqal5uVdBTCOEk2z+L0sIDLfdbVfEowfAKJB1/TBpuZz7TJ5yK6PCcK6XkhxVXYP3gqTFzyoVoWruhM7s2hhHlx1U3WHaJaRtNuNl4yvloYujysUKRtawsf4if792GH27ZBSOuIRMauRuFOfyhLMZt0f7Z185s9aRNIijODLWwuNXvIdKyjuXl93T6t0kSa/bw6i7nEwu0u7lOn8qeWPlu6lh2Tzh8cO5alaOdxEjAL6+oTA53Dmx+tFr8/PIelT4XrlVVkFbhmJmHqY4yoDSvG1aoxrvJXo3fPqqaFgQqVQhi8q6w/21Q0EO0zEi0djA3VOMDzdH5u1P5FXx5ryq1n7KbWsA0S7FMxFQl5+f/URWpLr8qyZ9zSedO86OdobY5qWynnS3ZSxJGSzdjDUqMqTHwDbmZW+LzTOi2X6RlnZL7pKshMYjGG2kO/UxWxoy2d4UQCLQUpemkVasdbilvHSfFMMLJxOLDh9RYA/g8E9hw0p8oOG8hs05+mlDZOAqLN6V4ekm3z0YasSzpNuLKYEBSpc/imgmDgm2XUfGuyrnL2bSCTc5+F3deiNULfksi0nsro7tVlslhj3c21oF1cN8uyphGAypU8eGVsMtfVDn5zheo6sp7djA32M4MJXYVj8CrpyvjrLtUpeWE7VUmyubzVQ53uFaJP7lStAUz4io2nohByTapJWPHbQn735zGuTth98tVVWc8ouYwhsoDRiT9/oU+9NDAdftsidZQ17SIWLwOj2s8uVmzcToGoHpiAGkO/WxpAKWM09D8lanBDoSXIy1cOCmj3Qw2QGbGDJqCP2DmZWd4p6AJB/F4gOqGBTQFv8dwxSivXkpBzq64nDkACKGb7p9E13xMK/3DsFVNOh1+ivJ2oygP5CRJJLqOYHglHldxp2YI0/eCH581z83WdJi0i/r/WLwRq/MVmsRdoAYo2G4lu9z7KLonhtBgi0te46vL98eI6qQlHyiUccqZDEc8A8Wbdd789FHQsLJ9ATDZbWbBdTBhJ3U+xbNUd/M1H3fO4BCaMr6zjoWnjlISrvFIe1bG6gXK0P/pZ/WE4Ouhyc8PT8PLpyhjLQQYBsy9RGmWDISBFcK8g7nNwDNiPOy6poVU1v6v1agZBELLqWn8mEnj5uHvq8jRIGAYLUhL9R5J3DBvoaIJB0IIy9VzTXT37orz9iQYXk7CiNBuhASacDE+f19i8WaWrb2ThBFGxWuhvnkxjcHvmVbyB9yuArzuUmW0TY4rhIPCnDkjosQ9FFnD2qpniCdCbU8WOf4tGV+wH0JobHK4quqLRzpnQehuGL8NlLQ+QXo9pQTDyy2fTBp/KgYks695EYcvRt0341ly81xqF0/AlR8gc0otuszFIfIYv5UqRmmuMGkQ0JoJUb9CZZH88bv2hcDG1VD2mXm2Riykmg4nW7Ad/SI8/zv45eXWKsWo6sd46MOqacHS17p74DKh0vq+fay9y40VK99TC7Vd87/fv1w1vbVqfWYzMhkRBjsaq2811u3fcEkcJKypfIKNJ5+Ppg1NUMyQCRKJILrmNT2mzz0RKw9MCCd+j/nNJTNjYyrrzMvZVPx7827vu5w5TJ9wCtX1H9AUXIJEkunbmKLcObiceaytep6EEaKzNZYYRgsVta8xZfxxCKExvuAAyqqf7xxzR8fpyOnUACEWb6Km4RMCoZ8RQicnc0tys7ZB17oviA4k0Vg9KyseaouzJ8+mIfA1ACWFB+DwKFW/Z46G8i9a+x22qCazh/y3fay8zNnUNnzcLSwiDY3A6lzqvykhY1I93uIAFe9uwKdnHEmiRW8r3InVZ5A1vY4TF6pH/GgAvrgdvri1tWlulxufEVO9FH96SXWHAWhY1To/i6ySjqXwLj8c+ZQKodT+rOLToVr4704QDVrHt2NBZeR7MtjvXGxdrPPe32H2yb1TQbQZXkaEwa5v+tIyXADQHPqJbP9mltsHAikTrKt7h/qmhSqDQSbI9G1EScEBOBztwUGPuxivewLhyOouXpxA01zkZM4yHd/pyCI/eydqGz/ptAAohJNM30Z43ebZGU5HNiWFB1FS2L39tVW4BCAYXolhxNA0J9n+TXHoGVTVv0u4pQJNOMnJ3IrC3F3bFi1bojUsL78Xw4iRTP2rqn+X+uYvmVZ6Erpm0Yp8AKhp7G5gQa0LNAS+oijvVzh0L1ml8LsPVM/E5nJVDNI1Jc/h8DNp/DGsqXwcKRPI1uvjcuTx2VnzEJpAcyYwYhoLLzykW9w6EXHStDyXr+5X3qfLr+LNQigP38yARptVsUrSYOdOTV2kYla27i9Wr0gj3Dkbok2prhgg1EJmT1Qsst7W0qQKevzjeh7HZmQwIgx2NN6A1YqSIRPEEwMgKtEDa6uepSn4Ex3zlJtDP/LT6h/JztiMcQX742iNqU4aN4/y6udpDv6M0BxImcDtLGRi8RGdsja6Upy3Ox5XMdUNHxCL1ePQ/eRn70hu1uw+6YNYLq4lt5MAlEHK8E5hqte6fXZZ9YvduttIGScWa6Cm/iOK8/fo5dwkochqwi1l6JqHrIyZbTHpeDxAfeBrYrF63K4iguHlWP37C3RaopU4vFPb3sueaF2gApDhmcTGk88jEF5OPB7A4yrC4y5hzu3L+OGaHNZ8mk/916WWi4yJsIsv7+kcLnB4VcjDzGALDZwdFvyyJsDEnWHVB90/7/R1bk7QlW8e6rlBb3KcLX+bxucyrD19aajtNqOHEWGwve5SmkM/mqZiaULH7bRo4T1ARFqqaQouwcpbbQx+T7ilnOkTTkPTHOiai4nFRxKPB2iJ1+HU/bicPfSVaiXbvwnZ/k0A1Si2uv5D1tW/jVPPoiBnJ7L9s9Iy3lIaeFzFRKLmxS5ORzaaSM8rjidCRFrKzY9DgobAV2kZ7Gisjki0CiGcVNa+QSxej5QJhNCpqH2N8fkHoGluyqqfbT2HOEI4U6YcSgw0rfc5sELoZPo27PReRmmM49+GcL3Gd69tD5r1YmzXmPWMX8Mb55l+FIdHdSbvyOGPw/1zVRglGlAhEiFUhsjU3a3nXbG4507yTh9sdIBS5+uJLX8Hn9/c3eMXmtq/Y7reqg/g0xvVYmnxFqp8v7h7pM5mGBkRBjs3cwuq698zSXkT6HpGa7unwaOmcQGpMilAEks00xT8npzM9uRgh8PfKVzSG9bVvUNt46dtxqrFiFBe8wrByCpKC1OXidU1fkFV/bskTDuzqsXE4ry90vbaDSOqfsEWHrthcZwkiUSYNVVPEYqsQaBjyCgdr2cy3FVR+0qrFkqiw7bU+eFIA49rYJ/Zvbkw66CNeOMP5l697lL61B1xepVu9Re3dDaozgzY9ChVMdkRX4HSKln+lsrq8GTDJkekfjIApXPSk0SqYcAuF6WX4THnYvj5RRVGSt6EdLcK9XQsff/uPwX88mCr3olUKYc/PAkH/1c1VbAZGYwIg63rXqaMP45VlY+qEmwkAoHDkcnkcccOuvZzMLyix89IGaOxi8HuK9F4Y2ss2yyX+zvysrbD6zY3UnWNX1BZ96a5oZM6uu6hOG8vdM1Nc/AnvJ4JOPTuz72xeBPV9e/TGPwBaSRMbpbteE3SFJMYMs7KioeIRNcBRspxzJ6gekIC0Xg97jSfYNIh0lJJ0FjF7re7+PiijQiWd7g+QoU/tj9b/Vm+UJXEr/tGbfNkQ+YElfucVapS4zY/xuwo6h44fW/1SpetfgcfXZ36M4kIPLQnnFfZc9MATzacvAgW3Q1f369S+2YeBtv/qb3DT9V38NP9+Z1K72WiQ8ed/VRGic3wMyIMNqh0LBV3XEos3ozbWYDPM6lfxjoUWUNNwydEY9U4nXkUZO9IhndKt88pj7BnxADJhzcHl1iq40gZpzHwranBltKgqv5da6/UKKK4cEcqal9CmToNMMjN3Ipx+fu2VVLG4k0sXXt7a5Pf1IWuQjgoyu3+DB9PhKiseZ3G4PekbFLYTzShE2kpHxCDLVE3l1BkNUhJzhyNfd97he/+tScrHtkBI65S6n79gDLGVd8r9byO3WiCVSrE8ZuHYOah/Z5SN7ImwEF3w4t/SO1lRxqVjGnH3o9WuPyw4znqZcZX96FK0c0wlHrgFsf3fBybwWfEGGxQ3VUyfSZL6H2gtvFz1tW91R5yiNUQDK+gMGdXCnM7i1a5nHmWMdz2uTnJ8ZtngPQWQ8ZT5nIbFgY5GqtLvdCoVVNe82y3t+ubF6Npborz9mg11nd0W2A0HU7zMaHwkG6FQIYRY0XZvSkXi60R9HST6Iqu9a8qI2gYvBEM4nZ+ycTwGrRkSEYmEDrMuvAddj27iKysaZ0U6d69xDol7n/nwozfDE5l36xjoSUAr/4Ry0tlxJWy30AQWAcY5icSj6gGBgONEYdlb6pK0OJZ7Xn0NqkZkxmYsXiAdSZhAyljVDd8QDRW3+n9wpxdECaFK0kEDtyuQjK7VCL2lQzPVIRFGbgmXGR6NzCfh3CkMPSARThCyji1jZ+RSERZUX4fhtFzswJVVDOXzIzuN9DG4HfEEs303lhr9NZYC6H3aQ3DiKswxmsLw8xdsYobq8sZLzoY6w5IGSOa9WEnYw0q/mw13eA6CAyiuOH4LVPrcQhd9YMcCCbuDKn+XdZ+NjDHSbJ6AdwwDp6ZB6/9SS3O3rWNenqxSc2YNNhNQWudSyklDYHOor9ZGTPJz94eIRwIOgcFNc1DfvYOTB1/Qidxpv7gdZfgdZe0lo13RBWz+H3mv0SXMwenI8di1J7n1hD4ikSihxSEVqSME4mWmW5rCnzf82JhJ5LeW2+NtZMJxYf3+rovvhduKIZ7d5Z8PNfNnjtNpPQdjXiKcVpi1d3eS9WXUBpKH2SwKN2+cxf5rnhzlJZ32DD4LBzm83CYFqNvoSllsK2p/qFPw5oSqIRH9lVrAC1NKtyUbEP28L6p95VS3USfOx6ePExVgqZqCjEWGVEhkYEiYURSLHAlSJi0wyrO24PczNmqolDGyPBOxeueMCgLnkIIJo87hoqaV2kMfqdKsWWCzIyNKCk4CENGqa77gIbmrzCMKG53McW5v8Lvm05p4cGtVYFxkgZQoIPQUnrfUiaIRmvSjteDhtORbXECPRtQIZxkeCbh0DMJtawlGqslfYMtyPJvTnHu3LTTJZN895hS9lOhDIEDgSOkscGfptN4Xym+7Vaa7ufUu2vWbHIEfPVf8xLzgk3S09HuK0LAMa/BvTt210/RXbDHP+GhukZuDtS13aolcH5eHkdlW/y7WeAvAs0pMWLm33XXAOZqL7rb/HoacVXpWb5QiVN1255QRnr5W+1rCkvfUM0n/vDp+lP8MyY9bJ+7FE2YF7BowkWGZ5LpNpczh4KcHSnMnYPPM3FQs1M0zUlp0SFsPPl8ppWexMaTz2di8ZEIobO87B7qGj8nYYSRJIi0lLN63RPUN3+NzzORaaV/UIUomheHnkl+9o7kZG6Z0h66HDk4nTndniCsEEIjN9Ok1xWQ45+FsLi+AH7vhkwedzQTig+nIGcOsVg9vfWu/Z5pvTbWUsJbfzGPO+sRjUU37E3cRFZACCf52Tt2e3/upUoOtVP0Sqg86ANv79XU+kTRZnBuGex5XWujhWLAodLyXjlb8su0TApe8hGUkqCUhKTkuro63goGexy7I/5xkL2R+Qqnw6NyuQeKtZ9YF/IAlh1vvrxbiWB1XACOBaC5TGWyrC+MSQ87wzsdhyOLaKyOznFWga57+9Rea7DQNTe6q73Apb75K2Lxpm7iRVLGqKx5jWz/ZnhcRUws7tyaOhKtor5xIVaGUdO8uF0FynXr0XYKxuXtZSkKlZUxk5rGT2hpqeqUxieEk8LcueT4Z1Fe/VKrCJMgVZcbcyQVta+Q7d+kVxoy4Tr1yG1F6Jti6vCRSQte4kgEmnCQlbGJqZZLVimcslgJJX3/pPICp+4Ou19JJ63uwcSdpUrjYyH4+DogrkrhQeBEsO2FhYSLE9Rsq6xgREpuqqtjz4zeucXbXlnBe8dPU+JardEuhxeyJ6nUxYEie5KKv5utnWt6603JhE9vNL8RG3FY8Y7SX/Hld98+1hiTHrYQgqklJ+DzTEAIB5pwI4QDr7uEqSW/N4kdDx6GEaO+eTGrKh9jzbonaQr+lFI3paH565Tx4XBkTbf34vEAlbX/SzmPSLSMNeueJte/FT3fpzXysrez3CqEztTxJ5CfvUNrBoeGy1lAaeEh5GVty/KyewiEl7bedHqfew0qhTIQ7l0ahMOTupdgwg1ncwh3sz2fMQ29fhfcZSeS7zrE8mkqqxQOugv+0gAXBeDol4bOWLfNOwqf/MvqyUGwyX9yOr23PBbD6GVfkpyNWzjtWyUGlTMVCmbAbpfDyQvNmxf0lW1OVSEdMzSHdc56qgVJ3QWhmv7PbTQwJj1sUD0Dp5b8jmisnmisDqcjB7draG/B8USQ5WX3EE8E24xwc2gpXncJk8cfh2Zy40jZsAC6xakNmWB5+b3E4k2qHVaqfWWMptDPFOTsRE3DByk+mcCQ8ZQNDTTNSXH+Ht1K1msbv2iVe+1vF1bZy4VNFWudMheWv9398AmHZPWBAZzCwS8rZ7Dp+b/i2R80dJcyiFucAPvdZG1MeiJkGDzW1MTTTU2EpWQ7r5eTc3LYwNV/pcOGVVheToEg77vOEgQeIdD6EM7LmQz739KHCfaCcVuq6ssPrlTXXSbUjVZzwFHPW2fGFM5UuuFmGHGVv74+MCY97I64nLn4fdOH3FgDlFe/rMIbHQyPlDHCLWXUNnxiuk92xiaWKX8SA5+78zezObiEeCJEuil28UQjdY0W3V3bEK3aKr1HacL0ztCaIWUCn2cyhhGjKfgjDc3fdEvHNGP/21R1X8dIiu6WOAslBWdWc56Wxz5HlFK/WCMeUZkK8Qh8/QA8f0Lf5hoyDOaXlXFrXR2r43GqEwleCwSYV1bGokjP+e494clRFYpWxDLb/+0dwAH+vsklDBW7XgS/XwBbnQjT94GdL4QzflYtzqyYc4l5g2CHV0nMDuTC6EhmzHrY6SClQV3j59Q0fkI8EcDpyCQ/e2fysrbp94JjwogSCP2CmSGVMk5d0xcU5u7SbVtu1jbUNn5OQibo6FYJ4aQgeyfCLRUIobemBWoEQsuQaWd+KHrOFJE0BX4gxySu2xNmjRj6gt+3EcHwSsprXmprbCwx8Hs3ZELxoZbef/6GSsNjwfXw0/NqwXDz+YIdzhasqopS92Q2y7tKiKN0Nn58Tmlu9KT30ZUnmppYE4/TcdnOAMJSclFVFa9P7P0CdothcFdDA482NtIkJZ4PNDAE49/xMfP2HPxr1XWOewyWHqO0WD1CkK/rnJs3cGX8g8X4reCgO9P//Ab7wh5Xq0VlzaHSKqUBGx4Ae/9r8OY50livDXZZ1XM0hX5q8whj8UbW1b1JpKWc0qJD+jW2YYRTCiolLIpXHLqP6RNOorz6VYLhZaoVFW58ngnUNH5MbeOngEQInfEFB6FpbvpSPdgTfY3z52Ru0doOrT9etoqhr658FCljnc4sEP6FippXUwpkZU1Q4Y39buqyoQp+edWke0zyqE5YswCy5/Vuts80NxOxiBnXJBKsiMWY1ovQSEJK/lBRwXctLSRvrZECdeNfeVgzaw4IsMcRpRSUO3HNNNBPCrOJy8WBfj+HZ2WRoY3NB+ftz4JZx6vGxrGwahCcv2GPu40p1luDHW6p6GSskyiRp+/Ij+6Ex9X3RFuH7kcgLM2o22kdonE6spk8/mgMI4ohYzQ0f9OmIdI2noSy6mdbNUIcAxKGSKIJl2nWRDpk+jbG6x5PuKW8S1d5By5HPvFEE0I48HkmteqPd12UdFCQs2O3Rg9Jklor4/L2RtfTl12VEn55OJe15pGo1kmmbmRrRThFwYqO8rR7wwehED9Go5g9B0knxHXJ9zfWcF1tCZsd5UB3rScBXFqVFo8d7lkMH+utwVYFMlal3AbNwR/7ZbCF0MnP3oEaE8Oj0t9263EMTXMhpIOahg9TGK/vyM7YlMZg5+pDIRzoWgbxXpaQC+HA7SrupiWd/v4ak8cfR23jZ9Q1foFhhHG7CinMndttzLrGhVTW/a9NVEvKBNmZW1CUuxs/r+7qHnc4BjotsVp8enuXHikNAqFfCLWUoWtesv2bdWrg/NZf4Jubi1IKKiFV9WBv2dHr5cVAwHS5WAIbOHsXJnolECCUyshrUDkjwvQpBvoo8qYTUhKVEo8Qg67AOdiEDYPXg0E+CYXI0XV+k5nJTPfgdWVKst4abKSBdRjBSJl6ly6FuXOJJZppbP6mtVWVGtPrKjHtrG5GLN6EkUKWNNJSzpTxx5Phm0ZZ5TvozhhuZwGFObvg921AuKWSxsC31DV+ZpqBIoQTh55JLN6ArnnIy9qWgpxd+lWGrwkHhTk7U5iTuuY5L3sbsjNnqXxtGcfnmdxmZB16BvGEeZ8sSaKTZGws3syK8vtIJIIYMopAp6r+HYrz9iI/eztCNfD5fyARsT4nhw8OvkdlLPSWk3Jz+V8w2M3IeoXgDzk5uHtpVNPJWteAaC899+GiLpHgutpaXg8EMIACXef03FwOzcwclYa7LBZjfnk5IcMgJCUaKix2ZGYmf87PH9RzWm8Ntt+3IbVNn5t6rqrPYv+VdYTQKMqdS1NgCVK2u3ahlrUsXXMb0yecbF3+3YaWUkda01wIIcjxb05FzMGMDWYCqunAqsrHVPstKdp6G3aYHULoTCqeh983fF3pdc1FlomoVn729pTXvGLy7yNwO4twOXPa3lmz7gli8UaSN0RJQonw172F113KindKVdaIRcKGrxDmvwyl1qnnKZnsdHLv+PFcVF1NRTyOjnIFTsrJ4aScnE6fbUgkeLG5WcW1nU4OyswkR++8XrB3RgYfhUIpvex8h4PcUeBdBw2Do8rKqIrH24Jf6xIJrqmtpTaR4ORc8+KskczZ69ZRl0i0PbcaqIKlp5qb2cHnY67PJJ1lgFhvDbbPMwmvu4RwpKxLtZ6Kr3o95k1xe0tl7f8wZFfd6QQJI0xl7RvdKhY7EoqsYVXFI5bbhdDJ8ZuXj6+teq7NczVHIqUkYaSKEXTHkHEiLZUIoeNxjRs0byLbP4um4I8EwsvajLYQTjThYELxYW2fa4nWtDVP6IqUMWobP0Hoh6c8Vsk2fTfWSWZ5PLw8cSKrYzFChsE0lwtXl2uzIBTirHXrMICW1tDATfX13DJuHDt42yVk98jI4I76elbEYqbetkcIzs3N7fO1r4rHWRiJ4BaCHb1efINo+J9vbqY+kei2UhGWkjsbGjgmO3tULZKuisVYFouZBhnDUvJgQ4NtsAeDpADTurq3qG9eDBgIdHKytqY4r3cNZ62QUrYurJl5SpKm4I9IKU1/eIYRZVXFI63G3gwHLkcuBbndww6xeBOB8C89NumFBGXVz5LhOSutVmc1DZ9QXf8eyawUoTkpLTi4TYJVSokkgUDvtyEXQjCx+EgC4WU0NC8mYUTwezcgN3OrTouN0Xg9At2y001LrJppe5g3zwXVPHcgF7EmWcSrmxIJzlq3rtMCZDKz5E+Vlbw3eXKb4XIJwcOlpVxXU8NLgQDJqTsBv6Zxfl4e+2f2vvwwISX/qKnhxUCA5CwTwF/z89m016Olx2uBgOWiqwNYFIkwJ00Dt6Slha8iETI1jd0yMvAPg6FfF4/jBKx+lRWJ3sow9I4+GexYLMZFF11EWVkZ0WiU0047jT32GBgj11eUtxhGE46Uncs7omlOxhfsx7j8vUkYEXTNM8Bl6wapF/yScfTuxq0x8H1K9b2sjBmUFh5sqrURiVYhcPRYNZmkIfANBTk7pfxMXdOi7t1uElHWVD3FpOL5BMK/UN+0CEPG0DUvBTk7k5+9Y78MtxCCTN8GKcNTLkdOyvN0Owvw5Cghp/euMEiE23/kugfypsMmqR3wAeHVYNByxUSiDNvhWe19uDI1jSuKiri0sJBgIkG9YZAApjqd6H28pv+pq+PlQIColJ0yUK6preXPQjCzT6OmpqeZpnMmAcPgtIoKfohGkajMm7/X1HBZQQEH9eHG1R8mO52m2TugzmWjXi4w95Y+GewXX3yRnJwcrr/+ehoaGvj1r389rAa7vulrqurfJpEIIZFkeKdSUnCApXhRV4TQTfse9hchdNzOQlOtZQC3s8hycS8aq02Zqud0ZFsKIzl0n0nM2hwp40TjqSsIpZRU1b1jmamyZt3jSNnezzFhhKiqf4+WWE2PDYX7i9tViNtZ1No9vvM5d1Th2+WvEHRW8PNdpdQvA1cmbP0H2O2yvpej94Y1sZhlrnZYStbGzP+tnUKQ43CQ08/jtxgGjzY1mc4hIiV3ORwMRq/dA/1+lkSjpl52HJjt6XmV98J16/i2pYWuV+iymhqmuVxsOgTZGUmKHQ529Hj4OBzuNh+3EPy+y5rFQNOnZ4p9992Xs846C1A/Zl0fOjGlrtQ1fk5F7SvEE82tnpZBMLyc5WV3E4sHetx/sCnO39O01FwIJ8X51jlkTmduii44OuGWMtbVvU0k2v1m4HGNx6Gn11ZLCCduZwqlfCCeaCaRoqWYIaPdQhKqofC3aZWT95dJ447C6chqk9RVIRkHRXm/6pSNM+mAJv70M1yaUGJOe9/Qt7zrvjDN6cRr4Rn7hGDqAGiOpKKyh0f1SiFYPABl9F05ODOTYoeDrt9kjxCcmZvbY/x8XTzOx5FIN+MIKkvmvw0NAzXVtPlncTGbut14hcCF+vdzC8Hf8vOZlcYNqD8IKfueGxQIBDjttNM48sgjOeiggzptW7RoEb5BCL5HIhE8rRdFkkC6XgBhEr+UGiQ2REsMsbSaCYa2GhyLaU/Y0iG+FZphrssNIIkhXS9ZnButYWQBaJCYjkhsQUtLEy7fKtBXtx6rNdLWsRCyq82QDkT0IES3n1THw0WRrufTe37ttKOGiG+BMDrnXxuiEbSVIFrAKEAYE1MeP61DYYBWgRQ1gBuRmISg8/ev43dnMJHAT0KwQNOIA9tIyQzD4DSXi5CJ0c6QkruiUQbTT2wGTnK5iFuFU6RkG8PgL/G+qSumIgg8quu8p+u0AOOkZK9Ego2kZLKUpLIS3wrB9U6n6XUDKDEM/mPxdDJQWH1vlgrBT5pGhpRsaxgM1DN6KBRi9mzzJpd9XnSsqKjg9NNPZ/78+d2MdZKZMwc+KrZkyZK2cUORMlZV6OZ5ysLA6alio0mDEZnrLTORci9aWr1ht6swrTznYDiL1ZWPIWWic5w2+d0VEkggnCsoGTeTsur3ESJmHtMVXf90IjSdyePm4/P0LJ7x/fIX6HWLL02jeNw48rPVv0HCiLKq8lHCkVXtH9JXAospLT7cNL2vd6ReOuv43Rks4lJyzrp1fBIOE5EqMPU+kKFpHJyRwcutuchhKfEKgUMI7h4/ns2G4LF+xtq1fBe1iMAKQaXbzcwNB6fWO9lEZmE4zF+qq3k6kUAHYsC8rCzOy8szjc27o1GMsjJL3dxJPh8zS0pMtw0UVt+bmYC55esfixYtstzWJ4NdU1PD73//ey699FJ23LF7p46hQhk9ayMylLrXPSGEhsdtoc5uQYZ3CrnZ21PbsCDl56SMUVn3FtCSZuxaIytjE0qKDkwpodoRlzOfaKz3osMdqxvLqp7tbKxbkSRYW/UM0yechruXXWZGGo80NvJxq7FOEgWihsGTzc04gfnZ2WRqGhOdTvbw+XpdWNNX/pKfz7EV1p2DxzsGN2nsm0iEkysraelifJ9oakIAF+R3l2uY5nIx2enkl2i02xK8VwiOH+SY8UijT9+UO+64g6amJm677TaOO+44jjvuOCKDEP/qCY+r2FKKVAgHOf5ZQzyjgSWeCFHX+AnplJYnjGCPetjtqAXCdI01QFHubpjf3zV0PQPRZZsQTrL9s9oWfmPxJppDSy3HlzJOXePnac9npPJgY6Pl4qKBClI90NjI3Q0NXFlTw3V1dVQPQhjCjK28XjZ1uUwjW24pOaGXvSAB1sZi/L26mt1XrWLv1au5ua6Oxi7x8qp4nFMqKphfXt7NWINa9Hy8qYmgiSaLlJKTcnJwi/ZvmIaKgR+amckcb3prNWOFPt1SL774Yi6++OKBnkuvEUJjfMEBlFU/16VARMOhZ5CXve2wzW0gaAr8MNAifK1oOB1ZPX+sA1kZm5CfXUFd02cgJRKjtYtPKROLjqSmcQH1TQsxZAsOPYP87F3Iz96+bf+WaFVKMSyASDRFf69hQkrJe6EQjzQ2Up1IMMvt5oScHKZbLBLWppGHmwyJhKXk6aYm3gwGeba0lIJB9nABbhw3jmPLymjuUFbtFII94/G2go+YlCyKRAgaBpu73RS1zqsxkeCppibeCoVwAjt4vTzQeoNKnvV/Gxp4MRDgqdJScnSdkGEwr6yMmkQi5b+9A/g5GmWrDrHisGFwSms6X7h1rhpKm+XywsJBX+AbiYz6wpls/yY4dC/r6t4h0lKB0Bxk+2dRlLsbujZy/0ETRpSG5sU0NH8DSLL9m5KbNRtd8yClZF3d29Sm6V33llQNdq33EYzL35O8rG1oDv2IIeNkeKbia60IHZe/J+Py90RKwzQ+r+v+HsM1LsfIKlOWUnJpdTWvBYNtaWkrYjFeDQb5d3GxacFHidPJql4sgsVRRTV3NzTw14KCgZq6JSUOB69NnMgbwSCfhsNkaxoHZ2Yily9HCMF7wSB/ra4m0Xq+MSnZx+/nj7m5HFteTtAw2p4gFre0dPsXjQLV8Th31tdzYUEBLzc309SaQ56KBCr3vCNX19byXTTa5pUnfwlr4nFWx+OM7ufnvjHqDTZAhncq00pPHO5ppE08EWZF2d3EEs1tTwYt9dXUNn7GtNKTaQh8TV3T5/RsrNPVwU5+TumHFOXujruPSoQuZw752TtYH8nEWEsp0TUPDi2DuGEu6CTQU/aRHA4+j0Q6GWtQhiUhJResW8eHU6Z0Kz8/OTubK2treyWpGgNeDQT6ZLCllHwWifBMUxPNhsHOXi+/zsrqZvw64tY0DsrM7FR0sgRVSXheVVW3kM6bwSBfhMPUd9DPAOtvXgx4KRDgwoIC3gmF0roW+brO9A5FJyHD4JVAwDSEEpaSe+rrOXCEd9YZDMaEwR5tVNW/QzTeREddNinjxBNBKmtf76SfYY6GrrnxeSb3UIKukePfAl3zEolW4HTmkpe1LV73uIE8nZQEwsupqH6FmIXynkJQlLcHXvf4IZtXOiT7M5ohgU/C4W66EYdkZvJTLMbjTU29UtPrbRR7bSzGM01NvBwIUNVBq+OLSIQ7Ghp4tLSUyb2oupPAvfX1pnOOSNljHndXkobW08OCajIefV1RUaeq2NrWLBIryoco7l+bSLBKCCYZxojQPLEN9jDQ0Pw15iKaRmsvxdQJz9kZmzK+YD9qGhbQHPoxxSclTcHvEZqTyeOO7dFQh1vKqWn4hGisBpczn/zsHdtCHn0hFFnTmpbY9ccl0HU/mtDxuSdSmDt3WHpu9kRdCiMlUaGMrgghuDA/n+OysnisqYlHm5pASiuhQEAZrZ16sXj2VFMT19TWEpfdEzgjUhKRksPWruX6oiJ2z0idHbw2FuNfdXW843IRD5m0Ze8jyVj0r/1+FlgoDwrgEL+fk3Nz2zRYElKiC0Gerqe8iRUNcry/Kh7nr1VVfBmJoDudGKtWcZDfz0X5+UOW1WOGbbCHGCnT6QZu7Zlpmo8JxYcC4HGPQxOuFD0apdqWiLKy4gE2nnSOpc5KXeMXVNa92WpcJZHoOppDP1Octyf5fQxVrKt7y0ItUKJrLjaceEafxh0qtvd6WdzSYvpYngA2N8mdDhsGa+NxcjSN8/Lz+VNeHm8Fg6yMxaiJx3ne5DHfIwR/TFNmdGU0yjW1taZz6jQPKTm/qorjs7M5y6LHY0U8zpGtC5DGAKoueoTgT63nM8fnY0uPhy8jkU6hFq8QnJeXx9HZ2ZTFYhy6Zg0/tcb+deBgv5+9fD7eDAZNtTtWxWKcXFHBuXl5zBjgHPaIYXB0WRnViYS6IQoBUvJSczO1iQS3jBu6J9SuDL+Pv54hhMDttI4fO3Q/GZ6pmHnZAgd5Wdu0/Z2ZMSNF+XpnpEzQGPjOdFss3kxl3RutN5Lkj0rdWNbVvUksniqcYU0ostZyWzRW32tp16HmiKysbjFqUGp623k8TOmQKRKXkutqa9ll1SqOKStj79WrOb68nOp4nP1bF+0uLSzkqsJCxuk6bqFqOzdzu7m/pMQy66QrTzY3ty0I9kRESh5obGSNxSLo7fX1BAwjrWXtDCEwW8J3oEqzfULgEYISh4NbiovZvNXD1oTgtnHjODs3l4kOB5maxlZuNzcVF3N0djbV8TgHdDDWoG6GzwUCrIjFmO504jNTswQWhMMcW17O9y0D+z16LRg0XShtAT4Oh1lhVXw0BNge9jBQlPcr1lY9a9o6rCh3d/y+aSwvu5uEEWnzUJXmR36nLi6acDC15ARWVjyEYUQwjJhlLraUMcIt5eSydbdtjYHvLCvJkJKGwLc9do8xQwgtZeceMQz+wjeRCLfW1/NNSwsZQnBEVhbHZ2fjNXnMzdV1Hiwp4azKSqpbY6pRYI7XyzVFnfVX/l5dzevBYCcvcnEkwryyMl6dNKltEXA/v599MzKoSiRwCUFuL3V41sZivYp3G1Lyv2CQP5gUmLwdDKap56huSAiBU0rcQqVnSpQ060GZmayIxXACU5zObgqNTiE4LieH40zmcF1tralOCMCSaJSHxo8nIiWX19SwxiRuHZaSa2pqeLh0YPTrAd5P0TxCoNYJBlv7xQrbYA8DWRkzGJe/D+tq3yDpSUsMinJ3IzdrSwA2mHA69c1f0hRcghA6uZlbkuXfrFuxi9tVwEaTziYYWcmqNe+DYy1m8XGBbtndJmGELSVKJQkSib7FNrMyZrZ69d2//BmeSZZqg4PFF5rGTRUVbUa1Cbizvp43gkEeLSkxjU1u5HLx6sSJ/BiNUpdIsIHLRXGX+Om6eJxXg8FuC3YGEJKS55qaOlXkCSG6jZEuM9xuPgqFLPWYuxIDvo9EiErZ7WmhNwmjLYCQklKHg7/l5+MUgtleb9uYG3UwYMuiUaoTCaY5nT3Gmt9LETeXqGyTSwsLqUyxyPhNSwsRw+hxgTNdMoSwzL/SwFLEayiwDfYwkZc1mxz/FoRa1oA08Hkmdoov67qHgpydetSpBmUA/N6piEQzOMvNs0aEICfTXAjL6y61jIVrwpV2/8muFOftQSC0rFXpL2keBJpwMa5g/z6N2VcSUnKbw9EtZa0FFQ99obmZIy0q/YQQ+DSNh1vLzpNVdvNbu6V8GYngBNNYa6S18GY7r5fHm5ooi8fZ3O3mqKysPhntIzIzlUJdLzJQPgiFmLNqFTcVF7N9h8XN3X0+XmrVNkkHiVqIzdX1tpBHR1bFYpxVWcmaDiL/u3i9XFtUZJlh0dNZJKsfe5rjQNaXHZKZyf+6pHMmScCgdpTpCTuGPYxomgO/dyp+3/S0my6kQuBkYvHhCOFEtCVFaQjhYHzBAZbVjZm+DdF1H93j5gJd85Lp27hP83E6spk+4dTWgiBfazfzWUyfcHK/OtL3hW9bWixDCWEpeaa52XLfbyIRDl+7lhdbU+hWx+PcXl/PvLIygoaBuwePqzoe55jycp5pbubjcJj7Gho4YM0aPguHe30ehQ4Ht4wbR4YQZLSWa/f0I44AzYbB6ZWVrOvgqZ6Wm4uv1ZvsSKqz0VA9GbsSMAzml5WxtFX3u7m1Q/pHoRBnVFpXsPaUHfNpJEJMyk43mq5s5HKZhrT6yrYeD3N8vm6etEcIzs/LI8sijFWfSFAei6W9xtAXbIM9xsj0bcSGE08nP3sn/L6NyM/enukTTiM3c0vLfYTQmFryu9YejU404UYIJx5XMVNLf9evDupORyYlBfszY8oFzJjyZyYU/RrXMAg89ZRVYaX/AfC36mpCsnP/nxZU9+yHGxvZ0eu19AA9QrA6HifSYf8o6iZxZmVlr3K1E1LycGMjf2stbkm2DEs3Cp6Qkiea2heQJzqdPFZayk5eL1pr6feGTie7eL2WY8akJCYlq7ssZL7Q3EyL7F7LGkWFLH6yWBj8S35+SiMUTCR4Jxjk3Lw801CERwj+YiIa1R+EENxQVMTfCgrY0OkkS0q29Xi4ddw45ps8hS2NRplfVsbuq1Zx0Nq1zF21iicaGwd0TknskMgYxOnIpjj/V73cJ4vpE04mEq0iFqvH6czF40rd2GA0sZnbbbnA5sL6MXdtLEaZRfy0BXi2uZlTcnO5pKCAf9TUdDL8HiHI0TSqLPK5JSpcsWcPudJJ/lJVxTuhUNsxGqTsVWgkinrS6Mg0l4u7xo/nmyVL2GjjjfFoGkujUY4qK+vmKYrWMS6rriaGWmC8vqiI6S4XC3qoaPympYWNTdLvSpxO5mdm8rDFE04Ytci3j9/P/SUlXFNT03YOG7lc/CU/n20GQQBKE4LfZGbym8xMJa86fbrp58rjcY4pKyPYerOKtebBX1dXRwtwfB8EtVJhG+xRjpSSxuB31DZ8guGqY0X5pxTk7JqyD2IqPK6iMWWok2RoGgcmErzqdHYyqgJVqn2cxQ8rLGVKDzZppA7JzKTU4eCO+np+jEbJ0XWOycpiQShEpUXoI0F6YlEAP7S0dDLWfUFDaYmY4aS9KnEDl4trCgv5a3U1GrQV6CQ7kAZa5/BzNMqx5eW8MGEC36RIrRNSpiyVn+Ry4RbC9CnIAWS37ruZ280jpaWEDQMJg9rtPV3ua2ho0z3vSERKbq2rY55FamhfsQ32KKe85iUaA9+pFEEBochq1qx7ksLcuX1KxRvLHJ1IMKmwkHsaGjBQhmgTt5srCwsptDBkk51Oy0d2Ddi+w+LbNl4v93Tx9oKGwSddikaSCDpnV6TizWCwx7BOT7iEYF5WeiqNe/v97Ozz8XYwyOpYjHsaGro9oUhUqOna2lpCJtKoSVogZWf0vTMyuKGuznSbLgQHddEMGch4dX95LxSyXBuRwC/R6ID2nLQN9igmHClrN9YdkDJGdf175Pq3wOFY/wRyrBDASbm5/DYnh/JYDL+m9Shp6hKCU3NzuaW+vpvRdQvBKT1UKB6alcVdJn0HdWCCw8FGTic/R6PkaprlTQMg1upV9hW3EPyxVVf6zMpKPgqHEcCuXi9nm1RCRgxDKfqFQjQaBg4hiJncMFqk5ONwuMc0w0iKVmCFDgfn5OVxU11dt2rI47KzOxUojTRSec8GKgd9ILEN9iimIfBtijJ3QVPox06VkTYKlxC9MgInZGdjSMmdrYY3ARTqOlcXFbFBD+Pk6Tp3jx/P6a0LjEk/dKLDwSyPhzmrVyOkamG8mcvFP4uLKTURbRrXD+0MHbisoICZbjdHlZUR7vAI/3YoxMfhMFcLQbIJVnksxvxWKdWQlD1qQvbk7zqBj0MhDuygDtiV47Oz2dTl4t6GBpbHYkxwODghJ4ddhjGFLh0O8fu5o6HB9OknS9PYsBcCXOlgG+xRjJGitFtKQ1U+2vQbIQQn5uZyXE4Oy6JRvEIw2aSiz4ygYfBdSwsz3W7ChsFmbjf7ZWTweHMzLzY3d8rdXhyN8ps1a3h7ypROMd8fWlr4p0XIIIlXCMtFPwO12Phic3O3Cr5kcc+Dus6ere+ds24dtR2kVFMZa58Q7O7z8WKKfG4NKIvHeScYZIrTyTSXi6BhsDwaJVvX24SfZnu9zB5lHWTmZ2fzbHMzlfF4p4pNjxBcXliY1nekN9gGexTj921AY/AHpEnBixAaGd7JwzCrsYtLCGa2xiObDYMnGxt5NRAAYH+/nyO76FB/F4nw+9bKymT896dolJ+iURZFIqZZK0Hg2upqripW/T9DhsGxZWUpC0eS3V8+CoVMy7wlEEok+MyijZ8EFmsaUkpWx+MsjcXSKqbxCsE2Xi9/zs/n7VCIZos4dgS4q76+LaySqWk0t6YlxlFPG9cVF6cdzx9J+DWNJ0tLubuhgRcCASKGwZYeD2fk5g5KRxzbYI9iMjNm4Kh7m1g8TsdaMCF0vO4SvO7B7Sa9vlKbSHDU2rXUGUbbo/CK+noea2zkiQkTyNd1Xmpu5q/V1d2805CULI5EUhrEV4NBrpQSIQSvBwKmFZQd0VDqdp+Ew6ZxZp8Q7JqRwYvBoOUYSW2QqtYqRSs5WK8QZGsaubrOMdnZHOz3owvBU6WlHLp2rakGh0yO17qtpdWwJ58Pf4nFOK68nJcnTEgZxx+pZOk65+Xnc94A54ObMXKWW216jSZ0ppWeqMrS0UE6EEIny7cJk8fNH+7pjVluqK2lKpHoFLdskZKqRIJ/1dayOhbjUhNjnaSjJqLV9mS6388mbbi6sqXHw95+P9t5vd2qLp2o+PeeGRlskiJbYYaUaK2hHqtAmwB29np5e/Jknp4wgd9kZqK3Hm+i08klPRTBpCJiGDxgsjhr05nRdzuz6YRDz2Dy+GOJJ4L8/Ms3bLzhVuj6yO1l2RNSShJGCE24hlwcKh2klLweCJiGMxLAa4EAuZqWtgqeGQIlfYoQaY1zSGva203FxVxXW8tzzc2I1vn8yufj0oICHELw5/x8Tu4gfpXELQTHtRYHFTkc7OT1ssAkvOIWghNNFPdAVftdXlvb5w6kceD+piZ0ITgrLw9tGAWWRjK2wR4jOPQMhMwZtcZaSkld0xdU13+AISMgVYxeaaBYZxcMNXGwlAOlddvyWKxHQ5spBM0p2o890dyMpGdlOB3avFyXEFxcUMD5eXnUtIo0dRRdmu3xcHRWFvc3Nnby2mNScp3TyaNr13JoZib/KCjgrHXr+DEaJSEljtYbx9/y8y3jsg80NpqGY3qDBB5paiIOXDAE4YXRiG2wbUYE1fXvU9P4cac0xebQz4TLythgwukj5kbkFIKJDgerLcrVJzkcbOxy8Wk4bBl7dgH/KCzk7zU1NJks1HU0ez01sNWgmzCSR9OYYFJcUhOP82hTU7cQiwE0CEFDNMqyujqebm7moZISlsZifBWJ4Nc0fuXzWYoegWrg25+niiRhKXmsqYlTc3NTVkeur9hXxGbYSRgRahoXmOSUSxJGhPrmL4dlXlacnZeHx0KI6Ky8PI7MzrZ8pBcoT3Vvv58XJ0xgXlYWOZpGpqaZdlbpum9H3MCRWVlpL9S9lmLRMUlYSpbHYjzS1MRmbjfHZmfz68zMlMYaoNTh6KETqSKdzzhRqYw23bENts2wE4qs6SAH2xkp4zQGvx/iGaVmH7+f8/Py8AmBv/Xla5Xe3Mfvp8Th4PqiIjxCtIU0XKhCiqdLSji8Vbek0OHgkoICFkyZwqdTpqQ8pgcVj3YJgQvI0TTOyMvjr70IHdR3WSi1IiIlT3VQ9UuHY7OzTW9iAhin6+zj8zHT5eJgv59/FRWR1UOFYE83r/WVPodEDMPgsssu46effsLlcnHllVcyebKd92vTe3pqFWZlzIeTo7OzOTQzk69bPcEt3O5OHWt+lZHBe5Mn83ogQE1rp5rdfL6UpcqlDge/WPRfRAiuKypCE4KQYZClab1emNvM7SZDCIJpGG2rnGortvV6OS47mwcbG9sqOr1C4BaCu8aP79azMmgYXF1ba6qx4tO0AdXfGEv02WC/9dZbRKNRnnjiCb766iuuvfZabr/99oGcm816gs8zGatENyGclp1yhhu3prFdisq8TE3jiDTFlgBOzs3l0urqbnFrNyoTJKmm5+plH8gkc3w+snWdcDyeMptDoFIFe8tZeXnsm5HBs83N1CQSbOPxcHBmpmm3mYMyM3mmuZmfotE2o62hFk6vKSwclVkiCSn5IBTiy0iELE1jP7+fCSOlNH3RokXsuuuuAGy55ZZ89515R24bm57QNAfF+ftQWft6pzi2QMflyCHHP2sYZzd07JeRwZKWFh5uakK0Vkc6hGC2x8OFA5A14RCCB0pKOKOyktWxGHEpTTNe3EJwWg+iVlZs7Hbz1zS8Y5cQ3F9SwpNNTTzZ1ESzYTDb4+Hk3NxRWfFYm0hwXFkZ1YkEodYqztsbGjg5J4dT+3gtzeizwQ4EAvg7yB7quk48HsfRYQFkyZIl/ZudCZFIZFDGHQuM7mvjBW0H0L8F0QQ4kImpRFs24aeflg7IEUbD9dkf2Bb4XNeJAbMMg2mRCMsHsKjkKmClEJQLwRuaxvetHrCGipWfFYuhL1/OUFyp2a0vAEIhEnV1Q3Lc3pDO9+bvTidrhSDR+mQQA5CSu+rqyF23jlkD1Daszwbb7/cT7LDqbBhGJ2MNMHPmzK679ZslS5YMyrhjgdF/bWYCveuU0xtGy/WZCcwZ5GPMkJKLqqtZFgwiW42JBBJCMHniRGaOcJW8oaSn7015PM7SNWtMezm2CMHb2dkcNX582sdbtGiR5bY+Z4lsvfXWfPDBBwB89dVXbLTRRn0dysbGZoj5OBzmzS6dwQ1Uhsj5VVX9LoJZnyiPxUgVxOna/7I/9NnD3muvvViwYAHz5s1DSsnVV189YJOysRlNhA2DR5uaeLqpibCUbOPxcGpubo9a2ekQNAx+aGnBLQSbut1tVY2paEwk+DAUIiol23m9pgtfT7bO1QxDSj4Ph9nZ9rLTotTpTCnQNXkAFx77bLA1TeMf//jHgE3ExmY0EjYM5peXsyoWa8tx/l8wyLuhEHeMG8e2fdR3llJya3099zU24kCFK1xCcEVhIbunaNp7f0MDN9XXt+2TAPb0+bi6qKhTSmFDD2l7ZhWYNuaMdzjYyu1mYSTSrV2YRwh+b6G/0hfswhkbm37wZFMTqzsYa2gPLVxUXd0WH06XxZEIfygvZ+sVK7i9tcFrQEqCUlJvGJxfVcXXFrrW74dC3FxfT1RKQlISlpKolLwTCnFTlwYI23k8WOVyxFA52zbpc31xMZOczraCHyet2TY5Od2kA/qDrSViY9MPnmlutuxkXp9IsCwW6xYakVLyaTjMy4EALVLyq4wM9szI4P1gkL9UV6fsjB5p9bzvMlnEut2k72Ryn8ebmvhTbm5bcc9RWVk82NjYrfLRLQQ7er1MHOD84bFOnq7zwoQJLAiHWRyJkKlp7Ov3M36A9b1tg21j0w9SiTPp0K2beFxKzqisZGEk0rbv+6EQt9TVUW8YKY11km8tdDaWR60jqQKoSiSY2GqwCxwO7i8p4Zx166hJJBCGQVzT2M3n46rCwh7nkA4thsFLgQCPNTXRIiU7ejyclZ+Pf4yKOmlCsKvPx66DGPu3DbaNTT/YyevlueZmS33srkUgDzc28kUk0skwh6RkrYX6nxlWOhu5uk7QYpyYlOR0qZCc6Xbz2sSJ/BiN8tWKFey5wQYD1vGlKZHg8LIyyjrMZ0UsxuPNzdwzbhzb2wuafWJs3upsbIaIE3NyunV5AaWj8fvs7LZy8iSPNDWZetGJ1ldPuIHDLMrdj83KMhVgSo7/Vmv/yY6I1j6VW0o5oO25rqut7WSskxjAKZWV3Z48bNLDNtg2Nv1gktPJfSUlTHM6cQtBRqty30k5Oabl3fWJvqtGe4RgssvFCa1qf105OjubbTweUwlTA7iytpYfh0C21JCSl0xuDkliwKvNzYM+j7GIHRKxseknm7ndvDRxImtjMYKGwVSXC5eFpzvJ6eQni1izA6X30dUD14ANnE6OzMriN5mZ3bz2tv2F4Ly8PD4rKzPVCIlKyYONjVxdVNSLs+s9sQ5d4q34OUW83cYa22Db2AwQ6SiznZqTw0UminweIZiXmUmew8HdDQ3EpSQuJZu73VxRWMiUNItw1sbjuIUwrVQ0gF+GwFC6hCBT01LmcttZKH3DNtg2NkPI3n4/y6NR7mxoQBcCiSpw2c3n4+z8fJxCcHx2NhXxOH5NI6+XUqolDoeld6sBU4bAUAohOD0nh2u65H4ncQAHZo6cPp2jCdtg29gMMafm5XFEdjYfhELEpGR7r7dT+bJTCCb10bDOcLspdThYHot107x2CcFxFvHvgeaY7Gy+aWnhlS5tyXTg/woLye2jpndvCRoGGuAdI6mEtsG2sRkG8nWd3wySl3nruHEcW15O0DDatJk1IfhTbq5l1/OBRgjBdcXFnBaNcnt9PesSCbZ2u5mfnT2g2ShWfB4Oc21tLUtbQ0Cbu91cVFAw6jvZ2AbbxmaMMcHp5I1Jk3gjGOSrSIR8Xedgv5/SYYgbT3W5uK64eEiP+Vk4zB8rKzst3n7V0sJvy8t5pKSEjUex0bYNto3NKCAuJe+GQnwWDpOpaRzk9zMtxUKkSwgO9Ps5sEOTkfWFay16RUak5N91ddzRC23qkYZtsG1sRjjV8TjHlZdT29p+ygE80NjIsVlZnDsArcPGEkHDsCzRl8Cn4fDQTmiAGRuReBubMcwFVVWUx+OEWr3GONAiJY82NfF+KDS8kxuBpFJjGY3NfTtiG2wbmxFMRTzONy0tpql6YSm5bwB7PY4FMjSNTSxi1BowZwClTocD22Db2IxgKuNxUi0Vmul1rO/8LT8fbxdPWkOJZp0zykNItsG2sRnBTHA4UrafmmpXDHZjc4+Hh0pK2MnrxYFqJvArn48nJ0wY0HZdw4G96GhjM4IpdDjY0ePh43C4mz6IRwhOHMD2U2OJmW43d4/ibBArbA/bxmaEc01RERu6XPiEQEN1hXG1FsIMZPspm5GP7WHb2IxwsnWdJ0tLWRiJsDgSIUPT2DsjY0gqBm1GFva/uI3NKEAIwbZeb5+7sA8GcSl5PxTi7WAQpxDs5/ezvceDGOWpcyMZ22Db2Nj0moBhcFx5OWtjsbb88FcCAbb2eLh13DicttEeFOwYto2NTa+5pqaGFdFom7EGlRe+KBLhwcbGYZzZ2KZPBru5uZlTTz2VY489lqOOOorFixcP9LxsbGxGKFEpeS0YNO1qE5GSh22DPWj0KSRy3333scMOO3DCCSewfPlyzjvvPJ577rmBnpuNjc0IpKmHvpT96Vtpk5o+GewTTjgBV6tSWCKRwD2K5QptbGx6R46u4wCs2vmWjPLilJGMkNJEh7ADTz31FA888ECn966++mpmzZpFdXU1J510EhdddBHbbbddp88sWrQIn8834BOORCJ4hkiEfbRhX5vU2NfHmt5em0d1nZd1nWiXxUW3lJwcjzM3RT/H0cZQf29CoRCzZ8823dajwbbip59+4txzz+XPf/4zc+fO7bZ90aJFlgftD0uWLGHmzJkDPu5YwL42qbGvjzW9vTZxKflLVRXvtKoFCsCQkmOzszk3L29MpfYN9fcmle3sU0hk6dKlnHXWWdx4443MmDGjX5OzsbEZfTiE4IbiYlZGoywIh3EKwVyfj2K7mGdQ6dPV/de//kU0GuWqq64CwO/3c/vttw/oxGxsbEY+U1wupqTofGMzsPTJYNvG2cbGxmbosQtnbGxsbEYJtsG2sbGxGSXYBtvGxsZmlNDntL6eWLRo0WAMa2NjYzPmGfA8bBsbGxubocUOidjY2NiMEmyDbWNjYzNKGLUGe9myZcyePZuWFisJmvUPW/a2O4ZhcOmll3LUUUdx3HHHsWrVquGe0oghFotxwQUXMH/+fA4//HDefvvt4Z7SiKO2tpa5c+eybNmy4Z4KMEo7zgQCAf75z3+2KQbaKGzZ2+689dZbRKNRnnjiCb766iuuvfZau/CrlRdffJGcnByuv/56Ghoa+PWvf80ee+wx3NMaMcRiMS699NIRJRg26jxsKSWXXHIJ5557Lt4R1N9uJHDCCScwb948wJa9TbJo0SJ23XVXALbccku+++67YZ7RyGHfffflrLPOAtTvStf1YZ7RyOKf//wn8+bNo6ioaLin0saI9rDNpF1LSkrYf//913vRqZ5kby+44AIuuuiiYZrdyCEQCOD3+9v+1nWdeDyOwxYpIiMjA1DX6Mwzz+Tss88e3gmNIJ599lny8vLYddddueuuu4Z7Om2MurS+vfbai3HjxgHw1VdfMWvWLB555JFhntXIoSfZ2/WNa665hi222IL9998fgDlz5vDBBx8M86xGDhUVFZx++ultcWwbxTHHHIMQAiEES5YsYcqUKdx+++0UFhYO78TkKGb33XeXkUhkuKcxYvjll1/kPvvsI5csWTLcUxkxvP766/LCCy+UUkq5ePFieeKJJw7zjEYO1dXVct9995Uff/zxcE9lRHPsscfKpUuXDvc0pJRS2s+FYwhb9rY7e+21FwsWLGDevHlIKbn66quHe0ojhjvuuIOmpiZuu+02brvtNgDuvvvuEbXIZtOZURcSsbGxsVlfGXVZIjY2NjbrK7bBtrGxsRkl2AbbxsbGZpRgG2wbGxubUYJtsG1sbGxGCbbBtrGxsRkl2AbbxsbGZpRgG2wbGxubUcL/A7YX3DHsR770AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_blobs\n", + "\n", + "X, y = make_blobs(n_samples=300, centers=4,\n", + " random_state=0, cluster_std=1.0)\n", + "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='rainbow');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A simple decision tree built on this data will iteratively split the data along one or the other axis according to some quantitative criterion, and at each level assign the label of the new region according to a majority vote of points within it.\n", + "The following figure presents a visualization of the first four levels of a decision tree classifier for this data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](images/05.08-decision-tree-levels.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Decision-Tree-Levels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that after the first split, every point in the upper branch remains unchanged, so there is no need to further subdivide this branch.\n", + "Except for nodes that contain all of one color, at each level *every* region is again split along one of the two features." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This process of fitting a decision tree to our data can be done in Scikit-Learn with the ``DecisionTreeClassifier`` estimator:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.tree import DecisionTreeClassifier\n", + "tree = DecisionTreeClassifier().fit(X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's write a utility function to help us visualize the output of the classifier:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def visualize_classifier(model, X, y, ax=None, cmap='rainbow'):\n", + " ax = ax or plt.gca()\n", + " \n", + " # Plot the training points\n", + " ax.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=cmap,\n", + " clim=(y.min(), y.max()), zorder=3)\n", + " ax.axis('tight')\n", + " ax.axis('off')\n", + " xlim = ax.get_xlim()\n", + " ylim = ax.get_ylim()\n", + " \n", + " # fit the estimator\n", + " model.fit(X, y)\n", + " xx, yy = np.meshgrid(np.linspace(*xlim, num=200),\n", + " np.linspace(*ylim, num=200))\n", + " Z = model.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n", + "\n", + " # Create a color plot with the results\n", + " n_classes = len(np.unique(y))\n", + " contours = ax.contourf(xx, yy, Z, alpha=0.3,\n", + " levels=np.arange(n_classes + 1) - 0.5,\n", + " cmap=cmap, zorder=1)\n", + "\n", + " ax.set(xlim=xlim, ylim=ylim)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can examine what the decision tree classification looks like (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "visualize_classifier(DecisionTreeClassifier(), X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you're running this notebook live, you can use the helper script included in the online [appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Helper-Code) to bring up an interactive visualization of the decision tree building process:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "27908facf15245bab6735b3bdfa456d6", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(Dropdown(description='depth', index=1, options=(1, 5), value=5), Output()), _dom_classes…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# helpers_05_08 is found in the online appendix\n", + "import helpers_05_08\n", + "helpers_05_08.plot_tree_interactive(X, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that as the depth increases, we tend to get very strangely shaped classification regions; for example, at a depth of five, there is a tall and skinny purple region between the yellow and blue regions.\n", + "It's clear that this is less a result of the true, intrinsic data distribution, and more a result of the particular sampling or noise properties of the data.\n", + "That is, this decision tree, even at only five levels deep, is clearly overfitting our data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Decision Trees and Overfitting\n", + "\n", + "Such overfitting turns out to be a general property of decision trees: it is very easy to go too deep in the tree, and thus to fit details of the particular data rather than the overall properties of the distributions it is drawn from.\n", + "Another way to see this overfitting is to look at models trained on different subsets of the data—for example, in this figure we train two different trees, each on half of the original data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](images/05.08-decision-tree-overfitting.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Decision-Tree-Overfitting)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is clear that in some places the two trees produce consistent results (e.g., in the four corners), while in other places the two trees give very different classifications (e.g., in the regions between any two clusters).\n", + "The key observation is that the inconsistencies tend to happen where the classification is less certain, and thus by using information from *both* of these trees, we might come up with a better result!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are running this notebook live, the following function will allow you to interactively display the fits of trees trained on a random subset of the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "f280b0c9da354fa395d5313c4f860380", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(Dropdown(description='random_state', options=(0, 100), value=0), Output()), _dom_classes…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# helpers_05_08 is found in the online appendix\n", + "import helpers_05_08\n", + "helpers_05_08.randomized_tree_interactive(X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as using information from two trees improves our results, we might expect that using information from many trees would improve our results even further." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ensembles of Estimators: Random Forests\n", + "\n", + "This notion—that multiple overfitting estimators can be combined to reduce the effect of this overfitting—is what underlies an ensemble method called *bagging*.\n", + "Bagging makes use of an ensemble (a grab bag, perhaps) of parallel estimators, each of which overfits the data, and averages the results to find a better classification.\n", + "An ensemble of randomized decision trees is known as a *random forest*.\n", + "\n", + "This type of bagging classification can be done manually using Scikit-Learn's `BaggingClassifier` meta-estimator, as shown here (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.tree import DecisionTreeClassifier\n", + "from sklearn.ensemble import BaggingClassifier\n", + "\n", + "tree = DecisionTreeClassifier()\n", + "bag = BaggingClassifier(tree, n_estimators=100, max_samples=0.8,\n", + " random_state=1)\n", + "\n", + "bag.fit(X, y)\n", + "visualize_classifier(bag, X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example, we have randomized the data by fitting each estimator with a random subset of 80% of the training points.\n", + "In practice, decision trees are more effectively randomized by injecting some stochasticity in how the splits are chosen: this way all the data contributes to the fit each time, but the results of the fit still have the desired randomness.\n", + "For example, when determining which feature to split on, the randomized tree might select from among the top several features.\n", + "You can read more technical details about these randomization strategies in the [Scikit-Learn documentation](http://scikit-learn.org/stable/modules/ensemble.html#forest) and references within.\n", + "\n", + "In Scikit-Learn, such an optimized ensemble of randomized decision trees is implemented in the `RandomForestClassifier` estimator, which takes care of all the randomization automatically.\n", + "All you need to do is select a number of estimators, and it will very quickly—in parallel, if desired—fit the ensemble of trees (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.ensemble import RandomForestClassifier\n", + "\n", + "model = RandomForestClassifier(n_estimators=100, random_state=0)\n", + "visualize_classifier(model, X, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that by averaging over 100 randomly perturbed models, we end up with an overall model that is much closer to our intuition about how the parameter space should be split." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Random Forest Regression\n", + "\n", + "In the previous section we considered random forests within the context of classification.\n", + "Random forests can also be made to work in the case of regression (that is, with continuous rather than categorical variables). The estimator to use for this is the `RandomForestRegressor`, and the syntax is very similar to what we saw earlier.\n", + "\n", + "Consider the following data, drawn from the combination of a fast and slow oscillation (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.RandomState(42)\n", + "x = 10 * rng.rand(200)\n", + "\n", + "def model(x, sigma=0.3):\n", + " fast_oscillation = np.sin(5 * x)\n", + " slow_oscillation = np.sin(0.5 * x)\n", + " noise = sigma * rng.randn(len(x))\n", + "\n", + " return slow_oscillation + fast_oscillation + noise\n", + "\n", + "y = model(x)\n", + "plt.errorbar(x, y, 0.3, fmt='o');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the random forest regressor, we can find the best-fit curve as follows (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.ensemble import RandomForestRegressor\n", + "forest = RandomForestRegressor(200)\n", + "forest.fit(x[:, None], y)\n", + "\n", + "xfit = np.linspace(0, 10, 1000)\n", + "yfit = forest.predict(xfit[:, None])\n", + "ytrue = model(xfit, sigma=0)\n", + "\n", + "plt.errorbar(x, y, 0.3, fmt='o', alpha=0.5)\n", + "plt.plot(xfit, yfit, '-r');\n", + "plt.plot(xfit, ytrue, '-k', alpha=0.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the true model is shown in the smooth gray curve, while the random forest model is shown by the jagged red curve.\n", + "The nonparametric random forest model is flexible enough to fit the multiperiod data, without us needing to specifying a multi-period model!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Random Forest for Classifying Digits\n", + "\n", + "In Chapter 38 we worked through an example using the digits dataset included with Scikit-Learn.\n", + "Let's use that again here to see how the random forest classifier can be applied in this context:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "dict_keys(['data', 'target', 'frame', 'feature_names', 'target_names', 'images', 'DESCR'])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import load_digits\n", + "digits = load_digits()\n", + "digits.keys()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To remind us what we're looking at, we'll visualize the first few data points (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# set up the figure\n", + "fig = plt.figure(figsize=(6, 6)) # figure size in inches\n", + "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n", + "\n", + "# plot the digits: each image is 8x8 pixels\n", + "for i in range(64):\n", + " ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n", + " ax.imshow(digits.images[i], cmap=plt.cm.binary, interpolation='nearest')\n", + " \n", + " # label the image with the target value\n", + " ax.text(0, 7, str(digits.target[i]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can classify the digits using a random forest as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.model_selection import train_test_split\n", + "\n", + "Xtrain, Xtest, ytrain, ytest = train_test_split(digits.data, digits.target,\n", + " random_state=0)\n", + "model = RandomForestClassifier(n_estimators=1000)\n", + "model.fit(Xtrain, ytrain)\n", + "ypred = model.predict(Xtest)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at the classification report for this classifier:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " precision recall f1-score support\n", + "\n", + " 0 1.00 0.97 0.99 38\n", + " 1 0.98 0.98 0.98 43\n", + " 2 0.95 1.00 0.98 42\n", + " 3 0.98 0.96 0.97 46\n", + " 4 0.97 1.00 0.99 37\n", + " 5 0.98 0.96 0.97 49\n", + " 6 1.00 1.00 1.00 52\n", + " 7 1.00 0.96 0.98 50\n", + " 8 0.94 0.98 0.96 46\n", + " 9 0.98 0.98 0.98 47\n", + "\n", + " accuracy 0.98 450\n", + " macro avg 0.98 0.98 0.98 450\n", + "weighted avg 0.98 0.98 0.98 450\n", + "\n" + ] + } + ], + "source": [ + "from sklearn import metrics\n", + "print(metrics.classification_report(ypred, ytest))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And for good measure, plot the confusion matrix (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.metrics import confusion_matrix\n", + "import seaborn as sns\n", + "mat = confusion_matrix(ytest, ypred)\n", + "sns.heatmap(mat.T, square=True, annot=True, fmt='d',\n", + " cbar=False, cmap='Blues')\n", + "plt.xlabel('true label')\n", + "plt.ylabel('predicted label');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find that a simple, untuned random forest results in a quite accurate classification of the digits data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "This chapter provided a brief introduction to the concept of ensemble estimators, and in particular the random forest, an ensemble of randomized decision trees.\n", + "Random forests are a powerful method with several advantages:\n", + "\n", + "- Both training and prediction are very fast, because of the simplicity of the underlying decision trees. In addition, both tasks can be straightforwardly parallelized, because the individual trees are entirely independent entities.\n", + "- The multiple trees allow for a probabilistic classification: a majority vote among estimators gives an estimate of the probability (accessed in Scikit-Learn with the `predict_proba` method).\n", + "- The nonparametric model is extremely flexible and can thus perform well on tasks that are underfit by other estimators.\n", + "\n", + "A primary disadvantage of random forests is that the results are not easily interpretable: that is, if you would like to draw conclusions about the *meaning* of the classification model, random forests may not be the best choice." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.09-Principal-Component-Analysis.ipynb b/notebooks/05.09-Principal-Component-Analysis.ipynb new file mode 100644 index 000000000..303bba21a --- /dev/null +++ b/notebooks/05.09-Principal-Component-Analysis.ipynb @@ -0,0 +1,1155 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: Principal Component Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Up until now, we have been looking in depth at supervised learning estimators: those estimators that predict labels based on labeled training data.\n", + "Here we begin looking at several unsupervised estimators, which can highlight interesting aspects of the data without reference to any known labels.\n", + "\n", + "In this chapter we will explore what is perhaps one of the most broadly used unsupervised algorithms, principal component analysis (PCA).\n", + "PCA is fundamentally a dimensionality reduction algorithm, but it can also be useful as a tool for visualization, noise filtering, feature extraction and engineering, and much more.\n", + "After a brief conceptual discussion of the PCA algorithm, we will explore a couple examples of these further applications.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Introducing Principal Component Analysis\n", + "\n", + "Principal component analysis is a fast and flexible unsupervised method for dimensionality reduction in data, which we saw briefly in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb).\n", + "Its behavior is easiest to visualize by looking at a two-dimensional dataset.\n", + "Consider these 200 points (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.RandomState(1)\n", + "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n", + "plt.scatter(X[:, 0], X[:, 1])\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By eye, it is clear that there is a nearly linear relationship between the *x* and *y* variables.\n", + "This is reminiscent of the linear regression data we explored in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), but the problem setting here is slightly different: rather than attempting to *predict* the *y* values from the *x* values, the unsupervised learning problem attempts to learn about the *relationship* between the *x* and *y* values.\n", + "\n", + "In principal component analysis, this relationship is quantified by finding a list of the *principal axes* in the data, and using those axes to describe the dataset.\n", + "Using Scikit-Learn's `PCA` estimator, we can compute this as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "PCA(n_components=2)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.decomposition import PCA\n", + "pca = PCA(n_components=2)\n", + "pca.fit(X)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The fit learns some quantities from the data, most importantly the components and explained variance:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-0.94446029 -0.32862557]\n", + " [-0.32862557 0.94446029]]\n" + ] + } + ], + "source": [ + "print(pca.components_)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.7625315 0.0184779]\n" + ] + } + ], + "source": [ + "print(pca.explained_variance_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "To see what these numbers mean, let's visualize them as vectors over the input data, using the components to define the direction of the vector and the explained variance to define the squared length of the vector (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def draw_vector(v0, v1, ax=None):\n", + " ax = ax or plt.gca()\n", + " arrowprops=dict(arrowstyle='->', linewidth=2,\n", + " shrinkA=0, shrinkB=0)\n", + " ax.annotate('', v1, v0, arrowprops=arrowprops)\n", + "\n", + "# plot data\n", + "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n", + "for length, vector in zip(pca.explained_variance_, pca.components_):\n", + " v = vector * 3 * np.sqrt(length)\n", + " draw_vector(pca.mean_, pca.mean_ + v)\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "These vectors represent the principal axes of the data, and the length of each vector is an indication of how \"important\" that axis is in describing the distribution of the data—more precisely, it is a measure of the variance of the data when projected onto that axis.\n", + "The projection of each data point onto the principal axes are the principal components of the data.\n", + "\n", + "If we plot these principal components beside the original data, we see the plots shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.09-PCA-rotation.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Principal-Components-Rotation)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This transformation from data axes to principal axes is an *affine transformation*, which means it is composed of a translation, rotation, and uniform scaling.\n", + "\n", + "While this algorithm to find principal components may seem like just a mathematical curiosity, it turns out to have very far-reaching applications in the world of machine learning and data exploration." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### PCA as Dimensionality Reduction\n", + "\n", + "Using PCA for dimensionality reduction involves zeroing out one or more of the smallest principal components, resulting in a lower-dimensional projection of the data that preserves the maximal data variance.\n", + "\n", + "Here is an example of using PCA as a dimensionality reduction transform:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "original shape: (200, 2)\n", + "transformed shape: (200, 1)\n" + ] + } + ], + "source": [ + "pca = PCA(n_components=1)\n", + "pca.fit(X)\n", + "X_pca = pca.transform(X)\n", + "print(\"original shape: \", X.shape)\n", + "print(\"transformed shape:\", X_pca.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The transformed data has been reduced to a single dimension.\n", + "To understand the effect of this dimensionality reduction, we can perform the inverse transform of this reduced data and plot it along with the original data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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ZY9X8OKsXlJG2bM6kLMpCBtuPtFMdDbBfgfix51n1/Hcoz/hbrnlVK2DD1/xZmrkkqIbfOVd6eun9nQ11FwVXC5JXQ5wK1PP6os3MX3/DpC/QNVdIoAsxCYqZsTme1xzN+XpXtaQsl3jIJGc7nOjIsGq+URhOad3xS9a99X0ibbu4Kp9E6Q5jD1DQUNr2wL9/Fm78LgSieFYaFw1F0VG8swt5eagoOHhoeKqO9d7P84f6u9jXnMBDYUVtlP8iQT6hJNCFmGDFztgs9jWBUZ2vd1VLNKCRs10CukZX1g9h89Cvefcb3yDY8Q6eByp9SyAVQMEBT4dcl7+WyiWfxXvhIcAPcA8VFYc8AdBNFCNAumw5LWs/zfJLP8r7gPetHFgTLyaGBLoQE2ywdcV7jhc7Ltz7NRPZPCc6MrSlLJq7ciwoD47qfL2rWhaWh0jsfJa1h5+iPLkfw8ug2jkUBVxPGRDmfbn+IlkdR+D9X+FQa4q6vU+i5VPYRoTtizexd9XdWLZHw8I4acuWcsMpIoEuSsJkDHEUq3dPuCd8k1kbF7fodvW8ZiKbZ8+pBEFDozpi0prKcbory/r6voE5oBoFv059x29+yrw9T7AstZegm8LrHhjpGeNWvFHMNvRcfxnb7rVUOt9zD43rtuC4Hic6MrQkc3S0ZYiFdExdlQqVKSSBLma9yRjiKKYNPR8opzqz2I5HyNQK4WvqCq6nFd2unt71iY4MQUMjaGhk8zZVkQDZvMPBthTvWnz2NQdUo+zdRuhXf8v7zuzBvzXp8796fdZVGbkuRYFA3N9kAv+DomfRrXjQoCzon3dxRWhaP1jnIgl0MetNxhBHj56g3nU8TYvWDEAia5PM2oWdfSojJgdakoUPFNvx2Hm8g5CpEw3ogEfOdlk1P46mKkW1q2cWaFvKojpiks3bZPMO9VURPM+j8fAZ0pbdZyLO+ek34B+/Ap1+dcpwZ+xfaDjc85SyOvjQw4W1yMvDJvGQQTRjYDkQDai8a3F50dc6FjPpL7OZQAJdzHojTWEfyVCh0Lvnryqw60QXWcvG1DUipkYqlyeoazQebmdpVaTwQVIbD7KGcl7e18qSSr9+u74qQixoFBbLGquzs0CTvHmsAxcI6SpZ2yUW0FkxL46pq7BvG+ft/SHhznfQ0mcAd5RTe3r65QqequG5rr+eCkp3lYtCLrKIY5dtZfmlHx3w054HaxeVD7ow2FiNNqRnwl9mM40Eupj1RprCPpzhQqF3z781bVNTa3I0kyfv2CwsD5PN27SnLRzX5UwqR2387BK1NbEAiyuDnLewbNh29Q+vyojJmZQ1ZJjVxIJ0ZmzaUxZ4Hic7MmQjJmVhg/N+dy+B3T/3x7i7jX6eZneduGqgeA6pshW0XPxX7HSXsvScpf4zugN6+SA/PZ7fQW9jCenJ/MtstpJAF7PeWBel6m24UOjd80/nPQK6iu14eN3h11PyVxk2OZP2S/8S2Tz7mhPsa07iOB6pnMN5C8qoiQUGtKt/eLUkcvzHzpNUREwMTcXQVI63p7l8RQ3lYZODrSlqY0HaUxZ52+Xavfezpn0bKk6vnvTY+f1vBceMkak6n4MrP4mz7ANYtgsnjhaeN1xAj+d30NtYQnq8f5mVIgl0Mev1DEe8dayjsO3Z8trR7V87XCj07nWGDYWc7aJrfjU2QM52iAb8MO7M5mnuyrL7VBcn2tNomsrSmgiJbJ6mk51k7SgLy0OFgNt+pJ2X97WSyNgEDBXP8zjdlaMznWORHWbNonJytsOx9jS/29/G/LIgL7/Twrx4kMqTL3LLrr/GdJOFNvcJ8yFnbPbVcys0V7GKU+/5K5JLrirsVNQT0FnbxfO8EQN6rAuDDWUsIT1RfxWUEgl0UTIc12PNwrJCD3Gs26/16AmF3r3O6rBOR8bC0BRMXaMzncP1PGqroqgqbDhvPq/ub+N0V5aysMnCijARUycS0HFcj4XlfsXHW8c62HGknaChc6glSchQOdRmMS8e5HBbkqqIyYnOLOfWOEQCOuXHX+Bdv/s28/LHuACPtFGFnk/0CfPevML/G56rBnAXv5u3z/nTs6saWnYhtHsC+vnmE6MO6JHWXxnN2PhYQnqi/iooJRLooiQUO546XCj07nW6Hpy/MA70rXKpjJqFYDrUmqItaZGzHY60pQkZGtUxE9txOdGRoSNtcbw9Q3U0wLH2DOm8Q872CJs6ecfF0DRSOZdbMv/KB7b9GMPNFNrpKRooGrHcyTHe5OzLBbbHN/Drhv/Oe5dVUV8V4UzKGjS0y8Mmq2uCg+52NFajHRsfS0hP1F8FpUQCXZSEYsdTRwqFnl5nMBWmYYQp64oCJxMZQppOJKCRyNq809xFPGjQkrRYX1eB7XrEgwa267GgLMSu450srgxT3/47PtP8fRbmDw46sUfxHFA0/9+jekf8MD9Z9195tOxLaKpCW9KiJZmlPGTyLkPjyJk0jutNSVXIaD9wxxrSsipjXxLooiSMZzx1IkKhI22xrzlBIpOnzbaoDBt0ZCws20FTDUxN4XBbEk1TydkOYVMjb7tURALcfGQr705uGzGoFc+md8+7//M9/KVoVTwcI0Lrmrt4ecGdZPa3Uh0NEgk4RANRbNfjneYkq7U4K2r1KakKGcsHroR08STQRUmYrvHUjrRVGBc/3pklFtA4lcvxxtEktbEAK+fFqIgEqIkGSHYvgrVi92PcdOiH6L1WJhwVz8NTtO5gh/7DKol576Xp2n/p86F2Zn8ruqqgAo4LIVPF8OBM2iLTPRFpKqpC5Abm1JBAFzNOMbP/pmM8tWdc+Hh7prBoluv4FTa6qmJoMC8eoixkcF7q9yz+3VeJZU8Ufb6eDZZtPYYWrkBLn/YPVK8gecVX2WGuZ8eBNiojJjWxAC3JHIdaE9gupPM2mqqQd1xsB0xNIRzQpyxU5Qbm1JBAFzPKeGb/FfunerHTx3vGhW3XI5G1WVgW4mRnlpZEjnhIZ0Hzf/LRQ9+lwjo55jYNStHIlS/nyLovc7Lm8sJ7UnjPdI319RXsOtnJr/54hoZFcd6/ah4vvdNKOm9jqCr7WxKgKKyoiaIpSlGhOls+cOciCXQxo0z17L+hPkDOrYn2mbGZzw1cTrZnXDga0DnUlqIibPLeoz/k4uafEPKSI69aOEr5QBUHLv8m+aUfKBwLW3bhPen/nlWGA7xrSTnRoMHC8jBXrKjhuabTNCeynL+wHAWPlOWQs13OrYmOKVSn4wNXjJ4EuphRpnr232AfIMmszba3T3PBorJCaO1uyTKvLdUn5BXFHwd+95EnuGHn9zHd7IS2LRVcCB/+BxqN9VSEzT43QXu/J/3fs2TOIRY0SOT8sfYF5SHOXxhjf4vKOdVRogGNheUhNFXhTMqivioy6jbJdPuZTQJdzCiTcfNsuCGCwT5AzqRyOK7bJ7Q8jz4hbx76Natfupdgrq3odg3GAzLhRZy8/O+ovvBDlIdNlL3NvHWsA9v1iAb0Qhj3vCf937NoQCORzRMNnn3PsrbLBYvKWL2g7Oy5ilg8S6bbz2wS6GJGmcibZx1pi1f2t/Kfe5sxdY1zqyMsrojQkbYKQwSDfYCcSfvrs/TWmXUIBlzqd/4Parc/2mfvzInQbizg5GVbSdZdVdjhp2d8vDOTJ5GzKQsaWLbDW8faWVwR5vIVNcDA96wibHK8Pc2Sykhh2r6mqlRGAn3OWcwHpVSrzGxFB7rrutx///3s2bMH0zTZunUr9fX1hceffvppfvzjH6PrOnfffTdXXXXVhDRYlLbx3jzr6Y2f6MhwoCXF0fYUZUEDU9M40JImZTmsmhcvDBEM9gGiqfQJv+jR57ll1/3U5g6j4A516jHzgB1l/4Vtqx4gHja4fHkN4e7Heo+P18aCVEUC/s5HOYdo0CAeMvpNfjr7nlVGTT6ybnGfGaAbzpvHgZbkgDXTx/pBKdUqM1vRgf7cc89hWRY/+clP2LFjB1//+tf53ve+B0BLSws/+tGP+PnPf04ul2PTpk1cdtllmKaMsc1lo62OGE+1Ss8Nu3TOpjOd40wyR1UkQMDQUBSFZNbmTCrXvcjW4B8gG86bz4GWJOV/+AcW/fG7KO7E9sbPUMYj0c/zVvDdLK+Nszpq9nkfBhsfVxSFVfP9XvBgQyWDvWf9x8bLQsa4q0ykWmVmKzrQGxsbueKKKwC48MIL2blzZ+Gxt956i4suugjTNDFNk7q6Onbv3s3atWvH32IxK03mZgQ9HxTbj5zB1DTOrYmSslxURaWse1naukodQ1dIZj3OpPMsnzdwNcaKEy+wtHtziCXZLhR3YsaFPRTa9Vr+Z/nnaNT/hEzewdRVlsQDWHmbw2fSnLfw7Nh27yGMiRzimKgqE6lWmbmKDvRkMkk0Gi18r2katm2j6zrJZJJY7Oz/YCKRCMnkwNXhmpqaij39tMlms7Oy3RNhPNe+uyVL3vUI6meL+bK2y/PNJ1hdExzmJ4eWyDm805qjqTVLWUAjZTnEAhpHT3hoCnSkbBwXWpJ59HwKPJeunEtzq4KSbuPQIYOygMqS33+Nd7X9epRrpAzCX1C8j6RaRvvl/43UgktJ5Bz+ZccZDrZbYKXQVAVFUbDSebpyLh2d8IqXZFHcQNNUMnmXhpogTalT5HN+hU3IUAloCjnH6/P4ZJP/3mfXtRcd6NFolFQqVfjedV10XR/0sVQq1SfgezQ0NBR7+mnT1NQ0K9s9EcZz7c1qc2HoAPyNII63pzneleWcSM2A4ZeRhmc60hanjrTjRTKcFwVFUdnXnCAQNnEsm65sHjMCju2wolwnaGic7MwSiMD7V81jaXUE89CvWbLti4Tt9vG9Mb3CPI/Kz8Ob2NdwN3979ZpCW1e0HcI1knh4BA0NTVVQFVhiaiypDKNpKi3JHBcurGDt4vI+17pyGvfNlP/eZ961NzY2DvlY0YG+bt06nn/+ea6//np27NjBypUrC4+tXbuWb3/72+RyOSzLYv/+/X0eF3NP76GDRDbPjqPttCUtwGPX8c4+O/OMZnim9yzNeNBAURQqwgZvHe2gvjpCUPerOt5pThANGlRETC6yXuey3X9PePdJFLxx7fLTwwNOU8v/CN/NH/R1hE2Nc6rCaOmz4+4HW1M0LChDVRVOd2aJBnSOtWfI5m2WLKlkxbw4saBR2Fyif1jLEIcYraIDfcOGDbz88svceuuteJ7Hgw8+yJNPPkldXR3XXHMNmzdvZtOmTXiexz333EMgEBj5RUXJ6l0d8c7pLo63p9E1jRW1UTRV4Z3mJM2JLMtqYpzqzFIdDQw7eaX3LM2c7RA0/DXFq2Imuq6QtxVq40FWzY/T8M73Wfi77+Bh92lTsWHuAsf0pfyvyMd5VbkIXdWoiQdY6LpURQN0pXOsmH92TLwrk6cmFiBkVrAvkODImTTZvE08bBANauw9nSAa0FlQFiSbHzgjVYjRKjrQVVXlgQce6HNs2bJlhX9v3LiRjRs3Ft8yUVJ6V0fsPp2gLGSwuCJCxNRJWTYdqRwdaYs/qa9i96kuUpZNyNSIdU+O6T95JR4yaEnkSFk2e091EQ+bdKTylIcMLsz+gcsOfZfw9oN4Th51gkoN8+i8vOBO3jz3z6iKBrBOd7E65/D64XaiIY15sQCpTJ6c7XHdmvl92prJ+7M3L6qr5KK6Sn53oIWjbWkMTSWga+Rshz8e7+hzc1SIsZKJRWLK9AwdvLyvlVTW5khbirCpdVd9aP4QiKJQFfGXmj3RkSmU6vWv7KiMmPz79mOc6szSkszRkPo9d2We4hz3SCHAPRjXeip5NURu3oX8fsHt/CZZTzheRd71KAcs22VFbYyU5VAbD9KSyNLclSMeNLh9/WJs1+OFPc3EQwaVEZMDLX5RQE/tdi7vr4V+dgBeKezxOZRiFxETc4cEuphSHWkLz/PoyliURwLkbZf9zQmqo0HO697ibWF5iN0nLdpS1oANintC7ddNp/joHz/DBfZbQ8bgaKtW+hepOOjsXXU3f1z2KeaXBbEsh8Tre1HyNi2JLC2dKgFT48qVtVREoGxhHM+jT3hbtlsY/z/Qkiws9tVTu31uTZTykMHJzixdWZtoQGPtojI6Mnm2H2kfENqTWfYpSocEuphSB1tTnLegDE1RSeZskjmbRNamNdGJofuxurw2Rn1VlNZkrs/kFYBTzzzABbu/y4UTOGPT1qK0xhvYc+6dnKy5DNeDRRUhru0Oyxf3NhMLaMSDBqqikMzZOK7HmVSOj65b3CdQe0K3//j/mZS/3EBvlu2yan688H1zV5aT3fcP+oe2LIolRkMCXUypszcINfY1J3jrWIZoUCdoqODBqwdaaTzczvLaGP/1woX+bMeffwp2/QzPdRjPCHP/bZNdNPau/gxd77kH23F550QXB453srgiTF1VuPC8fc0JqsIaS+edDd+MZZO17QG949EuXjXYFPqDbUmWVkUHDW1ZFEuMhgS6mDCjqh3vzLL7VIKqiH+8NhakMhzEchza0xaeB6qqENBVOt78JYtf/QKalZiwNioAegAu/yLa+7/CgrRFtjVFazKHqipsaJhPTSzQp3fsDTq+7Q065j3amZ2DTaFfUBaiJta3GqwntGVRLDEaEuhiTHqHdvccITzP3/He730HB90o4kRHhpOdWWpjAVK5PMlsnr2nE7geGJpKIpdnZeI1bm15hMr8SRjtBL2eLvcwA+ZubAnaDf8IKzcMeKx3jfdQpZIraqM8f+IU2bxdqEjpyub7VKT0XhTsZGeWpVWRwgfDUItXDVZfPlRoy6JYYjQk0AUwugqKRM7hVPcYsa4q/PF4Bx4KaxeVcbAtRTKbpzISQFGUXhtFnOKCReWkcza6Am3JHIsrI3Rl8uiaSmsyx9cObKLaPV1cw4cIcg+FjtgK9q75Iquv+D9GvHHYM6SR6K6uSeYcIqZKOKBz2fJq3t6n47genRkLQ1NZXBFm7eLywnvXM3a+pCJMUNc42JYkazssLA+NevGq4UJbFsUSoyGBLkZdQXG8K8/CuH9jbs+pLgxNoy2Z4/k9LQDMj5t9Sg39jSL83m7KcomHTHK2w6lOf1PlT+zbQn1y6GnMxbC1EG/Vfxzz6r8CQOm1Vdtweuraj5xJEzQ04kGdroxFZ9afjLRuYRijsmzQD7z+Nyxr4/7aNK3JHF2ZPAdbUyytZtz7bsqMUTESCfRZZjJqkUdbQZGyXEKGBkBLMkdbMkdA01Dx0DWFo+0ZLAdWdc+pOZO2ChtFRAMaOdul5vR/ctFbD1Bpj75HPtJ8zg6lnJfXPMDRqssoC+qYusaq7sdGe+NwaXWExsNn0BV//D5nO3jA0qoIB1tTxAIaDXWDD2/0v2GZyOY53JYk70LDgrjsuymmjAT6LDJZtcijraCImCotCb+UsOlkJwoK1bEgUVOnJh7g7ROddKatQXfJefeRJ1iw6wcYTqbodvaW0aL8P6GP8mzl7dTGg6ysiXGiLU02anLx0qqzzxvljcPysMmCshDpnL+wVzSgU18VIRrQaU9bDLceZP8blic6MqiKQlXEKAw/gZQYiskngT6LTFYt8mgrKMoCKr8/1Ebe9UhmHVKWTXva4vLl1WgKLCzvjr192zhv7w9Z37EPz86hOBbaODdQ9lDpjC1n28JPc7D8UgK6SjrnslIFVYGTXVmWVIbI2S6aqgyYkDQaC8tDWLbb531IW7b/PqSG/rn+Y99tqRyGprKwPFR4jpQYiqkggT6LjKcWebihmtFWUJxI2Jh6ENXxiAd1ArpK3vE40p7mwsUVNMwvo77jFZb/YSs4ech1+MMl49jxx0Ph0ILr+d+Lvkp9VZjGg2fItiYJ6jrzywK4nsKKeTG6snnW1VVwtD2NqatF3Tgc7n04OUyg9x/7Lg+ZVEcDhXVoQEoMxdSQQJ9Fiq1FHmmoZrQVFEc7LeoXBQmZ/s7zh8+kwINzOl7mupefINh5ANXNg6qDqoGioqhqn0Af7fqGpyrezf9e/V3KwwZdGYsDxzs52ZHG9SBi6igKHGpNU18VIWc7RAM6mbxfVdJ/RuZoDfc+nBzVz/rvV8/7Pd79O4UYKwn0WaTYWuTRDNWM5mac5wF4XPT6V6g7+f+ieP2XelX9JWndvP9/mtn9Mz36z9XsK2/EefXCr3Og7L14wLlhkz8cbMPUVOIBg2QuT97xiAUNgoZKe8oilcuTsWxqq6ITEpoTcVNSSgzFdJFAn0VGGxT9h1dOdGRYUhHu85xixnTry03WNf4l9S3PDnjMLwfvu76K5+RxNRUFDQWHwcLc0cMcWX0X2lV/yZmUxanTCQ6f6KIsYtKWtKiOBklZNrqhsawsgOVA3nUoC5mUhQxSOYd5ZSEqo+aMWn1QqlXEdJBAn2VGCorBhldOdmYI6lqhPhpGOaa7dxu88gh0HIbyev5kwY2saP2PQZ/aO6qV3kc9B1QVRw2i2Wk8FPJ6hPa1f0bLus8D/o1HM2WxtDpCR9qiakUNZ1I5Xj/cjq4qLKkMoyigqSrLKkMkcjY10QBtqRyLK8Jctrx6xgS5ENNJAr3EDDa8srQqysG2FNGgPvqhmt8+BC/9A7g2aAFwHZa2/MMgwywDeaqO4rl4aHh6CFcxyVWuoGXtp/mtsxYFhfXnVBae3/PXQu+218aDpPMOe0910ZXJU18VYV9zgu1H2wnqKiFdxdBUqqMBWUZWiG4S6JNgOjciGKwSpiYWIGs7w1Z/JHc+i/fyI+hdR/HMGMGOd1AVBVTDD/VUC5jlfWbaDzUa7nmghKs5cNk3aJv/vj43cY2j7aQthz2nukjmHKIBjYqwiaErvHGkHRWIBY1CyZ+mqqTzLhFTp64ywh8OncFQVaLdz+nZi1NqvIWQQJ9w070RwVCVMAOqP3qGU5qbcK00YTuLq5k44XloXQdRPBsPw1+AS1HBdf1VD40w5NNDnt9DJRVfRuxDf0f14is52u8mrqGptKfSmJpCLGiQyObZ35ygvjpCQFdRUcg7LntOdZG1Xeorw3Rk8nRlbcpCBmsXlRE29T7riPe/HyA7+4i5SgJ9gk33RgSjqoTpHk7xbAu/n+0vBKt6NmrqJHguoOB5NkrPfyKKiuJYsORSiC2EXT8D9+zwi2PGaV1zF4fXfA5TV/0PMBi4RGx5kOpogPa0RSJnEw0aWK6L7XqcWx1lz6kEQUPDcV32nExg6CoXLIqzvDZKLGj4myj3W5Cr9/2A6f5AFWI6SaBPsOneiGDESpi92/wwd53uFb17rertuniqhoqLp6j+eLnr+mvjug4oGly6xV+G9mP/RGev8Bzqw6P/TdwX9jRTEwv0uUH7+qE2bNsvR1w1P8ZbxzrYfridjG2zpCJMMmez+1QX9ZURysMGHgxZ4z3dH6hCTCcJ9Ak2EzYiKA+bXJR9AX5zP7S+4/doK5fDB77mD7O4Nq6io9J3BqeCh4uChwp4eKqJohlgZ0HVaV29mdp+a4prqsLOE50oeCyvjY3YEx7s/TE0tdDrTmZtdh3vwgHmx8MsKA/TlrKIBQ1akzmuXeOv/DXUB9Z0f6AKMZ0k0CfYtG9EsHcb/Pp+aH67eyaQCpoOrXvg3z/jP0cLgGN398LP1o7784YcXFXHMaJo0VpUOwXldXDpFtqcxdR2P7f30Ma76ysL1zmSwd6fnl53c1eWVw+2ksnbRAIa8ZBOZ9piYVmIeNCvfOkJ7qF62zPhA1WI6VJUoGezWe69917a2tqIRCI89NBDVFZW9nnO3XffTXt7O4ZhEAgEeOKJJyakwTPdtMwS7HWDEyvpj4EXgtoBT/WHS3IJ0E0IlaMkW/BQUXpNBvJ77S7Z+HLca/4bgTXX9T1P09lthIod2hjs/bl8RQ0A/9/OU6RyDpURg1goQDxoYNkOXZk8tusyryzI9iPtw97snPYPVCGmUVGB/q//+q+sXLmSP//zP+eXv/wljz32GF/96lf7POfw4cP88pe/RFGUIV6ldE3pLMG92+DZL4Fq+kMjrtNr7ZTuqfae46+t4tqgRkEz8CI1eOl2PMdBARwjRqKiAeN99xDtH+SDGM/QxlDvz/yyIH9SX0FX1uZUV5bObJ5kxqI5kWV+WYiykMHSam3Ym50y7V7MZUUFemNjI3fddRcA73vf+3jsscf6PN7a2kpXVxef/vSn6erq4lOf+hRXXXXV+Fs7AUqupO2VR/wwN8PgWGeDu3eVuOf5/6fqULsaLt2C9sojOOphUuFFHFz5SZxlH2BpdYToEO9FR9pid0uWZrWZeMgvZ5zooY14yMB2PJI5h7Kgwd5TXaTzDpGAwfx4kPZ0njrXG3GNcZl2L+aqEQP9pz/9KU899VSfY1VVVcRiMQAikQiJRN9d2fP5PJ/4xCe444476Ozs5LbbbmPt2rVUVVX1eV5T02h3Ap4YiZxDU0uWkKES0BROOx5v7XFpqAkSC2ijeo1sNjtl7a7a9UMq9/wYzU7j6GHOrLqVtvM/2ec5y1r24RhxyGYxFR3FtUHVUdw8vUPdc20cs4yTdR8l5SyGi79ZeMwAjNQpTqYYdFXBnvdNc/Oozcc57Xi0pW3/XmtYJ6Ap5ByPTN5/L5tSp4q63nzO4VhLFsWDYy0Z7JxLVFW5oDpEa6IdR/V4PdHGORX+phme55HIuQRT4RFeefym8vc+k8zV64bZee0jBvrNN9/MzTff3OfY5z73OVIpf4HoVCpFPB7v83h1dTW33noruq5TVVVFQ0MDBw8eHBDoDQ0N423/mGw/0s7q+MANDAxdHXJ7sf6ampqmpt2/fQjefhLwZ2vqTpbat5+ktroG3v+Vs897bTkkToMZAuZB13E/x7UA4BV67Ur1KtQPfI26flUqvQ3110vP+3b6xFGWnrMU8N+3nO0QCxoT+tfOyu42JLUW5sWDLKoIEwsa7DnVhWU7WA4sra8otKFuDL+78Ziy3/sMM1evG2butTc2Dr0Pr1rMC65bt44XXngBgBdffJH169f3efyVV15hy5YtgB/477zzDueee24xp5pQXZl8YU/MHiFDoytT/AYMk+bV7wKKX6Gidn9F6T7ey6VbwLXASkMgDqFqf9glWAZLLoZNP4P72uAzr/j140PoqVqxbJeKsIllu2w/0k5H2hryffM8f+LQlatqJ2ziTs8Y+GUraqirihQ2iVhYHqIrm0fX/J552rJJWzZLqyPjPqcQpaKoMfTbbruNr3zlK9x2220YhsHDDz8MwDe+8Q0++MEPcuWVV/LSSy+xceNGVFXlC1/4woAqmOkwmSVtEz42n0v666j0pmj+8d5WbgC+1b0q4hGoXgaXfoeOxVeebc+R9hHbM1zVSs/71ttklwL2r1bRVIXFFWHiIUNudgoxhKICPRQK8Z3vfGfA8S9/+cuFf//N3/xN8a2aJJNV0jYp080DUb/X3ftX5Dn+8f5WbujT++7fnpZEjsbD7SwoC7KwPDRouA9XtfKuJeVsP9JO1naL2quzGEOVN0qACzG0ooZcZquekOhZdbCw5sg4Q6J377anAiNs6hxs7bUR5d5t8M8fhm9f4H/du234F73ks/hj4Da43V/xuo+Pvj3JnM2RMyl0BdI5u89QSm/D9cJ73jdDVSb0fRtJz3knckhHiFI252aKTkZJ24g12b1rxYMV/k3MZ78EfGvoce2eG5+vfhcvl8QxIhxZeSed536KpWlr2HDr3Z4THRmChkZA1+jK2kOW+43010t52GR1TZCGVbUIIWamORfok6H32Hz06PPUvPV99K6j5ONLQPli31px8L9a+MeHuVHJ+79Cx3vu6bMAljWK4Zze7UnmbOJBg5ztEu0uzRxsApBMyBFi9pNAnwA9vduy479l4e/vx1ENLKOMcK7V74nnkhBf1PeHjJB/E3MExUyx793bjpgaXRkLD4X6Kn/uwFA3NGVCjhCz25waQ58sPb3bRW8/jq0YoIcJB3T0QMTvmbt5yGf6/lA+4y96NYJiSi173ysIB3Rsz6OuMkw0oEu5nxAlTHroYxQ5+Qq8dm9h4+Se9cHLwyZkjkO4wl8/vIcR6t6T0/KHWYyQH+au5f/sCIottezpbV9UV1EoqZShFCFKm/TQx2LvNuY3fsu/qdn75mZPxUp5/eA98ZpVcN23IDYPsh3+1+uGuSHay9LqSKFXXeyEGqkWEWJukB76WLzyCK5qDH1z89ItfsAP1hPvVys+WnKzUggxWtJDH4uOw3hasO+x3jc3V24ouic+nJ5Qf9eScgDePNoxaC25EGJukx46nN0got+4+ADl9ShtR4DQ2WP9b24W2RMfiWx+LIQYifTQeyb9DDUu3tulW1DdvD8l3/P8r6O8uTleo5qNKoSY0yTQe0/6URT/q2r6x/tbuYFT67804UMqozGrVooUQkwLGXLpOOz3zHsbZtJPasGlcPUnB31sMsnmx0KIkUgPfahSw1FM+plKE1G+KIQobbOuhz7h644PV2o4He0ZgpQvCiFGMqt66MPtqlO0cZQaTkp7hiEThIQQw5lVPfSDrSkWtLzE4rcfx0wcw4ot5th5f8bB8NXjW1SqyFLDYhbOEkKIyTKreuja/udY+vv70dPN2IEy9HQzS39/P9r+56alPVJ5IoSYSWZVoC/d+0Mc1cA1/BJD1wjjqAZL9/5wWtozHXttCiHEUGZVoIfTx7GVIK7nAeB6HrYSJJw+Pi3tkcoTIcRMMqsCXauoJ6xaqCg4roeKQli10Crqp6U9k7VHqRBCFGNW3RTl0i3oz34JXVHA7C4x9PJTMvV+KLLLjxBipphVPfTJWs1QCCFKwbh66Nu2beNXv/oVDz/88IDHnn76aX784x+j6zp33303V1111XhOddYkrWYohBCzXdGBvnXrVl566SUaGhoGPNbS0sKPfvQjfv7zn5PL5di0aROXXXYZpilDE0IIMVmKHnJZt24d999//6CPvfXWW1x00UWYpkksFqOuro7du3cXeyohhBCjMGIP/ac//SlPPfVUn2MPPvgg119/Pa+99tqgP5NMJonFYoXvI5EIyWRywPOamprG2t5pl81mZ2W7J4Jc+9y79rl63TA7r33EQL/55pu5+eabx/Si0WiUVOrsxgupVKpPwPcYbLhmpmtqapqV7Z4Icu1z79rn6nXDzL32xsbGIR+blCqXtWvX0tjYSC6XI5FIsH//flauXDkZpxJCCNFtQuvQn3zySerq6rjmmmvYvHkzmzZtwvM87rnnHgKBwESeSgghRD/jCvSLL76Yiy++uPD9nXfeWfj3xo0b2bhx43heXgghxBjMrolFQgghhiSBLoQQJUICXQghSoQEuhBClAgJdCGEKBES6EIIUSIk0IUQokRIoAshRImQQBdCiBIhgS6EECVCAl0IIUqEBLoQQpQICXQhhCgREuhCCFEiJNCFEKJESKALIUSJkEAXQogSIYEuhBAlQgJdCCFKhAS6EEKUCAl0IYQoERLoQghRIiTQhRCiREigCyFEidDH88Pbtm3jV7/6FQ8//PCAx7Zu3cobb7xBJBIB4LHHHiMWi43ndEIIIYZRdKBv3bqVl156iYaGhkEf37VrF0888QSVlZVFN04IIcToFT3ksm7dOu6///5BH3Ndl8OHD3Pfffdx66238rOf/azY0wghhBilEXvoP/3pT3nqqaf6HHvwwQe5/vrree211wb9mXQ6ze23386dd96J4zjccccdrFmzhtWrV/d5XlNT0ziaPj2y2eysbPdEkGufe9c+V68bZue1jxjoN998MzfffPOYXjQUCnHHHXcQCoUAuOSSS9i9e/eAQB9quGYma2pqmpXtnghy7XPv2ufqdcPMvfbGxsYhH5uUKpdDhw5x22234TgO+XyeN954g/PPP38yTiWEEKLbuKpc+nvyySepq6vjmmuu4cYbb2Tjxo0YhsGNN97IihUrJvJUQggh+hlXoF988cVcfPHFhe/vvPPOwr/vuusu7rrrrvG8vBBCiDGQiUVCCFEiJNCFEKJESKALIUSJkEAXQogSIYEuhBAlQgJdCCFKhAS6EEKUCAl0IYQoEYrned50nHi49QiEEEIMbf369YMen7ZAF0IIMbFkyEUIIUqEBLoQQpQICfQxSiQSfPrTn+b222/nlltuYfv27dPdpCm3bds2vvjFL053Myad67rcd9993HLLLWzevJnDhw9Pd5Om3JtvvsnmzZunuxlTKp/Pc++997Jp0yZuuukmfv3rX093k0ZtQpfPnQuefPJJLrnkEj7+8Y9z4MABvvjFL/Jv//Zv092sKTPSXrKl5LnnnsOyLH7yk5+wY8cOvv71r/O9731vups1ZR5//HGeeeaZwkY1c8UzzzxDeXk53/zmN+no6OAjH/kI11xzzXQ3a1Skhz5GH//4x7n11lsBcByHQCAwzS2aWsPtJVtqGhsbueKKKwC48MIL2blz5zS3aGrV1dXx6KOPTnczptwHP/hBtmzZAoDneWiaNs0tGj3poQ9jqP1U165dS0tLC/feey9//dd/PU2tm1zF7CVbapLJJNFotPC9pmnYto2uz43/2Vx77bUcO3Zsupsx5SKRCOD//v/iL/6Cz3/+89PboDGYG/9lFmmo/VT37NnDF77wBb785S/znve8ZxpaNvmK2Uu21ESjUVKpVOF713XnTJjPdSdPnuSzn/0smzZt4oYbbpju5oyaDLmM0b59+9iyZQsPP/wwV1555XQ3R0yidevW8eKLLwKwY8cOVq5cOc0tElOhtbWVT3ziE9x7773cdNNN092cMZHuxhg9/PDDWJbF3/3d3wF+L24u3SibSzZs2MDLL7/Mrbfeiud5PPjgg9PdJDEFvv/979PV1cVjjz3GY489Bvg3iIPB4DS3bGQyU1QIIUqEDLkIIUSJkEAXQogSIYEuhBAlQgJdCCFKhAS6EEKUCAl0IYQoERLoQghRIiTQhRCiRPz/g3u/IJb9dU8AAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X_new = pca.inverse_transform(X_pca)\n", + "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n", + "plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The light points are the original data, while the dark points are the projected version.\n", + "This makes clear what a PCA dimensionality reduction means: the information along the least important principal axis or axes is removed, leaving only the component(s) of the data with the highest variance.\n", + "The fraction of variance that is cut out (proportional to the spread of points about the line formed in the preceding figure) is roughly a measure of how much \"information\" is discarded in this reduction of dimensionality.\n", + "\n", + "This reduced-dimension dataset is in some senses \"good enough\" to encode the most important relationships between the points: despite reducing the number of data features by 50%, the overall relationships between the data points are mostly preserved." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### PCA for Visualization: Handwritten Digits\n", + "\n", + "The usefulness of dimensionality reduction may not be entirely apparent in only two dimensions, but it becomes clear when looking at high-dimensional data.\n", + "To see this, let's take a quick look at the application of PCA to the digits dataset we worked with in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb).\n", + "\n", + "We'll start by loading the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1797, 64)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import load_digits\n", + "digits = load_digits()\n", + "digits.data.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Recall that the digits dataset consists of 8 × 8–pixel images, meaning that they are 64-dimensional.\n", + "To gain some intuition into the relationships between these points, we can use PCA to project them into a more manageable number of dimensions, say two:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1797, 64)\n", + "(1797, 2)\n" + ] + } + ], + "source": [ + "pca = PCA(2) # project from 64 to 2 dimensions\n", + "projected = pca.fit_transform(digits.data)\n", + "print(digits.data.shape)\n", + "print(projected.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can now plot the first two principal components of each point to learn about the data, as seen in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(projected[:, 0], projected[:, 1],\n", + " c=digits.target, edgecolor='none', alpha=0.5,\n", + " cmap=plt.cm.get_cmap('rainbow', 10))\n", + "plt.xlabel('component 1')\n", + "plt.ylabel('component 2')\n", + "plt.colorbar();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Recall what these components mean: the full data is a 64-dimensional point cloud, and these points are the projection of each data point along the directions with the largest variance.\n", + "Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the data in two dimensions, and we have done this in an unsupervised manner—that is, without reference to the labels." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### What Do the Components Mean?\n", + "\n", + "We can go a bit further here, and begin to ask what the reduced dimensions *mean*.\n", + "This meaning can be understood in terms of combinations of basis vectors.\n", + "For example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$:\n", + "\n", + "$$\n", + "x = [x_1, x_2, x_3 \\cdots x_{64}]\n", + "$$\n", + "\n", + "One way we can think about this is in terms of a pixel basis.\n", + "That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image:\n", + "\n", + "$$\n", + "{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n", + "$$\n", + "\n", + "One way we might imagine reducing the dimensionality of this data is to zero out all but a few of these basis vectors.\n", + "For example, if we use only the first eight pixels, we get an eight-dimensional projection of the data (the following figure). However, it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.09-digits-pixel-components.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Digits-Pixel-Components)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The upper row of panels shows the individual pixels, and the lower row shows the cumulative contribution of these pixels to the construction of the image.\n", + "Using only eight of the pixel-basis components, we can only construct a small portion of the 64-pixel image.\n", + "Were we to continue this sequence and use all 64 pixels, we would recover the original image." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But the pixel-wise representation is not the only choice of basis. We can also use other basis functions, which each contain some predefined contribution from each pixel, and write something like:\n", + "\n", + "$$\n", + "image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n", + "$$\n", + "\n", + "PCA can be thought of as a process of choosing optimal basis functions, such that adding together just the first few of them is enough to suitably reconstruct the bulk of the elements in the dataset.\n", + "The principal components, which act as the low-dimensional representation of our data, are simply the coefficients that multiply each of the elements in this series.\n", + "the following figure shows a similar depiction of reconstructing the same digit using the mean plus the first eight PCA basis functions." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](images/05.09-digits-pca-components.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Digits-PCA-Components)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Unlike the pixel basis, the PCA basis allows us to recover the salient features of the input image with just a mean, plus eight components!\n", + "The amount of each pixel in each component is the corollary of the orientation of the vector in our two-dimensional example.\n", + "This is the sense in which PCA provides a low-dimensional representation of the data: it discovers a set of basis functions that are more efficient than the native pixel basis of the input data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Choosing the Number of Components\n", + "\n", + "A vital part of using PCA in practice is the ability to estimate how many components are needed to describe the data.\n", + "This can be determined by looking at the cumulative *explained variance ratio* as a function of the number of components (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pca = PCA().fit(digits.data)\n", + "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n", + "plt.xlabel('number of components')\n", + "plt.ylabel('cumulative explained variance');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This curve quantifies how much of the total, 64-dimensional variance is contained within the first $N$ components.\n", + "For example, we see that with the digits data the first 10 components contain approximately 75% of the variance, while you need around 50 components to describe close to 100% of the variance.\n", + "\n", + "This tells us that our 2-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance. Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in its features." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## PCA as Noise Filtering\n", + "\n", + "PCA can also be used as a filtering approach for noisy data.\n", + "The idea is this: any components with variance much larger than the effect of the noise should be relatively unaffected by the noise.\n", + "So, if you reconstruct the data using just the largest subset of principal components, you should be preferentially keeping the signal and throwing out the noise.\n", + "\n", + "Let's see how this looks with the digits data.\n", + "First we will plot several of the input noise-free input samples (the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_digits(data):\n", + " fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n", + " subplot_kw={'xticks':[], 'yticks':[]},\n", + " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", + " for i, ax in enumerate(axes.flat):\n", + " ax.imshow(data[i].reshape(8, 8),\n", + " cmap='binary', interpolation='nearest',\n", + " clim=(0, 16))\n", + "plot_digits(digits.data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now let's add some random noise to create a noisy dataset, and replot it (the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10.609434159508863" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rng = np.random.default_rng(42)\n", + "rng.normal(10, 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.default_rng(42)\n", + "noisy = rng.normal(digits.data, 4)\n", + "plot_digits(noisy)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The visualization makes the presence of this random noise clear.\n", + "Let's train a PCA model on the noisy data, requesting that the projection preserve 50% of the variance:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "12" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pca = PCA(0.50).fit(noisy)\n", + "pca.n_components_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here 50% of the variance amounts to 12 principal components, out of the 64 original features.\n", + "Now we compute these components, and then use the inverse of the transform to reconstruct the filtered digits; the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "components = pca.transform(noisy)\n", + "filtered = pca.inverse_transform(components)\n", + "plot_digits(filtered)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This signal preserving/noise filtering property makes PCA a very useful feature selection routine—for example, rather than training a classifier on very high-dimensional data, you might instead train the classifier on the lower-dimensional principal component representation, which will automatically serve to filter out random noise in the inputs." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: Eigenfaces\n", + "\n", + "Earlier we explored an example of using a PCA projection as a feature selector for facial recognition with a support vector machine (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n", + "Here we will take a look back and explore a bit more of what went into that.\n", + "Recall that we were using the Labeled Faces in the Wild (LFW) dataset made available through Scikit-Learn:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['Ariel Sharon' 'Colin Powell' 'Donald Rumsfeld' 'George W Bush'\n", + " 'Gerhard Schroeder' 'Hugo Chavez' 'Junichiro Koizumi' 'Tony Blair']\n", + "(1348, 62, 47)\n" + ] + } + ], + "source": [ + "from sklearn.datasets import fetch_lfw_people\n", + "faces = fetch_lfw_people(min_faces_per_person=60)\n", + "print(faces.target_names)\n", + "print(faces.images.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Let's take a look at the principal axes that span this dataset.\n", + "Because this is a large dataset, we will use the `\"random\"` eigensolver in the `PCA` estimator: it uses a randomized method to approximate the first $N$ principal components more quickly than the standard approach, at the expense of some accuracy. This trade-off can be useful for high-dimensional data (here, a dimensionality of nearly 3,000).\n", + "We will take a look at the first 150 components:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "PCA(n_components=150, random_state=42, svd_solver='randomized')" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pca = PCA(150, svd_solver='randomized', random_state=42)\n", + "pca.fit(faces.data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In this case, it can be interesting to visualize the images associated with the first several principal components (these components are technically known as *eigenvectors*,\n", + "so these types of images are often called *eigenfaces*; as you can see in the following figure, they are as creepy as they sound):" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(3, 8, figsize=(9, 4),\n", + " subplot_kw={'xticks':[], 'yticks':[]},\n", + " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", + "for i, ax in enumerate(axes.flat):\n", + " ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The results are very interesting, and give us insight into how the images vary: for example, the first few eigenfaces (from the top left) seem to be associated with the angle of lighting on the face, and later principal vectors seem to be picking out certain features, such as eyes, noses, and lips.\n", + "Let's take a look at the cumulative variance of these components to see how much of the data information the projection is preserving (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n", + "plt.xlabel('number of components')\n", + "plt.ylabel('cumulative explained variance');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The 150 components we have chosen account for just over 90% of the variance.\n", + "That would lead us to believe that using these 150 components, we would recover most of the essential characteristics of the data.\n", + "To make this more concrete, we can compare the input images with the images reconstructed from these 150 components (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# Compute the components and projected faces\n", + "pca = pca.fit(faces.data)\n", + "components = pca.transform(faces.data)\n", + "projected = pca.inverse_transform(components)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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gHNdsTrKhrzqI8kHGrJArdVwrFRsthMlp9FGO3I0Zjc86G+R5YCI3lCyNYfNnw5Z49BcDK+hzDLlHVXFxtf+JW8wIMGYckJSs03InhTPDGKdJlTij5kbZjQ/vJNpASRwwuDFCmN0QYrj4/vz8fKhPY92cReO9vq5uSLPZbOrCcp9nZ7m8rsSjKN6J4vId323jc+8pOfpMtEZ/eZazfMyxG0Kvf8lms2En2qTmOsG/kU2ed3x8rKmpqcROGU9Du4w6GGEMpH3ZpUkf411d3ic3nM6YOmM8qbksoQfMLX2C1eS5zlzFzjAOXnxNYhDoTG9ss2I7xM+Qh7T1UNKpHaGeMv6uOxSvT4tti9clekDDvMBUAvz5nrO7zJ3bbYJi9JZnEJSkAfpnAdlR84g9w6YwVnTVg2VPMTLv2GNsFP0EgMQgKl4HZ80fZv0Azv4z5i0Olhk/gal/j/nwvsXzx/9dR0fJInLrvotgtlKpqFKp6KWXXpo4vkxmuKHq8PBQrVZL7XY71CGiG9gUUoUemDL/cfmO2wVJQW59owXr4cw4u/B8DpiT2JaPa686iAKcONuAEjgQ8H9LyToZX3wG7MjalWiUYMXC4nl7j6BIJcVOb1wjbTQzMxP6wrsdFDrIQagwSh4JxQDSgZWDD48eGKPPA32LI17e8TCpLklB0XGWng7F0TmARNFZV3eGnkZwIOmREcrku9U87eJzgIHi3zwrri8bt4ZxipnxomS5XC7IBk6H9CLbcmN21Rm6mDWYnp4OKWCXD6fCY8CKQwQA93o9lUqlieOL5TBeQw9QZmZmtLCwEFJ5FGY7sIh3idHiuirmEyfr7BTP9OjY9YG5SgOikDEvlPejSjCWHsRlMpmw2YX/j2OnRgVl/u+YHXAdjr/LWJHZSc2dhrNDccAYP8tZOGeE3Z54+syZGq9DdFvjcxhH/vSN9D/zmxZEuYz5vKJLsV7RPJj2eaZfBCj+f2pCAX6wIeVyORyBAPCOnbAzQviQSe2suUbeHDi4LPoae8AjPVgX5vI+KkjCrrotcnvrvovaMOZhUgMUtdttVavVUNwtDVP+2WxW+Xw+2BW3m55Z8LH5ujsRgP1zux3XDTpri5zwOfwfm5/Gtf8nQBTKPErpY+XxnzsIwvDH6RuEYhSAig0b7AKold9RwNzv90MOP0b6ZzUHEvzbDRUL7uwQwuPCD4jyiMPBpc+DF8rFbIgDF3dSzh4MBoNgICY1ztZxBYsjRHes7rCkIWCampoKDEG8xZfPZbPZxG4xF3rG4b8ftUZOaT9MpAjgcgMmKShrp9MJERQGhm34yGbMhDqIcMPljJsDQuo6YuOJLDjTkCaCovk8jwMIgChSMkTr7sDdqXjA44aYP4yV5zjb4WOnts+B9KhalLMaz240GpKGjAM/Jy3M2GD0/A+y644HWfYA0MFybJxHGfuzwNdZTPOo5oCUPjDOeF39mXFQF6dIvLkcshYeeAFSpWQdnrNUUpLF8z6naQ6OYsDmz3L9dD0hOGU9PYgkrQND0W63ww5e31jk3/EUugcN9IVNQWlARqyDzB2y6cyRrzF/xzYd33dWBsd9h9vkUeyO+wiaA+E0u5z9XChngNBjwCp+AL3yuiiICMbhpQTu65GPmLVHZj1Ag51yto3fHR0dpUqpv+ogCgfoE4tgoORxusCRqRt53znFpPIZJtGFn+bfZ7szkTdbJnGitVrtATZo0vikoUFzJ+NGFyEBhbuR8rF75BdHXDSnn333g7NzrpSwT86gANwmNepMXPi8H+5kPJqIKfZMJqPj42O1Wq0wtxg31ghjxDzAYGQymQR7Nyo6jo143NdxzWUnBvPIJzKCYXHD6RRyzBLExssZOl9/d1i+xs7GeN/4fRo5dSPiBdOxY/b1823ggEcvtHVHOSq9FDOoHrnjkGPmZ3p6OuguID9NyiuXy+nw8FCHh4fhPZ42Z+zoutudmAk/K43jY4qZH492fawxaIr7/DDyybP9nV6v58Eca8TnYdr5vKes4z6yxjg0GFLvf+x8Y5YPdrbZbOro6Cg1iHIwO2remYMYNLh+ORCM1yoOWsvlstbX11Uul4NeA7R997Gvqwe86GcaEOXrxzO9PIGfAeb4dwyw3HfGoMnnYlSK0P0iTJgDmpiN4l1pGP1ut6t6vR5SeD4ugKYfNdLvn5YPlMvl0A/s6ihdYQw8VxoSI7ENjGU6DvaYJ45BmSSfrzqIotNQ7J7+cSVkgAgRk+l5Tl9YZ5piRssnm99hGCgwy+VygRGCgWL7+tTUVOLwwXFtamoqLIbTo/SHsXgxHQY+NqI+Fp+7+HMuNET6PM+39PIMj6ZGgctJ4/MiYubeo6AYNNJHd7ooMbvuGo1GOCm+1+uFrbXIR+yo/G//dzw+j5i97mVcGzUPGKKYkcHAjWLjRjnMGAh7BOjRv4NRX/M4AvbIMm29CTs5nS3yvjmA8AgNuSYaLRQKod7J9dj7G68TAZI7bwIgfo6eYFg7nU4APGlAYr/fDw7b15JD+7zuwufUo1lPjTgL5UEc+i0lT5eOGR5/buzE40g6TcNBwuQ5WGct3Vlhw5hb1g57GvfVnR2yAEuCjkoKgbCDKh+D2/B8Pq/Z2dkHinjPam4zRwWQbgv9j4NkBzysc2w/PPh2gDk3Nxe22ns2wfvmAIwdvWl3ccPAxmNg7Vhj3uvMp4/fg9O4rMGDFv+c2wpkmHX0usyY+XEdmNS4CQR/PSpAifvRarXCZwnUKpVK4kaMGDh5X9w2eiraa/vcF3owOUpHz2qvOojixNJRdK80jKjdKQMMMAQeiY8SEEkPKFcMrIgwAEh+DggnOiMEzhJNatlsNlwdk8vlwo4wT0/Q4sjJAcgoNM3frswIC1Gi7/bgGThDhCSmuHlfGgcc16v4+rjSuiOiH7CQAFJ3AM1mU81mM3FUQ7PZ1Pz8vIrFYiKKjBk6n5/Y4LjRTFsThfL5WjHOGDwxf6PObBnFXjiQ4PvO3LCmGGdJAcSwlj4uZN/ZoknNDz1FF9A1gguABuCFMbbbbTUaDR0cHIS1oWaKIIQW11k5sI7ZOmcSfa6YL+pU0sgowc9gMKTvqY/gyo98Ph/kyNlZdj6588LOxH0bFfTEax1/zhmh+HcY9DQNvWddcD4e5MCYel2a1554mpQ/OFGCBeTh+Pg4HFrKv/f29lSv1xOsQRzIug3imaRZxzW3dz7vbjM9SHGgxFrH7K4/24MV5LLZbKparQZAQtAX2xn3JdiVfD6vQqEQrjSbdOq1O3hnyTx1GIPjmJVzJneUnPJ51xnmjgCDnayUKTi75cA0ZqYmtTi15naLfsPg8VzkikCtVCrp+PhYy8vL4doptyU+l9KQIUOOmcNR+ID5oa/YGeZjXHvVQVSz2UwYUze6LBqUInnrTCYTjHUcRTrb5I7IBRLF9kn0nSlexH18fKxarabt7W3du3dP1Wo1sRBp2tHRUUh7uEN0Ojamhn0OACAONKXkmVHuPKGS/VkepTJ2KZmqmZqaSghMGgdVq9USkYSnC3wnD0rUbrfD5+bn50Oh9Pz8fAAHHjVg/I+Pj4NBOjo6SjA+zA3ywc/54zI1isad1LyGxusjfH5dMfmOMxY0jHXMQDjzwc8x2BgzZxX8/x5xOaPnqdFxDRDrjBN/CC4KhYLy+Xy4lgLWYnZ2NgDeRqOh/f19lUolLS0tqVKpJI5C8Ot+YtCEsSJgQU8YD8YeuYgPWh3XON6AfyNvMzMzKpfLWlxcDDrjQZczgjET4inimLWJyw1i5tQBbwya/Duj0oajGvPnfTpLxnyd8/m8FhYWgu4RrDjr5Hea+thbrZZ2d3d1//79oJftdjvcL8qBu16K4WyjdFoKUCqVwr2N49oohz3Kqcf67gyilNQ/9wUO0rLZbAgY6Lc7d7cto/Qrmz0tkF5aWlK321WtVps4PlgfTuJ23+C+TBqeGu9srTfAstsfgkAAi8+N+0bshtte37jggYyfrj6pUabCZiAPUlhDB1GsVbvdVr1elyRVKpVAZHC6O39cPt2H0Wd8DrLhNadOJviRQOCD/+dB1MnJSajwd8MZC02/39fh4aGq1aqazaYKhYKWl5dVLBZVLpcD8udZ7pQ8cpCG6NtBlAskhqJerwfwdO/ePe3v74cJpf4lTfNLcWN6m3fimJ0y9z7jQOIoyI17nI5wcEM05QyTs2Fu9FHSNIfg1et15fP5EGkx736kPwY7k8kEBSUFxFlG5XI5se3Zr75hLRqNhjqdjprNZlCMbHaY6jk6OgoGzBkTB51eDNput1Otn5+ZhGNw0OKsVAzO3NDzLNbco1jW2I0jY4zTgDgK32aOLGMIWD9uBBjXmENnEWEScCYAqHK5HJgL9LTdbmtnZ0e7u7sjizFheeh77LQAUM1mU/V6PXGX3yimFr0pFAqpWIxMJhNYq8PDw8C8eh0GFw6zfrCk0lBPnA135sPX2YMrd4Q+JzzH0wcxoGJu07LBBJusS7vdDjKLbBYKhaBzmUwmpDOdIXRWXko6dwKew8NDbW9va3NzUwcHB0E/ZmZmVKlUglxKyaMpHLwwBzCKk5rrnts3nKPrXByMuv7572P2j78pciYAIOglWHeQ5uvtOj09Pa1KpZJglcc1AgcCbr8Hlb66jYcF9iCDtaN20DcHedDiQT2/B9x4wTfvRH7iM8j8yqRJ7ZFHHtEjjzyifD7/AKDza7F8jE6eEDxTQgBuAJg5cETHpQcL75mDuJjcSztgq529GtdedRBFkaFHgg4UmOjDw8MQ8VKcdnR0lKCoy+WylpaWtLi4qEqlkjhcL3Zu7pxoGKJWq6WdnR3duXNHd+7c0fb2dsIZIYRpCq/L5bJ2dnZ0dHSkfD4fFouITVI48whjTf6X06DdWLhR8kgZx+BbYVEK/u1RtYMvmjNVzWYzlQM+PDwMaVAcQ6vVUqvVCqCHdZaGrAe7oCQFpYdJOj4+ThwLwe8okkfxMOA4eZS9XC6HLfgYFWcDnN1K01x+nKFENplXN3p8x0Gs//EUAhEgwBNn7Odp4chIn/hOI2cb/ewsSamAIrtrcLp+kzrj8cjTU3+5XE6lUinMPReSAgg7nU4IDlhvZAy5PTw8VL1eD8xGvV7X8fFxSIvEV2x40JFGB5FN1sq31+/t7eno6EiNRkP9fj+Ax5mZmcR5VvQbefXm+igN61sAaaQTXPdGBXgxwwGwnNS8GB87Wa/XEywd68pFtysrK0Fu2+12wpmgT5QuZDKZIHfo9f7+vur1urLZ0/PWAA7uaJEBbE88T6RludNw0hr6zQbYylEZB/+3s4iu/6PWzYMa6nHa7Xbi4moHu6MCJl/L6enpcOHu7u7u2PEdHR2pXC4He4ctxX7EQI/ia8YBMOUzLqs+R71eT41GQ1NTUyoWiwFIs5MY34ONRdfjo09mZ2dDNigNo/8VX/EVeuKJJ4Ivz2az4eYJ7DBr3Gq1ArPtbCH/9+wD48cuowf4Egd90vCibC/ax+4RjLN2fsfeuPaqgyjfHi0ld0+4s8rlclpYWNDCwkKYAIpbqcsYDAYqFotaWlrSlStXtLq6GhQU5+U5Zv4vDc8waTQa2t7e1ssvv6xbt25pd3c3OPVyuayZmRnVarVUaRJJ4UBHnMn09HSor8LB0Ue/S2p1dVXlcjnBrMUMBeeZ+C4XBw0eAQIOu91uwnB5JOW7chDESQ22CmcBHeqOFGVxJ+VHMBSLRQ0Gg1CLRoOhQKkw4EQlzWYzRG3Hx8chb8789nq9UIPmjIanK9I0B0acFQbLxuGRUMPODhHNusMnGvK6NeYI5+e77pwtZG6pE8OBScNrIwBSMANpGmwg3xl1vEW3O7yiw3fxZLPZIKNLS0uamZlRtVoN64vB8pSkp1+R393dXW1vbwcQNj09HQqeSR9ms9kgE6QSJ9WaSMPt+8gk4Bq9AfRTEwQYyOfzAXAwr/1+/4Fb5JFjL1qFKSuXyw+k1/1OPHfEDqpczia1TqcTUuPYBOaeWhPk4+joSAcHB8G5oOcEsoVCITgWP+bF5x2d29jYCCy0p1uZD+pAcUpeW0hgkfaycy/oRic8MIpTq8x1DNz936OAHfaQMgSY44ODg8BQwUo5S+O67XI3NzenpaWliSDK2TlnoZwFjW3/YDAIbLGDYGefWA90djAYqF6vh5+xDtgaz9DgW2G4CC5Ys1KppLW1tVQgmEwE4yFwxlZLw6NI7t+/r1qtpnK5rIWFhSBftVotZKOwh5JCStob4IcAALuKbrnfB8xTG4kf9SNqxrVXHUThNFl4rxdwxaBoFZpZGm6brFaryuVywcGCQI+Pj0MNB0WMRPQoPfQgBnZ3d1f37t3T5uamOp2OlpaWAgUOe7K9va3d3d0HctFnjS+fz6vZbCa2ZXvqBTDlabxcLhd+VywWEzluDBwRNAWesUFgfBTH0t9SqaSFhYUgJF7Y7LsU0xi3wWCQYBowPA5W3XgRxWKIScGWSiUVi0Wtra0lwKbXyRBpc1jb1NSU8vl8iKiIjpARlBSA4+uFoqRpXgAJ2KlWq+HKGxga2KRM5rRmb2VlJezocQMEM4ER43tsw2cjgm/3JaBw6tm3BPsWdU89phljqVRKGFQHZICCRqOhWq0WnDTOMJ/Pq1wuJ9If8/PzgS0+PDwM7EbsBJrNpg4ODlSr1VSr1dTtdrW0tKRSqaRKpRJqHllLAoFqtapWq6W5uTmtrq6mGh/GE3lFFpEl35nEes/NzQVdPTk5CewMdSuwhDBuBA8EFhRtOzAjQEGuvK7EAzPWPE2wRvqbvpKugx0tlUoqlUoPpChZXxwyDg4G2Zlsd+jUvAFg0XNYUMCoA09sGs6ToA8gMKl5ep558dIPB6Ax2+epRGm4c9sZKOwDz6fQOpvNhuxHo9EI/oSLcGFuisXiA1c+Ie9pQIZnB5hTT295/RJ95/cxkMO3eeBD0DU9PR1S5s1mM3HGk7M27XZbBwcHoWYZO1upVLS8vKxKpaK5uTmtrKxoeXl54vgIgt124TeQYdfHjY0Nra2tqVKpBFtZqVR0eHiog4MDHRwchHFIeiAtjE72ej3VajVtbm4Gv8/fgCeCHebN07bo6Lj2qoMoBBrD7/93hfdzeDBKg8EgbD+FEUD4T05OEmkBjDzgzBWQU1RrtZr29vYC3Xnp0iUtLS2FC0xZEJxTmly3R+CkF+NdAk61kkqjnxghj7g9coVajZ0CR0YA0AAahUIhgCsMmNdfITTkric1ojKibSK46enTW7ArlUrYZVGr1UIRqjTc8QMYAfxgMBuNhur1ekgdUGQIAzU3N6fl5eVQxAzYBBQzB6RfkbeY1p/UHJR5bQggAaDjLFOtVlO9Xtfi4qIWFxcTRyFgqJ0d9ej48PAwMDLunKlDYH4Gg0GgxtEFX0co+0kNYOdz4nQ3NUOAvGazGepZKpWKSqVSMGw4E4ASfYHhwMi3223t7e0lUuWsn6TADLnuAyBxFhx7Mamtrq4GI+o6ABAG5EkK4A/ATqTcaDQCsCPFSMrTU5cAf+yPAxB0ApYBI+47A91J8vlJDSbKgx8CFAAph0Yic9KwVhNgh+wxJmcrSPXEdUluI4ja0TWiej8biDQquimlO2rE5w094xnYHbe1zlB5zY5/n0bA58EtNgMQhP1ZWVlRPp/X8fFx+Js58IDSU/9pGqUbXnBNwE1fCKrddgNG2PjhoL7X6wXwAiufz+dVq9VUrVZDMMEOeWwjMoz+kbnA9hJQlMtlXbhwQVeuXJk4Pp7rZRHIKcFKs9lUt9sNpAX+0uucVldXVSqVtLe3FwgPWHCwA4EWwGx3dzfUTmK38TfU6xIoUp7C9UT46XFtovT+7M/+rD74wQ8maNL/9t/+28RJS9va7bby+Xwir+25TpQbYASIQvFgh2AEMPTQkUdHR4GBAn1i0EClrVYr1GS02+2w82dxcTEIJlEVwjY3N5eq3sSL2Yhc+X4+nw/C5YcBOsWOE5WGVLNT24A5csBEUdD4S0tLwfEC5Bi7FzHHggLLM6nBKCEfGHKcQ6/X097eng4ODhIpR56Pg4RB8giA+jCcPKmY+fn5kCO/deuW9vb2tLy8rKtXr2ppaSk4KE9lAtLdyKcx3tKpAcdgE7l7JCspAFZXPE/xFAqFMD7+Jq2JjJPeIuql2Bljxve82BSDz/fZys88pwEZ8RlJyIbXGviJ7chaPp/Xo48+qitXrujzn/+87t27F+aAdUSWAb3FYjE4HkAyKVDGDGikEJoAieiX+fCof1x7+eWXtb29raOjo/AMGkCcGkrAHX05OjrS1taWms2m9vb2tLKyosXFRS0vL4fIFxDVbrfVbrfVbDYTtWHoGDVJlAVMTU09kHp1Bw+LNKkRfLpcFYvFRD2ZA1CvQyWAZDddPJ/O9NA/ZIDfe8CC00OuYD8AbPzO1z0GNaMagYOU3JYPaxvXrsS66odj+nUtPE9KntXk13sROOzv72tzczOs4+LiopaWlrSyshKeRQ0d+uR+c1yjrtDJA8ZIHRGBCmCDMcEI4194BraOMpHFxUV1Oh3t7+/r9u3bIVAAIBKo9Xq9wDKtrq4GnSEL0+12w9hXV1d16dKlieNbWFgI9g5fBDvpgRrB4O7urm7fvq29vT1NTU2Fnb7NZlNLS0sql8uBzfa6O1jOarWqarUaTkgnQEMWYBOpdwOIt9tt1Wq1BMs8aQ0nepHf/d3f1X/+z/85derjYdvnP//5IJAUXnsNAywFEwBAcmGhSNuLkNneTdEc6JzoDJTf6XRUr9e1s7OjZrOp6enh6b3sgABs8QzQbJqiTyJBChTpC0rXarW0v7//wJlI09PTarVaKhaL4W/SG94fipHb7XbI+RK1sZMKA8Tcws4gcFD5zkJ4dD6ukS/HwHlxe7Va1d27d7W5uRmiUVI/3W5XGxsbCadGBICSzc/Pa3FxMRh/rt6hSJ8NANlsVs8//7xu3bqlGzdu6OrVq4n0q1P69PlhaoYcRBNRswMQAIwRcqPudS0wIJVKJYyNCIuUdK1WCylpUgi9Xi/Q6Mitp/QAb4AsTwPwnknNrxlC7qmfw9m7o6lUKjo6OkpQ+cViUcvLy0GHYATdAcPeSMNdecgLEWStVlOr1dLs7KzW1tZUKpW0tbWl+/fvq1wua2NjI0TtgJBJjVRhpzO8hqPf7yfYMa+JWlxcVLFYVK1WC0wH0W2j0VAmk9Hq6mpgqFln0pJE//QNmyIlDzb1OhWCG3eMaXWQdxCYoC9+kjzjBNjwblg92GOCDmyFpxoBSQR+sDHPP/+8Xn75ZVWrVe3s7OjKlSu6ceOGNjY2AgPmdT30z4+zmNS8lMFrJam39JQqYIgUOKCAP5ISQYOkhJxiywhqCLK9jgt5v3r1agAsLluAZy+VGNfic8oAFgBzWBJJIRAhdUx9pu8CJ5gFqCwuLibKLo6OjrSzsxMyFwTx6Oz09LS2t7e1tLSk69ev68qVK8rn8zo6OtLm5qYWFhZ06dIlzczMaHFxceL4SqVSWDuCdtbUy0AAMrBNn/nMZwJbdfPmTZXLZR0cHIRrZGCSAK+s99TUVNiItLGxoStXrgT76GUkrDUYwLEDPuP/Op331FNPhQj3T6ItLy/r5ORE29vbpx0ytsAZgzj/jZGu1+va2toK9J2U3B5MKqFcLocCWpiSTqej3d1dff7znw+GG4YDqp9JdzoS0JBG+Y+OjlQqlbS8vBx2+2DEqtWq7ty5o4ODgxCFAPoODg5C1DAzM6OVlRVNT09rdXVVMzMzqtfrgdKk4M4Lj09OThJRPHVQnt5hjhmjF7CnrYnyqBbwJ0n379/Xiy++qFqtFuqDdnd3AyNRqVR07do1ZTIZlcvlwFL51mqMPHUI9LfVamlpaUl7e3th9yTA6tatW2o0Gnr88ce1trYWnhc7BCnddQXSkO6XkltmieRgLjBEyA31QaRIcCgXLlzQ0tKSpqamtLe3p62trXBEgKeTGGun09He3l6IgElfMuc0ZxNxVmlSlv1+P8jJ3NxcYI6otaI4HoNMAIIOeH3S8vJy6Her1QqOxGta6N/s7KwuXboUNha0220tLi7q3r17KhaLunnz5gM7AjnR3p1ymvWD0SSyJhBrNBq6d++eDg4Ogp0D9LDTt9vtKp/Ph1q+2dnZsANYUnBuBHAY90KhoAsXLmhtbS0BRJEd1tkBKyyGMzqTGoyOgyYCQcbPuzkTis0yOC7fyecgwFPWBAg4vGKxGI69gEW4fv26NjY2lMvlQmF5XOAtKbBBfGZSQ38Bedg5L3aXhmkjT/V5vZOnIT29yZx3Op2ELnuNF/4GlnRtbS2x8Qlmw2XT65zGtUKhEOwbwAJGkzpfaq/IYLRaLW1vb6ter+v+/fthQ4dv+WdD1OLiYrjGhvOWtre3Ewzk8vJyWEtqbTc3N8NRP1evXtXy8rKy2WwI/Dc2NlLVJU5PT2t/fz9suHAGkvnDR1EGsrGxEZjEpaUlPf7442FdGo1GYPipefZ6MIgBUpgEtpAw+ESKyWHeIE6cOZ0UiE70ko8//rje+ta3amVlJQjEhz/84YmTlratrq4G50+0wyBw5tQvEHkwgdVqNVFk5udEoXQYRQqRoa4xBE7RFgqFEOUcHR1pb28vGE52CmFc/eybca3RaGh2djakC6grwLGy47BUKqlareqll15St9vV8vKyLl68GAScKNWdkVPsnhuXpM3NzUABZ7PZ4MBxdPHWVxykK3wakAi7BgOWzWbDjo4LFy7oxo0bIVK5e/euarWa5ufnw6mzntbg/dQAeGoMR+67ZqamprSxsRHm5Pr166GeiKJJUki+O4mzUNI22D932oeHh7p//75eeeWV4Hw9AnbFI/3lRbnLy8uh/s13rFCPBvN2fHysV155Ra+88kpIjW5tbQUjwzwiDy4LRH5pmhewElHTZ2oOYY1wRAA1HD+6St2EpxX9gE4odZzC5cuXg7O6cOFCSPUgV9euXdPKyopqtZqOj4/DXD1MTRt6R7E/toZ0P1vRYaenpqZ08eLFkEJAV7vdrlZXV8PGjG63G2rDcIDdbldbW1va3d0Ncgp4IyIn7QeAAsR4qQKOYFJzkMpawmRzfVK1WtXt27dDTdLKyopu3rwZWP52u53YmID9pCTi+Pg4pH0kBSYeoPyWt7wlOCRP23E0AmOJa2LQ5TRj9HpGgpLZ2dnAxmAbsGXYcNaPEg3PfDBvzN3W1pa2t7d1cHAQAAnglACD4AL9vHXrVgDPkrS+vp5gANOAqDiAhP3iGBdnTmq1mvb397W1taWXXnopBF9sMGCO0U/A0+XLlwNzlslktL29nbgDc3l5WRsbG+EoIQIrt22Hh4daX1/X3NxcqGVMk3KGeZQU0uqkxH0tOS9yaWlJc3NzunLlijqdjlZXV7WxsRE2opCBgqknPQchQHlDt9sN9ZD4pVKpFOqbpdNDPAlsPQ3qtdNjZXPS4H/zN39TH/7wh1PVVvzCL/yC/u7f/bvh/+9973v1Iz/yI2O/4wBBGqYLpOGZFtVqNRjP4+PjcOzA9vZ2gna7ePFiOONCUih+KxaLQRmIoJeWliSdMiZQ36BT6dTh7+zshNQbkQjGfdQ28FGt1WqpUqmoUqkEJkoaFjiurq6G6J5TWEHeS0tLQbBgcHBuudzpkQ8UyRJ1EeFPTU3ppZdeUr/f18WLF1UsFrW/v69GoxEof1IIXqyL4CBEk9rKykpgK4rFYuiD0/g8l6geoaRmAwBNjQkUP32RhtebSEO2cnFxUW9605uC81pcXAyFkr49mzlhnry4P03DGPH+4+Nj7ezsaGdnR8ViUY888oiKxaIODg704osvhjW/ePFicLSSAgDHMAEcSVtSqCydGrW1tbUwHiL2jY0NzczMhHoiio89jUO60ot3xzWvw4M18J10yLzvVsFJ4hg5ZoL0t0f3zB2n/0sKKRFAFfM0NTUVZNrnv9/vh4JY+gDjMKlR9wBwQ9YB5xcuXAggjp9zVIoz4Ds7O+r3+yHFjGPBMGNDpqZOT/6/d++ePvOZz+jWrVtaXl7W2tqalpeXtbKyovX19RD5E9R5YfLDNmc+er2eXnnlFW1tbYUiYOm0LkVSAI3M5fz8vPb29sLOOXYqTU1NJdJk/X4/7KLFEcOOOmPoO0uxVa5r9BVHlubAVCl5GCbgnVQ6qTcvGpYUGBU/i8hTerAYjKHb7erevXuhzAEbhoyvra2F9NDNmze1trYW9AG9jgPSNHV7Xk4hKQAAShykU1+1t7cXsiTsFM7lcqHUARnyjTYEbRxKTcC5tbUl6TTdzQnrAC4PnAhmKBtBN6hNTdtgt7EzyKFvQAGEE1isr68HfTg+Ptb6+rrW19fDUR2ZTEZra2sPlAJh5732l4D/ta99rfb39/Xf//t/12c/+1mdnJxodXVVly9f1urqatjd6in4cW2itgJMxqU+PvCBD+iDH/ygXnjhBf2X//JfJA23vU4CUdDGGH8vvgYgsSuAiS8Wi7p69aquXr2q//k//6fq9bqWlpZ06dKlkKbrdrshjUbtCrtPOOV8dnZWFy9e1MrKSqgrIfo8OjrSnTt3tLS0pMuXL+vixYvqdk+P8Ac0pKk38VoolBYH41uRoRjX1tYS38dgnJychB1eREiADObMjzN48skndeHCBfV6Pa2urmp2djacuI5y+G4baHJp9EGkZzW2Tvux/qQsHQBB4/IeN9LkoGFR4mJWp9xhXaBqAV6keHECgF6YAHLmpGs9RTepIXPUzsB6vvGNbwxb8qkBW1hYCCfqY4yIcg8PD0OBJY4FBsdTzoAfAPTrXvc6XblyRdPT06EGydOGkgJwRdap8Um7g9RBlK8DTjF27hh9mAtnDQFz7mgpRiZKpvbo4OBAjUZDCwsLARzjiLyOzeXB+51GTpFnwBzAE1bI09pEosgysgurBPB3OUYHXQ9KpZIuX76s/f19dTqd4Ly2t7cDg066kGDGAWfaNJA0rEuUhgwRDsh3E3oQJimwVX6QrTOj7LjFrvghwKwNzsvTaawNIMprWplfAlfXjzTr6PVC2HkYxqWlpdBfHB+MhqSQMvIjY2Lbsry8rNXV1QQbSDYD27a6uqobN27oxo0bWl9fDzaJlKpnQtI25JICad8ZR1kH5yNtbGyErAg2jl3m+/v7Ojw8DGksQBQgn0BocXFRTz75ZGASmUf0mXQpvmJpaUkXLlwIcg4TN2pT0qgGU0dAiK0hc0JtMoDQSy/QtUxmeMsEvo+zpOg7DHMmk9GFCxd06dKlYHuQtbW1Na2srOj27dvh2qKjoyNtb2+r2WwGWaIQflKbCKLu37+vP/fn/lzYxpjJZPT+978/8Zlv/dZv1Vd+5Vfql37pl/QDP/ADkk4VO835EZ6nRnBRMFA1lC+TxpUvpEdIx1UqlRAxUOUfF9OhcOweu3z5sp566indv39fU1NT4XiB9fV1vfnNb5Y03FmA86VIGAEY12KmTUruCsMRMbc4Bgw6YAkDG9e9EPV4WoW5QKBgt6iH8h0bRFFEmghtWiDFHAPIPA3HuHieGwZ+RvE08xIzIBhgxovBIkKGhXFn7oXyXgvBfBDFpU0HwY4QlbL+ACscBs6ZuSVdANtWr9fDHNF/wB9MD2CKs4hmZmZ07do1XbhwQVLyChU3drzPAQxOZlKjdtB1kXViPh1ouHy60Uee6YOkwM7A4vE3Tow5aLfbCSaOfvBsZMqNJXMwqdG3crkcdvmQHob2J8Xr6VBPSR0cHASjzxriqLE5MEH0jQ0lAFx2+0gKNRr1ej2UCuD0kKc0LBtzTl9xqDgX2G8H7siLdFoj5TcLAFRYb5cfZMqBbhz1ew0Sc4OM0VeeBcuShnlzZ43Ng12EYaMvgMJmsxmOIQDMoZPOptIIUi5duqTp6elQB4af4UgNCudXV1dDSYL3ywFUWiDlaVSvLaXui80MMEBetM66cFkymx/m5uYCkQAbi4zj+wis/Vw3bJLv5KROiayOy0CaMfol58g3/qBcLocaSsA6KXf6Q60aNpS1I9jBVmCPAH9gBQgU7Pfs7Kxe85rXhB2qADTe4QCNzNhZLdURB5PazMyMLl++rL/0l/6SNjc3w8/v3Lmjt7zlLWO/65QngIN78ED2KOVgMAgDI7p9+umndeXKlQSFHDM0GAYM1fLycqD1y+Wyrl27lsjNw9ZsbGwkwB39RHFJCY5rOHQ/w0caHmzmzsedEswM4I/PetExAAFBJqKAffEaBxQTx0FaE6MNFR8bzkltVHGzMxQO9LyWBro2rmPwfL5/n3WUFAyvp6FQIPpEX+JNCc4aPEy90OzsbMilUzMD8GGs1EjgTHD6sGIAXfrsa+nj92ACxpT+Izc+dk/hciaXz+GkFhfZ+noxz54mZPu4r7fv4sOZUdcF8PC6Ke87Pzs6OkoUROPI/dBR1haWI02DZc5mswkWGaaF+USfXEYHg4Gq1ap2d3eD80UvHbAzPk/jwIZLw7s2AZgwBxzMCRvl3/WU9LjmDB664cyhyywsEOMFyGGH3CnhqEhZIk+kmdhp66yzH7fhjFHMcpKySctCSclzqOKUmc+D2xoH46w9NoFn+S7lSqWiK1euKJfLBYeNbwEscQYY84gdwOYy7w4YJzXXbxh2Ul34BMYDUHX98DpidI4avKWlpQQDTr+KxaJu3LghSYkDb9ETCq/RX2ftvCg8DdvtttYDWc4vXFxcDPejNhqNBFCiNgwCg/IWZJ5xeWBKDRu7ZMkWDAaDUOe8sLCgp59+OrE7kSL6drsd3jOpnQmiPvCBD+jbv/3b9f73v/8BpPnDP/zDI7/z67/+65JOBeLzn/+8Ll26NBFExbQ1ggKzgXGam5sLSBIj6PQp+XA/zweD4UKNkaEQ7eTkRGtra4Eu9boPjB6OA6XjOWnqxKhV8uJFp7ddITzaigUDxce4srieHpGGZ2vxToyWAy2vCZGG99k9jNLT3PA7W+YRagyMcKJ+rgzrznM8pcczeQ+1LL4LA+PuII4xEyXzXP6kTVnSR1KHmczwmAh3WAA9ZJCIyFM/Dp5ZW08jIRs+h2woYH0xQqwb0bWnrRyETmqkDplbB+aMD0bNAbIbMsAFDgk9iyN1AJOnY2BgnK10J4HMSsmDEXnmpMYdb61WK6TzHTR5OorxO9DzzSUEX84aO8B3Fo6oOnbuvKdUKiUAqYNeZDpNTRu20lNUrB32i7n0GkvqzJCjcrkcQLvrYwxq41owXy8iegJHnoENyGazocCYtUX2xjXsFWPzeklpmJJ2EE+fkE0KkD1w5VmeHgJg7+zshENzATKtVkubm5thzZAH6cE7FaXkfX7jGmwwrL77B68jZcywZBShw4RTK0uNJXXB5XI5YauRe44qWFpaCmwRATZABP1mfK472LtJpS3OUPs9uMxfqVTSpUuXwllz+E3SzNQPl8tlZbPZcJQKa4uuwKgC8jnnrdFoaGVlJfhsymNcdjud0/tY0dnV1dVUR4ycCaI2NjYknd6+nLb9zM/8TPh3p9PRP/gH/2Did9y5SUNEDgggMmVbPywLE+A5WqhPoh6EShoeo+87dTAU7NqAOmTB3SBiKDFCaQtAcZaSAhBzgQQoMXZ3XESrXs8BWHAgxd8sOEbRaxs8enOGwRWU/jodP6k5g+VrSZ94l4MHB7iABgfNrIGzZrGTcPaLMQIC43lhDWLQmrYxb9LQGKDk7lAAELyL+gtqlzA8jAUDAXvFvCHX0Owcv+GRM7JEWgr5YR0eZnzMsadQGScAzp1FzJ4RcKC7bMNG/5w1ZX0PDw/DOJF33u8F3l4bxdr5nLkcnNWoEyLapq6Q2hVJ4d/MMe9gl+eFCxeCE6avyIannxmP18W4Djj4dKDjAQZzm1ZO4/oeTyWNAtKsmZ8t53eHOdsjPcguO3tDyszTn/yNgwegML/YHUmJzTaTmgdrLvPO3qOP0vDAYMbrwQlAygOBUqkU7kl01p/gwH0D70IGWUNp6GseRgfRB9bLS0B4lx/bwDh9Hjnp26/kwbY6S+xBNYfNetoe28LnXLbQDQfoqeqGjP2jZrPVagXZIfu0uroajk8AnK2urobawbh/9PHk5CRx8TZlJnNzp4dib29vBxnB15AyRJYZ15UrV7SyshKCrUmBzJkoYG5uTn/4h3+oy5cvpxYEb71eT7dv3574OWhfNyREgBhhpxKpWZKGDtoLUaE9MezSkA2CpvTaHSKhSqUSTimOUb8bAK/xeJjLTz1fi9NwJO20KAaXAklPQeEg+awzO0QPODvAhaecnOqOldGNEY5rUmO9uH7E2ZaY+mU+WC+/s8wdKgAYpoq1Y94Yg+fjnY3DGPic+5kx/C4NDU3js/5+amkYgzNWGLV+v5/YfeQpBp7r9SgYS2owPBXi7yBa5mBSnoMxcNCWpjkAQ4ccHGJ8+ayvmbOs9IuxEdh4Sj42gK7jDkIdeHtayK/BScNEDQaDsA2+Xq+H9CppCq//8HQ29XoXL17U6upqYFCwU8528h63PwRIgAjmwJkUB/7MM7roQGZccweFc3NW2UGZF3uT6nBmHqABmPb3s1boPHUqFO3SDwfG7mRdLqhtQ08mNWfpnDV0O+XsKfPCe112AUXo7ezs6bUhnKHkv5ueng67wLD3zGcctPN85MnZs0nt8PAwsGTOasYZBvQDv+eAkQ0w+D3sqzP0HjSjh2R58Kc+5zS3qYA5bPuk3Wu8C/nETnG9mrPRmczpLuuVlZXgK8hGkXYDuPpYqYUD9JLJmZ+f16VLl9TpdMIVU1447uMaDE43SlB71u8PS2nGtTNBFKm5V155RScnJ3rd616nT37ykyoUCvrVX/3Vkd9561vfGv7d7Xb1Pd/zPRMnt9VqBQPgtQY4Pa+lACi5o8Dw+Y4vznxigVwB3Vhi7DqdTthVxbvZKutRD6CHCCENiJL0wIFwHrnELIo0ZHc8ZeP5fzfgnvryOidnc2KwQTQYO94YZKSJpLiqhmdLQxDoBsRZMJR5VG2NGzgMpDsUf6Y/jwjcnRRj8giVZz4MG+U7flgv5BFZAhzQJ5gIT5fEcxKzavSfCJhzlHgXZ/zwWfoP0KSgFrlhPSc1B+IYXAdUXmeHPDl48kMeMYRepApgAATB5nAQKfMHKGTOHQDjsBxIxXozrsFcw564LjEeBzXdbjdEw8vLy4H5InVK6oNneMDhzLHLrae24+bAnnGnbdg0bJ+ULDaXhgAD5x/XKWFn+a5/D/mQkvWG6Bh99uMjnJXm+cyV2yV0ZVJzMBazgN6wA65jvMtZPu8jLJQfRsyW//X1dW1uburk5PRw0Wz2tHC73W6H2i70220s7/Sfj2vc2cZJ3J6acr3L5XJhQxN66X4EsEjA0Gq1wvgI8AAh+Ihut6udnZ3EDRFOIDD/zD2yCgFCXd+45ilrgguAY79/ejgvNqFcLodd38wfegteoMgfFhP5ZA4pJ8jlTo8OeuyxxzQ3Nxd2xna73cA0OUNVqVTCQcgETV8wE0Vq7h3veId+4Rd+IURv73jHO8582Bdyp169Xpc0XCxYImmoEAwQI+GGxg0PyNMpd6eg3Wm64aaKn900gCl2LHhtEUj68PAwUUR/VqMQkIXo9XqhlmYwGIQIzp0pTpHvoECx88eIuBN0hWPuXJG9dsAdEn+ckUpjyGHucGiMCWbB348CoRS+3g6EAMV+RhfspBfRxsXQDixYYwcHcaSf1lFBPxM9kyJwECcNIzvmgXSdA1oYCv7vtLinhRgrxcIYDo+++ZwfiMhBsaxnWhDlTtznMJYx77cHFdQ+ATipPwLI4rxhLDHofr8lYAudIJJ2IOfFo6Oc6KiWzWZDPRMpJh9bzOB4UDYYDMJJ0OVyWUtLSyHwcvYbHRjFipwFoph3D4JisJ+GDUam0DsPatwZMj4/PwxQQzDgshWnzOLn+LgovyB44FkOUN328CxpdC1R3Nh0wFydNcZRa+A2wvWBfsDC4WOcmYOpPDg4CPdCOoPjLL+/01uaNUQ3sGuweBAJzDN6w5zFejAYDMJZivfu3ZM0PCdtfn4+yBlyTqvVaiHlxd2OcdDn8wYxkHZ8BHTMP7YLVg27w5zGNt2vUmLu4wNmAYuMz/0P5/NxODfBGXMwNzcXbiFAv+njpDtyJxb17OzshH/3ej3t7++f+dmPfexjes973qO9vT2tra3pJ3/yJ/XUU0+NfT47CkaxKgyUfCkCxtUFLkA4KD5HESBGGoeMIea9GJ5erxcK6Tz9g9J7zp8DQF9++eVJ0xeYFXfCpOikBxWd8fP+OHJzFgog5BQ6fXXldhDpY/L6Ei/I95TepMZ84iidHZGGuw4ZB+8FRBF5EYVwXIGDDmqQvO5hFDjz3zsgJKXijjgtS4OM4iQ9enYHSV+I5l3OSE0TBJCCcxDiReasIRF6DNQymUzoPxEaRs3ZmjS1Ci6D/NvXzueYxtrQfxwQu5Y41y1Oi8AoMXZ0g+MNGGdcQ8eaet+Y9zQy6sDMdcqBoJcQIBec7I+esL7oE43/owMuJ/ze+83PXNc8ZelpmDQOijVBHkeBB96NHvj3WAuvAXJWl/4ic8gvDp3fAz4IYH09YRxjgJg2JUswS79GAX3+7YDV5yFmBT0g86DM31Gv10Nx+fb2dlhjfI0HFOg4+pGWJWV8BEGAYthfWFcH5fzbWSPsW7Va1ebmpprNZrh/kvXFxrsvgXy4f/++er2eLl26FMCEzy0yzg5gfA9HTIxrMLduq+PUpZ8b5nJLbSg2FzbOD7z2IIiie2l4oPPMzExgrjhChvfDRsI0+uGtHDA6rk0EUW9/+9v1Ld/yLbp586Y+97nPjWWifuInfkLvfe979dhjj+mzn/2s3v3udz9wplTcYCVc4N3pu/ODSscZeXQxGAyCE85kMuH+Iyh5jH42m33gfBcvHGSRMQReQ4AiUgtQrVYnTV+gTX0nghfGeXowBpLu6N3YS0o4GGfqYuPC38yhp7hisDiKiZjU4hojwCpjj1NV/X4/nMcR795z4wND5ZsDmBeP2hy4MYZRwJB58r6mdVD0M069uiGOmTTkhKsy/JwpjrvwbfGSghPjmRQ+ulPzefeLjwFP/MFgpTHkbpClIUiKx0pDdjl1nF2uUOVcpu16DGggsuY5nrpnXpBb9JDn4GhcpryG46zmzCPpUmcT+L2zGF5jwiWwROc+v8ggegAQo38x0IuDpFEginGm1UVnC90pxXLJXAAiJSUYDT9J2muIeL7vqMTeeC2Lg9K4Jg+Q6kEd856msTbYQx8v74hBNo2xOYvkNsVtqQPeXq+n3d1d/fEf/3EIyLvdbmA8isViKCnBUXsWINbZcc2DXAJ80oWsITLpIJA/6FGj0Qj3iXIuWqlUCnb/8PAwsTGC966srGh/f197e3vBX3AoaQykuU7o+Pg4gJNJjc01jMEZeMaCf/ca2l6vF+6GXV5eDsCNozh8jvE/gFFqyMhO8R5YaQ+qsUXHx8fhAFr8fLPZHDu2iRbou77ru/Tcc8/p1q1bun79+tizkUqlkh577DFJ0s2bN1NtD2QXktP8kkKulIng34PBIJHacyPKzwFP+/v7IdfKLhCMAYqDkWs2m4nTVNnFF2+JRelBqWlat9tVvV7XYDBIHNDoRhRBcIrfgSWRDs6IuUAJcC70GaPjUYTv7vAIPzZM/DtN40wtHweCHhtq+u4glGsEpqenw3UGgD0/gI10hYNFrz1iHpx98iJl2sMARJqnbTiYLZPJhNoEjBrPp//sFoF99LQzESyGySN0KGQcagwaeA564zfZe6TpKeJxzZ2sA1l3VC4XrAWOpNvt6uDgILGrxpkYT9/Exbb831Ni/J/vOMCGGSL1lwYkYij5DsbSgSdyJZ3KKQds4hiRM3f8HgDxHOTf6yjoowMlnFocNHmgkxboO0vuLWalPGDxVAnggJQZssl3XF4ZG33O5XLhtHnmlb6gC6MCNS8ETgv045RZLJfeXG7ZuQVzhj11Vhw21+WKMd+/f19bW1uJtGkmk9H+/n64/QLdjGtXH4aNctuFX/ICdUkhm4J+wPwxxvv37+vOnTtqt9vhsnppKHvooteE9funO4kvXryoarUarr1hl5+/nwwPgRLHdExqXvTtG4RYV99khZ/AZ+HHOYeP441iQO51flwfw117sEzITVwKQTYHkMizOIphXEt1SdPy8rJ+6Id+SO973/smfu4f/+N/rK/4iq/Q888/r36/r3/7b/+tJOk7v/M7R36HNEC32w0oGVoUsOHUL/SlMxa0TOb06hMuZ9zb21M2mw2UHlEk1Hwmkwk3ZBNtHhwcBGPoxoTns8BM/qRG5Ebut1AoJJwyCoExQen7/X5AyxgxjDgFh4Ald6D8iSMx3kF/3KCNMq4xZX5Wc6bBI0Xmy9kwScHBS9LBwYF2dnaCorL+OLGdnR1tbm6GCys3NjbCVSqcAI4Bp69urIk04pQBBjJtOg9DzRohQ+5EPY0J/Vyr1ZTJZEKkhtywBZf1JF2IbGDMYT+ctvdU9ygDwpi8xuVhWhxF4yh97jh4lDQB6Q4CEa8XcfaJukN0Xhqmc+m/H0rrRjLu3yiG7KzG/ACWmEevCSSNkMlkwk6ez3zmMzo+PtbKyoquX7+uhYWFB4w3uoeMIVduQzydFK8V68Vcuz6lbQ54Y/s4Sp+94N3vX4MpAEw6EMbJMe8AqlqtFgI3HJ8DI+bdi6XRUcBoGqC/t7cX0qsO+gEqvi6eXsUpNptNLSwsPMBq46ip33P7lMudnk1UKpX0uc99LmQSvHaNYmy/iB377jY1TUM2RgHCUXOEbmUymVAHdevWrVA6Iimcvs34crlcONHcQSwF5fPz8wG0NBoNLS4uJuqUCPIoH4CISDM2J0Kwa8iY+zhpuBuxVquFOibmdH19PTF210PGUygUdHJyEs5/XFpaCnLvbBV/kBvXTUiVSWxp6psu0yg1Z0rdunVLxWJRX/ZlX5aoqRrVfHs0yh5HsSg/ESqTGUfK/X5f1WpV29vb2tnZUaPRCIaexef0Uwp3uc+N00oxClxN4gxDv99PFO4CZsY1jAbF5EtLS0HpPTLFsQPSWMhRReXUClGP4IDM0wkOvFwQvIjV19VBD8+d1PwaEk9fIOSuIDxzZmZGlUol5Our1ap2dnbCFQvUkHFnm99gns/ntbi4qGaz+QBgRAlQJmdAXNEdgKRtON64rorULM9FoWu1WjgHhTvaiJLIscf1AByJgIFjOz6gxN/jDKKkxHhxgvFnzmrOtLoMxGwoEXypVAqH92FoMIgEAdns8GBbSaHmjWsrOJ3YdYBne51HDKRiJ5XGQQFUu93uAyeixwwJc99qtYIBhqHJZrPhNGXpdFPF3t6ejo+PtbCwEBwu7Hqv10ucP+XpctdnZ1Mc4MepwHHrxxwRUbtOxmklT2EB6gFJfr+a1yN6ypzfYQsBycg4KTaYe+TVmSGe6Y5zXHvxxRc1MzMTgKzPl4/Rxwaj62y2F7kTYMXpXuaI9SP74rdikPIpl8vh7lZ8Cd/3+Z7UcPCeJcHnEMhjC3wundm/e/eu9vb2wg6zk5MTffazn1WtVgtsC/YIAoH1mpmZ0YULF0JdMKd2Hx4ehuNWIDfiQDlNxon5Zs2QrVFkhaTAkGIzd3Z2dHBwEI41qFQqAcgPBoMA+sg8sV5kNvDrlJN4XSw22xlrDyAnnWOWGkRxj9y49s53vjMYFdrFixfHd+D/OBApec4K4MoVUBoCAM/P871utxvqMkCXCDwAaHNzMxTdcQVMt9sNtN1gMNDq6urIFBtgyM83mtS63dPCWb88UnqQ4kdJAFDValXVajXsCPJaJiLIg4OD8F1AiteMkDP29F+cHnGARvP02KRGOscdhRsBfybGEmd56dIl9ft9bW9va29vL1yGmcmc7kRbWVkJ1xVIp4aGk3gzmdO6N69l8XQeRpH5wrAzLn6eprE2GDqn3R08YJy5CBQQyBURrDn1AX5TfL/fD8DLgRQOi3nD8Dul787EKeu0IMPXyuXCv8uacO3S7OxsoMMplscpV6tV9fv98HMMJo4NkMA87e3tKZcb3kQfAyb6MQrkpWluK5hHSYn1dN0ikl1YWAjnS73yyitqt9taXl4OR5twVQTPbLfbicuvY9mLbZnrXQxW0wIoSamiZRq66QEipQ7YXUolCFw8FQ2zj40hoISNwuYyvzj6uP6LcacFUXfv3tX6+noISFw2PJ3OGLHVpGZgUwBuyLlnCnDIOGUAtKRwOCn2WjpdP44RcGDjTKDP87jmKW7mivnyul3sHfNH4fP9+/f1yiuvqFKpaHl5WSsrK4FQuHXrVmAbuUA6l8uFsQEWOeV7aWlJ9Xpd+/v7YR65Ms0PkUUf06TzpOH1UplM5gG76TKArJGZ4OqknZ2dRGDZarXCjs16va6trS3VarXATsIqraysqF6vh7SrEyMx6HZWmTF+wUxUfFzBs88+G37m50F5e8973qPf/d3f1draWujIpMJyJsRrdYgIAVJe1wLIYPE8qsSAe5Hq8fGxdnZ21O/3tb+/r93dXXU6nVCkfe/evaAs3FeEk8IYOOKHAk3rhHkWqRme6YKD48Dxo+A4Yj7DmMlb379/X/1+X4uLi1peXg43tnt9me+EcGOGgjqwkIaOJS2IIlKVhrVBnt7zsTob1ev1QlTFxZYIOKyFFw4iD0S8RBUojIPAs96NQ+M7aUEUSg/Ywfk5rU8jxVGr1ZTLnV4dce/ePRUKhXDqNYbw6OhI1WpV9Xo9rGm9XtfKyoouXLigUqmkVqsVjB5RG5S015qwXozLnfWk5t/3+eN91IFwnQSpG3ZcVSqVRJRKXz0o8LQgaeparaZqtRqYHN995YDf14FnO/MyqXn6ge8Q/TKf1FoA+iqVim7cuKG5uTnt7u7q8PBQ29vb6na72tjY0PLysi5evJg41XhqairsAPJ6K5qzC85C+TgfNgUkKTg63/pOlO/O2cG/NNz4AUPodSvScNu4M0aAg3hDBOltD6Q8RRLviOUZaWUUsH3x4sXERpwYcDooJuCFFSX49Noo0u/ValX7+/taWlpSJpPRiy++qE996lPK5XLa3d0N/sJ9AjUz+CdkMgbCadZyVBaAABzdIaDCscOwNhoNvfLKK+p0OlpaWgo1psViUVeuXNHMzIwODg5Cyp36sH6/H05p5w+1SgApTpx3G+EbULLZrGq12sTx4UPj9XaZYtySQuqdetsLFy4E4uDWrVvB7szPz4cM1L1797Szs6Nu9/Q4EoDzxYsXQ40s+u4pYPd3cfYiDVlyJoj60Ic+dOaXzgJRf/RHf6Tf/u3ffqhiOqew3YjH1DSOigieqAgQJinsoCCX3ev1tLW1pbt37waa79KlS+H8j1qtpv39/cB4cVN1Pp8P0QzC5jnUNGk8H5/XfIyKsnEcni/m8mOiXY6WIEo6Pj4Od/t4FFEqlRKGmuaI2w0ZzdmZh4n03eD6NlOcgwMajCvO35nHxcXFEOHzjJhR8qJLUg/Ij4NDDE481/TFWb80DaVDTjxiBAj6GhI9coHo1tZWGP/y8rL29vYCEGKnYrVaDbUKPJcajlwuF6hwZ908JcRa4LScHZzUvL6Ieh6MDLtZlpaWEkYLp+gMxMzMTDDEBDqkZlutlnZ2dkJUSz8zmeFOm9ioxWmuUc4oLRvlxdx+uKOzQW5bMpmMVlZWwgnGvV4v1HVdvHhRa2triVQ28+81mj6vrnu+ZqNSl963NCCDAJJnsUb+fHcQyL47NZwxfYCdx/612+1w7ZY7N8YF6wrA9vG4E4bRZOt+2pRzp9MJG0+8Roc5djaK/qOrlAOgW54+JuVH/wk6P/7xj+vWrVshjeuHmDJ3ADXPEnhLy0JJCiAtrvfyuiPqXyWFdzabTW1vb6tarerq1ashzYUdxIYUi8WQ3eCA5MHgtA4T5srPXWJnHzqLDrq8Yvs563FSc4Dr2RfPiCBPmUwmbMKam5vT448/rlKppBdeeEG1Wk33799XtVoNO0EpCTk6OkrUvl26dElra2thJzPlPVKyTtc3QyFbsb88q50Jot7znvekmhhvV69eDRHdwzScIoNwVsYLGjEEzky5U+FsGq4SQKlnZ2cDDcg2SunUmJRKJV24cEEHBweSpIWFhcQ2S19YZ6cckY9rOBLqlfi+G1gvZvQIb2VlRZ1ORzs7OyHfnc1mtbq6qscffzzsvsDJu3Fjx407Jd7rNHPM2DwMCyUld97h5L22gJ8BBFhX2LJutxvqnrhElz7GqUZP2TH3bMfO5XLhnkEHGTGQQGEfBugzjlG7oEY5fT+bxGsdYCi2t7fVbDaDggIiL168mADROHG+Hzsk/xM77Pjf45qnlj09yvbl5eXlAKAcaGHgnOXESTrbyE4ZaogIdLivDTmCKfBdqA7s4/oXKf1uS6+Tc2froCbeLUsakm3iCwsLYXxe7wVoQIf5jDTclcTn/PmMB53x4MfXelJz++JslDPdfM7fgV5RIwKAbLfbyufzwRlj93wjDbvwYIbZtXrWerh9k05ljmekKSzvdrvhpPBKpTISnPi68k7OBSLtE2/QISV9eHioW7duKZfLqVwua3FxMaSJCGqwY6TvmFuXK/7vDEuadFcs6y7fnj5ELwjqSTuWSqVQbxvXVaGnbOpwOcRv8B5qhefm5nTx4kVls9nEUT7IpAelacZHf5BVHwvy7uyPEysA4UuXLml6elp3797V7u5u4uaSXq8X7ruDCCkWi+FEga2tLbVarVBz6XPufnBmZiYAZz+0eFw7EwU899xzD0R+DPTDH/7wyO/cv39fX/d1X6dr166F705K53n+EXrXBdyFN045YASIdjHOIOqpqdNbqnFeHJWAceAQT6J+bob2hfeiUzdqTnuPa16PAYhwA+COMAZuCOvi4qKeeuqpUIPDRZO+M8ydDAWU/j4XFDcyDgLilF8aA45C0F+En7Qc6yANFRB6H8Do23C9f3E04Ovvxbc4YHdi7nCdKo7rotK0TCaTMEjIalxTRmTFjkFqny5fvhzmlegXuUJeqTlAdiuVSjjMjzn1lHecUvax8O80UZQ3jBoAcGFh4YG6NDfqrDOpMgwadTM8k7RBbPT4PSk0B5z8Lgb5brwdPI5rLtuslcuMs2KuP4A5UiPlcjnh6FxvXBZi0OeGOta9mHkYpY+TGgCB9fP1Yfz+e3f4ftArwQtgyo9KYRMO8kef3SFKw0MxSSeiKwQgzk45izSpcWRNvV7X8vJymN+YlXWQihwji8gcffPPspV+cXFRV65c0ZUrV0LaCLaKPnu/Y7ad+fY1SHMUzv3798Np+C4Pvlb4ElhggNTs7KwuXrwYrivxAmkACmvpdom54LgH7AvrODMzo9XV1VDAzRryTFj4NDbGfY2XVviBnowbfQK04yNIyfL/ZrMZ/HmxWAyMGgQK9dbILudNcf5ezAqj8wSGvV4v3GAyrp0Jon7nd35n4sTQPvCBD+jbv/3bdfHixUQheZpcMEoYF+L5dv1RYIWFy2QyIUqCdvVDvHCy0jDaBa3zez/91CPHUSyDNAQ+aZgohB3wwG4BTynERtbTWDAg3C7OXKHczEEMIPj3KEqdsbmBj8eY1vnu7e0l6tJQMAcpvMfpb0mBOSOaZUcT0RHg2dlGqGiAMFE/yuVUto/Jxz+Keh/XSFdJw3ONkFXfHSgNd6FhHHDIpHKXlpa0trYWwIQ7Vd+hAkh02WcdYxYG8Oa/HxWpn9V8S/vc3JyKxaIWFxdDfQ/A0wEca4JBhp1ytgInAyPMuVocAcH6YRQdbPt4Y5bGI+k0zdfHv0PETZqWjQ38H0fB97AXyKIzBg6ssC3+cw9g/Bn8jL/d3nigOK6trq6G+8BIk7hNjQMJ13kpeZ8ocsj3/RgPanD8yg8H8p7i5XBZf06/3w8BJXo9jr3yRt3SwcGBNjY2gl7E6W0PwNjYwNx6kEpgQh9Yf653KZfLunjxorrdrvb394N9Yr78ahCvS3S/Azi7f//+xPF97nOf05vf/OaEHLH23kdn7nK5XCjyBxiQ6fD+uH/wdBXr7nYHP+W3NFAnTD9IJWJj0wB9D1CwJzT+78cPZbPZkHHys71IV87Pz4f0s9+3F99ni+6xw5AjWBy48z7kBaDZ6XTCdTPj2kQU8Df/5t98AAzF50Wx4+xrvuZrJj3ugQbb5BSbO303DDHY8EXs9XoBVWPccWDuzDAq1AWA0jOZTMib4uR5pkdwPvlpQJQzYCcnJyHN5gYUxskjmBiEOPDzMzZosXGPjaUbYzfObkzjyCqNAd/d3dXKykpYr9g4xQYW58clkX7AmgNLL6T0ok5OykUmoFuRD3cYcVQfg5a0LZfLhfc7QHdmy9eB9zuQQlYZi98D5YybP8up87imjjE4gGJ+HUylBRoYYtICFKjGbGBco+bF2uhknC5wUI/s4oSQOYyWM2/uIOmDp8XTson0wfWXdxB9optE2jgjv6MLJ4ZjcpvkzKCDXAdINL7PZ/jb5zc+pmNcq1QqieMiHJzgIB3sxGA7ZquZL3eupO6kIVPgxx8A+pElPs+cMy8xE5aWLSWt9Morr+jChQth45CzQzFTyVqR/s/lcmH3lTd0NJMZbtxhsw5jhamKyzG46JdgImb9qtWqbt++rbW1tbHju3PnTqj7cZ1x0IG8soasL/NYr9eDXDsD6H7Pn+1zj3wgewS8kAxkbJy8QD7SpPNim8y8ukyQpgQP0B/OcQMw5XK5sFOYchA2haC/yDqAnbPtKPnxuwHpn9dXs6uf3dLj2kQUQG3UYDDQ888/r0996lMPfAbw9Jf/8l+eOJlxw5D6wVtO1bojiVkhnKg7bzeACA8K5IvjW60BS74NlugC1B/vhnJDOK7xfBTcHYAbUndI7ug9WqSfnkLiOT53fNf7eJYBdUDwhUT5Ozs7KpfLD0SDTtF6ipCC0mazqTt37oTdlNlsNpwhBMBl3mBHYEVwFhgQBzdxKiVu7tTSFpbDUCJbREWjnAPvx4Egn14PRoTqxh2DEa8DnwE8xKyhGwIfo+vOpMblm8vLy+EIg1F1ga4X0jDNiUF0Z0atCREez/L0OHPFMQHOPLqzYCy+QYO5SMO48R4H0qOAL+vLOmK4Aa/9fj+w1lLyJHbGFtsiXxNneWIGOP57FMt5VsNJ+FZ7twceXElJVjYOTP2ZROV8hvpDnxN0lYAAZxYHmMjNqPqwNE4Ythp9Rw/pq88zOoTtIWiLr6PBlsKWEqzs7OyE2pr19XVls1ltb28HJpwSE8bogNcdeLvd1ssvv6x79+5NBFEURnOgKAyR23rmwQONwWAQ0lrILjoYs32ZzGmNGAXb7I71E7vZqNTv9xMnuLMZy9fQ7e+kRn+RFWy+A9+Tk5NwwwM1spQxICsE1WygillAZNpJCtZ9dnY2gCgyFnGgwjOwX34C/1ltIojiAE1JevTRR/XBD35w4oQ9TCP6xMCw+JISjsAjDJwkRg/nzOBxcgiZo0w/dZc7hRBKImTQNZMtDc9z4ucY8UnNoxNJgR5kl4BHSwiY05goAhRmnF7w5zujFBeX0s4CR6OAVBrj1mg0AvXrTpv1dGFmLZrNpm7duqUXXnghbOvPZrOJaMId0tzcnFZWVvToo4/qkUceUblcDhGopKCQNI+6vAbN5yitA2YsyBYAyZ37YDCk+jlNHSX1c2ikoTPAaNF/r52jfxzK6Xe28T43jh75OhBPC/TZrk/tE4AdJ+5Uv6dCXU+kYS0Iuw0PDw+VyWRCPRFGmPv15ufntba2FjYUOHPpoB99I80Aa/Uwzdk8v4yYCB8K/+DgIFyuuru7m0jFLiwshGMqcArUVbJTLwYFzsg6mHOD7+DJI3bqUtK0+fn5IC9nybb/DN1kLePaFk/74JgB/M5KMrc8P5sdHh/gNgonGbPcpAgntStXrmhxcVHr6+vBKWIDHBg5o+vBabfbDWyK2zp0xAOZg4ODsOOZYmYO0G02m0EfM5lMYGnimwuOj4919+5dfeYzn0m1e21ubk47Ozu6cuXKyLvoXC8AzX4uFwXwnM7uxy6gy86+5nK5cM6epER6kgM52fjhaTgYRp5FcDepIUNkevD7LnNkGrhv1Ovy5ufnw+aWUqmkjY2N0Md40xZrjrzH8sC7Hdi7LMHCMYdeJz2qnQmiOO2ba1skhVNMv5gNMHJycpKIWHGAfq6SR9+jIm0+z2TwOSl5jpQXwELVstXcAYTTn54qcTpyUvOIq9/vq9VqqVarBYGQhjvyiCr29vbC6d0YJHZXzM/PJyhXnIAzdUQURDQxKxNHvK5scTp1Uuv1eiFiwSA5aKE5Y3J8fHoLeD6f19raWtg1CZ3ukSNgZH9/P4zvxo0boZbKx+NMCD+Pxxr/P00rFouq1+shOvNnwEqgjBgiB7g4aSJjWA6UE2aFc5f4HGnguMDXGTBpCPI8ZYoMp0mVrKyshOsdmDciUE8PAGgY/9HRkWq1WjBY6JYzor3e6QWiyDP0PHT50dFRYhciIJNxScOrQwBQpHPTNnckGE4KZXu94Q5gzqEhQgcQoEfcalAqlYLs4ZRKpZJWV1fD9RLOSHjq3W2By6P/Yd5hBNI035XHc5zti9OHzIs0lF3/nAc9gE6eT7E2m3mQXZiGbDabOFHaU8y+Hsh4mrW8efNmmI9qtarBYBA2DcXpSuYZZ0hNS7lcTpzr5X2TFEAIR9/cv39fq6urGgwG+tSnPqVXXnklBHtTU6dngq2srGhjYyMAa97bbDb1/PPPa3NzM1Ug88gjj4S6r0KhEGyv1z+5PlLqwPrU6/WQcrx165aOjo4CY0PwDYAELHI+GMzx3t5eYLW4WJp0Nv7Y+5LJZALYmdTYdcu72u12CAbd1vT7/XBTgKeQYT0Jzi9fvqy1tbWwGx2bSokIQRL1lw7iCGA9gIkZRCcHvmAm6h3veId+/dd/Xc8//3ygIufm5vTP/tk/mzhhD9M8OkFgWOzYkXtExITH9B01AaRgMJyHh4chQmZ7OfRmt3u6/ZrIQlLItbpyutHr9XqpokT6RR8pVut0OgFEeeoAwZ2ZmVG9XtetW7cStTAYJhyk7+zCGUBFl8vlBPXrxiyeV9C7n05MmmVcg4UBBLuxRFnpNyCJ+hu2jA8GA124cCFs0QWgYpQPDg4CgCfCy2QyunjxYnjnKGYO5+BONAZSaRrnGvEdQCMREkaF6MULp9k5guF1R8K8c/kpTBfpEvrbarVCZIwRIRoHYLisA6LSAmGMLMbCdcojfhqywYnIHCyKTgCIHSjQT3fMGP1GoxEAiDPSvm44au7n83Wc1BgLRpWaCI9OCVgWFxc1MzMTGDLOhuIoBoAzdVTNZlO1Wk17e3th3f3wUWyZMzCeRogZKW/IVJrG+zwI9HRX7MgBEi4rnkbiDzYllzvdLcUl0wAg7jXL5/Pa2NgIhc4epKCLHoQCZtMCfdae51WrVW1sbGh1dTXooAOiXm949xmpRp4DsPJ6VbeB0qlO7Ozs6Pbt2+r3++E2C4JrxlkqlcItCsx7u93W7du39eKLLwbwMKldunRJjUZjZIDu/tFrBflcPp8PJ+Xn83ktLCxoe3tbh4eHYccvqVgnBWB6pFNZe/TRR/XUU08FMILv8yOGnHxwdnFSI9j2HYWAJPfFCwsLoTyE+zk5UoQgj4OmWRtsPLq6uLgYADa2hwC03W4rmz3dPRzrHutHLRQZhUkg+EwQNTU1pb/6V/+qbt26pUcffTT8/MMf/vDEYwsepqHA0lDZvRYAY0xDiPidO0dSLvwOI+eT4hdNYjyJcFks6ExASFxfgLNKA6I8EqTfHNWP88Kgsrj0o9vtJmja3d3dcAyDAw3QvRsk5o86BdgNDLhT8cwdztgdc5rxMbe+Sw5nCKiBbeOwxRs3biTy+7zfDTl1GVC5HAjILpq5uTmtra0l1sZBrhtVb64wadrGxoZefPHFAGaRO0A2efpc7vSsqp2dHW1tbanT6ahUKgVgjsJnMpnAZhwfHweD7rUGHqVls9lwHYMbUp6HU/CaKRifRqORaowecblTYR3jGheMN/eKMR/FYvEBMI3c+/9hgHd3d0N6DyPplzP7Ll22GxMhponwpSFzze5YTtfm/7AoAF7fxeuHuwIoCFhIiRGgccXI3t6e5ubmEil7Z4odUDD3/O2/RycmNepa9vf3H0i1+Bywti4/8U47AKakwL46Q+3sNjdAnJychFPcK5VKmCtnLz0974dTYk8nNd/h5mUWAAO3xQ7U0J35+fnE9VHT09PhgFJPfyHDa2tr4RT3RqMRbBEF/D4u3gkoq9VqeuGFF3T//v3EZplxDQCBTfF6SbdhcVoYHYXBJeX8yCOPhMyKH4vgDDXBycWLF8PBzay3pLAJijlnrTyIS1u398ILL4QT/2/evBk23XABOYw7BABySHH70tKSSqWSKpWKHnvsMe3t7YUz55wkaTQa2t3dVbfbDeBROj27D72tVCphzUYBfYIhfNWkdiaI+pVf+RVtbW3px3/8x/VP/+k/nfigL7ShQF5g5oPDmGHkndaUThXfIw4HSnGhNlQsFDCCzwRms8MTwr043c/uwGimpdljEDU9PZ2gbb0wEyNFZOWXNPZ6PV26dCkxP8yF0/EAFyhMjOYoQ834JCVYDa8jmNRwNO12O5Gi8n7RN6+poU8cxjgYDALzxfoyF6Q2Dg8PA9Pm4CHe4QYA9KJBZwK89ixNW19f1+LiojY3N4MBhS0CPPpOFcZRKpW0vLwciukdsHoqAwbUHS3yEis3Z0f5mvmpyQ70YXrSyKjLitftICP83ovqObogn88HJ+S72TBirquAf+RheXlZBwcHwXB7cOIpOJgImAPve5rx8X4cHU6Y6JQ6EeQD4Mh6kRLC6FOTAvjiQEcCMt4Xvz9O50nJwn13emnrLvf399Vut8MFrR6EOPOJbHhqHTYJwMT6ccE0YKvX64UDR5vNpur1uu7evaujo6NwGGk+nw8BG3aBoAw7D9OMbjr7M65xejrzODs7q1qtFmStXC4/kHYBvNIvbL7PKf9Hxt1HsIkA9pyA13dbo6sEQc1mU6+88oo++9nPBsCVRkb7/X7IKFCTx3hif+cBCvJEisqDZ1LkrKkz3NIpmFxYWAjnS7HzmbFik7vdboL9xffgsyaluyTpf//v/61WqxUCSNKf6COHdFOm4ceuwHSzphT8r66uBjsHgCLQ5kwoGPODgwNdvHhR165dC6wda4aNwdY6Q8nPxrUzQVQud3rnzC//8i9PnKD/m+ZIF2XzIkdfJCIoIgyclt9957UK7ox4hudfMc6zs7NaW1sLyBfamLQDqQeiWS45TJsOwngRMcAwcdUJC8n4fJulsxPUJniRHw7TDxKl39DYjNWjSndmsZNintIARcBLu90OOypoOEHfjk7foMibzWaoVfAIn2iH+eJUZU+9wCTwPdgXZ+XilAljj880GtcWFxd17dq1cC8Tz/F3sR6FQkHXr18P/af405lD5sYZSGQEYIXyklJBH7wGi4DB74XDSSHnaYCis8EAfjeMHnF6XQa6iWyzzn50Af33uj1PO05PT2t5eTnQ/DRPv7GNvFarBWDhzO6k5il5ZN2ZNeSMmhsHOET4gEruEkOuSdMSVftzPJCIwYNH/Kyng3vmKI2DIkiRhvV1jA/Zxy7E9sMBba1WU6/XC4C+UqmE3x0eHgYGmCDV00d++K8zvYzFmVWvR+p0OoEZmDRG+swYKNimuD9OIxIAx1vmkUOvYXTb6M4dBopgF9uFbhIIU0u1u7ur559/Xnfu3Amyn7a21PUJoM+88XN/t/sVfIvPF2QAaXZuH0A3kS1q/Th3CUDKXLNObo/Y6ORBw7hGRmUwGGhnZ0cXLlxQPp9P1Dlik7E1vV5PxWJRJycn2tzcDLXExWIxMPn4Hy95gU3k+dji9fV1Xbx4UaVSKUEWELRgu6j186zTuDb5oKM/4XaWgXGA4tSwlARCGFXywqQCcELU+PB5DIekADz4OSACReFCX4rqjo6OtLe3p+3t7RCJp230HeNGNEfKkHnw9KXPgUc+zsbF0RyRMeDMaV8HFw5OASkIMPOaBkTB0mF0YJWcGXIhBEiQCuGSS4wdET4pTYBtrVZTp3N6qjTrzDvYouvskKdEmEtPHzhYntTm5+f1yCOP6JVXXtHt27fDOlAgSb+npqbC3XGAV6fPnXmIgYr30R0b6WUMGbLY7XZDWtjZGa8R2NjYeCANN6ohWwC9OGJHfhwIAfaRL8AaQIhgiAJXZ0b8wEYiaC+Kdn2jyJPidNeTtM1ZGGTdmSh3BF63g/Px9DD26eTkJBzsBxuCTXBnzvw4q4YcujyMYhVhXCY15nB2djbBtNFXTztj6+grrC71e6TwYR5YF6/hwpGif9StMKeABg9k4rpB7JGU3AE+aZwEWL1eL9jrhYWFUMPGnAMyHMDT3B7SF19bjmAhcGXMU1On14RNT08H8MdZRbVaTZubm3r55Zf16U9/Ws1mU6VSKXWwzbojU8gp6+a+BoJAGqZnqTFiTaThDk8ClHq9HjZvoYuNRiMwmTCqyAlXoMDYeAZjZmZGFy5cULfbDVemTVo77Aq+D+ANQM9kMiFYhgQg6IYxbTQaYV1iX4JtgEX0MbDxgzpcdBgbjr4xTzByviZntf8nQBSIG+PvghcXR2KMEJ5+vx8Kd6kxcireHaorGPVHPMeVCOBEREbdCjdF7+7uJgzOpOZKxHjYltpsNoMwYNhwJMwDRtydrxsFPudpT59fP6vImROMPcabyJj3j9pqGzcHYqNSgF44yFhYg3K5nCguBvA6EITJGQwGYXsrtK9H9KyFG2mn0v1zHKqa5joG6VT2VldX9cgjj2h/fz9x1hd9HQwGAfzFOyKRV+bHU3TuYPi5sz3UWknDs8K8PghgwbzikLPZrC5duqQnnnhi4vjoC39ip8PcuSEEAGG0HMS222212+2QfkUfHXDB7Po9lp6yQCYBZYBzrx1z+UvTmBuciqfSPY3oRdXMvQcCzJEzScyXp1Vi8ORpA3TA+wQgdlCTBkThRObm5sIWd9JY3mfmC0ALm4D8UCcG8OJzDkQ8OOC96CNz5UCTtXK75+zP4uKibty4MXGM9NcBtjtebGdcI+S7Cgk+nI2PU8M4WEAkhdmeNqxUKjo5OdHa2poqlUpI4b3wwgt66aWXtLW1FeY2ZhzPauiMX5fE5hT66bWJBFnuE6hJRZYJvmq1mmq1WoKVRz4JZqamprS4uBiYH1g3r71kLVn7lZUVtVotvfjiixPH5+UJ1JmhD2zOYNNVt9sNKVgCLOwGbJn7OmQVVtTvYaX/ZKlgzEn1kQ1BHvALyEWv15son686iCKN5bUcKKE0rNfw2gpJofAMMORbXd1Ikdv1+hyaR4w4HsAKRh+FrVarun//vu7fvx+uh0iTDkJopWGKDPTNVlo/xZnvOKhzcMPY6H8ckY/6LkYDx4TBRaDi+iHpdEcaJ9GPa850AFDYFcH6errB02rZbFYLCwvKZrMBUBJ90SfSI8ViMdQM+DUscbqFMbLOzurAOJA/T0OzS8O07rVr13T37t1w2jjP9EJ6r4HzYACnggPhDwbNZRtngVF0gMM7m81mqAFw4OMs48LCgl7zmtdMHJ8/3wG/AwOarx+GPZfLJXbCMM+AVE89u9H3k8CdKSQiBBDPzMyEonqeS8Sahi31tAeghvOinBUicgU4+Plcnk5xRiSeH/7v8k4K0QNEAAdzhlF3RpmDD9OMD+DA5gbW0cEeTC6gCAfEXWEw0NLwbDJPq3uDmZQUivFj+XAwyLOdaZudndWNGzdSBWs4YWQDW8EmIAqjq9VqIohmDPgAz3R4NsHl04Gt+xDqcUiJkYZ88cUX9elPf1q3bt3S7u5uSPN62npSY058Wz26jsxiC+OzAllTfCDgCxBHXRC1VqwxwJTnApp83vgb9o8/U1NT4aT8NGw378PHcySD+1d2X/sGL5hg1oRdsdhCScFfszPPj7Hwi8AJ6vC99Xo9nEmFnrJBBx80MzOjy5cvjx3Xqw6i3OhT7xSDKBTA01g4YRbaHannxN05YWxwgEycNLzPq9VqBRqbhWg2m9rd3dX9+/fDuTj0Ic34pOQ9YPTFi0ERYqf4vc9xfQ/g0sfngNGdg1OXROCeCvNdGDynUqno2rVrE8fnqRJqTbwOC2flaSJJIfrxHV0LCwthbbxeCBDl9+yhSB49OkXvaVrmhEjHGcA0jTleXFxMsFEYST97xIsikWOvefIUsxtYZyMxCsgMz/IUF2nQ+PnIzMzM6YWd6+vrE8fHOI6PjxPFqcyfgzxPF8RGLJ/Pa3FxUblcLhwl4jUxgAdP2Xoqn/4jp+yshQ1gyzMOjuc+bGMu3bm5zcCpeH2l67E0vLjVa498HeJghj9eVuByiUzwPgqD0+wA5n2sQavVUqPRCGDPa/Fw1F5TxvekYVDCdzxlwns8xUka0RnpOGjk516/l8vltLGxoZs3b6parU4cI/MMA4XNyufzunz5sq5fvx6cIAyErwn66Uw3tgtwFttMZ+NmZ2e1tLSky5cv6/LlyxoMBqrX6/rMZz6jj3/843rppZdC3Y+XmnipxaQ1RBbQXUkBWAMuSPG7rvM3rA1rg8/kLkN0jDWBLSsWi6F0BSYdO4a+eypfUrivDkA5qTlhAbBzEIUdI0PBIabMA+9Dfp3Vd33haAMP3P0dvJsaMOYX+QSAkqK9fv26rl69Ol42J47+T7ixMJ4CwcD5wZmgYaeivbDMDSpgiu9Jw4gQNsDPQ+r1eolt5ryDtMLBwYG2tra0t7eX2Eae1oA7G0HERy1GvV7X/v5+QN6ejkPJHSh42sY/48bC++bOm/H5cfoU9aEcRMDr6+t67LHHJo4NJoZUC8cUkJMGEOGc3agDnL3wn4aji8cnJU9XZpwYIGe+YiXCuRB5oKCTmlPCly9f1r1798J1NQBRSQEIu2PBWaLorvwewWGk+MN4AYpnjcHTsjgtr3eZn5+fWPgJaKHWg/cja/zxIIax0GJanXuqnHmQFObGa2pcXokA2+22dnd3Va1WlcvlAvitVCrBuFKfkqYhC+ius7NxATQ1F+iJlxmgJ6xtDDYcRLEmo1K3niZx9gk9oUg9DdB3p1goFHR8fBxS5K43ME5sG4fpRC99Uwhj88CHn3vqDhvsNjfWU/SE2pNs9nTL+pNPPqlLly7ps5/9bKo1hLFD9jni5MqVK7pw4UJgXPb29hIAKh4TaR3WAXAVB+/MycLCgtbX13X58mVduXJFlUpFd+7c0fPPP68/+IM/0EsvvRQOqfS0lW+qmdToZ6/XCweVcnyEn/INMHJgHIN03zyQyZxe0M7ZZfgA5BwQRS0UYIRiemfVGQ8XlHPESZqNAU4ESA9eg8Qh3sViMfweG+bHPkBE+NEc6CLj4QDOqampIHOAL4AtTCayCYPOesHWPfHEE1pZWRm7hq86iMLReh2CNIxoGJTvdEARAFkeDcaKAOCCgQKcIZQsLE4ZBM7n6/W6dnZ2tLu7G5T3YZoboLh/ksL5LkTmbjwRXo8Cva8OpJyVi9MJRO6dTieAJCKl+DgIdkvdvHkzVT0NV7bEfeQUX0+henrAwZP3nXVzR+Tpr1GpFwByTDcDKGE1uLaBNKE7jUnNZYlU7snJSaKQ2AvN/ef0wyNixuIpNP6OHRW6wPZdLjt12Xf2ESe8uLgYzsMZ1zCODoi9+JR14t8OGKSh8+doDklBx1zGkGWXTS9adXDDuWj1ej0UeDYaDS0sLISCXox92sbcMF8wp9Qeed0h8oHDZW7jNHH8R1ICOHlay+0YTC3P8/OXkG1n/cY1f/fMzIwqlYp6vV4oyGdcnvKNGSqcraelHYQ4YKev2AsCMtYY4On1bzixXO70gMrHHntMzzzzTGAEJjVP8RIALS0t6bHHHtPly5fDbq21tbWQrmc83vAvvpYOaj0rMjMzE85dunjxotbW1lQqlbS1taXf+73f03/9r/9Vd+7cSQQTMUMEUJ/UHNByiLDrB0AK3fY6Nd7hwSV2FlALk+tMoafyyAZg47z+zNlSSQFUzszMaHFxUTdv3pw4vph4ACAVCoXgnwgUG42GKpVKYLVZC8aG/HqQjV/z09WZP2TPy1n4P32Ls1MnJydaXV3V6173uol6+KqDKByKFz56dI1hRbEZMAYJpXbFjhkPnIBvN0e4+DzRCH8w/gAoaOJYKdM0FhlH5OCt3++H9BBULeDAD69EyeMUAXPkzIWDGVeAwWAQtmT7Vk5o9lwupwsXLuiZZ57RW97yFl2/fl1bW1tjx0YRqzt8Uq0YBT+O3w2xGw5PvXq0Lw2F3IESxg7wwthhE/guAIqaAGhx6OK0jQLNz3zmM/qDP/gDfe5zn9Py8rKKxeIDjJezUe4ce71eMAYuh57iRXbdEHiK02XfU71xGsJrN9KMjTl04M5aAeg8zYd+OXNGbVQmM7wJgPSlpy6doQFM4GgZb61WS5xbQ/RJLRipPU4Sn9RiNkVSAJdTU1OhoBZnBKPqOwcBCIyVcccBjrNQjBn5JkhjLQHDMSh18Dap0T9sml/nwXzRL06TB8zxfkkJ2XM7zBjjoDQGH84ywG76hhWc9cbGhp555hmtrKzo4x//eCq2zXdRAZaeeOIJve51r9OFCxeCH0G/uIwZRjwu9YhrZB00Mva5ublwr+Ty8rLm5ua0vb2tj3zkI/rt3/5t3bp164HAQEperYMDn9TwTdPT07p48aIKhUK4goh++8GS9NXrxOL6TO4KjMkCB1r4FlJhgEv8L36C1HylUtHly5e1vr4e7NtTTz018To4JzaYM4rAT05OwnEJ9Xpd1Wo1BEukIZ1dkxRYMw88/VxFX2tsTLvdTmSYvG/uVyEbnnzySV28eDFxZteo9qqDKLYvsniuvC6Moxw1hX++E8MLIkeliTBQcR2VR4bk1rlZ++DgIICQOE02qTmgw8HAJGCYTk5OQqHzpUuXEmkKL+z0/sZGy6N4j3zdmElD0Apw8uhuY2NDzz77rN72trfpxo0bmpqamgiiaJ52a7fb2traSkTH0MMov/8bUOWgyZ/n/faxoeSuBNLwkD3q2QBQ1IMVCoUQBaVpR0dH2tra0kc/+lF9+MMf1v/4H/9D+XxeTz75pK5du6ZqtRrOMCKid4CPPNPcmBFNudxLwwiWcRKJOuDyZ/l8FQoFXbt2LTWIims2HEQRmCB7owqvfd5hxmCtPP3n8kowEa8j57Dt7++H+hKe59Ek4GBhYWHi+GKd9T9EvhSzOmB0ltCLyGMQ5SAiZk49SPNAz8+miUEUzilNzSV98zFlMplwflGhUAgMbKfTCWc6ARIkJXYhSsOCZUCj66YDRwdgLoPYF5w+tq9UKmlpaUk3btzQo48+qt3dXe3s7KRKySL//X5f5XJZN2/e1LPPPqunn35aS0tL6na72tvb0+3bt7Wzs6N6vR7ORiqXy4kCYnwHgavrn4Modmk7k/GRj3xEH/rQh7S5uRmcO/MiJXeLYn/T7nKmHgqAQh2oM/kEJH78AXpYr9cDUEZPZ2ZmQq2vM1buXzkaw4NP6t46nU74fiaT0fLysq5du6ZSqRTma319XS+99NLE8Ul6QEbZZY2vxu/Ozc2F8ha/IsbLQhzsO2uXy+USm4hYOw5mJtjg3fh8dDaTyWhlZUVvfOMblc/ntb29Pbb041UHUcViMdD1Hq16VExzg03ECsviW8s9neLf9ZOQ+b4XIrPAgBqOlueAPQdRaQCUNIxyQfwosDS8DgMEzN1dMEVuoFhcTylhyDDUzpTBirCb6fDwMLFFHmfE+SCPPvqovvZrv1Zf/dVfrWvXroV06aRGZOvGlTHu7u4mjBKG22lofu6gMI7wY3aSsfr6+8Gk0rB+AkaD6MJP6E0DMCTp05/+tD7ykY/oP/2n/6TPf/7zarfbeuaZZ/SmN71Jr3nNa/SZz3xGH/vYx0Kq0Ov3nIlird0hee0CfzAE1DCwtReg7TS2z5l0GpRcvnxZTz/9tEqlUiomw400fcRxkrpkgwBGm5SXR/CjAgsf16hxSkOmkS3H+/v7Iar25mDZ5TtN87nCiCJjnEXlKSne5ek1xocDYjyM2Q0y6wZAxamhfwBET8uwhgQAvV5PKysrqcbG+vl6UxxPAFatVhMBCLv/6D+2xUsGeL7rHqDXDz5128g6djqdYP84x+/SpUvhfraXX345Ubc6rhFATE9P69KlS3r66af15JNP6sKFC8pkMrp3754+9alP6cUXX9TW1lao8Xv88ccDo3737t0Q7JBiJoBEXx08IuMcJHz//n196EMf0ksvvfRAYORyLQ13Xc7OzurChQsTxwcAWFxc1MrKSmAUCVbiWrper5c4UylO50unvsdtJEAqBuezs7OBSXKZoV8cvVGpVHTx4kVtbGwEFojU6qTmQZ+/d2FhIfgifHej0QjgutlshvET+AIO/fwsfCis4PHxsWq1mg4ODsLxEV4CATkRl+j0+6dHHD399NN65JFHEszdWe1VB1Fc+5DL5cL2QunB7fs4TQcWOHmKXH03TZzKw1jh4CmgRXHcsYOGuQ6BCMgNRdpGvQXRGcaTxfbUwaVLl/T444+H+9ek4WGkGCQieoydO1UWHCNOHRBnCXHK98nJSWBPCoWCXvva1+ptb3ubnn322XAXnTM745ofcMd60cfDw0Ntb28n6g/iqyFwbl4MHtPjzthIesCQcyaRbxGnno2ttBjz1dVVlUqlwAamab/8y7+s3//939fOzk5QROoCHnvsMc3OzmpnZ0fPP/98qLMhP+/G35kJT48wbgwBKUlnXer1eqJ+SBoybrSZmRmtrq7qDW94gx5//PEE+zOpIWcYaEAnfYQ58V1rBC6DwXDHFlv53Vl7LQRjx7jzLhghbpKXhkc9eOpaGtazOPAe1/x7Pu+kTKnTWVpaCgEUIAhG0QMKB8eMyaPhZrOZ2PXj4AidJ3XjwNUBWqfTUblcTlWXyLPpD2lRACC7NIvFYkjN8H6OjkCuY112MIk8uC1EnmGISTsdHR2FtDk6Twruxo0bunv3ru7evZuo/RvX6EO5XNbVq1d19erVcKXSwcGBXnjhBX3+858P96kRHHKjgV+ZtbW1lWDo49paQPbh4aH29vYCiIDl4vfIkesJz6Fe8uLFi6kOE0XmNzY2VC6XE/c58lyYMQfi6BBrTl9Ig+N32DgVp65gY1l3v7AYea7VapKk1dXVkCnxWrq0wSifd3u/uroqSbp161YANNRxbm5uhvIIQCV1l1w35cGNs/Ew2lz/gu3ywMHPLGMOs9msNjY29OY3v1kLCwva29ubKJ+vOoh68skn9b/+1/9KRNReK+B0PnQnhptolHvVEDqcI8/01BGK7zsn4vMquEiUCNwd38M2DArCTvSJ0UX4y+WynnzyST322GPa2trS9va26vV66DuoG+PthdOADN+FwC6uVqulXC6nSqWibDarRqMRnr2+vq6v/uqv1tve9jY99dRTqlQqwaDyzEktZvuYI8aLw9nb25OksGMMI9/tDncL0nBsUvJiSGc7WD+uW2AnGH0mguIohUKhEC6xhBZP2/7jf/yPgc7GWBJd5/N5Xbt2Tc8884x2d3dDFNxoNAKI8ajVQY9T0lLyVHrSV41GI8ikO+VYprPZrBYXF/XMM8/o2WefDQWb/r6z2iiGFyNLn5lvL9709DlGiDXz73tj7ZAvjp2oVquqVqva398PQMzZonjuHjaocYbA0+LS8Ey01dVV3b17V3t7e0GWSCUQeTP3oxgkanFgDD2Vx/w4CHFQRVDHn0qloqeeekpPPvmkdnd3x46N93hQ6EFHLpfT0tKSVldX1Ww2df/+/bCDz4vnY3lx+wszio2dnZ0NQa9nEahrmZo6PUeIGkwKkJ966inNzMzozp07qtfrIaCa1GDONjY2dOnSpbDbrN1u6/bt2+HCX1hn7CFrWSgUdPXq1bAp4e7du9rf3w8gAiAhDQ8E7fV6YTu8O3jfHIOsO5CAjV5cXNT169e1vLw8cXzNZjMwPdQB0Ty1Lg3PVpyeng5BmqfjmCtSkdhIr82KdYp6MnwsdwaS8rxw4YKeeOIJXb9+PZxHFT9r0vq5zKMDxWIx7Mj73Oc+l7Ah+DH6ia0AWPpxMtgKD7wAv9Tl+TmM+HsYcJiq1dVVvfnNb9aTTz4ZPlcsFscG3K86iHrrW9+qZrOpT3/60wHV+1ZDN3pMPobbmSPpweJRIjunQ91BQUeT9uFPoVDQzMzM2PNL0oIq30aJQXUWCsO6srKiRx99VCsrK8rn8zo4ONCnP/3pUAwHtYsz9ggFZA8zA4Dg/CJAys7Oju7du6ejoyNdu3ZNX/d1X6e3ve1teuyxxxLRhYO9SQ1GzOeFcefzeb3mNa/RxsaG/uiP/ki7u7sh102+u98/vTYi3lLrQMEdqhcY7+7uant7O9SsueFB6DlzBeNJlHh4eBiioEnNr4dx1oFxLyws6Omnn9bOzk7oG9H+8fFx+DzOmOf4AbKxM2632wEckhqJN184qKtUKnrd616nr/iKr9Dq6uqZIGZU42BAGE5anOL2Oh+MOEbXU/ExQ0ZDj/3oEtJ31K15Str/Zg4dSDs7Nal5SorvOnOQz+eDMcdpAuZIZUpDMMHaeU2Us9wOMh3YOMvKz7y4WToNNB577DG94Q1v0OLi4kQQ5eNzHWCu/OgN0iA7Ozt6+eWXdXJykriglnmhfwQAcf0WtivegQl7V6lUAnOysLCgJ554Qs8884yWlpZ0584d3b59O8hY2vUrFou6cuWKrly5Eg7p3dra0ssvv6z79+8nGEDa1taWWq2WFhYWAhu9tLSk69eva39/X5ubm/rkJz+pT37yk9rf30+UejA+Anpst282kIb6SLBHkOUF6ZNau93Wo48+qsuXL2t+fj4ELF4KISkBeNFFZ7AJtjwd7xtUPJj34AkGFHvl9WErKyt65pln9PrXv14rKysPxTzReA+23JkfDshcWFjQJz7xiXCtGrqXyw0vOwbA+0Yz+h8HloybwBPCxNP1AKjj42MVCgU98cQTevbZZ8PBrZlMZqIOvuoganV1VV//9V+vbrerW7duBcQI8kRAPCJF0BFsTyP4pHqxY5weJK3V6/VCtM9Os5s3b2owGGhvb0/37t0LYCtuaYSJMWB8nUHC+ObzeV25ciUo0MLCgt74xjeq0+noj//4jxMHDnp9jTteQBRAyusuqtWq6vW67t+/r0wmo9e97nX6pm/6plD/RGSB8MVzNa7RF/7udruhEHF1dVWPPfaYlpeX9alPfSqct8XuGijjk5OTAKRQMPoRHxcA4D04ONC9e/fCzkZfH5wjDN7CwkK4b09SmJc0W3NpXmvQ7w8vT2ZnycbGhr78y79ctVpNzz//vI6Pj8OBmJ628XopIiOvcUJmeD5reVYRsiSVy2W95jWv0Zd/+ZeH03Xd2U1qr33ta/Xiiy8mwKIXDXtazosvAffx+sfsm38XEIy8kVY+ODgIkfJZYCDWt7PA2lntrM8iJ0Tg3W43XHjM/ZblcjkYb9916Y3/M3avsxnFnPH/bDYbGKH5+XldvXpVr3nNa8LZR5OalzgANHGKvosSOeN8JdKWROroms8TmzFi4OBlBF5zwrlKFLZXKhW95jWv0Wtf+9pw0fTm5mYo/Ha7Pq7NzMzoypUreuqpp3Tt2jWVy2X1+31tb29rc3NT+/v7oeaH3aa5XE5bW1uq1+u6cuVKcOScmyRJm5ubIbgkbRXbZ+bTgzzmmf4DKvv9fti4wjEFaev2rl69qrW1tbC79saNG7pz5462t7cTBdVcc+NBi6RgH/m91/84y4h+YntZezIQHqhvbGzo9a9/vd74xjdqfX39AflI2+LvwARh54vFoh555BENBgN97GMf0+7ubmIDGf9mvj0woc8OHD1dz7p7ylo6rbPjvKhcLqfHH39cX/u1X6vLly8H/8nREP9Pg6i9vT299rWvDYWdr7zySgBS5DZBoTjX2FjgYDlLBto1jsa9hgKBwdlxqN8TTzyhN73pTdrb29NHP/rRhIACMhy8TGpEpQABZ44QitXVVT399NNaW1sLuV/u62k0Gvr93/997e7uhoPHML5OyQI+mBsvuAZE5fN5fe3Xfq3+wl/4C3rLW96itbW1B2oSPEpO05w+ZUxQ6uVyWWtra1pcXNTa2pqq1aq63a52dnYCAxXPSfx+jBdzSd2M57vdaTvImJmZUalUCgBqamoqsJxXr17Vn/kzfybVGD2VyDw3Go1Qb0V9ydWrV/VVX/VVqlarYfsziupyQ2rWWQlneXznFuPu9XqBjfRgYm5uTo888oieffZZPfroowmDmVZG3/72t+u3fuu39MlPfjJxbxTv8VopZ5ykZM0M42A9PGDwNCVrNhgMAoDiElPWzgHTw8rkqBaDF9dr+srZNUSh1JNUq1XNz8+HozpgqpFNjrNgd5+nxpgP/u8An/97rcby8rIef/xxXb16NUTgk9pZKTwvSmatcDpzc3O6fv16+Pfm5mY4FRpHia2VhudY8Sze5UXB8dldc3Nzeuqpp/T6178+sL61Wk3b29sJpjkNG1UqlfTUU0/pda97XWB37t+/rzt37oSrVmA5naHhnD9/B/L4yiuv6KMf/ag++9nPql6vJ0pIPAAYpUfObLpO+JlL3W5X1WpV/X5/4vVL2WxW169fD4zZ9PS0Ll++rJWVlVAfC4j1tJsz9M68+HgZEzp3VgkGsokPWVpa0hvf+EZ9+Zd/ua5evZrwPa6TaWpLfQ6RVWfX8dnXrl0LFw3DfmP3+JzXdVHb6tkpD1hgRmNbe3Q0vNC42+3q8uXL+rIv+zI98cQTodxjMBiE3axjxzb4v7FM/5ftox/96Kv16i9qe/Ob3zzy5+fj+9JoZ41P+tM/xvPxfWm0P+3jk/70j/F8fF/a7azxvaog6rydt/N23s7beTtv5+1LtT18hdh5O2/n7bydt/N23s7beTsHUeftvJ2383beztt5O29fSDsHUeftvJ2383beztt5O29fQDsHUeftvJ2383beztt5O29fQHtVjzj40161fz6+L412vjvvS7+dj+9Lv/1pH+P5+L6021nje9XPidrd3Q3H0/uBgnNzcyoUCg+cyTLq3io/2djPUPLzJPxnfmszh2rxfs6v4PoGDuPi7iG/gmR2dlbf/d3fPXZ873rXu8LVB5y/wmWc+Xw+nNnhp9Iylrj/0oPXXfAdPyOJ81z4mZS8P8yfwTkfnIlTq9W0t7cXrmz5sR/7sbHj+4mf+Ilwpsfy8rLW19dVqVRUKpUS53twVpZfHMnBhXG/WU8/DZqx+x/OLWJNOJiNn/G96elp5fN5zc7OqtFo6Pnnn9fHP/5xbW1t6Vd+5Vcmiaj+v//v/1O5XA6nMPulwhxCyEGMnAfm5x3Fh0S6LMbr4vda+Z1O/m+/1sIv0JZODxLlzkTOYfnpn/7pseN75zvfmbjPjYMuXd849Z6D7TiHiPOR+OMXmLKefM7/+FUWnOHiBxf6qdHcWl+r1bS7u6uXXnpJn/zkJ8Phsf/+3//7seP7i3/xL+rGjRt6/PHHtb6+Hg4I5RC/6elplUolFQqFxBlJo+TS9eqsP/G5Vn62HWe5+ZluvMfvzeNU/f39ff35P//nx47vueee09LSUrjWyA8BjU+3Z76Zez/ryk989rO6YvsZn9XD+X3x+Pg/5/dVq1Xt7u7q4OBAJycnQafm5ub0r//1vx47xp/7uZ/T3NxcONma87j8j/fd14D++llFzAXyy/lWLs/IMn8zd6yVpKCP6ChXNbXbbc3MzKhSqahQKISzns5qP/mTPxku911eXlaxWAznQNF8rfzMQj+JP7Yn/l0/Q899ptsplxfGys0CW1tbeumll/TCCy/ozp07ajQa4aDM97znPWPH9w3f8A16wxveoOeee07PPvusVldXdXJyov39/XDQrusX/XXbga2NZdT1J77JAV3wA1E5k89Pp+f8QOaN/3Ou35UrV84c26sOojiYzQ9Ic2c76vI/hCV2uH4iK0YQRxwrkjtmPwjPT8pGcWKF9PdMaiijG+T4virvjxvouPk4aLEBGWXU/btnnWiBQiK47pjHNQBRLpcL10dwsCWCi3Ogv34KuQOOeG3OOsTNx4Cy+3f545eiAkqz2Ww4gJMTiic1rqnBeAFwGKP3i3H6CfCMIz5wjp/5M3zd/SDC2GjE605z2cVITGp+4jUHB7Jm8bUQNIy5Oxm/1zE2hm60XY45cNYdkx/c6oYP3cM2EHxNaoVCQYuLi+FwVw5I5LscMAioYl6Ry1hn4kDN18fl2E96jwMXBxw+J74mOPlJLZ/Pq1QqqVgsJk5Nj2XF++kA2e8hi4H/WYEpB1P6SdjonB9Ki+wQFHMlFYd0chhi2hYfUut266xDJOO1wdbHshuf2B6fMI9c8rtRss2J936HZ5pDb8vlcgDxDnRHfZeT6H19R9l1l7lRh+/GB2f695hDblYoFovhirX9/X3t7Ozo4OAg3KowqeXzea2vr2t9fV2FQiEclMnlwPF9t37oKWsZ+3CXTWx77ANjwgE7FuuEn3Du2OAsX+ztiwqifu/3fk//6l/9q8SN5+973/vGfmd+fj4c/+6nB/vdcNKDp0aPciI+iX5kP82FyQXPhcnBDk7Cr+3wZ6Ux4DEQ9JOcWbD4tO0YHMbRrV+e6oIQ98/nwA2gfyaOXvyqlTQn0frp4IVCIdzRhWPwaIl++hyPAnyjDIevD8+WlBhTDDJoOEgMP1fBjLsb0Zuf6u5AOjawOA434LHzHNdiQMbfbkBY+1hmHSxi+OKTi89qnJDutwNwJY8zoThc1tevWnB9jNmNmD1Ghn0tfZ4Ac/HPeQfRqaRU19oUi8XEtT/O3nH3Y79/em+Y30/pAZifyu7N9XSU08YQu/P1NYmZYQfeMXsybnxcs+IyMQpIOSPsazOKiRrlXAHYfrsA48B+xHLszCVBFpe8Hx4epgJR7hfwDe4c4wAsvkopdrDunGGwvc+SEtdPMW8eGPqc+ve4vgdWfJLeSwpMWAzMpNHBF3LlPxsFGmL7E9uVOIAbBZ7R8Xw+Hy6yvn//fjgp3i82PqsVi8XAOkqnOsj9lH6xOmON/W98q0Ys2z5vsTy4Xp7lS/2ZTsCkaV9UEPVTP/VTete73qWNjY3U38HxeMTrgEIaotN4ol1BY1DE3zFrEQOKUZE+z0QZEBQiJ0mpo/w4XQeAii+TdWFwoxKDRRY4BlHeRhlqd8SjjLjPg6cW0ozP7xNzBoN+e19jps2jglHrF/8dryeGwucoZoGIIKFn+/1+uGojTXNlcsMcy1Icgftnve/xvPrzRxk9nu/sDE5iFJDKZrOanZ19YK3Pan7fogdAOIsYTPv1D74WDp6cifI/cWrM59XXOU4XxY7dA5FJjWs4+DxGm34jHw70WUcHQ86W+bhZN5flOFhDTj0S9nHHETi/SwOi/Dogt2H+XQcPDpy8TCLWzRhI4bg9fed24qwggGdhJ/L5fCiT8MudxzUHPvFzfZ7Psumx32DN3f6xFl4e4IAKh85YpOFF8OgJzwGc85xRGRVvBJ9+sW4sT/Td77iLf38WcPI1GhVw81y3bX7NGgC7UChoZWVFq6ur2t7eDtcjTWqMTxpeYwULxXy7LXdw6n7D2UJ+77LhVxPF8jhqrVlvDzgB/GkDmS8qiLpw4YK+6qu+6qG+46yKAxgijdgROEUuPcguuZLFQjROyaamphKGlb7MzMyE9Nv09HRId6Q14AiHG8dRRtsFwC8ZpjnoGAegfE7iKDeeP58fXwdJD0SUZzUMyqjLS31d3FgzFr9Q0r8TO2jGFPd51LtGMVsYHb4HmPILVcc1+hwbNvoVO/lY8XztvMVrPMoZuUw7CI5BsT+bNYGNmtSOj48DO8PceASOrLN+sbFBR7yOJAZSziL4Ra6M18GMp/ZjWWdsfi/fpAbIwKm5DjM2/vY7uFyHWC/XF/pDP2KWlzVz2YvH5S2W61gnz2p+LyeOJg6CXA/jgC22O7zfgZiPGTDl5Q+xE3Sw5Tbaa1z8YtlJzXUKWRwFREeBWf+M+wdns1lf/sAgueP2wDf2Q/zc68EAWmkY/fhuwlEMSezb/L3IZjxet5t+cTgyEa+tP9PHCGibmppSoVBQpVIJdVtp1s/1FTLi8PAwAV5iXz4qXcrfvv4eIIwCkzRnlR0DjNJL3p/GvnxRQdTy8rLe/e536+mnnw6D+c7v/M6x36HTdNijDXeaCElcv+QRoz8vBlE0Z4Ti38XOCKFxpxAX9U1qJycnwVnHAiklKcZRLFwcaTm4if9mDDwznoOzIv14vjAcaZqDKBdiB6I+Ln+/R8b++7OaAxnGShTjxovP8l6//JbvpK034Vm8z/vhY4kV1gFXXPfmINc/PwrsOwA8i0GMZd6j3jRG4Pj4WIeHh8GpeZRNWs/nzd/rgM3TQ6SxfR1iRm8UEI7HxnyjH9RDAdbSNHdmXpjvLDHjcEccp0fGBS2jwLUHBKOCON7tYENKAq8063dWKYD3Db2OHc4oHXXnFQdfsbONAzGXdX83/XTgzXynqakB+DpYjcFu/N7Yn/B7Bxy+ztKD2YqY1XUbFvsdD3gALP6cSWvImvBdB1Vx33xtabwnltMYUPgaxiy4gwt8TexnpqenVSgUAsObZv2Y46OjIzWbzQSI4rmxfJ7FYsfzcRZwZNyMLdYxZ/R53qhAdlIg80UFUZcvX5Z0uuPuYVvcUa+ZkIYD5G+PvGKEHlN9PrEedXo06sCFxjM6nU4w2kQog8EgVS4fKpTFGZdC9PG6oDs9OcpAxvN4FmiKnYE7w3juSA9Mag66vMYp/owLrVPgHgnzWf/bAavLwijAwtyOAlKxo8IQpGmxUvp4fD7juXaAHM9lDOBHOdt4N4mDqliO+DuepzTNd6vQ17MKnkf11aO/swBTLH+xXvP9GKTFay+dgiJ2UKXRQQI039HI82Mg5ePz9Yv/HpWKjIGUf34UqzQKfPA9l+m0DX1yeTur73Hk7ms4yinFazcK8Pofd4wxUAYET01N6ejoKJUT9uZgIQZ8cXBIGs4BbcxgIHeAbBr6fnx8HPrtO09HBQI0Z1g8MDmrOZs0ia3k79iGxP4rHmsclEij661GgTP8HnPPRoH5+XnV6/WxY+OZvV4vAaK8lipeizggoy4rDthHBTix/0cvY5+IPRg1124zJungFxVEvfOd79RHPvIRfe5zn9ONGzf0Dd/wDRO/4wbIfyaNrpcZhTxjhuCs6NaNln/H2S0WAEHr94f1M7Ozszo6OkpQm5NajIQRBmdh3Ai4Mab/Dihjxm3cnMYGLjasCFgcGWNQ0oyPPnmtS+zcRwELd7ajjFD8s3hM/MznUnoQpPq7fD6np6fDVvdJzZnDGLAzf/Ea+dhchmNA4C0OElwOcLQOeHw9naHMZrMhVZqmjWLReK7LSpySG1WU7Lrjabs4mqRvjNfX0tfO67xc1tiKnoaNYs2p/aLuy9/F/+Mxj/oTgw//44AlXv9Yr33+Y5t0FvMzqvkc+Zq7AxnlZEatcyyv8fz4O/z/sd06i0FDjgBSaXcB09ChGKx7cOF65sGZ26B4/fgMenxycpKYB3eo+ASfyzgwloabHtKMz4OzGMx4X8+qdfP19H7F8ybpgblz8BkHovHveTb1whTDT2qsS6fTCbVwnU4n4Qfdbjpginf7+ufpn487bqNIBT7rsu0/44/XT57Vvqgg6r3vfa9u3bqlN73pTfqN3/gNffSjH514zhCI/awoLR7UKBDljvUsdDoKVEhD9B5T6LFisauk0WiEZ5/lDEe1uBBwVIvHHDuUUdF9PMaYMYnnyOfZjWYMcAB8aVss0O7Q3QG7c4kd91mA2kGTA8IYLI2aW4/0GaPXgKRpcQQXvyemimMQxbqNigRHBQy+DkS8AKh4bD5+lx0YnbQGztkQB0GjdnL5EQMxUMXoxbu9YgAVA07e62ufyWQCaPR3+fPTpvQYH7s0XRd9HuMi63h8o+o0/DP0b5Szo3kUPRgMQj2m26VRDOBZLZY9b2c5XZfRs9KBPjcxu4tt8B2B9MVTemcx3V4X5ZsZxo2RPsWBzKh3xfoZtzh4c6AQgxZnR9FD5CS2VzEIjcHMWc0DMQcyo2QotndnMYruM3x+kFG3ww6Q6E9sd72NKuGYND7fBRnroa/JKF81KeiOfcEoH+Jrw9r5vMbyRKrv/68g6g//8A/1/ve/X5L0Pd/zPfqO7/iOid/xrcwxOIqFaFS0hFL7Z2PhGcXa8H2YIQy1R4VuED3ifpg2KkqTkqm0UY7TwR39jf/OZDIPCJv/zp1rrBCxYHmE58zcpDaKQfS5lx6MfJw2dxYJgfUxuTK7fIwyXKOYGebTi2K9MDlNc4M0qujf5zoG+zHrEjucUeviMhu/O05LjgKiowzhuOY7/nwsviXdd1/6mKgx8rqReAxuqJ0RdPDk0XQMVOMonzVFJ9M0amqQu5gpZLy+a20UiIplxgMcT0/HzjTefODBirOYbvvSFpYzhw7OYucb2xc/9DY+m0h6MG2ErfF1iG2zOx4PXrzuhLn3eU6jh6y7yx42mjaKFXYb57Ln34l9RMzqOvvhoNP/7TIfB7xpgD6pJZeJWIacDXL7FdsZB2/eD57jQNp/R/Nglf97ow/0NS3YR//wMQR53ldkiPPDXO4I5hzo0j9fr1j+XVZzuVw4Q8/9o5QkUhgjDPa49kUFUTjAUQM5q2HUfKBnLUw82d7cUfnfzjzFKa1RaBwgFUcQcaSX1rgB8Hg2342fFxvjWOH9feP6cFb/XQFdSc6iuNM2d7w+hlh5vc8e9TA/0lBgPRJzhiSug/Mxxkbf5wYAwjtYizQRInPnYxsFlOIaGd47ChC4bnjUFAPk2BE6M+XOlu/EP09jAOiTMz44OMCTs1AxwAdEUTfCHLuDdueHEXc2I/69zxXgJ07T+MnnacbntWVuuGN2jYL4+I+DZFq8Xr7+Dup9PWK75v3wYDKtbMZ94X2jnh+PlfX1E+TjwCy2n66r/N6dGmvlN0LETs4367iTHNdGnRfkzQPDWC9i3R3FHMcgCIAQg+gYfMZn4uH/RrFD4xp65MeHoJc+DtYXuxP7D1//2Aa7b/B3YJO9eJ91cxDnz3SbmmZ3nuuV9OBmiDgj5EcJTU1NqdPphF3y2A7XyfjvWDZ8HeJgw+fVa0M96B/Xvqgg6pu/+Zv11//6X9frX/96feITn9A3f/M3T/wORi0W8jgq9kicicUBx2miONJwA+ZOzNG7C4ILsDsJZwFGGcRRbWpq6sxToCWdufBxtHoWmxYbA198V8JRkX78rNgYpGndbvcBNiAGAe5ERhkCn1PmimjEr3BhDG7AUGSn2j01EjNZZ0Vf4xrfj0GRMw8eqcbG8yzWaNScxZ+JZcBTzs6wxb+HOk9TtOugheCCqzCoO3Kn6wwCBvfo6CjIG/UufgUM9WcOoOI6CEmJ8TAGio/94EKAVJozhjyVwJzyDBxjzMbEbEO8tr5mvIMGGOUP7/fI3nXMU0YeMMS7kdK0UQAhDs4cPFLXwvjcscbgb5QddfvIaeTs8uSzcVABE0EWII2tcZnjOx6A+fx6YHyWLYo/x/w4cxUHpB5YOKhz/XZbwLEaaRppTU+Ve12qy5I01JNsdniQaxyc8u9RTBK663bTAw2e6alpt2uezkszRorQ/TooachKuv47G3V0dBR01Oc+nmcPdmKC4qxsiR8UzHzzGQ88Jo3viwqivvd7v1dvfetb9eKLL+rtb3+7bt68OfE7nl5Bcb0gzyNTnzj+xMf2u4OJEbQb0FjBWFSYELZgcm+en64aMyTjWiaTSeTRRzEmcQqEP7Hyn/U93hPTtE5JOqBgLmL2hH7GNTLj2vHxcTCKvvtOGqaJoHBjwDE7O6uTk5OEU6OP8SnaDmA9KvQxuBNyUBjTtGkBcLyOGFopyQz5n5iJc4fm8zlqPUcBKY/4/FmMJQa+Lm84tjRjw7niKABRbGPmZxh4jDeOFFlgHgBO+Xw+nKbNLqk4hUPfXecoQGUnj6eGmEeMaZrmNWWuN3EffA5ZEwf/o1ipGHDEsuLPjted+Y+dJOv+MCDK2SHe5YGTA1jmgv/H6SCeF9fKMI+sDffEcUQG+krje3GA67ZgVIAYtzgwccDnn/F1cQDkIJE1xRaOYtg8cMnlcok79mIgwLtZe2Q9vsNzXMPWuXw7S4czZwye6s1mh4XwrDm+MGY0+Z6vNTba2UNA6ln+ZWpqKoCaNK1UKoW589sQPDhBtkYFAtgTP94k3i3pNZK+5s5yxQQK8+l66eRDGv37ooCoD3zgA/r2b/92vfe97w0C/MlPflKS9MM//MMTv+95YEeiceSDELkx8EP+nJ72wlcHHK40roD+c5xPs9lUs9lUq9UKfx8eHoYdemlBFKjaD/zjXR61srguRLHRiJkwTxPGtGX8fWc1eB6fc+DkDmtSOzo6SjCEjBUg6jUoDjowSuzu8FoSB1VuvEcZGubDldEvrHRj8bBj8zV02pl58/l3cBWDWN7vSuz/j516zATwrNgRe998LZ3NexgQNTMzE0APLBSXvvqVPgAXHKcDU9bMD1N0wIkBdVnGgFerVVWr1QCc/BoaN7QxCzipYU/cMDrQHAwG4coXxuiMDexaXMcTsxuM31k6N9B8Nl5z+sc8emCXxoi7TDsDhC0lWp+bm1M+nw+/9/G6nYhLCZytOD4+VqvVUq1WU7VaDQEmNjEGgcyDjysOitM0ZMDBJv4Apx5/3i+0j4FUDG7cFvsY4uDPPxsz3L5uHCrqTNG45gxQ/Gxp6MzxD+4n/Pf0m/nxMwp5jwcC6L1/lz57bR/PwH5NTU2FICtNzVelUglXL+Ev4vmM/SJHkUgK84nMYo/ii6JZb2e6JSX0I/YJXpftgJJnTWpfFBDFNS+PPPJI4udp0yVOvUpJhyElBcwROBGCR8pcKwCgcoqP58UGhndwn0+z2VS9Xle9Xg9ACkNxeHioVquVeoJdoL1ewOlLz4fPzc2FFJkfKOiRnLNGOCEEPAZU/N7HHBt3j6Ldsaeppzk8PEwcFTAYDAKt32w2w4FqDjZmZ2fDYW3FYjGMEwWLC057vdNdVUS+jUYjsIIAFb95nbvSCoVCMGTev1H/HtfcQMZgH4MS15Y4vUyLgbyDD38uRjR+n//OjWwMwPm5y8G4hoxNTU2pVCqpVCppZmYmOBvYRk+nso7SkL1Fjvv9fjjJOJvNBkdNdE4Eimw2Gg1Vq1Xt7Oxof39f7XY7wQh4rRLj9aBpUkOeHdC78Ww2m4FxAOj5Zdq8Z25uTv1+P8hUDDJY2xhQOpuIoXYGz0HKKBZiUvOxATx9LTKZ0w00+Xw+AXy9tmQwGDywo9LtJsxgq9VSo9EIug0D4kAjLpOA4fCgwgFtGjtK//zMJ5qzdvQ73lk1Kgjnucw3z3KfgfzDBJFeou9eK+jPIM08PT2dOq3uc+PBroN9Z1+dHRo1hy4XHoAhqz73jAnQ5SSGg2PPAHCXXrlcnjim1dXVAKJ8jeJgSRr6xMPDwyCnnO82NTUVwFUcLHhq0FOU+I/4gnHWP04FxzZ+EtD/ooCor/mar5Ek/fEf/7He/e53h5//w3/4D/Vt3/ZtE78fRyguFKBuNzJe7xGn3ubm5oJj97x1DNSk5IFax8fHajQa2t/fV7VaVa1WU6vVCvUYgDhHr2mU342hLxCMFp+hn264AQU4LpydgyCv2+LncUGnFwnGRm7UOnjUP6kxD54fB4xicJlDolEuK15YWAjXB+TzeXU6nQQgi8FTtVrV/v6+9vb2AjiThs4f8MT5M16/g9NmrqX0IMoBryu+FyH6bjEcMe/HMTnAiVk/DJ4/G8MHSHH2Br3wCM2jcq/jmdTy+Xz47MLCggqFgrLZbLgvsl6vBydcLBZVKpXCVSrIKDKGXrrRJ6hx/SWl1Gw2tbOzo62tLW1vb6tWq2kwGAT59zoI5pD0MMzKpObBiwMDZ9Ew5P1+P0TZAMpSqaRCoaCTkxPl8/kEwy0NgzzWNo7YASr+u5jNdJDM79KcUcMzmH+XH/8+z3VQ5cXdzLk03Pk1ysbwnqmpqcBQMjZPz1End3h4mGB+nEWXhkBkUnN2wYNoZ7hjNgadcOfM73w9WDdpyE5w/RE/a7fbidobTyXFdgY7QJotm81OBFHOYLr/i30h9sZBA2RBTBIAoBwUODD3QG8U+8kaum4QAONfy+WyKpXKxPUrl8uan59/oJ+Ac5dz1gmd9wyA+2v6DsB124jdoq6q3W6r3W4/UDAfl2MAENElAr5x7YsCon7t135N/+Jf/AtVq1X91m/9lqTThXvssccmfpcBISheSOdC7oj75OQkABzfvXN0dBQM2uHh4QORgv/bBaXVaqler2t/f1+7u7uqVqvhWfTJc9JEc2kiRU/5uBEgWkRgULyjo6MAovg37/eLRhknQsJljm683DAjIH4XYBzBuCJ7ZDWu8WzfpYKh9ohPStZT1Ov1kApYXFxUuVxWr9dLpBZYx0ajoYODA+3v72t/f18HBwc6OjpKFC0DoGBReF+sBIxtZmYmVaqLNQQgIGcOrmM5oE8YG0AA8uz1HBgnHBWpZIyXR1DohKd/eReAw9cRIzupLSwshItgi8Wipqeng9N0HaMOolQqBXqe6HJmZkbFYjEYJ/QHQ+RAW1IIfHZ2dnT37l3t7OyEy0wBUJVKJawncwY4g5lYWlqaOD4cysnJSdBjr7Pi//SJ7dWFQkHlclnLy8taXFxUsVgMwQrAUxqCHdbR6zp83M6CeLDif4iiPf0wqblzkYbMjNfoef0oNkUaMvDMLwArdtwA4Fwup0KhoFKplGBaHUAxj41GI2HrnA3xgCINiMImsj3d/YIzgh7YoAcO3DyYxF75mrG+zkjW6/VEQbOnk5zxd4bIa83SNA/0aXEqzWXM05rMv4Ml9y8xs+LlDDw/ZrXIKDjjTyDlWYVyuZxKB7FNcXqfP55Gk5KZBQd22JSTkxO1221Jw1Qf4yM4I2vRaDSCv8GW8r18Pq+FhQUVi0XNz8+HcUpDvf6iMFGf+MQn9KEPfSiBpn/8x388/Pu7vuu79F3f9V36xV/8Rf3AD/xAmkeG5lEbk+W5Xhy0V+d7xEV6jZQbP3eD4EWBXrvS7/fVarW0t7eng4MD1Wo1NRqNkMZiERFQ0C87hdLeGcQ7SQm4UUIJfCcawsQfwBeRAMpPH2DhcL6g7ji3Hzv8OJfthjRthMgaeV0OhkYaplw9HcpOLtg/BwQYI/p7dHT0wPrCcODQl5eXValUVCgUVCgUEgoHmPT8PoY7zc4unsNaI18ObtzpYcBJKwPwAMCsBfKHAacol3ni7/iEbXfGOEc/FsJPUvZCy3GtUqno6Ogo1ENJSjB9Xp/gRqlUKgU2EcfM2JEjZAL2EcdzeHio/f19bW5uant7O6TUeIbvFBoVmWezWc3Pz2tlZSXVGuLAPUp3tigGN91uV61WKwEmK5VKgs3ygMZ3p3lKjcAL2+Zy4UdIoHM0T81Pas7uObAGxMPYEXTgOGPnRIA6Kvp22XN2lfc7e+YMGODNWW1nIuLswFkNW8yzPGBDTggg/bTxuK7Mg3YYYbe5BC+sL+UBsG7UAPl6kSKShmAEoJFWB4vFYsImMOekveKib3TFN9cATuMg29cPP8ZzYtbbMy4Ew7wnn88HOwgLhf2d1GCMqT105sdZzk6nk8g84QuQNUAVY2i324FgQKZOTk7UbDZVq9XUbDZDraVnrygJyOVy4d0e3BIIpiFKUnnJH/uxH9P3f//3T8x9Pv744/rn//yf6wd/8Af1fd/3ffpbf+tv6a1vfevY7zBZXmTGoNyZAx7ceUpSu93WwcGBpOFFqs4iYbzd6EkKE729va3d3d1A9WWz2bDgHk3gpKBvnSYe16DMJQWD5vUesRJDJXs04Yjc6y5QehQ/vtaCGiscnKfyUFiPdqTkKb1pQIZT/7xzdnY2GHXGKCkBsjxCZyzOWKBcXvPGLq9SqRTmDWEHjLlTcqYHAOOALU2ULw0BN2szin2ShsXvAMRWqxXkj3Qj0bQzkuxuAmQCgllLr8PxKM6j6aOjo7CO8Rkqk1o+n9f09HRIWwFSkXXYGdcd2FhkL04pOojKZDJBZ+fm5sL46vV6qH/yOgnWs16vh7o235VDP3jnpOZpOk+3eLqA9SsUCkGXcMjUQHptH+/PZDLqdDqBza7X60EnAdfuTBkHDtl3Lfl6OTs/qXmN3PT0tIrFoiqVSmDyFhYWwnsIUrEt2Ez0z2vd3KEwBq8RcdabIMdruvjDHYeATLc9Z9XzxM3lytOMo5h4B3IE0p5qd51w8ODpdGQyl8uFtcUGwb6Q+vaaOUAH707LRM3PzycYNebHMysw9+iis4VeRxmPLZfLBVBNTRGlFrVaLaw/wAR/jK9FTovFYpBn34BCTfS4Bksdg2mff9ay1+uFm0EkBX1x2yklN4zwHPSVWmbGhs9xMM6csLmJeT48PAyBVBr7mQpEXbt2TX/lr/yViZ/7+Z//eb3vfe+TJP3cz/2cvv/7v38iiOKQPgaJEWUhUR6ciwsztRh+TgmRMiAM+lEaMib8nzqbRqORYBAQXhbVmTGn6NPWRHm6AxAFAmasGCQHf4AHr/WhDyw4bIU7NGmYHvTaEh+/R+XucOMdDZMayiYpgBjmpdVqqVqthlqXVqsV5g/FhMVwZV1YWAhOxY1hoVBIsDa1Wk0HBweq1+shxbK0tKS1tbUEO+LnuTD37ownNfrioMuZN2kYXXskR7+pCzs5OVGlUnmAFYN+brVaCVmG6fJCVmdkcUbMKevpRibNGLvdbiItyFoiD6Ru0FFPp3udkusJOoJDkhSieqLo2dlZlUqlAHDYjLC/v6/j4+PE8QjUKQEMRqU/zmoOoJCz+fn5sKYAY1o2mw0RvheuNptNTU9Ph9Qzz/ZCbr9g1R2OBzPOdKHHcYrd03uTmgdlgFUYQgdp9Nf13WuAnLmem5sL/YwL1dE/bDKMYr1eD+nYSqUS0vRuf5CRmC2a1ADLrBV9cBAFyPVz/VgDwJTf9easu689wTbMcLVaDTYT1mNhYUGrq6u6cOGCLl68qLW1tcSOMU+nptmg43VzBLu9Xi+x0YnsAp9FD7121202wDefz2t1dTVxHFC321W1WtXm5qb29/eD7+H7sJdkEUizobf47bm5uVRMVDabTZRPoHd+hA2lEq1WK0EiUHtJLWa8S893mfIMZJN+LiwsBB2kDpd1oka5VquFAMiD5Ek2JhWI+qZv+ib90A/9kB599NHws3e+850PPuz/GFzp9FyINAag2+2q0WgkBAdF8dw1g0EweHan0wl0HVEgCkr+XBoW83Y6nWBYpqZOD8KkBooxAOSg/D3KY6EkpTZwoF7fOcCYOp1OYvcfbJija8aysLAQFAjg5GkuUDyGkWfFO+GcqvfCSi+czOVyQXHGNS80JtJGkPf29rS7u6vDw8PgIDBCpVJJGxsbWlxcDGtBP11JyuWyMpmMisViUHKUJJfLBdrWaxqIJpaXl1Uul4PhcBDFOqdpns8H2Hsaj7XDeHskjPHHUVIU7SAIOYkL1r2mqNVqJSJhHJ0DLAdnzjpOanEqy3foACiofyJdms1mgwEHhEkKRp9UmNdiALJ7vZ7y+byq1aqmpqa0vLystbU19ft97e/v686dO9rZ2QkOnPFRTzc9PR36kQboM1ewpOg/6cm49kMaAj6CHt/R5sW10vAgSACV15vMzc1pYWEhyLmncll3r+eEqUJH06TUsVOAKAAgto1aMz6HDfH6MPQHMOwOBuYQENXr9dRsNkOfm81mSPfGNVeMzzMKnqpJy5bi+NGTmH0neEH+cJ7OgvN+t3O+cYG5JAinfCOXywUWTVIIDAkOYTpIyWEHp6enA/Ca1LxUg363Wi3t7++rXq+HnWmwxf1+X9VqVYeHh9ra2lK1Wg2y57Vwc3NzWl1dDYHryspK8Cv7+/thbpBVZ7F9NySMZblcDowe7Fuai9zJGHitZrz21NsVCoVEbRefg0Sgbgl7gn7Nzs6GchyYO2zY0dFRonQIOWaNwBteKoRvnJTSSwWifu3Xfk3f+I3fODGd98wzz+hHfuRH9IY3vEGf+MQn9PTTT0989szMTOg0g8BwekSG8kDTITC1Wi0gab6DcnihLSkPhCyfzwcWoNVq6eDgQJ1OJxg4PovjdzrelXBSY3His6skhQJWnCGG3VNdvvsDoXVK3QsL5+fnE9GZI3FPH5Df9yMgvMYmbapSUiJVRV/b7bYymUwiCibFhzEoFotaXl7W/Px8iE4x/L5BAMWiloZ6msPDwyAbCwsLIeJn/pyFQhYwBrQ0xpu55W8YKCJfqH6cCmDBWSPmwSlkDO5gMAiOD8OAE0Q3qtVqiAYB+AcHB2HnGADdaySccUjb3LAAFngm4GNtbS0wQTgrD4DY4bq1taVarRbmwusave6tVCppcXFRy8vLKhaLOjk50dbWlnZ2dgIzF6dckP2YQRrX/FyyQqGgmZmZkTWNpD5gc9ApzojDaZDKAFD7cQ+kEQBfPt5yuRy+JykAA98x5Cm9tA44riWs1+uq1WqJnbLUncHw4RDduWCvYDRJ3cIOeB9JrRSLRa2tranT6YRiXa8Xc3Dp5QKjNrec1egbcxYXpnt5A3aGufdCatYfMAJ7TRp7b28v1OhhU5DdxcXF4AvQjbm5OTWbTW1ubibsCZ9FVu/evTtxDdETSQk2ejAYBP+Ry+XCem5vb+vOnTva2toKa4uvcXBYKpW0srISGDPmZ3NzU8ViMbybtC/r77YIeUCf8R3U+E1qrDFyOj8/HwA9TNPKykqwY3wn7ocf20Hgvbi4GEgbbBKbkVjzbDYb/s87wRue5gNEwXSmqQ1OBaIqlYre8Y53TPzcP/kn/0S//du/rRdffFHPPfec/uyf/bMTv4MiQpfG6QgM0fHxsQ4ODrS7uxvSN5lMJkTDg8FACwsLIdrz9AQsCcKBAcCB4cRgDkC4HgV7ESiG82HSQb67wwujFxYWghHE2LhR9VowT29SsIyCSUOwiCFnR4KkxBEJcdGeU8+el08DMjwVBxjs9/taX1/X5cuXQ/+9aJOoi2gX9obPAZDiFEPMrFy4cEHr6+sh2vOifWlIPbO+gGNYh7SNNUMZ6SNRLoaKFJFHu37OkBf7AuKpw2GrOE7Fo+tCoaBWqxXGCEN1eHgY1tBBN7vr0jhg1hqQ4g7V60hOTk5Uq9XCGnvfS6WSpqenQ9HoyclJYIWdofFaL2QYZ14sFkM0ubS0pCtXriR20BGZ7+3tJbYupwVRzBEAAjkqlUrhkD7W2lPKg8FArVYrkSojYveCcOSi3W6HrdwwywQ21Wo1jBUH7ruFcaAeAacF+p7icSYTBg1H6QELIMb1jHn1VLrv0CQoKRaLCXbJ04XOIsS7Sxlfr9dLlCxMal57CYOGI3UGWFLQN78uyM8Cg+EulUqBXSWt3Gq1gh0lOPAU9dTUlCqVii5cuBB2bBKwEShiYwCbadJ5BM4EGdhD7HKv1wslEZ4Gm5qaCn6PxhhJO66trWl1dVUrKytaWloKulypVAIbnM1mQ/oXe+msIjYHAOQ7Th8G6AOkkRdqMZ0wQYaw+byPRsptMBgkNhNhjwFlZC/8CBfIFgrOm82m+v1+kAFn47wGb6xsThy9TlH1u9/9bj399NNBqb/zO7/zgc/9xm/8hiRpbW1NjUZDv/Ebv5HqnCgMCOjW89p+9Uqn0wnMBoroTmp1dVXFYvF0YP9nsf1sCgpg3akWi0Wtr6+HVAtODEPkEQKTyhykER6U3msyEBiPwqg1cGPAdzBwjAPBxfHCoPFsj8ra7XYi9+91JP5vZ6E8ypvUKpVKYFkATGyTRwEBwhhSBNNTPRhoB3GeCvC+oIAAZcApYMeZTMZFhN5oNBJp0jTN+8W8oLgrKyuJeSOyiVkFX39n/zCUyCljAdRIpwfVOUPpTCnjwBl7lIVcpGkeuMASeE0HqWLSqIzXa54wdF6Lx7O8xoQItFQqhfnC8bA2XkCKnOJgCJ6wE5Mac0cajjorghAH6B7J0y9kp9PphNpEgh7XZYIiAhvSQkS6BGgwRQAuUu2sHc6GOZvUYASQDU9JUpNE+hh2FztKDYrv4mLOvN4rrpfBUREckMZnw4HLpjP2rvu+aWRSY469iJ7/I//Ux7AuhUIhbNqQFNbcC+0Bi/SHonGcvQfM2Ww2AK9SqaTV1VWtra0lajjxFW7HH2YDkpdySMM0P3VPrN/CwkJYU+bbNwsgj2wwwDZjY9bW1nT16lV1Oh3t7+8natRYExgg9IV5pkYXe5smpe67VZElgCdF9b5Lzu0pqWLW1st9kHeejXx6mQjz5GUwsOT9fj+R/mUjFyDSa37PaqkLyyVpd3d37OdeeOEFSadC86lPfUqVSmUiiELwSLF5QSNUdMy6EAVD2x0eHobcKKgZQ+2pBpyMA6mVlZVQDMmiuSOHDfC6Ds85T2qeVsEJ0i9peDo7Asqc4Fw9KvI6A6+VQoFRQgdJrIfXWCF4Mcvjn0XoJzUvXsW5eHTNuN3goXh+kBtrxjiZ73gtmXPmESUEgEvDgwVdxlgDBwdpG2sD+GGTgAM03oszcpAIGHIa3B0Lz3cWy+cNmfRUHWvkO4l8uzMGM83utTj9iL65LvG5TqejRqORqH8DGMHUFgoFVSqVsJbuZDDUAEocGADKwRNr5EEBssCZLmlABmNgnh1U+NjG6QHzGwd6Ps/MGeOHrfR0AcCEdAFpKnaiIhsY/DQOmDGRzobpdcYL1ssDNObFjwFx3WCtnKEmSIEFIQXP730enTFyfeD9sONpjgCAbcaOsHbo4Pz8fAA/bjvYMQmIddYY24rthB2+cOGCcrlc4jxAT+NStL+4uBiKlEeVeOCn0tbtOVPn60ofWGNP/wMyvBaUwmhn3Jz1JHVGLefMzEzQP4AKBd3IQFyKQICUtnlq0oNjaaifnu5FjmMdoW/METYXXIBcYKMpBXEChLq3Uqmk7e3twJoDUJFJ9GZSunLsLNy/f18bGxv6lm/5llQT9SM/8iPh34PBQH/n7/ydid9B8Fz5SE95ioICY1AitTEU9uF8vDA9Bh6AJyjYTCajSqWiTqcTttTj8Dxi8nSTU/hpDLjXOkjJu86c7aJhmJxOlB6MEB14MXeOzJ2dcKGMn8E4PULgGWkMuBunmIGJaVmPXLwGw6MIZzc8tQBDguFwYfd0AobV01LMo0d4jDltw8EwDmf2eB6FwS43NAfSsbF0R+WOxUGjv5fn+xp66gGjmxZE0VcCGJgk5tHlyEEkrBr9caaN1Dg6G8spf1zWY3mPI03kAoofo5tmfOh1HF170bgzo/TDWRhPb+IgPe3jKZD5+flEwTe2h/44kPJ6E2e30kb5vsUeefIdzD73Dh79XchaDOBdTj2och3m/x5gev2gp4lj5jstiHJbTr89OPI1YV1YV/cPsJHYHn8efcEJs9ObIy7YsTYKSIzSZc9qTGoeLMEUsl6kpbANzlhxtIkHT4Dx+fn5kD4mOMEmlMtlra+vq9vtqlgsJjYKeGrby2IAFPFuyzTBNnoE8+flBsyVpJE2GuYdP8IYpqamVC6XQzoTH+Z2Ej+JXWLesK/5fD4QMV5jCYhKw5SOBVH/8l/+S73rXe9KXOXCoDnKwJuDip2dHd25c2fS3CZy9c7aIAwIN6kJlAHjxKSwIIAngIQzILlcLhxTDyhjmygG2Z2iv8N3l2HY0zgoB2P8n3/jAKVkJEIfnAWLQVRsjOgLkb0LtxsgHyPPA807yk8LMnyemCO+60rgRo/3esOA+5ri/ACvyApz4eApTg3G4NV/7oAyTXPFxRjFz/Y18d1ZjIk1dKcDuwJIZ2yMy50C8+wMGv3yIISx+c8mNa7m4BwYr7fyzRUAVtI5/mzAFToHle7skoNp30zi6VlkKAZOboRhdLwIdVyLD0YdtfYxCx0HFgAhgjjWFNviDAvzwnogOzEQ9q34yLhH5/RjUsOxOoOHPXA74GwT4MZlFVnyteL9cT+QLZxsDPzchuEwmWPXT7dN45rPDXPlTKIXsDNW1pwxU48Ie+YOm3f4oaTIOQGz18V6qpN+jdI1dGdSc5vkTAi+xmWNdcHxu2wB7LzWF5n195AShHHy3eEuy1675wEE9gggN6k5Yx6nZL3cggwU8xsHPzBOpOlgm8AIHph1u92wqxRAxNrBbJI9odCdeWbe0sjn2N++613vkiT96q/+6sRJkqTnnnsuTPDc3Jy+7/u+b+J3XOFgJHA+OC0ExSMlB1w8g22JbszdEYHO/eAx0hEwTa6YKD0CiGHxvHOa8Xlax51tHLU408XnXXlcAONI0KNABMjfw3P5rDQEFvTL++r9HNccQDjb5uOLfxanF6VhgbpvAqAexQ25U/jIAvOCErqB9nF66jDt+KQhCHU2ygG6y6IbZeTG6ee4P9DvyL4bSilZkOmgnvn0/8cMVdox8mzmENlGZhi37/pxvYLZIRiCvWK93Mg7u0zQ5c93EM1cAvJdLp2BSzM+1h3gin1hzM7mSclTuPk5DtYduEfNXr8H0PJ6mpg1wzHwewdQLguTGgCXjRXITZz68L8dBLjOOJjis7Hsxiy2gxr67OARR+X9Zeys/aTm4DcOdGNm0wMUL76GmWNtkTVnEqlPi1PnHqQ4S87ZTciu9+dhArUYvBBMsJbogNcV0S9YY3QWW+rBG31zW00KWlJIrbuNZU68fIU+eRqeox/GNQfVBI6+CSb2OQ5mfBOSkwcebLIuLiPIOMGKg7BRJAO6m8sNjwpBjse1sdL79V//9QklJjKdnZ3Vb/7mbz7w+b//9/++vvVbv3XihHpz4zg1NRUm1KnS6enpIDBxzQIgyhcABssNnQsokwaSLZfLAU17VBmnFlx5fUfLuOZAhehbUmLBnE5HSN0ZOlBwlghhj50KCh0b4Tj9xLzETsbBxqTmB336eJg3p6mZX8YX15sAonBu7uh8XlyZMNSsmY/X5wqjEzvjNM3Ba8zyxE7OjZBHbG68kAnfuYVC+7w7KGYOYhDlz3Pn4YfYTWruAJ0BZA3dSMUOi0CHehI3+A4smBuMN7sMGQPrH7MLUrI2EYABAE27yxLjzSXlkhIpUwCeszTuCDHaXjcUy6Wzdp4eczuBTsZyEsvLWYzZqOYMPY7TgYnLrqfr/Uwy1tQDLwdQ/D4OtFgbAHfMUPozmBvm9mFAlNfLuM7FARtz5vYQkM+VRuhwzDCTrgP4eeDJCdpe+I/dY1xuV3w90wTbR0dHiVQoc8kzvK9kWwBQjNF3gAPgfRexs4/MOc/097huxxkQ1pt/cy7XpOb2hZ3GHlB7/VU+nw/zxloQdGFX8N98zxl7gKQHFLBSgGr3pw4YnYHEnk4KZMZK73/4D/9Bg8FA73nPe/TX/tpf0zPPPKNPfvKT+jf/5t+M/PwHPvCBhwZR3H0DYgadIsQYhhjQeDQhDQ0xhtENIAuFsXADRo0UZ095SkhK1mzxXv5OY8Bjp+nFsQh7DG6cNfHIxp0xzUGaNNwKHBtmBwDSg3UZjtgf5vyddrsdDktFOQE/CHhs+Oinp0owAq5MgF03RO7MUZiZmZmg2M4OefrAt0G7Q07TMFpS8sJTb4Aq7zNy57t04v77mjrgQ0bcQLvDcLliHn0Nnd2a1LxW7Symzp0ma8bcUycCcCdFDqPkz3GH7+BPGkaEvGtUIMQY/QDISY11YCcaQINo089L8wDAQQXrwC5UdIn598/xLHcEvr7eXE/pa7wOk5rvzCQYHQU0+Lf3xVnu+PPO9MRyH8ueszVuk2nMH+snJQPaSQ1b6OnSswJCacgC+4GQDuCc7fE6RAAXNU/IarVaDTKJzDg4Qu7xDQ7C0oAorhqhP+g+/syDRd6FTcDxw8pg172eL5PJJBgZ5sKZXfrqAMXZN97pgXbaQIY1jmuLkSPe52lITy9DXIAT2AjgG9EcRMGwuay32+2ROAD5hIGCreKzkwLRsdKLIN6+fVvPPPOMJOnpp5/WSy+9NPLznU5H3/Zt36YbN24EwXnve987tgPcL8bA4hQNzIT/nMlxGpmFcEr8rMX1iNapu1g5z2og/Hq9PvZz0vCkZWd5HCR4c2H1SyLPMooeYaAAjqwROE/feTTh7IzXX3n0PanhzKBlUQTWhuc4EMWQuRFwo+PKjFP1FJorH33FyDBOgJMzNH6ERNrdh5LCttuY2aM/MTvkDsYjY1dyj36Rf1+jWB/i3/NMImIMZgyE0zBRvMtlwtMAzK+PkfWheJVT1Ll6iYahigETzsqPPeC5rv/uaBkj29bT7l5zGWi324lUqcu6r60zau704x2wrJWvrdcGMrfOkvicIMsu085OpgFR9B19i9NevN/1OQav2CP/XMxeEbT6ezyt5HaNwBcA6f3xdfXU4bjmRzD4nPE8T4d7+l0aFt4z96yN134RyPlF9QAN6tZgnUaxPh5AuA1+mPEhO5Qx0LCNzD9jxD748TKwrZzc7aQAz49rSdlxS/qMA5B5jweD2BdsDoftTmrYZ0gEvuug2FnheKeqX8jujBGssusJz3PWOJM5LS73ui8PTJkbD4CcrR3XUu1RLJVK+rmf+zk988wz+vjHP67V1dWRn/vRH/3RNI9LNN8SzpEGnnftdDqhIBCkTfOozyNcz/U75S4Nb6Q/OjpK0PMxHT4qmvIo8fDwMOEszmoIDEri9D1Fbp4SwPnGEbwbYAdb3W43GG3P8TMW5skNjqfvmCNH8ow7DYjyueQ5KLcXiruhgRXAUXsqxY1DXMToNUnMBX/7H5wfaS2fU3dQaQCGNIye3Cl5/YMbSwc5zKezOh7tAAycUfH58VOKXZ74nK+lg0MHUWnYNpi2mHnCCTnocwaK9AcHVgKI2FZOypu54eJTL+hkbLC0Dp4x+L471mXfvz+uORPNe1y/GZOvL99jjuNiegcMDsQ8uMvlcok6E3+2Azhf0zgd+zDNg6dRP0cX49+jh6Oag0m3VXFAxtji2hIHkTFIjedkXMN++vzFLLuzarH99rq/eG74HP2nUB5ghg0BtGOLAEueMfFnOZM6qXkA5DbO584DDAd+6OXx8bHq9br29/fDjkIPTOPgi985SyspcSK/s1Fua+IDWNOMDz2LswoO5n3zjgdPBE5sMIsDffdXjIeaLy+K50BUD6R9Hfk+6+33Bp7VUoGon/7pn9b73/9+feQjH9Gjjz6qv/f3/l7i90zE+973Pv3sz/5sENZ3vOMdI3fxeXMlcGTLojul5obMFZfJ9q2rHFA2GAyPzOd7MCeeO3VWi8VBAb0/3leEblKjPywmixgDHxoggvnh3XEaz52kR+/ZbDZskXUGw6lgr8eJaV0+n0b5MTJ+BggC6WNzYNxsNsNBhG6kiTLoN2AVhRilhP6H5/j4fBt5HFWnTeexVjAtKLvT9XHK0tkop94BB0SCDh6Rc45GyOWGO8IYb+yE/R2jGMW0a+gOyJ+Lvnl0D9voJ3v7XYl+qTegMZc7va6C9QU0shPH04Wct0R/HMDGFHyaVFAMDj2oYe6Qrxjs08/YSbI2pBb4eZyOhnHl3e7EY/mNWWgCkrTrJyXrHmNnHjOJOCNff4Cfp6vcZjA3OGi3Gz4+XzeARJxGJMh4GBllPePv+Bh5H8CJjRLOtmGnXJ8cACN/7XZbe3t7Ojg4CHqJU/VgAFl0f+S1N2kattQBr7OmHpS6XWWMtVot6J/XGWFjPFintshlpdvthpsuSNEDpJBjdIcgWFKqu/P8SqyYFXUg6n8YW6vVUqPRSBxZ4XaO+cFmcU2R+0NPwfJZ938+Bx7MANzGtVQgKp/P63u/93v1S7/0S/qe7/meB37/7/7dv9Mv/uIvand3V88991yYrGeffXbis31hQfieOnAqHOVmUZ11gdpjYur1uhqNRoLSwwAgcJlMJjAoXEfhDEVMx7ri4uAnNTeOGBnob1J9cZ4/jriYDwQCg+fUtqN6DDx9jxmuuKCZ37uyAwImNZQLoMLaxFQqa310dBSuo+H+OZgY/hBV1Wo17e3tBeeLIWf3DNEic+LPiP/4WOKoeFLDIGG8HRDHht3X25UQB+QgBZmPI2c3/GzLjaPaeM09FRc7tEktXmd/rkd8yBy7mCqVSjgPqVqtamtrK1zLwkYD+u/1GR4w4Zg80ocNwHG642W+mLM0ZwzF8+ABhQNwD1yOjo7CpeakW2EJPOp1J8f6etBEHz0YdMb0rDXkZ2nYYJ4hDQGe99HXztebd/IMT5nFAZDPGf1n95LbLGcW4jSu25qHSVfSv3j9Y2bYf+Z2zgEih2zSYiaDMbjNPTg40P3790N60pkJbC1y7j5jVDZjXGNefN7pDxkH3y3n9qPVamlnZ0fb29tBTl1WIRA4nR77JSmc1p3JZMKVKhxGyYXwcXbIN0hRfzSuodsekMXpO2eg0KN2u639/f2QbpQUUrMuF14L6sCo0WiElKeXTiDTLlfIjTOPpBDHtfRHjkr6vd/7vZEHaH7Hd3yHvuM7vkMf/OAH9fa3v/1hHpkowvXozynoGFRlMsOdHZ4fzWazAUnXarVw2jnV/tIwqvIItNfrhe/4WRMxfS8lU3ppzsfw2htXNsbpuXuez99uoDzCdCX29IdHYIARaWhQ4sJATrZ14x73I836uZGVFECQR07MIafqHh8fq9lshvRto9EIqaBM5vS05mq1qv39/ZDSpV/Ihjsiz9vHtU9ubOhHmjQQjTlyQxKzPfztNLADRV9Xz7U7g+CywHiazaZyueHhe56ailknd2Cx3I5rvoEhjuhdB9E3AFS5XA7BBDULXofh6Vdn1dBHAhdnKTxNx98xq+E2IS0Thdzwfwe7gAFf60ajoZ2dHdVqtXCdCGkCmDVpqFv0lQJm0rEcTOhspYMk/4M8xMxgmvE52+lzFbN4cVoGRsn7gd7ghAlSff6kIQhjbhmb65ezwm6HYlA0qR0eHiYAs4NC12vW0FP3Ltv+Pme3YEIkJWQS/0R6mgup0TlSRsgRzZm+tLYU8ObMR7/fDwHk8fFxIqtCv3u9nqrVqu7du6fd3d0AbJBLWCDWyVlXZCeTGV67ApODj/Cd8gAWiACXi3HNgwovD+APbJk0TL12Oh3VarUQzCBXMNUewHj5BuuGLW42m4n78+LmRISzpG5jx7WHAlGThOG1r32tPv7xjyubzepnfuZn9AM/8AP6yq/8yrHfcYaFd9B5pzaZeAx0zNyQIoCBwlFLCmexQM/6xaUgdFJMg8EgVP3DXI1Ko3kUPa5hQHq9XijaQ1h8nP6Ofr8f6NK4Xot3O+uA8ZKGoBQjyPjceHm9mIMQH2Pa6MnvAkQYGRepWQdSGFk/38PHQgqW+hk/gySOYvx57hRjqtdlBWPCc9I0T3Pyf8bI386Gse2XugF+7+kRB8X0KZ5zIjG+57tGvIbNHVKc7krTPHLzwOT/196ZxEiaXWX7jRwiKzMy5sipsrJGV1WXjd1tQ68sNWLBwismeWnLC68sSxbIatuALQsjjGSrjWQwghUImWZYwQIkBKyQwKBe0G1ZWLjdZXdV5RhjRmRW5RT/IvXceL+bkRGf/ff/I6M4Uqq7MmP47r3nnvOe95x7LsGJ33GWz+dVLpdDITmgWDpnrHEErBtAZ2FhIYCvYrEY1hfjl8lkQlrAnTDPQMDh9sAd3yhxVi1OK7GWsd7u7+8HA97tdnVychLSG3G3c5ze/Px8uEuSa6Q89cV8xClT9oDrgrMR44Q9fnR0lGjv4uIO01kg5pHnIWpnr0xNDfrxMGfO8HC/KUEn73NGyE//xvbGU1ajpN1uh4aIsDA+nwj22VOx/B77gM4AOv1ZWBtYCPYqZQhxUJbL5cIJNQ+I/LnSgihe65/FM/OZ1FK6zX327JkajYa2trbU7XZVKpV0enoa7oSDXYK1x5+wPvg82F/YL/T+6OgocViC+WVvpxmfBwXoitcqMaYY5GNLyRxxKg/mKZMZXG7vATrrhO/1uwCZV2ejhwUyqYmENC9qNpvqdrv66le/OvJ1X/ziF/X5z39eX//61/Wrv/qr+spXvjIWRHnEGUcJTCZRbBwtuUMECMEm8RkYalIK/NvBGIYc4AFVHU+if3fawk9fbIraUCg3pA4iiQZI9TEW0ldECoBBT58VCoXQgwcQEzMWSAwO+N2Psun9Ykv/jDg94SlKTr94RO7MHyBrYWEhzHGhUFC1WlW1WlU+n0+8P65h8dSpdBFMDMvLjxLmyVNqbqjRW4xvr9dL6BnGmvXjmdEl3sPrSAENcxYYv2GbHL2SkicHx4kbbT/tw9Fwv2iWDsGzs7OJlPDMzIwqlYoWFhYSxa0O2F233Ml2u91QpA4gcL32aNVTVWnH58+JEXUw5fpKap+9RY3F8fFxGD8XugIoPPKFrXDmw22VG27X/1jQgzQ6StT+7NmzRPdw5tjnyJ0HrAS6i4OiU7N/Pv9Fx5lXALCkBLiM55Xv9P93Fn2ctFqtcLkzNtrZNn8+T1NKg+P1/jv2ojPYBwcHAWB4kTa1OASvyPT0dAj0+BvrFqfcxonbFmfImEP+jk331Cx1W61WK+wjTqJRq9hsNoNOe00mtrlSqejq1ataXFxMlGhwmwcZFP7GmAj4xwlMlAfCHhQ5G4RdhVk6OjoKZRGnp6dhHPv7+8rlcjo7OwtBz/7+fgCPCOUfcdsGr58dxg6jo+MIhZHa+/rrr+u3fuu3dHZ2poWFhcASfOELX9AHPvCBC6/PZrO6e/eujo+P9cILL6QyADgUFieOwJzm9+gdlooNA0AiAiYSPDw8VLfbTaBUjDOfc3BwEJ6DGo84BTOMCk+zOdh8khJ3E3nhLOK0vEeNMGxsYJD3sHw/jAGG0ZG2O0vegxHxZ/H3jRM2o28EvtsNgtcZxH1KJIUTmDyDF/Lyb06CeY2K0/rMnUcTiDNXGKZhzuuyNfR5Y448lcPv/GQca4iRcfBE/UGn09He3l44kjw1dX5ZbbFYDMwMY43bfPg6+fOxDpfR17HwHgwbAIrLO6He474sAMg45cczA0C63W6CcqdWEbBJnZunfz1ydebRx43TGSesCakJJHa6BDPsE1KXMG0OXP3i67ir89zcXEgf+HicRY7BpYNf/j+NAWccpBo5hOGfxxili7dC8DuYcgC8p+m92N0djrMm2G2YME8xM7cOoIexyqOk3W4Hh+4MiINVt9G+t+M6Nt/7zE+v19Pe3l4Ahd1uV81mU+12W51OJzEWt2PuV5yh8u9LY0d5lpjF43mxr9hs9sDR0VF41pmZmXAhPIGQ60iz2Qy+RBpcD5TP5xMXLHs/Kvzj2dlZCJh5r/vicYL/wT54IMQaeFkBe7bf7wd7xIl4ThJubm4Gn+HBK/6cNiocfHFf6RmlmNmPgew4PzESRH35y1/W17/+da2trYXfPXnyRJ/61Kf013/91xden8lk9PLLL+ull17S3/3d36Wi2tkQToV6+s4pYpwJDoU6BQdJXn/EZ5AeIp+KUzg7OwuUJZEYUZhTeh45xvUE44Rn7vf7ge1irmIA5Q6BCNxrfFAqnglDCMrmhvFhTI8rin+vz79v4LSM1LCGmm7YHETxOujxmZkZ5fN5zc7OJjoKEx05xcuzeh0HRgKjjYGNGba4lsONbVrxZ0AfPY3H5zJOmAroZmcXm81mcHoeyUqDbvvUoXj0hqHB6TizwbPFqZI0Ub5/D87BLxr1Wia/8oV1IrWHoyQaRu97vZ62t7e1u7urra0tVatVlUqlMDc4Ui+G9fRWzLq5k0wDhL3olBOgfHacXnJ2O5/PhxQl7Ggul1O1WlWtVgsgk9S0O2fG4UEgke8wVhiJQVOa8XmqLmbH2RueTvdSBlImMAXoJWuN3cLGOgPvLAKg2u1JDLj4TgdRnmIZJY1GQ8vLyzo8PFSxWEywtB44uJ54um4YCGdPAeQPDg5ULpeVzWYTNY2kwaj1JIAHtHrg5IwrY08DMpzplpJF+Q5Sva6V7+UgR6VSSdQdTU9Ph70J05/NZsPJ6EwmE5hVGozm8/kAZtx3MAZvM8S8pxmfv86ZWR+nl11ICgdMvAFqq9UK9rLT6SSeFb0GQObzeVUqlQAqnViIQRTPwZhiZmyUjLSwJycnCQAlSWtra5dGR1/72tf0xhtv6KWXXtK3vvUtvfLKK2Mn14u3nZ1h0QFCGCkWn8nAcICWYzoVFOvKwUKdnp5qYWFBxWJxaCfxOLrBGPOTJoJyA0Nthy+WKxHikb07YV4zPT0dGCe/c8477ErJo8ls8NgoO43scxw/0yiJ02OX1QT0+/2EMc9kMiHyod5ESt5bhlGHdaPIGubKi+79KK9HgjFzE2+6ceLM6LD0gX/X1NRUaABHFDU1NRX6nNA110EtKbSZmZnAAGHQMFqxvrhuxiky/3caIByfAATAQft73xjS3G6wmH+MJM+WzWZVKBTU6XRUr9dDjRHrkM/nE3Uu7pDjiNzTQV6knGYNY4cOeHEQ4/MLCPY58KL6YrF4oQ2DO2q+w/dT7GB9L8RgKrY748TZn9PTQX8vPiOO+J3Fc2eJHWWPLS4uBsfd6/VCmgRAiW0GNNHny7+buYj1kD2TJtCWFA7+7O/vB7DA9/g6+/dhL1hTGHquQomL6/n/UqkUWDmYSfYv4nroY/XMiLN446Tb7QabJl289mtYETV1QN1u9wLhgL6hP9hY9AU94cYOUunS4CJm9BLf6nqLf+Lv4wR267Kykjg977V5pFfx1dgRUq3uGyj7oG6zWCwmnjWumfXAw4E98zgsMIllJIj62Z/9WX3sYx/TBz/4QeXzeXW7Xf3Lv/yLXnrppaGvz2az6vV6+pu/+RtJ0tbWln7xF39x5AN4GoiBxMjZX8OEY6AANkRBoFBqKDwi8JoZN06wBJzM4zl4L4bdo1mvYxolfMbh4WEAUYATN2BSEoHzdwwNzgbl8qZkXpwXz6VHyKRGYsMMgxGDoTQgyqlrB37+7zgK9KjVa3C84zyOzw0izxOzWw4avPVAnLt3qt8j8nHCEfVYR/lcB6E4W36H4fXojf+yXqwhrI/XpngRrP/EKcs4enLgOk5gVPzUDPPonYG9rUQcsDAPrCFMHDUM1WpVjUYjpBIYhxtKdwQ+tji6J8UNjT9OXP/QzRhkx0wSdieXyyXSI74mGG8HfPGaeOCHDGMMnc10fU8zPj+kMWztHUxJA/uCM2OP+vceHh4mdBv7SDqLMTOXblN5X8zyxeI6O04AMpzo9fvVGCN6gY0mNQ5TT02qM2rMO8EY4JGegwQHsHWMFduNk43tDGCHFNM46XQ6AdT458Tz5EDR9SO+GJy9QvANiIT9Z+28rQD392GXCKCYW/SEfQrgSHN3HmB82Lh4Fp7DbQvBpf/enx1AnM1mlc/nw+0JrCGgFH1GL9w3xP7XmWM/dHOZjARRn/zkJ/Wd73xHr732mlqtlhYXF/Xyyy/r3e9+99DXf+ITn9Dy8nJgry5jrFx8YnxiY0PnVK2zGX7c0tMc/hme30exnBE6Pj7WwsJCOBHn0Qwo1CcVZUjDRHkEDYPFovii+fjcGBEVsLm8zgLn44DSwZCneXg9P8M2vitTTI1fJr1eL5xkZM7dObHxXHExYn5Ul/nxzYmzwjl7qiyO4j2ydbYEw+P6dlkq5TLxPj/uMN3hMa9xY1cMG8/mtL+DEC+ajg2Vf75HvB5QxGyVA/VxsrCwEH68LgYDy/Oxh3y+3eDETtyNXaFQCIbZTxzGxpP5BUQ7KHSnxfelMeA8i5RkeT0Iwul5qgtAzFoAEN0+uD5ISvzNHZ8/g38n3+XAyvdjGhA1Pz8fanJ8X7lN9QCJuXSmA731cbm+4+Dd5gEOPYhA3Ea5fWeOkHh/Xib9/uDEbrfbDZ/teuMnAGHruRibveSsggda2JZOpxMYfQrl/ZAFbFUcjPkedV3d399Xo9FQPp8fOb5ms5k4+em65TaVucWWEHxxoMhrjrz21A9m+ef6Wnq/KNdjD46wB/ywLuOE74v3jT8DNtvLa7AFksKhCcoNYL4JOr3cwAMzQCHXS12WTvdnjAPWUTISRP393/+9PvShD+nGjRv6/d//ff3bv/2btra2dOPGjUANuvT7/bEn+GLh5JyzTDFYip26I3Le4wyANAAGMUvjxokNRbRNAZp3uY4pWgcbaXL5PAsRedxewZmXGKWzeYYVCDsA4t9EC7HhwtggOALmz422K1ga40aNS5w6G+bcJSUArJS8CBkAFDM9MaMUMwC8z5k8r5lxp+6OLS2QckaTOqDYMTBmZ94wdg6wHKTzGgcR/rywdf68MQjkO2Ow4czbOJmZOb+wc3Fx8YKjZM59Dvm7g3e+04OM+G+np4NGsA644toUL4xmPF6P6D9pUgkYZcTBq5844rXOMlND5akS171hTHpsoAlaGM8o3ePvzriNE+q2fK5iHXWw47oR24bYycYtEDwdwvz4OBkX4CUObh1cxumUUQIYoHu19zryE8zuD1gz/k47Bsbtp/bQVT4fBoRg2U+neXA4LIBhbg4PD1Wv17W7uzsWRO3s7KhQKCifzydKFJhXnwe+m/00M3N+WweBG2PzelU+xz+XQAVdcwbS/afPp9doAjjS2FFnz9EfD0LRAWfP/Googhg/te0BAHWd+EG+y9kv/hb7OiQOZoa9Zqhujvrjq6++qg996EP68pe/rI2NDX3+85/Xv/7rv+oLX/jC0IuF79+/r//8z//UgwcPwu/GAQ13FEQDvogOnPihuNYdCobQmSePPtkw/nuPoJgoFsCvXnDHxyL7JkwjbhjdqHt06I7agaFvomEpRHdSoO1+v5+IHp2ZQjzajJ20O/NRsrm5KWlQ2+Yb38GuNDhVSJGqU/SsqdfnIIyDeiEYEyh6f0539v67GAikYUmRhYUFtdvtBFsWg0afP9dH5pGIlr/7CVDXL2cD/d/OLsXOMQaGPt40IMrrnqgbwcFNT08njKyDBHc+Z2dngWVlfAQkGEJnlwFcOATYQ5wqzB2vdVBBCt8LXkeJ7y3X6zjC5/thSqmT8RosACuOJHYqvgcc+DMOr79wvfE19nRMmpS6p1nRKx+bB6DoFfbNnw29dabBGVKejxpF/wwHXl7rB/CQLgY0sX0YJZwKxdH3er0AdPg8Dx5iUONtbPr9frAfPs+kb6kv9ZpL0tCsFXuGLIFfoM7e4caFVqs1dnwwbOgHJQmMBZ1xEAc453XUXDIfPG+cfmddPICNSydYf9g8L7dw0Jg2EPU6UE4z+mEGvp92Bicn560YnG2DhcI3Isy5B+Z8JuIHOxD3CXEtlJf+jPODqVDAw4cP9du//duSpDt37ugf/uEfhr7u3//93/XP//zPicH90z/908jPJg8b02hMuKcRUHZH144qj4+PEzleNgqv88jKgRuADKdOs04/cukMmaTUAMoRN47F+1QxT9KAzvQjmt6c0yl5T+v5XMzMzCQK0WMn6sAzdrg8g/+Mk0ePHimTGRSIe9SD0XOAylHi3d1dbW9v6/Hjx9rd3Q1HixmT1wkVCgVVKhVVq1UtLS2pWq2G4lIU3w2nj8MBirN8zGcawXj4pZvOnvK5DlxiEIXj9ejG9cvnm/H7XuC/sQ47GPT9wxykifKpucNYum574ACDyKlCagQpOAZ8xHrlAYGfBJ2ZmQkHLgBNOHje7/Vtbtgw/mlAYnzQwpki1xkAQqfTCW0Z9vb2lM/nlcvlErWWzl7zu2FOJp5LAKWzV6xVHMSkDWTiFB2f5boRp04Av+gf8+GHefxzPc3Od7qDxo7yXb4vHKTxfPH+HCfVajWk2QBS/X4/NIiM7bP7BOwu+8fXCt10AAkggeWgeNubb7oOENQ5M3t0dKR6va56vZ6qJsrBhLOcUrJsgKCD+jzAIacJ/doTP8mH33TAx7zxd2cx5+fnw8EW5gwd4Pl4tjRAirUhEMEH4ucJ1nq9nlqtVuKicnw59/g58+QMmbODMW5wJtX1OK7XRVe4szVmsYfJSCTw8OFD/cmf/IlmZmb0ne98R+9+97v1xhtvXGqY//Zv/1aSVK/XVSqVUtUMHR4eJpCxKxDOwgcpXX6vG4vijA6G14viXNlxUK1WK5wg8vbxsCNxgXRslC4T5grDgsLHQMppTdJ+0sAAMV42kBfcuWONKeBhCuApg8uMWpySuEza7bauXLmipaWl0JNDGtzaHbMpPBNO1y949PogPy3G5mL9WBNOSF1WqxHTtj6eNIYboU4IUAJLwTy7k2AsznrEjAf/9pNJPk+u93HtRVzLw7wOGyfM2TjxFhNxx2vXSQw993TR2I5bArxPG8DCa1f82T1lwTHrUqkUGsX6vgDcEGl7T560TBvP4nUzBCo8E/NFITGpPHpboX/5fF75fD7ogYN+Z3HYo27b3NC7fvqe9OAnjY1hjbBz6Anv9zWYmpoKts0dBHbXDzvw/x6hx7YB5kBSaA/jjEkMDn1f4NTSsImUDPD8fIeXcXgwAuPBqTpsAhfO+0lSHxOfCfM9MzOjw8ND7e3thX5RMFacaiMNnsmcH0Di3sXNzU01m81UdpQ0Hv6K/SENGDyelcDZT2JTYI2uejADO5nJZMK1RYyNtCt/h+1hTK7frK2DKHR2nHgtmd9xR7E/voK6N07xYu8BUwA/5p89BzgEYEGesNbYVnTI7ZFnnfr9fgCkBwcHicMHl8lIEPVHf/RH+va3v62bN2/qu9/9rjY2NvSlL31JX/ziF4e+/lvf+pZ+/dd/Xfl8Xp1OR1/60pf0wQ9+cOQDsAm95sCNrteXxBGNlCzOlAa0oadHHGX7QoLO6era7XYD1euLwyZ1NAtiHyexMWSTeX8KB2Sez0ah3Hm4sYsdFM9Ns0b63KA0Hn3HVLqDOArg00bBMEwoKxuM+fFoZW5uLlxLMDc3p5WVFUlKGCM/keYpCsZOlOfRGkbMN7gbad8I6ECa8UkDJwx9TvEuc8kY+Zuf4jw+Pk4Up2KMcFAY/LjWB/DlTizWE8bI+9FvB1FpHBRGtVAohAiVteU7uLcLNo3+Qn61jddjeC+ms7OzC83uiEZhmxcXF8PRZD9hydg6nU5giGhH4umxUeKA0NeHdXE9mpo6b1FRKpV0dnbeYHBxcTGR2nEn5Ovvzg5dccDBuuOInBlz5+9OL62NQf8ymUzixKMznZ4KilkOAB5O1MfHc3EPGUEgaTUO5lB8PaxZp9tNB7JxiuUywVax//1wj1+F4q0PPEjDBqLfHsjGaV7mjnQfr+92uwlWThqk9Tzt3el0tLOzo+3tbXU6nUTTy8vEQdSwNJ5nC9wekAbHXgAkaKXC++IAzU9Fs0YECaT1Gbunhfk8T+elsaP7+/tBh+bm5hJ2gyDD7eT8/Hz4HawYhf37+/uB9HC7g+/j/V7Dhj9nvdBRT4nyWTDtsJH/VyDqwYMHevDggT784Q+H3/3VX/3Vpa//vd/7Pf35n/+5VlZWtL29rU9+8pNjQZQ3v5MGjtcjKF9ET1V5pAvDw8IQUXouFIaHqBZUD1jJZDLBmRNlxF1f+ZyDg4NUheUoHAZNGlxD4ewCG9ypVp7VKVvG7uLFghipZ8+eJQyLM3Ax9S8NjJTPUxomcXFxMcyhAzLG5oyCpBAN1mo1VSoVTU9PJ+aaNfU6hrgWhlOUnU4nOFvSicwBwNkLV50BSFtvIimkEaanp0PKl83tETBrBjPj1/JgsJx9ki62Ljg+Pg5AgVMnMB9eC+Ysn++JGECluZKhUCgkLsq9LGpj/YhgWXMixnK5nKijGaZfPu74mDlzR7NYD3i8+aEDwzQOmO/zNCB25+joKAQanMji+Dz7kZvsPT0W1xz5nLHvYnaD18ZOx+fI60NiXblMYlCJ7jiTweeiq6wT63B2dnaB/QUEsZ+dDQSg8DqCOPZKXB/kKSNss3dvTzNGT/UCOGBNPIUqJdvFeCqZguxhKVPeQxkBY0C3KTpnbXxusCfdblf1el2bm5va3t7W06dPVSwWx47PWXzqgDwgdGfurCVjzuVyCYbe95brl+9pQBi6ArCiVAHbi830rIUzjmmA/ubmZtgP9Fnzy43Za140DiOXy+VUKpVUqVRC+rbX64XAyq9AOzk5vw6m0+lcKKWYnZ1VtVoN19twGpXxYRtg2GHKxsnI0X/kIx+5VMH/4i/+4sLvpqenA7OwsrKS6gEo5CSn7mhXGrSmZzJwprwOQ0BawcGJU8gOLuLor98fNNn06AuJayag+tLQmNKgMBolJpUF0EGZPQICnWNwEI90HWA6Zc684fzY6BjFYf0vUFqc1bNnz4aewIwFIOG1DdDDAFqU1VkWImLP0UvJ9g6SAhPIGnrnduaOxqeed/cu77BBbBaAWBqAwTMA0rjjzk+quAF33QE4sa7DQB5r5XQ5eu39s7yQlfkkb+/jRA9+lCjf2zJ4TY9Hcm58vRGf6y5XnXjg4GNgbtjzrCfAiHUFKPp8UZdCIOG1cOMEHXRGBaBBug5Hy15nHrAJ8b7zOYkduAMlB17sAQeY7ANPBxN8pAliJCWCK2c+HcgAPpwFOz09TYBT11lS5F7c7wEq6ZmpqalEZ3tqxGBmvHbNU3h+3YbP0WVCDRS6zZrQgDFO/2L/0WuvgXK2hx9n9XHm9ATjuxjX06dPE21MYOUoC9nc3NTm5qbq9XpqMOx23xlKdNHr+mhFELOcBGuAQGypp5DRW+yN65if5nNb7gE6c+zAOS2IcsY3l8up2+0GFo9xwyYBJPl+dAmCo1gsqlarBTbUMyHYF4CQ95H00hfG4nrqvcggWcal1EeO/tOf/rR+8zd/U3/wB3+QmpX4sz/7M7344ov6j//4j1QI3DfH7OxsMAIewXmqj42HMAFEKgw6bnfAxqENPr/v9/uJe6FQSjaPOzYYK9DvjyKczCKCIppz+tlTPdSfxGPyNB6/9wjWDQR/Z4yk3uKTOcyjR/xnZ2eJe8YuE55LGuTuPZp1NO/g1tkgALQrLBsuPvUH8PK1iSNujBpAFWENiabT9hian59XoVDQwsJCYIn8+geelVQQV++wYWPAG7MRTiUzJwQPziYCKHFQgIG4oNtrC9PU1LgBB7x7ytg/yw06hsdrFRwY4IxIh2GccUI+f8wL4MtBt18uynp6hD5OYoaU72csDgA8rcfrHagxNnTeHRKCPfNoPQ4O45RyzGh4KnWceHE38wOY8dcA/qUBU9ntdsNBGp7Zwa+fsHNGy9ksmFI/CcyzkwlgHHwvIIrvGieHh4cJZov1z+VyOjg4CNdHDSvzQK+dhcK/xLrngRB2ycEI6S9fc1J4T58+1d7enjY3N7W7u6tut5tIj48SL1/BTjEObB7+kedlfYeVvHgAzf87O+lr6oXoAE7fw4iXpsBGT09Pq91ujx1fvV4P+kLmAJvKczto4nvxXYeHh+HmA88MMAafO+aCz8Zvzs3NqVAoJBg//DA66ffvMXfcpHGZjARRzz//vH7hF35B3/3ud/XzP//zYyfqK1/5ir7xjW/oa1/7mu7cuaPf+Z3fGfseb/DlE+AbmsmVdMEQId6hnN+j6B5FOijDYLlT9buSnJk6OTkvqG00GqHzchoE7jSsbzzSc3GagH87MHJE7EbZ03KenmMD4AQdvMDAMEYp2VWdGgfen2Z8fA5OlY0C6+UsmD8j4NeBjkfw3vDRaXo3ig4kMcyMg7Qfm43nOTg4CFRwGpmfn1epVFK5XA5pOnfEztJg7AgK3JExftaL53bn5OwURi+m9FlHv3cPHXOGKw2TKClR4wO4kQY1PKwJn+2n0WBYAXUYeQx+XEPmIN5ZCZx4NpsNf2NfNptN7e3thRNzfHfMGF8mznigD7BPh4eHAUBJSdaZuUYcDB8fHwf95Jm8KNv3qzMj/kxxwbDX/vlajxN/Ztd/7zjtNpD96nWUvN/3M2AagIyuOqtB/YnfNuCpaQAUOunZAJx0mmAN9snXU1IIaGH1fZ08ZUU9H/bdDxf4nnSdZH15Rhw7n0sDZNJ8+/v72t3d1c7OjtrtdkgVp2Ha/DmcicIPSskaRfYousYzoT+MzfXM7UhMSrD3/BJi5g72mM/GJxeLxVA3NE729/cTp3MpeSCNyV5k/bA9+EmYa54fP+41y24PpqenA0OKnnHCb2ZmJpQ67O/vJ9LTkAheR1cul0eObayX/PjHPz52gpBms6n3vOc9+sxnPqOvfvWr2t/fH8tGobhMkEdhLJYbJRbTHVcc7fsmGsZsALaYSDciHsHAgqC07XZbzWZTjUYjGN9xAvvT7/dD6guHf3BwkChY9fw81D7vlQZgx5XWjWw8Vo+OiVIBUM5C8V1eb0KhcRpxRo+7twBNONIYLPKMGFSn6h10+vFVLzzEaHiKknXyNJdHODCApH7TRFDMRbVaVa/XC4wIDBBrh/N04OEpPHTcDdwwRs7X0dMMzjKdnJxfug3oZ8/467LZbKg9GCdufJhT3wc8C86H+SRN7Sl0DJCUbCTqKQEvnPd0s4McadASo9FohMJUABRODUc2StzpUoOIXZmdnQ172fe8ByaxYBOcOWPunFFwlpf19XlwcOIpLj6HORonzjxLChF17Fx4VsByLpcL8z2sLipm0aSLt0EQKMQAChvn7HScCnTWdpywNuz1uL4NxtuDLU/fOFsT16y53fG5xOmynvSQQr8BqO12W71eL/iGer0eTqlSID1O2Nf4LsboLAvryX5B8H/oTJx29QL7YTpN8Oe1gOxtT8uyj5zViVnYy4TvBkTB6OOD3c6wF53JJTjAdzFeAkBvP4KOe32e2yLGQ+0UINwPymBTc7mclpeXR44tfbfIFPLyyy/rs5/9rKTze/d+4zd+Q3/6p3868j3DUlIoshtgT/e5wWCi44ly4+PoFJbL6wLceQ0zIBSb1ev1hEH3CylHjY/om+fEwIDOcUruvHxsGCIU2SVmntyISxf7aGHQ3RAyFlKis7OzoTfTOPF1Iw9NBMN4qUnxtXaq2Ouz4udmDXhfnFKSkpGv36zuIIT6DyJGxppGiLY5xbm3t5cwAHFdgW9+n39AsRskB1fxWsa1FIAoejPFEROv6ff7oXg/jYEDVGI0PahBl5z6dyfEWsAos57ewsPZIsaMU4ABYy1I1QD6uWwUwEp0yd1YadfQgzP2I2ACJ+zpUk/1DAMy6DZRtKfZEWc4fO8yJ273vBaKz5KUKlDz98HkcfAlTikDejxNTsTPfontblzj5eP0+ivG5ulpT/MSrFGykcvlVKlUUh3Q4Zlh0D2I8vnnOXkebI7POTWW6Kfrnv/bxzc/Px9aqnia99mzZ+p0Omq1WuEHxtRT2OMEXSGFxJq43yBoYCy8HoDJPDDPPKef8qYA28EZwT2fjZ6wrhxc8HIX6kRhptMI80vwzHOgr+hNJpMJpz19TbPZbCJ48ayE67X374pPbbv9hA1DV/3wA4Bvfn5+rB98R0GUJL3wwguSpBdffDE1Fe15aSZWGjgkSWHRPVctXexAPgxAOXDwFJhHfx55uxMEHGxvb2tnZ0eNRiPc/ZW2MNnrQKiVOT4+DukkNrxvODarpwI8GvQfp+DjtCcGmsjNnSOOEPofCntxcVGVSiUcEhglRGVurIkycZBxMTnPyUa9jFb3SNzBk4NFT3s4W8JmdOav3W6r3W6HOry0m59i7sPDw3C5JQwQdT2MydMIDnzRNY8wnaGImR/Wxtk2xuaN9Zgj5p0oLZvNqlKppGITd3d3g+GCMfDaHK9P8PV2XfXj4JlMJlFn6Klm5sn3GfPnegALtbe3p1arpampKRUKhUSdFSzBOOFZ2VMOPNE/n/9YLzwwYwyeUojTruxb5oN5YB8wBzArXo8ZM+tpQBQ6ACuH86WvEWy3gwjG5Hdykop1+zdszeIUs8/BsOCUZ2SckoJzWlpaSgUyAD7O1sGWLC4uBt3wlGSc7vVg2k9mAc7cF8A8lUqlcB0L39Hvn/cSarfbajQa2t3dDQ0iYVi8fjVNrzZsL+DSSw+wMV4c74JdRFecPXQA76UUnplxNif+f3yV+82pqamwBwmQx8nMzMyFefCUooNCvtefZXFxMaEnjCHObnhww0ERT4/C4rfb7XAQDXFbTPZkYWFBpVJp9NjGjv5HkEKhoL/8y7/UCy+8oNdffz1VTYZHCR65S+fFhB4FM2mkSmA5nOFxSpT34XxcqdyJxblUL/amWHBra0s7OzvhiGvazeH1DnyvI2Kvp+CkIc/BZvF8dByFsOHdaACU3IDHuXEMHnlhCuXz+XwAUFwkPUqoO3KwcHx8HJw3YyICcePlETfPFTugYfriDABz6SkY/z5pUPhZr9fV6XQCJZ3GAUuDJoI4ODa3nzC7LH3A2NyY+2bn3w6Iia68Fswjee9K7KcEHXgChtMA4UajoUwmE1oUsI+G1Z3x4zrnJ6Dy+fwF+t9/HFD7HMAiMp8HBwfa29vTzs6Oer1eaK7nc+Tp0lHCIQ2E7yDSdIDnKX/+jd7G4IG1c7vka81edJDkqWppwOQ6YGau45q6y8QDikwmE+rkSCkRMGC30Bf/rwcccSmEgydP9zEX/lpPO8cpaAAU6fGrV6+qUqmkrk18+vSp2u22+v1+cPL5fF7lcjn0FyOd7wy0r5WDf/aJsxhe91MoFAKI8nvtSJPRyoD0nZ809YAyTcbi8PAwMMHsw6Ojo3CY4vDwMNRnATJinQMQsj6sF/YSNt2zOQT2pCo5/eY3ZXggLymkgikVSFPTRpNT9NGDqDjLQgoUYJjP54NeDgNPcTqWtSYtik6AAzioQhDKnHmgChFQKpXGlkS8oyDqd3/3d/WHf/iH+sd//MfUheWkkzCMzqqcnJyEAtAYADhF7PUGl9VyOGhy2o7FcSMqDYr32u22dnZ2QvdZ6EuMwziJozEXUDH049zcnJ49e5Yo1PTWB06tM/Zh4+W7YmfG+Ji/4+PjUOdzdHSkxcVFlctlXbt2TRsbG6lAFEf+iZhIpzmbSGqNMbGOOKa4diYeH/92HWAsHinHFDep2263q2azGU4hEdWlifIR7//kqWV+PLrDwTuoct111m0YII6BC+uKLscpMU/lSYOWGkTSacaGHvgxfwcenv7xOcdAM7aYjfDUTkyZ8zmAGmoUYGmbzWa4s5C0Gyywp6TGCXrAM3uaw+tEPMhxxtNTVjhixIFlzMA4QBqmmw4w+v3BiS8+x4u1R4kz9rOz573FvCeeNKj3jEE+/48zcR2KwZOXCfgcuK6SRnIg5XM9MzOjYrGo9fV1Xbt2TdPT06lAFLaS5pUAnFqtpmq1qkKhkAicHcT52seBlqcn/f+9yJprf0gn7e/v68mTJ/rhD3+onZ2dRH9CWE58lqfARgn1qplMRpVKJfRRwjYzt9gv1gcf6fYGFofxOIByMIud8v5z3toBooD0N76PFgMwweMuV5bOgZGz0v79jIO9mM1mlc/nVSwWL9TEeiDjvo55jm0NjDalD04anJ2dJQ5WMFYwR7lcVrVaHRuovaMgqlKp6Od+7uf09ttv6/nnn0/NRDmlFrMTbEBpMGlMLJvBDQ+fKQ0iDxYKxfb3el2KG7azs/MTUM1mU1tbW9rd3Q3RwOzsbFDIcYKj87oBj/pOTk4SpwO8LxAFdkSjcZTrhpnfY8y9/sJpXAegdCDGuJVKJa2srOjmzZva2NjQ6urq2PGxufwzOWnF91Gk7n1XWEc2kvcq8nG4c/I0E58fpwH5PcaQgk/qahy8pSlolc5rhhqNhh4+fKjHjx9rf39f0uDiVzYsa+VzHYMLB4f+g14408G6ufFxQOwsFJEYAIDmnGn2IHuBmjFP2eDgOXUIYHLWhL/53z3IYB/78/OdGGguX6XQk/oSik6JIEmvY3DTGPBhESxjw3Dy49diOONFRM97Yz31scb7Ml5XnIKDLGnQGBInx+vHCXuP74EpkJRwmh4oup1lr/i/nQ2NGUlnR5kP/s26+slMUtiZTEb5fF7r6+u6ceOGarWams1mKqaGgxTY71KpFIBYrVZTLpcLAM7rWngun9NhqUbXaQeBgGppULD/5MkT/eAHP9CjR48CyOc9XpDNqdS0wRogt1gsqlwuh+CPVOPp6WloyxIf8fexuL8D6GBj40DBi7EJ5AHKjNf7JpXLZS0tLalWqwWGvlarjR2b13iiN35IyE/h9fv90KU8LjL3gNFtKiQDPh7g6evvvebQI+ogvVTi9PQ0AP1xJ/OkdxhEvfLKK9ra2tKbb76pbDarP/7jP9Yrr7wy8j2Li4uBWstkzu/Rmp6eTqShOA4rDZgdLzJEIbwy340EmyCOEDGa0LNshtPT01BTQEqh2WxqamoqdIaNexBdJplMJpx6wHl76iquWcKp0H/HnZV/JlGVMxqMkXF6qtLpUEmhmA8nVS6Xtba2pps3b+rWrVtaXV1VPp8fe4LN0yuZTCZEVNKA1SPP7+32eb0fI/bTJzHYcKDm7Ey8jm4sSePRkkJSKDbs9/upWwBsbm7q7bff1n/913/prbfe0snJiWq1msrlctAFotGnT5+GQlTmG70c5mwui4gZpzNP3lATcMY6ew0TNW3chedzMkyctej1euE5cLbHx8chQnU2FdAI8I+dM3roeufAgcgaHZIU9h0HOE5PT0NxK444m82Go8lpDz+wR2KWz9OjOA3XT9bFA6Z4rfx3cUATAw6vefK5cFaRVCosXxphnngOLmtlXXl+ryeK7aSvuzNQzgDEIArdZY8yn37SCf3L5/NaXV3Vu971Lt28eVP9fj91qxGYg1wup3K5rPX1dd26dUvXrl1TpVLR3Nxc6HtFxoA58QNJrIMHHq4fHpRNT0+r1+uFHn9nZ2fa2dnR9773Pf3gBz/Q3t5e4kCFlxmwb0mPjRPsoPdVy+fzKpVKF26rIJhwm+sMvffrigM0/x16w35we9Tv9wMT1mw21ev1tLCwoEqlovX19QSIShNs8z34P1Lp+Xw+2DEO/AA+qdEk+HYigjUcxo7H+5LvPzg4uFBjBmNHkMbp8tXVVd24cUP5fD6ROhwm7yiIeu211/TNb35TH/nIR/RLv/RLevXVV8e+Z3l5WZlMRru7u8HpE816Lj0+eRBvbD8JgmF3gxlT8KBOz4VKgz4m9BJqNpuhAA1Uz+vTgChpoNTuIOPUHouK8/XiV69ZcIZD0gXFZ3xSsh6LuWFeUahM5rwW5vr167p3754ePHigjY2N8BxpBAMwNTUVPpeThxhsDAPon2eJgZKU7PLszjdO7Z2eniYiGDYgrz04OFCj0QiMBie6MCRpmsFK0ltvvaX//u//1htvvKFHjx6Fdbpx44ZKpZJ6vZ62trYCTcxaujMexig4EPKxesqWNQacMj7mz5kd6VzXoKG5kmecoAelUinBJEmDglBPDUO5s/a+Xm6gWQfX3RjsA14olm+1Wtrd3Q1tRNjzfvR4ZmYmvD5tKoiSAV8bxuU1ZjgoT59SNxXXLfmYYv10vYY1871LAAWo8TosbCAXM48T7Aq6hN0jYPAriPxZYhA1LPB0iQF0DBJh9nwvMpfz8/NaWlrSvXv39Nxzz6lQKOj73/9+aEo5Tki9LC4uhmDv+vXrWlpaCleF9Ho91et1bW1tSTrfCxyugCX3rMZlp7LYXwDAw8PDkA579OiR3n77bW1vb4erwvxEbuyj5ufnU9Ulsl7ValXFYjHoF6k4fAIgAJAnKbDfrAMBe8wMOivooMMLzL0W6unT84uUqUPL5XJaXV3V6uqqyuVyCH7W1tbGriEsodcYAqKYa9LJh4eHajQaoes66UZP38Po+qEOB2msG4F1fFjGMQJ+otFo6OTkROvr67pz547W1tYCgI79tcs7CqIw9jjqNAb89u3bYRMQeXrdgCs6xoLNGuflUQY/2hsXQmIYEUetGBk2G8fIiQyhDKFW0+S6JSUcpZR0Lmw+Chmr1Wow2LBRfL8XU8dz60YPI8488bweuUChE9Vh3G7evKlCoZBoOzBubM4AUv/EuoHw6/V66IDsvTuYRxxzzAJ43QhAGaPgPVCgaSkgpIYCADUzM6N8Pq/FxcUQuaUFUa+//roePXqkt956S9vb2yqVSjo6OtL8/LzW1tYSAJxTH6S4OP3kqQVfJ9e/uJYIHQBA4fSlZEdt9AQjfPXqVa2srKQq+JQUCnL39/cT6UFJicMbzp4ARr19h6cVGLMzbVKytot6BU5N7u7u6vHjx3ry5Ek4kQdI47U4COY7zQlZdyQYXfay72NsS6PRCM6/UCiE18XO0ssOvP6GOXJmmXn2Nfa0LDYL1p0LmdPUJbrt8z3ln0vKBKfi7VWcAWYeEHfO7Ef0AEEHvZM/ukA6f2VlRQ8ePNBP/dRP6fr166Gzd71ev6A3wwTHW61WQxqvWq0GBoqTcq1WKzjDcrmsSqUSnDBACz1ijT1AiQuoW61WsEf7+/vB2QKg2OfoBPMBm4J9HSdkQYrFopaWloLfwS46+O90OsGmOwvI2gE43Ua4X3M7wnqS+qMZ5dTUVGgiCqO2tLSk1dVVVatVXblyRc+enV8mvLy8PBZEYSNgNwm8AYze9Bbfu7W1dQFEsc9Im+JTYmaYMXuWwlk33nt6eqpGo6HNzU11Oh3VajXdvn1bd+/eValUCn5zFJv/joKoj370o/rlX/5lNRoNffjDH9bHPvaxse+5ffu28vl86JQdMzyeGvBJiHP9cRQvKUSQDjj6/X5II6BQGDsiKHfaGG2Uk4sNpcEJm1HiNTzSQMm9boaCvmq1qtXVVT179kzNZjMogTRgqvzobJwqcOaO8RC5YDSIRKTzGrbr16/r/v37un37ttbX11UsFoPTSsNEeRGiR8R+dFY6p2p3NCJrVQAACa5JREFUdnbCHGQymZBOcybK63zcafvpRpwn4ImC0263GzYL48eYFYtFVatVzc/Ph+g/Tb5bkr797W+HuqhOpxNOj2SzWdVqtaAfnsbodDpBT2ESXTednXH9dN3DOfnFuwQYfDZ75cqVK1paWgrpWBrEpQH6N2/eDIwA9Qhx+pzvRIfYF0R8cQoLHccpxQwNeug3sj958kRvv/12cILUrHkk7XMHi5RGvMZrWBkAkSl1JxyYwBi7IfcaIeliyxEH+QCKYUEDtglwBbinwd/6+rrW1tYSNaPDxE9xelqRv3Elil9xAeBnTH5TgqeeGZ+n0J2tgg1mP2JbnCUol8t67rnn9P73v193795Vv9/Xzs6Onjx5kvoid5z88vJyONW3sLCgk5MTNZvN0Cnc7QCn7bxGjJIC1wdsCMXHns5zXeM1EAWeDvI9Kymk1Wu1Wio2sdvt6uTkJIAo1gMdmp2dDc8uSa1WK/hDfIxnJ/AT7DUvEPceeegJgdTBwUGwvwA5fNP6+nq4vBcdTtvwluCA1DX1S9TKPn36NLBP2O5Wq5UgEfzQih8OGuYT3cbAdLvfpk6t3W5re3tbrVZLV65cCf7w6tWrunLlSmha+/8NRH3zm9/Uq6++qocPH4Zc9ThZWVnRlStXAn1PFMhkxSySp/VYkJOTk9C3h8gX5+upQYxcDDSITgBQ7sg5vUB36JOTk8S9UuMEIIYzcYMnDQAgdPf6+now8tvb24kLVzH2XuAafxYbioZiXJTsTpmc73PPPaf3ve99un37tmq1WtgMAKg0TGIul0tsVjb2wsJCSCvhRLlfinmu1WrBWBDJeeoFgbngB7CCA261Won7vySF9Z2dnQ1RPVGP14GlkTfffDPUCPhcT09Pq1QqqVqtKpvN6uDgIDBf1BahozF9zv/HEZTrJwYvvvDawUwmc15zB4C6f/++NjY2tLi4GOpIxskHPvABfe9739P3v/99NZtN9fv9kLom9cu6EEHGhhodjeu9AL6MF11gLWEpYfr29vYkKRSVujFkfvhv2sMd7B3exz7GMXMaliiYtB4AiuPtFKE6kIrF03Re3MqaubPz54IVAShsbGxoeXlZ+Xxe9Xp97Phw/NLgNCJ7ESAF6KALPDUvnB7lv/4Z/jkuBAXooTe4BaRwwOHGjRt6/vnndf/+feXzef3whz/UkydP1G63NT09naqXWSaTUaFQ0MrKilZWVsKBgm63q8ePH+vx48eh9ALnz2lPnL0Hol7cTwoX++TAH5bGfQzsGrbP078nJyfh77VaLZwwGycEW+VyOdhiThzynehdPp/X6enphfsEsQeAOgf0/B0fwN+ZW7IIsL/oK0Dw9u3bunPnjpaXl8NrAZNpxucMkdvybDarlZUV9fv90M7B06u0qximf4ChYfsxriklEOEkPIze5uam2u12AkDduXNH5XI5rOXc3NzIu3LfURCVyWT0uc99Trdu3QqD/rVf+7WR76GR1vLycmgOhzI7W+Pf4YvmUZHXOsW1U54WcgNPpI+joN7Fi9tA7qBpotI0BhzHGxc2SkmHwFHRpaWlEOU6iiad6aeEGLdHwWxmxkUtCazWzMyMrl27pve+97168cUXde/ePVUqFc3MzIRIxWtsxgnPw1wwzrm5OdVqNa2vr+vs7CxclwJYJrIrlUqhdoMTLZ4qkQbdy51d49oWB1A4Ws+x03mdeh+AAMxNGtnZ2QlUMpS6R0R0XebuLA5KcOIMMIWjuuy0E7oQp0dgSKmVYZ4zmUwwcjdv3tS9e/dCOtbTS+PkxRdfVDabVafTCfUkACT0iHqvXC6nK1euJPqD5fP5wEjCYjoI9NQBIIJn63Q62t7e1qNHj1Sv1wMwpaYDXWHf+Rzg/MbJ9PR0YKVx9PzXe4ARnS4sLITO9OgpIMQDKNfROCXrYIT9ytp6WsPrOefm5rS0tKSNjQ2tr6+HeR0HomImTFLQV/4Ok0FQMTU1pd3d3VBIC4ADuDpL6gGV22NAFGvM92BDAT337t3T3bt3Va1Ww12InU4nBABpCq+xjysrK1peXg4HJlqtlvb29vTkyRPt7OyEDAPPu7u7q2azGQIdL/wGKDuD7PVc7n/4PMbGZzmr6MCLmp+pqXT9BOfm5lQsFsNVTblcTteuXdObb74ZahaxF7zWbT9MC7beQZ3XxaJrDqI8wwPoRk9qtZpu3bqlu3fv6vr16wHw0hfL22KMklwulwiEDg8PVa/X1ev1dOXKFV29ejWRwpQGLVbw1/439o/XDvNar73yLBCsGdkI+gbOzs6qVqvp/v37evDggdbW1lQoFML9uIuLi2o0GpeO7R0FUb/yK7/yI7+H1AqnLpgU0lBsYqfBAVJEvkwYERngwSMOKVmjISk4KIADtQhemxMDlvgE0jghd+6bjM/CWLG4GDoijdiJwtA5e4Fj8pSJ19Lg0ACIKysres973qOf+Zmf0XPPPafl5eVA5XqRJc5/nPj8+NiIQldWVoKDgtVotVrq9/sBRJXL5XCjt/c94jPZQMyFd5ylAzlGwQsM6SNTKpXCyTIYiFqtptXV1VQgwwua0TvSWOgoR2Jv3LgRmrN6OpbvxsDGuslrAOswdnxGv98PrB21GNw9dvXqVd26dUsbGxsqlUrKZDIJ8DZO7t+/r4ODg/DMBA9EpDC1nF6hZ44DKX4nDaJNP1Xk4MKZk263G65T6vf74bSOs1iwwV5USgoxjQF3B8R8eBAFoJqamgonyGBrAMIUF3sX5biOyMGwp7R9TkgDefABgCqXy7p69arW1tbC6cqFhQU9fPhw5PhwNs5ASUoAPdcZ9AiAyClW1oQ97SyaO1iCCGcc+Ru6UywWA6N27dq1YNMIpOiHx/Uc4wRnViwWQ62fXzROETQn8wCK1EjRusKLx72guNPpBGDAnnMGCBBPEBHPkadTvQddp9MZyljGAvPEHlpYWAisG72iPANBkT1jmZ6eDkw8ttz3B3tuGOvvZADfkc/ntby8rFu3bunOnTvBtsDks//wU2nG53WhlKxsbW3p1q1bKhaLWllZCUwUNgx7zVwTLJOV8ayF674DX0/Xe8d5amULhYKuX7+ud73rXdrY2FChUAjzBWgeJZl+Giv0/0hee+21/6mvfkflp3/6p4f+fjK+nwy5bHzS//4xTsb3kyH/28cn/e8f42R8P9ly2fj+R0HURCYykYlMZCITmchPqqTLSU1kIhOZyEQmMpGJTCQhExA1kYlMZCITmchEJvJjyARETWQiE5nIRCYykYn8GDIBUROZyEQmMpGJTGQiP4ZMQNREJjKRiUxkIhOZyI8h/wddex0kuImNlAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the results\n", + "fig, ax = plt.subplots(2, 10, figsize=(10, 2.5),\n", + " subplot_kw={'xticks':[], 'yticks':[]},\n", + " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", + "for i in range(10):\n", + " ax[0, i].imshow(faces.data[i].reshape(62, 47), cmap='binary_r')\n", + " ax[1, i].imshow(projected[i].reshape(62, 47), cmap='binary_r')\n", + " \n", + "ax[0, 0].set_ylabel('full-dim\\ninput')\n", + "ax[1, 0].set_ylabel('150-dim\\nreconstruction');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The top row here shows the input images, while the bottom row shows the reconstruction of the images from just 150 of the ~3,000 initial features.\n", + "This visualization makes clear why the PCA feature selection used in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) was so successful: although it reduces the dimensionality of the data by nearly a factor of 20, the projected images contain enough information that we might, by eye, recognize the individuals in each image. This means our classification algorithm only needs to be trained on 150-dimensional data rather than 3,000-dimensional data, which, depending on the particular algorithm we choose, can lead to much more efficient classification." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Summary\n", + "\n", + "In this chapter we explored the use of principal component analysis for dimensionality reduction, visualization of high-dimensional data, noise filtering, and feature selection within high-dimensional data.\n", + "Because of its versatility and interpretability, PCA has been shown to be effective in a wide variety of contexts and disciplines.\n", + "Given any high-dimensional dataset, I tend to start with PCA in order to visualize the relationships between points (as we did with the digits data), to understand the main variance in the data (as we did with the eigenfaces), and to understand the intrinsic dimensionality (by plotting the explained variance ratio).\n", + "Certainly PCA is not useful for every high-dimensional dataset, but it offers a straightforward and efficient path to gaining insight into high-dimensional data.\n", + "\n", + "PCA's main weakness is that it tends to be highly affected by outliers in the data.\n", + "For this reason, several robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components.\n", + "Scikit-Learn includes a number of interesting variants on PCA in the `sklearn.decomposition` submodule; one example is `SparsePCA`, which introduces a regularization term (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)) that serves to enforce sparsity of the components.\n", + "\n", + "In the following chapters, we will look at other unsupervised learning methods that build on some of the ideas of PCA." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3.9.6 64-bit ('3.9.6')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "513788764cd0ec0f97313d5418a13e1ea666d16d72f976a8acadce25a5af2ffc" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.10-Manifold-Learning.ipynb b/notebooks/05.10-Manifold-Learning.ipynb new file mode 100644 index 000000000..40d083ed2 --- /dev/null +++ b/notebooks/05.10-Manifold-Learning.ipynb @@ -0,0 +1,1110 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: Manifold Learning" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the previous chapter we saw how PCA can be used for dimensionality reduction, reducing the number of features of a dataset while maintaining the essential relationships between the points.\n", + "While PCA is flexible, fast, and easily interpretable, it does not perform so well when there are *nonlinear* relationships within the data, some examples of which we will see shortly.\n", + "\n", + "To address this deficiency, we can turn to *manifold learning algorithms*—a class of unsupervised estimators that seek to describe datasets as low-dimensional manifolds embedded in high-dimensional spaces.\n", + "When you think of a manifold, I'd suggest imagining a sheet of paper: this is a two-dimensional object that lives in our familiar three-dimensional world. \n", + "\n", + "In the parlance of manifold learning, you can think of this sheet as a two-dimensional manifold embedded in three-dimensional space. Rotating, reorienting, or stretching the piece of paper in three-dimensional space doesn't change its flat geometry: such operations are akin to linear embeddings.\n", + "If you bend, curl, or crumple the paper, it is still a two-dimensional manifold, but the embedding into the three-dimensional space is no longer linear.\n", + "Manifold learning algorithms seek to learn about the fundamental two-dimensional nature of the paper, even as it is contorted to fill the three-dimensional space.\n", + "\n", + "Here we will examine a number of manifold methods, going most deeply into a subset of these techniques: multidimensional scaling (MDS), locally linear embedding (LLE), and isometric mapping (Isomap).\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Manifold Learning: \"HELLO\"\n", + "\n", + "To make these concepts more clear, let's start by generating some two-dimensional data that we can use to define a manifold.\n", + "Here is a function that will create data in the shape of the word \"HELLO\":" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def make_hello(N=1000, rseed=42):\n", + " # Make a plot with \"HELLO\" text; save as PNG\n", + " fig, ax = plt.subplots(figsize=(4, 1))\n", + " fig.subplots_adjust(left=0, right=1, bottom=0, top=1)\n", + " ax.axis('off')\n", + " ax.text(0.5, 0.4, 'HELLO', va='center', ha='center', weight='bold', size=85)\n", + " fig.savefig('hello.png')\n", + " plt.close(fig)\n", + " \n", + " # Open this PNG and draw random points from it\n", + " from matplotlib.image import imread\n", + " data = imread('hello.png')[::-1, :, 0].T\n", + " rng = np.random.RandomState(rseed)\n", + " X = rng.rand(4 * N, 2)\n", + " i, j = (X * data.shape).astype(int).T\n", + " mask = (data[i, j] < 1)\n", + " X = X[mask]\n", + " X[:, 0] *= (data.shape[0] / data.shape[1])\n", + " X = X[:N]\n", + " return X[np.argsort(X[:, 0])]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's call the function and visualize the resulting data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = make_hello(1000)\n", + "colorize = dict(c=X[:, 0], cmap=plt.cm.get_cmap('rainbow', 5))\n", + "plt.scatter(X[:, 0], X[:, 1], **colorize)\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output is two dimensional, and consists of points drawn in the shape of the word \"HELLO\".\n", + "This data form will help us to see visually what these algorithms are doing." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multidimensional Scaling\n", + "\n", + "Looking at data like this, we can see that the particular choices of *x* and *y* values of the dataset are not the most fundamental description of the data: we can scale, shrink, or rotate the data, and the \"HELLO\" will still be apparent.\n", + "For example, if we use a rotation matrix to rotate the data, the *x* and *y* values change, but the data is still fundamentally the same (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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xVoAvlga6Ltj+oWHmxJX0dnDWr0QkTEZt6nunrNgSkZ59Fm66yQjrwmPSJOFbr64WXx5P6AeHyQT//CeKP7eO1xt9F50ghCXc8+fPZ9q0aUyePJk3m9TKffnll7n00ku57rrruO6669i5c6fhRkokAFU4OEIVvkj8xK1NbiGYYikPqsPx7YaZ0yJsff3EW8LATpCbGv1YDge89ppwW8SbH38UM24twvvL5xO9KgPxs5/FZpcfQvq4V69ezffff89rr72Gw+HgxRdfbLR/8+bN/OUvf2FgorQbkpx02HDxJus4QEXtS7jCADoxgC4U0h41kf3AbU+BnB5o5TtRA3W6CYU1Azb9VxSt6jwc2g80rvKg0Wg+OLCa+mm2osBjE2H2QvBFOfX2eEQH9nHjDDPTLzabCP+LBk3zfxfquqh4aDAhrVyxYgV9+/Zl7ty53HbbbYwdO7bR/i1btvD8888zffp05s+fb7iBEslrrGEf5XjR8KDhwcd6DrCQIv7BMqpo5ciDYCgKnPlLSnNHiqzJyAcQYXZ7v4ID38Lap+CTW2DV41BzyHBzY0b30Sxypl0G/Oni6Fub6TrceSd5L7wQ3kJhNBw4IIpAGZiWDogHQbQPgyAouh48OPH3v/89Bw8e5LnnnmP//v3MmTOHxYsXo9Q64p9++mlmzJhBZmYmd9xxB9OnT2dckydjUVER6enphhsfDk6nk9TUGF7VWoBEtzGe9uno/Nimkh/zqvCoGp1s6Zx2NI8Mr3gZrLK6+bzgAD7V/22q6NDensqIbXkJ/Rl6bOUMPPIyKr7QB9cifmIVxY9rSAc0NYUd3W/EZ4ohq68BRv2e++56EpO/t4tHvoCVe6IeVzOZ8LVty+6FC/F2iLEKYUPcbvqOGoVqs4X97qbTON5HB1BVlAZuFs1kwjF8OHubeCnCxW63MzRAmnxIV0lubi6FhYVYrVYKCwtJSUnh+PHjtG3bFl3Xuf7668nKygLg3HPPZevWrc2EG6B///5RGR8rxcXFrXbtcEl0G+Np37usZxPlaLUytTenhiM5Tm5lNG3IYDfHMHMYH/7dDLoCxzJcmNKt9D8lcT/DHzd9h6qqjSvphUBJyQPXcf/7ABMafVMOQR9jfKiG/Z4dg+HQmubbh3SFtfvBHf5n0BDV50M9dow+zz4Lb7wRo5G1aBr8/e8Rz+SbCrwCeNq0weJyiZDA1FTUnBwyFi6kf/fuUZlWVFQUcF/IOfzQoUNZvnw5uq5z5MgRHA4Hubm5ANTU1DBx4kRsNhu6rrN69Wrp65aETSUONnCgXrTrcOHlKb7kBVaQgglvGIuRmmJkDVXj8ZoyRa2SSHCVB9+veaAy+hls3DjtOvzGn4/tBWkh3EWhCjr5fPChQVE2n30G3brBPfcYMpz52DGRNfnnP8PLL4uFzihFO+S1Qh0wbtw41qxZw5VXXomu6zzwwAN8/PHH2O12pk2bxt13383MmTOxWq2MHDmSc889Ny6GSk4+NnMw6P4DVPIfVpOJlcogfuwsUrH4EjyyVVFg8C2w8s8RnBTiYaRaIKdHTGbFBUsGjH5AxKC7KsU2UyoUnAk3pMDfXwh8bnp6aD+zEU18t2+HK64wNFRPAdi6FV55Bb77zthmw00IK3PyniBPpMsvv5zLL7/cKHskPyGchI5vduHFFcBNUocNN+/32UMbutCFXIOsiwNtCqH/NChZVLuIFyO6Bl0TtNxrTj6c/zfwOsVDy1RbGe9YIbzwWmDXxNEwko2uvfbEv3Udjh8XM/VIqu89+6yIVokHW7bA/Plw553xGR+ZgCNpRbrTxpBAPg8+3GaN//Fd4sd4F14Ip82E1Daxj6X74Ovfw/5vYx8rXphTT4g2iMJLgwaJpJUIqX//eOUVePJJeP994Zro3BmysqB3bxgxAi67TBzjru35+dZbMHgwtG8PEyfCxo2wZk38hNvrFa6SOCJrlUgiQtd1lh/38NI+F3ucGkOyzNzSI5W+mZH/IfamPdmkBnWDRIIPnZ2U0QcDIw7iQffR4kvXYednUBJDSrTPDZv/K5oTJ6LbpCmqCl98IartPfkkVFWFnfBS/5CvqBB+aV1vnNW4Y4f4AuG/fuIJuO46UeypziXy8cewdGn8RLsOIzrDB0HOuCVho+k6U4qqOW9VNS8fcLPsmJcndjsZ8HUFz++JXHxVVGYzikLaGWajO4RbJaFQFOh1EZwRY0q3zwO7lxpjU0tgMsHnn4HHHXmWYh2hUtFdLiguhvvvb+zH1nWRjekzwFUViIwMUbskjkjhlgSlYZj/m4fcfHTU0ywS2avDHVtslLkj/yPMIpVBdMVkgNNEQ6MnbWMep8Vp25/YqgDq4KowyJgW4Lm/wdrvwGZ8DY9GOJ0n3CVNMaIBsD9UVbiDbrwxPuPXIl0lkmbstvtYUubhqd1ONlf7yFLbMdldzSdHPbgD3O8eHa5YW805eWZu7J5K74zwXCc2XHzIJnx+IihySaMSR1g1ikyawji1LxkY1x6qxVj/r9jOV0zQ4XRjbIk3mhdefBpcSfRmFCY6oNx3X3TdciJECreknoNOjSvWVrGhyoergVpWaSov7w8wc2nAinIv35Z7eXKXk1cHZ3F5J2vIc7ZxFCXAbLMKZ1iibUZl5P4OnJ3fK4yjEwxnJZRvJ6YSeokcXdKUsq2iJ2VLkZEhqvyFi8kkRDeKUrK62Yzyhz/EXbRBukoktei6zkWrqyiqbCzakeIDHBpc8301rjCKCulBBKtpYk4gvGis6VyKjTB7OSYSXruYMceKmsCFthridcCEAZDSQuIdTLQVRQi1qoqY68xMEaESKu3fYmm++JiWxrEbbzS0IXAwpHD/RDni0viuwkO5R/ilv6/yscvhi6CSRnDsGjy1O3QB+r509CveKgrmCG5Pt8nHSpKwpLBqFe6DWLBminGSgbb9YFg3mNCvtS0Rfu7Jk0W3m6eegvfeg5KSwEWhFAXS0kSVwldfFQ0XFAVyc+F3v6PsrrtazHQp3CcxPl1nxXEPn5a6qfEKcXT5dK75vpoeS8u5cHU1XZaU84stNRxy+jAZ/Ir3ux8cLD4a3MWSSQoTGIgZFVOt08SMynB6YIrg9tRU+JEk6BTTEJ8LVj4SWzKOyQp9L2+R13NDSMmBvpPgltGQ0sqlaRUFOnSA0aPhttvgvPOEa+Xpp/0fb7WKMMRPP4WpU0VKu9MpEoB+97u4VAEMhPRxn6S8sNfJ7ZtteHXxdLao8Hj/dJaWefik1INLA5cmxPyp3S4+K3XjjLZecgA8Ovxyq42LOwSfDQ6mOwW0ZSuH8KFzCh3pQBbdacPbrA/bZZJ0C5MH14AnVBlRFXqMh6rdYDsswucURbhYUnKFCHYf3QLGGkjvCZDXB85ZA0sCFFLq1g0OHYpv2J6ui9ZoQ4fCrFkntmuaEPCm2Z0ul0iVb4i1dd505Iz7JOTdQy5u3mTDo4slLx/g1ODOLXbeOeLB2SRqTweKbTo+HcwGT9x+sIUXIphLOmfTi3PoTQey+IISFvF92KKNDoPoGoOlrUDV3jDcJBrs+Vx0iHdXg9cmxN6cIQT8h3dg86vgiXNondHk9YH/fSQyHpty773w7bct8xbhcIhZdMMHRI8e/mfPKSnQt2/8bQoDKdxJzhdlHs5cUUH24mOc/nUFHxxxc/uW6IrN+xAx2UajRRAz68TDZ2xlBTsiu4guMjGTiqyuRB2/7akGxzERv73nC1jyqxMFnZKFjh1h714h1KeeKnzHK1fCvHlixn3llS1jR3U1lJWd+H7MGOjUqfkCpMXSsv0vgyCFO4n5vNTNZWuqWFPpo9oHG6t9XFVUzaFYwkIMxqzAqvLwFt/suHmOr1nFroivk+41kUXiNlLwS5czhY/aCDQ3fPn7+CWWxIvcXCHUW7aIVPSRI0/s+9//RLXASFEUKCwM/3ifT9hRh6qKBctzzhGukLqZ9pIl0KVL5PbEASncScyvi+3Ym3ginAn2d5uiQnWYvvMVbKcGV1QRzXaLj60cDN+1kgiY02D0H8BsUHcorx0+vR3WPQe2Fmiu25Dj22HVX2HJL0VbteM/xj6mySQWDqM5b9688I9PT28exte5s3iQHD4Mu3eLaJOzzorcljghFyeTmJKaOC7cGIRXh1FtwqtLXMIRvxmU4fIm32NhAwW0oz+dGUhnzCRoU906MjvDhX+HI+vh6Cbh+ji6MfrxfG44tBZKN8M5D0K6cXVgAlK2Fdb8Q8z6QbhsVv8Nhs0VjY1j4YEHYMWKyOpmqyoMGCBcHeEk0hQUBN7XxoAqjnFAzrgTGK+ms8Pmq4+1BrB5dV7e5+ShbbaEn1umqPD0wAwyw1zxTIllHlF7CQ8a2zjKx2zmGb7CTuiMz1ZHUaHTEDh1uhDBmNFFqOGOjw0YKwSuKtj8ygnRrkNzi+2xMmqUaFPWsye6ySSiPa65RnxlBOi1mZYmqg4G2t+QjAz4xS9it7OFkcKdoCzY76TjknJOX15B5yXlTC2qYm2Fl/yl5dy5xcaDPzrxJIhym4Gf90yhk1XcUDlmuKyDhVVn53Bj9/D9zmdRgMWgGbIHH1U4WcYPhozXImx/P/ZknDp0DY5vM2YsfzjLYeWjsPQ3IkzRH/ajUB28y1FYTJwIO3fyw6pVUFkpfN//+59InvFX19vphFNOgQcf9O8jN5lElmRqqggDvP762G1sYaSrJAH58piH2zbZGvmvPzzq4bOySqq9MVW1iBkFuLSdma/KvZhVhQvbmXlmYAZtrSaeHBCiX2AITqcrh6igiH0AMTdF0NAp5jCXclpM47QYRzYYO156nKJsdF34s21HIdTvqOgZRPXCamFPr4uh8zDxlhEJioKekdFYqO+7D95+u3G8dXo63HAD5OWJmXROjij6dOgQDBwo6oDn5sL+/SJ+O0EWGyNFCncCctummuaLjhrN4q9bg9vyU3j2tNgEOhAKCpcwEAvmqCJL/BFJ9mWrY4nwc80tFH0nK3bUdo9v8Eg3WaHXhMjG033C9WHNDC6s5dvFjDucB2vD2XjVHvh+Puz5Es76Fagxvl317w/LlgmBXrNG+KN//nP47W9PHDNrVuPkmjoGD47t2q2MFO4Ewu3TmLimOuyklZZmUKbK0wMMioAIgI7OWvYY0oLMjMpg4tNlOy70HAeVO8N3l1Tug4LxcObPYeN/4HARoIh2YQOuEUku4aBrUPIWp+z6HHYjHgY9xkL1AajeD6lthZjXHBQt13ILial++PEfYNcS0UQiVoYPh2++iX2cJEMKd4Lg8Wl0/aKCsjg6rhXCd7NkqHBrjxRWVfhw2u3ccUobZnZLQY1zNpsXzZAuNgqiScNpyZRN2Xm4iAbZH6YQ6R7Y/QXknys6yHudIoMyNTcyV0TJW7DrC1R8tam2Pti5+MR+Z/mJf9uPQsVOIfax8ON7xgj3TxQp3AnCH390xFW0AbJMUO0LLd4WBXqkm3i8fwaqolBcfJD+3TvH1bY6zKhkkUpVjH0odaASB8/xNZcxKDkEXFEgNU+UeY2k8FTZFsjoINwjB1bBnqUiLLDTUOh9KViCvCVpXiH+egQ9GDUPoNZWNowyasfnFj7yjATvD5qgSOFOEF4/GP+wNZcmIj4q/ExoUxQRc60qMLmTlWcGZsR9du0PBYUL6M97bMBrwOKkhs77bKQPHUglvHjyVuXw2shEW1FFIo/HBt89CZV7Tpy/83MR0z3mIeE+Aag5DFtfh2MlYlvXs6OrTqhaoPB8OPw9uGvAXRX5GK4qKdxRIoU7QUhtgTU0swrvD8vmyV0O3j/qwaeDSYGh2SZeH5JFfpqKAiitXCJ0IF2wYuILfuAoEXQvCYCKynZKGUgSRBCYI0zb17yw5ytY/2+aLxb6wFEGy+6DIbdCRkf45mHRzADAXetqieZFT/dCz/NFv8w1T0YzgFjkzOsdxbkSKdwGcXw7rHkW9n0DVQfFBKjj6XD+POg2IvT5vypM46ZN0RWHCpc2FpXReWbOaZuNrusccGpYVIWOKYkXedGXjvShA3/hM1wx+rx1AxY6W4ye58OGF8OfBes+KA8Rr+2uEmno5vQTol1/fpSfrSlFZEdW74vufICDq0R4oCRiEu8vNgHxueHwBrGI35DDG+DNq+Bv3eDpfrDqSTjwnViId5aLqKd/j4R3b6yN1grCrO4ppMfpt5GiQoYJXjkjs342rSgK3dJMCSnadSgojKQQNcYO8B40tnIIBxH4cVuLLmeFXlhMbRddxxtvgLRxNQoXktcem2iLC8d4/k8XOeMOwYb/wsd3iPUYzQvtToXrPhc1dP53IXgchHzV3PgfyOoE4x8JfIyqKNxVkMoTOyPLiAwVKdLJqnB7z1Ru7J5C19SWq9vh1XQ+POphY7WX3ukmJneykmqKXIDH0BsNja/ZHvrgIBRzmL0c527Ow5TI9UsUBVRz7QJgANr1h/3LjbtmsGvFC9UK+WNa/ronCfKRF4R9K+HDW2vr1zuFcB/dCP/oBe/Nqq1dH4bI6hp88ziUbgl+3G97pdEjTY3I331JOzPWIHpY4dGZ2rllRbvcozHw6wquW1/Ng9sc3LqphsJl5ex1RL4IpqAwjlO4jwsZQ2/ySA/YFT4UNty8ToCOK4lEVogImAPftowdUaNAbm9QAswLTVbx8Ol+TsuadRIhhTsI3/6fEOymuGsir1qpe+H5M8XDIBC5FpUNY3KZ2MES1i8mQ4UvjnkJVjXVB7x3pGUKLe2w+fjjD3bGrKxkh12jpjb0sMYHR906N22M3odvxcI4TuFOxjEkhqSanZRRk+jd4PtdFXx/tH7plqL9aTDyN1B4oXDDqBYxw1ZM0O0cOOvXMOzO2DMnf8JIV0kQKozJuq7Ha4cPb4M5Qap2ppsUru+WyqelHqpDTFDDSbBUFYLOyI1gS7WXp3Y5+c8BF5qOX1ePT4elZR5cPp2UKFwmDRlLX4rYG9W5CgqHqUrsbjl5vSC9g0h2SUaG3yn89P2miH6YpZvFYmanwWAJo2KfJCRyxh2EnucZP2bp1tDtAS/pYKFDiorFAMFVgCs7x6ehqUfTmbSmimHLK3l+nwuX5l+06/ABU9ZVsy8Kl0lDUjEzgp5RnetD4w3WsiJGn3ncGXlPdAuQrc3gWxovrmZ0hJ7jhYBL0TYMKdxBGP1bsU5kJKo5dLcqk6Lwzdk5TOwQXZHTFBXSVREb/szADLqnxeeV9LEdDj4v80TUdWfxUQ9nflOJPcqO8oep4m98wTr2RR1r4q1d7CwmQDnSRCC1jag3orSEO0GFlJzgyzUB/xBUYWOH0+G8x0VUjCTuSOEOQnpbmLlMvOUZhckaXonijikqbw/L5tF+aZG7OnTINCusHR1ZPWyATVVeflts467NNr485kEP0sPw+b0uHBGGSPuAaq/OGwcj9zPr6LzGGhx4cDfolaMAWU4zPWgTtph78LEy0obELU3nIS0g3Ar0+Rmc/bvAh2R2g07DGv8hqFbR3WbkPXDJczD8LkjLi7OtkjrCmk/Onz+fpUuX4vF4mD59OlOnTq3ft3TpUp555hnMZjNTpkzhqqtCLKwkGT1Gw6+PwJLfQtHzxFwM222DNybDLWtDH1vm1njrsBt3hNd06XDMrXPPVjsfnZUd9nlP7XJwb4kdtyZy8P69z8nYtmammCzke3UyzAr7HT7sPuidoeLQghum1H411XabDzaFcuD74RBVOP3EYutAutfMDZyNCw/lOPgPq/we25BEWKT0oeHEQxoW1KbzKEs6nDEbvv9XfBYkVQsUXgR9JoKiUpXRnxz7j42vZUoR1QdT28DRDbB/pXCFdBslhLuVs2x/qoQU7tWrV/P999/z2muv4XA4ePHFF+v3eTwe5s2bx6JFi0hLS2P69Omcd955tGvXAn3uWpDUHBh9L6x7IbqyDo3QhJ+7Yg/k9gh8mE/XGb2yku1Rlnj1AR+XebjkuyreGZoVNIb6uFvjmT1OHtrmoOGPZ9fg41Ivy5Qc5n5+nM4pKodcGiYFsswKQ3PMLCnz4A2g3wrCXdO0tnimCQZlRT6T9OELGAroU4URKVjohAVXCNFWUejVAguUOjrfspOv++zhLXbRmRwu4lS6ksvXbGclO9DQMaEylj6cRUHjn7HzMMjrC/tXQckbxhk2eI5I7TWdSL452OFicsx9YPdS8DmhTR8YMP3ETLrjGeJL0uqEFO4VK1bQt29f5s6dS01NDffcc0/9vh07dpCfn09OTg4AQ4cOZc2aNVxyySXxs7gBZSWw8wtxX/WbFLwIWqzUGOwOdYcowfFZqYeDTo1YnxNfHvPwh212Hu/vf2FofaWXc1dV4fDpAa/l0FXQYVcDv4jNp/NlmYc0lYDRLxYFciwKXrde/9agINw4V3WJ3P/UhVy/sm1BJb8yExr8/rNJoxKHn6OFaKdgZgzxqZNxiEpWsoNj2NHRKaMGr1l8dvup4L+sZgjdWcc+PLWfuheNpWwjBTODyW88YEo2tD0ldsNMKYACp88WbpimKCboO0l8SRKakMJdXl7OwYMHee6559i/fz9z5sxh8eLFKIpCTU0NWVlZ9cdmZGRQU1Pjd5zi4mLDjNZ1KHqoI3veywVAMet8cAuMeWEvbQc1Drx2Op2GXHvVw13QfdnEVEC+Fq9DZ8ljxznj3qMoin8bv6xIw+nLjPl6Tg2e323nxgbhcy4NvnVYcekKT5VnUOU1RXUdp67j9MGJ/M3GY7h0ndNMdpaTSp3jREGnxq2xbPOPFFojfywNz2jHym5H0NHRVFA1MPkUtrQt53v9IzLdFnqVZ1PdwRFwBUfTdfofyuJA5W4ORGxBcA5m2vm26xF8ih7oY8Gj+/iO3ehNt+NjibuY1B3N493THfvojoIaoa9OB1yWdpRnn4HbmocjpQt6hRkqmv9NGPW3Ei+kfScIKdy5ubkUFhZitVopLCwkJSWF48eP07ZtWzIzM7E16Pdms9kaCXlD+vfvb5jRxe/Avo9EI2uAOlflqrsK+OXBxnH9xcXFhlz7O/+TtyhR2P5qWwZe1JZB1/i38bxSN88WVeOJdcoNuFDp3qcfHx91s6HKx1N7Hbh1IvadN0cJ8O8T25bY0xvt0VCw6QqP2Dryzek5EV+xPzAEO8vYxhYOoqk6TvXEh1Sd4mFDp2PB5U2B7V3sTOwyIuosTH/48PEBXzRYNiXQxxLQPqfV5/9+dXaGQ5G7ShTVQuo599A5rW3IY436W4kXPzX7iooCZ/mGjCoZOnQoy5cvR9d1jhw5gsPhIDc3F4BevXqxZ88eKioqcLvdrF27lsEG9XJzVsCm12DTq+A43njfuhdE9b2meBxwYLUhl2/GKT8TZY+NQvfBuzPhhw/877+gnYX8NJMhGVImIOfT48z4voZHdjio0YwQ7fDQoJkLRge+q/BGHRJowUQxh/Gh+xXAcEatxmlIe7Q6DlHJE3wRcyErUT98Q/OF0/Io487T20MYoi1JLkLqwrhx41izZg1XXnkluq7zwAMP8PHHH2O325k2bRr33nsvs2fPRtd1pkyZQseOHWM2as1z8MkdJ7ojqWaY9BIMukZ87wuQwe2xwbaPoNtI4xe7h9wkyrZW7WuQBq8SVr/UQOgaLLwSJi5r/vxUFYXlI7O58LsqiiqbT7sjaUPWdHEwEVAg6lJPmzkYQLLDx4wp4kbCvtoqg9s4SiZWhpBPe7LwofE/Voct2qF+dxs4wA7KmMu5WOv+RFVzGGc2uILJKs4ZcltYNkmSi7AmdA0XJJty3nnncd55xqUYHt0CH89pvE3zwDvXwo5PRW/UgvNg/7fNZ926BqufBMcxmPicYSYBolfqLUWw9p9Q/Dakt4Mz7xIRJ69dFn12suaGZdf0ZNC2Rgv8AORZVa7oaGV9pSPmRcrWwox4iDbMqDQr4o0i2tR3B56Q3XFCSZwX4Wc+i4KwrunFx8t8y1Fq8OBDAdayl0mcThoWPGE+wRVgBIV8y86Ax2jo2HGzkQMMozb0qF1/4QMMp5HwKVeI8L3OQ41NQpAkDAmXgPP5bwLv27gA3rsBlv5efO+v+JjHDhv+AxW7jbctJQtG3QM3rYKpb8KKefDf8aIDUyzYDlrYusj/vks7WPFXMlvFiGXS+FBnboYJJnW0MCzHTIZJhAZmmaBHmsq/B2VGPX4h7TAF+elVFIbQnXQCp6jqwFJ+wBvmI/F79nGU6vooEB0RCfIBG7HjDnscHfiRI5hD/Ol50dhB2YkNphQYdleDmXcALOmiz2S3s6Von8QkXJGpspIwDtL8+7jrUC0i7DW3p1FWNeerh0RfVn/VAyNFc6sUL4LTpjffd0aOmRu7p/DSfhf2Wm1IN8EVHa0sOuSOKN28JRierTI6z4pN05nSycoF7cRrxDflXjZU+eiVrnJBewumGHxZ3WlDKhZs+PeZ6ehs5CBaGLPgcuy0x/+COoALDzs5xhr2+J1VKyiYUCJy3BzDRieyOUTwJ/7RpvvbD4Dz/w+OrBe9Hks3Na6lrVqhQHZO/ymQcMLdeUjsVfnc1bB3BQyYZoxN/lj/kjGiLdDxOAML2VMDMriycwqvHHChKHBt1xRGtzFzeSc3V6+ribGxl3Gc387Mx8OzsajNf5bReRZG5xnTrFdBYSBdREidn/061M+Mg+FDJ5MTs9IyatjIAbz46EcnKrDzAZswoQR0hejo5BDZqrUOHKEaKybcQez02+neki5m011Hwg9vw+4liDAVDXqMg94TIrJFkpwknHCPfQhK3os9w3f9S5CaC52vMcSsZgRaII2W9CBJfIqicG5bC+e2bSx8Uzqn8NdTffxiq6GxihFhVaBfpon3hmbRM6Pl6iufRUGjBJZgBPJ3tyODQ1RRQFvWsofPKK7vDL+GPfjQal0igXHj403WRWy/ho4Vc1DhDlpiTFFE2dQ+E8FRLnzaZuka+amQcD7uDgNgxgdgirDZdVM8dlj1f+B1xMcTfMokjPv0VJ2OA8M/XNd1ttX42Fjp4f6S1hXtXxemsv6cnBYVbYA2pDOD4SF9xeA3BwYFhTJqeIO1/JOv+ZRivGi1Ui18zIHcH03HqvQ3Mw5BV3KYxUjaE9jXP7xuYTIYphTI7CRF+ydGwgk3QO+L4er3A3c+ChdFBccRY17Pm9LrYmIuOFWHyQqnhflmsPy4hx5LKzh9eQVnrKgKGupnVvC7sBk5/n9QswL39Eqrb0Dc0vQgL+xYbAsmJjCATmTXzsB1fOi48VFGTVj+cBCi3awYVASoKFgxcSmnkUcGt3MuMxiGtcHsuq6Oyhj6RH0dyclNwrlK6vDYYi/opPkgrUN8GqGWvE1swq2IEENFhTMf209W5/yQpxx0alzyXRW2MD+XW7qn8PKB4BXwVMCqitR4f7SzwECzi4K8bF4/5EYDTIooO/C/MzLJsbTes38f5RH9CjqRzVGqm50TyRgqSpC5eBB0aKtkcAodOZOejfzifejIvVzEASoox05HsukQZMFUIklI4V7/XxH21+zvwyRinX1hvJla0mHorWBOj0/YRbQ+blMaTHlV2OeqgL4TYfue8HoxvrjPGbASX0MU4IK2Znqkqzw/MJNZG2oCpoYoiEp9RZW+Zt7WLikK+8a34YeSEvr378p9fXx8dNRNmqowuZOV9sZM56OmBlfYQurGx2K2xpS4Y8HEMPJZz/6IMyTz7FbuyBgbcL+CQjfa0I02Udsn+emQcMKt6/Dx7fifBmmgqs1TqP3Rrh+c/xfYFqcOVYOuhZ1LgoclNsWSDlcuFLP1Ta+K2bYpBQbenUP/P4Q+f59TwxXGG70OfHbMy7Lj3tpkFzOflHn9fqQ+4KxcMzsdGjVeHacmqvqlqLBoaBZqAzdInwwTvygwMO8/RrqSG5EQH6QyquuYUGlDGufTj1PoRA5pfMEPYS2M1lGdEp83P8lPk4TzcTsrgoihHrpfYx1lJSJFPV70nwy9Lqxto1eXYRxkfciSDpcvgOK3YOP/RCihxw7Oclj3cCd+/Dj0NcfmWciI4Dfm0cGhwccBRBsgTYWxbS2UnJvLH3qnMaG9hZ/3TGXTmFxGtonP+oBR5JDGkKYlUOOAD41y7LULmD7OpCcX0q9RKGEoLFrC/alJkpiEm3Fb6yqZxujh8Nhh9VNw4YVGWNUcRYWr3oLdX8KPH0NaG7HAuOdrePd6mtnvscObU/Fb20Rzq7xzPfzyAJiD9KOc0tnKIztMbK02pjySCShIN3FZRytmVeH+PnEsaB4nLmUgOymjXLfHnEpqQiEFC3Y/iT0+dGpwsYVDnE43htGTYfTEh8b/8UXAZCAQZvUqz4HYy/hIJEACzrhNFugxJsDOCP8wXdG9GYdFabGondK+P1z4OJxzv+hoU3OQwNWTgqitowweSRcZn4Gwqgrfnp3DbwtTSYlBpExAW4vCHT1TWXl2NmY/CTOtzWGnxl1bbPRdVs7olZW8e9i/MCooXMUQzJoS082sIJov/JrzGRmgfokHH7s51mibCZUrOAMLJr9p+GZUutGGvuXht5CTSEKRcDNugGs+gX+eBuUNermm5olONxW7w0/O6XGu8bY5yuG1n4mMY9UiaoKfcSNM+Ads/xS+fIjgGRtB0H2w4AK4L0h3nEyzwiP9Mzjg0njlQLD0jcD4EAuSfzs1vZEPO1E46tI4fXkF5R4djw4/2jXWr6/md73TuK9387eCTuRw8c7ulPexsJ9ybLgox964LnYAUjCjodOGdK5iCEv5gW8JnLrrr49lL9pzO2MoYi+VOMhHtPqy4aYbuRTSjhI9nFoOEkl4JKRwW9Lgru1waB3sWgodB0HhBaJ92PzBYDty4ljFLNwL/nzf2z6AtAG59Hso+jKvJe/B8j9D9QHoPgrsZXBgjajqV8f6F+FQkahs6I0xH8ZdA0c3Q4cgCTnF1V7ePBSdaNfx5XEvf9vpYFqXFLqntWzyTDB0XeeuLTWUufVGLyg2H/zpRwdze6SS7ScEMd1rZij96r+vxMESitnMoYDXUoEJDKQLOeSSxsus4gAVQe0L9DDIJZ3xDa4vkcSThBTuOjoPadwaz1XZvBKf7iVgiJzmgY2PdSTHDOc+EPn1v3tadHeveyhsXYRf37vXaWwDB1eIfpTLy2OvTqIDvy1xcN8PDobmmPlgWFaLh/fpus635V6OuDVG5FromKIwdV0N7x72XxnEqipsqvYxKi+wnQ7cLGQdezkWch1AAz5hM/dwYX31v2AoiDR5iaS1SWjhbsqe5f5nzsESdXwulW8eE+VYzRGk0fvc8MX9TWbyLVCJT1Gh21nBj+lgVTEb4OHQAE2H1RVeRn9byQ9jWy6GeI/dx+hvqzji0upT0ie0t7DkWODK1m5Np3Nq8IfLm6xjDyFalzXAiZe17OEHjoQM7zNjOlEfWyJpRRJucTIYGR1EI+qmKGrw9HhFgaoAXWHLd8HBosaV/jQvfHGfcFsYQgQiO2im+HmCMaGDhVSTkd0SYZtN4/vKlos1HrWykv1ODY8u3pg8Orx31BMwK9QEDMsxU5ge2K1ThYO9HI/4+bqe/aQQPPTRiolpDCVPzrglCUDSzLgr98L3L4iSrU3RtdqMSh9+Z8WaT9ThacjxHfDf86Byn2gsolpgwjMweBa8ewNsjTWlvRZTCuT0gOPbCdnmzJIuFjlDYVUVvhyRzaS11Rxyafg0DKnL/eFRD4Nz4h+7vbbCwwFXZAb3ylB5d1jwNPBgIXnB8OBjGPn8yFG/s+5h5HMJA2KqUSKRGElS3InuGvjXmQRNUvG58PvTmFI1hs0Ba4OJkrsGnh0gHgboYobtdcCHt8LWt0SSjM+IonsK5PWGs38FmZ1DH37pc7Vx7GFwapaZbWNz+WZkNhlmY2bfPdJa5nb48njkM/uDTo3KEPn+7cmMuI6IikIfOlBAO0bTCzMqVsxYUEnDws2M4lJOk6ItSSiSYsa98RUhtnqo1SYfoEJmB7AdBUsmFFx5nD4T2lFaLGKuAZbPqxX6Jmge+OYvYpZsSJMEHUq3iAdCOKyYJyJnTr+u+RuCPxRFYZtdw63F2joXLMDlHYNk/xjIgChKwNp98PgOB8+eFvjJZsZEV3LZHyIypA4TCmlYOZtCAMbQhyHks4fjpGGhJ3lSsCUJSVIIt7/GwAHRwFkJg66HvF7w1Z/y2P2WWGzM6Q6DroPNrwU+3VbWuBtUS1JWDF8+INqiXfMJ9Dgn9Dm77VrAyn6RcF/vVFJaKBHn/PZWMlWoicBuDfi2InQ0zcUM4AW+CXqMArQhg/50YiQFZDRIXc8khQGE8XokkbQiSTGdKPshsuO9Dtj8ioi/1lwqrkqx7dg2WPaH4K3Ruo+sbY7dMpPPZnid4iH11nRRcCsUw3LMMdfcTlXgyd1OOiwpZ/FR/35it6bzeamb9w67cGvhK+7mKg/vHHax135CdC2qwtKR2WSYxKJjuObvtfvQQ3woXcllOD1QAziPLJgYQj53Mpbz6ddItCWSZCEpZtxhNRBuQrRlV0vehrb9RAGpbR9GN4YROCvEz13n3gnE2LZmBmWbKarwEuF634lr6eD0AuhMKapm53lt6NjgabDMZuX0xcfxNBj/9CyVPItCYbqJSztYmdDByg67j2/KvXRKUTkrR2XEymp2OU6I/Jg8M0tHZFPu0blhgw100YwBRYi3I8TzwKHB2kofw3OD37YTGMggulLMIVRUOpLNfsrR0BlAF/Jl6VRJkpMUwm1JheDtAIzD64SjG0V2pmppPbeJ5g1v1q8oCkvOymbedgfP7HZwPMzcnLr5aFOtd2jw+A47fz1V+JIPOjXuOpLTLNZiQ7VQ2WXHffx7vxuLAqoimiyYFLB7m5ff/fq4l5s21FDl1fnR5jvxINDFzNusBE6mAjArCjvtoYUbaFbbeiBdQp4jkSQLSeEqGXwTUVV+i7b1ma5BzaHIRbvdqdFdzx8+F2z4D9iPhT42zaTw/05J59hFbdk2NpczskzB2swC0ClFCGxTdOCJXS7mbReZRy/uc4SVWu/RwaWJRcRqP6Jdx8sH3Lx9xNNo9g7ieK8e/Nfs1XUGZSVOer5E0lokhXCP+R1kd4/iRL3+P3FHtcJ1n8HE+eFFhITD8nnwTH+o2h/+Ob3TVe7tlUrfDDVoSskhV/DZ7f0/ONhQ6eGJHUaE14RPsLrhF7Sz0D8rKV4SJZK4khTCbU6F2SshJZuIZt6x9qwMF1Mq9LkYsrvC0FvgV4fg1g1gjrFZjO4Feyl8dEf45/zuBzuzN9kotmkRNtdqztAVVVT4IOZC11FiAtJV0ULtt73SeHOo7MMokUCSCDcIUbxtI/SZEOmZcRQdRcR8nzoZJr/aeNeeL8OIOw+Tbe+Hl35f5tb4v13OsJsJh6KFnntBrz+1s5UD5+fxx77pWBOwbrhE0hokjXCDaFQweDaoCfK2/LMX4J4ymPxK48xMgNRckYZvCLrI6AxFUaW3xWKxm6IgelUaSaoKfaNI1pFITnaSSrgBup4JeitPvBQzdD1L1DUJlKLe7woMnexXByiS1ZDOKSrecIK/DcAK3FOYymUdLFzf1coXZ2UxrbOxdU4sCszOj6Cko0TyEyHphDu7Kwy9mYCWKyYwxaEReWqu8LGntYWz7oSZXwRvzpCSJbIf09rWlpOtPdac7r/CYSi+fxEOfR/8mEHZZvpmmAwp+RoKqwpnt7Hw3vBsXj4ji42VXv53MDaveoZJiLVVgVMzTSwdkdMonlwikQgSxOkQGROehq7DYdkfofqgWIQ0p1Bf1zna5Bt/5BTAef8PBl0b+bn5o+CCx+Cj26kPl/CG2aW+KeU74MVRcOeP4uEViE/OzObKomrWVoqAbiPS4f3h0ODOzdVcvS50ZcKxeSoryrWAUSxmBdpYFNaOziHHrODRoZ1VCrZEEoiwhPuKK64gM1P4BLp168a8efPq9z388MOsW7eOjAzh5H322WfJyorv6r+iwBk3iC8QzQ6ObBQ1t9+dGV00iSlF1MFWTSL55ezfwJjfx576/tVD/gtaBaIu9txfX02vA1Y+ARf/LfD5HVNUlp+dwwGnj+02Hxd9V40rDuLtA/aF+XOd3cbKwiFp/H6bnXcPu0lVFS5pb8alwXGPzug8Mzflp9LGT0syiUTSnJDC7XK50HWdBQsW+N2/ZcsWXnjhBfLy8gw3Llws6dBtBHz9sP/ekyFR4ee7RCNizSP812aDSlgEauAQiFCNkHcvDW+crqkmrIrCkGwT31X4WjVC5Ow2ZtqnqMw/LZP5p7WiIRLJSULIKU5JSQkOh4Mbb7yRmTNnsn79+vp9mqaxZ88eHnjgAa6++moWLVoUT1uDouuw9rnozlVNIgKk+0joMcY40QZoU2jcWAA5+eEdt9vuo/9XFayrbF3RTlVhQodWqtglkZykhJxxp6amMnv2bKZOncru3bu5+eabWbx4MWazGbvdzrXXXsusWbPw+XzMnDmTgQMH0q9f827XxcXFcfkBAFzlJn54sQ3Vh9oReSiHTs4pTvaU7oZS423rd0cWK+/uApoRbgCdHjfspLg4tBP/7iPZlHtS0ML6PHRUCPNYcXzgz/mEI9sMLOhUTknJ0TDHjR6n0xnXeyxWEt0+SHwbpX0nCCncBQUF9OjRA0VRKCgoIDc3l9LSUjp37kxaWhozZ84kLU2EcYwYMYKSkhK/wt2/f4gyd1FSVgL/vhQ8DkK2BvOLonDWLWlxs69/f9j5MhwOGhESTAgbouBY24sRk8RbQjBW7T0eQTcYJaKPzqwoARcaFRQmdjBzXlsrs7qnkGNpF8HI0VNcXBy336ERJLp9kPg2/tTsKyoqCrgv5DRw0aJFPProowAcOXKEmpoa2rdvD8Du3buZPn06Pp8Pj8fDunXrGDBggEFmh8dHc0TjhEgWABuhB6/PbQTtQ34k4b8lrP47LLkn9HHG5q0Ilc41w79Oy+CrEVm0tyqkNTE7wwRvDsnk/eE5/KIwjRy52CiRxIWQM+4rr7yS++67j+nTp6MoCo888ggLFiwgPz+f8ePHM2nSJK666iosFguTJk2iT58+LWE3IFLK93xNzHWkjmwyxJyADLsNihcZ0w7NY4c1/4RxD4MlSLz63B6pPLzdEbLGdXgonN3GxDdn59ZvOXR+G9ZUePHq0CddxaXpdEszoQYLbpdIJIYQUritVitPPPFEo21Dhgyp//dNN93ETTfdZLxl4aCImtlRz7Zr2fsN7PwCCscbY1ZT8kfBWT8X/SwNQRc9NXN7BD7knl5pLClzs+x47EuTKYrGhPaNnxImRWFEm/h3hJdIJM1J6ndZRYHTZogY7FjwOeCTu4yxKRDj50HbUzAkDd7nhqwQbRHNqoInwvT3DBOc39ZMeoO7wqxApqJzWw+Zei6RJApJLdwAFz8JnQeLVPJYKNsKf7LA88Nh5xJDTGuEosCMjyC7m+g+H4uA65pIFgrF0TDfRNJUEbZ3a34qi8/M4vH+6fTLUOmcojCrWwpvdSunrcxklEgShqRMeW9ISjbcuBIOroUPb4HD66MfS/PCobXw2iS4+h3Rd9JI8nqJRJ89X8GxH2HrIti1BMKPKhFYM8Ord3JBOwvb9gZX71QVnh+Uydg8M93SxKC390zj9p4nXCPFxXHKm5dIJFFxUkyjFEWkvBu1yOi1w2e/MWaspqgmKDgPht0Kroq6reGLtjkdhs8NXuCqjj+fkua3A7wCZJog3QTvDsvi2q4p9aItkUgSn6SfcYMIB/z4DmM73hz7wbix/KHrcDBwmGYzVLOYZZ82Hc57OLxzcqwmto/N5br1NXxT7sWswMXtLZybZyHHonB5Jyu5MmRPIkk6Tgrh3v1lsBloZG6IOrLi3BRcUUSNFY8tvOM1Lwy8Ci79Z2SNJLqlmVg2Mic6IyUSSUJyUky3gsUzR7sKWHhBVKdFxODZkR2/+TX4R1+oPhQfeyQSSXJwUgh3z7HRNScIxoFVUVYajIDzH42wDZsuOr5/eGvcTJJIJEnASSHcJquo7GckR7fAXzvC9sXGjtsQS5qo+61aw4/a0L2w/RPQWruTr0QiaTVOCuGG2BseNEX3ic7qC6eA/ZixYzdk3J+g17RyTKnhz75bqK2kRCJJUE4a4e53RfzGLg6jw3q0qCYYfN9R7imDOZsgLUQxPcUk/O+hqgNKJJKTl5NGuE+bAZkh0sCjwecFV7Xx4zbFmgHt+sGsryGjk/9jLOmQ0QF+Nj/+9kgkksTlpAgHBOEvvvV7UXNk68LIzzelAnrzglWqCXpfbIiJYdG+P/zqIGx6FYrmg71MpMm3O0W0VOs/JVQUjUQiOdk5aYQbILMjTH0DvhkCX/2/8KJCUrLB5xFlUo9ugK1vnYittmTA4FnQoWVLjKMoMOga8SWRSCRNOamEu45Rv4V2p4qFRc3jPwFHtcAFj0FWV2hTAJ2Hiu0DroaNC8RM+/TroSBOpV4lEokkWk5K4QbR9FfgPwFH88Cnd5/43pwO0xZBn0vEl0QikSQqJ83iZFMiSmxBFJZ6daLMSpRIJInPSSvc1gwoPB9Qwg961jVYcCHMyxK1uRdcCMe2xc9GiUQiiYaTVrgBJr0E6Z09EZ1TulUk3mhe0VDhhRFgK42TgRKJRBIFJ7VwZ3aEAbeXRVbHpGH2uQ5eBxQ9b7RlEolEEj0ntXAD7FjYJqY63V4nHIqgbrZEIpHEm5NeuL3O2LrzmlKh02CDjJFIJBIDOOmFu9v4qvAPVptEoyhgThFtxiQSiSRROOmFu+/1x8PupaCaRQKOOU10Ue85FmZ/K+qDSCQSSaJw0ibg1GHN1uk5FnYvC3yMooI5Fcb8HkbfBywQpVPDacgrkUgkLc1JL9wAZ9wIe1eIbMmGqGZoPxC6ngmDb4RuZ53YJ0VbIpEkKj8J4T51MnxyJ7gqGm83WeGaj+LfGFgikUiM5KT3cYOoYz1zCWR2AWsmWLMhLQ+mvSNFWyKRJB8/iRk3QJeh8Mt9cGidKOPadXjk9UwkEokkEfhJSZeiQpdhrW2FRCKRxMZPwlUikUgkJxNSuCUSiSTJkMItkUgkSUZYPu4rrriCzMxMALp168a8efPq9y1cuJDXX38ds9nMnDlzGDduXHwslUgkEgkQhnC7XC50XWfBggXN9pWWlrJgwQLeeustXC4XM2bMYNSoUVit1rgYK5FIJJIwXCUlJSU4HA5uvPFGZs6cyfr16+v3bdy4kcGDB2O1WsnKyiI/P5+SkpJ42iuRSCQ/eULOuFNTU5k9ezZTp05l9+7d3HzzzSxevBiz2UxNTQ1ZWVn1x2ZkZFBTU+N3nOLiYuOsjgCn09lq1w6XRLcx0e2DxLcx0e2DxLdR2neCkMJdUFBAjx49UBSFgoICcnNzKS0tpXPnzmRmZmKz2eqPtdlsjYS8If379zfO6ggoLi5utWuHS6LbmOj2QeLbmOj2QeLb+FOzr6gocAeXkK6SRYsW8eijjwJw5MgRampqaN++PQCDBg2iqKgIl8tFdXU1O3bsoG/fvgaZLZFIJBJ/hJxxX3nlldx3331Mnz4dRVF45JFHWLBgAfn5+YwfP57rrruOGTNmoOs6d999NykpKS1ht0QikfxkCSncVquVJ554otG2IUOG1P/7qquu4qqrrjLeMolEIpH4RSbgSCQSSZIhhVsikUiSDCncEolEkmRI4ZZIJJIkQwq3RCKRJBlSuCUSiSTJkMItkUgkSYYUbolEIkkypHBLJBJJkiGFWyKRSJIMKdwSiUSSZCi6ruvxvkiw8oQSiUQi8c/QoUP9bm8R4ZZIJBKJcUhXiUQikSQZUrglEokkyQhZjzuZuOKKK8jMzASgW7duzJs3r37fwoULef311zGbzcyZM4dx48YllH0PP/ww69atIyMjA4Bnn302YBu4eDJ//nyWLl2Kx+Nh+vTpTJ06tX7f0qVLeeaZZzCbzUyZMqVV6rAHs+/ll1/mzTffJC8vD4CHHnqIwsLCFrXv7bff5p133gHA5XJRXFzMN998Q3Z2NtD692Eo+1r7PvR4PNx7770cOHAAVVX505/+RK9ever3J8I9GMrGFrkP9ZMEp9OpT5o0ye++o0eP6hMnTtRdLpdeVVVV/+9EsU/Xdf3qq6/Wjx071nIG+WHVqlX6rbfeqvt8Pr2mpkZ/6qmn6ve53W79/PPP1ysqKnSXy6VPnjxZLy0tTRj7dF3Xf/WrX+mbNm1qUZuC8eCDD+qvv/56/feJcB8Gs0/XW/8+/Pzzz/W77rpL13VdX7FihX7HHXfU70uEezCUjbreMvfhSeMqKSkpweFwcOONNzJz5kzWr19fv2/jxo0MHjwYq9VKVlYW+fn5lJSUJIx9mqaxZ88eHnjgAa6++moWLVrUorbVsWLFCvr27cvcuXO57bbbGDt2bP2+HTt2kJ+fT05ODlarlaFDh7JmzZqEsQ9gy5YtPP/880yfPp358+e3qG1N2bRpE9u3b2fatGn12xLhPgxmXyLchwUFBfh8PjRNo6amBrP5hFMgEe7BUDZCy9yHJ42rJDU1ldmzZzN16lR2797NzTffzOLFizGbzdTU1DR63cvIyKCmpiZh7LPb7Vx77bXMmjULn8/HzJkzGThwIP369WtRG8vLyzl48CDPPfcc+/fvZ86cOSxevBhFURLiMwxmH8Cll17KjBkzyMzM5I477mDZsmWt4hID4dKZO3duo22J8BnW4c++RLgP09PTOXDgAJdccgnl5eU899xz9fsS5fMLZiO0zH140sy4CwoKuOyyy1AUhYKCAnJzcyktLQUgMzMTm81Wf6zNZmtx/3Ew+9LS0pg5cyZpaWlkZmYyYsSIVpmJ5ebmMnr0aKxWK4WFhaSkpHD8+HEgMT7DYPbpus71119PXl4eVquVc889l61bt7aofXVUVVWxa9cuRowY0Wh7InyGENi+RLgPX375ZUaPHs2nn37Ke++9x7333ovL5QIS5/MLZmNL3YcnjXAvWrSIRx99FIAjR45QU1ND+/btARg0aBBFRUW4XC6qq6vZsWMHffv2TRj7du/ezfTp0/H5fHg8HtatW8eAAQNa1D4Qwf7Lly9H13WOHDmCw+EgNzcXgF69erFnzx4qKipwu92sXbuWwYMHJ4x9NTU1TJw4EZvNhq7rrF69moEDB7aofXWsWbOGkSNHNtueCPdhMPsS4T7Mzs6uF+OcnBy8Xi8+nw9IjHswlI0tdR+eNAk4breb++67j4MHD6IoCr/+9a/ZsGED+fn5jB8/noULF/LGG2+g6zq33norF110UULZ98ILL/DJJ59gsViYNGkS06dPb1H76njsscdYvXo1uq5z9913U1FRgd1uZ9q0afUr+rquM2XKFK655pqEsu/dd99lwYIFWK1WRo4cyV133dXi9gG88MILmM1mbrjhBgBeeumlhLkPQ9nX2vehzWbj/vvvp7S0FI/Hw8yZMwES6h4MZWNL3IcnjXBLJBLJT4WTxlUikUgkPxWkcEskEkmSIYVbIpFIkgwp3BKJRJJkSOGWSCSSJEMKt0QikSQZUrglEokkyZDCLZFIJEnG/wen6JHy9XlySQAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def rotate(X, angle):\n", + " theta = np.deg2rad(angle)\n", + " R = [[np.cos(theta), np.sin(theta)],\n", + " [-np.sin(theta), np.cos(theta)]]\n", + " return np.dot(X, R)\n", + " \n", + "X2 = rotate(X, 20) + 5\n", + "plt.scatter(X2[:, 0], X2[:, 1], **colorize)\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This confirms that the *x* and *y* values are not necessarily fundamental to the relationships in the data.\n", + "What *is* fundamental, in this case, is the *distance* between each point within the dataset.\n", + "A common way to represent this is to use a distance matrix: for $N$ points, we construct an $N \\times N$ array such that entry $(i, j)$ contains the distance between point $i$ and point $j$.\n", + "Let's use Scikit-Learn's efficient `pairwise_distances` function to do this for our original data:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1000, 1000)" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.metrics import pairwise_distances\n", + "D = pairwise_distances(X)\n", + "D.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As promised, for our *N*=1,000 points, we obtain a 1000 × 1000 matrix, which can be visualized as shown here (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(D, zorder=2, cmap='viridis', interpolation='nearest')\n", + "plt.colorbar();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we similarly construct a distance matrix for our rotated and translated data, we see that it is the same:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D2 = pairwise_distances(X2)\n", + "np.allclose(D, D2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This distance matrix gives us a representation of our data that is invariant to rotations and translations, but the visualization of the matrix in the following figure is not entirely intuitive.\n", + "In the representation shown there, we have lost any visible sign of the interesting structure in the data: the \"HELLO\" that we saw before.\n", + "\n", + "Further, while computing this distance matrix from the (*x*, *y*) coordinates is straightforward, transforming the distances back into *x* and *y* coordinates is rather difficult.\n", + "This is exactly what the multidimensional scaling algorithm aims to do: given a distance matrix between points, it recovers a $D$-dimensional coordinate representation of the data.\n", + "Let's see how it works for our distance matrix, using the `precomputed` dissimilarity to specify that we are passing a distance matrix (the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.manifold import MDS\n", + "model = MDS(n_components=2, dissimilarity='precomputed', random_state=1701)\n", + "out = model.fit_transform(D)\n", + "plt.scatter(out[:, 0], out[:, 1], **colorize)\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The MDS algorithm recovers one of the possible two-dimensional coordinate representations of our data, using *only* the $N\\times N$ distance matrix describing the relationship between the data points." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### MDS as Manifold Learning\n", + "\n", + "The usefulness of this becomes more apparent when we consider the fact that distance matrices can be computed from data in *any* dimension.\n", + "So, for example, instead of simply rotating the data in the two-dimensional plane, we can project it into three dimensions using the following function (essentially a three-dimensional generalization of the rotation matrix used earlier):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1000, 3)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def random_projection(X, dimension=3, rseed=42):\n", + " assert dimension >= X.shape[1]\n", + " rng = np.random.RandomState(rseed)\n", + " C = rng.randn(dimension, dimension)\n", + " e, V = np.linalg.eigh(np.dot(C, C.T))\n", + " return np.dot(X, V[:X.shape[1]])\n", + " \n", + "X3 = random_projection(X, 3)\n", + "X3.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's visualize these points to see what we're working with (the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits import mplot3d\n", + "ax = plt.axes(projection='3d')\n", + "ax.scatter3D(X3[:, 0], X3[:, 1], X3[:, 2],\n", + " **colorize);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now ask the `MDS` estimator to input this three-dimensional data, compute the distance matrix, and then determine the optimal two-dimensional embedding for this distance matrix.\n", + "The result recovers a representation of the original data, as shown in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "model = MDS(n_components=2, random_state=1701)\n", + "out3 = model.fit_transform(X3)\n", + "plt.scatter(out3[:, 0], out3[:, 1], **colorize)\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is essentially the goal of a manifold learning estimator: given high-dimensional embedded data, it seeks a low-dimensional representation of the data that preserves certain relationships within the data.\n", + "In the case of MDS, the quantity preserved is the distance between every pair of points." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Nonlinear Embeddings: Where MDS Fails\n", + "\n", + "Our discussion thus far has considered *linear* embeddings, which essentially consist of rotations, translations, and scalings of data into higher-dimensional spaces.\n", + "Where MDS breaks down is when the embedding is nonlinear—that is, when it goes beyond this simple set of operations.\n", + "Consider the following embedding, which takes the input and contorts it into an \"S\" shape in three dimensions:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def make_hello_s_curve(X):\n", + " t = (X[:, 0] - 2) * 0.75 * np.pi\n", + " x = np.sin(t)\n", + " y = X[:, 1]\n", + " z = np.sign(t) * (np.cos(t) - 1)\n", + " return np.vstack((x, y, z)).T\n", + "\n", + "XS = make_hello_s_curve(X)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is again three-dimensional data, but as we can see in the following figure the embedding is much more complicated:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits import mplot3d\n", + "ax = plt.axes(projection='3d')\n", + "ax.scatter3D(XS[:, 0], XS[:, 1], XS[:, 2],\n", + " **colorize);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The fundamental relationships between the data points are still there, but this time the data has been transformed in a nonlinear way: it has been wrapped up into the shape of an \"S.\"\n", + "\n", + "If we try a simple MDS algorithm on this data, it is not able to \"unwrap\" this nonlinear embedding, and we lose track of the fundamental relationships in the embedded manifold (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.manifold import MDS\n", + "model = MDS(n_components=2, random_state=2)\n", + "outS = model.fit_transform(XS)\n", + "plt.scatter(outS[:, 0], outS[:, 1], **colorize)\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The best two-dimensional *linear* embedding does not unwrap the S-curve, but instead discards the original y-axis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Nonlinear Manifolds: Locally Linear Embedding\n", + "\n", + "How can we move forward here? Stepping back, we can see that the source of the problem is that MDS tries to preserve distances between faraway points when constructing the embedding.\n", + "But what if we instead modified the algorithm such that it only preserves distances between nearby points?\n", + "The resulting embedding would be closer to what we want.\n", + "\n", + "Visually, we can think of it as illustrated in this figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![(LLE vs MDS linkages)](images/05.10-LLE-vs-MDS.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#LLE-vs-MDS-Linkages)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here each faint line represents a distance that should be preserved in the embedding.\n", + "On the left is a representation of the model used by MDS: it tries to preserve the distances between each pair of points in the dataset.\n", + "On the right is a representation of the model used by a manifold learning algorithm called *locally linear embedding*: rather than preserving *all* distances, it instead tries to preserve only the distances between *neighboring points* (in this case, the nearest 100 neighbors of each point).\n", + "\n", + "Thinking about the left panel, we can see why MDS fails: there is no way to unroll this data while adequately preserving the length of every line drawn between the two points.\n", + "For the right panel, on the other hand, things look a bit more optimistic. We could imagine unrolling the data in a way that keeps the lengths of the lines approximately the same.\n", + "This is precisely what LLE does, through a global optimization of a cost function reflecting this logic.\n", + "\n", + "LLE comes in a number of flavors; here we will use the *modified LLE* algorithm to recover the embedded two-dimensional manifold.\n", + "In general, modified LLE does better than other flavors of the algorithm at recovering well-defined manifolds with very little distortion (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.manifold import LocallyLinearEmbedding\n", + "model = LocallyLinearEmbedding(\n", + " n_neighbors=100, n_components=2,\n", + " method='modified', eigen_solver='dense')\n", + "out = model.fit_transform(XS)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.scatter(out[:, 0], out[:, 1], **colorize)\n", + "ax.set_ylim(0.15, -0.15);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result remains somewhat distorted compared to our original manifold, but captures the essential relationships in the data!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Some Thoughts on Manifold Methods" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compelling as these examples may be, in practice manifold learning techniques tend to be finicky enough that they are rarely used for anything more than simple qualitative visualization of high-dimensional data.\n", + "\n", + "The following are some of the particular challenges of manifold learning, which all contrast poorly with PCA:\n", + "\n", + "- In manifold learning, there is no good framework for handling missing data. In contrast, there are straightforward iterative approaches for dealing with missing data in PCA.\n", + "- In manifold learning, the presence of noise in the data can \"short-circuit\" the manifold and drastically change the embedding. In contrast, PCA naturally filters noise from the most important components.\n", + "- The manifold embedding result is generally highly dependent on the number of neighbors chosen, and there is generally no solid quantitative way to choose an optimal number of neighbors. In contrast, PCA does not involve such a choice.\n", + "- In manifold learning, the globally optimal number of output dimensions is difficult to determine. In contrast, PCA lets you find the number of output dimensions based on the explained variance.\n", + "- In manifold learning, the meaning of the embedded dimensions is not always clear. In PCA, the principal components have a very clear meaning.\n", + "- In manifold learning, the computational expense of manifold methods scales as $O[N^2]$ or $O[N^3]$. For PCA, there exist randomized approaches that are generally much faster (though see the [*megaman* package](https://github.com/mmp2/megaman) for some more scalable implementations of manifold learning).\n", + "\n", + "With all that on the table, the only clear advantage of manifold learning methods over PCA is their ability to preserve nonlinear relationships in the data; for that reason I tend to explore data with manifold methods only after first exploring it with PCA.\n", + "\n", + "Scikit-Learn implements several common variants of manifold learning beyond LLE and Isomap (which we've used in a few of the previous chapters and will look at in the next section): the Scikit-Learn documentation has a [nice discussion and comparison of them](http://scikit-learn.org/stable/modules/manifold.html).\n", + "Based on my own experience, I would give the following recommendations:\n", + "\n", + "- For toy problems such as the S-curve we saw before, LLE and its variants (especially modified LLE) perform very well. This is implemented in `sklearn.manifold.LocallyLinearEmbedding`.\n", + "- For high-dimensional data from real-world sources, LLE often produces poor results, and Isomap seems to generally lead to more meaningful embeddings. This is implemented in `sklearn.manifold.Isomap`.\n", + "- For data that is highly clustered, *t-distributed stochastic neighbor embedding* (t-SNE) seems to work very well, though it can be very slow compared to other methods. This is implemented in `sklearn.manifold.TSNE`.\n", + "\n", + "If you're interested in getting a feel for how these work, I'd suggest running each of the methods on the data in this section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Isomap on Faces\n", + "\n", + "One place manifold learning is often used is in understanding the relationship between high-dimensional data points.\n", + "A common case of high-dimensional data is images: for example, a set of images with 1,000 pixels each can be thought of as a collection of points in 1,000 dimensions, with the brightness of each pixel in each image defining the coordinate in that dimension.\n", + "\n", + "To illustrate, let's apply Isomap on some data from the Labeled Faces in the Wild dataset, which we previously saw in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) and [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb).\n", + "Running this command will download the dataset and cache it in your home directory for later use:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(2370, 2914)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import fetch_lfw_people\n", + "faces = fetch_lfw_people(min_faces_per_person=30)\n", + "faces.data.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have 2,370 images, each with 2,914 pixels.\n", + "In other words, the images can be thought of as data points in a 2,914-dimensional space!\n", + "\n", + "Let's display several of these images to remind us what we're working with (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(4, 8, subplot_kw=dict(xticks=[], yticks=[]))\n", + "for i, axi in enumerate(ax.flat):\n", + " axi.imshow(faces.images[i], cmap='gray')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we encountered this data in [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb), our goal was essentially compression: to use the components to reconstruct the inputs from the lower-dimensional representation.\n", + "\n", + "PCA is versatile enough that we can also use it in this context, where we would like to plot a low-dimensional embedding of the 2,914-dimensional data to learn the fundamental relationships between the images. Let's again look at the explained variance ratio, which will give us an idea of how many linear features are required to describe the data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.decomposition import PCA\n", + "model = PCA(100, svd_solver='randomized').fit(faces.data)\n", + "plt.plot(np.cumsum(model.explained_variance_ratio_))\n", + "plt.xlabel('n components')\n", + "plt.ylabel('cumulative variance');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that for this data, nearly 100 components are required to preserve 90% of the variance. This tells us that the data is intrinsically very high-dimensional—it can't be described linearly with just a few components.\n", + "\n", + "When this is the case, nonlinear manifold embeddings like LLE and Isomap may be helpful.\n", + "We can compute an Isomap embedding on these faces using the same pattern shown before:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(2370, 2)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.manifold import Isomap\n", + "model = Isomap(n_components=2)\n", + "proj = model.fit_transform(faces.data)\n", + "proj.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output is a two-dimensional projection of all the input images.\n", + "To get a better idea of what the projection tells us, let's define a function that will output image thumbnails at the locations of the projections:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from matplotlib import offsetbox\n", + "\n", + "def plot_components(data, model, images=None, ax=None,\n", + " thumb_frac=0.05, cmap='gray'):\n", + " ax = ax or plt.gca()\n", + " \n", + " proj = model.fit_transform(data)\n", + " ax.plot(proj[:, 0], proj[:, 1], '.k')\n", + " \n", + " if images is not None:\n", + " min_dist_2 = (thumb_frac * max(proj.max(0) - proj.min(0))) ** 2\n", + " shown_images = np.array([2 * proj.max(0)])\n", + " for i in range(data.shape[0]):\n", + " dist = np.sum((proj[i] - shown_images) ** 2, 1)\n", + " if np.min(dist) < min_dist_2:\n", + " # don't show points that are too close\n", + " continue\n", + " shown_images = np.vstack([shown_images, proj[i]])\n", + " imagebox = offsetbox.AnnotationBbox(\n", + " offsetbox.OffsetImage(images[i], cmap=cmap),\n", + " proj[i])\n", + " ax.add_artist(imagebox)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling this function now, we see the result in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(10, 10))\n", + "plot_components(faces.data,\n", + " model=Isomap(n_components=2),\n", + " images=faces.images[:, ::2, ::2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is interesting. The first two Isomap dimensions seem to describe global image features: the overall brightness of the image from left to right, and the general orientation of the face from bottom to top.\n", + "This gives us a nice visual indication of some of the fundamental features in our data.\n", + "\n", + "From here, we could then go on to classify this data (perhaps using manifold features as inputs to the classification algorithm) as we did in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Visualizing Structure in Digits\n", + "\n", + "As another example of using manifold learning for visualization, let's take a look at the MNIST handwritten digits dataset.\n", + "This is similar to the digits dataset we saw in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb), but with many more pixels per image.\n", + "It can be downloaded from http://openml.org/ with the Scikit-Learn utility:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(70000, 784)" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import fetch_openml\n", + "mnist = fetch_openml('mnist_784')\n", + "mnist.data.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The dataset consists of 70,000 images, each with 784 pixels (i.e., the images are 28 × 28).\n", + "As before, we can take a look at the first few images (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "mnist_data = np.asarray(mnist.data)\n", + "mnist_target = np.asarray(mnist.target, dtype=int)\n", + "\n", + "fig, ax = plt.subplots(6, 8, subplot_kw=dict(xticks=[], yticks=[]))\n", + "for i, axi in enumerate(ax.flat):\n", + " axi.imshow(mnist_data[1250 * i].reshape(28, 28), cmap='gray_r')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us an idea of the variety of handwriting styles in the dataset.\n", + "\n", + "Let's compute a manifold learning projection across the data.\n", + "For speed here, we'll only use 1/30 of the data, which is about ~2,000 points\n", + "(because of the relatively poor scaling of manifold learning, I find that a few thousand samples is a good number to start with for relatively quick exploration before moving to a full calculation). the following figure shows the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Use only 1/30 of the data: full dataset takes a long time!\n", + "data = mnist_data[::30]\n", + "target = mnist_target[::30]\n", + "\n", + "model = Isomap(n_components=2)\n", + "proj = model.fit_transform(data)\n", + "\n", + "plt.scatter(proj[:, 0], proj[:, 1], c=target, cmap=plt.cm.get_cmap('jet', 10))\n", + "plt.colorbar(ticks=range(10))\n", + "plt.clim(-0.5, 9.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting scatter plot shows some of the relationships between the data points, but is a bit crowded.\n", + "We can gain more insight by looking at just a single number at a time (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Choose 1/4 of the \"1\" digits to project\n", + "data = mnist_data[mnist_target == 1][::4]\n", + "\n", + "fig, ax = plt.subplots(figsize=(10, 10))\n", + "model = Isomap(n_neighbors=5, n_components=2, eigen_solver='dense')\n", + "plot_components(data, model, images=data.reshape((-1, 28, 28)),\n", + " ax=ax, thumb_frac=0.05, cmap='gray_r')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result gives you an idea of the variety of forms that the number 1 can take within the dataset.\n", + "The data lies along a broad curve in the projected space, which appears to trace the orientation of the digit.\n", + "As you move up the plot, you find 1s that have hats and/or bases, though these are very sparse within the dataset.\n", + "The projection lets us identify outliers that have data issues: for example, pieces of the neighboring digits that snuck into the extracted images.\n", + "\n", + "Now, this in itself may not be useful for the task of classifying digits, but it does help us get an understanding of the data, and may give us ideas about how to move forward—such as how we might want to preprocess the data before building a classification pipeline." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.11-K-Means.ipynb b/notebooks/05.11-K-Means.ipynb new file mode 100644 index 000000000..78e5feeb4 --- /dev/null +++ b/notebooks/05.11-K-Means.ipynb @@ -0,0 +1,1045 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: k-Means Clustering" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the previous chapters we explored unsupervised machine learning models for dimensionality reduction.\n", + "Now we will move on to another class of unsupervised machine learning models: clustering algorithms.\n", + "Clustering algorithms seek to learn, from the properties of the data, an optimal division or discrete labeling of groups of points.\n", + "\n", + "Many clustering algorithms are available in Scikit-Learn and elsewhere, but perhaps the simplest to understand is an algorithm known as *k-means clustering*, which is implemented in `sklearn.cluster.KMeans`.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introducing k-Means" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *k*-means algorithm searches for a predetermined number of clusters within an unlabeled multidimensional dataset.\n", + "It accomplishes this using a simple conception of what the optimal clustering looks like:\n", + "\n", + "- The *cluster center* is the arithmetic mean of all the points belonging to the cluster.\n", + "- Each point is closer to its own cluster center than to other cluster centers.\n", + "\n", + "Those two assumptions are the basis of the *k*-means model.\n", + "We will soon dive into exactly *how* the algorithm reaches this solution, but for now let's take a look at a simple dataset and see the *k*-means result.\n", + "\n", + "First, let's generate a two-dimensional dataset containing four distinct blobs.\n", + "To emphasize that this is an unsupervised algorithm, we will leave the labels out of the visualization (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_blobs\n", + "X, y_true = make_blobs(n_samples=300, centers=4,\n", + " cluster_std=0.60, random_state=0)\n", + "plt.scatter(X[:, 0], X[:, 1], s=50);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By eye, it is relatively easy to pick out the four clusters.\n", + "The *k*-means algorithm does this automatically, and in Scikit-Learn uses the typical estimator API:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.cluster import KMeans\n", + "kmeans = KMeans(n_clusters=4)\n", + "kmeans.fit(X)\n", + "y_kmeans = kmeans.predict(X)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's visualize the results by plotting the data colored by these labels (the following figure).\n", + "We will also plot the cluster centers as determined by the *k*-means estimator:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(X[:, 0], X[:, 1], c=y_kmeans, s=50, cmap='viridis')\n", + "\n", + "centers = kmeans.cluster_centers_\n", + "plt.scatter(centers[:, 0], centers[:, 1], c='black', s=200);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The good news is that the *k*-means algorithm (at least in this simple case) assigns the points to clusters very similarly to how we might assign them by eye.\n", + "But you might wonder how this algorithm finds these clusters so quickly: after all, the number of possible combinations of cluster assignments is exponential in the number of data points—an exhaustive search would be very, very costly.\n", + "Fortunately for us, such an exhaustive search is not necessary: instead, the typical approach to *k*-means involves an intuitive iterative approach known as *expectation–maximization*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Expectation–Maximization" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Expectation–maximization (E–M) is a powerful algorithm that comes up in a variety of contexts within data science.\n", + "*k*-means is a particularly simple and easy-to-understand application of the algorithm, and we will walk through it briefly here.\n", + "In short, the expectation–maximization approach here consists of the following procedure:\n", + "\n", + "1. Guess some cluster centers.\n", + "2. Repeat until converged:\n", + " 1. *E-step*: Assign points to the nearest cluster center.\n", + " 2. *M-step*: Set the cluster centers to the mean of their assigned points.\n", + "\n", + "Here the *E-step* or *expectation step* is so named because it involves updating our expectation of which cluster each point belongs to.\n", + "The *M-step* or *maximization step* is so named because it involves maximizing some fitness function that defines the locations of the cluster centers—in this case, that maximization is accomplished by taking a simple mean of the data in each cluster.\n", + "\n", + "The literature about this algorithm is vast, but can be summarized as follows: under typical circumstances, each repetition of the E-step and M-step will always result in a better estimate of the cluster characteristics.\n", + "\n", + "We can visualize the algorithm as shown in the following figure.\n", + "For the particular initialization shown here, the clusters converge in just three iterations.\n", + "(For an interactive version of this figure, refer to the code in the online [appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Interactive-K-Means).)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![(run code in Appendix to generate image)](images/05.11-expectation-maximization.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Expectation-Maximization)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *k*-means algorithm is simple enough that we can write it in a few lines of code.\n", + "The following is a very basic implementation (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.metrics import pairwise_distances_argmin\n", + "\n", + "def find_clusters(X, n_clusters, rseed=2):\n", + " # 1. Randomly choose clusters\n", + " rng = np.random.RandomState(rseed)\n", + " i = rng.permutation(X.shape[0])[:n_clusters]\n", + " centers = X[i]\n", + " \n", + " while True:\n", + " # 2a. Assign labels based on closest center\n", + " labels = pairwise_distances_argmin(X, centers)\n", + " \n", + " # 2b. Find new centers from means of points\n", + " new_centers = np.array([X[labels == i].mean(0)\n", + " for i in range(n_clusters)])\n", + " \n", + " # 2c. Check for convergence\n", + " if np.all(centers == new_centers):\n", + " break\n", + " centers = new_centers\n", + " \n", + " return centers, labels\n", + "\n", + "centers, labels = find_clusters(X, 4)\n", + "plt.scatter(X[:, 0], X[:, 1], c=labels,\n", + " s=50, cmap='viridis');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Most well-tested implementations will do a bit more than this under the hood, but the preceding function gives the gist of the expectation–maximization approach." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a few caveats to be aware of when using the expectation–maximization algorithm:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### The globally optimal result may not be achieved\n", + "First, although the E–M procedure is guaranteed to improve the result in each step, there is no assurance that it will lead to the *global* best solution.\n", + "For example, if we use a different random seed in our simple procedure, the particular starting guesses lead to poor results (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "centers, labels = find_clusters(X, 4, rseed=0)\n", + "plt.scatter(X[:, 0], X[:, 1], c=labels,\n", + " s=50, cmap='viridis');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the E–M approach has converged, but has not converged to a globally optimal configuration. For this reason, it is common for the algorithm to be run for multiple starting guesses, as indeed Scikit-Learn does by default (the number is set by the ``n_init`` parameter, which defaults to 10)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### The number of clusters must be selected beforehand\n", + "Another common challenge with *k*-means is that you must tell it how many clusters you expect: it cannot learn the number of clusters from the data.\n", + "For example, if we ask the algorithm to identify six clusters, it will happily proceed and find the best six clusters, as shown in Figure 47-6:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "labels = KMeans(6, random_state=0).fit_predict(X)\n", + "plt.scatter(X[:, 0], X[:, 1], c=labels,\n", + " s=50, cmap='viridis');" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whether the result is meaningful is a question that is difficult to answer definitively; one approach that is rather intuitive, but that we won't discuss further here, is called [silhouette analysis](http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html).\n", + "\n", + "Alternatively, you might use a more complicated clustering algorithm that has a better quantitative measure of the fitness per number of clusters (e.g., Gaussian mixture models; see [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb)) or which *can* choose a suitable number of clusters (e.g., DBSCAN, mean-shift, or affinity propagation, all available in the `sklearn.cluster` submodule)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### k-means is limited to linear cluster boundaries\n", + "The fundamental model assumptions of *k*-means (points will be closer to their own cluster center than to others) means that the algorithm will often be ineffective if the clusters have complicated geometries.\n", + "\n", + "In particular, the boundaries between *k*-means clusters will always be linear, which means that it will fail for more complicated boundaries.\n", + "Consider the following data, along with the cluster labels found by the typical *k*-means approach (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.datasets import make_moons\n", + "X, y = make_moons(200, noise=.05, random_state=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "labels = KMeans(2, random_state=0).fit_predict(X)\n", + "plt.scatter(X[:, 0], X[:, 1], c=labels,\n", + " s=50, cmap='viridis');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This situation is reminiscent of the discussion in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb), where we used a kernel transformation to project the data into a higher dimension where a linear separation is possible.\n", + "We might imagine using the same trick to allow *k*-means to discover non-linear boundaries.\n", + "\n", + "One version of this kernelized *k*-means is implemented in Scikit-Learn within the ``SpectralClustering`` estimator.\n", + "It uses the graph of nearest neighbors to compute a higher-dimensional representation of the data, and then assigns labels using a *k*-means algorithm (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.cluster import SpectralClustering\n", + "model = SpectralClustering(n_clusters=2, affinity='nearest_neighbors',\n", + " assign_labels='kmeans')\n", + "labels = model.fit_predict(X)\n", + "plt.scatter(X[:, 0], X[:, 1], c=labels,\n", + " s=50, cmap='viridis');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that with this kernel transform approach, the kernelized *k*-means is able to find the more complicated nonlinear boundaries between clusters." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### k-means can be slow for large numbers of samples\n", + "Because each iteration of *k*-means must access every point in the dataset, the algorithm can be relatively slow as the number of samples grows.\n", + "You might wonder if this requirement to use all data at each iteration can be relaxed; for example, you might just use a subset of the data to update the cluster centers at each step.\n", + "This is the idea behind batch-based *k*-means algorithms, one form of which is implemented in `sklearn.cluster.MiniBatchKMeans`.\n", + "The interface for this is the same as for standard `KMeans`; we will see an example of its use as we continue our discussion." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Examples\n", + "\n", + "Being careful about these limitations of the algorithm, we can use *k*-means to our advantage in a variety of situations.\n", + "We'll now take a look at a couple of examples." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 1: k-Means on Digits\n", + "\n", + "To start, let's take a look at applying *k*-means on the same simple digits data that we saw in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) and [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb).\n", + "Here we will attempt to use *k*-means to try to identify similar digits *without using the original label information*; this might be similar to a first step in extracting meaning from a new dataset about which you don't have any *a priori* label information.\n", + "\n", + "We will start by loading the dataset, then find the clusters.\n", + "Recall that the digits dataset consists of 1,797 samples with 64 features, where each of the 64 features is the brightness of one pixel in an 8 × 8 image:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1797, 64)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import load_digits\n", + "digits = load_digits()\n", + "digits.data.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The clustering can be performed as we did before:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(10, 64)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "kmeans = KMeans(n_clusters=10, random_state=0)\n", + "clusters = kmeans.fit_predict(digits.data)\n", + "kmeans.cluster_centers_.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is 10 clusters in 64 dimensions.\n", + "Notice that the cluster centers themselves are 64-dimensional points, and can be interpreted as representing the \"typical\" digit within the cluster.\n", + "Let's see what these cluster centers look like (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(2, 5, figsize=(8, 3))\n", + "centers = kmeans.cluster_centers_.reshape(10, 8, 8)\n", + "for axi, center in zip(ax.flat, centers):\n", + " axi.set(xticks=[], yticks=[])\n", + " axi.imshow(center, interpolation='nearest', cmap=plt.cm.binary)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that *even without the labels*, ``KMeans`` is able to find clusters whose centers are recognizable digits, with perhaps the exception of 1 and 8.\n", + "\n", + "Because *k*-means knows nothing about the identities of the clusters, the 0–9 labels may be permuted.\n", + "We can fix this by matching each learned cluster label with the true labels found in the clusters:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from scipy.stats import mode\n", + "\n", + "labels = np.zeros_like(clusters)\n", + "for i in range(10):\n", + " mask = (clusters == i)\n", + " labels[mask] = mode(digits.target[mask])[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can check how accurate our unsupervised clustering was in finding similar digits within the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.7935447968836951" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.metrics import accuracy_score\n", + "accuracy_score(digits.target, labels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With just a simple *k*-means algorithm, we discovered the correct grouping for 80% of the input digits!\n", + "Let's check the confusion matrix for this, visualized in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.metrics import confusion_matrix\n", + "import seaborn as sns\n", + "mat = confusion_matrix(digits.target, labels)\n", + "sns.heatmap(mat.T, square=True, annot=True, fmt='d',\n", + " cbar=False, cmap='Blues',\n", + " xticklabels=digits.target_names,\n", + " yticklabels=digits.target_names)\n", + "plt.xlabel('true label')\n", + "plt.ylabel('predicted label');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we might expect from the cluster centers we visualized before, the main point of confusion is between the eights and ones.\n", + "But this still shows that using *k*-means, we can essentially build a digit classifier *without reference to any known labels*!\n", + "\n", + "Just for fun, let's try to push this even farther.\n", + "We can use the t-distributed stochastic neighbor embedding algorithm (mentioned in [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb)) to preprocess the data before performing *k*-means.\n", + "t-SNE is a nonlinear embedding algorithm that is particularly adept at preserving points within clusters.\n", + "Let's see how it does:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9415692821368948" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.manifold import TSNE\n", + "\n", + "# Project the data: this step will take several seconds\n", + "tsne = TSNE(n_components=2, init='random',\n", + " learning_rate='auto',random_state=0)\n", + "digits_proj = tsne.fit_transform(digits.data)\n", + "\n", + "# Compute the clusters\n", + "kmeans = KMeans(n_clusters=10, random_state=0)\n", + "clusters = kmeans.fit_predict(digits_proj)\n", + "\n", + "# Permute the labels\n", + "labels = np.zeros_like(clusters)\n", + "for i in range(10):\n", + " mask = (clusters == i)\n", + " labels[mask] = mode(digits.target[mask])[0]\n", + "\n", + "# Compute the accuracy\n", + "accuracy_score(digits.target, labels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's a 94% classification accuracy *without using the labels*.\n", + "This is the power of unsupervised learning when used carefully: it can extract information from the dataset that it might be difficult to extract by hand or by eye." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 2: k-Means for Color Compression\n", + "\n", + "One interesting application of clustering is in color compression within images (this example is adapted from Scikit-Learn's [\"Color Quantization Using K-Means\"](https://scikit-learn.org/stable/auto_examples/cluster/plot_color_quantization.html).\n", + "For example, imagine you have an image with millions of colors.\n", + "In most images, a large number of the colors will be unused, and many of the pixels in the image will have similar or even identical colors.\n", + "\n", + "For example, consider the image shown in the following figure, which is from the Scikit-Learn `datasets` module (for this to work, you'll have to have the `PIL` Python package installed):\n", + "(For a color version of this and following images, see the online version of this book)." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Note: this requires the PIL package to be installed\n", + "from sklearn.datasets import load_sample_image\n", + "china = load_sample_image(\"china.jpg\")\n", + "ax = plt.axes(xticks=[], yticks=[])\n", + "ax.imshow(china);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The image itself is stored in a three-dimensional array of size `(height, width, RGB)`, containing red/blue/green contributions as integers from 0 to 255:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(427, 640, 3)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "china.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One way we can view this set of pixels is as a cloud of points in a three-dimensional color space.\n", + "We will reshape the data to `[n_samples, n_features]` and rescale the colors so that they lie between 0 and 1:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(273280, 3)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = china / 255.0 # use 0...1 scale\n", + "data = data.reshape(-1, 3)\n", + "data.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can visualize these pixels in this color space, using a subset of 10,000 pixels for efficiency (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def plot_pixels(data, title, colors=None, N=10000):\n", + " if colors is None:\n", + " colors = data\n", + " \n", + " # choose a random subset\n", + " rng = np.random.default_rng(0)\n", + " i = rng.permutation(data.shape[0])[:N]\n", + " colors = colors[i]\n", + " R, G, B = data[i].T\n", + " \n", + " fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + " ax[0].scatter(R, G, color=colors, marker='.')\n", + " ax[0].set(xlabel='Red', ylabel='Green', xlim=(0, 1), ylim=(0, 1))\n", + "\n", + " ax[1].scatter(R, B, color=colors, marker='.')\n", + " ax[1].set(xlabel='Red', ylabel='Blue', xlim=(0, 1), ylim=(0, 1))\n", + "\n", + " fig.suptitle(title, size=20);" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_pixels(data, title='Input color space: 16 million possible colors')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's reduce these 16 million colors to just 16 colors, using a *k*-means clustering across the pixel space.\n", + "Because we are dealing with a very large dataset, we will use the mini-batch *k*-means, which operates on subsets of the data to compute the result (shown in the following figure) much more quickly than the standard *k*-means algorithm:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.cluster import MiniBatchKMeans\n", + "kmeans = MiniBatchKMeans(16)\n", + "kmeans.fit(data)\n", + "new_colors = kmeans.cluster_centers_[kmeans.predict(data)]\n", + "\n", + "plot_pixels(data, colors=new_colors,\n", + " title=\"Reduced color space: 16 colors\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a recoloring of the original pixels, where each pixel is assigned the color of its closest cluster center.\n", + "Plotting these new colors in the image space rather than the pixel space shows us the effect of this (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "china_recolored = new_colors.reshape(china.shape)\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6),\n", + " subplot_kw=dict(xticks=[], yticks=[]))\n", + "fig.subplots_adjust(wspace=0.05)\n", + "ax[0].imshow(china)\n", + "ax[0].set_title('Original Image', size=16)\n", + "ax[1].imshow(china_recolored)\n", + "ax[1].set_title('16-color Image', size=16);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some detail is certainly lost in the rightmost panel, but the overall image is still easily recognizable.\n", + "In terms of the bytes required to store the raw data, the image on the right achieves a compression factor of around 1 million!\n", + "Now, this kind of approach is not going to match the fidelity of purpose-built image compression schemes like JPEG, but the example shows the power of thinking outside of the box with unsupervised methods like *k*-means." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.12-Gaussian-Mixtures.ipynb b/notebooks/05.12-Gaussian-Mixtures.ipynb new file mode 100644 index 000000000..082377b2d --- /dev/null +++ b/notebooks/05.12-Gaussian-Mixtures.ipynb @@ -0,0 +1,1106 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: Gaussian Mixture Models" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The *k*-means clustering model explored in the previous chapter is simple and relatively easy to understand, but its simplicity leads to practical challenges in its application.\n", + "In particular, the nonprobabilistic nature of *k*-means and its use of simple distance from cluster center to assign cluster membership leads to poor performance for many real-world situations.\n", + "In this chapter we will take a look at Gaussian mixture models, which can be viewed as an extension of the ideas behind *k*-means, but can also be a powerful tool for estimation beyond simple clustering.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Motivating Gaussian Mixtures: Weaknesses of k-Means\n", + "\n", + "Let's take a look at some of the weaknesses of *k*-means and think about how we might improve the cluster model.\n", + "As we saw in the previous chapter, given simple, well-separated data, *k*-means finds suitable clustering results.\n", + "\n", + "For example, if we have simple blobs of data, the *k*-means algorithm can quickly label those clusters in a way that closely matches what we might do by eye (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# Generate some data\n", + "from sklearn.datasets import make_blobs\n", + "X, y_true = make_blobs(n_samples=400, centers=4,\n", + " cluster_std=0.60, random_state=0)\n", + "X = X[:, ::-1] # flip axes for better plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the data with k-means labels\n", + "from sklearn.cluster import KMeans\n", + "kmeans = KMeans(4, random_state=0)\n", + "labels = kmeans.fit(X).predict(X)\n", + "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "From an intuitive standpoint, we might expect that the clustering assignment for some points is more certain than others: for example, there appears to be a very slight overlap between the two middle clusters, such that we might not have complete confidence in the cluster assignment of points between them.\n", + "Unfortunately, the *k*-means model has no intrinsic measure of probability or uncertainty of cluster assignments (although it may be possible to use a bootstrap approach to estimate this uncertainty).\n", + "For this, we must think about generalizing the model.\n", + "\n", + "One way to think about the *k*-means model is that it places a circle (or, in higher dimensions, a hypersphere) at the center of each cluster, with a radius defined by the most distant point in the cluster.\n", + "This radius acts as a hard cutoff for cluster assignment within the training set: any point outside this circle is not considered a member of the cluster.\n", + "We can visualize this cluster model with the following function (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.cluster import KMeans\n", + "from scipy.spatial.distance import cdist\n", + "\n", + "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n", + " labels = kmeans.fit_predict(X)\n", + "\n", + " # plot the input data\n", + " ax = ax or plt.gca()\n", + " ax.axis('equal')\n", + " ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n", + "\n", + " # plot the representation of the KMeans model\n", + " centers = kmeans.cluster_centers_\n", + " radii = [cdist(X[labels == i], [center]).max()\n", + " for i, center in enumerate(centers)]\n", + " for c, r in zip(centers, radii):\n", + " ax.add_patch(plt.Circle(c, r, ec='black', fc='lightgray',\n", + " lw=3, alpha=0.5, zorder=1))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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aSUlJzJo166LOpybQHDH3Wpcm2+vzQgU87fHoPj5+/FG2N57CZ2r4TZ1t9bl8MfspGrWWsOOtTpmGLdwipJRcljAw6n5jxoxh7NixBAIBTNNk165dAzLuUKLthtTWKs4wjGhpfpRLkiEdwzZNk/3792MYBoZhsHjxYlS1fzHiiMeSkgp/AzbFQqotLuJ2mfYk9AiLkAYmfy19n7+UbuVro6+mUffyWvVh3IYPBRG2TN1jBni56iCfGLGs03s3DpvDjvpTFHirOxTeSAFv1xwNu09fuPzyyykqKkLXdY4dO8Y111yD0+kckLEvBFJK6uvrKS8vp6KigsbGRtxuN83NzTQ3N4fNgFEUhdjYWGJjY4mLiyMuLo6kpCSGDx/O8OHDL6nzj/LRYUgb7Pz8fOrr69E0DYfDwZQpUwblONvqcvlj8cbQomKGLYEfZa0lM8yiXqzFzoL4cexqzA87ltcMlpD/uuhtLCgECG/c27Oz4VRY42tXLKxOmUbR2e0dbhKGNHm9+gjLkyczzjmsR+fYFZmZmaSlpVFbW4uu6xw+fJjLLut9j8kLhZSS8vJy8vLyKCkp4fDhw8TFxYXeC/en7T0glF3k9/upq6sL1RC0b1qcnJzM8OHDGT9+PJMmTQqNHyXKxWRIG+x9+/ZhmiaGYTB37lysVuuAH+NQ0xkeOrOhw2vlgUa+kvMMT8/6XCctEJ+pcai5+1xoE9kjYw3BUMruhgLerD5Cs+FjUfw4bkqbQ7zFyea6nLAefUDqPFT4Nl8ZczVTXMN7dJxICCGYM2cO7777LoZhsH//fpYsWTKkuq4bhsHp06fJzc0lLy+PpqYmpJSYponP58Nms2GaJqZpdgp3CCFQVTV0Pm1PbOfTZrhVVaWqqoqamhpOnDgBBG9qkydPZurUqaSlpQ3+CUeJEoYha7AbGhrIz89H14Ne7+zZs/s1nmYavFC5j7drjuE1NSbbhvGgayV/Ltkcdnu/1Hm7+ii3pM/r8PoHDacxw2Ru9IcGvYXfntmAv3XBssRXxzu1J/j9lHu6PFaJv57vn3qJB0cuZ03qjH7NYerUqWzbtg1N06itraWwsJDx48f3a8yBoKmpiYMHD3LgwAGam5uRUoYMrq7rIQ9aVVUyMzPJyMggMTExFO5wuVw4nc5OVbi6rody0Nv+rqmpoaKigpqaGgKB4JOSoihYLBZKSko4e/YsW7ZsYdSoUSxcuJBp06ZhsQzZn1CUDyFD9tuWm5sbLBzRdcaMGdMp77q3/PT06xx3nw3FkY/4yvhG3rP4I/RZBDjUfKaTwW7UW0KGdaBoU+ZrQ5MGTbqX5yr2sTJpKiXeug454O3xS51HSt/nyqRJONW+Z8/YbDamTp3K4cOHkVKSk5NzUQ12cXExe/bsIScnp4OBblswdDgcTJo0iXHjxmGz2Rg/fnyvnggsFgsJCQkkJCR0eq9NMKvsbDHx1ueZNvYwdptO4dkU3t01kzNnTEpKStiwYQPz5s1j8eLF0ZBJlAvCkDbYbY+4Eyf2XqWuPXmeCk54znZa9AsaXgFhBJcAUqydf4RnfQ39mktPMTDZ3ZjP36Z9gk11Jynx1RGIsNipCoUT7jIWJIzt1zEnTpzIoUOHMAyD3NxcrrvuugseFqmsrGTTpk3k5eUhpQzpxpimicvlYurUqUyYMIERI0aEvOaampoBnafFYiEjI4NJ6f+HlUMoBBtJTB5XyfiRNfzx6SupbUhE13W2b9/OBx98wJIlS1i6dOmQafgc5cPJkDTYPp8vlLUAkJWV1a/xsj3lmGE0PyQSm7CEzd4AuGf44g7//3f5B7xXd6Jfc+kNVmHBrlh4aNI6ttbl8seSjRFuLWAdAOGtkSNH4nA4MAyDxsZGKisrycgIL6zVX6Regmz+Bfi3gVAJiJVs3DOPA4dOh4SpNE1DSsmoUaOYM2cOEydOHLQsofNRZT429iM41/VHEWCzmtx7czX/fHEETU1NKIqCYRhs27aN/fv3s2zZMhYtWjQo6y1RogxJg52fn0+zzeDUCBNfkpPH6z/gFus8RjmS+zRegsWJKlS0MEY7zRaHLk0qAo2h1wRw//DLGdYuva9J9/Jc5b6IuiIDjQWVa1KmA2BVLFydOp3DzcXsbMjvVLQjBExzjej3MVVVZdy4ceTk5GCz2cjNzR0Ugy2NGmTtbSCbARMkqPrbLJn8Pnv3XY3XFzy/adOmsXDhQoYN638mTG+xcpRwT15CSDJSSnjwwYcpKCjg2OGNVFXX0OJzYRgG7733HgcOHGDt2rWMGTPmgs87yoebIWmwt5w+xI6ZGoYQoBhsrD3J+3W5fH/8TcyJH93r8ZYkZPHnki2dXrcrFm5Nm8fKlKnsaShgZ30+CVYnNw2bw4jzUvqyPeVYhXrBDLaJGTLYbTw4cjk5LeU06T58poZVqChC8K2x1/dbw6SNrKwssrOzMU2T/Px8li/vWu+7L8iWf4H0Qrsbj6qauJxepowroilwFcuWLbsohjo0RxKQWBB07vRjEo9N5LBows+4bEIF0jSpaYjj6ddnUVWXTE1NDY8//jiLFy9m1apVUW87yoAx5Ay2lJJXxCkMFWgtzTaR+KXO/xW/y2PTP93reKVDtfKjrLX87+nXMGVQ2dowDVYmTeXqlOkIIViWNIllSZMAONJczFNlu6gMNOFQrIyLGcYYR0qH4pWBIlIE3aqo7GzI5/ph5yo7E60x/GXqx9lRf4oTnrOk2+JZlTKNFGvsgM1n9OjgDdE0TSoqKjBNc+B1zgO7IIwhtNsMVi9PQMbeOrDH6wN+lhHLQ51eN3Hg41oS+BoKwYIcocCwpHq+9LEP+O1jV1PfaGKz2di9ezd5eXncdtttjBw58kKfQpQPIUPOYJe5a/Go4WPKbt1Pmb+hk/fbE6bFZvLUjM9wsLkYj+4nU3MyJWNsp+3+UbqNt2qOdljgO+45ixU1rH6HVajMih3JUXdpj71vm7CgSR2bsETO/jB1Sn11nfdVLKxMmcrKlMHpyuFyuYiLiwvJAdTU1Axo3rGmaZSVGYxIgfPvA1JacbrGE75Q/wIj7DTK35DANwk+CZgITPysROBG0PFzEwIsqsmD9yfz3BuJFBYWhrJNHnvsMW688caQfnuUKH1lyBnsupraiO9JwNJFD8XusCoWFicEU9XC9XMs9tbyVs2xsNkYGgYWqeJQrIDEbxrYFQsj7Il8ftRVHGou5q8lW8K2+IJg+MWQJvNix5BqjyXR4uJIczEnWnWuO20vLIyLuTghgfT0dE6fDqoBlpWVDZjBbmxs5N///jeKkcH9N53Eppx3nYWCj+sH5FgDgS5mUCtfxcYHCJrRmI0pRpAg/xNB53RQQQCX/Qy33/5pjh8/zpYtW/B6vZimyauvvkplZSXXXHPNoHdmivLhZcgZbG91I7Et0OSSQbelHWm2ONLtg6fX/EHjaYwuvGQTkzXJMxkbM4w6zc2EmHQONxXzH9lPYRFKRGOtINBbm+vubS7E4bEyypEc1oNuQxWCKxIn9e+E+kh6ejoFBQVIKSkrK2POnDn9HrOkpIRnn32W5uZm/P443tg6jZtXZqMoNhASMGjhk5hcvLh1eKwEWADYg7EPQGc8Vg518rIlYGMfDt5h5sxrGT16NC+//HKoYfSePXuoqqpi3bp10fS/KH1iyN3qq6urmZ1vwaKDVQanZxcWYhQb3xp7XZ/GNKXkQFMRT5Xt4rWqwxHV8YKx8cjxcYlEiqCK3rqMRdQG3LxVexRNGni7KMAxkRitfyBY3l7YUh2xAEcgeCBzGQ714ixWpaWlhcq+B0JutbCwkCeffJKmpqaQxxmX9lka1NcIiPmt3qqFGJ4kmTtQZUH/T6K/SIlDvkoya0nlOlK4nhj5GEgDL7cTztcRgIKHOH6LQ75CQkIC9957LxMmTMDv9+P3+ykoKOCJJ56gpWVIBH6iXGIMOYPd3NyMqwUW7dS43jqJ1cnTuD/zch6d/sk+hQh8hsY3857ll4Vv8VzlPp4o28mnTzzGMW/nUMTlCVmoXSxo2hUrlyeekzV9sWp/n6sedcwuPfLBilH3hLauM1JK3O7Iet09oaCggKeffhq/34/X68Vut7Nu3TrmzJmDje3Y2YdAR6Gl9U81iXwNZOQb4IXAwcvE8idU6hEYKHiI4Rlc/AlTDKeR32CQFvYTFPhw8QhIA5vNxtq1a7n88svRNA2/309ZWVnUaEfpE0PSYJumiUWHa5Om89UxV7M2bS5xlr49Qq6v+IBCb01IozogdfxS5+Ha7Z10qzMdSdyRvgAbnePkdmFhQfxYprkyQ6/VR/DU2+hr7Z1NaYuVXxxcrmB/Siklzc3NfR6nqKiI9evXh4x1bGws9957L6NGjQIghvUIfB32CV6zADZ29/m4/UYauPhHmLn5cPIaQjajidk08TMk4b+XAj8K9cF/C8HSpUtZs2YNhmHg8/moqKjgySefjDY/jtIr+hTD1jSN733ve5w9e5ZAIMAXvvAFVq1aNSATcrvdIbW12Nj+p6ttqjsZNntDAAebznTwmAHuGb6E+fFjeaf2OAUtVfhNnRRrLLPjRpHtKeczJx9jhD2JdRmLyIpJ45i7NOKx+5sEWOSt4R+l2zjuPgtAosXJ8uTJ3JQ2t9+pfPWaB00aDLPGdUqTjImJQVEUpJT4fD40Tet1LnFFRQXPPPMMgUAAn89HXFwcd911F4mJiaFtFMLH8IMed+TF58FG0NTJWLchsaJSgs40TFIREcW5JCYdP6NZs2ZhsVh466238Pl8lJeX88wzz/DAAw9ERaSi9Ig+fUtee+01EhMTeeihh2hoaOCWW24ZEIPd9gjeZrDbPL3+EDDDLyJKCNsZBmCSK4NJrnMVfgeaivjF6TeDncyBqkAzJ91lLEvsn8ZJOAQwL34sexsL+cXpNzr0dKzRPbxYdZCXqw7x9THXsCK59/rgpb56flO0gWJfLQJBosXJV8Zczey4UefmIAQulwufL2i0mpubSU7ueZWpx+Nh/fr1+Hw+fD4fLpeLdevWdTDWABpTsLE3zJOIgs7gaJ/3BEkskZ6PBFpoYdQUqQTkbGznLUCa2PCzEkRn73vatGmYpsnbb7+N3++nuLiYN954g7Vr1w4pOdsoQ5M+hUSuvfZavvrVrwKEpC0HAk3TQmpsVqt1QCrE5sWNDtsb0ZRmByMFwdznk+4yCr3VHUTvHy7ejL/VWIe2lTqb6rP7Pb/zcQorZ311/Oz062Eb8EJwEfMPZ96joZuQzPm0GAG+nfccp71VaNIgIHWqtGZ+cvo1Ss7LWHE6naFr0Ga4e4JhGDz33HM0NDTg9/uxWq3ceeedYdUWW3gQsHd4TWJDYyq6uHgxfIQVLzciO83NSoA5mOLcWkozP0JnMhIrJnYkVjTm4ua/Ig4/Y8YMrrrqKnRdR9M0Dh8+zJ49ewbtdKJ8eOiTh93m+brdbr7yla/wta99Lex22dm9M2g+ny+UlWCz2cLmSveWm2OmcbDpDD6phQyuTaisipmEbPRR0/rou7k5j+caD6EgMJHEKw6+Omw5dmGhVuvfwltPmWHPoNn0U+Kri7gg2YaJ5N2zh1kZ23XqX1vxBsCW5lP4Ta3TyJpp8MyZnXw65VyXGa/XS1NTE83NzeTm5tLY2Eh3SCnZunVrSPQf4Prrg3nV4T/LVBotPyIt5p84LfmY0kGDfzXVLfch6fln3/4cLaKOBMd72NVSfHoWDf7VmLL34aMa7iLTVUWcfQ9SWhFCo0Wbwln3VzDlublZlTLi4uuQigAJUkiavSOo8TYDbkAnzrYPh3oazRxGU2AZpoxhzJgxjB49mpycHIQQPP300zQ1NYUqTcPh8/l6/Zu61IieY9f0OXBWXl7OF7/4Re69915uuummsNtMndo7L8nj8TBs2DD8fj8Wi4XU1NS+Ti9EnUfHrOj4mkQyxzUyNP7BpjM813ioQ9VhteHml1UbyYpJ69Z49pb25egKggkxafznmDUI4Ms5z4TS/7pCAhanvdtrVFNTE9qm1nsMf5h4vomkTDZ3GCs+Pp6WlhacTidZWVldGpI2jh8/TlVVFQkJCQQCAa688koWLFjQzV7L8LAMT9t/YyAlpttDdaDtHC3yKAl8A4GBIECcfR/DXC/TwF8wRO81aAL8nHpZgyqKMcjAtGeS3N7plgbJfBaFGgQyFEVJiXkLe8xE/CwlkS+iUI+CF4mDdJ6kkd+ji8ncfvvtPPfcc5SVleF0Ojly5AjLli2LGArMzs7u9W/qUiN6jsHG45HoU0ikpqaGT33qU3zzm9/kjjvu6MsQ4SfTrgJsILpam1Ly88I38MuOXqUmTX5VtZEcTzkAz1fsC1siHpA6JyNUIvYHtfWyW1BYlTyVhybdxQhHErWaB4vo2UeiojAvvndqcKMdKZ1ankHwpjHWkdLhNSllKKbak8o8t9vNW2+9hWEYaJrG1KlTWbRoUa/m1y+kJJ4foeANCTYp+BE0E8sv+jysKVLRxDxMkdnpPSv7EXiCxrodwWySp4njN6hUndMcwYeCh3i+C1JisVhYu3ZtaL3A4/Hw5ptvRju6R4lInwz2X//6V5qamvjzn//M/fffz/3339+rOGfEybQzDKbZ/zZcBd4q3Lo/7Hsmkj8VbwKgMtAUdpuANPqkzmcVKklqZDexLTatY/Je3UnuPfpXfpD/ClvrciJqc7dHRXBF0kTGOnv3BLIieTJWoXaK6FuFym3p8zu81r7nYXcGW0rJm2++icfjwe/3ExcXx9VXX31BF9FUTiPoHLoSSKzkIKQnzF79PWY1RFhnUKjFxq5O1ZDBObmxkAcEw4vXXnttSAP85MmTHUJKUaK0p08hke9///t8//vfH+i5YLVaEUIghEDTtH4rxQW6KWop9dXTYviZEJNGTWNzp0CERShISSf9aYBMeyK1AXd48SYJzWbPb2AeM8Ch5jNA0NtVER3CIoJgMwMBpFhd3JWxuE8ZIjGqnV9OvJOHit6m3N+AQOCy2Pnq6KsZc57xb+tpCHS7+HvixAmys7NDn9maNWuw2+1d7jPwdHeDH8A+nFIiaEZnfCfvug2dLKycjDCA0iFtcNy4ccyaNYtjx46hqipvvfUW48aNG5AsqSgfLoZU8qeiKMTExBAIBJBS4vF4+tUrb2JMetfRYAGqULk7YzEHm850ML4KglRrHHWaG+O8QRyKhbszFhOj2vjZ6dc7L+Jh9DkJ20SiInAqNrxmgDRbHA8MX8qVyZP7NuB5jHGm8KepH6Mq0IRuGmTYEzupELalV7Z5yF19BoFAgA0bNoRCIbNnz2bs2LEDMtfeYDCeYMZJx0IUSVD7Q4p25yAlFk6iUo5OFoYY1+Pj2OUGXPwVhUZAwSQegURpJxcrsdPC53Hxe6ycCjOKiXZe2uKKFSsoKirC7XajKAobN25k7dq1PZ5XlI8GQ67SMS7uXCFHf8uibYqFz40ML8AvgNmxo7ArFsbHDGNxYuc2ZJNdGXxx1CpsQsUmLKgo2IWFSTEZPH52Oz8NY6wHAhPJNSnTeWXOl/nH9E/12FhLKXHr/h6Vy6fZ4sl0JIWVjPX7/WiahqIoWK3WLr3lPXv24Ha7CQQCxMbG9r3hgTSxyg+Ikf/AIV/CIo9ik3tQZA+1TIRKE99HYg19JsG/BS3cH9pMkTUk8QAJfJ1YHiKJB0mQX29tqNA1NrmlNS5di0BHEEChEZMkJHYkAp2xNPJLNDEbN/+FxIFs/ZlJgsbcw5dAdLymdruda665BtM00XWdw4cPD4iOS5QPF0PKw4aOBtvj6X/c8ZrUGQD8uWRLSL2jTUzq2tSZbKo9ya6GfPY2FXbYz0TyQWMBixPGc3/m5ZxwnyXFGodNUXm56mC/59UdDZqHP5ds5oy3lnHOYdyaNpfMMDrg2e4yHi/bQZ6nMpTNogjBgvixfGlU34qZ2q67EILY2NiIseiWlhZ27twZ6ma+dOnSvoVCpJdEvopKEQIvbXk0EkdQg1quoJnvguj66yoJetFts20bJY6HqJWLQTiJ5/uoFCM4F6O3cpRYfocm5+PkeRQaCbCAFj6OKYaHtnPxtw49HoPH0FCpp57HMMjsMEddTKdePoKTf2HlJAaZeLkPTYTXxR43bhxjx47lzJkzWCwWNm/ezF133dXjyxjlw8+QNtj90bFozzWpM1iaNJFt9bmU+xpxqFZerTjILwrf7LKLjM/U+U3RBmyKimaaqEJE7FzeE5yKtUtVvzYsQmVXYwGGDN5iTrVUsqU+mx9n3cL02HO9G0+6y/hB/sud4uimlOxrLOLbvhf432HX9nqebU82QoguwyHbt2/H5/MRCARITk5m+vTpEbftChf/wEJBu3Zcbb5xMM5r431iSKOFz3U5TgxPw/mNBQCJhp3NaHIuFvI7GOvgNgEcvIODLaFjOngbO1uol//AFMFrrhI+YyhYrl4UNnXQEGNx0/P1niuvvJInn3wSTdPIzs6mtLQ02q0mSoghFxJJSkoKLTwOROFMGy7VznWps5gVN4r1FR/Qgtajll8mEp+pY2D2y1grwFMzHuxW1MnemsWhSSPkMZtI/KbO78+81yHl659nt0fsWGNgUqe5Oe4r7/Vc2667ECJiSbrb7Wbfvn3ouo5pmlxxxRV9XiB28HbY3oltKPhx8hJ0k+6mcibsIqCCFwu5WNkbCk90xuywEBjM5fbi4u/ttgh/LQQGBsPDvtdb0tPTmTJlSmgBd+vWrQMybpQPB0POYGdmZiKEQFEUKisrB3Rsv6Hx09OvDeiYPUEAc+PGYFetPDjiSuztHpsFwTS98Y5U5seP4YERyxARdCxqNTc17aouC7xVXR43YOqUag29nm9FRQWKoqAoCsOHhzdEhw4dQtM0NE0jIyODiRP7rqvSlbE+t42X873n89GZEPYWLAEnrxLLX1vH6em8TGzsC/2/hXsxz1Pnk1jQGY0hBk5XZunSpUCwgjM/P5/a2osnhBVlaDHkQiJtBkJRFKqrqzEMY8C0St6oOdKjKsI2IjXI7Q1WoWJXLHy2dfHzmtQZDLcn8kLlfioCjUyMSePO9EWMcQYLVyr9TTx+dmfYsYIt0s7dY12qnUY9sgGyKRZSLb0vy66srAx5y5mZnQtGTNNk//79mKaJaZrMnz+/XznXARZgY2fEFDkAkzTsbMMhX0ClHIkTjen4WAetnm8L92FnM+E+NYGJaK2nlHSUdgpubSHcDaG9fKqPO1GpxckLSKwIdDQm08RPe3vKXZKcnExWVhanT5/GarWyf/9+1qxZM6DHiHJpMuQMdkxMDImJidTU1ODz+aitrR2wnoJHmkt6tJ0AprtGkOspR+tl/q5DWFiVMo0GvYXagIeZcSO4adgckqzncmpnxo1kZlz4uGS6PZ50Wxwl/vpOcxrtSO4wzo2ps3m+cn/YYhtB0GDPdfYu/un3+6mrqwvlxGdkZHTa5tSpUzQ2NqJpGk6nk0mT+tfKzMMXsHII8HWKL0Mws0JnJLH8AqXdop9KKQ624LN/HHig1VO3cn5H9vNvJeH+L8Me14afK0EaIFQQAg9foEXej0ohJilhKyAHgjlz5pCfn49hGBw+fJiVK1cOynGiXFoMuZAIBL3sNg+vtDSy3nRvibc4u3zfJixYhcqq5Gn8dOJtrEyZ1qGUW0EQo9j44sirwioAQrA6MtESw3fG3cBDk9fx8cylHYxsT/jmuOuIUWyh0IldCWa1TI8dwYMnHuMTxx/lbyVbuTplOosSxmETKpZ2H6VNqIy0J/PLiXdi7WXT4oqKCqSUKIrCsGHDwhbN7Nu3D9M0MQwjpPHcHwwxmnoex8eN6IzEIB0TB8FOj8Nx8yA2jncw1hA0tIIA6a4nELK+1fPu61wUTOytxxXI4EoCDt4ihbXY5JbQllLEoouZg2asAcaOHUtiYiKapuH1ejl+/PigHSvKpcOQ87AhmN6UnZ2NoiicPn2aefPmDci4ti6M14yYEdyesYBxMamh5gBfHLWSqa7hvFJ1kHqthWG2OFYkT8ErdRQhMMMsgplI3qw5yt3DF/d5nuOcw3h0+ifZXJdNkbeGsY5U3q/PZUO7ju5v1xxjV2M+f5xyH/cPv4zclkpiFTuxFjuxFgejHMEwQY27dwu3+fn5CCFQVZVx4zoXlLS0tHD69Gl0PejVz549u8/n2R5TZODmGx1fbPVsnfJZuqpUlFLBJnahM7mLhgLdIajnKWzswsVfEfhbzbYX8BLPz2iQaeiib5kwvZ6NEMyePZv3338f0zQ5ceIE8+fP737HKB9qhqSH3faIraoqxcXF+P3h9UB6S6E3svEaE5PCgoSxHTq5CCFYmjgRh2rFL3UKvTU8Xb6bp87uxJCRDUOL0bf5nnSX8c3cZ7nt8J/4YvZTaFLnS6NXkelIpMRf1yFLxcCkWffxRvURMh1JXJU8hYWJ45gamxky1r1FSklBQQGqqiKEYPLkzgU7+fn5Ie96+PDhJCQk9OIAPlzyN6TK1aTKFSTKB1BlTuTtW2+wwaKUrr+qAjDEBLRWbeoOh+1uWgAY2NmExEWwDfL5e/mJ4Z/djDSwtF1/wzAoLCzsIBcQ5aPJkDTYiYmJZGRkYLFYMAyDoqKiARk3wRo+JGIRComW8GJNT5btpKClGp+pYWDiNTW0bgRXFaGE9b674oT7LD/If5mclgo0aVCvt/Dv8r38/sx7HGo+E7Y7jiYN9jUWhhmtb9TU1NDY2IiqqtjtdsaM6awGmJubG1pszMrqXB0aEWmSxKdw8mqr92pg4TRJPIhFHu5yVz/Lu1yQFMLET1DL28udmLhaqwqDRePdLYcGQysSF49j5XBIXe/8bWzsxSY3dzPawJGQkEBaWlqoMKm4uPiCHTvK0GRIGmwIeheKoiCEID8/f0DGvDF1TgR5UYWrksPr026M0BOyK0xpcrDpTK/2eezsjk451X6ps6PhFEKKDjHq9rRvTlwdaGZrXQ77GwvRIrRG64r24ZCJEyd2ys4xDCO0ECal7JXBtrIHlZIOxrPt3/H8b5f7SpFEM99CYms1xK2vE/S+q1ruR4pkHPI54vkJKg2tY0volZq5hkoFJuFv7AKI5+cIGb4X5WCQlZWFaZpIKQfMcYly6TKkDbYQAovFwqlTpwZEvnVBwljWDpuLVajYhBrSpVYRvFi1n3qtcyl8T3Q5zicgDU56zvZqn0g51RahkGFPCKv5YVcs3DBsNlJK/lqylc+dfIKHSzbz66INfPz4IyG9754gpeT48eOh/Otw4ZC28JRhGCQmJvaqwYSdLWFfF4BCNciuK0D9Yg11PIOHzxBgYWtK3w008CfqfTeBbCGWv3coHRf0rnO9wMQkFtnqoYdDIltTBy8MEyZMQEqJYRicOXMmqpX9EWfIGuzhw4eTnp6OxWJB07QB0wi+P/NyHp76MVyKjTZfzSs13q05wddz1+PWO94Yprg6p7V1h02oEUMskYhVI2twjHWm8oVRK7G15nS33XCuTZnJovhxbKo9ycbaE2jSwGdqeM0AbsPPD/Nf6fENp7CwkIaGBqxWK06nkylTOsu3lpUFS7MNw2D06NG9yr1u0/mIhINXWzeU2OQmEuWnSZL34ZRPgQz2rjRJRZLc2sGlDokDk+BNw0oXsXA6xrEl4ePaEgcBrqCBh5HYwo4j0FAYeG3tSKSnp+NwODAMA6/X26NWbVE+vAxZgy2EYNGiRaiqiqqqHDp0aMC8i4KWalpMrUMRTdsi3ts1xzps+5mRy7Erll56aoIrk3onh3pj6pwOFZDBcYIa1tNjR7A6ZRr/nP4pHhyxnE+OWMafpn6Mz4y8EiEEr1QfCluiLpEc8vYsLfLw4cMoioKqqsyZMydsOl9ZWVno8Tw9Pb1X59fCvRHfE4CLR0FqxPN14vkRVvKwUIyLv5PMXVjkYRL4aqtkaT4q5Th5lSQ+iUXUIYkBwnvpAoLViAxrNcSda0mDMqxp2NhOMvchCETwsu0EaNf2TOrQxQJ0fxFCkJaWFmro0XbTjPLRZMgabICZM2dit9uxWCzU19cP2KLL+drXbQSkwb7zVPsmxqTz20l3cVnCBJItLmKVyJ6wQ1hwKFa+O/4GEq0xSCnJ8ZSzs+EUlf7wXW3auCNjAYsTxmMVKk7FilOxkmx18ZMJt4bCIQnWGNakzuCmYXMYbk8M7Rup2lGXBk09aKTQ2NjI6dOnsVgsCCEi9mFsM9hA2IKarpAiFS/ruognSxy8ho0DneLcCg0k8lWsHOmQix2UOG0mxflia+dye8TSdJ0Z1ImXkNgjLGBaUHBjZ0fruJ0rXSV2AsxHZxpWeYRE+UlSWUkqq4mVP0PIwWnWnJGREbru5eW914aJ8uFhSOZht2Gz2ZgzZw579uwhEAiwZ8+eXj+KhyPB4uzU1eXce51DGWOcqXx3/A0AfPbE47gDndP2bELlxmFzuGv4IhyKlQp/Iz/If5l6vSXo4UmTyxOz+PqYNajtyss1U2dnQz6Hms6QYovl++Nvoln3kWiNYUbsiA7bRmKaK5PdjQWdxKwUoTDBNqzb/T/44AMALBYLWVlZpKSkdNrG6/VSX1+PaZqoqtqnBsktfCIo4hS2bZaOnXfD7hf8tMN7sQKDWNs+GoWgWX6HeH4YZisbPm5p/Xd4L1yioOCOUGlpw8SFxlzcfBULeSTwX+3i5RoONmHhNA3yURjg1mhpaWmhp8uoh/3RZkh72EAoLGKz2SguLubMmd5lX4Tj6pRpKGEMoV2xcOOwrgtBmozwHqtAkG6Px6FYkVLyg4JXqAg0tcaUNTRpsLvhNM9W7A3t4zH8fDV3PQ+XbGZzfQ6vVR3iZ6ffQJM6s+NG9chYA9w3fEmn7BebUJnqGs54e2fj2566ujqOHTuGxWJBURQuu+yysNu1KfiZpklKSkqfqhuliCPAok7ViBIVjWkItF6FntpQRAsp8lri+AU6E5GomFgwsSGx4ubz6CKYBaSxuLWKsSPBY3fOcxateyk0YmMnKawjlt/SufxdQ6UQG+F1YPpD+/BTtKnBR5shb7BTUlKYO3duyKBs27at37HsTEcSH09ciE2oOBQr9taS9NvS5jM7blSX+06KiRy7nRwTDBPktVRSr3k6ebwBqfN69WE+aDzNb4ve4dt5z1PubwjlWBtIAlLnLyVbaNZ7nhUz2pnCryfeyZy40diEhQSLk1vT5vGD8Td3u+/OnTuRUmK1Whk7dmzEVL02bXLTNHtXLHP+OHwPg7GYODFxYOLEYARN/Agfq3sttiURqMKLggcFHxYKkLjw8GXcfINaXsQn7gxt7+YLSJydFiGJILYbFIqSCMzWLux+LGSHDasINOL5Pg45sIqQ8fHx5+bvdkczRT7CDOmQSBsrVqzgyJEj6LpOZWUlOTk5TJ0aPm+6pyyLzWLlyFnsbSzEkCbz48eQauu+f+THMy/nZF5Zhxi4TajMiB3JuJhg+KFO80Qs13Abfn55+s1Q5/RwKEJhX1MhKyPkhodjXMwwfjLh1h5vD0HdkJycHGw2G4qisHr16ojhpjaDLaUkJqZ3GTDtkSKBevlPLBzDwhkMRqIxB4TAJ28nhqdRaApdvfOV9Wj3elDoyUCIc9cyWJruxsmz6MzAYDQ6Se32i4NODQwiHyf81Qiv4xjc1iCWP6DJaRhkIWgOKv6J8FknPcFiseBwOPB6vZimicfjITa29yqMUS59+uVhHzlyhPvvv7/7DftJXFwcS5Ys6eBlD0S5erzFyeqUaaxJndEjYw0wISadn028namu4ahCIVa1szZtLv/dGuMObpPWZbFNV8Y6iMQcxMwDCHrKmzdvRgiB1Wpl6tSpXXY2aW5uDnl2/TYWQqCLWfjETcF2WW03CWGnnicJMB+JpTW0ERcmhKLgZykB5oXVDhGYWCjDznsk8tVWLRJAmiTyudZKy/P36UxkPzYYcomMhouHSeZ2UlhLKtcRK38WSk/sC7GxsaHr399ep1EuXfpssB955BG+//3vD5jOR3csXbqUmJgY7HY7zc3NvP/++xfkuOGwCRWvoaEg8Js6expPU+Q7JzI/zBbHlUmTwlZV9gRDSubHjx2g2Ybn4MGDnD17Frvdjqqq3cp3tj2KSykHzbuzy3dI5j6sZAMWDIbTyP/Dy1ramusG488mNvZj4TSSyIJewVCGHxd/R8h6rOxDoaZXcfJw8W5Q8XJ7hPfaGh/sR6Watma9DjaRwLd7ceSOuFznFB8HqnVelEuPPhvs0aNH88c//nEg59IlTqeT66+/HlVVsVgsHDlyZEAWIHtLg9bCd069QJGvBk0aaNKgxFfHf596kZrAuR/Sl0evZl36IhIsTgSQ2I20axt2xcK9GYt7LcnaG+rq6ti+fTsWiwWLxcKVV17JsGFdZ5O0rzR1OBxdbNk3LPIocTzUGotuQeBDpZRE/gsPDyCxhDQ/gql+/mCFZJisjvORqNjYg4W8HnW3OYcNSUyHm4KJAx8raRFfwsN/dBKaCh4vnOa2hpVsVNk3mQWn89z3ZyCqfqNcmvQ5hr1mzZputaqzs7P7OnxYVFUlLi6O6upqpJS8+OKL3H333dhsvY8P6rrep56RrzceD6vToZkGLxTv4Y7Ecx2xV1rGMT01lZ9VvYNH7/5JJEl18vmUZUyypA1YP8vzz9M0TV5++WWampoQQmC320lNTe32syopKaG2thYpJU1NTQPabxNgZNw/wervYOkEYMoAqu8vSDud3AtBsM2jRMGUdhThDZtRJ6Wk2e0BYnC6bKhKZIMXjDqoSFSqW+6mKXAFKc4XiLUewpCx1PtuoNG/AqhBsJSsxGdRlXoUYYT2j5TVZ5oCr+cwTYHEHl6Vc7jdbkzTpLq6mvz8/H5rkA9VfD7fgNuNoUZ/znFQP/X+LgyGY/To0Tz88MO43W58Ph/79u3j5ptv7nVudk1NTZ9yicub3GhhvDodkzLcncb8Wc57uM1AhByEczgUK58fvZLLEyf0ek5dUVNTgy9W5cmynRxzl6JokpSkFrICSThsdj772c/2qAjm4MGDNDU14fV6SU5O7tO16wqnrAoffBA+XM7GiDrXQoApVTzK17GzGRv7EefleSvCxB53TWvRzD+R+CKHRQS08HECXIbd1UyqS6Lz3zS2fr+sVkhtt9zRKP+Ji0datVJMhPATyesXCsTETcImen/tEhMTQ00lxo4dOyi/raFAdnb2h/bc2ujuHA8cOBDxvSGf1nc+sbGxodCIzWYjLy+P3bt3X7Djj3GmhO3iYkFhrKPjD7FWc3PGV9utsbYKhemxmSxOGD+gcwWo0Jr4z9z17Gk8jdvw06QEODNe5dg0uPLKK3tcsdj+hjgYaWU6k8JqXps4CbC4y8YEUlowGE8zP8BgeKhRrkRFYqeFu3Hyb2J4hma+jSRytWow5U+QyJeI5wck8FWSWYcqw8vYSpGEW3yLWvE2DTxKJB8oqBuYgs7MyBehC9oqHYE+d6ePculzST5XzZw5k5KSEvbu3YtpmuzcuZPU1NR+9xbsCdemzuSVqkOdskAsisoN5xXd+M1gZ5pI9tql2BjtSOXmtDlclpjV40KZ3vBy41H8pt7hpmGqgtokyJjT807fbVK3EBR/GihschtOnkWlotN7QYMbj4+bUCnCycvhU++EjkEmEhUva7GzDYG7tQNNMzE8B/g5l3FtDRtnDpawj8PFMwgCoXi3xEsiX6FWvgSic8y6DYORGKRioaNSY3Cx1EEjf+xzFWTUYEeBfhrskSNH8txzzw3UXHrFmjVrqK6u5vTp05imydtvv01iYuKANezVpYGK0inUkmKN5ScTbuU3RRto0IJpWvEWJ/85dg3p9vgO22bYEohRbGEV81KsLh6b/ul+l9l3R46/MqwitKIoHGk4w5TEET0ap/1C40AtesXIR4nhWQTB8SRKaEkx2K1xPm6+A8KKR34ZKyexkNvB0JrYafCvwOF4DRd/p30Ju4UzSESnEIlAi3APtSFwh+ZzbnuQBLCxC03OIJY/Y2M7AomfZXj4IqZIBSFolj8mga8COgr+1puDQgsPYnajWNgVXu85vZjBWPSNcmlwSXrYEFyAvPPOO3nkkUeora3F5/Px/PPPc9ddd/Urvrqz/hSPle2gKtCEQ7FxQ+os7stcgqVdGGSKaziPTPsE5YFGpJRk2hPDGl5FCL48ejW/KnyLgNRDXp1NWPjSqFWDbqwBnFgIJztlUVQSbD0vgImNjUUIgRBiQPKAhawjhvUdsjZE660lwAya+CmIxOAbUhLP91E506GgBgQ+bsCrjSLJ8acwYRMjYqz6XOmLvfXIsTTzfeL5UYTtNVTOEsvvUagLaY7Y2YyVQ9TLf7U2551MnXwWB2/i4HVUygCBi7/j4m80yR8SEFf27mIBHs85Sde4uL4b/iiXNpf0s1VMTAz33HMPMTExOBwOfD4fzz33XJ8zGHbV5/O7M+9SGWhCAl4zwGvVh/n9mfc6bSuEINOeyAhHUpeGd2HCOH456Q4uS5jASHsSlydM4JeT7mRBQucGtwONx+MhOc+DYoTzJwXL06b1eKy4uLjQeQ6EwbZxuFNBTHBWYOMIqdxOrPwlSD9WDmPlEEo7zzdocK1YySEz9vdhRZu6Q+LCzZeo51HqeAlNzEdjUoQSdQsKNSg0dziWwETgxsGb57YVCUjiWnO+TRQCrcU6AeL5b2Lkn3s9V7fbHbr+l1qVo5QSv9+P1+vF4/Hgdrvxer34/f5omX0vuWQ97DbS0tK47777eOqpp4Dgo+Ozzz7LunXrus0tPp/Hyjq36QrIoJreA4HmHldDns+EmPSQ2t+Fwu128+yzzxJTWk9GXCIVw8CiqlgUFRD8v/n347T0PB2yzasTQtDS0veKvTYkkR/rg2YpgJ33UKjHYFSnMAXQagiz+yGOZ6KThSHO9a5s4UFsHIF2Mq4SKwbjUKmIMA8/Vvbj5a7Qa06e73CDaX9uMbyALqcRECt6NEtd10NhKEVROhTRDBWam5spKyujsrKSpqYmmpubcbvdob/bx+Db03Y+cXFxxMXF0dDQQFVVFenp6WRmZnZwFKJ8CAw2wKhRo7jvvvt4+umngWCMdf369dx4442MH9+zzAtTSioC4bt5WIVKobemzwb7QlNZWckrr7xCc3MzihDMLbJz2cxVeIbZiLM6WTZsMg61d7nrbQZbUZROXU8UWUoMT2LjMCYptHA3Aa7scoEt2ASg6x+iQgAb+/EynODDYGcvuqvmvF0RXAiMR2d66DWr/AAXfyMow2UhKANrxce1uPkSLh5BtgrzdhxLxaTj2okgcjWiQCOGZwiwokdzbWo6F9RqC01dTNralRUXF1NWVkZZWVnoqavNY5ZShppdtP0JhxACv99PfX09Qgjq6uqoqKjo8DQxfPhwMjMzGTVqFGPHjv3Q5qD3hA/NmY8ZM4b777+ff/3rXwD4/X5eeuklli9fzoIFC7r9kitCEKvacRudC1wMTFJtl8ZjaE5ODhs2bMAwjFCY6I477mD69Ond79wFbesCiqJQW1uLrutYLBZUWUgin0fgQ2CiUk48P6WFdbTwYOQBhY0m+Qvi+Ra0hg3C0ebdBr+q5xvKrk1+V8JRkmQaeSiYHA3Y5E7i+SHte0IGqxpvwSO+CIBP3oyT1zvNAyx4uRVkCypVmAxDYx4K70acn0LPw3aVlZWhf/f2qXGg8Hq9nDp1itzcXPLz80PhjLZ+k6Zphv6EM85tAmNtGS5t2wYCHT93KSUtLS2hbTVNo6mpiby8PIQQ2Gw2JkyYwOTJk5k4cWK/hMguRT40BhuCnvYnP/lJ1q9fT0NDA36/n61bt1JVVcWaNWu6vTOvHTaXF6r2d8jqUBCMsCcxznlxfig9RUrJzp072b17N6qq4nQ6cTgcLF26tN/GGoKl0UlJSVRXVxMIBKipqSEjIwMXf0Lg7eDpCnzE8G+88g6kSIo4pibmUidfws4mXDwcIYSgA1prCXj7m6mNYDOCyB52JGNtkEk9T0NrSzZV5hPHTzoYawAFH05eokXejxTxGGIczfKbxPFQqwcuERg081UcvImT11pL6HX8LAXsyDBCUxIFjVkR530+VVVVIYcjMzOzx/v1F13Xyc7O5uDBg5w5cyZkZA3DCP1pM842m42MjAzS09NJSkrC5XLhcrmIjY3F5XKFbTnXdoy2uLbb7ebs2WBKZGVlJVVVVSGtIiEEqqqiaRrHjx/n5MmTCCEYM2YM8+bNY9q0aR8Jz/tDd4YZGRk8+OCDPPvss5SUlBAIBMjOzqayspLrrruO4cOHR9z3zoyFVGnNbK3LwSpUDGky0pHED7LWDuqcpZS4DT8OxYK1D4JR9fX1vPPOO5SUlGC1WrHZbKSmpnLPPfcMqOB9ZmYmtbVBkauKigoyMjKwcThsWEJiwcphAlwF0sDJizh5AYEbjVl4+ByGGIcUcfi4BSH9xPBoB6Md9K4zieWvHYxp8GgBJE7A2ysxJwGo1CDwIEnAIV8hlj9yfkOC9nOwcAqN+UCwe3tAXoGV/YBEYwExPI6D1zvkbtvZhZ/F2DgENHeYY7CY5xM9nnNFRUXIM+3q+ztQNDY2sn//fg4ePIjH48E0TXRdD3nSUkoSEhIYP358qFl2cnJyn/LDLRYLCQkJIY31lJSU0NOclJK6ujoqKyspLy/n9OnTNDQ0IIQI9R89ffo0RUVFbNiwgXnz5jF//nySkiI7CZc6HzqDDcG41wMPPMBbb73FwYMHURSF+vp6nnnmGRYtWhSxq4oqFL4yejX3D7+MQm8NKdZYxji77tjSX7bW5fDPs9tpNnwoCJYnT+GzI5fjUCIXaLQhpeTQoUNs27YNXdex2+1YrVYmTJjA7bffjtPpHHCDfeLECYQQocd0iS2CoJKOk1ewyUMolGLjWGjBzsYurBykQf4VQwTXGLysQ9BIDM+1eqkaAeag0NjJ8xWhv719imAHMz5qUeV+Yvm/LjNMBAYmyaH/K7ISgYcAlwc9dOnHySth5ujHzh4a+R/i+TW0xrRN4mnmhxhibM/mKiVVVVUhYziYHvbZs2fZtm0beXl5IU9a07SQkc7MzCQrK4usrCxSU1MHPZYuhCAlJYWUlBSmTZvGypUrqa2tpaCggIKCAsrKyggEAqiqiq7rbN++nZ07dzJx4kSuuOIKRo3quhnJpciH0mBD8M590003kZmZybvvvouqqqG+kKdOnWL+/PkR87WTrK5BVctrY3dDAX8q3tQhM2VrXQ61ATc/nnBLl/tWV1ezadMmSkpKsFgsOJ1OLBYLy5YtY8WKFYNSDddmLFRVpbi4GCklPq7DyaudjLYggI2DSA5xvkhp0CP3BfOS+VXri4IWPotXfgyVEkxSMEUqKXJNl3NqE4Dqje0Q6MTzw9Yc6cjGWqJgMAJDjEOR5cTzg3aSripu+RU05nURK1dI4Ccdro2Chzh+S508F5LpisrKSnw+Hw6HA6fT2a9uP5Goqalh8+bNnDx5Eiklmqah6zqmaRIXF8fs2bOZOXPmRU8nFEKQmppKamoqixcvxuPxcOzYMY4cOUJTUxOKomCxWMjJySEvL48pU6awatWqixb3Hww+tAYbCHUAz8rK4tVXX6WoqAhVVamvr+eVV14hPz+fK664YsCqI3vLk2U7O6URatLguPssJb46RjmSO+3T2NjIzp07OXnyJEDIq05LS+OWW24ZVA9s9OjR2O12NE2joaGBmpoaROqDWDmOSlGrB61Ca9dxiJzFIZDY2EOMfAwvt4Ri3VLEoDM5tJ3JMBS6ltE931h3txgJGiqlnSogzx/DIJNGfgVSJ5EvolDbmncdJI7f0sj/Rp4XnRewBQaCBmzsCmbSdEN+fn4ofjtmzJgB9WqbmprYunUrhw8fDnnTmqYhpWTs2LHMmTOHrKysIVsK73K5WLJkCYsWLeL06dMcPnyYwsJCNE3DarWSnZ1Nbm4us2fP5qqrrhqUm92F5kNtsNtISkrigQceYN++fWzcuBFVVfF4PBQWFnL69GmmTp3KZZddFrZb+GBS7g+fRqgKhTPe2g4G2+12s3fvXg4fPoxpmlitVqxWK6qqsnTpUpYvXz7oiy6qqjJhwgSOHTuGEIKCggKGDVtCg/wbVg5g5SQOXkOlsvvBCBadxPAYMTyGJifTwufRxPwO27TwCeL4Vdj85/Npq1wMdqsxW4tVwuX/ym6NddAPn4pJHDZ2tZasdxxL4CeGZ/BxO05e7DBHiR2JikLnnHVBCxYKemSwCwoKQjou48YNTLGVaZrs3r2bLVu2hLzpQCCAlJLJkydz+eWXD7ga42CiKAoTJkxgwoQJ1NXVsWvXLrKzs9E0DZvNxqFDhzh+/DjLly9n6dKlQ/YG1BM+EgYbgt72okWLmDx5Mlu2bGHjxo3ExMSgaRo5OTlkZ2czZswY5syZw4QJEy7Ih5pojaFW61w1KJGk2+ORUlJcXMzhw4fJz89HSonFYsFut6MoCpMmTWLVqlUdumoPNpMnT+bEiRMoikJBQQFLliwBIdBYgMYC7HIL9NBgwzkP3EYOVr5Ns/wmfnEuDOIXq1FkBS4ehzAZF21IBD6uxy2+A1Ji5Qhx/BCVujDH7G5OwRHtbEWhGpNkBN6w26qU0sjvCer8vdSqXWLg5QYsFGNjf5i5OjHoXiWxsbGRqqqqUFeggYjJ1tTU8Morr1BaWhoy1KZpMmbMmF6pNw5VkpOTufHGG1m4cCHbt28PedyGYbBp0yays7O55ZZbLtpTdX/5yBjsNhISErjllltITU2lpKSE3NxcrFYrmqZRUlLCmTNniIuLY+bMmUycOJFhw4YN2uLKnekLeOxsx+pKBcEwNZb6E2d47Nib1NbWIoTAYrFgtVpRFIVRo0axevVqxowZ08Xog8PEiRNDK/Tl5eU0NDSQmJgYet/HNbgo6RQOCOY+21ozKcIj8BPL7/HLVR3iu17xMbzyNuxswcWfOzTpbX8EB+9hyhRa+DSamENAzsbBljBpdd0b7eB8NKwcIVKjsGDYZBwIFQ9fwCM/hUJNcJFSOLHKQ1g5fp7nDcHayBXdHj83NxcIPtmMGzeu1406pJS4fQGcNiuKoINX7ff70XWdtLQ0VqxYcVG+S4NJeno6d9xxB8XFxbz//vtUVFRgsVg4e/Ysf/vb31ixYsUl6W1/5Ax2GykpKSxbtoySkhJ27twZMtyGYdDS0sLu3bvZtWsX8fHxZGVlMWHCBEaMGBExn7QvXJ86i1rNzatVh1AQ6KZBvEcw4mAl7wcqUVUVu92OxWJBCMHYsWO57LLLmDRp0kWrdnM6nYwfP568vDw0TePo0aNceeW5R3svt2LnHVTOhlL0TBz4uQaDNFw8SaQUuiA6KiWtxTLtEDH4uQG/vJ4Y/k4MzxJU5gsKPLWVszt5DokVL58AIrVlE6FKxjYPP3LX9K7yUAQePtnuv3ZMzqkfamIuXnkDTl5s3boNAwsl6ESWA5ZScuTIEVRVRVGUXufSv77nJH98eQcNHi+qojA5SWE01ZiGjt/vR1EUli1bxqJFi1DVyH0xL3VGjx7Nfffdx759+9i5cyctLS3Y7XY2bdpETk4O69atu6Ri2x9Zg93GqFGjuPvuu2loaODAgQMdck/bjPfhw4c5dOhQKM2orUAgLS2NuLg4XC5Xj+LHpmni8Xhobm6murqayspKRGUli+sCNDtNbAFwBRQsFjtqTPCHarPZmD17NgsXLhwyj3ELFy4kPz8fVVU5evQol19++bnzFw4a5N9w8C52NiOJwcvNaCwCjFY51cgGW2Ag6SJDRwha+Bw+uYZkPtHJyCr4iGE9XvkxrJyI4ElLTFJaPX4vBsNRKUGlvlfXwSQdXXRRACN1HLx3XoYMgI9YHqKBRyLuWlhYSENDQyg7ZMaMGeTn96wf5IZ9Ofxi/SZ8geCTm26YHK+SVFrsTLe7SU9P57rrrvtQZU90haIoLF68mKysLDZs2EB5eTkWi4XS0lL+/ve/c/fdd18yKYAfeYPdRmJiIqtWrWL58uXk5uaSk5PDqVOn8Pl8HcpvGxoaqKur4/jx4x32dzgcxMbG4nQ6Q2W1bZVhfr8/pFDWvmy3rQDArqo4/cEFROEMhj+ysrKYPHky06dPx26P3CHlYjBx4kQSEhIwDAOv10teXh7TprVT/hN2fNyEj5vO29NCk/whCXwfwrTpkijoZGGK7m9MCh4k1rA51MFO5W5MIntOKhWt1ZMqzfwPSkg6tWda3xIrPq7uchsLBRBmcVMAFk4hpAcpwt+cDh8+HAo9zZkzp1dPdn98ZWfIWLdhIqjW7cy8fAlXL7/8Q+1VRyI1NZV7772Xffv2sWPHjtDv8fHHH+fGG29k7ty53Q9ykYka7POwWCxMnz6d6dOnYxgGxcXF5ObmUlBQQE1NTcjgttdNaDPoDQ0N1Nd39tLadKStVmvo3+11FSCYyTJu3DgmT57M+PHjBzT0MtAoisKCBQvYuHEjiqJw4MABpk6d2qMwjSYWUyefxMm/cfAWwZCG2ZpV4aKpizS59gSNdSTjqiCJxcsdWMjrZITPpRxqgEYcP6aOF7GQ21oE092xaR1/XTfbqXRVOh8+Mh7san/69OnQ92XBggXdzOgcpikprwungA42q4XkkeM/ksa6jTZvOzMzk1dffRWv14tpmrz66qtUVFSwZs2aIR3XjhrsLmhb7GlLpwoEAlRUVIQUympqamhubg6FULpDCBHSV0hOTiYzM5PMzEyGDx+O0xkp3jr0ME2TGTNm8Nr6N6k+2UgF9ewdtZ/FKxb2bH8xHA9fxyO/go09qJzBYOS56sEeYGcr7dsQtBFs8zUWhIWAXIGPo60aH6I1za8zCm6sHETjMhxs6EEKoQU3X0C2NViIgMH41vBOxwwTiUBjJojwwkU7duwIHsViYcKECb1KN5XSxGFR8Omdv48SSE8cetKsF4NRo0Zx//338/LLL4ccsQ8++IDm5mZuv/32IXtTixrsXmCz2Rg9ejSjR4/u8LppmrS0tNDc3IzP5wt5321etM1mC8W6h+oXoT1SSpqamigrK6OioqKTvrHH46HgrTIqDtUjDYlQ4I87n2DvPYdYfOccbDYbNpsNu91OTExMSACok+ciVAIsBZb2eo4qxWEXBIMmvLUiTwg8fBWvvBM7O3DxMITNy/aTwLcIML/LMvU2JBYMsrqfpFBokj8mgW+0FswEWhsE22nm22F3qaioIDc3N6Rut2LFiu6P04phGLzwwguMtXvI0x3tSnxAVQRjhiUyJi2xx+N92ElISODee+/lrbfe4tSpU5imycmTJ9F1nXXr1g1JMamhN6NLEEVRiI2Nveilu31FSklZWRmnTp2itLSU8vLyUEuq9nrGbX/qTzVTdaQBDBCIkA3c9+9jjJiVTtLI+FB4pP3fbUL1SUlJJCUl9esHoTMDkz0ondIHbWhMRpHVrel1KqbIxMs67PI9LOR08rJF64hWDmEwrFUcKpIYlIrJCHR61sBYF7Ool89g501UitGZip9rkSL8d2X79u2h8NnUqVMZOXJkj47TZqxPnjzJaEsAt8Wg3IjFYbOiGSYTMpP5n7uuCLuvphvszimlsLKBzOQ4rpg+Gofto2EabDYba9euZevWrezfH8yZz83N5bnnnuOuu+4acg7WR+NTidIJTdMoLCwkNzeX3Nxc3G53j/WNKw80YGqdvVvTkJzclM/i+85lTrTF7IUQIU+9vLwcIQSJiYkhcZ/eNpb1cQMxPIUk0C41T9CWiRLDC0gcuOXn8YsbAWjmOyTyRUALa5CDHWyqaOE+HLyKQiNgBXQkDgQmOqNo4te9Ei8xRSpeHuh2uzblubbCqJUrV/ZsfNPk5ZdfJjs7m0AggK5r3LdsEnMXLqGkponkOCeZyeGbb9Q0tfCf/3gXtzeAN6DjsFp45N2D/PoTqxmbntjjc7yUEUKwYsUKLBYLe/bsASAvL48XXniBO+64Y0gZ7T4bbNM0+dGPfhR6fPvpT3/6oUu+/zBSU1PDvn37OHLkSIcMmDb5zDbjbLfbO+gbtz1BuFwufrfjEZoKT3ceXIK3ycf06dMJBAL4/X48Hg8ej6dDp/W2Rde6ujrq6+vJz88nMTGRzMzMHqvASRFHvfwbcfwaqzwCQiCxtxbm6ARzrP3E8X9I6SIgrsIQWdTJp4nh6Vap13ALgiZ+rqBFfObcfGUtFgowSQ2pC/YK6cfONlQKMBmJj5Wd4tc+n4933303JGA0d+7cHqfdvfPOOxw/fhy/34+maSxcuJDly5cjhCDB1fWN8Hev7qG2yYvZ+rn7NB2fBj99bjuPfOnGi97d5kIhhOCKK65ACMHu3bsByM7O5q233uLGG4fOdeizwd64cSOBQIBnn32Ww4cP88tf/pK//OUvAzm3KAOEaZrk5OSwb98+CgsLQ0a6vXSm0+lkypQpjB07NmSkI31JF14/h6KjJQR8WofXhVVgpvhpaGjodPPWNI2Wlhaampqor6/H7XZjGEbIeNfX19PQ0IDNZiMzM5OMjIxu0xlNMZJG/kBt7VnSUhpI4mudNEIEflw8GtTlBqRIwSO/gIOXI+iJmFgowWgnQCVFChp905lRZGVrRx4PCl5MHLj4Cw3yTxjiXHHQ+++/j9vtxuFw4HK5WLVqVY/GP3jwIB988EFIuGnu3LkhY90dXr/G0cKqkLFuT01TC6U1TYwadukUlQwES5cuRdM09u/fjxCCAwcOkJGRwcKFPVtQH2z6bLAPHDjAFVcEY2Jz5szplJcc5eIjpSQ/P59NmzZRU1MTEqJvU2RLSkpi4sSJZGVlkZmZ2eN0pqs+tpSNT2ynrqwezR80eqpVwZFmJW6sg02bNnHfffd1MLhWqzUkVD9q1KhQH7+6ujoaGxsxDCOUu15YWMiZM2cYMWIEo0eP7jbFUWLHQjkSJWwWSFBGtR3CipQphNM8EYCVg/hZ3aNr0R1x/ByFupBwlIIPiZ94vh/sekOwSObo0aPYbDZUVeWGG27oUaPd4uJi3nzzzZAmSJu2TE+9Qc0wI9boK0Lg03rfif5Spy084vF4yMnJQVEU3n77bVJTUwdMfKs/9Nlgu93uDotsbSLi7ReSsrOz+ze7QcTn8w3p+fWX0tJSdu/ezdmzZ7FYLKFQR1uJ+4wZMxg1alTox11X11kkqSu+9vSnef+p3Rx46ziqVWX+TTM4o5/Cr/moq6tjw4YNrF69ukvjER8fT3x8PIFAgOrqaqqrq0MtoYBQ/8C2riaRYom6rlPbEEtsghHWAGlGMjUNHXsoOuJGEWfrbLClVPB4LdR4e95zMRKK8JCSdBQhzlf5kyiygsb6ozQ0J/Diiy/S0tKC1+sNyZmG+262/842Nzfz3HPPhYo/UlNTWbRoUagjUE+QUpIa56CiIZyiIMSpOjU1/b8O2aV1PLfnFKW1bhJddm6eP45lUzLDfjd0fWCO2V/mz59PSUlJqD3bww8/zB133DEgZez9sT19NtixsbGhTAIIPnafv+o/derUvg4/6GRnZw/p+fWVxsZG3njjjVCaksViISYmBpvNxrx585g1axbx8fH9P1AqfOwHd/KxH9wZeik7O5s33ngDwzAoKioiOzu7R0UfMTExJCYmkpWVRV1dXagLd5sOdH19PR6Ph6ysrLDl+TU1NcQmLsZgNILCDqEOEwc+9VOd5EJNeRcmxztXNgorSsytpLr6Ly8qpBrMogn7poWEeBtvvB3MuU5NTSU2NpbPfe5zEb3rtu+sYRg8+uijoVRJh8PBxz72sT4Zk6+vvYwfPLMVTTdDoRG7VeWLNywkI73/Ugj7TpXx2zcO4deD3npFQwuPvZ9NYwA+sWp2p+1ramqGjLTrxz72MZ566im8Xi9Op5NDhw7x4IMP9jvdrzvbc+DAgYjv9bmkZ968eWzbtg0IltFOmhRZyCbK4COl5MCBA/z5z38mLy8Pv9+P1+tFVVUWLFjAZz7zGZYtWzYwxjoCU6ZMYfbs2SHBol27dlFYWNjj/RVFITU1lZkzZzJ58mQcDkcohNPmlZw4caJTp20AhKCR36IxC4kNkxhMHLTwAH6u77R5gMX4uLm1wtKKxIbEhpvPd4gt9wdJIgaRpG9VNmwsoLy8PCSfevvtt/coFLJt2zbKy8tDTyM333xznz2/WePS+d1n1nDF9NGMTIlj0aRMfnb/SlbOHphr8Ne394eMdRuabvLs9hNsOVo0IMcYLOLi4rjlllsQQuD3+6msrGTLli0XdU59vlVcffXV7Ny5k7vvvhspJT//+c8Hcl5RekFjYyOvvfYaBQUFGIaB3+9HSsmMGTOYPHnyBYu9CSFYtWoVtbW1Ib3lDRs2cOedd/bKa2oT2UpOTqa6upri4mICgQCKolBdXU1DQwMTJ07s5G1LkUQjv0eRNQgaMBgFIsLCpRB4+DI+uRYbu5BYCHBlj3RMenEiuOW3SOBbQKC1BF8ANo4U3MaxYyex2WxYLBbWrFlDVlb3xTjl5eVs37491Hjgqquu6rdw0bj0RL5zR++Ll7rDF9CpqPdEfP93r+5hYmYyI1MHz4noL5mZmVx11VVs3LgRTdPYtWtXr/LjB5o+G2xFUfjf/+2Z7kOUwSMvL48XX3wRn8/XmoOrk5iYyHXXXceIESMueDxQVVVuvvlmnn76aRoaGggEArzyyivccccdHXSze4IQgrS0NJKTkzlz5gyVlZWhXPHs7Gzq6urCPtmZIhXo2Q3CEKPxMrr7DfuIJuZSL/9GDE9h4RQGozlWsITnXs4NaZzPnTuXxYsXdz9Xw+CVV14JLTKOHDmS+fPnd7vfxcJqUbCogoAeXk/FME1e35fHF67ruVbKxWDOnDmcOnWK4uJiVFXllVde4XOf+9xF0fsZuionUbpESsmOHTtYv359aMFK13UWLFjAAw88wIgRI7ofpJ+czavgn99az09u+R1P//glakqDC5cul4tbbrklpOXt8Xh46aWXaGho6NNx2tQLp0+fjs1mC+WMV1RUcPjw4fAhkiGEIcbTLH5IvfgXu0/ex/Ov5IU6B40ePZobbrihR5kd+/fvp7KykkAggMVi4dprrx0y+cHhUBWFq2aNi1hjZEoor+vccWmoIYRgzZo1WK1W/H4/NTU1bN269aLMJWqwL0E0TeOll14KPab5fD7i4uK45557WLFixQW58x/ZdIL/ufbXbH1mN7kfFPDuP97nOyt+RuGRYgDS0tK49dZbQ4/8zc3NvPjii73ORmlPQkICs2fPJi0tDcMwMAyDpqYmTp48SVNTeIW6ocTRo0d5++23g5K6djuZmZnce++9PVrEqqmp4cCBA6FQyJVXXklSUtIFmHX/+Py180lLCB+Xt1lUZo4JH4I6fqaKnz23nW/88z3WbztOc0vnhsYXkoSEBJYvXx6qX9i1axcVFRUXfB5Rg32J4fF4eOyxxzh69CiBQACfz8eIESO47777LohXDWAaJn/96lMEvAFMI5iyZmgGPo+fR7/xTGi70aNHc8stt2C1WrFYLLjdbp5//nlKS0v7fOw2b3vcuHFIKUPhgcOHD1NdXd3vcxsM2p6G3nnnHVRVxeFwkJGRwf33399jlcZNmzZhmiaBQIARI0ZcEtrNAA6bhT9+7jpcDmuHfBlFCBw2C9fO6xi3L6lp5tuPb+Q7T2xix8kSThRX8+9tx/nsw2+Sd7aWLUeL2JNbSkC/8Dnis2fPZsyYMaE+mJs2bbrgc4ga7EsIt9vNE088wdmzZ/H7/QQCAWbPns26det6lF0wUJRkl6GdV+XYRmluOZ52eb1jx47ltttuC3nafr+fl19+maNHj/b5+EIIhg8fzrRp00K52YZhcPLkSSore94A+EIQCAR49dVX2b17N1arNeRZP/DAA8TEhJdXPZ/S0tJQ3q6UslfFMUOBOKeNP33uOhZMzEQRAkUI5mVl8H+fWUNczLlF4X9vO84PntvD0aIqDPNc3DugmzR6fHztkXf44xt7eejFXdzz0EscK6q6oOchhOCqq4IVs5qmcerUKc6cOXNB5xA12JcIbrebxx9/nMrKSnw+H4ZhsHr1aq655poLLk6jWJROglDtEWpHYzJmzBjWrVtHbGxsqIhny5YtbNmyBcMIekpSyh5pircnISGBWbNmhdL/2krwh4rRbmho4JlnniE/Px+73Y7dbmfChAm9MtZSSjZu3BiSEJgyZQrp6ZFSBftPdWMLuWdrafGHvyH3lYykWG5cOJExw+KxqILyejfZpeeeiIqrG1m/7QS6Gf57JVv/eAM6LQGdFr/GD5/ZiieC4zBYDBs2jGnTpoVkHd57770ufwsDTVSt7xKgpaWFJ598kurq6pBg0w033HDRCn9GTh6OKzEGf0vHxT4hBFlzxhAT1/kxPzMzk1tvuI0/fO3vlB2uAQHlExsoOlWMtTyWfS8fwef2kz5uGHd+7wZmXtWzc3M4HEyZMoXCwkJaWlqwWCyhkuKL1bNQSsnx48fZsmULgUAgtPh62WWXcfXVV/eqo0lBQQFFRUVomoaiKCxdOvDpdwBNLX5+8fwOTpZUY1FVdMNk7eLJfHL17AHx5rccLeL3r3+Av7Xc/WxtM394fS9ltc14AzobDhb0OswhJezMLuaauT3QJh9Ali5dSk5ODpqmUVpaSm5uLlOmTLkgx4562EMcXddZv359yLOWUnLjjTde1CpNIQRf/tuncLjsWO3BBU6b04YrMYYHf3df2H18Hj+/vONhyg7UYvhMDK9J/fEWPvh/2Wx/Zi8+d3BRqbKwmr99+WmOv5/b4/lYrVamT5+Oy+UKedrZ2dl9zkrpD22Lqxs2bEDXdZxOJ3a7nbVr1/ap/dTWrVtDGjBTp04lOTl5UOb9o2fe53hxNQHdpMWvEdANXtuby8t7ev45RMI0JY+8ezBkrNvwawZPv3+c1/bm9smj1wyDBs+FX4xMSEhgzpw5oe/a1q1bL5iXHfWwhzBSSt544w2Ki4vx+/2YpskNN9zA5MmTu995kJm4YDy/2fVDtj6zi/L8SsbNGc0Vdy7GlRD+UX/bs7tprvVgtP/RmiDDPAJrPo0Xf/UWM5b3/DzbBP9PnDiB1+tFCMHJkyeZN29ez7S2ZYAYnsDJawha0JiJmy9iiJ41KjAMgyNHjrBjx44OXnVKSgq33XZbnwotysrKKC0tDXnXg6UYd6aqgdOV9ehGx5CUXzN4fscJbrusf95jg8eHxxc59VI3ujZ2QgS96fOxqirTRl2cMvbFixdz9OhRNE2joqKC0tLSC9J5PWqwhzB79uzh8OHDHarahpL+SWJaPLd87doebXtk00kC3p7nS1cUdB2HDngDFJ84izPOQeLIYKWczWZj2rRpHD16FF0P6okcP36cuXPndhvnT+A7WDkSamxg5QBJ/Af18m9damBLKcnJyWHnzp3U19ejqipOpxNVVVm8eDGrVq3qc5rl/v37Q5kwU6dOHbSF5Yp6D6qiQJj2aA2eYNVsf8IiMXZrWIPbHYoAh83KuqXT+Pf24/g1I6RgbrMoTBiexPTRFyfs5XK5mDp1KseOHcNms7Fv376owf4oU1BQwLvvvhvS0pg5c+aQrmrrim3P7uHEjrxe7SNsgnfeeYf58+d3Kmvf/MQOXv7NBhRVwTQk8cNi+dLfP8HwCenY7XamTJnC8ePH0XUdt9tNTk4O06dPj3gsi8zByrEOXWiCvSGDWtpNdJZdME2TgoICdu/eTWVlZShdr82rXrt2bafen73B6/Vy7NgxdF1HSsmcOXP6PFZ3jB6W0Mm7biMtISZkrAO6wYu7stlwoAC/prNoUiYfWzGLtNbGvr6AzqYjhezNO0uCy871CyYyZWQqDpuFJZNHsDunNOKi4vkkxzm4c+l0rp2XFdx/ykj++d4hjhRV4rBaWDMvi3uXz7io2TJz5swJOQcnTpxgzZo1g56tFTXYQxC3282LL74Y0gXJzMzsVqp0qHLgnaM8/t3n0APhmgUAIhgTbx8aERZB6rxYcnJyyMnJYcSIEcycOZMJEyZwclseL/9mAwHvuZhnTUkdv733b/xi+/ew2i3ExcWRlZVFfn4+hmFQU1NDaWlpxLCEheOEa84rkFg51uE1j8fD0aNHOXr0KE1NTSG1PFVViYmJ4YorrmDhwoX9Ll46cuRI6MkqPT2dzMzMXkmn9obhybHMHZ/BodMVHRb+7FaVj68MKupJKfmff20hp7Q2tM2mI0XsyT3LX75wPTarha89soHaZi9+zUAA204Uc9/ymdy5bBpfunER+/PLO30POve9B6uq8PGrZnP51FGh3pJj0hL48X0rBuX8+0rb51JRUYHVauXQoUMsW7ZsUI8ZNdhDDCklb775ZqitVmxsLGvXrh2SHZx7wou/fjNiKMRiU7n1P69j10v7qSmtQ1EVNL/GyIXpxC+yIITANE3Onj3L2bNniYmJoeiFmg7GGgAJAb/OkY0nWHBD0MCkpaXR0tJCWVlZqClCSkpK2EIVSRISS9g+jyaJeL1eioqKyMvLo6CgANM0Oxhqm83GkiVLWLp0aa97U4ZDSsn+/ftD1Zxz5swZ9Jv1d+9cyl/fPsDmo0VIJE6blU+snMWqVtW+Y0VV5JXVdTDoppS0+DVe2JmNqgqqGltCnrokGAN/autRrpo1llNldWEbskmCHd0VIRAimHMtpeTv7xzkz2/t45YlU/jEqoHJVBkM5syZw1tvvYVhGOzfv5+lS5cO6lwvTSvwIebEiRNkZ2eH8jyvvfbaQX3MCvg0Nj+1g23P7kFKWHbHQlY/cCX2GNuAjF9ZFL760GKzcM8PbmHNp1dw81fWUHziLA2VjYyZOYrEtHhKS0s5cOAA+fn5KEow79vr9dJQEb4EXfdr1JY1dHht9OjRNDY20tLSghCC3NxcZs/u/OP3s4xYftN5TMPG+wfH8d72P4eMtKqqoSa5MTExzJs3j8WLFxMXF77JbV+oqamhpqYGXdex2WwXJGXMbrXw1ZsX84XrFtDi14iLsbXGtYMcKarEF+YpyTAl+/PL8Ab0sGEVRQj25p0lp7Q27P4AqqrwwMpZrH//OAHdRDclemvWyCt7ckiJc3LTokk9NoR+Tae0ppkEl53U+J7lu/eVyZMns3nzZnRdp6GhgcrKSjIyMgbteFGDPYRwu92hu7WmacyePZuxY8cO2vF0zeBnt/+ekuyzIa/1xV9Xseul/fzojf8Kpez1hOZaN021btLGpHTYL3VkMmfzOmsuqFaVsTOCizRCCMbMGMmYGedCFiNHjmTkyJG43W6OHDnC0aNHcbvdxKTZaSr0dhpPCklRTQE7dqgkJCSEGgYPHz6cU6dOYRgGjY2NlJWVMWLEiFB82+124/F4UOVnmTvuLwh0pDRRVcneoyN4b3s8FoslpPEthGD06NEsWLCAadOmDcqTT25uMJXOMAwmTJiAzTYwN89IlFQ3knu2lqRYB3PGZZAY2/kpId5px2ZRw+ZKxznt+LQIIS8ABE5b5Ouk6wY2Ve1Q3dhGQDf5y9sHeOb943x85SyuXzCRgGbg1w1iHdYORlxKyQs7s3nm/WMIRaDrJlNGpvK9O5eFPaeBwGKxMH78eLKzs7HZbOTm5kYN9keFd955B4/Hg9/vJy4ujuXLlw/q8fa/dZjSnLIOIYaAT6O8oJL1P3mFzIkZZM0Zw7jZkRfPPA0t/OXLT3Biey6qJZiJcet/Xsf1XwiWT9/2jev521f/1SEsoloUUkcmM2lR9x3IY2NjWbp0KUuWLKG4uJgPEvbz1k+3YWrtftwKWONUfDHNYbt1NDY24na7Q0Y3MzN8e6rX1NVMHFNLbIxOcXkabm8sMTFBL3PEiBFMnjyZKVOmhO16M5Dk5uZiGAamaTJhwoRBO45umPzyhR3sO1WOogR74zhsFn7x8ZWMSUvssO2iSZk8+u7BTmM4rCprl0ymoLyOV/bkBvtEtsOUkiWTRzAxM5nX9oZfeFYVwenKhi4zSRpb/Px9w0HePpBPUVUjAClxTv7j+gUsmhTU0Nl0pJCn3z/WId/7ZEk133tqMw9//rpBC1VkZWVx8uRJTNMkNzd3UH+3UYM9RCgvL+fYsWOhUMiaNWu67RreX/a9daRTtSJAwKux8fHtWKwqCMHEBeP4ryc/j83R2eP+zf1/ofBoMXrACDXkfem3bxGb7GL53Zex6Ma55OzJZ8u/doX2mbRwHF/8yyd79AMydANFDYYixo0bx7jPjmPmtFn841vPUF0cVP6LH+9k5Ork4HwhVMTQ9ndiYiJ1dXX4/X5UVcVisYT6WbZ1bW/7d2lVMLSRnJzM+ImZjBs3jkmTJg1oyKMrPB4PpaWloY7yg9l84t/bjrPvVHkHr9kb0Pnvp7bwxNfXhkIi2SXVfP9fWxCKCGqiElwstKgKq+eMJy0hhgP55VjV4PaaYSIARREkxzr581v7uWXJZOKcNprDrGdohiQhxo4MG+U+h183yC+vD/2/ssHDz5/bwU/vv4oZY9J45v3jnYpzDFNSXucm92wtU0YOTs722LFjUVUVwzAoKyujqalp0Do7RQ32EGHTpk1IKWk404x2RuG1vE0suG4Wi26ci6WLx8n+4Ii1BzM0wrg2pmESaPWW8vae5oVfv8Ht37iBF3/zJu+v303ApzF2xkgKj5WgB86rYGsJ8PJv3+aytfP55V1/4szJs+gBHYvNglDg+i+sJmFY11/orc/s4sWH3qS+spHYRBc3fenqkNc+fdlk/t+uH+N1+7DaLNQ31mOz2aisrKSqqorm5uZQqMPtduP1eklPT+fEiROoqkpLSwuZmZmkp6cTFxcX+pOUlMTw4cMZPnz4gCwe9oVTp04hpcQwDEaMGNFjzZG+8Ma+U2FDHC1+jY2HCymqaqDR42d3TkmnDuqKIlg5aywxdivffXIzAd1AymCGR6zDil/TkQgqGzxUNXjYn1/Gsqmj2XysMKwn/eoHuUzKTCGntKaTl94Vft3gqS1H+dUnVlPT1LmZMAQLb8rr3INmsB0OByNHjqSkpASbzUZeXl6Pepn2hajBHgIUFRWRn59P4aZyKvY2gCEpkmUc2XyCt/+2mf955evYnAMfx1x+92XsfvlAtwUtml9jy792cmrf6aCBbvWkT+2P3K+xrryB1/74LoXHSkLKfm0pXX/87D94+OgvcLjCP0G899g21v/kldC83PUeXvrNWzTXe7j7v9eGtnO2xiWFECQkJJCQkBC+A02rcNJzzz1HcXExLpeL6dOnc/fdd3d53heDoqIiTNPEMIwetQzrD5GEkzTd4E9v7sMwzIg+r2FKtp0oxjBlB6OvGSaGKVsb+rY+6RDMGNl24gw2i9rJC4agx37Dgomkxdl4/+TZHudrAxS0et3Dk2Iprum8KG1KyZi0/nc774oJEyZw5swZTNOkqKho0Ax2VEvkIiOl5J2336X8QC0Ve+qRugx5IP6WAGfzKnjv8W2DcuxJC8dz7YMrsDmsqKoSfOSNgM/jp/hkWchYd0fKiCS2PrM7vAyrgMObToTdzzRMXvjVG51uIn5vgHce2YrX7Qu7X1e0ZXesXLkSRVEwDIOcnJx+6XIPFm1piADDhw8f1GNNyAzfAEE3JXoXxroNX4TMEDNCMNqiKpgRDLFhSjTDwKoqKIqC0ot4c0sgqH3y8VWzsVs7VrRaVYUJw5MZnzG4zR7aPivTNCkrKxu040QN9kXmjcff4eWvb6JwQwUyzJNgwKex/dkPBu346757Mz/Z8C1u/cb1XP+5laE48PkkZcTj72HXD5vTxi3/eR0Bb/jt/S0BTu07Hfa9xppmAhGEgDS/xh8e/AeBPkpqpqenM2XKFDRNQ0rJ7t27+zTOYBEIBKiursY0TYQQgyqjCvDgNfM6GTiLIiK29DqftMSYXokeSSlRIjgFft3gj6/vZdPxYHOC9kZfVUQoPh4Oq6pwqKCCpVNH8cUbFpAQE8xosaoKl08ZyY/vXUHe2Vp+8u9tfOaPr/PTZ7eTX9b3zkfhGDZsGIqiYJomdXV1+Hy9dyx6Qr8M9nvvvcd//dd/DdRcPnJUFFXx5y88jhEwkV0oSw62EtiIycO55WvXcs8PbmX1J6/Efl74xea0ktjdI6US3M7hspOUHs8//usZWpojfGklbH5qJzm78zu95Yp3hlf6aeX49hz++a313Z5TJJYsWRLS58jOzqa5ubnPYw00bU2GTdMkOTl50NP5po0exi8+voqZY9JwWC0Mi49h0aQR3Xq3bd1iPrFyDrYwN/hI+/s0A70LCdWAYYaNXwsh+MNnr8VmCW+uVEXBGwjexK+ek8XT37iVf37lJp779h18585lHDtTybce38junFLO1jazK7uEbzz2HnvzznZ5nr3BYrGQmpoa0ncvLy8fsLHb02eD/dOf/pTf/va3vRadj3KOV//ydugDjoTNYWXZnYsu0Izgvh/dxsd/dieZE9JxJcYw66qp/PcLX6U0t5svoBnMLvG1+Kksqgm2DuviPqP5NV586I3Q/5vr3Ox57SBHt2az5Jb5qBF+nNKQ7Hn1AJ7G8AtM3TFs2DBGjhyJpmkYhsHBg51T1S4WbY/SpmkOiHcdKfzQnqmjUvn1J1fz8n+v48n/vIUH18zrcntVEVw5YzR/eHANK2aN5aqZY3FYzy2FOawWXGGyidroRpgv4jFb/BpzxmUQ7lYQ0A1mjU1vt71CSnwMDpsF05T84fW9HYSj2mLqf3h974A6QxkZGSF7OFgGu8+LjvPmzWP16tU8++yzAzmfjxQ5h0916VkDpI8bxtWfGtx87PYIIVh+z2Usv+ey0Gs+jx89zEJRWHrx/S9pvQm8/bfNPPeL11CtKiAwDQPVqmLo4Z0BKaGhojGilGt3zJkzJ5Q6d+DAAa644ope61QPBhUVFZimiWmafS6+MAyTf209xut78/D4NTKTY3nwmnksmdIzedeMpFhuWjSJV8LoYNssCp9cPZdblpyTvf3KTYu4fOooNhzMxxfQWT5jDK/vzQubvtdX/JrBn9/az9fWLuZIYSX+MF76ntxSrl/QWQq3vL4Zb4QQW7M3QFWDh/SkWAAa3D4QkOjqW4ZQWlpa6Anpohns559/nieeeKLDaz//+c+5/vrr+eCDrmOrbX3ohiI+n++izk9KSZNSByrhVC2BYDXgvb+4BXdLM+6Wvj2667pOTU1N3ydKcK5xKbE0Vg5sZ/LE9Hg+2LCf5375OppfD+VxA4R1pVoxDROcZui8enuOycnJSCmpq6ujvr6eDRs2DGq+c0/Jzs6mtrY25PWdf049Oc+/vHuU/aerCLTe7Mrq3PzihR18cc0s5o3rWcHP7QvGoAf8vHmw6JycqaowOTOJJeOSOs1hXJKNL6yaFvr/3hwHBRWdI1uqEkwh7UUCSIji6kY2HshleFIMRdUdfwuGKfnzW/sZlWBjeFJHGQeP2xe2ghLAlCbu5kZKK6r428bjlNd7AMhMjuWzq2cwJrV3ufdCCFpaWvB6vWRnZ0e0L/2xPd0a7DvvvJM777yzT4MPJe3m88nOzr6o8ysvLydzbiplO2rRPeE9SSEE4yaNITap71oiNTU1neRJ+8I931/LP76xvqNR7Qc2p43bv3Eju17YixbGAwoW1ciw4eyFN8xhxOhzHeL7co5Llixh7969xMTEoGnakPiubt68maSkJHw+H6NGjep0Tt2dZ1WDh32nq9DOezIJ6CbP7yngmoXTIuzZmS/enMq65bN5/3gxHl+AeVnDmTFmWI+Kne5ZMZvdeeWdHrZsFoW0BBflde5Qjn9P0QyT7Tnl1HvCr4sYpuR763fx2Wvnc9Oic6mdqamQlujibG1HIy+ArIxkkpKS+ea/XsfbTuekuKaZn7+8n0e/fCNJsT3rat9GTEwMDoeD+Pj4iN+p7mxPuGrdNi7+c+BHlNzcXBSrYPLHMrHHd15cUq0q06+Y3C9jPVAceOcoT/3Pi8EfYB+qe1WLSmJaPDaHFWecA3uMjTu/fSMLr59NfUVj2DCKNCVWpw3lvIa+aWNS+OKfP9GX0+jAxIkTQwUqeXl5Q2Itxu12h7zrvgh+na6oxxqhUUNpbXOv47XDElzcsXQqD6yazcyxaVQ1trD1WBEH8sswujC4h05XhDXsyXEx/OFz1/HlmxYxKiUOIXr3dQroBqqIbLJ0U/Lou4cobZeLXdfsDVtQI4H7Vszkzf2nwqYmaobBm/s7L4p3RWxsMLQipaS5uffXuydEC2cuErm5uZimicWl8h9P3M8L33ubqjPnHjUzxqfx+T/cfxFnGKQk+ywPf+GxTpKmovXxNlLMWijBUm/TMEFIfB4/CFj3vZu5ct2SkBrg9CsmU3SstJNOsj3Gxr0/vJXqkjr2vXEIi83CyvuXsfoTV4Q0S/pDRkYGLpcLv9+Px+Ph7NmzF6RjSCQ0TcPr9bamvil9qnBMjY+JuNAY57R16R0fPl3By7tzqG5qYfbYdG67fCrDWtcITFPyxzf2suloIZbWWL/NovLT+69iwvDOPSaf3X4ibBiirK6ZkupGVs8Zz+o546lu9PBBXhmv7M7hbF33Ib/JI1JQhODg6YqIYQ7DNNl0pJAHVgVldt89VBD2mihCsPNkMXVuX9jMFE03e536Z7fbsVqtmKaJpmn4/f4Br5jtl8FevHgxixcvHqi5fGRoamqivLwcwzBQFIXpc6Yyb9McTu0vpKKwisysdLLmje3R4+eZE6U8/8vXObW/kLhkF9d+diUr71/ao0W0I5tO8OzPX6Msv5KEYXHc9KWrWfXAFR2O+/bft3QqPQewWFWu/tSVlJ2qDBbBtP4mgguHEkMzQ9oQhmZiaMGc7Gd/9ipXrlsSGueaT69gw9+3oJ+3RqUFdOZePZPk4YkdqhsHCiEEWVlZHDt2DCklubm5F9Vgu91uIOiduVyuPgkVZQ1PIj3JRUl1U4c8ZrtV5ZbFkftjvrgrm6e2HA1VIBZXN/Le4dP834NrGJkazxv7TrHlWBGabqK1NnrwBnS+9+Rmnv6vW7G2u4FKKXFHyJOXEg4UlJM1PBmvX0MRguvnTyCnpLpHBvvYmWC4pyu/1TAl7nb9I0trm8MaZFNKSmubmToylUOnKzp52RZVQSJ5cVc200YNY8rIlG4/EyEELpcr9Fm63e6hZbCj9I38/OCjlq7rjBo1KvShTlo4nkkLu1ewa6PwaAk/vfV3+L0BkEHlvGd+/DJnjpfw6Yfu7XLffW8d5i9ffCJUhFJ7tp71//sKNaV13P39W0LbVRRUBb3k89D8OrVnG5gwbyxaINgk1h5j4/B7J9C1yI/LpmHy/r93c027zBcjzKq/AF7/47s88PN13VyFvpOVlcXRo0cxTZNTp06xevXqQTtWd7S0BB/bpZR91g8RQvCT+67iB09vpaK+GUVR0HSD5TPGcNeV4VukNXsDPLH5SIe4t2FKPH6Nrz36DmZr6Xk4j1Y3TPbnl3NZuwyU7oxaXXMLP312Ox/kBnOgnXYLNy+ehNWidIq9n0+gm/ch2AcyLdHFk5uPEmO3MDwpFru1czm8RVWYPCKFmxZN4o19ncMiumFypLAyJGo1ZeQwfnzfcmzdPN3FxMSEcvs9Hs+ArB91mPeAjhalR5SVlYXSf/rT92/9T17upLYX8AbY8fxe1n7lWlJHdX5chaBRePqHL3WqGPR7A7zz6Pvc9KVrcCUGjUbW/LEUHD7Tsds5YHVYOfTeMQ6+eyx8+XkEAl6Np3/4Iu+v381XHvk0uR8UoFrUTl68oZt88NrBHhvs5lo3z//6Dfa+fgiAxTfN5Y5v3UhcSmzEfdoU+wzDoKqqCk3T+t3aq6+0xdCllN02DO6KYQkx/OU/rud0RT21zV7GpyeS0oWI/9GiSqxqeGMZSWukDW9A5/W9eSyZPKKDoXbZrXgipNK9sS8f0zyny9fsDfDM1uNcNXMMW4+f6VMGSXtMCf/acoyAbmBRlZCq4Pmd162qwtrFk0lLdPGTj63g1y/uotnrRwKB1pztNiNvmAYnS6p4dtsJ7l85q8vjt//sBmNdJLroeBForxfRH7Hz/AjiS6pFJW9fQcT9/N4AdeUNYd+z2FSKT56rALv2M1dhtXe8rwtFYOommk/vlbFuw9BNik+e5X/X/q7rwqEI3lrAG+DpH73Eg5O/wQOjvsrv7/8H3135c95fvxt3vQd3vYet63fzP9f+Ohg7j4DdbicpKSkkDlVR0bnRwoWi/Y97IHSbx2cksXBiZpfGGujWY+yO48VVvNVucc4wTPQuDJVhdhZRlcCO7BKunT+R9mvMfb0KbWJUemvlpG4EGxmoikBVBBMzk/n1J1eHmgfPGJPGE19fyx8+ey2fvnoujjDVmwHd5O2D3S9Ctg9FDobBjnrYFxjDMKisrAwZqv6I4TtiHeF1NQS4EjtnGeQfLOLNP2+korAq4pjeZh8NrQLxEBRx+p+Xv84/vrmeouMlCGDS4ixyduf3axVcmjKoTWISNuSiWlUuu6Vzl3gpJb+652FOHz4TSjEsPFzSaTtDM2iuc7Pjhb2sfuCKiPNIT0+noaEBCKZaXqw4dvtreSH7F84el07fTWNwce75nSe5YWGwaKXJ6++yEUEkArrJu4cKOlRCDlSOhRCC5dPH8PP7V2JKSUyYTkpCCEYNSyD3bG1ER8EbqZH0eeO0MRhZIlEP+wJTVVUV6iaSkJDQL73jVQ8s6+T9QlBcKWPcsA6v7XhxLz+/4/fse+swJSfLurz7/+Ob62muc4f+P2bGSP737W/y95yH+Hvub/jOv7/U5zm3J+AN0FTr5r4f3Y7NYUVpFfixx9hIHZHErf95Xad9Tu07TdGxkh7lg/tbAhzdfLLLbdrKiQdbZa072ntmg60d0x6bReW/1y3DblX77G3Xu72hfo2xDluPxaPOpwuxyH5hGCZ+Tcdhs4Q11u2ZOTY97BOCAGaN6d65av/E2J/QViSiHvYFprKyEgg+LvW31dTar6xh4+Pb0fzuTu89/B+P8b9vfwsI6nY8/p3nOqbmdWETTMNkxwt7ue6zKzu83qZfbejB7BbD7GG5egRsThsjJmWw4LrZTFw4js1P7aSxqonZq6Zz+a0LwjYCLjh0JuwiZTgUVSExo2vRqrbPwDTN0GdzMWgz2G0x9cEmu6SG53acoLSmifEZSfz4nuXkV9RT09RCYUU9J0t63khA003u+vULrJw1js9dO58FEzLZlVPSK09biLZr0PmYLrsFu9VCXTtpXYfVgmGaKELg1w0E5xzj8+PgFovC/AmZPZpHeqKLa+dm8e7h06EYtiIEdqvKp66e2+3+7R2hwZA7iBrsC0zbCrKUkqSk/mn0Bnwa3uYwDWlNSUlOOTWldeCAwiPFvStQ8GpUFkUugc7Zk4/FrvbYcIZFgB4wOLkrj7EzRjFm+kg++cu7ut0tIS0ei9USNtXwfCw2lVX3L+tym8TEROBcscPFon07OL+/ZzK2fWXb8TP8v1f3hBbXztY180HeWX54z3Juv3wqXr/GD57eSk5pTYdGAsHa085IgiGN9w6fZtPRQhREr4y1qghWzBzDtuPFnd6zWVRuXjSZ+1fOotHj50BBGVWNLYxNS2ReVgYf5J5lZ3YJTpuFy6eM4g9v7KWpxR+62TisKpdNGUXW8J7/1r5w/QImjfj/7Z13fBR1+sffM7Ozu+khhZAQIJCQ0EIRCL0jnCgCCqKogF3PO7snp55654n9fnfnnXp2RWwoiIoigkgvERJ6AgmphPRGstk68/tj2ZWQ3fQG7Pv1yh/Z7Mx8JzP77Hee7/N8PsGs3pVCpcFEfFRXbpwUT2RIw7ZfJpPJmRZpC7VFT8BuZxwdUI5625ZgMpgQBBFXYiSSRsRQWYO3Xoesk5v0mK3z1tKnHuNdk8GMWE/HmXMMsoRGluxlh1D7067aHWg2fbidrZ/u5onVD9B7cMP54+EzB/PBsrqCYxpZsltUnU0R2awKNz5zTS0ndlc4roGqqlRXV6MoSocIQTm65ARBoLq6GlVV2ySXbbMp/GddYq0yN1W1V0S89u1e3r1vNl46mUevGcttr31Ta9uG7iCborptaHEgCQJD+oSRWVBOaZURvSwxsGco247kuEylB3jrWDhxIIIgEOirZ9qQ2mWvEwf1YuKgXs7f/xt5BV/vTmVnSg7eOpmrRsYyJT6qgZHXRhAEZ3NPU6mqqnJet7bwAfUE7Hbm3JbVlgbswLAAfLt429u7z0eFiJgwyivL6RUfiZefvk7FhCAJCAi1Fv1EScTb34vRV7uX2YxLiG60ep+s02A2WlDddaZZbNgsNt595BP+vuGxBven89ay7PM/8MpNb2A+m8e2mq387o7JzLpnGgc320V1hkwdgF+Q+5I+B5IkOfVEVFWlqqqqzQxU60Ov16PRaDCbzc6ftjBhTj9d5sw3n09xpYGyKiNBfl7sSsk9+6XcuukZjSRSXGnAYLYiCPYGln3p7qtzKmtM7ErJZbKLoFtttPDp1kNsOpCJTVEY0y+SJVOHsGTaEGenY3titVoxGo1otdpmd6s2hCdgtzMt1Ys4F0EQWPzcgloNMA7MJguv3f0eC56+EjFE5P537+CFhf9Bsdkw11jQ++jw9vfitldu4MuX1pF1OBdBgEGT+nHrSzfU6yHpE+jNtY/OYs2rP/w2e3aBzWKjqqxxutU5x/LIPJzDj2/9wrFdJ/AP9WPW3dMYNXtYnZlmn6G9eC35OVJ2p2GoqCEkOpDe/aIAGD+/6drhPj4+lJXZfQE7KmALgoCfn5/TqaSqqqrVA7bRbOWl1Tvc5qZVfivzU84+BbYWkigQGeJPRBc/fk3Lc46hoWYYk8XG59uO1AnYVpvCI+9tIKe40jmr35B0km1Hsvng/qvx99FjtSlsPpjJhuR0VBUuH9qHqYOjanVmtibV1Xa1P0fHoyeHfRHQmgEbYOSsofiu9OHtBz+mMLvE+bpiVTiw6SjVFdU8+dWDxFwWxT/3/pUdXyVSkFlEcEQQob2CCYkM5r53buOHN35m/0+HSNuXyXuPfsqCZbOJinefohg9ZzjZR09x8JdjVJVWt/g8VFXl73P/idloRrGpFOeW8vaDH3MyOYtFT82r835JIzFwvL3duqXysT4+PpSW2nUjHG3FHYGfn5/zXKqrqwkODq7znvTTZXy+/QhZhRX07hrAgvEDG52fXbsnlaLKumseYF9YG9AjBN+zX9SjYrvzwaYDzTyT2vjoZf5x6+X0CA1g7nNfNMkVHaDExTrNrpRc8kqr6qRgasxW/vbZNl5cOo0nV2wm5VSxM/2TdrqUDUkneXHpNDT1WI41F8e94/jybQs8AbudsdlszoDdWl11/cbEUO3ig2g1W0nbl0VhdjFde4bg28WHyYvG8tpd77L5451oZAmjwVQnXXHg56Mc2X6cZZ/fS7/RdUXhf3hrM58+uwZVUd2mOpqCIAp4+eupLjfUSpSaDGZ+em8Lv7tjCkk/HWLdG5s4U1xFr0GRLHziavqOaHqO0RXnXof2qNBwh5+fn/NporKyrvb4gawiXlt/ELPVhqpCTnEFu4+f4onrJjCyb8NVED8fzKjlcH4ueq2GR+b9ZloREezHvNFxrN2TirGx5hUuEAWBGpOFe/+33q6O2Iz7RSOKXPv8KgDG9Y/klulD2Z9+2u25HM0pYtPBDFLzSmrl6k0WGyfzy9h+NNtliqWlOK6ZKIptFrA9ddjtTFuU/VhMVgxuZk4arURBRpHz9w8e/5wj21KxmCzUVBndBlyr2cpz1/6bnz/e7vyCUVWVVxe/ycqnv0KxKi0K1tLZbjKdtxbfLj5YaiwuV7UkjcTbD63kk2fWUJhZTE2VkZTdaTx/3WsuPSGbgyAIznPsSJnV0FC73rQgCHVKDBVF5Z2fj9qtrs7+nxyLhf/6Zk+j0hfuvBYFAeaP609oQO0nvqXTh/LMoskMjurarNpqrSQCdsMCq01pVrAGKKs2YjBZMJgs/Hwwk/ve+hFvrfu5pigKbEg66TJXb7RY2XI4q1njaIjCwkLn9Wtpya47PAG7nTGdMVOaeoaqHKPLDr/mIOs0+LnRzbaabYRH2/3uTAYzu7/e12gTAlVRee/Rz7h7wGO89eDHPHPVqyT9dLjF4x0zdzjz/3QlE68fzQ1PzeMfu59xWXPt4Oj21Dq5cnONhY+f/qrFYzmf9mxaOZ+IiAgEQUAUxToBO7+8CoMbfY4qo5n8sobTUpcP7YPORf5WliQmDnRdFTSkdxgvLJlGv+4hyG58NmvvS8RHJyNLImab0ihtEEkUCDvbmStQf9+lTVE5U2PCq54GGFEQ8NZq3O6npe347sjPz0cURQRBIDw8vE2O4QnY7YSqqrz5yIdsfT6Zk98VkLG2kGUTnifrSG6T9uNqBigIAnMfuqKO27msl+k/Lgb/ED9sVpu9Q7AR7bXnU11uYOtnu0nfn9nkbV0REhnE7D/M4M7/u4npSybg5atn4vVjXHZtKoqK7MbUNetwbqsE2HP30RbdaY3F8SEXRZHCwsJa11qnkdzWNiuKis6F/sX5XDUylqiwQKdpriDYpVevGz+A7sHuF1oVRWX54qlcNaIvPjrZbjwgUCsP3K97MK/d+TvCAn2oMVublKeWNRK3XT6MB+eM4vlFY5mdEItUT9ujyWLjSE6R21m/43q6ylPrZYkZw1onlXb+MQsLC51PzRERjWvUaSqeHHY7seGDX1j35k8oVhXHs39l0RmeX/Aa/0l+Dk09j3hWs5UvX17Hpg+2UVNlJKJvGDc+cy1Dpv5m+XT5LRMxGy2s/ed6bFYFVVHoPyaGwuwSbo9+yG4oIImtJ9DQTPQ+Ovq6kJC99pFZnEg8SdbRU1iMZmSdDILAwieu5ovnvnGxJ9D76hpdq5x1JJfje9PxC/LlshnxtapgrFarcz8dacbr5+eHn5+fU/y+pKSE0FC7xECwvzfdg3zIKjpT6xIKAkSFBRLk17CVlVaWeOXWy9mVksuOYzn46GRmXBZNXPe6i5sA6/en8fHmQ5ScqcHfW8uCcQN4aO5oXlq9E5PFVkuSNLekkiqjmeIzNbW0uBuD0Wxl+art9vPBHmjrS5+IAlRWm9zey1ZFJTHtNJIoIJ6j0qeVJSYN6sVl0a0/+y0vL8doNKLT6fD29iYgoP4O2+biCdjtxKpXv8FoqNvBZrVYSdp4hJGz3NeN/uee9zn481Fn6V7eiQL+ddvbPPjBncRPsnvDCYLAVb+fzu9un0x5QSWl+eW8sPC139rRFRUaoSfclmi0GkJ7BjN0Wl1tZq2Xlr+sfZCUXWkcTzxJQKgfCbOHoffRse6/G+3/u3PlMfUaptw0rsFjWi02/n3HOxzekoKKvaFIEAT+9MnvnYuWBoPBGbBbo3KnJURERFBRYa+rLygocAZsgHtnDubvq3/FZLVhNFvRyxp0ssSyaxv+PzjQSCITBvZkgpsUiINv9x7n3Z+SnIt2lQYzH/9yCF+dto62NNhTFTuO5bRARsqOCg3OziVRJLOwvFGNPPLZ8/X31jFxYE/6RYa0SUOSQ+lRFEXCw8PbTMDLE7DbibICF80t2DvyygvK3W6Xn1HEgU1H6xjVmo0WPn12rTNgO9BoNYT0CGLFU19iMbaOYW5j0HrJdWzEHEiyhFYvM+7akVz3+NVOkafzEQSB/mP70n9s7cqUxz69l+Xz/+2saFFVlbhRMSx47KoGx/X9G5s4vCXF+WXnGOHLN73Bfw8sR9bJbd6d1hQiIyNJSUlBFEUyMjIYNGiQ82/dAn344IE5bDuSTVZRBb1CA5gwsCf6ep7OmoNNUWo50DgwWWyYLK4Xt80WG7IkuZ0Zu2trbyqyJBLdrYtdVa8RWBWFsEAfFk9t20aazMxM5/pDZGT93bUtwROw24m4kTH8+mNSnTykKApED4tyu13mwWwkWcTiQl7i1PHTbrfLOJDdrPyuRqup46/YEJIs1Tuj0Opl/r3/73j5Nt4uSVVVUvekcyr1NGG9Q/m/xL9ydPsJyvLL6TO0Fz0HdG94J8BPH2x1KUGr2FQObj7GsBmDMBgMztI+R4t4RxEbG8umTZuQJInMzExsNlutvLpeq+HyNsjBnktFtcnlLBrs96vqQtNaK0uM7BtBVlE5h7OKapXcaTUSS6cNZvyAXrz01Q5ST5WgEQVq6ikXlAQQRBHprDeo1aYwb3QcCycM5M7/rmt08FdV3Ob+WwtFUUhPT0eS7J+D2NjYhjdqJp6A3U7c8vfrObj1qF0D+iySLBJ9WRR9hvZyu11QeKDbqYm7yhCA4MggtyYF9WE1W3ll51M8OeNFjFWNEyESBMG1LvdZFJvC7rX7mXLj2Ebtr6qsmucXvEZ+ZhHqWW0P/xA/nlh9f628fWMwnjG6fF1VFKorDBgMBqduh7e3d4cuOoJdPTAwMJDi4mKMRiO5ubn06uX+/mgLfPQy7m46RVHRSGKt/LUsiYQH+TGkdxgDeobw1vr9bDyQgU1RCPbz4qbJ8YyM7U6gj56Xb72c3OJK8suqePXrXZS7MZgQRZEXlkwjs7ACvVZiVGzk2XHZDYVLXTTTuEKWRMb2b1uN87y8PGpqatDr9fj5+bXZgiN4qkTajb6X9eHlTU/Tc3B3EEHUCcRM7sEjK+6pf7uRffAP9UM4b9Vc66Xlirunud3u6vtmuGwv12g1zhpoV3TpFkBg14BGO8kIgkBE37B6Z9gmg5nS02WN2h/A2w+vJPf4aUzVJsw1FozVJopzS/n37e80eh8O4kZHu6wTUxSVuFHRznxxW3anNQVBEIiLi3PO1hz+n+2JTtYwZXBvtG7K+AQgxM8LAXtAnBwfxUtLpyGKAjpZwx9nJ7D6zwv4x20zCPDW8e/vErn5H19z93/XcfxUCZEh/ozoG8Et04eicVENIgoC4wf0YEDPUGaNiGHq4N7OYA0wb3Rco6piBOyljH0jXFvltRbp6ekIgoAkScTGxrapAUWzAvaZM2e4++67uemmm1i4cCFJSUmtPa6Lkv6j+vLX7x5h3JMDGXZ/HyImBaF1U7LmQBAE/vzFH+nWpys6by1efnpknYbxCxK44q4pbrcbNn0QCx67Clkv4+WnR+etI7RnMDc9ey0+AV6IUt2bSuel5ZqHZ3F8bzqSXM/D1zmbqqpK3on8emvK9T66etvcz8VYbeLApiN1PCQVm0L2sTyKc0obtR8HC5+Yg867djWJzkvLmDnDCYsKddY7i6LYZs0OTSUuLs4ZANLT0zukNvyeK4YzPCbCZemcxaZQUWPi00evZe2TC3lo7mh89LUnBwazlSdWbCbtdBnWszZdWUUVPPbhJgrL7TXjM4ZF88fZCXifU84piQLXjOnHQ3PH4I4Zw6KZEh+FViOhkyW8tBo0oogk2tMvoiDgpdXw0NzR/OGqka3zD3GDqqqkpaU566/j4ty707cGzUqJvP/++4wePZqlS5dy8uRJHn74YdasWdPaY7soCQsLQxRFRFGktLQUk8nUoMhPaI9gXtr6JJmHcqkoqiQqvgeBXRsWKLrirqkMviKOitxqvP280Oplnpz5EmYXgk16Hx3XPDKLyTeO5diuE24XBgFkraZW801D2tS+XXwYNn1Qve9xYKw2uZ2hSBqJqvJqt+bCrujRL4K/rXuEL178luN70vEJ9OF3d0xm6mK7TrajO00UxTZ9lG0KvXr1Qq/XY7FYqKioICcnp0Vmzc1BJ2t46vqJzHrmE5d/lyWJYzlFjO7neoHtp6R0ewv9ea9brDZe+HI73jotPUL8mZ0Qy5fLFmA8q953pqK8VmWMKwRB4P6rR3Hd+IEczCzARy8zsm8EBpOF9NNlBPrqie7WpV2s1vLy8igtLUWn0yHLMr17927T4zUrYC9dutQpzm2z2dpEBvJiRZZlQkNDOXXKbnRbUFDQqA+jIAiN0os+H523jgFj7Qt07y/7zOWCokYrMeP2yfgG+bDy6a/oGhWK5GIG7qCx0qoOlr6wsN4vgHPxD/HFJ9Cb8oK6WhqoKhF9m25a3D0unAffu9Pl3/Lz851567bqTmsqkiQRHx/P3r17MZvNJCcnt3vAdqCTJZdaIqqq1ludciKv1KXWh01RScktQQWSM/L5YX8af1k4wekIU9WEIBse5Ev4ORK6OlnDiL4N16O3JsnJyQiCgEajIT4+vtX0gdzRYMBetWoVH374Ya3Xli9fzuDBgykqKuLRRx/l8ccfd7ntsWPHWmeUbYDRaOyw8dlsNsrKylBVlePHj7eJbq4Dq9XqVIDLPJLjMnVhNdv4/s2NSJKEyWBG6yXba5ZlqU5qAmiyhshbD67g/o9uIziycapyc/80k5VPfF0rj67Vy8z641QqqyrgPEG9c8+xKVgsFnJycpxuMxUVFZ3mng0ICHCe04EDBxgyZAg6na7FyoTnYjRbySurxt9bS4iLxhuz1YafXovRRSmfJAqE+4puxxPiIyNLAhZb3XvF8Yrd8MDGi1/u4D+3TkYUhWZfy47AYDCQlJSEoigYDAYCAwMbdf+0JPY0GLAXLFjAggUL6ryemprKQw89xJ/+9CcSElxrEPfv39/l652BY8eOddj4qqqqKC4uxmAwcObMGUJCQtrsWMXFxc79x42MIetgbp0UhiAKWM02rKr9dUc9tazXYGvc2mO9VBZV8e59n/HilicRBAFFUdj4/la+/9/PnCmtJio+kuufmONsZJm+aBLdIsNY9eJ3nE4vICQyiHkPzXLbXHTuOTaFrKws9Ho9er2esLAwhgxpf9H7+jhx4gQZGRnU1NRw6tQpYmNjW+VeUVWVT7YcZtX2o0hnKz76RgTxxHXj6eL7W+B+ftV2ymvqVnFIosBfF00mrKv71MU1E3xYl5SJxdZwiahVUSm3iMR2D272tewI9uzZ4+xs7NGjBxMnTmzUdg3Fnn379rn9W7MWHdPS0rj//vt59dVXmTRpUnN2cUnTp489MEmSRFZWFhZLK0TFRjDztsl1WuAFwV5X66qKy2pqPanRklNlZB+1p4E+WPY5nz77NcU5pZiqTaTuTrer7+3+rSJi0MR+/HXdI7yV8jLLN/653k7Q5pKWluZc3IuJiWn1/beUkSNHIooikiRx4MCBVpN+Xb8/nVU7jmKy2jCYLJitNlJyi3lixWbnAmd5tZFdKblYXHTHaiQRL53Mqu1H+WLbEbKL6jaFdfH1YvniqXQN8EEnS079Ene4UxLsrCiKwoEDB5AkCVEUGTmybRc3HTQrh/3qq69iNpt57rnnAHuzwRtvvNGqA7uYCQ4OJjQ0lNOnT2M0GsnKymqXgBHcvQtPfPUA7zxkL5sD6DWwO1lHcrFZ6n4wJY2IoigoLh5rm4ooiVQWnaEgs4jNH++sU/lgrrGw8pnVPLve7vR+Or2Ab1/7ibT9GXTtGcKVv59epwOyJaiqWqvZoa1X95tD//798fX1xWq1UlVVxbFjxwgLC2vxfj/beqROY4xNUTldWsXxvFLiugdTXGFA1kgu28StVoX7316PcjY1tnLLYWYnxHL7jNqu4v0iQ/jggavJPesK889vdpN6qm6Vj07W0Kdbywyp25sjR45QUVGBXq/Hy8uLgQPryi20Bc0K2J7g3HLi4uKcFQonT55stxle78E9eG7jMqrKqp3+jX+a8Cx5aQV13qv10mK12jAb3NuANRar2UpUfA/eX/aZ2zK1rMN25cL05CyWX/svLCYrik0h70QBR3ee4Oa/Xdso/ZDGUFxcTEVFBTqdDp1O1+7NKY1BkiTGjBnDTz/9hCRJJCYmMm7cuBYvbLlrOhEEyC+rIq57MN26+GJxM6O3qSo262/X0KbY+C7xOCNiwhnap/aisCAI9AgNwKYoVLup7b9jxjDEetT5OhtWq5WdO3ciSRIajYZRo0a1+WKjA0/jTAfhKLCXJIm0tLRmCedXlxvIzyhqcis52EvtvP3t+crbXlmE1kv7WyWHYM9rG6tNLksA3aHRalyqDmq9ZKYvnYhfsC+Ht6W63d4ho/rBY59hMphrLZCaa8x8/MzqJo2nPs5Nh/Tt27fDOxzdkZCQgJ+fH1qtFoPBUG9+s7GEuzEnVhSVqK52lbmMgnK0Lv4n7uKqyWJj/f50t8f89cRpl1ZfoiBwOLvIxRadl+TkZCorK9Fqtfj4+DBmjPua8dbGE7A7iMjISHx8fNBoNFRXV5Oe7v5mPx9DZQ3/d8tb3DvkcZ6Y/jz3DFrGj+/80uyxxI2K5qm1DxLZLxxRI4BqTxkoNsW9Yo8Aovzb7aPz1pIwexivH36eK+6aSpfwADSyREhkEIuemseip+2+jPV9uQwY1xeLyULmYdca4aIokJ7UcrcQRVE4dOiQsx6+M6ZDHMiyzOTJk51fKImJidTUNK4t2x1Lpg2p0ykoSyL9eoTQq2sgmQXl/GXlZqpdGCb0CHFf/19tdP9lmpJbTI2La6+oKoeyCiiqqOa9n5J4ae0+3tmwn4KyjvPWrA+j0cju3buRJAlJkpg4cWK7ljV7tEQ6CFEUGTZsGNu2bUMURZKTk+nbt3E52pdveoOMA9lYzVasZz8jny//Bp9A72a5his2hfeXfc7p9MKzet24DNQarT3f2290DPMemcXxPens+TYJvY+OaYvHkzB7GKIocuMz13DjM9e4PFb/sbEc2HSkzuuCKHDTX69FlOxB1Ka4Liesz5mmsWRkZNTKP3bmaiaAYcOGsXPnToqKijCZTOzevZspU9x3uTbEuP49qLlqJO9uSHYG2YmDenHvrBEAfLbtiMvFRr1Ww9A+4RSUGzBaagdfnSwxfoD7WvFgPy90GgmTi9psL63Mnf9dh82mYLEpHMsrY11iGs/eNJlBvTpH96mDxMREjEYjer2ewMBARowY0a7H9wTsDmTEiBHs2LEDjUZDZmYmpaWlBAXV38WXc+wUWYdz6sxUzTVmVr+yrlkB+8DPRziVerpB/ZCQyCBe2fG08/fYEX246t7Lm3SsG/4yl2M7j9eRYk24cihhUfYysWEzBpG04RC284KGl78XUc1oHjqf5ORkZ/XFZZddhkbTuT8Goigybdo0UlJS0Gg07Nu3j7i4uBZ1Zk4f0oep8b2pNJjw0mnQnVPFkXa61KUJgV2DWyIyxI/MgnKsZxcdZY1IeBdfptRjbDtpUC/e3Zhc53WdLFFWVVPLf9HRyv7y6l188MDV7dKx2BgKCgrYu3cvGo0GSZKYOnVqu6fSPCmRDiQwMJDY2Fg0Gg2CIHDgwIEGt8lLK3B7k5ScarzA0rkc2pKK0Y1q2rk0tlvRgWJTOLTlGL98spOMgzmAPXXias0xedMRyvLLAbjlxesJiuiC3kfn3MbLT8+D793RYkeY8vJyMjIy0Gg0iKLI8OHDW7S/9qJ///5ERkai1WoRBIEffvgBq7VleueiKBDoq68VrAEiglyLYOllDb56LUUVhloPYKqictfvhqOtR5DJz1vHXxdNwlcv463T4K3VoNWIzBkVR4ULYw+A8uoaTpd2jtSIzWbjhx9+AECr1dKzZ0/i4+PbfRyde2pxCTBy5EhSU1ORJIlDhw4xatSoejsfw6PDsLkRWgqKaF5plH+wDxpZarDlXNY2fiW8MKuY5679F9UVBlSbXT+5z5Ce9BwUiepi/Dabws8rdnDto1cSEOLHy9ufYv+PB8k4kE1Ij2DGzBuOdyNssBpi7969AGg0GmJiYhp8ouksCILA1KlT2bRpEzabjdLSUnbs2NEmfRDXjR/AwcyCOqV/skZkz4k8ztSYa83ArYrKK2t2seKhufXOhgdHhfHJI9dwMLMQo8VKfK+uWG0Ka3aluHy/2aqw/VgO141vmqRuW7Br1y6KiorQ6/VotVrmzJnTITN/zwy7g4mOjiY0NBStVovZbGbPnj31vr/ngO70HNAdjbb2bEbrpeWaR2ZhrjGz8pnV3Bn3KEt63Me/Fr9LenL9C3Xj5ifUkW91RVif+kV5HKiqyis3v0np6XKMVSZMNWbMNWbSkjJJXJfs8ovBarKScyzP+btGlki4ahgLn5jDtMXjWyVYl5aWcujQIefsevTo0S3eZ3vi7+/PjBkz0Gg0yLJMYmIieXl5DW/YRAb16sofrhyJt07GW2u3IQvv4suzN07mWE6Ry3RJtcnCybNPSPUhaySGx4Qzrn8P/L11BPl50T3Yvaztyl8OUVHtWtO8vSgoKGDPnj3IsoxGo2HatGkEB7v2wWxrPAG7g3HMnERRRKPRkJSURGWlC+Gjc3h05T3ET+qPRqtB76ND76tjwWNXMn5+Ai/f9AYbP9iKobIGm1UhIymH5675l1t39iPbU3numn/9Nmt3E7e1XlqmL53QqHPKTcmj5FRpHc0Rq8lKRWGlSz1uWScTFd921koAO3bsQFVVZFkmKirK2XF6ITF8+HB69+7tTI2sW7cOg8HQ6seZPrQPnz16DcsXT+Vfd8zk3ftm0yPUvbGsAFib2Yn5yLyxbr0gRQF2p55q1n5bA6PRyLfffgv8lgoZNWpUh43HE7A7Af369SMyMhJZllEUhZ07d9b7fp8Abx7+6G5eS/o7f1v/J944/AJX3DWN9KQsTiZn1ZI+BTAbzXz10ro6+zmVeppXF79JcW4pimOBT7WLPmm0GnTeWrReMrJOw+x7pzNgbOOsj86UVrvNd6uqWufpAOwVKFNuHt+o/TeHgoICUlJSkGUZURSZPn16p1nMagqCIDBnzhxnw09FRQXffvttq7Wtn4uskYiLtJf6CYKAt06md1igy/dKokhMePPSS9HhXQjwcW0fp6gNm/K2FYqi8N1331FeXo5Op0Or1TJ3bv1pn7bGE7A7AYIgMH36dOcs+/Dhw04X5vrwC/IlIiYMWWfPLZ9MynSd31YhbX9GnZe/e32jSy1rjSxx3Z9nc/Oz87nxmWt5ZcfTzHt4VqPPp9egSLca2WFRITzx5f10j+2GrLM32vToH8GTax4gIKRtHF9UVWXz5s0IgoAsy84FvAuVwMBA5s2bhyRJaLVasrOz2bx5c7sc+77Zo9BrNU6nGFEQ0MkSD1ydgNTERelzmTCgJ5KbtNzIvh2jU75161YyMjLQarVIksScOXM6fM3Ds+jYSYiKiiImJoYTJ044V6RvvvnmJpWcBXT1ty8emupWD/i7CIbZR0+5lFs1GcwUZZewZPl1TTuJs/gEeDPrnmn88L+fa3UmavUyNz+7gD5De/HilicpK6hAFAUCQhs2Y2gJSUlJ5OTkoNPpnOVYFzr9+/dnypQpbN68GUVRSEpKIjQ0tM0VB/tGBPHmPbNYvTuF46dK6B7szzVj+rVYC2TRpEHsTMmh0mByzqj1ssTVCXGEBbr3Lm0rjhw5QmJiIrIsI8syEydOrOVg31F4AnYnYtasWbzxxhvYbDaKi4vZvXs348c3Pk0w7PJ4JE3ddIPOS8tVv69bLx3ZL4KcY3l1graslyk5Xc6G97YwavawZgXU+X+6krCoEL55bQPlBRX06B/BdcuuriXg1CXMfU60tSgvL2fbtm3Ohbpx48Y16GhyoTBx4kQKCws5fPgwqqqyadMmAgICiIqKatPjhnXx5Z4rWrdhJNBXzxv3zOKLLQc4lFtGgLeO2QmxjOiA2XVWVhYbNmxwPsH069evRY1KrYknYHcigoKCmD59Oj/88AOyLLNnzx5iYmLo1q1xLitavcyfv/gjLy16HbPRDAhYzRamLhnPuPl15R+v+v00EtclYa6pHbAtRgvJGw5xcPNRVj6zmmlLJnDdstnOuujGIAgCExeOZuLCjqvEUFWV9evXY7FY8PLyomvXrheVHLAjn11SUuJUflyzZg3XXntthznUtAQ/bx1zRvbhtis6Tg87NzeXNWvWoCgKXl5ehIWFMW/evE6z3uHJYXcyEhIS6NWrl9OC7fvvv8dkaripxUFUfA/+k/wcD31wF3f98yae+vEBbnz6Gpc3XI/+3Xng3TsIDAtA56VF0khO01VFUbGarNgsNja88wu/H7SMxO+T6z22qqpNtg9rS3799VdycnLQarVoNBrmzp3b6bsam4pWq+WGG24gMDAQvV6PoiisWbOG7Ozsjh7aBcepU6dYvXo1NpsNvV6Pv78/N9xwQ6eyQPQE7E6GY9ak1WrR6XSUlpby/fffN8k5W5REBoyLZeSVQ13mrs9l8JQB/Hv/szy3cRnhMV1ddiECmI0W3vjDhxTn1tUztpqtfPb3r7mj7yMs7XU/D415hl9/aLhrsy3JyMhgy5YttVIhncVkt7UJCAhgyZIl+Pv7o9frsVqtrF69mqyslgtlXSpkZ2fz5ZdfYrFYnMF6yZIldOnSuXS6PQG7ExIUFMRVV13lzKGlpaWxY8eONjueKIp069O1QZlWxaaw9Yu6jT1v/PFDNry7xd7erkJhZjGv3/sB+zccaqsh10tJSQnfffcdoiii0+no0aPHRZUKcUVQUBBLliwhICAALy8vFEVh9erVHD16tKOH1uk5duwYq1evxmq1otfr8fPzY/HixZ3SqswTsDspQ4YMYezYsc5V6l27drW5QexlMwejqUcPwmq2UZ5f2w6qKKeE/T8ewnyecJS5xsLHT33J2n//yKoXvuXEryeb9JTQXBx5XJPJhE6nIyAggIULF150qRBXhISEcMsttzjTI6qqsm7dOrZs2dIsvfWLHVVV2b59O999950zZx0QEMAtt9xC166dSyXQgSdgd2KmT59OTEyMsw50/fr1bfqYe+Xvp+MT6O22TV3no2PAuNoSsFmHc12aFgAUZpXw1cvrWPvvH3lh4X947c732jRwWCwW1qxZQ3l5OXq9Hp1Oxw033ICvr2vB/ouRoKAgZ8DR6/XIsszevXtZs2YNRmPHtnh3JkwmE2vXrmXXrl3Isoxer3d+4XXGmbUDT8DuxIiiyPz58wkNDa21oJSTk9MmxwsI8WP5pj8z+caxdYK2RisRHNGFEVfUrvPtEh5Y70KjYrWbIJgMZg78fISdX/3q/JvNaiNlVxqHt6ZgaqENmdVqZc2aNZw6dcpZbz137lzCw8NbtN8LkcDAQG6//Xbi4uKcHZEZGRmsXLmSoqILy92lLSgpKeGTTz4hLS3N+f/p27cvd9xxR4c3xjSEJ2B3cvR6PTfeeKMzN2mz2Vi9enWbVQEEhPpz20s38H97/sqYucPR++jwCfBmyo3jeOa7h2vNpg2VNXz0+BdYXTiTuMJkMLPpo20AHN1xnHsHP86ri9/kX7e/w+/jl7Hls13NGrPFYnH+TxwVITNmzGg3Y9TOiE6n4/rrr2fChAnOGWRZWRkrVqxg9+7dl2SKRFEUEhMT+eijjygpKXE+gYwdO5ZFixah17tuj+9MXPyJvYuALl26sGTJEt5//31UVcVoNPLVV18xe/bsNjPvDYkM4t43bqn3Pe8++ilZR3LdVpa4wmQwU15Yyas3v4npPH/GDx//gu6x4cRcFtXo/RkMBr777jsqKirQarXIsszUqVMZO3Zs4wd1keIwPujatStr165FFEVMJhPbtm0jLS2NmTNnXjRNRA1RUlLC+vXrycvLQ6PR4OXlhSzLXH311W3eHdqaNGuGbTAYuOeee7jxxhtZunQpBQV1Hbc9tC7BwcEsXbrUOdNWVZWvv/6aPXv2tMti3vmYDGb2rT/oVjPEFbJeQ8LsYWz73PUMz2K0sv6tnxu9v6KiIlauXEleXh46nc4ZrCdOnNjofVwKxMfHc+edd9K9e3f0ej16vZ78/HxWrFjBrl27sFga94R0IWK1Wtm7dy8fffQRp0+fdp5/9+7dufPOOy+oYA3NDNhffPEFAwcOZOXKlVx99dW8/fbbrT0uDy5wLIp06dIFvV6PJEls3bqVdevWtfuHzlhtpCnNX7JOQ2DXAGbcOonC7JI6ioJgX7UvzCpp1P7S0tL45JNPqKysRBAENBoNM2fO9ARrN3Tt2pXbb7+dadOmodPp8Pb2RhAEtm/fzrvvvsvBgwcvqjSJoigcPnyYd999ly1btgDg5eWFTqdjypQp3H777YSFhXXwKJtOs1IiS5cudco55uXl4e/ftuI9Hn4jKCiIO+64gy+++IKsrCzMZjMpKSmUlZVx1VVXtVuhv1+wLz4B3pQXutfuljQiiqLStWcIExaOYsatk/D29yJ2ZB92rvkV03m2ZJIsETc6ut7jKorC7t272blzJ6IootfrMZvNLFy4sNOb6XY0oigyYcIE4uLi+Prrr8nLy8Nms2EwGPjxxx9JTExkwoQJ9O3bt9O0YjcVVVVJT09n27ZtFBcXI0kSXl5eSJJEeHg4c+fOvSADtQNBbeB5etWqVXz44Ye1Xlu+fDmDBw9m8eLFHD9+nPfff7/Oh2Xfvn31Wl11NA7n4wsVm83Gtm3bOHz4MHBWZ1qjYcyYMcTHxzs/cFartc1qkPevP8ynf1lby7xX1muIHhGF3kdHeEwoY+YPr9NtaTZaeP7q/1BRdOY3HW4B9D46lq35PYHdXItClZSUsHnzZgoKCpzn5+/vz7Rp0+jevXubnGNnojXvWUVRnIp0DgMERygIDQ0lPj6emJgYZLnxtnCtQXPvV4vFQnp6OocOHaKwsBDAeY94eXkxYsQIBg0a1O6mua5o6DoaDAa3XqMNBuyGSE9P56677mLjxo21Xt+3b1+nNjg9duzYRTEjS0xMdBqyms1mrFYrPXr0YObMmXTp0oXi4uI2rSs98PNRVr34LafTCwmOCGTeQ1cwZm7DSm7lhZV89OQq9v1gfxTvNzqGpcuvo3tc3TI8RVHYu3cvO3fuRFEUdDodGo2GqKgorrvuOrKysi6Ka9kQbXHPms1mdu/ezY4dOzAajVitViwWC4qioNfrGTRoEEOGDGm3crem3q9lZWUcOHCAQ4cOYTQaEUXRaeWl0+kYO3YsY8aM6VR6IA1dx/piZ7OmXv/73/8ICwtj7ty5+Pj4dIpvrUuVkSNH0r17d77++msKCwuxWCzk5uby4YcfkpCQQO/evdv0+EOmDmDI1KabpAZ29ee+t25DVVVUVXXrhp6VlcWWLVsoKChAo9Hg7e2NRqNh8uTJjBs3rsUu6pc6Wq2WiRMnMmLECLZt2+bUgLbZbFgsFvbt28evv/5Kjx496Nu3L9HR0QQGBnbomMvLyzl58iQnTpwgOzsbQRBqpT4kSWLEiBFMnDgRH5/219JuS5o1wy4uLuaxxx7DbDZjs9l4+OGH63wjeGbY7YvVamXLli3s2LGj1mxbVVWmT5/OkCFDLqgv1vz8fLZt20ZmZiaiKDrrqyMiIpg7d26t1uGL7Vq6oz3O02AwkJyczK+//kppaSmKomC1WrFarc5FyZCQEGJiYujduzdhYWGtmjZxNcO2Wq0UFBSQkZFBWlqas/nH4dDkMFUODAxk5MiRDB06tFMH6pbMsFucEmnOQTsDF+uHPC8vj7Vr11JQUIDNZqOkpARvb28CAwNJSEigf//+TunWzoaqquTn55OYmEhqaiqCIDgDtSzLTJo0yeWs+mK9lufTnufpWLxLTEzk+PHjqKqKoijYbDZn8HY8GQUHB9OtWze6du1Kt27dCAgIcFahNPWYOTk5yLJMfn4+BQUFFBQUUFxcjKIoCILgDNKSJCGKIoIg0LdvX0aOHEl0dPQF8cTV7ikRD52XiIgI7rrrLg4cOMAvv/xCaWkper2eM2fOsGHDBrZu3crAgQMZMmQIwcHBHT1cwL5glJKSQnJyMvn5+c5A7TDMHTZsGJMnT/ZUI7UjgiAQExNDTEwMZ86c4fjx46SmpnLy5Ennk5vNZkNRFMrKyiguLq7VDyCKIr6+vvj4+ODr64uXl5cz4AqCgKIoKIpCTU0N1dXVVFVVUV1dzZkzZ5zFCo5Uh2MGLUmSs4Szd+/exMXFERsbe0ndF56AfRHiCHLx8fGsWrWK7OxsampqnHnJ/fv3s2/fPnr27ElsbCzR0dHtftNbrVays7NJS0sjNTXVuWDkWFAUBIH+/fszbdq0Ti3Gcyng5+fH8OHDGT58OGazmZMnT5KamkpOTg7FxcXO9zmCsGNdoqamBoPB4GysO/9h3jEDdwRyR0DW6/WIolhrthwcHEyPHj2Ii4sjOjq60z4ltjWegH0Ro9FoGDp0KPPmzSMpKYnExERKS0tRVdW5OJmdnc3GjRvp2rUr0dHRREVFtXpeEuwf1vLyck6dOkVaWpqzhvz8BSONRsOgQYNISEi4aA0HLmQcHof9+vUD7Kp3p0+f5vTp0+Tl5VFQUEBlZWWzlQF1Oh0RERGEhYURHh5OREQE3bp1u6BLcFsTT8C+BNDr9YwZM4bRo0dz8uRJZ45Yq9U6F5VKSkooKipi165dCIJAcHAwYWFhdOvWjS5duuDr64u3t3eDuUmLxUJVVZXzp7CwkPz8fAoLC50fYsdsytGtKQgCQUFBjBgxgqFDh3bq+n0PtdHpdERFRdUx/nXcB2fOnKGqqoqamhrnDBxwzqAdhgF+fn74+vqSlpZ2SaxHNBdPwL6EEASB6OhooqOjqaysJCUlhdTUVDIzM7HZbLXykuXl5ZSWlnLkyJFa+5AkCW9vb2d++dx8pMFgqOM/6XjcdaQ7HItFYO/ajIuLIy4ujl69el2w3XUe6iLLMl26dOl0FlsXOp6AfYni7+9PQkICCQkJmEwm0tLSOHHiBKdOnaq1gHRuTtLxYzQaqampqbNPx2KhIAi1Fpgcgdjb25vw8HD69OlDXFwcwcHBniDtwUMT8ARsD+h0OgYOHOjUjzabzc68ZH5+PhUVFc7H24Zyk5Ik4evr63zEDQ0NdeYiAwICPAHag4cW4AnYHuqg1Wrp1asXvXr1qvM3R27SZrM50yiONIeXl5ezfMuDBw+tjydge2gSjtykBw8e2p/O3xbkwYMHDx4AT8D24MGDhwsGT8D24MGDhwsET8D24MGDhwuENlXr8+DBgwcPTafd5VU9ePDgwUPr4kmJePDgwcMFgidge/DgwcMFwiUXsBVF4amnnmLhwoXcfPPNZGVldfSQWh2LxcKjjz7KokWLmD9/Pps2beroIbUpJSUlTJo0ifT09I4eSpvwv//9j4ULF3LNNdewatWqjh5Om2CxWHj44Ye5/vrrWbRo0UV3LQ8cOMDNN98M2H1Kb7jhBhYtWsTTTz/tVDBsDJdcwN64cSNms5nPP/+chx9+mBdeeKGjh9TqfPPNNwQGBvLJJ5/wzjvv8Oyzz3b0kNoMi8XCU089ddHqJe/Zs4ekpCQ+/fRTVqxYQX5+fkcPqU3YsmULVquVzz77jHvvvZd//vOfHT2kVuPtt9/mySefdCpZPv/88zzwwAN88sknqKrapAnVJRew9+3bx4QJEwAYOnQohw8f7uARtT6/+93vuP/++wGcWh8XKy+++CLXX399LVPei4nt27cTGxvLvffey913383kyZM7ekhtQu/evZ3SvlVVVWg0F49qRs+ePXnttdecvx85coSEhAQAJk6cyM6dOxu9r4vnv9JIqqqq8PX1df4uSRJWq/WiukEcjtFVVVXcd999PPDAAx07oDZi9erVBAUFMWHCBN56662OHk6bUFZWRl5eHm+++Sa5ubncc889rF+//qIT2PL29ubUqVNcccUVlJWV8eabb3b0kFqNmTNnkpub6/xdVVXn9fPx8eHMmTON3tclN8P29fWlurra+buiKBdVsHZw+vRpFi9ezJw5c5g9e3ZHD6dN+Oqrr9i5cyc333wzx44d47HHHqOoqKijh9WqBAYGMn78eLRaLX369EGn01FaWtrRw2p1PvjgA8aPH8+PP/7I2rVrWbZsWR0zjIuFc70qq6urm+SneskF7Msuu4ytW7cCkJycTGxsbAePqPUpLi7m1ltv5dFHH2X+/PkdPZw2Y+XKlXz88cesWLGC/v378+KLLxIaGtrRw2pVhg8fzrZt21BVlYKCAmpqaggMDOzoYbU6/v7++Pn5ARAQEIDVasVms3XwqNqGAQMGsGfPHgC2bt3KiBEjGr3txTe1bIDLL7+cHTt2cP3116OqKsuXL+/oIbU6b775JpWVlbz++uu8/vrrgH3h42JdmLuYmTJlComJicyfPx9VVXnqqacuyjWJpUuX8vjjj7No0SIsFgsPPvjgRevt+dhjj/GXv/yFf/zjH/Tp04eZM2c2eltPp6MHDx48XCBccikRDx48eLhQ8QRsDx48eLhA8ARsDx48eLhA8ARsDx48eLhA8ARsDx48eLhA8ARsDx48eLhA8ARsDx48eLhA8ARsDx48eLhA+H/YFZWE8+OYKAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "kmeans = KMeans(n_clusters=4, random_state=0)\n", + "plot_kmeans(kmeans, X)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "An important observation for *k*-means is that these cluster models *must be circular*: *k*-means has no built-in way of accounting for oblong or elliptical clusters.\n", + "So, for example, if we take the same data and transform it, the cluster assignments end up becoming muddled, as you can see in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+6W0q6p0YQHxkGF+/YSpXZScHx9h+0tZrxDAMnM5LYyKLQDBYCI+5C84X5rCwsEG55t1zxrP86hwsJvmiaSe9wavqlNU50Y3WfOaK+maefGUbB09VBtHavmOz2TCZTBiGgc/nw+cbns2XBIKhQAhzJ7R5cm3CHKzCku6QZYkvXDeZp740n//+6g3ERwbvul5V4+8bDwRtvf4gSRIhISGBkmzhNQsEnyGEuRO8Xi+qqgZS5axW66Be32JSGBkTziO3zkIJYjrdmarGoK3VX0JCQgIffM3NzUNsjUAwfBDC3Annz6Uzm81DZse4UbF8+5arUYJ0KOgIGdwPmK44/3UVcwAFgs8Qh3+d0NbLARiQ/OXesHBiOpsPn+bI2ep+HwrWNbn53rMfMGdcKnGRoUzLTMRsao1lbz9awsvb8qltcpGdPILPz5tAZuLAFamc/7qe/3oLBFc6Qpg7YTiNapJliZ99bh4bDp7ivX1FnKpswKf2TchUXedoSQ3HztVgNZswmxR+fd8Cdh0vZfXW/IDw7yosZf/JCn557wLGjRq4svE2htPrLRAMNSKU0Qnne3PDoWewosgsnjKaP3x5MWNTYvq9nm6A26fS5PLykxc+ZNWW/HbeuAF4/RpPvbu339fq1IbzXtf+fisxDAO3201DQwN1dXXU1dXR0NCAy+UadjncAkF3CI+5E86Pf/p8PgzDGDZeXbDn+rm8/k77dZysqEfTdJQgTlxp4/wUuZ7G8b1eL+Xl5ZSVlVFeXk5DQwNOp5Pm5uZO49SKohAWFobD4SAiIoLExESSkpJITEzEbrcHZS8CQTARwtwJFosFi8WC3+/H6/Xi9Xqx2YZHC83pWUkUV9QHbT1dNzA6+cwxKfKANfJ3uVwBT7mzPHHDMCgtLaWwsJDCwsJ2VYK6rgdK5tsqNNueA5+FRyRJwuPxUFtbiyzL5OfnB9YYMWIE2dnZ5OTkMGrUqCE/TxAIQAhzp0iSRFhYGC5X6wSQ5ubmYSPMy2fk8NqOAlQtOCEWVTfoSHvNisz8iWlIkoSm6+w+XsauwnOE2CwsmpxBenxkn69pGAYulytQAXjh1PHKykr27t3L0aNHaWlpCQhw25Tttlas52O1WrFarQFx1XUdn8+Hx+Np9zhJkpBlGUVRqKyspKamhp07d2K32xkzZgzTpk0jKSlp2HxDElx59EiYV6xYEfBoRo4cya9+9asBNWq44HA4qK6uBqClpYWYmP7HdoNBRKiNe+dN4LmNB4O2pt5BHDbMbuEri6fi82v8+PmNnKxswONTkSWJd/ac4L4FE7ltVm6frud2u9E0DUmSsNlsmM1mNE3j6NGj7Nmzh7NnzwYmx6iqGhBiWZaJiYkhPj6e+Ph4RowYQVhYGGFhYVgslg6v5ff7aW5uprm5mbq6OiorK6msrKS6uhqfz4ckSSiKgt/v55NPPmH//v0kJiYyffp0JkyYMKTpkoIrk26F2ev1YhgGL7zwwmDYM6xwOBwBr6mxcfgUZqzecoR/fHioT89tcwJ7ch7W7Pbh9au8/8lpisrrA5kgumHgUzWe//Ag1+amEB/Vu3J1l+bl6ZKP2L8kHEMxSHb72PDJdo5s2UNDQwO6ruP3+wPTtENCQsjMzCQjI4PU1NROBbgzzGYzUVFRREVFkZKSErhdVVVKSkooKiqiuLgYp9OJz+fDZDJRWlpKeXk5H374IfPmzSMvLw9FGb7d+gSXF90K87Fjx3C73Tz44IOoqsp3v/tdJk+ePAimDT1xcXFIkoQkSVRWDo8eE3VONy98dLjPz+9NgoJJkfmkuJwP9hd3mJ5nGLC9oIRbe+E1a4bOD4+/RomnFs3SGnIoCXHzWNk7XOOUUTxqwJPOyclh0qRJpKSkDEhYwWQykZ6eTnp6Otdddx3l5eUcOnSIgoICXC4XiqKgaRr/+te/2LFjBwsWLGDcuHEixCEYcLoVZpvNxhe/+EXuuOMOTp8+zZe//GXef//9wGgggIKCggE18kI8Hs+gXNPlclFTU4NhGBQXF5OXlzfg12xDVVVqamouuv3DIyUYAzYlsD2GYeD1uPD5O8520A2DJmdzh3Z2xifuEsq9DWjn70GWUDHYmevHZ5dBNiNLEsdNtdilOkJqQ/q7lR5hsViYNm0a48ePp6CggIMHD1JbWwu0toAtLCxk1KhRzJ8//6KYeGcM1t/qUHIl7BEGd5/dCnN6ejqpqalIkkR6ejqRkZFUV1eTmJgYeExubt/ijH2loKBgUK45atQoPv74Y7xeL263m6ioqEH7OltTU9NhTNseUoeENCjibAAL8nKoc+u8uu0o/gsOGxVZZsGUbGJiInq85rlzBXiNDoRelvCFKvCpM6pjUKY28n+12/nWqOuYG53Tj530npEjRzJv3jw++eQTdu/ejdfrxWQy4XK52LhxI4sXLyYvL69b73mw/laHkithjxD8fe7bt6/T+7rNDXrttdf49a9/DbSelDc3NxMbO/CVYMOB0NBQIiIiUBQFVVWHRUP3q7KSBix97UKiQm2s+6SYG6dlERsR0q4Nqc2scMPU0YyK7bkoq6pKZfFZJK2TD5UOtuU1VJ4t3TIkRSJms5mrr76aL33pS0yZMgVVVXG73bhcLt566y1Wr16N1+sddLsElz/dCvPtt9+O0+nk7rvv5jvf+Q5PPvlkuzDG5U5qaiqKoiBJEidPnhxqc4iPCuPOa8diHoCCjwupaGjh7xsP8viqzfz+S4t5YOFkxqfGcXV2Mj+5czZfXTK1x2s1Nzfz8ssvox8oo7fOvlPz8L8lH/J0ySYOOUsGXaTtdjsLFixg5cqVRERE4PF48Hq9HDt2jGeffZa6urpBtUdw+dOtwlosFv7rv/5rMGwZluTk5HDo0CFkWaa4uJhrrrlmqE3i3vkTmZQWz9u7j1PR0ExCVBi7j5f1uX9GV3hVjZLqJvaeKOOWGTncMqP3IYXy8nLWrFlDc3MzsqqSvKWRsjkxKLKMLCv4ULvUatXQeb/2CBKwoe4oU8PT+EHaDQM2XbwzRo4cyf3338/WrVvZt28fuq5TWVnJM888w5133kl6evqg2iO4fLlyXN8+kpmZiaIogWKEpqamQRkz1R0T0+OZmN46N0/TdO7+zzcGRJgBPH6VLflnWTCp98Jz9uxZ3nzzTbxeb6CD3JTwVG5pTKVYaiArNwefGZ4+t6nbtQzAo/vZ13SaHQ1FXBuV1Wt7+ovZbGbBggUkJCSwbt063G43hmHw4osvcscddzBmzJhBt0lw+SHqT7vBarWSlpYWCN+cOHFiiC26GEWRefTO2djMJiym9oeTFpOMSZZJjO7faCybpfef4WfOnOGNN94IDB2wWq0sXLiQtLQ0rIqZHCOa65MmEWGyY+rFn6JH9/NB7ZFe2xNMxo4dy8qVKwkJCcHtduPz+XjllVeuiOwEwcAjPOYeMHbsWIqLi1EUhQMHDjBlypRhl8s6MT2e5759MxsPnqKysYWUmHAkWge8Xp2TjCxJ3Pe7N3H3oZ+z1dTa2a43nDt3jjfffBOfz4eqqoSGhrJixYpAap0kSURFRQFgkU1YZBOq3vPmTH5j6Ps3JyYm8vnPf55XXnmFhoYGoPWw/K677iI7O3tojRNc0giPuQeMHz8eq9WKyWSirq6Os2fPDrVJHRIZZuO2a3L5xtJpLLsqm5uuymZRXgbhIVbC7BZS+9jbIiHaweRPwyY9oaGhoZ0oh4WFcfvtt+NwOKirq0OWZSRJCmT3THaM6jD9T0FG6SBVQwLyHKP6tJdgEx4ezsqVK4mMjMTj8eDz+Xj11VepqKgYatMElzBCmHuA1Wpl0qRJmEwmJEniwIEDQ21Sn4iPDOsoI61byuua0fSeZUJ4vV7efPNNPB4Pqqpit9tZsWIFkZGRVFZWYhgGiqIQERFBSEhr4YhVNvGj9BuxSiYsUmsoxiqZMEly+0KUTzGAtVUHcGvDY7J2WFgYd911FxEREYFOhKtWraKlpWWoTRNcoghh7iHTpk1DkiTMZjNFRUWXZIrU8hk5WMy9L5DRDQO3r/uZfIZh8N5771FTU4OqqiiKwrJly4iOjkbTNCoqKgLeclJSUrvn5YQm8PTY+7kv6RoWRueioXdciPIpXsPPprrCXu9loHA4HKxYsQKz2YzX66WhoYFXXnlFjMwS9AkhzD0kLi6OjIwMTCYThmGwffv2oTap14wZGcNds8f1+nkOu4UwW/cd1vbu3cuJEycCneAWLlwYqBAtLy/H7/cjyzIWiyVQ1fhezSHuPfIM9xz+C18reJ56fwtO1YtmdN3S1KurFLmHR/+SNmJiYrjxxhvRdR2v18uZM2fYtWvXUJsluAQRwtwLFixYgCzLmM1mjh07NmwaG/UUwzBYf+Bkr8IZFpPMwknp1DS5unxcbW0t27ZtQ9d1dF0nLy8vUL7q9/spKytDlmVkWSYtLQ1ZlvnIeZxnS7fSqLpRDR2P7mdt1X72N53utgbFIplIskb2YieDw+jRo5kzZw6qquL3+9m/fz/nzp0barMElxhCmHvByJEjyc3NxWw2I0kSW7YMTalwXzlRVkd9s6fHhXcWk4yuw3t7i/jin97midVb8HbQ0EjXddatWxfomxwbG9uuEKesrCwQ2rDb7SQkJODW/Kxq+ASv3n49FR0/3Q8AUCSJ66LH9nAng8v06dMZNWpUYCTZmjVrOh17JRB0hBDmXtLmNVssFk6fPk1h4fCJc3ZHo8vbq2o53Widqt3i9ePXdPYWlfE/7+zFp2psPnKGl7fm8/Gxc+zd9wmlpaVomoYsyyxatCjQ7MnlcgW85bZGWACPF7+Jnz6k7skmYsxhPJF5KxHmwek611skSWLJkiWYzWYMw6CmpobNmzcPtVmCSwiRx9xLYmNjmTp1Knv27EFVVTZs2EBKSgqhoaFDbVq3ZCVF96o68MLRVT5V56NDp9h9vBSfquH1q1jNJiTVy2SrhKLrzJgxI5AGp+t6oCBHURTCw8OJjY2lsKWCEy29CwPZJDNfHzWfdHsMabaYYZdHfiERERHMnTuXtWvX4vf72blzJ9OnTx8WVaOC4Y/wmPvAokWLiIyMxGq14vF42LBhw1Cb1CMiQ23EhvfMy+xM91TdoNHlxe1T0Q1w+1RcukyBN5Lw8HCmTZsWeGxpaSktLS2BkvacnNY+G8ddFR2mwXWFamhkhcSTbo8d9qLcxqRJk4iLi8Pv9+P3+9m0adNQmyS4RBAecx+wWq3cfPPNvPDCC5jNZo4fP05+fj7jxvU+42GwiQi1Ul7f3O3jehc6l2jQ7Uy9alIghNHc3My5c+cCB37p6emBvOUoU2iv86lVdJ4p2YRZNlHjc9Ks+WjRvMRbw7kr4SpmRWb2csWBR5IkZsyYwYYNG1BVlf379zNz5swrpm2uoO8Ij7mPjB49milTpmA2m1EUhQ8++IDy8vKhNqtbpmUmXdRPIxhIwKjUDAB8Ph/Hjh0DPgthJCcnBx57VUR6n9r8728uYXfTKU56aqjyN9GieznpruZ3Z9axprLzpuNDSUpKCmlpafh8PnRdZ+vWrUNtkuASQAhzP1i8eDFxcXHYbDZ0XQ+0thzO3DQ9ixCrKegtMyNDrESEWtF1nWPHjgWGmprNZsaMGdMu/GCRTShS8P70vLrKi+Uf49H8QVszmFx77bUYhoGqquTn54uKQEG3CGHuB1arlbvvvpuQkBBsNhstLS2sWbMGn294lAp3RESojT995QbmTUglxGom1GbuNKxgkmW6H5ZioGDw9RumAFBcXExzczMmkwlZlhk7dix2u739Mwyj2wKS3iJLMjsaTlDvH36il5iYSFJSEn6/H03T2L9//1CbJBjmCGHuJ9HR0dxxxx2YTCasVisVFRWsWbMGv394em8AsREhPHLrLF7/8R28+N0VKJ1MQ5FlCA+xBsRZojW3+ears4iz6VgllWjJzT3T4pmcHsepU6eorq5GURRkWWb06NGBDnLn06S6g74nt+7jf0s+4ov5z/F40RqaVU/Qr9EfJk+ejK7raJrG3r170fXgfjAJLi+EMAeBjIwMlixZgslkwmKxcPbs2WEvzm3YLCauzk7GdIE4y5JEeIgVl1cNHATKskR8ZBg3Tx7FeKWcGdYyJtpqWXj1JE6fPk1FRUUgAyMxMbFdXLndNRULcp/aKXWN11DxGxoHm0t44uTbQV+/P+Tk5GC32/H7/TQ0NAzbDoWC4YEQ5iBx1VVXsXDhQsxmMxaLhTNnzvD666/j8Qwvz60jvn3z1aTGRWAzm7CaFewWEyPC7TS0ePCpnyW2abpBZUMLqz5q/Squ6zppaWmUl5dTXl6OLMsoikJcXBxZWZ1PF7HKJqZFDNwYJtXQOdFSSYln+DSaMplM5OTkBPqIXEqFSYLBRwhzEJk9ezbz58/HbDZjtVo5d+4cL7300rDvROewW/jzV5bwi3vn85XFU/npXXNYfnUOUgderU/V2HOqrjVO/GnntMrKShRFwWQyERsbe9FhX0fEmQe20EJF49wwEmZoHVPW9roVFhZeUuX8gsFF5DEHmblz56IoChs2bECSJOrr63nppZe46aabhvWwTkmSGDcqlnGjWnNsT1bWd5rL7FdV3Kqb2tpa8vLyAuGL+Ph4cnJyelQAcrB5YL/KG8DuxlMcdpayz3maUMXKTbGTmBc1ZtCHuLaRkpKCxWJB0zTq6uqoqakROc2CDumRx1xbW8vcuXMpLi4eaHsuC6699lpuu+02rFZrIK74+uuvs3379kumP+/V2cnIHaRkmGSJMG81paWlREREEBoaiqIopKWl9chTbiPcZO/0PgWpw8klvWVD3VHerjlAmbeBE65Knir5kD+dXd/vdfuKyWQiNTU18Ddw+vTpIbNFMLzpVpj9fj+PPfYYNpttMOy5bJgwYQIPPvggkZGR2Gw2FEVhx44dvPTSS1RXVw+1ed0yMiac5TNysJ7XWN9qUjDrXpoKP0ZRFGJjYzGbzYwbN47U1NRerb8sdhJW6eIvbBbJxC8zb+Nno1cQbQrFLAWvGMajq2ytP8EZd23Q1uwtycnJ6LqOYRiUlZUNmR2C4U23wvyb3/yGlStXEhcXNxj2XFYkJSXxla98hdTUVGw2Gzabjerqal544QW2b98+7LM2HrhuMj//3DzmjBtFdlwYWZZGws9uxWZuTYdLSkoiLy8v0PQeWidYb6w9yotlO9lafxy/3vE3hBkRo5kbmolZUrBIJmyyGYtk4jupixjnSGZSeAr/nXsPCZaIoO5JNTT2O88Edc3eEB/fOjtR0zQhzIJO6TLG/MYbbxAdHc3s2bP5y1/+0unjBntku8fjuaTGxF999dXYbDZ27doV6Mu7YcMGdu7cybRp08jNzQ30mGhDVdXAROmhwjAMvDVncVQewFdbi2EYnKirxWKxBOYgut1u3O7WvOQyfyO/qvoAv9E6FsoqmXhG3syjcYuJNl3cPOkOxySuc+RwxFOGWTKRZ08mVLMG9u3UPJR7G4K6Jx2DluYWauTBeW0v/D2aTCZcLhdut5vGxkYOHTqE2dz9dJjhzKX2fuwrg7nPLoX59ddfR5Ikdu7cSUFBAT/84Q956qmnLjqwaJtUMVgUFBQM+jX7y7hx47j++utZu3YtJSUlaJqGz+djz549FBUVMXPmTHJycjCZWn8lNTU17TzRwcQwDE6fPs3OnTspLS1FlmWio6PRdZ2IiAiys7NxOBxkZma2iyk/dvQ9WnRfIL3Oa6j4NY3nnXv4RdZtF12npqaG3Jg0cknr0I5mdw3mChOqHtxKyihHxKC9th39HpOTk3E6ndhsNuLj4wNe9KXKpfh+7AvB3ue+fZ33d+lSmF966aXA/9977708/vjj4hS5H8TExPDAAw+wf/9+Nm3ahNPpRFVVGhsbeffdd9m0aRMTJkxg0qRJQ2Kfy+UiPz+fgwcPUl9fjyzLWK3WQFXjmDFjUBQFv9+Pw+FoJ8plnnqqfE0XNSfSMchvKaNF8xKqWHtlT7wlHLWTUEh/6Cy8Mlg4HA6ampqA1i58l7owC4KPSJcbZGRZZurUqUycOJFdu3axbds23G53wIPevXs3u3fvJioqiry8PDIyMoiMjBwwe1paWjh16hRFRUWcOnUqMAKq7cDSZDIxbdo05syZQ1lZGYcOHcLn8xEWFtZuHY+utqahdZBiJyHh09VeC7NdsTA9Ip0djUX92eJFJFiDG7fuLaGhoYEcZqfTOaS2CIYnPRbmF154YSDtuOIwm81ce+21gWko+/bto7GxEV3XUVWVc+fOUVdXx8aNG4mNjSU1NZWEhATi4uKIjo7uU7N4wzBwOp1UVFRQVVXF2bNnKSsrwzCMQNVeSEgIsixjs9mYPHkyV199daDfRZuIGIZx0cSWUfZo5E46xo0whxHZQYy5J3wh6Rp2NRb3urF+V3iDHBrpLWFhYUKYBV0iPOYhxm63M2fOHK699lqOHz/O3r17KSoqQpIkQkJC2hUjtL2ZrVYrI0aMIDQ0lLCwMMLCwggJCcFkMiFJUqC6zO1209zcTEtLC83NzdTV1eFytU67liQpMPG7rUAEWjuhXXXVVYwfP/6iQ6m25xqGEWh634ZJUvjGyPn86ewGfIaKQaunbJEU/m3Uwj5PHUm0RTLZkco+5+k+Pb8j/qfkI2ZH9awQZiAICQnBMAwMwwi8pgLB+QhhHibIssyYMWMYM2YMTU1NrFu3Dp/PFwgvtL2RNU1D13UqKysDt3VV2itJUuCnLWbcNlWk7faUlBRycnLIycnp8lDs/I5obYeU5zMnOodYi4NXK/dS6q0n3R7LXfHTSQ/p37nEN1Pm8+DR5/q1xvm4dR8lnjrCTXZsihmbfHFWRLXPybs1hzjtrmG0PZYbYiYywhLWwWq95/wMHNFlTtARQpiHIeHh4YwfP57c3NyAOJeWllJeXk5ZWdlFjdY7E+c24T0fq9Ua6A+clJREenp6jwfJ9kREcsOSeCzs5h6t11NireEkWiIo9zUGZT0D+EnR67i01pDGVREZ/FvKQsJMrTHwYy3lPHriDVRDR0PnoLOEtdUHeDLrNrJC+n9Qd/7vRAizoCOEMA9zLBZLwJuFVhFuamqivr6e5uZmnE5nIFyh6zq6rge8Y7vdjsPhICwsDIfDQURERJ/j09Dq1bcx2A14vpN6PT888WrQIs2N5/WE3t5wgiPN53g6937sspmfFa3Fa6iB+/2Ght/Q+N3pdTw19r5+X/v81+7811QgaEMI8yWGJElEREQQETH4mQXnhy/aCmUGi9ywJH6fczffKVwVxGPAz2hU3Xz3+GomhaXQrHs7fEylr4laX3O/QxrnV3xeWFgkEIBo+ynoBW0hD0mShmRu3eiQOH6ZedsAtNhvpcLbwPu1hzu9P1jfElpaWgJhpgvTDgUCEMIs6AUOhwNoFeahGjo7wTGSX2XdTrI5Iuh/vDodpmEHiLU4gnIA2CbM8NlrKhCcjwhlCHpMm3c3lMIMMC4smf8b/wWcqgfZgHuOPIPKwB+ifTv1uqCs09zcHBBm4TELOkJ4zIIeEx7eOnVEkiScTueQZxQ4TDb2N5cMuChLSFwbmcW4sJFBWa+pqSlw6Cc8ZkFHCGEW9BibzUZ4eDiKoqCqKrW1Q9fXuI2uYsLB5Ksj5wVlnZaWFpxOZ6C4Jzo6OijrCi4vhDALekVSUlLA26usrBxia8ClDnx5tV02c8IVnL22vWayLJOQkCDS5QQdIv4qBL0iMTExkFFQUVEx1OYw2TFqwK9hAKZO+oD0loqKikCeeWJiYlDWFFx+CGEW9IqkpKSAsJSUlAypLcdbKni7+sCAX0eSYHyQ4svnzp0LfLAlJSUFZU3B5YcQZkGvSE1NxWQyYTKZqKmpoaGhYUjs0A2DX576Fx5j4MdzfX/UEsxy/wtBPB4PJSUlgUKdjIyMfq8puDwRwizoFRaLhfT09EDF2smTJ4fEjiJXZaDXxYVIwKyI1nmCdtmM3M+SFC1IWR+nTp1C13UURSEpKSmQ5SIQXIjIYxb0mpycHE6cOIEsy5w4cYIpU6YMug0+Q+tUcCUkvpe2mDp/C6fc1USbQvl/RW+063/RG+QgtQctLi4OdPZr630iEHSEEGZBr8nOzgZae2eUlJTQ0NAwoFNWOiIrJB69E082IyQWi2wiwRpBgjWCTXXH0Iy+e71rKj/hlyf/hY6BROuE7x+k3YCpF+ENl8vFiRMnUBQFSZKEMAu6RIQyBL0mPDyczMzMQKz04MGDg26DVTbx5eR5WKXPfAsZCZts5usj5wdua9G8/Pnsxn4VoRxuKUX/tFjbAHY2FvOdwlW9WiM/Px9VVTGbzSQlJYk5f4IuEcIs6BNXXXVVYBzV4cOHB73bHMD1MeP4WeZypoenM8oWzYLoXP6QczfZoQmBx+xrOo0yAJNKTntqOeWu7tFjDcPg4MGDKIqCLMtMnz59yKanCC4NRChD0CcyMzOJjIyktrYWt9tNfn7+kEz3HheWzLiw5E7v1w1jQNqEAnzccJJ0e/fTWYqKiqivr8dms2Gz2Rg/fvwAWSS4XOjWY9Y0jR//+MesXLmSu+++m+PHjw+GXYJhTpvn1zYvcOfOne36DA8X8hyj+hVf7ooES/dZFbqus23btsC3iylTplw0S1EguJBuhfmjjz4CYPXq1Tz88MP8/ve/H3CjBJcG06dPJywsDIvFgtPpZP/+/UNt0kVEmEO4L3FWu1h0MJCRmBPd/QHe8ePHqampwWKxYLVaueaaa4Jqh+DypFthvu6663jiiScAKCsrE7mXggAWi4W5c+eiKAomk4ldu3bhdru7f+Igszx+Ck9krmBOZDYjzKEo/TxakYAnMlegdFOm7ff72b17d+D1mTVrVo/nKwqubHrkRphMJn74wx+yfv16/vSnP110f0FBQdAN6wqPxzPo1xxsLpU92u12fD4fTqcTwzBYu3Yt113Xs77FqqpSU1MzwBa2EouFBxzTwTGdIm81O1pO4TNUJttHctpXx/aWk7gNH35DD2RgdIQE/GfCcqK9dmq8Xdu+fft2GhsbURQFTdOIioq6JH6nveVS+VvtL4O5T8noxbyc6upq7rzzTt555x1CQkIA2LdvH1OnTh0wAzuioKCA3NzcQb3mYHMp7bGwsJBVq1bh8/nw+XysWLGCzMzMbp9XU1NDTEzMIFjYMxpVNw8ceRa/oXX6GLts5j+z72KUfUSXa5WWlrJq1SpcLhexsbEsW7Zs0N8ng8Wl9LfaH4K9z660s9vvdGvWrOHpp58GWr2jtgY2AkEbOTk5TJgwAbPZjCzLrF+/fliGNLojwmTnweRrsXQTj06wdj0I1+/38/777wdS4kaPHj0k1ZGCS5duFfb666/n6NGjfP7zn+eLX/wiP/nJT7DZbINhm+AS4oYbbsDhcGC1WmlpaeHdd98d8gknfeGm2Mn8Ovt2xoQkIF1Q8m2WFFbGX4VF7ly4DcNg/fr11NfXY7VasVgs3HzzzSJvWdAruo0xh4SE8Mc//nEwbBFcwoSEhLBs2TJWrVqFxWLh5MmTbN26lblz5w61ab0mKySe3+bcxfqafP7v3CZ8n/bYsEl+djfu4troLOIsHXvN27ZtY8+ePYEpL1lZWTQ1NeF2uzGZTERERIh0OUG3iAITQdDIyclh9uzZbN26FV3X2b17N7GxsYwdO3aoTeuQZtXDutojHHKeI87iYGnsxHYFI4WuCgwMUixOHk/dTZa9EQOoV9/BZnyZOvd8KivrqaiooLKykqNHj7Jnz55AznJSUhI+n4+qqqrAmpIkERsbS1JSEomJiSQlJZGQkBBUsfZ4PFRUVFBWVkZ9fT1OpxOn00lzczMejyfwTaZtvFVYWBgOhwOHw0FERAQJCQkkJSWJeYRDiBBmQVBZsGABVVVVHDt2DF3Xef/997HZbMOu93C1z8l3C1fh0vz4DBUZiQ/rjvFvoxYyP3oMmqHzUV0BZsnDM9kf4VB8KJ9GIxIsTnTjd1iUP7D72AT2HEnF6XRSXFxMeHg4ZrOZ0NBQUlJSAmLYhizLlJWVUVFRETirkSSJuLg4JkyYQF5eXq9T6nw+H8XFxRQWFlJSUtJuFqNhGBiGga7rtJ3zt/23LbzS0NAQaN7f9gOtE7xHjhxJVlYW2dnZQqgHESHMgqAiSRK33norf/3rX6mqqsLj8bB27VpWrFhBWlraUJsX4K+lW2hSPYHUOB0Dn6HyP2c3MiMiAwkJ1dC5IfosFkkLiHIbEmC16Nyy4AhllRLbTmkBUY6IiCA9PR2bzUZLSwshISH4/X78fj+NjY0BYWxrAdom1pWVlXz00UeMGzeO6dOnM3LkyE5j036/n/z8fPLz8zl16hSqqmIYBpqmoes6uq6jaRq9SLpq3denh/uyLOP3+2lqauLYsWMAJCcnk5ub26cPD0HvEMIsCDpWq5V77rmH5557jvr6ejweD2+88QbLli0jKytrqM0DYE/jqQ7zlRVJ5nDzOaaHpzPCFEqWrZEQ5eL0uTa9tFg0bpx3Dpd6IzExMYwYMYKpU6cG0kkvTAlsC21UVlZSU30Gu+kgzc5mis7E4PVaMJvNHDx4kEOHDpGQkMD06dOZOHFiINRRV1fH3r172b9/P263OyDAqqoGvGJZlomJiSE+Pp7Y2FhCQ0MJCwsjLCwMm80W8NQNw8Dn89Hc3Bz4qa9vDc1UV1fj9XqB1g8Qk8nE2bNnKS0t5aOPPmLs2LFMnz6dlJSUoP5eBK0IYRYMCBEREdx///38/e9/p6GhIeA5z5kzZ1h0V+vy6gbs37+fxPxmTs9x4NYU7B2IcxsjE11MnhCJT4tj0qRJAVHuCIvFwsiRIxmdnI+DpzCQwQDD8LP+42v5cIcDn8+HyWSitLSUiooKtm3bxpw5cygqKiI/Pz/gGfv9fjSt1a7Y2FgyMzNJT08nPj4+0JK1O6xWa4chCl3Xqa2t5cyZMxQXF3Pu3Dl8Pl8gLn3o0CEOHz5McnIyaWlpV0Qe82AihFkwYERFRfHAAw/wj3/8g7q6OrxeL5s3b6a6uprrr79+yOyq9jlJtY+gyFV1kc+sGTrH1+2i/Ow5IgyDkx8moH7+KLqsIXeg5oYBFpOH66f+D15jKi5TBoYR8plL3QGKcQoHv0XC2/oBIbX+LJ61g9E5T7JrXz0FBQW43W4Mw+DEiROsWbOGxMREUlJSAjHjiIgIJk2axJgxY4iI6Dq3urfIskxsbCyxsbFMmzYNt9tNcXExhw4dorS0NPDhUVJSwoEDB6ioqOC6664Tk7+DhBBmwYASGRnJl770JV5++WXOnj2Lz+ejoKCAmpoarr766kGv/PtH6XbWVu9HgnairCAhGRJZR1XKy84FYrWJ3hiOnPw+UzNfwCyfA9prriSBJOmAjp1d2LkLjUSajR/il/I6tMHOGqCjTnx+Ro7YSuTi7zFnzhw2bdrEhg0b8Hg8WCwWTp8+TUVFBfPmzeO6664jPT190Iq97HY748ePZ/z48VRWVnLgwAGOHj0aKCQqKiqiuLiY6dOns2jRIiwWy6DYdbkihFkw4ISGhnL//ffzzjvv8MknnyDLMjU1Nbz22mssXLiQq666KjDcNdgUuSr5W+k2ClsqMEsyHt2PdoGfLAFpDVaijjZhbzHwqyqyLDNt2jSuvvrq1rCCZw5N9TuJD3me2MjTyNLFTnHrP3VMlBLBD6g3/gJcHCaQqULqYKKKhI5MJR6Ph+PHjxMSEsLChQvZu3cv5eXlhIeHEx0dTVNTE6dOnSI1NXVIqnDj4+NZvHgxM2fOZMeOHezevRuXy4XFYmH37t0UFRVxyy23DKvD3ksNIcyCQUFRFJYtW0ZCQgIffPABiqLQ0tLCtm3bOHHiBHPnziU1NTWo1yx2VfGjE6/h1VsLRHydJChIGmjVzVidGpqukZVhYebMeUTFjCHc9DoO5TVMchONxggOFS/iZPnVTM9Zg9nk7eLqPuy8BHytg3umYGEvEp52t+vYqGvOYe/BvaiqiqZpmM1m5s+fj6qq7Nu3D5/Px4jIJprr1vH+O2dYtOQerFZrH1+h/hEeHs6SJUvIyMjg8OHDnDx5ElVVqa2t5e9//zszZ85k0aJFooVDHxDCLBg0JEniqquuIiMjgzVr1lBTU4PNZqO6uppXXnmF9PR0Zs+eHbR5eM+X7QiIcmfIGEyPrGR0RgvJ4T6WzjuJzeIF3mqzGklqVfTIsBpmjX+NoyUrUJSuy80ldMx0PFTCy1JC+CcyfiRaD+8MFFTVyq6DIwOHeoZhkJycTEpKCjalmAVXebGyBZvFTXOTwrp/nuSxRXsxh6Sy4J5rmXPXTEzmgfnm0RXR0dHceuutHD16lA8//BC3243FYmHnzp1UVVVx++23Y7fbB92uSxkhzIJBJyYmhgcffJDVq1dz8uTJQPny6dOnOXXqFJmZmUyePJm0tLR+ZW8Uuiq6vH+U1cn/jN5MiKJi0nUsJr2DM7v2brZJ8TM2dRteaQk2PkCiY6/ZQEIlreP7pFAajGcI5SmsbMEwDKoaJ7D32AK8PjOapmK328nKyiIsLIwo819wmN5pd62ju0J46Xdx+DwKcI4Xj7/O7rf384NV3xwSD1WSJMaNG0dqairr1q3j5MmT6LpOUVERzzzzDHfffTexsd2P4RK0IoRZMCTIskxeXh433ngjmzZt4sCBA5hMJvx+PydPnqSoqIioqCgmTpxIdnY2kZGRvb6GQ7HRonUWbjD4Y8ZWRpg9rdkWvXA0Famceh5CYxR2XkamtS9ze0234OZzna6hSzE4+Sl1fj+HDh3C6XR+euCoER0dHZhCbpWP4jC9gyy138eUOU4mX9PC7o2tgyt8bj8n9p5i86qdVJ+tpam2mYnzcpm6ZCKKafC86LCwMG699VZ27NjBjh070HWdmpoann32We69916Skzufzyj4DCHMgiElIiKCW265hVmzZrFx40aOHTuG2WxG0zSamprYvHkzmzdvJjY2ltGjRwfydHvSW+KWuDz+XrbtonCGrMN4Wy0Riq/DFLjuMRjBLfiZQiN/BDTCeRSFyta8ZCw4+QGqNAbovJm+3+/nwIEDtLS0BCr3Ro4cSUpKymdl0cp6JHwXPdcearD47tqAMAN4XT7+9sPVyJKEpursXLOPxIw4Hl3zMLaQwYtDS5LENddcQ0xMDO+9916gJP3555/nnnvuEUUpPUAIs2BYEBsby8qVK6mtrQ1UtrU13NE0jbq6Ompqavj444+RJIkRI0aQkJDAiBEjCAsLC1S32Wy2QL+HufbRHLOfY3vLSRQkDAM0rx/7qwWkZjRhpOu9fgcYtKUdu7CwHTOfUM9z1EsvIRvnkPCikQZS116q3+/n4MGD7UQ5MzOTuLi4Cx7pC8S4L8RmvzjObWhGIOvE2+Kl9Hg57/zPBm575MbebTQI5OTkEBERwWuvvRYQ5xdffJH777+fpKSkQbfnUkIIs2BYMWLECBYvXsyCBQs4cuQIR48e7bAXRENDA3V1dT3q+TzFBk0RMo2VNVTtLMQWEcGZ0gislq5j0G0YgIEZCX+7cIWEAXgI4R8082N0aSQYfqx8hNnYh04sJnkG0D5X2zAM8vPzaW5uDuwrOzu7w5xul34tocZ2ZKl9Boe7ReKjNVHd2u73qmx+eSe5s7Joqm0mc0oaMSOje7TvYJCQkMBdd93FK6+8EhDnl156ia985StBL4q5nBDCLBiWmM1m8vLyyMvLC3RPO378OOfOnaOmpqZdp7QLf85HkiTskoSt0k3JvlM4QkMJDQ0lOWUsJTXRjIrdjSJ/Fipo84jP/7dOGDKuDu2U0LGwu/X/DSeRfBWZGmTcGJgZHfkSTuOn+KR5geecOHGCxsbGQOZFVlZWB6KsYVd2Y5WPoBrRmKlEkj7N4DCgocbEznUOJNlAkmUM/dOucR041/XljfzuC61TiDS/xjW3TefB3949aIeEsbGx3HnnnaxevRqPx4MkSaxatYoHH3xQFKJ0ghBmwbDHYrGQm5sb6Mfg9XqpqKigvLychoaGdv2GvV5vu37DFouFkJAQPvnkE5KTkwkJCSE5OZkHHngAq8WCizWEsAqJBlSy0In+NMfYjU4UMg0oNHdpn0wtduPvKNSgUI5Ea0xbwo8kQTi/pMa4CqQQysrKKC8vD3j+qampF2UrSLhItH4fk1yOLLnRDQsgoekhyJIbMEgYpfPLVef46N056KYc4rJj+NtDq+loXKGhG3iaPzs83PHmPkaOSWLJl+f3/ZfSS2JjY1m+fDmvvvoqXq+X8vJy1q5dy+233z7kfVOGI0KYBZccVquV1NTUHhek7Ny5k9LSUiIiItB1nVtvvTVQlOFhBR5WIBl1RPIQJk4ABgYWJJwBke0KCYNQXsRA6fDxBjIW9lDrnEJRUVEgbt7WMP9CIs3PY5JLkKXWsm1ZavXoZQyqvd/HopSiaVbCcuayNCeBshOVbPjbVuzhdlwN7g695vPxuX28/5ePBlWYAVJSUli4cCEffPABkiSRn5/PyJEjmTlz5qDacSkghFlwWdPQ0MDGjRtRVRVVVZk1a1YHB2wQzuMonAsUfEC3+nYB/nbPvRDD8AWGB6iqSlhYGBkZGR16i2GmjQFRbo9GXcHT/PIbk6k604jZeoicq0dTuLsYza+ja/pncZgLm4FcgLO+pVe7CxaTJk2iurqa/fv3oygKGzduJDs7mxEjup46fqUhaiUFlzW7d+/G7/fj8/mIi4tjxowZFz1GMuowk3+RsPbmC7aEjkbMp+lyF96ncrIkHpfLhaqqKIpCdnZ2p/1BpA4bHIGuwVt/i6DqTCPQerB3ZEshfo/aKsrwmRh386mSMWlUj/Y1EMyfP5+4uDh8Ph9+v581a9ZckoN7BxIhzILLFr/fz/79+wPx3GuvvbZDMZRpwuhFhUlHmteauaHQlqsRuM0At5rNydP1gcO+1NTUDifNy9QTomzDp4/GMC7+WNA12Lup/+OdLHYzd/2/W/q9Tl9RFIUbbrgBaD0vKCkpYffu3UNmz3CkS2H2+/088sgjfO5zn+P2229n48aNg2WXQNBv8vPzcbvd+P1+IiMjSU9P7/BxGiPpVelfB0iAiYp2WR0SrR3orHIh4SGtB34REREd9AIxiDL/lZH2+4ix/A6LXAQYXDgVyu1S0NT+HZSFhNv40cvfInNKWr/W6S9t317aQkybNm0KtBAVdCPMb731FpGRkfzzn//kr3/9K0888cRg2SUQ9Js9e/YEDtomTZrUeXqYZKKFr2HQ3ovtzDPuDAkNuYM4sySpJEYfQZKkDuPKocpGHKZ/IUt+ZMmFLHk/7fPcfh17iM5d36qir5itJn708rfInj48BuPOmDGDqKgofD4fbrebbdu2DbVJw4YuhXnJkiV8+9vfBlpzJAeqZ65AEGxKS0spLS3F7/djMpkYP358l4/3SLfQxGP4yUTHjs7FoYY2OvNZuxJtwzCIj4/vsMtahPm1iwpIOsJsNZh3c0O3j+uMrGnpZEwObmvV/qAoCtdee23gQHTXrl00NTUNtVnDgi6zMtom4TY3N/PQQw/x8MMPd/i4goKCoBvWFR6PZ9CvOdiIPfaPDRs2UF1djWEY5OTk4HK5cLk6LhL5jFzgt8SFPEu07d0Op0NJtMaNO0y9/bS+48L7dF3hTEU2ozJGdGiDbKvv2aagw8PFnlJTVk/+7gLiM4Lb5U1VVWpqOu8J0hVtJfVVVVU0NDTwz3/+k7lz5wbVvmAxmO/JbtPlysvL+eY3v8nnPvc5li1b1uFjBnsQY0FBwWU//FHsse8YhsHatWuJjIzE6/UyZ86cno+wMjxEs77DCSPQsfB2dntbjPh0xXjCo6d3WoLs1XNRpF2d9sRoQ1VNbHy97+XUVWdq+M+7/sK1t1/Fg/+xMmiFHRdOAu8tS5Ys4bXXXsNqtVJfX09GRsaQNf/vimD/ve7bt6/T+7r8+K2pqeHBBx/kkUce4fbbbw+aQQLBQFJfXx9ogGSz2Xo1IFSmrkuvtDMp6+h2SWoVZ8NQSEhI6HTNBv99GLQvTdYNGcOQMAz503/bKDlh5uU/9yPfVwe/x8/m1TvY9trwyYJIS0sjOjoaVVXxer0cPnx4qE0acroU5v/7v/+jqamJ//3f/+Xee+/l3nvvDTQiEQiGK+Xl5QDouk58fHyvPEOd6C695d4iy5AUU9KlB+g3Mqjw/haPNg7DUNCMUJzqcso9f6BJXUazOo8TZ+7ne7eNw+Pq/zmPrhr848evdJo7rGs6n3xwmFd+9Rbrn9uMs67rkvT+IkkSeXl5aJqGpmns3r37op4nVxpdhjIeffRRHn300cGyRSAICmVlZRiGga7rXXqqHSLZ8BpXY2VLrwpMukJWJCS9BYPQTh/j07Op8P7Xxbf7cwBwG0143XuDZBF4Wrz8v4W/5u5/X86EubmBDy+X080Ty39P9ZlaPC1eLDYzq3+xlu89/zXGXpMdtOtfyNixY9myZQuqqlJVVUV5efkV3RpUFJgILjvKy8vRdT2QCdFbZJr6lHnRGTZTJaPst5NgfQST1LNWoxcSGR9OxuRRyKbgvWVLjpXxH3f/L1/N/QH//Pmb1JXVs/qJNZQXVeJpaW165PP48bp8/OHBZ1B93fcN6Ss2m42srKxAG9TCwsIBu9algBBmwWWFYRgBYQb6KMydZxgY2NGx9kqgW3OSDazyYRKsD180HbunfPmPnyMhIxZriAVZCd5b19Xo5t2nNvLQ1J/y4QvbUX0X52IbukH+to6HywaLzMzMwDedK12YRRMjwWVFQ0MDbrc7cPDXl2bsfiahUHZRrNnAjpPHUDhNKH+DTnpadIYkgUIjYcr7OLXlvbYrPMbBY+98h+JPzlBeVMn+D45QsKMIQzMw9AGOyUqtXekGkrS0tMBg3oqKChobG6/YZvrCYxZcVjQ3tx5U6bpOdHR0n1LCXNyDga2dV2xgRicJiUbsvEpvRbkNSTJwmNf26bmtz5fInJrG7Luu5qFnv8iyhxYNyrBV1acyZmbmgF7DarWSkpKCprV67CdPnhzQ6w1nhDALLiv8/s8E02Tq2xdCXRpJA/+Ln6kYKOjY8XADLu7Awe9RqOvXwaBZqiDG8kuizM9iksr6sRLsWrN/QGO/AFa7heXfuQFHdNiAXgdg5MiRgUk0bdk1VyIilCG4rFDVz0Sqr8IMoEmjaeQP7W6LNu5AwtvxE3qFQZhpK4ZhwmF6ixrf93Bpc/q00kCFF2RFxhEdysgxSSz92kImLRg7INe5kPj4+ECcuaysfx9alzJCmAWXFW1fg4Hg9nYxdBT6llFxIW3RFUlSkVCJtfwH1T4fbm3ORYUm3TFp4Vi2rPoYTQ1uP2Or3cJvtz1GSPjFvT0GkrbDWl3XqaysRNf1QZtNOJy48nYsuKw5X4zP9577jSRjMFBlwioxlj8x0v55zFLv4qo3fGMBIREhKObgxpm/+uf7Bl2UobU/j8PhQNd1/H4/9fU97yNyOSGEWXBZYTabA/8fVGEG/IztNE2uPzkRktQ610/GSbz1p9BJ5WFHRMQ6eOydh5l/3yzMNnPvxq50gmJWyN9yrP8L9ZHw8PBAuqPT6RwyO4YSIcyCy4q2uLIkSUEXZh95nd4XjCrBVoF2YZV718EsPMbBtKWTWkMkQcia0/waR7cPbM5yV4SGhgZKstuybK40hDALLiva8l4lSaK2tjaoPRcMIjEwd3JfsJCQ6b0YnT5UEtRc5qiEocsfDgsLC/zehMcsEFwGOBwOwsLCkGUZn89HXV1d0Nb2MhepA9/4/HFSPaG141xnbz0Vr9771pIRceHIQcpnttot3PDVhYF/67qOx+UdtMZCISEhgZS5lpahmeY91IisDMFlhSRJJCYmBiZhVFZWMmJEP1plnochReM0voeD/6Q1DqxhYEXCR2995irv/yPW+h9I+AJ9mHXDRpN/BTrhvbZtwrwxmC0K3iDomMlq4o9fegbNrxEWFUZTTROGAWabmRXfXcLN31rc/4t0df3z0hyv1OnZwmMWXHYkJSUhSRKSJFFZWRnk1S18OmYVUJDoWxzbIhdR4fkdLu0qVD0Kr55Bre9hGtT7+rSe2Wri4ee/TEhE/zMpWhpc+Nx+NFWnsbop0PDf7/HzypNv8+pv3u73Nbri/GpNIcwCwWVCYmIikiQhyzIVFcHJPQaQjUoc/LrVy0VFQkNCo7fesiRBhPl1zPJZqn0/o8r3M3xaOmGmd4kwrUKmb3PvUnKTuOcXtw34u/rtP68f0LDG+WtfiTnMIEIZgsuQtj6+sixTVVWFYRhBGaNkZT0dpbJ12iK0s9mAtKbHxVj+i3D9n1jkksDjbHI+4eY1lHn+jGb0vjNe7jWZSEgYQTyOvBBd02mobCQqIXJA1j8/m+ZKFeYrc9eCy5q2A0BFUfD5fJw5cyYo68o0IvWweVFXotyGJKntRLn1Ng2ZJqLNz/TJxvXPbhlQUW7DYu9dhWJvaGlpCYSi2gZCX2kIYRZcdkiSxLhx41AUBUmSOHDgQFDW9TENnYtjuP0tLunoNruyq9drnTtWzvpnt/amPqVPxKREYw+zXdQ8yef2UXKsjKaa/qW4NTc3B77hOByOfq11qSJCGYLLkunTp7Nr1y7MZjNFRUU0NTURHt77bIfz8TMdjdFInAg0MzJQPu1v4QGMICY09z70sudfBwa805zZZiZtQgoPZnwXTdUYOSaJWx5ZxPZje3nrzx8gyRKaX2P8nDF87c/3ERoR0utruFyuK16YhccsuCyJiYkhPT09kHp16NCh/i8qyTTwB1q4F40ENKLxcCNeFgCm1lwN6bOfvp6PGQZoRhgRpudRqO3x8zRVH7hDOQlGT0klNiWaAxuOoPpUDN2g5GgpT335ed78w/t4XT48zV78XpXDm4/xuy/8pU+XamxsDMSWhTB3wcGDB7n33nsH2haBIKhMnz4dWZZRFIVDhw616zzXZyQrbul+6qRXqZPW0iw9gpWPOo0991UnzXIdEebXSLZ/CYt0okfPmbxoHBZbx5WJ/caAUwdLKDtRedHoKU3VUb3tPXXVp3Lq4BlKj/cuK6alpYXm5mZkWcZsNhMZGdlfyy9JuhXmZ555hkcffRSvNxh9aAWCwWPMmDE4HA5MJhMtLS0cPz4w/R86m+HXV8+5Le4sSz5kyU2M9bc9et7oKalMXjQOxfLZ21o2S5gsJqyhrZ3xLHYztlArKWOSeh0t0bXeBa8Vk0LFqapePactvVGWZRISEq7YrIxuY8yjRo3iz3/+Mz/4wQ8Gwx6BIGjIssy0adP48MMPkWWZrVu3kpGRgdUa3PadfsZh4XCn97eJc18z9kxSOYpUi2Z0XcEoSRJLH5lPuXqW+vwWDA2uv3ceNz64iPztxzl54AzRiVHMuGUKZouJVb9cy/pnN/fNqB6g+jWSsxJ69ZyKiopADnpb2uOVSLcfR4sXL+7XJAiBYCiZNm0aISEhWK1Wmpqa2LJlS9Cv0cJDGN1Mzu5IlFt7ZvT0Kt0/UFVVNm7cgGO0jdG3JTD/e9O59Vs3YQuzMXXxRO744TIW3nctoREhWOwW7vrJzT29eJfIJhmTpb1GmC0mcq4eTUJGXK/WKi0tDaTKJSYmBsW+S5GgKG5BQe/aFPYXj8cz6NccbMQeg0dOTg7r168HYMeOHcTGxjJy5MggXiGGeuWXpEf8AKSOv+5fKMBtYY6e4NdicbaEAK4uH/fxxx8HQgGGYTB9+nRqazs/PNQ1HcUk92n6iSRL7brZhUWH4G7ytI6F0nTGLxzDyseXUVNT0+M1vV4vhYWFgeZFfr9/WL0HBvM9GRRhzs3tfTes/lBQUDDo1xxsxB6Dx5gxYwJvKrfbze7du8nNzQ1ySCMGt3EXNl5D7uAgsC2coRrRmKSed7wzDNBIJCSkNe2s7HgFR7YUYraYmbJkPBFxrSmAlZWV5OfnY7VaURSFhQsXMnr06G7Xj4gLp66socf2BOw6T5R1Vaepupm41Bh+sOobOKLDsIfZer1mQUEBNpsNu91OSkoK06dP7/UaA0mw/1737dvX6X0iRiG47JEkiZtuuokzZ86g63ogpLFo0aKgXqeFrwB+bMbrSBgXecSSBCbqehVrbi02OYRh6Lz02Bo+fvMTdFVDVmRe/807rHzsFmbcNoX169ej6zpms5mUlBTy8jpv6n8+rkZ3z43pgrYy7fryRuJGxfRpjaKiokB8OScnJyh2Xar06Mhz5MiRvPLKKwNti0AwYISFhXHDDTegKAomk4kDBw4E/2upZKJF+jaN0h/Q9M7T1nqbpWHofv78pefY9spu/J7Wrm9+r4rfq7L652t557X3qK2tRVEUzGYzS5Ys6XFvEHsXc/0ujBt3h8/rp7qk53nX5+N2uykqKsJkMiFJkhDmoTZAIBgsJkyYwJgxY7BYLCiKwrvvvktxcXHQr6MyETqZdKIZ0b1ayzAgf08I+ZuPY2gXK7rfp7Ln7QPIsowsy8yZM6dXub+LvjAHi/1iW+0OG08X/IYxM7oPh7Shqzr1lY09fvz55Ofno6oqZrOZxMTEwLTsKxUhzIIrBkmSuPnmm4mLi8NmsyFJEm+99VbQmhx9diET9dp3UTUzbe2EDUNGN2xU+x769N89W0rX4ZdfTev8AQZoHgNFURg7dmyPQxhtLP36QibMzcViM2O2teY4h4Tb+eGqb2INsfKl392DLaznsfitL3/cq+tD60HlgQMHUBQFWZaZPn16ULoBXsqIGLPgiiIkJIR7772X5557jrq6OtxuN2+88QbLli0jMzMzeBeyLuaT435iQ98iIqwej5qFbn+AEGUHBmZkqWdd6vZvdeBq7tp/Com3kpmZyeLFi9n+2h7+9T/raaxuImNyKrf/cBnpE1M6fa7JrPCd575CSUEpx3efxDEijMnXjQ9UECakx/Lvb32XJ+/4M87a7mcRNtX0fl5hcXEx9fX12Gw2bDYbEyZM6PUalxvCYxZccYSHh3PfffcRHh6O3W7HMAzWrl3LkSNHgnudETPZcnA5H+z9GlsOLKTFMwKbfKTHogxQdtqM39f123Tc3GyWLVvGa7/+F3/74WrOFZbjrGvh4IdHeWL57zix92S310nJTWbh/bO56qa8i8q6U3KT+fqfezZZZfSU1B49rg1d19m6dWugdD4vLw+zeYDKyi8hhDALrkiioqJ48MEHiY6ODoQ13nvvPd5++21crq7zhXvKiBEjCA0NRVEUdF3n3Llz+I3ELgaxfobHLeHzSFSctaJ30eJj1FUJrLz3LlwNbtb9dRM+t6/d/T63nxcee72/W8Hv7b5rnclq4vZHburVugUFBdTU1GCxWLBarVxzzTV9NfGyQgiz4IqlTZzj4+Ox2WxYLBYKCwt57rnngtZXIyUlJZACVllZSbVzIUYPIojNjQrfWjqGt/6eRGdNLeLHjuCn//x+a2vTT053mkVxcv8Zmhv6NqXV0+Jl/XOb+dsPV3f5OEmW+NHqfyN90qger62qKtu3b0dRFBRFYebMmYSFhfXJzssNIcyCKxqHw8GDDz5IXl4eFosFu92O1+tl7dq1QfGew8PDiYqKQlEUAApOuKn2/gjDkLs8ABwRb/DoqkzmfWEmI8aEY4szIbUugSXCxNIfzeM/NzyOPbS1kCM0IqTLlp/fnPBjivef7pXtjdVN/GDOE6z6xVoaq7qeQ3jDVxcwZkbvYvQ7duygsbERi8VCaGgos2bN6tXzL2fE4Z/gisdms7F8+XLGjRvHW2+9RVNTE36/n8LCQs6ePcv06dMZP358oPqut4wePZqGhgZMJhNOp5Pic2n4kv5Ggu0HKNQj4b+o6EQ3FHYdTaTceor4RWEoSgSSJJGUmMwNS5cwYkT7hkZZ09Oxh9nwNHfcBVJTdX77+af438O/QlZ65o+t/mWrIHdXsh0R72D5w0t6tOapg2fZ9vpuGusaqaaMyNGtI8AWLFgQ9OZSlzJCmAWCT8nKyuKb3/wm77//PgcOHMBkMuH1etm8eTPbt28nJyeHyZMnB6Zw95TQ0FBSU1M5ffo0sixz9uxZoqImUco/sMrHsMt7cJjeQZK86LqB1yfz/JrxHD9dEuhLbDKZmD17NlOmTOmwFaYsyzzy0jf4ycJfdWqH1+3j+J6TPfZs97xzsEtRlhWJ5Jwk/u3v9xPSRaFKGy8/+Rbr/voRfm9rk33ZLBGR3sINP5zL1KlTe2TTlYIQZoHgPC70np1OJ7qu4/f7OXr0KPn5+cTHxzN58mTS0tJwOBw9EulRo0ZRU1OD0+kMeOMTJkzAredQWhdLUVEm1eU78HjclFc5kGQFs7k1dpGcnMzixYsv8pLbqC2rZ9dbn+B1+QgJt+Nq6rjMWpIkPC296KveSWhEVmRG5iSw7FvXc/WyKdTVd9/74/ThEtb99SN87s8yUnS/QeMpFzFqwhWft3whQpgFgg7IysrioYceIj8/n927d1NWVobFYkFVVaqrq1m3bh3QmhcdHx9PQkIC8fHxxMfHdyjWkiSRlZXF5s2bqa2tpaamhi1btqAoCqqqfvoYC7Jsw2SWkSSJzMxM8vLyGDVqFKcOnuW1n79LXUUDE+fmMu/zswiNCGHz6p38/cevYOg6mqojy50LnK7rZE1L7/FrMG3pJHa+ufcir1kxKzz65nd65CW3sePNvR1mduh+nc2rPmbZl3sWCrlSEMIsEHSC2Wxm8uTJTJ48mdLSUvbs2cORI0cwm81omhbwpM+cOcPp06cDh29tPSsURcHtdmOz2VBVFVVVaWpqora2Fk3T8Pl8REREEB8fH+hBHBoaysSJE5k4cWJgeOzG57fy0uNvBEIAJ/ac5N2nP+R7//gqf//Ry+0ET9ONi1pyApitZm57ZGmvhqOufHQ5+VsLaWl04XP7kRUZk1nh/ifv7JUoQ+uoqc4OJ/0DPED2UkQIs0DQA5KTk0lOTub666/nwIEDHD9+nPLy8sDINcMw0HUdXW8diKppGpqm0dLSEsjIMJlMjBgxgpaWFkpKSlBVlbq6OkJDQ5kyZQpjxowhOzs78HiAlgYXL/77G/g9n4UAfG4/qk/jbz9c3WG0wdAN4tNiiYhzUHWmlvj0GG765iLyrhvfqz1HxoXzmy2PsmX1xxzeXMCIpCgW3j+b1HG972WdMSMF+XkJ3d/eYGuIles+P7vX613uCGEWCHpBSEgIs2bNYtasWRiGQW1tLeXl5ZSVlVFeXt5OrNs4P9vA4XCQm5vL0aNHaWpqCnjWo0eP7rDX7+Etx1BMF3d41jWdM0fOXeQZtyErEo+t/W7/9+uws+TL81ny5fl9XqOiooJPTu4mPN1O0yl3QJxtIVZG5iRx/Rfm9dvOyw0hzAJBH5EkiZiYGGJiYgL9HQzDCIQtVFXl6NGjjBs3DpPJFPiB1mkdzz//POfOncPr9bJu3TpUVWXKlCntrtEaM+44btyZKJssCtOXTg7aPvvDuXPneOONN/D7/Yy5YxSu034otYAuMf/ua7n+/rlYbJahNnPYIYRZIAgikiRhNpsD/R7Cw8M7rGazWq3cc889PP/885SVlQGwceNG6urqmD9/fiCcMX7uGHS1i5rsC5BNMo7oMG746oIg7KZ/HDlyhA8++ADDMLDZbISGhvKN/7jvip7l11NE5Z9AMETY7Xbuv/9+UlJSsFqtmM1m9u/fz2uvvRaoOAxx2Pnif30Oi82MYmp9u0pdZF4kZcbz5MYf4xgxdKXNuq7z0Ucf8d577wGt+3Q4HHzhC18QotxDhMcsEAwhNpuN++67j7Vr15Kfn48sy5SUlPDiiy+yePFiUlNTuebW6aRPHMWHL26jvryRylPVnD5cctFakiwx9ppsHNFDJ8oNDQ28//77lJSUYDabsVgsxMfHc/fddxMVFTVkdl1qCGEWCIYYi8XC7bffTnx8PB9++CGyLON0OnnllVeYPHkyc+fOJSkznnsevw2AI1uO8fsv/AXvBZ3kzBYTc1fOHIotYBgG+/fvZ+vWrfj9/sA3gDFjxrBixQpRbt1LhDALBMMASZKYM2cOcXFxrF27FlmW8fl8HDx4kFOnTjFnzhxycnKQJInxc8aw8AuzWf/cFgxNB0lCkuDW7y8ldXzXqWzN9S00VDURkxKNLSQ4YllVVcX69es5d+4cJpMJu92OoijMnTuXuXPniqq+PiCEWSAYRowZM4bk5GT+9a9/UVhYGGh89Pbbb7Nnzx7mzJlDamoqn3tsBfM/P4tPPjjcOo5p6WRiUjqfJ+h1+Xjmey+x992DmCwKuqpz/RfncudPbu6w90ZPqKurY9u2bezfv5/Q0NCAlxwbG8vy5ctJTk7u68twxdOtMOu6zuOPP05hYSEWi4Vf/OIXpKb2bkqBQCDoOQ6Hg5UrV3L48GHee+89ZFlGVVWqqqp45ZVXSE5OJi8vj+zsbG78+nU9WvOpb/2DgxvzUX0q6qeVdh/8bQtWu4UV31vaY9sMw+DcuXOBIhvDMJAkiZCQEBRFYdasWcybNy+QFijoG92+ehs2bMDn8/Hyyy9z4MABfv3rX/PUU08Nhm0CwRWLJElMnDiRrKwstm3bxq5duzCZTKiqSnl5OaWlpYHy7ZycHGJiYjoNGdRXNHBwY/5FvSp8bh/vPv0htzy8pNtWoE6nkxMnTnDw4EFqamqQJAmTyYTFYsHlcjFu3DgWLFhATExM0F6DK5luhXnfvn3Mnt1aMjl58uSgz0UTCASdY7fbWbRoEVdffTWbNm0KtCPVNA2v18vHH3/Mzp07iYiIYPTo0WRkZJCQkIDd/lkvi+qztZgspg6bCPk9ftxOD6GR7XtotHnop0+fpri4mIqKCqC1D4jVasVkMiFJEhkZGcyfP5958+YN6OtwpdGtMDc3N7dLkG/rhnX+V5WCgoKBsa4TPB7PoF9zsBF7vDwI5h6zsrJISkri6NGjHDlyhJaWz8ZFuVwuysvL2bZtG9Ba2BIXF0d0dDSSX8bn6XgArGJVOFZUgMfroaWlhYaGBqqrq6mrq0PXP+sqd743bjabycnJYdy4ccTGxl4Rv0cY3L/XboU5LCys3R+ArusXxY86qvEfSAoKCgb9moON2OPlwUDscdq0aWiaxvHjx8nPz+fEiRN4vd5AI6W2zncVFRWBqkJHhpXGYhfGeU6zZJKImhzChx99+NltkoSiKISHhwcmV7fNLExLSyM3N5cJEyZgs9kGdI/DkWDvc9++fZ3e160wT5kyhY8++oilS5dy4MABsrOzg2aYQCDoG4qikJubS25uLpqmcebMGQoLCykpKaGyshJNay3jNgwDwzDIXj6SU+9XUJPvbB1jJUHi1dEkXzsCWZYDbUfP94xHjBjByJEjycrKIjMzs50YCwaWboV50aJFbN++nZUrV2IYBk8++eRg2CUQCHqIoihkZGSQkZEBfBYfLi8vp76+HqfTidPpJGlkEi1NLjxOL1aHGZPFhNlsxuFw4HA4CAsLIyIigsTERBITE0VRyBDSrTDLsszPf/7zwbBFIBAEAZPJRFJSEklJSUNtiqCPiCZGAoFAMMwQwiwQCATDDCHMAoFAMMwQwiwQCATDDCHMAoFAMMwQwiwQCATDDCHMAoFAMMyQDMPoeNRuD+mqrFAgEAgEnTN16tQOb++3MAsEAoEguIhQhkAgEAwzhDALBALBMOOSm//idDr5zne+g8vlwmKx8Nvf/pbY2NihNivoaJrGr371K44cOYLP5+Nb3/oW8+fPH2qzBoTi4mLuvPNOduzYcdk1znE6nTzyyCM0Nzfj9/v50Y9+RF5e3lCbFRSuhLFzfr+fn/zkJ5SWluLz+fj617/OwoULB/y6l5zH/MYbb5Cdnc0///lPli5dyrPPPjvUJg0Ia9euRVVVVq9ezVNPPcWZM2eG2qQBobm5md/85jdYLJahNmVAeO6555gxYwYvvvgiv/rVry6rhmDnj5373ve+x69//euhNinovPXWW0RGRvLPf/6Tv/71rzzxxBODct1LzmPOzs7m5MmTQOub+nId+rht2zaysrL4yle+gmEY/PSnPx1qk4JO276++93v8o1vfGOozRkQvvCFLwQ+dDRNu6y+EVwJY+eWLFnC4sWLgda/V0VRBuW6w1rVXn31Vf7xj3+0u+2xxx5j+/btLF26lMbGRl566aUhsi54dLTPqKgorFYrTz/9NHv27OHHP/7xJb3XjvaYlJTE0qVLGTNmzBBZFVw62uOTTz7JxIkTqa6u5pFHHuEnP/nJEFkXfHoydu5SJzQ0FGjd60MPPcTDDz88OBc2LjG++c1vGqtWrTIMwzAKCgqMm266aYgtGhgefvhh4/333w/8e9asWUNozcBw3XXXGffcc49xzz33GOPHjzc+97nPDbVJA8KxY8eMpUuXGps2bRpqU4LKk08+abzzzjuBf8+ePXsIrRk4ysrKjBUrVhivvvrqoF3zkvtoCw8Px+FwAK2jb86fR3g5MXXqVDZv3szixYs5duwYiYmJQ21S0Fm/fn3g/xcsWMDf/va3IbRmYCgqKuLb3/42f/jDHy6bbwZtXAlj52pqanjwwQd57LHHmDlz5qBd95IrMKmsrOTRRx/F5XKhqioPPfQQ11xzzVCbFXR8Ph///u//TnFxMYZh8PjjjzNu3LihNmvAWLBgAe+9995lFYMF+PrXv05hYSHJyclA63Djp556aoitCg5tWRnHjx8PjJ0bPXr0UJsVVH7xi1/w3nvvBcZ2ATzzzDMDPv/wkhNmgUAguNy55NLlBAKB4HJHCLNAIBAMM4QwCwQCwTBDCLNAIBAMM4QwCwQCwTBDCLNAIBAMM4QwCwQCwTBDCLNAIBAMM/4/X49TjYTWRKsAAAAASUVORK5CYII=", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.RandomState(13)\n", + "X_stretched = np.dot(X, rng.randn(2, 2))\n", + "\n", + "kmeans = KMeans(n_clusters=4, random_state=0)\n", + "plot_kmeans(kmeans, X_stretched)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By eye, we recognize that these transformed clusters are noncircular, and thus circular clusters would be a poor fit.\n", + "Nevertheless, *k*-means is not flexible enough to account for this, and tries to force-fit the data into four circular clusters.\n", + "This results in a mixing of cluster assignments where the resulting circles overlap: see especially the bottom-right of this plot.\n", + "One might imagine addressing this particular situation by preprocessing the data with PCA (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), but in practice there is no guarantee that such a global operation will circularize the individual groups.\n", + "\n", + "These two disadvantages of *k*-means—its lack of flexibility in cluster shape and lack of probabilistic cluster assignment—mean that for many datasets (especially low-dimensional datasets) it may not perform as well as you might hope.\n", + "\n", + "You might imagine addressing these weaknesses by generalizing the *k*-means model: for example, you could measure uncertainty in cluster assignment by comparing the distances of each point to *all* cluster centers, rather than focusing on just the closest.\n", + "You might also imagine allowing the cluster boundaries to be ellipses rather than circles, so as to account for noncircular clusters.\n", + "It turns out these are two essential components of a different type of clustering model, Gaussian mixture models." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Generalizing E–M: Gaussian Mixture Models\n", + "\n", + "A Gaussian mixture model (GMM) attempts to find a mixture of multidimensional Gaussian probability distributions that best model any input dataset.\n", + "In the simplest case, GMMs can be used for finding clusters in the same manner as *k*-means (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.mixture import GaussianMixture\n", + "gmm = GaussianMixture(n_components=4).fit(X)\n", + "labels = gmm.predict(X)\n", + "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But because a GMM contains a probabilistic model under the hood, it is also possible to find probabilistic cluster assignments—in Scikit-Learn this is done using the `predict_proba` method.\n", + "This returns a matrix of size `[n_samples, n_clusters]` which measures the probability that any point belongs to the given cluster:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0.531 0.469 0. ]\n", + " [0. 0. 0. 1. ]\n", + " [0. 0. 0. 1. ]\n", + " [0. 1. 0. 0. ]\n", + " [0. 0. 0. 1. ]]\n" + ] + } + ], + "source": [ + "probs = gmm.predict_proba(X)\n", + "print(probs[:5].round(3))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can visualize this uncertainty by, for example, making the size of each point proportional to the certainty of its prediction; looking at the following figure, we can see that it is precisely the points at the boundaries between clusters that reflect this uncertainty of cluster assignment:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "size = 50 * probs.max(1) ** 2 # square emphasizes differences\n", + "plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis', s=size);" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Under the hood, a Gaussian mixture model is very similar to *k*-means: it uses an expectation–maximization approach, which qualitatively does the following:\n", + "\n", + "1. Choose starting guesses for the location and shape.\n", + "\n", + "2. Repeat until converged:\n", + "\n", + " 1. *E-step*: For each point, find weights encoding the probability of membership in each cluster.\n", + " 2. *M-step*: For each cluster, update its location, normalization, and shape based on *all* data points, making use of the weights.\n", + "\n", + "The result of this is that each cluster is associated not with a hard-edged sphere, but with a smooth Gaussian model.\n", + "Just as in the *k*-means expectation–maximization approach, this algorithm can sometimes miss the globally optimal solution, and thus in practice multiple random initializations are used.\n", + "\n", + "Let's create a function that will help us visualize the locations and shapes of the GMM clusters by drawing ellipses based on the GMM output:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from matplotlib.patches import Ellipse\n", + "\n", + "def draw_ellipse(position, covariance, ax=None, **kwargs):\n", + " \"\"\"Draw an ellipse with a given position and covariance\"\"\"\n", + " ax = ax or plt.gca()\n", + " \n", + " # Convert covariance to principal axes\n", + " if covariance.shape == (2, 2):\n", + " U, s, Vt = np.linalg.svd(covariance)\n", + " angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n", + " width, height = 2 * np.sqrt(s)\n", + " else:\n", + " angle = 0\n", + " width, height = 2 * np.sqrt(covariance)\n", + " \n", + " # Draw the ellipse\n", + " for nsig in range(1, 4):\n", + " ax.add_patch(Ellipse(position, nsig * width, nsig * height,\n", + " angle, **kwargs))\n", + " \n", + "def plot_gmm(gmm, X, label=True, ax=None):\n", + " ax = ax or plt.gca()\n", + " labels = gmm.fit(X).predict(X)\n", + " if label:\n", + " ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n", + " else:\n", + " ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)\n", + " ax.axis('equal')\n", + " \n", + " w_factor = 0.2 / gmm.weights_.max()\n", + " for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\n", + " draw_ellipse(pos, covar, alpha=w * w_factor)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this in place, we can take a look at what the four-component GMM gives us for our initial data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gmm = GaussianMixture(n_components=4, random_state=42)\n", + "plot_gmm(gmm, X)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Similarly, we can use the GMM approach to fit our stretched dataset; allowing for a full covariance the model will fit even very oblong, stretched-out clusters, as we can see in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gmm = GaussianMixture(n_components=4, covariance_type='full', random_state=42)\n", + "plot_gmm(gmm, X_stretched)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This makes clear that GMMs address the two main practical issues with *k*-means encountered before." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Choosing the Covariance Type\n", + "\n", + "If you look at the details of the preceding fits, you will see that the `covariance_type` option was set differently within each.\n", + "This hyperparameter controls the degrees of freedom in the shape of each cluster; it is essential to set this carefully for any given problem.\n", + "The default is `covariance_type=\"diag\"`, which means that the size of the cluster along each dimension can be set independently, with the resulting ellipse constrained to align with the axes.\n", + "A slightly simpler and faster model is `covariance_type=\"spherical\"`, which constrains the shape of the cluster such that all dimensions are equal. The resulting clustering will have similar characteristics to that of *k*-means, though it is not entirely equivalent.\n", + "A more complicated and computationally expensive model (especially as the number of dimensions grows) is to use `covariance_type=\"full\"`, which allows each cluster to be modeled as an ellipse with arbitrary orientation.\n", + "\n", + "We can see a visual representation of these three choices for a single cluster within the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![(Covariance Type)](images/05.12-covariance-type.png)\n", + "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Covariance-Type)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Gaussian Mixture Models as Density Estimation\n", + "\n", + "Though the GMM is often categorized as a clustering algorithm, fundamentally it is an algorithm for *density estimation*.\n", + "That is to say, the result of a GMM fit to some data is technically not a clustering model, but a generative probabilistic model describing the distribution of the data.\n", + "\n", + "As an example, consider some data generated from Scikit-Learn's `make_moons` function, introduced in [In Depth: K-Means Clustering](05.11-K-Means.ipynb) (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_moons\n", + "Xmoon, ymoon = make_moons(200, noise=.05, random_state=0)\n", + "plt.scatter(Xmoon[:, 0], Xmoon[:, 1]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "If we try to fit this with a two-component GMM viewed as a clustering model, the results are not particularly useful (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gmm2 = GaussianMixture(n_components=2, covariance_type='full', random_state=0)\n", + "plot_gmm(gmm2, Xmoon)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But if we instead use many more components and ignore the cluster labels, we find a fit that is much closer to the input data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gmm16 = GaussianMixture(n_components=16, covariance_type='full', random_state=0)\n", + "plot_gmm(gmm16, Xmoon, label=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here the mixture of 16 Gaussian components serves not to find separated clusters of data, but rather to model the overall *distribution* of the input data.\n", + "This is a generative model of the distribution, meaning that the GMM gives us the recipe to generate new random data distributed similarly to our input.\n", + "For example, here are 400 new points drawn from this 16-component GMM fit to our original data (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Xnew, ynew = gmm16.sample(400)\n", + "plt.scatter(Xnew[:, 0], Xnew[:, 1]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "A GMM is convenient as a flexible means of modeling an arbitrary multidimensional distribution of data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### How Many Components?\n", + "\n", + "The fact that a GMM is a generative model gives us a natural means of determining the optimal number of components for a given dataset.\n", + "A generative model is inherently a probability distribution for the dataset, and so we can simply evaluate the *likelihood* of the data under the model, using cross-validation to avoid overfitting.\n", + "Another means of correcting for overfitting is to adjust the model likelihoods using some analytic criterion such as the [Akaike information criterion (AIC)](https://en.wikipedia.org/wiki/Akaike_information_criterion) or the [Bayesian information criterion (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion).\n", + "Scikit-Learn's `GaussianMixture` estimator actually includes built-in methods that compute both of these, so it is very easy to operate using this approach.\n", + "\n", + "Let's look at the AIC and BIC versus the number of GMM components for our moons dataset (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n_components = np.arange(1, 21)\n", + "models = [GaussianMixture(n, covariance_type='full', random_state=0).fit(Xmoon)\n", + " for n in n_components]\n", + "\n", + "plt.plot(n_components, [m.bic(Xmoon) for m in models], label='BIC')\n", + "plt.plot(n_components, [m.aic(Xmoon) for m in models], label='AIC')\n", + "plt.legend(loc='best')\n", + "plt.xlabel('n_components');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The optimal number of clusters is the value that minimizes the AIC or BIC, depending on which approximation we wish to use. The AIC tells us that our choice of 16 components earlier was probably too many: around 8–12 components would have been a better choice.\n", + "As is typical with this sort of problem, the BIC recommends a simpler model.\n", + "\n", + "Notice the important point: this choice of number of components measures how well a GMM works *as a density estimator*, not how well it works *as a clustering algorithm*.\n", + "I'd encourage you to think of the GMM primarily as a density estimator, and use it for clustering only when warranted within simple datasets." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: GMMs for Generating New Data\n", + "\n", + "We just saw a simple example of using a GMM as a generative model in order to create new samples from the distribution defined by the input data.\n", + "Here we will run with this idea and generate *new handwritten digits* from the standard digits corpus that we have used before.\n", + "\n", + "To start with, let's load the digits data using Scikit-Learn's data tools:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1797, 64)" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import load_digits\n", + "digits = load_digits()\n", + "digits.data.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next, let's plot the first 50 of these to recall exactly what we're looking at (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_digits(data):\n", + " fig, ax = plt.subplots(5, 10, figsize=(8, 4),\n", + " subplot_kw=dict(xticks=[], yticks=[]))\n", + " fig.subplots_adjust(hspace=0.05, wspace=0.05)\n", + " for i, axi in enumerate(ax.flat):\n", + " im = axi.imshow(data[i].reshape(8, 8), cmap='binary')\n", + " im.set_clim(0, 16)\n", + "plot_digits(digits.data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We have nearly 1,800 digits in 64 dimensions, and we can build a GMM on top of these to generate more.\n", + "GMMs can have difficulty converging in such a high-dimensional space, so we will start with an invertible dimensionality reduction algorithm on the data.\n", + "Here we will use a straightforward PCA, asking it to preserve 99% of the variance in the projected data:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1797, 41)" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.decomposition import PCA\n", + "pca = PCA(0.99, whiten=True)\n", + "data = pca.fit_transform(digits.data)\n", + "data.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result is 41 dimensions, a reduction of nearly 1/3 with almost no information loss.\n", + "Given this projected data, let's use the AIC to get a gauge for the number of GMM components we should use (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n_components = np.arange(50, 210, 10)\n", + "models = [GaussianMixture(n, covariance_type='full', random_state=0)\n", + " for n in n_components]\n", + "aics = [model.fit(data).aic(data) for model in models]\n", + "plt.plot(n_components, aics);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "It appears that around 140 components minimizes the AIC; we will use this model.\n", + "Let's quickly fit this to the data and confirm that it has converged:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True\n" + ] + } + ], + "source": [ + "gmm = GaussianMixture(140, covariance_type='full', random_state=0)\n", + "gmm.fit(data)\n", + "print(gmm.converged_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now we can draw samples of 100 new points within this 41-dimensional projected space, using the GMM as a generative model:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(100, 41)" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data_new, label_new = gmm.sample(100)\n", + "data_new.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we can use the inverse transform of the PCA object to construct the new digits (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "digits_new = pca.inverse_transform(data_new)\n", + "plot_digits(digits_new)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The results for the most part look like plausible digits from the dataset!\n", + "\n", + "Consider what we've done here: given a sampling of handwritten digits, we have modeled the distribution of that data in such a way that we can generate brand new samples of digits from the data: these are \"handwritten digits,\" which do not individually appear in the original dataset, but rather capture the general features of the input data as modeled by the mixture model.\n", + "Such a generative model of digits can prove very useful as a component of a Bayesian generative classifier, as we shall see in the next chapter." + ] + } + ], + "metadata": { + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.13-Kernel-Density-Estimation.ipynb b/notebooks/05.13-Kernel-Density-Estimation.ipynb new file mode 100644 index 000000000..9f0ce72c3 --- /dev/null +++ b/notebooks/05.13-Kernel-Density-Estimation.ipynb @@ -0,0 +1,913 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: Kernel Density Estimation" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In the previous chapter we covered Gaussian mixture models, which are a kind of hybrid between a clustering estimator and a density estimator.\n", + "Recall that a density estimator is an algorithm that takes a $D$-dimensional dataset and produces an estimate of the $D$-dimensional probability distribution that data is drawn from.\n", + "The GMM algorithm accomplishes this by representing the density as a weighted sum of Gaussian distributions.\n", + "*Kernel density estimation* (KDE) is in some senses an algorithm that takes the mixture-of-Gaussians idea to its logical extreme: it uses a mixture consisting of one Gaussian component *per point*, resulting in an essentially nonparametric estimator of density.\n", + "In this chapter, we will explore the motivation and uses of KDE.\n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Motivating Kernel Density Estimation: Histograms\n", + "\n", + "As mentioned previously, a density estimator is an algorithm that seeks to model the probability distribution that generated a dataset.\n", + "For one-dimensional data, you are probably already familiar with one simple density estimator: the histogram.\n", + "A histogram divides the data into discrete bins, counts the number of points that fall in each bin, and then visualizes the results in an intuitive manner.\n", + "\n", + "For example, let's create some data that is drawn from two normal distributions:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def make_data(N, f=0.3, rseed=1):\n", + " rand = np.random.RandomState(rseed)\n", + " x = rand.randn(N)\n", + " x[int(f * N):] += 5\n", + " return x\n", + "\n", + "x = make_data(1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We have previously seen that the standard count-based histogram can be created with the `plt.hist` function.\n", + "By specifying the `density` parameter of the histogram, we end up with a normalized histogram where the height of the bins does not reflect counts, but instead reflects probability density (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hist = plt.hist(x, bins=30, density=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that for equal binning, this normalization simply changes the scale on the y-axis, leaving the relative heights essentially the same as in a histogram built from counts.\n", + "This normalization is chosen so that the total area under the histogram is equal to 1, as we can confirm by looking at the output of the histogram function:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "density, bins, patches = hist\n", + "widths = bins[1:] - bins[:-1]\n", + "(density * widths).sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "One of the issues with using a histogram as a density estimator is that the choice of bin size and location can lead to representations that have qualitatively different features.\n", + "For example, if we look at a version of this data with only 20 points, the choice of how to draw the bins can lead to an entirely different interpretation of the data!\n", + "Consider this example, visualized in the following figure:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "x = make_data(20)\n", + "bins = np.linspace(-5, 10, 10)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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3794ElAcAAABMD75QAwAAAEYiCAMAAMBIto9GIH7znzrtdAkT8uv1dzldAgAARptcZnDuN2G82fygY/tOJO4IAwAAwEgEYQAAABiJIAwAAAAjEYQBAABgJIIwAAAAjEQQBgAAgJEIwgAAADASQRgAAABGIggDAADASARhAAAAGIkgDAAAACMRhAEAAGAkgjAAAACMRBAGAACAkQjCAAAAMBJBGAAAAEYiCAMAAMBIBGEAAAAYiSAMAAAAI/mcLgDusfLwRUkXnS7jE73Z/KDTJQD4BPOfOp3Arbl7Hk1OqvSSKn0AN3FHGAAAAEYiCAMAAMBIBGEAAAAYyfYZ4Wg0qrq6Og0MDCgjI0MNDQ3Kz8+PLT927Jg6Ojrk8/m0efNmrVixQv/5z3/0wAMPKBAISJLuv/9+rV+/fvq6AAAAACbJNgh3dXVpZGREnZ2d6uvrU3Nzs/bt2ydJunz5so4cOaITJ05oeHhYVVVVWrZsmf7617/qoYce0tNPPz3tDQAAAABTYftoRDAYVElJiSSpqKhI/f39sWWvv/667r33XmVkZCgnJ0d5eXk6f/68+vv7de7cOa1bt05PPPGELl26NH0dAAAAAFNge0c4HA7L7/fHXnu9Xo2Ojsrn8ykcDisnJye2LDs7W+FwWHfddZcWL16sr3zlKzp16pQaGhq0d+/eW7YdCoUS1IZzhoaGUqKPZDGRY805ST1uOZ/Jcm0lQ40Aklsi54yTs9U2CPv9fkUikdjraDQqn8837rJIJKKcnBwtWbJEWVlZkqTy8vJxQ7AkFRYWxlW8G4RCoQn0we9dTJSJXDMTOyfTjXOeSM6fz5tm4toKBoNxb8PZ48W1D5ggkXPGydlq+2hEcXGxenp6JEl9fX2x/wFOkpYsWaJgMKjh4WENDg7qwoULCgQC+v73v6/f/va3kqSzZ89q0aJFiegBAAAASBjbO8Ll5eXq7e1VRUWFLMtSY2Oj2tralJeXp7KyMlVXV6uqqkqWZWnbtm3KzMxUTU2Ndu7cqfb2dmVlZamhoWEmegEAAAAmzDYIp6Wlqb6+fsx7BQUFsZ/XrFmjNWvWjFn+uc99TkeOHElQiQAAAEDi8YUaAAAAMBJBGAAAAEYiCAMAAMBIBGEAAAAYiSAMAAAAIxGEAQAAYCSCMAAAAIxEEAYAAICRbL9Qw83mP3Xa6RL+30WnCzDGxM855ySVuOfPuvRJ19abzQ/OYB0AgHhxRxgAAABGIggDAADASARhAAAAGIkgDAAAACMRhAEAAGAkgjAAAACMRBAGAACAkQjCAAAAMBJBGAAAAEYiCAMAAMBIBGEAAAAYiSAMAAAAIxGEAQAAYCSCMAAAAIxEEAYAAICRCMIAAAAwEkEYAAAARvLZfSAajaqurk4DAwPKyMhQQ0OD8vPzY8uPHTumjo4O+Xw+bd68WStWrNC1a9f03e9+V0NDQ7rjjjvU1NSkrKysaW0EAAAAmAzbO8JdXV0aGRlRZ2enampq1NzcHFt2+fJlHTlyRB0dHXr++ef14x//WCMjI2ptbdVDDz2ko0ePauHChers7JzWJgAAAIDJsg3CwWBQJSUlkqSioiL19/fHlr3++uu69957lZGRoZycHOXl5en8+fNj1iktLdUf//jHaSofAAAAmBrbRyPC4bD8fn/stdfr1ejoqHw+n8LhsHJycmLLsrOzFQ6Hx7yfnZ2twcHBcbcdCoXiKv7X6++Ka/1EGBoa0qxZs5wuIyFSpRf6cJdU6UOy7yXemZYoTtaRqLls0nWTLOjDXZzuI5FzZmhoyLG5ZRuE/X6/IpFI7HU0GpXP5xt3WSQSUU5OTuz9WbNmKRKJaM6cOeNuu7CwMN76HRcKhVKiDyl1eqEPd0mVPqSZ6SUYDMa9jVQ43lw37kMf7pIqfUjOzlbbRyOKi4vV09MjSerr61MgEIgtW7JkiYLBoIaHhzU4OKgLFy4oEAiouLhY3d3dkqSenh4tXbo0ET0AAAAACWN7R7i8vFy9vb2qqKiQZVlqbGxUW1ub8vLyVFZWpurqalVVVcmyLG3btk2ZmZnavHmzduzYoWPHjulTn/qUWlpaZqIXAAAAYMJs7winpaWpvr5eHR0d6uzsVEFBgR599FGVlZVJktasWaMTJ07o5MmTeuCBByRJn/nMZ/T888+ro6ND+/bt0+zZs6e3i2lWV1eXFPt+/7NO1vtRiazFDX3NRA3j7ePD7020hrq6uluuCbttJ2qZXV1TXe6GawCJw2ydOmZrYvbBbI1vn6nAY1mW5cSOg8Fg0jwy4fF49HGHabqfa/mkfX/cZyezzodNRy9TrSWebU3nOUlkP3b7+HAfH97vRGvweDySNOaaGG/dT9reVJd92EfPh916idjndJmp59jimY3M1vj3/XGfZbYyW9//nMRsTSQnZyvfLAcAAAAjEYQBAABgJIIwAAAAjEQQBgAAgJFsf30apN27dyfFvt//rJP1flQia3FDXzNRw3j7+PB7E61hvHXstp2oZROta6b2CXditk4dszUx+2C2xrfPVMBvjYgT3+ziPvThLqnSh8RvjZhJXDfuQx/ukip9SPzWCAAAAGDGOXpHGABwq3jvCAMAbjXebHUsCAMAAABO4tEIAAAAGIkgDAAAACMRhAEAAGAkx4PwhQsXtHTpUg0PDztdypQMDg7qscce07p167R27Vq99tprTpc0KdFoVLt27dLatWtVXV2tt956y+mSpuT69euqra1VVVWVHn74Yf3+9793uqS4XL16VcuXL9eFCxecLiUuP/3pT7V27Vp985vf1PHjx50uZ0quX7+umpoaVVRUqKqqKmnOCbPVWcxWd2K2uodbZqujQTgcDmvPnj3KyMhwsoy4tLW16Utf+pJeeOEFNTU1qb6+3umSJqWrq0sjIyPq7OxUTU2NmpubnS5pSk6dOqW5c+fq6NGjOnjwoH7wgx84XdKUXb9+Xbt27dKsWbOcLiUuf/7zn/Xaa6+pvb1dR44c0b///W+nS5qS7u5ujY6OqqOjQ1u2bNGzzz7rdEm2mK3OY7a6D7PVXdwyWx0LwpZl6emnn9b27duVlZXlVBlxe+SRR1RRUSFJunHjhjIzMx2uaHKCwaBKSkokSUVFRerv73e4oqn5+te/rieffFLSzWvL6/U6XNHU7dmzRxUVFbrjjjucLiUuL7/8sgKBgLZs2aLHHntMX/3qV50uaUoWLFigGzduKBqNKhwOy+dz9xdyMlvdgdnqPsxWd3HLbJ2RvR4/flyHDx8e895nP/tZrVq1Svfcc89MlJAQ4/XR2NioJUuW6PLly6qtrdXOnTsdqm5qwuGw/H5/7LXX69Xo6Kjr/2P/UdnZ2ZJu9vPEE0/oO9/5jrMFTdHJkyeVm5urkpISHThwwOly4vLee+/pX//6l/bv369//OMf2rx5s37zm9/I4/E4XdqkzJ49W//85z+1cuVKvffee9q/f7/TJcUwW92L2eouzFb3cctsdez3CJeXl2vevHmSpL6+Pi1ZskQvvviiE6XEbWBgQNu3b9f3vvc9LV++3OlyJqWpqUlf+MIXtGrVKklSaWmpenp6HK5qat555x1t2bIl9ixbMvrWt74lj8cjj8ejUCik+fPna9++fbr99tudLm3SfvSjHyk3N1cbNmyQJH3jG99QW1ubPv3pTztc2eQ0NTUpIyNDNTU1euedd7R+/Xr96le/cu0dSmarOzBb3YXZ6j5uma2O/dX0d7/7Xeznr33ta/r5z3/uVClx+dvf/qYnn3xSzz77bFLdgXlfcXGx/vCHP2jVqlXq6+tTIBBwuqQpuXLlijZs2KBdu3bpy1/+stPlTNmHA0t1dbXq6uqSclBLN7/B5xe/+IUeffRRXbp0Sf/73/80d+5cp8uatDlz5ig9PV2SdNttt2l0dFQ3btxwuKqPx2x1B2aruzBb3cctszW5/o3GhVpaWjQyMqIf/vCHkiS/3699+/Y5XNXElZeXq7e3VxUVFbIsS42NjU6XNCX79+/Xf//7X7W2tqq1tVWS9LOf/Szp/6eIZLZixQr95S9/0cMPPyzLsrRr166kfL7wkUce0c6dO1VVVaXr169r27Ztmj17ttNlpTxmqzswW92H2ZpYfMUyAAAAjOT47xEGAAAAnEAQBgAAgJEIwgAAADASQRgAAABGIggDAADASARhAAAAGIkgDAAAACP9H4FUpE14/F18AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=(12, 4),\n", + " sharex=True, sharey=True,\n", + " subplot_kw={'xlim':(-4, 9),\n", + " 'ylim':(-0.02, 0.3)})\n", + "fig.subplots_adjust(wspace=0.05)\n", + "for i, offset in enumerate([0.0, 0.6]):\n", + " ax[i].hist(x, bins=bins + offset, density=True)\n", + " ax[i].plot(x, np.full_like(x, -0.01), '|k',\n", + " markeredgewidth=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "On the left, the histogram makes clear that this is a bimodal distribution.\n", + "On the right, we see a unimodal distribution with a long tail.\n", + "Without seeing the preceding code, you would probably not guess that these two histograms were built from the same data. With that in mind, how can you trust the intuition that histograms confer?\n", + "And how might we improve on this?\n", + "\n", + "Stepping back, we can think of a histogram as a stack of blocks, where we stack one block within each bin on top of each point in the dataset.\n", + "Let's view this directly (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(-0.2, 8.0)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "bins = np.arange(-3, 8)\n", + "ax.plot(x, np.full_like(x, -0.1), '|k',\n", + " markeredgewidth=1)\n", + "for count, edge in zip(*np.histogram(x, bins)):\n", + " for i in range(count):\n", + " ax.add_patch(plt.Rectangle(\n", + " (edge, i), 1, 1, ec='black', alpha=0.5))\n", + "ax.set_xlim(-4, 8)\n", + "ax.set_ylim(-0.2, 8)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The problem with our two binnings stems from the fact that the height of the block stack often reflects not the actual density of points nearby, but coincidences of how the bins align with the data points.\n", + "This misalignment between points and their blocks is a potential cause of the poor histogram results seen here.\n", + "But what if, instead of stacking the blocks aligned with the *bins*, we were to stack the blocks aligned with the *points they represent*?\n", + "If we do this, the blocks won't be aligned, but we can add their contributions at each location along the x-axis to find the result.\n", + "Let's try this (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_d = np.linspace(-4, 8, 2000)\n", + "density = sum((abs(xi - x_d) < 0.5) for xi in x)\n", + "\n", + "plt.fill_between(x_d, density, alpha=0.5)\n", + "plt.plot(x, np.full_like(x, -0.1), '|k', markeredgewidth=1)\n", + "\n", + "plt.axis([-4, 8, -0.2, 8]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result looks a bit messy, but it's a much more robust reflection of the actual data characteristics than is the standard histogram.\n", + "Still, the rough edges are not aesthetically pleasing, nor are they reflective of any true properties of the data.\n", + "In order to smooth them out, we might decide to replace the blocks at each location with a smooth function, like a Gaussian.\n", + "Let's use a standard normal curve at each point instead of a block (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from scipy.stats import norm\n", + "x_d = np.linspace(-4, 8, 1000)\n", + "density = sum(norm(xi).pdf(x_d) for xi in x)\n", + "\n", + "plt.fill_between(x_d, density, alpha=0.5)\n", + "plt.plot(x, np.full_like(x, -0.1), '|k', markeredgewidth=1)\n", + "\n", + "plt.axis([-4, 8, -0.2, 5]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This smoothed-out plot, with a Gaussian distribution contributed at the location of each input point, gives a much more accurate idea of the shape of the data distribution, and one that has much less variance (i.e., changes much less in response to differences in sampling).\n", + "\n", + "What we've landed on in the last two plots is what's called kernel density estimation in one dimension: we have placed a \"kernel\"—a square or \"tophat\"-shaped kernel in the former, a Gaussian kernel in the latter—at the location of each point, and used their sum as an estimate of density.\n", + "With this intuition in mind, we'll now explore kernel density estimation in more detail." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Kernel Density Estimation in Practice\n", + "\n", + "The free parameters of kernel density estimation are the *kernel*, which specifies the shape of the distribution placed at each point, and the *kernel bandwidth*, which controls the size of the kernel at each point.\n", + "In practice, there are many kernels you might use for kernel density estimation: in particular, the Scikit-Learn KDE implementation supports six kernels, which you can read about in the [\"Density Estimation\" section](http://scikit-learn.org/stable/modules/density.html) of the documentation.\n", + "\n", + "While there are several versions of KDE implemented in Python (notably in the SciPy and `statsmodels` packages), I prefer to use Scikit-Learn's version because of its efficiency and flexibility.\n", + "It is implemented in the `sklearn.neighbors.KernelDensity` estimator, which handles KDE in multiple dimensions with one of six kernels and one of a couple dozen distance metrics.\n", + "Because KDE can be fairly computationally intensive, the Scikit-Learn estimator uses a tree-based algorithm under the hood and can trade off computation time for accuracy using the `atol` (absolute tolerance) and `rtol` (relative tolerance) parameters.\n", + "The kernel bandwidth can be determined using Scikit-Learn's standard cross-validation tools, as we will soon see.\n", + "\n", + "Let's first show a simple example of replicating the previous plot using the Scikit-Learn `KernelDensity` estimator (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.neighbors import KernelDensity\n", + "\n", + "# instantiate and fit the KDE model\n", + "kde = KernelDensity(bandwidth=1.0, kernel='gaussian')\n", + "kde.fit(x[:, None])\n", + "\n", + "# score_samples returns the log of the probability density\n", + "logprob = kde.score_samples(x_d[:, None])\n", + "\n", + "plt.fill_between(x_d, np.exp(logprob), alpha=0.5)\n", + "plt.plot(x, np.full_like(x, -0.01), '|k', markeredgewidth=1)\n", + "plt.ylim(-0.02, 0.22);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result here is normalized such that the area under the curve is equal to 1." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Selecting the Bandwidth via Cross-Validation\n", + "\n", + "The final estimate produced by a KDE procedure can be quite sensitive to the choice of bandwidth, which is the knob that controls the bias–variance trade-off in the estimate of density.\n", + "Too narrow a bandwidth leads to a high-variance estimate (i.e., overfitting), where the presence or absence of a single point makes a large difference. Too wide a bandwidth leads to a high-bias estimate (i.e., underfitting), where the structure in the data is washed out by the wide kernel.\n", + "\n", + "There is a long history in statistics of methods to quickly estimate the best bandwidth based on rather stringent assumptions about the data: if you look up the KDE implementations in the SciPy and `statsmodels` packages, for example, you will see implementations based on some of these rules.\n", + "\n", + "In machine learning contexts, we've seen that such hyperparameter tuning often is done empirically via a cross-validation approach.\n", + "With this in mind, Scikit-Learn's `KernelDensity` estimator is designed such that it can be used directly within the package's standard grid search tools.\n", + "Here we will use `GridSearchCV` to optimize the bandwidth for the preceding dataset.\n", + "Because we are looking at such a small dataset, we will use leave-one-out cross-validation, which minimizes the reduction in training set size for each cross-validation trial:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.model_selection import GridSearchCV\n", + "from sklearn.model_selection import LeaveOneOut\n", + "\n", + "bandwidths = 10 ** np.linspace(-1, 1, 100)\n", + "grid = GridSearchCV(KernelDensity(kernel='gaussian'),\n", + " {'bandwidth': bandwidths},\n", + " cv=LeaveOneOut())\n", + "grid.fit(x[:, None]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now we can find the choice of bandwidth that maximizes the score (which in this case defaults to the log-likelihood):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'bandwidth': 1.1233240329780276}" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grid.best_params_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The optimal bandwidth happens to be very close to what we used in the example plot earlier, where the bandwidth was 1.0 (i.e., the default width of `scipy.stats.norm`)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: Not-so-Naive Bayes\n", + "\n", + "This example looks at Bayesian generative classification with KDE, and demonstrates how to use the Scikit-Learn architecture to create a custom estimator.\n", + "\n", + "In [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) we explored naive Bayesian classification, in which we create a simple generative model for each class, and use these models to build a fast classifier.\n", + "For Gaussian naive Bayes, the generative model is a simple axis-aligned Gaussian.\n", + "With a density estimation algorithm like KDE, we can remove the \"naive\" element and perform the same classification with a more sophisticated generative model for each class.\n", + "It's still Bayesian classification, but it's no longer naive.\n", + "\n", + "The general approach for generative classification is this:\n", + "\n", + "1. Split the training data by label.\n", + "\n", + "2. For each set, fit a KDE to obtain a generative model of the data.\n", + " This allows you, for any observation $x$ and label $y$, to compute a likelihood $P(x~|~y)$.\n", + " \n", + "3. From the number of examples of each class in the training set, compute the *class prior*, $P(y)$.\n", + "\n", + "4. For an unknown point $x$, the posterior probability for each class is $P(y~|~x) \\propto P(x~|~y)P(y)$.\n", + " The class that maximizes this posterior is the label assigned to the point.\n", + "\n", + "The algorithm is straightforward and intuitive to understand; the more difficult piece is couching it within the Scikit-Learn framework in order to make use of the grid search and cross-validation architecture.\n", + "\n", + "This is the code that implements the algorithm within the Scikit-Learn framework; we will step through it following the code block:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.base import BaseEstimator, ClassifierMixin\n", + "\n", + "\n", + "class KDEClassifier(BaseEstimator, ClassifierMixin):\n", + " \"\"\"Bayesian generative classification based on KDE\n", + " \n", + " Parameters\n", + " ----------\n", + " bandwidth : float\n", + " the kernel bandwidth within each class\n", + " kernel : str\n", + " the kernel name, passed to KernelDensity\n", + " \"\"\"\n", + " def __init__(self, bandwidth=1.0, kernel='gaussian'):\n", + " self.bandwidth = bandwidth\n", + " self.kernel = kernel\n", + " \n", + " def fit(self, X, y):\n", + " self.classes_ = np.sort(np.unique(y))\n", + " training_sets = [X[y == yi] for yi in self.classes_]\n", + " self.models_ = [KernelDensity(bandwidth=self.bandwidth,\n", + " kernel=self.kernel).fit(Xi)\n", + " for Xi in training_sets]\n", + " self.logpriors_ = [np.log(Xi.shape[0] / X.shape[0])\n", + " for Xi in training_sets]\n", + " return self\n", + " \n", + " def predict_proba(self, X):\n", + " logprobs = np.array([model.score_samples(X)\n", + " for model in self.models_]).T\n", + " result = np.exp(logprobs + self.logpriors_)\n", + " return result / result.sum(axis=1, keepdims=True)\n", + " \n", + " def predict(self, X):\n", + " return self.classes_[np.argmax(self.predict_proba(X), 1)]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Anatomy of a Custom Estimator" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Let's step through this code and discuss the essential features:\n", + "\n", + "```python\n", + "from sklearn.base import BaseEstimator, ClassifierMixin\n", + "\n", + "class KDEClassifier(BaseEstimator, ClassifierMixin):\n", + " \"\"\"Bayesian generative classification based on KDE\n", + " \n", + " Parameters\n", + " ----------\n", + " bandwidth : float\n", + " the kernel bandwidth within each class\n", + " kernel : str\n", + " the kernel name, passed to KernelDensity\n", + " \"\"\"\n", + "```\n", + "\n", + "Each estimator in Scikit-Learn is a class, and it is most convenient for this class to inherit from the `BaseEstimator` class as well as the appropriate mixin, which provides standard functionality.\n", + "For example, here the `BaseEstimator` contains (among other things) the logic necessary to clone/copy an estimator for use in a cross-validation procedure, and `ClassifierMixin` defines a default `score` method used by such routines.\n", + "We also provide a docstring, which will be captured by IPython's help functionality (see [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next comes the class initialization method:\n", + "\n", + "```python\n", + " def __init__(self, bandwidth=1.0, kernel='gaussian'):\n", + " self.bandwidth = bandwidth\n", + " self.kernel = kernel\n", + "```\n", + "\n", + "This is the actual code that is executed when the object is instantiated with `KDEClassifier`.\n", + "In Scikit-Learn, it is important that *initialization contains no operations* other than assigning the passed values by name to `self`.\n", + "This is due to the logic contained in `BaseEstimator` required for cloning and modifying estimators for cross-validation, grid search, and other functions.\n", + "Similarly, all arguments to `__init__` should be explicit: i.e., `*args` or `**kwargs` should be avoided, as they will not be correctly handled within cross-validation routines." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next comes the `fit` method, where we handle training data:\n", + "\n", + "```python \n", + " def fit(self, X, y):\n", + " self.classes_ = np.sort(np.unique(y))\n", + " training_sets = [X[y == yi] for yi in self.classes_]\n", + " self.models_ = [KernelDensity(bandwidth=self.bandwidth,\n", + " kernel=self.kernel).fit(Xi)\n", + " for Xi in training_sets]\n", + " self.logpriors_ = [np.log(Xi.shape[0] / X.shape[0])\n", + " for Xi in training_sets]\n", + " return self\n", + "```\n", + "\n", + "Here we find the unique classes in the training data, train a `KernelDensity` model for each class, and compute the class priors based on the number of input samples.\n", + "Finally, `fit` should always return `self` so that we can chain commands. For example:\n", + "```python\n", + "label = model.fit(X, y).predict(X)\n", + "```\n", + "Notice that each persistent result of the fit is stored with a trailing underscore (e.g., `self.logpriors_`).\n", + "This is a convention used in Scikit-Learn so that you can quickly scan the members of an estimator (using IPython's tab completion) and see exactly which members are fit to training data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we have the logic for predicting labels on new data:\n", + "```python\n", + " def predict_proba(self, X):\n", + " logprobs = np.vstack([model.score_samples(X)\n", + " for model in self.models_]).T\n", + " result = np.exp(logprobs + self.logpriors_)\n", + " return result / result.sum(axis=1, keepdims=True)\n", + " \n", + " def predict(self, X):\n", + " return self.classes_[np.argmax(self.predict_proba(X), 1)]\n", + "```\n", + "Because this is a probabilistic classifier, we first implement `predict_proba`, which returns an array of class probabilities of shape `[n_samples, n_classes]`.\n", + "Entry `[i, j]` of this array is the posterior probability that sample `i` is a member of class `j`, computed by multiplying the likelihood by the class prior and normalizing.\n", + "\n", + "The `predict` method uses these probabilities and simply returns the class with the largest probability." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Using Our Custom Estimator\n", + "\n", + "Let's try this custom estimator on a problem we have seen before: the classification of handwritten digits.\n", + "Here we will load the digits and compute the cross-validation score for a range of candidate bandwidths using the ``GridSearchCV`` meta-estimator (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.datasets import load_digits\n", + "from sklearn.model_selection import GridSearchCV\n", + "\n", + "digits = load_digits()\n", + "\n", + "grid = GridSearchCV(KDEClassifier(),\n", + " {'bandwidth': np.logspace(0, 2, 100)})\n", + "grid.fit(digits.data, digits.target);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next we can plot the cross-validation score as a function of bandwidth (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "best param: {'bandwidth': 6.135907273413174}\n", + "accuracy = 0.9677298050139276\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.semilogx(np.array(grid.cv_results_['param_bandwidth']),\n", + " grid.cv_results_['mean_test_score'])\n", + "ax.set(title='KDE Model Performance', ylim=(0, 1),\n", + " xlabel='bandwidth', ylabel='accuracy')\n", + "print(f'best param: {grid.best_params_}')\n", + "print(f'accuracy = {grid.best_score_}')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This indicates that our KDE classifier reaches a cross-validation accuracy of over 96%, compared to around 80% for the naive Bayes classifier:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8069281956050759" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.naive_bayes import GaussianNB\n", + "from sklearn.model_selection import cross_val_score\n", + "cross_val_score(GaussianNB(), digits.data, digits.target).mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "One benefit of such a generative classifier is interpretability of results: for each unknown sample, we not only get a probabilistic classification, but a *full model* of the distribution of points we are comparing it to!\n", + "If desired, this offers an intuitive window into the reasons for a particular classification that algorithms like SVMs and random forests tend to obscure.\n", + "\n", + "If you would like to take this further, here are some ideas for improvements that could be made to our KDE classifier model:\n", + "\n", + "- You could allow the bandwidth in each class to vary independently.\n", + "- You could optimize these bandwidths not based on their prediction score, but on the likelihood of the training data under the generative model within each class (i.e. use the scores from `KernelDensity` itself rather than the global prediction accuracy).\n", + "\n", + "Finally, if you want some practice building your own estimator, you might tackle building a similar Bayesian classifier using Gaussian mixture models instead of KDE." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.14-Image-Features.ipynb b/notebooks/05.14-Image-Features.ipynb new file mode 100644 index 000000000..a1189fad1 --- /dev/null +++ b/notebooks/05.14-Image-Features.ipynb @@ -0,0 +1,729 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Application: A Face Detection Pipeline" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This part of the book has explored a number of the central concepts and algorithms of machine learning.\n", + "But moving from these concepts to a real-world application can be a challenge.\n", + "Real-world datasets are noisy and heterogeneous; they may have missing features, and data may be in a form that is difficult to map to a clean `[n_samples, n_features]` matrix.\n", + "Before applying any of the methods discussed here, you must first extract these features from your data: there is no formula for how to do this that applies across all domains, and thus this is where you as a data scientist must exercise your own intuition and expertise.\n", + "\n", + "One interesting and compelling application of machine learning is to images, and we have already seen a few examples of this where pixel-level features are used for classification.\n", + "Again, the real world data is rarely so uniform, and simple pixels will not be suitable: this has led to a large literature on *feature extraction* methods for image data (see [Feature Engineering](05.04-Feature-Engineering.ipynb)).\n", + "\n", + "In this chapter we will take a look at one such feature extraction technique: the [histogram of oriented gradients (HOG)](https://en.wikipedia.org/wiki/Histogram_of_oriented_gradients), which transforms image pixels into a vector representation that is sensitive to broadly informative image features regardless of confounding factors like illumination.\n", + "We will use these features to develop a simple face detection pipeline, using machine learning algorithms and concepts we've seen throughout this part of the book. \n", + "\n", + "We begin with the standard imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## HOG Features\n", + "\n", + "HOG is a straightforward feature extraction procedure that was developed in the context of identifying pedestrians within images.\n", + "It involves the following steps:\n", + "\n", + "1. Optionally prenormalize the images. This leads to features that resist dependence on variations in illumination.\n", + "2. Convolve the image with two filters that are sensitive to horizontal and vertical brightness gradients. These capture edge, contour, and texture information.\n", + "3. Subdivide the image into cells of a predetermined size, and compute a histogram of the gradient orientations within each cell.\n", + "4. Normalize the histograms in each cell by comparing to the block of neighboring cells. This further suppresses the effect of illumination across the image.\n", + "5. Construct a one-dimensional feature vector from the information in each cell.\n", + "\n", + "A fast HOG extractor is built into the Scikit-Image project, and we can try it out relatively quickly and visualize the oriented gradients within each cell (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from skimage import data, color, feature\n", + "import skimage.data\n", + "\n", + "image = color.rgb2gray(data.chelsea())\n", + "hog_vec, hog_vis = feature.hog(image, visualize=True)\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=(12, 6),\n", + " subplot_kw=dict(xticks=[], yticks=[]))\n", + "ax[0].imshow(image, cmap='gray')\n", + "ax[0].set_title('input image')\n", + "\n", + "ax[1].imshow(hog_vis)\n", + "ax[1].set_title('visualization of HOG features');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## HOG in Action: A Simple Face Detector\n", + "\n", + "Using these HOG features, we can build up a simple facial detection algorithm with any Scikit-Learn estimator; here we will use a linear support vector machine (refer back to [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) if you need a refresher on this).\n", + "The steps are as follows:\n", + "\n", + "1. Obtain a set of image thumbnails of faces to constitute \"positive\" training samples.\n", + "2. Obtain a set of image thumbnails of non-faces to constitute \"negative\" training samples.\n", + "3. Extract HOG features from these training samples.\n", + "4. Train a linear SVM classifier on these samples.\n", + "5. For an \"unknown\" image, pass a sliding window across the image, using the model to evaluate whether that window contains a face or not.\n", + "6. If detections overlap, combine them into a single window.\n", + "\n", + "Let's go through these steps and try it out." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1. Obtain a Set of Positive Training Samples\n", + "\n", + "We'll start by finding some positive training samples that show a variety of faces.\n", + "We have one easy set of data to work with—the Labeled Faces in the Wild dataset, which can be downloaded by Scikit-Learn:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(13233, 62, 47)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import fetch_lfw_people\n", + "faces = fetch_lfw_people()\n", + "positive_patches = faces.images\n", + "positive_patches.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us a sample of 13,000 face images to use for training." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2. Obtain a Set of Negative Training Samples\n", + "\n", + "Next we need a set of similarly sized thumbnails that *do not* have a face in them.\n", + "One way to obtain this is to take any corpus of input images, and extract thumbnails from them at a variety of scales.\n", + "Here we'll use some of the images shipped with Scikit-Image, along with Scikit-Learn's `PatchExtractor`:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(512, 512)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.camera().shape" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from skimage import data, transform\n", + "\n", + "imgs_to_use = ['camera', 'text', 'coins', 'moon',\n", + " 'page', 'clock', 'immunohistochemistry',\n", + " 'chelsea', 'coffee', 'hubble_deep_field']\n", + "raw_images = (getattr(data, name)() for name in imgs_to_use)\n", + "images = [color.rgb2gray(image) if image.ndim == 3 else image\n", + " for image in raw_images]" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(30000, 62, 47)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.feature_extraction.image import PatchExtractor\n", + "\n", + "def extract_patches(img, N, scale=1.0, patch_size=positive_patches[0].shape):\n", + " extracted_patch_size = tuple((scale * np.array(patch_size)).astype(int))\n", + " extractor = PatchExtractor(patch_size=extracted_patch_size,\n", + " max_patches=N, random_state=0)\n", + " patches = extractor.transform(img[np.newaxis])\n", + " if scale != 1:\n", + " patches = np.array([transform.resize(patch, patch_size)\n", + " for patch in patches])\n", + " return patches\n", + "\n", + "negative_patches = np.vstack([extract_patches(im, 1000, scale)\n", + " for im in images for scale in [0.5, 1.0, 2.0]])\n", + "negative_patches.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have 30,000 suitable image patches that do not contain faces.\n", + "Let's visualize a few of them to get an idea of what they look like (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(6, 10)\n", + "for i, axi in enumerate(ax.flat):\n", + " axi.imshow(negative_patches[500 * i], cmap='gray')\n", + " axi.axis('off')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our hope is that these will sufficiently cover the space of \"non-faces\" that our algorithm is likely to see." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3. Combine Sets and Extract HOG Features\n", + "\n", + "Now that we have these positive samples and negative samples, we can combine them and compute HOG features.\n", + "This step takes a little while, because it involves a nontrivial computation for each image:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from itertools import chain\n", + "X_train = np.array([feature.hog(im)\n", + " for im in chain(positive_patches,\n", + " negative_patches)])\n", + "y_train = np.zeros(X_train.shape[0])\n", + "y_train[:positive_patches.shape[0]] = 1" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(43233, 1215)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X_train.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are left with 43,000 training samples in 1,215 dimensions, and we now have our data in a form that we can feed into Scikit-Learn!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4. Train a Support Vector Machine\n", + "\n", + "Next we use the tools we have been exploring here to create a classifier of thumbnail patches.\n", + "For such a high-dimensional binary classification task, a linear support vector machine is a good choice.\n", + "We will use Scikit-Learn's `LinearSVC`, because in comparison to `SVC` it often has better scaling for a large number of samples.\n", + "\n", + "First, though, let's use a simple Gaussian naive Bayes estimator to get a quick baseline:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.94795883, 0.97143518, 0.97224471, 0.97501735, 0.97374508])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.naive_bayes import GaussianNB\n", + "from sklearn.model_selection import cross_val_score\n", + "\n", + "cross_val_score(GaussianNB(), X_train, y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that on our training data, even a simple naive Bayes algorithm gets us upwards of 95% accuracy.\n", + "Let's try the support vector machine, with a grid search over a few choices of the `C` parameter:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9885272620319941" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.svm import LinearSVC\n", + "from sklearn.model_selection import GridSearchCV\n", + "grid = GridSearchCV(LinearSVC(), {'C': [1.0, 2.0, 4.0, 8.0]})\n", + "grid.fit(X_train, y_train)\n", + "grid.best_score_" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'C': 1.0}" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grid.best_params_" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This pushes us up to near 99% accuracy. Let's take the best estimator and retrain it on the full dataset:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "LinearSVC()" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model = grid.best_estimator_\n", + "model.fit(X_train, y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 5. Find Faces in a New Image\n", + "\n", + "Now that we have this model in place, let's grab a new image and see how the model does.\n", + "We will use one portion of the astronaut image shown in the following figure for simplicity (see discussion of this in the following section, and run a sliding window over it and evaluate each patch:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "test_image = skimage.data.astronaut()\n", + "test_image = skimage.color.rgb2gray(test_image)\n", + "test_image = skimage.transform.rescale(test_image, 0.5)\n", + "test_image = test_image[:160, 40:180]\n", + "\n", + "plt.imshow(test_image, cmap='gray')\n", + "plt.axis('off');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, let's create a window that iterates over patches of this image, and compute HOG features for each patch:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1911, 1215)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def sliding_window(img, patch_size=positive_patches[0].shape,\n", + " istep=2, jstep=2, scale=1.0):\n", + " Ni, Nj = (int(scale * s) for s in patch_size)\n", + " for i in range(0, img.shape[0] - Ni, istep):\n", + " for j in range(0, img.shape[1] - Ni, jstep):\n", + " patch = img[i:i + Ni, j:j + Nj]\n", + " if scale != 1:\n", + " patch = transform.resize(patch, patch_size)\n", + " yield (i, j), patch\n", + " \n", + "indices, patches = zip(*sliding_window(test_image))\n", + "patches_hog = np.array([feature.hog(patch) for patch in patches])\n", + "patches_hog.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can take these HOG-featured patches and use our model to evaluate whether each patch contains a face:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "48.0" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "labels = model.predict(patches_hog)\n", + "labels.sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that out of nearly 2,000 patches, we have found 48 detections.\n", + "Let's use the information we have about these patches to show where they lie on our test image, drawing them as rectangles (see the following figure):" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.imshow(test_image, cmap='gray')\n", + "ax.axis('off')\n", + "\n", + "Ni, Nj = positive_patches[0].shape\n", + "indices = np.array(indices)\n", + "\n", + "for i, j in indices[labels == 1]:\n", + " ax.add_patch(plt.Rectangle((j, i), Nj, Ni, edgecolor='red',\n", + " alpha=0.3, lw=2, facecolor='none'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of the detected patches overlap and found the face in the image!\n", + "Not bad for a few lines of Python." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Caveats and Improvements\n", + "\n", + "If you dig a bit deeper into the preceding code and examples, you'll see that we still have a bit of work to do before we can claim a production-ready face detector.\n", + "There are several issues with what we've done, and several improvements that could be made. In particular:\n", + "\n", + "**Our training set, especially for negative features, is not very complete**\n", + "\n", + "The central issue is that there are many face-like textures that are not in the training set, and so our current model is very prone to false positives.\n", + "You can see this if you try out the algorithm on the *full* astronaut image: the current model leads to many false detections in other regions of the image.\n", + "\n", + "We might imagine addressing this by adding a wider variety of images to the negative training set, and this would probably yield some improvement.\n", + "Another option would be to use a more directed approach, such as *hard negative mining*, where we take a new set of images that our classifier has not seen, find all the patches representing false positives, and explicitly add them as negative instances in the training set before retraining the classifier.\n", + "\n", + "**Our current pipeline searches only at one scale**\n", + "\n", + "As currently written, our algorithm will miss faces that are not approximately 62 × 47 pixels.\n", + "This can be straightforwardly addressed by using sliding windows of a variety of sizes, and resizing each patch using `skimage.transform.resize` before feeding it into the model.\n", + "In fact, the `sliding_window` utility used here is already built with this in mind.\n", + "\n", + "**We should combine overlapped detection patches**\n", + "\n", + "For a production-ready pipeline, we would prefer not to have 30 detections of the same face, but to somehow reduce overlapping groups of detections down to a single detection.\n", + "This could be done via an unsupervised clustering approach (mean shift clustering is one good candidate for this), or via a procedural approach such as *non-maximum suppression*, an algorithm common in machine vision.\n", + "\n", + "**The pipeline should be streamlined**\n", + "\n", + "Once we address the preceding issues, it would also be nice to create a more streamlined pipeline for ingesting training images and predicting sliding-window outputs.\n", + "This is where Python as a data science tool really shines: with a bit of work, we could take our prototype code and package it with a well-designed object-oriented API that gives the user the ability to use it easily.\n", + "I will leave this as a proverbial \"exercise for the reader.\"\n", + "\n", + "**More recent advances: deep learning**\n", + "\n", + "Finally, I should add that in machine learning contexts, HOG and other procedural feature extraction methods are not always used.\n", + "Instead, many modern object detection pipelines use variants of deep neural networks (often referred to as *deep learning*): one way to think of neural networks is as estimators that determine optimal feature extraction strategies from the data, rather than relying on the intuition of the user.\n", + "\n", + "Though the field has produced fantastic results in recent years, deep learning is not all that conceptually different from the machine learning models explored in the previous chapters.\n", + "The main advance is the ability to utilize modern computing hardware (often large clusters of powerful machines) to train much more flexible models on much larger corpuses of training data.\n", + "But though the scale differs, the end goal is very much the same the same: building models from data.\n", + "\n", + "If you're interested in going further, the list of references in the following section should provide a useful place to start!" + ] + } + ], + "metadata": { + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/05.15-Learning-More.ipynb b/notebooks/05.15-Learning-More.ipynb new file mode 100644 index 000000000..7eac4c547 --- /dev/null +++ b/notebooks/05.15-Learning-More.ipynb @@ -0,0 +1,57 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Further Machine Learning Resources" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This part of the book has been a quick tour of machine learning in Python, primarily using the tools within the Scikit-Learn library.\n", + "As long as these chapters are, they are still too short to cover many interesting and important algorithms, approaches, and discussions.\n", + "Here I want to suggest some resources to learn more about machine learning in Python, for those who are interested:\n", + "\n", + "- [The Scikit-Learn website](http://scikit-learn.org): The Scikit-Learn website has an impressive breadth of documentation and examples covering some of the models discussed here, and much, much more. If you want a brief survey of the most important and often-used machine learning algorithms, this is a good place to start.\n", + "\n", + "- *SciPy, PyCon, and PyData tutorial videos*: Scikit-Learn and other machine learning topics are perennial favorites in the tutorial tracks of many Python-focused conference series, in particular the PyCon, SciPy, and PyData conferences. Most of these conferences publish videos of their keynotes, talks, and tutorials for free online, and you should be able to find these easily via a suitable web search (for example, \"PyCon 2022 videos\").\n", + "\n", + "- [*Introduction to Machine Learning with Python*](http://shop.oreilly.com/product/0636920030515.do), by Andreas C. Müller and Sarah Guido (O'Reilly). This book covers many of the machine learning fundamentals discussed in these chapters, but is particularly relevant for its coverage of more advanced features of Scikit-Learn, including additional estimators, model validation approaches, and pipelining.\n", + "\n", + "- [*Machine Learning with PyTorch and Scikit-Learn*](https://www.packtpub.com/product/machine-learning-with-pytorch-and-scikit-learn/9781801819312), by Sebastian Raschka (Packt). Sebastian Raschka's most recent book starts with some of the fundamental topics covered in these chapters, but goes deeper and shows how those concepts apply to more sophisticated and computationally intensive deep learning and reinforcement learning models using the well-known [PyTorch library](https://pytorch.org/)." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/06.00-Figure-Code.ipynb b/notebooks/06.00-Figure-Code.ipynb new file mode 100644 index 000000000..31ad5c89f --- /dev/null +++ b/notebooks/06.00-Figure-Code.ipynb @@ -0,0 +1,2905 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Appendix: Figure Code" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Many of the figures used throughout this text are created in-place by code that appears in print.\n", + "In a few cases, however, the required code is long enough (or not immediately relevant enough) that we instead put it here for reference." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import seaborn as sns" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "import os\n", + "if not os.path.exists('figures'):\n", + " os.makedirs('figures')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Broadcasting\n", + "\n", + "[Figure Context](02.05-Computation-on-arrays-broadcasting.ipynb#Introducing-Broadcasting)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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jC7ZeyN2HNTU1ACBLIZIzi6gv3lqjWPg0ikXPfSx6RNLx5hrFwqdBLHruY9Ejko631ygWPo3x9oTSAhY9IukoYY1i4dMYb08oLWDRI5KOEtYoFj6NuP0aGBa9oZG7D8+dOwdAnkIkZxZRX5S0Rinqk1vIfZ5+u70SyD039uzZgxEjRkiaYbfbUV5ejnnz5kma05N1/PhxxX3+q9pwjfIMJaxRiil85D5enO4+9iGRdJRyfrHwERGRrvBvfEREpCssfEREpCssfEREpCssfEREpCssfEREpCssfEREpCssfEREpCssfEREpCssfEREpCssfEREpCssfDK5cuUKJk+ejPb29kFtk1J+fj7Ky8uHvJ0GZ6jjzHEg8iwWPpls2LABy5Ytg7+/v0vbli5divHjxyMwMBAzZszA4cOHB5050DEKCgrw3HPP9bv/QNtpcPqbA+6OExENkiDJWa1WERYWJurr613eVl1dLW7evCmEEOKTTz4RYWFhoqura1C5rhwjNjZWVFVV9XuMgbaTa5zNAU+MExG5TnHP+KKjo7F27VrExsYiJCQEmzdv7rVtzZo1uOuuuzBx4kQUFxcP6tinTp3Cfffdh8DAQKSlpeGLL75wKffatWtYunQpxo0bh0mTJmHr1q2ObadPn0ZmZiYCAgIQHh6O3/72t3fkfvnllwgICEBkZKTL26ZNmwZ/f38IIWCz2dDU1IQrV64M6vG6coysrCynL6MNtD06Ohp1dXX9bpNqLDds2ICYmBiMGjUKsbGxKC0tvSN706ZNSEtLw+jRozF//nyX9+uvzTU1NbjnnnsQGBiIX//61zAYDDhz5gwA53MEcD4HPDFORDQIXi68d4iKihKzZ88WbW1t4oMPPhBGo1HYbDbHth//+MeiublZVFVViVGjRol//vOfLh23u7tbJCcni//5n/8RNptN/OEPfxDjx493/KbtLDc3N1csW7ZM3Lx5U5w5c0bcdddd4siRI0IIIRYtWiSeeuopYbfbxbVr18SBAwfuyC4qKhK5ubl9tsvZtp///OfC19dXABALFixw6XEO9hgbN24UDz74YL/7D7Q9KipKnD9/vt9tUoylEEJs2bJFnDp1SnR3d4u//vWvwtfXV1y+fLlX9tSpU8XJkyeFzWYThw8fdnm//tqclJQk1q9fLzo7O8UzzzwjAIjTp08LIZzPESGcj7MQ7o8TEblOkYXv/fffF0II0dnZKQA4Xh6KiooSv//97x33nTVrltiyZYtLxz137pwYMWKE6OjocNw2YcIEYTabneZeuHBBGAwGce3aNcd+v/jFL8Szzz4rhBDikUceEXl5eaKhoaHf7BdeeEE8/PDDg97W05bt27eLnTt3uvQ4B3uMLVu2iOzs7H737Wv7Sy+9JAIDA0VgYKAwGAzCaDSKwMBA8dOf/rTX/aQay76YTCaxf//+XtmvvfbakPbrq81nz57tNX/q6+sdhW+gOSLEwOPckzfUcSIi1ynupU4ACAkJAQDH19N3dHQ4tplMpl7/f+nSJZeOeenSJQQFBcHPz89x2/jx4/H99987za2vrwcATJo0CUFBQQgKCsK2bdscuRs2bEBAQADuvfdexMbGYufOnXdkBwcHo7W1tc92OdvW05bFixfjN7/5Db799luXHutgjtHS0oKgoKB+9+1re0FBASwWCywWCyZOnIgTJ07AYrGgrKzsjv2lGEsAKC4uxrRp0xASEoKgoCA0NTXBZrP1uk9cXNyQ9uurzZcuXUJwcLBj/tze9oHmCDDwOPfkDXWciMh1iix8zty+mFy+fLnXAuSMyWSCxWJBZ2en47bvv/8e48aNc7rfhAkTMHLkSFy9etWx2N+4cQNvv/02ACAiIgLvvPMOLly4gF/96ld48skn7zhGcnIyvvvuuz6P72zb7ex2O2prawe832CP8e233yI5ObnffQba7o6hjuU//vEPrFy5Em+++aZjXIKCgiCE6HW/4cOHD2m/vowbNw7Xr1+H1Wq9o+0DzRHA9XEGhjZOROQ61RW+rVu3oqWlBUeOHMHhw4cxe/Zsx7bGxkbExsbigw8+uGO/SZMmIT4+Hhs3bkRXVxdKSkrQ2dmJGTNmOM0LDw/HT37yExQUFKCtrQ02mw2HDh3C8ePHAQB//vOfceHCBRgMBhgMBhiNxjuOkZ6ejubmZjQ0NLi07fvvv8e2bdvQ3NyMrq4uvPXWW6irq0NaWlqvfQ0GA9atW9dnu109RmVlJXJzc/t9/ANtd8dQx7KtrQ0GgwEmkwl2ux0vv/wyLBbLgHlD3Q8AYmJiEB8fj8LCQthsNrz++uuObQPNEaD/OeCpcSIi16mu8GVmZmLy5MnIy8tDUVERoqKiHNtsNhvOnj2LlpaWO/YzGAx477338NFHH2Hs2LF4+eWX8ac//QmjRo0aMLOkpASXL19GbGwswsLCsGbNGnR1dQEAvvrqK6SlpWHMmDHYtGkT3n333Tv29/X1xRNPPIGSkhKXtvn4+OCPf/wj7r77bgQHB+PNN9/Ezp07MWnSJMd9bt68CQAICwvrs82uHKOqqgpGoxHp6el9HmOg7QBQV1eH6Ojofrc7M9SxnDJlCp555hmkp6cjPDwcra2tmDhx4oB5Q92vx/bt27Fjxw6EhoZi9OjRAIBhw26dQs7mCND/HPDEOBHRIHn7j4yDERUVJfbu3evtZgxJU1OTiI+Pd7yL1NVt/dm/f78wGo3CYrEMuU15eXnio48+GvJ2d6h5LIW4NWYARFtb26D2Gew4CyHtOBDp0fABKyN5RGhoKE6dOjXobf05fPgwfvaznyEwMHDIbdq1a5db2/Xms88+Q3h4OGJiYlBUVISMjAyXXjHoMZRxBjgORJ7GwqdSa9as8XYTdKeurg6PPPIIWlpakJKSgnfeecfbTSKiITAI4cJb2oiIiDRCdW9uISIicgcLHxER6QoLHxER6QoLHxER6YpqCp+c78FhlrpotQ+1mqVVWh0vLWapovBVVlbioYcekqVTmKUuWu1DrWZplVbHS6tZir+cobKyEgsWLBj0l7BS3xQ+3IPCueFZWpobcuI89Cw55qGin/H1TKidO3dC3PruQMn+mc1mhIaGwmw2azZLSzg3ODeUgPNQpfNQKJTZbBahoaGOL4pllvtZCh7uQdHLeMmZpZW5ISe9zA05s+Sah4qc7XoZZLmztLC4ebsPtZqlhbkhJ2+Pl1azdFv4vN3xWs5S++KmhD7Uapba54aclDBeWs3SZeFTQsdrOUvNi5tS+lCrWWqeG3JSynhpNUt3hU8pHa/lLLUubkrqQ61mqXVuyElJ46XVLF0Vvi+//FK2jtdzlhoXN6X1oVaz1Dg35KS08dJqllzzUBHX8bW2tiIgIMDbzdAEZ8NpMBicblcizg3P0drckBPnoecoYR4qovAB8p54es1S6+KmpD7UapZa54aclDReWs2Sqy2KvoCdiIjI01j4iIhIV1j4iIhIV1j4iIhIV1j4iIhIV1j4iIhIV1j4iIhIV1Rb+JYvXw6TyYSpU6cyi3qpqKhAfHw8YmNjsX79ekmz5Bqv+vp6ZGdnY8qUKUhMTMSrr74qaR65T4tzo6OjA+np6Zg2bRoSExOxdu1aybIkJcvnw7hgsE3Zv3+/OHr0qEhMTGSWi1kKGu5BGUy7u7q6RExMjDh79qzo7OwUycnJora2VpIsIeSbGxcuXBBHjx4VQgjR0tIi4uLiPPq41Do35KTXuXG77u5u0draKoQQwmq1ivT0dHH48GGPZck1D1X7jG/mzJkICQlhFvVSVVWF2NhYxMTEwNfXF4sWLcLu3bsly5NrvMLDw5GamgoAMBqNSEhIQGNjo+S5NHRanBsGgwFjxowBANhsNthsNhgMBkmypKTawkfUl8bGRkyYMMHxc2RkpOYKRF1dHY4dO4YZM2Z4uymkMHLMDbvdjpSUFJhMJuTk5KhyHrLwEanIjRs3kJ+fj8LCQn5oMvUi19zw8fFBdXU1GhoaUFVVhZMnT0qWJRUWPtKUiIgI1NfXO35uaGhARESEF1vkOTabDfn5+ViyZAny8vK83RxSEG/MjaCgIGRnZ6OiokKWPE9i4SNNmT59Ok6fPo3z58/DarXivffew/z5873dLLcJIbBixQokJCRg9erV3m4OKYicc6OpqQkWiwUA0N7ejr1792Ly5MmSZkpClrfQuGCwTVm0aJEYP368GD58uIiIiBBvv/02sxTyjilPG2y7P/roIxEXFydiYmLECy+8IGmWXHPjwIEDAoBISkoS06ZNE9OmTRMfffSRx7LUOjfkpNe5cbvjx4+LlJQUkZSUJBITE8Xzzz/v8r6uZMk1D/l9fDrKUut3rimpD7Wapda5IScljZdWs/h9fORRlZWVAJx/+7EadXR04OzZs8xyw549ewBob26Qusi5Rg2XPIG8rrKyEgsWLAAAVV5z05+Ojg58+umnuHbtWq83tLir5wS8ndVqxdGjR2G325GZmamZrCNHjmDdunUAtDU3SF1kX6NkeUHVBXI2RU9ZZrNZhIaGCrPZrNq/4/TV7vb2dlFWViba29uF2Wxm1hCyPvnkExEQECA++eQTj2ZplbfPZa1meWON4kudGtbzW9TOnTuRlZXl7eZ4TM8zvVmzZmHkyJHMGoI9e/Y45sb9998vaRZRf7y1RrHwaRSLHrP6w6JHSuDNNYqFT4NY9JjVHxY9UgJvr1EsfBrj7QklFa0WIhY90hslrFEsfBrj7QklFbmKg5azWPRICZSwRrHwaURVVRUAeH1CeZrdbgcAWYqDVrMOHz4MACx65FVKWqMU9ckt5D5nw6nWT+fg3PAMZ2NfWVnp9cVI6TgPPUMJa5SinvEJIWT5p+UsLTKbzU4f90DbB/NPy1nkPq2uG3JmKYGiCh8REZHUWPiIiEhXWPiIiEhXWPiIiEhXWPiIiEhXWPiIiEhXWPiIiEhXVFv4li9fDpPJhKlTpzJLZuvWrXN8eakSnTlzBps2bcJrr72Gzz//XNKs3bt343e/+x3eeOMNSXOam5vx7rvvoqioCG+88Qa++OILSfPIfXKdy/X19cjOzsaUKVOQmJiIV199VbKsjo4OpKenY9q0aUhMTMTatWsly5KSagvfsmXLUFFRwSzqpbu7G+Xl5ViyZAlWrVqFkydPoqmpSbK8lJQULF26VLLj9xg2bBjuv/9+rFq1CitWrMCRI0ckfVzkPrnO5eHDh2Pjxo345ptv8MUXX6CoqAjffPONJFl+fn7Yt28fjh8/jurqalRUVKjylzDVFr6ZM2ciJCSEWdRLY2MjQkJCEBwcDB8fHyQmJuLUqVOS5UVFRcHf31+y4/cwGo0IDw8HcGvxCQsLQ0tLi+S5Upo7dy6CgoL6/Dd37lxvN89tcp3L4eHhSE1NBXBrniQkJKCxsVGSLIPBgDFjxgAAbDYbbDabKj/Kbbi3G0DkSa2trQgICHD8HBAQINki4C0WiwUXL15EZGSkt5vilrKyMm83QXPq6upw7NgxzJgxQ7IMu92OtLQ0nDlzBqtWrZI0SyosfOSSuXPnOv5e1tHRAQAoLCwEAGRmZnIRk4nVakVpaSnmzJkDPz8/bzeHFOTGjRvIz89HYWFhr1/+PM3HxwfV1dWwWCx48MEHcfLkSUW/J6EvLHzkktsLW88bW5T4Bhej0djrJcCWlhYYjUYvtshz7HY7SktLkZSUhISEBG83x20PPPAADhw40Oe2++67Dx9//LHMLVIvm82G/Px8LFmyBHl5ebJkBgUFITs7GxUVFSx8RN4UERGBq1ev4vr16wgICEBtba1sC4GUhBD48MMPERoaioyMDG83xyNY2DxDCIEVK1YgISEBq1evljSrqakJI0aMQFBQENrb27F3716sWbNG0kwpqPbNLYsXL0ZGRga+++47REZGYtu2bcwiDBs2DLm5uSgpKUFRURGmTJkCk8kkWd6uXbuwbds2XL16Fa+88gq+/vprSXLq6+tx4sQJnD9/Hps3b8bmzZtx+vRpSbLIM+Q6lw8ePIji4mLs27cPKSkpSElJQXl5uSRZFy9eRHZ2NpKTkzF9+nTk5OSo8o1Iqn3Gt2PHDmZ5iRJf4rxdXFwc4uLiZMnKz8+XJWfixImqvWZKr+Q6lzMzM2X7rrvk5GQcO3ZMliwpqfYZHw1OZWUlAOfffqxGHR0dsr1rk1lE0pFzjVLtMz5yXWVlJRYsWAAAqrzmpj8dHR349NNPcf78ecdJ467q6uo+b7darTh69CgaGhoQERGhuSy73e6RHKKhkH2NEgohZ1P0lGU2m0VoaKgwm82ytsWTzGbzHbe1t7eLsrIy0d7e3ud2ZnkvS6u8fS5rNcsbaxRf6tSwnt+idu7ciaysLG83x2N6nunNmjULI0eOZJbCs4j64601ioVPo1j0mKWELKL+eHONYuHTIBY9Zikhi6g/3l6jWPg0xtsTSipaLQ5azSLqjxLWKBY+jfH2hJKC1WqVbcFmFpG0lLBGsfBpRFVVFQB4fUJ5mt1ux9GjR2VZsJlFJB0lrVGKuo5PzmvMtJrl7QnlaT4+PgDg9Msu+7tGbSguXLigySwALHoeoNV1Q29rlKIKn5DpU0UMBoNms7QoIyNjwJPFkyeTVrPIfVpdN/S2RvGlTiIi0hUWPiIi0hUWPiIi0hUWPiIi0hUWPiIi0hUWPiIi0hUWPiIi0hXVFr7ly5fDZDJh6tSpzKJezpw5g02bNuG1117D559/LmnW7t278bvf/Q5vvPGGpDnNzc149913UVRUhDfeeMPphe+kDHKdy/X19cjOzsaUKVOQmJiIV199VbKsjo4OpKenY9q0aUhMTMTatWsly5KSagvfsmXLUFFRwSzqpbu7G+Xl5ViyZAlWrVqFkydPoqmpSbK8lJQULF26VLLj9xg2bBjuv/9+rFq1CitWrMCRI0ckfVzkPrnO5eHDh2Pjxo345ptv8MUXX6CoqAjffPONJFl+fn7Yt28fjh8/jurqalRUVKjylzDVFr6ZM2ciJCSEWdRLY2MjQkJCEBwcDB8fHyQmJuLUqVOS5UVFRcHf31+y4/cwGo0IDw8HcGvxCQsLQ0tLi+S5NHRyncvh4eFITU0FcGueJCQkoLGxUZIsg8GAMWPGAABsNhtsNptiPo1lMFRb+Ij60traioCAAMfPAQEBaG1t9WKLPM9iseDixYuIjIz0dlNIYerq6nDs2DHMmDFDsgy73Y6UlBSYTCbk5ORImiUVFj4iFbFarSgtLcWcOXPg5+fn7eaQgty4cQP5+fkoLCzs9cufp/n4+KC6uhoNDQ2oqqrCyZMnJcuSCgsfaYrRaOz1EmBLSwuMRqMXW+Q5drsdpaWlSEpKQkJCgrebQwpis9mQn5+PJUuWIC8vT5bMoKAgZGdnq/I9CSx8pCkRERG4evUqrl+/DrvdjtraWsTHx3u7WW4TQuDDDz9EaGgoMjIyvN0cUhAhBFasWIGEhASsXr1a0qympiZYLBYAQHt7O/bu3YvJkydLmikF1Ra+xYsXIyMjA9999x0iIyOxbds2ZhGGDRuG3NxclJSUoKioCFOmTIHJZJIsb9euXdi2bRuuXr2KV155BV9//bUkOfX19Thx4gTOnz+PzZs3Y/PmzTh9+rQkWeQZcp3LBw8eRHFxMfbt24eUlBSkpKSgvLxckqyLFy8iOzsbycnJmD59OnJycjB37lxJsqSkqO/jG4wdO3Ywi/oUFxeHuLg4WbLy8/NlyZk4caJqr5nSK7nO5czMTNm+Ty85ORnHjh2TJUtKqn3GR4NTWVkJQL4v0pRLR0eHZG/dZhaRfORco1T7jI9cV1lZiQULFgBQzjcge0JHRwc+/fRTdHd3O04ad1VXV/d5u9VqxdGjR2G32zWZxUsjyJtkX6OEQsjZFD1lmc1mERoaKsxms2zt8LS+2t7e3i7KyspEe3s7sxSWpVXePpe1muWNNYovdWpYz29RO3fuRFZWlreb4zE9z/RmzZqFkSNHMkvhWUT98dYaxcKnUSx6zFJCFlF/vLlGsfBpEIses5SQRdQfb69RLHwa4+0JJRWtFgetZhH1RwlrlOH//uDodQaDQba32ms5KzQ0VHNFb8+ePbDZbLIs2Myi/mh53dDbGsVnfBpRVVUFAF6fUJ5mt9tx9OhRWRZsZhFJR0lrlKKu45PzGjOtZnl7Qnmaj48PoqOjZf2ySy1mRUdHs+h5gFbXDb2tUYp5qZOIiEgOfKmTiIh0hYWPiIh0hYWPiIh0hYWPiIh0hYWPiIh0hYWPiIh0hYWPiIh0hYWPiIh0hYWPiIh0hYWPiIh0hYVP4a5cuYLJkyejvb3d5X3y8/NRXl4uYasGLzo6Gn/729+8ku2sD4fSv57ibJyUOIZqp5VzidzHwqdwGzZswLJly+Dv7++4benSpRg/fjwCAwMxY8YMHD58uNc+BQUFeO655+RuqmL11YfOtg3Uv67YvXs3MjIy4Ofnh2XLlvV5H2fjxDH0PJ5L5CBIsaxWqwgLCxP19fW9bq+urhY3b94UQgjxySefiLCwMNHV1dXrPrGxsaKqqkq2tg4kKipK7N27V/bc/vrQ2TZX+ncgZrNZ7Nq1S/z85z8Xjz/+eL/3czZOShtDNdPSuUTuU9wzvujoaKxduxaxsbEICQnB5s2be21bs2YN7rrrLkycOBHFxcWDOvaGDRsQExODUaNGITY2FqWlpXdkb9q0CWlpaRg9ejTmz58/4H7O2gsANTU1uOeeexAYGIhf//rXMBgMOHPmDADg2rVrWLp0KcaNG4dJkyZh69atvfb98ssvERAQgMjIyF63T5s2Df7+/hBCwGazoampCVeuXOl1n6ysrCG/RNNfPwzU5tOnTyMzMxMBAQEIDw/Hb3/7217HPXDgQJ/9NFD/Ohvzofahs22u9O9AsrKykJeXh5CQkAHv1984uTKG0dHRqKur6/N2b51HPRmePJfcOY8A751LpFBeLrx3iIqKErNnzxZtbW3igw8+EEajUdhsNse2H//4x6K5uVlUVVWJUaNGiX/+858uH3vLli3i1KlToru7W/z1r38Vvr6+4vLly72yp06dKk6ePClsNps4fPjwgPs5a68QQiQlJYn169eLzs5O8cwzzwgA4vTp00IIIXJzc8WyZcvEzZs3xZkzZ8Rdd90ljhw54ti3qKhI5Obm9vlYfv7znwtfX18BQCxYsOCO7Rs3bhQPPvigy31zu/76YaA2L1q0SDz11FPCbreLa9euiQMHDvQ6Zn/9NFD/Ohtzd/rQnf511XPPPef0GZ+zcXJlDKOiosT58+f7vN1b51FPhifPJXfOIyG8dy6RMimy8L3//vtCCCE6OzsFAMfLE1FRUeL3v/+9476zZs0SW7ZsGXKWyWQS+/fv75X92muvDWo/Z+09e/asGDFihOjo6BBCCFFfX+84YS9cuCAMBoO4du2a47i/+MUvxLPPPuv4+YUXXhAPP/xwv+3o7OwU27dvFzt37rxj25YtW0R2dvaAj6Uv/fXDQG1+5JFHRF5enmhoaOjzmP310w/9sH/7G3N3+9Cd/nXVQIXP2Tj1t+2ll14SgYGBIjAwUBgMBmE0GkVgYKD46U9/6riPN8+jngxPnUvunkdCeO9cImVS3EudABwvD/n6+gIAOjo6HNtMJlOv/7906ZLLxy0uLsa0adMQEhKCoKAgNDU1wWaz9bpPXFzcoPfrr72XLl1CcHAw/Pz87mh7fX09AGDSpEkICgpCUFAQtm3b1uvxBAcHo7W1td/H4+vri8WLF+M3v/kNvv32217bWlpaEBQUNGCf9KevfhiozRs2bEBAQADuvfdexMbGYufOnb3276+fBurf/sbc3T50p389xdk49betoKAAFosFFosFEydOxIkTJ2CxWFBWVtbrft48jwDPnUvunkeAd88lUp7h3m7AYN0+oS9fvuzy19j/4x//wMqVK2E2m5GRkQGDwYCQkBCIH3wB/fDhw4e0X1/GjRuH69evw2q1wtfXt1fbJ0yYgJEjR+Lq1avw8fHpc//k5GS88sorA+bY7XbU1tYiISHBcdu3336L5OTkAfftzw/7wZU2R0RE4J133oEQAlu3bsWTTz6JBQsWOM1xpX/7G3N3+9Cd/vUUZ+Pk7hg6I/V5BHjuXHL3PAK8ey6R8ijyGZ8zW7duRUtLC44cOYLDhw9j9uzZjm2NjY2IjY3FBx98cMd+bW1tMBgMMJlMsNvtePnll2GxWAbMG+p+ABATE4P4+HgUFhbCZrPh9ddfd2wLDw/HT37yExQUFKCtrQ02mw2HDh3C8ePHHfdJT09Hc3MzGhoaHLd9//332LZtG5qbm9HV1YW33noLdXV1SEtL65VdWVmJ3NzcPtvlrJ+cGajNf/7zn3HhwgUYDAYYDAYYjcYBj+lK//Y35kPtQ2fbXO1fADAYDFi3bl2fj8tut6OjowN2u93x/11dXXfcz9k4OdvmLmfnEdD/HHHnfBjqvu6eR4B05xKpk+oKX2ZmJiZPnoy8vDwUFRUhKirKsc1ms+Hs2bNoaWm5Y78pU6bgmWeeQXp6OsLDw9Ha2oqJEycOmDfU/Xps374dO3bsQGhoKEaPHg0AGDbsVreXlJTg8uXLiI2NRVhYGNasWdNrcfT19cUTTzyBkpISx20+Pj744x//iLvvvhvBwcF48803sXPnTkyaNMlxn6qqKhiNRqSnp/fZJmf9NBBnbf7qq6+QlpaGMWPGYNOmTXj33XcHPJ4r/etszIfSh862udK/AHDz5k0AQFhYWJ+Pq7i4GP7+/li/fj1KSkrg7++PF154odd9nI3TQGPYo66uDtHR0U7v0xdnfQr0P0fcOR/c2ded8wiQ7lwilfLmHxgHy1vXgnlKU1OTACDa2toGtU98fLzjWiNX5OXliY8++mgoTVQcT4y5sz4cSv8KIcT+/fuF0WgUFotlyO1yNk5SjqEez6Oe/fR8LtH/p7q/8anNZ599hvDwcMTExKCoqAgZGRkYNWqUy/uHhobi1KlTg8rctWvXYJupac76cCj9CwCHDx/Gz372MwQGBg65Xc7GiWPYm7vnEcBzif4/Fj6J1dXV4ZFHHkFLSwtSUlLwzjvveLtJ5AFr1qzxdhN0hecReZJBCBfenkhERKQRqntzCxERkTtY+IiISFdY+IiISFdY+IiISFdY+IiISFdUUfisVisOHDiguSzg1kdbaTFLLlqdG1rN0iqtjpdWsxR/HZ/VasXChQuxe/duWXP37dsHg8Egaca5c+dQW1uLefPmSZrTk2WxWLB69WrJs+TirbmhVd3d3ZLPeS3iPPQsOeahogtfz4QCgM7OTsdXlUidtXv3bmRnZ0uWBdz6RumxY8ciJibG5U/Gdzfr6tWrkubIyVtzo7S0VJNZu3fvZtEbAs5Dz2bJNQ8V+1KnNwdZajU1NQCApKQkTWXJRQ8LgNbmvBbpZW5ocR4qsvBpdZABFj13aXVuaDVLq7Q6XlrN+iHFFT4tdzyLnnu0Oje0mqVVWh0vrWb1RVGFT8sdz6LnHq3ODa1maZVWx0urWf1RTOHTcsez6LlHq3NDq1lapdXx0mqWM4oofFrueBY992h1bmg1S6u0Ol5azRqIIi5n+PLLLx3XwPj5+cmSuWfPHhw6dKjf7ZWVlW5n2O12lJeXY968ef0er7q62u2cnqzjx49r6jo9wDtzQ6tZUr/dXss4Dz1HCfNQEYXvvvvuAwDI9dWABoMBOTk5Tu/jqWvrfHx8BjyWJ7O0xhtzQ6tZ3l5s1Izz0HNZSpiHinipk4iISC4sfEREpCssfEREpCssfEREpCssfEREpCssfEREpCssfEREpCuqLXwVFRWIj49HbGws1q9fL2nWmTNnsGnTJrz22mv4/PPPNZOlVXLOjeXLl8NkMmHq1KmS5tTX1yM7OxtTpkxBYmIiXn31VUnzyH2chwomFGIwTenq6hIxMTHi7NmzorOzUyQnJ4va2lqPZd2+3W63i1dffVVcu3ZNdHV1iTfffFNcvnzZ5Syz2ezydjmz1ERJc+OH9u/fL44ePSoSExMHtd9gsy5cuCCOHj0qhBCipaVFxMXFSTbnqW+ch9qZh6p8xldVVYXY2FjExMTA19cXixYtcnyckKc1NjYiJCQEwcHB8PHxQWJiIk6dOqX6LK2Sc24AwMyZMxESEiLZ8XuEh4cjNTUVAGA0GpGQkIDGxkbJc2loOA+VTZWFr7GxERMmTHD8HBkZKVnnt7a2IiAgwPFzQEAAWltbVZ+lVXLODW+pq6vDsWPHMGPGDG83hfrBeahsqix8RHp148YN5Ofno7CwsNcvSURyUvs8VGXhi4iIQH19vePnhoYGRERESJJlNBrR0tLi+LmlpQVGo1H1WVol59yQm81mQ35+PpYsWYK8vDxvN4ec4DxUNlUWvunTp+P06dM4f/48rFYr3nvvPcyfP1+SrIiICFy9ehXXr1+H3W5HbW0t4uPjVZ+lVXLODTkJIbBixQokJCRo7quntIjzUNlUWfiGDx+OTZs2Yfbs2UhISMDChQuRmJgoSdawYcOQm5uLkpISFBUVYcqUKTCZTKrP0io55wYALF68GBkZGfjuu+8QGRmJbdu2SZJz8OBBFBcXY9++fUhJSUFKSgrKy8slySL3cR4qm+H/3kLqdUr6/ilPtqWystLp9+0NtF2pWXJS0tzQapacbVErJY2XVrPkaosqn/FJyWq1yppnt9s1mSUnrfahXFlyz3mivsg5DxXxDexKYbVasXDhQgCA2WyGwWBw+5jV1dX9bjt37hzMZrPHvjl9oKza2lrMmjXLI1lKUVNTg7179zquLfKEysrKPm/v6cN58+ZpJstms+FXv/oVgFt/v/HEnCcarNvXXjnmIQvf/7m94wEgOzvbY8fu6+XFmpoajB07FjExMR59+XGgLC2pqakBAKSmpsrah1rJslqtmDNnDoKDg7Fnzx4WPfKKH669csxDvtSJ3h1fWloqeV7Pgp2UlKSpLDlptQ/lyuopesCtz5QcMWKEpHlEfZF77e2h+8L3w4739fWVNE+Li6jctNqH3ip6Us95or7IvfbeTteFj0VPfbTahyx6pCfeLHqAjgsfi576aLUPWfRIT7xd9AAdFz4WPXXRah/KmcWiR0rg7aIH6LDw3X6tiBwdf+7cOQDyLGxyZnmDnI9LS1m3z3kWPfIWuddeZxR1OYOcb6detWoVDh061O/2/q6vGgy73Q6z2YyYmJh+j+fs2rvBZtXW1mL58uUeOZ5S9FzEnZycLFumVrNY9Nwn5xql1SxvFz1AYYVPzo/NycnJcXofT10/5ePjM+CxPJmlNT4+PjCbzZr82Dc5s8xms9cXGy1Qykd7qTlLCfNQdy91EukRL04n+v9Y+IiISFdY+IiISFdY+IiISFdY+IiISFdY+IiISFdY+IiISFcUdR3fYCxfvhxlZWUwmUw4efKkpFm7d+/G3//+d4wePRpPPfWUZrK06syZM6ioqEB3dzdSU1ORmZkpWZZc49Xc3Iy//OUvuHHjBgwGA1JTU/GjH/1Isjxyn1xrVH19PR577DFcunQJBoMBTz75JJ5++mlJsjo6OjBz5kx0dnaiq6sLDz30EJ5//nlJsqSk2md8y5YtQ0VFhSxZKSkpWLp0qeayhmrdunVYt26dt5vRp+7ubpSXl2PJkiVYtWoVTp48iaamJsny5BqvYcOG4f7778eqVauwYsUKHDlyRNLHRe6Ta40aPnw4Nm7ciG+++QZffPEFioqK8M0330iS5efnh3379uH48eOorq5GRUUFvvjiC0mypKTawjdz5kyEhITIkhUVFQV/f3/NZWlRY2MjQkJCEBwcDB8fHyQmJuLUqVOS5ck1XkajEeHh4QBuLT5hYWFoaWmRPJeGTq41Kjw8HKmpqQBuzZOEhAQ0NjZKkmUwGDBmzBgAgM1mg81mU+WHI6i28BH1pbW1FQEBAY6fAwIC0Nra6sUWeZ7FYsHFixcRGRnp7aa4Ze7cuQgKCurz39y5c73dPFWqq6vDsWPHMGPGDMky7HY7UlJSYDKZkJOTI2mWVFT7Nz4iPbJarSgtLcWcOXPg5+fn7ea4payszNtN0JQbN24gPz8fhYWFvX758zQfHx9UV1fDYrHgwQcfxMmTJzF16lTJ8qTAwkcumTt3Lj7//HMAt/7ADQCFhYUAgMzMTMUsYkajsddLgC0tLTAajV5skefY7XaUlpYiKSkJCQkJ3m4OKYjNZkN+fj6WLFmCvLw8WTKDgoKQnZ2NiooK1RU+vtRJLikrK4PFYoHFYkFBQQEKCgocPyul6AFAREQErl69iuvXrzu+qik+Pt7bzXKbEAIffvghQkNDkZGR4e3meMQDDzyAMWPG9PnvgQce8HbzVEMIgRUrViAhIQGrV6+WNKupqQkWiwUA0N7ejr1792Ly5MmSZkpBtc/4Fi9ejMrKSly5cgWRkZF4/vnnsWLFCkmydu3ahbq6Oty8eROvvPIKsrKyHH9MVnOWFg0bNgy5ubkoKSmBEMLxtwipyDVe9fX1OHHiBEwmEzZv3gwAmDVrFuLi4jyeJZePP/7Y202QlFxr1MGDB1FcXIykpCSkpKQAAF588UXk5uZ6POvixYt4/PHHYbfb0d3djYULF6ry77GqLXw7duyQLSs/P1+TWVoVFxcnW0GQa7wmTpyItWvXypJFniHXGpWZmSnb9+klJyfj2LFjsmRJSbWFTypWq1XWvJ5vGFdTltKu4VNjH+o5i6gvcq69LHy3sVqtWLhwIYBb31jtietTqqur+9127tw5mM1mj31z+kBZtbW1mDVrlkeylKKmpgbl5eWy9aGc48W5QXpx+9orhJD82kAWvv9ze8cDQHZ2tseOnZWVdcdtNTU1GDt2LGJiYvrcLlWWltTU1AAA5s2bJ2sfajWLyBt+uPbKcUE839WJ3h1fWloqeV7Pgp2UlKSpLDlptQ+1mkXUF7nX3h66L3w/7HhfX19J87iwuU+rfajVLKK+yL323k7XhY9FT3202odazSLqizeLHqDjwseipz5a7UOtZhH1xdtFD9Bx4WPRUxet9qFWs4j64+2iB+iw8N1+rYgcHX/u3DkA8iw2cmbJSat9qNUsor7IvfY6o6jLGeT8XqdVq1bh0KFD/W6vrKx0O8Nut8NsNiMmJqbf4zm7vmqwWbW1tVi+fLlHjqcUPY9Lrj6Uc7w4N9RHzjVKq1neLnqAwgqfXB+7YzAYkJOT4/Q+nrp+ysfHZ8BjeTJLa3x8fFy6Tk+t48W5oS5yrlFazfJ20QN0+FInERHpGwsfERHpCgsfERHpCgsfERHpCgsfERHpCgsfERHpCgsfERHpiqKu43NVfX09HnvsMVy6dAkGgwFPPvkknn76aUmympub8Ze//AU3btyAwWBAamoqfvSjH6k+S8vOnDmDiooKdHd3IzU1FZmZmZJl7d69G3//+98xevRoPPXUU5LlcG6oi5xrVEdHB2bOnInOzk50dXXhoYcewvPPPy9JVg+73Y57770XERERKCsrkzRLCqosfMOHD8fGjRuRmpqK1tZWpKWlIScnB1OmTPF41rBhw3D//fcjPDwcnZ2d2LJlC+6++26EhYWpOkururu7UV5ejkcffRQBAQHYunUr4uPjJevDlJQUpKen489//rMkx+/BuaEucq5Rfn5+2LdvH8aMGQObzYbMzEw88MADkv5i9OqrryIhIQEtLS2SZUhJlS91hoeHIzU1FQBgNBqRkJCAxsZGSbKMRiPCw8MB3JpgYWFhkg22nFla1djYiJCQEAQHB8PHxweJiYk4deqUZHlRUVHw9/eX7Pg9ODfURc41ymAwYMyYMQAAm80Gm80m6UeQNTQ04KOPPsLKlSsly5CaKgvf7erq6nDs2DHMmDFD8iyLxYKLFy8iMjJSU1la0traioCAAMfPAQEBaG1t9WKLPI9zQ13kWKPsdjtSUlJgMpmQk5MjadYvf/lLbNiwAcOGqbd8qLflAG7cuIH8/HwUFhb2WuykYLVaUVpaijlz5sDPz08zWaQunBvqItca5ePjg+rqajQ0NKCqqgonT56UJKesrAwmkwlpaWmSHF8uqi18NpsN+fn5WLJkCfLy8iTNstvtKC0tRVJSEhISEjSTpUVGo7HXS4AtLS0wGo1ebJHncG6oi5xrVI+goCBkZ2ejoqJCkuMfPHgQH374IaKjo7Fo0SLs27cPS5culSRLSqosfEIIrFixAgkJCVi9erXkWR9++CFCQ0ORkZGhmSytioiIwNWrV3H9+nXH1/HEx8d7u1lu49xQFznXqKamJlgsFgBAe3s79u7di8mTJ0uS9dJLL6GhoQF1dXV477338K//+q8oKSmRJEtKqnxX58GDB1FcXIykpCSkpKQAAF588UXk5uZ6PKu+vh4nTpyAyWTC5s2bAQCzZs1CXFycqrO0atiwYcjNzUVJSQmEEI6/e0hl165dqKurw82bN/HKK68gKyvL8aYGT+LcUBc516iLFy/i8ccfh91uR3d3NxYuXIi5c+d6PEdLVFn4MjMzZfv+qIkTJ2Lt2rWay9KyuLg42QpCfn6+LDmcG+oi5xqVnJyMY8eOyZJ1u6ysLI99X6TcVPlSp5SsVquseXa7XZNZctJqH2o1i6gvcq69qnzGJxWr1YqFCxcCAMxms0euhamuru5327lz51BbW+uxb8ceKMtisWDWrFkeyVKKmpoaHD9+XLY+lHO8ODdIL25fe4UQkl6HCLDwOdze8Z2dnfD19fXYsft6OaCmpgZjx47F8uXLPZYzUFZSUpJHs7ytpqYGADz+5gGljBfnBunBD9deqYsewJc6AfTu+NLSUo8Wvb70LNhyLDZyZslJq32o1Syivsi99vbQfeFj0VMfrfahVrOI+uKtogfovPCx6KmPVvtQq1lEffFm0QN0XPhY9NRHq32o1Syivni76AE6Lnwseuqi1T7UahZRf7xd9AAdFr7brxWRo+PPnTsHQJ7FRs4sOWm1D7WaRdQXuddeZxR1OYMcb2PtsWrVKhw6dEjSjJ7PioyJiUFlZaXkWRaLRXMLW8/junr1qix9KOd4cW6oj5xrlFazvF30AMAg5PpcHQWR4wJJIiLqTSlrry4LHxER6Zfu/sZHRET6xsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES6wsJHRES68v8AXDqwws6ZJ+sAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Adapted from astroML: see http://www.astroml.org/book_images/appendix/fig_broadcast_visual.html\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "\n", + "#------------------------------------------------------------\n", + "# Draw a figure and axis with no boundary\n", + "fig = plt.figure(figsize=(6, 4.5), facecolor='w')\n", + "ax = plt.axes([0, 0, 1, 1], xticks=[], yticks=[], frameon=False)\n", + "\n", + "\n", + "def draw_cube(ax, xy, size, depth=0.4,\n", + " edges=None, label=None, label_kwargs=None, **kwargs):\n", + " \"\"\"draw and label a cube. edges is a list of numbers between\n", + " 1 and 12, specifying which of the 12 cube edges to draw\"\"\"\n", + " if edges is None:\n", + " edges = range(1, 13)\n", + "\n", + " x, y = xy\n", + "\n", + " if 1 in edges:\n", + " ax.plot([x, x + size],\n", + " [y + size, y + size], **kwargs)\n", + " if 2 in edges:\n", + " ax.plot([x + size, x + size],\n", + " [y, y + size], **kwargs)\n", + " if 3 in edges:\n", + " ax.plot([x, x + size],\n", + " [y, y], **kwargs)\n", + " if 4 in edges:\n", + " ax.plot([x, x],\n", + " [y, y + size], **kwargs)\n", + "\n", + " if 5 in edges:\n", + " ax.plot([x, x + depth],\n", + " [y + size, y + depth + size], **kwargs)\n", + " if 6 in edges:\n", + " ax.plot([x + size, x + size + depth],\n", + " [y + size, y + depth + size], **kwargs)\n", + " if 7 in edges:\n", + " ax.plot([x + size, x + size + depth],\n", + " [y, y + depth], **kwargs)\n", + " if 8 in edges:\n", + " ax.plot([x, x + depth],\n", + " [y, y + depth], **kwargs)\n", + "\n", + " if 9 in edges:\n", + " ax.plot([x + depth, x + depth + size],\n", + " [y + depth + size, y + depth + size], **kwargs)\n", + " if 10 in edges:\n", + " ax.plot([x + depth + size, x + depth + size],\n", + " [y + depth, y + depth + size], **kwargs)\n", + " if 11 in edges:\n", + " ax.plot([x + depth, x + depth + size],\n", + " [y + depth, y + depth], **kwargs)\n", + " if 12 in edges:\n", + " ax.plot([x + depth, x + depth],\n", + " [y + depth, y + depth + size], **kwargs)\n", + "\n", + " if label:\n", + " if label_kwargs is None:\n", + " label_kwargs = {}\n", + " ax.text(x + 0.5 * size, y + 0.5 * size, label,\n", + " ha='center', va='center', **label_kwargs)\n", + "\n", + "solid = dict(c='black', ls='-', lw=1,\n", + " label_kwargs=dict(color='k'))\n", + "dotted = dict(c='black', ls='-', lw=0.5, alpha=0.5,\n", + " label_kwargs=dict(color='gray'))\n", + "depth = 0.3\n", + "\n", + "#------------------------------------------------------------\n", + "# Draw top operation: vector plus scalar\n", + "draw_cube(ax, (1, 10), 1, depth, [1, 2, 3, 4, 5, 6, 9], '0', **solid)\n", + "draw_cube(ax, (2, 10), 1, depth, [1, 2, 3, 6, 9], '1', **solid)\n", + "draw_cube(ax, (3, 10), 1, depth, [1, 2, 3, 6, 7, 9, 10], '2', **solid)\n", + "\n", + "draw_cube(ax, (6, 10), 1, depth, [1, 2, 3, 4, 5, 6, 7, 9, 10], '5', **solid)\n", + "draw_cube(ax, (7, 10), 1, depth, [1, 2, 3, 6, 7, 9, 10, 11], '5', **dotted)\n", + "draw_cube(ax, (8, 10), 1, depth, [1, 2, 3, 6, 7, 9, 10, 11], '5', **dotted)\n", + "\n", + "draw_cube(ax, (12, 10), 1, depth, [1, 2, 3, 4, 5, 6, 9], '5', **solid)\n", + "draw_cube(ax, (13, 10), 1, depth, [1, 2, 3, 6, 9], '6', **solid)\n", + "draw_cube(ax, (14, 10), 1, depth, [1, 2, 3, 6, 7, 9, 10], '7', **solid)\n", + "\n", + "ax.text(5, 10.5, '+', size=12, ha='center', va='center')\n", + "ax.text(10.5, 10.5, '=', size=12, ha='center', va='center')\n", + "ax.text(1, 11.5, r'${\\tt np.arange(3) + 5}$',\n", + " size=12, ha='left', va='bottom')\n", + "\n", + "#------------------------------------------------------------\n", + "# Draw middle operation: matrix plus vector\n", + "\n", + "# first block\n", + "draw_cube(ax, (1, 7.5), 1, depth, [1, 2, 3, 4, 5, 6, 9], '1', **solid)\n", + "draw_cube(ax, (2, 7.5), 1, depth, [1, 2, 3, 6, 9], '1', **solid)\n", + "draw_cube(ax, (3, 7.5), 1, depth, [1, 2, 3, 6, 7, 9, 10], '1', **solid)\n", + "\n", + "draw_cube(ax, (1, 6.5), 1, depth, [2, 3, 4], '1', **solid)\n", + "draw_cube(ax, (2, 6.5), 1, depth, [2, 3], '1', **solid)\n", + "draw_cube(ax, (3, 6.5), 1, depth, [2, 3, 7, 10], '1', **solid)\n", + "\n", + "draw_cube(ax, (1, 5.5), 1, depth, [2, 3, 4], '1', **solid)\n", + "draw_cube(ax, (2, 5.5), 1, depth, [2, 3], '1', **solid)\n", + "draw_cube(ax, (3, 5.5), 1, depth, [2, 3, 7, 10], '1', **solid)\n", + "\n", + "# second block\n", + "draw_cube(ax, (6, 7.5), 1, depth, [1, 2, 3, 4, 5, 6, 9], '0', **solid)\n", + "draw_cube(ax, (7, 7.5), 1, depth, [1, 2, 3, 6, 9], '1', **solid)\n", + "draw_cube(ax, (8, 7.5), 1, depth, [1, 2, 3, 6, 7, 9, 10], '2', **solid)\n", + "\n", + "draw_cube(ax, (6, 6.5), 1, depth, range(2, 13), '0', **dotted)\n", + "draw_cube(ax, (7, 6.5), 1, depth, [2, 3, 6, 7, 9, 10, 11], '1', **dotted)\n", + "draw_cube(ax, (8, 6.5), 1, depth, [2, 3, 6, 7, 9, 10, 11], '2', **dotted)\n", + "\n", + "draw_cube(ax, (6, 5.5), 1, depth, [2, 3, 4, 7, 8, 10, 11, 12], '0', **dotted)\n", + "draw_cube(ax, (7, 5.5), 1, depth, [2, 3, 7, 10, 11], '1', **dotted)\n", + "draw_cube(ax, (8, 5.5), 1, depth, [2, 3, 7, 10, 11], '2', **dotted)\n", + "\n", + "# third block\n", + "draw_cube(ax, (12, 7.5), 1, depth, [1, 2, 3, 4, 5, 6, 9], '1', **solid)\n", + "draw_cube(ax, (13, 7.5), 1, depth, [1, 2, 3, 6, 9], '2', **solid)\n", + "draw_cube(ax, (14, 7.5), 1, depth, [1, 2, 3, 6, 7, 9, 10], '3', **solid)\n", + "\n", + "draw_cube(ax, (12, 6.5), 1, depth, [2, 3, 4], '1', **solid)\n", + "draw_cube(ax, (13, 6.5), 1, depth, [2, 3], '2', **solid)\n", + "draw_cube(ax, (14, 6.5), 1, depth, [2, 3, 7, 10], '3', **solid)\n", + "\n", + "draw_cube(ax, (12, 5.5), 1, depth, [2, 3, 4], '1', **solid)\n", + "draw_cube(ax, (13, 5.5), 1, depth, [2, 3], '2', **solid)\n", + "draw_cube(ax, (14, 5.5), 1, depth, [2, 3, 7, 10], '3', **solid)\n", + "\n", + "ax.text(5, 7.0, '+', size=12, ha='center', va='center')\n", + "ax.text(10.5, 7.0, '=', size=12, ha='center', va='center')\n", + "ax.text(1, 9.0, r'${\\tt np.ones((3,\\, 3)) + np.arange(3)}$',\n", + " size=12, ha='left', va='bottom')\n", + "\n", + "#------------------------------------------------------------\n", + "# Draw bottom operation: vector plus vector, double broadcast\n", + "\n", + "# first block\n", + "draw_cube(ax, (1, 3), 1, depth, [1, 2, 3, 4, 5, 6, 7, 9, 10], '0', **solid)\n", + "draw_cube(ax, (1, 2), 1, depth, [2, 3, 4, 7, 10], '1', **solid)\n", + "draw_cube(ax, (1, 1), 1, depth, [2, 3, 4, 7, 10], '2', **solid)\n", + "\n", + "draw_cube(ax, (2, 3), 1, depth, [1, 2, 3, 6, 7, 9, 10, 11], '0', **dotted)\n", + "draw_cube(ax, (2, 2), 1, depth, [2, 3, 7, 10, 11], '1', **dotted)\n", + "draw_cube(ax, (2, 1), 1, depth, [2, 3, 7, 10, 11], '2', **dotted)\n", + "\n", + "draw_cube(ax, (3, 3), 1, depth, [1, 2, 3, 6, 7, 9, 10, 11], '0', **dotted)\n", + "draw_cube(ax, (3, 2), 1, depth, [2, 3, 7, 10, 11], '1', **dotted)\n", + "draw_cube(ax, (3, 1), 1, depth, [2, 3, 7, 10, 11], '2', **dotted)\n", + "\n", + "# second block\n", + "draw_cube(ax, (6, 3), 1, depth, [1, 2, 3, 4, 5, 6, 9], '0', **solid)\n", + "draw_cube(ax, (7, 3), 1, depth, [1, 2, 3, 6, 9], '1', **solid)\n", + "draw_cube(ax, (8, 3), 1, depth, [1, 2, 3, 6, 7, 9, 10], '2', **solid)\n", + "\n", + "draw_cube(ax, (6, 2), 1, depth, range(2, 13), '0', **dotted)\n", + "draw_cube(ax, (7, 2), 1, depth, [2, 3, 6, 7, 9, 10, 11], '1', **dotted)\n", + "draw_cube(ax, (8, 2), 1, depth, [2, 3, 6, 7, 9, 10, 11], '2', **dotted)\n", + "\n", + "draw_cube(ax, (6, 1), 1, depth, [2, 3, 4, 7, 8, 10, 11, 12], '0', **dotted)\n", + "draw_cube(ax, (7, 1), 1, depth, [2, 3, 7, 10, 11], '1', **dotted)\n", + "draw_cube(ax, (8, 1), 1, depth, [2, 3, 7, 10, 11], '2', **dotted)\n", + "\n", + "# third block\n", + "draw_cube(ax, (12, 3), 1, depth, [1, 2, 3, 4, 5, 6, 9], '0', **solid)\n", + "draw_cube(ax, (13, 3), 1, depth, [1, 2, 3, 6, 9], '1', **solid)\n", + "draw_cube(ax, (14, 3), 1, depth, [1, 2, 3, 6, 7, 9, 10], '2', **solid)\n", + "\n", + "draw_cube(ax, (12, 2), 1, depth, [2, 3, 4], '1', **solid)\n", + "draw_cube(ax, (13, 2), 1, depth, [2, 3], '2', **solid)\n", + "draw_cube(ax, (14, 2), 1, depth, [2, 3, 7, 10], '3', **solid)\n", + "\n", + "draw_cube(ax, (12, 1), 1, depth, [2, 3, 4], '2', **solid)\n", + "draw_cube(ax, (13, 1), 1, depth, [2, 3], '3', **solid)\n", + "draw_cube(ax, (14, 1), 1, depth, [2, 3, 7, 10], '4', **solid)\n", + "\n", + "ax.text(5, 2.5, '+', size=12, ha='center', va='center')\n", + "ax.text(10.5, 2.5, '=', size=12, ha='center', va='center')\n", + "ax.text(1, 4.5, r'${\\tt np.arange(3).reshape((3,\\, 1)) + np.arange(3)}$',\n", + " ha='left', size=12, va='bottom')\n", + "\n", + "ax.set_xlim(0, 16)\n", + "ax.set_ylim(0.5, 12.5)\n", + "\n", + "fig.savefig('images/02.05-broadcasting.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Aggregation and Grouping\n", + "\n", + "Figures from the chapter on aggregation and grouping" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Split-Apply-Combine" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def draw_dataframe(df, loc=None, width=None, ax=None, linestyle=None,\n", + " textstyle=None):\n", + " loc = loc or [0, 0]\n", + " width = width or 1\n", + "\n", + " x, y = loc\n", + "\n", + " if ax is None:\n", + " ax = plt.gca()\n", + "\n", + " ncols = len(df.columns) + 1\n", + " nrows = len(df.index) + 1\n", + "\n", + " dx = dy = width / ncols\n", + "\n", + " if linestyle is None:\n", + " linestyle = {'color':'black'}\n", + "\n", + " if textstyle is None:\n", + " textstyle = {'size': 12}\n", + "\n", + " textstyle.update({'ha':'center', 'va':'center'})\n", + "\n", + " # draw vertical lines\n", + " for i in range(ncols + 1):\n", + " plt.plot(2 * [x + i * dx], [y, y + dy * nrows], **linestyle)\n", + "\n", + " # draw horizontal lines\n", + " for i in range(nrows + 1):\n", + " plt.plot([x, x + dx * ncols], 2 * [y + i * dy], **linestyle)\n", + "\n", + " # Create index labels\n", + " for i in range(nrows - 1):\n", + " plt.text(x + 0.5 * dx, y + (i + 0.5) * dy,\n", + " str(df.index[::-1][i]), **textstyle)\n", + "\n", + " # Create column labels\n", + " for i in range(ncols - 1):\n", + " plt.text(x + (i + 1.5) * dx, y + (nrows - 0.5) * dy,\n", + " str(df.columns[i]), style='italic', **textstyle)\n", + " \n", + " # Add index label\n", + " if df.index.name:\n", + " plt.text(x + 0.5 * dx, y + (nrows - 0.5) * dy,\n", + " str(df.index.name), style='italic', **textstyle)\n", + "\n", + " # Insert data\n", + " for i in range(nrows - 1):\n", + " for j in range(ncols - 1):\n", + " plt.text(x + (j + 1.5) * dx,\n", + " y + (i + 0.5) * dy,\n", + " str(df.values[::-1][i, j]), **textstyle)\n", + "\n", + "\n", + "#----------------------------------------------------------\n", + "# Draw figure\n", + "\n", + "import pandas as pd\n", + "df = pd.DataFrame({'data': [1, 2, 3, 4, 5, 6]},\n", + " index=['A', 'B', 'C', 'A', 'B', 'C'])\n", + "df.index.name = 'key'\n", + "\n", + "\n", + "fig = plt.figure(figsize=(8, 6), facecolor='white')\n", + "ax = plt.axes([0, 0, 1, 1])\n", + "\n", + "ax.axis('off')\n", + "\n", + "draw_dataframe(df, [0, 0])\n", + "\n", + "for y, ind in zip([3, 1, -1], 'ABC'):\n", + " split = df[df.index == ind]\n", + " draw_dataframe(split, [2, y])\n", + "\n", + " sum = pd.DataFrame(split.sum()).T\n", + " sum.index = [ind]\n", + " sum.index.name = 'key'\n", + " sum.columns = ['data']\n", + " draw_dataframe(sum, [4, y + 0.25])\n", + " \n", + "result = df.groupby(df.index).sum()\n", + "draw_dataframe(result, [6, 0.75])\n", + "\n", + "style = dict(fontsize=14, ha='center', weight='bold')\n", + "plt.text(0.5, 3.6, \"Input\", **style)\n", + "plt.text(2.5, 4.6, \"Split\", **style)\n", + "plt.text(4.5, 4.35, \"Apply (sum)\", **style)\n", + "plt.text(6.5, 2.85, \"Combine\", **style)\n", + "\n", + "arrowprops = dict(facecolor='black', width=1, headwidth=6)\n", + "plt.annotate('', (1.8, 3.6), (1.2, 2.8), arrowprops=arrowprops)\n", + "plt.annotate('', (1.8, 1.75), (1.2, 1.75), arrowprops=arrowprops)\n", + "plt.annotate('', (1.8, -0.1), (1.2, 0.7), arrowprops=arrowprops)\n", + "\n", + "plt.annotate('', (3.8, 3.8), (3.2, 3.8), arrowprops=arrowprops)\n", + "plt.annotate('', (3.8, 1.75), (3.2, 1.75), arrowprops=arrowprops)\n", + "plt.annotate('', (3.8, -0.3), (3.2, -0.3), arrowprops=arrowprops)\n", + "\n", + "plt.annotate('', (5.8, 2.8), (5.2, 3.6), arrowprops=arrowprops)\n", + "plt.annotate('', (5.8, 1.75), (5.2, 1.75), arrowprops=arrowprops)\n", + "plt.annotate('', (5.8, 0.7), (5.2, -0.1), arrowprops=arrowprops)\n", + " \n", + "plt.axis('equal')\n", + "plt.ylim(-1.5, 5);\n", + "\n", + "fig.savefig('images/03.08-split-apply-combine.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## What Is Machine Learning?" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "# common plot formatting for below\n", + "def format_plot(ax, title):\n", + " ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + " ax.yaxis.set_major_formatter(plt.NullFormatter())\n", + " ax.set_xlabel('feature 1', color='gray')\n", + " ax.set_ylabel('feature 2', color='gray')\n", + " ax.set_title(title, color='gray')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Classification Example Figures\n", + "\n", + "[Figure context](05.01-What-Is-Machine-Learning.ipynb#Classification:-Predicting-Discrete-Labels)\n", + "\n", + "The following code generates the figures from the Classification section." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.datasets import make_blobs\n", + "from sklearn.svm import SVC\n", + "\n", + "# create 50 separable points\n", + "X, y = make_blobs(n_samples=50, centers=2,\n", + " random_state=0, cluster_std=0.60)\n", + "\n", + "# fit the support vector classifier model\n", + "clf = SVC(kernel='linear')\n", + "clf.fit(X, y)\n", + "\n", + "# create some new points to predict\n", + "X2, _ = make_blobs(n_samples=80, centers=2,\n", + " random_state=0, cluster_std=0.80)\n", + "X2 = X2[50:]\n", + "\n", + "# predict the labels\n", + "y2 = clf.predict(X2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Classification Example Figure 1" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the data\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "point_style = dict(cmap='Paired', s=50)\n", + "ax.scatter(X[:, 0], X[:, 1], c=y, **point_style)\n", + "\n", + "# format plot\n", + "format_plot(ax, 'Input Data')\n", + "ax.axis([-1, 4, -2, 7])\n", + "\n", + "fig.savefig('images/05.01-classification-1.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Classification Example Figure 2" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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iEZGJaVKHcMJ2MIYoMjDYJuQTndtl8L5ZFfjdLjwuA4NkaUKvO3lcu96IiIyMST0nnO9z43EZg27IXl0wcXfFOZLSPB+XLaxhb0eIznCcfL8n2UM+jv1xbcchGrfxul1jdp9dx3E41B1le2sPCdthanGAqcVBVYQSkVExqUPYMAwW1xaxdld7Wq/X7TJYVFOUo5aNDW6XwbSS4x96dhyHdw528c6BTuJ2credqcVBltWVjKniH7bj8ML2FvZ1hFML03a1hcjzdrByTtWQq+U7I3He2tfB3o4whgH1JUEWTClSUQsRGdKkDmGAmeUFOA6s39tB3HFwHIcCn4fl9aVagDRCXt/TznuHugd80dndFqKlJ8r751XjGSPD21sOdbO3IzxgZCRuO3RF4ry6s5UzG8szPq4tFOOxTQcHrCh/71A3O9tCXDS3mjzf0EFsOw6bm7p4t6mLcNymwOdm4ZQi6jX3LjLhTfoQBphVUUBjeT5dkThul6F6uCMoHEuw+VBX2l60DhCO22xr6WF2ZUFO2na4jQc7M05N2MCejhCxhJ1xPnzNrta0W7ocIBq3eXNfO6c2lA16TcdxeG5bM/s7wiR6n6I9HOelna20hWOcWFN8PC9JRMa4sdEFGQNchkFRwKsAHmEHuyKDzqcmbOcIhUGyKxwffGN6l2EQyXA+lrA51B3N+BgH2HmE19fUHeVAZyQVwH0StsM7BzoJxVSdTGQiUwjLqBpq9TmQtj/taIglbGKJwQO2T4F/8C9gjkPG+WvbgaFeon2EFfbbW3oGLYxiYLCnfex8SRGRkadun4yqKYV+Bsshj8tgRnn+qF27qSvC2t1ttIWS94KXBL0srSuhssCf8ecXTinkxR2taUPSbgMay/MyFjDxuQ2CXjfd0cw91op835BtHCqkHZy0YfyhOI5DS0+MnliC4oCHooDWNIiMdeoJy6jyul2cWFOUVvzDZUBR721Po+FQd4Q/v3eI1lAMh+TQcGsoxp/fO8Sh7kjGx0wryWN+VSEuA9yGkfp/dWGAk6aWZHyMYRicNLUYd4besNswWFw79Jzu1OLgoNXJDKC6MPMXhsO1h2I8+PZ+nnyviZd2tPCnjQd5bNNBwhrOFhnT1BOWUTevupB8v4c397XTGYnjdbmYWZHPgimFo3a/8Ot70m87g2QBltf2tHPhnKqMj1tUU8Ssinz2tIdI2A7VhYEjrpKfVpKH0wCv7WkjGk9GftDnZvm0Uiryhw7RqcUB8nxuuiLxAb1etwE1RQGKh9GbjSVsHt98kOhhE8vN3VH+vOUQF82tOuK0gIjkhkJYsmJaSZBpJdnZh9juLbgxmObuKLbjDLpgLOh1M6vi6FZs15fmMa0kSHc0gWFAntc9rOBzGQYXzK7i1V2t7G4PYWCAAbPK84/Yi+6zraU746puh+T9y4e6o4MOwYtIbimEZcIxev8bbDp1tPqEhmEMubhrMD6PixUzyoknbCIJm4DHfVQjBE1d0bTV1X0cx6E1FFMIi4xRmhOWCccwjCHnUqsL/WOyDKXH7SLf5znqIfqg1z3oFwuXYeAbI8VQRCSd/nXKhHTy1JKMC548LmPQRVbjVWN5/qBfKhyS884DjjkOB7sibG3uZn9nGGeSblQiMhZoOHoCsh0H23HwuCbvd6zioJcL51axbm87+zrCQHKh0+KaYoqPoxyp4zg0dUfZkdrgIcjU4kBOe9YlQS/zqwt450BXajGaQbIXfHp96YAqX12ROH9+r2lAYRKv28W5MytGvUxrNG7TGYnj97iOadheZCLSv4QJpDsaZ+3uNva2J0Mn3+/mpNoS6rK0IGqsKQ54ObuxYsSez3YcntvazIGuyIANHvJ9blbOrsI3xAYPo21RTTFTCgO829RFTzROadDH3KqCAfcK247D45ub0qpwxe0ET2xu4rKFU0bli1vCdli7u5XtLT24DAPbcSgKeDljepnuZZZJb/J2lSaYUCzBIxsPsrc9nLovtiuS4IXtLWxt7s5187LOcRzCsQTRIUpRHq3NTV3s7wwPqHAVtx06I3HW7G4dsescq8oCP2fOKOfCudWcUl+aFnB7O8KDVg6zHYedraNTneulHS1sb+kh4UDMdkg4yXu2H9vUlLEUqMhkop7wBLHxYCcx205bEZxwHF7f0870srwxuRhpNOxq7eH1ve2pHl9p0MuyaaWU5Q1dvepI3m3qyrgK2XaSPeJ4wh4zO0Jl0haKDVoiM247tPREaRzhCmbd0Ti720MZK38lbIctzV2cUD25twyVyW3sfmLIUdnVlvmDDpK9nPbe0o0T3c7WHl7c0Up3NIHtJAOyuSfGE5ubaA8f33sQjg3eazMMg8gw6lPnUsDjGnTltctgVPY+PtQdHXwDD8dJzdeLTFYKYRnXIvEEneEYCTu5F/Rrg1TKitsOb+3rOK5rFfiHDqmAZ+RDbCTVl+QNevO0AaNSx3uwkpx9Mm0NKTKZaDh6gmgozWPjwc6MvWG3yziuFcFjUU80wcs7W1JbJTrAjNIgkSFqJR9vr2vBlCJe3pl5g4dZ5fmjVoJzpPg8Lk5vKOXFHa04joNN3ypqWDqtlLxR6AlPKQwMes7jMpg5iht4iIwHCuEJYl5VAVubu4nEB84Luw2DZXUlE2o+OJaweXTTAUK9w8N9OxFta+lhqAHh462fXF8SpD0U452DnRgYODgYJG99WjJ1eCUmc21aaR6leT42H+qiPRSj0O9hdmXBqK1SdrsMTq0v5aUdrQNGKNwug+oCP7VFg4e0yGSgEJ4g/B43F82r5o097exs68F2kguSFtcWUzPBPui2tXRnXPU8WOlGSPb46kuP71YtwzA4sbaYWZUF7GkPYdsOU4a5ycJYUuD3ZLVgSX1pHvl+Dxv2d9DaE8PvcTGnsoDpZXnaWEImPYXwBBL0ujl9ehmnU4bjOBP2A25Pe3jQwHUbycVY/U8bJIdiF04ZmVW4eV43s49yg4fJrjzPN6L3bItMFArhCWqiBjAw5NyrYRgsrinkQFeUg50RXEZyB6dFtcWjsvpXROR4ZCWEDcNYDawGqK+vz8YlZQJrLMvnQGck4z2vjgOzKgqYX61VtyIy9mXlk8pxnDscx1nmOM6yysrKbFxSJrDa4gDleT7ch/X23YbBSXXFuu2lH8dxaOqKsG5vO+v3ttPaM/g+yyKSfRqOlnHHZRicO6uCTU1dbG7qIpKwKQl4WTClaMItQjseCdvhqS2HaOmJpkYNNh7sYmpxgNOnl02oFfMi45VCWMYll2Ewr6qQeVWFuW7KUYnbDtGETcDjGvUQfGNvO4e6IwPuHU84DnvaQ2xq6hp3753IRKQQFsmCaNxm7e42drb1YGBgGDC7Ip8Ta4tHJYxtx2Frc3fmms1OskesEBbJPYWwyChLbiF4kI5InGS9iuQ9VJuauumOJlgxo3zErxlL2KkiJpmEh6gsJiLZoxAWGWV72sN0RxMcnol9Q8Md4diIV6zyul2pvXszGe+3azmOw6HuKK2hZPGPqcWBUdkLWWS0KYRFRtnuttCgWwg6wP7OyIiHsMtI1mV+71D69otul8H8qvFbbCQUS/DUe4foisaxHSc1nH/G9DKmFh9fVTSRbNNXR5FRNmRxEQxGa9+HxbXFVBb4U9c3SN7GNa04yOzK8RvCz25tpj2c3BvZdpKL3eK2w/PbWuiMxHPdPJGjop6wyCirLw2yvbUnbfclAAeH2lHqvbldBu+bVUlzd5S9HSFchkFdcXBc76jVForRFopl3JHRdhw2NXWytK406+0SOVYKYRn3xnqd7OoCP1UFPg52RtN2EppbWTAqWwj2V57vozzfN6rXyJb2cAzDIOO+yA7Q2hPLdpNESCQShEIhwuEwBQUFuN1u3n77bcLhMKFQiKqqqkEfqxCWcSkat1m3r51tLckeZqHfw4k1RdSX5uW6aWkMw+DsxgrePdjFu01dROIJCvweFlQX0XCcOztNNkf6wpLnG98LziR3bNsmHA7jdrvx+/1s2bKFnp4ewuEwwWCQhQsX8vLLL7Nt27ZUuK5evZo333yTBx98kEAgQDAY5JJLLqGmpoYtW7akjvl8g38JVgjLuBNP2Dzy7gG6Y39ZcdwZifPSjlZC8QRzK8fe/a8uw2B+dSHzq8de28aTinwfPreLuJ1+i5XbMMbkn71kj+M42LaN2+3m4MGDdHV1EQqFAFiwYAHvvvsumzZtSvVaL7vsMjo6Ovj5z39ONBrF7/ezcuVKli5dyquvvorH4yEQCDBlyhQAqqurKSoqSoWrYRiceOKJLF68OG007sorrxxWmxXCMu5sbekmFMt8y8+6vR3MLM/X7SoTVHJUoZwn3mvCdpKlOQ2SX3JOmFI4YYbdBbq7u1MhGg6HmTdvHvv27RswzHvGGWdQWFjInXfeSTgcJhwOs3z5ci666CKeeeYZuru7CQaDlJSUsGDBAoLBIDU1NQSDwVSQFhQU8LnPfQ6/3z8gSK+77rq0Nk2fPn3EX6dCWMad7a2hQfcTdgFNXVHVkJ7ASvN8fPCEGra1dNPUHSXodTGrvGBcLzibiOLxeCpAQ6EQNTU19PT08M4776SOz507lxkzZnDXXXfR3d1NOBxm6tSpXH/99Tz55JPs3r07FZZz5szBcRw8Hg+VlZUEg0EKCwvJz8/nhhtuIBAIEAgEcLuTUxJXX311Wpvq6+sz7uTX95hcUAjL+DN4IaihTskE4vO4mFtVyNxcN2SCSyQSqRAtLCzEMAzeffddQqEQoVCIKVOmMHfuXB566CGampoIhUIEg0E+9rGP8dRTT/HGG2+kep1XX301sViM1tZWgsEgpaWl5OfnYxgGF1xwAX6/PxW4AB/4wAfS2lNbW0ttbW3a8fLyka86ly0KYRkR+zvCvHOwk65InKKAl/nVhVQV+EflWg2lQdpC0Yy9YcdJzhuKHCvbcbBtB7fLGNOr7ofLtm0ikQhutxuv18vWrVtTwZqfn8/8+fN58cUX2bVrF6FQiEgkwm233cZrr73GH/7wh1QwXnbZZVRUVLBp06bUMY8nGSELFizAMAyCwWAqRFeuXMnKlSvT2nPxxRenHaurqxvdN2EMUwjLcXtzXzvvHOhK3X7TFU1woDPCibVFo7JJQGN5PhsPdiXnhfsddxsGC2sKtZ+wHJOeaIK1u9vY2xHCcZIrrU+sKWJ6WX6um5a24Ki7u5tQKIRhGMyfP5+NGzfy3nvvpcL18ssvp7m5mV/96ldEIhF8Ph+rVq1iyZIlvPjii6le59SpU4HkgqPi4uJUrxXgpJNO4uSTT077InLVVVeltW/GjBmj/yZMUIYzRJH30bBs2TJnzZo1Wb2mjJ7OSJw/vrM/Y6/UZcAHF9SMSp3icCzBa3va2NWW/MAMet0sqimisTz3H5gy/kTiCR5+5wDhuD3guNswOGlq8YhWGOvu7k6FaCQSYc6cOezZs2fAqt0VK1bg9/u5++67U8dOO+00LrjgAn75y1+mbpspLy9n5cqVbNu2jUOHDqV6ovX19RiGQTQaJRAI4NJCxZwzDGOt4zjLDj+unrAcl+0tmbfL67OztYe5o9AbDnjdnDG9fMINHUpubGrqIpqw044nHIc39rbTWJ6fKv/ZvzBDKBSitraWzs7O1FxpOBxm/vz5TJs2jbvuuiv1cw0NDVx99dU8+uij7Nu3j0AgQF5eHrNnz8a2bVwuF+Xl5QSDQfLz8wkGg1x33XWp3mnf4qFMq3ZnzJiRsTfaN1wsY5f+hOS4RBP2oIuhbAdiQyX0CHAZBi63wleOTl9hhr4KR9ua2mnbtQ07FiERixIoqSC/qo4D654j1tXOD59PUFJUxI033shjjz3Gm2++mQrH6667jkgkQnNzM8FgMDWs63K5WLlyZWr+tG+u9Iorrkhrz7Rp05g2bVra8YqKilF/LyS3FMJyXKoKAmxt7sm4S5DHZWiRlIwax3FSC47cbjfbt29P9UQLCwuZM2cOL7zwAnv27CEUChGPx7nlllt4+eWXeeSRR/D7/QSDQa666irseIyu/Ttwe/24vD7oHVUpqJmBx+3itJnV1JaXAHDRRRdx0UUXDWhLQUEB73//+9PamOl2GJH+FMJyXKYWB/B7XCSiAxdJGUC+z031KK2QlonBcRwcx8HlctHU1JSaK3W73cyZM4e3336bbdu2pcL1qquuYu/evdx3332Ew2G8Xi+XXnopCxYs4Nlnn031Tvt6lVVVVRQXFw+49WXZsmUsX758wPRFm7uDqOu8tLUN+VVT8boN5kyvTW2ZKDKStDBLjltPLMHz25pp7YniMgwSjkNlvp8VM8rwe1TLd7Lo7u6mp6eHUChELBZj5syZ7N69m82bN6fmRc8++2xcLhf33HNP6l7TFStWcN5553H33XcTj8cJBAJUVVVx3nnnsWXLltQwbyAQYMaMGTiOQywWG9EFR9G4zR83Hsi44n7ZtBIt+JPjNtjCLIWwjJiuSJzuaJwCv4d8nwZZxhvbttMWHLW3t7N58+bU8QULFjBlyhR+9rOfpY41NjZy+eWXc++993Lw4EECgQCFhYVcc801bN++nW3btqXmRGfNmoXf708VbAgEAmNm8VA4lmDd3nZ2tIZIOA4lAQ8n1hYzdZS2mpTJRSEsMgk4jjNgwVEikWDLli2pXmddXR0zZszggQceoK2tjVAoRElJCddddx0PPvgg77zzTiocb7zxRtra2njttddSw7mzZ8+moqKCHTt2pH4uLy8Pr3dilYwc69tjyvijEBYZJxzHIRqN4na7MQyDnTt3pnqnRUVFzJo1i+eee479+/cTCoVwHIePfvSjvPDCCzz++OP4fD6CwSDXXHMNwWCQxx57LBWiM2fOZMaMGWzevBm3200wGCQvL4/i4uJcv2yRCU33CYtk0eELjvr2JXW73cyaNYsNGzawY8eOVLh+6EMfYvv27TzwwAOpn7v88suZPXs2Tz/9dKrX2dDQAEBlZWXqVpi8vOQeysuXL+e0005Lmyf90Ic+lNa+2bNnj/6bICJHpJ6wZIXjODR1Rdne2oPtOEwtDjK1ODAuVpz29PSkdniJx+PMmDGDXbt2sWXLltTQ7znnnEM8HufXv/51KljPOusszjnnHO666y5s2yYYDDJlyhTe9773sWnTptS8aDAYpLGxkUQiQTQaJRgM5nRXFxEZeeoJS87YjsNzW5s50BVJ3U+8qy1Evs/NyjlV+Ea51nNfYYa+hUS1tbW0tramQjQUCrFo0SLKyspSq3bD4TCzZ8/m0ksv5Xe/+x0tLS0EAgGKi4uZMWMGsVgMx3EoLi5mypQp+P1+CgoK+NCHPpRW3P7mm29Oa9OcOXPSjrndbnw+3VctMpkohGXUbWrqYn9XhES/gh5x26EzEmftrlZOn37kbcj6CjP0LTiKxWIDdoOZNm0aDQ0N/O53v6Ojo4NwOExZWRlXX301DzzwAJs2bUoN6d5888309PRw4MCBVIlAn8+H1+vlnHPOSfVO++4r/fCHP5zWnsbGRhobG9OOV1VVHcc7JSKTjUJYRt27B7tI2Mk5UicRB8OFYUBXy0E27I3gbcmjvLSUGTNm8Oyzz3Lw4MFUwYbrr7+eZ599lj//+c94vV6CwSA33HADLpeLDRs2DCjCADB//nw8Hk8qXAEuv/zytJWudXV1GbdP024wIpJNCmE5an23b/Rt4h0KhfB6vTQ2NvLWW2+xa9euVA/12muvpWnnFvavf4FENILhMqhZeh7B8ik0b1yL2+dne7gEX+/QbUVFBSUlJQQCgVSInn766Zxxxhlp86TXXHNNWtvmzk3f5l23mojIWKUQnsT6qhuFQiESiQQNDQ3s3LmTbdu2pUL0vPPOo6enh9/+9repnz333HNZsWIFv/vd73C5XASDQWpra2lsbMTtdlNaWjpgX9KqqfX4S6twef24+gXptDMvxeMyuGJRbWqHmvnz56e1c6wUcxARGWmDfrpZluUGPg7UAX8yTfP5fuf+0TTNf8pC+2QI/Qsz9FU4am5uHlBr98QTT6SwsJB777039XPz5s3joosu4t5776Wjo4NAIEBZWRkNDQ1EIhHi8TiFhYVUVVXh9XopKyvjyiuvTAVrX2GG2267La1NmUL0xGkVvLKrdcCcMIDbgFkVf9kiTkRkshmqi/FfQB7wCvA9y7KeNk3zC73nrgQUwiOgrzBD34KjSCTCjh07Ur3OhoYG6urquP/++1PF7aurq7nsssv4zW9+w5YtW1KLiG699Va6urpSe5UGg0G8Xi9+v5+zzjor9XN995XedNNNae2ZPXt2xntIq6urj/k1NpQGaQ9F2djUhYGBg4MB1BQFWVyrIhEiMnkNFcLLTdM8EcCyrNuB/7Qs637gepKb5Egvx3GIx+O4XC4cx2HPnj2pXmdpaSkNDQ08/fTTNDc3p+ZPr7nmGp566imeffbZVOWim266iXg8zvr161MhatvJjcbnzZuXqoRUUFAAwNVXX50239nQ0JAq6NBfppW82WIYBounljC7spA9HSFs22FKUYDiwMQqdSgiAn/pXPWNSA516+FQIZx6lGmacWC1ZVlfBZ4ECo6mQYZhrAZWw9jeX7OvcElfWPa9eQ0NDaxfv569e/emhn+vvfZaNmzYwCOPPEIoFALguuuuo6amhieeeCLV6+ybzywvL6ekpGTAqt0VK1Zw1llnpS04uvbaa9PadsIJJ6QdG28LjvJ8bmZXHNVfHRGRnOjrXPWNSvZ1rDL9OtPvPR5PqjO1aNGiQa8zaMUsy7LuBu42TfNPhx3/OPBD0zSPqRuTjYpZfW9GKBTCtm2mTZvGjh07BpQJXLlyJW1tbfz+978fsAjptNNO44c//GHqdphp06Zx9tlns2HDBjo6OlLzonPmzCEajaYqHHk8nnEXiiIiE108Hh9QrGe4QdrXuepfN6AvVPv+P9ivA4FAWudqXG3g0FeYIRQKEYlEmDJlCocOHUrNlYbDYZYsWUIgEOD+++9PHVu4cCHnn38+P/nJT+ju7iYQCFBZWckVV1zBxo0b2bNnT+pNOuGEEzAMg9bW1tQxn8+nIBURGWMOr3o3VO/08GOJRGLQoDxSoI7k7mBjJoQXLlzo3HHHHUyfPp2amppUiIZCIWpqarj00ku555572L59e+rNWL16Ndu2beOtt95KvTkLFy6koKCAnTt3po7l5+fj9/uz+npEROTI+neujrZXGo1G8fv9xxSkY6VzNWZqR8fjcTo7O7FtG8MwmDt3burNLSwsBJJzq4e/aYOVCZw5c2ZW2i0iMtk5jkMsFjvmedK+ab7BgrR/jYH+PxcIBMZEkI6GrIdwQUEBq1atSv1+4cKFaT8zUd9sEZGxYLgLjjId6yvQM1gPtLCwcNAg1e5g6Y4YwpZlGcANQKNpml+3LKsemGKa5iuj3joREckokUgc8zyp4zhDzpOWlZUNGrSqYDeyhvNu/idgA+cBXwc6gfuAU0axXSIiE55t26l50qMN0lgsNmSQFhUVUV1dPeiCI404jg3DCeFTTdM82bKs1wFM02y1LEubnoqIkF6Y4WiCNBKJpIrwZArS/Px8ysvLM573+/0K0glgOCEc660j7QBYllVJsmcsIjIh9C/McLRBenhhhv5zoH2/Ly4uzji86/f7cblcuX75kkPDCeHvAb8FqizL+iZwNfCPo9oqEZFjkEgkjilIQ6EQhmEMObybqUc6WGEGkeEaMoQty3IB24D/DzifZM3oy03TfCcLbRORSWi4hRkynTtSYYaSkhKmTJmS8fxIFmYQGa4jFuuwLOt10zRPGqkLZqNspYjkVv/CDEcbpNFoNG04N9PvM/1aC45krDqeYh1PWJZ1FXC/aZrZLa8lIjnTvzDDscyT+ny+IYO0rzBDpnlSBalMFsMJ4U8AXwDilmWFSQ5JO6ZpFo1qy0RkRBzrTjChUAi32z3k8G5fYYZMvVMtOBI5siOGsGmahdloiIgMbriFGTKdU2EGkbFrOBWzzs503DTNZ0a+OSITlwoziMjhhvM190v9fh0AlgNrSVbQEplURrMwQ15eXuo2mMODVPOkIhPTcIajP9D/95ZlTQP+Y7QaJDLajrcwg9vtHnInmL7CDJkWJWmeVET6O5YJn93A/JFuiMjROp7CDMCQt7uoMIOIZMNw5oS/T2/JSsAFLAFeG8U2ySTSV5jhWIL0SIUZiouLU4UZMs2Tiojk2nB6wv0ra8SBe0zTfH6U2iPj0JEKMwwVpNFoFL/fP2QB+4qKioxB6vP5NE8qIuPacEK4xDTN7/Y/YFnW3xx+TMa34RZmGCxkvV7voEHaVy5QhRlERAYaTgjfBBweuDdnOCZjwNEuOOp/ToUZRESya9AQtizreuDDwAzLsn7f71Qh0DLaDZvMMhVmGO486ZEKM5SWllJbW6vCDCIiY8BQn7ovAPuACuDf+h3vBNaPZqMmAsdxjrnC0ZEKMxQWFlJVVaXCDCIi49ygIWya5g5gB3B69poztoxUYYZMgarCDCIi48vhVe9qampoaWlh69atqQxYvHgxhYWF/PrXv04dmz9/8Lt6h3OL0mnA90neG+wD3ED3eNrA4Xh2gukrzDBYz1SFGURExo++uznC4TCFhYVEIhG2b9+e+txvaGigrq6O+++/n66uLsLhMFVVVVx++eXcf//9bNmyJfV5f8stt9DV1cWBAwcIBALk5+fj9Xrx+/2cc845AzpdgxnOJODtwHXAvcAy4KPAnBF5N47CcAozDHYOBi/MEAgEBu2RBoNBFWYQERlj+u7mcLvdOI7Dnj17Up/3ZWVlNDQ08PTTT3Po0CFCoRA+n49rrrmGP//5zzz77LN4vV4CgQA33XQT8XicN998M/W5b9s2APPnz09tx1lQUADAVVddlTZK2dDQQENDQ1obZ8yYMazXMqyVOKZpvmdZlts0zQRwp2VZrwNfHtYVDmPbNi0tLUe9crd/YYZMYdlXmCHTORVmEBEZexwnWQeqLyz79qGePn0669evZ8+ePakO1nXXXceGDRv405/+RDgcBuC6666jpqaGJ598Mu3zvqKiIrVndX5+PgBnnnkmZ599dlrn6tprr01rW6Yh5NGYJhxOCPdYluUD3rAs619ILtY65nHW1tZW7r777oxhqcIMIiIjz3EcDr39Mu3b3sZXUELN8gvw5o3cLrU9PT2pDpNt29TX17N9+3Z27tyZCtfzzz+f9vZ2fv/736eOnXfeeZx22mncd999qd7ptGnTmD59Om63m9LS0lQWOI7D7NmzaWhoSKt697GPfSytTQsWLEg7NhY7ZMMJ4Y+QDN1PA58HpgFXHesFy8vL+exnP3usDxcRkaMQbj3IC9/8GKGW/dixKC6Pl/V3fZ2TPvnPTD3tYiC96l1NTQ2HDh1ix44dqXA96aST8Pv9/Pa3v00dW7hwIStXruSee+6hu7ubYDBIRUUF9fX1qS04CwsLqaysxOPxUFFRwRVXXJHqYPWF4ic/+cm0dmcKUb/fj9/vH903LMuMvuGAoViWFQTqTdN893gvuGzZMmfNmjVH/kERkcM4doJYTxeeYD4ut+5r769/1bvCwkJCoRA7d+5k3S++Q1frIQq69xOMtLK95nQSbh8JT4BZi5dzxbUf5p577mH79u2pcFy9ejXbtm3jrbfeSh1bsGABhYWF7Ny5MzVCmZ+fj8/ny/VLHxcMw1jrOM6yw48PZ3X0B4B/JbkyeoZlWUuAr5um+cERb6WISAZ2PMbG+25n+6O/IBGL4HJ7qD/3ak64/gu4fYFcN29ExeNxDMPAtm327duX6nWWl5czbdo0nnrqKVpaWgiHwwQCAa688kqeeOIJXnjhhdTdHLfccgs9PT2sfel52kJxXG4/juHCAEq6duNOxPA4caa0FgPJudXDp/saGxtpbGxMa1+mY3LshvNV8mvAcuApANM037Asa3jLvkRERsCa736Og2++gB1NLshJxGPsePLXtG9/mxVf/dmYWy/SN8LY3NycWmDq9/upr69n3bp17Nu3j3A4TDQa5ZprrmHdunU88cQTqap3N954I2VlZTz++ONpC47KyspSC476Vu2eddZZnHvuuQMWHBUXF3PegnreeO5HxEPdqeOlnbtSv47vTQ5ujrX3bzIZTgjHTNNstyyr/7Ejj2GLiIyA9h0bBwRwHzsWoX3HOzS/8yoVJywflWv3v3PDtm3q6urYtm0bu3fvTp278MILaWpq4uGHH04F7gUXXMDSpUv55S9/mQrR6dOnU19fj2EYFBcXU11dnVpwNHfuXGbMmEEwGMTj8aRC8ZZbbklr04knnph2bLAh4WDZFBx7kI9rw0Ve9bRjf3NkRAwnhDdYlvVhwG1Z1mzgsyRLWg6bYRirgdUA9fX1R91IEZm8Dq57FicRy3guEQ6xf+0Tg4Zw/6p3kUiE6upqmpqa2LlzZyowTz75ZNxuNw888EDq2JIlSzjnnHP43//9X8LhMMFgkOrqaurq6ujp6SESiZCfn095eTkul4uqqiouu+yy1Pxp390cn/70p9PalClE+2oWjLSSmYsIlFTQfWAXh/ed3F4fjas+MuLXlKMznBD+DPAVIAL8AngE+KejuYjjOHcAd0ByYdZRtlFEJjPDhW14iXl8eONh4m4f3cEKEi4fCbeP8piLRCLB7373u1Svta6ujosuuoif//zn7Nq1K1Vw4bbbbqOtrY3du3enArNvHnXFihUDbpcE+MQnPpHWnAULFmRcuVtTUzPqb8XRMgyD5X/7Q57/+g0kohESkRCG24PhcjPnyk9ROiv9C4Fk11C7KP3MNM2PALeZpvkVkkEsInJM4vE4LlcyMPfv358azq2oqGDq1Kk8+eSTtLe3EwqFyM/P57LLLuPRRx/llXV7sWd8ALcdZd72PxH1FtBSNAO3HcODTfmCU3G5XMyePTu1areoKFlV94Ybbkib75w9ezazZ89Oa9/MmTOz8j5kW+HURlZ+9wn2vPgwLZteJ1BSybSzL6egZnqumyYMcYuSZVlvAyuBPwLnAgP+JpumeUzbGeoWJZHxzXGc1OrcUChEIBCgrq6ON954gwMHDhAOh0kkElx55ZW89tprPPXUU6ljN998MwUFBdx///2pXuf8+fOZP38+r7/+OoZhpHYKq62tJRKJ4HK52HCnxZ4X/kCi37yw2xegctEKTvnC97WwSMa8Y7lF6UfAE0AjsJaBIez0HheRcejw2uq1tbVs3bqVvXv3poZ0V61axZ49e3j00UdTxy6++GIWLFjAz3/+81Svc+bMmdTV1QGkCjP0FayfN28eM2fOTK3u7QvLW2+9Na1NJ510UtqxvsIMiz/+dYqnz+e9B39CqOUA/uIyGi/6KDMv+ZgCWMa1IxbrsCzrh6Zp/tVIXVA9YZHj178wQzQapbKykqampgGrdpctW0YikeDhhx9OHVu6dCkrVqzg9ttvJx6PEwwGqa2t5QMf+ADr16/nwIEDqXBdvHgxsViMtra2ARueKPREjt5gPeFhVcwaSQphkb+Ix+OEQiEKCgro7u5O7QYTDoeZOXMmJSUlPPjgg6mea0NDAytXruSuu+5iz549qc1Lbr31VjZu3Mi7776bGuZdsmQJfr8/tTCp777SiVb2T2Q8OOaKWSIytEQigWEYxOPx1JxoKBSisrKSmpoannjiCTo7O1P7l15yySX88Y9/5LXXXsO2bYLBIJ/61Kc4dOgQa9euTfU64/E4brc7NZwbDAZTC44++tGPpu1XPW/ePObNm5fWvlmzZmXlfRCRo6cQFull2zZtbW2pnmjfUO3rr79OU1NTavu0D37wg7z66qs899xzqSL1H//4x/F6vTzyyCOpXqff76empoaSkhLKysoGhOj73vc+zj///AHzpNOnT2f69Olp7Vq8eHHascMDWETGJ4WwTCj9d4IBmDJlClu2bBlwS8zFF1/Mjh07eOKJJ1K91ksvvZSZM2fys5/9LNUTnTNnDrW1tdi2nSrM0Hf/6AknnJC6Jab/Npsf//jH09q0dOnStGOjUZhhLHAch30vP8KWP/6UcGsTxdPnM/uDH6d0VvoXCRHRnLCMMY7jpOZJY7EY5eXlHDx4MLW5dygU4pRTTiESifDII4+kgnX58uWceuqp/Md//AeO4xAMBpk2bRqXXHJJqifbF64nnXQSkUgkteCor9eq3uXxcRyHN/7rK+x9+U8kIslV1xgGbq+fE2+1mHaW9nyRyUsLsySrEolEquhCV1dXajeYcDjMrFmzyM/P549//GPqWGNjI+eeey4/+clP2L9/P4FAgLKyMj72sY+xYcMGNm/enBrmXbp0KW63m927d6eOFRYWasFRjjVvXMNL/2/1XwK4H7cvwKofPYcnkJ+DlonknhZmyVGzbRvDMIjFYjQ1NaV6nVVVVVRXV/P444/T3d1NKBSitLSUVatW8dBDD7F+/XoSiQSBQIDPfe5zHDx4kFdffTXVE21oaMDj8aQK1gcCAUpKSgC4+eabB+wEA4OXCcxU9Wiyiod7CDXvw1dYhr+oNCdt2PnU/SQi4cwnXW4OvP40U09/f3YbJTLGKYQnAdu2aW9vTw3n5uXlMWXKFF577bXUVmsul4tLLrmEl156iZdeeim1zdonP/lJbNvm4YcfHnCvaHV1NUVFRakFR8XFyX1Jzz//fC688MIBC45mzpyZsSTgkiVL0o4dHsAytEQsyoa7/y87n/4tLpcbOxGjfP4pnPSJbxEorcpqW2LdHQy6wZptEw93Zz4nMokphMeJvp1gwuEwhmFQVVXFli1bOHDgQOr4+9//fjZv3szTTz+dOnbZZZdRV1fHT3/609T857x585gyZQrxeJxAIEBpaWlqX9KFCxcyd+7c1DxpX5DedtttaW1avjx955pgMDi6b8QkEu1qp2XTa7jcXsrnL8u4ef3a73+Rg+ufxY5GsHuPHXrrJZ41r+e8f/1DVje8rzxxBU1vvZBxONrBpmx2ekWs0RJq3s++NY9jRyNULDiVksaFWbu2yNFQCGdR/wVHZWVlHDhwYMCq3VNPPZWuri4ef/zx1LHTTz+dpUuX8t3vfje128v06dO5+OKLaW1tpbOzM3Xri+M41NbWcvHFF6cCNxAI4HK5+NznPpfWnkwh2hfGkjuO4/DOr77D1j/+Ly6Pt/eYzaKP/gP1516V+rmufds4uO5Z7Fhk4OPtBNGuNva89Cfqz748a+2eduYHefe+20lEI+DYqeMur5/yeadQWJed+5Xfufd7bHnoJ4CBYydwuT2Uzl7M8r/9IR6/viTK2KKFWUcpkUgQiUTIy8ujs7OT/fv3p4Z5Z8+ejd/v59FHH00dmzVrFmeddRZ33HFHqiRgZWUlN910E+vXr2fLli2pxUWnnHIKhmGwa9euAcUZtOBocnnvoZ/w7n0/SOtRun0B5lz1aQ5teImuvVtxuT2Emvdjx6MZn6fmlAs45fPfy0aTU7oP7GLN975A557NuNw+7HiEmmUrWXzbN/AE8kb9+ntfeZTXf/j3ae+dy+tj6hkf4KRPHNUurCIjRquj+zl8wVFfYFZXV1NRUZHqiYbDYcrLyzn//PN54IEHePvtt4nFYgSDQb74xS+yefPmAQuOTjnlFEpLS3nrrbdSIVpSUkJxcXGq+pHq7spQHDvBnz5xRu/8agaGAcP8N1t31uWc/Ff/PIKtG77uA7uItB8if0oD/qKyrF336a9cTfu2DRnPubx+Lvqv57VCW3JiQq6Otm2bjo6OVGDm5+dTVVXF2rVraW1tJRwO4/V6WbVqFS+88AKvvvoq4XCYSCTCpz/9aXp6enj44YdTPdFAIEBlZSUFBQWpBUd9q3YvuOACVq1aNWCedO7cucydOzetXZl2g/F4xvVbLVkSaW8mEcvcswWGHcBufzCrQ9GHy6+eRn71tKxft+fgrkHPGW434ZaDFNTOyGKLRIaW02ToX5ghFArhdrupqKjgvffeS90SE41Gueiii9i4cSPPPfdcKnCvvPJKKioquPPOO1MBunDhQqqqqohGo/j9foqLi1NlAhctWsS8efNSq3tdLhdlZWWsXr06rV2nn3562rG+rdlERpMnkI9jJ47rOdz+IJWLVlB+Qvqc/0QXKK0adBTBScTxF5dnuUUiQ8t6CLe1tfGDH/yAM888kxNPPJFvf/vb+P1+gsEgM2fOZNWqVTQ3N9Pe3k4wGKS0tDS14GjVqlWpYd5gMIjL5eLzn/982jUyhWhhYWE2Xp7IcfEE86lceDoH1z8Htn3kB/TyFZfjJBL4i8povPgmGt531aSc+ph5yS28edc30uaEDY+X6iXn4M1PLmBsfudV9rz4ME4ixpSlK6k+6WwMl26Pk+zL+pzw4sWLnccee4zi4mItOBLJINS8n2f+8UPEQ10kosniFy6vP7kAK8O/V08gn8Uft5h6xiXZbuqYkyqd+dIfk8P6jo07kEdeeQ0rzLvxBPJ55d8+RfPGNb2FRRzcgTzyqxs486s/wxPUfLGMDi3MEhlHYt0d7HjqPva9/Agur49pZ1/Btsd/QceOd3HisdTPGS43gbJqzv/3P+Ly+HLY4rGlbesG9rz4B+KREFUnnsmUk8/FcLnZ/Psf8+79P8CODqzs5fL4qDvzAyxZrdXTMjoUwiLjXKynk9d/9GUOrnsWl8eHHY9RMnMRyz7zb1mvjjVePfqpcwi3Hsx4zuX1c/GPX8Ht1ZcZGXkTcnW0yGTizStk+RduJ9x+iJ6DuwmWVRMsr8l1s8aVSEfrEGcd4qEu3N7s3VIlohAWGUE9TXvo2LUJf3EFJY0LR2VxVKC4gkBxxYg/72SQV1lL9/4dGc+53F68+UVZbpFMdgphkREQ6+li7fe/wKG3X8Hl8eLYNv7iMk75/PcpbpiX6+aNa9GuNnY/9yDdB3ZSWDeLqadfgjfv2Mqrzr7sE7x55zdIRA+rqOULMH3VDbjc+kiU7NKcsMgIeOGfbqZl0+tpJSQ9eYWs/M4j+Apzs73geHdw3bO8+p2/wcHBjoZx+4MYhotT/+4OyueenPyZ9c/zzq++Q8eOjbh9AerO/ADzPvTZjO+54zi8/fNvs+2xX4BBcrW5YTDlpPdx8qe/rRCWUaOFWSKjpGP3Zp75x2vSVtxCcrHP3Ks+xewPpu9CJUOLdrby2GfOS92m1Z8nWMCF//kM+199nHU//uqAnzE8XgKlVZz7z78btMccat7H/tf+jJNIULloBYVTG0ftdYiAFmaJjJq2rRswDFfGc3YswqG3X1YIH4Ndzz042O7E2IkYz371Ojp3b067d9qJx4i0H2L7E79i9gduzfj4YHkNMy748Ai3WOToZf7kEJFh8+UXDb4AyzDwF6lU4rHo3r894+gCgB2N0Llr06C1tO1ohN3PPjCazRMZEQphkeNUeeKZyd2NMnD7AjScf22WWzQxFE6dhdt37Pv/Hm8NbpFsUAiLHCe318fSz/xbctFQv/rDbn+QaWdfkVpAJEenbsWl4Dq2W7xcXh+1p100wi0amh2PDbq3s8hgNCcsMgKql5zNOd+6jy0P/5TW99YTKKui8cIbqTxxRa6bNm5584s47Us/4uVv/xWO45CI9GB4vAPKdmZiuFx4ggXMuPCGrLSzffvbvPWz/0vLu2txHCiZuYiFH/l7ymYvycr1ZXzT6miRScCxEzRteIlI2yGKps2hePr8rF4/1t3BvlcfJ9rVRknjQsrnnzLsQibxcA97X36E0KG92Ik4W/74U+zDdknqY7jcVC05m0U3/yN5FbUj+RIyat+xkee+dgOJSM+A425fgNP/4X8om5O+t7hMTlodLTJJtb63jpf/9a+xoxEcHLAdCupmctqXfpSV/XV3P/8Qb/z3/8EwDOx4DJfHR17lVM74yp3Dur4nkEf9OVcAyft8D7z+FJ17tgzsERsuguVTOPf/PnDMhTyOxdu/+Ne0AAZIRMO89bN/5uxv/DprbZHxKStzwoZhrDYMY41hGGuampqycUkRASIdLbz4rVuJdrQQD3eTCPeQiIbo2LGRl/7fakZ7JKxj1ybW/ff/wY6GSURCOIk4iUgPXfu28cp3PnPUz2cYBmd85U4qF5yGy+vHk1eIy+unbO7JnGXdk9UAdhyHQxteGvR8+7a3M97jLNJfVnrCjuPcAdwByeHobFxTRGDHk/diJ+Jpx51EnK5922jb+halMxeN2vW3PPxT7AxzuE4iTvv2d+jcs/WoC2X4Cko47e/uINx6kO4DuwhW1GRl6DmjUagNLpOLVkeLTGAtm17HjkUyn3SgY+fGUb1+x853B71VyOX20L1/+zE/d6C0ivJ5S3MWwIZhULnoDJL1L9OVzDoRty+Q3UbJuKMQFpnAguVTMFyZ/5kbLteoFxLJq6obtLfo2AmC5VNG9fqj7YQP/y3uQJDDg9jtD7LwI18eseskohEOrnuOfWueOMJ2jDLeaGGWyAQ2/fxr2f3sA5nnJl0uqhafOarXn3nxTRx8/en06xsGwfIaihqyu0p7pBXVzeasr/+St3/+bZrefAHHcaiYfwon3PAlSmYsGJFr7HrmAdbf9fVUaVQ7HqXhvGtY+JEvD/oFS8YPhbDIBFY8fT6zL1vN5gfuIBGLgmPj8vgw3G5O+fz3cHl8o3r9sjknMfvyT7Dptz/CsRM4iThufx5uf4DlX7x9VPZbzraiutmc9nd3JBe5Oc6IBuOhDS+z/n++lvYlZudT9+HNL2Le1Ue/uE3GFt0nLDIJtG19i22P/oJQ8z5KZ53I9JXXZ3UouHPPVnY981si7c2Uz1tK7envx+M/9pKUk8XzX/8IzRszf156AvlcdMcLo/5FSkaG7hMWmcRKGhdy0ie/dVSP6Wnaw8H1z2PHIrj8AXz5xVQuOA1vftFRX79waiMnXP/Fo37cZNe+891BzzmOQ6h5P/nV9VlskYw0hbCIDODYCd7476+y54U/pIaQAQy3BwwXcy7/BHOu+KsxOZQcD/ew95VHCTXtIa96GrXLLxzXK5S9eYXEezoznnMSMbx5hVlukYw0hbCIDLDpgTvY++LDabc29YXxew/+mGBFLfVnX56D1g2ueeNaXv72J3DsZJ1pdyCPt+76Jqd9+cejei/0aJq+8jrevf8H2NGBfxaGy0XZ3KX4Cktz1DIZKVpaJyIpjp1g68N3DVnpKREJ8e5vvp/FVh1ZrKeLl//lE8RD3akykolwD7GeDl7654+P28pVjRd9lOL6ebj7zZ+7fAG8BSUsWf1POWyZjBT1hEUkJdbTSWKQzRH6Cx3ah52I43KPjY+QPS/+Ace2M56z7Th7X3mUaWd+MMutOn5un58VX/0Ze195lJ1P3UciGqZm2fnUn3s1voLiXDdPRsDY+BckIlnRvv0dtj/xK8ItByibezL1516Nv+gvQ5qeQD4YRx4gc/v8A/ZOzrXOPVtIRDN/eUiEe+jevzPLLRo5Lo+XujMuoe6MS3LdFBkFCmGRSWLjfbez5cGfYMejOLZN04YX2fzAHZzxlTspaVwI/OUDf/fzDw26Qb3h8TLt7MvH1MKs/OoG3L5AxmFntz+PvMqpOWiVyJFpTlhkEmh9bx1bHvwJiWg4NWxrRyPEQ128/K9/PWAod8FHvkx+zfQB85B9XL4A+dX1zL/uC1lr+3DUrbh00PKYhmFQe+qqjOccx6Ft61vseeEPtGx+Y9R3lRI5nHrCIpPAtkd/kayYlUEi3EPzxjVUnLAcAG9eAed88zfsf+3P7H3pj4Sa95OIRvAVlFB31geZetrFuH3+bDb/iHwFxZzyhe/z6r9/BhyHRDSc/BJhGJz6pR/iCeSlPabn0F5e/pdP0NO0B8PlwrEdAqWVnPqlH1FQMz37L0ImJYWwyCQQOrQXnMwLlwDCbQP3+XZ5vNQuv5Da5ReOdtNGTNWiFVzw/T+z+/mH6N6/g8KpjUw945KM99I6doLnv/4Rwi37B4wCdB/YyfNfv5GV33sSt1eVqGT0KYRFJoGSmYtoeW8dTqa9fe0ERXWzc9CqkecrKKZx1Q1H/LkDrz9NtKs9fUW14xCPhNj38iPUnfmBUWqlyF9oTlhkEphx4Q0Zbycy3B6K6udSVD8nB63KnfYd75AId2c8lwj30LrlzSy3SCYrhbDIJJBXOZXlX7gdT7AATyAfty+I2x+kqH4uy//2h7luXtb5CktxDVLO0uXxESipyHKLZLLScLTIJFG56AxW/eh5Dq57lmhHM8XTT0jdmjTZTD3tYjbc/S+ZTxoGdeOwsIeMTwphkUnE7fVRs+z8XDcj53yFpSy57Ru88eOv4sRjOHYCw+XG8HhZ+JG/z+o2jzK5KYRFZFKqO/MDFM84gW2P3E3Hrk0U1DYyY9WNFNfPzXXTZBJRCIvIpFU4dSYn3mLmuhkyiWlhloiISI4ohEVERHJEw9EiImNUpL2ZpjdfwMGhctEZBIp169REoxAWERljHMfhnV99h60P/xTDk/yYdhJxZlx4Ayd8+EtjagcrOT4ajhYRGWN2PHkv2x65GzseJRHuIRHuwY5F2f74L9n++D25bp6MIPWERUTGmE2//SGJSCjteCISYtNvf8SMCz6cg1YN1LZ1Axvv/S7NG9fi8nqpW/FB5lzxV/iLSnPdtHFFPWERkTHEsROEW/YPej7S3jzotpTZcujtV3j+6zdycN1zJCI9xLra2f74PTz9D1cQ7WzNadvGG4WwiMhYYrhwZ9j/uI/L68Pl8WaxQQM5jsMbd/wjiWgYcP5yPBEn0tHCe3+4M2dtG48UwiIiY4hhGDScexUuT/p+xi6Pj/pzrsjpwqyeg7vT9p/u48Rj7H7u91lu0fimOWERESDUvJ/3HvofDrz2JIbbw7SzLmPGqhvx5hVmvS3zrvkbDm1cQ/e+HSQiPQC4/XnkVdVxwnVfzHp7+rPjMQxj8P6bk4hnsTXjn0JYRCa9rr3beOar15KIhFIhsul3/8WOP/+Gc751H76Ckqy2xxPI5+yv/4r9a55g94t/AAemnn4xNaeszNhDzqaCmgbcPl/qy8EALjdVS87OfqPGMYWwiEx6635iEg91gfOXOU47FiHc2sSm+/+ThR/9h6y3yeXxUnvaRdSedlHWrz0Uw+XmhOu/xJt3faN3XvgvPL4Acy7/ZI5aNj5lZU7YMIzVhmGsMQxjTVNT5rkEEZFciPV00rLpjQEB3MdJxNilOc409edeyYm3WvhLKnF5/bg8XkpmLWbF135OfnV9rps3rmSlJ+w4zh3AHQDLli1L/5suIlnXtnUD2x79Od0Hd1Iy/QRmrLpxUn6AJiIhDJcLJzHI+Wgkuw0aJ6ad9UHqVlxKuK0Jt9eHr1D3Bx8LDUeLTEKbH/wxm+77QfJ+U8emdfM6djx5L0s/8+9MWfq+XDcvq/zFFXjzC4m0ZQ7bslmLs9yi8cNwuQiWVee6GeOablESmWQ692zl3d/cnpzPc2wguaI1EQ2z9vYvEg9nWHAzgRkuF/Ov+TxuXzDtnNsXYN41f5ODVslkoRAWmWR2PvUbHHuQsVfDYP/aJ7PboDGg/twrOeHDX8QTLMATyMftz8NfUsnSz/47ZXNOynXzZALTcLTIJBNuPTjovZxOPE60oyXLLRobZlx4Aw3nfYiOnZsxPB6K6mZjuNRPkdGlv2Eik0zZ7JNw+9OHXoFk+Eyfl+UWjR0uj4+SxgUU189VAEtW6G+ZyCRTd9ZluNzptYcNl5tgeQ3l807JQatEJieFsMgk480r4Iyv/i+B8im4A3nJOVBfkKL6uZzxD/+jDeNFskhzwiKTUHH9XC743pO0vLuWcMsBCmobKZ4+P9fNEpl0FMIik5RhGJTPW5brZohMahqOFhERyRGFsIiISI4ohEVERHJEISwiIpIjCmEREZEcUQiLiIjkiEJYREQkRxTCIiIiOaIQFhERyRGFsIiISI4ohEVERHJEISwiIpIjCmEREZEcUQiLiIjkiEJYREQkRxTCIiIiOaIQFhERyRGFsIiISI4ohEVERHJEISwiIpIjCmEREZEcUQiLiIjkiEJYREQkRxTCIiIiOaIQFhERyRGFsIiISI5kJYQNw1htGMYawzDWNDU1ZeOSIiIiY15WQthxnDscx1nmOM6yysrKbFxSRERkzNNwtIiISI4ohEVERHJEISwiIpIjCmEREZEcUQiLiIjkiEJYREQkRxTCIiIiOaIQFhERyRGFsIiISI4ohEVERHJEISwiIpIjCmEREZEcUQiLiIjkiEJYREQkRxTCIiIiOaIQFhERyRGFsIiISI4ohEVERHJEISwiIpIjCmEREZEcUQiLiIjkiEJYREQkRxTCIiIiOaIQFhERyRGFsIiISI4ohEVERHJEISwiIpIjCmEREZEcUQiLiIjkiEJYREQkRxTCIiIiOaIQFhERyRGFsIiISI4ohEVERHLEk42LGIaxGljd+9uIYRhvZeO6k1gFcCjXjZgE9D6PPr3Ho0/vcXbMzXTQcBwnq60wDGON4zjLsnrRSUbvcXbofR59eo9Hn97j7BjsfdZwtIiISI4ohEVERHIkFyF8Rw6uOdnoPc4Ovc+jT+/x6NN7nB0Z3+eszwmLiIhIkoajRUREckQhLCIikiMKYRERkRxRCIuIiOSIQlhERCRHslK2UkSOjmVZnwX+CnjNNM0bjvKx04EzTNP8xSi17dPA54CZQKVpmip5KHKM1BMWGZv+GrjgaAO413Tgw0f7IMuy3MP80eeBlcCOo72GiAyk+4RFxhjLsn4E3AK8C/wPyZv8vw8sBLzA10zTfKC3x/szIL/3oZ82TfMFy7JeAuYD24CfAq3AMtM0P937/A8B/2qa5lOWZXUB/0UyVD9FMsA/C/iAl4G/Nk0zMUg7t/c+r3rCIsdIPWGRMcY0zU8Ce4H3mab5HeArwJOmaS4H3gd827KsfOAgyd7yycC1wPd6n+LvgWdN01zS+/ih5AMvm6a5GGjufZ4VpmkuARLAsfTERWSYNCcsMvZdCHzQsqy/7f19AKgnGdS3W5a1hGRgzjmG504A9/X++nxgKfCqZVkAQZJBLyKjRCEsMvYZwFWmab7b/6BlWV8DDgCLSY5qhQd5fJyBo16Bfr8O9xtuNoCfmqb55ZFotIgcmYajRca+R4DPWJZlAFiWdVLv8WJgn2maNvARoG9hVSdQ2O/x24EllmW5LMuaBiwf5DpPAFdbllXVe50yy7IaRvSViMgACmGRse8bJBdkrbcsa0Pv7wH+E7jJsqx1wDygu/f4eiBhWdY6y7I+T3I18zbgbZLzxq9luohpmm8D/wg8alnWeuAxoObwn7Ms67OWZe0G6nrb9OOReZkik49WR4uIiOSIesIiIiI5ohAWERHJEYWwiIhIjiiERUREckQhLCIikiMKYRERkRxRCIuIiOSIQlhERCRH/n8hZhSDw0RDHAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Get contours describing the model\n", + "xx = np.linspace(-1, 4, 10)\n", + "yy = np.linspace(-2, 7, 10)\n", + "xy1, xy2 = np.meshgrid(xx, yy)\n", + "Z = np.array([clf.decision_function([t])\n", + " for t in zip(xy1.flat, xy2.flat)]).reshape(xy1.shape)\n", + "\n", + "# plot points and model\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "line_style = dict(levels = [-1.0, 0.0, 1.0],\n", + " linestyles = ['dashed', 'solid', 'dashed'],\n", + " colors = 'gray', linewidths=1)\n", + "ax.scatter(X[:, 0], X[:, 1], c=y, **point_style)\n", + "ax.contour(xy1, xy2, Z, **line_style)\n", + "\n", + "# format plot\n", + "format_plot(ax, 'Model Learned from Input Data')\n", + "ax.axis([-1, 4, -2, 7])\n", + "\n", + "fig.savefig('images/05.01-classification-2.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Classification Example Figure 3" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the results\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "\n", + "ax[0].scatter(X2[:, 0], X2[:, 1], c='gray', **point_style)\n", + "ax[0].axis([-1, 4, -2, 7])\n", + "\n", + "ax[1].scatter(X2[:, 0], X2[:, 1], c=y2, **point_style)\n", + "ax[1].contour(xy1, xy2, Z, **line_style)\n", + "ax[1].axis([-1, 4, -2, 7])\n", + "\n", + "format_plot(ax[0], 'Unknown Data')\n", + "format_plot(ax[1], 'Predicted Labels')\n", + "\n", + "fig.savefig('images/05.01-classification-3.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Regression Example Figures\n", + "\n", + "[Figure Context](05.01-What-Is-Machine-Learning.ipynb#Regression:-Predicting-Continuous-Labels)\n", + "\n", + "The following code generates the figures from the regression section." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "\n", + "# Create some data for the regression\n", + "rng = np.random.RandomState(1)\n", + "\n", + "X = rng.randn(200, 2)\n", + "y = np.dot(X, [-2, 1]) + 0.1 * rng.randn(X.shape[0])\n", + "\n", + "# fit the regression model\n", + "model = LinearRegression()\n", + "model.fit(X, y)\n", + "\n", + "# create some new points to predict\n", + "X2 = rng.randn(100, 2)\n", + "\n", + "# predict the labels\n", + "y2 = model.predict(X2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Regression Example Figure 1" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot data points\n", + "fig, ax = plt.subplots()\n", + "points = ax.scatter(X[:, 0], X[:, 1], c=y, s=50,\n", + " cmap='viridis')\n", + "\n", + "# format plot\n", + "format_plot(ax, 'Input Data')\n", + "ax.axis([-4, 4, -3, 3])\n", + "\n", + "fig.savefig('images/05.01-regression-1.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Regression Example Figure 2" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits.mplot3d.art3d import Line3DCollection\n", + "\n", + "points = np.hstack([X, y[:, None]]).reshape(-1, 1, 3)\n", + "segments = np.hstack([points, points])\n", + "segments[:, 0, 2] = -8\n", + "\n", + "# plot points in 3D\n", + "fig = plt.figure(figsize=(8, 6))\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "ax.scatter(X[:, 0], X[:, 1], y, c=y, s=35,\n", + " cmap='viridis')\n", + "ax.add_collection3d(Line3DCollection(segments, colors='gray', alpha=0.2))\n", + "ax.scatter(X[:, 0], X[:, 1], -8 + np.zeros(X.shape[0]), c=y, s=10,\n", + " cmap='viridis')\n", + "\n", + "# format plot\n", + "ax.patch.set_facecolor('white')\n", + "ax.view_init(elev=20, azim=-70)\n", + "ax.set_zlim3d(-8, 8)\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.yaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.zaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.set(xlabel='feature 1', ylabel='feature 2', zlabel='label')\n", + "\n", + "# Hide axes (is there a better way?)\n", + "ax.w_xaxis.line.set_visible(False)\n", + "ax.w_yaxis.line.set_visible(False)\n", + "ax.w_zaxis.line.set_visible(False)\n", + "for tick in ax.w_xaxis.get_ticklines():\n", + " tick.set_visible(False)\n", + "for tick in ax.w_yaxis.get_ticklines():\n", + " tick.set_visible(False)\n", + "for tick in ax.w_zaxis.get_ticklines():\n", + " tick.set_visible(False)\n", + "ax.grid(False)\n", + "\n", + "fig.savefig('images/05.01-regression-2.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Regression Example Figure 3" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from matplotlib.collections import LineCollection\n", + "\n", + "# plot data points\n", + "fig, ax = plt.subplots()\n", + "pts = ax.scatter(X[:, 0], X[:, 1], c=y, s=50,\n", + " cmap='viridis', zorder=2)\n", + "\n", + "# compute and plot model color mesh\n", + "xx, yy = np.meshgrid(np.linspace(-4, 4),\n", + " np.linspace(-3, 3))\n", + "Xfit = np.vstack([xx.ravel(), yy.ravel()]).T\n", + "yfit = model.predict(Xfit)\n", + "zz = yfit.reshape(xx.shape)\n", + "ax.pcolorfast([-4, 4], [-3, 3], zz, alpha=0.5,\n", + " cmap='viridis', norm=pts.norm, zorder=1)\n", + "\n", + "# format plot\n", + "format_plot(ax, 'Input Data with Linear Fit')\n", + "ax.axis([-4, 4, -3, 3])\n", + "\n", + "fig.savefig('images/05.01-regression-3.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Regression Example Figure 4" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the model fit\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "\n", + "ax[0].scatter(X2[:, 0], X2[:, 1], c='gray', s=50)\n", + "ax[0].axis([-4, 4, -3, 3])\n", + "\n", + "ax[1].scatter(X2[:, 0], X2[:, 1], c=y2, s=50,\n", + " cmap='viridis', norm=pts.norm)\n", + "ax[1].axis([-4, 4, -3, 3])\n", + "\n", + "# format plots\n", + "format_plot(ax[0], 'Unknown Data')\n", + "format_plot(ax[1], 'Predicted Labels')\n", + "\n", + "fig.savefig('images/05.01-regression-4.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Clustering Example Figures\n", + "\n", + "[Figure context](#Clustering:-Inferring-Labels-on-Unlabeled-Data)\n", + "\n", + "The following code generates the figures from the clustering section." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.datasets import make_blobs\n", + "from sklearn.cluster import KMeans\n", + "\n", + "# create 50 separable points\n", + "X, y = make_blobs(n_samples=100, centers=4,\n", + " random_state=42, cluster_std=1.5)\n", + "\n", + "# Fit the K Means model\n", + "model = KMeans(4, random_state=0)\n", + "y = model.fit_predict(X)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Clustering Example Figure 1" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the input data\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "ax.scatter(X[:, 0], X[:, 1], s=50, color='gray')\n", + "\n", + "# format the plot\n", + "format_plot(ax, 'Input Data')\n", + "\n", + "fig.savefig('images/05.01-clustering-1.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Clustering Example Figure 2" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the data with cluster labels\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "ax.scatter(X[:, 0], X[:, 1], s=50, c=y, cmap='viridis')\n", + "\n", + "# format the plot\n", + "format_plot(ax, 'Learned Cluster Labels')\n", + "\n", + "fig.savefig('images/05.01-clustering-2.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Dimensionality Reduction Example Figures\n", + "\n", + "[Figure context](05.01-What-Is-Machine-Learning.ipynb#Dimensionality-Reduction:-Inferring-Structure-of-Unlabeled-Data)\n", + "\n", + "The following code generates the figures from the dimensionality reduction section." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Dimensionality Reduction Example Figure 1" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_swiss_roll\n", + "\n", + "# make data\n", + "X, y = make_swiss_roll(200, noise=0.5, random_state=42)\n", + "X = X[:, [0, 2]]\n", + "\n", + "# visualize data\n", + "fig, ax = plt.subplots()\n", + "ax.scatter(X[:, 0], X[:, 1], color='gray', s=30)\n", + "\n", + "# format the plot\n", + "format_plot(ax, 'Input Data')\n", + "\n", + "fig.savefig('images/05.01-dimesionality-1.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Dimensionality Reduction Example Figure 2" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.manifold import Isomap\n", + "\n", + "model = Isomap(n_neighbors=8, n_components=1)\n", + "y_fit = model.fit_transform(X).ravel()\n", + "\n", + "# visualize data\n", + "fig, ax = plt.subplots()\n", + "pts = ax.scatter(X[:, 0], X[:, 1], c=y_fit, cmap='viridis', s=30)\n", + "cb = fig.colorbar(pts, ax=ax)\n", + "\n", + "# format the plot\n", + "format_plot(ax, 'Learned Latent Parameter')\n", + "cb.set_ticks([])\n", + "cb.set_label('Latent Variable', color='gray')\n", + "\n", + "fig.savefig('images/05.01-dimesionality-2.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Introducing Scikit-Learn" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Features and Labels Grid\n", + "\n", + "The following is the code generating the diagram showing the features matrix and target array." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(6, 4))\n", + "ax = fig.add_axes([0, 0, 1, 1])\n", + "ax.axis('off')\n", + "ax.axis('equal')\n", + "\n", + "# Draw features matrix\n", + "ax.vlines(range(6), ymin=0, ymax=9, lw=1, color='black')\n", + "ax.hlines(range(10), xmin=0, xmax=5, lw=1, color='black')\n", + "font_prop = dict(size=12, family='monospace')\n", + "ax.text(-1, -1, \"Feature Matrix ($X$)\", size=14)\n", + "ax.text(0.1, -0.3, r'n_features $\\longrightarrow$', **font_prop)\n", + "ax.text(-0.1, 0.1, r'$\\longleftarrow$ n_samples', rotation=90,\n", + " va='top', ha='right', **font_prop)\n", + "\n", + "# Draw labels vector\n", + "ax.vlines(range(8, 10), ymin=0, ymax=9, lw=1, color='black')\n", + "ax.hlines(range(10), xmin=8, xmax=9, lw=1, color='black')\n", + "ax.text(7, -1, \"Target Vector ($y$)\", size=14)\n", + "ax.text(7.9, 0.1, r'$\\longleftarrow$ n_samples', rotation=90,\n", + " va='top', ha='right', **font_prop)\n", + "\n", + "ax.set_ylim(10, -2)\n", + "\n", + "fig.savefig('images/05.02-samples-features.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Hyperparameters and Model Validation" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Cross-Validation Figures" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "def draw_rects(N, ax, textprop={}):\n", + " for i in range(N):\n", + " ax.add_patch(plt.Rectangle((0, i), 5, 0.7, fc='white', ec='lightgray'))\n", + " ax.add_patch(plt.Rectangle((5. * i / N, i), 5. / N, 0.7, fc='lightgray'))\n", + " ax.text(5. * (i + 0.5) / N, i + 0.35,\n", + " \"validation\\nset\", ha='center', va='center', **textprop)\n", + " ax.text(0, i + 0.35, \"trial {0}\".format(N - i),\n", + " ha='right', va='center', rotation=90, **textprop)\n", + " ax.set_xlim(-1, 6)\n", + " ax.set_ylim(-0.2, N + 0.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 2-Fold Cross-Validation" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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jJO0wxjzeaZMISTd7MRsAwBt9vR7gGlsgqchaWyFJxpipkv63Maa/tbbc08kAAJ4I61d8kv5GUvWFb6y1/y5psqSVxpj5nk3Vy8yePVurVq267PeXMm3aNL300ktXfd8AcK2F+yu+k5JukvTVhQXW2g+MMVMkbZE03KO5erUXX3xRffte3b8amzdv1urVq/Xxxx9f830BwK8J939xPpb03yV92HmhtXZ7x2HPLZ5M1ctFR0eH5b4AQAr/Q53/U9KZS62w1v5fSVMl/a+QTnSVVVZWasKECfr555+7LF+8eLGKiorU2NiooqIiZWVlKSMjQ7m5udq2bduvPubFhx+PHz+uoqIipaWlKScnR5s2bep2n9dff13Tp09XRkaGJk6cqJKSEp06dUqStGvXLi1fvlxnzpxRSkqKUlJSgodJL97XyZMnVVxcrLvuuktpaWmaO3euvvzyy+D6zZs3KyMjQx999JGmTZumjIwMzZkzR01NTVf+5AFwUliHz1q7zVr77K+sr7XWzg7lTFdbTk6OWlpa9OGHv7yobW1tVW1traZMmaLW1laNGzdOL7/8st5++21NmjRJCxYsUENDz8/iWLZsmRobG/XKK69o3bp1evfdd3X06NEu2/Tp00dLlizRpk2b9Nxzz2nfvn169tnzT31qaqqWLFmiqKgo1dTUqKamRvn5+Zfd12effab169frzTffVFRUlAoKCnT27NngNn6/Xxs2bFBpaaneeOMNNTc3q6ys7AqeNQAuC+vwuSA6Olrjxo1TVVVVcNnWrVsVERGh7Oxs+Xw+5ebmasyYMUpISNDjjz+uW2+9Ve+//36PHv+rr77S9u3bVVJSojvuuENJSUlatWqVzp0712W7vLw8ZWZmKj4+Xunp6XryySf13nvvKRAIKDIyUoMHD5YkxcbGKjY2VgMHDuy2ryNHjqi2tlYlJSVKS0vTmDFjtHr1ap0+fbrLz9fe3q7i4mKlpKTI5/Np1qxZ2rVrl6y1v+cpBOCYcH+PzwlTp05VcXGxzpw5o6ioKFVVVWnSpEnq37+/WltbVVFRoW3btunYsWNqb29XW1ubRo8e3aPHbmhoUJ8+fZScnBxcNnz4cN14441dttu5c6c2bNighoYGtbS0KBAIyO/364cfflBcXNwV7ev2228PLhsyZIhGjx6tQ4cOBZf169dPiYmJwe/j4uLk9/t16tQp3jME8JsIXxgYP368IiIiVFNTo8zMTO3cuVMVFRWSpLVr1+qDDz7QwoULlZCQoKioKC1dulR+v/+K9mGMuey6b775RvPmzdODDz6oefPmaejQoTp48KAWL158xfvpyf4jIiIuuS4QCFyVfQEIbxzqDAP9+vVTTk6OqqqqVF1drZiYGKWnp0uS9uzZo/vuu0/33HOPfD6fhg0bpsbGxh4/dmJiogKBgOrq6oLLvv32Wx07diz4/f79++X3+7V48WKlpqZq5MiR+v7777s8TmRk5G+GadSoUQoEAvr000+Dy1paWlRfX69bbrmlxzMDwK8hfGFi6tSp2rFjhyorKzV58mT16XP+P+3IkSO1detWHThwQF988YWefvpptbW19fhxExMTdffdd2vFihXau3evPv/8cy1btkz9+/cPbpOQkKBAIKCNGzeqqalJW7Zs0caNG7s8Tnx8vM6dO6cdO3boxIkTOnOm+4dtb775ZmVnZ6u0tFSffPJJcN5BgwZp8uTJv/OZAYCuwvZQpzFmfU+3tdb+07WcJRTGjh2ruLg4HTp0SGvWrAkuX7RokZ555hnl5+dryJAhysvL6/bBlN+ycuVKrVixQnPnztXQoUNVWFioH3/8Mbje5/Ppqaee0quvvqry8nKlpqZq4cKFWrRoUXCb1NRU5ebmasmSJfrpp59UWFioJ554otu+ysrK9Pzzz6uoqEhtbW1KTU1VRUWFBgwY8DueFQDozoTrJ+GMMTU93NRaa/+u84K6urrwfFLQq3T+wBBwrdTV1Sk5Ofnyb9I7KGxf8Vlrs72eAQDQ+/AeHwDAKWH7iu9ixpgxkv5eUoKkfp3XWWvneDIUACDknAhfx9UY/k3Sf0oaK2mXpFsk9Zf0Hx6OBgAIMVcOdZZKWmGtvVPSOUl5kkZK+oukWu/GAgCEmivh80n6147bfkkDrbVndT6IC7waygVcaBZAb+NK+JolXTgR7FudvzK7dP5Q7w2eTAQA8IQr4dsp6Y8dt6skrTXGlEj6ky66SC262717tx555BFlZGTozjvv1MMPP6z6+npJ0t69e5Wfn6/09HRNnDhRZWVlamlpkSQVFxdr9+7deuutt4LX4bv4ckYAEGphewJ7Z8aYUZIGW2s/M8YMlLRW0t2SvpD0pLX2687bcwL7L9rb2zV+/HhNnz5dDz30kPx+vw4ePKikpCS1t7dr5syZmjdvnrKysnTy5EmtWbNGw4YN0wsvvKDm5mYVFhYqMTFR8+fPlyTdcMMN3X7JtKs4gR2hwAns3TnxqU5rbUOn262SCj0c57py+vRpNTc3a8KECRoxYoSk879MWpKWLl2qe++9V7NmzQpuv3z5cs2YMUPHjx9XTEyMIiMjNWDAAMXGxnoyPwBczInw4feLjo7W/fffr4KCAmVmZiozM1M5OTm66aabdODAAX399deqrq7udr/GxkbFxMR4MDEA/LqwDZ8x5pSkUdbaH4wxzZIue/jSWvtXoZvs+rNy5Url5eVp+/btqq2tVXl5udatW6dAIKDp06fr0Ucf7Xafnl58FgBCLWzDJ6lI5z/NKUn/6OUg4cDn88nn8+mxxx5TQUGB3nnnHSUlJenQoUNKSEi47P16ch0+AAilsA2ftfZ1STLG9JV0TNJOa+1xb6e6/jQ1NamyslLZ2dmKi4tTU1OT6uvrlZubq6ysLM2cOVOlpaWaMWOGBg0apMOHD6u2tlYlJSWSpOHDh2vfvn06evSoBg4cqOjo6OC1AgHAC2Ebvguste3GmD9L+ltJhO8KDRgwQEeOHNHChQt14sQJxcTEaMqUKZozZ44iIyP12muvqby8XLNnz1YgEFB8fLwmTpwYvH9+fr6Ki4v1wAMP6OzZs6qurlZ8fLyHPxEA17lyOsNOScXW2r/0ZHtOZ0AocDoDQoHTGbpz5ZjTP+v8SesPGGNGGGP+0PmP18MBAEIn7A91dqjq+Ppndf10p+n4njOqAcARroSPq7EDACS5E77DkhrtRW9oGmOMpBHejAQA8IIr7/EdlnTjJZb/oWMdAMARroTvwnt5Fxss6WyIZwEAeCisD3UaY9Z33LSSnjXGtHZaHSEpQ9LeUM8FAPBOWIdPUkrHVyMpSVJbp3VtkvZI+pdQDwUA8E5Yh89amy1Jxpg/SZpvrT3l8UgAAI+FdfgusNbO9noGAEDv4MqHWwAAkET4AACOIXwAAKcQPgCAUwgfAMAphA8A4BTCBwBwCuEDADiF8AEAnEL4AABOIXwAAKcQPgCAUwgfAMAphA8A4BTCBwBwCuEDADiF8AEAnEL4AABOIXwAAKf09XqA3sgY8521dpjXcyC81dXVeT0CHGCM+c7rGXobY631egYAAEKGQ50AAKcQPgCAUwgfAMAphA8A4BTCBwBwCuEDADiF8AEAnEL4AABOIXwAAKcQPgCAUwgfAMAphA8A4BTCBwBwCuEDADiF8AEAnEL4AABOIXwAAKcQPgCAUwgfAMAphA8A4BTCBwBwCuEDADiF8AEAnEL4AABOIXwAAKcQPgCAUwgfAMAphA8A4BTCBwBwyv8HToPaLrYzOxcAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_axes([0, 0, 1, 1])\n", + "ax.axis('off')\n", + "draw_rects(2, ax, textprop=dict(size=14))\n", + "\n", + "fig.savefig('images/05.03-2-fold-CV.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 5-Fold Cross-Validation" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(8, 5))\n", + "ax = fig.add_axes([0, 0, 1, 1])\n", + "ax.axis('off')\n", + "draw_rects(5, ax, textprop=dict(size=10))\n", + "\n", + "fig.savefig('images/05.03-5-fold-CV.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Overfitting and Underfitting" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "def make_data(N=30, err=0.8, rseed=1):\n", + " # randomly sample the data\n", + " rng = np.random.RandomState(rseed)\n", + " X = rng.rand(N, 1) ** 2\n", + " y = 10 - 1. / (X.ravel() + 0.1)\n", + " if err > 0:\n", + " y += err * rng.randn(N)\n", + " return X, y" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.pipeline import make_pipeline\n", + "\n", + "def PolynomialRegression(degree=2, **kwargs):\n", + " return make_pipeline(PolynomialFeatures(degree),\n", + " LinearRegression(**kwargs))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Bias-Variance Tradeoff" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "X, y = make_data()\n", + "xfit = np.linspace(-0.1, 1.0, 1000)[:, None]\n", + "model1 = PolynomialRegression(1).fit(X, y)\n", + "model20 = PolynomialRegression(20).fit(X, y)\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "\n", + "ax[0].scatter(X.ravel(), y, s=40)\n", + "ax[0].plot(xfit.ravel(), model1.predict(xfit), color='gray')\n", + "ax[0].axis([-0.1, 1.0, -2, 14])\n", + "ax[0].set_title('High-bias model: Underfits the data', size=14)\n", + "\n", + "ax[1].scatter(X.ravel(), y, s=40)\n", + "ax[1].plot(xfit.ravel(), model20.predict(xfit), color='gray')\n", + "ax[1].axis([-0.1, 1.0, -2, 14])\n", + "ax[1].set_title('High-variance model: Overfits the data', size=14)\n", + "\n", + "fig.savefig('images/05.03-bias-variance.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Bias-Variance Tradeoff Metrics" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "\n", + "X2, y2 = make_data(10, rseed=42)\n", + "\n", + "ax[0].scatter(X.ravel(), y, s=40, c='blue')\n", + "ax[0].plot(xfit.ravel(), model1.predict(xfit), color='gray')\n", + "ax[0].axis([-0.1, 1.0, -2, 14])\n", + "ax[0].set_title('High-bias model: Underfits the data', size=14)\n", + "ax[0].scatter(X2.ravel(), y2, s=40, c='red')\n", + "ax[0].text(0.02, 0.98, \"training score: $R^2$ = {0:.2f}\".format(model1.score(X, y)),\n", + " ha='left', va='top', transform=ax[0].transAxes, size=14, color='blue')\n", + "ax[0].text(0.02, 0.91, \"validation score: $R^2$ = {0:.2f}\".format(model1.score(X2, y2)),\n", + " ha='left', va='top', transform=ax[0].transAxes, size=14, color='red')\n", + "\n", + "ax[1].scatter(X.ravel(), y, s=40, c='blue')\n", + "ax[1].plot(xfit.ravel(), model20.predict(xfit), color='gray')\n", + "ax[1].axis([-0.1, 1.0, -2, 14])\n", + "ax[1].set_title('High-variance model: Overfits the data', size=14)\n", + "ax[1].scatter(X2.ravel(), y2, s=40, c='red')\n", + "ax[1].text(0.02, 0.98, \"training score: $R^2$ = {0:.2g}\".format(model20.score(X, y)),\n", + " ha='left', va='top', transform=ax[1].transAxes, size=14, color='blue')\n", + "ax[1].text(0.02, 0.91, \"validation score: $R^2$ = {0:.2g}\".format(model20.score(X2, y2)),\n", + " ha='left', va='top', transform=ax[1].transAxes, size=14, color='red')\n", + "\n", + "fig.savefig('images/05.03-bias-variance-2.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Validation Curve" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 1, 1000)\n", + "y1 = -(x - 0.5) ** 2\n", + "y2 = y1 - 0.33 + np.exp(x - 1)\n", + "\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "ax.plot(x, y2, lw=10, alpha=0.5, color='blue')\n", + "ax.plot(x, y1, lw=10, alpha=0.5, color='red')\n", + "\n", + "ax.text(0.15, 0.05, \"training score\", rotation=45, size=16, color='blue')\n", + "ax.text(0.2, -0.05, \"validation score\", rotation=20, size=16, color='red')\n", + "\n", + "ax.text(0.02, 0.1, r'$\\longleftarrow$ High Bias', size=18, rotation=90, va='center')\n", + "ax.text(0.98, 0.1, r'$\\longleftarrow$ High Variance $\\longrightarrow$', size=18, rotation=90, ha='right', va='center')\n", + "ax.text(0.48, -0.12, 'Best$\\\\longrightarrow$\\nModel', size=18, rotation=90, va='center')\n", + "\n", + "ax.set_xlim(0, 1)\n", + "ax.set_ylim(-0.3, 0.5)\n", + "\n", + "ax.set_xlabel(r'model complexity $\\longrightarrow$', size=14)\n", + "ax.set_ylabel(r'model score $\\longrightarrow$', size=14)\n", + "\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.yaxis.set_major_formatter(plt.NullFormatter())\n", + "\n", + "ax.set_title(\"Validation Curve Schematic\", size=16)\n", + "\n", + "fig.savefig('images/05.03-validation-curve.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Learning Curve" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "N = np.linspace(0, 1, 1000)\n", + "y1 = 0.75 + 0.2 * np.exp(-4 * N)\n", + "y2 = 0.7 - 0.6 * np.exp(-4 * N)\n", + "\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "ax.plot(x, y1, lw=10, alpha=0.5, color='blue')\n", + "ax.plot(x, y2, lw=10, alpha=0.5, color='red')\n", + "\n", + "ax.text(0.2, 0.83, \"training score\", rotation=-10, size=16, color='blue')\n", + "ax.text(0.2, 0.5, \"validation score\", rotation=30, size=16, color='red')\n", + "\n", + "ax.text(0.98, 0.45, r'Good Fit $\\longrightarrow$', size=18, rotation=90, ha='right', va='center')\n", + "ax.text(0.02, 0.57, r'$\\longleftarrow$ High Variance $\\longrightarrow$', size=18, rotation=90, va='center')\n", + "\n", + "ax.set_xlim(0, 1)\n", + "ax.set_ylim(0, 1)\n", + "\n", + "ax.set_xlabel(r'training set size $\\longrightarrow$', size=14)\n", + "ax.set_ylabel(r'model score $\\longrightarrow$', size=14)\n", + "\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.yaxis.set_major_formatter(plt.NullFormatter())\n", + "\n", + "ax.set_title(\"Learning Curve Schematic\", size=16)\n", + "\n", + "fig.savefig('images/05.03-learning-curve.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Gaussian Naive Bayes\n", + "\n", + "### Gaussian Naive Bayes Example\n", + "\n", + "[Figure Context](05.05-Naive-Bayes.ipynb#Gaussian-Naive-Bayes)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_blobs\n", + "X, y = make_blobs(100, 2, centers=2, random_state=2, cluster_std=1.5)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu')\n", + "ax.set_title('Naive Bayes Model', size=14)\n", + "\n", + "xlim = (-8, 8)\n", + "ylim = (-15, 5)\n", + "\n", + "xg = np.linspace(xlim[0], xlim[1], 60)\n", + "yg = np.linspace(ylim[0], ylim[1], 40)\n", + "xx, yy = np.meshgrid(xg, yg)\n", + "Xgrid = np.vstack([xx.ravel(), yy.ravel()]).T\n", + "\n", + "for label, color in enumerate(['red', 'blue']):\n", + " mask = (y == label)\n", + " mu, std = X[mask].mean(0), X[mask].std(0)\n", + " P = np.exp(-0.5 * (Xgrid - mu) ** 2 / std ** 2).prod(1)\n", + " Pm = np.ma.masked_array(P, P < 0.03)\n", + " ax.pcolorfast(xg, yg, Pm.reshape(xx.shape), alpha=0.5,\n", + " cmap=color.title() + 's')\n", + " ax.contour(xx, yy, P.reshape(xx.shape),\n", + " levels=[0.01, 0.1, 0.5, 0.9],\n", + " colors=color, alpha=0.2)\n", + " \n", + "ax.set(xlim=xlim, ylim=ylim)\n", + "\n", + "fig.savefig('images/05.05-gaussian-NB.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Linear Regression\n", + "\n", + "### Gaussian Basis Functions\n", + "\n", + "[Figure Context](05.06-Linear-Regression.ipynb#Gaussian-Basis-Functions)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.linear_model import LinearRegression\n", + "\n", + "from sklearn.base import BaseEstimator, TransformerMixin\n", + "\n", + "class GaussianFeatures(BaseEstimator, TransformerMixin):\n", + " \"\"\"Uniformly-spaced Gaussian Features for 1D input\"\"\"\n", + " \n", + " def __init__(self, N, width_factor=2.0):\n", + " self.N = N\n", + " self.width_factor = width_factor\n", + " \n", + " @staticmethod\n", + " def _gauss_basis(x, y, width, axis=None):\n", + " arg = (x - y) / width\n", + " return np.exp(-0.5 * np.sum(arg ** 2, axis))\n", + " \n", + " def fit(self, X, y=None):\n", + " # create N centers spread along the data range\n", + " self.centers_ = np.linspace(X.min(), X.max(), self.N)\n", + " self.width_ = self.width_factor * (self.centers_[1] - self.centers_[0])\n", + " return self\n", + " \n", + " def transform(self, X):\n", + " return self._gauss_basis(X[:, :, np.newaxis], self.centers_,\n", + " self.width_, axis=1)\n", + "\n", + "rng = np.random.RandomState(1)\n", + "x = 10 * rng.rand(50)\n", + "y = np.sin(x) + 0.1 * rng.randn(50)\n", + "xfit = np.linspace(0, 10, 1000)\n", + "\n", + "gauss_model = make_pipeline(GaussianFeatures(10, 1.0),\n", + " LinearRegression())\n", + "gauss_model.fit(x[:, np.newaxis], y)\n", + "yfit = gauss_model.predict(xfit[:, np.newaxis])\n", + "\n", + "gf = gauss_model.named_steps['gaussianfeatures']\n", + "lm = gauss_model.named_steps['linearregression']\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "for i in range(10):\n", + " selector = np.zeros(10)\n", + " selector[i] = 1\n", + " Xfit = gf.transform(xfit[:, None]) * selector\n", + " yfit = lm.predict(Xfit)\n", + " ax.fill_between(xfit, yfit.min(), yfit, color='gray', alpha=0.2)\n", + "\n", + "ax.scatter(x, y)\n", + "ax.plot(xfit, gauss_model.predict(xfit[:, np.newaxis]))\n", + "ax.set_xlim(0, 10)\n", + "ax.set_ylim(yfit.min(), 1.5)\n", + "\n", + "fig.savefig('images/05.06-gaussian-basis.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Random Forests" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Helper Code\n", + "\n", + "The following will create a module ``helpers_05_08.py`` which contains some tools used in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting helpers_05_08.py\n" + ] + } + ], + "source": [ + "%%file helpers_05_08.py\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.tree import DecisionTreeClassifier\n", + "from ipywidgets import interact\n", + "\n", + "\n", + "def visualize_tree(estimator, X, y, boundaries=True,\n", + " xlim=None, ylim=None, ax=None):\n", + " ax = ax or plt.gca()\n", + " \n", + " # Plot the training points\n", + " ax.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap='viridis',\n", + " clim=(y.min(), y.max()), zorder=3)\n", + " ax.axis('tight')\n", + " ax.axis('off')\n", + " if xlim is None:\n", + " xlim = ax.get_xlim()\n", + " if ylim is None:\n", + " ylim = ax.get_ylim()\n", + " \n", + " # fit the estimator\n", + " estimator.fit(X, y)\n", + " xx, yy = np.meshgrid(np.linspace(*xlim, num=200),\n", + " np.linspace(*ylim, num=200))\n", + " Z = estimator.predict(np.c_[xx.ravel(), yy.ravel()])\n", + "\n", + " # Put the result into a color plot\n", + " n_classes = len(np.unique(y))\n", + " Z = Z.reshape(xx.shape)\n", + " contours = ax.contourf(xx, yy, Z, alpha=0.3,\n", + " levels=np.arange(n_classes + 1) - 0.5,\n", + " cmap='viridis', zorder=1)\n", + "\n", + " ax.set(xlim=xlim, ylim=ylim)\n", + " \n", + " # Plot the decision boundaries\n", + " def plot_boundaries(i, xlim, ylim):\n", + " if i >= 0:\n", + " tree = estimator.tree_\n", + " \n", + " if tree.feature[i] == 0:\n", + " ax.plot([tree.threshold[i], tree.threshold[i]], ylim, '-k', zorder=2)\n", + " plot_boundaries(tree.children_left[i],\n", + " [xlim[0], tree.threshold[i]], ylim)\n", + " plot_boundaries(tree.children_right[i],\n", + " [tree.threshold[i], xlim[1]], ylim)\n", + " \n", + " elif tree.feature[i] == 1:\n", + " ax.plot(xlim, [tree.threshold[i], tree.threshold[i]], '-k', zorder=2)\n", + " plot_boundaries(tree.children_left[i], xlim,\n", + " [ylim[0], tree.threshold[i]])\n", + " plot_boundaries(tree.children_right[i], xlim,\n", + " [tree.threshold[i], ylim[1]])\n", + " \n", + " if boundaries:\n", + " plot_boundaries(0, xlim, ylim)\n", + "\n", + "\n", + "def plot_tree_interactive(X, y):\n", + " def interactive_tree(depth=5):\n", + " clf = DecisionTreeClassifier(max_depth=depth, random_state=0)\n", + " visualize_tree(clf, X, y)\n", + "\n", + " return interact(interactive_tree, depth=(1, 5))\n", + "\n", + "\n", + "def randomized_tree_interactive(X, y):\n", + " N = int(0.75 * X.shape[0])\n", + " \n", + " xlim = (X[:, 0].min(), X[:, 0].max())\n", + " ylim = (X[:, 1].min(), X[:, 1].max())\n", + " \n", + " def fit_randomized_tree(random_state=0):\n", + " clf = DecisionTreeClassifier(max_depth=15)\n", + " i = np.arange(len(y))\n", + " rng = np.random.RandomState(random_state)\n", + " rng.shuffle(i)\n", + " visualize_tree(clf, X[i[:N]], y[i[:N]], boundaries=False,\n", + " xlim=xlim, ylim=ylim)\n", + " \n", + " interact(fit_randomized_tree, random_state=(0, 100));" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Decision Tree Example" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(10, 4))\n", + "ax = fig.add_axes([0, 0, 0.8, 1], frameon=False, xticks=[], yticks=[])\n", + "ax.set_title('Example Decision Tree: Animal Classification', size=24)\n", + "\n", + "def text(ax, x, y, t, size=20, **kwargs):\n", + " ax.text(x, y, t,\n", + " ha='center', va='center', size=size,\n", + " bbox=dict(boxstyle='round', ec='k', fc='w'), **kwargs)\n", + "\n", + "text(ax, 0.5, 0.9, \"How big is\\nthe animal?\", 20)\n", + "text(ax, 0.3, 0.6, \"Does the animal\\nhave horns?\", 18)\n", + "text(ax, 0.7, 0.6, \"Does the animal\\nhave two legs?\", 18)\n", + "text(ax, 0.12, 0.3, \"Are the horns\\nlonger than 10cm?\", 14)\n", + "text(ax, 0.38, 0.3, \"Is the animal\\nwearing a collar?\", 14)\n", + "text(ax, 0.62, 0.3, \"Does the animal\\nhave wings?\", 14)\n", + "text(ax, 0.88, 0.3, \"Does the animal\\nhave a tail?\", 14)\n", + "\n", + "text(ax, 0.4, 0.75, \"> 1m\", 12, alpha=0.6)\n", + "text(ax, 0.6, 0.75, \"< 1m\", 12, alpha=0.6)\n", + "\n", + "text(ax, 0.21, 0.45, \"yes\", 12, alpha=0.6)\n", + "text(ax, 0.34, 0.45, \"no\", 12, alpha=0.6)\n", + "\n", + "text(ax, 0.66, 0.45, \"yes\", 12, alpha=0.6)\n", + "text(ax, 0.79, 0.45, \"no\", 12, alpha=0.6)\n", + "\n", + "ax.plot([0.3, 0.5, 0.7], [0.6, 0.9, 0.6], '-k')\n", + "ax.plot([0.12, 0.3, 0.38], [0.3, 0.6, 0.3], '-k')\n", + "ax.plot([0.62, 0.7, 0.88], [0.3, 0.6, 0.3], '-k')\n", + "ax.plot([0.0, 0.12, 0.20], [0.0, 0.3, 0.0], '--k')\n", + "ax.plot([0.28, 0.38, 0.48], [0.0, 0.3, 0.0], '--k')\n", + "ax.plot([0.52, 0.62, 0.72], [0.0, 0.3, 0.0], '--k')\n", + "ax.plot([0.8, 0.88, 1.0], [0.0, 0.3, 0.0], '--k')\n", + "ax.axis([0, 1, 0, 1])\n", + "\n", + "fig.savefig('images/05.08-decision-tree.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Decision Tree Levels" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from helpers_05_08 import visualize_tree\n", + "from sklearn.tree import DecisionTreeClassifier\n", + "from sklearn.datasets import make_blobs\n", + "\n", + " \n", + "fig, ax = plt.subplots(1, 4, figsize=(16, 3))\n", + "fig.subplots_adjust(left=0.02, right=0.98, wspace=0.1)\n", + "\n", + "X, y = make_blobs(n_samples=300, centers=4,\n", + " random_state=0, cluster_std=1.0)\n", + "\n", + "for axi, depth in zip(ax, range(1, 5)):\n", + " model = DecisionTreeClassifier(max_depth=depth)\n", + " visualize_tree(model, X, y, ax=axi)\n", + " axi.set_title('depth = {0}'.format(depth))\n", + "\n", + "fig.savefig('images/05.08-decision-tree-levels.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Decision Tree Overfitting" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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efdd2QghRNNsi9zcbvPA8MDwiEDOYgWhb5P426WxJ6bF6IAS2eoxVY2YZ0BORe39iwYqMwHhKOvu2SuKnMRAtc2JnkMPbb8ymv34iPnwQQsw+UjAoUYudaOFKN/qEovz2gy4wf7ETfzhk+sTjkfdo0vlmm4BVFABR0jmSdn+YumNnbB5a7kanG6Zwc+TeJ+tMhRDiyHbF7h4H+MgKN3ydCywJGTu3R96Pdsfu3qSzJenewP/iRj/4pGbMBWABxE9E7mdn05a9p3nhBRXETyWCS8gvSykDn3eGHzzyjyB1fdL5hBDieEnBoEQtd6PnDn/xDFMEf5ETXykFAzGVeqweuDfQtySdQwghZpJtsbt9W+x+LOkcpaTdOF1/zuh3L3biRR5xakfkbotn2VP3OTp+miKkRh5TBL9em6cDkIKBEGLGk4JBiXLz2/2N6zHhEDckkUcIIYQQYqIYhF2xuyfpHFOFQVGhfsHMiAu9X4HpVC88v0GbiwwwsDt2/rwt8rZNeVAhhJgkKRiUqF6r7vLJnDS8JAEALCPqt0q6CgshhBCiJHlgZ50Xnp0ibmg3+uHtsbsj6UxTqcXoa5dSfMqY67Vcm3H+WOj9T01n31dGfI4ipJhhT3KjC6vIfu2+MHX79KUWQohjJwWDEnV/6P3tqenspS5jEQE+AzkLdD8Q+L9JOpuYWeYoUzvXiZd2G92yzzgtSecRQggxOzXpuP4sP/gyAWUEOHO0sYvd6OYbs+lvlVrzXJ+se7IXXlhJduUgqx2PhN4tGVbBRM/zcOjfW6XszxuUfTkDlgDdbdXvHwi9cQWAJU60qJz4PCJ4AEAERYA/3zFvfyDkOyyo0NbGQgiRKCkYlKiAVfTXTNmH13vhmVXKLhu0at/DoXdXBCo4xW22adZx42o3epZH3Nxr1X0Pht4N0nxvYgiMi1K519Uo+5zhzs1rObznxmz632OQSTqfEEKI2WWDF75JAbXDSyoJQAX4ojVudNPjkfdIwvGeVEE2fXE6+x8aaFCEVCWbXGM6+9Lbcqn39lg9MNHz3Z5L/7aM7J8atWnqNLpjgFW20PsatFnOgBlbOlFAukbZyi6r+yb1AwkhxBSSgkEJMyD7YOj/A8AJtQxhmRMtXe+FXyTAIYKTInPaU9PZZ1yfKfvQbC6YLHeiZSvd8A0eYVkE7N8VuT88ngaXJ3vhmdXKXjGyc3MafMZZfu45dwTp3xctuBBCCAEgTXz62P5LBPiN2pzxeISSKRic4gdXOPleUR4AKEKKGHqDF77wllz6x5M5Z4ZVsCtWR+zV0GfV/nl6XL0ADMR9Vg1OZlwhhJhq45rqCTEV1nnBKZelMx+4LJ35wDo33HCk965ywzcqQoooX9BSBN8B5p/shedOZUYNVqd4wcYLU9mXne4FF7jgaSuoLdBx8zov/EJKYYMiVPiE1Svd6BMr3XDlZM/ZpM1TCnVurtX2suNPLIQQQoxmgXFP5xmIIqAngTiHVUn2jOFiwTAiuBXKnjGV426N3CdCYLtlPDlj0jKCTqN+lvTMPwKjXpmaCrLpJHMIIUrPjJphUEm2bL0XPDWteHG/VZsfCr1bAlZR0rnEkV2Qyl5Zp+xLCPkv5+VudE6NNv97ey5dsB+DR1g+9pgipKqVWQPg1slkcMAKAB3uC9kn6z41nf2cCywmwK9VNmh24lfemk1/sI+nvuq/0g2fN3YbTQK8pU78kq2R99nJnJMBwwwmGr1wlFG4c7MQQghxPDqN/k2jNq8f2QAQgNkSejcnFqqACNTiM580cjYEMzhimtI+PwzCTdn0v53pB8+vVvZiC2RaY+d394f+HVM57tEsd6Jla7zwQw7QCIAGme68PZf6elaWggohMIMKBg3K1Jybyn2dgDJF8CvIXNyYzr7gxmz6A5NpUiOmR7Uy5fXKvnRkJZ8Av0HZl1eSvbafVWbsZ2KgzQOWjTxmGbkMq70THb+MrH9eKveOcuILAagc00P3hd7XOozTNfJ9p3rhpS6wZPgih4AUMRpP9YMXTXZ64kR4hHlE0COPEYFc8NzJnnNf7Fy7yo3OJYzq3Bx0Gl2wc7MQQghxPO4O/D+f6+f8Bm2vJKA8AnY+EXrfPGh1T9LZRtoWub87xQsvGvn9yEC4M3J/NdVj51iFt+XSvwTwy6ke61iUkfXXeeFnFaF8+Fg5+OzzUrm3/z1b9vUkswkhSsOMWZJwshe8TAGVwzd0ipDSQNMpXvC0pLOJw5urzaJCT7QZiJudeGGhz+yJnR9axpNFIGYYBjKPTuIJxQWp3AfLiM8ngkMElSI++Sw/+ByN2TO5RtlzxjwRARHcSmXPmuiYk9Fv6b6RUxSB/B7Og5YemOw5N0fe4+1G/8AycpaRZUbYa9WfNwX+3447sBBCCDEGg3BHkP7dHzLlr7gmU/b8P2fK37stdrcnnWus3bG77/HI/ZfA4lHLGAwYW56I3H8rxaxTbY0bnYUx9wNE8CqIL3bA+jAfE0KcQGbMDIMyxacOr2kfpgh+leLTAcgT0xLVZXQruZE79jgB7kGj2wp95pHQf8AwfWKxE73MITQNWrr/4dD/+eG6Dh9OjTKVQw2YnhyfCFozale50Zotkbd5+HgEdKQYdmyzpphxcCJjTtaDof+XS9LZp4ExRxFSlpFjYOCh0D+upx13Bak/p8j+ba42cw8a3VloRocQQghRbKW+ReDWyNu6NfL+OekcSXOIU0DBPS+VQ6xjll2VhDjRzZiCQczU4oCbR67HZkYcMO1PMpc4sg6ruweYbi4HXzj8BN8yggGmmwtNUawgm65RtmZr5G5+PPI+djxjlxGXDe2JPBb7xJUjD+yI3Gs2eOElY6fv74mnfnoiAAyyyv0tm37v0J7QqzOsdj4SejcNssod77lzrMKjdW4WQgghxIlnZ+Te06zNW0ceY4YNGZtlO2shBDCDCgY7Y+d/17jR+uEbOmYwA9GWyL0m6Wwz0TInWrLQiS8BgL2xc9OO2N1VTjYVMEXH0qlXg9UiJ16YY8q0GKfjSO+9KZv+1kY/t71e22cC4ING/+UfgX/t2PNdlM6+uYr46QwYAGZfrL99X5i6bbI/Y4vRbZzv2Dx6qQHg7IzcUdsV7ordPWniTyx1o7e4wEIDtO+Nne9P577RAavoniB1A4AbpmtMIYQQYqo5YH12Kvf8GmUvA2C7jLr27iD1p1KfhXAi6LC6+4DR/zlPm3cMLSElBgYfCP2vJJ1NCFEaiPnwv6t/u/2050xjlqNa64brl7jRaxxgXsi0/YnI/cHO2N2VdK6Z5mw/9/Qmbd48oiu/sUCfAmqR3wv4ultzqe/FIFvo86vdcO0qN/pnAlIEqBDYdmcu9dkeq/snm+k8P/v8Bm1fObKPgGUED4XeB3bF7qSfjq92wzWr3eiTQ/9TEUD7Yv2Ne8PULZM9pxBCJOmFy++f8YXyUru+EFPraenMVWniM8fMNLzxhmzZf070XNXKlK91w0tSxE1dVj/8SOjdI4WH41erTOVSJz4lBAY2h95Dh7sGFELMXoe7vpgxMwwA4PHIe+TxyPtw0jlmsnKyqSZt3jymwZ9SjHrKz933qpR9+vmpXHxzLv2DQp9f7UafUIQn9+n1GKvO9oP3XZct+9Rkc9Vp+6xxTQcBZ7ETX7ordsflOFZbIm/z/th53RovPEcB7s7I3dRhdfdkzyeEEEKIY9es48Yy4o0jd0tSBL8SfGmtMj/pnsDDhvk6nnuGH/wHAC/fxyp+ZrM2j/4tm/60kRvc49JtdX93qCc9q1MIMXvNmF0SRHHMd+LFyE/5H4Vo1H/3q5W9vNDnV7nRGQU+66SITysj6xf6zLEYMdthJKXAXoHjEzLAKntPkLrxH0HqrzOxWFCrTOVpXnDeOjfcoMHy/1khhBAzRq2ycxmIxh5nIKpTds5EzrXOC99EQPnIHbN84nXrvXDctYkQQojiKMkZBjXKVMzTZkm3Ve0txmlPOs9s0mtVJx3D3zsBPoHBYxrnKjr8FjtUuMvuMemz6qYaZZ898gkEA+EB45zQSwc2+rlL52nz9qG+DljqRgP3BP5VrcbpTDqbEEKI2WGBjpvLlK3cFbk7QtC4rZCPR4vRO1e6UaHiv24xekKNq1PE68buZqQIqVplTgGwaez75yhTu9yNziNA74ydO+S7UwghJq7kCgbnp7IvbFD2FQzEBDhZDu+9MZv+96jIX2AnqjbjHMxweE8afKYaujlnHj3DgBk2YDw8tlgAAFtD79756eyoL2tmmIDx2PF09P9H4P/s4lR2pQesAmAIcLut+s2WyHt8suec6Rp1XDdPm7cTwRv+myCGf6oXvO8vWedfEw0nhBBixqsiW35+OvsxD1jBQLzGjbArdv7jodAfd/M9Wd1W9x+06pd1yr6YMHTdAYTtRv8gwyqYyLkM0K2A8pHHLCMImMY9XDrZC85Y6sQfQf5hBjVq85p9cSw9jCbABTs+sTvRba2FELNLSRUMVrvh2nplXz50g+QBQAp8xtmp3Atvy6V/mXS+2eLmbPrL56RyL6vOdyumiLHXB9YyYAFYBrIPhv43C322j9Xgztj5/FInvgoAA1AG6Lg39P/jeDJlWYV/yZb/61InWlylbOP+2NnaWWDbxbEIjDVutH6ONqeETD2bI/fmHqsHjidLqVjqxBsZ4JFlGyIoH1jngp1SK6I5YHWqH1xSp+z5BujeGbl/3CFNSYUQYkJcsLPSjU6yQLQ1crdM5dr8s1O5d3jAKiI4w9ddS5z4w/tj500Hre4t1ji35dK/OMkNH2924qcAsPti5/otkbd5oudpifVPFzjmvcNLEpjBAOLHI+/Gke9zwHqpE39gbG+kBY559+bI/qMYWxbPZg5YX5jOvqmK+GkAdAzs3xx6X9keuzuSziaEmH4lVTCYr+NLhr+whimCV6Ps0wBIwaBIQlB8Sy59NYCrh48167hxoROfEjD1PhZ69x3pZvTh0L/vich91TInXh0wDe6MnZ2FZiNMxs7Y3Q1g97G8l8B4ajr7nnLiCwjwGQgbtXnVQ6F31fHsrFAqYiCHfBFnLGMLH08MgXFpOvtxn/gkRUgxw673wovLlf3Cw6F/b5K5zvFzz23Q9kUKKM8xPfxw6H3ngHHaksokhBCHs9oN1652o49j6Kn4SjfKPhR6H90du/uKPZYCUxnxeUQYt9RwhRudczDQ1xVzvMci76HHIu+h4znHfWHqdiBHzY55pQZqA6bHH4vc/xm7S9NCJ14IjP+5GDCLnXjV8eaY7S5I5V5bSXzZ8DJRh7FwnRd+rs3o18tsAyFOPCVVMBh6ws0YvxZetsuZYi3GaW8xzvXH+v6AVfR45D0ylZmOZpUbrS4nvnD4CQIBPjO8tV74zl2xe1WS2YphS+j9Y346+/aRx5gRDjDdUmrdoFe70drhYgGQnwlBgL/Yid/2cOi/Oalc5/m5F9Rr+4rhfyMp8Gln+MG/d2XVm3KswqRyCSHEWC7YWe1GH1d0aMo9M1Ine+FH98TO24pVmD9G0zrYRNwXpm5DiCN28x9g6ivUr4mA1Ao3+tdlbtTbZvQv7gn8v0/zn2vJIzCqlL185OwMIhAz1FovPG9TkPp7kvmEENOvpDqu7zPODRjTSdcygi6j/pxQpBmlgmz6DD930Rl+7qJKsmVJ5wGAJh03bPCCjQt03Fzsczdoc/LYCwIi0FAfhBlvgFX2scj9aMxoYUbEjHiQ6e47cqnvJJ1trFplV1CBpzkaaHQS3NmhXtsXj7noUQT467zwnKQyCSFEISvdaC3G3KgTgRRQP1+bon+HWhBnmO5kxqgZhQRol2ztUidaUuwxp0uHcbqyTA9YPnRNyflHT6QIaYcwt1mbt53tB1ckFrKEjZ3tO3RMO0BJXFsKIaZXSc0w2Bp5W+uU/X9N2rwJQ43vBplu/UeQ+kPS2UrdSW64fkV+GiMDwPx0Vm2Pnc88GvoPFnOcSrJla7zwXAco32f0PXtj90Ch9xEYl6Szb60ifjoD0VIndtZyuOnGbPrf4yI9HQ+YuhiIxt6oWmBW9DAAgG2Rt2175L61QdnaLFOuVKcCDjDtn5NvVDpqe0wL9Bbr73uiKL/HR8X443B94vokMgkhxOFYIEaBJ/sEUFxgW8JiuDuX+vb56Wy9x1jOgCUgxYCtV3xlvRe+cJETX3NzLv3jyZ5/jo7rVrvR03zixi6j730o9O6arhlyt+VSXzonlXtzJfgSDF0njFx+oQj+HG1eBkAeSo3AIASMh3zg5DE7UvDe2LknsWBCiMSU1AwDALg7SF13fTb9ykdD719uy6Xe8Pds2TeSuuGYKRywWuFG/6wIKUVID/3HX+7EH3HBRSsKLXeiZU9JZ7/frM1bG7V57ele+I3zUtkXFHrvqV54XiXxpURwFaGMCF6a+MyNfq5o1fzHQu92BgLmQ+v5LSPoMPoXxRqjWBqUqVnphivLyPpHf/doDEKH1d2lWiwAgMdC74EYaGXGk9P8LSNoMfqHSWViEELgiaGmWCOOw7THjqxfFUKUlK2Ru4WB7MjfWcwwEbBnqrYD7GM1eG2m/Kp7A//dMdAKgBXBI4JDBL9G2ecucaJFkzn3Midacq4f/Fe9si+pVPy0hU783svS2X9To3v5TpkMq+CGbNm3/i9T/uJOq64u9B4FVE9HlpnmwdD/pgV6LCNjGTlmhB1W/XSfcVqSziaEmH4lVzAA8h3zt8fujmJ26J3NljjxUhSeLUJL3Wh5scZZ44XvV4QyRUgRwSWCN0fZV83VccPY987R5inD69mHKYJfq+1lxcqTYRXcG/gfzDHdZxlBzOhsN/r7dwf+H4s1xvFywOqydOb956dy31vrRp++LJ29+mw/d3nSuYrNgOwt2fRHuqz6bcTYm7N4ZGfsfOGeIHVDkrk2h963GMhYRsAMtoxggOnv22J3e5K5hBBiLAOyD4XeR2OgZeh3VhgBOzYF/memeuwDRre6wGKicTMcqFmbUydzztVu+FZC/noBABQh5ROvXeeFpx9v3onqNPpRLjBLIwK2TXeWmaDFOO3XZsreuCt2/qPF6O/eHfhvuyOX/t3I96TIeo06rtMJLjsUQkyPklqSII5dBdl0kzbNB61qzzFlqHDxRwdMg8UazwHmjz3OgFnoxKe0GufvY46HzOCxFx/MxZ1WecA4bQeyzqeKec5iOjuVe0EZ8blEcIen6zdp84YVbrh1W+TNqguVAVbZW3PpnwH4WdJZhu2M3d1dVr1prRtd7BJXtRt9/xORuyXpXEIIUcju2N23J3beNk+buQaIp2pmwVicX+KfIyA95ngcApN6eOMRVo69BiAgVavsGgDTunvOE5G7eaET310GPntoV6UIgNkSet+ezhwzSQwyD4X+prHHFZguTOVeU6PsswGQBbJ7YuebD4b+PxKIKYSYBlIwmIHOT2Vf2KDsK3hozXivVdeGwG6PsYwo/3fKDBMD+4q1FVPAFCG/i8XYxnYcMI27mNgfO9eucKOzCIcazllGrt3qa4qRZyopMJ3lB1c0aPMcAF6/VTdvCvz/zbAKJnquWmWfOXYfaALchTq+dLYVDEpVr9WDdwVa1qgKIWYEBmG/cVqne8xuq35fq+wLh7+zmMEMRI+F3p2TOacBuhxg7uhxkMsyTfu2tgzC37Pp/1jnhac2KHNGBOraHHo3HrS6Z7qzzHRn+cEV1co+m4b+nWjAW+zEH+q26r17Ynd/0vmEEMUn04hmmPVecGq9si8jgjfUG8CtUvYZ3UbdmGN6kBmGGSbH9NDdudQnizVuBIr7mP5qGU/eNDPDMpB5LPTuH/v+xyLvkXajf2gZOcvIMiPsser/7gv8W4qVaapcmMq9rlGb1zmEeQ6hoUbZ51yUzn5ikqcrtFZT9nASQghRUm7Ppf6326rfWsYgMzhgPHJ/4H8oO8ktaA/E+sdjrhkMA9nHQu+IWyJOFQbhkdB/4KZc2fduz6V/J8WCyWnQ5rkFHoQ4S524aEtOhRClRWYYzDDN2jyjUG+AOm2f+udM+QfSZD0g3wei2GPfmk3/v/NTubBa2csJ8HNMD22NnB9cnM6+s5z4bAtkDxr9u7sC/08Mwl1B6k8+2b82atPYZfTBQVa5YmcqtjKyfo2yzyI6tKUQETyPsWK5Ey3bHrs7JnK+Hquur1Ojt/ZjINxvnJuKGFsIIYQ4LhbEt+bSPwfw82Kc774wdZtFEM9z4pdroDbL9MBDoffDmXAtIA5v5MzREZQGy5aLQsxSUjCYYQ7TqwAYOj7ZQoEC00Innp9jyrUdZs1kDDI359I/APADAkMB6vKyzH9qoJEIjgIq52jzugtSucpbc+n/BYCAVbQ3VjNmilqNsjWMgi2cTaWyTQAmVDC4O5f6zSXp7JIy8MahJSROp1FXPxF5so5eCCHErPZA6N/1QOjflXQOUTz9Vt1apewVig5to8xA0GqcRGaOCCGm3qwuGDhgvcELz61WZl2O6cBjkXdDr9VFaQKYlFaj/7aE4tNGzjKwjOCg0ddN9pyr3HDVajf6FwLKCFAhgq135lKf67G6/3CfYRDWesEpCqgd7psADO2EoOwLNfiX07XXcjG1G90BIATGT7drMXrrRM8XgeLrs2VfnKvjhhplG/fHzq5+Vpli5RVCCCGEmC73BP7PLkxn17qMRcg/YNG9Vl37eOQ+nHQ2IcTUmLUFAwesn1aW+ZwLLFWEVCVzcJHOvfSewH9/i3Hak843rEnHDUud+CwDBFtC764+VkcsaDwceptqlf1jjbLPYyAkwBtkuv2ewP/rZMZPk/XWuNGnFOHJqWQeY/XZfvD+67JlR+yBUEY8BwVmPBDgpon9AabsZDIlKQbZvbH+9kLHvG9oVwNiIOi16k+Hm3lxLFqN09lqMC3droUQQoiZoFaZyrVueKlP3Nhl9YOPhN6mmfiw4UQywCr7l0zZB1e60aoK4sZWo7ceMM60N7IUQkyfWVswOMUPzh8uFgD5J9/McNd54Wtass6Xk84HABv93KXztHk7AwyAm9PZt2yJ3H/bEnmbD/cZBuHmXPrH9cr8X5M2iw5a1XI8N7Kr3egMjGnCRwQnBT6lnGzqSGsNW41+tFmbcbP3DdAxOAOLBcPuD1N3dNto3xInepoipFpj55bHIk8q50IIIUSRLHKi+ad64ZcBuIrgVar4srnaPHp9Nv0pC+Kk84nDYxCeiLwnADyRdBYhxNSbtQWDGmVPG9sckAgqDd6QVKaRapSpmKfN24ngjbzjXulGH3oict/IR2mkf9Dq3oNWH/dNrBq/TeIwUkfZRWNP7O5f7sR/rVT2sqEmODEDZnvkfuNo+Uvdrtjdsyt2v5d0DiGEEGI2WutGbyGgjCh/waAIKR+8br0XnvFQ6N+TdD4hhBB5s7ZgEDC1lDOHakS3eyD/9DupTCMtceJ1Q03wRuXTQHWTNg2txzFrYCK2Ru59C5x4VGGAGSYEthzLWvubcqn/XuNGtzfp+OwYNLA1cm84nhkPQgghhJj9fOI1w8WCYYqQqlV2PQApGAghRImYtQWDzaH31/NSuRcwwx3+QrKMYG/s/DTpbACQY+oHCj6Gp+w0TufvZ5XZGTufX+rEVyG/NEIZoOu+wP/3Y/k8g/B45D36eOQ9OrVJhRBCCDFbWKBbAelRxxhBwFQyfaaEEELM4oJBp9U9D4TeB9e60Rt98JoY6NgXOz95OPTvSzobADwRuY+vcKMeYnhE+WUBzAgzTP+Y7p0cHg79+7ZG7quXOfGaCMhui9ytM31JgRBCCCFK14FYX73AMf+kKL8rETMsgPDR0Lsp2WRCCCFGmrUFAyC/xn5P7H4q6RyFWBDfHfj/fLoXvjsFPg2AGWC66fZc6r+TyJNjFT4WeQ8lMbYQQgghTiz3hanbGAHPc+JXaKA2x/TII6H3Pdl6eGr8ZcuGVySdQQhR2l64HNcUOj6rCwbFpsD5pQ1F6t7bYZyu67LOJzVYWcDKU/3jp8BEAMm2TEIIIURpuz/0b78/9G9POsdsd/fBJRs33bUS/ma9NeksQogSdkXhw1IwOAa1ylRu9IP3pInPBMCDTLfdlUv91wCrovQaOBFubpc60eImbdZlmQ4+Gnr3xCBTzPOnyXrnpXJvqyC+BIDKMT1wX+h9o8M4XcUcRwghhBBiJqrZPLgp6QxCiJlHCgZHQWCcm8p92gUWDfcaKAOff34qV3ldtuyTSecrdQTGJens2yqJL0W+yaNZ6MT9d+VSH+y0uqdY41yQyr2/jPhMovy/6RT4lLP84LN/zui3y8wNIYQQQgghhJg4dfS3nNiWOvESB5g3fCMKAIrgpog3zNFxXZLZpssCHTdfls588Nllg//zjHTm48udaNmxfnaNG62rJH6qIviK4ClCWgP1p/rBG4uVr0aZijLijTRiC00iaA3UrXKjNcUaRwghhBBCCCFOJDLD4ChSxFUAxi0ZYCAuJ67oAGb1lPcmHdef7gdfISBNBKXBjeu88GQAV22P3R1H+3yjNhsJ+Q7Iw4igy8BnFitjmrgMBf6OAHCKuLJY4wghhBBCCCHEiURmGBzFrtjZAuSXIozEQLQ3dvYlEGlarXGjZxPgEeX/rRCBCPCWu9HLjuXzMdDHQDT2uAWK1gW51eh2CwyMPU6AszNyHyvWOEIIIcRM4IBVrTKVGizXeUIIIY6LfJEcRYZVsC/WX2NGaBmBZeQsI9gRO/9+IjQrTBEvIYI78hgRyCVedCyffyJybxrbQYAZ3GPUX4qVkUF4InK/OPR3k7OMgBnhfqP/s4/VYLHGEUIIIUrd2X7umVeUZX56USr3w2eVZX5ypp97StKZhBBCzFyyJOEY3Bembt9r4seXOfHZDMRPRO5dPVb3J51rOgwwPZxiPnlkfwBmmBzTo8fy+axVWcbQfpSHcIWypwL4VbFybom8zS2x8/rVXniOArxdsfOPNuMcLNb5hRBCiFJ3shec0aTNGxXllwIS4M7T5h1r3LBtc+TJjDtRVBwbh1vazuNssAGOPqCa5vyNytN9SecSQhSXFAyOUYdxujqMc23SOabbQ4H/l4vT2csVo1YRPMsIAQSPht7Pj+Xzq9zoDIzpL0AE5QNrK8imi7U1ZQXZ9BxtmraE3l0yq0AIIcSJaL6OnzdcLBhGgLfQiZ8jBQNRTGyMtlt3fg7GLAGQQojQ7txzJS1ofr+qqWpJOp8QonikYCCOqJ9V5qZs+j0bvODpFYrXZZl2PBZ61x60uvdYPs8AH+alou11eGEq+9I6Za9kICbA6bHqmltyqR/JdopCCCFOJIpQPvYYEUgzVySRR8xefKDt/CeLBXkeAIfbOl6PmqrPJZdMCFFsUjAQRzXAKntHkP4/AP830c8+Ebn3LnTiUceYEeeYHinG7IJTvGBjrbIvIoJH+S8rVCv7rNO8cMd9oX/r8Z5fCCGEmCm6jbp5jraLRs4ysIzgoNU3JZdKzEacCzbgULFgmEJs1iaRZyKYGegbaITnZiidGtc0WwgxmjQ9FFNqkFXuicj9pGH0WUaWGUEI7Lwn8P+jGOefq83likZ/YSlCqlHHVxTj/EIIIcRMcU+Q+nPA9PjIJs05pvvvD/wbk852oqhXprpZx4102AmWs4TjHAAQjjuuqGP6wxw729652j629ft274Fv2+27f2S2bP8Ih5F39E8KceKSGQZiym2OvMe2Re5rFjvxkoApu884xVzbVrDoRVIME0IIcYKJQPFfs+mPr3CjldXKLuwyeueO2N2ZdK4TQRXZ8nNTuQ+niNcDYAN0Px56n98euzuSzjYVVFPD9XbHnhchfy8xfM0VUE3V1QnGKogtEwYG65lguf3gpwCkn3wxis+0u/a9Ta9a+o3kEgpR2qRgIKZFDLJT8aXZbvRfF1J80shZBpaR67T6r8UeSwghhCh1DMLWyNsKYGvSWU4k56Ry70sRn0yUv7Z2gKZ1XviZfUa/NmAVHe5zC3TcvMYLX5EiXh0y7doauT/bGbu7pi34JFFZup8WNH+A2zpei9ish6J2qqn6qWpuui/pbCPZlvZTuKvn/WAuB6ALvMVDGF7Clr9Jimb5tBAhJkcKBmJGeyD07qhWdm21slcwEBLgDTDdfG/g35B0NiGEEELMfuVkU2ni04eLBSOoNW50+oOhf3ehz83VccPpfvBVAlJEUBrcdLIXnsrAB3fF7p5piH5cVE1VK2qqvph0jsPh/sE6Ptj9UWD0ziEFKDATIAUDIQqRgoGY0RiEm3Lp7zUo85tGbRZ1WrWv3ThdI99z98ElG7s7q1YmlfFIahv6tgLA2fW7Ng0fG5l3+PWJKNWfVQhRHC9cjmuSziCEOEQXfnI9/Jp7uNfWuNHzCfCI8lP6iUBgeCvd6CW7YvfLU5H1RGI7uy7E0ZeoGjj6IdLKHuV9QpywpGAgZoVOq3s6re4ZeWz4xnvTXSvhb9YlOzXzpOdsu/gv9VUraxv6to7NG6wxK4O5aisAcHO06XDnoBZ3o99qVwIo6Z9VCFEE0tJViJLSx2owAna6jOXDN/9D9LbIvf9wn0uRXTp2VgIRlAdePGVhTyTMPg5fMMgAICjqVvObvz6NqYSYcaRgIGa123at3lq1mVCzefCwN9vDOIw8xLFPZen+6cg27DGswIbXbV4JjM/bg3LEg6lNZnl249HO42/WW4/l5xRCCCFEcT0Q+F863Q8+pxgVABiA3h07/97HavBwnxlg9bDHdrUiPNmlnxlxxtKj05F5tqOaqrs4k30JRs8AieE6d1FF+U1wnX5qqN8svQuEODIpGIgTHkeRZ3fufRfC6HwABKVaqKnh31V97a6pHNfsa7kAff2vrHgMc/Y/QAed99JBAF1H/aAQQgghSsoB47S1ZvSbVrnRWpc4vSNyHx1klTvSZx4JvT9emMo93TKqFMGzjIiB7KOR98vpyj2bqbqaPaa3/2oMZl4NIEL+Gq9NLZz3X9P9cEiImUwKBiJRBMZcbRqzTNkeqxP55W137nsrwug8DK8ztHYBt7R/jisrXkeeO36P4SIw+1rOR0/fPwHwCUC4jedue796o/7n4FtAKjsVY4rZh6PIs/tan4Vc7gKQ6qWaqt+puXMeTjqXEEKciCyIN0feY8f6/h6rB27Opt99sh88o5z4pCzTtsdC79qDVvdOZc4TiV668Pc8kLmJe/vWwnW6aE79FiJKOtaMxb39Tdw/sAqe2368f5ZsmfhA6/k8mLkIRANUW/NnNaduWxHjiiKRgoFIzCo3XLXKjT6sgRoAlGW69/Zc6itHq8gXExujEYaXYHRTIgKgub3zLFrQfNuUDNw38EqM7tpLbKAr/9p2sp2/+B9TMuYEcWwcbmm7kLO50+A4B1Rj/XVUUd6ddC6Rx5bJbtv1GRi7FIAPWHBn18kmir6pF867Jel8Qgghjq6P1eDtufRvAfw26SyzFVWU9VBF2Z1J55jJmBl2++7XIxc8C4ABQHywe69atvij5HuTetBlt+58P6LobAApAJbbOi40QfBVvaD5jmJmF8fvaJ1DhZgSFWTTa9zoUw6hkQgeEdwU8ennpnLvmNYglhUKdzcmtjY9dePa2nHHDLm6J6yZsjEngI3RduuOz3Nv/9sRRpcgk73S7tr3X7arZ0HS2UQet3eeDGOXYHThyUffwBuZZTmmEEIIIYqD2zpPRi64HIAHIA0gBWOX2L0HXjmZ89mD3YsRReciXywA8vekPnr7386WZQpIiZGCgUjEai88C/kn+U9SBK+c+AIHfNjtiYqNXCeC1lsAjN1OR6namnunbGDXeXTsmORwGKyu3DllY04At7SfC2MX49AvchdAmtsPvjHBWGIEzgWLUKjYxVwDY2X2mBBCCCGKgvsHzsfoBxQA4CIIL5jUCQezKzD+2htgLkMuVzGpc4opIwUDkQidr1AWqiAqVfj4lKF5jV8BUQ/yW+xkAYSorPguVZZPWQNCaprz/wAMAggAAC5ifyH2DlwypyTWbnE2tx6HigXDCHG8Ook8YjxK+zuRnxY45gXqglbx9CcSQgghxKxElEWhG3wauo6dqJS37zCvRPD9w+4sIpIhT6FEInZE7qZmbd468hgzbMB4JARN682Oqq5q44ryN3Jb56kwppzqah6k8rIpbTikaqpaOeW9xbZ2XhxV6FOaX5KLFr4kc/P2B0qkhuc6+xGEAcZWk5VqTyaQGIsaGx7l7t6tiM0q5P+eGECI6srvSkMnIYQQQhQL1df+jfe3PhujZzYGKCv7w6TON6d+Cx/s2QFjVgBPbisaoKLsp6TV+MKESFSJ3J2IE02n1T37Yv0NZoSWkbGMrAHa7w/9ryaRh7Q2al7TvWrhvFumuljw5Jip1KBesuDPuQtW/K3y6c4BKqHynZo75wYQchhdTQ6oturHSWUSoxER1Iql/4bK8u9B60fgurdRY8NH9YLmu5LOJoQQQojZQ9VW76e6mi8NzcgNAQRIp65Ri+f/aTLny1/DLP44ytK/glJ7odVmqqn+ql6y8JqiBhdFUUK3KOJEc2+YuuWJyN6zzI3WBUwDT0TuZguSbm0lgFKpQbVw/vtsa/trEMUboKidaqp/ppobH0g6mziEHB3rxQv+AuAvSWcRQgghxOyl5jVt4rmNr8VgphYpv59cJzqe85HrhnrZol8A+EWRIoopIgWDBKx0w5ULdHwpAfqAcW7YHHmPJ50pKf2sMg+G/qakc4jxqKqiU1dVfCXpHEIIIYQQ4vhwEKbsnv2vRxBeDMAi5f9dLZ7/E3Ld8FjPQYoYU9jjS5QmKRhMs7P93DOatHkT5bvO0yoVXVKvzf/enkv/JulsQgghhBBCiNnH7tzzUcRmDYZ7BuSCy+2OPU169fLPJZtMlDopGEyjNFmvSZs3KTrUSI4Av0HZV9Qo89ceq/uTzCeEEEIIIcSR2M6uZdzTdzEAS7XVN6n62t1JZxJHZnt6m0cVC/I8RPEZ3D9YN5U7g4mZTwoG02ieNgtQYBs0BqJ52iztsfqhBGIJUZLMngNPRf/AK8FcA603U1PDd1VdzZ6kcwkhhBAnKrNr37MxMPha5GfKglvan2MGM/+pF82/IeFo4kiCsB5AjNEFAwCIOQhqpGAgjkQKBtOo26rOoaUIoxDg9FjVlkQmIUqR2XvgYvT1vx3D2zoas54PtH2Jff8tVJ7uSzadEEIIMTtxLldu97W+DEF4LhT1U2XFr9SC5juGX8PA4Osw9il138DbOIpum8haeDG9qKZ6O3d06cKvVcnDGHFEsq3iNOqyum+A6SbLCIaPWUaYZbrvgHGkYCDEsP6BlwOHlu4AIACObe98SkKJhBBCiFmNrVV2x94vIRdcAeZGGLuce/reZ3bveyYAcG//UgCFOuNb7u1fML1pxUSQ72VRVfEd5LdENMjPNghRU/UNcpw42XSi1MkMg2l2Uzb97bP93N46bS8HoHqsuv7uXOq3SecSoqRYri5w1IMxDcP/g7O5Cru/9eUIwo1Q1EPVVb9U85rumcaUQgghxMxgLNn9rWdzGC2glL+dmuY8SGr0Vtbc2nE6rG3A6NmwPgYGX8XMf0HK70CBmbIAXEqlZt2UdtvavoF7B54BsEOVFX+j5sZNRJR0rEnTi+b/3Xb3bubu3vMBWKqruU3VVLUmnUuUPikYTDMDsncE6d8D+H3CUYQoXa7zEKL4bIyeBZWjsvQDAMCxcezOPf8By3MAODA8l7t6rjLGfFMvnHdLEpGFEEKIUhR2wKv99uZncl/kAfB4MBNxT992tXLpx8jRTz5d5jCai0L3BoxKWKtVdVWbael4CHG8AYeWJQTw3LupoqxnOn6W6WJ27n0eBjOvQv7nJO7qOY0z2T/rFUt+eLzn5v6Belh2UFXRNt0FCFVbvR+11b+c1kHFjCcFAyHEUdneviZkcs1UVbGLyqf+okDNbfye3XfgJDB85JcmBHCdB2hu430AwK3tZ8NyDUb/DvPRN/BaAFIwEEIIIYbs+w91nhqIKnGoCK9hzAq7v+VSSqd2cd/ABSAK4Hk7kZ+uPnoWgaJW0toAgFq++PN29/6XIwguBWCR8v+qliyYVTegHISpoWLByKWRKeSC5/BA5veTLY7wwGCt3XvgX2HsEgCAonZqbvqsqq3ef9yhZwhmBu9vPY8HBp8BkKXK8r/QvKa7Z/LMjROBFAyEEIfFxmi7bdeHEMVnAoj5YLeLdOp3evniq6dyXKqubFeppW+xbR0XIIrnUHn6EWqa89DwFwpHUTPGd/oFmOunMpcQQojS9Fh/89zbD6548aDxlla72Uef2rD5t4vLunqSzpWEJh03nOyFr0sTn2qB7i3zemtvsLVj+5b5GMi8gPsH65H/PjXI5gy02gVjFwNIYWitO9XVfHv4Q+Q6kV6x+McAfjxtP9A044HBuSiwqxmAkPsHFk+2YGD3HvgojF0GIN980PJ8PtD2Ga6ufCMpZScdeAax23e/HrngcuT/fYG7e9dxLvg/vXzxTxOOJo5ACgZCiMOyew48F1F8BvIXE/kb9Gzuebal/RHV3PjAVI5NvpfVi+ZfX/C1VGorD2YjDH/pDlNKOv0KIcQJ5uG++fP/3Lb+KwzyANK5wF36y/1nPuXlC/7xzgXpnhNqZ51ysqmz/OArCqgigtJA1Xs/s5fNIHDz/9WOfKsF81wcmnXgAHBg7DzUVH0Dg9lzoFUP1ddeeyI9AQcAKkt3cOF7JJfK0wcmc07uG2gYKsSMvG4hMJdxZ9dqamx4fFJhZxAezFQjFzwbo2ewpJDNvYCzud9TOjWYVDZxZFIwEEIcXjb3NIyekgcAHvcPPBVTXDA4Emqa8xD39m1GbNZg5FOQ+trvJJVJCHHs7j64ZGPSGcTscU/vkhcwKAUMz2smx0KV3di55lmrylq3dXdWrUw24fS5Yu7eZTa1v0IrfnJGgZ9iev1HWscWDMzQf1JjTuGpyoqttKD5tmmIW5IonRpEyv/z0JPw4WugAJ57J1VVdkzmnGytC4ALvQTLhRpJzjo8MLgA+V0axv68MQ8MzqN0amsCscQxkIKBEOJICk3JA/Lb8SSGFLFauewTfKD1Is5kz4bWB6mh9k+qprolyVxCiGPzh/2nbko6g5g9KlLBG4kwahE0g9zuML2xY2/d/Pu3Lj3gb9YnxM3IS99wYJ7TzOOu7+fMi/Lb6AFlyN+4GoydpZenkPJ7pzZl6VPLF3+f97bs5sHBK8DQKEv/VS2a95fJno+qK1v4QGsXLM8FRv1bZWqofez4E5c+Ki/fzx1d45eTAi5VlMv1WwmTgoEQ4vDK039C/+AbMXqWQUg1VQWXCkwn0srSwnk3Abgp4ShCCCESxIytAOYSHdpZh2DDcifcf//WpS1Nv8/9LMF406p3p2fsyXSW1vzkzAFm8P7dqQ4AdUOHCPmZBYz8A4Dh+4EAvnc9+V5uWkOXICICLZr3dwB/P9x72BjNvf3zyPd7qTx9xKUvRASa2/gZbmn/DJiH/+xBc+o/TY6T6EOY6UIVZT3wvb8iCC/FoZktOaT8aymdGkgymzgyKRgIkTCtLJaU9Vd6TlAGIJN0npHUwvnX2R27FyIXPAP5pxGEivIfqBNgrZ0QQoiZIYidn6fc+CxmeETQABtFnFmWbt90AHMXJJ1vOn3/fzbcf8GFex+trQ3Wac0paxFaS+ZL71roYPwSQ4ZSe8C2HqAQZak/qcULfj9V2ZgZ3Nm1CkHYQNVVm6myvGuqxppqdn/rWdzd+14ADgMarnunWr7oa0e6+Vd1NXu5pur13HFwLSw7NKfu0ROlWDBMrVjyXd7X8gQPZJ4BwFJF+V9owVzZ3arEHbFgIGsMhZhar3ndw+uf+8Kt73M9k1LEz3zWpQe3v2/TM3+bdK5hpIj1iiX/w9nczziTbaDKihby3DDpXGL2GL6A5IHBk0k73TS34XbyvCDpXEKImSM2+kAOeI/nmBcReOkcb+DgMxof+05Ltmqlf9/BeWZz68cAKKoov57mN90xm7dwi2PNb3r9FZ9+29vvP2vtSQdP7+vz2n/6k3V/2/Zw71cKLKEnuM4WvXLpf011Ls4FZXbHns/C2vkALPf0uShL/1IvW/SLqR672Li3v5G7ez+Mkbs1RdE5dte+V+kVS354pM+SUpaa5jw6xRFLFhGBFs67EcCNSWcRx+6IBQNZYyhmMmpxN+rt6U1AriQLXytWdlVc+dLNHx85bXB5Zc+yL7z575d/5N5L7kgy21iUTg1K91pRbMwMu3XXuxCGFyP/lCbi/v7X04LmD6rqqrak8wkhZo7Y6LbY6P8EgEvrH9+4qKyr5/b311xUcdP+82FYAwD39K7jXG61XrHkB8mmnVph4NhvfG3jXQDuevKgn70ZueA5GL0lcUhVFbdORya798DrYO1ijLz3yGRfbDsO3qfm1M+o/hK2q/tCjO5DAAAecsHTAfxw+hMJMbXG7skqhJgmL33Z4+eOrfY7ip11SzrWO46ZvY8/hBjC7QfXIgwvQn6arAaQAqOSWzrelnA0IcQM17nZK++5ic6noWLBkBRywbN5MFOdWLCEqEXzfw6tnwAQIL/8MUI69X+qac4j0xIgDM/H+AeVHvf2nzct4xcTQ6PwPZTcV4lZSXoYCJEQx7FOfguo0UUDAiulmRAX3H6nJDHno87maZ6i+Hhg8FSMX1OrEMcnJxBHCDGL7L21rJkUDJtx17ohDwwupPKyE2onAPLcUK9d8S/2YPcS5IImqqrcOhU9BDgIU7at40KEcTOVpR6nuXPuJaUsQFGBJREGSs24BotUU3UnZ7IvwehdJiL43gm7FaWY3aRgIERC/njNirs3ntXyxpHHDMPuaq3ZHgaOTSrXRNievmZuaX83jFkHIId06k9qycKrSasZkV8kzNG9yG/zNbpoQCTdkoUQx2XZBYOdd3+lTo+fOQ6Pysv2J5GpFKj62l0Adk3Fubl/sM7u2f9VMKcBpDiXy3Fv/xNq1dJ/Qzr1R2SyL8Xo3/dG1dfeNBVZppKqq9lr+ge+N7SLVAxAQ+sdauG87yWdTYipIAUDIRJy7z3NXTfdtOgbF168971MxEoxdwep3o/94CnXJJ3tWHAUu7y/9UtgrkT+iiyNbO45dude0isW/yjpfKL0qcaGm23/4KuRX1M7fFUfoLzsVwnGEkLMYG+Y9+jKN8/b8rbKhXH9y7b24pf/2Wh/+uUmxUwAkIPv3UQV5d1J55yNbEvba8BchUNP3lMwZhUfaD9fLVnwW7t9dx2C8BkAGEQZqq3+OlVXzsh+NXrxgms5m7uFe/pWwXO7VH3t7qQzCTFVpGAgRIK+/MVzbvnKDeeaF7/5nnO8imDr52+5tKWyTaEGpd9fkNs6zgazh9Fr9nzkcs9myz8mRTNmSYVIBqVTgzSv6Spu63wHjFkDon6UpX+lFs//U9LZhBAzz+mV7dX/tOjBzzjEaQDwfcZL3tlhwdR29VfndVN52XW0oPmGpHPOWlF8KkZP0weAFGezZyilbtErl/43h+GPkAsrUVF+cLqvE2x373zu7T+dtOqnpoY7j3dHnqGG0PcXK58QpUoKBkIkrKu/LLyrq7GlVvW18PipkyWLYzPyKcJIHqzVUPqE2ltYTI6qq9mDupqPJJ1DCDHzvWX+IxcRRjU5hO9Z9dJ3tXs//8tFH04q12zEYeTxwe6ToFVADfWbSRFD0UEYrhvz1ghaPzmLgDwvQAJb55ode16KTPZKAMRAzL39b6Z5TVepupp9051FiJlGCgaixDGlveh5WvHzAKQs485c6P7AsupPOtmJjqorH+CBcTMhGFptI6c4xQLb0bWCO7veCGOWQqlWqq3+gWpufLAY5xZCCDG7VDpRpQLcsce15rIk8sxW9kDbGdzVcxUAC4C4o6tfLWj+V6qu+vnQ8eE+BQwgVo311yUWFoDt7p03VCwY3lLSBcDc1vFPqKv5UILRhJgRZPsPUdLK/Og1WvEriVBPhHJFuKTMj74I8Mx5FD9LqdrqAyhL/wr5pnURgCyAQWqa8/VinN/29DVzW8fnhhoqlsHaZXyw+6O2vXNtMc4vhBBidrm5e/69FhSOPGYsuLMjfV9SmWYbzgVp7ur5CIAUgDIAaTA32AOtH1bzmu5BTdVXoNR+AAG0foyaG6+iyoqDiWbu7T+twGGCsavYWLkXEuIoZIaBKGHsKOJnEx3qqEsEhxn1nmNODmPnoSTTCUAvW/QL2917G/f2nUFa91Njw53ke0XZIok7Dj4H458UedzV+1I0NnyiGGMIIYSYWlrZaiJOx0a1FtixoKj+e//6LU+r23Pt6vLuZxNgLQgDgRd/6xtnfHdKBz6BcGf3aQDMmMMKxi7lTLZSL2i+E8CdCUQ7LHJ0H4/PDAAhFMmuTkIchRQMRMlS+aZFhdbIkyKun+48ojBVW70ftdXF36LK2GaM//snWNtY9LGEEEIUlSKbTnvRh4mwAYCFi/4w1l8MY2fLVI575cNXfP8Dy29ruaJuHz0wUF/3yV88jWvvibqmcswTiqLo8K+pQjfliaOmhru5t++tYKQwckeedOoaIpmwKsTRyDQcUbIsUz+AQl/yKrbqsSkdu7t3vtm6853m8W2fNTv2vJCDMD32PTyQqeFMtnIqc5zQUv69AMY2RorhuTK1VAghSlzai95NhA1EcIngE6HBc8wniTg11WNvzVV03hWk/nxz35wtodGyY08R0Zz6B5DvXTBSDEc/RCk/k0CkoyLXDWne3A9D68eQ76uQQzp1jVq68OqkswkxE8gMA1HCCGGsv+455uPIF7ccAKFl+mNs9JTt22s7u5Zza8fnkW+Oo5DJrrbbd1+mVi55L7luaHv6mvlA20dg7QIAgNaPq0Xzv0Tl6b6pyjTTcW9/k+3pPY20HqCmhn+Q64ZH+wzVVv+DM5lnw3Id8mslcyAaUM1Nv5yynNYqbu9cj9hUUF3Nw1SWluaaQggxQQR2iHAO0bjrTPKd+Kxc5N6SSDBx3Mh1Ipo756Pc1vkvYK4GoKD1ZrVo/n8kne1IVG31AdRW/zNbJhBYZhYIceykYCBKWhg7DxtLb/cc8xQilMdG3TnV0xm5o+sNyN+gDvNgbYNtab9QLZh3A+9v/QyY6zE8Q8eYk+ye/f+i166QreEKMDv3Ph+DmVcBYAYs9/ZFNG/uVeowyxjYWGW3734XwvBi5J9ieAAOIp36m1rY/Ovj3Tf5cLhvoMHuPfAFMFcCYO7pc1BZ8R29eP7fpmI8IYSYxRQKNywgFNjFQMwsqqFuB9fXvol7++eSowOqKO+eyvGYGXbvgUsxMHglLFfCc+9TzU0/oMryCS81IUUlO+OEBzI1ANNU/3kKMVFSMBAlz1jdmQ31r6ZvQLO0wNEUgnAVdx48AOYKjF7O48CYldw/WDeZL6+jIia3Klzu+NE6ZnQGkXPzTNlW0vb2NQ0VC7wnDzJS3Nr+XtRWF9zKyO7Z/1yE4YUYfVFZj2zuBba1o0Uvmn/DsYzNlonb2k/jwewGOLpTNTbcfKQZA/ZA63vB3ICRf7f9A2/j/oH7k+7wLIQQMwmDQgYeA2Md0ajvSxUavSmxYKJoiAhUU9U6HWPZ3fufhYHB12F4u8YwusDu2b9OrV72FnKcomzjnCTuH6yz+w78C4xdiuF7M6JOVFX8SC+cJ7NxROKkh4EQY2m9r8DRHDx3J4z1kV//NpZlY7wCx48Lg+Gf3/URrz68Uit+oVb82jI/+m9Hm/nFHmsqcE/faRj/50UwdiXH8ZMFS2aG3ddygXl825cwmHk1Du3hPJKHvoG3cGyOWuhkZtitOz7CB3s+glzwQgxkXmd37Plv291b8M+NjdGIzXqM/53Itqt349HGE0IIMVoudL4CoI0ZWWZkmBHERn3FWiXL92YJ5ml6WD+YeRlGXxdoMJdza8c50xNgatm9Bz4BY1cg/6CEABCY56C3/91mb8sFCccTQmYYCDEW1df8gNsPfgr5p+IEIAJRv5rbeBMUWT7YPXaaJYOom6ori19pXxstJd+eRpR/2k4Enxme78ZvjY3+eNHHKzLSeoDHN0cCgBhKPXnc7tz7UmSyL8LopSCFKB4YmEM11S1HehO3dpyCKD5txPk8AC63dbwNtdUfGx+UGPktl8YWDCwpKso2kUIIcSIxVh8cyKm3eo5ZTcQVYawfY1bZpHOJ48PMsDv3vhiZ7AsBlEPrLdTU8C1VV7PnsJ+JjcNtHRs5ihuoouxR1VC3YyLjgbmqwEtp7u17iy1L71J1NYUe9MwItrt3PqxtRuGHuD76B14B4LZpjiXEKDLDQIgxVGPD4zR3zkfgOndCqZ1I+X9QSxe+l3wvR64bUn3t5wDkAGQAZEDop7lzPjcVDXS4OV4CGn0TTQQiYG3RB5sC1NTwDxBijJ5lECDlX0dDBQMOIw+Z7Itx9GIBAChKp3uO9ibOZNcXOB8hNgX/3EgpC8+7EcDYZoxMjQ13H0MuIYQQ4xDC2NkSRO69UiyYHeyuvS9EJvsSABUACMas5gNtX+RcUFbo/TyQqbFbtn+Hu3vfi4HB13FrxxfNEzvffayzE4gIUGpnwRcZ1dzS/jk2ptAW3DODsR4Kz1zNs7Zm2rIIcRgyw0CIAlRD3XY01H2h4GvNjQ9yfc2rubN7A4himlP/MDl6atbQZVQfYAKMn6LfOyXjFdnwVkbc2v5eGLsSQIyU/1e1dOH3h9/DmWw9jvRleUiAlP8n8r2jX3Q6zkHkt2Qc/edG1HO4j6ilC/7b7tybQhidh/yskU5qrP/yMY0nhBBCnAgyuRdidEGeAGjb1nmBXjz/r2Pfbg+0vmGoUfShm/owvJDbOm6muY0PHcuQNKf+W9zW8VkAY7e4JjB73N55CjU3zcgtl6muZhe3dWTBBbcbtXCdh6c9lBBjSMFAiEkgzwtoXtOUN26ih7xHeE10IQMeUb7j9NA60J9N9djFomqr96O2+kMcxw6UsjRiKQIAUEVZBxcuGERw3bsQRSuhVIjysj+oRfPGXYwUHLOp4WY7MPBqMFwcmkkVoLL854f7DLluqFct+zIHYRpRlEJ5WbdsuySEEEKMwFxoJoEHY6oLvj+MzsTIYkGezwOZjQCOqWCg5tRts0RXcWv711BodrQpeLM9I5AipsaGT3Nbx6eQL4gM/1mFIOTU3MbvH+HjQkwLKRgIUcIoo4LokcoP6NWDH1KeXQCgJzbq57nIvSnpbBN1uE7G5DgxKst/iP7BN+BQ34gcfO9mvXLptyc1VsrP0vzmD3Bbx5sQxSeDqBeVFT/Xi+bdeNTP+l4WMqtACCGEGM/RjyA2GzD6xj2iyor7C76faHBod6mRYmg1oZmSqqF2l2nv3AtrF2H0lp2aGmofmMi5So2aU7eNa6tfY9s7NyCXWwHLZXDdVtXUcDOlfLkeEYmTgoEQJc60pVrDCv5fbo5m7VZUevGCa21bx17u6b8czCmqKLuB5s+9/XjOqWqqWlFT9ZliZRRCCCFOdDS38T95f8u/g+Ehfx9hkfL/qubUbSv4gfL0bzCQeTNGb5VsVEP9MW2RPGrs5sYv8IG2z4N5+OGCQm31lynlZybxo5QUcnSs5zXdB+CYllbYnr65CIIGqq7aLkUFMdWkYCCEKAmqac4jaJrzSNI5hBBCCFGYqqlq5bL0G7mt41yOTS1VVjyoGmoLNiXk/sE6DGZfPOZwLzU2fIYqy7smPHZt9X6uqng9tx/cAGtTVF/74GwoFkwEh5Fnd+z+l6GtoGPu6HJQWfE/evH86w77mUy20rZ1XorYNFJZ6kFqbtw0dnmoEEciBQMxa3FztMkAG4Nyu7IH5UnHQc3mwVk7Q0AIIYQQxcdR5Nn9bZciCE6D1i2qsf6PVFXZkWQm8tyQFs67+Wjvswda3zqu4SGQgqJJN4omrQ01NxZe/nACsHv2v3qoWOAN/QfoH3iT7ep5vNDWlra7dz7vb/0y8jM8PA6Cy7h/8FG1atmnSNGxbVUhTnhSMBCzGjdHmwK4COYm+zvRb80XLaRoIIQQQohjwXHs2K27vgRr5wPwEcWx3XPgmdTceJWqr92VdL6jiuIzML7hoct9A2eioW57EpFmvCB4CoYLBYc43N17Eepqrh77dm7reAuAMhzq+5BCHK/j1vYzaF7TPVOcVswSUjAQs14prP0P4MLfnHQKIYQQYvbjWfLclFvaL4C183Boi2AHgOaOg29Afe3HE4x2bIiyQ/0GRoqh1GAieWYFOszGUii8xCA2azC6SSQApDiTXQ9ACgbimEjBQAghhBBCzHiuEy/3HPOum7rXLL+le3Vfk997J8DdSeeaLM4FawCM3TKQEJsVSeSZsHTqD8hkX4JDBQ8AMGpO3a1JRZrxfP965HLPxehZBobqagovEVHUDcvpMUcDuE77VEUUs8/4vUyFEGIasbHK7Nr7XPPY1m+ax7Z+zezZfxlPw+MhNkbbto71tq1zLVs7Y38Xcmwce6DtTLuv5QLO5sZuXSWEECcErWyN75jPKcJygGChqlqDmqeqBdGypLNNmuvuARCMO65Vy/SHmTi1ZOGvkU5dg/zPYKBoP8rSv7Ztnc+wLe2nsuWxT77FUagl838G19kEIAKQAZBDVeW3VG31/oIfqKy8GqP/DVkQQtXUcNQeFEIMkxkGQozD8ByzUileYi3tCWO9ZfxsLlEsdtuuDyKKNmL4CUTfwFvt9t2L9Yol35uyMTsOruT2zk+AoQEQd3blqLnxY4UaBpUy29WziFvaPgvOb1fFPX0Oaqq+ohc035F0NiGEmE6eEz8VY65rGeSq+fHKtueXvcLfrLcmFG3SaPHS3vLrHosQW5eGHvIxIQo2zL8rWl6+cSLnSqKHEilivXzxj9nYq3lgsI73tXwemeyLAficyYbc27dZrVz2CdLSsf9YkePEevXyL3L/YB0HQS1VV+0h14kO9369sPk2S2DuG3gFrK2F6zxCc+d8j1IpWRYijpkUDIQYhXW5H/4rEdYDICiw65gtmZz3Scbku/qKwmxvXxOi6CyMnlrnIxdcwbnc/07FFxobq7i989/AqDx0kFPc0v5xrq1+E9HMKQ5xa8eHwajCyIpWT9/7uaH2QbkYEEKcSIhQg0LXtQpeMFdtTbr58eS44eCGVf9T8+t9FzkHsstshdMz8LSmmzPn1O89zDr2IyjfmFTjZdLK2vbOFw3tmDD8d5RCbNbwgdYLaOG8W3ggU8NdPadDqyw1NtxzpJtgAVBledexbk2pFjTfDuD2KY4kZjEpGAgxQsqLLiXCyUQj1tsx1qS86PJs6F2TYLTEMDPsrn3PQyZ7JZgroPUWamr4dlGexmdyzQBijO/4G/NgtmFKCgYHu1YNP5EfgcBcxd29C6muZm+xx5wKPJiphrXNGD/9xXBnzym0YK7MMhBCnDCMUfcqxzwTI9b8M8Mw475SaH48WVGzg44zl9w45ugxf77mvw9s9B8YfKUeYNcor1YtbP4bqQSe6IfRRoy/70hxJne22bPfRd/A25Fv3Mfc0xtTc9M/z7RZf0LMVjN23a4QU0ErvnhUsQAAEXyl+OKkMhUDG6vsvpbzzdad7zI79lzJA5maY/2s3b3vORjMvArMVQAUjFnDB9q+yNlc+fHmosqKXcC4m3cAUFRZMTVrNInM4V6BUjNnFonWEQqvlWFolZ3uOEIIkQRXmyVpL3ypUnapZdzDjIAZMTOyAHpykTtly9tKXcMndz6v/PquD7ttwTI1GC5E/8Cb7dZdH0wkjKKeAkdjKOofKhZ4yBd70mBUcGtHMjmFEOPIDAMhRmL0M8BE427E+hPJUwRsrbJbd3wSsVmN/JdxaHftfRHNa/rwMVXvB/PrDUccIQCObe+8SC9ecO3xZKOKsh6kUn9ALvesoWwMIERF+Y/Ic0MA4L7+Obaz+ymwtoyqKu5WjQ2PH9eY9XXbuP3gAJhTOHTDbaFUq6qpmhGNpACAUn4GrnMvovh0HCq6MIhCaqx/KMlsQggxHdJe+CKt+OXIX88aANZY+j6AFDN1BJFz14m6nFB1R67/yOAryY76/vYRRWfZ7t75h22SNyRayXWZZ/GLbA1OokHsSv+dfuXfRwcmm4eqq37BXT0fxujriRiO04IgHFvIJ1i7gLO5ckrL8johkiYFgxnO0abJ1eYpREjFRt0exs6Ma+pTSiKj/+A55gyM+EJjRhDH+v8SjHVcuLXjjBHFAiBfxXe5vfNNqKs5+j7OzIVmEngwtroY+dTyRT/ilvZHuH/gMhBFVF15nWqa8ygA2NaODdzZ9THkZ0M5nAueZfoG/qRXLPnhZMcjRUzzmj7GLW0fg+UG5GcW7FcLmj9djJ9nOqnFC75id+97H6L4zPwBtZeaG79EWh9uFoUQQswKWtk6rfgVRE8WTFX+OL9kIOe9Ib9f/YnLfzxTd5iXYmSyi3CEgkG0hKv7X8/fgEIZFBxOYenglXw+NN7vb6J9w+/jTLbSdhy8AJbLqLpy05EeQqh5TZuMMd9E38BrwVwPpXZRQ+13EJtKHswU+ggPzaQTQiRMCgYzmO9GZ7raXgVAA9CeY56llf11NvR+kXS2mSqMnccU8bccbd8MoAxANjbqB0HsPJBwtEnjTHYdCu/jvPqYTuA4jyCOT8XoJUwhVZQ9UIx8RASa13Qv0HTvyOPMDD7Y/U/AmKcjueDZtqfvL6qmqnWyY6ra6gNcU/V27u2fS0SWqitn5H7ElPKzevXyz3EQpmGMQ2XpGTsTRgghJsLV5iTkF/OPXdZWqZWtM1YfTCBWyQjWlRf8+ZngZU5urDKNh99lwT4lewlUXAY1dJ+goMDwBy+hd2b7y39bs3lwk+04uIrbOj+N/LWB5sHMy3M6vC139tLDN9dbszIL4DsjjlQiNqrij30WsWUamvXHhNjWlm3u31BzSlKNGoUQh0jBYMZi5Wr7T2PW2/ta8Uu0stcbq46pc6oYLxe5NyPiWxRxmWXKzPinFK7TilyQw9iigVLHdDFFzXP+i/e1fBkMD/nZCTF87yaaU7+5+GFHyOYqwVxb4BWLvoGTcBwFA2CoUHGc5ygV5HvSs0AIcUKxTAdRuI8LWVYD052n1NhqJw42VPzEf2jgNcPLElhTFC5Ib+l+SUXXkXZZSM83zVqNuUcgkK2zc6M1ZmUPl6H8iW3vVEB65Fuc/T0XZ5cOPBwtLu879qTK5hYt+2HtT3a/QPdEc0HgcHH5YwffvuxPXp9Z2YP8JMfJFg44m6tAFKdQWd45k3ZBEqKUSMHgqBhEnGamXLFuHF1tFjnaXAjARkbfEht9xHVkhTjK1mP8U2MAiBxt1hirpEP6cSG2TLNi3ZxqmnOzHRh85dAN//AsgYCqKq8+ps9XV7VxOvUmbus8j2NTRxVlD6k59VO/9MXzssivSR37e4rhuZ1TPr4QQoiSFcb6cc8xHcyYR5T/nmBGYJluYKYg6XyloPNjS66p/kHLvvSdvc8mw6ngpPK/d71nwY1woyNez7LGcmYsIjq0gxEzLAgP504zP4vd6MKK35rxyxKJTcXtrdx1zsL7FXHaMvUXrumMFjSn0Hrx6ut0S5DiMh3baicGGEGLioO5jKqbJn6jz7kgbXft+yDi+DQAFkRd1NTwBdVQt2PCJxPiBCcFgyPw3egcV9u3A6gCkIkt/TgXetcdzzlTXvgMR/GbkV9GAK3iF8XKfjMXuTdP5DyGVT8K73KhmKnjeDKK2YVSflYtnPd+29LxOsTxBhB1UXXlz9T8uXcf8zk8L6CF8248+juLhxwdI536A7K55+LQsoQYSnVSY8PD05lFCCFEqSFkAvef0170ZgDnAAiNpWuzofvzpJOVkt7XN9/f+/rm+yfymSBy/lTmR5czg4jgMsMACILY+TkA2HInQoEpCkyE6OW1p1akwrcjf53bGxn9jSByjml80+znRp2vOdpELe5hl04cid2975+GllPm73WY53Jrx2e5uvK15OabKgshjo0UDA7Dc+KVrrYfGDHlv9JR/CbfjbqCyJ3UtChFNu0ofvPIii0A7Wj7Tor4DgYdc3MXZspZpusU+GnDGZkRAdgXxloaH4pRqKqyQ1dV/nvSOSZKLV10td29rw+Z7PPAnILn3qUWNP+A1AxfJiKEEOK4WVb9g4H/laRzzDaWVX82dN/jO/FzSfF6ZtoRRvp3sdXtAMApbcycyvuc9v5TMFTQZ8AGz68xvMw7d8S1c72rzb8YS++OjZ62JYAcRR6i+CyMv88hbj94Bs2fe+d0ZRFiNpCCwWG42jwbGHVjDyL4jrYvDCJMqmDgaLscQDz2vACs45iFUexMaJpUJnD/X9qLurTiZwHwLNPtudD54bFM/xJiJiBFrJcu/D8Ax7xLBWeylba143JE8VL47mOquelvssZfiNlLkS1PefEbFPG5AAJj6Y/Z0P3tjO8/I8QYROy52iy3TD2x0VO6DbCxqjcTej853OvZ85f/tfIvm3cjm7sCgG+r0zuCVzU0EWHsUgXtaXNZbPQxLYMsCssah+lvAWvHXoMLIY5CCgaHV0k0/pcNARWTPeFQg55Cf+aOtap74mckmw29XwP49WQzCXEsOJOthNYR+V7u6O9ODvcP1Ns9+78ORgqAhyg6027b9Ry1fPF7KeUX3Ldp0mOFkcc9fUsp5R+kqgrpqSBEIhhlfvR5AAuG1rFXaMUvK/Oj6kzgfT/pdEIUS8qNLnC0fQ8AC8BhN34iG7iftqySKYhrxXr54p8A+AkA9K8p3win//2F3glCoe2Zpwz5XhZabYOxKzF6+a6m+tr7pjOLELOBFAwOw1h1G5FdT3SosSAzQmPp1smeMza6hd34UTDWDS9LYEbIjE1mUgWDidPK1vlO/CwiXmyZHslFznWc1JeNKHm2q2cRt3Z8GNbOAwC47p1q6cKvk1ea6/9sa8dLwSjHUI8QAD6Y62xL+zP10oW/LdY4Zs+BS9DX/w4AlgEHjvOQWr7oC7IuUojp5TnmJABNw03vgPxsQAW+gsBXM0j+PylmPK1Mg6Pte0ctaWWsTnnRmzOB/40Eo41icupxnbanEI3a6jKIzfQ34lbz5n7Z7mv5HJgrkO+3oFFT9dXj3X7YdnYt587uV8OYxXD0dppT/2NVV7OnOKmFKE1SMDiMXOTcVK7CcwGcOnSIGdiVi9zfH895M4H32bQXvVqBnwrAWqa/ZoPpadDjaNOccuOvAPCI4BLzqeV+dPlg4P1TfhcIMZuwsYr7+pvJ9/om8wXJUexyS9vnwajA8NS+KDrb7tr7Lr1qWWmuGY3i9ThULBjmIQg2AChKwcB2985HX/+7MHJpURxvsLv3v0avWPL/ijGGEOLYKOKGw7xESnGZsVIwEOP5bnSWo+0LCagwlm7Nhe7vSrm45DnmfIyZYk8EVwEXASiZgkHQkbqhbFGmgRlNyOdVlun6MNbT3qiYqivbVGX5m7nj4EmITRnV1z5MKf+4HpDZg92LubXjC8h//xOiuI4PtG2wSr1HzZJtmoUoRAoGh0V2MPA/6znxSqV4mbW0L4z1o8fbH4CZwkzgfQ/A94qT89j5TvwqAGmi/PQsInjMqEu50WXZ0PvjdOcRU8e2tJ/GXd0fBMNlQMN171bLFn2VXOfYG2u2d54Bxth1gB7C6AKO4m9O5FzTRqt9sHY+RmeO4Ti7izUEd/degEJFiVzwVABSMBBiGsVGPe5oW+hapt9Y6p32QBPGTsqNz1fKnspMLWHs/NVY1ZN0qtks5YWXO4rfMNyYTyu+siwVnjGY8z5cwj2gDtePo6T6dLBRwUDOe4/nmPWKuDG26vGp7rVwJKSUpaY5jxTrfNzZ/RIALg79QyEALnccfB5qqr5brHGEKDWFtuUTI4SxszUXuteFsXPcxYKkEWH1cLFgxDFfEa9PKpMoPu4frOOD3f8CRiWAFAAXUXSW3b3vdRM6kbVpHL5pUEkWG6m+9n8BhDh0EWUBhKqx4ZrkUgkhpkpsdYex9FtmBMxgZkTMCKJYf630mx6yLk+Fn3O0fadWuFQrfknai/7L0WZ+0slmL1aO4leP6OIPIngELBla3lKSwljfgTHFAWZElmlCW3JPD0IYO4/kIveGJIsFU8KYhRh/76QRm8VJxBFiukjB4ATCwH7mgl84uxKKJKaAPdg9buoi8k/AL5vIeaiu5n6Mf5JuodWOUt11QDXU7aC5cz4Cx7kfRB1w3Ttp/tz3F7MpIdVW3wbAjDkcIuXfUKwxhBDHLht6Pw1j/VFr6bfG0i9zofPOIHYeSDrX0aTc+DwClgz3Shpan16ecuOvl6eCz3lOLMX8IlPEKeBQb6pRryku2UKNsbozMurLzMgyI8OMkIFHsqErs9qmk+c+hPxuZyOF8L0Hk4gjxHQpyaeEYmpEsb7ac8xJzPCIQMwwAHJh7FybdDZRRMwOCs8MGHvzf0RUXtaDqspvo6//ncjfIDOIAmpu/HIxYk4V1VC3HQ11n5iy89dW7zf9g98eanpokG96+LBaNP/HUzWmEOLIwtjZEgJbks4xEUrZDSMbKwMA5X9zewSs9xzzbwR8OoidhxIJOAtZpgyAfgC1Y14iY2l7ApGOWRC5d1kbfdTV9mkM9Iax+2fpPzW9VHPjr+2ufReCuQyADyAAUa+a1yjLesWsJgWDE0gYO1sZ+GdPm5cDWGAZj4aR83Nj1QxY5zkZTAA0QGOrwaMosmmtbLOxqs2yGpymcFOGaqvu4sHMK8ccjuG5d070XHrRvBs5k72Hu3pOhVIZamp4gLQe+3T9hKMXzbuRw/AO7ulbQr7fTdWV7UlnEkLMLIqwjvnJIsE4RPAdx7wmiJ0PTm+y2YwQGfUdV9v3A3CJoJiRY8b9UezsSDrdkaS98KVa8YuRX0Nv0l70/DDWnwxjp2hr9MWRUXlZj1q26B22tePpCKPl8L3Nqrnx79A6sp1dy8jz+kplm2WOjcMtbedzLlgH19mr5s65gVKpGX+NK5IhBYMSQcQpR9kmY6nDsirqfvEjRbGzLYqdT0/V+UsDqzI/epUifg4Al4GdYeR8PTJ619h3pr3wSq34pQBiwDiW6ZpM4P5oJverUDXVLaZ34LvoH3gr8lPnFLTapxbOm1RDHipL91NZetLbic5W5HkBNTbMqCeaQojS4CjTCKDxcMWCYQTMnZZA08zRptnV5lIipGOjbgtj5/HpGjuI3Dstx//savMsYlQZq27JRc5xf8c52jT5TvwqIqxlYH8U65+GsfPE8ZxTK1vju/GVivg0APNG9KFSAOA55n1hrN84k69ZZhpKpwb10oW/G/7f9kDbmdzV8wEAigENRz+qli76QpJLNzmOHbt155dg7AIAKQRhYLfvfolaOP99pVLQEDOLFAxKQNoLX6AVvwL5Bm3aMv0hE7g/li+AyUl70UsV8XOebGrEWOa78eeNpTeOLMb4bnSmVnzl0LpRDwAU+FkpN96Zi9xbkklfHHrx/Os5l7uDu3tXw3V7qL52Bx3tynQW4L6BBtvVfT4YpOpq7qTqyrakMwkhxFhKcS3yBV3vcO8ZauJ4XDecpch3ozNdba9Cfpmc9hzzdEfbP2QC7yfTlWHo4cnXi3U+rWxNyo2/huGdqBhzhpoo/utkiwaKbHnai74BoIIIDhdu4VmjFdcYSz2TzS4mjwcGa7mr5yrgUBNNxGa93b3vLXrVsqL9+5ooe6DtkieLBXk+GI5tbX+Vrqr4WlK5xMwlTQ8T5rvxqVrxK4jgEyFNBE8RPzvlxhclnW2m0oqfO6YDMgHQnmvOH/k+R9lnFlg/mtLaXjFNUacUpVKDqrnpPtVQd0IUC+z+1rPtnv3fwUDmNRjMvNruPfBts/fAxUnnEkKIsaJY70SBa7Dhm0JmRMj3GPr+9Cabakyutu8ZuuZxiEBDuzU9XyvTUMyRFNnylBc9Pe2FL5jqnSd8J74CgDdi22oC4LmOecWkz+nGzwBQRpR/uHeYr3G2lqZsVqo4MtvZfW6Bwy7C6CI+TIVnWmSD0zC+uadGFG9IIo6Y+WSGQcIcZS4feXMLPHnT+ixEmNFPuRNUqAOyQ+DKMccO1wRwQs0BZws2VnFr+0YOwqXkuXtpbuPd5Ogj9n8oFRwbh7t734exT+t6+9/FTeFd5HlBMsmEEGI8BoWxUd9ytH0PDhUOrGXcRIwyZjoQxM6fjVVdSeYsNp2fWVFW4KXY1XaNsfq2sS+42ixytF1vGV1B5NxztL5EAOA58UrPMZ9Bfqqm1ip+pXXiGwDKMKMvjJ0bjVXdx/8T5RHxYiK4o4+BwFgw2XMq4uVDMyALYkZgma5nUDjZMcRxUzjc9tNJcvR+RFEEjP43CaWk35KYFCkYJK/g3wHJ382kMfAwGBtGrPUDABMbfe/I9xmrriey60bOMmBGzlh13bSFPW4MzzEnqUZzoT2L+k0nP6I7acLr5jiKPLt11xdh7XwAKc5ks9w30KmWLfogpfyS3EJxJO7pXYTCX9CGu3tXUNOcR6c705GwsYp7+xaQ7/VSedksbToqhDiSXOTe4ljzhKvzs98io2+PjW5NOtdUspYGDvMSWaaOsQfL/PCNivhyANCAcXU4mA2dDxmrDx5+FIbnmPcTIT3yqAKeCTCDEKe96KVhrD8axs7W4/hxnmSZHibm00c+AGKGZcZjx3HOzcR81phzAvnlq/3G0p+zofuL48ktjo+qr7nTDgy+bszhGK57e5IzO1Vjw1/s7n3PRf5eYjhIQLXVP0sslJjRSm5Jgla2Ju2Fz0174UtcbZYknWeqxVb9jRmjtsVhRhBbuj6pTKVIka0s94MPVqSCX1Wkgp+V+eFrAC44EyAInW8D6BvarzhgRmgs/T4yevfI9+Ui5w7LdB0zImYMMiOyTLfkQufv0/JDHTdGmR++z3PMJ5zy+GKsjZ7Z+37+n+AUnnCTLLu/9Zmwo9a7pWHtXLu/9flFjTxFyPd6UXhmiIbn9UxznCOyB9rOtI9vvZoPtH3Z7tz7fbNl+1Ucxe7RPymEmG1io1uzofebbOj9ZrYXC4D8zArL9CdmPDnra2j5xb4w1qOayHpOvFoRP5MI3tB/0gDqUm78liOMoFJu9AwA88a+QpR/6k8ElwhpzzHvLtbPlYvcvwHoHP65hn6mTBA5P5342RiuEy8zlnYD6GVGOHROAyAbRM57BnL+q7Oh93OAbLF+BjFxVFlxEDVVXwGQA5ABEEDrrWrxvO8km6u8i+Y1fQiOcy+Afmi1jeprP6vmzpEtWsWklNRTbM+J13uO+TccmkL2EkebX2RD71dJZ5sqQeTcqVW0ToEvBxACcJlxRy50/zpdGbQyDb5rXqaI1zFjTxg7Py+0o0ByGGV+9HnkOwQ7AHwFfk6ZH1VlAu9bY98dW902mFNv8Nz4LEWoiYx6IDb6wPjzEjKB9z2t7G+0souMpf1HfmpRWjzHrFeEc5+cIaHhgqEzz+a3+g/SJyd0smxwNjB6aQwAF0F4NoCfFyXwFKLKioNwnIcQx6fg0BS8CFpvU7XV+5PMNhL3D9SPa5AUxRvtrn2v0yuX/E9yyYQQYnpkAveHaS86qBU/F4BvmW7Nhc5Pxk4S08qejjHLzIZmDp5+uHOX++EHiLBxqIfA0SwGWBXjppuZcoOB976UG12miNcz0+4gdq41VvVM5DyONnNTbvxpAHXIF8ENM+5hoIKZ9oSx/n1stDTzLSF6QfMd3NhwD3f3roDn9pbKNYeqq9mLuppPJZ3jcJgZ6B+YA9fNUFq2eyx1JVQwYHiOed+Y9fxaK36ZVuaGmXQjNzGETOD9P63sbx1tFxlDB2Krp22NUX5GR/x15BvraADzfDc+HeCrIlMaexJ7jlkLYM5w4x8gvz+1Aj+FiP8fM+XGfoZBcRC5dxzL+Y1VPRP9Uk8CDaq0u8W/hHJqka2wW/QZvQsx9iafoLgS6yd8cq06YIzF6FlHDKVmzPY7atnCL9rd+9+AIHwKAAXPvVUtml9SN+G2s/sCjJ/Z5SEILgVQUlmFEGJqEGdD7w8A/nCUN/YDiDB+J4mCTf5cbRYR4ayxfaGA/FT+AjPEM8hP7y8KZsplQ++PAP442XOk3PijAJpGZFUAzo0MfT6IvDuPP6WYCuS5ITU1THr5yYnGtneu4Y6uD4G5GgDBdf+hli78Knmu9OMoUSVTMNCKawDUFHgpdrVdZ6ye1Q0AjVVdSTQ38p34cgCpoWIBiEDM8DzHvDIyzqenO08hirgWQKF2s6zIlhvW4woGh8fwXXOqVvZsZvSGsf6bsbpkb4prNg9uArCxfz6Ve4+Wfw8WPoFcGlBPoy3pHNZmYoxptIQY/RMdh+prf88t7edjdAEipLrqXx/fTzB9yPMCvXLpfwH4r6SzHMHI9YQjnZCNNoUQ4nCC2LmlzItePfIYMwJj6feF3q+VXY4CBYChdf8RM9Twtc7QeX6VdG+6kRxl5iA/k3IUIsDV/J4gghQMxIzHuVw5tx/8JDCix0gUbbS79r1Fr1o6btawKA0l08NgaFuYgnuQWKZZ1SW4lBDx0kKdfYmwKKlMY0VGP4axnV7zBiZaZCnzw/e42vyLIr5CK74y7cX/6Tnx2uIkLR7b2bXMbN35LrNl+1Xe4y1r3K3+alhKEcgFAAJ5dnfah4VlHvH/G4PI3YpfTnQ8VV+7ixrqPgWldgGIodQ+qqv5gmps2Fy0H0qAaqvuwPgL2gieO64zuBBCnMisVX1BrP+VGbuYwczIGku/yYbu7wu93zDtReEKQCYbOm9lxu1D/YraY0vfz4bub6f0B5ggzl8DH66CUa7Ilk9nHiGmgm0/eA7G/zv3EIZPYcuTruCxZbJdPQu4f7Du+BKKQkpmhsFQI5zrFfiy4elkQw1eusJYl1SH89nEMj1GzKcV6OxbMjeK+SUD9GOt+NUYWtMHgMNYfwWgY97o1tXxUkW4cMTP6gJwPce8O4ydd0xB9EnxHj2wlls7noN8PuU93hpVBlE0eOmqUf9/pUj58e01Dzvn9II9XguLPtri3hXf7R/sWUMbJzzwmnIA+MmIIwrAxM8zQzAAdlUjK0qr0OwnxjRsIVkO/wFznbu943IQGTAUp932zCWr7uUyb9b+WYuiuybpAEIUxgBAE/luPpIodrZFsfMegB0A8ZFmBESx3uY5ZjMYa0dcRwbG0k+N1Z2Dgf5yMTJNlfxsx7iDGXMLLJ9gzzGn5yJ1awLRhCgeZg+HnWnJk/rdYds6T+LOro+AOcWAhqMfUUsWfmEm7PI1U5RMwQAAMoH7P2kv6teKnwXAY8Y/spH73WJ98Yjxgsi5rsyPns2MGiJ4nL9pCoLYmfDWK74bnedq+1IA1ZZxbxC5PylWb4Bs6P2fq839jjZnAwjC2Ll1onsoO5pPQuFfUvPzFyNH39t5ysWWvCfar8CIpQFk2fV3HnSy3RnY2kPbVzMQc6+7I3dLw/dGnWPhtKWdscigUgf4FIAFAAzgKtb4ivFx11SPPbhw5Sanc/5P04+2r4pr/O7sKc27j/4pIYQoXUTsp73wrYpwCQDFjHtykftNY1WRto09lu9nQibnfSrlRc/Wii9hIBsb9fsgcu8uToaplwv1J1OeKbSsjhxt35amsDkbur8ByEx7OCGKQNXWbLL9g28cc9jA0Q+SUhPuKcK5oIw7Dn4Ch3b5AmKz3u7e/269etmXji+tGFZSBQOAbDb0fgZA9gmdJpZVNhO47/Hd+JmKeAODdgWRvmaiTSZTbvRUR9u3D1f1FfDUtBedOpjz3spFuhGPjN4TGb1nsp+3jHadn50wVgaYjqfLR+d0hGWwdmyDJ4AROR0DFNaWufn/CQYQW3fyzZVOBCoTOdV/2vI8t33wqSAKgiU11/Q+c+WNOqT3AFhMI38HGnyQDN7EGj1TnStuKMv0X7zkgakeRwghpkOZF36QCKePaE58etqLPjOQ8949nX0CGBRnQ+/3AH4/bYNOkiJb7rvxMxTxWsu0PYidP8fW2c8wD4KxYeROD0MzDiq14ivL/XD+YOB/NbHgQhwHqqroRFXFf6Jv4B3IX3sTFHWr+c3fmMz5uOPg2Ri/pN1FFJ3LxmjSWoprRVBiBQORBMsqkw293wKY9Ho+R9tXjVzWQATNjArfjc/NRW5JTKELIudeV4e9zHCHL2qGpiv+olQaH5k6NwsiO9yl6UnM1mr8kIHLAMwFsN26+B47kO2VjqD+6gc/qjLheuJ8l+3UE53v0H1Bc99zT95I43u4sIpxttG4LoGoQggxI2llq4eKBU/2GiKCw4wm1zErotjZlmS+UqTIVpT50TcAVBHBI+bTy7zo2dnQfU8udP8j7UX/xoyFALyRyxOGrrMu0Mp+v3izN4SYXnrR/Bs4m7ubu3rWw3H6aE79ZlKTm03OzBqFL+IJXCIX97OAFAzEOIpsecqNX6AUn81ARxTrX4Wx8/hRPlaoyYhPxHOnIuPkkM2E7gdTbvxaBT4bwEBs6Te50L0+6WTD2Nc2WlBzq7en+wIMLUtgQmxTzo7sujl/hsKfE444Y6QfbFmsMuG64WIBABDDd1v7X4DIMNxxGxMwirjFlhBCnAiIuBz52XtjmxNbRahKIFLJILCb9qOXK+JLAbC1dH0mdH/hu/GzAVQPF1mI4DKDfDe+MhN43x3I+e8bnrmJsdsnA5EiW2cgBQMxc1E6NUjz5x73ciFVX7vJ9g28bcxhA0c/RI4uidnDs4EUDMQY7JT50ZcBNBLBBWOR55iTifgLQeTee9hPATsIWDHmcGisKpnmiUC+63Im8L4J4JtJZzmcYOOSO/xecz8PDDwfzOl4XvW27mcu/ybUkQul5Xtz0jRvBK8ttwZEGDdbA6Sc3tx2U1+2HERPVg2IWXudYUCW5c9RlDppeihKRmxUC1zkMHINcZ6OYnW0hw3jKLJlrmPXWEZPFOsdxZgBSGBHKa4ylnoAmrbCcJkfXkWEU4nyhWul+PnlfjgfdKhY8GRGgqPA6/P/nVNa2QsxvlgAACo2ev/Upxei9FF5WS9qqr6Mnr4PIF+4VFCqQy2YJ8t2ikgKBlPIc+L1rmNeRUATMx4JIufHsdUdSec6kpQbnwOgbkTVmwD4rrZvDCIctmAQxfq/PMd8FoAeqpTnmPFwGOuHpyn67EEEtbD5FgC3AED/mvKNttIPj+Wj1f9o2wkMrRE7wXEf7bGWnzf2ODFH1Ttyn+ipSl9lXawFYMCI0y25L1XuyjyYQFQhhJjBiMNYf8lzzMeHDwCg2KhvWVYT6lI+9FR9eG2z8h3Tkgncj1pW/ZPLxkh70Uu04hcP5Ypio76Ti9xbJne+Y+co0ziyWAA8uaTgbMu4kYG1I3o+DO9QtRsAyrzwHUTYMHI5wlDtO4yN+g6DjumaQIgTgV7QfBc31r+KD/asgesMUH3tdiqw1YiYPCkYTBHfiTe4jvnYiHX9F6a8+PRMQG+b/Bff1CPihQDSBV5qOtLnwtjZai2903PM00HcYK3alIucu0qlN8Bs5287OKf8+h1vsbmoFgCg1H41f+5nqbqyfboyDC5Mr801eJcCUP7B8O8Ve7KJbodK1ZVtaPf+hiB8KvJPvhhAiKqK/3EiDDRs6v5YUOs2GF9XpNpze5SV5QhCCDEZYew8Ehv1Rs815xDghrG6e6LNkx1l5jjavmPoBtsDAGYsTHvROwYD/4uTyZVy44u14itHXIv5jrbvdjk+MNW9FZTieuQLH2MbGUfGqLuVYy9ghiKCYs5/P4Wx80uAFREuGFlMGBIbS7/IRe4NU5n7aKjFHTcLr2dN+ZTMzCs0lhCFkOcF1NwoD32miBQMpojjmFePaQKomOH5bnzpUAffkmSZdmhwFuOLBvuO9tnY6o441D+dmmTisCyj+i/bPkmRacRwhcbaxXZ/yydVVcXbp6PK2nNS5XPCGvc1GLowyixIXxhVOj+vfbR/0o00i0GtWPIdPtB2Pw8MXgKiHNVU/0U11m8Zft3vjjqB6ISfjSGEEMfLsurPhWrSPYFcx5wz9tjQTfM5+Xrvkb7LGFpxnWXKMFNu+Kij7fNGXosND+Vqe3kUT+3SxNioXZ5jCl1nq9A4Dxq27/ed+BUAVjFjVxg7P8vvBMUa45vyAv+/vTsPl6SsDj/+Pe/7VnXfGZZhkx2FiIq7IqCIAhpUEmI0auK+EONCTHA3auICxqhxxSTGLUrUxGhcouangqggoIgaEEEQWURAEFlnud1V7/ue3x/dd6bn3p71dnfd5Xyeh4ehurvq9L1Md9Wp854DSZFG+xbMXMD7q6YuhM5hg4mCtfu3L4Tpw0Z9kT/sWMaYsRm65NESBmMivU72G28TWiJ6QBPxbK1uHS4sfHW9KgeI0FIlA3UV/Ueajm2hcpKnypAeBrgq+h9ldWu3dR/x1rDP7exE66YM+CtnP77y153Del/Gc01dcvMBEvOesvHZlCPrbnr7nQfIrqu2exTl1ohtN1WtKp6HyOBdlFa9c/HMuMJ/M6xL2/zzGBURod9UZ9HM4TbGmOVJ4pCmMwBpc8mCMsT7lyG9CtgRkKzy7XXd4l9BEkMqJkVworpiZGFvQlY3HbN8PDg9kQ0NIeuY3EdUpYrJ3xiTf/fcV0pSmBmtONidV+roh54HTFLvAn4mQTD8sVHb1PmPMWYyLGEwJqpcDhw+OEdXlU7OboGv6Ze8tlO+vl3Wj3OihytySx39//Sy3ma2MsT7lSG9mf4M2OCzq5P/h24dfrK1+1h1+doLL+OedO+TDm5d7q9cdfnaC2c/fsd9Vh62qaaGYZ3uhaBzptCCkvPsrtUjLx1MpduHuTNwAfTOg1c+3nfTr0d5vDkHAUkrw6G59IcCuCr9xK+NP5LhMRmzFFjTQ7PkdKM/b0WZTxzcpkqVVTZZgu9d3qUM6c2DVQQOPWZFq75rXbf8VMry3f6ShPUJbVU6MbvvjuVNzNKpyq8XPl5e+Hw0kOvkz66T/9WWX1d8YKqs/16VXel9l4WY3Gkpu9vHHrQxxsxiCYMx6cbwiXYR769KOdMEELihW4fvjeeISruIx3ifHwekmNzXu3U4f3t6CChSTVfl14CvjTzMJUVdGdLfiGzcGbrw6bVV7Z+tyFaPc1l1+doLuZxNZtBnJxE2iiIHl5WnMnudpEhXdl11zbDXjDJbL4lVvstzZ/+fpiLS3a04W32xTetYt1WY5mUoR0u/m3Rqh2PTVAhxitPGeVxjjNlW7aI+Kvj8ZGAqZTmnUxVftAZ2PTm7u+ro31aE9Gp6n+delR9PV8XHNvWaMsRHMetER4SWQ48HPtWpii+uaFcPQLk3vbG5Pquc3a3DxKrO6hSuqRNDv4s3JWV325pO+dIypHuL6I519JduawNJMxkS2dPV/KHAXur4YSr5LoKN8zNLiiUMxiQmf+O0ykvLEJ/gRPdL6i7qVuHsbbmI3BYrWvVLnOhjZ7Lshc/3dlIfNF2Vnx7H8QwUPh/A3GZGvcdCulcVw2WTiEOcy7Ln7qfozbecgq4vX0xyt91PEefG3shPPXcgnKPKUTMX7QpdhAvUM9ZkgSRWoRwrA/O/BVqqHC2JT6nH7sYYYxaEqbJ6snf6zJnvae/0qSva1YPXdsq/sQbBPd0YLu5G/7zg895ZZXXO7q4tvKQFG5Xtz+g1TUTqtZ3W3xYhHuRF943Z/TIm/5uRBz4WQhXDFVt+nmmKq7mnq3k7EAQCiQeHaR4Xp/gbxBopm6XDEgZjlLK7Y7oqPzvu43iXd3Wixw3O9BWh7Z0+yUn+Yla3btwxLEeqrGP4iYpTlbH+zLXTXZF/feOJdKujECLt9jfk4ANfwG133gcU2WO3S8X7NM4YBsU2H/RdriFzPIA6zkgt/mfcx5XMnkANzF56UUtmL0sYGGMWBvXe6dNnNUMuUQ4qQ7q3XRgOkhyTv2FrnhmTv8C7+GcMfBerElU37ltTx3B1DVePOFCzzLmaFwkbqkwF2gp39xWHpZb1TjJLhyUMlgDv8n5AxdyLpuhd3isnZ1+SYxCz/60Sr0I5eGb8kSoJuLlO7tpxHVdVyddcdwopHwgUKDDd+WO99vrd/L0O+sC4jrtZQk5tvgJ8ZZKHzZ5fu3ro51jIHuu7YYxZEJzTlWzinMuJ7gNYwmA71MlfF3z6jHf6bFhfBv676br4cJNxmWXjwNkbBKY0cy+s2bJZQixhsASk7K6HNKw0PqTsbpp4QMvIdLd421RZvxx4KIDCzzpV8Z5xlpfqrbcfRMoHsHGCqEVVP1o7nY9Ju93YVIKJc6xTx3+SeToblodU6vgcjuXzczCNkMQOruJPRDkU4aYc+HwuGOtsd7M45SyrgWnmJvZdyu6qBkJaMqar8kve5e8WPt0vq9xWRX+ZLfEwE/JbYP/BDQodHDc2FI8xY2EJgwkoQzw4+Pz7gMTkvlPF8PNR7j9ld1tWOcOhj51pwKdKJ2X5si1HGK+sbvXabutUQUsEVCfQvKqqd4Oha+OSdro7LauEAZDafMFV/MIljgMke87MJT9tOq4FTxHf5UmSeSLQQvhBKvk39axpOrRFIVP6Lu8DdhUoVLmHq3koyltyyaVNh2cWGtGY3L8En18BFCI4VTqqfN+mEM1fyu72lN25Tcdhlpcc+KSLvHagf1ME1qSCMTU4N6YZljAYs3ZZHT8wg1fKkI71Ln92uiq/MMrjrOsWH24X8eezpiT8YHv3513avV3E54nwAIXfxeT/Y1tGBS43ilSTGuInO+90hd52x5xxiQi17LTjzZOJYmHJJZdkWOAjSxcW3+F5ovzh+hMd5Rjf5V5xipfZzbkt8zVHAzvPNNyU3i3Nlou8IJe8utnozELUqYvzC403Fz7/gaiuTNmd06nD95uOyyx3SrusjwtOnw7spPCzbh0+sniaQzYnl1wIvM1F/gzYXYUf55LP4rDJJ2ZJsYTBGIloKzg9cbDJEdDyTp/hJH8zq5vXnTzv8q5liI8X0T1ydj/p1OFcajlnnmHjJK+cKuP7gB1FcAK7Fj69HvSd3br40Xz3b+ZHVk7dxcoVp7N23XPoXawkIMsuq94/iakIo+ZqDnCRP0bZsz+S6Bv2ZTtmSjGYLAAQCAp7uJr755KfNRneopA5cLDZ1YD9Jh6LWTTqGK6qIx9sOg5jZrTL+vHB6QvXn6sqD2kX8d3rsrzQRjluWS65OJdc3HQcxoyTJQzGKPi0L72Ludli8PnAKrrtviNa+Hhgq0jvAIIIhZN81EpXPW5tt3wzyLzudbeKeCzQFsHNbBOhVfj8nG6NJQwWAH/g/l/Jt97+U73zrkeAVG63Xb4nO+/426bj2lau5hBXcwpQCDgy9w4dHhOneBUy9O+OGQHJrIANf783ekzZfcLhLE6OKzXRGZI0uLaJcIwxZnuEudM7nCpFWaRHdSp3RpOxGWMWBksYjFHK7neQ5paOQ8hZ5lU6XhbpRfQu6gV6YxSB+7SK9NBuHX48n32LsM+sqogZd5vPfs1oud12uZbddrm26Tjmw9W8cNZd7pbCPr7i4anFeU3GtpSp407gTpiTHPDZc1kDIS06qeTcMM1TFfYUKLWXHI654ONNx2bMclOG+IDCp+MAF5P/VjeGi5qOaRHZaci2lqC7TTwSY8yCNPQOkxmNnN1dWeVsVboz21TpqvKjmP287gYLHDyTLFi/TWh7yYfMZ78AOculqnQGt6miCpfPd9/GzHLA7A0CbTIHNRHMsiGQAx9Q6CrUCqrQVeF/NDDaShXF+y5H+g5PcRUPQpdIhwShjm1erY7/ULgE4axU8opccGXToRmznEyV1ZPLkN4kwtHO8egipDdOldXTm45rsVD4ueqcLkzdlLe/CtYYs7RYhcGYresW/zRV1td5p8cDLmU5c7oqvjiCXd8K7D24QZVORuY9RrFThx+s9NUTUQ4Uoa1KDdRVHf5tvvs2ZpabgLsPbuiPJPp1Q/EsG7nkYnWc5CLHAlPq+UEuRjwLPrMydHgPsAtQSqZ2kSviFG9ZEktOHNOpzReBUXymG2O2kZM85Z0+S2T9WF1EaHmnT3OS/zerWz2i4+xYhPQAVNZ0o/8ZyKLrF7Qp3Tp8qF3Ed6sS6FX8dVT5YRW99bJZoCSyl4scA7TUc74lqs24TTRhIGjRKuIjRHSPlN2lVfSXL/1ZuZKnq/LLwJdHudeY3KeCzyfPLB1QJQHT3TqMYJSLpLWd8o3tIh7lXX5wVrmpiuGbKbvb579vYzbIgY+7yBuBUnrNN2rg9lTacoRJ0MAtKfC5ce3fd/kzYA/ZMHveK9zbVzw6tfjOuI5rjFkegs/70RtlV856qAo+H1BFN+8Rp+2iPjb4/Jf940gR0tpOFV4Xs79lvvteCGLyN6zL8sJWkY4WdNeU3U+70f906Z+fL06u4jAXeS3gAS+ZEyTx36nNfzUdm1m6JpYw8C7vOlXW7wWmgNK7VBc+/XBtt3y3fShtu05dnNuirgufnwHskpWLunVxuqp0t/jirSKxUxffBb47mv0ZM1cuuQjhb13kaarcTR0XppIvItRNx2bmT5QjBpIFvW29JScPB0sYGGPmJ2Z3czm8V1SZ8vwrLr3LuwSf/7JfwVACqNJqlfGVseNfP/v5hU/3cE53q6P7xaiqGyYhq1s7Xbn/13QcZgsU5yInD/Z+Alpk/lQSZ6rntsZiM0vaxBIG7aL+c2BnEXx/kwcObxXpId06/N+k4lhKunVxQbfmgqbjMGY+csEVueBtTcdhxuIOZi+dgqTwu2bCMcYsJf1eUd9y6GMGKi67qpyfsr91vvsvQjoU2Gj5gQgO5RBBS0Uq6C2NmGrVpwjcA0iFTyFm+WSnKr823xiMmSGJ3WFoU/LoIvdOnu9POiazPEys6aEIDxlIFsxoeZcfNqkYzLYRtFjRqp6zQ7t7+g7t7idXlNWzQK3vhTFmq+TA5xRmVz3FXGB3sowxI7GuW/xryvJxVa5R5Vcpy+lru+UHRrLzXtPqoWWwOjA2u13GPxc4SISWCCtEKIPT5xU+zWnsa8z2UsddDL92myJx5JzWlcaMyCQv/u4Cdpi1Lapa+cxCtaJVvbaf6CkBnNMnr2xV+67ttt7VdGyjVPh4UPD54UCniv6clL3d/RwBiezpav5ElINUuCyXfEk9dzQdl9mCTNsl9lfHLfP9feWSH4vyQRLPozfC8boc+FcN3DCSWI0xBtHpqvwG8I1R77kb/Q+Dz7P7IwDgne6cstwG4ESPEmH20ogQfDqyTv66UcdllilHB+EMVZ4gbLgJ289oHeFqHpZLftRUeGbpmljCICb3+eDzS2ZKxmY2VzGcNakYlialXda/H5z+Ab0pDGdMV8U35tvBN7h0t8FkAUD/z0d4l3dN2S2JRM9UWT3NO/1Teuus01QZn1FH/Xub4Tw/EtnbV7wPaAl4lIN8l8ekgjcgoJ4bEJZMl+mlwnf4Q8k8n96dswLhnNjmg/P5XaUW5wDnjCpGY8xip9K/2F4DEpuOZnOcMEXv83D2+XK38On+KbuZz7Zh7yOD9eMxoxXbfDRMcxSw8+B2gbZLHJOxhIEZvYklDDp1OKstdRmcPgPYWeGXVfT/nLK7Y1IxLEUrWvVfONHHzSRivNMXrGxVB6/ttuZVjuec7sbwzsO1d3m3pZAw8C7v6p0+feCugAMoQnpFN/rn95r2m+3ha54OtKX/MxUoFHbyNafRO4GqcuDdueSiJuM0G7iae0nm+YPNlFQ5ynf5VWqPdsqLMWZ5ahX1I4rexIEpIKUsn5+uis8v1ObXWWUdDC/0ziq3Dfz5TIf+0eBNFkDr6EcwucqYAb0E/m3MShho7//TqpGYzJI3sR4GIHSq8utrOq3nrum0/nhtp/WqOoarJ3f8pcdJ3tGJPmGwaqO/fu7R3qXd5rPvmNy1DE8o+Tr5X81n3wtF4dMhDL8rsNK7vOuk41lSlINl1ueLgAh46SUSdnKRN0ra+AvPNEDxZKYk8vvMShAKtCRzfEORGWOWkMLHAwufXynCTiIUIrS90z9tF/GYuc9WmSqrE3Zodz+6Q7v7qRWt6iVO8opJx6wqVVY5U3VDLxZVInBbFf36kY3rusVnVDlflVqVjipr6uTeFbP/7TYczffeo92rMJunjq8M6Q9U5cA3GwnILHnWwG4R8z7vSe9u7ex1c5V3unfKbHeH4KxuOmb5eHB64sD+65jcR1RlSWQws8qmfj6S1a2ZaDBLjXCVKvvMThrM5iKPSI4zfJfjJPMYoJMDX7U1eBOgON/hz0V5PL21kNObeOb23fpTnGR2UsdqZENzMGPM8lSE/ARmj1kVWsHnJ1FvPMJ5Rat+jhP9o5kbIg593IpWfZ81nfLlk65GWNctPjJV1qt9b+lnS5UfduriwxtXIUpc222910n+qHO6U0zuN1u/NFRlRat+thN9Ir3z8luq6N9XxfDzMbwdswSkFmf5DvuiPJHe0pesno/lgiuajs0sTZYwWMRScjcQ0rDfYRmzm3eTnU5Vfr3w8fLC56MB6uS/Wyd/7Xz3u1BU0V9ehnSzKvuJ9P4uqNLNKmepyuzMrdkGqeA/fcXhCqWAV4ae4glKCB1eg/KwmVJ4F7mvZD6V2nxlwmEvK77Dc0V5nMzMFoeVzPo1KXTVccY277vLYyTxQnr7Tur4dGrz1ZEEboxZlARdIbKJDu8bP68YTBYAiBBU2bsM6ZDJX0hLnq7KzwCf2dIzs7rVObF6W/Y+VdZPcqJPHHi/e5UhvTVl95KlsPzTjIFAmuLfyXxOMruo5xZkaMWsMSMxwSUJZtSyuumU5T9nlcp1ssqXc3Z3jeIYdQrXrKvKT66ryk8upWRBj7CuW7whK+eoMq3KnSnLF9d1i480Hdlip4EbU8nLEc5S+CVwow5Z/qGOX6EcNrhuvl8G/2zUEprjJMofzPq5C1ArJIV1ChXChanFl7Zlv67iEEm8VGAH6SWMpiTzXFdx+MjfhDFm0YjZnatKZ3CbKlXOslFTVOd0JZs4P3WidxtjiI3wTv94VkNwAF+GeHQjAZnFw9HRwG8sWWDGzU7IF4AixHsGlx+kyJ1V7c/L6jZVGjzHdFV+oRXiVcGnxwEuZvetbh2snHsrZXVr1nVb7wfe33AoS44GfhMD/wQgiR19l1MV9qFXPufV80+i7Mjw5poiiV00cMuEw14eeoW0s09Qew8J/6Gey9Rxswa2ecSoS5zAkF4ILvKkXPLD7QnXGLP4detwgXf1OQ49ht7kAVG4ZrouPj/4vJTlTmA1MLuXkI/JXT6ZaCeqPWRbkLmjyI0xphGWMGjYilb1Iid6HBBA69DKL+jU4bUx+a2eU96N4SIbA2gWMvWsjlO83EUORNk5B67AMS2RfX0a+jmU1XP7xANdLnoLDy5WeOCsPhOaC87XwFZ//gyxUoYvMp4ass0Ys2wI67rlPwWfvhRcPjir/KaK/oq5HxeidfKnFT69nl5/FQ90s8r/i9nfPPm4x0uVC4GjRPADm6uY3QVNxWTMbK7iwS7yVGCVOs5LJV/CbVwxZJYuSxg0qAjxnk70uIFSNK9Kq1XEl8XkX99ocMaMmkAuuGZwkwZuoOYHqhwu/bss/XXz/24lduOVSj7oK/5RexfyAjh1/Oc8kwWo42wS95WBu2b93+l35xmyMWYJiMnfsKWbIt06/CRl+avCp8eKsDImd14Vw6Wbe81i1amLj02V9b1UWUX/szirfK2K4RcNh2YMAL7LoyXxV+uXMWb2Ch0eHqd4RX/Mo1niLGHQoODyg5j1OxBBUA5pKCRjJi62ea+vOJbEYxCms+drueSipuNa6jRwS/T8uat5qCirsueiUSwBSSVnhw4PU+VwestPHHBZavG/8w7aGLPg9cc6S8p+m5Y0BZ/2LkN8mhPukVV+1q3DF/vNBpe0lN2dazrlS1tFepCI7haTuzQm/5um45ooRXyXp0jmiUAL4cJU8lH13Nl0aEuFJFahrFTPjciQ2Z1K4Ts8U5THAFkdZ6QWn0NIkjhxVs+jUmEvV/OQXPLjSb4P0wxLGDRIVe4ArWGjMjQAG+lnlg8hpxZnAWc1HcqyI6RccuGI95njFP/oag6QzEHquC4XXD3SYxhjFhzv0u5TZXwjsH9vS/xNpw5/H5O/aUuvLXzav1XE9wCFCN6h95gq62PWdYu/zOq2aerA4iS5W4f/azqKpvSn9pwwc1GqyiN9l3vGKU6yO9jzlJkKHV4LPJBe75BODrwrl/xs8GlhmjcAD5iZnETmT0KHfWKb98ncfiIAQTL7gSUMlgObktCgbvTnA7XqhkyfKt2U5QsNhjVSwad9Vra7p+7Q7n5hh3b39KmyOoEhiU1jzNKSC65LLb5ryQJjloepMr4ZOFCEUoQS2L9dxFO25ju/DPGZQGtmHX9/1PGKVhGPH2vQpnlKGEwWAEjvRtouruaBDUa2JIQuJ9HrV1QItAVWucibyKyceY5E9mIwWUCvWTHKkZLZSWFY0i+p46oJvAWzAFjCoEGqbrpTh9co/EyVpMpdKct/TFfFNo0xW6ic5Kl2Ef9R4IEiFCLs4p0+b6qsT2g6NmPMZLmaQ8I6Tg3r+FiY5mSJ7N50TMaY0Qg+7QPsJbLhvLL/51VFSAdt6fUiHCSycfdDEUoneq/RR2sWEsm0mVtpCyCi7DbpeMZO8a7iUN/lkYMX7WM6lkN5pEAx+yFf8/CZP0tmd4aMvgaiZHbNgQ8rdLW3zBCFLnBFLjauUjBLly1JaFhM/saY/BubjmMcyiIdRa+8cP1JgAgt7/RpwNeai8yMheJ8xRGSOUyF23LgDA38tumwTPNcxf1c5C0D5abH+IrDkvBS9SyDcmNjljbpnU8OKyXIwy5WZlPlKmDPwYSDKlVWuWKEYS4IwaU9i5COAKmr6M9P2S3rdfrqWAP8Dthr1kMu+6V1QSqRfX3FP9C7ky8h4dXz3tTi/DEedtjNYWHgGjAHrnFx6DWhZM/1OK5GeK2L/JHCLuo4P5V8e+g8JLMkWcLAjI2guzJrHnvfjpOOxYyZQujwepQHCbRRoq94Ylb+LhcsuRO+kVPwFcdK4vGAqufrqeScpfJl7CLPnV1uqtByNcclzxebjM0YM391cr9uFaxhYDpKX6yiv3JLr+/G8Jl2EQ9VpRTBq1IDa7t1+AaAd3kXJ3lVTP7XiizaCTrtoj4u+PxiQEDzVJlPrKI/tYrhp03H1hiBHHi/i7yFDWM0a3X8jwYW/RhNiezrIo8GRDKPAnbeaPRw4pVkLsaxdvQHJwP/p/Bg2biKQ3Jgw9hOx1p1nE7muWxI8EX1/CuOCnpTrnLBaSOP0SwKljAwY5Oyu9i79BQGx6spqnBZg2GZMXA191ufLGD93abgak7KBSc3HN6C5zu8WJTHrh9FmPg93+H30hSfaDi0Udl79ob++sgDmgjGGDNqot3an9oq0ilsuODIVfSngmyxaV1M/oYOnFyG9CeCHqhZLunG8D+q0lnZ6v6NCIcBsVUkYnKnderivLG+nTFwklcGn1/c7++wXhnSq6vonweybBs85ZLL1PNiV3M0sFI9F+SCXzYd13zNjCOkd04kgBtyHyD7Ln+cS/533lMhMit9zaNRdlHHxbng0tTiA77LqQp70ltS4NXzfvXcMfjS1OarruZSiRyNkNXznVxw3bziMQC4moNc5FkoByD8IhV8WgOLahKKJQzM2FTRXx58/p5DH0Wv0qACYrcOH2o4NDNikrkPw8tO7zHhUBYdSawS5XGDZbv9Ko0TJPHfS6JkX7hClcMH76oodNSxJOeqG7Mc1SlcUyf//DKk+wpIN/rL2IZqgJj8TTH5fxnctqJVvUCEh4lQ0P+MDD6/IuR09WIbPViEdAi9deKzKy+ngs97Lbb3M2rquT15vtx0HCOjFJJ42WB13Sa0RXmy7/IUFb6S2py+PdWFEtnfV7yL3rVdKZknucS5sc1pcYq/cpHfQ9kxBy7H0Rm2j1xwNdaoeKRczT1czTuBUkBU2cNXHJqEl6lnm0bPNskSBmaMhHXd4oNlSGd6lx+kyO1V7b+X1U03HZkZMeEmegmhqVmP3N5ANKOlOFdzqGT2Vccvc8HPRrlUQBL7AjVzEy61ZPZaqAkDSewqmV2z57qZksVNSQWf9BUP0F6X5qLfMOnmVHD2hMI1xkyEpCqGS0a1Nyf6+7PvyAOu8OmomPznR3WcSVCVOxm+ntzlLDZOe4lxkQNg7khIZUPmfODPrf6GP3Q1P88lP9zW4/mKk4AVA4n5tiqPcpFv5oIrcrHwJxq4Loe6xEuB3YA16vh0avHNxbw800WeQT9ZACDgFEpX8UeLqYrUEgZmzIQqhsuBy5uOxGw9ieztap4gveY2308lP0A2PRsrlVwQplndvyAM0Ouiq57PTC7qMejNL34XcDegkEx0kcvjFG9FSKM4hHquJw6tzgjZc+MojjFSSggdXoVyOFC7Gqeef00tvr3JlwRuSMJJruYPUPZT4eJUctaWEg3GmGVvUw3bFt2Uryr6K8uQblZl3/7YSFSpVPlhVrcgE8Nm+6njdoZXXub+tAG/US8DetWFLvH7mW1PGAD3mb0/oJDEg1gEvaRcl8Nc4m8H3sPOZE7yXVam9iLudaTsP+T3HFhkFbiL7gPXGDNeruIBvuI0UZ4oyjGSeEXo8NrNjtIWYmrxKhXOUrhN4Vr1vD+1OHNigY+Br3gKsLfAlEDo9xg4xFccM6pjqOdOFb6mbCgR7Jfrf2ksTZDmyXd4Osph/ZnOKwTaknipRPbf3OvUc1tq8+k4xTtSm69bssAYsyVZ5ex+A8RBKSa/6HoYgLCuKt6oyg9Viap0s8q31nXL9zcdmRk99dyGcKGy4buu/+eLY5tnwSZL/7f3ZsSwpFOFcOt27m+iXOKlQy6sRTLPRBfv9aoKl+qs36lCpcLIKrEmwSoMjDEbcZG/nNXRvq3Kw1zkXrngF5t6nXruTFP882SinAzJHCmz1psKtMgcCZw1quOkNp/wFVeQeDxCVsc3UjnQwXgBEeW42T8TILjI0Snw6UaCWogUD2i/S7UxZjtMV8UnV7Sq/VDuTe+kO8QsH6mTv77p2LZHzu6utd3WO5qOY6QU7yIHqbBOAzc0Hc5CEtu823d4FspxgKjwndTi33FU6vkqvYvk9edbCt3s+eb2HEsdnyPzvPXji3tVDFUqWCzJtV02sb1AaSOsm2g0I5JL/st3OVKhJVD2l2TemUq+3nRs28ISBsaYDXoXOXM62gNOEvdmMwmDBStT+oon9ccZrcmBL+aSC7fy1XcA+w1u6H8J3zbSGAX6c5jHOYt5VIatJlyUJcLjIIldfJeXAw8CMsK5scW/bKrJlDFm01Sls7bT+tvg075OdNeY3C+tD9LC4Sru7yKvp3c94ai4PrV46+wO/MuWENMUpwOnz34olXzbdzgQ5Xh6zTCDOj6bSy7ankOlFl/zXRKZP6U3vvySVPLhRfTdcwMMnZy0ZrEmCwDU87vU4iRXczzKQSpclkq+iWNRfY5ZwsAYMygBa+h92QyK6hbXCBgAFEKHU4Hfm7kr7iL3lMy/pfaWs7s58N8ucvCsLsd1DnxtXCHPoQTf5bGiPFzht7ngqxpo7O6aCt9GOWFWlUGtnnOaimnBUPBd3g7sJb0EilPlkaHLyjjFqU2HZ8xiFZO/Aezu9YKSmXKRN8ng6Gy4h+/yyriCNzUZ2qIgkKb4uCT+SzJ3y57fzOsiUqB/XrOo7lzPyAX/5Gr+gV5vh5lVsJo971/MTQ+hX4Hr+WzTccyH3REyxmwgoI5P90umANBe5vvWXPCTBiPbLq7mvsCBgxe3Ai3JPAfd8ldQLvmJev5J+xUFCr/Jgb/PBb8aY9gbKC5M83bJvFCUQ0V5nK94n6u470SOP0Rq8xngpwqVwjqFSh0fzwXXNhXTQuEi9wZ2E/Az26RXTvlgSezUYGjGGDNSvuZQ2Li7Uf+z7/7kOROTzCaoZ00uuHqx3XEGQCl8l6N8hz9yNXefz65yweWp4K8UfqRwK/DTVHBybm11RagZI6swWIbKEO8ffHosQEz+rCqGnzUdk1k4Upuv+y6rSTwV2FGFH6QW/7EY12KLsu8mHmqjTG1NmVtqcTZwNopsblLEOLjeCdndZyoc+idj3kVelEtevskXKs53eYpknkBv3eS3U5vPImz1TPRNEuq4glMksqdkds9hkZ7ojIOyA0PGaAEZZSVw14QjMsYY0yeJXV3sTfhJBT9YiI2FFwuJ7OEr3k2vwiRIRiXyjTTFx7Z3n1pwfSo4ZXRRmlGxhMEyM1VWT/FOn07/jmsZ0lHe5c9MV+WXm43MLCSpxbnAuU3HMV/quFrS0EqC1VtKFkhkD1F2zoFrEeKkkwUAkvk9Bso9Bwxb57de6PDXKI+UDbOdnxSmOTCuGF1ZvAZuVrh5VPtbCnLgMhc3VBcMWKuemyYekDHGjEkq+HGY9f3a7wb/s4WYRPZdHiWJk+lVRWhIvDgHTsklk71ppoirebBkDlLH9bngwsV4Q8ZXvBTYWQar1ZXHu5qzc8GVzUVmxsGWJCwjTvJK7/QZIrREkP4/Le/02U7yiqbjM2bUcsFVCD+ZGVmooApd9Xx4kwsSMu2wjrf6ig+5mreFaT7tuxwxwbA3EK6HoQ2LfrvJlyR2RnnUrEkXJfAgiew1hijNDMe0ek7rL9fozPyTC97ZRMLJGGPGxjGdA6cqrFGY7i9lvDa1eG/Toc2RmZLEXwuU0utW3xZou8hrt2Z54sgoIUzzdhd5vWSe7SKvDNOctkiXcDxQ5l5HFpJ4aCPRmLGyCoNlJPh8AL316LNHosXg8/5VdFc0EJYxYxXbvNNXHE1vSsLqHPja5rLfocsLgfsLFMz8XUm8RhIvVr/pecau4nAXeTKwgzq+l0q+jNswf3mzFFzk7ig75MCVM69LJT8I0zxbIfTjmRm79IlN7UoyuwE1/ecP/igks4did7rHKbX4niQucZHDgJgKLsAt3g7PxhizKbnkklzwnIU+VrHfXyYNeagtiX0mFbfv8vvAPQcS+lMKe/uKJ6c2/zGJGEZoHXOvJ2pgdQOxmDGzhMEykrK7GdLsiwiAoveYMQuDRPZxNY8X2DF7vt8v2dvOnZFTi+8A39mq5yvHyNyLbVzNkcnz1WEv8R2Ol8yJ608CMnuHDofGKV63pbglsbPvcgqwD5BcxOXAP+aSCxFibPMq3+WpKIcDt+bA53PJJZvaX/Zc7+qh1WMhB67efDRmFNRzR/Kc2XQcxhgzdkJa8CXowhqGV1V7ZHJ9DER5xKypS73GuJlHwOJKGKjjS2SeMTMlQ3tLPVIubGLSUmQJg2UkZXebKucCR4r0PrBU6WaV76Xs7mg2OmN6XMWDXeSN9O6qexc5yiXOi1N8YFv3JZF9XOKe6rgxB345j8JDYVNLuBQnmefMXgKgcKCrOSSX/HxzO/ZdTgb2l4HPYxd5nXpOVM9dONZuao7zUI5KPR8h8WI2JD5qdXzaGjwZY4xZbnLgl67mtwr7zkyx0d7d8IvVc8cEQ7lVIQ8p5b9tgjHMX2Zlv8nvtPbOMxxwdS44TT1rGo7OjIElDJaZtd3yA1NlfZV3+niAlOUb01Xxv03HZQwwU5r/slkX321VjnEVX83lVt4hVwgd/hLlWCBJwrmaK2Obt2xxmYBwrvZ6AAxWGWgOnLeJY7UZ3pgQUfaDzSQMFA88dMjJQ3aRw5PnW5uNdRNSi2+5mqskcizgNXB2LvjF9uzLGGOMWdQEUou/9V3+WuGhQEY4L7b4l0mGkQNfcTWPYuAcR6GbA/89yTjmRQmhw3uAPQSKfmVBlQP/nguuaTo8Mx6WMFh2JE9X5VeArzQdiVnEFMbSJqh38b3bkEe8i5yYS/52a3bjao5AOVoG1tcp3MtX/Elq89nNvTa2+HDosKfCPemteXTqOU0Dvxv6gt60hTXAqtmPqOOqrQh3WDM8Zfh4vq2WC67BvryNMcYY1HNHXMEpKA7QJhrR5oJrUd7mIi8G9gVuUc/HN7fMcKHxFUcCu87cVJHe2WCrf472V81GZ8bFEgbGmK3mKh7gIifR+6K7XT2npxbfHtkBhC69xpx+482gcF8U2ZoveZd4tMy66y9QkjkGNp8wwDEdV/B6iewjmZ1z4KrNViUIqOdDJF5JrwOzKHQQ/i8XW6iIEBLCBaocLht/HksquGALb9MYY4wx22ISIwwV72oeIsqOOXCx+g1LDnLJxbnkpLHHMC7KAbPPr/r2nngsZmIsYWCM2SoS2ddF3jSwXGAXEi91FatzyYWjOQgK/FjhyCEFDI5eIiFuxZ7WbWKd4FbPhtbAjQo3bs1zU4vvu5rXu8gJCjv2pyRsVeOf2OKDocMblPVdnOsceJf1GzDGGGMWF4ns6SveSe+i2vmEU8cnUpulsfxXuFqhMyRp8OtG4jETYQkDY8xWcTV/wKzPDOmVoT1tZAkDIJV8wlccwUCVQX+N3JXIViULyIFvuJpjmLVOUD3/M6o45xyz4Je54P3b/ELH2riCN0pkD1FW5sB1E7kDYowxxpiR8hUnA6s2umGReYFELtTAb5uLbDRSyQVhmhsU9hNoaW/5ZJ0DH206NjM+w7t+G2PMLNJbs+aHPLRqlMfRwM3q+HeFSqGrvaqA1anc+ovxXHCVek5TWN3fT0cdn08l3x1lrKOkgVtywbWWLDDGGGMWoV4j4/sOqW5Ulzi0iZBGTkixzevU8SmFSxC+nQtelUsuazo0Mz5WYWCM2Srq+AGJQwfL0BRqFX4w6mOlNl+SyPku8RBgdSq4cE4fgcwKl9g7e24aVr6fWnwP5TzJrFLHXVtbnWCMMcYYs80yJf1myXMegXWTD2hMHFVqYw3UlxFLGBizFZzklWWRHinoypj8j+rkl91arVTyvTDNMQr3o/fZUQO3phb/NY7jaeDmFPjG3AfAd3mmZP4EiK4mqPCV1Obf50xuEPJgs6HG9No0OqseMMYYY5YYRXyHPxflCYAbHCTVX1KZrZGxWcwsYWDMFhQhHtQK6e30MsbBu/is4NPnpqvyc03HNlFCjlO81dXcTzL3UscNueBHk74I9hVHSOZJ/ZGJvbGJygm+4urU4txJxrJFmTJ0eRHKsfSWc1yUWpy2IJIYxhhjzBIniVWu4pmiPBS4NQc+m0v+b5TH8F2eKMrjZ41yhl61wfW54D04OqM85qKgFC6ynzpuU8+dsx4LQLYbKYuDJQyM2YJWSK8QYcXgNu/0T4NLZ8fsb24qrkYI5JJLgUsbCyFx/JCRiW0Sx8PCShiELiejHDEzr1jhQb7LP8QpXtLEDGhjjDFm2ciUvsv76DUh9MDdXOQNwLtzObo7/pI5YWCC1PqjK5yZVvAvozrOYuK7PEYSL6G3HKNAOC+2+YAkdvcVLwcOARLCd2KbDyPUjQZsNsuaHhqzGSLaBvYb8lAOIT9w0vEYgDkLD2YsrM+zzEqUhw/eceifsKxyNYc0GJkxxhizpLmae4YOpwG7DTZs7k93ev6ID1cO2eYEHiuRvUZ8rAXP1dxdEicJtAVWCBQoj/Adnuor3gEcIr2fT4FyTOjwsqZjNpu3sE6wjVlgVKnplZTNfUi5Y8LhGEA9Zyobl/YpdNRzRlMxDSPKFAytIlBRdpx0PMYYY8xyIJG9Xc3bBfbZxB2GPUZ5PBXO0Vnniv3jel/znFEea8FR5pzpSORYhozhFuUEegkEN7C9RDmKPKdCwywgljAwZrMkZZWvq9Kd2aLa63bbrcNPGgxs2Uol56pwhkKtsFahRvhOKvlO07ENUsfvYNaavZ6Qg40fMsYYY8bB1ZxAfyngJlw1yuOlFp+BudOaBBy6RCsKleCn+YswzefDNF8O63izJHbtPzpsBPfmtouoJQwWMksYGLMF67rFJ7LKV1RZp0pSuGi6Cq8BGVZ5YMZNIE3xsdTiz3Pg71OLF8YpPrTJhQpNEcgF71KYVugodBUq9fyrelY3HZ4xxhizFPUrC+ZcnPZvhndywUdGekBHRx1fVYauw79xpMdaIEKHk0R5nECrXzHwYN/lnShOA2cz62ehUCl8m1mVB/0pEjep567JRW+2lTU9NGaLJK/rlp8CPtV0JGYD9dyhfmEvC8kFV2TPib7m4SitXPBD9fyu6biMMcaYpUqFC1HuP9iIsH9helUqeYcGfjvqY+aCb/guT1TwMyX3Ct1c8OlRH2vDQVkJgJtb3TBWmRbK0TJQxSHgFXZyNffPJT+VxKfIPBeI9K43f5qmON13uY7Mi+iPm+y9lDqs47PADTnwb/3m2mYBsYSBMcaMk2NtanFW02EYY4wxy0Eq+VbocJzCvgLtft+jNanFW8Z1J1s9d6aSV/qaZ6lyP+CGXPCZXHDFqI8liVW+y2tg/XKHK1OLd05qZHO/R9OmHtsZILX5CpmzXOT31HGLBn7T336GJH7sIg9DWSmZZwgc2H/5wS7yFoTX5YKrJ/BWzFayhIExxhhjjDFmaXBUcYrX+IqHa+beOK5LBefgNvSjGgcN3BwD7x3nMQB8lzcBB84su1C4t+9yapziLyexPFMddwC3wpwJECEHLln/X461ueSnc17vuTV5vhmmOZm5vSZKF3laLnjniMM282A9DIwxxhhjjDFLhxBTi3PTFB9PLc4cd7JgUiSyN7D/rFGRDtjDRe4xmSAgF7x7oEdTrVCp4xPbtFRU2UtmXYsKCLr8RlEudFZhYIwxxhhjjDELnChtemv/Z8tAe1Jx5IJf9Hs0HYkylQM/1MBN27IPdfyYzMEC5fptUKvjx6OP2MyHJQyMMcYYY4wxZoHLgV+5mgrm9BHIOXDlRIPp9Wg6c3tfnkr+N3R4jMLuA70m7kglXxphlGYELGFgjDHGGGOMMQudkHPB21zNW9dvAXLg7QiLa9y3YzpOcbKvOEozB+G4NhV8D0fVdGhmY5YwMMYYY4wxxphFoD+y+bm+5iGApIL/W7Q9GoQ6tfgO8J2mQzGbZgkDY8z8KUESu6rnNoTYdDjGGGOMMUuWo0otLmg6DLM8WMLAGDMvvsMTJfNsemVxqo5PpTZfnXggSuEiB6lw18y8X2OMMcYYY8z2s4SBMWa7uYpDJfMcgdb6jZnnuoobczm5Lre+yxGSeCWgQKDiytjmVBzrJhWDMcYYY4wxS43b8lOMMWY4F/mjjZIFgEDLJU4Y64EVJLK/RPaVyK6SeI3AlMCK/niee4UuLx1rDMYYY4wxxkxCpuW7HOeneZHvcixKMalDW4WBMWY+hs/81Y2TCKMkkf19xZuAnektg5ie8xwoVHkkynt6/YONMcYYY4xZfCSxg+/yfmAngbYmOmGap8Y2r8bNPQ8eNaswMMZsN3WcpWzcmVehq55vb9cOMytcxYNdzYHosAMivuIU4G4C7X51w84wuSyrMcYYY4wxk+IqngLsIv0bdf1/7+krjp/E8a3CwBiz3VKLs0KHB6tyBBCBgHBBKrc9YeC7PEYSJ/X341zNDanF36lnzcxzXOSe9JYdrK8bEJDZuQWFGuE8qy4wxhhjzFInkb1c5FigpZ7zc8Evmo7JjI4oD5VZN8cESjKHAl8c9/EtYWCM2X5CjlP8o0T2dYm7Z8+vNHDDNu8mcjdJnNTvP1ACKNzdV7w0TvGPA0/dVFVUpZDp/ROAy2OLD21rHMtCpvQ1R6Hsi/CLVHIhQm46LGOMMcZsO1fxMBd5HeABL5k/lMQXUpvPNh2bGRHhJlXuMXjDTCEhk5kKZgkDY8y8aeCGtB2Jghku8gjYuB5AIKjyiMFtOXClq+kCU+uP3ZuMcFtsc5JLHNgfq3jz9sYylCKS2UEdaxfzxbUkdvJd3gfsKNBW6IRpro1TvAEhNh2fMcYYY7aB4lzk5FkNqFtkniaJM9RzW2OxmZHJgc+7moey8e85poIvT+L41sPAGLMQ1DD0Qjxt9F9CzgVvUbhDYVp7DQ9vTSVvxRFzwZWjThb4Lo8O03zKdzk9TPMZ35nMerFxcBVPZ+4auHv4imObjcwYY4wx20oSuzK8AXXtIveZdDxmPHLBL3PgLQq/UFircFkueIMGrp/E8a3CwBjTuFxwvu/ygsFtChUytxdCLrg6B57vIgcDOQd+iQxtkThvruY+kvirgcx9IHOiq7gll/xoHMccJ1EOlVmf+wJtMocBZzYUljHGGGO2gzrWwNCOTU4dt0w6HjM+ueTSXPLqJo5tFQbGmMap544c+HuF1QqdftPCn8QWHx/6gl6lwRW54MpxJQsAXOQE+j0VNhyalos8eVzHHLNbZ29QSAq/bSIYY4wxxsyDo6PCGYMTq7RXtXl9DlzZYGRmCbEKA2PMgpBLLsoFz5HEPgir1XNn0zGh7CjDM/crJh7LCOTAZ13k72atdaxzwdcaC8oYY4xZzjJTvsvTRHkkcJd6/ju1uGBrX57afMx3uZXMCUChwnmpxek2KcqMiiUMjDELh5AntR5ra6jnbBL3HbzAVqjUcXaTcW2vXPJT4F0u8nxgT+CaXPARDdzUbGTGGGPMMqRI6PAOYN/+pKi9Sbzad/hYavPNrdqHkFObLwBfGGeoZvmyhIExxmxCKvlu6HCEKg+F9UsfrkytxXtHPpdcmEsubDoOY4wxZrlzNQ8C9pKB5Y/Sm3LwHJRvWpWAWQgsYWCMMZsi5DjFP7iagyRzoDp+nQO/sC9wY4wxxsyXZPYB/JCHdgAKev0IjGmUJQyMMWYLcsHVwNVNx2GMMcaYpUM9v5Q8dKz0LViywCwQNiXBGGOMMcYYYyasX7V4kUIHQCErdHPgQ1bNaBYKqzAwxhizOGRW+JqHo7Rz4EINNmPaGGPMIiYQ27zDVzySzCMV7tTA/+aC65oObbsozlccjnIQwnWp5AcIsemwzPxYwsAYY8yC52oOdjVvozfm0vmKEzXy0a3uIm2MMcYsREJOLb4HfK/pUOYlU4YO7wT2EZhSmA7TPCO2eTWO6abDM9vPliQYY4xZ2BRczWsEpgTaAqVAKZm/kMROTYdnjDHGLHe+4nhgP4EpgP6/9/IVf9xsZGa+LGFgjDFmQZPMKmC3IQ8lF3nghMMxxhhjzCySebhAa6NtUEjmiKZiMqNhCQNjjDELmgrdzTx21yRjMcYYY8wQwm+VjSc+KChi/YYWO0sYGGOMWdgc0wjnKVQzm/onJatzwc8ajMwYY4wxQA58ibmjIKsc+EIT8ZjRsYSBMcaYBS+2+SDCWQp1P1nw09TidcjQ+dXGGGOMmaBccG0OnKJwTf+7+tc58A+54IqmYzPzY1MSjDHGLHxCHaf4EMqHAGeJAmOMMWZhySWX5JKTm47DjJYlDIwxxiweAmDJAmOMMcaYSbAlCcYYY4wxxhhjjJnDEgbGGGOMMcYYY4yZwxIGxhhjjDHGGGOMmcMSBsYYY4wxxhhjjJnDEgbGGGOMMcYYY4yZwxIGxhhjjDHGGGOMmcMSBsYYY4wxxhhjjJnDEgbGGGOMMcYYY4yZwxIGxhiziElkP1dxPzKtpmMxxhhjlq1M6Sru62oOaDoUY0YpNB2AMcaY7ZBZGTq8CTgISC7i1fOB1OLcpkMzxhhjlhNXcbiLvBrIgHc1v04t3qye1U3HZsx8WYWBMcYsQqHLS4CDBVoCKwRakni5JHZvOjZjjDFmuZDEzi7yWoH2zPcxcA9fcXLTsRkzCpYwMMaYxUg5UoZUibmaRzQRjjHGGLMcucjh9CoL1hMIKA9D7VrLLH72P7ExxixOuo3bjTHGGDN6eRPb7fvYLAmWMDDGmMVIOFuhnr05F5zXRDjGGGPMcpQDPwRkcJtCRPg+sslkgjGLhiUMjDFmEYotPgpcolApTCuszYF3quf2pmMzxhhjlgv1rM6Btyms7n8fV8DPY4t/bjo2Y0bBpiQYY8xi5OjEFbxFErtLZqccuA4hNh2WMcYYs9zkkotzwXNc5O4qrNHALU3HZMyoWMLAGGMWMfX8Tj2/azoOY4wxZlkTci64pukwjBk1W5JgjDHGGGOMMcaYOSxhYIwxxhhjjDHGmDksYWCMMcYYY4wxxpg5LGFgjDHGGGOMMcaYOSxhYIwxxhhjjDHGmDksYWCMMcYYY4wxxpg5LGFgjDHGGGOMMcaYOSxhYIwxxhhjjDHGmDksYWCMMcYYY4wxxpg5LGFgjDHGGGOMMcaYOURVm47BGGOMMcYYY4wxC4xVGBhjjDHGGGOMMWYOSxgYY4wxxhhjjDFmDksYGGOMMcYYY4wxZg5LGBhjjDHGGGOMMWYOSxgYY4wxxhhjjDFmDksYGGOMMcYYY4wxZo7/D8cMgEhiqS5eAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "model = DecisionTreeClassifier()\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "visualize_tree(model, X[::2], y[::2], boundaries=False, ax=ax[0])\n", + "visualize_tree(model, X[1::2], y[1::2], boundaries=False, ax=ax[1])\n", + "\n", + "fig.savefig('images/05.08-decision-tree-overfitting.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Principal Component Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Principal Components Rotation" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "from sklearn.decomposition import PCA" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "def draw_vector(v0, v1, ax=None):\n", + " ax = ax or plt.gca()\n", + " arrowprops=dict(arrowstyle='->',\n", + " linewidth=2,\n", + " shrinkA=0, shrinkB=0)\n", + " ax.annotate('', v1, v0, arrowprops=arrowprops)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "rng = np.random.RandomState(1)\n", + "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n", + "pca = PCA(n_components=2, whiten=True)\n", + "pca.fit(X)\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", + "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", + "\n", + "# plot data\n", + "ax[0].scatter(X[:, 0], X[:, 1], alpha=0.2)\n", + "for length, vector in zip(pca.explained_variance_, pca.components_):\n", + " v = vector * 3 * np.sqrt(length)\n", + " draw_vector(pca.mean_, pca.mean_ + v, ax=ax[0])\n", + "ax[0].axis('equal');\n", + "ax[0].set(xlabel='x', ylabel='y', title='input')\n", + "\n", + "# plot principal components\n", + "X_pca = pca.transform(X)\n", + "ax[1].scatter(X_pca[:, 0], X_pca[:, 1], alpha=0.2)\n", + "draw_vector([0, 0], [0, 3], ax=ax[1])\n", + "draw_vector([0, 0], [3, 0], ax=ax[1])\n", + "ax[1].axis('equal')\n", + "ax[1].set(xlabel='component 1', ylabel='component 2',\n", + " title='principal components',\n", + " xlim=(-5, 5), ylim=(-3, 3.1))\n", + "\n", + "fig.savefig('images/05.09-PCA-rotation.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Digits Pixel Components" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "def plot_pca_components(x, coefficients=None, mean=0, components=None,\n", + " imshape=(8, 8), n_components=8, fontsize=12,\n", + " show_mean=True):\n", + " if coefficients is None:\n", + " coefficients = x\n", + " \n", + " if components is None:\n", + " components = np.eye(len(coefficients), len(x))\n", + " \n", + " mean = np.zeros_like(x) + mean\n", + " \n", + "\n", + " fig = plt.figure(figsize=(1.2 * (5 + n_components), 1.2 * 2))\n", + " g = plt.GridSpec(2, 4 + bool(show_mean) + n_components, hspace=0.3)\n", + "\n", + " def show(i, j, x, title=None):\n", + " ax = fig.add_subplot(g[i, j], xticks=[], yticks=[])\n", + " ax.imshow(x.reshape(imshape), interpolation='nearest', cmap='binary')\n", + " if title:\n", + " ax.set_title(title, fontsize=fontsize)\n", + "\n", + " show(slice(2), slice(2), x, \"True\")\n", + " \n", + " approx = mean.copy()\n", + " \n", + " counter = 2\n", + " if show_mean:\n", + " show(0, 2, np.zeros_like(x) + mean, r'$\\mu$')\n", + " show(1, 2, approx, r'$1 \\cdot \\mu$')\n", + " counter += 1\n", + "\n", + " for i in range(n_components):\n", + " approx = approx + coefficients[i] * components[i]\n", + " show(0, i + counter, components[i], r'$c_{0}$'.format(i + 1))\n", + " show(1, i + counter, approx,\n", + " r\"${0:.2f} \\cdot c_{1}$\".format(coefficients[i], i + 1))\n", + " if show_mean or i > 0:\n", + " plt.gca().text(0, 1.05, '$+$', ha='right', va='bottom',\n", + " transform=plt.gca().transAxes, fontsize=fontsize)\n", + "\n", + " show(slice(2), slice(-2, None), approx, \"Approx\")\n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import load_digits\n", + "\n", + "digits = load_digits()\n", + "sns.set_style('white')\n", + "\n", + "fig = plot_pca_components(digits.data[10],\n", + " show_mean=False)\n", + "\n", + "fig.savefig('images/05.09-digits-pixel-components.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Digits PCA Components" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pca = PCA(n_components=8)\n", + "Xproj = pca.fit_transform(digits.data)\n", + "sns.set_style('white')\n", + "fig = plot_pca_components(digits.data[10], Xproj[10],\n", + " pca.mean_, pca.components_)\n", + "\n", + "fig.savefig('images/05.09-digits-pca-components.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Manifold Learning" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### LLE vs MDS Linkages" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "deletable": true, + "editable": true, + "tags": [] + }, + "outputs": [], + "source": [ + "def make_hello(N=1000, rseed=42):\n", + " # Make a plot with \"HELLO\" text; save as png\n", + " fig, ax = plt.subplots(figsize=(4, 1))\n", + " fig.subplots_adjust(left=0, right=1, bottom=0, top=1)\n", + " ax.axis('off')\n", + " ax.text(0.5, 0.4, 'HELLO', va='center', ha='center', weight='bold', size=85)\n", + " fig.savefig('hello.png')\n", + " plt.close(fig)\n", + " \n", + " # Open this PNG and draw random points from it\n", + " from matplotlib.image import imread\n", + " data = imread('hello.png')[::-1, :, 0].T\n", + " rng = np.random.RandomState(rseed)\n", + " X = rng.rand(4 * N, 2)\n", + " i, j = (X * data.shape).astype(int).T\n", + " mask = (data[i, j] < 1)\n", + " X = X[mask]\n", + " X[:, 0] *= (data.shape[0] / data.shape[1])\n", + " X = X[:N]\n", + " return X[np.argsort(X[:, 0])]" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "def make_hello_s_curve(X):\n", + " t = (X[:, 0] - 2) * 0.75 * np.pi\n", + " x = np.sin(t)\n", + " y = X[:, 1]\n", + " z = np.sign(t) * (np.cos(t) - 1)\n", + " return np.vstack((x, y, z)).T\n", + "\n", + "X = make_hello(1000)\n", + "XS = make_hello_s_curve(X)\n", + "colorize = dict(c=X[:, 0], cmap=plt.cm.get_cmap('rainbow', 5))" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits.mplot3d.art3d import Line3DCollection\n", + "from sklearn.neighbors import NearestNeighbors\n", + "\n", + "# construct lines for MDS\n", + "rng = np.random.RandomState(42)\n", + "ind = rng.permutation(len(X))\n", + "lines_MDS = [(XS[i], XS[j]) for i in ind[:100] for j in ind[100:200]]\n", + "\n", + "# construct lines for LLE\n", + "nbrs = NearestNeighbors(n_neighbors=100).fit(XS).kneighbors(XS[ind[:100]])[1]\n", + "lines_LLE = [(XS[ind[i]], XS[j]) for i in range(100) for j in nbrs[i]]\n", + "titles = ['MDS Linkages', 'LLE Linkages (100 NN)']\n", + "\n", + "# plot the results\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6),\n", + " subplot_kw=dict(projection='3d'))\n", + "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0, wspace=0)\n", + "\n", + "for axi, title, lines in zip(ax, titles, [lines_MDS, lines_LLE]):\n", + " axi.scatter3D(XS[:, 0], XS[:, 1], XS[:, 2], **colorize);\n", + " axi.add_collection(Line3DCollection(lines, lw=1, color='black',\n", + " alpha=0.05))\n", + " axi.view_init(elev=10, azim=-80)\n", + " axi.set_title(title, size=18)\n", + "\n", + "fig.savefig('images/05.10-LLE-vs-MDS.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## K-Means" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Expectation-Maximization\n", + "\n", + "[Figure Context](05.11-K-Means.ipynb#K-Means-Algorithm:-Expectation-Maximization)\n", + "\n", + "The following figure shows a visual depiction of the Expectation-Maximization approach to K Means:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_blobs\n", + "from sklearn.metrics import pairwise_distances_argmin\n", + "\n", + "X, y_true = make_blobs(n_samples=300, centers=4,\n", + " cluster_std=0.60, random_state=0)\n", + "\n", + "rng = np.random.RandomState(42)\n", + "centers = [0, 4] + rng.randn(4, 2)\n", + "\n", + "def draw_points(ax, c, factor=1):\n", + " ax.scatter(X[:, 0], X[:, 1], c=c, cmap='viridis',\n", + " s=50 * factor, alpha=0.3)\n", + " \n", + "def draw_centers(ax, centers, factor=1, alpha=1.0):\n", + " ax.scatter(centers[:, 0], centers[:, 1],\n", + " c=np.arange(4), cmap='viridis', s=200 * factor,\n", + " alpha=alpha)\n", + " ax.scatter(centers[:, 0], centers[:, 1],\n", + " c='black', s=50 * factor, alpha=alpha)\n", + "\n", + "def make_ax(fig, gs):\n", + " ax = fig.add_subplot(gs)\n", + " ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + " ax.yaxis.set_major_formatter(plt.NullFormatter())\n", + " return ax\n", + "\n", + "fig = plt.figure(figsize=(15, 4))\n", + "gs = plt.GridSpec(4, 15, left=0.02, right=0.98, bottom=0.05, top=0.95, wspace=0.2, hspace=0.2)\n", + "ax0 = make_ax(fig, gs[:4, :4])\n", + "ax0.text(0.98, 0.98, \"Random Initialization\", transform=ax0.transAxes,\n", + " ha='right', va='top', size=16)\n", + "draw_points(ax0, 'gray', factor=2)\n", + "draw_centers(ax0, centers, factor=2)\n", + "\n", + "for i in range(3):\n", + " ax1 = make_ax(fig, gs[:2, 4 + 2 * i:6 + 2 * i])\n", + " ax2 = make_ax(fig, gs[2:, 5 + 2 * i:7 + 2 * i])\n", + " \n", + " # E-step\n", + " y_pred = pairwise_distances_argmin(X, centers)\n", + " draw_points(ax1, y_pred)\n", + " draw_centers(ax1, centers)\n", + " \n", + " # M-step\n", + " new_centers = np.array([X[y_pred == i].mean(0) for i in range(4)])\n", + " draw_points(ax2, y_pred)\n", + " draw_centers(ax2, centers, alpha=0.3)\n", + " draw_centers(ax2, new_centers)\n", + " for i in range(4):\n", + " ax2.annotate('', new_centers[i], centers[i],\n", + " arrowprops=dict(arrowstyle='->', linewidth=1))\n", + " \n", + " \n", + " # Finish iteration\n", + " centers = new_centers\n", + " ax1.text(0.95, 0.95, \"E-Step\", transform=ax1.transAxes, ha='right', va='top', size=14)\n", + " ax2.text(0.95, 0.95, \"M-Step\", transform=ax2.transAxes, ha='right', va='top', size=14)\n", + "\n", + "\n", + "# Final E-step \n", + "y_pred = pairwise_distances_argmin(X, centers)\n", + "axf = make_ax(fig, gs[:4, -4:])\n", + "draw_points(axf, y_pred, factor=2)\n", + "draw_centers(axf, centers, factor=2)\n", + "axf.text(0.98, 0.98, \"Final Clustering\", transform=axf.transAxes,\n", + " ha='right', va='top', size=16)\n", + "\n", + "\n", + "fig.savefig('images/05.11-expectation-maximization.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Interactive K-Means\n", + "\n", + "The following script uses IPython's interactive widgets to demonstrate the K-means algorithm interactively.\n", + "Run this within the IPython notebook to explore the expectation maximization algorithm for computing K Means." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "ed1359fd1a134c999ea35ab6a9fc5796", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(Dropdown(description='frame', options=(0, 50), value=0), Dropdown(description='n_cluster…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "from ipywidgets import interact\n", + "from sklearn.metrics import pairwise_distances_argmin\n", + "from sklearn.datasets import make_blobs\n", + "\n", + "def plot_kmeans_interactive(min_clusters=1, max_clusters=6):\n", + " X, y = make_blobs(n_samples=300, centers=4,\n", + " random_state=0, cluster_std=0.60)\n", + " \n", + " def plot_points(X, labels, n_clusters):\n", + " plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='viridis',\n", + " vmin=0, vmax=n_clusters - 1);\n", + " \n", + " def plot_centers(centers):\n", + " plt.scatter(centers[:, 0], centers[:, 1], marker='o',\n", + " c=np.arange(centers.shape[0]),\n", + " s=200, cmap='viridis')\n", + " plt.scatter(centers[:, 0], centers[:, 1], marker='o',\n", + " c='black', s=50)\n", + " \n", + "\n", + " def _kmeans_step(frame=0, n_clusters=4):\n", + " rng = np.random.RandomState(2)\n", + " labels = np.zeros(X.shape[0])\n", + " centers = rng.randn(n_clusters, 2)\n", + "\n", + " nsteps = frame // 3\n", + "\n", + " for i in range(nsteps + 1):\n", + " old_centers = centers\n", + " if i < nsteps or frame % 3 > 0:\n", + " labels = pairwise_distances_argmin(X, centers)\n", + "\n", + " if i < nsteps or frame % 3 > 1:\n", + " centers = np.array([X[labels == j].mean(0)\n", + " for j in range(n_clusters)])\n", + " nans = np.isnan(centers)\n", + " centers[nans] = old_centers[nans]\n", + "\n", + " # plot the data and cluster centers\n", + " plot_points(X, labels, n_clusters)\n", + " plot_centers(old_centers)\n", + "\n", + " # plot new centers if third frame\n", + " if frame % 3 == 2:\n", + " for i in range(n_clusters):\n", + " plt.annotate('', centers[i], old_centers[i], \n", + " arrowprops=dict(arrowstyle='->', linewidth=1))\n", + " plot_centers(centers)\n", + "\n", + " plt.xlim(-4, 4)\n", + " plt.ylim(-2, 10)\n", + "\n", + " if frame % 3 == 1:\n", + " plt.text(3.8, 9.5, \"1. Reassign points to nearest centroid\",\n", + " ha='right', va='top', size=14)\n", + " elif frame % 3 == 2:\n", + " plt.text(3.8, 9.5, \"2. Update centroids to cluster means\",\n", + " ha='right', va='top', size=14)\n", + " \n", + " return interact(_kmeans_step, frame=(0, 50),\n", + " n_clusters=[min_clusters, max_clusters])\n", + "\n", + "plot_kmeans_interactive();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Gaussian Mixture Models" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Covariance Type\n", + "\n", + "[Figure Context](http://localhost:8888/notebooks/05.12-Gaussian-Mixtures.ipynb#Choosing-the-Covariance-Type)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.mixture import GaussianMixture\n", + "\n", + "from matplotlib.patches import Ellipse\n", + "\n", + "def draw_ellipse(position, covariance, ax=None, **kwargs):\n", + " \"\"\"Draw an ellipse with a given position and covariance\"\"\"\n", + " ax = ax or plt.gca()\n", + " \n", + " # Convert covariance to principal axes\n", + " if covariance.shape == (2, 2):\n", + " U, s, Vt = np.linalg.svd(covariance)\n", + " angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n", + " width, height = 2 * np.sqrt(s)\n", + " elif covariance.shape == (2,):\n", + " angle = 0\n", + " width, height = 2 * np.sqrt(covariance)\n", + " else:\n", + " angle = 0\n", + " width = height = 2 * np.sqrt(covariance)\n", + " \n", + " # Draw the Ellipse\n", + " for nsig in range(1, 4):\n", + " ax.add_patch(Ellipse(position, nsig * width, nsig * height,\n", + " angle, **kwargs))\n", + "\n", + "fig, ax = plt.subplots(1, 3, figsize=(14, 4))\n", + "fig.subplots_adjust(wspace=0.05)\n", + "\n", + "rng = np.random.RandomState(5)\n", + "X = np.dot(rng.randn(500, 2), rng.randn(2, 2))\n", + "\n", + "for i, cov_type in enumerate(['diag', 'spherical', 'full']):\n", + " model = GaussianMixture(1, covariance_type=cov_type).fit(X)\n", + " ax[i].axis('equal')\n", + " ax[i].scatter(X[:, 0], X[:, 1], alpha=0.5)\n", + " ax[i].set_xlim(-3, 3)\n", + " ax[i].set_title('covariance_type=\"{0}\"'.format(cov_type),\n", + " size=14, family='monospace')\n", + " \n", + " draw_ellipse(model.means_[0], model.covariances_[0], ax[i], alpha=0.2)\n", + " ax[i].xaxis.set_major_formatter(plt.NullFormatter())\n", + " ax[i].yaxis.set_major_formatter(plt.NullFormatter())\n", + "\n", + "fig.savefig('images/05.12-covariance-type.png')" + ] + } + ], + "metadata": { + "jupytext": { + "formats": "ipynb,md" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.2" + }, + "widgets": { + "state": { + "a65a11f142ca44eebc913788d256adcb": { + "views": [ + { + "cell_index": 92 + } + ] + } + }, + "version": "1.2.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/Untitled.ipynb b/notebooks/Untitled.ipynb new file mode 100644 index 000000000..363fcab7e --- /dev/null +++ b/notebooks/Untitled.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/data/births.csv b/notebooks/data/births.csv new file mode 100644 index 000000000..4a5bb7aef --- /dev/null +++ b/notebooks/data/births.csv @@ -0,0 +1,15548 @@ +year,month,day,gender,births +1969,1,1,F,4046 +1969,1,1,M,4440 +1969,1,2,F,4454 +1969,1,2,M,4548 +1969,1,3,F,4548 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-0,0 +1,45 @@ +order,name,height(cm) +1,George Washington,189 +2,John Adams,170 +3,Thomas Jefferson,189 +4,James Madison,163 +5,James Monroe,183 +6,John Quincy Adams,171 +7,Andrew Jackson,185 +8,Martin Van Buren,168 +9,William Henry Harrison,173 +10,John Tyler,183 +11,James K. Polk,173 +12,Zachary Taylor,173 +13,Millard Fillmore,175 +14,Franklin Pierce,178 +15,James Buchanan,183 +16,Abraham Lincoln,193 +17,Andrew Johnson,178 +18,Ulysses S. Grant,173 +19,Rutherford B. Hayes,174 +20,James A. Garfield,183 +21,Chester A. Arthur,183 +23,Benjamin Harrison,168 +25,William McKinley,170 +26,Theodore Roosevelt,178 +27,William Howard Taft,182 +28,Woodrow Wilson,180 +29,Warren G. Harding,183 +30,Calvin Coolidge,178 +31,Herbert Hoover,182 +32,Franklin D. Roosevelt,188 +33,Harry S. Truman,175 +34,Dwight D. Eisenhower,179 +35,John F. Kennedy,183 +36,Lyndon B. Johnson,193 +37,Richard Nixon,182 +38,Gerald Ford,183 +39,Jimmy Carter,177 +40,Ronald Reagan,185 +41,George H. W. Bush,188 +42,Bill Clinton,188 +43,George W. Bush,182 +44,Barack Obama,185 +45,Donald Trump,191 +46,Joseph Biden,182 diff --git a/notebooks/data/state-abbrevs.csv b/notebooks/data/state-abbrevs.csv new file mode 100644 index 000000000..6d4db366f --- /dev/null +++ b/notebooks/data/state-abbrevs.csv @@ -0,0 +1,52 @@ +"state","abbreviation" +"Alabama","AL" +"Alaska","AK" +"Arizona","AZ" +"Arkansas","AR" +"California","CA" +"Colorado","CO" +"Connecticut","CT" +"Delaware","DE" +"District of Columbia","DC" +"Florida","FL" +"Georgia","GA" +"Hawaii","HI" +"Idaho","ID" +"Illinois","IL" +"Indiana","IN" +"Iowa","IA" +"Kansas","KS" +"Kentucky","KY" +"Louisiana","LA" +"Maine","ME" +"Montana","MT" +"Nebraska","NE" +"Nevada","NV" +"New Hampshire","NH" +"New Jersey","NJ" +"New Mexico","NM" +"New York","NY" +"North Carolina","NC" +"North Dakota","ND" +"Ohio","OH" +"Oklahoma","OK" +"Oregon","OR" +"Maryland","MD" +"Massachusetts","MA" +"Michigan","MI" +"Minnesota","MN" +"Mississippi","MS" +"Missouri","MO" +"Pennsylvania","PA" +"Rhode Island","RI" 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b/notebooks/helpers_05_08.py new file mode 100644 index 000000000..09d900083 --- /dev/null +++ b/notebooks/helpers_05_08.py @@ -0,0 +1,82 @@ + +import numpy as np +import matplotlib.pyplot as plt; plt.rcParams['figure.dpi'] = 600 +from sklearn.tree import DecisionTreeClassifier +from ipywidgets import interact + + +def visualize_tree(estimator, X, y, boundaries=True, + xlim=None, ylim=None, ax=None): + ax = ax or plt.gca() + + # Plot the training points + ax.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap='viridis', + clim=(y.min(), y.max()), zorder=3) + ax.axis('tight') + ax.axis('off') + if xlim is None: + xlim = ax.get_xlim() + if ylim is None: + ylim = ax.get_ylim() + + # fit the estimator + estimator.fit(X, y) + xx, yy = np.meshgrid(np.linspace(*xlim, num=200), + np.linspace(*ylim, num=200)) + Z = estimator.predict(np.c_[xx.ravel(), yy.ravel()]) + + # Put the result into a color plot + n_classes = len(np.unique(y)) + Z = Z.reshape(xx.shape) + contours = ax.contourf(xx, yy, Z, alpha=0.3, + levels=np.arange(n_classes + 1) - 0.5, + cmap='viridis', zorder=1) + + ax.set(xlim=xlim, ylim=ylim) + + # Plot the decision boundaries + def plot_boundaries(i, xlim, ylim): + if i >= 0: + tree = estimator.tree_ + + if tree.feature[i] == 0: + ax.plot([tree.threshold[i], tree.threshold[i]], ylim, '-k', zorder=2) + plot_boundaries(tree.children_left[i], + [xlim[0], tree.threshold[i]], ylim) + plot_boundaries(tree.children_right[i], + [tree.threshold[i], xlim[1]], ylim) + + elif tree.feature[i] == 1: + ax.plot(xlim, [tree.threshold[i], tree.threshold[i]], '-k', zorder=2) + plot_boundaries(tree.children_left[i], xlim, + [ylim[0], tree.threshold[i]]) + plot_boundaries(tree.children_right[i], xlim, + [tree.threshold[i], ylim[1]]) + + if boundaries: + plot_boundaries(0, xlim, ylim) + + +def plot_tree_interactive(X, y): + def interactive_tree(depth=5): + clf = DecisionTreeClassifier(max_depth=depth, random_state=0) + visualize_tree(clf, X, y) + + return interact(interactive_tree, depth=(1, 5)) + + +def randomized_tree_interactive(X, y): + N = int(0.75 * X.shape[0]) + + xlim = (X[:, 0].min(), X[:, 0].max()) + ylim = (X[:, 1].min(), X[:, 1].max()) + + def fit_randomized_tree(random_state=0): + clf = DecisionTreeClassifier(max_depth=15) + i = np.arange(len(y)) + rng = np.random.RandomState(random_state) + rng.shuffle(i) + visualize_tree(clf, X[i[:N]], y[i[:N]], boundaries=False, + xlim=xlim, ylim=ylim) + + interact(fit_randomized_tree, random_state=(0, 100)); diff --git a/notebooks_v1/00.00-Preface.ipynb b/notebooks_v1/00.00-Preface.ipynb new file mode 100644 index 000000000..7d635a808 --- /dev/null +++ b/notebooks_v1/00.00-Preface.ipynb @@ -0,0 +1,203 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "| [Contents](Index.ipynb) | [IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Preface" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## What Is Data Science?\n", + "\n", + "This is a book about doing data science with Python, which immediately begs the question: what is *data science*?\n", + "It's a surprisingly hard definition to nail down, especially given how ubiquitous the term has become.\n", + "Vocal critics have variously dismissed the term as a superfluous label (after all, what science doesn't involve data?) or a simple buzzword that only exists to salt resumes and catch the eye of overzealous tech recruiters.\n", + "\n", + "In my mind, these critiques miss something important.\n", + "Data science, despite its hype-laden veneer, is perhaps the best label we have for the cross-disciplinary set of skills that are becoming increasingly important in many applications across industry and academia.\n", + "This cross-disciplinary piece is key: in my mind, the best extisting definition of data science is illustrated by Drew Conway's Data Science Venn Diagram, first published on his blog in September 2010:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Data Science Venn Diagram](figures/Data_Science_VD.png)\n", + "\n", + "(Source: [Drew Conway](http://drewconway.com/zia/2013/3/26/the-data-science-venn-diagram). Used by permission.)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While some of the intersection labels are a bit tongue-in-cheek, this diagram captures the essence of what I think people mean when they say \"data science\": it is fundamentally an *interdisciplinary* subject.\n", + "Data science comprises three distinct and overlapping areas: the skills of a *statistician* who knows how to model and summarize datasets (which are growing ever larger); the skills of a *computer scientist* who can design and use algorithms to efficiently store, process, and visualize this data; and the *domain expertise*—what we might think of as \"classical\" training in a subject—necessary both to formulate the right questions and to put their answers in context.\n", + "\n", + "With this in mind, I would encourage you to think of data science not as a new domain of knowledge to learn, but a new set of skills that you can apply within your current area of expertise.\n", + "Whether you are reporting election results, forecasting stock returns, optimizing online ad clicks, identifying microorganisms in microscope photos, seeking new classes of astronomical objects, or working with data in any other field, the goal of this book is to give you the ability to ask and answer new questions about your chosen subject area." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Who Is This Book For?\n", + "\n", + "In my teaching both at the University of Washington and at various tech-focused conferences and meetups, one of the most common questions I have heard is this: \"how should I learn Python?\"\n", + "The people asking are generally technically minded students, developers, or researchers, often with an already strong background in writing code and using computational and numerical tools.\n", + "Most of these folks don't want to learn Python *per se*, but want to learn the language with the aim of using it as a tool for data-intensive and computational science.\n", + "While a large patchwork of videos, blog posts, and tutorials for this audience is available online, I've long been frustrated by the lack of a single good answer to this question; that is what inspired this book.\n", + "\n", + "The book is not meant to be an introduction to Python or to programming in general; I assume the reader has familiarity with the Python language, including defining functions, assigning variables, calling methods of objects, controlling the flow of a program, and other basic tasks.\n", + "Instead it is meant to help Python users learn to use Python's data science stack–libraries such as IPython, NumPy, Pandas, Matplotlib, Scikit-Learn, and related tools–to effectively store, manipulate, and gain insight from data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Why Python?\n", + "\n", + "Python has emerged over the last couple decades as a first-class tool for scientific computing tasks, including the analysis and visualization of large datasets.\n", + "This may have come as a surprise to early proponents of the Python language: the language itself was not specifically designed with data analysis or scientific computing in mind.\n", + "The usefulness of Python for data science stems primarily from the large and active ecosystem of third-party packages: *NumPy* for manipulation of homogeneous array-based data, *Pandas* for manipulation of heterogeneous and labeled data, *SciPy* for common scientific computing tasks, *Matplotlib* for publication-quality visualizations, *IPython* for interactive execution and sharing of code, *Scikit-Learn* for machine learning, and many more tools that will be mentioned in the following pages.\n", + "\n", + "If you are looking for a guide to the Python language itself, I would suggest the sister project to this book, \"[A Whirlwind Tour of the Python Language](https://github.com/jakevdp/WhirlwindTourOfPython)\".\n", + "This short report provides a tour of the essential features of the Python language, aimed at data scientists who already are familiar with one or more other programming languages." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Python 2 vs Python 3\n", + "\n", + "This book uses the syntax of Python 3, which contains language enhancements that are not compatible with the 2.x series of Python.\n", + "Though Python 3.0 was first released in 2008, adoption has been relatively slow, particularly in the scientific and web development communities.\n", + "This is primarily because it took some time for many of the essential third-party packages and toolkits to be made compatible with the new language internals.\n", + "Since early 2014, however, stable releases of the most important tools in the data science ecosystem have been fully compatible with both Python 2 and 3, and so this book will use the newer Python 3 syntax.\n", + "However, the vast majority of code snippets in this book will also work without modification in Python 2: in cases where a Py2-incompatible syntax is used, I will make every effort to note it explicitly." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Outline of the Book\n", + "\n", + "Each chapter of this book focuses on a particular package or tool that contributes a fundamental piece of the Python Data Sciece story.\n", + "\n", + "1. IPython and Jupyter: these packages provide the computational environment in which many Python-using data scientists work.\n", + "2. NumPy: this library provides the ``ndarray`` for efficient storage and manipulation of dense data arrays in Python.\n", + "3. Pandas: this library provides the ``DataFrame`` for efficient storage and manipulation of labeled/columnar data in Python.\n", + "4. Matplotlib: this library provides capabilities for a flexible range of data visualizations in Python.\n", + "5. Scikit-Learn: this library provides efficient & clean Python implementations of the most important and established machine learning algorithms.\n", + "\n", + "The PyData world is certainly much larger than these five packages, and is growing every day.\n", + "With this in mind, I make every attempt through these pages to provide references to other interesting efforts, projects, and packages that are pushing the boundaries of what can be done in Python.\n", + "Nevertheless, these five are currently fundamental to much of the work being done in the Python data science space, and I expect they will remain important even as the ecosystem continues growing around them." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using Code Examples\n", + "\n", + "Supplemental material (code examples, figures, etc.) is available for download at http://github.com/jakevdp/PythonDataScienceHandbook/. This book is here to help you get your job done. In general, if example code is offered with this book, you may use it in your programs and documentation. You do not need to contact us for permission unless you’re reproducing a significant portion of the code. For example, writing a program that uses several chunks of code from this book does not require permission. Selling or distributing a CD-ROM of examples from O’Reilly books does require permission. Answering a question by citing this book and quoting example code does not require permission. Incorporating a significant amount of example code from this book into your product’s documentation does require permission.\n", + "\n", + "We appreciate, but do not require, attribution. An attribution usually includes the title, author, publisher, and ISBN. For example:\n", + "\n", + "> *The Python Data Science Handbook* by Jake VanderPlas (O’Reilly). Copyright 2016 Jake VanderPlas, 978-1-491-91205-8.\n", + "\n", + "If you feel your use of code examples falls outside fair use or the per‐ mission given above, feel free to contact us at permissions@oreilly.com." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installation Considerations\n", + "\n", + "Installing Python and the suite of libraries that enable scientific computing is straightforward . This section will outline some of the considerations when setting up your computer.\n", + "\n", + "Though there are various ways to install Python, the one I would suggest for use in data science is the Anaconda distribution, which works similarly whether you use Windows, Linux, or Mac OS X.\n", + "The Anaconda distribution comes in two flavors:\n", + "\n", + "- [Miniconda](http://conda.pydata.org/miniconda.html) gives you the Python interpreter itself, along with a command-line tool called ``conda`` which operates as a cross-platform package manager geared toward Python packages, similar in spirit to the apt or yum tools that Linux users might be familiar with.\n", + "\n", + "- [Anaconda](https://www.continuum.io/downloads) includes both Python and conda, and additionally bundles a suite of other pre-installed packages geared toward scientific computing. Because of the size of this bundle, expect the installation to consume several gigabytes of disk space.\n", + "\n", + "Any of the packages included with Anaconda can also be installed manually on top of Miniconda; for this reason I suggest starting with Miniconda.\n", + "\n", + "To get started, download and install the Miniconda package–make sure to choose a version with Python 3–and then install the core packages used in this book:\n", + "\n", + "```\n", + "[~]$ conda install numpy pandas scikit-learn matplotlib seaborn jupyter\n", + "```\n", + "\n", + "Throughout the text, we will also make use of other more specialized tools in Python's scientific ecosystem; installation is usually as easy as typing **``conda install packagename``**.\n", + "For more information on conda, including information about creating and using conda environments (which I would *highly* recommend), refer to [conda's online documentation](http://conda.pydata.org/docs/)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "| [Contents](Index.ipynb) | [IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/01.00-IPython-Beyond-Normal-Python.ipynb b/notebooks_v1/01.00-IPython-Beyond-Normal-Python.ipynb new file mode 100644 index 000000000..5d01277e6 --- /dev/null +++ b/notebooks_v1/01.00-IPython-Beyond-Normal-Python.ipynb @@ -0,0 +1,152 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Preface](00.00-Preface.ipynb) | [Contents](Index.ipynb) | [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# IPython: Beyond Normal Python" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are many options for development environments for Python, and I'm often asked which one I use in my own work.\n", + "My answer sometimes surprises people: my preferred environment is [IPython](http://ipython.org/) plus a text editor (in my case, Emacs or Atom depending on my mood).\n", + "IPython (short for *Interactive Python*) was started in 2001 by Fernando Perez as an enhanced Python interpreter, and has since grown into a project aiming to provide, in Perez's words, \"Tools for the entire life cycle of research computing.\"\n", + "If Python is the engine of our data science task, you might think of IPython as the interactive control panel.\n", + "\n", + "As well as being a useful interactive interface to Python, IPython also provides a number of useful syntactic additions to the language; we'll cover the most useful of these additions here.\n", + "In addition, IPython is closely tied with the [Jupyter project](http://jupyter.org), which provides a browser-based notebook that is useful for development, collaboration, sharing, and even publication of data science results.\n", + "The IPython notebook is actually a special case of the broader Jupyter notebook structure, which encompasses notebooks for Julia, R, and other programming languages.\n", + "As an example of the usefulness of the notebook format, look no further than the page you are reading: the entire manuscript for this book was composed as a set of IPython notebooks.\n", + "\n", + "IPython is about using Python effectively for interactive scientific and data-intensive computing.\n", + "This chapter will start by stepping through some of the IPython features that are useful to the practice of data science, focusing especially on the syntax it offers beyond the standard features of Python.\n", + "Next, we will go into a bit more depth on some of the more useful \"magic commands\" that can speed-up common tasks in creating and using data science code.\n", + "Finally, we will touch on some of the features of the notebook that make it useful in understanding data and sharing results." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Shell or Notebook?\n", + "\n", + "There are two primary means of using IPython that we'll discuss in this chapter: the IPython shell and the IPython notebook.\n", + "The bulk of the material in this chapter is relevant to both, and the examples will switch between them depending on what is most convenient.\n", + "In the few sections that are relevant to just one or the other, we will explicitly state that fact.\n", + "Before we start, some words on how to launch the IPython shell and IPython notebook." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Launching the IPython Shell\n", + "\n", + "This chapter, like most of this book, is not designed to be absorbed passively.\n", + "I recommend that as you read through it, you follow along and experiment with the tools and syntax we cover: the muscle-memory you build through doing this will be far more useful than the simple act of reading about it.\n", + "Start by launching the IPython interpreter by typing **``ipython``** on the command-line; alternatively, if you've installed a distribution like Anaconda or EPD, there may be a launcher specific to your system (we'll discuss this more fully in [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)).\n", + "\n", + "Once you do this, you should see a prompt like the following:\n", + "```\n", + "IPython 4.0.1 -- An enhanced Interactive Python.\n", + "? -> Introduction and overview of IPython's features.\n", + "%quickref -> Quick reference.\n", + "help -> Python's own help system.\n", + "object? -> Details about 'object', use 'object??' for extra details.\n", + "In [1]:\n", + "```\n", + "With that, you're ready to follow along." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Launching the Jupyter Notebook\n", + "\n", + "The Jupyter notebook is a browser-based graphical interface to the IPython shell, and builds on it a rich set of dynamic display capabilities.\n", + "As well as executing Python/IPython statements, the notebook allows the user to include formatted text, static and dynamic visualizations, mathematical equations, JavaScript widgets, and much more.\n", + "Furthermore, these documents can be saved in a way that lets other people open them and execute the code on their own systems.\n", + "\n", + "Though the IPython notebook is viewed and edited through your web browser window, it must connect to a running Python process in order to execute code.\n", + "This process (known as a \"kernel\") can be started by running the following command in your system shell:\n", + "\n", + "```\n", + "$ jupyter notebook\n", + "```\n", + "\n", + "This command will launch a local web server that will be visible to your browser.\n", + "It immediately spits out a log showing what it is doing; that log will look something like this:\n", + "\n", + "```\n", + "$ jupyter notebook\n", + "[NotebookApp] Serving notebooks from local directory: /Users/jakevdp/PythonDataScienceHandbook\n", + "[NotebookApp] 0 active kernels \n", + "[NotebookApp] The IPython Notebook is running at: http://localhost:8888/\n", + "[NotebookApp] Use Control-C to stop this server and shut down all kernels (twice to skip confirmation).\n", + "```\n", + "\n", + "Upon issuing the command, your default browser should automatically open and navigate to the listed local URL;\n", + "the exact address will depend on your system.\n", + "If the browser does not open automatically, you can open a window and manually open this address (*http://localhost:8888/* in this example)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Preface](00.00-Preface.ipynb) | [Contents](Index.ipynb) | [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/01.01-Help-And-Documentation.ipynb b/notebooks_v1/01.01-Help-And-Documentation.ipynb new file mode 100644 index 000000000..39879ee90 --- /dev/null +++ b/notebooks_v1/01.01-Help-And-Documentation.ipynb @@ -0,0 +1,355 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb) | [Contents](Index.ipynb) | [Keyboard Shortcuts in the IPython Shell](01.02-Shell-Keyboard-Shortcuts.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Help and Documentation in IPython" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you read no other section in this chapter, read this one: I find the tools discussed here to be the most transformative contributions of IPython to my daily workflow.\n", + "\n", + "When a technologically-minded person is asked to help a friend, family member, or colleague with a computer problem, most of the time it's less a matter of knowing the answer as much as knowing how to quickly find an unknown answer.\n", + "In data science it's the same: searchable web resources such as online documentation, mailing-list threads, and StackOverflow answers contain a wealth of information, even (especially?) if it is a topic you've found yourself searching before.\n", + "Being an effective practitioner of data science is less about memorizing the tool or command you should use for every possible situation, and more about learning to effectively find the information you don't know, whether through a web search engine or another means.\n", + "\n", + "One of the most useful functions of IPython/Jupyter is to shorten the gap between the user and the type of documentation and search that will help them do their work effectively.\n", + "While web searches still play a role in answering complicated questions, an amazing amount of information can be found through IPython alone.\n", + "Some examples of the questions IPython can help answer in a few keystrokes:\n", + "\n", + "- How do I call this function? What arguments and options does it have?\n", + "- What does the source code of this Python object look like?\n", + "- What is in this package I imported? What attributes or methods does this object have?\n", + "\n", + "Here we'll discuss IPython's tools to quickly access this information, namely the ``?`` character to explore documentation, the ``??`` characters to explore source code, and the Tab key for auto-completion." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Accessing Documentation with ``?``\n", + "\n", + "The Python language and its data science ecosystem is built with the user in mind, and one big part of that is access to documentation.\n", + "Every Python object contains the reference to a string, known as a *doc string*, which in most cases will contain a concise summary of the object and how to use it.\n", + "Python has a built-in ``help()`` function that can access this information and prints the results.\n", + "For example, to see the documentation of the built-in ``len`` function, you can do the following:\n", + "\n", + "```ipython\n", + "In [1]: help(len)\n", + "Help on built-in function len in module builtins:\n", + "\n", + "len(...)\n", + " len(object) -> integer\n", + " \n", + " Return the number of items of a sequence or mapping.\n", + "```\n", + "\n", + "Depending on your interpreter, this information may be displayed as inline text, or in some separate pop-up window." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because finding help on an object is so common and useful, IPython introduces the ``?`` character as a shorthand for accessing this documentation and other relevant information:\n", + "\n", + "```ipython\n", + "In [2]: len?\n", + "Type: builtin_function_or_method\n", + "String form: \n", + "Namespace: Python builtin\n", + "Docstring:\n", + "len(object) -> integer\n", + "\n", + "Return the number of items of a sequence or mapping.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notation works for just about anything, including object methods:\n", + "\n", + "```ipython\n", + "In [3]: L = [1, 2, 3]\n", + "In [4]: L.insert?\n", + "Type: builtin_function_or_method\n", + "String form: \n", + "Docstring: L.insert(index, object) -- insert object before index\n", + "```\n", + "\n", + "or even objects themselves, with the documentation from their type:\n", + "\n", + "```ipython\n", + "In [5]: L?\n", + "Type: list\n", + "String form: [1, 2, 3]\n", + "Length: 3\n", + "Docstring:\n", + "list() -> new empty list\n", + "list(iterable) -> new list initialized from iterable's items\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Importantly, this will even work for functions or other objects you create yourself!\n", + "Here we'll define a small function with a docstring:\n", + "\n", + "```ipython\n", + "In [6]: def square(a):\n", + " ....: \"\"\"Return the square of a.\"\"\"\n", + " ....: return a ** 2\n", + " ....:\n", + "```\n", + "\n", + "Note that to create a docstring for our function, we simply placed a string literal in the first line.\n", + "Because doc strings are usually multiple lines, by convention we used Python's triple-quote notation for multi-line strings." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll use the ``?`` mark to find this doc string:\n", + "\n", + "```ipython\n", + "In [7]: square?\n", + "Type: function\n", + "String form: \n", + "Definition: square(a)\n", + "Docstring: Return the square of a.\n", + "```\n", + "\n", + "This quick access to documentation via docstrings is one reason you should get in the habit of always adding such inline documentation to the code you write!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Accessing Source Code with ``??``\n", + "Because the Python language is so easily readable, another level of insight can usually be gained by reading the source code of the object you're curious about.\n", + "IPython provides a shortcut to the source code with the double question mark (``??``):\n", + "\n", + "```ipython\n", + "In [8]: square??\n", + "Type: function\n", + "String form: \n", + "Definition: square(a)\n", + "Source:\n", + "def square(a):\n", + " \"Return the square of a\"\n", + " return a ** 2\n", + "```\n", + "\n", + "For simple functions like this, the double question-mark can give quick insight into the under-the-hood details." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you play with this much, you'll notice that sometimes the ``??`` suffix doesn't display any source code: this is generally because the object in question is not implemented in Python, but in C or some other compiled extension language.\n", + "If this is the case, the ``??`` suffix gives the same output as the ``?`` suffix.\n", + "You'll find this particularly with many of Python's built-in objects and types, for example ``len`` from above:\n", + "\n", + "```ipython\n", + "In [9]: len??\n", + "Type: builtin_function_or_method\n", + "String form: \n", + "Namespace: Python builtin\n", + "Docstring:\n", + "len(object) -> integer\n", + "\n", + "Return the number of items of a sequence or mapping.\n", + "```\n", + "\n", + "Using ``?`` and/or ``??`` gives a powerful and quick interface for finding information about what any Python function or module does." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exploring Modules with Tab-Completion\n", + "\n", + "IPython's other useful interface is the use of the tab key for auto-completion and exploration of the contents of objects, modules, and name-spaces.\n", + "In the examples that follow, we'll use ```` to indicate when the Tab key should be pressed." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Tab-completion of object contents\n", + "\n", + "Every Python object has various attributes and methods associated with it.\n", + "Like with the ``help`` function discussed before, Python has a built-in ``dir`` function that returns a list of these, but the tab-completion interface is much easier to use in practice.\n", + "To see a list of all available attributes of an object, you can type the name of the object followed by a period (\"``.``\") character and the Tab key:\n", + "\n", + "```ipython\n", + "In [10]: L.\n", + "L.append L.copy L.extend L.insert L.remove L.sort \n", + "L.clear L.count L.index L.pop L.reverse \n", + "```\n", + "\n", + "To narrow-down the list, you can type the first character or several characters of the name, and the Tab key will find the matching attributes and methods:\n", + "\n", + "```ipython\n", + "In [10]: L.c\n", + "L.clear L.copy L.count \n", + "\n", + "In [10]: L.co\n", + "L.copy L.count \n", + "```\n", + "\n", + "If there is only a single option, pressing the Tab key will complete the line for you.\n", + "For example, the following will instantly be replaced with ``L.count``:\n", + "\n", + "```ipython\n", + "In [10]: L.cou\n", + "\n", + "```\n", + "\n", + "Though Python has no strictly-enforced distinction between public/external attributes and private/internal attributes, by convention a preceding underscore is used to denote such methods.\n", + "For clarity, these private methods and special methods are omitted from the list by default, but it's possible to list them by explicitly typing the underscore:\n", + "\n", + "```ipython\n", + "In [10]: L._\n", + "L.__add__ L.__gt__ L.__reduce__\n", + "L.__class__ L.__hash__ L.__reduce_ex__\n", + "```\n", + "\n", + "For brevity, we've only shown the first couple lines of the output.\n", + "Most of these are Python's special double-underscore methods (often nicknamed \"dunder\" methods)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Tab completion when importing\n", + "\n", + "Tab completion is also useful when importing objects from packages.\n", + "Here we'll use it to find all possible imports in the ``itertools`` package that start with ``co``:\n", + "```\n", + "In [10]: from itertools import co\n", + "combinations compress\n", + "combinations_with_replacement count\n", + "```\n", + "Similarly, you can use tab-completion to see which imports are available on your system (this will change depending on which third-party scripts and modules are visible to your Python session):\n", + "```\n", + "In [10]: import \n", + "Display all 399 possibilities? (y or n)\n", + "Crypto dis py_compile\n", + "Cython distutils pyclbr\n", + "... ... ...\n", + "difflib pwd zmq\n", + "\n", + "In [10]: import h\n", + "hashlib hmac http \n", + "heapq html husl \n", + "```\n", + "(Note that for brevity, I did not print here all 399 importable packages and modules on my system.)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Beyond tab completion: wildcard matching\n", + "\n", + "Tab completion is useful if you know the first few characters of the object or attribute you're looking for, but is little help if you'd like to match characters at the middle or end of the word.\n", + "For this use-case, IPython provides a means of wildcard matching for names using the ``*`` character.\n", + "\n", + "For example, we can use this to list every object in the namespace that ends with ``Warning``:\n", + "\n", + "```ipython\n", + "In [10]: *Warning?\n", + "BytesWarning RuntimeWarning\n", + "DeprecationWarning SyntaxWarning\n", + "FutureWarning UnicodeWarning\n", + "ImportWarning UserWarning\n", + "PendingDeprecationWarning Warning\n", + "ResourceWarning\n", + "```\n", + "\n", + "Notice that the ``*`` character matches any string, including the empty string.\n", + "\n", + "Similarly, suppose we are looking for a string method that contains the word ``find`` somewhere in its name.\n", + "We can search for it this way:\n", + "\n", + "```ipython\n", + "In [10]: str.*find*?\n", + "str.find\n", + "str.rfind\n", + "```\n", + "\n", + "I find this type of flexible wildcard search can be very useful for finding a particular command when getting to know a new package or reacquainting myself with a familiar one." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb) | [Contents](Index.ipynb) | [Keyboard Shortcuts in the IPython Shell](01.02-Shell-Keyboard-Shortcuts.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/01.02-Shell-Keyboard-Shortcuts.ipynb b/notebooks_v1/01.02-Shell-Keyboard-Shortcuts.ipynb new file mode 100644 index 000000000..f50e9fb1c --- /dev/null +++ b/notebooks_v1/01.02-Shell-Keyboard-Shortcuts.ipynb @@ -0,0 +1,207 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb) | [Contents](Index.ipynb) | [IPython Magic Commands](01.03-Magic-Commands.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Keyboard Shortcuts in the IPython Shell" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you spend any amount of time on the computer, you've probably found a use for keyboard shortcuts in your workflow.\n", + "Most familiar perhaps are the Cmd-C and Cmd-V (or Ctrl-C and Ctrl-V) for copying and pasting in a wide variety of programs and systems.\n", + "Power-users tend to go even further: popular text editors like Emacs, Vim, and others provide users an incredible range of operations through intricate combinations of keystrokes.\n", + "\n", + "The IPython shell doesn't go this far, but does provide a number of keyboard shortcuts for fast navigation while typing commands.\n", + "These shortcuts are not in fact provided by IPython itself, but through its dependency on the GNU Readline library: as such, some of the following shortcuts may differ depending on your system configuration.\n", + "Also, while some of these shortcuts do work in the browser-based notebook, this section is primarily about shortcuts in the IPython shell.\n", + "\n", + "Once you get accustomed to these, they can be very useful for quickly performing certain commands without moving your hands from the \"home\" keyboard position.\n", + "If you're an Emacs user or if you have experience with Linux-style shells, the following will be very familiar.\n", + "We'll group these shortcuts into a few categories: *navigation shortcuts*, *text entry shortcuts*, *command history shortcuts*, and *miscellaneous shortcuts*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Navigation shortcuts\n", + "\n", + "While the use of the left and right arrow keys to move backward and forward in the line is quite obvious, there are other options that don't require moving your hands from the \"home\" keyboard position:\n", + "\n", + "| Keystroke | Action |\n", + "|-----------------------------------|--------------------------------------------|\n", + "| ``Ctrl-a`` | Move cursor to the beginning of the line |\n", + "| ``Ctrl-e`` | Move cursor to the end of the line |\n", + "| ``Ctrl-b`` or the left arrow key | Move cursor back one character |\n", + "| ``Ctrl-f`` or the right arrow key | Move cursor forward one character |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Text Entry Shortcuts\n", + "\n", + "While everyone is familiar with using the Backspace key to delete the previous character, reaching for the key often requires some minor finger gymnastics, and it only deletes a single character at a time.\n", + "In IPython there are several shortcuts for removing some portion of the text you're typing.\n", + "The most immediately useful of these are the commands to delete entire lines of text.\n", + "You'll know these have become second-nature if you find yourself using a combination of Ctrl-b and Ctrl-d instead of reaching for Backspace to delete the previous character!\n", + "\n", + "| Keystroke | Action |\n", + "|-------------------------------|--------------------------------------------------|\n", + "| Backspace key | Delete previous character in line |\n", + "| ``Ctrl-d`` | Delete next character in line |\n", + "| ``Ctrl-k`` | Cut text from cursor to end of line |\n", + "| ``Ctrl-u`` | Cut text from beginning of line to cursor |\n", + "| ``Ctrl-y`` | Yank (i.e. paste) text that was previously cut |\n", + "| ``Ctrl-t`` | Transpose (i.e., switch) previous two characters |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Command History Shortcuts\n", + "\n", + "Perhaps the most impactful shortcuts discussed here are the ones IPython provides for navigating the command history.\n", + "This command history goes beyond your current IPython session: your entire command history is stored in a SQLite database in your IPython profile directory.\n", + "The most straightforward way to access these is with the up and down arrow keys to step through the history, but other options exist as well:\n", + "\n", + "| Keystroke | Action |\n", + "|-------------------------------------|--------------------------------------------|\n", + "| ``Ctrl-p`` (or the up arrow key) | Access previous command in history |\n", + "| ``Ctrl-n`` (or the down arrow key) | Access next command in history |\n", + "| ``Ctrl-r`` | Reverse-search through command history |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The reverse-search can be particularly useful.\n", + "Recall that in the previous section we defined a function called ``square``.\n", + "Let's reverse-search our Python history from a new IPython shell and find this definition again.\n", + "When you press Ctrl-r in the IPython terminal, you'll see the following prompt:\n", + "\n", + "```ipython\n", + "In [1]:\n", + "(reverse-i-search)`': \n", + "```\n", + "\n", + "If you start typing characters at this prompt, IPython will auto-fill the most recent command, if any, that matches those characters:\n", + "\n", + "```ipython\n", + "In [1]: \n", + "(reverse-i-search)`sqa': square??\n", + "```\n", + "\n", + "At any point, you can add more characters to refine the search, or press Ctrl-r again to search further for another command that matches the query. If you followed along in the previous section, pressing Ctrl-r twice more gives:\n", + "\n", + "```ipython\n", + "In [1]: \n", + "(reverse-i-search)`sqa': def square(a):\n", + " \"\"\"Return the square of a\"\"\"\n", + " return a ** 2\n", + "```\n", + "\n", + "Once you have found the command you're looking for, press Return and the search will end.\n", + "We can then use the retrieved command, and carry-on with our session:\n", + "\n", + "```ipython\n", + "In [1]: def square(a):\n", + " \"\"\"Return the square of a\"\"\"\n", + " return a ** 2\n", + "\n", + "In [2]: square(2)\n", + "Out[2]: 4\n", + "```\n", + "\n", + "Note that Ctrl-p/Ctrl-n or the up/down arrow keys can also be used to search through history, but only by matching characters at the beginning of the line.\n", + "That is, if you type **``def``** and then press Ctrl-p, it would find the most recent command (if any) in your history that begins with the characters ``def``." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Miscellaneous Shortcuts\n", + "\n", + "Finally, there are a few miscellaneous shortcuts that don't fit into any of the preceding categories, but are nevertheless useful to know:\n", + "\n", + "| Keystroke | Action |\n", + "|-------------------------------|--------------------------------------------|\n", + "| ``Ctrl-l`` | Clear terminal screen |\n", + "| ``Ctrl-c`` | Interrupt current Python command |\n", + "| ``Ctrl-d`` | Exit IPython session |\n", + "\n", + "The Ctrl-c in particular can be useful when you inadvertently start a very long-running job." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While some of the shortcuts discussed here may seem a bit tedious at first, they quickly become automatic with practice.\n", + "Once you develop that muscle memory, I suspect you will even find yourself wishing they were available in other contexts." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb) | [Contents](Index.ipynb) | [IPython Magic Commands](01.03-Magic-Commands.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/01.03-Magic-Commands.ipynb b/notebooks_v1/01.03-Magic-Commands.ipynb new file mode 100644 index 000000000..e5ee9d164 --- /dev/null +++ b/notebooks_v1/01.03-Magic-Commands.ipynb @@ -0,0 +1,238 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Keyboard Shortcuts in the IPython Shell](01.02-Shell-Keyboard-Shortcuts.ipynb) | [Contents](Index.ipynb) | [Input and Output History](01.04-Input-Output-History.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# IPython Magic Commands" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The previous two sections showed how IPython lets you use and explore Python efficiently and interactively.\n", + "Here we'll begin discussing some of the enhancements that IPython adds on top of the normal Python syntax.\n", + "These are known in IPython as *magic commands*, and are prefixed by the ``%`` character.\n", + "These magic commands are designed to succinctly solve various common problems in standard data analysis.\n", + "Magic commands come in two flavors: *line magics*, which are denoted by a single ``%`` prefix and operate on a single line of input, and *cell magics*, which are denoted by a double ``%%`` prefix and operate on multiple lines of input.\n", + "We'll demonstrate and discuss a few brief examples here, and come back to more focused discussion of several useful magic commands later in the chapter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pasting Code Blocks: ``%paste`` and ``%cpaste``\n", + "\n", + "When working in the IPython interpreter, one common gotcha is that pasting multi-line code blocks can lead to unexpected errors, especially when indentation and interpreter markers are involved.\n", + "A common case is that you find some example code on a website and want to paste it into your interpreter.\n", + "Consider the following simple function:\n", + "\n", + "``` python\n", + ">>> def donothing(x):\n", + "... return x\n", + "\n", + "```\n", + "The code is formatted as it would appear in the Python interpreter, and if you copy and paste this directly into IPython you get an error:\n", + "\n", + "```ipython\n", + "In [2]: >>> def donothing(x):\n", + " ...: ... return x\n", + " ...: \n", + " File \"\", line 2\n", + " ... return x\n", + " ^\n", + "SyntaxError: invalid syntax\n", + "```\n", + "\n", + "In the direct paste, the interpreter is confused by the additional prompt characters.\n", + "But never fear–IPython's ``%paste`` magic function is designed to handle this exact type of multi-line, marked-up input:\n", + "\n", + "```ipython\n", + "In [3]: %paste\n", + ">>> def donothing(x):\n", + "... return x\n", + "\n", + "## -- End pasted text --\n", + "```\n", + "\n", + "The ``%paste`` command both enters and executes the code, so now the function is ready to be used:\n", + "\n", + "```ipython\n", + "In [4]: donothing(10)\n", + "Out[4]: 10\n", + "```\n", + "\n", + "A command with a similar intent is ``%cpaste``, which opens up an interactive multiline prompt in which you can paste one or more chunks of code to be executed in a batch:\n", + "\n", + "```ipython\n", + "In [5]: %cpaste\n", + "Pasting code; enter '--' alone on the line to stop or use Ctrl-D.\n", + ":>>> def donothing(x):\n", + ":... return x\n", + ":--\n", + "```\n", + "\n", + "These magic commands, like others we'll see, make available functionality that would be difficult or impossible in a standard Python interpreter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running External Code: ``%run``\n", + "As you begin developing more extensive code, you will likely find yourself working in both IPython for interactive exploration, as well as a text editor to store code that you want to reuse.\n", + "Rather than running this code in a new window, it can be convenient to run it within your IPython session.\n", + "This can be done with the ``%run`` magic.\n", + "\n", + "For example, imagine you've created a ``myscript.py`` file with the following contents:\n", + "\n", + "```python\n", + "#-------------------------------------\n", + "# file: myscript.py\n", + "\n", + "def square(x):\n", + " \"\"\"square a number\"\"\"\n", + " return x ** 2\n", + "\n", + "for N in range(1, 4):\n", + " print(N, \"squared is\", square(N))\n", + "```\n", + "\n", + "You can execute this from your IPython session as follows:\n", + "\n", + "```ipython\n", + "In [6]: %run myscript.py\n", + "1 squared is 1\n", + "2 squared is 4\n", + "3 squared is 9\n", + "```\n", + "\n", + "Note also that after you've run this script, any functions defined within it are available for use in your IPython session:\n", + "\n", + "```ipython\n", + "In [7]: square(5)\n", + "Out[7]: 25\n", + "```\n", + "\n", + "There are several options to fine-tune how your code is run; you can see the documentation in the normal way, by typing **``%run?``** in the IPython interpreter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Timing Code Execution: ``%timeit``\n", + "Another example of a useful magic function is ``%timeit``, which will automatically determine the execution time of the single-line Python statement that follows it.\n", + "For example, we may want to check the performance of a list comprehension:\n", + "\n", + "```ipython\n", + "In [8]: %timeit L = [n ** 2 for n in range(1000)]\n", + "1000 loops, best of 3: 325 µs per loop\n", + "```\n", + "\n", + "The benefit of ``%timeit`` is that for short commands it will automatically perform multiple runs in order to attain more robust results.\n", + "For multi line statements, adding a second ``%`` sign will turn this into a cell magic that can handle multiple lines of input.\n", + "For example, here's the equivalent construction with a ``for``-loop:\n", + "\n", + "```ipython\n", + "In [9]: %%timeit\n", + " ...: L = []\n", + " ...: for n in range(1000):\n", + " ...: L.append(n ** 2)\n", + " ...: \n", + "1000 loops, best of 3: 373 µs per loop\n", + "```\n", + "\n", + "We can immediately see that list comprehensions are about 10% faster than the equivalent ``for``-loop construction in this case.\n", + "We'll explore ``%timeit`` and other approaches to timing and profiling code in [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Help on Magic Functions: ``?``, ``%magic``, and ``%lsmagic``\n", + "\n", + "Like normal Python functions, IPython magic functions have docstrings, and this useful\n", + "documentation can be accessed in the standard manner.\n", + "So, for example, to read the documentation of the ``%timeit`` magic simply type this:\n", + "\n", + "```ipython\n", + "In [10]: %timeit?\n", + "```\n", + "\n", + "Documentation for other functions can be accessed similarly.\n", + "To access a general description of available magic functions, including some examples, you can type this:\n", + "\n", + "```ipython\n", + "In [11]: %magic\n", + "```\n", + "\n", + "For a quick and simple list of all available magic functions, type this:\n", + "\n", + "```ipython\n", + "In [12]: %lsmagic\n", + "```\n", + "\n", + "Finally, I'll mention that it is quite straightforward to define your own magic functions if you wish.\n", + "We won't discuss it here, but if you are interested, see the references listed in [More IPython Resources](01.08-More-IPython-Resources.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Keyboard Shortcuts in the IPython Shell](01.02-Shell-Keyboard-Shortcuts.ipynb) | [Contents](Index.ipynb) | [Input and Output History](01.04-Input-Output-History.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/01.04-Input-Output-History.ipynb b/notebooks_v1/01.04-Input-Output-History.ipynb new file mode 100644 index 000000000..c8e5463fe --- /dev/null +++ b/notebooks_v1/01.04-Input-Output-History.ipynb @@ -0,0 +1,222 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [IPython Magic Commands](01.03-Magic-Commands.ipynb) | [Contents](Index.ipynb) | [IPython and Shell Commands](01.05-IPython-And-Shell-Commands.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Input and Output History" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Previously we saw that the IPython shell allows you to access previous commands with the up and down arrow keys, or equivalently the Ctrl-p/Ctrl-n shortcuts.\n", + "Additionally, in both the shell and the notebook, IPython exposes several ways to obtain the output of previous commands, as well as string versions of the commands themselves.\n", + "We'll explore those here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## IPython's ``In`` and ``Out`` Objects\n", + "\n", + "By now I imagine you're quite familiar with the ``In [1]:``/``Out[1]:`` style prompts used by IPython.\n", + "But it turns out that these are not just pretty decoration: they give a clue as to how you can access previous inputs and outputs in your current session.\n", + "Imagine you start a session that looks like this:\n", + "\n", + "```ipython\n", + "In [1]: import math\n", + "\n", + "In [2]: math.sin(2)\n", + "Out[2]: 0.9092974268256817\n", + "\n", + "In [3]: math.cos(2)\n", + "Out[3]: -0.4161468365471424\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We've imported the built-in ``math`` package, then computed the sine and the cosine of the number 2.\n", + "These inputs and outputs are displayed in the shell with ``In``/``Out`` labels, but there's more–IPython actually creates some Python variables called ``In`` and ``Out`` that are automatically updated to reflect this history:\n", + "\n", + "```ipython\n", + "In [4]: print(In)\n", + "['', 'import math', 'math.sin(2)', 'math.cos(2)', 'print(In)']\n", + "\n", + "In [5]: Out\n", + "Out[5]: {2: 0.9092974268256817, 3: -0.4161468365471424}\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``In`` object is a list, which keeps track of the commands in order (the first item in the list is a place-holder so that ``In[1]`` can refer to the first command):\n", + "\n", + "```ipython\n", + "In [6]: print(In[1])\n", + "import math\n", + "```\n", + "\n", + "The ``Out`` object is not a list but a dictionary mapping input numbers to their outputs (if any):\n", + "\n", + "```ipython\n", + "In [7]: print(Out[2])\n", + "0.9092974268256817\n", + "```\n", + "\n", + "Note that not all operations have outputs: for example, ``import`` statements and ``print`` statements don't affect the output.\n", + "The latter may be surprising, but makes sense if you consider that ``print`` is a function that returns ``None``; for brevity, any command that returns ``None`` is not added to ``Out``.\n", + "\n", + "Where this can be useful is if you want to interact with past results.\n", + "For example, let's check the sum of ``sin(2) ** 2`` and ``cos(2) ** 2`` using the previously-computed results:\n", + "\n", + "```ipython\n", + "In [8]: Out[2] ** 2 + Out[3] ** 2\n", + "Out[8]: 1.0\n", + "```\n", + "\n", + "The result is ``1.0`` as we'd expect from the well-known trigonometric identity.\n", + "In this case, using these previous results probably is not necessary, but it can become very handy if you execute a very expensive computation and want to reuse the result!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Underscore Shortcuts and Previous Outputs\n", + "\n", + "The standard Python shell contains just one simple shortcut for accessing previous output; the variable ``_`` (i.e., a single underscore) is kept updated with the previous output; this works in IPython as well:\n", + "\n", + "```ipython\n", + "In [9]: print(_)\n", + "1.0\n", + "```\n", + "\n", + "But IPython takes this a bit further—you can use a double underscore to access the second-to-last output, and a triple underscore to access the third-to-last output (skipping any commands with no output):\n", + "\n", + "```ipython\n", + "In [10]: print(__)\n", + "-0.4161468365471424\n", + "\n", + "In [11]: print(___)\n", + "0.9092974268256817\n", + "```\n", + "\n", + "IPython stops there: more than three underscores starts to get a bit hard to count, and at that point it's easier to refer to the output by line number.\n", + "\n", + "There is one more shortcut we should mention, however–a shorthand for ``Out[X]`` is ``_X`` (i.e., a single underscore followed by the line number):\n", + "\n", + "```ipython\n", + "In [12]: Out[2]\n", + "Out[12]: 0.9092974268256817\n", + "\n", + "In [13]: _2\n", + "Out[13]: 0.9092974268256817\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Suppressing Output\n", + "Sometimes you might wish to suppress the output of a statement (this is perhaps most common with the plotting commands that we'll explore in [Introduction to Matplotlib](04.00-Introduction-To-Matplotlib.ipynb)).\n", + "Or maybe the command you're executing produces a result that you'd prefer not like to store in your output history, perhaps so that it can be deallocated when other references are removed.\n", + "The easiest way to suppress the output of a command is to add a semicolon to the end of the line:\n", + "\n", + "```ipython\n", + "In [14]: math.sin(2) + math.cos(2);\n", + "```\n", + "\n", + "Note that the result is computed silently, and the output is neither displayed on the screen or stored in the ``Out`` dictionary:\n", + "\n", + "```ipython\n", + "In [15]: 14 in Out\n", + "Out[15]: False\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Related Magic Commands\n", + "For accessing a batch of previous inputs at once, the ``%history`` magic command is very helpful.\n", + "Here is how you can print the first four inputs:\n", + "\n", + "```ipython\n", + "In [16]: %history -n 1-4\n", + " 1: import math\n", + " 2: math.sin(2)\n", + " 3: math.cos(2)\n", + " 4: print(In)\n", + "```\n", + "\n", + "As usual, you can type ``%history?`` for more information and a description of options available.\n", + "Other similar magic commands are ``%rerun`` (which will re-execute some portion of the command history) and ``%save`` (which saves some set of the command history to a file).\n", + "For more information, I suggest exploring these using the ``?`` help functionality discussed in [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [IPython Magic Commands](01.03-Magic-Commands.ipynb) | [Contents](Index.ipynb) | [IPython and Shell Commands](01.05-IPython-And-Shell-Commands.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/01.05-IPython-And-Shell-Commands.ipynb b/notebooks_v1/01.05-IPython-And-Shell-Commands.ipynb new file mode 100644 index 000000000..6fe0dd875 --- /dev/null +++ b/notebooks_v1/01.05-IPython-And-Shell-Commands.ipynb @@ -0,0 +1,255 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Input and Output History](01.04-Input-Output-History.ipynb) | [Contents](Index.ipynb) | [Errors and Debugging](01.06-Errors-and-Debugging.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# IPython and Shell Commands" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When working interactively with the standard Python interpreter, one of the frustrations is the need to switch between multiple windows to access Python tools and system command-line tools.\n", + "IPython bridges this gap, and gives you a syntax for executing shell commands directly from within the IPython terminal.\n", + "The magic happens with the exclamation point: anything appearing after ``!`` on a line will be executed not by the Python kernel, but by the system command-line.\n", + "\n", + "The following assumes you're on a Unix-like system, such as Linux or Mac OSX.\n", + "Some of the examples that follow will fail on Windows, which uses a different type of shell by default (though with the 2016 announcement of native Bash shells on Windows, soon this may no longer be an issue!).\n", + "If you're unfamiliar with shell commands, I'd suggest reviewing the [Shell Tutorial](http://swcarpentry.github.io/shell-novice/) put together by the always excellent Software Carpentry Foundation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quick Introduction to the Shell\n", + "\n", + "A full intro to using the shell/terminal/command-line is well beyond the scope of this chapter, but for the uninitiated we will offer a quick introduction here.\n", + "The shell is a way to interact textually with your computer.\n", + "Ever since the mid 1980s, when Microsoft and Apple introduced the first versions of their now ubiquitous graphical operating systems, most computer users have interacted with their operating system through familiar clicking of menus and drag-and-drop movements.\n", + "But operating systems existed long before these graphical user interfaces, and were primarily controlled through sequences of text input: at the prompt, the user would type a command, and the computer would do what the user told it to.\n", + "Those early prompt systems are the precursors of the shells and terminals that most active data scientists still use today.\n", + "\n", + "Someone unfamiliar with the shell might ask why you would bother with this, when many results can be accomplished by simply clicking on icons and menus.\n", + "A shell user might reply with another question: why hunt icons and click menus when you can accomplish things much more easily by typing?\n", + "While it might sound like a typical tech preference impasse, when moving beyond basic tasks it quickly becomes clear that the shell offers much more control of advanced tasks, though admittedly the learning curve can intimidate the average computer user.\n", + "\n", + "As an example, here is a sample of a Linux/OSX shell session where a user explores, creates, and modifies directories and files on their system (``osx:~ $`` is the prompt, and everything after the ``$`` sign is the typed command; text that is preceded by a ``#`` is meant just as description, rather than something you would actually type in):\n", + "\n", + "```bash\n", + "osx:~ $ echo \"hello world\" # echo is like Python's print function\n", + "hello world\n", + "\n", + "osx:~ $ pwd # pwd = print working directory\n", + "/home/jake # this is the \"path\" that we're sitting in\n", + "\n", + "osx:~ $ ls # ls = list working directory contents\n", + "notebooks projects \n", + "\n", + "osx:~ $ cd projects/ # cd = change directory\n", + "\n", + "osx:projects $ pwd\n", + "/home/jake/projects\n", + "\n", + "osx:projects $ ls\n", + "datasci_book mpld3 myproject.txt\n", + "\n", + "osx:projects $ mkdir myproject # mkdir = make new directory\n", + "\n", + "osx:projects $ cd myproject/\n", + "\n", + "osx:myproject $ mv ../myproject.txt ./ # mv = move file. Here we're moving the\n", + " # file myproject.txt from one directory\n", + " # up (../) to the current directory (./)\n", + "osx:myproject $ ls\n", + "myproject.txt\n", + "```\n", + "\n", + "Notice that all of this is just a compact way to do familiar operations (navigating a directory structure, creating a directory, moving a file, etc.) by typing commands rather than clicking icons and menus.\n", + "Note that with just a few commands (``pwd``, ``ls``, ``cd``, ``mkdir``, and ``cp``) you can do many of the most common file operations.\n", + "It's when you go beyond these basics that the shell approach becomes really powerful." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Shell Commands in IPython\n", + "\n", + "Any command that works at the command-line can be used in IPython by prefixing it with the ``!`` character.\n", + "For example, the ``ls``, ``pwd``, and ``echo`` commands can be run as follows:\n", + "\n", + "```ipython\n", + "In [1]: !ls\n", + "myproject.txt\n", + "\n", + "In [2]: !pwd\n", + "/home/jake/projects/myproject\n", + "\n", + "In [3]: !echo \"printing from the shell\"\n", + "printing from the shell\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Passing Values to and from the Shell\n", + "\n", + "Shell commands can not only be called from IPython, but can also be made to interact with the IPython namespace.\n", + "For example, you can save the output of any shell command to a Python list using the assignment operator:\n", + "\n", + "```ipython\n", + "In [4]: contents = !ls\n", + "\n", + "In [5]: print(contents)\n", + "['myproject.txt']\n", + "\n", + "In [6]: directory = !pwd\n", + "\n", + "In [7]: print(directory)\n", + "['/Users/jakevdp/notebooks/tmp/myproject']\n", + "```\n", + "\n", + "Note that these results are not returned as lists, but as a special shell return type defined in IPython:\n", + "\n", + "```ipython\n", + "In [8]: type(directory)\n", + "IPython.utils.text.SList\n", + "```\n", + "\n", + "This looks and acts a lot like a Python list, but has additional functionality, such as\n", + "the ``grep`` and ``fields`` methods and the ``s``, ``n``, and ``p`` properties that allow you to search, filter, and display the results in convenient ways.\n", + "For more information on these, you can use IPython's built-in help features." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Communication in the other direction–passing Python variables into the shell–is possible using the ``{varname}`` syntax:\n", + "\n", + "```ipython\n", + "In [9]: message = \"hello from Python\"\n", + "\n", + "In [10]: !echo {message}\n", + "hello from Python\n", + "```\n", + "\n", + "The curly braces contain the variable name, which is replaced by the variable's contents in the shell command." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Shell-Related Magic Commands\n", + "\n", + "If you play with IPython's shell commands for a while, you might notice that you cannot use ``!cd`` to navigate the filesystem:\n", + "\n", + "```ipython\n", + "In [11]: !pwd\n", + "/home/jake/projects/myproject\n", + "\n", + "In [12]: !cd ..\n", + "\n", + "In [13]: !pwd\n", + "/home/jake/projects/myproject\n", + "```\n", + "\n", + "The reason is that shell commands in the notebook are executed in a temporary subshell.\n", + "If you'd like to change the working directory in a more enduring way, you can use the ``%cd`` magic command:\n", + "\n", + "```ipython\n", + "In [14]: %cd ..\n", + "/home/jake/projects\n", + "```\n", + "\n", + "In fact, by default you can even use this without the ``%`` sign:\n", + "\n", + "```ipython\n", + "In [15]: cd myproject\n", + "/home/jake/projects/myproject\n", + "```\n", + "\n", + "This is known as an ``automagic`` function, and this behavior can be toggled with the ``%automagic`` magic function.\n", + "\n", + "Besides ``%cd``, other available shell-like magic functions are ``%cat``, ``%cp``, ``%env``, ``%ls``, ``%man``, ``%mkdir``, ``%more``, ``%mv``, ``%pwd``, ``%rm``, and ``%rmdir``, any of which can be used without the ``%`` sign if ``automagic`` is on.\n", + "This makes it so that you can almost treat the IPython prompt as if it's a normal shell:\n", + "\n", + "```ipython\n", + "In [16]: mkdir tmp\n", + "\n", + "In [17]: ls\n", + "myproject.txt tmp/\n", + "\n", + "In [18]: cp myproject.txt tmp/\n", + "\n", + "In [19]: ls tmp\n", + "myproject.txt\n", + "\n", + "In [20]: rm -r tmp\n", + "```\n", + "\n", + "This access to the shell from within the same terminal window as your Python session means that there is a lot less switching back and forth between interpreter and shell as you write your Python code." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Input and Output History](01.04-Input-Output-History.ipynb) | [Contents](Index.ipynb) | [Errors and Debugging](01.06-Errors-and-Debugging.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/code_listings/01.06-Errors-and-Debugging.ipynb b/notebooks_v1/01.06-Errors-and-Debugging.ipynb similarity index 62% rename from code_listings/01.06-Errors-and-Debugging.ipynb rename to notebooks_v1/01.06-Errors-and-Debugging.ipynb index 7d6b3364e..a7625d5ef 100644 --- a/code_listings/01.06-Errors-and-Debugging.ipynb +++ b/notebooks_v1/01.06-Errors-and-Debugging.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [IPython and Shell Commands](01.05-IPython-And-Shell-Commands.ipynb) | [Contents](Index.ipynb) | [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,26 @@ "# Errors and Debugging" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Code development and data analysis always require a bit of trial and error, and IPython contains tools to streamline this process.\n", + "This section will briefly cover some options for controlling Python's exception reporting, followed by exploring tools for debugging errors in code." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Controlling Exceptions: ``%xmode``\n", + "\n", + "Most of the time when a Python script fails, it will raise an Exception.\n", + "When the interpreter hits one of these exceptions, information about the cause of the error can be found in the *traceback*, which can be accessed from within Python.\n", + "With the ``%xmode`` magic function, IPython allows you to control the amount of information printed when the exception is raised.\n", + "Consider the following code:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -48,6 +90,19 @@ "func2(1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling ``func2`` results in an error, and reading the printed trace lets us see exactly what happened.\n", + "By default, this trace includes several lines showing the context of each step that led to the error.\n", + "Using the ``%xmode`` magic function (short for *Exception mode*), we can change what information is printed.\n", + "\n", + "``%xmode`` takes a single argument, the mode, and there are three possibilities: ``Plain``, ``Context``, and ``Verbose``.\n", + "The default is ``Context``, and gives output like that just shown before.\n", + "``Plain`` is more compact and gives less information:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -91,6 +146,13 @@ "func2(1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``Verbose`` mode adds some extra information, including the arguments to any functions that are called:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -134,6 +196,36 @@ "func2(1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This extra information can help narrow-in on why the exception is being raised.\n", + "So why not use the ``Verbose`` mode all the time?\n", + "As code gets complicated, this kind of traceback can get extremely long.\n", + "Depending on the context, sometimes the brevity of ``Default`` mode is easier to work with." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Debugging: When Reading Tracebacks Is Not Enough\n", + "\n", + "The standard Python tool for interactive debugging is ``pdb``, the Python debugger.\n", + "This debugger lets the user step through the code line by line in order to see what might be causing a more difficult error.\n", + "The IPython-enhanced version of this is ``ipdb``, the IPython debugger.\n", + "\n", + "There are many ways to launch and use both these debuggers; we won't cover them fully here.\n", + "Refer to the online documentation of these two utilities to learn more.\n", + "\n", + "In IPython, perhaps the most convenient interface to debugging is the ``%debug`` magic command.\n", + "If you call it after hitting an exception, it will automatically open an interactive debugging prompt at the point of the exception.\n", + "The ``ipdb`` prompt lets you explore the current state of the stack, explore the available variables, and even run Python commands!\n", + "\n", + "Let's look at the most recent exception, then do some basic tasks–print the values of ``a`` and ``b``, and type ``quit`` to quit the debugging session:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -162,6 +254,13 @@ "%debug" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The interactive debugger allows much more than this, though–we can even step up and down through the stack and explore the values of variables there:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -204,6 +303,15 @@ "%debug" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This allows you to quickly find out not only what caused the error, but what function calls led up to the error.\n", + "\n", + "If you'd like the debugger to launch automatically whenever an exception is raised, you can use the ``%pdb`` magic function to turn on this automatic behavior:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -251,9 +359,50 @@ "%pdb on\n", "func2(1)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, if you have a script that you'd like to run from the beginning in interactive mode, you can run it with the command ``%run -d``, and use the ``next`` command to step through the lines of code interactively." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Partial list of debugging commands\n", + "\n", + "There are many more available commands for interactive debugging than we've listed here; the following table contains a description of some of the more common and useful ones:\n", + "\n", + "| Command | Description |\n", + "|-----------------|-------------------------------------------------------------|\n", + "| ``list`` | Show the current location in the file |\n", + "| ``h(elp)`` | Show a list of commands, or find help on a specific command |\n", + "| ``q(uit)`` | Quit the debugger and the program |\n", + "| ``c(ontinue)`` | Quit the debugger, continue in the program |\n", + "| ``n(ext)`` | Go to the next step of the program |\n", + "| ```` | Repeat the previous command |\n", + "| ``p(rint)`` | Print variables |\n", + "| ``s(tep)`` | Step into a subroutine |\n", + "| ``r(eturn)`` | Return out of a subroutine |\n", + "\n", + "For more information, use the ``help`` command in the debugger, or take a look at ``ipdb``'s [online documentation](https://github.com/gotcha/ipdb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [IPython and Shell Commands](01.05-IPython-And-Shell-Commands.ipynb) | [Contents](Index.ipynb) | [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/notebooks_v1/01.07-Timing-and-Profiling.ipynb b/notebooks_v1/01.07-Timing-and-Profiling.ipynb new file mode 100644 index 000000000..76f0db5cb --- /dev/null +++ b/notebooks_v1/01.07-Timing-and-Profiling.ipynb @@ -0,0 +1,548 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Errors and Debugging](01.06-Errors-and-Debugging.ipynb) | [Contents](Index.ipynb) | [More IPython Resources](01.08-More-IPython-Resources.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Profiling and Timing Code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the process of developing code and creating data processing pipelines, there are often trade-offs you can make between various implementations.\n", + "Early in developing your algorithm, it can be counterproductive to worry about such things. As Donald Knuth famously quipped, \"We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil.\"\n", + "\n", + "But once you have your code working, it can be useful to dig into its efficiency a bit.\n", + "Sometimes it's useful to check the execution time of a given command or set of commands; other times it's useful to dig into a multiline process and determine where the bottleneck lies in some complicated series of operations.\n", + "IPython provides access to a wide array of functionality for this kind of timing and profiling of code.\n", + "Here we'll discuss the following IPython magic commands:\n", + "\n", + "- ``%time``: Time the execution of a single statement\n", + "- ``%timeit``: Time repeated execution of a single statement for more accuracy\n", + "- ``%prun``: Run code with the profiler\n", + "- ``%lprun``: Run code with the line-by-line profiler\n", + "- ``%memit``: Measure the memory use of a single statement\n", + "- ``%mprun``: Run code with the line-by-line memory profiler\n", + "\n", + "The last four commands are not bundled with IPython–you'll need to get the ``line_profiler`` and ``memory_profiler`` extensions, which we will discuss in the following sections." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Timing Code Snippets: ``%timeit`` and ``%time``\n", + "\n", + "We saw the ``%timeit`` line-magic and ``%%timeit`` cell-magic in the introduction to magic functions in [IPython Magic Commands](01.03-Magic-Commands.ipynb); it can be used to time the repeated execution of snippets of code:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100000 loops, best of 3: 1.54 µs per loop\n" + ] + } + ], + "source": [ + "%timeit sum(range(100))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that because this operation is so fast, ``%timeit`` automatically does a large number of repetitions.\n", + "For slower commands, ``%timeit`` will automatically adjust and perform fewer repetitions:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 loops, best of 3: 407 ms per loop\n" + ] + } + ], + "source": [ + "%%timeit\n", + "total = 0\n", + "for i in range(1000):\n", + " for j in range(1000):\n", + " total += i * (-1) ** j" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes repeating an operation is not the best option.\n", + "For example, if we have a list that we'd like to sort, we might be misled by a repeated operation.\n", + "Sorting a pre-sorted list is much faster than sorting an unsorted list, so the repetition will skew the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100 loops, best of 3: 1.9 ms per loop\n" + ] + } + ], + "source": [ + "import random\n", + "L = [random.random() for i in range(100000)]\n", + "%timeit L.sort()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this, the ``%time`` magic function may be a better choice. It also is a good choice for longer-running commands, when short, system-related delays are unlikely to affect the result.\n", + "Let's time the sorting of an unsorted and a presorted list:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sorting an unsorted list:\n", + "CPU times: user 40.6 ms, sys: 896 µs, total: 41.5 ms\n", + "Wall time: 41.5 ms\n" + ] + } + ], + "source": [ + "import random\n", + "L = [random.random() for i in range(100000)]\n", + "print(\"sorting an unsorted list:\")\n", + "%time L.sort()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sorting an already sorted list:\n", + "CPU times: user 8.18 ms, sys: 10 µs, total: 8.19 ms\n", + "Wall time: 8.24 ms\n" + ] + } + ], + "source": [ + "print(\"sorting an already sorted list:\")\n", + "%time L.sort()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice how much faster the presorted list is to sort, but notice also how much longer the timing takes with ``%time`` versus ``%timeit``, even for the presorted list!\n", + "This is a result of the fact that ``%timeit`` does some clever things under the hood to prevent system calls from interfering with the timing.\n", + "For example, it prevents cleanup of unused Python objects (known as *garbage collection*) which might otherwise affect the timing.\n", + "For this reason, ``%timeit`` results are usually noticeably faster than ``%time`` results.\n", + "\n", + "For ``%time`` as with ``%timeit``, using the double-percent-sign cell magic syntax allows timing of multiline scripts:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 504 ms, sys: 979 µs, total: 505 ms\n", + "Wall time: 505 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "total = 0\n", + "for i in range(1000):\n", + " for j in range(1000):\n", + " total += i * (-1) ** j" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on ``%time`` and ``%timeit``, as well as their available options, use the IPython help functionality (i.e., type ``%time?`` at the IPython prompt)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Profiling Full Scripts: ``%prun``\n", + "\n", + "A program is made of many single statements, and sometimes timing these statements in context is more important than timing them on their own.\n", + "Python contains a built-in code profiler (which you can read about in the Python documentation), but IPython offers a much more convenient way to use this profiler, in the form of the magic function ``%prun``.\n", + "\n", + "By way of example, we'll define a simple function that does some calculations:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def sum_of_lists(N):\n", + " total = 0\n", + " for i in range(5):\n", + " L = [j ^ (j >> i) for j in range(N)]\n", + " total += sum(L)\n", + " return total" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can call ``%prun`` with a function call to see the profiled results:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " " + ] + } + ], + "source": [ + "%prun sum_of_lists(1000000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the notebook, the output is printed to the pager, and looks something like this:\n", + "\n", + "```\n", + "14 function calls in 0.714 seconds\n", + "\n", + " Ordered by: internal time\n", + "\n", + " ncalls tottime percall cumtime percall filename:lineno(function)\n", + " 5 0.599 0.120 0.599 0.120 :4()\n", + " 5 0.064 0.013 0.064 0.013 {built-in method sum}\n", + " 1 0.036 0.036 0.699 0.699 :1(sum_of_lists)\n", + " 1 0.014 0.014 0.714 0.714 :1()\n", + " 1 0.000 0.000 0.714 0.714 {built-in method exec}\n", + "```\n", + "\n", + "The result is a table that indicates, in order of total time on each function call, where the execution is spending the most time. In this case, the bulk of execution time is in the list comprehension inside ``sum_of_lists``.\n", + "From here, we could start thinking about what changes we might make to improve the performance in the algorithm.\n", + "\n", + "For more information on ``%prun``, as well as its available options, use the IPython help functionality (i.e., type ``%prun?`` at the IPython prompt)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Line-By-Line Profiling with ``%lprun``\n", + "\n", + "The function-by-function profiling of ``%prun`` is useful, but sometimes it's more convenient to have a line-by-line profile report.\n", + "This is not built into Python or IPython, but there is a ``line_profiler`` package available for installation that can do this.\n", + "Start by using Python's packaging tool, ``pip``, to install the ``line_profiler`` package:\n", + "\n", + "```\n", + "$ pip install line_profiler\n", + "```\n", + "\n", + "Next, you can use IPython to load the ``line_profiler`` IPython extension, offered as part of this package:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext line_profiler" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the ``%lprun`` command will do a line-by-line profiling of any function–in this case, we need to tell it explicitly which functions we're interested in profiling:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "%lprun -f sum_of_lists sum_of_lists(5000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As before, the notebook sends the result to the pager, but it looks something like this:\n", + "\n", + "```\n", + "Timer unit: 1e-06 s\n", + "\n", + "Total time: 0.009382 s\n", + "File: \n", + "Function: sum_of_lists at line 1\n", + "\n", + "Line # Hits Time Per Hit % Time Line Contents\n", + "==============================================================\n", + " 1 def sum_of_lists(N):\n", + " 2 1 2 2.0 0.0 total = 0\n", + " 3 6 8 1.3 0.1 for i in range(5):\n", + " 4 5 9001 1800.2 95.9 L = [j ^ (j >> i) for j in range(N)]\n", + " 5 5 371 74.2 4.0 total += sum(L)\n", + " 6 1 0 0.0 0.0 return total\n", + "```\n", + "\n", + "The information at the top gives us the key to reading the results: the time is reported in microseconds and we can see where the program is spending the most time.\n", + "At this point, we may be able to use this information to modify aspects of the script and make it perform better for our desired use case.\n", + "\n", + "For more information on ``%lprun``, as well as its available options, use the IPython help functionality (i.e., type ``%lprun?`` at the IPython prompt)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Profiling Memory Use: ``%memit`` and ``%mprun``\n", + "\n", + "Another aspect of profiling is the amount of memory an operation uses.\n", + "This can be evaluated with another IPython extension, the ``memory_profiler``.\n", + "As with the ``line_profiler``, we start by ``pip``-installing the extension:\n", + "\n", + "```\n", + "$ pip install memory_profiler\n", + "```\n", + "\n", + "Then we can use IPython to load the extension:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext memory_profiler" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The memory profiler extension contains two useful magic functions: the ``%memit`` magic (which offers a memory-measuring equivalent of ``%timeit``) and the ``%mprun`` function (which offers a memory-measuring equivalent of ``%lprun``).\n", + "The ``%memit`` function can be used rather simply:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "peak memory: 100.08 MiB, increment: 61.36 MiB\n" + ] + } + ], + "source": [ + "%memit sum_of_lists(1000000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that this function uses about 100 MB of memory.\n", + "\n", + "For a line-by-line description of memory use, we can use the ``%mprun`` magic.\n", + "Unfortunately, this magic works only for functions defined in separate modules rather than the notebook itself, so we'll start by using the ``%%file`` magic to create a simple module called ``mprun_demo.py``, which contains our ``sum_of_lists`` function, with one addition that will make our memory profiling results more clear:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting mprun_demo.py\n" + ] + } + ], + "source": [ + "%%file mprun_demo.py\n", + "def sum_of_lists(N):\n", + " total = 0\n", + " for i in range(5):\n", + " L = [j ^ (j >> i) for j in range(N)]\n", + " total += sum(L)\n", + " del L # remove reference to L\n", + " return total" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now import the new version of this function and run the memory line profiler:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "from mprun_demo import sum_of_lists\n", + "%mprun -f sum_of_lists sum_of_lists(1000000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result, printed to the pager, gives us a summary of the memory use of the function, and looks something like this:\n", + "```\n", + "Filename: ./mprun_demo.py\n", + "\n", + "Line # Mem usage Increment Line Contents\n", + "================================================\n", + " 4 71.9 MiB 0.0 MiB L = [j ^ (j >> i) for j in range(N)]\n", + "\n", + "\n", + "Filename: ./mprun_demo.py\n", + "\n", + "Line # Mem usage Increment Line Contents\n", + "================================================\n", + " 1 39.0 MiB 0.0 MiB def sum_of_lists(N):\n", + " 2 39.0 MiB 0.0 MiB total = 0\n", + " 3 46.5 MiB 7.5 MiB for i in range(5):\n", + " 4 71.9 MiB 25.4 MiB L = [j ^ (j >> i) for j in range(N)]\n", + " 5 71.9 MiB 0.0 MiB total += sum(L)\n", + " 6 46.5 MiB -25.4 MiB del L # remove reference to L\n", + " 7 39.1 MiB -7.4 MiB return total\n", + "```\n", + "Here the ``Increment`` column tells us how much each line affects the total memory budget: observe that when we create and delete the list ``L``, we are adding about 25 MB of memory usage.\n", + "This is on top of the background memory usage from the Python interpreter itself.\n", + "\n", + "For more information on ``%memit`` and ``%mprun``, as well as their available options, use the IPython help functionality (i.e., type ``%memit?`` at the IPython prompt)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Errors and Debugging](01.06-Errors-and-Debugging.ipynb) | [Contents](Index.ipynb) | [More IPython Resources](01.08-More-IPython-Resources.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/notebooks_v1/01.08-More-IPython-Resources.ipynb b/notebooks_v1/01.08-More-IPython-Resources.ipynb new file mode 100644 index 000000000..ad87f002d --- /dev/null +++ b/notebooks_v1/01.08-More-IPython-Resources.ipynb @@ -0,0 +1,99 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb) | [Contents](Index.ipynb) | [Introduction to NumPy](02.00-Introduction-to-NumPy.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# More IPython Resources" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this chapter, we've just scratched the surface of using IPython to enable data science tasks.\n", + "Much more information is available both in print and on the Web, and here we'll list some other resources that you may find helpful." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Web Resources\n", + "\n", + "- [The IPython website](http://ipython.org): The IPython website links to documentation, examples, tutorials, and a variety of other resources.\n", + "- [The nbviewer website](http://nbviewer.jupyter.org/): This site shows static renderings of any IPython notebook available on the internet. The front page features some example notebooks that you can browse to see what other folks are using IPython for!\n", + "- [A gallery of interesting Jupyter Notebooks](https://github.com/jupyter/jupyter/wiki/A-gallery-of-interesting-Jupyter-Notebooks/): This ever-growing list of notebooks, powered by nbviewer, shows the depth and breadth of numerical analysis you can do with IPython. It includes everything from short examples and tutorials to full-blown courses and books composed in the notebook format!\n", + "- Video Tutorials: searching the Internet, you will find many video-recorded tutorials on IPython. I'd especially recommend seeking tutorials from the PyCon, SciPy, and PyData conferenes by Fernando Perez and Brian Granger, two of the primary creators and maintainers of IPython and Jupyter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Books\n", + "\n", + "- [*Python for Data Analysis*](http://shop.oreilly.com/product/0636920023784.do): Wes McKinney's book includes a chapter that covers using IPython as a data scientist. Although much of the material overlaps what we've discussed here, another perspective is always helpful.\n", + "- [*Learning IPython for Interactive Computing and Data Visualization*](https://www.packtpub.com/big-data-and-business-intelligence/learning-ipython-interactive-computing-and-data-visualization): This short book by Cyrille Rossant offers a good introduction to using IPython for data analysis.\n", + "- [*IPython Interactive Computing and Visualization Cookbook*](https://www.packtpub.com/big-data-and-business-intelligence/ipython-interactive-computing-and-visualization-cookbook): Also by Cyrille Rossant, this book is a longer and more advanced treatment of using IPython for data science. Despite its name, it's not just about IPython–it also goes into some depth on a broad range of data science topics.\n", + "\n", + "Finally, a reminder that you can find help on your own: IPython's ``?``-based help functionality (discussed in [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)) can be very useful if you use it well and use it often.\n", + "As you go through the examples here and elsewhere, this can be used to familiarize yourself with all the tools that IPython has to offer." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb) | [Contents](Index.ipynb) | [Introduction to NumPy](02.00-Introduction-to-NumPy.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/02.00-Introduction-to-NumPy.ipynb b/notebooks_v1/02.00-Introduction-to-NumPy.ipynb new file mode 100644 index 000000000..e527c4355 --- /dev/null +++ b/notebooks_v1/02.00-Introduction-to-NumPy.ipynb @@ -0,0 +1,191 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [More IPython Resources](01.08-More-IPython-Resources.ipynb) | [Contents](Index.ipynb) | [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "# Introduction to NumPy" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This chapter, along with chapter 3, outlines techniques for effectively loading, storing, and manipulating in-memory data in Python.\n", + "The topic is very broad: datasets can come from a wide range of sources and a wide range of formats, including be collections of documents, collections of images, collections of sound clips, collections of numerical measurements, or nearly anything else.\n", + "Despite this apparent heterogeneity, it will help us to think of all data fundamentally as arrays of numbers.\n", + "\n", + "For example, images–particularly digital images–can be thought of as simply two-dimensional arrays of numbers representing pixel brightness across the area.\n", + "Sound clips can be thought of as one-dimensional arrays of intensity versus time.\n", + "Text can be converted in various ways into numerical representations, perhaps binary digits representing the frequency of certain words or pairs of words.\n", + "No matter what the data are, the first step in making it analyzable will be to transform them into arrays of numbers.\n", + "(We will discuss some specific examples of this process later in [Feature Engineering](05.04-Feature-Engineering.ipynb))\n", + "\n", + "For this reason, efficient storage and manipulation of numerical arrays is absolutely fundamental to the process of doing data science.\n", + "We'll now take a look at the specialized tools that Python has for handling such numerical arrays: the NumPy package, and the Pandas package (discussed in Chapter 3).\n", + "\n", + "This chapter will cover NumPy in detail. NumPy (short for *Numerical Python*) provides an efficient interface to store and operate on dense data buffers.\n", + "In some ways, NumPy arrays are like Python's built-in ``list`` type, but NumPy arrays provide much more efficient storage and data operations as the arrays grow larger in size.\n", + "NumPy arrays form the core of nearly the entire ecosystem of data science tools in Python, so time spent learning to use NumPy effectively will be valuable no matter what aspect of data science interests you.\n", + "\n", + "If you followed the advice outlined in the Preface and installed the Anaconda stack, you already have NumPy installed and ready to go.\n", + "If you're more the do-it-yourself type, you can go to http://www.numpy.org/ and follow the installation instructions found there.\n", + "Once you do, you can import NumPy and double-check the version:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.11.1'" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy\n", + "numpy.__version__" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For the pieces of the package discussed here, I'd recommend NumPy version 1.8 or later.\n", + "By convention, you'll find that most people in the SciPy/PyData world will import NumPy using ``np`` as an alias:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Throughout this chapter, and indeed the rest of the book, you'll find that this is the way we will import and use NumPy." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Reminder about Built In Documentation\n", + "\n", + "As you read through this chapter, don't forget that IPython gives you the ability to quickly explore the contents of a package (by using the tab-completion feature), as well as the documentation of various functions (using the ``?`` character – Refer back to [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)).\n", + "\n", + "For example, to display all the contents of the numpy namespace, you can type this:\n", + "\n", + "```ipython\n", + "In [3]: np.\n", + "```\n", + "\n", + "And to display NumPy's built-in documentation, you can use this:\n", + "\n", + "```ipython\n", + "In [4]: np?\n", + "```\n", + "\n", + "More detailed documentation, along with tutorials and other resources, can be found at http://www.numpy.org." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [More IPython Resources](01.08-More-IPython-Resources.ipynb) | [Contents](Index.ipynb) | [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/02.01-Understanding-Data-Types.ipynb b/notebooks_v1/02.01-Understanding-Data-Types.ipynb new file mode 100644 index 000000000..82b128e48 --- /dev/null +++ b/notebooks_v1/02.01-Understanding-Data-Types.ipynb @@ -0,0 +1,830 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Introduction to NumPy](02.00-Introduction-to-NumPy.ipynb) | [Contents](Index.ipynb) | [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Understanding Data Types in Python" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Effective data-driven science and computation requires understanding how data is stored and manipulated.\n", + "This section outlines and contrasts how arrays of data are handled in the Python language itself, and how NumPy improves on this.\n", + "Understanding this difference is fundamental to understanding much of the material throughout the rest of the book.\n", + "\n", + "Users of Python are often drawn-in by its ease of use, one piece of which is dynamic typing.\n", + "While a statically-typed language like C or Java requires each variable to be explicitly declared, a dynamically-typed language like Python skips this specification. For example, in C you might specify a particular operation as follows:\n", + "\n", + "```C\n", + "/* C code */\n", + "int result = 0;\n", + "for(int i=0; i<100; i++){\n", + " result += i;\n", + "}\n", + "```\n", + "\n", + "While in Python the equivalent operation could be written this way:\n", + "\n", + "```python\n", + "# Python code\n", + "result = 0\n", + "for i in range(100):\n", + " result += i\n", + "```\n", + "\n", + "Notice the main difference: in C, the data types of each variable are explicitly declared, while in Python the types are dynamically inferred. This means, for example, that we can assign any kind of data to any variable:\n", + "\n", + "```python\n", + "# Python code\n", + "x = 4\n", + "x = \"four\"\n", + "```\n", + "\n", + "Here we've switched the contents of ``x`` from an integer to a string. The same thing in C would lead (depending on compiler settings) to a compilation error or other unintented consequences:\n", + "\n", + "```C\n", + "/* C code */\n", + "int x = 4;\n", + "x = \"four\"; // FAILS\n", + "```\n", + "\n", + "This sort of flexibility is one piece that makes Python and other dynamically-typed languages convenient and easy to use.\n", + "Understanding *how* this works is an important piece of learning to analyze data efficiently and effectively with Python.\n", + "But what this type-flexibility also points to is the fact that Python variables are more than just their value; they also contain extra information about the type of the value. We'll explore this more in the sections that follow." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A Python Integer Is More Than Just an Integer\n", + "\n", + "The standard Python implementation is written in C.\n", + "This means that every Python object is simply a cleverly-disguised C structure, which contains not only its value, but other information as well. For example, when we define an integer in Python, such as ``x = 10000``, ``x`` is not just a \"raw\" integer. It's actually a pointer to a compound C structure, which contains several values.\n", + "Looking through the Python 3.4 source code, we find that the integer (long) type definition effectively looks like this (once the C macros are expanded):\n", + "\n", + "```C\n", + "struct _longobject {\n", + " long ob_refcnt;\n", + " PyTypeObject *ob_type;\n", + " size_t ob_size;\n", + " long ob_digit[1];\n", + "};\n", + "```\n", + "\n", + "A single integer in Python 3.4 actually contains four pieces:\n", + "\n", + "- ``ob_refcnt``, a reference count that helps Python silently handle memory allocation and deallocation\n", + "- ``ob_type``, which encodes the type of the variable\n", + "- ``ob_size``, which specifies the size of the following data members\n", + "- ``ob_digit``, which contains the actual integer value that we expect the Python variable to represent.\n", + "\n", + "This means that there is some overhead in storing an integer in Python as compared to an integer in a compiled language like C, as illustrated in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Integer Memory Layout](figures/cint_vs_pyint.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here ``PyObject_HEAD`` is the part of the structure containing the reference count, type code, and other pieces mentioned before.\n", + "\n", + "Notice the difference here: a C integer is essentially a label for a position in memory whose bytes encode an integer value.\n", + "A Python integer is a pointer to a position in memory containing all the Python object information, including the bytes that contain the integer value.\n", + "This extra information in the Python integer structure is what allows Python to be coded so freely and dynamically.\n", + "All this additional information in Python types comes at a cost, however, which becomes especially apparent in structures that combine many of these objects." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A Python List Is More Than Just a List\n", + "\n", + "Let's consider now what happens when we use a Python data structure that holds many Python objects.\n", + "The standard mutable multi-element container in Python is the list.\n", + "We can create a list of integers as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L = list(range(10))\n", + "L" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "int" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(L[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or, similarly, a list of strings:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L2 = [str(c) for c in L]\n", + "L2" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "str" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(L2[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of Python's dynamic typing, we can even create heterogeneous lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[bool, str, float, int]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L3 = [True, \"2\", 3.0, 4]\n", + "[type(item) for item in L3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this flexibility comes at a cost: to allow these flexible types, each item in the list must contain its own type info, reference count, and other information–that is, each item is a complete Python object.\n", + "In the special case that all variables are of the same type, much of this information is redundant: it can be much more efficient to store data in a fixed-type array.\n", + "The difference between a dynamic-type list and a fixed-type (NumPy-style) array is illustrated in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Array Memory Layout](figures/array_vs_list.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At the implementation level, the array essentially contains a single pointer to one contiguous block of data.\n", + "The Python list, on the other hand, contains a pointer to a block of pointers, each of which in turn points to a full Python object like the Python integer we saw earlier.\n", + "Again, the advantage of the list is flexibility: because each list element is a full structure containing both data and type information, the list can be filled with data of any desired type.\n", + "Fixed-type NumPy-style arrays lack this flexibility, but are much more efficient for storing and manipulating data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fixed-Type Arrays in Python\n", + "\n", + "Python offers several different options for storing data in efficient, fixed-type data buffers.\n", + "The built-in ``array`` module (available since Python 3.3) can be used to create dense arrays of a uniform type:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import array\n", + "L = list(range(10))\n", + "A = array.array('i', L)\n", + "A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here ``'i'`` is a type code indicating the contents are integers.\n", + "\n", + "Much more useful, however, is the ``ndarray`` object of the NumPy package.\n", + "While Python's ``array`` object provides efficient storage of array-based data, NumPy adds to this efficient *operations* on that data.\n", + "We will explore these operations in later sections; here we'll demonstrate several ways of creating a NumPy array.\n", + "\n", + "We'll start with the standard NumPy import, under the alias ``np``:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Creating Arrays from Python Lists\n", + "\n", + "First, we can use ``np.array`` to create arrays from Python lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 4, 2, 5, 3])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# integer array:\n", + "np.array([1, 4, 2, 5, 3])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember that unlike Python lists, NumPy is constrained to arrays that all contain the same type.\n", + "If types do not match, NumPy will upcast if possible (here, integers are up-cast to floating point):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 3.14, 4. , 2. , 3. ])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.array([3.14, 4, 2, 3])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we want to explicitly set the data type of the resulting array, we can use the ``dtype`` keyword:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., 2., 3., 4.], dtype=float32)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.array([1, 2, 3, 4], dtype='float32')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, unlike Python lists, NumPy arrays can explicitly be multi-dimensional; here's one way of initializing a multidimensional array using a list of lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[2, 3, 4],\n", + " [4, 5, 6],\n", + " [6, 7, 8]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# nested lists result in multi-dimensional arrays\n", + "np.array([range(i, i + 3) for i in [2, 4, 6]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The inner lists are treated as rows of the resulting two-dimensional array." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Creating Arrays from Scratch\n", + "\n", + "Especially for larger arrays, it is more efficient to create arrays from scratch using routines built into NumPy.\n", + "Here are several examples:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a length-10 integer array filled with zeros\n", + "np.zeros(10, dtype=int)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1., 1., 1., 1., 1.],\n", + " [ 1., 1., 1., 1., 1.],\n", + " [ 1., 1., 1., 1., 1.]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x5 floating-point array filled with ones\n", + "np.ones((3, 5), dtype=float)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 3.14, 3.14, 3.14, 3.14, 3.14],\n", + " [ 3.14, 3.14, 3.14, 3.14, 3.14],\n", + " [ 3.14, 3.14, 3.14, 3.14, 3.14]])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x5 array filled with 3.14\n", + "np.full((3, 5), 3.14)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create an array filled with a linear sequence\n", + "# Starting at 0, ending at 20, stepping by 2\n", + "# (this is similar to the built-in range() function)\n", + "np.arange(0, 20, 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0. , 0.25, 0.5 , 0.75, 1. ])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create an array of five values evenly spaced between 0 and 1\n", + "np.linspace(0, 1, 5)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.99844933, 0.52183819, 0.22421193],\n", + " [ 0.08007488, 0.45429293, 0.20941444],\n", + " [ 0.14360941, 0.96910973, 0.946117 ]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x3 array of uniformly distributed\n", + "# random values between 0 and 1\n", + "np.random.random((3, 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1.51772646, 0.39614948, -0.10634696],\n", + " [ 0.25671348, 0.00732722, 0.37783601],\n", + " [ 0.68446945, 0.15926039, -0.70744073]])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x3 array of normally distributed random values\n", + "# with mean 0 and standard deviation 1\n", + "np.random.normal(0, 1, (3, 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[2, 3, 4],\n", + " [5, 7, 8],\n", + " [0, 5, 0]])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x3 array of random integers in the interval [0, 10)\n", + "np.random.randint(0, 10, (3, 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1., 0., 0.],\n", + " [ 0., 1., 0.],\n", + " [ 0., 0., 1.]])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create a 3x3 identity matrix\n", + "np.eye(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., 1., 1.])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create an uninitialized array of three integers\n", + "# The values will be whatever happens to already exist at that memory location\n", + "np.empty(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## NumPy Standard Data Types\n", + "\n", + "NumPy arrays contain values of a single type, so it is important to have detailed knowledge of those types and their limitations.\n", + "Because NumPy is built in C, the types will be familiar to users of C, Fortran, and other related languages.\n", + "\n", + "The standard NumPy data types are listed in the following table.\n", + "Note that when constructing an array, they can be specified using a string:\n", + "\n", + "```python\n", + "np.zeros(10, dtype='int16')\n", + "```\n", + "\n", + "Or using the associated NumPy object:\n", + "\n", + "```python\n", + "np.zeros(10, dtype=np.int16)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Data type\t | Description |\n", + "|---------------|-------------|\n", + "| ``bool_`` | Boolean (True or False) stored as a byte |\n", + "| ``int_`` | Default integer type (same as C ``long``; normally either ``int64`` or ``int32``)| \n", + "| ``intc`` | Identical to C ``int`` (normally ``int32`` or ``int64``)| \n", + "| ``intp`` | Integer used for indexing (same as C ``ssize_t``; normally either ``int32`` or ``int64``)| \n", + "| ``int8`` | Byte (-128 to 127)| \n", + "| ``int16`` | Integer (-32768 to 32767)|\n", + "| ``int32`` | Integer (-2147483648 to 2147483647)|\n", + "| ``int64`` | Integer (-9223372036854775808 to 9223372036854775807)| \n", + "| ``uint8`` | Unsigned integer (0 to 255)| \n", + "| ``uint16`` | Unsigned integer (0 to 65535)| \n", + "| ``uint32`` | Unsigned integer (0 to 4294967295)| \n", + "| ``uint64`` | Unsigned integer (0 to 18446744073709551615)| \n", + "| ``float_`` | Shorthand for ``float64``.| \n", + "| ``float16`` | Half precision float: sign bit, 5 bits exponent, 10 bits mantissa| \n", + "| ``float32`` | Single precision float: sign bit, 8 bits exponent, 23 bits mantissa| \n", + "| ``float64`` | Double precision float: sign bit, 11 bits exponent, 52 bits mantissa| \n", + "| ``complex_`` | Shorthand for ``complex128``.| \n", + "| ``complex64`` | Complex number, represented by two 32-bit floats| \n", + "| ``complex128``| Complex number, represented by two 64-bit floats| " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "More advanced type specification is possible, such as specifying big or little endian numbers; for more information, refer to the [NumPy documentation](http://numpy.org/).\n", + "NumPy also supports compound data types, which will be covered in [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Introduction to NumPy](02.00-Introduction-to-NumPy.ipynb) | [Contents](Index.ipynb) | [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/code_listings/02.02-The-Basics-Of-NumPy-Arrays.ipynb b/notebooks_v1/02.02-The-Basics-Of-NumPy-Arrays.ipynb similarity index 60% rename from code_listings/02.02-The-Basics-Of-NumPy-Arrays.ipynb rename to notebooks_v1/02.02-The-Basics-Of-NumPy-Arrays.ipynb index 171b019db..f9dad509a 100644 --- a/code_listings/02.02-The-Basics-Of-NumPy-Arrays.ipynb +++ b/notebooks_v1/02.02-The-Basics-Of-NumPy-Arrays.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb) | [Contents](Index.ipynb) | [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,40 @@ "# The Basics of NumPy Arrays" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Data manipulation in Python is nearly synonymous with NumPy array manipulation: even newer tools like Pandas ([Chapter 3](03.00-Introduction-to-Pandas.ipynb)) are built around the NumPy array.\n", + "This section will present several examples of using NumPy array manipulation to access data and subarrays, and to split, reshape, and join the arrays.\n", + "While the types of operations shown here may seem a bit dry and pedantic, they comprise the building blocks of many other examples used throughout the book.\n", + "Get to know them well!\n", + "\n", + "We'll cover a few categories of basic array manipulations here:\n", + "\n", + "- *Attributes of arrays*: Determining the size, shape, memory consumption, and data types of arrays\n", + "- *Indexing of arrays*: Getting and setting the value of individual array elements\n", + "- *Slicing of arrays*: Getting and setting smaller subarrays within a larger array\n", + "- *Reshaping of arrays*: Changing the shape of a given array\n", + "- *Joining and splitting of arrays*: Combining multiple arrays into one, and splitting one array into many" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## NumPy Array Attributes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First let's discuss some useful array attributes.\n", + "We'll start by defining three random arrays, a one-dimensional, two-dimensional, and three-dimensional array.\n", + "We'll use NumPy's random number generator, which we will *seed* with a set value in order to ensure that the same random arrays are generated each time this code is run:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -18,9 +74,16 @@ "import numpy as np\n", "np.random.seed(0) # seed for reproducibility\n", "\n", - "x1 = np.random.randint(10, size=6) # 1D array\n", - "x2 = np.random.randint(10, size=(3, 4)) # 2D array\n", - "x3 = np.random.randint(10, size=(3, 4, 5)) # 3D array" + "x1 = np.random.randint(10, size=6) # One-dimensional array\n", + "x2 = np.random.randint(10, size=(3, 4)) # Two-dimensional array\n", + "x3 = np.random.randint(10, size=(3, 4, 5)) # Three-dimensional array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each array has attributes ``ndim`` (the number of dimensions), ``shape`` (the size of each dimension), and ``size`` (the total size of the array):" ] }, { @@ -46,6 +109,13 @@ "print(\"x3 size: \", x3.size)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another useful attribute is the ``dtype``, the data type of the array (which we discussed previously in [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -65,6 +135,13 @@ "print(\"dtype:\", x3.dtype)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Other attributes include ``itemsize``, which lists the size (in bytes) of each array element, and ``nbytes``, which lists the total size (in bytes) of the array:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -86,6 +163,28 @@ "print(\"nbytes:\", x3.nbytes, \"bytes\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In general, we expect that ``nbytes`` is equal to ``itemsize`` times ``size``." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array Indexing: Accessing Single Elements" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are familiar with Python's standard list indexing, indexing in NumPy will feel quite familiar.\n", + "In a one-dimensional array, the $i^{th}$ value (counting from zero) can be accessed by specifying the desired index in square brackets, just as with Python lists:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -152,6 +251,13 @@ "x1[4]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To index from the end of the array, you can use negative indices:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -196,6 +302,13 @@ "x1[-2]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In a multi-dimensional array, items can be accessed using a comma-separated tuple of indices:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -286,6 +399,13 @@ "x2[2, -1]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Values can also be modified using any of the above index notation:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -311,6 +431,14 @@ "x2" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind that, unlike Python lists, NumPy arrays have a fixed type.\n", + "This means, for example, that if you attempt to insert a floating-point value to an integer array, the value will be silently truncated. Don't be caught unaware by this behavior!" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -334,6 +462,33 @@ "x1" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array Slicing: Accessing Subarrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as we can use square brackets to access individual array elements, we can also use them to access subarrays with the *slice* notation, marked by the colon (``:``) character.\n", + "The NumPy slicing syntax follows that of the standard Python list; to access a slice of an array ``x``, use this:\n", + "``` python\n", + "x[start:stop:step]\n", + "```\n", + "If any of these are unspecified, they default to the values ``start=0``, ``stop=``*``size of dimension``*, ``step=1``.\n", + "We'll take a look at accessing sub-arrays in one dimension and in multiple dimensions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### One-dimensional subarrays" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -467,6 +622,15 @@ "x[1::2] # every other element, starting at index 1" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A potentially confusing case is when the ``step`` value is negative.\n", + "In this case, the defaults for ``start`` and ``stop`` are swapped.\n", + "This becomes a convenient way to reverse an array:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -511,6 +675,16 @@ "x[5::-2] # reversed every other from index 5" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multi-dimensional subarrays\n", + "\n", + "Multi-dimensional slices work in the same way, with multiple slices separated by commas.\n", + "For example:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -582,6 +756,13 @@ "x2[:3, ::2] # all rows, every other column" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, subarray dimensions can even be reversed together:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -606,6 +787,16 @@ "x2[::-1, ::-1]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Accessing array rows and columns\n", + "\n", + "One commonly needed routine is accessing of single rows or columns of an array.\n", + "This can be done by combining indexing and slicing, using an empty slice marked by a single colon (``:``):" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -644,6 +835,13 @@ "print(x2[0, :]) # first row of x2" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the case of row access, the empty slice can be omitted for a more compact syntax:" + ] + }, { "cell_type": "code", "execution_count": 30, @@ -663,6 +861,17 @@ "print(x2[0]) # equivalent to x2[0, :]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Subarrays as no-copy views\n", + "\n", + "One important–and extremely useful–thing to know about array slices is that they return *views* rather than *copies* of the array data.\n", + "This is one area in which NumPy array slicing differs from Python list slicing: in lists, slices will be copies.\n", + "Consider our two-dimensional array from before:" + ] + }, { "cell_type": "code", "execution_count": 31, @@ -684,6 +893,13 @@ "print(x2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's extract a $2 \\times 2$ subarray from this:" + ] + }, { "cell_type": "code", "execution_count": 32, @@ -705,6 +921,13 @@ "print(x2_sub)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now if we modify this subarray, we'll see that the original array is changed! Observe:" + ] + }, { "cell_type": "code", "execution_count": 33, @@ -747,6 +970,22 @@ "print(x2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This default behavior is actually quite useful: it means that when we work with large datasets, we can access and process pieces of these datasets without the need to copy the underlying data buffer." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Creating copies of arrays\n", + "\n", + "Despite the nice features of array views, it is sometimes useful to instead explicitly copy the data within an array or a subarray. This can be most easily done with the ``copy()`` method:" + ] + }, { "cell_type": "code", "execution_count": 35, @@ -768,6 +1007,13 @@ "print(x2_sub_copy)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we now modify this subarray, the original array is not touched:" + ] + }, { "cell_type": "code", "execution_count": 36, @@ -810,6 +1056,17 @@ "print(x2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reshaping of Arrays\n", + "\n", + "Another useful type of operation is reshaping of arrays.\n", + "The most flexible way of doing this is with the ``reshape`` method.\n", + "For example, if you want to put the numbers 1 through 9 in a $3 \\times 3$ grid, you can do the following:" + ] + }, { "cell_type": "code", "execution_count": 38, @@ -832,6 +1089,17 @@ "print(grid)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that for this to work, the size of the initial array must match the size of the reshaped array. \n", + "Where possible, the ``reshape`` method will use a no-copy view of the initial array, but with non-contiguous memory buffers this is not always the case.\n", + "\n", + "Another common reshaping pattern is the conversion of a one-dimensional array into a two-dimensional row or column matrix.\n", + "This can be done with the ``reshape`` method, or more easily done by making use of the ``newaxis`` keyword within a slice operation:" + ] + }, { "cell_type": "code", "execution_count": 39, @@ -930,6 +1198,32 @@ "x[:, np.newaxis]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will see this type of transformation often throughout the remainder of the book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array Concatenation and Splitting\n", + "\n", + "All of the preceding routines worked on single arrays. It's also possible to combine multiple arrays into one, and to conversely split a single array into multiple arrays. We'll take a look at those operations here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Concatenation of arrays\n", + "\n", + "Concatenation, or joining of two arrays in NumPy, is primarily accomplished using the routines ``np.concatenate``, ``np.vstack``, and ``np.hstack``.\n", + "``np.concatenate`` takes a tuple or list of arrays as its first argument, as we can see here:" + ] + }, { "cell_type": "code", "execution_count": 43, @@ -954,6 +1248,13 @@ "np.concatenate([x, y])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can also concatenate more than two arrays at once:" + ] + }, { "cell_type": "code", "execution_count": 44, @@ -974,6 +1275,13 @@ "print(np.concatenate([x, y, z]))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It can also be used for two-dimensional arrays:" + ] + }, { "cell_type": "code", "execution_count": 45, @@ -1036,6 +1344,13 @@ "np.concatenate([grid, grid], axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For working with arrays of mixed dimensions, it can be clearer to use the ``np.vstack`` (vertical stack) and ``np.hstack`` (horizontal stack) functions:" + ] + }, { "cell_type": "code", "execution_count": 48, @@ -1091,6 +1406,22 @@ "np.hstack([grid, y])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similary, ``np.dstack`` will stack arrays along the third axis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Splitting of arrays\n", + "\n", + "The opposite of concatenation is splitting, which is implemented by the functions ``np.split``, ``np.hsplit``, and ``np.vsplit``. For each of these, we can pass a list of indices giving the split points:" + ] + }, { "cell_type": "code", "execution_count": 50, @@ -1112,6 +1443,14 @@ "print(x1, x2, x3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that *N* split-points, leads to *N + 1* subarrays.\n", + "The related functions ``np.hsplit`` and ``np.vsplit`` are similar:" + ] + }, { "cell_type": "code", "execution_count": 51, @@ -1189,9 +1528,27 @@ "print(left)\n", "print(right)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, ``np.dsplit`` will split arrays along the third axis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb) | [Contents](Index.ipynb) | [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/notebooks_v1/02.03-Computation-on-arrays-ufuncs.ipynb b/notebooks_v1/02.03-Computation-on-arrays-ufuncs.ipynb new file mode 100644 index 000000000..5296859e5 --- /dev/null +++ b/notebooks_v1/02.03-Computation-on-arrays-ufuncs.ipynb @@ -0,0 +1,1109 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb) | [Contents](Index.ipynb) | [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Computation on NumPy Arrays: Universal Functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Up until now, we have been discussing some of the basic nuts and bolts of NumPy; in the next few sections, we will dive into the reasons that NumPy is so important in the Python data science world.\n", + "Namely, it provides an easy and flexible interface to optimized computation with arrays of data.\n", + "\n", + "Computation on NumPy arrays can be very fast, or it can be very slow.\n", + "The key to making it fast is to use *vectorized* operations, generally implemented through NumPy's *universal functions* (ufuncs).\n", + "This section motivates the need for NumPy's ufuncs, which can be used to make repeated calculations on array elements much more efficient.\n", + "It then introduces many of the most common and useful arithmetic ufuncs available in the NumPy package." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Slowness of Loops\n", + "\n", + "Python's default implementation (known as CPython) does some operations very slowly.\n", + "This is in part due to the dynamic, interpreted nature of the language: the fact that types are flexible, so that sequences of operations cannot be compiled down to efficient machine code as in languages like C and Fortran.\n", + "Recently there have been various attempts to address this weakness: well-known examples are the [PyPy](http://pypy.org/) project, a just-in-time compiled implementation of Python; the [Cython](http://cython.org) project, which converts Python code to compilable C code; and the [Numba](http://numba.pydata.org/) project, which converts snippets of Python code to fast LLVM bytecode.\n", + "Each of these has its strengths and weaknesses, but it is safe to say that none of the three approaches has yet surpassed the reach and popularity of the standard CPython engine.\n", + "\n", + "The relative sluggishness of Python generally manifests itself in situations where many small operations are being repeated – for instance looping over arrays to operate on each element.\n", + "For example, imagine we have an array of values and we'd like to compute the reciprocal of each.\n", + "A straightforward approach might look like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.16666667, 1. , 0.25 , 0.25 , 0.125 ])" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "np.random.seed(0)\n", + "\n", + "def compute_reciprocals(values):\n", + " output = np.empty(len(values))\n", + " for i in range(len(values)):\n", + " output[i] = 1.0 / values[i]\n", + " return output\n", + " \n", + "values = np.random.randint(1, 10, size=5)\n", + "compute_reciprocals(values)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This implementation probably feels fairly natural to someone from, say, a C or Java background.\n", + "But if we measure the execution time of this code for a large input, we see that this operation is very slow, perhaps surprisingly so!\n", + "We'll benchmark this with IPython's ``%timeit`` magic (discussed in [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 loop, best of 3: 2.91 s per loop\n" + ] + } + ], + "source": [ + "big_array = np.random.randint(1, 100, size=1000000)\n", + "%timeit compute_reciprocals(big_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It takes several seconds to compute these million operations and to store the result!\n", + "When even cell phones have processing speeds measured in Giga-FLOPS (i.e., billions of numerical operations per second), this seems almost absurdly slow.\n", + "It turns out that the bottleneck here is not the operations themselves, but the type-checking and function dispatches that CPython must do at each cycle of the loop.\n", + "Each time the reciprocal is computed, Python first examines the object's type and does a dynamic lookup of the correct function to use for that type.\n", + "If we were working in compiled code instead, this type specification would be known before the code executes and the result could be computed much more efficiently." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introducing UFuncs\n", + "\n", + "For many types of operations, NumPy provides a convenient interface into just this kind of statically typed, compiled routine. This is known as a *vectorized* operation.\n", + "This can be accomplished by simply performing an operation on the array, which will then be applied to each element.\n", + "This vectorized approach is designed to push the loop into the compiled layer that underlies NumPy, leading to much faster execution.\n", + "\n", + "Compare the results of the following two:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.16666667 1. 0.25 0.25 0.125 ]\n", + "[ 0.16666667 1. 0.25 0.25 0.125 ]\n" + ] + } + ], + "source": [ + "print(compute_reciprocals(values))\n", + "print(1.0 / values)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the execution time for our big array, we see that it completes orders of magnitude faster than the Python loop:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100 loops, best of 3: 4.6 ms per loop\n" + ] + } + ], + "source": [ + "%timeit (1.0 / big_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vectorized operations in NumPy are implemented via *ufuncs*, whose main purpose is to quickly execute repeated operations on values in NumPy arrays.\n", + "Ufuncs are extremely flexible – before we saw an operation between a scalar and an array, but we can also operate between two arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0. , 0.5 , 0.66666667, 0.75 , 0.8 ])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.arange(5) / np.arange(1, 6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And ufunc operations are not limited to one-dimensional arrays–they can also act on multi-dimensional arrays as well:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1, 2, 4],\n", + " [ 8, 16, 32],\n", + " [ 64, 128, 256]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.arange(9).reshape((3, 3))\n", + "2 ** x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Computations using vectorization through ufuncs are nearly always more efficient than their counterpart implemented using Python loops, especially as the arrays grow in size.\n", + "Any time you see such a loop in a Python script, you should consider whether it can be replaced with a vectorized expression." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exploring NumPy's UFuncs\n", + "\n", + "Ufuncs exist in two flavors: *unary ufuncs*, which operate on a single input, and *binary ufuncs*, which operate on two inputs.\n", + "We'll see examples of both these types of functions here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Array arithmetic\n", + "\n", + "NumPy's ufuncs feel very natural to use because they make use of Python's native arithmetic operators.\n", + "The standard addition, subtraction, multiplication, and division can all be used:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [0 1 2 3]\n", + "x + 5 = [5 6 7 8]\n", + "x - 5 = [-5 -4 -3 -2]\n", + "x * 2 = [0 2 4 6]\n", + "x / 2 = [ 0. 0.5 1. 1.5]\n", + "x // 2 = [0 0 1 1]\n" + ] + } + ], + "source": [ + "x = np.arange(4)\n", + "print(\"x =\", x)\n", + "print(\"x + 5 =\", x + 5)\n", + "print(\"x - 5 =\", x - 5)\n", + "print(\"x * 2 =\", x * 2)\n", + "print(\"x / 2 =\", x / 2)\n", + "print(\"x // 2 =\", x // 2) # floor division" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is also a unary ufunc for negation, and a ``**`` operator for exponentiation, and a ``%`` operator for modulus:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-x = [ 0 -1 -2 -3]\n", + "x ** 2 = [0 1 4 9]\n", + "x % 2 = [0 1 0 1]\n" + ] + } + ], + "source": [ + "print(\"-x = \", -x)\n", + "print(\"x ** 2 = \", x ** 2)\n", + "print(\"x % 2 = \", x % 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, these can be strung together however you wish, and the standard order of operations is respected:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-1. , -2.25, -4. , -6.25])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "-(0.5*x + 1) ** 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each of these arithmetic operations are simply convenient wrappers around specific functions built into NumPy; for example, the ``+`` operator is a wrapper for the ``add`` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 3, 4, 5])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.add(x, 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following table lists the arithmetic operators implemented in NumPy:\n", + "\n", + "| Operator\t | Equivalent ufunc | Description |\n", + "|---------------|---------------------|---------------------------------------|\n", + "|``+`` |``np.add`` |Addition (e.g., ``1 + 1 = 2``) |\n", + "|``-`` |``np.subtract`` |Subtraction (e.g., ``3 - 2 = 1``) |\n", + "|``-`` |``np.negative`` |Unary negation (e.g., ``-2``) |\n", + "|``*`` |``np.multiply`` |Multiplication (e.g., ``2 * 3 = 6``) |\n", + "|``/`` |``np.divide`` |Division (e.g., ``3 / 2 = 1.5``) |\n", + "|``//`` |``np.floor_divide`` |Floor division (e.g., ``3 // 2 = 1``) |\n", + "|``**`` |``np.power`` |Exponentiation (e.g., ``2 ** 3 = 8``) |\n", + "|``%`` |``np.mod`` |Modulus/remainder (e.g., ``9 % 4 = 1``)|\n", + "\n", + "Additionally there are Boolean/bitwise operators; we will explore these in [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Absolute value\n", + "\n", + "Just as NumPy understands Python's built-in arithmetic operators, it also understands Python's built-in absolute value function:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 1, 0, 1, 2])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([-2, -1, 0, 1, 2])\n", + "abs(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The corresponding NumPy ufunc is ``np.absolute``, which is also available under the alias ``np.abs``:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 1, 0, 1, 2])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.absolute(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 1, 0, 1, 2])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.abs(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This ufunc can also handle complex data, in which the absolute value returns the magnitude:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 5., 5., 2., 1.])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([3 - 4j, 4 - 3j, 2 + 0j, 0 + 1j])\n", + "np.abs(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Trigonometric functions\n", + "\n", + "NumPy provides a large number of useful ufuncs, and some of the most useful for the data scientist are the trigonometric functions.\n", + "We'll start by defining an array of angles:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "theta = np.linspace(0, np.pi, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can compute some trigonometric functions on these values:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = [ 0. 1.57079633 3.14159265]\n", + "sin(theta) = [ 0.00000000e+00 1.00000000e+00 1.22464680e-16]\n", + "cos(theta) = [ 1.00000000e+00 6.12323400e-17 -1.00000000e+00]\n", + "tan(theta) = [ 0.00000000e+00 1.63312394e+16 -1.22464680e-16]\n" + ] + } + ], + "source": [ + "print(\"theta = \", theta)\n", + "print(\"sin(theta) = \", np.sin(theta))\n", + "print(\"cos(theta) = \", np.cos(theta))\n", + "print(\"tan(theta) = \", np.tan(theta))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The values are computed to within machine precision, which is why values that should be zero do not always hit exactly zero.\n", + "Inverse trigonometric functions are also available:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [-1, 0, 1]\n", + "arcsin(x) = [-1.57079633 0. 1.57079633]\n", + "arccos(x) = [ 3.14159265 1.57079633 0. ]\n", + "arctan(x) = [-0.78539816 0. 0.78539816]\n" + ] + } + ], + "source": [ + "x = [-1, 0, 1]\n", + "print(\"x = \", x)\n", + "print(\"arcsin(x) = \", np.arcsin(x))\n", + "print(\"arccos(x) = \", np.arccos(x))\n", + "print(\"arctan(x) = \", np.arctan(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exponents and logarithms\n", + "\n", + "Another common type of operation available in a NumPy ufunc are the exponentials:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [1, 2, 3]\n", + "e^x = [ 2.71828183 7.3890561 20.08553692]\n", + "2^x = [ 2. 4. 8.]\n", + "3^x = [ 3 9 27]\n" + ] + } + ], + "source": [ + "x = [1, 2, 3]\n", + "print(\"x =\", x)\n", + "print(\"e^x =\", np.exp(x))\n", + "print(\"2^x =\", np.exp2(x))\n", + "print(\"3^x =\", np.power(3, x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The inverse of the exponentials, the logarithms, are also available.\n", + "The basic ``np.log`` gives the natural logarithm; if you prefer to compute the base-2 logarithm or the base-10 logarithm, these are available as well:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [1, 2, 4, 10]\n", + "ln(x) = [ 0. 0.69314718 1.38629436 2.30258509]\n", + "log2(x) = [ 0. 1. 2. 3.32192809]\n", + "log10(x) = [ 0. 0.30103 0.60205999 1. ]\n" + ] + } + ], + "source": [ + "x = [1, 2, 4, 10]\n", + "print(\"x =\", x)\n", + "print(\"ln(x) =\", np.log(x))\n", + "print(\"log2(x) =\", np.log2(x))\n", + "print(\"log10(x) =\", np.log10(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are also some specialized versions that are useful for maintaining precision with very small input:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exp(x) - 1 = [ 0. 0.0010005 0.01005017 0.10517092]\n", + "log(1 + x) = [ 0. 0.0009995 0.00995033 0.09531018]\n" + ] + } + ], + "source": [ + "x = [0, 0.001, 0.01, 0.1]\n", + "print(\"exp(x) - 1 =\", np.expm1(x))\n", + "print(\"log(1 + x) =\", np.log1p(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When ``x`` is very small, these functions give more precise values than if the raw ``np.log`` or ``np.exp`` were to be used." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Specialized ufuncs\n", + "\n", + "NumPy has many more ufuncs available, including hyperbolic trig functions, bitwise arithmetic, comparison operators, conversions from radians to degrees, rounding and remainders, and much more.\n", + "A look through the NumPy documentation reveals a lot of interesting functionality.\n", + "\n", + "Another excellent source for more specialized and obscure ufuncs is the submodule ``scipy.special``.\n", + "If you want to compute some obscure mathematical function on your data, chances are it is implemented in ``scipy.special``.\n", + "There are far too many functions to list them all, but the following snippet shows a couple that might come up in a statistics context:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from scipy import special" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "gamma(x) = [ 1.00000000e+00 2.40000000e+01 3.62880000e+05]\n", + "ln|gamma(x)| = [ 0. 3.17805383 12.80182748]\n", + "beta(x, 2) = [ 0.5 0.03333333 0.00909091]\n" + ] + } + ], + "source": [ + "# Gamma functions (generalized factorials) and related functions\n", + "x = [1, 5, 10]\n", + "print(\"gamma(x) =\", special.gamma(x))\n", + "print(\"ln|gamma(x)| =\", special.gammaln(x))\n", + "print(\"beta(x, 2) =\", special.beta(x, 2))" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "erf(x) = [ 0. 0.32862676 0.67780119 0.84270079]\n", + "erfc(x) = [ 1. 0.67137324 0.32219881 0.15729921]\n", + "erfinv(x) = [ 0. 0.27246271 0.73286908 inf]\n" + ] + } + ], + "source": [ + "# Error function (integral of Gaussian)\n", + "# its complement, and its inverse\n", + "x = np.array([0, 0.3, 0.7, 1.0])\n", + "print(\"erf(x) =\", special.erf(x))\n", + "print(\"erfc(x) =\", special.erfc(x))\n", + "print(\"erfinv(x) =\", special.erfinv(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are many, many more ufuncs available in both NumPy and ``scipy.special``.\n", + "Because the documentation of these packages is available online, a web search along the lines of \"gamma function python\" will generally find the relevant information." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Advanced Ufunc Features\n", + "\n", + "Many NumPy users make use of ufuncs without ever learning their full set of features.\n", + "We'll outline a few specialized features of ufuncs here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Specifying output\n", + "\n", + "For large calculations, it is sometimes useful to be able to specify the array where the result of the calculation will be stored.\n", + "Rather than creating a temporary array, this can be used to write computation results directly to the memory location where you'd like them to be.\n", + "For all ufuncs, this can be done using the ``out`` argument of the function:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0. 10. 20. 30. 40.]\n" + ] + } + ], + "source": [ + "x = np.arange(5)\n", + "y = np.empty(5)\n", + "np.multiply(x, 10, out=y)\n", + "print(y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can even be used with array views. For example, we can write the results of a computation to every other element of a specified array:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 0. 2. 0. 4. 0. 8. 0. 16. 0.]\n" + ] + } + ], + "source": [ + "y = np.zeros(10)\n", + "np.power(2, x, out=y[::2])\n", + "print(y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we had instead written ``y[::2] = 2 ** x``, this would have resulted in the creation of a temporary array to hold the results of ``2 ** x``, followed by a second operation copying those values into the ``y`` array.\n", + "This doesn't make much of a difference for such a small computation, but for very large arrays the memory savings from careful use of the ``out`` argument can be significant." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Aggregates\n", + "\n", + "For binary ufuncs, there are some interesting aggregates that can be computed directly from the object.\n", + "For example, if we'd like to *reduce* an array with a particular operation, we can use the ``reduce`` method of any ufunc.\n", + "A reduce repeatedly applies a given operation to the elements of an array until only a single result remains.\n", + "\n", + "For example, calling ``reduce`` on the ``add`` ufunc returns the sum of all elements in the array:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "15" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.arange(1, 6)\n", + "np.add.reduce(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, calling ``reduce`` on the ``multiply`` ufunc results in the product of all array elements:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "120" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.multiply.reduce(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we'd like to store all the intermediate results of the computation, we can instead use ``accumulate``:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1, 3, 6, 10, 15])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.add.accumulate(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1, 2, 6, 24, 120])" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.multiply.accumulate(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that for these particular cases, there are dedicated NumPy functions to compute the results (``np.sum``, ``np.prod``, ``np.cumsum``, ``np.cumprod``), which we'll explore in [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Outer products\n", + "\n", + "Finally, any ufunc can compute the output of all pairs of two different inputs using the ``outer`` method.\n", + "This allows you, in one line, to do things like create a multiplication table:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1, 2, 3, 4, 5],\n", + " [ 2, 4, 6, 8, 10],\n", + " [ 3, 6, 9, 12, 15],\n", + " [ 4, 8, 12, 16, 20],\n", + " [ 5, 10, 15, 20, 25]])" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.arange(1, 6)\n", + "np.multiply.outer(x, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``ufunc.at`` and ``ufunc.reduceat`` methods, which we'll explore in [Fancy Indexing](02.07-Fancy-Indexing.ipynb), are very helpful as well.\n", + "\n", + "Another extremely useful feature of ufuncs is the ability to operate between arrays of different sizes and shapes, a set of operations known as *broadcasting*.\n", + "This subject is important enough that we will devote a whole section to it (see [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ufuncs: Learning More" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "More information on universal functions (including the full list of available functions) can be found on the [NumPy](http://www.numpy.org) and [SciPy](http://www.scipy.org) documentation websites.\n", + "\n", + "Recall that you can also access information directly from within IPython by importing the packages and using IPython's tab-completion and help (``?``) functionality, as described in [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb) | [Contents](Index.ipynb) | [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/code_listings/02.04-Computation-on-arrays-aggregates.ipynb b/notebooks_v1/02.04-Computation-on-arrays-aggregates.ipynb similarity index 66% rename from code_listings/02.04-Computation-on-arrays-aggregates.ipynb rename to notebooks_v1/02.04-Computation-on-arrays-aggregates.ipynb index acdad9950..53e6462fd 100644 --- a/code_listings/02.04-Computation-on-arrays-aggregates.ipynb +++ b/notebooks_v1/02.04-Computation-on-arrays-aggregates.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) | [Contents](Index.ipynb) | [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,26 @@ "# Aggregations: Min, Max, and Everything In Between" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Often when faced with a large amount of data, a first step is to compute summary statistics for the data in question.\n", + "Perhaps the most common summary statistics are the mean and standard deviation, which allow you to summarize the \"typical\" values in a dataset, but other aggregates are useful as well (the sum, product, median, minimum and maximum, quantiles, etc.).\n", + "\n", + "NumPy has fast built-in aggregation functions for working on arrays; we'll discuss and demonstrate some of them here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summing the Values in an Array\n", + "\n", + "As a quick example, consider computing the sum of all values in an array.\n", + "Python itself can do this using the built-in ``sum`` function:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -41,6 +83,13 @@ "sum(L)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The syntax is quite similar to that of NumPy's ``sum`` function, and the result is the same in the simplest case:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -63,6 +112,13 @@ "np.sum(L)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "However, because it executes the operation in compiled code, NumPy's version of the operation is computed much more quickly:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -85,6 +141,23 @@ "%timeit np.sum(big_array)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Be careful, though: the ``sum`` function and the ``np.sum`` function are not identical, which can sometimes lead to confusion!\n", + "In particular, their optional arguments have different meanings, and ``np.sum`` is aware of multiple array dimensions, as we will see in the following section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Minimum and Maximum\n", + "\n", + "Similarly, Python has built-in ``min`` and ``max`` functions, used to find the minimum value and maximum value of any given array:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -107,6 +180,13 @@ "min(big_array), max(big_array)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "NumPy's corresponding functions have similar syntax, and again operate much more quickly:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -150,6 +230,13 @@ "%timeit np.min(big_array)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For ``min``, ``max``, ``sum``, and several other NumPy aggregates, a shorter syntax is to use methods of the array object itself:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -169,6 +256,23 @@ "print(big_array.min(), big_array.max(), big_array.sum())" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whenever possible, make sure that you are using the NumPy version of these aggregates when operating on NumPy arrays!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multi dimensional aggregates\n", + "\n", + "One common type of aggregation operation is an aggregate along a row or column.\n", + "Say you have some data stored in a two-dimensional array:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -191,6 +295,13 @@ "print(M)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By default, each NumPy aggregation function will return the aggregate over the entire array:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -213,6 +324,13 @@ "M.sum()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aggregation functions take an additional argument specifying the *axis* along which the aggregate is computed. For example, we can find the minimum value within each column by specifying ``axis=0``:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -235,6 +353,15 @@ "M.min(axis=0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function returns four values, corresponding to the four columns of numbers.\n", + "\n", + "Similarly, we can find the maximum value within each row:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -257,6 +384,62 @@ "M.max(axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The way the axis is specified here can be confusing to users coming from other languages.\n", + "The ``axis`` keyword specifies the *dimension of the array that will be collapsed*, rather than the dimension that will be returned.\n", + "So specifying ``axis=0`` means that the first axis will be collapsed: for two-dimensional arrays, this means that values within each column will be aggregated." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Other aggregation functions\n", + "\n", + "NumPy provides many other aggregation functions, but we won't discuss them in detail here.\n", + "Additionally, most aggregates have a ``NaN``-safe counterpart that computes the result while ignoring missing values, which are marked by the special IEEE floating-point ``NaN`` value (for a fuller discussion of missing data, see [Handling Missing Data](03.04-Missing-Values.ipynb)).\n", + "Some of these ``NaN``-safe functions were not added until NumPy 1.8, so they will not be available in older NumPy versions.\n", + "\n", + "The following table provides a list of useful aggregation functions available in NumPy:\n", + "\n", + "|Function Name | NaN-safe Version | Description |\n", + "|-------------------|---------------------|-----------------------------------------------|\n", + "| ``np.sum`` | ``np.nansum`` | Compute sum of elements |\n", + "| ``np.prod`` | ``np.nanprod`` | Compute product of elements |\n", + "| ``np.mean`` | ``np.nanmean`` | Compute mean of elements |\n", + "| ``np.std`` | ``np.nanstd`` | Compute standard deviation |\n", + "| ``np.var`` | ``np.nanvar`` | Compute variance |\n", + "| ``np.min`` | ``np.nanmin`` | Find minimum value |\n", + "| ``np.max`` | ``np.nanmax`` | Find maximum value |\n", + "| ``np.argmin`` | ``np.nanargmin`` | Find index of minimum value |\n", + "| ``np.argmax`` | ``np.nanargmax`` | Find index of maximum value |\n", + "| ``np.median`` | ``np.nanmedian`` | Compute median of elements |\n", + "| ``np.percentile`` | ``np.nanpercentile``| Compute rank-based statistics of elements |\n", + "| ``np.any`` | N/A | Evaluate whether any elements are true |\n", + "| ``np.all`` | N/A | Evaluate whether all elements are true |\n", + "\n", + "We will see these aggregates often throughout the rest of the book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: What is the Average Height of US Presidents?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aggregates available in NumPy can be extremely useful for summarizing a set of values.\n", + "As a simple example, let's consider the heights of all US presidents.\n", + "This data is available in the file *president_heights.csv*, which is a simple comma-separated list of labels and values:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -279,6 +462,13 @@ "!head -4 data/president_heights.csv" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use the Pandas package, which we'll explore more fully in [Chapter 3](03.00-Introduction-to-Pandas.ipynb), to read the file and extract this information (note that the heights are measured in centimeters)." + ] + }, { "cell_type": "code", "execution_count": 14, @@ -303,6 +493,13 @@ "print(heights)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have this data array, we can compute a variety of summary statistics:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -328,6 +525,14 @@ "print(\"Maximum height: \", heights.max())" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that in each case, the aggregation operation reduced the entire array to a single summarizing value, which gives us information about the distribution of values.\n", + "We may also wish to compute quantiles:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -351,6 +556,15 @@ "print(\"75th percentile: \", np.percentile(heights, 75))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that the median height of US presidents is 182 cm, or just shy of six feet.\n", + "\n", + "Of course, sometimes it's more useful to see a visual representation of this data, which we can accomplish using tools in Matplotlib (we'll discuss Matplotlib more fully in [Chapter 4](04.00-Introduction-To-Matplotlib.ipynb)). For example, this code generates the following chart:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -388,9 +602,27 @@ "plt.xlabel('height (cm)')\n", "plt.ylabel('number');" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These aggregates are some of the fundamental pieces of exploratory data analysis that we'll explore in more depth in later chapters of the book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) | [Contents](Index.ipynb) | [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/02.05-Computation-on-arrays-broadcasting.ipynb b/notebooks_v1/02.05-Computation-on-arrays-broadcasting.ipynb similarity index 87% rename from code_listings/02.05-Computation-on-arrays-broadcasting.ipynb rename to notebooks_v1/02.05-Computation-on-arrays-broadcasting.ipynb index ffc2af7f0..c1cae6ddf 100644 --- a/code_listings/02.05-Computation-on-arrays-broadcasting.ipynb +++ b/notebooks_v1/02.05-Computation-on-arrays-broadcasting.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb) | [Contents](Index.ipynb) | [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,24 @@ "# Computation on Arrays: Broadcasting" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We saw in the previous section how NumPy's universal functions can be used to *vectorize* operations and thereby remove slow Python loops.\n", + "Another means of vectorizing operations is to use NumPy's *broadcasting* functionality.\n", + "Broadcasting is simply a set of rules for applying binary ufuncs (e.g., addition, subtraction, multiplication, etc.) on arrays of different sizes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introducing Broadcasting\n", + "\n", + "Recall that for arrays of the same size, binary operations are performed on an element-by-element basis:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -42,6 +82,13 @@ "a + b" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Broadcasting allows these types of binary operations to be performed on arrays of different sizes–for example, we can just as easily add a scalar (think of it as a zero-dimensional array) to an array:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -64,6 +111,16 @@ "a + 5" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can think of this as an operation that stretches or duplicates the value ``5`` into the array ``[5, 5, 5]``, and adds the results.\n", + "The advantage of NumPy's broadcasting is that this duplication of values does not actually take place, but it is a useful mental model as we think about broadcasting.\n", + "\n", + "We can similarly extend this to arrays of higher dimension. Observe the result when we add a one-dimensional array to a two-dimensional array:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -113,6 +170,15 @@ "M + a" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the one-dimensional array ``a`` is stretched, or broadcast across the second dimension in order to match the shape of ``M``.\n", + "\n", + "While these examples are relatively easy to understand, more complicated cases can involve broadcasting of both arrays. Consider the following example:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -163,6 +229,52 @@ "a + b" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as before we stretched or broadcasted one value to match the shape of the other, here we've stretched *both* ``a`` and ``b`` to match a common shape, and the result is a two-dimensional array!\n", + "The geometry of these examples is visualized in the following figure (Code to produce this plot can be found in the [appendix](06.00-Figure-Code.ipynb#Broadcasting), and is adapted from source published in the [astroML](http://astroml.org) documentation. Used by permission)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Broadcasting Visual](figures/02.05-broadcasting.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The light boxes represent the broadcasted values: again, this extra memory is not actually allocated in the course of the operation, but it can be useful conceptually to imagine that it is." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Rules of Broadcasting\n", + "\n", + "Broadcasting in NumPy follows a strict set of rules to determine the interaction between the two arrays:\n", + "\n", + "- Rule 1: If the two arrays differ in their number of dimensions, the shape of the one with fewer dimensions is *padded* with ones on its leading (left) side.\n", + "- Rule 2: If the shape of the two arrays does not match in any dimension, the array with shape equal to 1 in that dimension is stretched to match the other shape.\n", + "- Rule 3: If in any dimension the sizes disagree and neither is equal to 1, an error is raised.\n", + "\n", + "To make these rules clear, let's consider a few examples in detail." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Broadcasting example 1\n", + "\n", + "Let's look at adding a two-dimensional array to a one-dimensional array:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -175,6 +287,28 @@ "a = np.arange(3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's consider an operation on these two arrays. The shape of the arrays are\n", + "\n", + "- ``M.shape = (2, 3)``\n", + "- ``a.shape = (3,)``\n", + "\n", + "We see by rule 1 that the array ``a`` has fewer dimensions, so we pad it on the left with ones:\n", + "\n", + "- ``M.shape -> (2, 3)``\n", + "- ``a.shape -> (1, 3)``\n", + "\n", + "By rule 2, we now see that the first dimension disagrees, so we stretch this dimension to match:\n", + "\n", + "- ``M.shape -> (2, 3)``\n", + "- ``a.shape -> (2, 3)``\n", + "\n", + "The shapes match, and we see that the final shape will be ``(2, 3)``:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -198,6 +332,15 @@ "M + a" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Broadcasting example 2\n", + "\n", + "Let's take a look at an example where both arrays need to be broadcast:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -210,6 +353,28 @@ "b = np.arange(3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, we'll start by writing out the shape of the arrays:\n", + "\n", + "- ``a.shape = (3, 1)``\n", + "- ``b.shape = (3,)``\n", + "\n", + "Rule 1 says we must pad the shape of ``b`` with ones:\n", + "\n", + "- ``a.shape -> (3, 1)``\n", + "- ``b.shape -> (1, 3)``\n", + "\n", + "And rule 2 tells us that we upgrade each of these ones to match the corresponding size of the other array:\n", + "\n", + "- ``a.shape -> (3, 3)``\n", + "- ``b.shape -> (3, 3)``\n", + "\n", + "Because the result matches, these shapes are compatible. We can see this here:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -234,6 +399,15 @@ "a + b" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Broadcasting example 3\n", + "\n", + "Now let's take a look at an example in which the two arrays are not compatible:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -246,6 +420,29 @@ "a = np.arange(3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is just a slightly different situation than in the first example: the matrix ``M`` is transposed.\n", + "How does this affect the calculation? The shape of the arrays are\n", + "\n", + "- ``M.shape = (3, 2)``\n", + "- ``a.shape = (3,)``\n", + "\n", + "Again, rule 1 tells us that we must pad the shape of ``a`` with ones:\n", + "\n", + "- ``M.shape -> (3, 2)``\n", + "- ``a.shape -> (1, 3)``\n", + "\n", + "By rule 2, the first dimension of ``a`` is stretched to match that of ``M``:\n", + "\n", + "- ``M.shape -> (3, 2)``\n", + "- ``a.shape -> (3, 3)``\n", + "\n", + "Now we hit rule 3–the final shapes do not match, so these two arrays are incompatible, as we can observe by attempting this operation:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -269,6 +466,16 @@ "M + a" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note the potential confusion here: you could imagine making ``a`` and ``M`` compatible by, say, padding ``a``'s shape with ones on the right rather than the left.\n", + "But this is not how the broadcasting rules work!\n", + "That sort of flexibility might be useful in some cases, but it would lead to potential areas of ambiguity.\n", + "If right-side padding is what you'd like, you can do this explicitly by reshaping the array (we'll use the ``np.newaxis`` keyword introduced in [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -315,6 +522,14 @@ "M + a[:, np.newaxis]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Also note that while we've been focusing on the ``+`` operator here, these broadcasting rules apply to *any* binary ``ufunc``.\n", + "For example, here is the ``logaddexp(a, b)`` function, which computes ``log(exp(a) + exp(b))`` with more precision than the naive approach:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -339,6 +554,45 @@ "np.logaddexp(M, a[:, np.newaxis])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on the many available universal functions, refer to [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Broadcasting in Practice" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Broadcasting operations form the core of many examples we'll see throughout this book.\n", + "We'll now take a look at a couple simple examples of where they can be useful." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Centering an array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the previous section, we saw that ufuncs allow a NumPy user to remove the need to explicitly write slow Python loops. Broadcasting extends this ability.\n", + "One commonly seen example is when centering an array of data.\n", + "Imagine you have an array of 10 observations, each of which consists of 3 values.\n", + "Using the standard convention (see [Data Representation in Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb#Data-Representation-in-Scikit-Learn)), we'll store this in a $10 \\times 3$ array:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -350,6 +604,13 @@ "X = np.random.random((10, 3))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compute the mean of each feature using the ``mean`` aggregate across the first dimension:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -373,6 +634,13 @@ "Xmean" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And now we can center the ``X`` array by subtracting the mean (this is a broadcasting operation):" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -384,6 +652,13 @@ "X_centered = X - Xmean" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To double-check that we've done this correctly, we can check that the centered array has near zero mean:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -406,6 +681,28 @@ "X_centered.mean(0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To within machine precision, the mean is now zero." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting a two-dimensional function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One place that broadcasting is very useful is in displaying images based on two-dimensional functions.\n", + "If we want to define a function $z = f(x, y)$, broadcasting can be used to compute the function across the grid:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -421,6 +718,13 @@ "z = np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use Matplotlib to plot this two-dimensional array (these tools will be discussed in full in [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -456,9 +760,27 @@ " cmap='viridis')\n", "plt.colorbar();" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a compelling visualization of the two-dimensional function." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb) | [Contents](Index.ipynb) | [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/02.06-Boolean-Arrays-and-Masks.ipynb b/notebooks_v1/02.06-Boolean-Arrays-and-Masks.ipynb similarity index 60% rename from code_listings/02.06-Boolean-Arrays-and-Masks.ipynb rename to notebooks_v1/02.06-Boolean-Arrays-and-Masks.ipynb index 10e24c2da..e17269f9d 100644 --- a/code_listings/02.06-Boolean-Arrays-and-Masks.ipynb +++ b/notebooks_v1/02.06-Boolean-Arrays-and-Masks.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb) | [Contents](Index.ipynb) | [Fancy Indexing](02.07-Fancy-Indexing.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,25 @@ "# Comparisons, Masks, and Boolean Logic" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This section covers the use of Boolean masks to examine and manipulate values within NumPy arrays.\n", + "Masking comes up when you want to extract, modify, count, or otherwise manipulate values in an array based on some criterion: for example, you might wish to count all values greater than a certain value, or perhaps remove all outliers that are above some threshold.\n", + "In NumPy, Boolean masking is often the most efficient way to accomplish these types of tasks." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Counting Rainy Days\n", + "\n", + "Imagine you have a series of data that represents the amount of precipitation each day for a year in a given city.\n", + "For example, here we'll load the daily rainfall statistics for the city of Seattle in 2014, using Pandas (which is covered in more detail in [Chapter 3](03.00-Introduction-to-Pandas.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -29,12 +70,21 @@ "import numpy as np\n", "import pandas as pd\n", "\n", - "# use Pandas extract rainfall inches as a NumPy array\n", + "# use pandas to extract rainfall inches as a NumPy array\n", "rainfall = pd.read_csv('data/Seattle2014.csv')['PRCP'].values\n", - "inches = rainfall / 254 # 1/10mm -> inches\n", + "inches = rainfall / 254.0 # 1/10mm -> inches\n", "inches.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The array contains 365 values, giving daily rainfall in inches from January 1 to December 31, 2014.\n", + "\n", + "As a first quick visualization, let's look at the histogram of rainy days, which was generated using Matplotlib (we will explore this tool more fully in [Chapter 4](04.00-Introduction-To-Matplotlib.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -70,6 +120,38 @@ "plt.hist(inches, 40);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This histogram gives us a general idea of what the data looks like: despite its reputation, the vast majority of days in Seattle saw near zero measured rainfall in 2014.\n", + "But this doesn't do a good job of conveying some information we'd like to see: for example, how many rainy days were there in the year? What is the average precipitation on those rainy days? How many days were there with more than half an inch of rain?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Digging into the data\n", + "\n", + "One approach to this would be to answer these questions by hand: loop through the data, incrementing a counter each time we see values in some desired range.\n", + "For reasons discussed throughout this chapter, such an approach is very inefficient, both from the standpoint of time writing code and time computing the result.\n", + "We saw in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) that NumPy's ufuncs can be used in place of loops to do fast element-wise arithmetic operations on arrays; in the same way, we can use other ufuncs to do element-wise *comparisons* over arrays, and we can then manipulate the results to answer the questions we have.\n", + "We'll leave the data aside for right now, and discuss some general tools in NumPy to use *masking* to quickly answer these types of questions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison Operators as ufuncs\n", + "\n", + "In [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) we introduced ufuncs, and focused in particular on arithmetic operators. We saw that using ``+``, ``-``, ``*``, ``/``, and others on arrays leads to element-wise operations.\n", + "NumPy also implements comparison operators such as ``<`` (less than) and ``>`` (greater than) as element-wise ufuncs.\n", + "The result of these comparison operators is always an array with a Boolean data type.\n", + "All six of the standard comparison operations are available:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -213,6 +295,13 @@ "x == 3 # equal" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is also possible to do an element-wise comparison of two arrays, and to include compound expressions:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -235,6 +324,28 @@ "(2 * x) == (x ** 2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As in the case of arithmetic operators, the comparison operators are implemented as ufuncs in NumPy; for example, when you write ``x < 3``, internally NumPy uses ``np.less(x, 3)``.\n", + " A summary of the comparison operators and their equivalent ufunc is shown here:\n", + "\n", + "| Operator\t | Equivalent ufunc || Operator\t | Equivalent ufunc |\n", + "|---------------|---------------------||---------------|---------------------|\n", + "|``==`` |``np.equal`` ||``!=`` |``np.not_equal`` |\n", + "|``<`` |``np.less`` ||``<=`` |``np.less_equal`` |\n", + "|``>`` |``np.greater`` ||``>=`` |``np.greater_equal`` |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as in the case of arithmetic ufuncs, these will work on arrays of any size and shape.\n", + "Here is a two-dimensional example:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -285,6 +396,23 @@ "x < 6" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In each case, the result is a Boolean array, and NumPy provides a number of straightforward patterns for working with these Boolean results." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Working with Boolean Arrays\n", + "\n", + "Given a Boolean array, there are a host of useful operations you can do.\n", + "We'll work with ``x``, the two-dimensional array we created earlier." + ] + }, { "cell_type": "code", "execution_count": 14, @@ -306,6 +434,15 @@ "print(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Counting entries\n", + "\n", + "To count the number of ``True`` entries in a Boolean array, ``np.count_nonzero`` is useful:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -325,10 +462,18 @@ } ], "source": [ - "# how many values less than six?\n", + "# how many values less than 6?\n", "np.count_nonzero(x < 6)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that there are eight array entries that are less than 6.\n", + "Another way to get at this information is to use ``np.sum``; in this case, ``False`` is interpreted as ``0``, and ``True`` is interpreted as ``1``:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -351,6 +496,13 @@ "np.sum(x < 6)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The benefit of ``sum()`` is that like with other NumPy aggregation functions, this summation can be done along rows or columns as well:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -370,10 +522,19 @@ } ], "source": [ - "# how many values less than six in each row?\n", + "# how many values less than 6 in each row?\n", "np.sum(x < 6, axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This counts the number of values less than 6 in each row of the matrix.\n", + "\n", + "If we're interested in quickly checking whether any or all the values are true, we can use (you guessed it) ``np.any`` or ``np.all``:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -393,7 +554,7 @@ } ], "source": [ - "# are there any values greater than eight?\n", + "# are there any values greater than 8?\n", "np.any(x > 8)" ] }, @@ -439,7 +600,7 @@ } ], "source": [ - "# are all values less than ten?\n", + "# are all values less than 10?\n", "np.all(x < 10)" ] }, @@ -462,10 +623,17 @@ } ], "source": [ - "# are all values equal to six?\n", + "# are all values equal to 6?\n", "np.all(x == 6)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``np.all`` and ``np.any`` can be used along particular axes as well. For example:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -485,10 +653,33 @@ } ], "source": [ - "# are all values in each row less than four?\n", + "# are all values in each row less than 8?\n", "np.all(x < 8, axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here all the elements in the first and third rows are less than 8, while this is not the case for the second row.\n", + "\n", + "Finally, a quick warning: as mentioned in [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb), Python has built-in ``sum()``, ``any()``, and ``all()`` functions. These have a different syntax than the NumPy versions, and in particular will fail or produce unintended results when used on multidimensional arrays. Be sure that you are using ``np.sum()``, ``np.any()``, and ``np.all()`` for these examples!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Boolean operators\n", + "\n", + "We've already seen how we might count, say, all days with rain less than four inches, or all days with rain greater than two inches.\n", + "But what if we want to know about all days with rain less than four inches and greater than one inch?\n", + "This is accomplished through Python's *bitwise logic operators*, ``&``, ``|``, ``^``, and ``~``.\n", + "Like with the standard arithmetic operators, NumPy overloads these as ufuncs which work element-wise on (usually Boolean) arrays.\n", + "\n", + "For example, we can address this sort of compound question as follows:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -511,6 +702,21 @@ "np.sum((inches > 0.5) & (inches < 1))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So we see that there are 29 days with rainfall between 0.5 and 1.0 inches.\n", + "\n", + "Note that the parentheses here are important–because of operator precedence rules, with parentheses removed this expression would be evaluated as follows, which results in an error:\n", + "\n", + "``` python\n", + "inches > (0.5 & inches) < 1\n", + "```\n", + "\n", + "Using the equivalence of *A AND B* and *NOT (NOT A OR NOT B)* (which you may remember if you've taken an introductory logic course), we can compute the same result in a different manner:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -533,6 +739,33 @@ "np.sum(~( (inches <= 0.5) | (inches >= 1) ))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Combining comparison operators and Boolean operators on arrays can lead to a wide range of efficient logical operations.\n", + "\n", + "The following table summarizes the bitwise Boolean operators and their equivalent ufuncs:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Operator\t | Equivalent ufunc || Operator\t | Equivalent ufunc |\n", + "|---------------|---------------------||---------------|---------------------|\n", + "|``&`` |``np.bitwise_and`` ||| |``np.bitwise_or`` |\n", + "|``^`` |``np.bitwise_xor`` ||``~`` |``np.bitwise_not`` |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using these tools, we might start to answer the types of questions we have about our weather data.\n", + "Here are some examples of results we can compute when combining masking with aggregations:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -547,7 +780,7 @@ "Number days without rain: 215\n", "Number days with rain: 150\n", "Days with more than 0.5 inches: 37\n", - "Rainy days with < 0.1 inches : 75\n" + "Rainy days with < 0.2 inches : 75\n" ] } ], @@ -555,7 +788,19 @@ "print(\"Number days without rain: \", np.sum(inches == 0))\n", "print(\"Number days with rain: \", np.sum(inches != 0))\n", "print(\"Days with more than 0.5 inches:\", np.sum(inches > 0.5))\n", - "print(\"Rainy days with < 0.1 inches :\", np.sum((inches > 0) & (inches < 0.2)))" + "print(\"Rainy days with < 0.2 inches :\", np.sum((inches > 0) &\n", + " (inches < 0.2)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Boolean Arrays as Masks\n", + "\n", + "In the preceding section we looked at aggregates computed directly on Boolean arrays.\n", + "A more powerful pattern is to use Boolean arrays as masks, to select particular subsets of the data themselves.\n", + "Returning to our ``x`` array from before, suppose we want an array of all values in the array that are less than, say, 5:" ] }, { @@ -582,6 +827,13 @@ "x" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can obtain a Boolean array for this condition easily, as we've already seen:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -606,6 +858,13 @@ "x < 5" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now to *select* these values from the array, we can simply index on this Boolean array; this is known as a *masking* operation:" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -628,6 +887,16 @@ "x[x < 5]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is returned is a one-dimensional array filled with all the values that meet this condition; in other words, all the values in positions at which the mask array is ``True``.\n", + "\n", + "We are then free to operate on these values as we wish.\n", + "For example, we can compute some relevant statistics on our Seattle rain data:" + ] + }, { "cell_type": "code", "execution_count": 29, @@ -654,10 +923,36 @@ "days = np.arange(365)\n", "summer = (days > 172) & (days < 262)\n", "\n", - "print(\"Median precip on rainy days in 2014 (inches): \", np.median(inches[rainy]))\n", - "print(\"Median precip on summer days in 2014 (inches): \", np.median(inches[summer]))\n", - "print(\"Maximum precip on summer days in 2014 (inches): \", np.max(inches[summer]))\n", - "print(\"Median precip on non-summer rainy days (inches):\", np.median(inches[rainy & ~summer]))" + "print(\"Median precip on rainy days in 2014 (inches): \",\n", + " np.median(inches[rainy]))\n", + "print(\"Median precip on summer days in 2014 (inches): \",\n", + " np.median(inches[summer]))\n", + "print(\"Maximum precip on summer days in 2014 (inches): \",\n", + " np.max(inches[summer]))\n", + "print(\"Median precip on non-summer rainy days (inches):\",\n", + " np.median(inches[rainy & ~summer]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By combining Boolean operations, masking operations, and aggregates, we can very quickly answer these sorts of questions for our dataset." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aside: Using the Keywords and/or Versus the Operators &/|\n", + "\n", + "One common point of confusion is the difference between the keywords ``and`` and ``or`` on one hand, and the operators ``&`` and ``|`` on the other hand.\n", + "When would you use one versus the other?\n", + "\n", + "The difference is this: ``and`` and ``or`` gauge the truth or falsehood of *entire object*, while ``&`` and ``|`` refer to *bits within each object*.\n", + "\n", + "When you use ``and`` or ``or``, it's equivalent to asking Python to treat the object as a single Boolean entity.\n", + "In Python, all nonzero integers will evaluate as True. Thus:" ] }, { @@ -726,6 +1021,13 @@ "bool(42 or 0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When you use ``&`` and ``|`` on integers, the expression operates on the bits of the element, applying the *and* or the *or* to the individual bits making up the number:" + ] + }, { "cell_type": "code", "execution_count": 33, @@ -814,6 +1116,15 @@ "bin(42 | 59)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the corresponding bits of the binary representation are compared in order to yield the result.\n", + "\n", + "When you have an array of Boolean values in NumPy, this can be thought of as a string of bits where ``1 = True`` and ``0 = False``, and the result of ``&`` and ``|`` operates similarly to above:" + ] + }, { "cell_type": "code", "execution_count": 37, @@ -838,6 +1149,13 @@ "A | B" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using ``or`` on these arrays will try to evaluate the truth or falsehood of the entire array object, which is not a well-defined value:" + ] + }, { "cell_type": "code", "execution_count": 38, @@ -861,6 +1179,13 @@ "A or B" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, when doing a Boolean expression on a given array, you should use ``|`` or ``&`` rather than ``or`` or ``and``:" + ] + }, { "cell_type": "code", "execution_count": 39, @@ -884,6 +1209,13 @@ "(x > 4) & (x < 8)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Trying to evaluate the truth or falsehood of the entire array will give the same ``ValueError`` we saw previously:" + ] + }, { "cell_type": "code", "execution_count": 40, @@ -906,9 +1238,28 @@ "source": [ "(x > 4) and (x < 8)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So remember this: ``and`` and ``or`` perform a single Boolean evaluation on an entire object, while ``&`` and ``|`` perform multiple Boolean evaluations on the content (the individual bits or bytes) of an object.\n", + "For Boolean NumPy arrays, the latter is nearly always the desired operation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb) | [Contents](Index.ipynb) | [Fancy Indexing](02.07-Fancy-Indexing.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/02.07-Fancy-Indexing.ipynb b/notebooks_v1/02.07-Fancy-Indexing.ipynb similarity index 81% rename from code_listings/02.07-Fancy-Indexing.ipynb rename to notebooks_v1/02.07-Fancy-Indexing.ipynb index bc698089c..00cc188a5 100644 --- a/code_listings/02.07-Fancy-Indexing.ipynb +++ b/notebooks_v1/02.07-Fancy-Indexing.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb) | [Contents](Index.ipynb) | [Sorting Arrays](02.08-Sorting.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,26 @@ "# Fancy Indexing" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the previous sections, we saw how to access and modify portions of arrays using simple indices (e.g., ``arr[0]``), slices (e.g., ``arr[:5]``), and Boolean masks (e.g., ``arr[arr > 0]``).\n", + "In this section, we'll look at another style of array indexing, known as *fancy indexing*.\n", + "Fancy indexing is like the simple indexing we've already seen, but we pass arrays of indices in place of single scalars.\n", + "This allows us to very quickly access and modify complicated subsets of an array's values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exploring Fancy Indexing\n", + "\n", + "Fancy indexing is conceptually simple: it means passing an array of indices to access multiple array elements at once.\n", + "For example, consider the following array:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -30,6 +72,13 @@ "print(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose we want to access three different elements. We could do it like this:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -52,6 +101,13 @@ "[x[3], x[7], x[2]]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, we can pass a single list or array of indices to obtain the same result:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -75,6 +131,13 @@ "x[ind]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When using fancy indexing, the shape of the result reflects the shape of the *index arrays* rather than the shape of the *array being indexed*:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -100,6 +163,13 @@ "x[ind]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Fancy indexing also works in multiple dimensions. Consider the following array:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -125,6 +195,13 @@ "X" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Like with standard indexing, the first index refers to the row, and the second to the column:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -149,6 +226,15 @@ "X[row, col]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the first value in the result is ``X[0, 2]``, the second is ``X[1, 1]``, and the third is ``X[2, 3]``.\n", + "The pairing of indices in fancy indexing follows all the broadcasting rules that were mentioned in [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb).\n", + "So, for example, if we combine a column vector and a row vector within the indices, we get a two-dimensional result:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -173,6 +259,14 @@ "X[row[:, np.newaxis], col]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, each row value is matched with each column vector, exactly as we saw in broadcasting of arithmetic operations.\n", + "For example:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -197,6 +291,22 @@ "row[:, np.newaxis] * col" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is always important to remember with fancy indexing that the return value reflects the *broadcasted shape of the indices*, rather than the shape of the array being indexed." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Combined Indexing\n", + "\n", + "For even more powerful operations, fancy indexing can be combined with the other indexing schemes we've seen:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -218,6 +328,13 @@ "print(X)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can combine fancy and simple indices:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -240,6 +357,13 @@ "X[2, [2, 0, 1]]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also combine fancy indexing with slicing:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -263,6 +387,13 @@ "X[1:, [2, 0, 1]]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can combine fancy indexing with masking:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -288,6 +419,23 @@ "X[row[:, np.newaxis], mask]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these indexing options combined lead to a very flexible set of operations for accessing and modifying array values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Selecting Random Points\n", + "\n", + "One common use of fancy indexing is the selection of subsets of rows from a matrix.\n", + "For example, we might have an $N$ by $D$ matrix representing $N$ points in $D$ dimensions, such as the following points drawn from a two-dimensional normal distribution:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -314,6 +462,13 @@ "X.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the plotting tools we will discuss in [Introduction to Matplotlib](04.00-Introduction-To-Matplotlib.ipynb), we can visualize these points as a scatter-plot:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -340,6 +495,13 @@ "plt.scatter(X[:, 0], X[:, 1]);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's use fancy indexing to select 20 random points. We'll do this by first choosing 20 random indices with no repeats, and use these indices to select a portion of the original array:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -387,6 +549,13 @@ "selection.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now to see which points were selected, let's over-plot large circles at the locations of the selected points:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -411,6 +580,23 @@ " facecolor='none', s=200);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This sort of strategy is often used to quickly partition datasets, as is often needed in train/test splitting for validation of statistical models (see [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb)), and in sampling approaches to answering statistical questions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Modifying Values with Fancy Indexing\n", + "\n", + "Just as fancy indexing can be used to access parts of an array, it can also be used to modify parts of an array.\n", + "For example, imagine we have an array of indices and we'd like to set the corresponding items in an array to some value:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -433,6 +619,13 @@ "print(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use any assignment-type operator for this. For example:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -453,6 +646,13 @@ "print(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice, though, that repeated indices with these operations can cause some potentially unexpected results. Consider the following:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -474,6 +674,16 @@ "print(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Where did the 4 go? The result of this operation is to first assign ``x[0] = 4``, followed by ``x[0] = 6``.\n", + "The result, of course, is that ``x[0]`` contains the value 6.\n", + "\n", + "Fair enough, but consider this operation:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -498,6 +708,17 @@ "x" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You might expect that ``x[3]`` would contain the value 2, and ``x[4]`` would contain the value 3, as this is how many times each index is repeated. Why is this not the case?\n", + "Conceptually, this is because ``x[i] += 1`` is meant as a shorthand of ``x[i] = x[i] + 1``. ``x[i] + 1`` is evaluated, and then the result is assigned to the indices in x.\n", + "With this in mind, it is not the augmentation that happens multiple times, but the assignment, which leads to the rather nonintuitive results.\n", + "\n", + "So what if you want the other behavior where the operation is repeated? For this, you can use the ``at()`` method of ufuncs (available since NumPy 1.8), and do the following:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -519,6 +740,25 @@ "print(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``at()`` method does an in-place application of the given operator at the specified indices (here, ``i``) with the specified value (here, 1).\n", + "Another method that is similar in spirit is the ``reduceat()`` method of ufuncs, which you can read about in the NumPy documentation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Binning Data\n", + "\n", + "You can use these ideas to efficiently bin data to create a histogram by hand.\n", + "For example, imagine we have 1,000 values and would like to quickly find where they fall within an array of bins.\n", + "We could compute it using ``ufunc.at`` like this:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -530,7 +770,7 @@ "np.random.seed(42)\n", "x = np.random.randn(100)\n", "\n", - "# compute a histogram by-hand\n", + "# compute a histogram by hand\n", "bins = np.linspace(-5, 5, 20)\n", "counts = np.zeros_like(bins)\n", "\n", @@ -541,6 +781,13 @@ "np.add.at(counts, i, 1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The counts now reflect the number of points within each bin–in other words, a histogram:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -564,6 +811,21 @@ "plt.plot(bins, counts, linestyle='steps');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course, it would be silly to have to do this each time you want to plot a histogram.\n", + "This is why Matplotlib provides the ``plt.hist()`` routine, which does the same in a single line:\n", + "\n", + "```python\n", + "plt.hist(x, bins, histtype='step');\n", + "```\n", + "\n", + "This function will create a nearly identical plot to the one seen here.\n", + "To compute the binning, ``matplotlib`` uses the ``np.histogram`` function, which does a very similar computation to what we did before. Let's compare the two here:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -590,6 +852,14 @@ "%timeit np.add.at(counts, np.searchsorted(bins, x), 1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our own one-line algorithm is several times faster than the optimized algorithm in NumPy! How can this be?\n", + "If you dig into the ``np.histogram`` source code (you can do this in IPython by typing ``np.histogram??``), you'll see that it's quite a bit more involved than the simple search-and-count that we've done; this is because NumPy's algorithm is more flexible, and particularly is designed for better performance when the number of data points becomes large:" + ] + }, { "cell_type": "code", "execution_count": 26, @@ -616,9 +886,29 @@ "print(\"Custom routine:\")\n", "%timeit np.add.at(counts, np.searchsorted(bins, x), 1)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What this comparison shows is that algorithmic efficiency is almost never a simple question. An algorithm efficient for large datasets will not always be the best choice for small datasets, and vice versa (see [Big-O Notation](02.08-Sorting.ipynb#Aside:-Big-O-Notation)).\n", + "But the advantage of coding this algorithm yourself is that with an understanding of these basic methods, you could use these building blocks to extend this to do some very interesting custom behaviors.\n", + "The key to efficiently using Python in data-intensive applications is knowing about general convenience routines like ``np.histogram`` and when they're appropriate, but also knowing how to make use of lower-level functionality when you need more pointed behavior." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb) | [Contents](Index.ipynb) | [Sorting Arrays](02.08-Sorting.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/02.08-Sorting.ipynb b/notebooks_v1/02.08-Sorting.ipynb similarity index 75% rename from code_listings/02.08-Sorting.ipynb rename to notebooks_v1/02.08-Sorting.ipynb index cd0e03624..8be3373c0 100644 --- a/code_listings/02.08-Sorting.ipynb +++ b/notebooks_v1/02.08-Sorting.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Fancy Indexing](02.07-Fancy-Indexing.ipynb) | [Contents](Index.ipynb) | [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,18 @@ "# Sorting Arrays" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Up to this point we have been concerned mainly with tools to access and operate on array data with NumPy.\n", + "This section covers algorithms related to sorting values in NumPy arrays.\n", + "These algorithms are a favorite topic in introductory computer science courses: if you've ever taken one, you probably have had dreams (or, depending on your temperament, nightmares) about *insertion sorts*, *selection sorts*, *merge sorts*, *quick sorts*, *bubble sorts*, and many, many more.\n", + "All are means of accomplishing a similar task: sorting the values in a list or array.\n", + "\n", + "For example, a simple *selection sort* repeatedly finds the minimum value from a list, and makes swaps until the list is sorted. We can code this in just a few lines of Python:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -47,6 +81,17 @@ "selection_sort(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As any first-year computer science major will tell you, the selection sort is useful for its simplicity, but is much too slow to be useful for larger arrays.\n", + "For a list of $N$ values, it requires $N$ loops, each of which does on order $\\sim N$ comparisons to find the swap value.\n", + "In terms of the \"big-O\" notation often used to characterize these algorithms (see [Big-O Notation](#Aside:-Big-O-Notation)), selection sort averages $\\mathcal{O}[N^2]$: if you double the number of items in the list, the execution time will go up by about a factor of four.\n", + "\n", + "Even selection sort, though, is much better than my all-time favorite sorting algorithms, the *bogosort*:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -84,6 +129,28 @@ "bogosort(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This silly sorting method relies on pure chance: it repeatedly applies a random shuffling of the array until the result happens to be sorted.\n", + "With an average scaling of $\\mathcal{O}[N \\times N!]$, (that's *N* times *N* factorial) this should–quite obviously–never be used for any real computation.\n", + "\n", + "Fortunately, Python contains built-in sorting algorithms that are *much* more efficient than either of the simplistic algorithms just shown. We'll start by looking at the Python built-ins, and then take a look at the routines included in NumPy and optimized for NumPy arrays." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fast Sorting in NumPy: ``np.sort`` and ``np.argsort``\n", + "\n", + "Although Python has built-in ``sort`` and ``sorted`` functions to work with lists, we won't discuss them here because NumPy's ``np.sort`` function turns out to be much more efficient and useful for our purposes.\n", + "By default ``np.sort`` uses an $\\mathcal{O}[N\\log N]$, *quicksort* algorithm, though *mergesort* and *heapsort* are also available. For most applications, the default quicksort is more than sufficient.\n", + "\n", + "To return a sorted version of the array without modifying the input, you can use ``np.sort``:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -107,6 +174,13 @@ "np.sort(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you prefer to sort the array in-place, you can instead use the ``sort`` method of arrays:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -127,6 +201,13 @@ "print(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A related function is ``argsort``, which instead returns the *indices* of the sorted elements:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -148,6 +229,14 @@ "print(i)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first element of this result gives the index of the smallest element, the second value gives the index of the second smallest, and so on.\n", + "These indices can then be used (via fancy indexing) to construct the sorted array if desired:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -170,6 +259,20 @@ "x[i]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Sorting along rows or columns" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A useful feature of NumPy's sorting algorithms is the ability to sort along specific rows or columns of a multidimensional array using the ``axis`` argument. For example:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -246,6 +349,22 @@ "np.sort(X, axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind that this treats each row or column as an independent array, and any relationships between the row or column values will be lost!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Partial Sorts: Partitioning\n", + "\n", + "Sometimes we're not interested in sorting the entire array, but simply want to find the *k* smallest values in the array. NumPy provides this in the ``np.partition`` function. ``np.partition`` takes an array and a number *K*; the result is a new array with the smallest *K* values to the left of the partition, and the remaining values to the right, in arbitrary order:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -269,6 +388,16 @@ "np.partition(x, 3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the first three values in the resulting array are the three smallest in the array, and the remaining array positions contain the remaining values.\n", + "Within the two partitions, the elements have arbitrary order.\n", + "\n", + "Similarly to sorting, we can partition along an arbitrary axis of a multidimensional array:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -294,6 +423,27 @@ "np.partition(X, 2, axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is an array where the first two slots in each row contain the smallest values from that row, with the remaining values filling the remaining slots.\n", + "\n", + "Finally, just as there is a ``np.argsort`` that computes indices of the sort, there is a ``np.argpartition`` that computes indices of the partition.\n", + "We'll see this in action in the following section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: k-Nearest Neighbors\n", + "\n", + "Let's quickly see how we might use this ``argsort`` function along multiple axes to find the nearest neighbors of each point in a set.\n", + "We'll start by creating a random set of 10 points on a two-dimensional plane.\n", + "Using the standard convention, we'll arrange these in a $10\\times 2$ array:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -305,6 +455,13 @@ "X = rand.rand(10, 2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get an idea of how these points look, let's quickly scatter plot them:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -330,6 +487,15 @@ "plt.scatter(X[:, 0], X[:, 1], s=100);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll compute the distance between each pair of points.\n", + "Recall that the squared-distance between two points is the sum of the squared differences in each dimension;\n", + "using the efficient broadcasting ([Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb)) and aggregation ([Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb)) routines provided by NumPy we can compute the matrix of square distances in a single line of code:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -341,6 +507,13 @@ "dist_sq = np.sum((X[:, np.newaxis, :] - X[np.newaxis, :, :]) ** 2, axis=-1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This operation has a lot packed into it, and it might be a bit confusing if you're unfamiliar with NumPy's broadcasting rules. When you come across code like this, it can be useful to break it down into its component steps:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -413,6 +586,13 @@ "dist_sq.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just to double-check what we are doing, we should see that the diagonal of this matrix (i.e., the set of distances between each point and itself) is all zero:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -435,6 +615,14 @@ "dist_sq.diagonal()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It checks out!\n", + "With the pairwise square-distances converted, we can now use ``np.argsort`` to sort along each row. The leftmost columns will then give the indices of the nearest neighbors:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -464,6 +652,15 @@ "print(nearest)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the first column gives the numbers 0 through 9 in order: this is due to the fact that each point's closest neighbor is itself, as we would expect.\n", + "\n", + "By using a full sort here, we've actually done more work than we need to in this case. If we're simply interested in the nearest $k$ neighbors, all we need is to partition each row so that the smallest $k + 1$ squared distances come first, with larger distances filling the remaining positions of the array. We can do this with the ``np.argpartition`` function:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -476,6 +673,13 @@ "nearest_partition = np.argpartition(dist_sq, K + 1, axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to visualize this network of neighbors, let's quickly plot the points along with lines representing the connections from each point to its two nearest neighbors:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -497,7 +701,7 @@ "source": [ "plt.scatter(X[:, 0], X[:, 1], s=100)\n", "\n", - "# draw lines from each point to its 2 nearest neighbors\n", + "# draw lines from each point to its two nearest neighbors\n", "K = 2\n", "\n", "for i in range(X.shape[0]):\n", @@ -506,9 +710,59 @@ " # use some zip magic to make it happen:\n", " plt.plot(*zip(X[j], X[i]), color='black')" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each point in the plot has lines drawn to its two nearest neighbors.\n", + "At first glance, it might seem strange that some of the points have more than two lines coming out of them: this is due to the fact that if point A is one of the two nearest neighbors of point B, this does not necessarily imply that point B is one of the two nearest neighbors of point A.\n", + "\n", + "Although the broadcasting and row-wise sorting of this approach might seem less straightforward than writing a loop, it turns out to be a very efficient way of operating on this data in Python.\n", + "You might be tempted to do the same type of operation by manually looping through the data and sorting each set of neighbors individually, but this would almost certainly lead to a slower algorithm than the vectorized version we used. The beauty of this approach is that it's written in a way that's agnostic to the size of the input data: we could just as easily compute the neighbors among 100 or 1,000,000 points in any number of dimensions, and the code would look the same.\n", + "\n", + "Finally, I'll note that when doing very large nearest neighbor searches, there are tree-based and/or approximate algorithms that can scale as $\\mathcal{O}[N\\log N]$ or better rather than the $\\mathcal{O}[N^2]$ of the brute-force algorithm. One example of this is the KD-Tree, [implemented in Scikit-learn](http://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KDTree.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aside: Big-O Notation\n", + "\n", + "Big-O notation is a means of describing how the number of operations required for an algorithm scales as the input grows in size.\n", + "To use it correctly is to dive deeply into the realm of computer science theory, and to carefully distinguish it from the related small-o notation, big-$\\theta$ notation, big-$\\Omega$ notation, and probably many mutant hybrids thereof.\n", + "While these distinctions add precision to statements about algorithmic scaling, outside computer science theory exams and the remarks of pedantic blog commenters, you'll rarely see such distinctions made in practice.\n", + "Far more common in the data science world is a less rigid use of big-O notation: as a general (if imprecise) description of the scaling of an algorithm.\n", + "With apologies to theorists and pedants, this is the interpretation we'll use throughout this book.\n", + "\n", + "Big-O notation, in this loose sense, tells you how much time your algorithm will take as you increase the amount of data.\n", + "If you have an $\\mathcal{O}[N]$ (read \"order $N$\") algorithm that takes 1 second to operate on a list of length *N*=1,000, then you should expect it to take roughly 5 seconds for a list of length *N*=5,000.\n", + "If you have an $\\mathcal{O}[N^2]$ (read \"order *N* squared\") algorithm that takes 1 second for *N*=1000, then you should expect it to take about 25 seconds for *N*=5000.\n", + "\n", + "For our purposes, the *N* will usually indicate some aspect of the size of the dataset (the number of points, the number of dimensions, etc.). When trying to analyze billions or trillions of samples, the difference between $\\mathcal{O}[N]$ and $\\mathcal{O}[N^2]$ can be far from trivial!\n", + "\n", + "Notice that the big-O notation by itself tells you nothing about the actual wall-clock time of a computation, but only about its scaling as you change *N*.\n", + "Generally, for example, an $\\mathcal{O}[N]$ algorithm is considered to have better scaling than an $\\mathcal{O}[N^2]$ algorithm, and for good reason. But for small datasets in particular, the algorithm with better scaling might not be faster.\n", + "For example, in a given problem an $\\mathcal{O}[N^2]$ algorithm might take 0.01 seconds, while a \"better\" $\\mathcal{O}[N]$ algorithm might take 1 second.\n", + "Scale up *N* by a factor of 1,000, though, and the $\\mathcal{O}[N]$ algorithm will win out.\n", + "\n", + "Even this loose version of Big-O notation can be very useful when comparing the performance of algorithms, and we'll use this notation throughout the book when talking about how algorithms scale." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Fancy Indexing](02.07-Fancy-Indexing.ipynb) | [Contents](Index.ipynb) | [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/notebooks_v1/02.09-Structured-Data-NumPy.ipynb b/notebooks_v1/02.09-Structured-Data-NumPy.ipynb new file mode 100644 index 000000000..ea4ee0bec --- /dev/null +++ b/notebooks_v1/02.09-Structured-Data-NumPy.ipynb @@ -0,0 +1,603 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Sorting Arrays](02.08-Sorting.ipynb) | [Contents](Index.ipynb) | [Data Manipulation with Pandas](03.00-Introduction-to-Pandas.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Structured Data: NumPy's Structured Arrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While often our data can be well represented by a homogeneous array of values, sometimes this is not the case. This section demonstrates the use of NumPy's *structured arrays* and *record arrays*, which provide efficient storage for compound, heterogeneous data. While the patterns shown here are useful for simple operations, scenarios like this often lend themselves to the use of Pandas ``Dataframe``s, which we'll explore in [Chapter 3](03.00-Introduction-to-Pandas.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Imagine that we have several categories of data on a number of people (say, name, age, and weight), and we'd like to store these values for use in a Python program.\n", + "It would be possible to store these in three separate arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "name = ['Alice', 'Bob', 'Cathy', 'Doug']\n", + "age = [25, 45, 37, 19]\n", + "weight = [55.0, 85.5, 68.0, 61.5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this is a bit clumsy. There's nothing here that tells us that the three arrays are related; it would be more natural if we could use a single structure to store all of this data.\n", + "NumPy can handle this through structured arrays, which are arrays with compound data types.\n", + "\n", + "Recall that previously we created a simple array using an expression like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "x = np.zeros(4, dtype=int)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can similarly create a structured array using a compound data type specification:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[('name', '``, which means \"little endian\" or \"big endian,\" respectively, and specifies the ordering convention for significant bits.\n", + "The next character specifies the type of data: characters, bytes, ints, floating points, and so on (see the table below).\n", + "The last character or characters represents the size of the object in bytes.\n", + "\n", + "| Character | Description | Example |\n", + "| --------- | ----------- | ------- | \n", + "| ``'b'`` | Byte | ``np.dtype('b')`` |\n", + "| ``'i'`` | Signed integer | ``np.dtype('i4') == np.int32`` |\n", + "| ``'u'`` | Unsigned integer | ``np.dtype('u1') == np.uint8`` |\n", + "| ``'f'`` | Floating point | ``np.dtype('f8') == np.int64`` |\n", + "| ``'c'`` | Complex floating point| ``np.dtype('c16') == np.complex128``|\n", + "| ``'S'``, ``'a'`` | String | ``np.dtype('S5')`` |\n", + "| ``'U'`` | Unicode string | ``np.dtype('U') == np.str_`` |\n", + "| ``'V'`` | Raw data (void) | ``np.dtype('V') == np.void`` |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More Advanced Compound Types\n", + "\n", + "It is possible to define even more advanced compound types.\n", + "For example, you can create a type where each element contains an array or matrix of values.\n", + "Here, we'll create a data type with a ``mat`` component consisting of a $3\\times 3$ floating-point matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0, [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])\n", + "[[ 0. 0. 0.]\n", + " [ 0. 0. 0.]\n", + " [ 0. 0. 0.]]\n" + ] + } + ], + "source": [ + "tp = np.dtype([('id', 'i8'), ('mat', 'f8', (3, 3))])\n", + "X = np.zeros(1, dtype=tp)\n", + "print(X[0])\n", + "print(X['mat'][0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now each element in the ``X`` array consists of an ``id`` and a $3\\times 3$ matrix.\n", + "Why would you use this rather than a simple multidimensional array, or perhaps a Python dictionary?\n", + "The reason is that this NumPy ``dtype`` directly maps onto a C structure definition, so the buffer containing the array content can be accessed directly within an appropriately written C program.\n", + "If you find yourself writing a Python interface to a legacy C or Fortran library that manipulates structured data, you'll probably find structured arrays quite useful!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## RecordArrays: Structured Arrays with a Twist\n", + "\n", + "NumPy also provides the ``np.recarray`` class, which is almost identical to the structured arrays just described, but with one additional feature: fields can be accessed as attributes rather than as dictionary keys.\n", + "Recall that we previously accessed the ages by writing:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([25, 45, 37, 19], dtype=int32)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['age']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we view our data as a record array instead, we can access this with slightly fewer keystrokes:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([25, 45, 37, 19], dtype=int32)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data_rec = data.view(np.recarray)\n", + "data_rec.age" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The downside is that for record arrays, there is some extra overhead involved in accessing the fields, even when using the same syntax. We can see this here:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1000000 loops, best of 3: 241 ns per loop\n", + "100000 loops, best of 3: 4.61 µs per loop\n", + "100000 loops, best of 3: 7.27 µs per loop\n" + ] + } + ], + "source": [ + "%timeit data['age']\n", + "%timeit data_rec['age']\n", + "%timeit data_rec.age" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whether the more convenient notation is worth the additional overhead will depend on your own application." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## On to Pandas\n", + "\n", + "This section on structured and record arrays is purposely at the end of this chapter, because it leads so well into the next package we will cover: Pandas.\n", + "Structured arrays like the ones discussed here are good to know about for certain situations, especially in case you're using NumPy arrays to map onto binary data formats in C, Fortran, or another language.\n", + "For day-to-day use of structured data, the Pandas package is a much better choice, and we'll dive into a full discussion of it in the chapter that follows." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Sorting Arrays](02.08-Sorting.ipynb) | [Contents](Index.ipynb) | [Data Manipulation with Pandas](03.00-Introduction-to-Pandas.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/03.00-Introduction-to-Pandas.ipynb b/notebooks_v1/03.00-Introduction-to-Pandas.ipynb new file mode 100644 index 000000000..9a5487ae9 --- /dev/null +++ b/notebooks_v1/03.00-Introduction-to-Pandas.ipynb @@ -0,0 +1,167 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb) | [Contents](Index.ipynb) | [Introducing Pandas Objects](03.01-Introducing-Pandas-Objects.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Data Manipulation with Pandas" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the previous chapter, we dove into detail on NumPy and its ``ndarray`` object, which provides efficient storage and manipulation of dense typed arrays in Python.\n", + "Here we'll build on this knowledge by looking in detail at the data structures provided by the Pandas library.\n", + "Pandas is a newer package built on top of NumPy, and provides an efficient implementation of a ``DataFrame``.\n", + "``DataFrame``s are essentially multidimensional arrays with attached row and column labels, and often with heterogeneous types and/or missing data.\n", + "As well as offering a convenient storage interface for labeled data, Pandas implements a number of powerful data operations familiar to users of both database frameworks and spreadsheet programs.\n", + "\n", + "As we saw, NumPy's ``ndarray`` data structure provides essential features for the type of clean, well-organized data typically seen in numerical computing tasks.\n", + "While it serves this purpose very well, its limitations become clear when we need more flexibility (e.g., attaching labels to data, working with missing data, etc.) and when attempting operations that do not map well to element-wise broadcasting (e.g., groupings, pivots, etc.), each of which is an important piece of analyzing the less structured data available in many forms in the world around us.\n", + "Pandas, and in particular its ``Series`` and ``DataFrame`` objects, builds on the NumPy array structure and provides efficient access to these sorts of \"data munging\" tasks that occupy much of a data scientist's time.\n", + "\n", + "In this chapter, we will focus on the mechanics of using ``Series``, ``DataFrame``, and related structures effectively.\n", + "We will use examples drawn from real datasets where appropriate, but these examples are not necessarily the focus." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing and Using Pandas\n", + "\n", + "Installation of Pandas on your system requires NumPy to be installed, and if building the library from source, requires the appropriate tools to compile the C and Cython sources on which Pandas is built.\n", + "Details on this installation can be found in the [Pandas documentation](http://pandas.pydata.org/).\n", + "If you followed the advice outlined in the [Preface](00.00-Preface.ipynb) and used the Anaconda stack, you already have Pandas installed.\n", + "\n", + "Once Pandas is installed, you can import it and check the version:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'0.18.1'" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas\n", + "pandas.__version__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as we generally import NumPy under the alias ``np``, we will import Pandas under the alias ``pd``:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This import convention will be used throughout the remainder of this book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reminder about Built-In Documentation\n", + "\n", + "As you read through this chapter, don't forget that IPython gives you the ability to quickly explore the contents of a package (by using the tab-completion feature) as well as the documentation of various functions (using the ``?`` character). (Refer back to [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb) if you need a refresher on this.)\n", + "\n", + "For example, to display all the contents of the pandas namespace, you can type\n", + "\n", + "```ipython\n", + "In [3]: pd.\n", + "```\n", + "\n", + "And to display Pandas's built-in documentation, you can use this:\n", + "\n", + "```ipython\n", + "In [4]: pd?\n", + "```\n", + "\n", + "More detailed documentation, along with tutorials and other resources, can be found at http://pandas.pydata.org/." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb) | [Contents](Index.ipynb) | [Introducing Pandas Objects](03.01-Introducing-Pandas-Objects.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/code_listings/03.01-Introducing-Pandas-Objects.ipynb b/notebooks_v1/03.01-Introducing-Pandas-Objects.ipynb similarity index 61% rename from code_listings/03.01-Introducing-Pandas-Objects.ipynb rename to notebooks_v1/03.01-Introducing-Pandas-Objects.ipynb index b726f9ab4..2e5f8f7b3 100644 --- a/code_listings/03.01-Introducing-Pandas-Objects.ipynb +++ b/notebooks_v1/03.01-Introducing-Pandas-Objects.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Data Manipulation with Pandas](03.00-Introduction-to-Pandas.ipynb) | [Contents](Index.ipynb) | [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,17 @@ "# Introducing Pandas Objects" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At the very basic level, Pandas objects can be thought of as enhanced versions of NumPy structured arrays in which the rows and columns are identified with labels rather than simple integer indices.\n", + "As we will see during the course of this chapter, Pandas provides a host of useful tools, methods, and functionality on top of the basic data structures, but nearly everything that follows will require an understanding of what these structures are.\n", + "Thus, before we go any further, let's introduce these three fundamental Pandas data structures: the ``Series``, ``DataFrame``, and ``Index``.\n", + "\n", + "We will start our code sessions with the standard NumPy and Pandas imports:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -19,6 +52,16 @@ "import pandas as pd" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Pandas Series Object\n", + "\n", + "A Pandas ``Series`` is a one-dimensional array of indexed data.\n", + "It can be created from a list or array as follows:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -46,6 +89,14 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we see in the output, the ``Series`` wraps both a sequence of values and a sequence of indices, which we can access with the ``values`` and ``index`` attributes.\n", + "The ``values`` are simply a familiar NumPy array:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -68,6 +119,13 @@ "data.values" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``index`` is an array-like object of type ``pd.Index``, which we'll discuss in more detail momentarily." + ] + }, { "cell_type": "code", "execution_count": 4, @@ -90,6 +148,13 @@ "data.index" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Like with a NumPy array, data can be accessed by the associated index via the familiar Python square-bracket notation:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -136,6 +201,31 @@ "data[1:3]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we will see, though, the Pandas ``Series`` is much more general and flexible than the one-dimensional NumPy array that it emulates." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ``Series`` as generalized NumPy array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From what we've seen so far, it may look like the ``Series`` object is basically interchangeable with a one-dimensional NumPy array.\n", + "The essential difference is the presence of the index: while the Numpy Array has an *implicitly defined* integer index used to access the values, the Pandas ``Series`` has an *explicitly defined* index associated with the values.\n", + "\n", + "This explicit index definition gives the ``Series`` object additional capabilities. For example, the index need not be an integer, but can consist of values of any desired type.\n", + "For example, if we wish, we can use strings as an index:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -164,6 +254,13 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the item access works as expected:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -186,6 +283,13 @@ "data['b']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can even use non-contiguous or non-sequential indices:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -236,6 +340,19 @@ "data[5]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Series as specialized dictionary\n", + "\n", + "In this way, you can think of a Pandas ``Series`` a bit like a specialization of a Python dictionary.\n", + "A dictionary is a structure that maps arbitrary keys to a set of arbitrary values, and a ``Series`` is a structure which maps typed keys to a set of typed values.\n", + "This typing is important: just as the type-specific compiled code behind a NumPy array makes it more efficient than a Python list for certain operations, the type information of a Pandas ``Series`` makes it much more efficient than Python dictionaries for certain operations.\n", + "\n", + "The ``Series``-as-dictionary analogy can be made even more clear by constructing a ``Series`` object directly from a Python dictionary:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -269,6 +386,14 @@ "population" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By default, a ``Series`` will be created where the index is drawn from the sorted keys.\n", + "From here, typical dictionary-style item access can be performed:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -291,6 +416,13 @@ "population['California']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Unlike a dictionary, though, the ``Series`` also supports array-style operations such as slicing:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -316,6 +448,30 @@ "population['California':'Illinois']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll discuss some of the quirks of Pandas indexing and slicing in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constructing Series objects\n", + "\n", + "We've already seen a few ways of constructing a Pandas ``Series`` from scratch; all of them are some version of the following:\n", + "\n", + "```python\n", + ">>> pd.Series(data, index=index)\n", + "```\n", + "\n", + "where ``index`` is an optional argument, and ``data`` can be one of many entities.\n", + "\n", + "For example, ``data`` can be a list or NumPy array, in which case ``index`` defaults to an integer sequence:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -341,6 +497,13 @@ "pd.Series([2, 4, 6])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``data`` can be a scalar, which is repeated to fill the specified index:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -366,6 +529,13 @@ "pd.Series(5, index=[100, 200, 300])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``data`` can be a dictionary, in which ``index`` defaults to the sorted dictionary keys:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -391,6 +561,13 @@ "pd.Series({2:'a', 1:'b', 3:'c'})" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In each case, the index can be explicitly set if a different result is preferred:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -415,6 +592,36 @@ "pd.Series({2:'a', 1:'b', 3:'c'}, index=[3, 2])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that in this case, the ``Series`` is populated only with the explicitly identified keys." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Pandas DataFrame Object\n", + "\n", + "The next fundamental structure in Pandas is the ``DataFrame``.\n", + "Like the ``Series`` object discussed in the previous section, the ``DataFrame`` can be thought of either as a generalization of a NumPy array, or as a specialization of a Python dictionary.\n", + "We'll now take a look at each of these perspectives." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### DataFrame as a generalized NumPy array\n", + "If a ``Series`` is an analog of a one-dimensional array with flexible indices, a ``DataFrame`` is an analog of a two-dimensional array with both flexible row indices and flexible column names.\n", + "Just as you might think of a two-dimensional array as an ordered sequence of aligned one-dimensional columns, you can think of a ``DataFrame`` as a sequence of aligned ``Series`` objects.\n", + "Here, by \"aligned\" we mean that they share the same index.\n", + "\n", + "To demonstrate this, let's first construct a new ``Series`` listing the area of each of the five states discussed in the previous section:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -439,11 +646,19 @@ } ], "source": [ - "area_dict = {'California': 423967, 'Texas': 695662, 'New York': 141297, 'Florida': 170312, 'Illinois': 149995}\n", + "area_dict = {'California': 423967, 'Texas': 695662, 'New York': 141297,\n", + " 'Florida': 170312, 'Illinois': 149995}\n", "area = pd.Series(area_dict)\n", "area" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have this along with the ``population`` Series from before, we can use a dictionary to construct a single two-dimensional object containing this information:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -513,6 +728,13 @@ "states" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Like the ``Series`` object, the ``DataFrame`` has an ``index`` attribute that gives access to the index labels:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -535,6 +757,13 @@ "states.index" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Additionally, the ``DataFrame`` has a ``columns`` attribute, which is an ``Index`` object holding the column labels:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -557,6 +786,24 @@ "states.columns" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Thus the ``DataFrame`` can be thought of as a generalization of a two-dimensional NumPy array, where both the rows and columns have a generalized index for accessing the data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### DataFrame as specialized dictionary\n", + "\n", + "Similarly, we can also think of a ``DataFrame`` as a specialization of a dictionary.\n", + "Where a dictionary maps a key to a value, a ``DataFrame`` maps a column name to a ``Series`` of column data.\n", + "For example, asking for the ``'area'`` attribute returns the ``Series`` object containing the areas we saw earlier:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -584,6 +831,34 @@ "states['area']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the potential point of confusion here: in a two-dimesnional NumPy array, ``data[0]`` will return the first *row*. For a ``DataFrame``, ``data['col0']`` will return the first *column*.\n", + "Because of this, it is probably better to think about ``DataFrame``s as generalized dictionaries rather than generalized arrays, though both ways of looking at the situation can be useful.\n", + "We'll explore more flexible means of indexing ``DataFrame``s in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constructing DataFrame objects\n", + "\n", + "A Pandas ``DataFrame`` can be constructed in a variety of ways.\n", + "Here we'll give several examples." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### From a single Series object\n", + "\n", + "A ``DataFrame`` is a collection of ``Series`` objects, and a single-column ``DataFrame`` can be constructed from a single ``Series``:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -645,6 +920,16 @@ "pd.DataFrame(population, columns=['population'])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### From a list of dicts\n", + "\n", + "Any list of dictionaries can be made into a ``DataFrame``.\n", + "We'll use a simple list comprehension to create some data:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -702,6 +987,13 @@ "pd.DataFrame(data)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even if some keys in the dictionary are missing, Pandas will fill them in with ``NaN`` (i.e., \"not a number\") values:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -754,6 +1046,15 @@ "pd.DataFrame([{'a': 1, 'b': 2}, {'b': 3, 'c': 4}])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### From a dictionary of Series objects\n", + "\n", + "As we saw before, a ``DataFrame`` can be constructed from a dictionary of ``Series`` objects as well:" + ] + }, { "cell_type": "code", "execution_count": 26, @@ -822,6 +1123,16 @@ " 'area': area})" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### From a two-dimensional NumPy array\n", + "\n", + "Given a two-dimensional array of data, we can create a ``DataFrame`` with any specified column and index names.\n", + "If omitted, an integer index will be used for each:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -879,6 +1190,16 @@ " index=['a', 'b', 'c'])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### From a NumPy structured array\n", + "\n", + "We covered structured arrays in [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb).\n", + "A Pandas ``DataFrame`` operates much like a structured array, and can be created directly from one:" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -958,6 +1279,18 @@ "pd.DataFrame(A)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Pandas Index Object\n", + "\n", + "We have seen here that both the ``Series`` and ``DataFrame`` objects contain an explicit *index* that lets you reference and modify data.\n", + "This ``Index`` object is an interesting structure in itself, and it can be thought of either as an *immutable array* or as an *ordered set* (technically a multi-set, as ``Index`` objects may contain repeated values).\n", + "Those views have some interesting consequences in the operations available on ``Index`` objects.\n", + "As a simple example, let's construct an ``Index`` from a list of integers:" + ] + }, { "cell_type": "code", "execution_count": 30, @@ -981,6 +1314,16 @@ "ind" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Index as immutable array\n", + "\n", + "The ``Index`` in many ways operates like an array.\n", + "For example, we can use standard Python indexing notation to retrieve values or slices:" + ] + }, { "cell_type": "code", "execution_count": 31, @@ -1025,6 +1368,13 @@ "ind[::2]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``Index`` objects also have many of the attributes familiar from NumPy arrays:" + ] + }, { "cell_type": "code", "execution_count": 33, @@ -1044,6 +1394,13 @@ "print(ind.size, ind.shape, ind.ndim, ind.dtype)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One difference between ``Index`` objects and NumPy arrays is that indices are immutable–that is, they cannot be modified via the normal means:" + ] + }, { "cell_type": "code", "execution_count": 34, @@ -1068,6 +1425,23 @@ "ind[1] = 0" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This immutability makes it safer to share indices between multiple ``DataFrame``s and arrays, without the potential for side effects from inadvertent index modification." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Index as ordered set\n", + "\n", + "Pandas objects are designed to facilitate operations such as joins across datasets, which depend on many aspects of set arithmetic.\n", + "The ``Index`` object follows many of the conventions used by Python's built-in ``set`` data structure, so that unions, intersections, differences, and other combinations can be computed in a familiar way:" + ] + }, { "cell_type": "code", "execution_count": 35, @@ -1145,9 +1519,27 @@ "source": [ "indA ^ indB # symmetric difference" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These operations may also be accessed via object methods, for example ``indA.intersection(indB)``." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Data Manipulation with Pandas](03.00-Introduction-to-Pandas.ipynb) | [Contents](Index.ipynb) | [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.02-Data-Indexing-and-Selection.ipynb b/notebooks_v1/03.02-Data-Indexing-and-Selection.ipynb similarity index 67% rename from code_listings/03.02-Data-Indexing-and-Selection.ipynb rename to notebooks_v1/03.02-Data-Indexing-and-Selection.ipynb index 23cb52e64..9cce1353f 100644 --- a/code_listings/03.02-Data-Indexing-and-Selection.ipynb +++ b/notebooks_v1/03.02-Data-Indexing-and-Selection.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Introducing Pandas Objects](03.01-Introducing-Pandas-Objects.ipynb) | [Contents](Index.ipynb) | [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,37 @@ "# Data Indexing and Selection" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In [Chapter 2](02.00-Introduction-to-NumPy.ipynb), we looked in detail at methods and tools to access, set, and modify values in NumPy arrays.\n", + "These included indexing (e.g., ``arr[2, 1]``), slicing (e.g., ``arr[:, 1:5]``), masking (e.g., ``arr[arr > 0]``), fancy indexing (e.g., ``arr[0, [1, 5]]``), and combinations thereof (e.g., ``arr[:, [1, 5]]``).\n", + "Here we'll look at similar means of accessing and modifying values in Pandas ``Series`` and ``DataFrame`` objects.\n", + "If you have used the NumPy patterns, the corresponding patterns in Pandas will feel very familiar, though there are a few quirks to be aware of.\n", + "\n", + "We'll start with the simple case of the one-dimensional ``Series`` object, and then move on to the more complicated two-dimesnional ``DataFrame`` object." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Data Selection in Series\n", + "\n", + "As we saw in the previous section, a ``Series`` object acts in many ways like a one-dimensional NumPy array, and in many ways like a standard Python dictionary.\n", + "If we keep these two overlapping analogies in mind, it will help us to understand the patterns of data indexing and selection in these arrays." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Series as dictionary\n", + "\n", + "Like a dictionary, the ``Series`` object provides a mapping from a collection of keys to a collection of values:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -58,6 +111,13 @@ "data['b']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also use dictionary-like Python expressions and methods to examine the keys/indices and values:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -124,6 +184,14 @@ "list(data.items())" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``Series`` objects can even be modified with a dictionary-like syntax.\n", + "Just as you can extend a dictionary by assigning to a new key, you can extend a ``Series`` by assigning to a new index value:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -152,6 +220,28 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This easy mutability of the objects is a convenient feature: under the hood, Pandas is making decisions about memory layout and data copying that might need to take place; the user generally does not need to worry about these issues." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Series as one-dimensional array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A ``Series`` builds on this dictionary-like interface and provides array-style item selection via the same basic mechanisms as NumPy arrays – that is, *slices*, *masking*, and *fancy indexing*.\n", + "Examples of these are as follows:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -253,6 +343,24 @@ "data[['a', 'e']]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Among these, slicing may be the source of the most confusion.\n", + "Notice that when slicing with an explicit index (i.e., ``data['a':'c']``), the final index is *included* in the slice, while when slicing with an implicit index (i.e., ``data[0:2]``), the final index is *excluded* from the slice." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Indexers: loc, iloc, and ix\n", + "\n", + "These slicing and indexing conventions can be a source of confusion.\n", + "For example, if your ``Series`` has an explicit integer index, an indexing operation such as ``data[1]`` will use the explicit indices, while a slicing operation like ``data[1:3]`` will use the implicit Python-style index." + ] + }, { "cell_type": "code", "execution_count": 11, @@ -327,6 +435,16 @@ "data[1:3]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of this potential confusion in the case of integer indexes, Pandas provides some special *indexer* attributes that explicitly expose certain indexing schemes.\n", + "These are not functional methods, but attributes that expose a particular slicing interface to the data in the ``Series``.\n", + "\n", + "First, the ``loc`` attribute allows indexing and slicing that always references the explicit index:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -373,6 +491,13 @@ "data.loc[1:3]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``iloc`` attribute allows indexing and slicing that always references the implicit Python-style index:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -419,6 +544,37 @@ "data.iloc[1:3]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A third indexing attribute, ``ix``, is a hybrid of the two, and for ``Series`` objects is equivalent to standard ``[]``-based indexing.\n", + "The purpose of the ``ix`` indexer will become more apparent in the context of ``DataFrame`` objects, which we will discuss in a moment.\n", + "\n", + "One guiding principle of Python code is that \"explicit is better than implicit.\"\n", + "The explicit nature of ``loc`` and ``iloc`` make them very useful in maintaining clean and readable code; especially in the case of integer indexes, I recommend using these both to make code easier to read and understand, and to prevent subtle bugs due to the mixed indexing/slicing convention." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Data Selection in DataFrame\n", + "\n", + "Recall that a ``DataFrame`` acts in many ways like a two-dimensional or structured array, and in other ways like a dictionary of ``Series`` structures sharing the same index.\n", + "These analogies can be helpful to keep in mind as we explore data selection within this structure." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### DataFrame as a dictionary\n", + "\n", + "The first analogy we will consider is the ``DataFrame`` as a dictionary of related ``Series`` objects.\n", + "Let's return to our example of areas and populations of states:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -493,6 +649,13 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The individual ``Series`` that make up the columns of the ``DataFrame`` can be accessed via dictionary-style indexing of the column name:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -520,6 +683,13 @@ "data['area']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Equivalently, we can use attribute-style access with column names that are strings:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -547,6 +717,13 @@ "data.area" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This attribute-style column access actually accesses the exact same object as the dictionary-style access:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -569,6 +746,15 @@ "data.area is data['area']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Though this is a useful shorthand, keep in mind that it does not work for all cases!\n", + "For example, if the column names are not strings, or if the column names conflict with methods of the ``DataFrame``, this attribute-style access is not possible.\n", + "For example, the ``DataFrame`` has a ``pop()`` method, so ``data.pop`` will point to this rather than the ``\"pop\"`` column:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -591,6 +777,15 @@ "data.pop is data['pop']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In particular, you should avoid the temptation to try column assignment via attribute (i.e., use ``data['pop'] = z`` rather than ``data.pop = z``).\n", + "\n", + "Like with the ``Series`` objects discussed earlier, this dictionary-style syntax can also be used to modify the object, in this case adding a new column:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -665,6 +860,23 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This shows a preview of the straightforward syntax of element-by-element arithmetic between ``Series`` objects; we'll dig into this further in [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### DataFrame as two-dimensional array\n", + "\n", + "As mentioned previously, we can also view the ``DataFrame`` as an enhanced two-dimensional array.\n", + "We can examine the raw underlying data array using the ``values`` attribute:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -691,6 +903,14 @@ "data.values" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this picture in mind, many familiar array-like observations can be done on the ``DataFrame`` itself.\n", + "For example, we can transpose the full ``DataFrame`` to swap rows and columns:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -758,6 +978,14 @@ "data.T" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When it comes to indexing of ``DataFrame`` objects, however, it is clear that the dictionary-style indexing of columns precludes our ability to simply treat it as a NumPy array.\n", + "In particular, passing a single index to an array accesses a row:" + ] + }, { "cell_type": "code", "execution_count": 26, @@ -780,6 +1008,13 @@ "data.values[0]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and passing a single \"index\" to a ``DataFrame`` accesses a column:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -807,6 +1042,17 @@ "data['area']" ] }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Thus for array-style indexing, we need another convention.\n", + "Here Pandas again uses the ``loc``, ``iloc``, and ``ix`` indexers mentioned earlier.\n", + "Using the ``iloc`` indexer, we can index the underlying array as if it is a simple NumPy array (using the implicit Python-style index), but the ``DataFrame`` index and column labels are maintained in the result:" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -862,6 +1108,13 @@ "data.iloc[:3, :2]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, using the ``loc`` indexer we can index the underlying data in an array-like style but using the explicit index and column names:" + ] + }, { "cell_type": "code", "execution_count": 29, @@ -917,6 +1170,15 @@ "data.loc[:'Illinois', :'pop']" ] }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "The ``ix`` indexer allows a hybrid of these two approaches:" + ] + }, { "cell_type": "code", "execution_count": 30, @@ -972,6 +1234,16 @@ "data.ix[:3, :'pop']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind that for integer indices, the ``ix`` indexer is subject to the same potential sources of confusion as discussed for integer-indexed ``Series`` objects.\n", + "\n", + "Any of the familiar NumPy-style data access patterns can be used within these indexers.\n", + "For example, in the ``loc`` indexer we can combine masking and fancy indexing as in the following:" + ] + }, { "cell_type": "code", "execution_count": 31, @@ -1021,6 +1293,13 @@ "data.loc[data.density > 100, ['pop', 'density']]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any of these indexing conventions may also be used to set or modify values; this is done in the standard way that you might be accustomed to from working with NumPy:" + ] + }, { "cell_type": "code", "execution_count": 32, @@ -1095,6 +1374,23 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To build up your fluency in Pandas data manipulation, I suggest spending some time with a simple ``DataFrame`` and exploring the types of indexing, slicing, masking, and fancy indexing that are allowed by these various indexing approaches." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Additional indexing conventions\n", + "\n", + "There are a couple extra indexing conventions that might seem at odds with the preceding discussion, but nevertheless can be very useful in practice.\n", + "First, while *indexing* refers to columns, *slicing* refers to rows:" + ] + }, { "cell_type": "code", "execution_count": 33, @@ -1147,6 +1443,13 @@ "data['Florida':'Illinois']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Such slices can also refer to rows by number rather than by index:" + ] + }, { "cell_type": "code", "execution_count": 34, @@ -1199,6 +1502,13 @@ "data[1:3]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, direct masking operations are also interpreted row-wise rather than column-wise:" + ] + }, { "cell_type": "code", "execution_count": 35, @@ -1250,9 +1560,27 @@ "source": [ "data[data.density > 100]" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These two conventions are syntactically similar to those on a NumPy array, and while these may not precisely fit the mold of the Pandas conventions, they are nevertheless quite useful in practice." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Introducing Pandas Objects](03.01-Introducing-Pandas-Objects.ipynb) | [Contents](Index.ipynb) | [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.03-Operations-in-Pandas.ipynb b/notebooks_v1/03.03-Operations-in-Pandas.ipynb similarity index 65% rename from code_listings/03.03-Operations-in-Pandas.ipynb rename to notebooks_v1/03.03-Operations-in-Pandas.ipynb index f157f6fce..6206ac790 100644 --- a/code_listings/03.03-Operations-in-Pandas.ipynb +++ b/notebooks_v1/03.03-Operations-in-Pandas.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb) | [Contents](Index.ipynb) | [Handling Missing Data](03.04-Missing-Values.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,28 @@ "# Operating on Data in Pandas" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One of the essential pieces of NumPy is the ability to perform quick element-wise operations, both with basic arithmetic (addition, subtraction, multiplication, etc.) and with more sophisticated operations (trigonometric functions, exponential and logarithmic functions, etc.).\n", + "Pandas inherits much of this functionality from NumPy, and the ufuncs that we introduced in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) are key to this.\n", + "\n", + "Pandas includes a couple useful twists, however: for unary operations like negation and trigonometric functions, these ufuncs will *preserve index and column labels* in the output, and for binary operations such as addition and multiplication, Pandas will automatically *align indices* when passing the objects to the ufunc.\n", + "This means that keeping the context of data and combining data from different sources–both potentially error-prone tasks with raw NumPy arrays–become essentially foolproof ones with Pandas.\n", + "We will additionally see that there are well-defined operations between one-dimensional ``Series`` structures and two-dimensional ``DataFrame`` structures." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ufuncs: Index Preservation\n", + "\n", + "Because Pandas is designed to work with NumPy, any NumPy ufunc will work on Pandas ``Series`` and ``DataFrame`` objects.\n", + "Let's start by defining a simple ``Series`` and ``DataFrame`` on which to demonstrate this:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -112,6 +156,13 @@ "df" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we apply a NumPy ufunc on either of these objects, the result will be another Pandas object *with the indices preserved:*" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -138,6 +189,13 @@ "np.exp(ser)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or, for a slightly more complex calculation:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -201,6 +259,32 @@ "np.sin(df * np.pi / 4)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any of the ufuncs discussed in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) can be used in a similar manner." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## UFuncs: Index Alignment\n", + "\n", + "For binary operations on two ``Series`` or ``DataFrame`` objects, Pandas will align indices in the process of performing the operation.\n", + "This is very convenient when working with incomplete data, as we'll see in some of the examples that follow." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Index alignment in Series\n", + "\n", + "As an example, suppose we are combining two different data sources, and find only the top three US states by *area* and the top three US states by *population*:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -215,6 +299,13 @@ " 'New York': 19651127}, name='population')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what happens when we divide these to compute the population density:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -241,6 +332,13 @@ "population / area" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting array contains the *union* of indices of the two input arrays, which could be determined using standard Python set arithmetic on these indices:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -263,6 +361,14 @@ "area.index | population.index" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any item for which one or the other does not have an entry is marked with ``NaN``, or \"Not a Number,\" which is how Pandas marks missing data (see further discussion of missing data in [Handling Missing Data](03.04-Missing-Values.ipynb)).\n", + "This index matching is implemented this way for any of Python's built-in arithmetic expressions; any missing values are filled in with NaN by default:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -291,6 +397,14 @@ "A + B" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If using NaN values is not the desired behavior, the fill value can be modified using appropriate object methods in place of the operators.\n", + "For example, calling ``A.add(B)`` is equivalent to calling ``A + B``, but allows optional explicit specification of the fill value for any elements in ``A`` or ``B`` that might be missing:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -317,6 +431,15 @@ "A.add(B, fill_value=0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Index alignment in DataFrame\n", + "\n", + "A similar type of alignment takes place for *both* columns and indices when performing operations on ``DataFrame``s:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -488,6 +611,15 @@ "A + B" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that indices are aligned correctly irrespective of their order in the two objects, and indices in the result are sorted.\n", + "As was the case with ``Series``, we can use the associated object's arithmetic method and pass any desired ``fill_value`` to be used in place of missing entries.\n", + "Here we'll fill with the mean of all values in ``A`` (computed by first stacking the rows of ``A``):" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -548,6 +680,34 @@ "A.add(B, fill_value=fill)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following table lists Python operators and their equivalent Pandas object methods:\n", + "\n", + "| Python Operator | Pandas Method(s) |\n", + "|-----------------|---------------------------------------|\n", + "| ``+`` | ``add()`` |\n", + "| ``-`` | ``sub()``, ``subtract()`` |\n", + "| ``*`` | ``mul()``, ``multiply()`` |\n", + "| ``/`` | ``truediv()``, ``div()``, ``divide()``|\n", + "| ``//`` | ``floordiv()`` |\n", + "| ``%`` | ``mod()`` |\n", + "| ``**`` | ``pow()`` |\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ufuncs: Operations Between DataFrame and Series\n", + "\n", + "When performing operations between a ``DataFrame`` and a ``Series``, the index and column alignment is similarly maintained.\n", + "Operations between a ``DataFrame`` and a ``Series`` are similar to operations between a two-dimensional and one-dimensional NumPy array.\n", + "Consider one common operation, where we find the difference of a two-dimensional array and one of its rows:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -597,6 +757,15 @@ "A - A[0]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "According to NumPy's broadcasting rules (see [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb)), subtraction between a two-dimensional array and one of its rows is applied row-wise.\n", + "\n", + "In Pandas, the convention similarly operates row-wise by default:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -661,6 +830,13 @@ "df - df.iloc[0]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you would instead like to operate column-wise, you can use the object methods mentioned earlier, while specifying the ``axis`` keyword:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -724,6 +900,13 @@ "df.subtract(df['R'], axis=0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that these ``DataFrame``/``Series`` operations, like the operations discussed above, will automatically align indices between the two elements:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -811,9 +994,27 @@ "source": [ "df - halfrow" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This preservation and alignment of indices and columns means that operations on data in Pandas will always maintain the data context, which prevents the types of silly errors that might come up when working with heterogeneous and/or misaligned data in raw NumPy arrays." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb) | [Contents](Index.ipynb) | [Handling Missing Data](03.04-Missing-Values.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.04-Missing-Values.ipynb b/notebooks_v1/03.04-Missing-Values.ipynb similarity index 56% rename from code_listings/03.04-Missing-Values.ipynb rename to notebooks_v1/03.04-Missing-Values.ipynb index cbc74da02..180ca09e7 100644 --- a/code_listings/03.04-Missing-Values.ipynb +++ b/notebooks_v1/03.04-Missing-Values.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb) | [Contents](Index.ipynb) | [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,66 @@ "# Handling Missing Data" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The difference between data found in many tutorials and data in the real world is that real-world data is rarely clean and homogeneous.\n", + "In particular, many interesting datasets will have some amount of data missing.\n", + "To make matters even more complicated, different data sources may indicate missing data in different ways.\n", + "\n", + "In this section, we will discuss some general considerations for missing data, discuss how Pandas chooses to represent it, and demonstrate some built-in Pandas tools for handling missing data in Python.\n", + "Here and throughout the book, we'll refer to missing data in general as *null*, *NaN*, or *NA* values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Trade-Offs in Missing Data Conventions\n", + "\n", + "There are a number of schemes that have been developed to indicate the presence of missing data in a table or DataFrame.\n", + "Generally, they revolve around one of two strategies: using a *mask* that globally indicates missing values, or choosing a *sentinel value* that indicates a missing entry.\n", + "\n", + "In the masking approach, the mask might be an entirely separate Boolean array, or it may involve appropriation of one bit in the data representation to locally indicate the null status of a value.\n", + "\n", + "In the sentinel approach, the sentinel value could be some data-specific convention, such as indicating a missing integer value with -9999 or some rare bit pattern, or it could be a more global convention, such as indicating a missing floating-point value with NaN (Not a Number), a special value which is part of the IEEE floating-point specification.\n", + "\n", + "None of these approaches is without trade-offs: use of a separate mask array requires allocation of an additional Boolean array, which adds overhead in both storage and computation. A sentinel value reduces the range of valid values that can be represented, and may require extra (often non-optimized) logic in CPU and GPU arithmetic. Common special values like NaN are not available for all data types.\n", + "\n", + "As in most cases where no universally optimal choice exists, different languages and systems use different conventions.\n", + "For example, the R language uses reserved bit patterns within each data type as sentinel values indicating missing data, while the SciDB system uses an extra byte attached to every cell which indicates a NA state." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Missing Data in Pandas\n", + "\n", + "The way in which Pandas handles missing values is constrained by its reliance on the NumPy package, which does not have a built-in notion of NA values for non-floating-point data types.\n", + "\n", + "Pandas could have followed R's lead in specifying bit patterns for each individual data type to indicate nullness, but this approach turns out to be rather unwieldy.\n", + "While R contains four basic data types, NumPy supports *far* more than this: for example, while R has a single integer type, NumPy supports *fourteen* basic integer types once you account for available precisions, signedness, and endianness of the encoding.\n", + "Reserving a specific bit pattern in all available NumPy types would lead to an unwieldy amount of overhead in special-casing various operations for various types, likely even requiring a new fork of the NumPy package. Further, for the smaller data types (such as 8-bit integers), sacrificing a bit to use as a mask will significantly reduce the range of values it can represent.\n", + "\n", + "NumPy does have support for masked arrays – that is, arrays that have a separate Boolean mask array attached for marking data as \"good\" or \"bad.\"\n", + "Pandas could have derived from this, but the overhead in both storage, computation, and code maintenance makes that an unattractive choice.\n", + "\n", + "With these constraints in mind, Pandas chose to use sentinels for missing data, and further chose to use two already-existing Python null values: the special floating-point ``NaN`` value, and the Python ``None`` object.\n", + "This choice has some side effects, as we will see, but in practice ends up being a good compromise in most cases of interest." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ``None``: Pythonic missing data\n", + "\n", + "The first sentinel value used by Pandas is ``None``, a Python singleton object that is often used for missing data in Python code.\n", + "Because it is a Python object, ``None`` cannot be used in any arbitrary NumPy/Pandas array, but only in arrays with data type ``'object'`` (i.e., arrays of Python objects):" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -42,6 +124,14 @@ "vals1" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This ``dtype=object`` means that the best common type representation NumPy could infer for the contents of the array is that they are Python objects.\n", + "While this kind of object array is useful for some purposes, any operations on the data will be done at the Python level, with much more overhead than the typically fast operations seen for arrays with native types:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -69,6 +159,13 @@ " print()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The use of Python objects in an array also means that if you perform aggregations like ``sum()`` or ``min()`` across an array with a ``None`` value, you will generally get an error:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -93,6 +190,22 @@ "vals1.sum()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This reflects the fact that addition between an integer and ``None`` is undefined." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ``NaN``: Missing numerical data\n", + "\n", + "The other missing data representation, ``NaN`` (acronym for *Not a Number*), is different; it is a special floating-point value recognized by all systems that use the standard IEEE floating-point representation:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -116,6 +229,15 @@ "vals2.dtype" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that NumPy chose a native floating-point type for this array: this means that unlike the object array from before, this array supports fast operations pushed into compiled code.\n", + "You should be aware that ``NaN`` is a bit like a data virus–it infects any other object it touches.\n", + "Regardless of the operation, the result of arithmetic with ``NaN`` will be another ``NaN``:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -160,6 +282,13 @@ "0 * np.nan" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that this means that aggregates over the values are well defined (i.e., they don't result in an error) but not always useful:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -182,6 +311,13 @@ "vals2.sum(), vals2.min(), vals2.max()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "NumPy does provide some special aggregations that will ignore these missing values:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -204,6 +340,22 @@ "np.nansum(vals2), np.nanmin(vals2), np.nanmax(vals2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind that ``NaN`` is specifically a floating-point value; there is no equivalent NaN value for integers, strings, or other types." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### NaN and None in Pandas\n", + "\n", + "``NaN`` and ``None`` both have their place, and Pandas is built to handle the two of them nearly interchangeably, converting between them where appropriate:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -230,6 +382,14 @@ "pd.Series([1, np.nan, 2, None])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For types that don't have an available sentinel value, Pandas automatically type-casts when NA values are present.\n", + "For example, if we set a value in an integer array to ``np.nan``, it will automatically be upcast to a floating-point type to accommodate the NA:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -280,6 +440,54 @@ "x" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that in addition to casting the integer array to floating point, Pandas automatically converts the ``None`` to a ``NaN`` value.\n", + "(Be aware that there is a proposal to add a native integer NA to Pandas in the future; as of this writing, it has not been included).\n", + "\n", + "While this type of magic may feel a bit hackish compared to the more unified approach to NA values in domain-specific languages like R, the Pandas sentinel/casting approach works quite well in practice and in my experience only rarely causes issues.\n", + "\n", + "The following table lists the upcasting conventions in Pandas when NA values are introduced:\n", + "\n", + "|Typeclass | Conversion When Storing NAs | NA Sentinel Value |\n", + "|--------------|-----------------------------|------------------------|\n", + "| ``floating`` | No change | ``np.nan`` |\n", + "| ``object`` | No change | ``None`` or ``np.nan`` |\n", + "| ``integer`` | Cast to ``float64`` | ``np.nan`` |\n", + "| ``boolean`` | Cast to ``object`` | ``None`` or ``np.nan`` |\n", + "\n", + "Keep in mind that in Pandas, string data is always stored with an ``object`` dtype." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Operating on Null Values\n", + "\n", + "As we have seen, Pandas treats ``None`` and ``NaN`` as essentially interchangeable for indicating missing or null values.\n", + "To facilitate this convention, there are several useful methods for detecting, removing, and replacing null values in Pandas data structures.\n", + "They are:\n", + "\n", + "- ``isnull()``: Generate a boolean mask indicating missing values\n", + "- ``notnull()``: Opposite of ``isnull()``\n", + "- ``dropna()``: Return a filtered version of the data\n", + "- ``fillna()``: Return a copy of the data with missing values filled or imputed\n", + "\n", + "We will conclude this section with a brief exploration and demonstration of these routines." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Detecting null values\n", + "Pandas data structures have two useful methods for detecting null data: ``isnull()`` and ``notnull()``.\n", + "Either one will return a Boolean mask over the data. For example:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -317,6 +525,13 @@ "data.isnull()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As mentioned in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb), Boolean masks can be used directly as a ``Series`` or ``DataFrame`` index:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -341,6 +556,24 @@ "data[data.notnull()]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``isnull()`` and ``notnull()`` methods produce similar Boolean results for ``DataFrame``s." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dropping null values\n", + "\n", + "In addition to the masking used before, there are the convenience methods, ``dropna()``\n", + "(which removes NA values) and ``fillna()`` (which fills in NA values). For a ``Series``,\n", + "the result is straightforward:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -365,6 +598,14 @@ "data.dropna()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a ``DataFrame``, there are more options.\n", + "Consider the following ``DataFrame``:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -427,6 +668,16 @@ "df" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We cannot drop single values from a ``DataFrame``; we can only drop full rows or full columns.\n", + "Depending on the application, you might want one or the other, so ``dropna()`` gives a number of options for a ``DataFrame``.\n", + "\n", + "By default, ``dropna()`` will drop all rows in which *any* null value is present:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -472,6 +723,13 @@ "df.dropna()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, you can drop NA values along a different axis; ``axis=1`` drops all columns containing a null value:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -523,6 +781,17 @@ "df.dropna(axis='columns')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this drops some good data as well; you might rather be interested in dropping rows or columns with *all* NA values, or a majority of NA values.\n", + "This can be specified through the ``how`` or ``thresh`` parameters, which allow fine control of the number of nulls to allow through.\n", + "\n", + "The default is ``how='any'``, such that any row or column (depending on the ``axis`` keyword) containing a null value will be dropped.\n", + "You can also specify ``how='all'``, which will only drop rows/columns that are *all* null values:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -646,6 +915,13 @@ "df.dropna(axis='columns', how='all')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For finer-grained control, the ``thresh`` parameter lets you specify a minimum number of non-null values for the row/column to be kept:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -693,6 +969,26 @@ "df.dropna(axis='rows', thresh=3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the first and last row have been dropped, because they contain only two non-null values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Filling null values\n", + "\n", + "Sometimes rather than dropping NA values, you'd rather replace them with a valid value.\n", + "This value might be a single number like zero, or it might be some sort of imputation or interpolation from the good values.\n", + "You could do this in-place using the ``isnull()`` method as a mask, but because it is such a common operation Pandas provides the ``fillna()`` method, which returns a copy of the array with the null values replaced.\n", + "\n", + "Consider the following ``Series``:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -721,6 +1017,13 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can fill NA entries with a single value, such as zero:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -748,6 +1051,13 @@ "data.fillna(0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can specify a forward-fill to propagate the previous value forward:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -776,6 +1086,13 @@ "data.fillna(method='ffill')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or we can specify a back-fill to propagate the next values backward:" + ] + }, { "cell_type": "code", "execution_count": 26, @@ -804,6 +1121,15 @@ "data.fillna(method='bfill')" ] }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "For ``DataFrame``s, the options are similar, but we can also specify an ``axis`` along which the fills take place:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -929,9 +1255,27 @@ "source": [ "df.fillna(method='ffill', axis=1)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that if a previous value is not available during a forward fill, the NA value remains." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb) | [Contents](Index.ipynb) | [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.05-Hierarchical-Indexing.ipynb b/notebooks_v1/03.05-Hierarchical-Indexing.ipynb similarity index 62% rename from code_listings/03.05-Hierarchical-Indexing.ipynb rename to notebooks_v1/03.05-Hierarchical-Indexing.ipynb index e6376f41d..1122989bb 100644 --- a/code_listings/03.05-Hierarchical-Indexing.ipynb +++ b/notebooks_v1/03.05-Hierarchical-Indexing.ipynb @@ -1,5 +1,33 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Handling Missing Data](03.04-Missing-Values.ipynb) | [Contents](Index.ipynb) | [Combining Datasets: Concat and Append](03.06-Concat-And-Append.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,11 +35,30 @@ "# Hierarchical Indexing" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Up to this point we've been focused primarily on one-dimensional and two-dimensional data, stored in Pandas ``Series`` and ``DataFrame`` objects, respectively.\n", + "Often it is useful to go beyond this and store higher-dimensional data–that is, data indexed by more than one or two keys.\n", + "While Pandas does provide ``Panel`` and ``Panel4D`` objects that natively handle three-dimensional and four-dimensional data (see [Aside: Panel Data](#Aside:-Panel-Data)), a far more common pattern in practice is to make use of *hierarchical indexing* (also known as *multi-indexing*) to incorporate multiple index *levels* within a single index.\n", + "In this way, higher-dimensional data can be compactly represented within the familiar one-dimensional ``Series`` and two-dimensional ``DataFrame`` objects.\n", + "\n", + "In this section, we'll explore the direct creation of ``MultiIndex`` objects, considerations when indexing, slicing, and computing statistics across multiply indexed data, and useful routines for converting between simple and hierarchically indexed representations of your data.\n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -19,11 +66,39 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## A Multiply Indexed Series\n", + "\n", + "Let's start by considering how we might represent two-dimensional data within a one-dimensional ``Series``.\n", + "For concreteness, we will consider a series of data where each point has a character and numerical key." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The bad way\n", + "\n", + "Suppose you would like to track data about states from two different years.\n", + "Using the Pandas tools we've already covered, you might be tempted to simply use Python tuples as keys:" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -54,11 +129,23 @@ "pop" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this indexing scheme, you can straightforwardly index or slice the series based on this multiple index:" + ] + }, { "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -80,11 +167,23 @@ "pop[('California', 2010):('Texas', 2000)]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But the convenience ends there. For example, if you need to select all values from 2010, you'll need to do some messy (and potentially slow) munging to make it happen:" + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -105,11 +204,36 @@ "pop[[i for i in pop.index if i[1] == 2010]]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This produces the desired result, but is not as clean (or as efficient for large datasets) as the slicing syntax we've grown to love in Pandas." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The Better Way: Pandas MultiIndex\n", + "Fortunately, Pandas provides a better way.\n", + "Our tuple-based indexing is essentially a rudimentary multi-index, and the Pandas ``MultiIndex`` type gives us the type of operations we wish to have.\n", + "We can create a multi-index from the tuples as follows:" + ] + }, { "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -129,11 +253,25 @@ "index" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that the ``MultiIndex`` contains multiple *levels* of indexing–in this case, the state names and the years, as well as multiple *labels* for each data point which encode these levels.\n", + "\n", + "If we re-index our series with this ``MultiIndex``, we see the hierarchical representation of the data:" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -158,11 +296,34 @@ "pop" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here the first two columns of the ``Series`` representation show the multiple index values, while the third column shows the data.\n", + "Notice that some entries are missing in the first column: in this multi-index representation, any blank entry indicates the same value as the line above it." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now to access all data for which the second index is 2010, we can simply use the Pandas slicing notation:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -183,11 +344,38 @@ "pop[:, 2010]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result is a singly indexed array with just the keys we're interested in.\n", + "This syntax is much more convenient (and the operation is much more efficient!) than the home-spun tuple-based multi-indexing solution that we started with.\n", + "We'll now further discuss this sort of indexing operation on hieararchically indexed data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### MultiIndex as extra dimension\n", + "\n", + "You might notice something else here: we could easily have stored the same data using a simple ``DataFrame`` with index and column labels.\n", + "In fact, Pandas is built with this equivalence in mind. The ``unstack()`` method will quickly convert a multiply indexed ``Series`` into a conventionally indexed ``DataFrame``:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -239,11 +427,23 @@ "pop_df" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Naturally, the ``stack()`` method provides the opposite operation:" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -267,11 +467,25 @@ "pop_df.stack()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Seeing this, you might wonder why would we would bother with hierarchical indexing at all.\n", + "The reason is simple: just as we were able to use multi-indexing to represent two-dimensional data within a one-dimensional ``Series``, we can also use it to represent data of three or more dimensions in a ``Series`` or ``DataFrame``.\n", + "Each extra level in a multi-index represents an extra dimension of data; taking advantage of this property gives us much more flexibility in the types of data we can represent. Concretely, we might want to add another column of demographic data for each state at each year (say, population under 18) ; with a ``MultiIndex`` this is as easy as adding another column to the ``DataFrame``:" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -348,11 +562,24 @@ "pop_df" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In addition, all the ufuncs and other functionality discussed in [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb) work with hierarchical indices as well.\n", + "Here we compute the fraction of people under 18 by year, given the above data:" + ] + }, { "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -404,11 +631,35 @@ "f_u18.unstack()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This allows us to easily and quickly manipulate and explore even high-dimensional data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Methods of MultiIndex Creation\n", + "\n", + "The most straightforward way to construct a multiply indexed ``Series`` or ``DataFrame`` is to simply pass a list of two or more index arrays to the constructor. For example:" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -471,11 +722,25 @@ "df" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The work of creating the ``MultiIndex`` is done in the background.\n", + "\n", + "Similarly, if you pass a dictionary with appropriate tuples as keys, Pandas will automatically recognize this and use a ``MultiIndex`` by default:" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -505,11 +770,36 @@ "pd.Series(data)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Nevertheless, it is sometimes useful to explicitly create a ``MultiIndex``; we'll see a couple of these methods here." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Explicit MultiIndex constructors\n", + "\n", + "For more flexibility in how the index is constructed, you can instead use the class method constructors available in the ``pd.MultiIndex``.\n", + "For example, as we did before, you can construct the ``MultiIndex`` from a simple list of arrays giving the index values within each level:" + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -528,11 +818,23 @@ "pd.MultiIndex.from_arrays([['a', 'a', 'b', 'b'], [1, 2, 1, 2]])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "You can construct it from a list of tuples giving the multiple index values of each point:" + ] + }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -551,11 +853,23 @@ "pd.MultiIndex.from_tuples([('a', 1), ('a', 2), ('b', 1), ('b', 2)])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "You can even construct it from a Cartesian product of single indices:" + ] + }, { "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -574,11 +888,23 @@ "pd.MultiIndex.from_product([['a', 'b'], [1, 2]])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Similarly, you can construct the ``MultiIndex`` directly using its internal encoding by passing ``levels`` (a list of lists containing available index values for each level) and ``labels`` (a list of lists that reference these labels):" + ] + }, { "cell_type": "code", "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -598,11 +924,36 @@ " labels=[[0, 0, 1, 1], [0, 1, 0, 1]])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Any of these objects can be passed as the ``index`` argument when creating a ``Series`` or ``Dataframe``, or be passed to the ``reindex`` method of an existing ``Series`` or ``DataFrame``." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### MultiIndex level names\n", + "\n", + "Sometimes it is convenient to name the levels of the ``MultiIndex``.\n", + "This can be accomplished by passing the ``names`` argument to any of the above ``MultiIndex`` constructors, or by setting the ``names`` attribute of the index after the fact:" + ] + }, { "cell_type": "code", "execution_count": 18, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -628,11 +979,36 @@ "pop" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With more involved datasets, this can be a useful way to keep track of the meaning of various index values." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### MultiIndex for columns\n", + "\n", + "In a ``DataFrame``, the rows and columns are completely symmetric, and just as the rows can have multiple levels of indices, the columns can have multiple levels as well.\n", + "Consider the following, which is a mock-up of some (somewhat realistic) medical data:" + ] + }, { "cell_type": "code", "execution_count": 19, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -739,16 +1115,30 @@ "data[:, ::2] *= 10\n", "data += 37\n", "\n", - "# create the dataframe\n", + "# create the DataFrame\n", "health_data = pd.DataFrame(data, index=index, columns=columns)\n", "health_data" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here we see where the multi-indexing for both rows and columns can come in *very* handy.\n", + "This is fundamentally four-dimensional data, where the dimensions are the subject, the measurement type, the year, and the visit number.\n", + "With this in place we can, for example, index the top-level column by the person's name and get a full ``DataFrame`` containing just that person's information:" + ] + }, { "cell_type": "code", "execution_count": 20, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -815,11 +1205,48 @@ "health_data['Guido']" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For complicated records containing multiple labeled measurements across multiple times for many subjects (people, countries, cities, etc.) use of hierarchical rows and columns can be extremely convenient!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Indexing and Slicing a MultiIndex\n", + "\n", + "Indexing and slicing on a ``MultiIndex`` is designed to be intuitive, and it helps if you think about the indices as added dimensions.\n", + "We'll first look at indexing multiply indexed ``Series``, and then multiply-indexed ``DataFrame``s." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Multiply indexed Series\n", + "\n", + "Consider the multiply indexed ``Series`` of state populations we saw earlier:" + ] + }, { "cell_type": "code", "execution_count": 21, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -844,11 +1271,23 @@ "pop" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can access single elements by indexing with multiple terms:" + ] + }, { "cell_type": "code", "execution_count": 22, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -866,11 +1305,24 @@ "pop['California', 2000]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The ``MultiIndex`` also supports *partial indexing*, or indexing just one of the levels in the index.\n", + "The result is another ``Series``, with the lower-level indices maintained:" + ] + }, { "cell_type": "code", "execution_count": 23, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -891,11 +1343,23 @@ "pop['California']" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Partial slicing is available as well, as long as the ``MultiIndex`` is sorted (see discussion in [Sorted and Unsorted Indices](#Sorted-and-unsorted-indices)):" + ] + }, { "cell_type": "code", "execution_count": 24, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -918,11 +1382,23 @@ "pop.loc['California':'New York']" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With sorted indices, partial indexing can be performed on lower levels by passing an empty slice in the first index:" + ] + }, { "cell_type": "code", "execution_count": 25, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -944,11 +1420,23 @@ "pop[:, 2000]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Other types of indexing and selection (discussed in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb)) work as well; for example, selection based on Boolean masks:" + ] + }, { "cell_type": "code", "execution_count": 26, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -970,11 +1458,23 @@ "pop[pop > 22000000]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Selection based on fancy indexing also works:" + ] + }, { "cell_type": "code", "execution_count": 27, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -997,11 +1497,26 @@ "pop[['California', 'Texas']]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Multiply indexed DataFrames\n", + "\n", + "A multiply indexed ``DataFrame`` behaves in a similar manner.\n", + "Consider our toy medical ``DataFrame`` from before:" + ] + }, { "cell_type": "code", "execution_count": 28, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1100,11 +1615,24 @@ "health_data" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Remember that columns are primary in a ``DataFrame``, and the syntax used for multiply indexed ``Series`` applies to the columns.\n", + "For example, we can recover Guido's heart rate data with a simple operation:" + ] + }, { "cell_type": "code", "execution_count": 29, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1127,11 +1655,23 @@ "health_data['Guido', 'HR']" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Also, as with the single-index case, we can use the ``loc``, ``iloc``, and ``ix`` indexers introduced in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb). For example:" + ] + }, { "cell_type": "code", "execution_count": 30, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1191,11 +1731,23 @@ "health_data.iloc[:2, :2]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "These indexers provide an array-like view of the underlying two-dimensional data, but each individual index in ``loc`` or ``iloc`` can be passed a tuple of multiple indices. For example:" + ] + }, { "cell_type": "code", "execution_count": 31, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1218,11 +1770,23 @@ "health_data.loc[:, ('Bob', 'HR')]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Working with slices within these index tuples is not especially convenient; trying to create a slice within a tuple will lead to a syntax error:" + ] + }, { "cell_type": "code", "execution_count": 32, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1238,11 +1802,24 @@ "health_data.loc[(:, 1), (:, 'HR')]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "You could get around this by building the desired slice explicitly using Python's built-in ``slice()`` function, but a better way in this context is to use an ``IndexSlice`` object, which Pandas provides for precisely this situation.\n", + "For example:" + ] + }, { "cell_type": "code", "execution_count": 33, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1310,11 +1887,53 @@ "health_data.loc[idx[:, 1], idx[:, 'HR']]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "There are so many ways to interact with data in multiply indexed ``Series`` and ``DataFrame``s, and as with many tools in this book the best way to become familiar with them is to try them out!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Rearranging Multi-Indices\n", + "\n", + "One of the keys to working with multiply indexed data is knowing how to effectively transform the data.\n", + "There are a number of operations that will preserve all the information in the dataset, but rearrange it for the purposes of various computations.\n", + "We saw a brief example of this in the ``stack()`` and ``unstack()`` methods, but there are many more ways to finely control the rearrangement of data between hierarchical indices and columns, and we'll explore them here." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Sorted and unsorted indices\n", + "\n", + "Earlier, we briefly mentioned a caveat, but we should emphasize it more here.\n", + "*Many of the ``MultiIndex`` slicing operations will fail if the index is not sorted.*\n", + "Let's take a look at this here.\n", + "\n", + "We'll start by creating some simple multiply indexed data where the indices are *not lexographically sorted*:" + ] + }, { "cell_type": "code", "execution_count": 34, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1342,11 +1961,23 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "If we try to take a partial slice of this index, it will result in an error:" + ] + }, { "cell_type": "code", "execution_count": 35, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1366,11 +1997,26 @@ " print(e)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Although it is not entirely clear from the error message, this is the result of the MultiIndex not being sorted.\n", + "For various reasons, partial slices and other similar operations require the levels in the ``MultiIndex`` to be in sorted (i.e., lexographical) order.\n", + "Pandas provides a number of convenience routines to perform this type of sorting; examples are the ``sort_index()`` and ``sortlevel()`` methods of the ``DataFrame``.\n", + "We'll use the simplest, ``sort_index()``, here:" + ] + }, { "cell_type": "code", "execution_count": 36, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1396,11 +2042,23 @@ "data" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With the index sorted in this way, partial slicing will work as expected:" + ] + }, { "cell_type": "code", "execution_count": 37, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1423,11 +2081,25 @@ "data['a':'b']" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Stacking and unstacking indices\n", + "\n", + "As we saw briefly before, it is possible to convert a dataset from a stacked multi-index to a simple two-dimensional representation, optionally specifying the level to use:" + ] + }, { "cell_type": "code", "execution_count": 38, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1486,7 +2158,9 @@ "cell_type": "code", "execution_count": 39, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1543,11 +2217,23 @@ "pop.unstack(level=1)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The opposite of ``unstack()`` is ``stack()``, which here can be used to recover the original series:" + ] + }, { "cell_type": "code", "execution_count": 40, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1572,11 +2258,27 @@ "pop.unstack().stack()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Index setting and resetting\n", + "\n", + "Another way to rearrange hierarchical data is to turn the index labels into columns; this can be accomplished with the ``reset_index`` method.\n", + "Calling this on the population dictionary will result in a ``DataFrame`` with a *state* and *year* column holding the information that was formerly in the index.\n", + "For clarity, we can optionally specify the name of the data for the column representation:" + ] + }, { "cell_type": "code", "execution_count": 41, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1653,11 +2355,24 @@ "pop_flat" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Often when working with data in the real world, the raw input data looks like this and it's useful to build a ``MultiIndex`` from the column values.\n", + "This can be done with the ``set_index`` method of the ``DataFrame``, which returns a multiply indexed ``DataFrame``:" + ] + }, { "cell_type": "code", "execution_count": 42, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1729,11 +2444,38 @@ "pop_flat.set_index(['state', 'year'])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In practice, I find this type of reindexing to be one of the more useful patterns when encountering real-world datasets." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Data Aggregations on Multi-Indices\n", + "\n", + "We've previously seen that Pandas has built-in data aggregation methods, such as ``mean()``, ``sum()``, and ``max()``.\n", + "For hierarchically indexed data, these can be passed a ``level`` parameter that controls which subset of the data the aggregate is computed on.\n", + "\n", + "For example, let's return to our health data:" + ] + }, { "cell_type": "code", "execution_count": 43, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1832,11 +2574,23 @@ "health_data" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Perhaps we'd like to average-out the measurements in the two visits each year. We can do this by naming the index level we'd like to explore, in this case the year:" + ] + }, { "cell_type": "code", "execution_count": 44, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1911,11 +2665,23 @@ "data_mean" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By further making use of the ``axis`` keyword, we can take the mean among levels on the columns as well:" + ] + }, { "cell_type": "code", "execution_count": 45, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1965,9 +2731,56 @@ "source": [ "data_mean.mean(axis=1, level='type')" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Thus in two lines, we've been able to find the average heart rate and temperature measured among all subjects in all visits each year.\n", + "This syntax is actually a short cut to the ``GroupBy`` functionality, which we will discuss in [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb).\n", + "While this is a toy example, many real-world datasets have similar hierarchical structure." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Aside: Panel Data\n", + "\n", + "Pandas has a few other fundamental data structures that we have not yet discussed, namely the ``pd.Panel`` and ``pd.Panel4D`` objects.\n", + "These can be thought of, respectively, as three-dimensional and four-dimensional generalizations of the (one-dimensional) ``Series`` and (two-dimensional) ``DataFrame`` structures.\n", + "Once you are familiar with indexing and manipulation of data in a ``Series`` and ``DataFrame``, ``Panel`` and ``Panel4D`` are relatively straightforward to use.\n", + "In particular, the ``ix``, ``loc``, and ``iloc`` indexers discussed in [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb) extend readily to these higher-dimensional structures.\n", + "\n", + "We won't cover these panel structures further in this text, as I've found in the majority of cases that multi-indexing is a more useful and conceptually simpler representation for higher-dimensional data.\n", + "Additionally, panel data is fundamentally a dense data representation, while multi-indexing is fundamentally a sparse data representation.\n", + "As the number of dimensions increases, the dense representation can become very inefficient for the majority of real-world datasets.\n", + "For the occasional specialized application, however, these structures can be useful.\n", + "If you'd like to read more about the ``Panel`` and ``Panel4D`` structures, see the references listed in [Further Resources](03.13-Further-Resources.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Handling Missing Data](03.04-Missing-Values.ipynb) | [Contents](Index.ipynb) | [Combining Datasets: Concat and Append](03.06-Concat-And-Append.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.06-Concat-And-Append.ipynb b/notebooks_v1/03.06-Concat-And-Append.ipynb similarity index 76% rename from code_listings/03.06-Concat-And-Append.ipynb rename to notebooks_v1/03.06-Concat-And-Append.ipynb index 5756b7536..7566c851c 100644 --- a/code_listings/03.06-Concat-And-Append.ipynb +++ b/notebooks_v1/03.06-Concat-And-Append.ipynb @@ -4,7 +4,42 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Combining Datasets: Concat & Append" + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb) | [Contents](Index.ipynb) | [Combining Datasets: Merge and Join](03.07-Merge-and-Join.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Combining Datasets: Concat and Append" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some of the most interesting studies of data come from combining different data sources.\n", + "These operations can involve anything from very straightforward concatenation of two different datasets, to more complicated database-style joins and merges that correctly handle any overlaps between the datasets.\n", + "``Series`` and ``DataFrame``s are built with this type of operation in mind, and Pandas includes functions and methods that make this sort of data wrangling fast and straightforward.\n", + "\n", + "Here we'll take a look at simple concatenation of ``Series`` and ``DataFrame``s with the ``pd.concat`` function; later we'll dive into more sophisticated in-memory merges and joins implemented in Pandas.\n", + "\n", + "We begin with the standard imports:" ] }, { @@ -19,6 +54,13 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For convenience, we'll define this function which creates a ``DataFrame`` of a particular form that will be useful below:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -76,7 +118,7 @@ ], "source": [ "def make_df(cols, ind):\n", - " \"\"\"Quickly make a dataframe\"\"\"\n", + " \"\"\"Quickly make a DataFrame\"\"\"\n", " data = {c: [str(c) + str(i) for i in ind]\n", " for c in cols}\n", " return pd.DataFrame(data, ind)\n", @@ -85,6 +127,13 @@ "make_df('ABC', range(3))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, we'll create a quick class that allows us to display multiple ``DataFrame``s side by side. The code makes use of the special ``_repr_html_`` method, which IPython uses to implement its rich object display:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -111,6 +160,23 @@ " " ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The use of this will become clearer as we continue our discussion in the following section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Recall: Concatenation of NumPy Arrays\n", + "\n", + "Concatenation of ``Series`` and ``DataFrame`` objects is very similar to concatenation of Numpy arrays, which can be done via the ``np.concatenate`` function as discussed in [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb).\n", + "Recall that with it, you can combine the contents of two or more arrays into a single array:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -136,6 +202,14 @@ "np.concatenate([x, y, z])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first argument is a list or tuple of arrays to concatenate.\n", + "Additionally, it takes an ``axis`` keyword that allows you to specify the axis along which the result will be concatenated:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -161,6 +235,29 @@ "np.concatenate([x, x], axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simple Concatenation with ``pd.concat``" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pandas has a function, ``pd.concat()``, which has a similar syntax to ``np.concatenate`` but contains a number of options that we'll discuss momentarily:\n", + "\n", + "```python\n", + "# Signature in Pandas v0.18\n", + "pd.concat(objs, axis=0, join='outer', join_axes=None, ignore_index=False,\n", + " keys=None, levels=None, names=None, verify_integrity=False,\n", + " copy=True)\n", + "```\n", + "\n", + "``pd.concat()`` can be used for a simple concatenation of ``Series`` or ``DataFrame`` objects, just as ``np.concatenate()`` can be used for simple concatenations of arrays:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -191,6 +288,13 @@ "pd.concat([ser1, ser2])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It also works to concatenate higher-dimensional objects, such as ``DataFrame``s:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -317,6 +421,15 @@ "display('df1', 'df2', 'pd.concat([df1, df2])')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By default, the concatenation takes place row-wise within the ``DataFrame`` (i.e., ``axis=0``).\n", + "Like ``np.concatenate``, ``pd.concat`` allows specification of an axis along which concatenation will take place.\n", + "Consider the following example:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -437,6 +550,23 @@ "display('df3', 'df4', \"pd.concat([df3, df4], axis='col')\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We could have equivalently specified ``axis=1``; here we've used the more intuitive ``axis='col'``. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Duplicate indices\n", + "\n", + "One important difference between ``np.concatenate`` and ``pd.concat`` is that Pandas concatenation *preserves indices*, even if the result will have duplicate indices!\n", + "Consider this simple example:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -564,6 +694,26 @@ "display('x', 'y', 'pd.concat([x, y])')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the repeated indices in the result.\n", + "While this is valid within ``DataFrame``s, the outcome is often undesirable.\n", + "``pd.concat()`` gives us a few ways to handle it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Catching the repeats as an error\n", + "\n", + "If you'd like to simply verify that the indices in the result of ``pd.concat()`` do not overlap, you can specify the ``verify_integrity`` flag.\n", + "With this set to True, the concatenation will raise an exception if there are duplicate indices.\n", + "Here is an example, where for clarity we'll catch and print the error message:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -586,6 +736,17 @@ " print(\"ValueError:\", e)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Ignoring the index\n", + "\n", + "Sometimes the index itself does not matter, and you would prefer it to simply be ignored.\n", + "This option can be specified using the ``ignore_index`` flag.\n", + "With this set to true, the concatenation will create a new integer index for the resulting ``Series``:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -710,6 +871,15 @@ "display('x', 'y', 'pd.concat([x, y], ignore_index=True)')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Adding MultiIndex keys\n", + "\n", + "Another option is to use the ``keys`` option to specify a label for the data sources; the result will be a hierarchically indexed series containing the data:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -837,6 +1007,24 @@ "display('x', 'y', \"pd.concat([x, y], keys=['x', 'y'])\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a multiply indexed ``DataFrame``, and we can use the tools discussed in [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb) to transform this data into the representation we're interested in." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Concatenation with joins\n", + "\n", + "In the simple examples we just looked at, we were mainly concatenating ``DataFrame``s with shared column names.\n", + "In practice, data from different sources might have different sets of column names, and ``pd.concat`` offers several options in this case.\n", + "Consider the concatenation of the following two ``DataFrame``s, which have some (but not all!) columns in common:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -979,6 +1167,15 @@ "display('df5', 'df6', 'pd.concat([df5, df6])')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By default, the entries for which no data is available are filled with NA values.\n", + "To change this, we can specify one of several options for the ``join`` and ``join_axes`` parameters of the concatenate function.\n", + "By default, the join is a union of the input columns (``join='outer'``), but we can change this to an intersection of the columns using ``join='inner'``:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -1110,6 +1307,14 @@ " \"pd.concat([df5, df6], join='inner')\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another option is to directly specify the index of the remaininig colums using the ``join_axes`` argument, which takes a list of index objects.\n", + "Here we'll specify that the returned columns should be the same as those of the first input:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -1246,6 +1451,23 @@ " \"pd.concat([df5, df6], join_axes=[df5.columns])\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The combination of options of the ``pd.concat`` function allows a wide range of possible behaviors when joining two datasets; keep these in mind as you use these tools for your own data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The ``append()`` method\n", + "\n", + "Because direct array concatenation is so common, ``Series`` and ``DataFrame`` objects have an ``append`` method that can accomplish the same thing in fewer keystrokes.\n", + "For example, rather than calling ``pd.concat([df1, df2])``, you can simply call ``df1.append(df2)``:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -1369,9 +1591,32 @@ "source": [ "display('df1', 'df2', 'df1.append(df2)')" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind that unlike the ``append()`` and ``extend()`` methods of Python lists, the ``append()`` method in Pandas does not modify the original object–instead it creates a new object with the combined data.\n", + "It also is not a very efficient method, because it involves creation of a new index *and* data buffer.\n", + "Thus, if you plan to do multiple ``append`` operations, it is generally better to build a list of ``DataFrame``s and pass them all at once to the ``concat()`` function.\n", + "\n", + "In the next section, we'll look at another more powerful approach to combining data from multiple sources, the database-style merges/joins implemented in ``pd.merge``.\n", + "For more information on ``concat()``, ``append()``, and related functionality, see the [\"Merge, Join, and Concatenate\" section](http://pandas.pydata.org/pandas-docs/stable/merging.html) of the Pandas documentation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb) | [Contents](Index.ipynb) | [Combining Datasets: Merge and Join](03.07-Merge-and-Join.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.07-Merge-and-Join.ipynb b/notebooks_v1/03.07-Merge-and-Join.ipynb similarity index 82% rename from code_listings/03.07-Merge-and-Join.ipynb rename to notebooks_v1/03.07-Merge-and-Join.ipynb index 08433401a..c46383e57 100644 --- a/code_listings/03.07-Merge-and-Join.ipynb +++ b/notebooks_v1/03.07-Merge-and-Join.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Combining Datasets: Concat and Append](03.06-Concat-And-Append.ipynb) | [Contents](Index.ipynb) | [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,17 @@ "# Combining Datasets: Merge and Join" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One essential feature offered by Pandas is its high-performance, in-memory join and merge operations.\n", + "If you have ever worked with databases, you should be familiar with this type of data interaction.\n", + "The main interface for this is the ``pd.merge`` function, and we'll see few examples of how this can work in practice.\n", + "\n", + "For convenience, we will start by redefining the ``display()`` functionality from the previous section:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -35,6 +68,41 @@ " for a in self.args)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Relational Algebra\n", + "\n", + "The behavior implemented in ``pd.merge()`` is a subset of what is known as *relational algebra*, which is a formal set of rules for manipulating relational data, and forms the conceptual foundation of operations available in most databases.\n", + "The strength of the relational algebra approach is that it proposes several primitive operations, which become the building blocks of more complicated operations on any dataset.\n", + "With this lexicon of fundamental operations implemented efficiently in a database or other program, a wide range of fairly complicated composite operations can be performed.\n", + "\n", + "Pandas implements several of these fundamental building-blocks in the ``pd.merge()`` function and the related ``join()`` method of ``Series`` and ``Dataframe``s.\n", + "As we will see, these let you efficiently link data from different sources." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Categories of Joins\n", + "\n", + "The ``pd.merge()`` function implements a number of types of joins: the *one-to-one*, *many-to-one*, and *many-to-many* joins.\n", + "All three types of joins are accessed via an identical call to the ``pd.merge()`` interface; the type of join performed depends on the form of the input data.\n", + "Here we will show simple examples of the three types of merges, and discuss detailed options further below." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### One-to-one joins\n", + "\n", + "Perhaps the simplest type of merge expresion is the one-to-one join, which is in many ways very similar to the column-wise concatenation seen in [Combining Datasets: Concat & Append](03.06-Concat-And-Append.ipynb).\n", + "As a concrete example, consider the following two ``DataFrames`` which contain information on several employees in a company:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -145,6 +213,13 @@ "display('df1', 'df2')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To combine this information into a single ``DataFrame``, we can use the ``pd.merge()`` function:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -212,6 +287,32 @@ "df3" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``pd.merge()`` function recognizes that each ``DataFrame`` has an \"employee\" column, and automatically joins using this column as a key.\n", + "The result of the merge is a new ``DataFrame`` that combines the information from the two inputs.\n", + "Notice that the order of entries in each column is not necessarily maintained: in this case, the order of the \"employee\" column differs between ``df1`` and ``df2``, and the ``pd.merge()`` function correctly accounts for this.\n", + "Additionally, keep in mind that the merge in general discards the index, except in the special case of merges by index (see the ``left_index`` and ``right_index`` keywords, discussed momentarily)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Many-to-one joins" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Many-to-one joins are joins in which one of the two key columns contains duplicate entries.\n", + "For the many-to-one case, the resulting ``DataFrame`` will preserve those duplicate entries as appropriate.\n", + "Consider the following example of a many-to-one join:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -371,6 +472,31 @@ "display('df3', 'df4', 'pd.merge(df3, df4)')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting ``DataFrame`` has an aditional column with the \"supervisor\" information, where the information is repeated in one or more locations as required by the inputs." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Many-to-many joins" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Many-to-many joins are a bit confusing conceptually, but are nevertheless well defined.\n", + "If the key column in both the left and right array contains duplicates, then the result is a many-to-many merge.\n", + "This will be perhaps most clear with a concrete example.\n", + "Consider the following, where we have a ``DataFrame`` showing one or more skills associated with a particular group.\n", + "By performing a many-to-many join, we can recover the skills associated with any individual person:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -568,6 +694,39 @@ "display('df1', 'df5', \"pd.merge(df1, df5)\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These three types of joins can be used with other Pandas tools to implement a wide array of functionality.\n", + "But in practice, datasets are rarely as clean as the one we're working with here.\n", + "In the following section we'll consider some of the options provided by ``pd.merge()`` that enable you to tune how the join operations work." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Specification of the Merge Key" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We've already seen the default behavior of ``pd.merge()``: it looks for one or more matching column names between the two inputs, and uses this as the key.\n", + "However, often the column names will not match so nicely, and ``pd.merge()`` provides a variety of options for handling this." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The ``on`` keyword\n", + "\n", + "Most simply, you can explicitly specify the name of the key column using the ``on`` keyword, which takes a column name or a list of column names:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -721,6 +880,23 @@ "display('df1', 'df2', \"pd.merge(df1, df2, on='employee')\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This option works only if both the left and right ``DataFrame``s have the specified column name." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The ``left_on`` and ``right_on`` keywords\n", + "\n", + "At times you may wish to merge two datasets with different column names; for example, we may have a dataset in which the employee name is labeled as \"name\" rather than \"employee\".\n", + "In this case, we can use the ``left_on`` and ``right_on`` keywords to specify the two column names:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -881,6 +1057,13 @@ "display('df1', 'df3', 'pd.merge(df1, df3, left_on=\"employee\", right_on=\"name\")')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result has a redundant column that we can drop if desired–for example, by using the ``drop()`` method of ``DataFrame``s:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -947,6 +1130,16 @@ "pd.merge(df1, df3, left_on=\"employee\", right_on=\"name\").drop('name', axis=1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The ``left_index`` and ``right_index`` keywords\n", + "\n", + "Sometimes, rather than merging on a column, you would instead like to merge on an index.\n", + "For example, your data might look like this:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -1055,6 +1248,13 @@ "display('df1a', 'df2a')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can use the index as the key for merging by specifying the ``left_index`` and/or ``right_index`` flags in ``pd.merge()``:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -1206,7 +1406,15 @@ } ], "source": [ - "display('df1a', 'df2a', \"pd.merge(df1a, df2a, left_index=True, right_index=True)\")" + "display('df1a', 'df2a',\n", + " \"pd.merge(df1a, df2a, left_index=True, right_index=True)\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For convenience, ``DataFrame``s implement the ``join()`` method, which performs a merge that defaults to joining on indices:" ] }, { @@ -1363,6 +1571,13 @@ "display('df1a', 'df2a', 'df1a.join(df2a)')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you'd like to mix indices and columns, you can combine ``left_index`` with ``right_on`` or ``left_on`` with ``right_index`` to get the desired behavior:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -1516,6 +1731,29 @@ "display('df1a', 'df3', \"pd.merge(df1a, df3, left_index=True, right_on='name')\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these options also work with multiple indices and/or multiple columns; the interface for this behavior is very intuitive.\n", + "For more information on this, see the [\"Merge, Join, and Concatenate\" section](http://pandas.pydata.org/pandas-docs/stable/merging.html) of the Pandas documentation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Specifying Set Arithmetic for Joins" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In all the preceding examples we have glossed over one important consideration in performing a join: the type of set arithmetic used in the join.\n", + "This comes up when a value appears in one key column but not the other. Consider this example:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -1636,6 +1874,15 @@ "display('df6', 'df7', 'pd.merge(df6, df7)')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we have merged two datasets that have only a single \"name\" entry in common: Mary.\n", + "By default, the result contains the *intersection* of the two sets of inputs; this is what is known as an *inner join*.\n", + "We can specify this explicitly using the ``how`` keyword, which defaults to ``\"inner\"``:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -1681,6 +1928,14 @@ "pd.merge(df6, df7, how='inner')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Other options for the ``how`` keyword are ``'outer'``, ``'left'``, and ``'right'``.\n", + "An *outer join* returns a join over the union of the input columns, and fills in all missing values with NAs:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -1816,6 +2071,14 @@ "display('df6', 'df7', \"pd.merge(df6, df7, how='outer')\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *left join* and *right join* return joins over the left entries and right entries, respectively.\n", + "For example:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -1944,6 +2207,31 @@ "display('df6', 'df7', \"pd.merge(df6, df7, how='left')\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output rows now correspond to the entries in the left input. Using\n", + "``how='right'`` works in a similar manner.\n", + "\n", + "All of these options can be applied straightforwardly to any of the preceding join types." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Overlapping Column Names: The ``suffixes`` Keyword" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, you may end up in a case where your two input ``DataFrame``s have conflicting column names.\n", + "Consider this example:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -2101,6 +2389,14 @@ "display('df8', 'df9', 'pd.merge(df8, df9, on=\"name\")')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because the output would have two conflicting column names, the merge function automatically appends a suffix ``_x`` or ``_y`` to make the output columns unique.\n", + "If these defaults are inappropriate, it is possible to specify a custom suffix using the ``suffixes`` keyword:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -2254,6 +2550,32 @@ "display('df8', 'df9', 'pd.merge(df8, df9, on=\"name\", suffixes=[\"_L\", \"_R\"])')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These suffixes work in any of the possible join patterns, and work also if there are multiple overlapping columns." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on these patterns, see [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb) where we dive a bit deeper into relational algebra.\n", + "Also see the [Pandas \"Merge, Join and Concatenate\" documentation](http://pandas.pydata.org/pandas-docs/stable/merging.html) for further discussion of these topics." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: US States Data\n", + "\n", + "Merge and join operations come up most often when combining data from different sources.\n", + "Here we will consider an example of some data about US states and their populations.\n", + "The data files can be found at http://github.com/jakevdp/data-USstates/:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -2268,6 +2590,13 @@ "# !curl -O https://raw.githubusercontent.com/jakevdp/data-USstates/master/state-abbrevs.csv" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's take a look at the three datasets, using the Pandas ``read_csv()`` function:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -2443,13 +2772,25 @@ } ], "source": [ - "pop = pd.read_csv('state-population.csv')\n", - "areas = pd.read_csv('state-areas.csv')\n", - "abbrevs = pd.read_csv('state-abbrevs.csv')\n", + "pop = pd.read_csv('data/state-population.csv')\n", + "areas = pd.read_csv('data/state-areas.csv')\n", + "abbrevs = pd.read_csv('data/state-abbrevs.csv')\n", "\n", "display('pop.head()', 'areas.head()', 'abbrevs.head()')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Given this information, say we want to compute a relatively straightforward result: rank US states and territories by their 2010 population density.\n", + "We clearly have the data here to find this result, but we'll have to combine the datasets to find the result.\n", + "\n", + "We'll start with a many-to-one merge that will give us the full state name within the population ``DataFrame``.\n", + "We want to merge based on the ``state/region`` column of ``pop``, and the ``abbreviation`` column of ``abbrevs``.\n", + "We'll use ``how='outer'`` to make sure no data is thrown away due to mismatched labels." + ] + }, { "cell_type": "code", "execution_count": 21, @@ -2538,6 +2879,13 @@ "merged.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's double-check whether there were any mismatches here, which we can do by looking for rows with nulls:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -2565,6 +2913,13 @@ "merged.isnull().any()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some of the ``population`` info is null; let's figure out which these are!" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -2650,6 +3005,16 @@ "merged[merged['population'].isnull()].head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It appears that all the null population values are from Puerto Rico prior to the year 2000; this is likely due to this data not being available from the original source.\n", + "\n", + "More importantly, we see also that some of the new ``state`` entries are also null, which means that there was no corresponding entry in the ``abbrevs`` key!\n", + "Let's figure out which regions lack this match:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -2672,6 +3037,14 @@ "merged.loc[merged['state'].isnull(), 'state/region'].unique()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can quickly infer the issue: our population data includes entries for Puerto Rico (PR) and the United States as a whole (USA), while these entries do not appear in the state abbreviation key.\n", + "We can fix these quickly by filling in appropriate entries:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -2701,6 +3074,16 @@ "merged.isnull().any()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "No more nulls in the ``state`` column: we're all set!\n", + "\n", + "Now we can merge the result with the area data using a similar procedure.\n", + "Examining our results, we will want to join on the ``state`` column in both:" + ] + }, { "cell_type": "code", "execution_count": 26, @@ -2793,6 +3176,13 @@ "final.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, let's check for nulls to see if there were any mismatches:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -2821,6 +3211,13 @@ "final.isnull().any()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are nulls in the ``area`` column; we can take a look to see which regions were ignored here:" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -2843,6 +3240,14 @@ "final['state'][final['area (sq. mi)'].isnull()].unique()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that our ``areas`` ``DataFrame`` does not contain the area of the United States as a whole.\n", + "We could insert the appropriate value (using the sum of all state areas, for instance), but in this case we'll just drop the null values because the population density of the entire United States is not relevant to our current discussion:" + ] + }, { "cell_type": "code", "execution_count": 29, @@ -2935,6 +3340,14 @@ "final.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have all the data we need. To answer the question of interest, let's first select the portion of the data corresponding with the year 2000, and the total population.\n", + "We'll use the ``query()`` function to do this quickly (this requires the ``numexpr`` package to be installed; see [High-Performance Pandas: ``eval()`` and ``query()``](03.12-Performance-Eval-and-Query.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 30, @@ -3027,6 +3440,14 @@ "data2010.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's compute the population density and display it in order.\n", + "We'll start by re-indexing our data on the state, and then compute the result:" + ] + }, { "cell_type": "code", "execution_count": 31, @@ -3068,6 +3489,16 @@ "density.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a ranking of US states plus Washington, DC, and Puerto Rico in order of their 2010 population density, in residents per square mile.\n", + "We can see that by far the densest region in this dataset is Washington, DC (i.e., the District of Columbia); among states, the densest is New Jersey.\n", + "\n", + "We can also check the end of the list:" + ] + }, { "cell_type": "code", "execution_count": 33, @@ -3095,9 +3526,30 @@ "source": [ "density.tail()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that the least dense state, by far, is Alaska, averaging slightly over one resident per square mile.\n", + "\n", + "This type of messy data merging is a common task when trying to answer questions using real-world data sources.\n", + "I hope that this example has given you an idea of the ways you can combine tools we've covered in order to gain insight from your data!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Combining Datasets: Concat and Append](03.06-Concat-And-Append.ipynb) | [Contents](Index.ipynb) | [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.08-Aggregation-and-Grouping.ipynb b/notebooks_v1/03.08-Aggregation-and-Grouping.ipynb similarity index 76% rename from code_listings/03.08-Aggregation-and-Grouping.ipynb rename to notebooks_v1/03.08-Aggregation-and-Grouping.ipynb index 87fb2956c..be00723d1 100644 --- a/code_listings/03.08-Aggregation-and-Grouping.ipynb +++ b/notebooks_v1/03.08-Aggregation-and-Grouping.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Combining Datasets: Merge and Join](03.07-Merge-and-Join.ipynb) | [Contents](Index.ipynb) | [Pivot Tables](03.09-Pivot-Tables.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,23 @@ "# Aggregation and Grouping" ] }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "An essential piece of analysis of large data is efficient summarization: computing aggregations like ``sum()``, ``mean()``, ``median()``, ``min()``, and ``max()``, in which a single number gives insight into the nature of a potentially large dataset.\n", + "In this section, we'll explore aggregations in Pandas, from simple operations akin to what we've seen on NumPy arrays, to more sophisticated operations based on the concept of a ``groupby``." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For convenience, we'll use the same ``display`` magic function that we've seen in previous sections:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -35,6 +74,16 @@ " for a in self.args)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Planets Data\n", + "\n", + "Here we will use the Planets dataset, available via the [Seaborn package](http://seaborn.pydata.org/) (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)).\n", + "It gives information on planets that astronomers have discovered around other stars (known as *extrasolar planets* or *exoplanets* for short). It can be downloaded with a simple Seaborn command:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -150,6 +199,28 @@ "planets.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This has some details on the 1,000+ extrasolar planets discovered up to 2014." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simple Aggregation in Pandas" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Earlier, we explored some of the data aggregations available for NumPy arrays ([\"Aggregations: Min, Max, and Everything In Between\"](02.04-Computation-on-arrays-aggregates.ipynb)).\n", + "As with a one-dimensional NumPy array, for a Pandas ``Series`` the aggregates return a single value:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -223,6 +294,13 @@ "ser.mean()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a ``DataFrame``, by default the aggregates return results within each column:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -316,6 +394,13 @@ "df.mean()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By specifying the ``axis`` argument, you can instead aggregate within each row:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -343,6 +428,14 @@ "df.mean(axis='columns')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pandas ``Series`` and ``DataFrame``s include all of the common aggregates mentioned in [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb); in addition, there is a convenience method ``describe()`` that computes several common aggregates for each column and returns the result.\n", + "Let's use this on the Planets data, for now dropping rows with missing values:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -455,6 +548,87 @@ "planets.dropna().describe()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can be a useful way to begin understanding the overall properties of a dataset.\n", + "For example, we see in the ``year`` column that although exoplanets were discovered as far back as 1989, half of all known expolanets were not discovered until 2010 or after.\n", + "This is largely thanks to the *Kepler* mission, which is a space-based telescope specifically designed for finding eclipsing planets around other stars." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following table summarizes some other built-in Pandas aggregations:\n", + "\n", + "| Aggregation | Description |\n", + "|--------------------------|---------------------------------|\n", + "| ``count()`` | Total number of items |\n", + "| ``first()``, ``last()`` | First and last item |\n", + "| ``mean()``, ``median()`` | Mean and median |\n", + "| ``min()``, ``max()`` | Minimum and maximum |\n", + "| ``std()``, ``var()`` | Standard deviation and variance |\n", + "| ``mad()`` | Mean absolute deviation |\n", + "| ``prod()`` | Product of all items |\n", + "| ``sum()`` | Sum of all items |\n", + "\n", + "These are all methods of ``DataFrame`` and ``Series`` objects." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To go deeper into the data, however, simple aggregates are often not enough.\n", + "The next level of data summarization is the ``groupby`` operation, which allows you to quickly and efficiently compute aggregates on subsets of data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## GroupBy: Split, Apply, Combine\n", + "\n", + "Simple aggregations can give you a flavor of your dataset, but often we would prefer to aggregate conditionally on some label or index: this is implemented in the so-called ``groupby`` operation.\n", + "The name \"group by\" comes from a command in the SQL database language, but it is perhaps more illuminative to think of it in the terms first coined by Hadley Wickham of Rstats fame: *split, apply, combine*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Split, apply, combine\n", + "\n", + "A canonical example of this split-apply-combine operation, where the \"apply\" is a summation aggregation, is illustrated in this figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](figures/03.08-split-apply-combine.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Split-Apply-Combine)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This makes clear what the ``groupby`` accomplishes:\n", + "\n", + "- The *split* step involves breaking up and grouping a ``DataFrame`` depending on the value of the specified key.\n", + "- The *apply* step involves computing some function, usually an aggregate, transformation, or filtering, within the individual groups.\n", + "- The *combine* step merges the results of these operations into an output array.\n", + "\n", + "While this could certainly be done manually using some combination of the masking, aggregation, and merging commands covered earlier, an important realization is that *the intermediate splits do not need to be explicitly instantiated*. Rather, the ``GroupBy`` can (often) do this in a single pass over the data, updating the sum, mean, count, min, or other aggregate for each group along the way.\n", + "The power of the ``GroupBy`` is that it abstracts away these steps: the user need not think about *how* the computation is done under the hood, but rather thinks about the *operation as a whole*.\n", + "\n", + "As a concrete example, let's take a look at using Pandas for the computation shown in this diagram.\n", + "We'll start by creating the input ``DataFrame``:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -530,6 +704,13 @@ "df" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most basic split-apply-combine operation can be computed with the ``groupby()`` method of ``DataFrame``s, passing the name of the desired key column:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -552,6 +733,17 @@ "df.groupby('key')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that what is returned is not a set of ``DataFrame``s, but a ``DataFrameGroupBy`` object.\n", + "This object is where the magic is: you can think of it as a special view of the ``DataFrame``, which is poised to dig into the groups but does no actual computation until the aggregation is applied.\n", + "This \"lazy evaluation\" approach means that common aggregates can be implemented very efficiently in a way that is almost transparent to the user.\n", + "\n", + "To produce a result, we can apply an aggregate to this ``DataFrameGroupBy`` object, which will perform the appropriate apply/combine steps to produce the desired result:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -608,6 +800,36 @@ "df.groupby('key').sum()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``sum()`` method is just one possibility here; you can apply virtually any common Pandas or NumPy aggregation function, as well as virtually any valid ``DataFrame`` operation, as we will see in the following discussion." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The GroupBy object\n", + "\n", + "The ``GroupBy`` object is a very flexible abstraction.\n", + "In many ways, you can simply treat it as if it's a collection of ``DataFrame``s, and it does the difficult things under the hood. Let's see some examples using the Planets data.\n", + "\n", + "Perhaps the most important operations made available by a ``GroupBy`` are *aggregate*, *filter*, *transform*, and *apply*.\n", + "We'll discuss each of these more fully in [\"Aggregate, Filter, Transform, Apply\"](#Aggregate,-Filter,-Transform,-Apply), but before that let's introduce some of the other functionality that can be used with the basic ``GroupBy`` operation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Column indexing\n", + "\n", + "The ``GroupBy`` object supports column indexing in the same way as the ``DataFrame``, and returns a modified ``GroupBy`` object.\n", + "For example:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -652,6 +874,14 @@ "planets.groupby('method')['orbital_period']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we've selected a particular ``Series`` group from the original ``DataFrame`` group by reference to its column name.\n", + "As with the ``GroupBy`` object, no computation is done until we call some aggregate on the object:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -685,6 +915,22 @@ "planets.groupby('method')['orbital_period'].median()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives an idea of the general scale of orbital periods (in days) that each method is sensitive to." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Iteration over groups\n", + "\n", + "The ``GroupBy`` object supports direct iteration over the groups, returning each group as a ``Series`` or ``DataFrame``:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -714,6 +960,23 @@ " print(\"{0:30s} shape={1}\".format(method, group.shape))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This can be useful for doing certain things manually, though it is often much faster to use the built-in ``apply`` functionality, which we will discuss momentarily." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Dispatch methods\n", + "\n", + "Through some Python class magic, any method not explicitly implemented by the ``GroupBy`` object will be passed through and called on the groups, whether they are ``DataFrame`` or ``Series`` objects.\n", + "For example, you can use the ``describe()`` method of ``DataFrame``s to perform a set of aggregations that describe each group in the data:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -902,6 +1165,30 @@ "planets.groupby('method')['year'].describe().unstack()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at this table helps us to better understand the data: for example, the vast majority of planets have been discovered by the Radial Velocity and Transit methods, though the latter only became common (due to new, more accurate telescopes) in the last decade.\n", + "The newest methods seem to be Transit Timing Variation and Orbital Brightness Modulation, which were not used to discover a new planet until 2011.\n", + "\n", + "This is just one example of the utility of dispatch methods.\n", + "Notice that they are applied *to each individual group*, and the results are then combined within ``GroupBy`` and returned.\n", + "Again, any valid ``DataFrame``/``Series`` method can be used on the corresponding ``GroupBy`` object, which allows for some very flexible and powerful operations!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Aggregate, filter, transform, apply\n", + "\n", + "The preceding discussion focused on aggregation for the combine operation, but there are more options available.\n", + "In particular, ``GroupBy`` objects have ``aggregate()``, ``filter()``, ``transform()``, and ``apply()`` methods that efficiently implement a variety of useful operations before combining the grouped data.\n", + "\n", + "For the purpose of the following subsections, we'll use this ``DataFrame``:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -987,6 +1274,17 @@ "df" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Aggregation\n", + "\n", + "We're now familiar with ``GroupBy`` aggregations with ``sum()``, ``median()``, and the like, but the ``aggregate()`` method allows for even more flexibility.\n", + "It can take a string, a function, or a list thereof, and compute all the aggregates at once.\n", + "Here is a quick example combining all these:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -1074,6 +1372,13 @@ "df.groupby('key').aggregate(['min', np.median, max])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another useful pattern is to pass a dictionary mapping column names to operations to be applied on that column:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -1136,6 +1441,16 @@ " 'data2': 'max'})" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Filtering\n", + "\n", + "A filtering operation allows you to drop data based on the group properties.\n", + "For example, we might want to keep all groups in which the standard deviation is larger than some critical value:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -1311,6 +1626,24 @@ "display('df', \"df.groupby('key').std()\", \"df.groupby('key').filter(filter_func)\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filter function should return a Boolean value specifying whether the group passes the filtering. Here because group A does not have a standard deviation greater than 4, it is dropped from the result." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Transformation\n", + "\n", + "While aggregation must return a reduced version of the data, transformation can return some transformed version of the full data to recombine.\n", + "For such a transformation, the output is the same shape as the input.\n", + "A common example is to center the data by subtracting the group-wise mean:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -1384,6 +1717,18 @@ "df.groupby('key').transform(lambda x: x - x.mean())" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### The apply() method\n", + "\n", + "The ``apply()`` method lets you apply an arbitrary function to the group results.\n", + "The function should take a ``DataFrame``, and return either a Pandas object (e.g., ``DataFrame``, ``Series``) or a scalar; the combine operation will be tailored to the type of output returned.\n", + "\n", + "For example, here is an ``apply()`` that normalizes the first column by the sum of the second:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -1533,6 +1878,32 @@ "display('df', \"df.groupby('key').apply(norm_by_data2)\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``apply()`` within a ``GroupBy`` is quite flexible: the only criterion is that the function takes a ``DataFrame`` and returns a Pandas object or scalar; what you do in the middle is up to you!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Specifying the split key\n", + "\n", + "In the simple examples presented before, we split the ``DataFrame`` on a single column name.\n", + "This is just one of many options by which the groups can be defined, and we'll go through some other options for group specification here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### A list, array, series, or index providing the grouping keys\n", + "\n", + "The key can be any series or list with a length matching that of the ``DataFrame``. For example:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -1653,6 +2024,13 @@ "display('df', 'df.groupby(L).sum()')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course, this means there's another, more verbose way of accomplishing the ``df.groupby('key')`` from before:" + ] + }, { "cell_type": "code", "execution_count": 26, @@ -1778,6 +2156,15 @@ "display('df', \"df.groupby(df['key']).sum()\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### A dictionary or series mapping index to group\n", + "\n", + "Another method is to provide a dictionary that maps index values to the group keys:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -1892,6 +2279,15 @@ "display('df2', 'df2.groupby(mapping).sum()')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Any Python function\n", + "\n", + "Similar to mapping, you can pass any Python function that will input the index value and output the group:" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -2010,6 +2406,15 @@ "display('df2', 'df2.groupby(str.lower).mean()')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### A list of valid keys\n", + "\n", + "Further, any of the preceding key choices can be combined to group on a multi-index:" + ] + }, { "cell_type": "code", "execution_count": 29, @@ -2069,6 +2474,15 @@ "df2.groupby([str.lower, mapping]).mean()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Grouping example\n", + "\n", + "As an example of this, in a couple lines of Python code we can put all these together and count discovered planets by method and by decade:" + ] + }, { "cell_type": "code", "execution_count": 30, @@ -2198,9 +2612,31 @@ "decade.name = 'decade'\n", "planets.groupby(['method', decade])['number'].sum().unstack().fillna(0)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This shows the power of combining many of the operations we've discussed up to this point when looking at realistic datasets.\n", + "We immediately gain a coarse understanding of when and how planets have been discovered over the past several decades!\n", + "\n", + "Here I would suggest digging into these few lines of code, and evaluating the individual steps to make sure you understand exactly what they are doing to the result.\n", + "It's certainly a somewhat complicated example, but understanding these pieces will give you the means to similarly explore your own data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Combining Datasets: Merge and Join](03.07-Merge-and-Join.ipynb) | [Contents](Index.ipynb) | [Pivot Tables](03.09-Pivot-Tables.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.09-Pivot-Tables.ipynb b/notebooks_v1/03.09-Pivot-Tables.ipynb similarity index 65% rename from code_listings/03.09-Pivot-Tables.ipynb rename to notebooks_v1/03.09-Pivot-Tables.ipynb index 8b476307e..717549875 100644 --- a/code_listings/03.09-Pivot-Tables.ipynb +++ b/notebooks_v1/03.09-Pivot-Tables.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb) | [Contents](Index.ipynb) | [Vectorized String Operations](03.10-Working-With-Strings.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,26 @@ "# Pivot Tables" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have seen how the ``GroupBy`` abstraction lets us explore relationships within a dataset.\n", + "A *pivot table* is a similar operation that is commonly seen in spreadsheets and other programs that operate on tabular data.\n", + "The pivot table takes simple column-wise data as input, and groups the entries into a two-dimensional table that provides a multidimensional summarization of the data.\n", + "The difference between pivot tables and ``GroupBy`` can sometimes cause confusion; it helps me to think of pivot tables as essentially a *multidimensional* version of ``GroupBy`` aggregation.\n", + "That is, you split-apply-combine, but both the split and the combine happen across not a one-dimensional index, but across a two-dimensional grid." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivating Pivot Tables\n", + "\n", + "For the examples in this section, we'll use the database of passengers on the *Titanic*, available through the Seaborn library (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -173,6 +215,23 @@ "titanic.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This contains a wealth of information on each passenger of that ill-fated voyage, including gender, age, class, fare paid, and much more." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pivot Tables by Hand\n", + "\n", + "To start learning more about this data, we might begin by grouping according to gender, survival status, or some combination thereof.\n", + "If you have read the previous section, you might be tempted to apply a ``GroupBy`` operation–for example, let's look at survival rate by gender:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -224,6 +283,17 @@ "titanic.groupby('sex')[['survived']].mean()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This immediately gives us some insight: overall, three of every four females on board survived, while only one in five males survived!\n", + "\n", + "This is useful, but we might like to go one step deeper and look at survival by both sex and, say, class.\n", + "Using the vocabulary of ``GroupBy``, we might proceed using something like this:\n", + "we *group by* class and gender, *select* survival, *apply* a mean aggregate, *combine* the resulting groups, and then *unstack* the hierarchical index to reveal the hidden multidimensionality. In code:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -283,6 +353,24 @@ "titanic.groupby(['sex', 'class'])['survived'].aggregate('mean').unstack()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us a better idea of how both gender and class affected survival, but the code is starting to look a bit garbled.\n", + "While each step of this pipeline makes sense in light of the tools we've previously discussed, the long string of code is not particularly easy to read or use.\n", + "This two-dimensional ``GroupBy`` is common enough that Pandas includes a convenience routine, ``pivot_table``, which succinctly handles this type of multi-dimensional aggregation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pivot Table Syntax\n", + "\n", + "Here is the equivalent to the preceding operation using the ``pivot_table`` method of ``DataFrame``s:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -342,6 +430,26 @@ "titanic.pivot_table('survived', index='sex', columns='class')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is eminently more readable than the ``groupby`` approach, and produces the same result.\n", + "As you might expect of an early 20th-century transatlantic cruise, the survival gradient favors both women and higher classes.\n", + "First-class women survived with near certainty (hi, Rose!), while only one in ten third-class men survived (sorry, Jack!)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multi-level pivot tables\n", + "\n", + "Just as in the ``GroupBy``, the grouping in pivot tables can be specified with multiple levels, and via a number of options.\n", + "For example, we might be interested in looking at age as a third dimension.\n", + "We'll bin the age using the ``pd.cut`` function:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -420,6 +528,13 @@ "titanic.pivot_table('survived', ['sex', age], 'class')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can apply the same strategy when working with the columns as well; let's add info on the fare paid using ``pd.qcut`` to automatically compute quantiles:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -531,6 +646,36 @@ "titanic.pivot_table('survived', ['sex', age], [fare, 'class'])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a four-dimensional aggregation with hierarchical indices (see [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb)), shown in a grid demonstrating the relationship between the values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Additional pivot table options\n", + "\n", + "The full call signature of the ``pivot_table`` method of ``DataFrame``s is as follows:\n", + "\n", + "```python\n", + "# call signature as of Pandas 0.18\n", + "DataFrame.pivot_table(data, values=None, index=None, columns=None,\n", + " aggfunc='mean', fill_value=None, margins=False,\n", + " dropna=True, margins_name='All')\n", + "```\n", + "\n", + "We've already seen examples of the first three arguments; here we'll take a quick look at the remaining ones.\n", + "Two of the options, ``fill_value`` and ``dropna``, have to do with missing data and are fairly straightforward; we will not show examples of them here.\n", + "\n", + "The ``aggfunc`` keyword controls what type of aggregation is applied, which is a mean by default.\n", + "As in the GroupBy, the aggregation specification can be a string representing one of several common choices (e.g., ``'sum'``, ``'mean'``, ``'count'``, ``'min'``, ``'max'``, etc.) or a function that implements an aggregation (e.g., ``np.sum()``, ``min()``, ``sum()``, etc.).\n", + "Additionally, it can be specified as a dictionary mapping a column to any of the above desired options:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -546,8 +691,8 @@ " \n", " \n", " \n", - " survived\n", " fare\n", + " survived\n", " \n", " \n", " class\n", @@ -571,32 +716,32 @@ " \n", " \n", " female\n", - " 91.0\n", - " 70.0\n", - " 72.0\n", " 106.125798\n", " 21.970121\n", " 16.118810\n", + " 91.0\n", + " 70.0\n", + " 72.0\n", " \n", " \n", " male\n", - " 45.0\n", - " 17.0\n", - " 47.0\n", " 67.226127\n", " 19.741782\n", " 12.661633\n", + " 45.0\n", + " 17.0\n", + " 47.0\n", " \n", " \n", "\n", "" ], "text/plain": [ - " survived fare \n", - "class First Second Third First Second Third\n", + " fare survived \n", + "class First Second Third First Second Third\n", "sex \n", - "female 91.0 70.0 72.0 106.125798 21.970121 16.118810\n", - "male 45.0 17.0 47.0 67.226127 19.741782 12.661633" + "female 106.125798 21.970121 16.118810 91.0 70.0 72.0\n", + "male 67.226127 19.741782 12.661633 45.0 17.0 47.0" ] }, "execution_count": 8, @@ -609,6 +754,23 @@ " aggfunc={'survived':sum, 'fare':'mean'})" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice also here that we've omitted the ``values`` keyword; when specifying a mapping for ``aggfunc``, this is determined automatically." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "At times it's useful to compute totals along each grouping.\n", + "This can be done via the ``margins`` keyword:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -680,6 +842,25 @@ "titanic.pivot_table('survived', index='sex', columns='class', margins=True)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here this automatically gives us information about the class-agnostic survival rate by gender, the gender-agnostic survival rate by class, and the overall survival rate of 38%.\n", + "The margin label can be specified with the ``margins_name`` keyword, which defaults to ``\"All\"``." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Birthrate Data\n", + "\n", + "As a more interesting example, let's take a look at the freely available data on births in the United States, provided by the Centers for Disease Control (CDC).\n", + "This data can be found at https://raw.githubusercontent.com/jakevdp/data-CDCbirths/master/births.csv\n", + "(this dataset has been analyzed rather extensively by Andrew Gelman and his group; see, for example, [this blog post](http://andrewgelman.com/2012/06/14/cool-ass-signal-processing-using-gaussian-processes/)):" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -700,7 +881,14 @@ }, "outputs": [], "source": [ - "births = pd.read_csv('births.csv')" + "births = pd.read_csv('data/births.csv')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Taking a look at the data, we see that it's relatively simple–it contains the number of births grouped by date and gender:" ] }, { @@ -788,6 +976,14 @@ "births.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can start to understand this data a bit more by using a pivot table.\n", + "Let's add a decade column, and take a look at male and female births as a function of decade:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -862,6 +1058,14 @@ "births.pivot_table('births', index='decade', columns='gender', aggfunc='sum')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We immediately see that male births outnumber female births in every decade.\n", + "To see this trend a bit more clearly, we can use the built-in plotting tools in Pandas to visualize the total number of births by year (see [Introduction to Matplotlib](04.00-Introduction-To-Matplotlib.ipynb) for a discussion of plotting with Matplotlib):" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -873,7 +1077,7 @@ "data": { "image/png": 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c/Xps2XcRlQpG9muciqG2Ghtm3x9xy3MkURBCWK09mQcor6pgeJBlRxN+zUFj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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -883,11 +1087,29 @@ "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", - "sns.set() # use seaborn styles\n", + "sns.set() # use Seaborn styles\n", "births.pivot_table('births', index='year', columns='gender', aggfunc='sum').plot()\n", "plt.ylabel('total births per year');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With a simple pivot table and ``plot()`` method, we can immediately see the annual trend in births by gender. By eye, it appears that over the past 50 years male births have outnumbered female births by around 5%." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Further data exploration\n", + "\n", + "Though this doesn't necessarily relate to the pivot table, there are a few more interesting features we can pull out of this dataset using the Pandas tools covered up to this point.\n", + "We must start by cleaning the data a bit, removing outliers caused by mistyped dates (e.g., June 31st) or missing values (e.g., June 99th).\n", + "One easy way to remove these all at once is to cut outliers; we'll do this via a robust sigma-clipping operation:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -901,6 +1123,15 @@ "sig = 0.74 * (quartiles[2] - quartiles[0])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This final line is a robust estimate of the sample mean, where the 0.74 comes from the interquartile range of a Gaussian distribution (You can learn more about sigma-clipping operations in a book I coauthored with Željko Ivezić, Andrew J. Connolly, and Alexander Gray: [\"Statistics, Data Mining, and Machine Learning in Astronomy\"](http://press.princeton.edu/titles/10159.html) (Princeton University Press, 2014)).\n", + "\n", + "With this we can use the ``query()`` method (discussed further in [High-Performance Pandas: ``eval()`` and ``query()``](03.12-Performance-Eval-and-Query.ipynb)) to filter-out rows with births outside these values:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -912,6 +1143,13 @@ "births = births.query('(births > @mu - 5 * @sig) & (births < @mu + 5 * @sig)')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we set the ``day`` column to integers; previously it had been a string because some columns in the dataset contained the value ``'null'``:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -924,6 +1162,14 @@ "births['day'] = births['day'].astype(int)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can combine the day, month, and year to create a Date index (see [Working with Time Series](03.11-Working-with-Time-Series.ipynb)).\n", + "This allows us to quickly compute the weekday corresponding to each row:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -940,6 +1186,13 @@ "births['dayofweek'] = births.index.dayofweek" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using this we can plot births by weekday for several decades:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -951,7 +1204,7 @@ "data": { "image/png": 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/DBo0iNTUVN5//30WLlzImjVr2LhxIy0tLSxYsIDk5GTWrl3LwIEDWbp0Kdu2\nbWP16tW8+OKL9gzZoZpa2th5vISvT5TQbDTh5aHkoZQI7k0McupaABKJhBitLzFaXy5cqmPLoSJO\n51dz7rNTRASpeWCs9rZvZRQE4SqfadOp37Obmq+2ok4eJ8qnC13KrolAbm4uTU1NLFy4EJPJxNNP\nP82bb76Jv78/AO3t7SiVSrKyshg+fDhyuRyVSoVWqyU3N5f09HQWLVoEQEpKCqtXr7ZnuA7TbGxn\n14kSdhwrocnYjqe7gocnhTMhKRgXRc/a4aNDvHn6h94Uljew5VARJ8/r+OvnWYT2UzFrrJZht3Fn\ngyAIVgofH9Rjx1G/by+NJ46hvrIUrSB0BbsmAq6urixcuJD58+dTWFjIokWL2LFjBwAnT57k008/\n5eOPP2b//v3XraLk7u6OXq+/bslFDw8P9Hq9PcPtdsZWE7tPXmL70WL0zW14uMr5wYRIJg0LxlXZ\ns68DagPVLJ0XxyWdnq2Hizh2toLVX2bT38+dB8ZoGTmkX7dOdBSEns7n/hnUH9hHzdYteN4zConY\nf4QuYtejjVarJSwsrON3b29vdDod6enp/OMf/+C9997Dx8cHlUp13UHeYDCgVqtRqVQd6y0bDLYv\nuXi391Tam7HNxFeHCvj8mwvU61vxcFPw6PTBzBofgbtr963t3x3tpNF4kjSkP6U6Pet3n2dP+iXe\n33KGLYeL+MHkaCYOD0Uhd/4vNGfvU85CtJNt7qidNJ4YUsah27sPWeE5/EaN7PrAnJDoU/Zn10Rg\nw4YNnD9/nhUrVlBRUYHBYODo0aOkpqayZs0a1GrrrWbx8fG89dZbtLa2YjQayc/PJzo6mqSkJNLS\n0oiLiyMtLY0RI0bYtF1nXYCird1E2qkyth4uot7QipuLjAeTtUy7JxR3VwWGxhYMjS3dEkt3L9Sh\nBH48OZr7hoew7WgxB7LKeHvdKT7Zfpb7R4UxPr4/Sie9DCIWNbGNaCfb3E07uU+6D/buo+DTdZjC\nB/f6eTeiT9nmbpMlu64s2NbWxgsvvEBZWRlSqZRnn32WxYsXExQUhEqlQiKRMHLkSJYuXcr69etJ\nTU3FYrGwZMkSpkyZQktLC8uXL0en06FUKlm1ahV+fn6dbtfZOk67ycz+rMtsOVRIbaMRF4WMKSNC\nuG/kAIdV93P0DlbbaGT70WLSTpXS2m7Gy0PJfSMHMCEpyOkuizi6rXoK0U62udt2Klv9NvqT6QQ/\n/RweV0rfoZK9AAAgAElEQVTc9laiT9nGqRMBR3GWjtNuMnMou5zNBwupbmhBKZcyaXgI00cNQO3u\n2Gp+zrKDNRha2Xm8hN0nrbdKqtwUTL0nlMnDQnB3dY6EwFnaytmJdrLN3bZTS2Ehxa/8FreBgwj9\nzQtdF5gTEn3KNmKJYSdkMps5klPBfw4WoKtrQS6TMnVEKDNGD8BLJZYIvZbaQ8kPJkQyfdQAdqdf\n4uvjJWzcl8/2o8VMHh7C1BEheDo4aRIEZ+Kq1eIeO5SmnGyaL1zALTra0SEJPZxIBLqQ2Wzh2NkK\nNh0spKKmCblMwqRhwcwco8XHUyQAt6JyUzB7XDjT7gllT0YpO44Vs+VQIV8fL2FiUjD3jQwVSZQg\nXOE7cxZNOdlUb91MyFPPODocoYcTiUAXMFsspJ/TselAAWVVBmRSCRMSg5g5Roufl6ujw+tR3Fzk\nzBgdxuThIew7VcZXR4vYfmWVxXsTgrh/9AB81aJNhb7NfeAg3KIH0pSdRUtRIa5hWkeHJPRgIhG4\nCxaLhYwLVXy5v4BLOj1SiYRx8f2ZNVaLxtvN0eH1aC4KGVPvCWVCUjAHT19m25Eidp+8xN5TpSTH\nBTJjdBj9fER9dqHv8p05i9K3VlGzbQtBS5Y6OhyhBxOJwB2wWCxk5VXz5f4CiioakUhgTGwgDyZr\nCfAVB6eupJBLmZAUzLj4/hzJqbhShvkyB7LKGTUkgJljwgjy93B0mILQ7dxjh+ISpkV/Mh1jWRku\nQUGODknooUQicBssFgs5BTVs3F9AweUGJMDImH7MHhdOfz9xMLInuUzKuPj+jB0ayPHcSrYcLuRw\nTjlHcsoZPrgfD4wJY0CAWHhE6DskEgm+M2dxefXb1H61lcCFixwdktBDiUTARmcLa9h4oICLl+oB\nGD5Iw+xx4YRoVA6OrG+RSiWMGhLAPTH9OHWhis2HCjmRW8mJ3EoSo/yZOTaMyCAvR4cpCN1ClZiE\nMiiYhqOH8XtwDgqNxtEhCT2QSAQ6cb6kji/355NbXAdAYpQ/c8aHi7NPB5NKJAwbqCEp2p/sgho2\nHyzk1MUqTl2sIlbrwwNjtQwa0PtLVgt9m0QqxXfGTMr/+R4127cR8Nh/OTokoQcSicBNXCyt58v9\n+ZwprAUgPtKP2ePCCe+vdnBkwrUkEglxEX4MDfflXHEdmw8VklNYS05hLQNDvHggWUus1rfXL8Uq\n9F2e94yietNGGg7ux2/Wg8i9RQIs3B6RCHxHweUGvtxfwOn8agBitT7MHh9BVLAYbnZmEomEwWE+\nDA7z4WJpPVsOFZKVV82fUzMJ7+/JA2O1JEb5i4RA6HUkMhk+02dSueZDandsR/PwAkeHJPQwIhG4\noriikS/3F3DqYhUAgwd4M2d8BANDvR0cmXC7ooK9eGp+AkXljWw5XEj6OR1vbzhNiEbFA2PDGDGo\nH1KpSAiE7mexWGhrN3f5+6rHJlOzZRN1aXvwnfEAMhsrtQoCiESASzo9mw4UkH5OB0BUiBdzx0cQ\nEyaG13q6sEBPfjk3jlKdnq1Hijh6poJ3N+UQ6FvAzDFhjI4NQCZqugt21m4yc76kjsyL1WTmVVGn\nb+XJObHER/p32TakCgU+06ajS11L7e6d+M95qMveW+j9+mzRocvVBjYdKOD42UosQHh/NXNTwvvM\n9eS+WMyjoqaJrUeKOJxdjslswd/LlZljwhg7tD8K+c0Tgr7YVndCtNNVDYZWTudXk3mxiuyCGlpa\nTQC4KGWYzdav3KfmJ3TpCYfZaKRg+XNYTO2Ev/5nZG49f1Ez0adsI6oP3sCtOk5FbRP/OVDAkTMV\nWCwQFuDJnPHhxEf69YkE4Ft9eQerqm/mq6PF7M+8TLvJjI+nC/ePGkBKQhBKhex7z+/LbXU7+nI7\nWSwWSir1ZOZVk3WxivyyBr79YtV4u5IQ5U9ClD+DQr25XGfk5X8fQSaV8uyPErt0/lH11s1Ub9yA\n/7wf4DvjgS57X0fpy33qdohE4AZu1HF0dc1sPljIoexyzBYLIRoVc8aHkxTdNyeQiR0MahuN7DhW\nzN5TpbS2mVG7K7hv1AAmJAbj5nL1qploK9v0tXZqbTNxtqiWzDzrmX9toxGw3toaHeJ15eDvR6Cv\n+3XfMRqNJzsO5rN6YzYuShm/WZBEWGDXXNM3NTVRsPxZJHI54Sv/hNSlZxfq6mt96k6JROAGru04\n1fUtbDlcyIGsy5jMFoL8PZgzLpxhgzRI+2AC8C2xg13V0NTK18dL2J1+iZZWEx6ucqbeE8qU4SG4\nuypEW9moL7RTTUMLWVcO/GeLamm9MvHPw1VOXKQfCZH+DI3wxcNVcdP3+Ladjpwp5/3/nMHDTcHy\nR5II7qLFyaq++JyabVvQ/OjH+EyZ2iXv6Sh9oU91BZEI3IBO10hto/HKuvRltJssBPi6M3uclpGD\nA8SMccQOdiOGljZ2p1/i6+MlGFracXORMWlYCJNGhuGplCKXiYmFt9Ib+5TZYqHgcgOZF61D/sWV\n+o6/Bft7EB9lPfhHBqttnnh6bTvtyyzjw69y8fJQ8vyjwwjogkJa7Y0NFCx/DpmHivDXXkci77lz\nwntjn7IHkQh8R21DCx9tzWFvRhntJjMab1ceTA4XM8S/Q+xgN9dsbGfvqVJ2HC2moakNsNY60AZ6\nEhGkJirYi8hgL3w8e/awa1frLX2q2djOmcIaTl2s4nRe9TV9QMLgAT4kRPkTH+l3xxVGv9tOX58o\nYe2uC/ipXVj+42H4e939JL/Kzz6lbtdOAh5/Aq+Ue+/6/Rylt/QpexOJwHc89PwWWttM+KldmZWs\nZezQQHEmdwNiB+ucsc3EyfM6SqubyM6r4lKlAfM1u4uPpwuRwV5EBqmJDPYiLECFQv79yYZ9RU/u\nU5W1TR0T/XKL6zBdmdmv9lCSEOlHQpQ/Q7Q+uCrv/uz6Ru209XAhG9Ly6efjxvM/Hoa36u6SzLba\nWgpfWIbcxxftK68hkfXMftmT+1R3uttEoOeOGd2Ep7uCGaOjGB/fXyQAwl1xUcgYExvY8WVkbDVR\nWN5AXlkDeaX15JXWdxQ8ApBJJYRdM2oQEaTGT+3aJyejOjuT2czFS/UdE/0uVzd1/C0s0LPj4B8W\n6Nktc4lmjtHS0mpi6+Ei/vTZKZY/koSnu/KO30/h44N67Djq9+2l8cRx1KNGd2G0Qm/T60YE2tpN\n1NU2df7EPk5k2ra7WVtZLBaq6lvIK6snr9SaHJRU6jvOJgG8VEoig7yIDFYTGeSFNtDzhrco9gbO\n3qf0zW1k51eTmVfN6bxqmoztACgVUoaE+ZIY7U9chJ/dL/ncqj+t3X2BXScuMSBAxW8WJOF+i0mH\nnWnVVVL44vMo+wcRtuL3SHrgpVFn71POQowIfEdfHpoVupdEIkHj7YbG243RQwIB6y1lheWN5F8Z\nNbhYVs/J8zpOnreuXCmTSgjppyIqyIuIYOslBY2XGDWwB4vFQll1E1kXq8i8WMWF0nq+Pe3xU7sw\nKjaAhEh/Bg/wdorkTCKRsGByNK1tJvZlXubN9Zk8+3DiHV+OUGr64TlyFI1HDmPIPIUqaVgXRyz0\nFr0uERAER1IqZAwM9e6oUWGxWKhpMHaMGuSX1VNU0UhReSO7T1pfo3ZXEHHtqEF/zy65Ft0XtbWb\nOVdSa13O92IVVfUtAEiAyGAvEq7M8g/WeDhl8iWRSHj8vsG0tpk5cqaCv36exVPzE+44UfGd8QCN\nRw5TvXUzHolJTvmZBccT3zaCYEcSiQQ/L1f8vFwZGRMAWA9WxRWN1nkGZQ3kldVz6mJVR8EriQRC\nNSoirkxEjAr2op+Pm/gSv4l6vdF6b39eNTkFNRjbrMv5urnIuGdwPxKi/IiL8Lura+7dSSqV8NOZ\nMRjbTGRcqGL1l9ksnRd3R3OeXIKCUSUNR5+RTtOZHDxih9ohYqGnE4mAIHQzhVxqvdvgmqVlaxuN\n5JXWk1/WwMWyegovN1JcqWdvRikAKjcFEUHqjjsUwvurr1v9sC+xWCwUV+jJvFhFZl4VBZevXkMO\n8HXvmOgXHeLVYycMy2VSFs8eyttfZJGVV817/8nhF7Nj7+gWaN+Zs9BnpFOzdbNIBIQb6pvfJILg\nZHw8XRgxuB8jBvcDrBXrSir1V0cNSuvJyqsmK68asA51B2s8rrukEOjn3mtXyzS2mjhTVGNd2OdK\nBT+wzrmICfMhIdKP+Ch/An3vfkEeZ6GQS/nl3DjeWpfJiXM6FFtzWfhAzG3/P3bVanGPHUpTTjbN\nFy7gFh1tp4iFnsruicC8efNQqaxLZ4aEhLB48WKef/55pFIp0dHRrFixAoB169aRmpqKQqFg8eLF\nTJgwAaPRyLJly6iurkalUrFy5Up8fER5YKH3k8ukhPdXE95fzZQrj9XrjR2XEvJKGyi83MAlnYF9\nmWUAuLvIraMGVy4pRASp72rWuaNV1TdfWc63mrNFtbSbrMv5qtwUjB0aSEKUP7FaX9xde+/5jItC\nxn//IJ5Vqac4nFOOi1LGY9MG3vZlIt+Zs2jKyaZ662ZCnnrGTtEKPZVd96DWVmvW/tFHH3U8tmTJ\nEp555hlGjBjBihUr2LVrF4mJiaxZs4aNGzfS0tLCggULSE5OZu3atQwcOJClS5eybds2Vq9ezYsv\nvmjPkAXBaXmpXBg2UMOwgRrAOmpQqjNcSQysIwfZBTVkF9R0vKa/n/t1ix4F+Xk47RLbZrOF/LIG\nMvOss/wv6QwdfwvRqKwT/aL8ieivdtrPYA9uLnKe/mECr3+awd6MUlwUUn44Meq2kgH3gYNwix5I\nU3YWLcVFuA4Is2PEQk9j10QgNzeXpqYmFi5ciMlk4umnn+bMmTOMGDECgJSUFA4ePIhUKmX48OHI\n5XJUKhVarZbc3FzS09NZtGhRx3NXr15tz3AFoUeRy6SEBXoSFujJpGEhgLWA0re3LuaXNZB/uYHL\nWZc5kHUZsE6gC++vJiLIi6hg60+Vm+NGDZpa2skprCHzYhVZedXom68u6RwX4UdClB/xkX5dsuxu\nT+bhquDZhxP546cn2XGsBBeFjDnjI27rPXxnzqL0rVXUbN1M0JKldopU6Insmgi4urqycOFC5s+f\nT2FhIYsWLeLa9Ys8PDzQ6/UYDAY8Pa8uiODu7t7x+LeXFb59riAIN6d2V5IY5U9ilD9gPcsurTJc\nGTGwXlI4U1jLmcLajtcE+LoTFaTuuEshWONh17ocFTVNVyb6VXO+5Opyvl4qJSkJQSRE+TEkzBcX\npePv7Xcmag8lz/0oiZWfpPOfg4W4KGTcP9r2M3v32KG4hGnRn0zHWFaGS1CQHaMVehK7JgJarZaw\nsLCO3729vTlz5kzH3w0GA2q1GpVKdd1B/trHDQZDx2PXJgu3crerLPUVop1s15PbKiBAzbDY/h3/\nbmxq5VxRLeeKasktquF8cS0Hs8s5mF0OgKtSxsABPgwK82FwmC+DwnzwsnHt+xu1U7vJzJmCao6f\nqeD4mXJKrxnyjw715p4hgdwzJIDIYK8+c4vknfYnjcaT1345nuff2c/6vXn4+bgzc5ztIwOyBT8k\nd+XrNO3ZSchTv7qjGLpbT973egq7JgIbNmzg/PnzrFixgoqKCvR6PcnJyRw7doyRI0eyb98+Ro8e\nTVxcHG+++Satra0YjUby8/OJjo4mKSmJtLQ04uLiSEtL67ik0BmxJGXnxNKdtuuNbRXm706YvzvT\nhgdjtli4XGXouDshv6yB0xeryLqyrgFAP28360qIV+5SCNGovndr3rXt1NjUyul860S/7IJqmo3W\ne/tdFDKGDdRYZ/lH+l2XYFRV9Y0Rv7vtT1LgmYcTWfnJSd7deJpWYzvj4vt3+joAS8RglEFB6NL2\noZo2E4VGc8dxdIfeuO/Zg1NXH2xra+OFF16grKwMqVTKsmXL8Pb25qWXXqKtrY3IyEheeeUVJBIJ\n69evJzU1FYvFwpIlS5gyZQotLS0sX74cnU6HUqlk1apV+Pn5dbpd0XE6J3Yw2/XFtmpqaSP/cgP5\npdZ1DfJLGzrW5gdQyq1lmSODvTpuYVS4Ktl7vIjMi9Xkldbz7ReLv5crCVH+JET5MSjUB4W8Z97b\n31W6qj9dqtTzx09P0mRs5xcPxnYsWNWZhsOHKP/Xe3jdO5GAx/7rruOwp764790Jp04EHEV0nM6J\nHcx2oq3AbLFQUdNkLa50Za5BaZWeG317SCQQHexFQpQ/8VH+BPm595khf1t0ZX8quNzAG2szaGs3\n88u5cSRG+3f6GovJROFLz9NeW0v4yjeQezvvLdli37ONSARuQHSczokdzHairW6s2dhO4eUGLpY1\nUFDWgNrThcEhXgyN8HPonQjOrqv70/mSOv687hRms4Vfz08gVuvb6Wvq0vZSueZDfKZNR/PDH3VZ\nLF1N7Hu2udtEoG+P0QmCcMfcXOTEaH2ZNVbLf/8gnmWPjmB0bKBIArrZwFBvfvVQPABvb8jifEld\np69Rj01G7uNDXdoeTOJurD6v00Tg20WBBEEQBOcUq/XlyTlxmEwW3lqfScHlhls+X6pQ4DNtOhaj\nkdpdO7spSsFZdZoITJs2jd/97ndkZWV1RzyCIAjCHUiM9mfRrCEY20z8OfUUlypvfabvlTIBmcqT\num92YWpu7qYoBWfUaSLw1VdfkZCQwJ///GdmzZrFv/71L3Q6XXfEJgiCINyGkTEBPHF/DIaWdv6U\neorymqabPlfq4oL3lKmYm5qo37O7G6MUnE2niYCbmxtz5szhww8/5L//+7/56KOPmDp1Kk8++SRF\nRUXdEaMgCIJgo3Hx/fnx1IE0GFp5Y20GVXU3P9v3njQZqZsbtV/vwGw0dmOUgjPpNBEoKiri7bff\n5r777uPTTz/lueee4+jRozz88MMddQAEQRAE5zF5eAjzJ0RS22jkjc8yqG288UFe5u6B98TJmBob\nqd+/r5ujFJxFp4nAE088gUQi4d///jcffPABs2bNwsXFhXvvvZcJEyZ0Q4iCIAjC7bp/dBgPJmvR\n1bXwp88yaDDceOK399RpSJRKand8haW9/YbPEXq3ThOB3bt3s3TpUoKDgwGwWCyUlJQA8P/+3/+z\nb3SCIAjCHZs9Lpz7RoZyubqJVamnMLS0fe85ck81XikTaK+toeHwQQdEKThap4nAJ598wrBhw4iJ\niSEmJoYhQ4bwxBNPdEdsgiAIwl2QSCT8cGIUE5KCKanU8+a6TJqN3z/r97nvfiRyOTVfbcNiMjkg\nUsGROk0E/v3vf7Np0yZmzJjB119/zauvvkpCQkJ3xCYIgiDcJYlEwqPTBjImNpD8sgb+8nkWxrbr\nD/YKHx/UY8fRVllB44njDopUcJROEwE/Pz9CQ0MZNGgQ58+fZ968eRQUFHRHbIIgCEIXkEok/HTm\nYEYM0nC+pI6/fXGatnbzdc/xuX8GSCTUbNuCxWy+yTsJvZFNtw8eOXKEQYMGsWfPHnQ6HQ0Nt161\nShAEQXAuMqmUnz8YS3ykH9kFNby7KZt209UDvlLTD8+Ro2ktvYQh85QDIxW6W6eJwEsvvcQ333zD\n+PHjqaurY/r06Tz66KPdEZsgCILQheQyKU/OGUpMmA8ZF6r499azmM1X6875zngAgOqtm+mF9eiE\nmxDVB/sgs8WMj68b9bViARFbiApothHtZBtnaKeW1nZWpZ4ir7SBlIT+/Nf0wR2losv+9jb6jHSC\nn34Oj9ihDo3TGdqqJ7jb6oPym/1h0qRJt6whvnu3WJKyp2lqa+Zg2VH2XjpIY2sjUd4RxPvHEq8Z\ngq+r89YkFwSha7kq5Tw9P4E31p5iX+ZllAoZCyZHI5FI8J05C31GOjXbtjg8ERC6x00TgTVr1mCx\nWPjb3/5GaGgo8+bNQyaTsXnzZi5dutSdMQp3qbq5hj0lBzh0+RhGUytKmZJQryDO1V7kXO1F1l/Y\nRIgqiHj/IcRrYglRBd0yCRQEoedzd1XwzMMJ/PHTDHaduISrUsa8lEhctVrcY4fSlJNN88ULuEVF\nOzpUwc5umgh8u4DQuXPneO211zoe/+lPf8q8efPsH5lw1wobitldvI+MytNYsOClVDNdO5lxQaMI\nCwrgwqVLZOnOkFWVw/naPC7py9hWuAsfF2/iNbHE+w8h2jsCmVTm6I8iCIIdeLoree5Hiaz85CRb\nDhXhopAxc4wW35mzaMrJpmbrZoJ//YyjwxTs7KaJwLWOHDnC6NGjAUhLS0MmEwcGZ2W2mDlddYbd\nxfvIqy8EIFjVn8mhKQwPSEAuvfq/3NvFi5SQMaSEjKG5vYUz1efIqsohpzqXtEsHSbt0EDe5G7F+\ng4j3j2WI3yDc5K4O+mSCINiDt8qFZT9KYuUn6WxIy0epkDF1xCDcogdiOJ1FS3ERrgPCHB2mYEed\nThY8c+YMy5cvR6fTYbFYCA4O5vXXXycqKqq7YrxtfXFySauplSOXT/BNyX50zdUADPEbxOTQFAb5\nRH1vqP9Wk3BMZhMX6vLJqsohS3eGWmMdAHKJjGifSBI0scT5D8Hbxcu+H8pJiAlLthHtZBtnbaeK\n2iZWfnySekMrP7l/MMNlVZS+9WdUw0cQtGSpQ2Jy1rZyNnc7WdDmuwZqa2uRSCR4e3vf1Qa7Q1/q\nOPXGRvZdOsj+0iMY2puQS2SMDBzGxNDxBKkCb/o6W3cwi8XCJX0ZWbocsqrOcElf1vG3MM9Q4jVD\niPePpb9HQK+dVyC+jGwj2sk2ztxOpTo9f/w0A0NzG4seiKH/xn9gLC4i7Hev4hIU1O3xOHNbOZNu\nSwR6kr7Qccr05ewu2ceJ8gzaLSY8FO6kBI8hJWQsamXnneJOd7Dq5lpOV50hsyqHi3X5mC3WBUn8\nXX2vzCuIJcIrrFfNKxBfRrYR7WQbZ2+novJGXl+bgbHVxK9iLbh9+RHqMckELuz+svPO3lbOQiQC\nN9BbO47FYuFc7UV2FadxtuY8AP3c/JkYOp7R/YejlCltfq+u2MGa2prIrs4lq+oMZ6pzMZqsZU49\nFO4M9YshXhNLjO9AXG4jLmckvoxsI9rJNj2hnS5eqmdV6ilMJhPP1OxAWqMj/NU/otBoujWOntBW\nzsDuiUBWVhbx8fF3tZHu1ts6Tru5nfSKTHaX7KNUfxmASK9wJg9IIc4/Bqmk0wUiv6erd7A2czvn\na/PIqsrhtC6H+lbreyukcgb5RBOvGUKc/xCbRiucjfgyso1oJ9v0lHY6W1jDm+uzGNKQx4zL+/Ga\nMImARx/v1hh6Sls5mt0Tgccff5za2lpmz57N7Nmz0XRzRngnekvHaWpr4kCpdQGg+tYGpBIpSZo4\nJg9IIUwdelfvbc8dzGwxU9x49dbEy4YKACRI0KoHkHDl1sQAj3522X5XE19GthHtZJue1E5ZeVW8\n83kmPyv8Em9LMxEr/4S8G+eJ9aS2cqRuuTRQWlrKpk2b2L59O/3792fu3LlMnjwZhUJxVxu3l57e\ncaqaq/mm5ACHLx+n1dSKi0xJctAoJoSMw8+ta1YA7M4dTNdUbb0DoSqHvLpCLFi7XIC7pmNlQ616\nwB2NbHQH8WVkG9FOtulp7XQit5JDH33B9MojyMZNIvIn3Tcq0NPaylG6bY5AWVkZW7Zs4bPPPiMw\nMJDq6mqee+45pk6delcB2ENP7Tj59UXsLt5Hpi4bCxa8XbyYGDqO5KCRuMndunRbjtrB9K0GsqvP\nkqXL4WzNeVrNbQB4KlTE+VvnFQzyiUYpc54kU3wZ2Ua0k216YjsdOlWCy9//gKulDe8XXyU4LKBb\nttsT28oR7J4IrF+/nk2bNqHT6ZgzZw5z584lMDCQiooK5s6dy6FDh265gerqah566CE++OADjEYj\nK1asQC6Xo9VqefXVVwFYt24dqampKBQKFi9ezIQJEzAajSxbtozq6mpUKhUrV67Ex8e2s+Ge1HHM\nFjNZuhx2Fe+joKEIgFBVEJMH3MuwfvF2m33vDDtYq6mNc7UXyNLlcLrqLI1tegCUUgUxfoOI9x/C\nUL8YVEoPh8bpDG3VE4h2sk1PbafjH6zD6+A2TgQkMWXZz+nn3bUnJzfSU9uqu9mt6NC3jh8/zq9+\n9StGjRp13eMBAQGsWLHilq9tb29nxYoVuLpaV6N75513WLp0KePHj+e5555j7969DB06lDVr1rBx\n40ZaWlpYsGABycnJrF27loEDB7J06VK2bdvG6tWrefHFF+/iozoXo6mVw5ePs6fkAFVXFgAa6jeY\nyQNSiPaO7LX35F9LKVMQ52+dRGi2mClsKO6YV5CpyyZTl40ECZHeWuslBP9YNO5+jg5bEPqk4Y/M\n5lz6XobqcvjLx0d59vHR+KrFSqO9QaeJwOuvv05ubi5r1qxBLpczatQoIiIiALjvvvtu+do//vGP\nLFiwgH/84x8ADBkyhNraWiwWCwaDAblcTlZWFsOHD0cul6NSqdBqteTm5pKens6iRdb7VlNSUli9\nevXdflanUG9sYO+lgxwoPUJTezNyqZzkoJFMCh1PoEf3DLc5I6lESoSXlggvLXOiZlBuqOxY2TCv\nrpCLdQV8cXELQR6BHcWRQj2DnXZegSD0NlIXF/pNn071l18QVpLJG5+58vyPh+Hl0bNvDxZsSATW\nrFnDxx9/zMSJE7FYLHzwwQcsWbKEuXPn3vJ1X3zxBX5+fiQnJ/Puu+9isVgICwvj97//Pe+++y6e\nnp6MHDmS7du34+l5dVjD3d0dvV6PwWBApVIB4OHhgV6vt/lD3e0wiT0U1V1iy7ndHCg+jslswtNF\nxQ8GzeS+qBS8XNUOickZ2+lbGo0ncdpIfsyD1LU0kF6axfGyLE6Xn2V70TdsL/oGHzcvRgTFc09w\nArH9BqKw47wCZ24rZyLayTY9tZ185s+hbud2xhnOc6Iqhr98nsWrS5JR2zEZ6Klt1ZN0mgisW7eO\nDRs2dByUn3zySR599FGbEgGJRMLBgwc5d+4cy5cv5+zZs2zatInIyEg++eQTVq5cyfjx4687yBsM\nBkRVeOkAACAASURBVNRqNSqVCoPB0PHYtclCZ5zlmpLFYuFszXl2F+8jt/YCYJ0pPyl0PCMDh6OU\nKWhtBF1j98fbs669SYhXJxCvTsAY3crZmvNk6XLIrjrL13n7+TpvP64yl2vmFQzGXeHeZVvvWW3l\nOKKdbNPT28lrwiRqtm1hvpeOtZflvLj6AMsWJOHmYlMNu9vS09uqu9h9joCbm9t1twm6ubmhVHae\n/X388ccdvz/++OP87ne/45e//GVHQhEQEEBGRgZxcXG8+eabtLa2YjQayc/PJzo6mqSkJNLS0oiL\niyMtLY0RI0bcyedziDZzOyfKM/imZD9lhnIAor0jmDwghVi/wWI4+y64yJQkaoaSqBmKyWwiv76Q\nrKozZOlyyKjMIqMyC6lESrR3RMetib6uXXPLpSDcKZPZxGVDBSWNpchqLAzzHnZdJdCexHvqNGp3\n7SSy8ATjUn7KgRwdb63P5JkfJuKi7D1Li/clN+2J77zzDgDe3t4sWLCAGTNmIJfL2b59O1qt9o42\n9sorr/DUU08hl8tRKpW8/PLL+Pv789hjj/HII49gsVh45plnUCqVLFiwgOXLl/PII4+gVCpZtWrV\nHW2zOxnamthfeoS0SwdpaG1EKpEyIiCRyaEpDFCHODq8XkcmtVZDjPaJZF7UA1w2VHTMKzhXe5Fz\ntRdZf2ETIaqgjnkFIaqgPjERU3CcNlMbZYZyihtLKbnyX5mhnHZze8dzSkIreCh61v9n787DoizX\nB45/32EYtmHfREBARUFBU3BLRVwq00zTyhUq26zjKbPFOtUxT6fUytNm2mLLLzSXzCwrLbWUXEFc\nUBRcwA1FZd/Xmd8fKkmpTMIwA3N/rovrqmHmfW9uZ7nneZ/nfkwY5Y1TOzrhHBVN/oZfGO2cS2Wo\nFwmHzvP+qmSevLsL1mopBpqbay4fvFwIXMvUqabZltIQTT2UdL40m99ObWHH2UQqdVXYWtnSt3VP\nov37mu230ZY+5JZfUVC7AuFw3jFq9DUAuNq4XNocqRPBLm0NWp7Z0nPVWCwxT+XVFWQWn639wD9V\nnMnZknO1m3HBxe27W2tb4e/oi5/Wly1nt5NZlMXDYTHc5BVuwuhvXFVeHhnPP4O1uwd+r/yXhd8f\nYu/RbG5q78Hjd4WhtmqcUU9LfE7dCNl06Cqa4omj1+svNgA6FU/yhRT06HG1cWGgfz9ubt0TO7V5\nL6uxpBdYWXU5B3PSSM5OISUnlbLqcgDs1HZ0du9IF4/OdHLveM1/M0vKVUO09DyVVpVxujjzim/6\nZzhfeqG2UyaAtcoaP21r/B19a398HLzqXAYo1xTxwi9zUClWPN/jyWa7JPbcl59TEL+ZVg9PwS6i\nB++uTObg8Tx6hnrxyIjOqFQNH3lr6c+pxiKFwFUY84lTo6thX3YKG0/Gc7zwJABtHP0Y3CaKbp7h\nzWb7XUt9gdXoajiSn147ryCvIh+4+K0t2LUdXT07E+7RCRcb59rHWGqu/q6WlKeiyuI/vuVf+sku\nz61zH1srW/wd637oe9t71jsHyNPTkR+SN/HloeX4a1vzdMQ/jLrixVgqz5/n+Isz0LT2JWDmf6is\n1vO/FXs5crqAvuGteGBYKKoGXoZrSc8pY5JC4CqM8cQpry5n+9ld/Hbqd3LK81BQCPMIZbB/FO1d\ngprddWd5gV0c1TldfIbkCykkZx/kdPGZ2t8FOPrX7pgYFtCOvJxSE0baPDTH55Rer6egspBTRZl1\nrunnVxTUuZ+DtT3+Wt86H/oedm4N2vlzyaGVbDubQL/WvRgfMqax/qQmdfaTjyjauZ3W/3gCbbfu\nlJZX89ayPRzPKmJQd18m3tKhQe+NzfE5ZQpNUghUVlai0Wg4ceIEGRkZREVFoVKZ78z3xnzi5FcU\nsOnUVrac2UFZdTnWKjW9fCIZ5N8fb3vz34nxWuQF9lc5ZXnszz7IvuwUjuan117nVRQFF40zbrYu\nuNm64m7ritvlHztX3GxcmuU3usZm7s8pvV5PTnlunQ/800VnaltbX+ascazzge/v6IurjUujFfuX\n81RZU8W8pA84XXyG+zqNo2er7o1y/KZUkZnJiZkvYhvUFv9/vYyiKBSXVTH3q91kXijh9l5tuDv6\nxjulmvtzylwYvRCYP38+J0+eZNq0adx77720b98ePz8//vvf/zboxMbUGE+c00Vn2Hgqnl3n9qLT\n63C01jLA72b6+/Yxee/7xiAvsOsrrSrlQE4qqblHKKwpIKswm/yKgjrXg6/kpHG8VBy44G7rVls0\nXP6xVds08V/Q9MzpOaXT6zhfml13eL/4DGXVZXXu52brevHDXutbO8zvbGPcBl9X5ul8aTZzE99F\np9fxXI8n8GmG3UXPfPA+xXuS8J3+LA6dOgNQUFLJnCW7OZdbyqj+QdzZN+iGjm1OzylzZvRCYPTo\n0SxbtowvvviC/Px8nnvuOUaPHs2qVasadGJjutEnjl6v52BuGhtPxpOWdxSAVvZeDGrTn57e3VvU\ntz55gRnucq5qdDXkVxSQU55H7qWfi/+dT255Hnnl+bWrE/7MQW1/cfTgL8WCG+62Ltip7Zrd5aU/\nM9VzqkZXQ1bp+brf9IvPUFlTWed+XvYedYb3/Rxbo7Vu+qL+z3nac34/iw7E0crBm+ci/4mNVfNq\n2Vt+/Dgn//sKdh1D8H/2+drbcwvLmb14NzmF5Ywd1J7berb528eW9ynDGL2hkE6nQ6PR8NtvvzFt\n2jR0Oh1lZWX1PaxZqaqpIvHcHjae+p2sknMAdHBtz2D//nRy7ygNgARwsW+Bu50b7nZuV/29Tq+j\nsLLoYoFQ9tdiIetSQ5mrsbWyqTOC4P6nokFr7dDsC4XGcHmN/qkrZu5nlpyts0ZfQcHHwbvO0L6v\n1sdsV/J08wpnoF8/fju9hWVpq4gNHdus/q1tAwOx7xxGacoByo4ewa59MABuTrY8O6EbcxYnsfzX\no9hYWxHdzdfE0YqrqbcQ6NOnD3fccQe2trb06NGDSZMmMXDgwKaIzeiKK0v4PXM7m09vo6iqGJWi\nood3dwa36Y+/ozxhxd+jUlS42DjjYuNMW+fAv/xer9dTXFVyRXGQ95ei4XInyj+zVlnXudzg/qei\nwUnj2OIK1oqaSjKLz9T5pv/nNfpWl9foa6/80G+Fppl9qx7VfhgZhSdJyNpNe+cg+vr2qv9BZsRt\n+AhKUw6Q++MafJ+cXnu7l4sdz47vxpwlu4n7OQ2NtYqbw3xMGKm4GoMmC545c4ZWrVqhUqk4dOgQ\noaGhTRHbDatvKOlc6QV+PfU7O88mUaWrwk5tS7/WvRngdzOuti5NFKVpyZCb4ZoqV3q9nrLqMnIu\nXWqoO6Jw8aek6uqrF6wUK1xtnHGzc7vqpEZXG2ejL21tSJ4urtE/U+ea/rmrrtH3+dMafe9m16r3\nWnnKLc9jTsK7VOgqeSZiKv6OrU0Q3Y07Nfd1yo4cps2/Z2HbJqDO706eK+KNr/ZQVlnNYyPDiAzx\nMuiY8j5lGKPPETh16hTLli2r3T74stmzZzfoxMZ0tSeOXq/nWMFxNp6MZ3/2QfTocbd1ZaB/f/r4\nRGJrpsOGxiIvMMOZU67KqyvqFAmX5ydcLhYKK68ep4KCi41znXkJtasebBtn5YOheaqzRv/Sh392\nWU6d+9ha2eB3eY2+9o81+s2lT8f1XC9PB7IPsTD5czzs3Hm+xxPYqe2aOLobV3Igmcx3/oc2IpLW\nj/218+yxMwW8tWwv1dU6/jkmnC7tPOo9pjm99syZ0ecI/POf/6RPnz5ERkY2q+tWl9Xoath7YT8b\nT/7OiaJTAAQ4+TOkzQC6enRuEW8swnLYqm1orW1Fa22rq/6+qqaK3IpLIwpll0cU8sktzyW3PJ/0\nghMcKzh+1cdeXvnwx0hCw1Y+GLxGX21PiGvwpW/5rS+t0XdvcZc6DBHmEcqtAQP55cRvLD60kofC\nJjWb9137zuHYBARSvDuJijNnsGldd0SjXWtnpt3dhbdX7OODbw8w7Z6uhAaYZwt2S1PviMDIkSP5\n7rvvmiqeRnHhQhHl1eVsO5PAb6e3knupAVAXj04MahNFO+fAZvPiMhaptA3XknJVo6shr6Lgr5cd\nLhUNeRUF1175YG1/lTkKV6x8cLJi74nDdYb3r7dG3+/St30328Zbo98c1Pd8qtHV8P7eTziSn87d\nwXcy0L9fE0bXMEVJuzi7cD5ON/el1eSHr3qfA+k5vLsyGbWViqfH3kR7P+er3g9a1mvPmIw+ItCt\nWzfWr1/P4MGDzbqJ0GXZpbmsOvozWzMTKK8px1plTZRvHwb698OrGTcAEqIxWKms8LBzw+M6Kx8K\nKgr/csnh8s/1Vj78mZutK11dwpp0jX5LYKWy4oHOE5id8A6rjv5AoJM/Qc4B9T/QDGi7dUfTujWF\nO7bjfucorD3++p4b1tadx0aFseDbA7z99T6eG9+NgFYN+yATDXPNEYGQkBAURamdF3C5Ytfr9SiK\nwqFDh5ouyr9h/Ip/UKPX4ajREu3Xl36+vU2yVtjcSaVtOMnVHy6vfMi5dKnhylUPjvb2eGu8TbpG\nvzkw9PmUlnuU9/d+gouNM8/3fLLZ5LNw+zayPv0Y5+hBeE+Kveb9dqRk8cmagzjYWTNjQjd8PbV/\nuY+89gxjtBGB1NTUaz6osrLymr8ztdaO3gxo3Y/IVt2wbmaziYUwd4qi4KjR4qjREuhUt0GMvGk3\nro5u7RkedCs/ZPzMlweXM6XL/c1i3oRjz17kfPcthVvicb/jTtQuV1+J1btzKyqrdXyxNpW3lu3l\n+Und8Xa1b+JoBUC9z6qxY8fW+X+dTseYMea7QcZbQ1+mT+seUgQIIZq92wIHEurWgZScVNaf2GTq\ncAyiWFnhevsw9NXV5P2y7rr3jeramvGDgykoqeStpXvILmhZzeqai2sWArGxsYSEhLBv3z5CQ0MJ\nDQ0lJCSELl26EBR0Y32jm4IlTToSQrRsKkXF/Z3G42LjzJr0nzmSd8zUIRnE6eZ+WLm4kL/5N2qK\ni69731t6+DM6qi05hRW8tWwv+cUVTRSluOyahcCXX35Jamoq48eP59ChQxw6dIjU1FQOHDjAe++9\n15QxCiGExdJqHHgwbCKKovBZylcUVJj/5ReVtTVut96OvqKCvA2/1Hv/O24OZHifAM7nlfHWsr0U\nlZrv5eeWqN5LAzt27GiKOIQQQlxDW+dARrUbRmFlEV+kfFWnzbK5ch4QjZXWkfxfN1BjwP40o6Pa\nMiTCjzPZJcxbvpfS8qomiFIAWL3yyiuvXO8OSUlJlJeXo9FoKCsro6ioiKKiIhwdzXe5R6lUk/Vy\ncLCRPBlIcmUYyZNhbjRPQU5tyCw+y8HcNPTo6eja3gjRNR5FrUZfXU3p/mSs7O2xC+5w/fsrCmFt\n3cgvriD5WC5pp/IZ0N2fyorq6z5OXHxONUS9M+r27dvHvn376tymKAobN25s0ImFEEIYTlEUJoXe\ny+nEd1l3fCNtnQPp7N7R1GFdl8ugweT9vJa8X37GZfAtqDTX3wxKURRibwuhskrHjoPneO7935k8\nLAS/qywtFI3HoE2HmhtZwlQ/WeplOMmVYSRPhmlonk4WnmZe0gfYqG14occ0s98oLXvVSnJ/+gHP\n8RNxHXyLQY+prtHx1YYjbNqTidpKxT3R7Rgc6YdKJoNfldE2HXr//ff55z//yQsvvHDVBza3TYdE\nXfKmbTjJlWEkT4ZpjDz9nrmdZWnfEuQUwFPdp5j1ninVRYVkzHgGKwctQbPfQFEbvrQ7/Vwx7yzb\nQ3FZFWFBbkweHoqLtmHD4C1RQwuBa84RKCkpISgoiKKiInx9ff/yY85bEct1yvrJ9VzDSa4MI3ky\nTGPkqY2jH+fLsjmYm0ZFTSWdzPgSgcrGhpqiQkoPpmDt7o5tQKDBj+0Q5M5NQa5kZpdwICOXrfuz\n8Hazx8e9eXRZbCoNnSNwzULgcq+A0NBQvLy8yM/PR6vV0rt3b7p169agkxqbvBnVT960DSe5Mozk\nyTCNkSdFUQh168C+CykcyDmEr9aHVg5ejRRh49O09iP/1w1UZmbiEj0IxcB9axwcbKiprqF3J28c\n7TUkH8thR8o58ooqCA1wRW1l/p0Wm0JDC4F6s7h27VpGjhzJ6tWrWbFiBaNGjSI+Pr5BJxVCCNEw\ntmobHgqbhLXKmsWHVpBdlmPqkK7J2s0N5779qDp/jqJdiX/78YqiMDjCj3/fF4mfp5b4fWd45fME\nMs4WGiFay1NvIbBw4UJWrVrFe++9x/z581myZAlvvfWWwSfIyckhOjqajIwMcnNzefzxx4mJiWHC\nhAmcOnUKgBUrVjBmzBjGjRvHpk2bAKioqOCJJ55g4sSJPProo+Tl5d3YXyiEEC1Ua20rxnW8i7Lq\nchYdWExVjfmuvXcdOhwUhdyffkCvu7E+CL6eWl6+L5LbevpzLq+M1+OSWLPtODpdi5vz3qTqLQTU\najWenn9sJenr64vawMke1dXVzJw5E1tbWwDefPNN7rzzTuLi4njyySdJT08nOzubuLg4li9fzqJF\ni5g3bx5VVVUsXbqUDh06sGTJEkaOHMmCBQtu8E8UQoiWq7dPJDf79OBUUSYrj64xdTjXpPHywrFn\nbyozT1OSvK/+B1yDtVrF2EHBPDPuJpwcNHwbn87cr3aTnS/7FNyoaxYCq1evZvXq1fj5+TFlyhTW\nrl3L+vXrefLJJ+nY0bCJKXPnzmX8+PF4eV28drV7926ysrJ44IEH+OGHH+jVqxfJyclERESgVqvR\narUEBgaSmppKUlISUVFRAERFRbF9+/ZG+HOFEKLluafDKHy1PmzJ3EFi1h5Th3NNbsPuACD3xzU0\ndOV6p0A3Zk3uSWRHT46cLmDm5wlsT8lqjDAtzjW/2u/cuRMABwcHHBwcaucF2Nsbtk3kqlWrcHd3\np2/fvnz44Yfo9XoyMzNxcXHh888/54MPPuDjjz8mMDCwTpdCe3t7iouLKSkpQavV1sZQXM/GFVdq\n6FIKSyF5MpzkyjCSJ8MYI0/PRU3h+V9ms/TwKroEBOPn5NPo52gwzxCKevcid8dONGcycLmpa/0P\nuU6uPIF/P9yHjYmn+Hh1Mp+sOUja6QIeG9MVrZ11Iwbesl2zEGhon4BVq1ahKApbt24lLS2NGTNm\nYGVlxcCBAwEYNGgQb7/9NuHh4XU+5EtKSnByckKr1VJSUlJ7299paSxrmesna74NJ7kyjOTJMMbK\nkxo7JoTczacHFvNm/Ec8G/lPbKyu38nPFLRDhpK7YyfpX63A37ftde9raK66Brky8/4efLLmIPF7\nMkk5ls1Dd3SiYxvXxgrbrDW0sDTa2ovFixcTFxdHXFwcISEhvPHGG0RHR9dOBkxMTCQ4OJjw8HCS\nkpKorKykqKiI9PR0goOD6datG5s3bwZg8+bNREZGGitUIYRoEbp7dWGAX1/Olpxjedq3DR5+Nwbb\nwCDsO4dRlpZK2dEjjXZcL1d7np/UnZH9gsgrquSNr/awctMxqmvMf4MmU2vSRZgzZszgu+++Y/z4\n8WzZsoUpU6bg4eFRu4rg/vvvZ/r06Wg0GsaPH8+RI0eYMGECX3/9NVOnTm3KUIUQolka3X44AU7+\n7MxKYvvZv79Urym4DR8BXJwr0JisVCpG9gvi+Und8XCx5acdJ3jtyyTO5pQ06nlaGtlrwELJMK7h\nJFeGkTwZpinylFOWx5zEd6jSVfFMxFT8HFsb9Xw34tTc1yk7cpg2/56FbZuAq96nIbkqq6jmqw2H\n2bo/C41axdjBwUTf1BqlBe5XYPRLA7///jujR49myJAhDB48mEGDBjF48OAGnVQIIYTxuNu5Ettp\nLFW6ahYdiKOsutzUIf2F2/BLKwh++sEox7ezUfPg8E48PioMa7WKuJ/TeP+b/RSWSPfLP6u3IcB/\n//tfnn/+eYKDg1tkJSWEEC1RuEcnbmkTzfqTm1hy6GseDJtkVu/h9p3DsQkIpDhpF5Vnz6DxMc6o\nRWSIF21bO/Hpj4fYezSbf3+6k8nDO9GlnbtRztcc1Tsi4OrqysCBA/Hz86uz6ZAQQgjzNqLtbbRz\nDmLPhf1sPr3N1OHUoSjKxb4Cej25a3806rncnGx5etxN3DuwPaUV1bzz9T6W/HKYyqoao563ubjm\npkOXZWRkEB8fj6IonDt3jjNnznDmzBmzLgZk45P6yQYxhpNcGUbyZJimzJNKURHq3oHErD0kZx8k\nxK0DrrbOTXJuQ2hataJ4VyKlaak49bkZK/u6uwo2Zq4URaG9nzNd23tw+HQBycdy2H0km/a+zjg3\n862Njbb74GUffvghFy5cICkpiZ07d7Jz504SEhK46667GnRiY5I3o/rJm7bhJFeGkTwZpqnzZKu2\nxc+xNTuzkjiUe5hePhForMyj2Y6iKKjsbCnenYS+ugZtl7oNhoyRK2etDf3CfSirrCH5WA6/J59F\no7aira+TWV06+TsaWgjIqgELJTO8DSe5MozkyTCmytNPGev5MWM9Ye4hPNrlflSKeWzhq6+p4fiL\nz1Odn0fQnLdQu7jU/s7YuUo+lsNnPx2isKSS0ABXHhweipuTrdHOZyxGXzWwa9cuHnvsMe677z5i\nY2OZNGkSgwYNatBJhRBCNK2hgYMJdevAgZxUNpzcbOpwailWVrjePgx9dTV5v6xr0nN3aefOfx7s\nyU3tPTh0Io+ZnyWQmHq+SWMwB/UWAi+99BJDhgyhpqaGiRMnEhAQwJAhQ5oiNiGEEI1Epai4r9M4\nXGycWZP+M0fy0k0dUi2nm/th5eJC/ubfqPkb+8o0yrntNfxzTDixt3WkqlrHwtUH+PSHg5RVVDdp\nHKZUbyFga2vLmDFj6NmzJ05OTvz3v/8lMdE8u1UJIYS4NkeNlsmdJwLwecoSCivN41KOytoat1tv\nR19RQd7G9U1+fkVRiO7my8wHehDQypGtB7KY+VkCRzMLmjwWU6i3ELCxsSE/P5+goCD27duHoiiU\nlpY2RWxCCCEaWTuXQEa2u52CyiI+T1mKTm8evfidB0RjpXUkf+N6asrKTBKDj7sDL8ZEMLxPADkF\n5cxZvJvVv6dTozOPHBlLvYXA/fffz1NPPcXAgQNZvXo1w4cPJywsrCliE0IIYQSD/aPo4tGZw3lH\n+Sljg6nDAUBlY4PLkFvQlZZSsOlXk8WhtlIxZkA7npvQDVdHDd9vPc6cxbs5n9dyvwAbtGpAr9fX\njgQcP36ckJAQVCrzmHF6NTJzuX4yw9twkivDSJ4MYy55Kq0qZU7ie+SW5/GPrg8S6t7B1CFRU1pC\nxoxnUNTWBM19C29fd5PmqrS8isW/HGbHwXPYaKyYMCSYfuE+ZrfM0OirBgoKCnj55ZeJjY2loqKC\nuLg4iopM/yQWQghx4+yt7XkobBJWioovDi4lrzzf1CFhZe+Ay8DB1BQVUvC76Vc22Nta88idnXl4\nRCdUCnz+UyoLVh+guKzK1KE1qnoLgZdffpnw8HDy8/NxcHDAy8uLZ599tiliE0IIYURtnPwYE3wn\nxVUlfJayhBqd6VvuutxyK4pGQ966teiqzOMDt0/nVsx6oCfBfs4kpV3g35/uJOV4rqnDajT1FgKn\nT59m7NixqFQqNBoNTz31FFlZWU0RmxBCCCPr79ubCK+upBec4Lv0taYOB7WjE85RA6jOy+XEl4ub\nfDnhtXi42DFjQndGR7WlqLSKecv2smzjEaqqm/9EwnoLASsrK4qKimqviRw/ftys5wcIIYQwnKIo\nTAgZg7e9JxtPxrPvQoqpQ8L1tmGotFrOfP8D6c9M4+wnH1F6OA1TN8JVqRTuuDmQf8VE4O1qxy+J\np3j1/3aRecE8ipUbVe9eAz4+Pjz77LOcPXuWPXv28MEHH/Diiy8SGBjYNBHeAOl3Xj/pC284yZVh\nJE+GMcc8qVVqgl3asePsLg7kHKS7Vxfsre1NFo+VnR3O/aJwbu1FSeYZytJSKdy6heKkRPQ1NWi8\nW6HSaEwWn6ujDf27tKa4rIr96Tls2X8WO40VQT6m2a+gSfYayM3NJTk5mZqaGrp27YqHh0eDTmps\n5jAj19yZy8zl5kByZRjJk2HMOU87zu4i7tAK/B19ebr741ibeHMiT09Hzp8vpCwtlYL4TRQl7YKa\nGhRraxwje+IcPRDbtu1MOot/z+ELfL42leKyKsLauvHgsNAm382woasG6i0EcnNz+fHHHykoqNth\naerUqQ06sTGZ64vMnJjzm5G5kVwZRvJkGHPP0+JDX7P9bCL9ffswrqNpd5n9c66qiwop3LqFgvjN\nVJ0/B4DG1w+XAdE49r4ZK3vTjGLkF1fw2Y+HOJCRi9bOmgeGhdAt2LPJzt/QQqDeSwOTJk1Cp9Ph\n5ORU5/aePXs26MTGZG7DbubIHIcnzZXkyjCSJ8OYe55C3DpwIOcQB3IO4W3nQWutj8li+XOuVDY2\n2LUPxmXgYOw7dERXVUnZ0SOUJO8jf+N6qi6cx8rJBbWLS5OOEthq1PTq7I2DnTXJx3LYkXKO/OIK\nQtu4orYy/pw6o18aGDNmDN98802DTtLUzLnaNhfm/q3EnEiuDCN5MkxzyNO50gu8kfgeOvTMiHyC\nVg5eJonDkFxVFxRQuPX3i6ME2RcAsPFvg/OAaJx690Fla9cUodY6faGYj78/yOkLxXi72fPIiE4E\n+TjV/8AGMPqIQG5uLsePH8fJyYmSkhKKioooKirC0bFhJzYmc662zYW5fysxJ5Irw0ieDNMc8qS1\ndsDDzp1d5/ZyJP8YvX0isVJZNXkchuRKZWuLXXAHXAYNwa5de/QVlZQdOUzJvr3kbdxIdU42apeL\nowRNwclBQ78uPlRW1ZB8LIet+8+iUhTa+zobbZSioSMC6vruUFRUxMcff4yrq2vtbYqisHHjxgad\nWAghhPmK8O7KsYIMNp/exrK0b4kJvdfsWuteSVGpcAgLxyEsnOr8PAq2XBwlKIjfREH8JmwCP9dV\nAQAAIABJREFUg3CJisaxZy9UtrZGjcVarWLc4GDC27nz6Q8HWRWfzoH0HB4a0QkP56YdoTBEvZcG\nhgwZwg8//ICtkRPXmMx92M0cNIfhSXMhuTKM5MkwzSlPVbpq3k5ayImiU0wMuYebW/do0vM3NFd6\nnY6SA/spiN9Eyb69oNejsrXFsffNuAyIxsa/TSNGe3XFZVX839pUkg5fwM5GTcytHejduVWjnsPo\nlwZ+++03+vfvj1arbdCJmpK5D7uZg+YwPGkuJFeGkTwZpjnlyUpREeIWzM6sJPZnpxDmHoqTTdNd\nFm5orhRFQePdCqeevXHq1x+VrR2VZ89QlnqIgs2/UXJgP6hUaLxboajrHSC/IRprK3qEeOHuZEvy\nsRwSDp3nXG4poQGuWKsb53KL0ScLTp48meTkZIKDg7G2/mNN6ZdfftmgExtTc6m2Tak5fSsxNcmV\nYSRPhmmOedqffZAPk7/Ay86D53o8gZ26aUaIjZErfU0NJfuT/ygE9HpUdnY49emL84CB2Pj6Nur5\nrnQur5RP1hwk/Uwh7k42PHRHJzq2ca3/gfUweh+BhISEq95u6PLBnJwcxowZw+eff05QUBAAa9as\nYcmSJSxbtgyAFStWsHz5cqytrZkyZQrR0dFUVFTw7LPPkpOTg1arZc6cOXXmKVxPc3uRmUJzfDMy\nFcmVYSRPhmmueVp99CfWn9xEN68uPNh5YpPMFzB2rqpysin4fTMFv8dTc6lXjm37YFwGRKON6GGU\n7oXVNTp+2HacNduOgx6G9QlgZL+gBi0zbGghUO9YSEP6BVRXVzNz5sw68wsOHjxYZzlidnY2cXFx\nfPvtt5SXlzN+/Hj69u3L0qVL6dChA1OnTuWnn35iwYIFvPjiizccixBCiBs3ou1tpBecYM/5ZDa7\nBBHt19fUITWYtbsHHqPG4H7HSIr37aUgfhOlKQfIOnoE1dKvcOrbD5eoAWh8WjfaOdVWKkb1b0tY\nkDsfr0nhx+0nOJCRyyMjOuHj7tBo5/k7jNrpYO7cuYwfPx4vr4trUPPz83nnnXfqfKAnJycTERGB\nWq1Gq9USGBhIamoqSUlJREVFARAVFcX27duNGaoQQojrsFJZMTlsAlprB1Yd+YHjhSdNHVKjUdRq\nHCMi8XvqGQJnv4Hr7cNRrKzIX/8zx1/+F6femE3hzh2Nui1yez9nZk3uSd+wVpzIKmLWF4ls2pNp\nko2VjFYIrFq1Cnd3d/r27Yter6empoYXX3yR559/Hju7P5ZPFBcX1+lJYG9vT3FxMSUlJbUTFB0c\nHCg2k60ohRDCUrnYOPNA5wno9Do+PbCEkqpSU4fU6DSeXniOuYe2b/4PnymPYx/aibLDaWR98iEZ\nz07nwtfLqDyX1SjnsrNR8+AdnZgysjNqlYovf07j/W/2U9jEk0mNM02Si4WAoihs3bqV1NRU7rzz\nTvz8/HjllVeoqKjg2LFjzJ49m169etX5kC8pKcHJyQmtVktJSUntbX+ngVFDr5dYCsmT4SRXhpE8\nGaY558nTsztZVcP4OuVHlh37huf6TUGlGG9w2ZS58vIZDLcPpuzMGbJ+Xs/5XzeR9/M68n5eh3OX\ncFrddgtuvXqism7Y5kzDPR3pGe7LO8t2s/doNrM+T+TJcd2ICPFupL/k+gzafbChYmJiePXVV2u3\nLs7MzOTpp59m2bJlZGdnM3nyZFauXElFRQVjx45l9erVLFmyhJKSEqZOncqPP/7Irl27mDlzpkHn\na44TcZpac52wZAqSK8NIngzTEvKk0+v4YO+npOYdYVS7YdwSEG2U85hbrnRVVRTvTqJg82+UHU4D\nwMrRCad+/XGOGoDGs2GtmHV6PT8nnGTV5nRqdHoGR/hxT3Q7NNbXX2Zo9MmCjUFRlGte9/Dw8CAm\nJoYJEyag1+uZPn06Go2G8ePHM2PGDCZMmIBGo2HevHlNEaoQQoh6qBQV93cez+yEd/g+fR2BTm0I\ndm1r6rCMTmVtjVOv3jj16k3l2TPkx2+mcNsW8tb+SN7aH7HvHIZzVDTarjfdUF8ClaJwe68AOgW4\n8fGaFDYmnSb1RB4Pj+hEG2/jjYw0yYhAUzOnCtJcmVulbc4kV4aRPBmmJeXpaH4G7+75CEdrB17o\n+RSOmsZtPNcccqWrqqR41y4K4jdRduQwAFbOLjhfGiWwdve4oeNWVNXw9W9H+XV3JmorhdFR7bi1\npz+qqyzbNHpnweaouXTtMqXm1N3M1CRXhpE8GaYl5cnN1hVrlZp92SmcKsqkR6tujdpfoDnkSrGy\nwsbfH+d+/dFG9EBRqag4kUHpwRTyN66nPCMdla0t1p5eKCrD51KorVR0aedBkI8jB9Jz2X0kmyOn\nC+gU6IadTd3RhoZ2FpRCwEI1hxeYuZBcGUbyZJiWlqe2zgGcKs7kYO5hFKCDa7tGO3Zzy5XayQmH\n8C64DL4Fa29vagoKKEtLpShhJ4Vbf6emrAxrL2+s7AzfeMjbzZ6bw3w4m1PCgYxctu4/i5eLHa09\n/ug5IIXAVTSnJ46pNLcXmClJrgwjeTJMS8uToih0cuvI7vP72J99iCCnADzt3Rvl2M01V4pajW2b\nAJz7D0DbrTuoFCoyLo0SbPiF8hPHUdldGiUwYATFRmNFr07eODtoSD6Ww46D58guKLu0X4FKCoGr\naY5PnKbWXF9gpiC5MozkyTAtMU/WVta0dQ5k59ldHMhJpUerbtg2wn4ELSFXamdntF26Xhwl8PSk\nOj//4ijBzh0Ubt2CrqICjZcXKtvrjxIoikKQjxMRHT05llnI/vRcElPP0dbHCb9WTg2KUQoBC9US\nXmBNRXJlGMmTYVpqnlxsnLG3tmfPhf0cLzxFr1bdG9xfoCXlSlGrsQ0IxCUqGoeuNwFQnpFBacp+\n8jasp+LkSVT29lh7eF53lMDRXkO/Lj5U63QkH81hy/4sxt/asUGxSSFgoVrSC8zYJFeGkTwZpiXn\nKcDRj3OlFziYm0aVrppQtw4NOl5LzZXaxQVt15twHTwYtbsH1Xl5lKUdomjHdoq2b0NfWYm1lzcq\n26uPqqhUCp0D3ejo78LBE7ncFd2+QfHI8kEL1RyW5ZgLyZVhJE+Gael5Kq8uZ+6u9zhfms2j4ffR\nxbPzDR+rpefqMr1eT3lGBgXxv1GUsBN9ZSVYWaHt1h2XAQOx6xhyzRUHlVU1+LZ2adD5pRCwUJby\nAmsMkivDSJ4MYwl5yiw+y5u73ketsub5Hk/iYed2Q8exhFz9WU1pKUU7tpG/eROVmacBsPbyxjlq\nAE59+6F2/Ot8AOkjcBUtcSipsbXUITdjkFwZRvJkGEvIk5PGEWeNE7vP7yO94Di9fCKwuoH5ApaQ\nqz9TWVtjG9QW5+iBOISFg66G8mNHKT2wn/yN66k8k4mVgxa1u0ftXAJZNXAVlvbEuRGW+AK7UZIr\nw0ieDGMpefJ39CW3PI+UnFRKq8oI8wj528ewlFxdjaIoWLu5oe0WgcvAwahdXKm6cIGytFQKt22l\nKHEnVNeg8W6F1rUZ7DUghBDC8oztMIqThaeJz9xGe5dAIrxvMnVIzZKVgwOuQ27BZfAQyo4cpmDz\nJoqTErmwYinZq76m1TfLG3R84+0dKYQQwqJprDQ8FDYJGysNS1JXcq7kvKlDatYURcG+Q0d8Hn6U\ntm+9g+e941B73NheBleSQkAIIYTReDt4MTHkbipqKll0YDGVNZY51N/YrLRaXG8dStB/5zT4WFII\nCCGEMKoI75uI8r2ZMyVZLD+82tThiD+RQkAIIYTRjQ6+gzaOfuw4u4vtZxJNHY64ghQCQgghjM5a\npebBsEnYqe1YfvhbMovPmjokcYkUAkIIIZqEh50bsaH3UqWrZtGBOMqqy00dkkAKASGEEE2oi2dn\nhrQZwPnSbJamfkMLbG7b7EghIIQQoknd2XYo7ZwDSTq/j/jM7aYOx+JJISCEEKJJWamsmBw2Ea21\nA98cWcOJwlOmDsmiSSEghBCiybnYOHN/5/Ho9Do+PbCY0qpSU4dksaQQEEIIYRKhbh24PXAwOeV5\nfHloucwXMBEpBIQQQpjM7UFDCHENZn/2ITac3GzqcCySFAJCCCFMRqWouL/zeJw1Tnyfvo6j+Rmm\nDsniSCEghBDCpBw1WiaHTQTgswNLKKosNnFElkUKASGEECbX3iWIO9sOpaCykC9SlqLT60wdksUw\neiGQk5NDdHQ0GRkZHDp0iIkTJxIbG8tDDz1Ebm4uACtWrGDMmDGMGzeOTZs2AVBRUcETTzzBxIkT\nefTRR8nLyzN2qEIIIUxocJsowj1CSc07wtrjG00djsUwaiFQXV3NzJkzsbW1Ra/X8/rrr/Pvf/+b\nL7/8kltuuYVPPvmE7Oxs4uLiWL58OYsWLWLevHlUVVWxdOlSOnTowJIlSxg5ciQLFiwwZqhCCCFM\nTKWoiAkdi5utK2szNhB/fKesJGgCRi0E5s6dy/jx4/Hy8kJRFN5++206duwIXCwSNBoNycnJRERE\noFar0Wq1BAYGkpqaSlJSElFRUQBERUWxfbt0nxJCiJbOwdqeh8ImYaWyYv7OL3hj1/scyjksBYER\nGa0QWLVqFe7u7vTt27f2H9DDwwOA3bt389VXX3H//fdTXFyMo6Nj7ePs7e0pLi6mpKQErVYLgIOD\nA8XFMnlECCEsQYCTP//q+RQ3+0dwsug08/ct4t09H5FecNzUobVIamMdeNWqVSiKwtatW0lNTWXG\njBksXLiQnTt38tFHH/Hxxx/j6uqKVqut8yFfUlKCk5MTWq2WkpKS2tuuLBbq4+lp+H0tmeTJcJIr\nw0ieDCN5qp8njoQFtGVU3m0s2/89u88eYF7SArr7hDEu/E4CXf1NHWKLYbRCYPHixbX/HRMTw3/+\n8x+2bNnCihUriIuLw8nJCYAuXbrwzjvvUFlZSUVFBenp6QQHB9OtWzc2b95MeHg4mzdvJjIy0uBz\nX7hQ1Oh/T0vj6ekoeTKQ5MowkifDSJ4M5+npiEO1Cw+GxhLtc5zv09ey++wBdp89QIRXV4a3vRVv\ne09Th2lyDS0sjVYIXElRFGpqanj99ddp3bo1//jHP1AUhZ49ezJ16lRiYmKYMGECer2e6dOno9Fo\nGD9+PDNmzGDChAloNBrmzZvXFKEKIYQwQ+1cApnWbQqpuUf4Pn0tSef3sefCfnq3imRY0BBcbV1M\nHWKzpehb4AwMqbbrJ99KDCe5MozkyTCSJ8NdK1d6vZ59Fw6wJv1nskrPo1as6O/Xh9sCBuGo0Zog\nUtNqFiMCQgghRGNRFIWbvMLp4tmZxKw9/JjxC7+d2sLWMwkM8u/PYP8o7K3tTB1msyGFgBBCiGZJ\npajo5RNBhHdXtp1JYO3xjaw7vpH409u4JSCaaL++aKw0pg7T7EkhIIQQollTq9RE+d1Mb59INp/e\nxi8nfuO7Y2v57dQWhgYOpm/rnqhV8nF3LZIZIYQQLYLGSsMtAdH08+3FxpPxbDz1OysOr2bjyc0M\nC7qFnq26o1Jki50/k4wIIYRoUezUdtzR9jb+0+d5Bvn3p6CyiLhDK3ht5//Yc36/dCn8ExkREEII\n0SI5arSMCR7BIP/+rD2+ge1nd7HoQBxtHH0Z0XYooW4dUBTF1GGanBQCQgghWjRXWxcmhNzNkDYD\n+CH9F5LO7+ODfZ9e2vr4dtq5BJo6RJOSQkAIIYRF8LL3ZHLYRG4tGsia9J85kHOI/+1eQGf3EEa0\nvQ1/R19Th2gSUggIIYSwKH6OrXms6wOkFxzn+2PrSMlJJSUnle5eXbgj6Fa8HbxMHWKTkkJACCGE\nRWrrHMiT3R4lNe8I3x9bx+7zyey9cIDerSK4PWgIbraupg6xSUghIIQQwmIpikKoWwdCXIPZl53C\nmvSf2XY2kYSs3fT37cNtgS2/bbEUAkIIISyeoijc5BlGF49Ol9oWr+e301vYejaBQX79GNxmQItt\nWyyFgBBCCHFJ3bbFiaw7voF1J35lc+Z2bm0TzQD/vti0sLbFUggIIYQQf3KxbXEfevtEsPn0Ntaf\n2MR36Wv59fTvl9oW98K6hbQtbhl/hRBCCGEEddsW/86vp+L5+vB3bDwZf7FtsXc3rFRWpg6zQaTF\nsBBCCFGPi22Lb2XWpbbFhZVFLD60gtcS3mb3+WR0ep2pQ7xhMiIghBBCGKhu2+KNbD+byKcHFuN/\nqW1xp2bYtlgKASGEEOJvuti2eAxD2kTxY8Z6ks7tY8G+T2nnHMSd7YbS3iXI1CEaTC4NCCGEEDfI\ny96TBzpP4IWe0wj3COVYQQZv717IB/s+5VRRpqnDM4iMCAghhBAN5Kv1YUqXB0gvOMH3x9ZyMCeN\ngzlpdLvUtriVGbctlkJACCGEaCRtnQN4stujpOUd5ftj69hzPpm95/fT2yeS2wOH4G5nfm2LpRAQ\nQgghGpGiKIS4BdPRtT3Jl9oWbz+bSGLWbvr59ua2wEE4aRxNHWYtKQSEEEIII1AUha6eYYR7dGLX\nub38kP4Lm05vZduZBAb692dImyjsre1NHaYUAkIIIYQxqRQVPVt1p7tXF7afTWRtxgZ+PvEr8Znb\nuaXNAKL9+5m0bbEUAkIIIUQTUKvU9PftQ69WEcRnbueX47/xffo6fju9haEBg+nra5q2xVIICCGE\nEE1IY6VhSJsB9G3dk19P/s7GU/F8feQ7NpzczPCgW+jZqnuTti02eh+BnJwcoqOjycjI4OTJk0yY\nMIFJkyYxa9as2vusWLGCMWPGMG7cODZt2gRARUUFTzzxBBMnTuTRRx8lLy/P2KEKIYQQTcZObcfw\nS22LB/tHUVRVzOLUr3kt4X9N2rbYqIVAdXU1M2fOxNbWFoDZs2czffp0Fi9ejE6nY8OGDWRnZxMX\nF8fy5ctZtGgR8+bNo6qqiqVLl9KhQweWLFnCyJEjWbBggTFDFUIIIUzCUaNldPAdvNL7Ofq27sWF\nshw+PbCYNxLfIyUnFb1eb9TzG7UQmDt3LuPHj8fLywu9Xs/BgweJjIwEICoqim3btpGcnExERARq\ntRqtVktgYCCpqakkJSURFRVVe9/t27cbM1QhhBDCpC63LX651zNEet/E6eKzLNj3GW/vXsjR/Ayj\nnddohcCqVatwd3enb9++tdWMTvfHMIeDgwPFxcWUlJTg6PjHekp7e/va27VabZ37CiGEEC2dl73H\nFW2LO3Gs4PjFtsV7P+Vk0elGP5/RJguuWrUKRVHYunUraWlpzJgxo851/pKSEpycnNBqtXU+5K+8\nvaSkpPa2K4uF+nh6mk+jBnMmeTKc5MowkifDSJ4MZ8m58vR05KagDhzOTmfp/u9IOZ/Gwdw0evt1\nZ2z4CHydWjXKeYxWCCxevLj2v2NjY5k1axZvvPEGiYmJ9OjRg/j4eHr37k14eDhvv/02lZWVVFRU\nkJ6eTnBwMN26dWPz5s2Eh4ezefPm2ksKhrhwocgYf1KL4unpKHkykOTKMJInw0ieDCe5usgVTx4P\ne4jU3CN8n76OHad3s/P0Hnr5RDAs8BZC2rRp0PGbdPngjBkzePnll6mqqqJdu3YMHToURVGIiYlh\nwoQJ6PV6pk+fjkajYfz48cyYMYMJEyag0WiYN29eU4YqhBBCmJU/2hYfZE36Onac3UVi1h6Wtpnf\noOMqemNPRzQBqSDrJ5W24SRXhpE8GUbyZDjJ1bXp9Dp2ndvLj+m/sGDkaw06ljQUEkIIIZqZy22L\nI71vavixGiEeIYQQQpiASmn4x7gUAkIIIYQFk0JACCGEsGBSCAghhBAWTAoBIYQQwoJJISCEEEJY\nMCkEhBBCCAsmhYAQQghhwaQQEEIIISyYFAJCCCGEBZNCQAghhLBgUggIIYQQFkwKASGEEMKCSSEg\nhBBCWDApBIQQQggLJoWAEEIIYcGkEBBCCCEsmBQCQgghhAWTQkAIIYSwYFIICCGEEBZMCgEhhBDC\ngkkhIIQQQlgwKQSEEEIICyaFgBBCCGHBpBAQQgghLJjamAfX6XS89NJLZGRkoFKpmDVrFtXV1cyc\nORO1Wk1gYCCvvfYaACtWrGD58uVYW1szZcoUoqOjqaio4NlnnyUnJwetVsucOXNwdXU1ZshCCCGE\nRTHqiMCvv/6KoigsXbqUJ598kv/973988MEHTJ06lSVLllBRUcGmTZvIzs4mLi6O5cuXs2jRIubN\nm0dVVRVLly6lQ4cOLFmyhJEjR7JgwQJjhiuEEEJYHKMWAkOGDOHVV18FIDMzE2dnZ0JDQ8nLy0Ov\n11NSUoJarSY5OZmIiAjUajVarZbAwEBSU1NJSkoiKioKgKioKLZv327McIUQQgiLY/Q5AiqViuef\nf57XXnuNESNGEBAQwGuvvcbw4cPJzc2lZ8+eFBcX4+joWPsYe3t7iouLKSkpQavVAuDg4EBxcbGx\nwxVCCCEsilHnCFw2Z84ccnJyuPvuu6moqOCrr76iXbt2LFmyhDlz5tC/f/86H/IlJSU4OTmh1Wop\nKSmpve3KYuF6PD0Nu5+lkzwZTnJlGMmTYSRPhpNcGZ9RRwS+++47Pv74YwBsbGxQqVS4uLjg4OAA\ngLe3N4WFhYSHh5OUlERlZSVFRUWkp6cTHBxMt27d2Lx5MwCbN28mMjLSmOEKIYQQFkfR6/V6Yx28\nrKyMF154gezsbKqrq3nkkUdwcXHhzTffRK1Wo9FoePXVV2ndujVff/01y5cvR6/X89hjjzFkyBDK\ny8uZMWMGFy5cQKPRMG/ePNzd3Y0VrhBCCGFxjFoICCGEEMK8SUMhIYQQwoJJISCEEEJYMCkEhBBC\nCAsmhYAQQghhwZpVIZCQkEBISAg//fRTndtHjBjBCy+8YKKozMfcuXOJiYnh9ttvZ+DAgcTGxjJt\n2jRTh2WW7r//fvbv3w9AVVUVkZGRfPbZZ7W/j4mJITU19brHqKysZNCgQUaN01T+/FyKiYmhT58+\nPP3006YOrVnJzMwkIiKC2NhYYmJiiI2N/Uur9Keffprq6moTRWgePv74Yx544AFiYmK47777SElJ\nueZ9V6xYQU1NTRNGZx7+To7+riZpKNSY2rZty08//cSwYcMAOHz4MOXl5SaOyjzMmDEDgG+//ZaM\njAymT59u4ojMV9++fUlKSiI8PJxdu3bRv39/Nm/ezOTJk6msrOTs2bOEhIRc9xh6vR5FUZoo4qZ1\ntedSQkICy5cvN3FkzU9wcDBffvnlNX8/b968JozG/Bw7doxff/2VZcuWAZCamsrzzz/P6tWrr3r/\nDz/8kFGjRmFlZdWUYZrU383R39WsRgQAQkJCOHPmTG0nwu+//54777wTgDVr1nD33XczceJE/vWv\nf1FdXc23337LtGnTmDJlCsOHD2+0xDUXCQkJdQqCfv36AZCVlcXDDz9MbGwsjzzyCOfOnaOyspLH\nHnuMmJgY7rnnHrZt22aqsI3u5ptvZteuXQDEx8dzzz33UFRURHFxMXv27KFHjx4kJiYyYcIEYmJi\nePHFF6mpqaG0tJTHH3+cmJgYZs2aZeK/oullZGTwyCOPMGbMGObPnw9cHD3JyMgAYNmyZcyfP5/M\nzExGjBhBbGwsn376KV999RX33nsv48aNq91x1FL8eYV2QkIC9957L5MmTeK7775j0KBBVFZWmig6\n09NqtWRlZbFy5UrOnTtHSEgIX3/9NYmJidx3333ExsZy9913c+LECVauXEl2drbFfcm5Wo5WrFhx\nzdfeuHHjeOqppxg9ejSvvPJKvcdvdiMCALfeeivr16/nrrvuIjk5mUceeYSUlBTmz5/P6tWrsbOz\nY86cOSxfvrx234JFixZx4sQJpkyZwqhRo0z9JzSpq31rnTt3LrGxsfTv35/t27fz5ptvMmXKFPLz\n81m0aBE5OTkcP3686YNtIp06dSI9PR2AxMREpk+fTp8+fdi2bRtpaWn069ePl156iaVLl+Lm5sa7\n777LqlWrKCoqokOHDkybNo3k5GR27txp4r+kaVVVVbFgwQKqq6sZOHAgU6dOveZ9c3JyWL16NVZW\nVtxzzz3MnDmTsLAwli1bhk6nQ6Vqdt9DbsjRo0eJjY2tHUG65557qKysZMWKFQC89957Jo7QtLy9\nvVm4cCFxcXF88MEH2NnZMW3aNHJycnjrrbfw9PTko48+Yt26dTz66KMsXLiQt99+29RhN6lr5eha\nI5LHjx/n888/x8bGhiFDhpCTk3PdZnzNrhBQFIU77riDmTNn4ufnR48ePdDr9ej1etq3b4+dnR0A\nkZGRbN26lS5duhAaGgqAj4+PRVfeVzp8+DAfffQRn3zyCXq9Hmtra9q3b8/YsWOZPn061dXVxMbG\nmjpMo1EUhZCQEOLj4/H09MTa2pr+/fuzadMm0tLSmDhxIi+//DLTpk1Dr9dTWVnJzTffTE5ODtHR\n0QB06dIFtbrZvYQaJDg4GLVajVqtvurQ7JXffv38/Grv8/rrr/PZZ59x+vRpunXr9pdvyS3Zny8N\nJCQkEBQUZMKIzMvJkydxcHDg9ddfByAlJYWHHnqIGTNm8Oqrr+Lg4MC5c+fo3r07QO37vSW5Vo68\nvLxq73NlTgICAmo/C728vKioqLju8ZtlSe7n50dZWRlxcXG1lwUUReHo0aOUlZUBF19sgYGBtb+7\nzNKeQDY2Npw/fx64OHEpPz8fgHbt2vHMM8/w5ZdfMmvWLIYOHcrhw4cpKSnho48+Ys6cObVbSLdU\nffr04aOPPqrd6joiIoKUlBR0Oh2urq74+PiwYMEC4uLiePTRR+nduzft27dnz549ABw8eNDiJnld\n7RuIjY0NFy5cAC7m5Gr3XbFiBbNmzSIuLo6UlJTaHFqCq73nXDkaYmnvSX+WlpbGf/7zH6qqqoCL\nH2JOTk7Mnj2bOXPmMHv27DofeCqVyuJydq0cubi41L6/X/nau5IhuWq2X2eGDRvG999/T0BAACdP\nnsTV1bX2mqSVlRVt2rThmWee4ccff6zzuJY6uetawsLCcHR0ZOzYsbRt2xZ/f38Ann0IrzU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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -968,6 +1221,16 @@ "plt.ylabel('mean births by day');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Apparently births are slightly less common on weekends than on weekdays! Note that the 1990s and 2000s are missing because the CDC data contains only the month of birth starting in 1989.\n", + "\n", + "Another intersting view is to plot the mean number of births by the day of the *year*.\n", + "Let's first group the data by month and day separately:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -992,10 +1255,19 @@ } ], "source": [ - "births_by_date = births.pivot_table('births', [births.index.month, births.index.day])\n", + "births_by_date = births.pivot_table('births', \n", + " [births.index.month, births.index.day])\n", "births_by_date.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a multi-index over months and days.\n", + "To make this easily plottable, let's turn these months and days into a date by associating them with a dummy year variable (making sure to choose a leap year so February 29th is correctly handled!)" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -1025,6 +1297,14 @@ "births_by_date.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Focusing on the month and day only, we now have a time series reflecting the average number of births by date of the year.\n", + "From this, we can use the ``plot`` method to plot the data. It reveals some interesting trends:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -1034,9 +1314,9 @@ "outputs": [ { "data": { - "image/png": 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XldTSlH5BEASh3bz11lucPn2aZcuWtelxq6urmTdvHsuXL2fYsGFteuycnBylZZ2Pj0+b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\n1Kn0798frVbLRx99R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yYhU6hxyIRGOCH7nMkF3wihgGW1eVYHOzGSNWL3pHXSgvVkEqyX+zKjEohYSb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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1046,29 +1326,36 @@ "source": [ "# Plot the results\n", "fig, ax = plt.subplots(figsize=(12, 4))\n", - "births_by_date.plot(ax=ax)\n", + "births_by_date.plot(ax=ax);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "In particular, the striking feature of this graph is the dip in birthrate on US holidays (e.g., Independence Day, Labor Day, Thanksgiving, Christmas, New Year's Day) although this likely reflects trends in scheduled/induced births rather than some deep psychosomatic effect on natural births.\n", + "For more discussion on this trend, see the analysis and links in [Andrew Gelman's blog post](http://andrewgelman.com/2012/06/14/cool-ass-signal-processing-using-gaussian-processes/) on the subject.\n", + "We'll return to this figure in [Example:-Effect-of-Holidays-on-US-Births](04.09-Text-and-Annotation.ipynb#Example:-Effect-of-Holidays-on-US-Births), where we will use Matplotlib's tools to annotate this plot.\n", "\n", - "# Add labels to the plot\n", - "ax.text('2012-1-1', 3950, \"New Year's Day\")\n", - "ax.text('2012-7-4', 4250, \"Independence Day\", ha='center')\n", - "ax.text('2012-9-4', 4850, \"Labor Day\", ha='center')\n", - "ax.text('2012-10-31', 4600, \"Halloween\", ha='right')\n", - "ax.text('2012-11-25', 4450, \"Thanksgiving\", ha='center')\n", - "ax.text('2012-12-25', 3800, \"Christmas\", ha='right')\n", - "ax.set(title='USA births by day of year (1969-1988)',\n", - " ylabel='average daily births',\n", - " xlim=('2011-12-20','2013-1-10'),\n", - " ylim=(3700, 5400));\n", + "Looking at this short example, you can see that many of the Python and Pandas tools we've seen to this point can be combined and used to gain insight from a variety of datasets.\n", + "We will see some more sophisticated applications of these data manipulations in future sections!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb) | [Contents](Index.ipynb) | [Vectorized String Operations](03.10-Working-With-Strings.ipynb) >\n", "\n", - "# Format the x axis with centered month labels\n", - "ax.xaxis.set_major_locator(mpl.dates.MonthLocator())\n", - "ax.xaxis.set_minor_locator(mpl.dates.MonthLocator(bymonthday=15))\n", - "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", - "ax.xaxis.set_minor_formatter(mpl.dates.DateFormatter('%h'));" + "\"Open\n" ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/03.10-Working-With-Strings.ipynb b/notebooks_v1/03.10-Working-With-Strings.ipynb similarity index 57% rename from code_listings/03.10-Working-With-Strings.ipynb rename to notebooks_v1/03.10-Working-With-Strings.ipynb index 852405942..75c004b84 100644 --- a/code_listings/03.10-Working-With-Strings.ipynb +++ b/notebooks_v1/03.10-Working-With-Strings.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Pivot Tables](03.09-Pivot-Tables.ipynb) | [Contents](Index.ipynb) | [Working with Time Series](03.11-Working-with-Time-Series.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,24 @@ "# Vectorized String Operations" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One strength of Python is its relative ease in handling and manipulating string data.\n", + "Pandas builds on this and provides a comprehensive set of *vectorized string operations* that become an essential piece of the type of munging required when working with (read: cleaning up) real-world data.\n", + "In this section, we'll walk through some of the Pandas string operations, and then take a look at using them to partially clean up a very messy dataset of recipes collected from the Internet." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introducing Pandas String Operations\n", + "\n", + "We saw in previous sections how tools like NumPy and Pandas generalize arithmetic operations so that we can easily and quickly perform the same operation on many array elements. For example:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -31,6 +71,14 @@ "x * 2" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This *vectorization* of operations simplifies the syntax of operating on arrays of data: we no longer have to worry about the size or shape of the array, but just about what operation we want done.\n", + "For arrays of strings, NumPy does not provide such simple access, and thus you're stuck using a more verbose loop syntax:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -54,6 +102,14 @@ "[s.capitalize() for s in data]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is perhaps sufficient to work with some data, but it will break if there are any missing values.\n", + "For example:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -79,6 +135,14 @@ "[s.capitalize() for s in data]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pandas includes features to address both this need for vectorized string operations and for correctly handling missing data via the ``str`` attribute of Pandas Series and Index objects containing strings.\n", + "So, for example, suppose we create a Pandas Series with this data:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -108,6 +172,13 @@ "names" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now call a single method that will capitalize all the entries, while skipping over any missing values:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -135,6 +206,23 @@ "names.str.capitalize()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using tab completion on this ``str`` attribute will list all the vectorized string methods available to Pandas." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tables of Pandas String Methods\n", + "\n", + "If you have a good understanding of string manipulation in Python, most of Pandas string syntax is intuitive enough that it's probably sufficient to just list a table of available methods; we will start with that here, before diving deeper into a few of the subtleties.\n", + "The examples in this section use the following series of names:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -147,6 +235,27 @@ " 'Eric Idle', 'Terry Jones', 'Michael Palin'])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Methods similar to Python string methods\n", + "Nearly all Python's built-in string methods are mirrored by a Pandas vectorized string method. Here is a list of Pandas ``str`` methods that mirror Python string methods:\n", + "\n", + "| | | | |\n", + "|-------------|------------------|------------------|------------------|\n", + "|``len()`` | ``lower()`` | ``translate()`` | ``islower()`` | \n", + "|``ljust()`` | ``upper()`` | ``startswith()`` | ``isupper()`` | \n", + "|``rjust()`` | ``find()`` | ``endswith()`` | ``isnumeric()`` | \n", + "|``center()`` | ``rfind()`` | ``isalnum()`` | ``isdecimal()`` | \n", + "|``zfill()`` | ``index()`` | ``isalpha()`` | ``split()`` | \n", + "|``strip()`` | ``rindex()`` | ``isdigit()`` | ``rsplit()`` | \n", + "|``rstrip()`` | ``capitalize()`` | ``isspace()`` | ``partition()`` | \n", + "|``lstrip()`` | ``swapcase()`` | ``istitle()`` | ``rpartition()`` |\n", + "\n", + "Notice that these have various return values. Some, like ``lower()``, return a series of strings:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -175,6 +284,13 @@ "monte.str.lower()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But some others return numbers:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -203,6 +319,13 @@ "monte.str.len()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or Boolean values:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -231,6 +354,13 @@ "monte.str.startswith('T')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Still others return lists or other compound values for each element:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -259,6 +389,41 @@ "monte.str.split()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll see further manipulations of this kind of series-of-lists object as we continue our discussion." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Methods using regular expressions\n", + "\n", + "In addition, there are several methods that accept regular expressions to examine the content of each string element, and follow some of the API conventions of Python's built-in ``re`` module:\n", + "\n", + "| Method | Description |\n", + "|--------|-------------|\n", + "| ``match()`` | Call ``re.match()`` on each element, returning a boolean. |\n", + "| ``extract()`` | Call ``re.match()`` on each element, returning matched groups as strings.|\n", + "| ``findall()`` | Call ``re.findall()`` on each element |\n", + "| ``replace()`` | Replace occurrences of pattern with some other string|\n", + "| ``contains()`` | Call ``re.search()`` on each element, returning a boolean |\n", + "| ``count()`` | Count occurrences of pattern|\n", + "| ``split()`` | Equivalent to ``str.split()``, but accepts regexps |\n", + "| ``rsplit()`` | Equivalent to ``str.rsplit()``, but accepts regexps |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With these, you can do a wide range of interesting operations.\n", + "For example, we can extract the first name from each by asking for a contiguous group of characters at the beginning of each element:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -284,7 +449,14 @@ } ], "source": [ - "monte.str.extract('([A-Za-z]+)')" + "monte.str.extract('([A-Za-z]+)', expand=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or we can do something more complicated, like finding all names that start and end with a consonant, making use of the start-of-string (``^``) and end-of-string (``$``) regular expression characters:" ] }, { @@ -315,6 +487,45 @@ "monte.str.findall(r'^[^AEIOU].*[^aeiou]$')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ability to concisely apply regular expressions across ``Series`` or ``Dataframe`` entries opens up many possibilities for analysis and cleaning of data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Miscellaneous methods\n", + "Finally, there are some miscellaneous methods that enable other convenient operations:\n", + "\n", + "| Method | Description |\n", + "|--------|-------------|\n", + "| ``get()`` | Index each element |\n", + "| ``slice()`` | Slice each element|\n", + "| ``slice_replace()`` | Replace slice in each element with passed value|\n", + "| ``cat()`` | Concatenate strings|\n", + "| ``repeat()`` | Repeat values |\n", + "| ``normalize()`` | Return Unicode form of string |\n", + "| ``pad()`` | Add whitespace to left, right, or both sides of strings|\n", + "| ``wrap()`` | Split long strings into lines with length less than a given width|\n", + "| ``join()`` | Join strings in each element of the Series with passed separator|\n", + "| ``get_dummies()`` | extract dummy variables as a dataframe |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Vectorized item access and slicing\n", + "\n", + "The ``get()`` and ``slice()`` operations, in particular, enable vectorized element access from each array.\n", + "For example, we can get a slice of the first three characters of each array using ``str.slice(0, 3)``.\n", + "Note that this behavior is also available through Python's normal indexing syntax–for example, ``df.str.slice(0, 3)`` is equivalent to ``df.str[0:3]``:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -343,6 +554,16 @@ "monte.str[0:3]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Indexing via ``df.str.get(i)`` and ``df.str[i]`` is likewise similar.\n", + "\n", + "These ``get()`` and ``slice()`` methods also let you access elements of arrays returned by ``split()``.\n", + "For example, to extract the last name of each entry, we can combine ``split()`` and ``get()``:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -371,6 +592,17 @@ "monte.str.split().str.get(-1)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Indicator variables\n", + "\n", + "Another method that requires a bit of extra explanation is the ``get_dummies()`` method.\n", + "This is useful when your data has a column containing some sort of coded indicator.\n", + "For example, we might have a dataset that contains information in the form of codes, such as A=\"born in America,\" B=\"born in the United Kingdom,\" C=\"likes cheese,\" D=\"likes spam\":" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -442,10 +674,18 @@ ], "source": [ "full_monte = pd.DataFrame({'name': monte,\n", - " 'info': ['B|C|D', 'B|D', 'A|C', 'B|D', 'B|C', 'B|C|D']})\n", + " 'info': ['B|C|D', 'B|D', 'A|C',\n", + " 'B|D', 'B|C', 'B|C|D']})\n", "full_monte" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``get_dummies()`` routine lets you quickly split-out these indicator variables into a ``DataFrame``:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -533,6 +773,30 @@ "full_monte['info'].str.get_dummies('|')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With these operations as building blocks, you can construct an endless range of string processing procedures when cleaning your data.\n", + "\n", + "We won't dive further into these methods here, but I encourage you to read through [\"Working with Text Data\"](http://pandas.pydata.org/pandas-docs/stable/text.html) in the Pandas online documentation, or to refer to the resources listed in [Further Resources](03.13-Further-Resources.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Recipe Database\n", + "\n", + "These vectorized string operations become most useful in the process of cleaning up messy, real-world data.\n", + "Here I'll walk through an example of that, using an open recipe database compiled from various sources on the Web.\n", + "Our goal will be to parse the recipe data into ingredient lists, so we can quickly find a recipe based on some ingredients we have on hand.\n", + "\n", + "The scripts used to compile this can be found at https://github.com/fictivekin/openrecipes, and the link to the current version of the database is found there as well.\n", + "\n", + "As of Spring 2016, this database is about 30 MB, and can be downloaded and unzipped with these commands:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -545,6 +809,13 @@ "# !gunzip recipeitems-latest.json.gz" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The database is in JSON format, so we will try ``pd.read_json`` to read it:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -567,6 +838,15 @@ " print(\"ValueError:\", e)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Oops! We get a ``ValueError`` mentioning that there is \"trailing data.\"\n", + "Searching for the text of this error on the Internet, it seems that it's due to using a file in which *each line* is itself a valid JSON, but the full file is not.\n", + "Let's check if this interpretation is true:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -591,6 +871,14 @@ "pd.read_json(line).shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Yes, apparently each line is a valid JSON, so we'll need to string them together.\n", + "One way we can do this is to actually construct a string representation containing all these JSON entries, and then load the whole thing with ``pd.read_json``:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -599,7 +887,7 @@ }, "outputs": [], "source": [ - "# read the entire file into a python array\n", + "# read the entire file into a Python array\n", "with open('recipeitems-latest.json', 'r') as f:\n", " # Extract each line\n", " data = (line.strip() for line in f)\n", @@ -631,6 +919,14 @@ "recipes.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see there are nearly 200,000 recipes, and 17 columns.\n", + "Let's take a look at one row to see what we have:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -670,6 +966,15 @@ "recipes.iloc[0]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is a lot of information there, but much of it is in a very messy form, as is typical of data scraped from the Web.\n", + "In particular, the ingredient list is in string format; we're going to have to carefully extract the information we're interested in.\n", + "Let's start by taking a closer look at the ingredients:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -700,6 +1005,15 @@ "recipes.ingredients.str.len().describe()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ingredient lists average 250 characters long, with a minimum of 0 and a maximum of nearly 10,000 characters!\n", + "\n", + "Just out of curiousity, let's see which recipe has the longest ingredient list:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -722,9 +1036,18 @@ "recipes.name[np.argmax(recipes.ingredients.str.len())]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That certainly looks like an involved recipe.\n", + "\n", + "We can do other aggregate explorations; for example, let's see how many of the recipes are for breakfast food:" + ] + }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 25, "metadata": { "collapsed": false }, @@ -735,7 +1058,7 @@ "3524" ] }, - "execution_count": 33, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -744,9 +1067,16 @@ "recipes.description.str.contains('[Bb]reakfast').sum()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or how many of the recipes list cinnamon as an ingredient:" + ] + }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 26, "metadata": { "collapsed": false }, @@ -757,7 +1087,7 @@ "10526" ] }, - "execution_count": 34, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -766,6 +1096,13 @@ "recipes.ingredients.str.contains('[Cc]innamon').sum()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We could even look to see whether any recipes misspell the ingredient as \"cinamon\":" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -788,6 +1125,26 @@ "recipes.ingredients.str.contains('[Cc]inamon').sum()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is the type of essential data exploration that is possible with Pandas string tools.\n", + "It is data munging like this that Python really excels at." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### A simple recipe recommender\n", + "\n", + "Let's go a bit further, and start working on a simple recipe recommendation system: given a list of ingredients, find a recipe that uses all those ingredients.\n", + "While conceptually straightforward, the task is complicated by the heterogeneity of the data: there is no easy operation, for example, to extract a clean list of ingredients from each row.\n", + "So we will cheat a bit: we'll start with a list of common ingredients, and simply search to see whether they are in each recipe's ingredient list.\n", + "For simplicity, let's just stick with herbs and spices for the time being:" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -800,6 +1157,13 @@ " 'rosemary', 'tarragon', 'thyme', 'paprika', 'cumin']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then build a Boolean ``DataFrame`` consisting of True and False values, indicating whether this ingredient appears in the list:" + ] + }, { "cell_type": "code", "execution_count": 29, @@ -918,6 +1282,14 @@ "spice_df.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, as an example, let's say we'd like to find a recipe that uses parsley, paprika, and tarragon.\n", + "We can compute this very quickly using the ``query()`` method of ``DataFrame``s, discussed in [High-Performance Pandas: ``eval()`` and ``query()``](03.12-Performance-Eval-and-Query.ipynb):" + ] + }, { "cell_type": "code", "execution_count": 30, @@ -941,6 +1313,13 @@ "len(selection)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find only 10 recipes with this combination; let's use the index returned by this selection to discover the names of the recipes that have this combination:" + ] + }, { "cell_type": "code", "execution_count": 31, @@ -972,9 +1351,39 @@ "source": [ "recipes.name[selection.index]" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have narrowed down our recipe selection by a factor of almost 20,000, we are in a position to make a more informed decision about what we'd like to cook for dinner." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Going further with recipes\n", + "\n", + "Hopefully this example has given you a bit of a flavor (ba-dum!) for the types of data cleaning operations that are efficiently enabled by Pandas string methods.\n", + "Of course, building a very robust recipe recommendation system would require a *lot* more work!\n", + "Extracting full ingredient lists from each recipe would be an important piece of the task; unfortunately, the wide variety of formats used makes this a relatively time-consuming process.\n", + "This points to the truism that in data science, cleaning and munging of real-world data often comprises the majority of the work, and Pandas provides the tools that can help you do this efficiently." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Pivot Tables](03.09-Pivot-Tables.ipynb) | [Contents](Index.ipynb) | [Working with Time Series](03.11-Working-with-Time-Series.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/notebooks_v1/03.11-Working-with-Time-Series.ipynb b/notebooks_v1/03.11-Working-with-Time-Series.ipynb new file mode 100644 index 000000000..c9b4d828b --- /dev/null +++ b/notebooks_v1/03.11-Working-with-Time-Series.ipynb @@ -0,0 +1,1960 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Vectorized String Operations](03.10-Working-With-Strings.ipynb) | [Contents](Index.ipynb) | [High-Performance Pandas: eval() and query()](03.12-Performance-Eval-and-Query.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Working with Time Series" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pandas was developed in the context of financial modeling, so as you might expect, it contains a fairly extensive set of tools for working with dates, times, and time-indexed data.\n", + "Date and time data comes in a few flavors, which we will discuss here:\n", + "\n", + "- *Time stamps* reference particular moments in time (e.g., July 4th, 2015 at 7:00am).\n", + "- *Time intervals* and *periods* reference a length of time between a particular beginning and end point; for example, the year 2015. Periods usually reference a special case of time intervals in which each interval is of uniform length and does not overlap (e.g., 24 hour-long periods comprising days).\n", + "- *Time deltas* or *durations* reference an exact length of time (e.g., a duration of 22.56 seconds).\n", + "\n", + "In this section, we will introduce how to work with each of these types of date/time data in Pandas.\n", + "This short section is by no means a complete guide to the time series tools available in Python or Pandas, but instead is intended as a broad overview of how you as a user should approach working with time series.\n", + "We will start with a brief discussion of tools for dealing with dates and times in Python, before moving more specifically to a discussion of the tools provided by Pandas.\n", + "After listing some resources that go into more depth, we will review some short examples of working with time series data in Pandas." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Dates and Times in Python\n", + "\n", + "The Python world has a number of available representations of dates, times, deltas, and timespans.\n", + "While the time series tools provided by Pandas tend to be the most useful for data science applications, it is helpful to see their relationship to other packages used in Python." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Native Python dates and times: ``datetime`` and ``dateutil``\n", + "\n", + "Python's basic objects for working with dates and times reside in the built-in ``datetime`` module.\n", + "Along with the third-party ``dateutil`` module, you can use it to quickly perform a host of useful functionalities on dates and times.\n", + "For example, you can manually build a date using the ``datetime`` type:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "datetime.datetime(2015, 7, 4, 0, 0)" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from datetime import datetime\n", + "datetime(year=2015, month=7, day=4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or, using the ``dateutil`` module, you can parse dates from a variety of string formats:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "datetime.datetime(2015, 7, 4, 0, 0)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from dateutil import parser\n", + "date = parser.parse(\"4th of July, 2015\")\n", + "date" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "Once you have a ``datetime`` object, you can do things like printing the day of the week:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Saturday'" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "date.strftime('%A')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the final line, we've used one of the standard string format codes for printing dates (``\"%A\"``), which you can read about in the [strftime section](https://docs.python.org/3/library/datetime.html#strftime-and-strptime-behavior) of Python's [datetime documentation](https://docs.python.org/3/library/datetime.html).\n", + "Documentation of other useful date utilities can be found in [dateutil's online documentation](http://labix.org/python-dateutil).\n", + "A related package to be aware of is [``pytz``](http://pytz.sourceforge.net/), which contains tools for working with the most migrane-inducing piece of time series data: time zones.\n", + "\n", + "The power of ``datetime`` and ``dateutil`` lie in their flexibility and easy syntax: you can use these objects and their built-in methods to easily perform nearly any operation you might be interested in.\n", + "Where they break down is when you wish to work with large arrays of dates and times:\n", + "just as lists of Python numerical variables are suboptimal compared to NumPy-style typed numerical arrays, lists of Python datetime objects are suboptimal compared to typed arrays of encoded dates." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Typed arrays of times: NumPy's ``datetime64``\n", + "\n", + "The weaknesses of Python's datetime format inspired the NumPy team to add a set of native time series data type to NumPy.\n", + "The ``datetime64`` dtype encodes dates as 64-bit integers, and thus allows arrays of dates to be represented very compactly.\n", + "The ``datetime64`` requires a very specific input format:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(datetime.date(2015, 7, 4), dtype='datetime64[D]')" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "date = np.array('2015-07-04', dtype=np.datetime64)\n", + "date" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once we have this date formatted, however, we can quickly do vectorized operations on it:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['2015-07-04', '2015-07-05', '2015-07-06', '2015-07-07',\n", + " '2015-07-08', '2015-07-09', '2015-07-10', '2015-07-11',\n", + " '2015-07-12', '2015-07-13', '2015-07-14', '2015-07-15'], dtype='datetime64[D]')" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "date + np.arange(12)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of the uniform type in NumPy ``datetime64`` arrays, this type of operation can be accomplished much more quickly than if we were working directly with Python's ``datetime`` objects, especially as arrays get large\n", + "(we introduced this type of vectorization in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb)).\n", + "\n", + "One detail of the ``datetime64`` and ``timedelta64`` objects is that they are built on a *fundamental time unit*.\n", + "Because the ``datetime64`` object is limited to 64-bit precision, the range of encodable times is $2^{64}$ times this fundamental unit.\n", + "In other words, ``datetime64`` imposes a trade-off between *time resolution* and *maximum time span*.\n", + "\n", + "For example, if you want a time resolution of one nanosecond, you only have enough information to encode a range of $2^{64}$ nanoseconds, or just under 600 years.\n", + "NumPy will infer the desired unit from the input; for example, here is a day-based datetime:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.datetime64('2015-07-04')" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.datetime64('2015-07-04')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a minute-based datetime:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.datetime64('2015-07-04T12:00')" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.datetime64('2015-07-04 12:00')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the time zone is automatically set to the local time on the computer executing the code.\n", + "You can force any desired fundamental unit using one of many format codes; for example, here we'll force a nanosecond-based time:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.datetime64('2015-07-04T12:59:59.500000000')" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.datetime64('2015-07-04 12:59:59.50', 'ns')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following table, drawn from the [NumPy datetime64 documentation](http://docs.scipy.org/doc/numpy/reference/arrays.datetime.html), lists the available format codes along with the relative and absolute timespans that they can encode:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "|Code | Meaning | Time span (relative) | Time span (absolute) |\n", + "|--------|-------------|----------------------|------------------------|\n", + "| ``Y`` | Year\t | ± 9.2e18 years | [9.2e18 BC, 9.2e18 AD] |\n", + "| ``M`` | Month | ± 7.6e17 years | [7.6e17 BC, 7.6e17 AD] |\n", + "| ``W`` | Week\t | ± 1.7e17 years | [1.7e17 BC, 1.7e17 AD] |\n", + "| ``D`` | Day | ± 2.5e16 years | [2.5e16 BC, 2.5e16 AD] |\n", + "| ``h`` | Hour | ± 1.0e15 years | [1.0e15 BC, 1.0e15 AD] |\n", + "| ``m`` | Minute | ± 1.7e13 years | [1.7e13 BC, 1.7e13 AD] |\n", + "| ``s`` | Second | ± 2.9e12 years | [ 2.9e9 BC, 2.9e9 AD] |\n", + "| ``ms`` | Millisecond | ± 2.9e9 years | [ 2.9e6 BC, 2.9e6 AD] |\n", + "| ``us`` | Microsecond | ± 2.9e6 years | [290301 BC, 294241 AD] |\n", + "| ``ns`` | Nanosecond | ± 292 years | [ 1678 AD, 2262 AD] |\n", + "| ``ps`` | Picosecond | ± 106 days | [ 1969 AD, 1970 AD] |\n", + "| ``fs`` | Femtosecond | ± 2.6 hours | [ 1969 AD, 1970 AD] |\n", + "| ``as`` | Attosecond | ± 9.2 seconds | [ 1969 AD, 1970 AD] |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the types of data we see in the real world, a useful default is ``datetime64[ns]``, as it can encode a useful range of modern dates with a suitably fine precision.\n", + "\n", + "Finally, we will note that while the ``datetime64`` data type addresses some of the deficiencies of the built-in Python ``datetime`` type, it lacks many of the convenient methods and functions provided by ``datetime`` and especially ``dateutil``.\n", + "More information can be found in [NumPy's datetime64 documentation](http://docs.scipy.org/doc/numpy/reference/arrays.datetime.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dates and times in pandas: best of both worlds\n", + "\n", + "Pandas builds upon all the tools just discussed to provide a ``Timestamp`` object, which combines the ease-of-use of ``datetime`` and ``dateutil`` with the efficient storage and vectorized interface of ``numpy.datetime64``.\n", + "From a group of these ``Timestamp`` objects, Pandas can construct a ``DatetimeIndex`` that can be used to index data in a ``Series`` or ``DataFrame``; we'll see many examples of this below.\n", + "\n", + "For example, we can use Pandas tools to repeat the demonstration from above.\n", + "We can parse a flexibly formatted string date, and use format codes to output the day of the week:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Timestamp('2015-07-04 00:00:00')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "date = pd.to_datetime(\"4th of July, 2015\")\n", + "date" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Saturday'" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "date.strftime('%A')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Additionally, we can do NumPy-style vectorized operations directly on this same object:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-04', '2015-07-05', '2015-07-06', '2015-07-07',\n", + " '2015-07-08', '2015-07-09', '2015-07-10', '2015-07-11',\n", + " '2015-07-12', '2015-07-13', '2015-07-14', '2015-07-15'],\n", + " dtype='datetime64[ns]', freq=None)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "date + pd.to_timedelta(np.arange(12), 'D')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the next section, we will take a closer look at manipulating time series data with the tools provided by Pandas." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pandas Time Series: Indexing by Time\n", + "\n", + "Where the Pandas time series tools really become useful is when you begin to *index data by timestamps*.\n", + "For example, we can construct a ``Series`` object that has time indexed data:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2014-07-04 0\n", + "2014-08-04 1\n", + "2015-07-04 2\n", + "2015-08-04 3\n", + "dtype: int64" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "index = pd.DatetimeIndex(['2014-07-04', '2014-08-04',\n", + " '2015-07-04', '2015-08-04'])\n", + "data = pd.Series([0, 1, 2, 3], index=index)\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have this data in a ``Series``, we can make use of any of the ``Series`` indexing patterns we discussed in previous sections, passing values that can be coerced into dates:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2014-07-04 0\n", + "2014-08-04 1\n", + "2015-07-04 2\n", + "dtype: int64" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['2014-07-04':'2015-07-04']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are additional special date-only indexing operations, such as passing a year to obtain a slice of all data from that year:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2015-07-04 2\n", + "2015-08-04 3\n", + "dtype: int64" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['2015']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Later, we will see additional examples of the convenience of dates-as-indices.\n", + "But first, a closer look at the available time series data structures." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pandas Time Series Data Structures\n", + "\n", + "This section will introduce the fundamental Pandas data structures for working with time series data:\n", + "\n", + "- For *time stamps*, Pandas provides the ``Timestamp`` type. As mentioned before, it is essentially a replacement for Python's native ``datetime``, but is based on the more efficient ``numpy.datetime64`` data type. The associated Index structure is ``DatetimeIndex``.\n", + "- For *time Periods*, Pandas provides the ``Period`` type. This encodes a fixed-frequency interval based on ``numpy.datetime64``. The associated index structure is ``PeriodIndex``.\n", + "- For *time deltas* or *durations*, Pandas provides the ``Timedelta`` type. ``Timedelta`` is a more efficient replacement for Python's native ``datetime.timedelta`` type, and is based on ``numpy.timedelta64``. The associated index structure is ``TimedeltaIndex``." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most fundamental of these date/time objects are the ``Timestamp`` and ``DatetimeIndex`` objects.\n", + "While these class objects can be invoked directly, it is more common to use the ``pd.to_datetime()`` function, which can parse a wide variety of formats.\n", + "Passing a single date to ``pd.to_datetime()`` yields a ``Timestamp``; passing a series of dates by default yields a ``DatetimeIndex``:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-03', '2015-07-04', '2015-07-06', '2015-07-07',\n", + " '2015-07-08'],\n", + " dtype='datetime64[ns]', freq=None)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dates = pd.to_datetime([datetime(2015, 7, 3), '4th of July, 2015',\n", + " '2015-Jul-6', '07-07-2015', '20150708'])\n", + "dates" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any ``DatetimeIndex`` can be converted to a ``PeriodIndex`` with the ``to_period()`` function with the addition of a frequency code; here we'll use ``'D'`` to indicate daily frequency:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "PeriodIndex(['2015-07-03', '2015-07-04', '2015-07-06', '2015-07-07',\n", + " '2015-07-08'],\n", + " dtype='int64', freq='D')" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dates.to_period('D')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A ``TimedeltaIndex`` is created, for example, when a date is subtracted from another:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "TimedeltaIndex(['0 days', '1 days', '3 days', '4 days', '5 days'], dtype='timedelta64[ns]', freq=None)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dates - dates[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Regular sequences: ``pd.date_range()``\n", + "\n", + "To make the creation of regular date sequences more convenient, Pandas offers a few functions for this purpose: ``pd.date_range()`` for timestamps, ``pd.period_range()`` for periods, and ``pd.timedelta_range()`` for time deltas.\n", + "We've seen that Python's ``range()`` and NumPy's ``np.arange()`` turn a startpoint, endpoint, and optional stepsize into a sequence.\n", + "Similarly, ``pd.date_range()`` accepts a start date, an end date, and an optional frequency code to create a regular sequence of dates.\n", + "By default, the frequency is one day:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-03', '2015-07-04', '2015-07-05', '2015-07-06',\n", + " '2015-07-07', '2015-07-08', '2015-07-09', '2015-07-10'],\n", + " dtype='datetime64[ns]', freq='D')" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.date_range('2015-07-03', '2015-07-10')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, the date range can be specified not with a start and endpoint, but with a startpoint and a number of periods:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-03', '2015-07-04', '2015-07-05', '2015-07-06',\n", + " '2015-07-07', '2015-07-08', '2015-07-09', '2015-07-10'],\n", + " dtype='datetime64[ns]', freq='D')" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.date_range('2015-07-03', periods=8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The spacing can be modified by altering the ``freq`` argument, which defaults to ``D``.\n", + "For example, here we will construct a range of hourly timestamps:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-03 00:00:00', '2015-07-03 01:00:00',\n", + " '2015-07-03 02:00:00', '2015-07-03 03:00:00',\n", + " '2015-07-03 04:00:00', '2015-07-03 05:00:00',\n", + " '2015-07-03 06:00:00', '2015-07-03 07:00:00'],\n", + " dtype='datetime64[ns]', freq='H')" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.date_range('2015-07-03', periods=8, freq='H')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To create regular sequences of ``Period`` or ``Timedelta`` values, the very similar ``pd.period_range()`` and ``pd.timedelta_range()`` functions are useful.\n", + "Here are some monthly periods:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "PeriodIndex(['2015-07', '2015-08', '2015-09', '2015-10', '2015-11', '2015-12',\n", + " '2016-01', '2016-02'],\n", + " dtype='int64', freq='M')" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.period_range('2015-07', periods=8, freq='M')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And a sequence of durations increasing by an hour:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "TimedeltaIndex(['00:00:00', '01:00:00', '02:00:00', '03:00:00', '04:00:00',\n", + " '05:00:00', '06:00:00', '07:00:00', '08:00:00', '09:00:00'],\n", + " dtype='timedelta64[ns]', freq='H')" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.timedelta_range(0, periods=10, freq='H')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these require an understanding of Pandas frequency codes, which we'll summarize in the next section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Frequencies and Offsets\n", + "\n", + "Fundamental to these Pandas time series tools is the concept of a frequency or date offset.\n", + "Just as we saw the ``D`` (day) and ``H`` (hour) codes above, we can use such codes to specify any desired frequency spacing.\n", + "The following table summarizes the main codes available:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Code | Description | Code | Description |\n", + "|--------|---------------------|--------|----------------------|\n", + "| ``D`` | Calendar day | ``B`` | Business day |\n", + "| ``W`` | Weekly | | |\n", + "| ``M`` | Month end | ``BM`` | Business month end |\n", + "| ``Q`` | Quarter end | ``BQ`` | Business quarter end |\n", + "| ``A`` | Year end | ``BA`` | Business year end |\n", + "| ``H`` | Hours | ``BH`` | Business hours |\n", + "| ``T`` | Minutes | | |\n", + "| ``S`` | Seconds | | |\n", + "| ``L`` | Milliseonds | | |\n", + "| ``U`` | Microseconds | | |\n", + "| ``N`` | nanoseconds | | |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The monthly, quarterly, and annual frequencies are all marked at the end of the specified period.\n", + "By adding an ``S`` suffix to any of these, they instead will be marked at the beginning:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| Code | Description || Code | Description |\n", + "|---------|------------------------||---------|------------------------|\n", + "| ``MS`` | Month start ||``BMS`` | Business month start |\n", + "| ``QS`` | Quarter start ||``BQS`` | Business quarter start |\n", + "| ``AS`` | Year start ||``BAS`` | Business year start |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Additionally, you can change the month used to mark any quarterly or annual code by adding a three-letter month code as a suffix:\n", + "\n", + "- ``Q-JAN``, ``BQ-FEB``, ``QS-MAR``, ``BQS-APR``, etc.\n", + "- ``A-JAN``, ``BA-FEB``, ``AS-MAR``, ``BAS-APR``, etc.\n", + "\n", + "In the same way, the split-point of the weekly frequency can be modified by adding a three-letter weekday code:\n", + "\n", + "- ``W-SUN``, ``W-MON``, ``W-TUE``, ``W-WED``, etc.\n", + "\n", + "On top of this, codes can be combined with numbers to specify other frequencies.\n", + "For example, for a frequency of 2 hours 30 minutes, we can combine the hour (``H``) and minute (``T``) codes as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "TimedeltaIndex(['00:00:00', '02:30:00', '05:00:00', '07:30:00', '10:00:00',\n", + " '12:30:00', '15:00:00', '17:30:00', '20:00:00'],\n", + " dtype='timedelta64[ns]', freq='150T')" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.timedelta_range(0, periods=9, freq=\"2H30T\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these short codes refer to specific instances of Pandas time series offsets, which can be found in the ``pd.tseries.offsets`` module.\n", + "For example, we can create a business day offset directly as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DatetimeIndex(['2015-07-01', '2015-07-02', '2015-07-03', '2015-07-06',\n", + " '2015-07-07'],\n", + " dtype='datetime64[ns]', freq='B')" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from pandas.tseries.offsets import BDay\n", + "pd.date_range('2015-07-01', periods=5, freq=BDay())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more discussion of the use of frequencies and offsets, see the [\"DateOffset\" section](http://pandas.pydata.org/pandas-docs/stable/timeseries.html#dateoffset-objects) of the Pandas documentation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Resampling, Shifting, and Windowing\n", + "\n", + "The ability to use dates and times as indices to intuitively organize and access data is an important piece of the Pandas time series tools.\n", + "The benefits of indexed data in general (automatic alignment during operations, intuitive data slicing and access, etc.) still apply, and Pandas provides several additional time series-specific operations.\n", + "\n", + "We will take a look at a few of those here, using some stock price data as an example.\n", + "Because Pandas was developed largely in a finance context, it includes some very specific tools for financial data.\n", + "For example, the accompanying ``pandas-datareader`` package (installable via ``conda install pandas-datareader``), knows how to import financial data from a number of available sources, including Yahoo finance, Google Finance, and others.\n", + "Here we will load Google's closing price history:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
OpenHighLowCloseVolume
Date
2004-08-1949.9651.9847.9350.12NaN
2004-08-2050.6954.4950.2054.10NaN
2004-08-2355.3256.6854.4754.65NaN
2004-08-2455.5655.7451.7352.38NaN
2004-08-2552.4353.9551.8952.95NaN
\n", + "
" + ], + "text/plain": [ + " Open High Low Close Volume\n", + "Date \n", + "2004-08-19 49.96 51.98 47.93 50.12 NaN\n", + "2004-08-20 50.69 54.49 50.20 54.10 NaN\n", + "2004-08-23 55.32 56.68 54.47 54.65 NaN\n", + "2004-08-24 55.56 55.74 51.73 52.38 NaN\n", + "2004-08-25 52.43 53.95 51.89 52.95 NaN" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from pandas_datareader import data\n", + "\n", + "goog = data.DataReader('GOOG', start='2004', end='2016',\n", + " data_source='google')\n", + "goog.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For simplicity, we'll use just the closing price:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "goog = goog['Close']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can visualize this using the ``plot()`` method, after the normal Matplotlib setup boilerplate (see [Chapter 4](04.00-Introduction-To-Matplotlib.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import seaborn; seaborn.set()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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eLa1T7JqZiwG5d2NAJiKKoM9/OIl7/v6tZD9xsHLHDIBcJi0c8cjP88XHDMi9\nGwMyEVEEfbDhGAxtHdh5uCbk13rrWaclxeG62bbqTBMzUjzOU+/Bak9ERBGy7dA58fF7a49gSGo8\nJo3yH0SrXQpITB8/0Os1VxeOwhUz06GQs4/Vm/GnR0QUIR99c0zy/LlVuwO+5sutFeLjWdmDfV7H\nYNz78SdIEdXQYsLGPVVi5jei/kQXYhatnYfOoarO1kO+9fLxktrH1PdwyJoi6tmVu3CmzghdnApT\nx6b1dHOIIqqh2YRErRpNeltFpiSt7wD9303Hsebb4+LzCRnJ3d4+6lnsIVNEnbF/269pbA1wJVHf\nYrUKaGgxIS0xDo/eOh0AkJvl+0upazAGABXTYfZ5/AlTz+DQG/UzTYZ2WAUBKQkxUKtsOfytVu9T\nN6Z2CzQx0gFM5qfu+zhkTT0iVm37g3SsqglKuRzpg3tfIniiUDS0mAAAyboYyOW2L6TeAvLKr4+I\ntY1dKRX8EtvX8SsX9QiVUo4zdQb8+e0deOytbWg3W0LOXkTUmzgCcpI2Bgr7CJHFS/Jpb8EY8EyT\nSX0Pf8IUMa4rqy0WARXVzpKdi5/7Bv/ecMzby4h6PZPZgtc/OwDAHpAVjoDs+SV0YFKc1/dQyNlD\n7usYkCli9h2vFx9bBQEms0Vy/ostFe4vIeoTPvqmHG3ttt/3CRnJPoesrYKAcy4LHlVK559obnnq\n+ziHTBEjd/mGb7FY8f7XR3uwNUSRs/+E88togkYNQ5sZgLSHvOdoLf7+71LJ626ZNx5b952JTCOp\nxzEgU8RYXBLf1za1eU2E32rqQFwMfy2p77AKAmLsq6odHMPPHRYBLcZ26DRqbNxTJZ7/0bThyBye\ngKvmjMFsP9m5qG/hkDVFjGPIDgCMpg6v17gOaxP1Bf/ecAzHzzQDgFjH2BGQ95bX4Z7nv8Ohkw2S\nL6LD0uJRMHEwh6n7GQZkihiTS0CubzZ5vSacknRE0apRb5Ksjbjz2mwA0ukbAPjv5hOSNRVZI5Ii\n00CKKhwbpIh58/ND4uO95XVer2E9V+pLlr78vfh41JAEMSGIeyEIhVwGY5tt1OjZO2chJSE2co2k\nqMEeMkWEr2ISAxKlf3gsFu5FpsiwCgLe+V8Z9hyt7bbPaO9wfsG8t2iy5NxzdxWKj/cdr8fBkw0A\nwGDcjzEgU0SYO7z3fC+bMRKF2YNx1awMAECHl0QJRN3h5NkWrNtZ6bGyuau0tTvXSeSNS4M2TiU5\nn6yLwRvHYA6vAAAgAElEQVRLL+qWz6beiQGZIqLNPj/mnvTgomnDsOiqiZhiX+xSUa332J9M1B0c\nFZcC2binSlyUFYo6+zqJC3KH4q7rcoJaoDUo2XtSEOofGJApIhwrrJN0MeKx0UMTxD9SSVrb8dJj\ndXj6vV2RbyD1O8FUHGvSm/DW54fwp/+3Hc//uxRNeu+LEb2pa7ItUEwNYQj60dtmBH0t9T0MyBQR\np6pbAADD0+LFY679hVSXueRweiNEoTrXEDggL3tti/h499FafPr9yaDff+vBagCBA/K880YCANRK\nucd+ZepfGJApIhy1XaeNddZ/5fKt/uOLLRX4+Nvynm6GSBAEfL3ztPj8Hx+WotXL3nhDm/SYr8WJ\n7iprDdi87ywAYGCAYeiiuZm44YLRuOfGyX6vo76PAZm63Z6jtaiqNQCQ9oT1RnNPNYkibPX6o/hk\n0wkAtqBmbPOeGCZSjlVKR2F2HanFOpcADXgPvsFUXLJaBTzi0rMePTTB7/UymQxXzszAhIyUgO9N\nfRsDMnU717k612xE53zM4Y0cpO32NvUlVbUGfLGlIujeW3c4W2/E51tOel1N7zrv2mGxYtFT6/Hr\nv23EybMtkWwiANtWp2fe34W/vLPD45wmVroK2tvvpyOhxwcbjuLZld7XOriurp4zZSizbVHQAgZk\nq9WKhx9+GPPnz8fNN9+Mo0ePoqKiAgsWLMAtt9yCxx57TLx29erVuOGGG3DTTTdhw4YN3dlu6kW+\n3OrMVBSnVuCmH2UBAPJchq8B4G+/OR8AYDJz61OwjpxuxLLXtmD1+qM4WtnUI20wtJnx8Ks/4IP1\nx/D9/rMe50+fc5bZdD2/uxP7fw+eqMezK3eF3NP+rvSMuN/XXWK8Wnz8xmcH8cJH+wAAP71ojHg8\nPtb2hfLzHypw4ESD1x0BZpe99NfOHhVS+6h/C5ipa926dZDJZHj//fexdetW/PWvf4UgCCguLkZ+\nfj6WL1+OtWvXIjc3FyUlJVizZg3a2towf/58FBYWQqVSBfoI6uMGJmvELSBKhRyXTh+B7FEpSEmI\nkVyXoFFjYHIcTO09O5zZmzz5zk7xsft8ZyS8/cUhbNjtLIpwukYvOS8IApa+8J34/M3/c2Zrq6o1\nQBCEsHqQz6zcDQDYXnYOc6YMDXh9RXULPvym3GOe+Dc3Tsbz9n3IjgGGAyfq8d1eZ4Wl1IRY3H9T\nLp5buRtrt58WdwQAtt7/wGSN5D3P1tmmZ/LHD5RcSxRIwIB88cUX46KLbJvXq6qqkJiYiM2bNyM/\nPx8AMGfOHGzatAlyuRx5eXlQKpXQarXIyMhAWVkZsrOzu/dfQFFPp7F9KRuUHCf+8R06IN7rtbEq\nBVqMwe0PJWBwqgZn6owAgPYe2L/tGowBePRYW1p9rxPYdugcRg1JEFcZB8t1aN6xtcifs/VGPPrm\nNo/jf/11IZK0MVhwcRbeW3sEJ84244U1ez2uSx+sE1O6Nhna8fpnB8VzD7+6Ba89eKHk+qfs2/ZK\nuzEDGPVNQc0hy+VyLF26FI8//jiuuuoqyX8Q8fHx0Ov1MBgM0Ol04nGNRoOWlsjPEVH0adS3Qwbg\n8TvOC3htjFqBtnZLj86H9iauvWJfBTsiIXu0bUGSawGRz7ecxL3P23rHaqX3PzWr14deE9t1nvq/\nm08EvN6x2tnVv343V+y9OuaFP/OxpSk1MdZnT9fq5/c0f/zAgG0jchX0oq4nn3wSX375JZYtWwaT\nyfkfvsFgQEJCArRaLfR6vcdxoka9Cbp4tUdCfW9i1AoIgjQHMHl34EQ9mg3O0YRggpvFau2yAh7m\nDmfwvfv6yZAB2HG4BlarLUh9sP6YeD43a4D4+I6rJ6JobmbYn/ve2sOS58Y2373wHWU1+NQtaKuV\ncsnvojzAkLlcJguqRrcgCKiuNyJJa5uLvvmSsQFfQ+Qq4G/Zf/7zH1RXV+OXv/wlYmJiIJfLkZ2d\nja1bt2LGjBnYuHEjCgoKkJOTgxUrVqC9vR0mkwnl5eXIysry+97JyRooleFvhE9L0wW+iDxE+r41\nG9oxdIA2qM8dMkCLfeX1EBSKgNfvPVqLh1/ahEvPS8fdP8ntqub6FS2/c+cajHjWPo/qKjVV61Ha\nz9Vv/74RZRUN+M8z1/i9Lhh6+3D0eZMGY+iQRHFf+e1Pr8fkMQMk1971k6m4vLIJ3+6uxEXnZSAu\nRokPNtgCdlKyBtsPnkNyQgzGpwfe+rNxzxnJc7la5fXnsqvsnNch6LhYpeT6hATnPuFErRrvPHY5\nBEHAa5/sw7RxA8VrL5+Vgc+99MibTBaMGZ6Ej9YfxZuf7gcADBkQj5HDkwP+W4IRLb9zvU1vvG8B\nA/Kll16Khx56CLfccgs6OjqwbNkyjB49GsuWLYPZbEZmZibmzZsHmUyGhQsXYsGCBeKiL7Va7fe9\nGxqMYTc8LU2HmhoOiYcq0vetw2JFW7sFSoUsqM9NirfNN+8/UoPYAB3qh1/aBAD435aTuLYwHSVf\nlmHM8CRcOHVYp9vtTbT8zm3YXYm3vygTnz+zZBYeeGkzAOAvb27Br66Z5PO1ZRW2FcZnq5ug6sSX\nYcAZkM1mi8d9cZ0/vXr2aFhMZqQP0CD94iy06tvQqgdyRqdib3kd/vz6Fuw4XAMAePWBuQH3+o4c\nqEWFy8rtxkaj19+VP7z6vedB2HJYu7bXYHDOQ2tilOK5a+0FTxzPL546DMNTNcgYrENifAx+/beN\nAICte6uQGKPAJxudIxQKWXC/74FEy+9cbxPN983fF4WAATkuLg5/+9vfPI6XlJR4HCsqKkJRUVGI\nzaO+bO8xW93jw6cag7p+cIptxeq5EL+s3flX2x/H7/dX44IpQzvd+4tWVkGQBOOHbpkmSbay5UC1\nJCCfqTNg3Y5KXH/BaMmwa1cU1XLMnzpGfAckxqLWbZHVS8UXYPiwJK9/HKdmDcDe8joxGANA2alG\nTAqQICNBqwbOAYXZg7Fp31l0dHJ6w3W7kybW95/EZF0MZk4aLD6/89psvPjxPry/9giOnGoUdxIA\nQIyaKR4odPytoW6173h9SNfHqm1/EI+cDryn1tdK7bP14Y+8RLvH/9928fHd1+cga3gSAOD2qyaI\nx10XxL2/9gi+3nka/918QnLcYu38ojnB/h6OOdilN0+TnP/19TmIUfvuhXur+/vcyt2oDVD0wfHP\n2Ftu+7LnukXJH0fPO94t6E7OdA6vJ4ewTck1Jeb2shrJOXUnRx+of2JApm4jCALW76oEANx/U3Bz\nvI5VusEkjUj3kdFr2WtbQu5h9wZ7y+twwp7dKn2wDlNdEqsUTBqMRPtiItdg68iSdrpGj2fed2aW\n8rc6OFiOj3GMRqQkxOKPLtWKxo5I8vv6EQO9//yaDP63vTm+WEyfMAgA8L9tp7xep1TIMXKgFktv\nnoY/LZoh9n5dF5i5u7wg3e9nu9JpfE/JDUnV+DxH5AsDMnWbqjpnUMwalhjUawSXkhPuSSbctdsz\neuWMTvU4d+qc/9f2Rp98d1x8/MurJ0rOyWUyMcA5ArLFakW1vaLRvvJ6HKpwThtYu6KH7DZkDQAK\nhfOJNs5/UqBkl1KcGpfhdJWPLVLOz7X9/6ghOpdjnv8ei9UKtVqBsSOSMCxNK36Gt+xejr3yvr4k\neJOkVSMuxrMnnD0qRcxGRxQKBmTqFKtVgMHHtpMDJ2zD1QUTB0EdbFk5l7+rL328z/dlgiD2pPLG\npXmc95eQojcSBAEDkmxDpE/8sgBDUj2H6xX2yOgItmdqfY8SdMWQtaOX7bptKNy5+1uvGI8fTRse\nVNsc/z7XYeHyKmmxCKsgQBCc9wQArpxp6/0W5gzxeM+//LIATy+eGVTxCAeZTIYX7rtAcmzs8EQU\n/zQ3pPchcuBvDXXKsyt34e6/fYv6Zs+MSY5jl0wfEfT7uf4trq73PZf4xdYKMXezt57Yf749jtue\nXBdU4oho95eSHVj01HpsOVANtUqONB/l/BT2IOAIaN6+lIwdbhupeOvzQx7nQuX4Wbn2kFX2NigV\nwQVmx7D2xIwUqFRy+/v6D8iCIEAGSL7kuY+mOHrBrgvZCnOG4O+/OV9SAtQhPlYlfuEJ1R1XTcTY\n4Ym4fs5oPLBgaljvQQQEscqayJdWU4c4DHq0sgkz3BbpOLbFuC+i8Uetcn5H9PeH+f9csip565U5\nes9rNpbjavv2ld6ousEoKRoxKFnjM5GFY6jX1G6BJkYpfiEaNyIJZacakaBRQWuf93QsiOoM90Vd\ngG0e+bc35XrtwXtz/0+nwGS2Ii5GCYX951jb2IaBSXFe52iPn2nGYfuCP9fsX47pi89/OIkTZ1tw\nqf1LoGNe3cHfvG+4ZmYPxszswYEvJAqAAZnC9ofXnTVf29o98ygbWm29lEBzia4mjUpBgkaFZqMZ\nF+cP93mda8rIAfZtP6kJsajz0lPvzVoM0l5uqpeVyQ4x9i8zjj3JDhfkDsWUMQOQNy4NaqUcOw/X\n+F39HKyth84BsKWmvPUK5yrviSHU9VUpFeJ+aEee81c+sSXXGDlQi0ddFokBwJ9cVpkPd5nv3Xqo\nGjVNrVi73VbTuNq+qM91SxNRtOOQNYXFYrVK9l16m/cztJkhkwGxQaQddJDLZFhyra0gyd7yeuwo\nO+f3+nuLJmN4mhbLfpaPx26bjmfvnCXZjgLY9uL2Vu5buLQa319uXLfvuNLFqzHvvJFIS4pDojYG\n2aNTYGq3+Jz7D0ZDiwlrNpYD8L9qORTuAx0V5/SS1KDutHEqFP9kCgDgWGWzGIwBoKLaNoTNakvU\nmzAgU1j+8aE0JWGHxQqrVYAg2P73/b6zOHK6CYIQOFewO0dPqbreiBfW7PO7Itixwnr00ARoYlVI\nSYjFRdOkPeu/28vr9UZv/N9ByfMpPoIuYEu04U2C2zCtDLb7e/ffvg2rTR0WK+5/YZP43PEFqrMU\nXqYe7v3Hd1jy3Dfi9Ie7+ACjL+5D1kTRjAGZQlZdb0SpPQPXGPt2psoaPW5/ej0+31KBbYfO4V+f\nHgj7/d3nhL0NQ8fHKjEsLd5rLd0UnbRXpDf23hXXjsxQP7lwDJ69cxamjfUdkH3VFR7mlkBlUoYz\nx3JDS+gVog6caJA8D/ULly/pg72nFDSZLfjz29u9FsUItHqfPWTqTTiHTEHrsFix7F9b0Kh3/hGf\nPn4gjlY2iQn//73hGCakO//gzwpjsYt7T+lcYyvS3FbACoKzp+du2rg0XDkzXSynZzR57jvtDayC\ngO/320oHzp4yBPGxgefiX3/wQuwoq8GkUSk4VtmEuFilxxecS6aPwMp1trzL97+wCW8svSikdtW4\nZNLqyopGjqxjgO0LiGv1qiZDu7iSeuRALe77qS3RjK+yjg6cQ6behD3kPuzE2WZJibzOqmtqw7nG\nVrE04pUz073uAT540tmDun7O6JA/xyMgN3hufxIgeMw5OshlMtxwQaa4xWegPZgfPtUYMAtUNDnm\nsro6mGAM2HrJ+eMHIi5GiezRqcgc6pmQRSaTSZJyhOrdr2zlD/PGpXVpIY+4GCUeu20GVtx9Pi6a\nNgwpCc42trVbxJ75tLFpYqB17SH/+PxR+Oe9czDSZbFXAgMy9SIMyH3U2Xoj/vjWdvzlnZ2S49X1\nRny17RSajaEHptZ2aU9z9NAEr/mIHX4+b5zf8764b00p+bLM4xqr4HuI1mH+xbbe2+TMVFQ3GPHk\nuzsluaCjnePfN2Z4cFnOQuE6VP31jtP4+Ntyr0PCb31+CLc9uU6SitQxBH7j3MwuL+IxYqAWifFq\nqFUKPHtnId5YepH4pe7f9nKNcS7b6Fx7yONHJkETq8SVLtvcmKCDehP+tvZRJ+05jx3/71Dyfwfx\n/tdHcO/z3+GR17agNYTh3O2HpAn0p2bZescP3TLN49ob52bigtzwek86PyuJHQTbmLVfjp62VRDw\nxZYKAN7no6PRibPNeH+trSeaPSr4bUThePerw/hk0wn88pkN+PyHk5JzG/dUAQCeW+WsvayQyxCj\nVmBQcmTyNU/OlKZGdd3X7ppm01GYhMPU1FsxIPdRjr2cgDRv8VmXLUCVtQZsD7CtyNUme1WdrOGJ\nkiICWcOT8PDCPMm1V4SQpN+dt16NR65iwXObjDuZ/YKqWoM4F9sbCIKAP761HcfP2L5MxQSbdjQE\n40d6L/zwwYZjsAoCfjhwFj+43DO53PkzaTK0RzTojRykk+SM1rgM37v+rjiu0YSwzY4omjAg9zEV\n1S0w2vf/Ojy7chcsVis6LFaxQL1DKH/sHXPHD92SJ0nKANhWW184zdYjHjUkIczWO101Kx1XzkwX\ntzWZzNK58GCGrB0B+1BFo5jJCQD2nwitJGSklVVIa0d3R0CeYa+U5E1NQyte/eQAXv2vc6V8db0R\nFdUtsAoCWozmiM/NtpqcP39fAdeR+nLogHhMHz8Qv7xmotfriKIVv0r2IcY2Mx59cxu0cSrEqhXi\nH7FDFY244+kNkpq5Dv4S+X+5tQItRjOuv2A0mvTtaDdbMMhHHmUA+OmFYzAwKQ5zu2Chz/VzMgEA\nr9u3T7UYzeKQJGDPZxygh+xrfvMfH5bi5fvndrqN3aXarXRkZxZg+XJB7lCkD9ZJMl85HHL70ubw\n380ncNXMDFgFAfE92At1T8W66MoJiFUrxO1Xcrmsy/ZGE0USA3If4shU5CuJwsmzniUJW4xmbDt0\nDmOHJyLRZc9ms7Edq+xbY+LjlFDI5bBYBb85e9UqBS6bMbIz/wQPKnvv0FEsQLDPB1usQsAessrH\ngp4RacGX2OsJjuxUc3OHQqmQIyfTs7xkZ8lkMmT42Pd7+FST5PnMSYPx/f6zSB+kw9Pv2xYJBiqR\n2NXuuHoi/mXvsSe67S32Vr2JqDfikHU3+HTzCXy/L/JzlvvchmIvyB2KB+ZPFdc+nThrK1F36xXj\nxa0hK78+gpc+3ofXXBJ5vPrf/bj3+e/E5x+sP4aVXx8BAMSpI/sdbrs9X/Kb9oxVB0404AP7attA\n63vdk0I45j2PVTXDYvVcUdzTth06hy+2VGDfcdvP8bLzRmLBJWO7LPGGO19faFzn2y+bMULc2lRV\nZxBHXX42b3y3tMmXgonOIfZQcqMT9SbsIXexU+f0+Mie4zctKa5btqz4MjE9GUdPO3s3VxSkIy0p\nDhfnj8BX20/hiP3csAFa3H9TLu5xCbpl9l7R/uP1+GF/tc/PmD0lsr0RR2+/4pytd79upzNfccA5\nZLch63Ejk7D1oC3AHzrZiEndvHo5FMY2s6T+c+awhIisYr44fzj2HqvDzZeORZvJghfdalDnjE6F\nxj5E7Pp7EemgKJPJsOxn+ZLFXUR9DXvIXczRowOAI5WNfq7seo7qShmDdXj2zllidiv3ObdhafEe\nf1A7LFZUVLdItrcAwMxJzp7J5MxUyTxuJMye7PwCsOdoLXYdqRWfB9PLffTW6UgfZBuaTdLGYFia\nbQ9tNNVJbja249dueaXdM5N1lwUXj8UTv5qJ7FGpyB8/0GOLUWpCrEe+6PzxAyPSNnejhyYEXdaR\nqDdiQO5irquBOzoiOyxqNNl6k3dely1JyHGVS6KEaeMGIkalgEzmufDl0Te3iY9HDtLipeILcMfV\nk8SA7poSM1IWXjYOgC0wuBeJOFbZHPD1IwfpsOznebjtigm4pnAU7iuyVQeCn1rLkSQIgmR6wCFr\nWORGVly5ruiOUSkwMDnOY4vTois8FwcSUedxyLqLudYFNlsi+0ffsWLafR+vXC5D0dxM1DebcPdN\nU1Ffb9uLPH38QAxdNANvfn4I5VXO4DZpVAp+dc0ksWbu8/fMxuFTjZJcw5Hi+Ld0JqGHQi7H+fae\ntiZWibgYBarqjHj6vZ34+bzxGJQSmQQX7gRB8NlTn5M7NLKNsXMNyP+8b7bXaYGuqKVMRJ7YQ+5i\nrvVbP918AuYAveTqBqPHNpdwWexfALyVsbu8IB03XzoWCrdgPSxN65HecuRArWRIWyaTYdzI5C5P\nk9hZ4QYGTYwS+lYzDlU04un3d3Vxq7zbdaQG9/3zO7G+sSAIWLF6Dz7+9rjkuh+fPwov3DcHCnnP\n/Kfpek9d2/DordMBAAsuzop4m4j6CwbkLtagl5az23rQ9wKpVlMHHnrlB/zxra7Jr+zoIXsLyP5M\nHSMt6ec6xB0NBiR65sN+/Pbz8PxvZof1fnExzi8bDS2mLi3A4cu7Xx1Gk75dXPBXVWsQV1MDwOUF\nIzEoOQ4XThuGuB7c4+ta0MHVyEE6vLH0IlycPyLCLSLqPzhk3UnnGozQxKpw+pzea2/r9c8O+twn\nWWVPYxlKPmlfahpbUXHOlmox1N5VTmYq5kwZgukTBmFgUlyPBgRvxgxLRG2Tc8j6rutyMHRA+It7\n3BeDtRjNSEno3mHYgUlxqG82oarW9jM3maVtuPb8USiaO6Zb2xAMx7SEa81kIoqM6PrL28u0my1Y\n+soPSIxXh1XWz3XRV1t7h8cKZqtVwKp1R9FhtWLBxVl+A+0f39oGgz15hkIRWg9ZG6fCLy6P3oU6\n7qt8vZV8DEWs21B3V3whCqTZaFtwV1VrwKuf7Jdk37rtiglQKaNjXnbMsEQ8f89sj3tERN3Pb0Du\n6OjAww8/jMrKSpjNZixevBhjxozB0qVLIZfLkZWVheXLlwMAVq9ejVWrVkGlUmHx4sWYO3duJNrf\no07X2Ho7gYKxLc2jZ5Bs1LdLHg9Okf44vtp+Cl9tPwUAGJoajx/lDff6/sa2DjEYA6EPWUe7SRkp\n+HqHbf/x2C7Y1+2eG7q9m1fDG9s6cKbWWdTjhwPOaYwEjQozJvTMNiJfmHiDqGf4DciffPIJkpOT\n8fTTT6O5uRk//vGPMX78eBQXFyM/Px/Lly/H2rVrkZubi5KSEqxZswZtbW2YP38+CgsLoVL17f+w\nXWvK+mPusEoKqQO2YPv+2iPi87qmNgx2W+1beqxOfNzW7tmLM3dY8cKavWJaScC2QjpQwozexnWh\n0YJLxnb6/dxHImoaW7ukIIYvp861QACgVMjQ4bby/rfzp3r8bhBR/+R3svHyyy/HPffcAwCwWCxQ\nKBQ4cOAA8vPzAQBz5szB5s2bUVpairy8PCiVSmi1WmRkZKCszLOofF/TbJAG5JmTBiF3zAA8MH+q\n5Li3HphrMAZs9WaPVTmzbAmCgEqXXtWGXVUe77HzcA1Kj9XhaKXtdXKZDPf/NDf0f0iUyxisg1ol\nxzWFGRg5yHv+5VDc9CPpXO3L/9nv48rOqa434l//3Y+dh23JTK6ameFxTWfmwomob/EbkOPi4qDR\naKDX63HPPffgvvvuk9SljY+Ph16vh8FggE7n/EOp0WjQ0tLSfa2OEiX/Oyx5ftWsDPzmxsnIchtW\nDbT1yeGJkp3i4/fXHpFsoaprbvOoCey+N/f2q6N3Hrgz4mKUePn+ubh29ugueb+ByRq8sfQiXDq9\ne1cMP/TqD/h+f7U47TBuZBJGD5X2xLsrTzUR9T4BF3WdOXMGv/71r3HLLbfgyiuvxDPPPCOeMxgM\nSEhIgFarhV6v9zgeSHKyBspOLGZJS+t8bylcW/adER+rVQr89OKxmDzeVgnJPXDqEuKQ5tITqqzx\nrLoEAFZBQFqaDsY2M9ba50wHpWhQbd+7qoxVS/YMt7uVTpyRMwxpQSS56Mn7Fk3i450Lq4K9J8Fe\n1+AlkUl+zlDkThiMrQeqscJeNam//Cz6y7+zO/Dehac33je/Abm2thaLFi3CH/7wBxQUFAAAJkyY\ngG3btmH69OnYuHEjCgoKkJOTgxUrVqC9vR0mkwnl5eXIygqcQKChEwkx0tJ0qKnpmV54s6Edj7+5\nVXz+8v0XAICkPffcOBmf/XASR0834Wx1M7aUVkKllGPGhEFY/OQ6ALbcvA8umIZfPbsBgK23dLqy\nEUv++o34Pn/4eT7e/PwQth86hxc/2I3brpgAY5sZidoYnLUH9twxA3D7VRMgt1gC3pOevG/Rxmh0\nTjkEc0+CvXer1h3Bl1tPeRxvaWoFAEwckYDRQxMwOTO1X/ws+DsXPt678ETzffP3RcFvQH7llVfQ\n3NyMF198ES+88AJkMhl+//vf4/HHH4fZbEZmZibmzZsHmUyGhQsXYsGCBRAEAcXFxVCr1f7eulc7\n4lJR6aaLvO8dnTJmAErL63D0dBNKy+vwb3vJwBkTnMUaBiTGQqWU4+4bcvCPD/di9NAE/Llkh+R9\n1Co56ux/yLccqMaxyibUNrXh/p/mipWL7ro+u8cyO/VmrgMZVqvQZZnIvAXjZT/LFx8r5HLJcyIi\nIEBA/v3vf4/f//73HsdLSko8jhUVFaGoqKjrWhbFahpbxcezp/jOOVxnT2bhCMaALSnF8DQtTtfo\nccfVEwEAUzJtmbIci7McRg3RQSGXY/GPs/Hgy98DgJggw7UqE4NxeFyrYN3+9Hos/vEkyRcmf77e\ncRqpibHIdcty5p505ParJiAhXu0xd0xE5I5/ycPgGpD95VO+2ksKys9/qIBCIYNKKRcDqa+emaMX\nlZYUh19c7r0gvK+9yRSYexrIYFdbNxvb8e5Xh/G8W/UpAPjPdyfEx7+bPxWzsocge1Sqx3VERO4Y\nkMPgCMgv3DfH7ypZb1WEyqua0dDcFjD5wpOLZ0r2Ew9KltbHjVUr8NhtM/CTC3s+3WJvFRejxLzz\nRkqO3fP8tzC0mf2+7sQZ73NTlTV6fOpSvWl8D5SrJKLei6kzw1DT2AqdRhUw57PGy/mDFQ0wtVtQ\nMEk6NPpi8Ry89ulBFOYMxphhidBppHPwIwZqxcc3XDAaV3rZ00qhc08R2WI048MNx/Czed5HJABp\nqk1zhxUqpe177SmX1fOLfzypi1tKRH0dA3KIzB1WVDe0IkETOAuZt6Fok71e8oBE9x6vEr++Psfn\ne2liVXhj6UUhtpYCUXvZdhcoA5vJ7KwOdbSyCRPsPeHjVc6e8/Tx0ZUOk4iiH4esQ/RtqS1jlqNY\nQM1kW7kAABUFSURBVCCO0oGpbjWHVSEWgKDuEaPy/E/A4KfYhCAI2LTXuQf9GXuFr6pag5gA5JrC\njD6XvpSIuh8Dcog27T0LAB7ZuHzJzbKtwm0xSgtQ6Fu7v8IQBeatylKbn4C87dA5ybY3AKisNeCt\nLw6Jz2dlD+66BhJRv8GAHCJHj8rXqmd340bY6steOG2Y5LgAwdvlFGHedozlZvku7+haocvhkde2\nSLKzJWpjPK4hIgqEc8ghMpmtUCrkGJIaXFGAaWPTsPTmaRiepsXxMy04fKoRAHBlQXp3NpOCJIPn\n0LJj/7irTXvPYOuhUuSPHeBxDgCOVTYDAB5cMNWjvCMRUTAYkENktQpQhDD/K5PJMNbeS76vaAqq\n6gxIH6xjUYEoERfr+Z9Ao965qKuyRg+ZTIbXPzsIAHD86BddOQGb953FwZMNktdm2X/WREShYkAO\nUqupAy3GdlisVijCDKYxakW31t2l0OWMTsG8GSNRMGkQ9pbX4cNvymFodS7Ye+T1rZLrdx+1lVJM\njFfj19fn4K4VGyXn+UWLiMLFgGxX39yGqjqD16xKPxw4i1c/OQAASNbFdFnOY+p5CrkcP7HnIx85\nSIfv91fjjL26lr7V90r6CRnJUMjluLxgJD7/oQIAcEGu7zSqRESBMCDb/fbFzQCA5++ZLcmi9fR7\nO3GoolF8HmiPKvVuVbUGALYvYaeqvZfJTEuKFdOeuiZ/WXBx4ApnRES+9OuA3GrqwDv/O4zLZjhz\nGhvazGJANndYJMGY+o93/3cYhjbv259cF23tP14vPva2hYqIKFj9etvT1ztO4/v9Z/Hom9vEYw+9\n8gO2HKgGYNtfSv2Tr2AMAC0uQ9lXeikgQkQUjn4ZkM/WG/HM+7uwx75Ax90rn+yHVRBQYR+yjItR\n4KX7LxDTIf7mhskRaytFD6XC9p9Lk8te5IzBvouNExGFot8NWVutAh5+9YeA193+1Hrx8b1FUxCj\nUuDWK8bjomnDMG4kq/j0VXnj0rCjrEZ8PiwtHvcVTUGsWolDlU345wd7JNc75pC595iIOqvfBWS9\nW2m9kQO1WHxtNlJ0MdiwqxIr1x31eM3IgbZeUKxayWDcx/3qmkn45TMbxOexKgVS7HnIB6d4JoOR\nyWR47q5CseITEVG4+l1ANrrNDY4bmYzB9rrFl84YiQunDcevnt0gnmeFpf5FqZBDp1GhxV485FhV\ns3huctYAXFOYgZxM6da4ZB1TZRJR5/W7r/UV1bYSeUqFDDFqBX6UP1xyXqWU4+GFeQBsdYep/xF8\npBmXyWS4dvZoZA4NrrAIEVEo+l0P2bFN5bc3TUXW8ESvZfLGDEvEirvPhy4ucM1j6ntcE4LcfMnY\nHmwJEfUn/S4gf1tqq2WblhTnt2ZtYrw6Uk2iKHbh1GGBLyIi6gL9asjatURekpYBl7wrujATALDk\n2mymSSWiiOlXPeT6Zlvay+njB/rtHVP/dvl56bhsxkgWiiCiiOpXPeSqOlvmrSGpmh5uCUU7BmMi\nirR+FZAPnrDVrk1ndiUiIooy/WLIWhAE3PH0Bljtc8ijuW2FiIiiTJ/vIQuCgKfe3SkG4yGpGq6g\nJiKiqBNUQN6zZw8WLlwIAKioqMCCBQtwyy234LHHHhOvWb16NW644QbcdNNN2LBhQ7c0Nhxn6404\nfLoJABAXo8Sfbj+vh1tERETkKWBAfu2117Bs2TKYzbZkCU888QSKi4vxzjvvwGq1Yu3ataitrUVJ\nSQlWrVqF1157Dc8995x4fXc7eroJm/ae8Xn+pD0zFwD8457ZXKxDRERRKWBATk9PxwsvvCA+379/\nP/Lz8wEAc+bMwebNm1FaWoq8vDwolUpotVpkZGSgrKys2xqtbzVD32rGrsM1+Ms7O/D6ZwfR1u69\nfm2ryQLAVjSAe0qJiChaBVzUdckll6CyslJ87ppcIz4+Hnq9HgaDATqdc+WyRqNBS0sLOksQBI/9\nws3Gdtz7/Hce17771WHccEEmkrTSRP9Ge3WnuJh+sX6NiIh6qZCjlFzu7FQbDAYkJCRAq9VCr9d7\nHA8kOVkDpdKzjqzFYsW1v/svhqTG45WHfiQJyo88udbre23aexab9p7Fx89cA4W9J/z2/x3Ah9+U\nAwBGj0xGWhq3OwHgfegE3rvw8L6Fj/cuPL3xvoUckCdOnIht27Zh+vTp2LhxIwoKCpCTk4MVK1ag\nvb0dJpMJ5eXlyMrKCvheDQ1Gr8c/WG+rSXymzoD9R85hULItkUerqQOVNQa/73ntA5/g0VunY0hq\nPD74+ojzRIcFNTWd77X3dmlpOt6HMPHehYf3LXy8d+GJ5vvm74tCyAH5wQcfxCOPPAKz2YzMzEzM\nmzcPMpkMCxcuxIIFCyAIAoqLi6FWh7+16PMtFeL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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "goog.plot();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Resampling and converting frequencies\n", + "\n", + "One common need for time series data is resampling at a higher or lower frequency.\n", + "This can be done using the ``resample()`` method, or the much simpler ``asfreq()`` method.\n", + "The primary difference between the two is that ``resample()`` is fundamentally a *data aggregation*, while ``asfreq()`` is fundamentally a *data selection*.\n", + "\n", + "Taking a look at the Google closing price, let's compare what the two return when we down-sample the data.\n", + "Here we will resample the data at the end of business year:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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I/tXpWsrUde30BQghxCjkraqi5l9/QfXPfhoZh021mZg+KXVQ97EnGQf92vtr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\nSDQRrtcwNjWS2oYECk85aPBUMSs9zzfVLYQQQgwHIReQna6eA/KFk5I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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "goog.plot(alpha=0.5, style='-')\n", + "goog.resample('BA').mean().plot(style=':')\n", + "goog.asfreq('BA').plot(style='--');\n", + "plt.legend(['input', 'resample', 'asfreq'],\n", + " loc='upper left');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the difference: at each point, ``resample`` reports the *average of the previous year*, while ``asfreq`` reports the *value at the end of the year*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For up-sampling, ``resample()`` and ``asfreq()`` are largely equivalent, though resample has many more options available.\n", + "In this case, the default for both methods is to leave the up-sampled points empty, that is, filled with NA values.\n", + "Just as with the ``pd.fillna()`` function discussed previously, ``asfreq()`` accepts a ``method`` argument to specify how values are imputed.\n", + "Here, we will resample the business day data at a daily frequency (i.e., including weekends):" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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51bR+3HpVH6rrjLzw/kEOnSxXJIuDC7UelQqGSqEWQgjh5FQqFTOSYnjg5sHY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\nt5WdsoQQmjO5GHlyUDsUsGZTJjZt9iwS4qqcqhr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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(2, sharex=True)\n", + "data = goog.iloc[:10]\n", + "\n", + "data.asfreq('D').plot(ax=ax[0], marker='o')\n", + "\n", + "data.asfreq('D', method='bfill').plot(ax=ax[1], style='-o')\n", + "data.asfreq('D', method='ffill').plot(ax=ax[1], style='--o')\n", + "ax[1].legend([\"back-fill\", \"forward-fill\"]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The top panel is the default: non-business days are left as NA values and do not appear on the plot.\n", + "The bottom panel shows the differences between two strategies for filling the gaps: forward-filling and backward-filling." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Time-shifts\n", + "\n", + "Another common time series-specific operation is shifting of data in time.\n", + "Pandas has two closely related methods for computing this: ``shift()`` and ``tshift()``\n", + "In short, the difference between them is that ``shift()`` *shifts the data*, while ``tshift()`` *shifts the index*.\n", + "In both cases, the shift is specified in multiples of the frequency.\n", + "\n", + "Here we will both ``shift()`` and ``tshift()`` by 900 days; " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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PZ8zRFHy9nGnT1Mvq869NmgI9U94zn/921sO9ad/cu8S+/v4eJCRdZsrCkvPl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yMQCJBOp2lqaqKzs/OHc77/5tjX18fo6Cj9/f1YrVaCwWCxL+HVFNq7UChEKpViamoKwzCoqKgg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\niIgJKJBFRERM4A/3oO5fXZCK2gAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(3, sharey=True)\n", + "\n", + "# apply a frequency to the data\n", + "goog = goog.asfreq('D', method='pad')\n", + "\n", + "goog.plot(ax=ax[0])\n", + "goog.shift(900).plot(ax=ax[1])\n", + "goog.tshift(900).plot(ax=ax[2])\n", + "\n", + "# legends and annotations\n", + "local_max = pd.to_datetime('2007-11-05')\n", + "offset = pd.Timedelta(900, 'D')\n", + "\n", + "ax[0].legend(['input'], loc=2)\n", + "ax[0].get_xticklabels()[2].set(weight='heavy', color='red')\n", + "ax[0].axvline(local_max, alpha=0.3, color='red')\n", + "\n", + "ax[1].legend(['shift(900)'], loc=2)\n", + "ax[1].get_xticklabels()[2].set(weight='heavy', color='red')\n", + "ax[1].axvline(local_max + offset, alpha=0.3, color='red')\n", + "\n", + "ax[2].legend(['tshift(900)'], loc=2)\n", + "ax[2].get_xticklabels()[1].set(weight='heavy', color='red')\n", + "ax[2].axvline(local_max + offset, alpha=0.3, color='red');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see here that ``shift(900)`` shifts the *data* by 900 days, pushing some of it off the end of the graph (and leaving NA values at the other end), while ``tshift(900)`` shifts the *index values* by 900 days.\n", + "\n", + "A common context for this type of shift is in computing differences over time. For example, we use shifted values to compute the one-year return on investment for Google stock over the course of the dataset:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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TN8ADznlo7vBi8YV6WdsUOrwfYu3cMRHDejrLm2a0c14UPXSDcw8KKnYSeMfO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\n3AkrUPtYNzSZQnoN8GpH8aR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YZW6ttfXABazdVYovfj0hfTDbNqtkgBJaohgMzF4SiX4O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\ns8WKLX+cR/+C9qIXklwJca4XpW+t/AP3XGvf80A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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ROI = 100 * (goog.tshift(-365) / goog - 1)\n", + "ROI.plot()\n", + "plt.ylabel('% Return on Investment');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This helps us to see the overall trend in Google stock: thus far, the most profitable times to invest in Google have been (unsurprisingly, in retrospect) shortly after its IPO, and in the middle of the 2009 recession." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Rolling windows\n", + "\n", + "Rolling statistics are a third type of time series-specific operation implemented by Pandas.\n", + "These can be accomplished via the ``rolling()`` attribute of ``Series`` and ``DataFrame`` objects, which returns a view similar to what we saw with the ``groupby`` operation (see [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb)).\n", + "This rolling view makes available a number of aggregation operations by default.\n", + "\n", + "For example, here is the one-year centered rolling mean and standard deviation of the Google stock prices:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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oI9alHq/MJKtypznncf+w9cmNdc6sOW2AeZXZu0sBnLukErs1N9/ZYprcOtYg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\nX4vfgTqYSFNT4+Jwoier9nFKOB4hkoj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xs3ZDctpMWdnjUHx7vXfpu+kLe9jTvY9/ffE7\nfOLcD6Mq2Tc/CU3LqTw20QYGl6T1+yI81fEbPJF+3lz2VuZZFgDJ4eFgJE7VNCcumUz5k/ZURaHK\nLUlVQkwmCcjjlJqHjMWTVbIA3BlDu6e6AyMG5HwFPMbKHwugomBWrUQGN45PJWldv3ILldaKUTeb\nB3DYTNRV/v/t3XlgFOX9P/D3zOzsfSSbbBJCyEEIdwAb8AKRHrZ41VK1CAWP2oNv6wVotR6AFcWK\nRytif3y/alVqK1RBbW2tYBUUKCKHKAgGkkBOcm/2yh4zz++PTWZ3yX3tLtnP6y+e3dndmYfNfua5\nPo8OJr0aGpGP6lKt3tCqhYiAPNLW+xatwAu4edJCvPH12/ikai+ONRYjRz0FXn9oNrzHK8GoG9pr\nbl+qE5BkZBoykGvKwXnmi5Tn0636qOWG7o6xrQVsNkR/Ah8hiY4C8gC1B+H+BFcpbJBZllmn6ys9\n3gC8fqnDjjcOnxMflX+CDys+wazMCzFBvFhZZ9z+w56qS+nVefAcF9fjhWfvadvXLl2RV2HB+Gsx\nPf08jEnKQ2l15BIjn18ChniiUvuNm88vozB1OsZpz0O9PTizOivNEBfBGAgOnUzJT+lyS01CyNCh\ngDwAXp80oFZu+Cxsf0DusMbX7vQqwSMnI5glq8Z1Bu+VfYiDtZ8jwCSYRCNSdSnwekLnMdwSJxjC\nguVAxjALkkd3+ng0JsOHL4erqo/c3OLsm61YG27fH0LOFd3+ugUCAdx///2orKyE3+/HkiVLMGbM\nGNx3333geR4FBQVYuXIlAGDz5s3YtGkTRFHEkiVLMGfOnGicf0y1dxH3RO5kowOvT0Jx2/gxADQ6\nWju0UsPHdT3eADRaGY9++gxkJiNdn4ZLsy7GBFMhNCoNSj2Ra4iHk/AEIElDkLpzb+1eeOucuCx7\nDozqwe8pCEgyAoHOo35epplSQRJCAPQQkN955x0kJyfjiSeeQEtLC6655hqMHz8ey5Ytw/Tp07Fy\n5Ups374d06ZNw8aNG7F161a0trZiwYIFmDlzJkRxeK9XPHsdq04jwOOVYNKrYbeHdhRijHXYmuir\nU5FJLpqdPqQn68HzHCqd1UjX2yJa0DzPQS/qMCdrJsYkjcaU1Inw+iUcO9UMIJRUIjyRx3ARnikq\nbRBmIFsMarS0ZVRjjGFv7T7U+2rx3+rP8PPCm5CflDvgz2jX6gvA19aLIqr4Dj0qYhdbCRJCEk+3\nAfnyyy/H3LlzAQCSJEEQBBw9ehTTp08HAMyePRu7du0Cz/MoKiqCSqWC0WhEbm4ujh8/jsmTJw/9\nFcTQ2XsLW4wajM7UID3dgorqUOtXloGeGkF2jxNbvzqAYveXKHdU4tZJi8F7RijP1zS4kWHV49qC\nq5XHKuoi19CmW3XQdDFL9lymEQWMHmmGbpDSdqZYtNBpBNTbW9HY4sXVaYvQpDmGd0rew7MHN2DR\nhB9FbFLRX7VNblTUObGtYSvG6Cfim3kzlI0+2sVqvTEhJP50GyZ0Oh30ej2cTifuvPNOLF26NKL7\n0GAwwOl0wuVywWQKZRbS6/VwOBydveWwEt6lDARbb6JK6LCWs7ucy27JhZ2N7+G1qvX4z5l/o9JZ\njcLUiWho6PiaszN/nb3RgmEYZ1Ay69WDuhmEXisqk8VUnAqX5czBL6f+BCpexMtH/4qPKnYN+DOq\n6t041PJfnPacxClPMUQVj7wRpogx2q52pCKEJJ4eb8+rq6tx2223YdGiRbjyyiuxdu1a5TmXywWz\n2Qyj0Qin09nh8d6w2WKTInCgSqvssLRlsyoYlQSTQR0xFpiZYYarbamONcUY0RJqbGlVXtvsO4nj\nVYdhVadgirUICy/4NgRZi69Kgzsx5Ywwo7reCZ9fhiVJH5EtK8cTQHPbVnlmgxp5o5LP+Qk50fw+\n+MHB5WfK59psRRidkYnn9r6MmWPOg83Uv3ORJBl2lw+l0hHsb/kEJpUZl+d8HyMyLNBpVMgZZcXB\n47XK5w6Wc/VvKdao3vqP6m5wdRuQ6+vrceutt2LFihW48MILAQATJkzAvn37MGPGDOzcuRMXXngh\nCgsL8cwzz8Dn88Hr9aKkpAQFBQW9OoG6unOvJe0PSDgRttFBIM2AJm+otWqzmZBqFOHz+FBvb0Vt\nbQsaHV7wHIfMVAMOFdcDCI45X5I1HQ2NXuRpx0MjquBuYjhSWhn6sFQ9vB4/Wlw+fPxZOSblWeEP\nSNBrRTQ2ueBw+ZGTYUKyQURDQ2R36LnGZjNF9fvQ0OhWxvrbP1cDI5ZN+xW4Vg51rf07lxMVduyu\n3Y29zR9Cy+txWcoP4XUC9mYXnG0JSAxqHnqNatCuN9p1N1xQvfUf1V3/dHcT021A3rBhA1paWvD8\n889j/fr14DgODzzwAFavXg2/34/8/HzMnTsXHMdh8eLFWLhwIRhjWLZsGdTq4ZtYwBU2dpyV1vms\n3OC2dcHWaqPDi1P1dVDzmog0jWaDGgIv4PsTZ+FIaSNEFY8jZY0R78NxkekMj7S1nDNT9crevslD\nMPM4EYQPJQQkWenh6KobWWZyj0lWAKDW2YQD9l0wCEZcYZuPJDEFY7IsEdnABmNyGiFkeOFYbzaV\nHULn4h1WdYMLZxqDLavCfGuHtIvtd46nzzhQXF+OLxyf4aT7KC5ImoP5Uy5DabUD7taAkv6RMdbp\nPsRJJjVyM8zwB2QlEHdmMNJuxoNo33GfaXKjOmxNcO4IU5drghlj2PDFy0jSJKEwdSIMzIpknRkW\nQ8fjDxXX44y3EjrBgGk52RAFfsgnb1FrpX+o3vqP6q5/+t1CJp0LX7rSWYYlxhgO1X6BD8o/RklL\nGQAgSWWFXjCiuiG4J3H4y7pqkeVmhPYCzk43dpihCwAakdaw9leqRRsRkMuqHZhW0HlAdgXcOOOu\nwxf1X+Hjyj0AAJFTY6x1NH459SfKcQ1tE/3SNSMxdpRlUDYNIYQkBgrI/dCe8nJSnrXTYHq0rhj/\n9+VGAMBIbS4mGb+BbG0+OI6D1y/BF5Ch6iFf9PicpIiyupPlTCNtBuquHgCB55Fu1Sm9HQBQVe9C\nRkrHvNJG0YD7z1+GrxqOo7S5Al/Xl8Pub0SZ/bRyDGMM5bWhmyYKxoSQvqCA3A9yW0Duaqu6ibYC\nXJX3PUy1TUZtdWQglWUGSWJQnxWQJ+Qm46uyJljNGtiSOm4MH368SS8iO90Ud5tAnIvODry1TR4I\nPId0a8cdr0RehSm2SRhtHIscBNeZTxljVZ73+UM9J7QzEiGkrygg94PD7Qe4rnP+chyHy/OCm87X\noj7iufbW9dkta40odDsWrBYFTMhJhiBwlGpxEHGd/B86PX6kd/Oa8E1B7E6/0ksRnq+6LztSEUII\n0ENiENKRxxucYS3LEv5Vuh3vlm7r0+vbW1GGfmySoFELFIwHWWf3VL4ecpRLYSlTqxqC2dIYYzhZ\nFconHi+7NxFCzh30695HjS2t8Ms+/LPub/hH6fv47MxByKzrHZ/SrZ0vbznXE3gMF50FTqmbhQcB\nSY6YXOdvu8FqbPECbS/LH9m7pDiEEBKOuqz7qNnjxnv1b6DGW4EpqZOweMKPul2b2t41LQgcJCn0\nQ9/q691OUWRodXZjpFN3/WfRcFa6VAA4fcYBpyeUGEY9iCk+CSGJg1rIfdAa8OLtyk2o8VagMGUy\nfjp5EfRi9wkeLAY1eJ5D5llbK9KmAvGhsxZyd3sudzaRr7HFG7GXtUhL0Qgh/UC/HH3g8DnR7GvC\naN043DJxAQS+55aQTqNC4WgrUixa2JJCM2/TkilTUzzorIXsOGvTDgCorHMqKU+DrzvrNW1Z0wpG\nWWj8mBDSL9RM6wObPgULcm4G82khqnpfde3d1iNtRmSmGmiHnzgXPqmr1RecxFfXHOyqbmkL1lk2\nI+wuH+xOX8Rru1oKRwghPaGA3EuMMTAAJpUFTr+/360gCsbxxaBVId2qQ5JRA4fHj6o6F8KndB07\n1RxxfIsrGIAFIZg97ainKWJuwNnrxwkhpLfo16ONLDNIMus02Ya71Y+vy4OJIHQaARRThw+O4zCi\nbXxfp1Gh2eFVlrZ1l+bdpBfBcxysZi3qmjxtr6fJXISQ/qOA3OZklR0uT0DZLOLTmgOo8zRgRvIs\nVNW5lOM8XgmggDxsef0SGAsmB5G7CMhqkVd6SMK7qPNHWqJyjoSQ4SnhA7LT44deq4LLE2wVeX0S\nPqz+AP8s3QadSotkbwH0gjHyRTHdH4sMpfbu55Iqe5fDC+HDFe2taQCUtIUQMiAJHZCdHj9OVNiV\nrkbGGF47uhWHmj9DijYZS6bcgtrqhK6ihCXLQFd3XgE5lAjGatJ0mNhFCCH9kbC39F6/hMaW4MxZ\njzc4q/YLx75gMFbbcPf022AWUpTjczJMUAmhJB8kcQUCoUBtNqhjeCaEkOEkIZt/lXVO1DW3RkzO\n8ss+HHEehF4w4rsp1wEBDcprg5tvZ6TokWzSQOA5VNa7MCrN2MU7k+HIoFOBMcCWpMOpmsgN2WnW\nPCFksCRcQJYZU9aUhs/ZMWq0+GHmIrh8bhhVJpRUhjYKsLS1gswGNbWIhrm8ESaUVkcG3YKs4N7U\n4ekxw5kN6ohMXYQQ0h8JF5DD14wCgFEnYkxWcHasx2vGqRpHRJ5prVqgNJcJxGLUQCU4EZA6jh+3\nz6g+u1E8OpM2kyCEDFzCjSHLcuQPbfiPq06jwvicZGWsGADG5yRH69RIvOiiF1qnUSEnw0TfCULI\nkEi4gNy+ubwgBDcB6Gw8uH09aVdbJ5JhrptlbckmDTQidU8TQgZfwgVkh9sHxhj2tLyPY/5dUKk6\n2X5Po0JhvhUZVn0MzpDEWnhCkBEp9B0ghERHwg2OVje48bnjU3xuP4RsfxYCcgBqoeNELeHs7XxI\nwghbZgxbEvWSEEKiI+GiTqn7a+yz70CSxoIlU27uNBiTxGbSiwCC3dOdbc9ICCFDIaFayCeaS/Fh\n4z8gciKWTLkFFg3NjiUd5Y+0wN3qh5Zm1xNCoihhWsiMMWw98S5kJuPKkT/EKFNmrE+JxDG9Vuz3\nFpuEENIfCdME4DgOC0YvxIGKYoyzjI316RBCCCEREqaFDAAOB4dsXT4sRk2sT4UQQgiJkBAtZMYY\nPj/RoJRNOjGGZ0MIIYR0NCxbyD7Jh22nPoLMgutXjp5qUp4z6UWaOUsIISTuDLsWstvvxh8Pv4wS\nexk0ghoXj7gQfn8wMCeZ1MjNoJnVhBBC4k+vWsiff/45Fi9eDAA4ffo0Fi5ciEWLFuHhhx9Wjtm8\neTOuvfZa3HDDDfjoo4+G5GQ70+oLwOEObhDf7LXjmQP/DyX2MhSlTcXFmefD4w0ox9K2iYQQQuJV\njy3kF154AW+//TYMBgMAYM2aNVi2bBmmT5+OlStXYvv27Zg2bRo2btyIrVu3orW1FQsWLMDMmTMh\nikM7VivLDMdONQMA0kZI+OPhl9DY2oRLs2biuoKrwXM8ApIXADAiVU/ZtwghhMStHiNUTk4O1q9f\nr5SPHDmC6dOnAwBmz56N3bt34/DhwygqKoJKpYLRaERubi6OHz8+JCfMGENJVQu+KGnA4ZOhiVpb\nvv4nGlubcPXo7+H6gu+D54KX5peC3dVa2hCAEEJIHOuxhXzZZZehsrJSKbOwxPsGgwFOpxMulwsm\nk0l5XK/Xw+GI3OS9KzabqdPHG+weyDJgS47MJVzb5AanEmA0RgbYbxuvxvikyVgw41vKYwFJRoPL\nD4tFh4x0M4z66KXJ7Oq6SPeo3vqP6q5/qN76j+pucPV5Uhcf1u3rcrlgNpthNBrhdDo7PN4bdXUd\nA7fHG8Dx08Gu6MJ8a0RX8+fF9V2+VyrycKK0HmaDGhzH4dCJemUrPXuzGx6Xt1fnNFA2m6nT6yLd\no3rrP6q7/qF66z+qu/7p7iamz4OqEydOxL59+wAAO3fuRFFREQoLC7F//374fD44HA6UlJSgoKCg\n3ydcVhP6T66ud0Nu28O4pW3yVndKqx040+SB1y9F7GurUtH4MSGEkPjV5xbyvffei4ceegh+vx/5\n+fmYO3cuOI7D4sWLsXDhQjDGsGzZMqjV/e8e9vok5d/19lbU21sjnhdVPLJsBpRWBwO31ayBy+OH\nt215U02DGzUNbuV4jVqgvMSEEELiGsfCB4VjoLMuj6NljfD55U6ODmrvxj7U1n09ebQVKoFHQJLx\nZUljxLHZ6UaYDWqohOi1kKkrp3+o3vqP6q5/qN76j+quf7rrso7LxCABqft7hPYx5dGZZrha/Uqw\nVQk81CIPn1+GWuSRnW6CkdJkEkIIOQfEZUAWBQ5eufOgPCbLovzbbFDDbIjsGp+Ya4UsM0qPSQgh\n5JwSlwFZZoBG5JFu1eP0meDs7Ul5Voi9nJhFwZgQQsi5Ji4DsiQzqEQeVrMWVrM21qdDCCEkwUgO\nB1xfHob5oplR+8y4WwsUkGTIMlOWOhFCCCHRJntb0fDu3+E8/HnUPjPuWsjltcEuam83s6wJIYSQ\noSSm2pD9wErwGk3UPjOuWsj1zR7YnT0n/yCEEEKGguz3gUnBXBiCTgcuipsSxVVArqhzKf8On01N\nCCEkevxNTbE+hZhx7N2LshX3w1teHvXPjpuA3NgSysY1OtNM64cJISQKAs1NqHjqCUht+xG0lpag\nfM0jYIFAD68cnswzZyF98c1QpaRE/bPjJiDbXcGu6tQkbYe1xYQQQoaGYEmCJicX7q+DW+YySULa\ngh+DUwWnGAWam5RgnQg4joN+/AQIen3UPzsuArLd6VXGjpNN0RtAJ4SQRCX7gr+5HMfBdt2PYPpG\nEQBAN6YAxvOC/2aMofqF/4Wn5ITyOs/JE5Dcro5veI6TvV7YP9kZ056BuAjItc0e5d9atdDNkYQQ\nQgaKyTJOr34Y7q+Odn9cIADDpELoRo9RHqt5YQMCTc1KuWn7+wjY7UN2rtEiuZxw7N2Lpm3vx+wc\nYrrs6dMjNeBkCS5PAILAoXB09PvsyfDhrawAp1ZDbUuL9akQEpcYY+A4DhzPw3b9fEiu7lu6vCjC\nevkVodfLMpK+fRnUI0Yo79fw9laYL7x4SM87GkRrCrKW3wMmx27JbcxbyM2OYLdJkpG6qsnA2D/5\nGM4D+5Vy+9KFzsh+X4fWgdza2sXRhJz7PCUlqHzmSSXgGAqnwDR9Rp/eg+N5JH/nu6GlQIxh5NK7\nIRiNAADJ7YLvTM2gnne0RXOZ09liHpDbWc0UkEnfeIqLceq3K5Wy6RtF0I0pUMpV659F6+lTSvnM\nq3+C3No2PCJJqPzD08p4kdzaitL7fw3JQdvJkeGlfYddbW4ueK0W/ob6QXtvjuehG50f/BxZRtXz\nz6H5Px8M2vtHA5NllD/5OzR/9J9Yn0psA/K4nGSY9CLyRphg0NIyJ9Kz8O27Nbk5UCUlKWVdwVjo\n8oNjXbLXC8nlgjo9Q3neefAgZK8XAMBrdbAtWKS0ov2NjbDMmg3B1PVepYPJeeggvOWnlXKMtyUn\nw1Tdpr/CsXcPgGDwzPzl7UM2pMPxPFK+/wPY5i8YkvcfKhzPw3bt9UAMW8btYnoGFqMG+SMtsMRR\nd7XkdMJ5cH+33Z0kRHI40PLpf7t8nskyJI+ny+f7qm7TX5WuZl5UY+QdSzs9jtdokP2bByPS3uWs\negSCyayUky6dozyvycxE6g+vU55r/s92eE6GZpYOhvCg69j3aUTigTN/egEtbT+cJLFVv7AB3orQ\nd0NyuXp9w9ayZxfqt7yhlHUTJqL11KluXjG49GPHKV2+vjM1kP3+qH12XzFJUoaptHmjkTR7TmxP\nCHHUZR1L4WvsAi0tqN3014i7pVgO8sc72e9D3ebXlXLA0YLS++5Ryt6KcpQ/9kjo+ZYWlD+xRimz\nQAC+mtCYk+zzRWQJ8lZVRnQl6Ubnw7Fvb7/OVWWx9Gp8KNDcjMb3/gWVdfAmGdp37kDDW1uUcsrV\n10A3brxSZoxBm5unlD3FX9NNYYJwHtyP1tISpeyrqgInhnIxnH7st/BVVSnlpvffUyZjsUAATdtD\ns4I1OXkRwdw4ZSrSYtBibS0rQ/njj8JbVhr1z+4t1xeHUfXH5+Lq7yzhAzILBHDqtyvgrawAAKiS\nk5G++GZwXHBPZfdXR1H13B9ieYpxhckyGv7+tvKDIFpTkLZgkfK87HZDExZYRGsKdGPHKuVAQz04\ndejHxltRgZoX/1cpt5aVouaFDUpZcjrR8t9Qy9E443yk33jL4F7UWVRJSchdvQZicjIA9HtdYvs6\nTwDQjR0b0UWtzsiAGJYJaMStP1e6171VVahav67HGbDk3OQ4sB/N/9mulCW3B/VhN2s5Kx6GOj0d\nQPDvTZuTC3VG8LvBGAse235jKQio3/KGMjdCk5mJzF/dEaUr6Zo6MxMj71gKXcHYng+OEsntRu1f\nX1N6G/QTJkI9YgSYP372TxBWrVq1KpYn4HZHvzICdjsktwuCTg+O58HrdOB1OohWK3hRhDotNMbS\nsncPDIVToc5om+YfCPTYyjIYNDG5rmhxHjwA95EvYJw6DUDwR6CdYDRGzNzk1WrlOCB4wxO+bmmf\n9QAAERBJREFUREJyOMDrdNCNzg/Wm6sVkssF/fgJbe9ngn7CBGUWZ/uN0lDjhOB6eBYIoPLZZ8Ab\njBHj0T0J2JtRtvIBmGZcAEGng2A0wXzBRb18NYOuYCy0WaMAAN7y03B89qkyeaYzw/07N1RiUW+s\ntRWN7/0TlksuBQCIVitMRdPBqztmKOQ4DqaiGRGzmvXjxivfRY7joBudD1VqqvKdjdYs4e7qjhME\nqNpuaIHQcqtY4gQB9W9sCtZXUjI4lQqGyVPAqaI7f8lg6HqIlmMxnk1SVxf9Wa31b22Br7oKmf9z\nW59ex2QZpx/9LdJvugXa7Jwuj7PZTDG5rqHEAgEllR5jDMznG/RtyeKx3gJ2Oxre3oq0RTf2+YfO\nvnMHxIwM6MeOG9A5nHn1ZYg2G6yXXwkgOEzAi5E/3vFYd+eCaNSb7PWi5k8vIOOWnyp/M7LXG9Vt\n/YZCb+pOcrtQ/8bfoEpJQcqVV0fpzLoWsDdDMFtienNgs3U9cXTYdFmzQKDbsYDwceCUq74P47Tz\n+jyzNWC3Q52eDs2obOUzHQf2D/sZsowxlD/5O7iPHwMQvCs/139MektlsSD9xpuVYNz84Qddblju\nq6lG/VtvKmXL7EsHHIwBwPajG5D0zW8r5eo/rofz4P5uXjF0/I0NEV3p3vLT8Dc2KmXJ40nYTQm6\nwms04EQRzgOfRTyWCDiehyo5WekN6IvBmLvDGEPNSy8o81RUlqSYt9S7M2wCsuuLz1H1x+eUsr++\nLmKWbNX6Z+E5UQwA4FQqmC+a2ef/GDE5GSN+/j/K65wHD6B527+VcqC5Gb662oFeStzhOA7WuVfA\n1zbOnsgcn+6N6Fps+Mc7CDhaAACqZCtadu8a1HWeAMBrteC1WgBtPRVqNfQTJyvP1299E1Lbcq7B\n5jl5Av66uojPch46oJSbtr0P99Ejoef/tgn2j3eGym9tQcvuXUNybvEmPIA49n8WMdkx4+ZbYb5o\nZixOK6Z4rQ4pV18DldkMxhiad3zU5czrxn/9M2KCZ82L/xcxYa0/OI6DbkwBmrb9e0DvEy3DJiCD\n46GfOEkpOg9/jpY9u5Wy+YKLeszb2lea7BzYbliolFv27ELzB9uUsqekBK4vDg/qZwJtXcZRbpUb\np52HpG99J6qfGY9GLrtbmajCGEPzhx8g0BBsIfIaDXJ/+xjElNQh+3xOpULmkl8pLazW06fQsmeX\ncpMgeTxo3vFhr9+vfuubqN8aatU37/gI9W9vVcrOgwdg3/2JUjYUToE6LV0pm84/H9qcXKUspqVB\nk52tlP11dRDTQ8fXv70V3srKXp/fQATszWgtK1PKA/2bCe8Z8Dc1RdSbp7gYVet+r5TF1FT4aqqV\ncvv4biLzFH+Npm3vKXXhrayEp7g4dACT0fjvfypFXq+Hafr5Stm+6+OImx7Xl4eVMmMM/vrQjWPw\n7YLPWWZfirQfLx706xkKwyYgG6edh+SwgKEvGAfzRaHJQ6bzL0DK1dcM6meq09Mjfow0o0ZFfoF2\nfhjxR9lf/sbGiLWFkr0Zpb9erpSZLEesaQ04WuD68osu369l7x7Uvv5az59bV4fa1/8yLHd26S9e\nVIcmz3Acch95DOqwSW3tLdlo0YzKxqh7fqP00rSeLIZjb2hduPPwIVSGrRJwf3U0ouWmKxgLXqcL\nvSGHiB4Ay8xZMBROUcrm8y+MmDlrmDwFmlGjlLJ17hVKchYAyLjl1oiy/eMd4DWh97fv+rjXKUsD\njha4j32llP1NTWj4xztK2Vdbi+adHyllz4li1G8N/d24j3yJ8rWP9+qzzuYpKcHpxx4JBQCfF479\n+5TnxbS0iGChzcntco18otJkjgz2MLavU66siAjASd/5LtJu+LFSTv/xYiXxj7+xEWdefRlo+54z\nWUblH54JvbkkofSB+5Qik2WcefVlZfgklukw++LcOMt+0IwaFfFDEA2GyVMiUjcmf/dymGfNVsrV\nG56Hp6Sks5dGkFwulD+xRrmjFwwGNH2wHZLbDSD4ZdONCV2bt6IcZza+rJT9tbVoCGvluI99hfIn\nf6eUVWYLWCA03t56qqzT3gNepwPz+eD+8ssezzlRCXpDp7Njo4XjOIg2m1LWZOdG9NoIOr2yhAYI\ntiTCh1UMkwthnRvaPCBp9hxl8hgAqEdkdju7u8fzU0XuX5O7ajVUbT0I3qpK1G1+HZwYnOXqb2xE\n2UP3K8dKDgcqnnkyVG5uxpk/v6KUA40NcH1+SCnLbhfsH4V6B3Rjx8ES9vfHqVTQT5iolN3HvkLl\n22EBva424ubTcWC/ktlNm5cH45SpkNv+BsWUVGTdGbopVlksyFp6d6/qJFEJRmPEZFjduHER3z1e\nre5ybF0wGJC19O7QMCNjSL3uR6FAKwgwX3ChcrzsdsNXXYWWvV0nLYpHCbnsaai1LwdQmUzg235s\nJIcDTf/5ANYrrgInCGCMBZf8tH0BfWdqwGk04AQBvFqN5g+2Qz9pEgSDAZxKBcusS6BqS+so6PQR\nS4ukFgd4nVb54eQEAWJaurJ2UXK7ITU1wlA4FQCgSk2FYcpU5ct95pWXIJjM0ObmAghmkRJtNgg6\nHYxTp0EzMmvoKw20dGcg2uuO12igsoTSiYopKTBMCo03q21pMJ9/QSxOEUDwR7f9eyfo9NCPn6B0\n8TNvKzzFX8N8YXB5WMBuh/3jHUj65reCx5tM4EU1NNk54DgOgsEAw+QpEAyG4HvrDdAXjIPKYgmW\nNRpoRo5UPltMtUVMsqvb9DqSJowDbMG/kzMbXwGvEpXXNLy1BZAZNKOywXEcDJMLlZsvjueVz01U\nA/175bVaiL1MvsOpVBBTQzeeHM9HNH44jlP2cAaC3zPLJbOhDRs+iRe07CnKuloOEL4Wz/31cdS+\nthE5qx4Bx3GoeOZJmGZcAMusSzocO9S8lRUQ09KVm4fSB+7FyNvvUtZeRwst3ek/qru+k/0+pGUk\no74h2Cpu2bsHoi1NubFtLSsDr1FDPSKzu7dJWPSd65/ulj3FdD/kRBMeYJnPh5Srr1EeS/n+DyLG\n0qI5Nf/sFrDt+hsgGIxR+3xCYoEX1RFji2cnbmnvMSIkWiggx4hhcmFEOdrj3d0xTjsv1qdACCEJ\nZ1ADMmMMq1atwvHjx6FWq/Hoo49iVNgMTEIIIYR0blBnWW/fvh0+nw+vv/46li9fjjVr1vT8IkII\nIYQMbkDev38/LrkkOClp6tSp+JKWyxBCCCG9MqgB2el0wmQKzSBTqVSQaS9hQgghpEeDOoZsNBrh\nCksvJ8sy+B4ypHQ3BfxcNlyva6hRvfUf1V3/UL31H9Xd4BrUFvI3vvEN7NixAwBw6NAhjB0bP5tT\nE0IIIfFsUBODhM+yBoA1a9YgLy9vsN6eEEIIGbZinqmLEEIIIcN4cwlCCCHkXEIBmRBCCIkDFJAJ\nIYSQOEABmRBCCIkDtLlELwUCAdx///2orKyE3+/HkiVLMGbMGNx3333geR4FBQVYuXIlAGDz5s3Y\ntGkTRFHEkiVLMGfOHMiyjDVr1uDIkSPw+Xy4/fbbcemll8b4qobeQOvN6XRi6dKlcLvd0Gg0WLt2\nLVJSereH6rmuL3UHAI2NjViwYAH+/ve/Q61Ww+v14p577kFDQwOMRiMef/xxJCcnx/CKomegded0\nOnH33XfD5XLB7/fjvvvuw7Rp02J4RdEx0Hprd/LkScyfPx+7d++OeJz0gJFeefPNN9ljjz3GGGPM\nbrezOXPmsCVLlrB9+/YxxhhbsWIF27ZtG6urq2NXXXUV8/v9zOFwsKuuuor5fD62ZcsW9vDDDzPG\nGKupqWGvvPJKzK4lmgZab6+88gpbu3YtY4yxzZs3s8cffzxm1xJtva07xhj7+OOP2Q9+8ANWVFTE\nvF4vY4yxP/3pT2zdunWMMcbeffddtnr16hhcRWwMtO6effZZ5W+0pKSEzZs3LwZXEX0DrTfGGHM4\nHOznP/85u/jiiyMeJz2jLuteuvzyy3HnnXcCACRJgiAIOHr0KKZPnw4AmD17Nnbv3o3Dhw+jqKgI\nKpUKRqMRubm5OHbsGD755BOkpaXhF7/4BVasWIFvfvObsbycqBlIvR0/fhxjx46F0+kEEEzNKopi\nzK4l2npTd3v27AEACIKAl19+GRaLRXn9/v37MXv27A7HJoKB1t0tt9yCG264AUCw1ajRaKJ8BbEx\n0HoDgBUrVmDZsmXQarXRPflhgAJyL+l0Ouj1ejidTtx5551YunQpWNgSboPBAKfTCZfLFZHPu/01\nTU1NOH36NDZs2ICf/vSn+M1vfhOLy4i6gdSbw+FAUlISdu3ahSuvvBIvvvgirrvuulhcRkz0pu4c\nDgcA4KKLLoLFYol43ul0wmg0Kse239gkgoHWndFohFqtRl1dHX79619j+fLlUb+GWBhovT333HOY\nM2cOxo0bF/E46R0KyH1QXV2Nm266CfPmzcOVV14Zkafb5XLBbDbDaDRG/PC1P56UlKS0imfMmIGy\nsrJon37MDKTe1q9fj5/97Gd499138eKLL+K2226LxSXETG/qLhzHccq/w3PLn33DkwgGUncAcPz4\ncfzkJz/B8uXLlRZiIhhIvb3zzjt44403sHjxYtTX1+PWW2+N2nkPBxSQe6n9y3XPPfdg3rx5AIAJ\nEyZg3759AICdO3eiqKgIhYWF2L9/P3w+HxwOB0pKSlBQUICioiIlz/exY8eQmZkZs2uJpoHWm8Vi\nUVp5Vqs1YvOS4a63dRcuvFUSnlt+x44dCRVUBlp3J06cwF133YUnn3wSs2bNit6Jx9hA6+3999/H\nq6++io0bNyI1NRUvvfRS9E5+GKBZ1r20YcMGtLS04Pnnn8f69evBcRweeOABrF69Gn6/H/n5+Zg7\ndy44jsPixYuxcOFCMMawbNkyqNVqXH/99Vi1ahXmz58PAHj44YdjfEXRMdB6u+OOO/Dggw/iL3/5\nCwKBAFavXh3rS4qa3tZduPDWyoIFC3Dvvfdi4cKFUKvVeOqpp6J9CTEz0Lp7+umn4fP58Oijj4Ix\npvTWDHcDrbezH6du676hXNaEEEJIHKAua0IIISQOUEAmhBBC4gAFZEIIISQOUEAmhBBC4gAFZEII\nISQOUEAmhBBC4gCtQyZkmKisrMT3vvc9FBQUgDEGr9eLcePG4aGHHup2h6wbb7wRr776ahTPlBDS\nGWohEzKMpKenY+vWrXjrrbfwr3/9C9nZ2bjjjju6fc2nn34apbMjhHSHWsiEDGO33347Zs2ahePH\nj+PPf/4ziouL0dDQgLy8PKxbtw5r164FAMyfPx+bNm3Czp07sW7dOkiShKysLDzyyCMddvMhhAwN\naiETMoyJoojs7Gx88MEHUKvVeP311/H+++/D4/Fg586dePDBBwEAmzZtQmNjI55++mm89NJL2LJl\nC2bOnKkEbELI0KMWMiHDHMdxmDhxIrKysvDaa6+htLQUp0+fVjbqaM9FfPjwYVRXV+PGG28EYwyy\nLCMpKSmWp05IQqGATMgw5vf7lQD8+9//HjfddBOuvfZaNDU1dThWkiQUFRXh+eefBwD4fL6E2l2L\nkFijLmtChpHwvWIYY1i3bh2mTZuG8vJyXHHFFZg3bx6sViv27dsHSZIAAIIgQJZlTJ06FYcOHVL2\n6l6/fj2eeOKJWFwGIQmJWsiEDCN1dXWYN2+e0uU8ceJEPPXUU6ipqcHy5cvx3nvvQa1WY9q0aaio\nqAAAfOtb38I111yDN998E4899hjuuusuyLKMjIwMGkMmJIpo+0VCCCEkDlCXNSGEEBIHKCATQggh\ncYACMiGEEBIHKCATQgghcYACMiGEEBIHKCATQgghcYACMiGEEBIH/j9PK2OZcai62gAAAABJRU5E\nrkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rolling = goog.rolling(365, center=True)\n", + "\n", + "data = pd.DataFrame({'input': goog,\n", + " 'one-year rolling_mean': rolling.mean(),\n", + " 'one-year rolling_std': rolling.std()})\n", + "ax = data.plot(style=['-', '--', ':'])\n", + "ax.lines[0].set_alpha(0.3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with group-by operations, the ``aggregate()`` and ``apply()`` methods can be used for custom rolling computations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Where to Learn More\n", + "\n", + "This section has provided only a brief summary of some of the most essential features of time series tools provided by Pandas; for a more complete discussion, you can refer to the [\"Time Series/Date\" section](http://pandas.pydata.org/pandas-docs/stable/timeseries.html) of the Pandas online documentation.\n", + "\n", + "Another excellent resource is the textbook [Python for Data Analysis](http://shop.oreilly.com/product/0636920023784.do) by Wes McKinney (OReilly, 2012).\n", + "Although it is now a few years old, it is an invaluable resource on the use of Pandas.\n", + "In particular, this book emphasizes time series tools in the context of business and finance, and focuses much more on particular details of business calendars, time zones, and related topics.\n", + "\n", + "As always, you can also use the IPython help functionality to explore and try further options available to the functions and methods discussed here. I find this often is the best way to learn a new Python tool." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Visualizing Seattle Bicycle Counts\n", + "\n", + "As a more involved example of working with some time series data, let's take a look at bicycle counts on Seattle's [Fremont Bridge](http://www.openstreetmap.org/#map=17/47.64813/-122.34965).\n", + "This data comes from an automated bicycle counter, installed in late 2012, which has inductive sensors on the east and west sidewalks of the bridge.\n", + "The hourly bicycle counts can be downloaded from http://data.seattle.gov/; here is the [direct link to the dataset](https://data.seattle.gov/Transportation/Fremont-Bridge-Hourly-Bicycle-Counts-by-Month-Octo/65db-xm6k).\n", + "\n", + "As of summer 2016, the CSV can be downloaded as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# !curl -o FremontBridge.csv https://data.seattle.gov/api/views/65db-xm6k/rows.csv?accessType=DOWNLOAD" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once this dataset is downloaded, we can use Pandas to read the CSV output into a ``DataFrame``.\n", + "We will specify that we want the Date as an index, and we want these dates to be automatically parsed:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Fremont Bridge West Sidewalk \\\n", + "Date \n", + "2012-10-03 00:00:00 4.0 \n", + "2012-10-03 01:00:00 4.0 \n", + "2012-10-03 02:00:00 1.0 \n", + "2012-10-03 03:00:00 2.0 \n", + "2012-10-03 04:00:00 6.0 \n", + "\n", + " Fremont Bridge East Sidewalk \n", + "Date \n", + "2012-10-03 00:00:00 9.0 \n", + "2012-10-03 01:00:00 6.0 \n", + "2012-10-03 02:00:00 1.0 \n", + "2012-10-03 03:00:00 3.0 \n", + "2012-10-03 04:00:00 1.0 " + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv('FremontBridge.csv', index_col='Date', parse_dates=True)\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For convenience, we'll further process this dataset by shortening the column names and adding a \"Total\" column:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "data.columns = ['West', 'East']\n", + "data['Total'] = data.eval('West + East')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's take a look at the summary statistics for this data:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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50%33.00000028.00000065.000000
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" + ], + "text/plain": [ + " West East Total\n", + "count 35752.000000 35752.000000 35752.000000\n", + "mean 61.470267 54.410774 115.881042\n", + "std 82.588484 77.659796 145.392385\n", + "min 0.000000 0.000000 0.000000\n", + "25% 8.000000 7.000000 16.000000\n", + "50% 33.000000 28.000000 65.000000\n", + "75% 79.000000 67.000000 151.000000\n", + "max 825.000000 717.000000 1186.000000" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.dropna().describe()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Visualizing the data\n", + "\n", + "We can gain some insight into the dataset by visualizing it.\n", + "Let's start by plotting the raw data:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import seaborn; seaborn.set()" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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tj8t7zgtGo2U41IqszWJH7s3W28BIHoyFBRDKO+bx0otbqe9dTrXe8N6kSRM8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\neHt7Y8KECfDz88P8+fMxatQo+Pv7IyAgoMr7XVn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "data.plot()\n", + "plt.ylabel('Hourly Bicycle Count');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ~25,000 hourly samples are far too dense for us to make much sense of.\n", + "We can gain more insight by resampling the data to a coarser grid.\n", + "Let's resample by week:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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W5D7tRhaNGNdRt/jTlfNJwSDkYBD20jLYywYBiMf5FVmGHImAdbri8U0S/l7B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NKz6nnpwC4AphcNvlj73Zv70etFZtUXD1j1tnb72Hush5pyu9afutHdzPMNL3LU1cS4ns9z95cv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\nYUGtd2NoHkGcIy18PjMphsykY717rT10Q9HEdV2csuFIaOX+5LhpZJ6bQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "weekly = data.resample('W').sum()\n", + "weekly.plot(style=[':', '--', '-'])\n", + "plt.ylabel('Weekly bicycle count');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This shows us some interesting seasonal trends: as you might expect, people bicycle more in the summer than in the winter, and even within a particular season the bicycle use varies from week to week (likely dependent on weather; see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) where we explore this further).\n", + "\n", + "Another way that comes in handy for aggregating the data is to use a rolling mean, utilizing the ``pd.rolling_mean()`` function.\n", + "Here we'll do a 30 day rolling mean of our data, making sure to center the window:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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YWIjhw4ejsLAQOTk5kMvlEIvFqKioQFpaGvbu3Yv8/HwIhUKsW7cOjz76KKqqqsBxnI3F\noDPwxhvrcfz4r2AYBrfe+nvcccdd+PjjbdDr9bj66ixIJBL8/e9/A8uy0Gg0PrVOJgiCIFxj3dTI\nGwRSKTiDAZzBACYMGtEFRYKOUjG6deuG6dOnY+rUqeA4DnPnzoVYLEZeXh4WLFiAqVOnQiwWY/36\n9QCA5cuXY/78+WBZFrm5ucjKygIAZGdn4/777wfHcVi6dKlf5E6Z8kCHT/MeHcsHDfinn35AfX0d\n3n77fRgMBsyc+Siys0dh6tTpqK6uxtixudi9eyeWLVuNxMREvP/+VhQWfocbb7zJL7ITBEEQ7eF8\njCFgzD0NWI0GQit3eKgIuELQu3dvfPLJJx2OTZkyBVOmTLGZI5VK8frrr7c7XlZWFnbs2NFuPD8/\nH/n5+X6SOrwoLy9HVtZIAIBIJMLQocNQXn7eZk63binYsGEtoqOjceVKDa69NicUohIEQXQZfFUI\nBOZ4Olang+Mix8GFChNFAJmZmSgpOQYAMBgMOH78V6Snp4NhBGDNzTNee20VlixZhhdffAlJScmW\nTofU8ZAgCCIwcAYDAHht7ucVCV6xCDWhd1oQLrnhhgk4duwInnrqUej1Btx6623o128AdDo9Pv74\nAwwaNBiTJt2Gp556DFJpNBITE1FXVwfAs8pZBEEQhPv4mnbIRJksBJyBFAKiA2677Xab7dmz57ab\nc9VVQ/DRR6YCTBMm3OzwOJs3v+N/4QiCIAjfXQZhZiEglwFBEARBeIGvWQa8IsHadU0MFaQQEARB\nEIQX+JxlQBYCgiAIgoh8LApBJwkqJIWAIAiCIDxEX1+Hlp/3AfCDhSBMggpJISAIgiAID7m0cZ3l\ntddBhSLTfupz5/wik6+QQkAQBEEQHqKvrra89tpCIDGlHTZ9/RUURf7pm+MLpBAQBEEQhA8wIi8t\nBBKp5bWquNhf4ngNKQQEQRAE4QF8hUIebwvACaRtCoH9MUMBKQQEQRAE4QFGdatfjiOQRltthb7M\nPCkEBEEQBOEBnEbrl+NYWwiMKpVfjukLVLqYIAiCIDyA1WgAAKLkZKRMud/r4zDmbodAeCgEZCEg\nCIIgCA9gtSaFIG7MWMTmjPb6OKKEBERfNcR0TJXSL7L5AikEBEEQBOEBrNbkMmAkEp+OwwgESJ+/\nAOKevcCqNf4QzSdIISAIgiAID+BdBtZpg74gkErBatR+OZZPcoRaAIIgCIKIJDizhUAg9c1CwCOQ\nSsEZDCFPPSSFgCAIgiA8gI8h8JeFgHc98K6IUEEKAUEQBEG4iep4CRQHfwHgewwBD59+yLsiQgWl\nHRIEQRCEGxhbVajctMGybV1HwBf4AkWhVgjIQkAQBEEQbqC/UmuzLfCXhcDc5IjTkcuAIAiCIMIe\no1Jhs+23GAJzt0RWr/fL8byFFAKCIAiCcIN2CoGfsgyYKLOFgBQCgiAIggh/jErb8sKMv+oQmC0E\npBAQBOEzRpUKuuqqUItBEJ0aex+/v2IILBYCnc4vx/MWUggIohNw5cO/o3zJImgrKkItCkF0Wjij\n0WabEfjnFsrHENi7JIINKQQE0QlQHDoIANCcLwuxJATReQlUJUFGbFIIrnz8IRRFhwKyhjuQQkAQ\nnQhjGHRMI4jOCmcIjI+fjyEAgKZvvg7IGm7JEbKVCYLwO6E2ORJEZ4YzGF1P8gLGSiFgxOKArOEO\nAVcIiouLMX36dADAyZMnMW3aNDz00EN4/PHH0dDQAADYuXMn7rnnHjzwwAP44YcfAABarRZz5szB\ntGnT8OSTT6KxsREAcOzYMdx3332YOnUqCgoKLOsUFBRgypQpyMvLQ0lJSaA/FkGEDRzHWV4bFaQQ\nEESg4F0G8TdORM8ZT/ntuEKZ3PI6lApBQEsXb926FZ9//jlkMhkAYPXq1Vi6dCkGDx6MHTt24J13\n3sFjjz2Gbdu24bPPPoNGo0FeXh5yc3Oxfft2DBo0CPn5+dizZw+2bNmCxYsXY9myZSgoKEBaWhpm\nzJiB0tJSsCyLw4cPY9euXaiqqsLs2bPx6aefBvKjEUTYYB2ZHOrSpwTRmeEVgsRbb4M4NdVvxxUl\nJbetoQ9dx8OAWggyMjKwefNmy/bGjRsxePBgAIDBYIBYLEZJSQmys7MhEokgl8uRmZmJ0tJSFBUV\nYfz48QCA8ePH48CBA1AqldDr9UhLSwMAjBs3Dvv27UNRURFyc3MBAD179gTLshaLAkF0ZliNGo1f\nf9W2HeK0JYLozPAKASMS+vW4wri4tjW0oVPqA6oQTJo0CUJh2xfXrVs3AMCRI0fw8ccf45FHHoFS\nqURsbKxlTkxMDJRKJVQqFeRykxlFJpNBoVDYjNmPOzoGQXR26r/4F+r/+Q/LdqjzmAmiM8MZeYUg\nysVMz2AYBhnLVwIAjGq1X4/tCUHvdrhnzx789a9/xdtvv43ExETI5XKbm7dKpUJcXBzkcjlUKpVl\nLDY2FjKZrN3c+Ph4REVFWeZaz3eHlBT35vmDYK5F+IdwP2f1ymabbYHREPYyBwP6DiKPSDhndeZH\n6JTuCRDJZf49eMoQVKd0A3SakH0XQVUIPv/8c+zcuRPbtm1DnNlEkpWVhU2bNkGn00Gr1aKsrAwD\nBw7EyJEjUVhYiOHDh6OwsBA5OTmQy+UQi8WoqKhAWloa9u7di/z8fAiFQqxbtw6PPvooqqqqwHEc\nEhIS3JKptjY4QVgpKbFBW4vwD5FwzjQttpYwfas67GUONJFw3ghbIuWcaVpN5vz6JjUEatbvx+fE\nUhgaGwP6XXSkbARNIWBZFqtXr0avXr3w9NNPg2EYjB49Gvn5+Zg+fTqmTp0KjuMwd+5ciMVi5OXl\nYcGCBZg6dSrEYjHWr18PAFi+fDnmz58PlmWRm5uLrKwsAEB2djbuv/9+cByHpUuXButjEURIMbS0\nADBFJnN6PdgQt08liM5MWwxBYG6dAqkUrEYNjuPAMExA1ugIhrPOWeqCkIWAcEYknLPzSxbCqFSi\n7+q1qFizCkaFAv03/cWrYxnVauiqqhDdr1+79wyKFgjlsSG5SHlKJJw3wpZIOWcX16yEpvw8Bv31\nbwE5/qVN69F6/FcM2PxXv/VJsKcjCwEVJiKICIbT6SCQSiGMkYERi92yEBiaGqE8eqTdeMXa1ahY\n/TJ0NdU24y0/70fZc3OgOPiL3+QmiEiE0+lsqgr6G4E0GoApeygUkEJAEBEIx3Fg9TqwOh0EYtOT\nhEAiAafTmd7TanFp0wa0njzRbt+KtWtwefMbUJedsxnXXTI1RlKfPmUz3vDfPQCA5p8KA/FRCCIi\nMDQ1QVtx0dKZMBAIok3tlFl1aFIPSSEgiAikbtcOlD03B6xSaalsxv/P6XRQHi1C6/ESXFr/art9\n9bVXAACas2cAmF0F5jEA0NXU2MwXmQN0WZVtL3gicNR9thvn5j8LVk9ppOFCxSurAABGRUvA1hCG\n2EIQ9LRDgiB8p/F//7W8FpgVAYGVQuDsKca6cJG2shKsXofK1zdYlAOgTWHg4Wsb0M0p8FS/9zfo\nqiqhKTN1rdTX1ECSlh5iqQgA0NfVBnwNQbRZIQhRLQJSCAgiguA4DmxrKxiJBJzWFC/AmF0GjDkI\nidVpnRYoMra01S1o2fcTdDXVNsoAACiPHUXryROIGTLUtE9rq+l/KvYVUFitFi37frIZMzQ3k0LQ\nhbD8hrWhyRYilwFBRBCtx3/FuWeetigDACCQ2FoIWK0OrLrV8r61VcDQYhvJba8MAACMRlxa/yo4\n1pRnzT+tsCoVOGNgur0RjjtVqs+chr428E+mhGM4gwHKo0eCdoPmAxZDVXGUFALCr6h+LYGuutr1\nRMIrVMd/bTfGBxXylgJOp7M81QOAwdxVFPCsTrqhoR41H22DoaHevDMXsieXroCjxlQNX/4LF15e\nalHOiOCiLD6Ky5vfQOVfNgVlPT4OiNXrg7KePaQQEH6B4zgoig6j8vUNKF+yMNTidFoYBylPjNg0\nxlsKFId+sTHvV739psX/6ckNXVddjebvv7UZo14JgcNZp0pWrYbWnAFCBBfeOqMuPQmYa3CkPDAt\nYOvxsT9ciOJ1SCEg/ILySBGq3iywbBuVSnqqCQBsq4NIf3NpMd5S0PjVf9D0zf8sb2svXsClDetM\nUz24oVe/3774CnVTDBwdBZKR2yA0GJuteoVwHOIn3ozEWyYFbD3G4jIgCwERwajP2OauX1j+Z5Qv\nWWQp9Un4B0eBfbxfnzc3OkJ/xZRK6ElpY2NTU/u1qDRywHBmIQCCE+FOtMHqdDC0tFhKg/OIu/cI\n6LoCs7WPM4RGIaAsA8IvsK22TzeGxkYAgLrsHGIGDQ6FSJ0So4NaAHxLVt5C4AyugxgA2chrYair\nhVGptJw7R5CFwP+0lp7Ele0fIbr/AKdz6nbtgPrMafR8YiYgYCAIYHEcAqh+dyuUhw9C3Ku3zbgo\n0b2med7CuwxC9TsjCwHhFwwtzQ7HNefOORwnvIO3EKTcnwdRcjIAgDOYLQSSjm8S+poay/mQ2vUr\niM0ZhYyXVkDaf6DDfaNSUk1rkULgd1TFx6CrvITmH3/oeN6xozibPxPnX5jXoTWB8A19Qz2Uhw8C\nAHSXK23eEyUkBnRtiiEgOgXGFsfVu+p270RT4fdBlqbzwraqEJWSgsRJt1rqnrdZCDpWCMqXLITi\n4AEAQLd770f3Rx6zvCeQmEqmdn/oEXS7+15AKAQARHXvgUFb30f8jRNM65PLwO94FGvDcTAqFFCf\nO2vZ16hUQnPxAi6uXgFtZaWLAxCuOP/CPKfvCWXygK7Npx2yFENARDIdlfO8su3vMASw3GdXwqhU\nQmC+KMmvGQkAiBlodsmYb+LuIIyORvTgNleOQGpSCIQxMUj6/e0QJZqehPjKaZYqiBpSCPyJoaUF\nraUnPd6Pzzqofm8rzj03GxdXLoem7Bzq/rHL3yJ2KVwpZwJZTEDX5zOGOEo7JCIZo1IJUXIy+ixd\n7vB9vV19fMJzOIMBnF5vuXkn/+FOpL2wCAnmqGdW1drR7jYIYmIQlZTctm2+8fMIY2SmcfNaAplp\nu9Wu8RHhGxdXvARd5SWH70ky+zrdT3/FVF5acfAXgOMA840sVDeSzgLb2vFvSBgdYIWAXAZEpMPf\nqMSpPSDtk+FwjuZ8GRSHD4LjuCBL13ngA434PumMSISYQYPBCEw/45ihwwCBez9pQXQ0GKHQklst\njI2zed++3gGvIDT/8B0avvoPAEB35QrOv7gA6jMOqh0SbtFRAGefF/+MgX9tn/oJAJoL5VAc/AVC\nuW1vez5o1KhQoLLgdYeFrAjnGFUdl+dmRIGNwxdQ2iERCli9Hpc2bUCL2afsC0ZzmVxBTLTTObU7\ntqPqrS1opQuU13B2CoE9ovh4DHr7XST9/nbTvGjn54OPP+i/8S9Im/cCopKSbN635EOb00Z5CwFg\ninjnOA6N//sv9FdqglbFrbPhTDnudve9SJ32EBiBwKS0OUBbfh5Vb78JY7NtaqihoQFXPv4Qtbt3\nQnXsKKreftPvcndmjB5Y2QIBnzqsPFoEXXVV0NcnhaCLoq24iNbjJah++y2fj8Wb2fgbUMayFUid\n+qDDua0nT/i8XleFtTQz6jh4UJ6dA0l6OnrNfhY9HpuB5Dv+2G4Ob1UQyuWWJkY275ufhHgTNG8h\n4NHXVFsisB0WSyJcYnSSmZN4621ImHiTV8c0NDag6btv0LLX1CTJlQmcsKWjv2XefRZIrC1zFa+9\nEvD17KE6BF0U6972HMeBMZuOvTqWucKawOxfk6SlQ5KWjisff9hurr6+zut1ujoWC4ELhUCakYmM\nl1ZYtjXl51H/r38CAFKnPwJpnz4u17K3EESlpiLu+lyoz5yBvvYKypcs8uozEG3wcQD22FsFkn5/\nO5r3/WRbNc8DOJa1KIBExxgdKARR3Xsg5d4pkPbt52CPNppVOpReaMToIaleX0+tz5OxuRmsTufy\n9+5P6K+ki2JoarR63b4inSfwCoEwxjbgJiWvfc1vfX29T2t1ZfiUP8ZFASJ7hPFtxVTirs91eWED\nAIGdhYARCNDj0ScQf8N4j9YmnKNzohDY0+3ue9F//eter9NRSeSuCseyDq971g9KfHwNIxRCPjLb\nZQ2Cj/5iLgcAAAAgAElEQVR3Cn/91284c8k7xc0R3iqB3kIKQRfFuhuesyhn949l+hHZ+6wTb56E\nQVvfhyixzT/tqMUr4R6uYgicIYprCxgUOGiO5Ij4iTcDMGUyWCOMjXU0PWTd2SKN6vf/hur3/gZj\nqwrqs6c92jdj+Sok//FuRKWkeLSfo3LXXZ3aXTtQNv9Z6Kou24zzlUB7PzsPsqwRAABG6N5t8qk/\nXo13F96EQen+q2ZoVAfX5UMugy4KZ1XCVnelBjIM9/pYbS4D50FslrkOSu8S7uFuDIE9vAmakbjv\nA40ZNBgD3363nanZPqqdR32qFLKrvf8b6gpwLGvx7SsOHrBJERTGx7t8GpT07g1J795o2feTR+uy\nGrIQ2NP09VcAAGVJMZJ69rKMW+KhYmSW65mhxb2HGF/crs4IdgwIWQi6KNY17Q0++vX5Pgb2LgOH\nc9VqVKxbS50QvaAthsAzCwEA9H9jC/qv3+jRPo78zs4sBOQKco21idpaGUh7fiEyV6yGJCPTYpnp\nCPvshOS77kHM1cMhHeC47DSVOW6j9fQpsFY5/vZKGG8hEMpkiBubCwCIzx3n1rEv1ihwtrIZzUrH\nxbv+c+AC9hy44PI4fRYvReyo0QAAliwERDCwLkHra6qNJe3QSdEOexO3uvQktJcqnNYsIBzTFkPg\neZCRO8qaW8dxYiFo+Pe/IB9xDUQJgW3+EsnYpwjySDMyIJBGI+PPy9w6Dqc3BXrGXT8OsaNGI2bY\n1WD+7w+o+8en0JxtXxOCFAITmgvluPTqGoh7p1nG7IMI+W2hTAZx9+7IXPMqohJtU3Kd8c4XJ1BZ\np8Jt1/XBlAntG1XJY6Lw3p5SfH24AhvznSsZ0r79EDNsOBSHDtq4doMBKQRdFGuXgbdpY4amJlSs\nXQ19rSk4yr64DU/PWfmo3fkJmKgoqI4eAQDoq6tJIfCQtsJEoet0J5S31XLPXPkKtJcrUbXlLzA0\nNKCy4HVkLHkpZLKFO84u7p4GiVoCPSViyIZnWcadpcWxWlIIAEBfZ7KEWsdM2XcP5V2aArMCLTY3\n9XKHFY+PcTj+xf5yRIuFuCUnHcP7JUMS5brEOL8+uQyIoGDtMmgtLcXFV1Z53HO99cRvFmUAMKWm\nOULSqzfSnp0HcY+eljFHbXyJjuG03mUZ+BOBTIbY0dchJW8axD162GQsaCsuhkyuSMBZ/IynKYGc\nwawQiGwDRJ1ZjshCYMLRg4/q6BFLoyjAdF0SREf7NU1Tb2Dx8Tdn8Pne80iQSxAtcf0czlv0gm0h\nIIWgi2K5SDAM2FYVNGfPoP7LLzrch+M4m4hl69exo0a7jGC3ybF1USKUsIXjONTtNjWuCWZesj0M\nw6DnjJlIvNnUP8HaYiCUyZztRsB/EeO9Zs2GKDERibf8zmZcFBfvcD5HCgHUZ86g5u/vOXyvYs1K\ny2tOq7VU8fQEjuNwoVqB8uoWXGkyxVTp9EZs+edx1Ddr8PRdw3GhWoHDpe6lmvIBjcFOGSWFoAui\nu3IFrb8dBwBLVzsA4FyYFpu//xbnns1H03ffAGhLIUx7YRF6PjnL5brW/jpKhfIM677s3sQQBApr\nJdBaOSDaY90iPObqrA5mdozs6uHo99pGRCUn24zLc0Yh6f/+gLR5L9iMW1sDuyo1297v8H0+UJPV\nab36fRmMLN7dcxIvv38Y735pqsZa26TGgN7xuO26PhiSkYjBfRJQeKwST28sxPGyjoNwQ+UyoBiC\nLoj6jKljnak8bVuqjOLQQXAsix6PP+nwaV9RdBgA0HLwF6jPnIbi0EEA7t8Ikib/H1qP/wp9ba3H\n7omujo2LJUwzNAQepDV2RTRl5wAA/dZvgvrsGbQeL/Hr8RmBAN3uugcAkPHyahga6lG5aX2XTzvk\nOA6GxoYO57DqVrAaLYwtLRDFex4YGyUSYvmjo23G9v9WjR+OVqKmoQeG90vGLTlpGD+iFziOc+k2\n4LsqBrsOgUsLwWeffdZu7KOPPgqIMERwMCpMT/Y9n3wKgG0Kk7LosMV6YE31u+9AfaoUAKA5d9ai\nDACAUOaeQhCVnIy+a16DMD4B2ouu02+INqyDQKX9+odQkvb0eGImAPJVu8LQ1AhBdDRE8QngjMaA\nriXp1Qsic8Oqxq/+C21FRUDXC2eMLc0uTe+6qiqcf2EuAIDxsPCXM6ZMGIC1M69Ht3gpfiy+jLkF\n+9Ci0iFGGgWNzgi2g86voXIZOFVT3n//fSiVSnzyySeorGwzVxoMBnz55ZeYNq19WVpHFBcXY926\nddi2bRsuXryIhQsXQiAQYODAgXjpJVNE8s6dO7Fjxw5ERUVh5syZmDBhArRaLZ5//nnU19dDLpfj\nlVdeQWJiIo4dO4bVq1dDJBLh+uuvR35+PgCgoKAAhYWFEIlEWLRoEbKyvDfJdXaMCpPpUhifYOql\nboe24iLk14xs275UgZb9+9om2O3jqe9YnJoK9dkz4AyGgLcT7SzwZt+UvGlhV5c+bsx1qP/n7qA/\nzUQS+vo66K7UQigzPfnJs0ZA0icDibfeFrA1rbMOqv/+bpfMAGne+xNq3nfcQtoapdn6CXgXo6PV\nG1HT0Ip4uQQf/LcUZyub8dIjo/DDsUr8dr4RD08eDKlEhNSEaOgNRnxaeA4D0+Jx3dAeDo/HCIVg\nJNLwyTLIyHCcEiaRSPDKK+51Ydq6dSuWLFkCvTlNZs2aNZg7dy4+/PBDsCyLb775BnV1ddi2bRt2\n7NiBrVu3Yv369dDr9di+fTsGDRqEjz76CHfeeSe2bNkCAFi2bBk2bNiAjz/+GCUlJSgtLcWJEydw\n+PBh7Nq1Cxs2bMDLL7/s6ffQpTCYi3GIYuMcasP2DYgUVj8WR3h6UxclJgEch/OLnif/ppvw35On\nZYuDhSA6hmrmO8GoVOL8gvngtBpLrQ6BNBoZS5cjbsx1AVvX2oXDddHfmTvKAGBqAMbjTQxBXbMG\nW788iWXvHsTRM3W48ZpeqG1SI6N7HKbeMhC9U2RITTA99TcqdeieGIP0FFeWVQ7aixdQ/++Og739\nidMr+cSJEzFx4kTcdttt6N/fOxNlRkYGNm/ejBdeMAW5/Pbbb8jJyQEAjB8/Hvv27YNAIEB2djZE\nIhHkcjkyMzNRWlqKoqIiPPHEE5a5b775JpRKJfR6PdLSTIUlxo0bh3379kEsFiM311RVqmfPnmBZ\nFo2NjUhM7LgZRVfFUF8PMAxEiYnoNfNpXN5SAP2VGsv7yiNHUGUwoPuDD0Mglfr9JsSnJxoaG6H6\ntQSxOaP8evzOCGcuSuRNlcJgIIiJAafVgjMa23Xr6+qoz7T1LAimQmezlv+r6kYcyX+8GzFDh6Fi\n9Yp27+kut/U08MZC0LubDC8/Nhocx+HMpWb06ibD67uKwQEY3CcB4igh0lNNCkBqQjR+Nyrd5TF5\nJa7+s91InHRrULKLXNoeL1++jHvuuQe33HILbr75Zss/d5g0aRKEVhcH65KbMpkMSqUSKpUKsVbl\nUGNiYizjcnOwmkwmg0KhsBmzH3d0DMIx+rpaiJKSwIhEkKSlo+/qtTZ9uNlWFRQHfkbNtvfRvG+v\n04wAab9+SJh0q8frJ0xo6/VOwYXuYeljELYWgtD4PCMB65LFBifVCgMBIxIhfqLpt6avb2hX8rir\nIemTAWlmX8t29KDBltc2Tdd86EnAMAwGpSdAHh2FxQ/l4OHJVyFGIvLlkACA5h++h+ZCuW8HcQOX\ntt6VK1di4cKFGDhwoM/NGwRWvk+VSoW4uDjI5XKbm7f1uMocWc3f8HklwnpufHw8oqKiLHOt57tD\nSop78/xBMNdyBsdxOKNQQNavr408px10q1P8cgCKXw4gdvDgdu8BwDWvrITQmxtUSixkr6zCrwsX\nQ8LqwuJ7cUa4yNYqMGUWJHVPRHyYyGRNU2IcVACYspOo3X8AA5+Zjai40MkZLucNAC4f+tnyOuO+\ne4N7zXn2aZxQNKPxcBGSYoQQycO3VkQgvhfrfpLJvbohrns8+OLOg2Y+DvWlSpzesMlmH6lU7LEs\nLSod6pvVSEmMATgOCzbvxZDMJORPuQbXDuvZbv57X/wGqViIvFuvcnrM1vvuxaWdnwIAanduBwQC\njP7gXUS5eW/zBpcKQWJiIiZOnOiXxYYOHYpDhw5h1KhR+PHHH3Hddddh+PDh2LhxI3Q6HbRaLcrK\nyjBw4ECMHDkShYWFGD58OAoLC5GTkwO5XA6xWIyKigqkpaVh7969yM/Ph1AoxLp16/Doo4+iqqoK\nHMchwc2a6rW1wWnHm5ISG7S1OoLVasEZDGDF0TbyRKWk2lQdtEZx6pTD8fpmLRhG5/A9V+j0JuVS\nWdcYFt+LI8LlnAGAotaUNqUwCKALE5ms0TEmC9PZNzYDAMo++xJJv789JLKE03nT19ejtcJUKrff\nhjcgjIsLumys3FSwqPr0BUjSXZuqQ0EgzhlnMNhst+gArdUaLVpAZ2xvJNdo9R7LUny2DrsLz+GO\n3L64dlAK7pvQHzoDi/MXGyCPbp/CLZcIIY+O6nCd6En/h1490nD5DbPCwrKo2HvIZxdrR8qOS4Ug\nOzsba9aswQ033ACJ1dPgqFGeC7VgwQL8+c9/hl6vR//+/TF58mQwDIPp06dj6tSp4DgOc+fOhVgs\nRl5eHhYsWICpU6dCLBZj/fr1AIDly5dj/vz5YFkWubm5lmyC7Oxs3H///eA4DkuXLvVYtq4CXyGQ\nj3bmSZv7PFoO7IfySJHTErT91m1Eyy8HULdrBwDf2n0KzK4fKlDkHqz5ewrX4j/2ra+tzeRdFVMw\n4TwAgCSzL0Rxjnt9BBq+4ZShuSlsFYJAYJ8GK7JrUiSQxTh0wTGM51k8IwZ0w4gB3WzGvthXjslj\n+mDUVe1Luk8Y2dvlMRmGgaS37fnSVl4KaMyVS4WgpMRUPOPEiROWMYZh8MEHH7i1QO/evfHJJ58A\nADIzM7Ft27Z2c6ZMmYIpU6bYjEmlUrz++uvt5mZlZWHHjh3txvPz8y0piIRzWHNnQ/tUwaiUFCT/\n4U4oi4853VeUkIio5G5O3/cEYYxpfVII3MOoNDddcbPmQ7CxVwgoBdE2WyeUZZ35UrxdrU4E3x1U\nIJOh19NzIDT/jcqvzYby2FEIpNGOg3T9EIA5NDMJQzPd65LYEfZ/N4amRp+P2REuFQJHN3AicuEt\nBIIYJxcoFwVTolJS/CIHIxRCEB1NTY7cxKhSghGLXfaLCBVCu9bXip/3IyoxCcl33eNz7FGkYh1A\nGFKFINqUftjVFALO3B1Ufm02YqwCCHvNmm157SjFMO56562JndHQooFKY0BqYjQkUULs+O4M9v1a\njdUzrnPoMvjuyCWUVyvw8OTBEHZQV8TegsFpbV20HMui8euvIB9xjU3zOG9xqRBMnz7d4Q/aXQsB\nEV7w3bOEThQCzq4srjA2DuLevZF8+x0ATLEGAGyyErxFKJdTkyM3YTUaS33zcMSRbA17vkTM1cNt\nLsZdCUNDW7lcpwp4EOALFHW1EsaWduFRztP1rFMzY8eMRfeHHvEqNbTodC1+Kr6Mx28fij7dY3HT\ntWmYPCYDMqnjW2xirAQiocBRXTgb7O+9+vo6sFqtRcaW/ftQt2sHWvbvQ+bylY4O4REuFYLZs9u0\nKYPBgG+//RZxIfKFEb7D8hYCZ08snK1CIIiJRvr8BZZtYUwM+ixeaqpy6CMCmRz68vOofH0Dkn5/\nO6IHDvL5mJ0VVq0O626CQieRz9oL5aQQIExcBl0sJZQzZ051VGjIOrdfIJV4XSdiUk46JuW0+ftT\nEjrumDhyoHeWVs25szj3zNMYUPAWGJHIUj9GV3nJq+PZ41IhGD3atmHD9ddfjylTpuCZZ57xiwBE\ncLFYCJxcoOwtBI6Q9u3nF1l4GVS/lkBTXo7+G9/wy3E7I6xGjahu/onfCASieMetd3U1NQ7HuwL6\n+raOdv6wqHlLm4Wgi7kMeIWgg+/e2iQfrkW/7OEMBqiO/wr5NSP9HoPlUiG4bFXBieM4nD17Fk0U\nQRyxsGafvTOFIHrAIOirq4Mii3XEvFHRAo7juqy/uSM4gwGcXu9Vn/ZgIXRiNeT7ZnRFrCsUcg7q\nfAQLS9EoFy4DdVkZFAd/RvKdd1sC8CIZi8ugAwuBtbLASL3v1lnT0Aq9gUWvbjIIBK6vYSXn6lB0\nqhaTx/RBz2TPrUf6K6YUcZuCSn7ApULw4IMPWl4zDIPExEQsWbLEr0IQwYMP4nPm00yd9iBkQ4fB\n0NyE2h3bIRs2PGCy2HdJNCoVEMWSO8oe/smODw4LRwTRjuMbupqZmoczGGBosLIQhLCJl7tZBtVv\nv2mqYhoXH7IaEv6E05sUgg4tBFYPIL6Ulf7uSCVOXGjAkodyIBG4Lt0tjxajX684l22QAaDnjKeg\nLD4KxS8HLGP6+jroG+otnWsB+KVZnMu9v/vuO58WIMIHo1qN5sLvATi3EAiixIgdPQYcx0Hcoydi\nhgwNmDz2cQyGhgZSCBzA31TD2ULgzLLTVRUC3jUnSe8DSXofJHpR4ttf8C4D5bGj0F6uhKSX4xx4\nvoy47orjAmWRBqfjXQbu9QDwRSHIu2WgR/P79YpDv17uXetiR49B7OgxNgpB07dfo+nbr23mXVy9\nAukLF/vU88BlBYaGhgY8++yzGDNmDHJycpCfn4+6ujpXuxFhSMu+vZbXAlnHEesMw0A2PCugTzb2\nRXYMjYHNsY1UeFOvfa5/uGIdcNpV6xHwwbvSvv3Q49HHbVoRBxt+bU6rxYWlix3Ose5zYKjvHNd3\n3k0jELsXv2HdHTIS0V68AMWhX3w6hkuFYOnSpRg+fDi+/fZbfPfddxgxYgQWL3b8R0WEN9Ypfh2l\n4gSLdkU3zG2ZiTaUJcW4tHEdgPB2GQBAXO4NEMhkyFy2An2WLkdU9+5d10LAu+bCIDOEsctz19Ve\nadfoiNO2uRN460akw1pcBu5d6xiJd9fERoUWB0/WwOhGQDZPZa0S7/+nFMVn/at8+dpO3qVCUFFR\ngcceewxyuRxxcXF44oknbAINiciBDyiUZ+eEWBIT9rnrTd99AzaEwVfhyOU3NsLYYgrMC2eXAQD0\n+NNjGPD6ZghjYyHtkwFBdAyMzc1o/OZ/oRYt6BjDrNS0depd+aIXULd7l2Wb4zhoLraVK+8s9Qra\nXAZuZniw3nWDVKn1+K7oEg785n5GjVQsQmbPWCTHua/kR3Xv7nIOF2iFgGEYVFVVWbYvX74MUQgD\nZAjv4Z9aUu7LC7EkPLZ+Z13lJVz54P3QiBIBRIrLgIevqlj7ycchliS4sDodLheYyq6HS+2ItHkv\nQD4y27Ld+N89ltct+/fh0qtrLNtsaytUvx2HsqQYDf/ZE7Ftk/mgQnd96t5mgqSlyrHwwWxcf3UP\nt/dJjpdiwjW9kZbqvsKYNu8FdH/kMUDoPGiR1fqWWuryzv7MM8/g/vvvx4gRI8BxHIqLi7FixQqf\nFiVCA9vaccphsJGkmQp5iHunWQprtPy8Dz0eeyKUYoUN9t3awt1CYE9X7VPR+tuvltfh8luL7j8A\n3E03Q3m0qN179n5no0KBSrObCgAk6emQXR24bKNAwbpRhwAA0hctQdO3X0PuRcM+a7xJmeaVLXf2\njUpKRvy4G3Dlw7/DmYrGanyzELhUCCZOnIgRI0agpKQELMvi5ZdfRlKS700biOBjVKkAodBhh69Q\nEJWUhP6vb4ZRqUD54oWWcVajjribXyCw9+WGewyBPda1/Fm9LiziVoKBtSIUTs2o7OMZOJYFIxC4\nDHjUXCiPSIXAknbowkIQ3X8AovsP8GoNnd6In0qq0KubDEMyEj3at+RcHXZ8dxb5dw/3rBaBXUyI\nMDbOUu/DVwuBS5fBgQMHMGvWLEyYMAGZmZmYMmUKjhw54tOiRGgwtqogjJGFVfEfoUzWrh5BZ0l7\n8hX7J+xIU5IYYdvzhrGp6wSM6q1KFotTXft9g4XQLmaHD/h0ld2jq4rMmDFLDIEocFUiDUYOl+tV\nqK73vElbcnw0Hpw0CAly7x7QEm6ZhJ4zn0ZcblszpoDHEKxduxYvv/wyAKBfv354++23sWrVKp8W\nJUIDq1KFjQnTGoFMhoRJt0LcOw1AW/BjV4bVqFG36xObsUirHtf72bmW15oL5aETJMjwxWLSFyyG\nKMH3nh/+QpRg+wTLy6l3kUZu3ZMhkmAtMQSBUwhipCJM/91gTLw2zeN9e3eTYUhmklvFiRzCCBCb\nMwqJt/wOokST1d7X8tQuFQKtVotBg9qazvTv3x8GO98mEf5wHAejShUWaVD2MAyD1PvzEH/DjQBM\nloyuTs0H70P1a4nNWKRZCKQZmeg151kAsDRh6Qrw5tuo1NQQS2ILIxJB3LOXZduoVIBjWRibOy5F\nb4jQUvVtvQw6mauKMd+2zfEHooQE9F1rivkIeNphv3798Nprr+H06dM4ffo0Nm7ciMzMTJ8WJYIP\np9UALBuWFgIe3qTJdpI8aF9Qnz3bboyRhkfshyeIzEWKulKNCWNLC8AwYZNyaE2fpcuQfOddAIDq\n9/6Gi6ttA8QdpbZF6rnjdO7FEPhCXZMa3x25hEtXPA+gvVijwGvbj+KnYs9cMlHmGD7rrCNGIAAj\nFgdeIVi1ahXUajXmzZuHBQsWQK1WY+VK3/suE8ElnAqlOIOvS9BZCqP4hFUb6vgbJyDp9j9EZFnn\nNoUgMp8yvUHf2ABhfDyYDtLDQoUgSgxRUjIAQF9TDW35eQBA7KjR6LduE6JS2ls1OK3GZRfUys1v\noObDD/wvsA9YKhUGsNOkRmfEpVoVmlSe34iT4qT4/dgMDOvrWZB+72eeQ/zEm5B02//ZjAskUnA+\nugxcOi/i4+OxdOlSnxYhQo/RRZfDcEBAFgIL1gF5sWPGImbQ4BBK4z3C2FiAYWCM0KdMT+FYFobG\nRkgz+4ZaFKcIY9tbLgTRMRAlJFgCfKNSu9u4eTidFoyVy4rV6QCOg0AigaG5GaqjpkDz7g8+FGDp\n3YPVaqG9VGHKqgpg3Zy0VDkeutW736Y8OgrDMj3P2IvqloLu09p/zwKpxGcLAVUY6iJY2h476XIY\nDvAug4Z/f4GEm26BKD4+xBKFDusnsnA0PbsLIxRCGBsbsWZnT9HX1gJGI6JSUkItilOE8th2Y3xj\nn9S8aRAlJCD5D3cAYFDz93ehOHQQmvPnbRqdXVj+Z3B6PTKWrUTtju3BEt1tqt55y6YTYFeAkUhh\nVNW7ntgBLl0GROeAN8PblwsOJ6xbMl9Y1rVbbLNWgZXhbNVxB1F8QpdxGWjNBbYkvdNDLIlzHCkE\njLkWgVAuR8qU+yGQRkMglVrGL61/FdrLlQAA7eXL0NfUwNDQgIurXobiYFsXvnCpaqg6djQo65RX\nt+D7I5fQ0OK5qZ7jOGzYeQzv7TnpF1kEEglYjcanc+BSIdi6dStqa2u9XoAID4IRYOMr1nnSRoWi\n09RU9xTOaLRJH7Kv0xBpCOPjwWm1KP/zi6EWJeDwrhFRcvgWb3NkcXJWnMg6s0VbYep3oD5VahnT\n11TbzG/6+iuTqT6EuIp38CcqtQEVV5Ro1XqeeccwDG4b3Qc3Z3uesugIgUQCsGy7Cqee4NJloNFo\n8OCDDyIjIwN33XUXbrnlFkQFMEiDCAyWnNwwTsGxr6Cob2hw2ru9M2OfSxxIH2gw4BU9XdVlS3W8\nzgprbvdsXwQonHDUE8NZSqu1osD/XXakqNfuNNXOGLT1fR8k9I1gKiTD+iZ5HBRozRAvYgicwV8/\nOa0W8PIe7fKXmZ+fj6+++gozZszAL7/8gjvvvBMvv/wyTp70j5mDCA6Wql1hbCFgGAbxE26ybBsa\nfPOHRSr8BVeeMwoDCt4KsTS+Y10JrzP3N9DVXkHdPz4FYArSC1ccVSp1ZiEQxba5FwyNjdCUl9t0\nSgxHNOfap+x2BQRik0LA6rwPLHRLVVer1bh06RIqKiogEAgQFxeHlStXYv369V4vTAQXzvxH4m7n\nr1DR/cGH0P2hPwEAjC1dKyiIh201KQSiuDiXdeYjAVnWNZbXnTnbQHmkrXFQOCsEjhA46W8ijGsL\n7DU01OPiymXBEcgH+NLnUT16IPWhRwK61vHz9fj+aCXUXrgMAODjr0/jlQ/bN5zyBoG1hcBLXNoi\n582bhwMHDuDGG2/EU089hZycHACATqfDuHHjMG/ePK8XJ4KHu52/wgGh+anEYK741tXgLQSRVpnQ\nGYm3ToamvAzKosOofGMD+r22MdQiBQRr106kBYI6Uzytrxf6CClhzJkb/PTOfwbiHj0DulazUoeL\nNQqMHuJdVcqxV/fA6CHdwXGczz1meIXAl9RDlxaCsWPH4uuvv8bq1astygAAiMVi/Pvf//Z6YSK4\nREJQIY8wzlSAp6ulDfEYzU1nHPl6IxFGIEDM0KsBuG6kE8nw1o/Y68aGfcps6vSHIbtmpGXbWRGl\nmKHDEHd9LoDI+T3ysQ6MJPDWtdzhPfHw5Ksgk3r3oNW3ZxwGpMX7peEcH0NQt3uX18qbUwtBQUGB\n5fW7777b7v38/HykhHGuLWELFwFBhTx8FLRRGRkXIH/DdjKFAABis3NwZdv7oRYjoBhaTApB8u13\nhlgS1yTcOBEJN07EpfWvofXkb+0aH/EIoqLQ49EnoD5zBjpzSqU9sqwRMKpUNr57zmgMWaVGXiHo\nDO42T+AtBK0nT6Du053oOWOm58fwt1BEeMJaggrD32XAm8r5H7ahuTmoqUShxuIy6EQKgVAuR8zV\nwwEAhqbOaSUwtphcXMIwtw5Y02v2M8hc86rLQkodFcdKeWAaej09x2bM14p5vmBRCJzERfiTAyeq\n8aOHvQis+bboElZtO4yaBt+rs1pnaXlb/t2phSA/Px8AsGjRIqxZs8argxPhA28hiITOX/yNkFWr\noa+vR/niBYgdMxY9/vRYiCULDhYLQSeJIeDhY0PK5j+H9Bf/jOh+/UMskX/RVV0GExUVUU+mArEY\nYrpJa+kAACAASURBVAf9C9rN66AWhlAub/eZWa02ZKmXrFYLRiwOeHpro0KLssoW+FKLaVjfJPTp\nLkeC3Hflhc8yAACBxLvrvMtv7PTp01BRf/qIh087DPcsA8AcyCQUQnPuLC6/WQDOYEDLvp/Cpgpa\noOmMLgPAtkKe0lz7vjOgr6tFxWuvQF9bi6juPfziDw43BB102hRER7e7+fKBfcFGfeY0tBfKg+Ku\n+LH4Mg6duoJbcrwvLNQjKQYD0xIgEfsur7VFhG/s5CkuswwEAgEmTpyIvn37QmK14AcfeNfZymAw\nYMGCBaisrIRIJMKKFSsgFAqxcOFCCAQCDBw4EC+99BIAYOfOndixYweioqIwc+ZMTJgwAVqtFs8/\n/zzq6+shl8vxyiuvIDExEceOHcPq1ashEolw/fXXWywchAk+NzUSsgwYhgGMRrBGo6UbG2AKahLF\nRV7HP0/hFQJhJ1MIrG+UvqRGhRvnF71g6U0fe212iKUJDNZPn/bw51UYF2dxm9gX1woW1e/9zbS+\nOvBVTu8c1xd3jgufJlaMlVXA23ofLhWC559/3qsDO6OwsBAsy+KTTz7B/v37sXHjRuj1esydOxc5\nOTl46aWX8M033+Caa67Btm3b8Nlnn0Gj0SAvLw+5ubnYvn07Bg0ahPz8fOzZswdbtmzB4sWLsWzZ\nMhQUFCAtLQ0zZsxAaWkprrrqKr/KHslwEZR26Ax9XW3XUAg6Wdohj/VFytDSOVJK+a5/PFHdu4dQ\nmsBhX0UUMPUeEcra3AKZK9fgyvaPoPh5v88KAWc0ou6z3Ygfd4NHqYN8h8ZIqe55/Hw9/rW3HLdd\n1wcjB/oWpG/dIdXbbB6XLgOGYRz+85bMzEwYjUZwHAeFQgGRSIQTJ05YUhrHjx+P/fv3o6SkBNnZ\n2RCJRJDL5cjMzERpaSmKioowfvx4y9wDBw5AqVRCr9cjLc1kuhk3bhz279/vtYydEVanAyMSRUzZ\n2G5T7kfM0GFI+sOdECWaIqDZLuK66mxphzwJt0yyvO4s59LQaJveJYqLnIBCT3AUoNd/01+QuWqt\nZVsYI4Okt+ka7GtQYeupUjT+dw/KlyzyTE7zb6bP4qU+re8Ol64ooWjV+XSM9BQ57p3QH/17+/53\nY62EGZoavepp4FKNeuONN9oWMRhw6tQp5OTkYNSoUR4vBgAymQyXLl3C5MmT0dTUhLfeeguHDx+2\neV+pVEKlUiHWqmxmTEyMZVxujniVyWRQKBQ2Y9ZruENKSvvOX4EimGvZc4kzQiCRhFQGT0h58D4A\n9wEAqtN64Nybf0WMwBh0+YOxXv2BX1C6dh2u2bQesow+qDGarDmp6SkQRMiTjlukXI30z3fj5/um\ngtFpAvrdBuvvpKmq3GY7OS0F8gj5jXmCJikO/DNn1rq1iIqPgzS1/U3M0C0edQDkYsbjc2A9XyBt\ne3DplhTjVkwAq9fjtFqN+OFXI+3aYR6t7Sksy2HFB4fRI1mGFx8Z7fVxUlJiMcBPXofEcaNQ93Ec\n9M0tAMchQQKIkzw7By6vNtu2bbPZrqio8Cnr4P3338cNN9yA5557DjU1NZg+fTr0VgEQKpUKcXFx\nkMvlUFqZGK3H+SBHXmnglQj7ue5QWxucXPeUlNigreUIfasGEEWFVAZvaeVMf6aNF6tgPFsBUXwC\nAFNXs4Y9X0LSJwPyrBF+XzdY56zsr1sBlsWZd95Dz5lPo7nkVzBRUahv7JzdHgUxMuiaWwL23Qbz\nt6a4XGez3aIF1BH4G3OF2uphU5PQHRoACgefs1Vvsh431zYBHnwP9uesuaqtj8nlk+chdsMVwxdO\nMkZJgnL+//yQyaodTtfUvuvfQM0H76H5x0LUVtZCbGx/i+9IUfPYfpyeno6ysjJPd7MQHx9veZqP\njY2FwWDA0KFDcfDgQQDAjz/+iOzsbAwfPhxFRUXQ6XRQKBQoKyvDwIEDMXLkSBQWFgIwxSPk5ORA\nLpdDLBajoqICHMdh7969yM7unME93sLqdRBEQA0CR/BlYOt270TZ/OegMQca1n22G/X//AcuvxHZ\npXDF3U0+UtWvJTj79JMAvI8SjgQEMhmMqs7R5Mg+eE0QE1kli93F3ap/fDaCrzEEfNdIADC6WcI8\nEgsS1TWpsebDIvz753K/HZOPPSpfssjS18FdXFoIFi2y9eGcO3cOgwYN8mgRax5++GG8+OKLmDZt\nGgwGA+bPn49hw4ZhyZIl0Ov16N+/PyZPngyGYTB9+nRMnToVHMdh7ty5EIvFyMvLw4IFCzB16lSI\nxWJLg6Xly5dj/vz5YFkWubm5yMrK8lrGzgbHsmBbWyEKcF3vQCGwrgvPcVCfPQtpZl+ofi0JnVB+\nRChvfxOJSu2cwWmAqTWw7pK6U7RCtr5xAZF1M/IE6+DBjuAVB9bHtEOjVYyJuxHzwVQINDoD6lu0\nSJSLEeNl2WIAiJWJcff4fkiO85/M1rFHzT8VIuWeKW7v61IhGD26zT/CMAwmT56MsWPHeihiGzEx\nMdi0aVO7cXvXBABMmTIFU6bYfhipVIrXX3+93dysrCzs2LHDa7k6M4amRnA6XcTeZOyrpOlqqgAA\nbKvpouEoAjqSYHXtA5Myli4PgSTBQWgucsO2tnZYAS8S4C0E3R/+EyTpfSJewXGGu5YPfzTYAWz7\nJrhvIQhedk5VfSve+eIEJlzTC78b3cfr40iihBjcx3HZaG+xVgg8rdbo8q/3rrvuwrBhw6BSqdDU\n1ITU1FSII6C4DdGGrroaACDu0SPEkniH0K5Kmra8HIrDBy0XY06rtXRzjETszc49Z87qtE+aQJvF\npzO4DfiMEEl6BqSZ4ZOT7m/c7YHC/936bCGwapPtbhneYFoI+vaMw+oZ1/mkDPCUXW7BB/8txemK\nJj9IZqsQWKciurWvqwn//Oc/MWvWLFy6dAmXL19Gfn4+Pv30U8+lJEKGvsasEHSPTIXAvkOj5nwZ\nqt7aYnMj5a0FkYi9vzU2x/uo5UiANz8bO0HqIe8y6GwpovYI3CxDbFEIfIwhMDS35dHbu2WcEYkx\nBAAgFQuRnipHnMw/D9rWqa+eKmYu1Yf33nsPu3btQqI5F3zmzJl46KGHcO+993ooJhEqIt1C4E7d\ni7J5zyJz1Vq3opHDDVatBiMSeZU3HIkIok03F9bLBizhRGctM22PpHdvpE5/GNH9B3Q4T2COIeA0\n3rsMjEolNBcuAAwDcBzYVjU4jnN5HQimy6BZqUWr1oDkOCnEUb6VHe7VTYZe3fwXjGrdXMtTK5xL\nCwHLshZlAACSkpI6Za3uzoyu2uRzj4pQC4G7qE+XhloEr2A1akSlpCLp97ejx2MzQi1OwOGfNpt/\nKgyxJL7DtnYNhQAwtUyWpKV3OIexxBB4byFQFh8DjEbE3zgRAND03Teo+9R1fBirNq3JBMFCcOxs\nHd7Y/Ssu1IRPyiGPtYXAUF/fwcz2uFQIBg8ejFWrVuHUqVM4deoUVq1aRSWBIwx9XR2E8tiQdR8L\nFrqamlCL4BEcy6Li1TUwKhQQREvR7e57ETf2+lCLFXCEZguBsugwdGZ3VqRiVLeCEYkgiOCS4P6E\nEYkAodCnoEJ9rSlVLmbIEMtY41f/dbkfr4QEw2Vw4zW9sWbGdRiYluDzsTQ6A7b97xS+PlzhB8kA\nUUIC0ua9AMB07fcElwrBypUrERUVhRdffBGLFi2CSCSyNB8iwhtd7RW0/LwPxpbmiOrR7i36CFMI\ntBcvQn36FACA1UVuUKSnWGeFGBoaOpgZ3nAcB/2VKxYXCGFy7wkkEp9iCAxNpvgBcY9eNuOulIw2\nl0FkxRCIhAL0SpYhLcV/GTcxQ4ZCkt4H+vo6j7rEuowhkEqleOGFF3wSjggN5S8usDReEUW4QtBr\nznNQFR+D4uABm2DCxEm3gjMa0PTdt9BdiSyFwPrp2DrNqrNjXSBL3+CZSTOcaP7+24gOZg0UAonU\nJ5eBocmUYRCVnGQzrrlQjphBg53u1xZUGHj3zZXGVrAckJoYDYGPLnSRUICbs71voez0uN26QVtx\nEUalAqJY9yr3urQQ7Ny5E2PHjsWQIUMwZMgQXHXVVRhiZcohwhgrzTDSLQTyrBHoPv1hcKyttiuM\ni0fq1OkQ9/5/9s46Pu76/uPP01xO4u5ppG2kQt2ghhaXAoUCQ4YMGDBs+zGGbR0wxmCDoRujuLS4\nFEqpUNdU0jZt4y4XObfv74/LXe5id0kuUsjz8eijl+995XN3X3l/3vJ6J2E7yR4unqVVIbPnDONI\nhhZlbj7qKU7Z15PZQ6Bd+x0AoaeeNswjGVmIFQpsDQ39DgfZ21oRyeVdHuym48d73c6VQzAUHoJv\nt5fzjw/34XD4P/seamThToOqL50PfXoIXnrpJd58802ysrL6P7JRhpzObqKfSxc2odPMw2F2eguk\noaFYKiuoeOZpEu74LeKTQCvD1uo0CCLOu4DI8y4Y5tEMHSKRiMgLLkK3a2eXboEnE66GOzFXXzvM\nIxlZCA4HACX/9yDZr73R5+3tbW1I1F319j1LEbvDHTIYggTP5Wf27KnoD5//VIxWZ+GaAO7X9T30\nJXzj00MQGRk5agychHQu6ZL42exppKPI9D4XBauzVM/V8MhQeJC27VuHfFz9wd5uEITMnvOzVbjr\nCVmEc/Zi7WMW9GDjapjVtmuHz3Vtra3I4xN+cb+dL6wDTBS169qQaLoaBK6Kjp5whwxOQuXS+EgV\nWUmBnbT1RxOiRw/BJ598AkBCQgK33norixYtQurRivXCCy/s7zhHGQJcDxsXJ3sOgYvE39yJ8fgx\nZJGR1L3/LuFnnQ14h0TMlZXDNbw+YWsPGfxcvDd9QawIRqxUjjgPQd1b/6Nlw3pEcjmaKT23eBds\nNhw6HZLEwMd+f044rNY+VWA4zGYEi6VbSWuXB6DHbY1GxArFoBtoL316gIPFTdywJIdJWVEB2efU\ncTEB2Y8nLoNACIRBsG3bNsDZe0CpVLJr1y6v90cNgpGNrdVb/1sWHfgTbjiQaDSoJ00GIPneBzqW\nezRAslSdHAaBvbUFsUJxUs5oAoE0IhJLdRXmygqCRsiDtW3XTgCEbvpLeGJtN2Sk4YHVof+54TAa\n+2QQ2HXO5FqXhyD1kcex1FR3USbt9lgm45CEC/LSI9leWMe2wtqAGQSDQUA9BCtWrBj4iEYZNjwT\n1uDklS32F892wX0V4xgubG3du0Z/KcgiIrBUlFP6p4dI+t39KMfnDOt4HFYrDpecskiEqaSYoNS0\nboXYXCWuP/frqj9EXnARjZ+uBlzaAP6HK13VNpL2rPigpGSCkpKpkb3q7hvRGYfVQuvmzVjr65En\nJHS7TiCZOyGeWXmxA64u8GRTQTWHy7QsXZhJiDIw+U/9MQhGg18/Uzw9BGGnn3nSd5XzRbBHOZK1\nqbFPtbfDhWA2n3Q104FEGhHpft22Y/swjsSJVza2IFD2xKNo13QVxDEWFVH17xcAkEWO3BnicBF5\n3gWELVwM9M1dDR0GgbSToSxWBGOpru5Wi6D2jf9St/KN9vWG5nqSiMUBVeyNClUwPjUcmSRwj2RX\nlYavUIvXNgE7+igjClcOQdL9vyfm8iuHeTSDj3LceNKe+CvK3DwEiwVhgO1XBxtBEHCYzYjkv8xw\nAXQkFgKYKwKj0jYQXO5qT9q2b3O/dj2Myp/8s7vaRawOnAb9z4n+Njmyu5tFeYs9iYLkCGYTJ+6/\nx13F4KJt2xb3a8Fm789w/aa4upVXPz/IoZLA5r6MSw1nTn48wUF9607YG6MeglHcuDwEv6SENXlc\nnLuaorub+0ii+uV/g8Pxi80fAO/KF9OJ4+4ky+HC0U33RVdzmPqPP+T4b39D84Yfvd7v3Jp7FCf9\nNQhcTZHECu/rwtX4y6HXd6mr9wwT2AdZKCpUJScnLSJgnQkHE9dvYPezWyT4oUOwceNGnn32WVpb\nWxEEwd11au3atf0f6SgBw9rUhG7nDsIWLkIklWIqK6XiqRXuC/HnUm7oL64bdNvOHYSfefaIbcSl\n2+l0kQ+0TezJjGciKDgFaYazGqa7znC2hga0369B+/WXANS9+YbX+6MGQfe4DQIfiYCdcVicBkFn\nz5lnJ1BrfR2yyI5wk+Ah+z3YHTQjQhTMyY8P+H4PlTSx5UANC6ckkR4fmHu2qD1k0LpxA7FXX+vW\nzegNnwbBE088wYMPPkhWVtaIvbkGCsFmczbnOImo/d9/MBw8gMNsIvK8C2hZv87rIfNL6MLmiStX\nouGjDxDJZIQvOn2YR9QVW3Oz+7W1vn4YRzK8iIK84719fXgEGrvOObvs3Iq6/r13etzm556b01/E\n7d9LX9vvdsgPd8oF8Pg9XL0O3Nt4iJV1NghqmwxY7Y6A9gkYDEKUcrJTwgKWUAidvkM/n90+Qwbh\n4eEsWLCApKQkEhMT3f9+bhiOHqHoNzdjOHJytdA1V1YA0LplM9BVE//nbsR1xvMGrS/YN4wj6RmD\nR5tme1trL2v+vOl8bpb/7UmMRUeHaTTOsAVAwu2/RZmXT9jCRT63EatGcwi6w6Wd37n82Reuck9x\nJw+BZmZHF1B7a6uXweYwm90Tn5irlntt9/qXhXyw7lifxtAb2wtrefXzQ9Q2BdYTkRSjZt6EBCJD\nA5cU6RmO9Febwed0eMqUKaxYsYJ58+YR5HGAadN6Fu04GRHMZrDbMRYdRTn25Gnv7Lqp2rRNNH39\nJbrdu3xs8fPGU/LUUl3lrE0egmYnfcEzBhq99IphHMnwEpyVjWriJASbDcPBA2C3U/7UCjJfeHnI\npacFux39wf1IwyNQ5uahysvHUl9H8w/O0GhQWjrhZ5xJzSsveW33SzO4/aW/uTwdHgJvgyDqokuQ\nhobS+Olq6j94j+b160j/85MIDgeCxYJi7DiS73uwy/7mT07AbHV0Wd5f4iKUWNMcAU3+GyxEYjFh\ni09HFhPr9zY+P1VBQQEAhw4d6jiQSMSbb77ZjyGOXGTt9cQnU392QRDcFrhgtdLw8YfDPKLhxzNE\nYmtq4tjtt5J0/+977ZI21Li8OMkP/h/Bmb9cWXCRVEriHXfRtnOH0yAAEATqP3iP6Muv7JOgzUAx\nFh3FodejmTrd/ZCXR8eQ9ep/EWxWxDI5DqsVWWws6gmTkMXHu+WyR+mKKz/EoetjyKCHHAKJSoVq\n4iS3voFLB8IVIugpNDo7L7Dx/pRYDSmxgdcOqdUa+GJzCbnpEczMCZy2RcwVV/VpfZ8GwcqVK/s9\nmJMJVzKTvY8uruHEYTSAvfsyG2lUFOGLzxziEQ0/3dUht2xcP7IMgk5qbL90PBPEAFp+/AGRWETM\nsuU9bBE4TKUlSMPC0e3ZDeDuwuhCJBIhkjm9FWKZjPQ/PznoY/o54E4q7GP5r6OHKgPoWjFla2ul\nZcN6r+N1pr7ZyLo9lWQnhzEpc+RqRgQHSclIDB32XAefBsHOnTt5/fXXMRgMztpph4Oqqip++OGH\noRjfkCGSyxFJpYOepRpI7K09uONEIsb89W9DO5gRQnBGJrHX3YCp+AQt69cBw5+s5sJu0GM4dNBt\ndI5mqDuRRUV3WWYoLBz049r1esoefwSJRuN0q0okBGdlD/pxfwm4Zvh9NQiEdg9Bd+W40rAwZ3Jc\nu+hYy/ofafxkFeCdqOtCZ7Sycs0RWnQWpgWoV8B3O8oprW1j2eJslIrAhQ1ClHLmTxr+3Dyfn+ih\nhx7ipptuYvXq1SxfvpwNGzaQkzO8EqODgUgkQqxUDnodayBxJaSJ5HJv7fWTQKVvMAmdOw+RWOw2\nCPzNsB1stN98TdNXX7j//iWrFHoi0WiIvvIqEKD+vbedCwf5J2vbtQPDoYOAM4QjWK3Io2OGNEzx\nc0YkFiOSyzGVFGOprUUe618c25VD0KNgl4dBYC4vcy/uTohMLBIxKTOKUJWc1AC5+VPjNAQHSZFJ\nB+8EdQhCQGWR+4LP1EOFQsEll1zC9OnTCQkJ4YknnmDHDt+tQU9GJEoVDv3J4yGwtasRdpZPDZk1\nZziGM6KQhHnEdz0ykocTz5a6Iqn0pCtxHUzCF52OZqqnu35wb4jV/36BlvU/uv92mEze58woA0Yc\nFIRgNlPyfw/4Xrkdh8Xi9Nb2lBXvoVLoWUUUs/zaLqsqFVIWnpJEZYOeG59ax/++OczxyoGJX2Un\nhzF3Qjwyqe+a/r5ysKSJXz/9I99sK/O98iDh844UFBREc3Mz6enp7Nu3j1mzZmE4idzqfUGsUmGp\nq3WLL410rA0NAKhPmYJ2TT3RV1xFcGYmspifR2fDgeCZ8GUfIeerZ6mUaNQ70AWxRwhlMD119h4S\n3ToLJY0yMASP/CZ/NV4Ek6lLyWGP67Y3NEv4zR0oUlJ7XO/8OenkpEWwdlcFxdWtCEBm4shTcB2b\nHMYLd88bFGPDX3z+Qtdddx133303//znP7n00kv5/PPPycvLG4qxDTkSlQocDsylpSjS0oZ7OD5x\nxVlD5y8k8oKLBr0P+MmENLzDIOhOknaoEQTBK2HV35veLwlPd729rQ3B4RiUc9qm7V6HfjSnI7B4\n5mNZGxv86gzpsJgRdZNQ2BvypORul5fWtLGhoIrp42IYmxJOWpyGx97Yid5k67dB8MEPxzDb7Cw/\nI/BJytIANjbqLz5HcPbZZ/Of//wHtVrNqlWrePrpp3n66aeHYmxDjqj9hlT2xCPDOg5/EAQBc2kx\n0shIZOHho8ZAJyRKFamPPD5i8kIcer1Xi+busqgHgs3uoLJBT13zyEig7C9J9//e6bq32/uckNYT\ngsNB3btvu0M2PXmMRkWGBg9Le5mgLxxGI+Kgnr1nyQ/8AWXeBGSunASRCFl4RLfrBiukJESqUMid\n8971e6uYkx/Hklk9exN8MS41nKykwfUuOBzDlwPm8ynS0tLCH//4R6655hrMZjMrV66krW1kN47p\nL5bqKvfrntyKIwVbczP2tjYUKWnDPZQRS1BSMrKY2BFROdKlwYgocAacIAgcLG7iXx8XBLwL21Cj\nzB6Lcux4IHC69MaiozSv/Y7q9pbFrv0q8/JJ+M0d7vWkv7C+H0OJtcG3RLfDZMRhNCIND+9xneCs\nbJLuusedNyVRq3sMRcSEBbNoShKpcc6EwlCVnGadGYm4/+HgCRmRAdUJ8MRitXPL337k+Y8LBmX/\n/uDzrvTHP/6R/Px8mpubUalUxMTEcN999w3F2IYcqYel6ZnBOhLR73XWTQel9t/a/SUgUakQbDYc\nnlUYw0Dn0kchQImOe4rqueHJdTz3UQFp8SEjonRpoIiVzta3jj50aeuNzmJjLo+RZup01JOnuJd7\nqlyOElj8Me70+/cD3m2xe8IlRNSbN6EzU8fFsGhKEvuON9KqH977QXfIpGKeu3Mev710wrCNwadB\nUFFRweWXX45YLEYul3P33XdTUzMwNb9XXnmFK664gksuuYSPP/6YsrIyli1bxtVXX82jjz7qXu+D\nDz7gkksu4YorruDHH38EwGw2c+edd3LVVVdx8803o22Xgd27dy9Lly5l2bJl/Otf/+rXuOJ+dSNB\naekAmMpKB/QZB5vWLT+BWEzI7LnDPZQRjcT1cBnmsEGXroY9CEr1ldy0CO5eOpGHr5vKDUvGB2Sf\nw42k/WYfqGRQT7U8h8nkriRyGR7B7aJVo8m4gSXinHPdr/3p6unqJSGL9l2i6Aq/iXppH77naD1v\nrTlCrbbjPCoqb+HHPZU06/oejnIIAi9+coCvtg7Os0EkEhEklwxrQrtPg0AikdDW1uYeZElJCeIB\nxKu3b9/Onj17eO+991i5ciXV1dWsWLGCe+65h7feeguHw8H3339PQ0MDK1eu5P333+e1117jmWee\nwWq18u6775Kdnc3bb7/NBRdcwIsvvgjAI488wt///nfeeecdCgoKOHy4702KpGFhxN90CwDmEW4Q\nmCurCEpM9Mua/iUjVjrjwvZhTixs/OwTr7+FABkEcpmE/DGRpMWF0NBiorj65FHa7Am3hyBABoFn\nw6/i/3uQ+g/eBToa8CTccRdJ9z1IcEZmQI43ipPICy8m6f7fA/4ZBK4wrcaPPjkuyfbe1D7DNEHE\nRSiRe2Ttz8qL467LJvZPfliAqWOjSYkd3ORTuyNwvRf6is8n+5133sny5cupqqritttuY9myZdx1\n1139PuCmTZvIzs7mtttu49Zbb2X+/PkcOnSIqe01yKeeeiqbN2+moKCAKVOmIJVKUavVpKWlcfjw\nYXbt2sWpp57qXnfr1q3odDqsVitJSUkAzJ07l82bN/drfLLoaEQyGcajR9Cu+SZgrt1A4rBaEMwm\nJJrRmKcvJJr2NqzDmBNiqa/DeNhbeS9Q55XgIUL13toiPt1UHJD9DicdIYPAJEjaPBrs2Fs6FO0k\nYc7kMElw8EnV0OxkQSQWu2WpHSbfv6Wt3XDzJ3SjmTYdgNA5PXtI0+NDWDw1mXBNYBJ4xWIR08fH\nkpce6XvlfvLXt3Zx+7MbB23/vvBZdjhv3jxyc3MpKCjAbrfz2GOPERXVf01orVZLVVUVL7/8MuXl\n5dx66604PCwilUqFTqdDr9ej8bD+lEqle7m6vcWtSqWira3Na5lreUVFRb/GJxKLkYaFYa2vp/6D\n9xArggk99bR+ftrBwd7mfLiNxjx94/qOtGu+QTEmY8BKdIIgoNuxneDssU4pVT8wFZ9wv1aOz8FQ\neIjg7IFJ5BaWaglRyXnifzsZnxrOnZdO4K7LJg5onyaLjRadhdgI5YD2M1Akwc7jd0nE7AeW+jra\ntnQ/OeisjT9K4HHF+P3yELS2OAW7egkDuAg//UxU+RMJSkjo03jMVjtHyppRB8uIjQhGKhYTJPev\n7v+vb+/GarPzx2sHr9Pv766YjFQyfCEDnwZBU1MTX375JS0tToWnwvba99tvv71fBwwLCyMjIwOp\nVEp6ejpBQUHUepSk6PV6QkJCUKvV6DxmdZ7L9e3uX5fR4DIiOq/rD9HRXR+q1VGRWOvbs2JrQdf2\n1wAAIABJREFUK7pdpz8Eaj+6tnZBopiIgO3zZ0tCDPWAft9eDN9+Tvqvuiqa9Ybn9yvY7dSu/YHq\nV14idEI+eY8/4tc+THrntRN3zlmMuekGGjb9RPjUqUiV/WvLLAgCa1cfIEwTxNuPn43JbCNU3f1N\n1GK1I5f5d8O77/kNWO0OVtw2d1jbu0rjI6kGgkX2fp/fru1Kvlzd5b3YMxajiI0lNmnkNrv5ueAI\nD+Y4IHXYev0trW1tmCvKUWdkEBPjp+cztneD7otNJ6is13HdubkEtV8D2jYTn2wqpqQ9tPbITTOZ\nMs4/WeU/3TQLvdFKdNTPtzzV51V/0003kZ2dTWJiYLKXp0yZwsqVK7nuuuuora3FaDQyc+ZMtm/f\nzvTp09mwYQMzZ84kPz+fZ599FovFgtls5sSJE2RlZTF58mTWr19Pfn4+69evZ+rUqajVauRyOeXl\n5SQlJbFp0ya/DZb6+q4llIKyw9vQVlHd7Tp9JTpaE5D9GI4ecUt2WiRBAdnnzxm90HGKNx0oRN2H\n76vzb1b96ku0bdsKQEvBfmrL6/3qR9Bc6vRWKWafRkOjHsZPQqu3gb7/v93tF+Xx3toiHnh+Aw9e\nPZlH1j9JiiqVGaELSYpWIwjw6BvbyUgI5dfn53ptu/lANTNyYpG05wLtO9bAxMwobjhnPEqFFF2r\nEc8Ay4mmCt4+9AnLcs8nIzyl32P2F2N7Anj1mrXIZsxFouzbDdjzd2urdRrPqkmT0e/dA4BizgKC\nEhNHr50hQiSVYmrV9fp9q4zN4HAgSUgK2O+ilInRKKQ0Neq8RH+uP3scqzeeYEZOLCmRyj4dT0r3\nz4xA4hAERDBoyYW9GWZ+TQNWrFgRsMHMnz+fnTt3cumllyIIAo888giJiYk89NBDWK1WMjIyOOus\nsxCJRCxfvpxly5YhCAL33HMPcrmcK6+8kgceeIBly5Yhl8t55plnAHj00Ue59957cTgczJkzhwkT\n+l+6IZJ0zKhc8sAjAYfVSsVTHb/FaMjAN15JRwNs+uQyBlyU/PEPJD/w+2679Xlira8HkQhp5MBj\nj6s2nOCLzSXERii5aF46k8aF8sahd6nUVeMwKindfYwls9LIHxPBby+dSHykt/vfZnfw454qiiq0\nXHtWDmaLnec/LuDm83OZPr77mdJ7hZ9TYylj1aG13DfnVwP+DL5wVYZY6+soe/xR0lc81e99WZuc\nugzRS690GwT+hnpGCQxiRTCCj5CBrT2B1FVOGAjyx0SSP6brNZcUo+aOS4avtK833l5zlB/2VPDE\njTOIjxx6T4RPg2Dx4sV8+OGHzJw5E4nHgzKhj7EbT+69994uy1auXNll2WWXXcZll13mtUyhUPDc\nc891WXfChAm8//77/R6TJ54JaK6OgsONpbbGqxkLdCTMjdIznomX9tb+NzYRujEmbNomKp//B2mP\n/bnXba0N9UjDwhDL5P0+vouZObHYHQ4mZkTRrDPz3I+fII4/BkC1/TinTY+j4Jia8jodZ0xL6rK9\nVCIma0YF26r3sOnIVcwdm8VLv5uP0eJMcmxsMVHVqPe6kQYrRGCGu2ctH/D4/UHiEdu31tcNSMLY\npm1CoglBFt1htLmSFkcZGsQKBQ5z7waBfRAMgp44VtmCts3MhDGRmK12QlS9X5dmu4W9VUW8s7qJ\nUycmcMlpGYM2tssXZXLl6VnD1u3Qp0HQ1tbGK6+8QriHepRIJGLt2rWDOrDhJGzhYndrVIfB4Hdj\njsHC1txMyf892GW5ZwOf4Wb93kqKKlq4YG46DoeAKliGOnj4W8lKPJJNrQ0NOKzWfiUW2poau11u\nqar0+cCy63R+6bj7Q0KUisvmO8vjBEEgf8yveHL3s9QbnZ6sPXX7OSNmChsLi/na+CJnJi/mnDGL\nsdkd7ryAktZyjHYDb277kfpaCRedOoaC4828sW4nEpuSVqOJmXkx/PrsUwBotbaikamRiofmGuj8\nULBUVxPUj5ClIAjYtFrkcfGIRCLCFp+OYLGM2MZldc1G3vu+iMnZUXy3o5yKej2Xzs+godnIxadl\njIjrqT+IFArsjb17Wl0GgSSABsFba44QEaLgnJne4m2f/VSMttXMG18XMj41gtsvzu91P9+UrGVP\nXQGPXn/XoJ87DmysLd2EyW7m9JTTUMqG1nj1eYWvWbOGLVu2oPgFdWdTT5pM5r9eouaN19Ht3IFd\nrxu2h6/DYuHEvd5lnuqp01FmZ6MYQN203mTFbLETERKY33V8ajgfrjvO5gM1SMQi7lk6kXGp4djs\njmHt3iWWyZCGh2PTakEQsNbX9zkzGaDVI1M94pxzafrqC/ffNq3WXV7VGcFmQzCbB6WTnkgkIjhI\nxv1T76C0rZzPjn1Dha6KnLRwNIkN/PcgrKn4nk9XSQnXBPHMb+bQ1Gri9JhzebX1RUIjrOwpauCC\nuemoNQKO7B/JjcylUlfFPrOWGm02326voE6iJTo4CqvNjkQsRjwA6Vd/P5cn5tKSfhkEDr0ewWJB\n2q7VEXPFVQEZ32ChVsgI1wTx368OE6KSs3hqEnKpGKlUjNU2fLXp/tDUamJ7YR0Wq50ZObFelSpi\nhQKHydRrF1mbwVmWGCgPwVdbS9leWMfSBV3vkZeelkFjq4lJmVF+PeArddXUGxuRB9kH/QHdZNLy\n2YlvAJgRd8qQGwQ+/XDJycnuCoNfEmKFwh1/tg9j7wbtmm+6LAuZOYuwhYsH1NDocKmWx97YwZYD\nA1OddBETruSpW2dz12UTuO3CPP737RFueHIdr39Z6HvjQWbM088SdelSAKy1/fu8lipnn4u0Pz9J\n6IJF3u/1sE+HyUjVC88DgWmco20zs+KtXXy3o9xruVIWzPiIbKQE48DBT4UVjIvIcr9/2gJ47Ean\nzsfRimY++q4aESLi4mFmbiy3/X09NTrnDC4iOIwms1P987k9L1Or2IFgl1JTI/CbZzdQP0TNk9L/\n+jQxV18DOEsH+4O13atzsoh3tdqbiMqq5HfXp/LwjbnIUgpRJdSwbHE22wtrOV7Vgs6qp6Kto+fK\ntyU/8NBPf6Gw6aiz4Zl96CV59SYrz31UwAfrjlFWp+N4lffzQqxQgCAg9CIf3hEyCMwDMC1Ow9kz\nU5iT39UzlxKrYXJWtN+z/ahgp7HfYBq8PiHvH/mEJ3c8z+4jHZ7Ib0vXsat236Adszt8eghEIhFL\nliwhKysLmYer9c033xzUgY0EXEl7w2UQWGpraPxkVZflgYiBThkbQ256BHuLGjhSpmVsSs8NRfzB\n7rBzuPUQeWnjECNFo5RT12zgaHkzR8ubSYhSDavL0+Wyt/RTdtvWnn8gjYjwSjqFnnMTWjZtRL/f\n2agkEB4ClULKhfPSaBMacQgOxJ0aJMVoQjmhA7lax/vfljIzZRZbG7awXf8NusIT/GbSjczMiWNm\nThwPb15Pg7GRc+amsmByIn/Y8ggADsE5E41VRmMw2mihmhfOeAyb3YFUIh4yd7ssKhrluBwAtN98\nReicuT6TNztja08olIYPnpBMIChrq+DNfZ/Q3CTBqC4mJjiKOmOHi10jimR/RRVSaTIvHHgbi7SF\nP874HbGqGLbW7ERrbmZV0RfYBTs2h43HZv9+SMdf3eB8mF9z1lh+Kqhmb1EDs/Pi3e+L23UFHCaT\n+3Vn3AZBgDzROWkR5KT1bgi26Mys3ljM1HHRXcSGth2qRSwWkRSt4nixFWSw4oNN3LnoDMb72G9/\nSNEksqFyM2W84V62vWY3comcKbED0xfpCz4NgltuuWUoxjEicXkIKp55isx/vzpgUZu+Yqmudr8O\nHjeeyHPPR7d7J8GZWb1s5T9NrWb2HW9kRg/Z5f5S22TghQ1f0hiyg8kxE7g+dxn7jBtYmHY6BpON\n99YWIZdJePCqUwIy7v4gi3F+RlNpSa+uy56wt7YgVqrc50Dib+/BeKyIpi8/79FgtGk7ZhQS1cAT\nQOUyCbqgMv536F32tuXx6/xrvN7XyJzH+LrxfcJM01kQEgvtz5VDTUd54M0vaTWZuHjydGKUURQ2\nHeWVgv+xdOyFWBzO2duWqu0AJKkTOGQ8js0hQiQSIZNK0Fn1NJtaSNJ0hFwqG/Q068zkDsJN0uXq\nF6xWSh99mMx//rtP29va+5xIIwZm7A423xdtp9pSBu2niKcxALCnopjisG/RSPIxS51Ki49vewaF\nVMHy8ZfxduFH1BnqSVQnUGGs4nBTEYebilBIFZS1lnNT/jWDashlJoXy6PVO5cDummuJFc4wQG/t\nrAejysAXL392kMNlzaTHe1drbarcyraGYsLbJlFU0czxEitBWXDW3CgiI0XYHLaA59M46AgJ3TX5\nFvRWPa8eWEmLeWi98z4/1fTp04diHCMSqUdZn7msdMi1zm3toZq4G24iZNYcAJTjAtPApqnVhFop\n49fn5VDXbOSNrwu5fGFWvwRpQlRyQuJaaDTAocbDNJm0/FC+EZVMRWZmOjKNmnExqWw+UI3Z6mDB\n5KHvyOcy7nQ7t6NNTSXi7CV92t7W2oo0tCP7XZU/AVFQUK8GgbWxwyAIVGZ7td4p4rWv/gAfHP2E\nY83FPDjtt4hFYqbGTqK0tZyjzcdJHWtgRsJkwoNDeOPguzhwoEtajxjIy17IJNlFfHzsc/Y1HGRf\nw0FOS5pDeVslZ6Ut5P0jq1mUtIA9dftJVDt/qwMNhfy74L8AXJp1PllBk/hiSwn1zSZSYtWDYhCI\n5R3Z3/2RMba3SxaPVEXCijodj76xA3FaGdIoyAoZS1HrkS7r6U3ORj5isbPSJVWTjNFupM7QgM0q\nJkQWTrWtkmpDLXbBzrel6ziqPUaiOp5KXTU6qx6NfHAqkrRtZj7/qZiLT8tg/d5K9hY1cP+yyV55\nQx0egp5/Q7s7h2Dg10lpTRvfbC9jbn48uek9n5f3LzsFvclKq96CwyEgFouo0xr4YO+P2IObmJ2i\nYoxqPBMmTeLfBXtYU7mGNZVrWJg8D6U0mLPTFw94rC5SNMnt/yeRGZbuzL0Sy2g2D22VW+Casv8M\nUWR0lJdYqqt6WTPw2A0GDIXOSgfJICQ0fvZTCQ+9ug1BgE0F1YAIu0PAYOq7xn5wkJQwtdPVZ7Zb\neHHff9zvPbv733xQ+V8+3VrIJzsLGK4Eb4nHA7nh4w/7tK1gs+HQ6ZB0Ur90h5R03RsEDs+GSgOT\nQADgp/3VbDrs7AiXGzmO9RWbqdRVs6rImeCYpEngjsk3ESwNplJXjUauZkrsRC7JvMBrP1+UfUGY\nIpQrx17sXjYxKpffTbmN3MhxPDb79xQe1+PAQRDO781m6nDlflz0OfuL69heWEdxdStLZqXyz48L\nOFrezEjCrneWDwcifyNQFBxv4KVPD2AwWYkOC+am83JITXR6nRRy79vxDXlXc1HmEvZbfwCgrM55\nnuWHT8RksaEQKynYK6LmuPP+4Lq0pGLnw9hVKttk0g7a59l6sIYN+6rZf7wRu0PAZLVTVqvzSoJ0\nhQGEHjwEbbt3UbfW+RnFwQMPGYRpgpgwJtKvEOX7Pxzj+Y/3u8tuwzUKgmXOMWyu38TKklf55NhX\nzI+fz7TYyQD8UL6Rb0rWusNr/cUhOHh+zyu8VPBfEtVx3Dnp1yyMXsKNT63js59KCAsKoXmkeQh+\nycgio4i/+TaqX37R3T9gKBBsNoofvNfd7W0wKhyuO3scV52ezZHyZlQKGfljInny7d0EyZ2ufU9l\nL1+s3nCC6YlnM3ZsBseai9lZuxcApbTD/bcv6H1IgfDEJGDoPQSdy0btBr3fCniuzmqeHgIAabvX\noWXDeoKzxhIya7b3MTy0+H3VYftDTloETaLJ7GrVu8sMAZotHbMIsUhMekgKh5qO0GbRoZGryY3K\nJlh2OSKRiP8deo+99fuBKwkN6jBwwhXe51j+WDWfb4eEUOcMKy8+hZjC8dRJCrEbVKyv383ccy1c\nkX0RbXqBslode4sayE4evGqcvpaMujpcDkaFR39xCDAuNRyHABKRwJTsaL7ZYUQpVXK8thGRRMQj\nsx5AhIjIYGeoY/WxLwGYlpRDlTGE7zdpMSY3EyFO4OozsrlOMo5GYxMHGg/zYdGn7t4wrgTDNsvg\n3bsWTUnicFkzH60/zp9vmoHV5uCt745y5yUT3E2FXAZBT9dA9Yv/dL+WBMBDEKqSMyvPvzLf68/x\n9rjKpGImJCey2WMC6HCI+PpTBZk5gjusYxPstJhbu1w3feF4cwlHtE4NkXpDA2MjMnGEC7x63xjE\nYhEHtopos+io1FWTqI73sbfAMGoQ+MAVx+xpFjgYmEpLvFq/dn4QBQqZVExpTRvNOjOpcRruvWKS\n83h9MAYAjBYb63ZX8NvLZjEvcRYFDYew2C3umYonWyp301IVTnp8CMkxwyesZGts9NsgcHUq7JzU\n5jnzrHn9FTTTZ3glHLpcpCKZjNA58wY0Xm2bmSNlWqYlTOK8PKfh8Xbhh2yu3kGc0ntcKZpEDjUd\n4avi77l87IVEKyOJVkZid9jZVr0LAQFZewz0sVkPcqKllBilt66/WCQmPyqHFI1T3EgqkfCn050q\nhUUVzfzj6F/YVQfxqljUbeM4a0YKi6Z0FUIaKDFXLafubadoWevmn1Dl5HqJDPWGy0Mj7qP08WBx\noqqVmkYDepOVO5/biDikkYi8QvQ2HSmaJGIUY1GoLEQFe7u5b5t4PUe1xzkvYz4ikYiKjCpW7PiJ\n7Ogkt2v+hQ9OYA9uhmhoszoNgMb2rPhWy+Ddu+QyCXcv7Uh6u+S0jC7CPS6DQPvtN6jyvBUChU6t\nfodT78XFBZnn4BAEmowtHG0pwmgU+PV5OYREmnnh0Hr3elpzc78MAkEQePfIKqIUEahlKnRWPU2m\nZmJVMU5BonZXz0151/B92XoEQeCVgv9xSuxEpsZOCtTH7Jbh//ZHOC6lu6GsNLDW1Xr9HWiX5xeb\nS5BJxSyemsRZM5za9P/5qpCDxU08ecssSmpa+XFPFZcvzPTKKVi55gg6g5Xrzh7H4VItk7OdN+Y5\nefHY7B0X9p9m3kelroaciGyywzPZXLWdjLB0/rP/HQ7VFlNRXs61Z40N6Gfyh9TH/kzTl1/Qtm0L\nlpoaZDGxPWY9e9Ky0XkTCJ3n3fWyc9mnpaqKoORk998OoxFZbCzpf35ywGPXG63sPdaARCImrr3G\ne2n2haSFpjAzbqrXuqclz8FgMzE7wbsrm0Qs4Y7JN3ktiwyOIDK4a5w1XhXLLROu63YsWUlh3B58\nI//a9xpfFH9LnkVFdnTgjQGAsAWLEOx26t97h7qVbwCQ/dobfm1r1+tBLA5Y5vpACVPLqWrQMzkr\nilMnxnPQWILepuPWCb8iN3Jcj4l/uZHjyI3saM9sdVhJ0SSRqE6gqkGPKljG0vkZbCgIpvrYRBYs\nmsZbutfc67eYh7dnQ3CW81o3FB7q8l5PSrBWmx2RSNTnyQnAl1tKqGowsPzMbBTy3h9xrg6fGqUM\npULGG18XUtVg4J7LL8YmMvPekdWcnnIaqSFxmGzeIY+y1kqS1InIJX1LNm80afmpahsAV469mHeP\nrOKNQ+/y5Lw/AU6Dwe4QSFDHcU3O5RxqPMK+hoMkawbfszpqEPjApXQ3VB4CU0kJpmJnT/vQ+QsJ\nzsoOeIZwSqyao+Ut7uY2AGfPSGHpgkz0Jht7ixrYd7yB06clkxgkpbbJwNpdFazbXcnM3FgOl2n5\ndnsZ/1y1n9z0CO64ON+ro15YUChhQU6vRlRwBOdnnAVAuDyCKlsV156VTVbS0As9BSUkosrLp23b\nFqpffhFZbCypjzzuU1LY1tqCJCSk25lp1KVLafjoAwDMFeVdDAJpWGAy3JNi1NxyQZ7XMplExpyE\nGV3WDZFruHzshQE5bk+MCUtzv775zOmIEKEzWvl2exnKICmnT0vu1828Ozon0vpbJeLQ65GoVCNG\nmTAiRMH1S5yfZXJ2NC/s2sGhFkhQx/VpjBHSeJalXk9jq4mHXttGiEpOdKiC8WnhZOtz2LvfwpU5\nN6FWyLEHNQ/ag6RVb+Gh17YxOy+OKxY5K58MJht1zQbC1UHuDpxBycmIpFKnSFcn1Vfjka5JlAB7\nihp47YtCblgynhk5fauCGpcSTpg6yK/zb29RA59sLOaKxVlMyoyiPmodZo0RuXQyCrGKG/Oudq+r\nkAbxxOw/cKjpCO8c/pgPiz6lpLWc63KvAODHip+w2q2cnjq/12O6wn1RwZFMjM5jY+VWTolxek5s\ndgc3/+1H8tIj3Z6XxvYckAjF4FfLjBoEPhAHB4NE4tXfYLCwNTdTtuJxsNsBCJk9l+AxYwJ+nAkZ\nUUzI8HYRuxppPP3uHqx2B3//zRz3Teqfq/ZjNNt46JqpfL+rnNe/KOTp22aj1Rn4tnQdX5dVc3ba\nIuSS3h+sSaExVJsqCY8UOFrezL5jDVw6P2NIb9hSDwlua20t5vJygsf0rk1u1+l6DNtEnHUO8tg4\nql54HltrC207t6PKm+C8AVosQ1pGNZQESeRckHE2wVIFYpGYVz47yL7jjSxbnEVlg55dR+rJSAgh\nPCTIy/DsD7LoGK+/bQ0NfoUN7Hr9iAkXGM02jle2MC41nA+LVrOpfYYITgOuL3y7vYxvtpVx12UT\nufHc8UwbF4tM2vEdC4LAy58dpLpR6y4HHAw0ShlP3DgDu6MjY/ZYZTOrNpzg/DnpnJLd8RupJk5C\nt2sndoMBqUdyrqn4BABR8+YQPG+he/n08bHkj4mkvE7X5zLhjMRQMhL9C7POzI1jZq4z38BoM6E1\nNyIVSxH3cM6GK8LIDBvD1NhJ7Kzdy47a3TSaGsmPzOHTE18DMCthGmpZz+ddvcEpPrQk/XQ0cjW/\nn96hRCuViHnlvvle18x7R5xaNBq5mmd2vUBu5DjOSnOKo+2t249dcDA5Jr+LLkl/GDUIfCASiZCo\nNZhOHKfimaeJvPCiQSs/NJeXuY0BGLzcgd6478rJ7tevfXGIILmEVr2F2y/OZ0xCCFdHZKM4V4pY\nJOJg8wl2Nv8EzVClq+HWib13wjsjdQHT4iZzoKGQoiI7kxN6dpMOFtJwb/e4L0NPcDhwGAxIEnqe\nZblKGpu+/ByHwYBmxkxirnTOLAKRJAVwoLgRk9nOhIxIL2/McHJG6gJMNjNryzZwKOQb7r3+ZtJD\n49l8oJpXPjuIAKTGavjTr6b53FdvdA7rmMpKfRoEgiBgN+j9zjcYTPQmK9/tKKeoooWwaLOXMaCS\nKftc037xqWOYmRNLSmz3hsSPeyo5WNzEstOz2bivigrxHspMx7h3yu1Iusnr6S8ikahLY6DuJhvQ\nkdjpMOjBwyCwt5eTpiy7Ap3M+/O8/0MRRRUt/P7qKYMualatq+OvO57FJthJ1ST3um6sMppf5S5D\nKpKytWYnJ1pKOdFS6n7/UOMRpsd1r7niEBxuD0F0cNfvCejRgK7UVbfn+3Sc05+f+JZmc4vbwzBQ\nRg0CP5Co1dhbmjEUHsRQeJDMF172K/bcVyydcgckIYFvb1xY0sSOI/Xkj5ej1ggkaxJQSDtirOV1\nOjbuqyIpRk2d1si41HD+dtts90NIqZCx+2g9kSEK6oz17u3qjPU+LfkEtdMSf3HffxirziUjsau7\ne7Dx9BAAOHwYBA6DAQSh1zwOV/mhKxHUcPiwu8IgUB4CbauZzcWHKBNbmJlwivu7HH4EVh1zlj2+\nVfghf5x5L4fLmpmTH8+l8zNQKwN/I/enBNhhNILdPqwVBrVNBrYcrOGzn0rISQvn/DlpHGjc7bVO\nZD/cwFKJuFtjoKJOx/MfFzB3QjzP3TmP0to2fthVgTmuhbK2Sip11aSEBCbXQxAENh+oYWxKGFGh\nvs9xl76A3bMUF3C0XycSpQqccgvUNBmw2hxce1bfJwxGs4231hwlIUrJkllpPte32R00tpp4b99G\nbIJzMuZvulhaaDJba3Z6LZsVP81dntiZL0+s4euStSRrEjklZkKXRF5P1uwoJyc1nKQYNQ/PvI9K\nXTX/PfgO0FG9ZbZbqDXUIyBw+7oH+N2U2xgTmubf4HtgVIfAD1wzQBe25sDX9eoK9rpj0S4C0S63\nMxEhChKjVBQ07+Yfe16itLUCramjflylkBIRoqC2yUBKrJpZubFeM1JBENh5pI61uytoNDq/hwem\n3cl9U+7w6+KNU8UQHhTGccMRrJKhT3byFLsB37khbrW78J5v3J3PD3tLM42rnW6+QBkEM/KiKQtZ\nw9qKH93Z4yMBT2NS5tDw9/f3smByItcvGU91o55/fbyffccacHTTProvBKWmuV9b63z3NrC1d9eT\nRvV80x1sRCKw2h3cvXQit1+cTzkFJKkTSAtJ4a7Jt/DsaU9wUye1yYEQGaogPlLFmPgQxGIR6fEh\nLJmdRn21c94XSC3+Q6VaXv+ykPv/vYXi6o7EQJvdQVltG9WN3g/+Dg+BwWu5o12QSKrq8KSV1bbx\nSruKYF8Jkkto1pn9Flir0xr5+/t70To6JM0TernWPeluhp8aktzjfXB7zW4EBBpNTVyfexWqHhoX\nNbQY2Xqwxq2NEKuM5pSYCYjbyw9clQ1akxbBQ+DkmV0v+jXu3hj1EPiBRO19w9ft2knEOecGbP+6\ngr1UPf+PgO2vJyxWO5sP1DApK4qCaudN9fm9r5AVNoa7TnFKVEeEKNyVB57sriugsq2Kc8ecya/P\nywXgp6pWrA4rCao4v92eYpGY7PAMttXs4tGtTxHbuIiHLzszQJ+w7/gKGVjb5Ydl4T0rnnWnQti2\nfavzvQAZBGVtFe7XCkngvVMD4Zrxl1PX1szqVSLUwW0o5E4DMilGTXmdjuc+KuAPy6eQ6WdctzuS\nfnc/lspKyp/8M3aD3uf6Lm9bX/sfBJKYcCWaYDnvrj3K9PmtfFe+llC5hr/M/aN7nQgfeTd9IThI\n6lUCCM4HntjuNNpaA1htkJsWwav3z6dFZ/Fy55ssdl77opBJWVFcfGpH/pPrGun829l8F17YAAAg\nAElEQVSNBkQyWbu+hFOnYPr4WKaPj8VitVPdqEelkHUJTfSEWCTyCnv6IiFKxZO3zObBTd9De+8l\ntdS/cuh4VSxzEmZQa6jjWHMxN+RdTX5Ujtc6giDQZtURJAlyJwdOjzsFm8OGrIfqhKjQYP547dQu\nhsWtE69nQ8VmJkfns6NmD9tqdvn9Of1l1CDwg84zwIZVHyGNiiJk+syA7N9w6KDX36l/erzLMQPB\noRItpbVtRCboONbsrGRQSBQUNZ/gREsJRdoT1BsbuTTrPK+ZHzi7qlXoqnAgkBmWTou5lSkxE7vN\ncvfFzPip7pN54SmJ7sY5Q0XcDTeh27Mb3e5dAfEQ9OYZcVWpDASj2cbOIx3hpHjVSAkXOJkRPwUh\nTmDJ/Xi1RlYpZDx2w3QUcsmAc0UkSqVTOVQkQr93D83r1xF22oIe1zdXOA2o/rRNDiRjU8JQR7fw\nbslqABTSoU0ynZARSb01jVVVm2ixBEYGt6Smlde+KGTRlKQuMuTqYOdv3hmX5kcXD4HR0KPRfLS8\nmbe/O8oFc9PdiX++ePGTAyRFqTh/brpf64OzMVubRUdGSDo35i33u713aFAIy8ZdQnlbFUe1x0hS\nJyATS7E6bHx09FMuH3sRz+5+CblYxvkZZyEgcFrSbC7NOt/nvru7XsZFZDEuIotHtjxJvbGjK2Je\n5HgONDq1Ur4uXsvZ6Yu6bOsvowaBH3R3U9ft2BEwg8DW7O0akyclDUqy3aSsKCZmRvJR0ecATImZ\n6FTKssO68k3srnN25otVRjMvcaaXUTAlZiIVuirWlK6jVl/HvoaDTIjK7dc4ssMzeHLun1DKgvnf\n10fYsHkPdy+d2K8+Cv0hZNYcVHkTnAaBDwVKV4OizsmI/tLf7Tyx2BxYm8O5LOZO5k2MD2hiWKAQ\niUTdylIH8jcVicXQHnqoW/m/3g2CMmeSV1ByV2/XUFCnNbBqwwlm5sSRl5JCSJWGVktbr3HjwWJi\nahKrqqDJGBhp6YRIFbdckEtDs4mj5c1+qVO6PQSdcwgMRsQqbw/b8coWVMEy8sZEsuLmWX6PSxAE\nZuXGOsV9/OSnqm2sOvoVAHqdmBBF3w34ZE0CyR4Nv/bW7edo83FazK2caClxrlOXyKVZ55Pkp+Jg\nXbOR7YdqyU4O6/L9uvobnJY0h/zI8WSHZ1DcWsZze15mX8OBUYNgsOlO2MRSU93Nmv3DptWCSIQi\nI3NQdAc8EYlE6K165GIZy8cv5bUDb3GgsRCZ2Om+kolltFraeGDjo4yNyOJg42FOS5rDmNBU9z72\nNTg9Gj3FwPxBLXfOGK49axy1WgNymdjdYGQoEKtUIBL59hA0+WcQRF12OaZjx9DMnIXpWBHa7751\nbhc2ML2F2iYDn24qZmZubLfZ2ycDBpONE1UtZCSGBtRA6C2J1VxWhiQ0dFBkv/1BqZAxISOSVuoQ\nkczjs3/Prtp95EQOvSDX/sM6bEdnMD55Sq/rHdUeIzNsjM/yNblMQlK0modf3446WMbzv/VW4axq\n0GM027xK/8TdeAjM5eXY21qRdcrz+GprKQ6HwG8v61vbX5FIxOQs/0NEdoeddw5/DIDUGM2SiQt9\nbOEfTSYtdYYGSlvLESFCQMAu2FmQPNfvfVisdoxmW7ee0whFGLWGepTSYMZHZgOQGZZOWFDogGWq\nRw0CPwhylZyJRO4ZiqWmGofVMuDEP+1332I6fgxJaCgpD/7fQIfaKyeqWokMCeK63Cux2C3IJDKu\nzbmCLdU7CJYGs61mF0vST+eT406L+WDjYQDWV/xEdtgYxoZnEh0c6S6bGqjhsuNwHW+tOcKM8bHs\nOFJHSoymSwx0sBCJxYhVKp85BC4lNWloSK/rRZx5NrSnQmimTCVk3qnodu9C4UPjwB+yU8KIjQhM\n+eJw8N3OcrRtZuIilQE1CHS7diCSy1FP8JZztba2YtM2ocwLTClWXzFZbHy47hj5Y4N5u/QNfmyM\n5uGZ9zEjvvcH8mAxNz+J0yYlu2fOpa3lxKvivBT2BEFwVv+EZ/ksH3bx99vndDsbX73hBFa7g7s8\nHugSVdccgtJHnbkUrq6uLu64ZIJ7THVao1O1Lyqw1SImm4l32+v7AXJTYjklKTBt5VNDnGWLpW0V\nTIrJZ09dAbHKvuWyJEWruWxB9+Xtt0z4Fd+W/sDiFG/lVI1MTaW+ul/t3V2MVhn4gTIvn7ibbibt\nL092lJ8Jgl/Zzr6of/9dYGikkb/cUsILnxwAcIsIKWXBLEo51R2DkklkiEViktQdLrCz0xaRFZ7B\nnZN/zYWZ5wCgkg78ATU+NZxlF4WRNr6NhVPiOFym9ZJAHmwkarVPD4FdrweJBFFQ3+RvgxISiTz3\n/AEZTYIgEBuhJCpUQWGpFkN7G9yRiN1hp9Go7VYmd/6kBCJCgojQDFxCWOGhAVL90otUPf+PLm11\ntbv3ONdNS2U4kErElNXp2FvrVOGrNdT72GJwkUnF7gd3la6Gp3b+k+f3vOy1jt5qwOqwIQgi6pqd\n36fdYcdgNXTZ36ebinn49e2YLPZuk/1+c3G+lzEAHjkE+q77szU1dlnm4vmPC/hmW5mPT+ikok7H\nv1btZ9cR3/fl70p/ZGftXia2hz2r9TU+tvCflHZlyLLWCpaPX8p1OVcyOyFwAlExyiiWj1+KQuqd\nXKySK7E5bO6mVv1h1EPgByKRiJAZzlhW5nMv0PDpapo+/xR7a+uAGvd5zk47q7ENBi7LuztOTzkN\nMSKywsbgEBxEK6OQiqVEB0dx7piOKoBgaTAPTLuzz+pq3aEOlrGzcTuHmo7wt1MfZfq4BCzWoUsw\nFCHC3taGuaqKoISEbtdxdUUcagElq81OYamW/3xZyJiEUDRKWZ/coUPNiZZS/rHnJc5MXeiWqnYR\nqg5ibHIYf3lrF6dPTe6zFK0niXfeTeXzz2I6fsy9zFRainLsOKxNjdR/8B4SizNbXT1peGbkUomY\nP103je01u9nTLt/vEBwBUZLrL3aHA5PFzvEWZzJxcav3Q1bb3mb30FED79Sv4+YFC1hV9AWbq3fw\n8Ix7iVV13J8WTUliclYUEZruq12Kq1tp1pm9zld3DkG77oDgUYYaf/Nt7tetBgvVDXrio1SEKOV9\n6rwaqpYzMyeWmHDfkxVXHP7CzCWEGseybX8zx1NayEgYuBicsj2UelhbRKOxiWlx/lc9eLL1YA1m\nq51TJyb4df9xqSPqrfouxoK/jHoI+oGrAqDimado+uqLfu+nZeMG9+u4628c8LgGQnpoKjfmL3fH\noOKVMdw39Xa3TrcnKZokd6+CgVBnqOdQk3MWpZAoCFJaUSqGzkYVtWsS1L/3do/rOPT6LklPQ8Er\nnx9i9YZiHrx6Cleckca82QqQDryF8mAR0V4bXanrXjQoJlzJ0gWZTMiIHNBxJCoVYfO9kwldM8y6\nt95Et3MHLQX7gY5OpcPF9LhTmBIzEYlIQoNx+LQjbHYHtz6zgb+89xPvHXFWO/xh+t1e69TrneM7\nZ+o4tKoCXtz3HzZX7wBgV+0+93rldTp+2F2BRCzqUTFTZ7Ty2aYSKhs6wgOidi+bvdVpeDjaFQpV\nEyaimdYxe65rMvLxhhMcPOEcz84j9fzm2Q18svGElxHRHRqlnKnjYvzqotrcbgCFBYWSH5tNgjqW\nhMjAhSWuzbmCWGU0IUH9nzjVNBnYfKAGbZuZFp3Z5/pzEmawbNwl/FS13f35+sqoh6AfSD10CRpW\nfUTYotP7pVxoKj4OQNrjf0Ee3/0MNVDojFZqtQZCNWKieilpTNEk8puJN/RLQa2vVOo63HRbqnfw\n9uGPiNfPIlOZx2ULMgasge+L2Ouup+yxP+Ewd3+xNe3chb2tDVlM/2e0/eXGJTnUNxuJDQ/meEsJ\nz+7+d7ez75GCy0A80HiYL0+sYVvNbuYmzuCMVOfDO1wTRHgPM8q+0jnB09rUROPnn6Iv2Oe1PBAl\nn31ly8Eath+qZcm8eNJjIrks+wKWj1/aY835UCCViPn3706luKqVZ9sz6uOUMdgdTmW+JlMz+yud\nHoPNpQVohSYvwZsD9UWcM+Z0wNl102J19Jr8mz8mkvwxkQiC4BXPVqSnYzxciPH4MaQhzvOl82+U\nmRTKH67u8OwsmJzI8coWjpY3Y7E5CAqQbHeLpRWlNBi5REZOWgQ5aYE1HqfHndKjfLG/XDhvDNPG\n6fj9K1uZlBmFSATp8SGcOb37ypnMsHS2Vu9kS/UOjDYjl4+9qM/HHPUQ9IPOGgH+SKl2xlJXh75g\nHyKpFFns4NeV1zYZeH3jOv6043E+O/5Nj9a2UqYkJ3Ksl4twsIgKds4WY5RRbKp0Jio2qw9wsLiJ\nv7271+eMYKAoUlIRq9Vu+VRPzBXlFD7+FyAwpYN9JUgu4attpTz5zh53P3uNfOgfcP7iWQr5Vcn3\nNJqakIu948sNzUY2H6imqXVgno7OHSQtFeU0frq6y3qd21MPNvXNRnQGK+mpMp499DfeO7IajVw9\nrMaAC4lYTGZSGGdprkU4PI+NB0t5auc/OaI9xiNbn2R7y48AGMXOmXmb3s5D0+4HoM5c4364v/H1\nYb7aWsqH6473erw3vznMzX9bT6u+I56tHOts4Vy+4glsLc4SSLHK9zl947k53L/sFJ/GwOYD1byw\nen8XlcTuaDa3EhrUe6LwSCAhSsVN5+ZgdwjERShJi9OgM/acS+TqqdBk6p+a7qiHoB90kTLWNkGa\n/0IYDquVkj84LzZpRMSQ3LgyEkOZcoqEH8rh29IfOHfMGYgY3rawyZoEbp90IzHB0Ty8ZQUAJkHH\nLeemExsSNiRxe4lS1aU2GkD73Rr3685yx0OFKkiGNEyMzuK8uEeyQQDw6/xrKGur5JuStQBes0yA\n4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9NLSBzs3yJ5Tui49oLl82Lb4YoVK3j00Ucxm80MGjSIWbNmIUkSN910E4sXL8Zut7Ns\n2TJUKhWLFi1ixYoVLF68GJVKxbp16wBYvXo1Dz30EDabjeTkZIYP7/0pcoW3N2SewKrToWglR8BS\n5agT7hIR0StbXr7fk8tP+wpIiPSmSF4NctBcIFcu18WcWTsPdw8ltewQVpUOi9XGoBBPPNxUhPhq\nqNQZUMhl6OpNHMur7lCmcVskhQLXQV0vltNV7+/ZyXHbTh6780aC3f35taiGGK+BeHUyQ/h8Zbfb\nWf3bWgBWjl1GiHcQL9w3CYVMoq7BjLYD29jOR64uCu6ZNwyAPcX7AMfv6sVIbzI09tRwVbhS1lBO\n0DmWgZ58+3eyCnW8eN+kZksASj/HEl9ni7JZTlXoO3sr43s/HENXb+LuuUM7dbyLTX5pHZmFNYyM\n9sNT64LRaqJEX4pG6Yava8f6sfRpQPD222f28G/YsKHF/QsWLGDBggXNblOr1bz44ostHjt8+HA2\nbtzo/EF2wunEQlNxURsBgWNppLea5SgVMqJCPLjxssE8/fu3mBpUKGTnRQzYKf5ujg+Q/Noivt+b\nQ1G2O4suGUxeaS1XTIjAYrWz9r39TBga1K2AoC/sOlTMwROV1ASV8kzqc/xz8ipmhk9lZvjUvh6a\n09Sazyzn/WPPc7wyYy1l1Q08+34qcydFMWtc693b+kJdgxm1St6h7ZCP/98e/D1d+fO1wxp3VARp\nOlcZ7kKhViiJ9YplqPcQhgVG88nxr1g4eF6bBagAbp4Vx3e7c9idXsLMpDNbsSVFywCwps7Ie1uO\nMS4+kEEDWl8GjAr2aHVmYGxCYLMmSq2pNtagVWouyM+/jioo15NZoCMuwhtPIK+2oNNdUsUmeCdS\nR0QCYMzNafV+86kdCMpeCgimjw7lrquHIJNJ6M31aC7AwjYA/qe6ItaYdJRp93Lz9T5U1xmx2uyY\nLTZcXRSsunUMl41pv/7D+abBaGFcQiBP/GF2422Z1RfGTpDO8FC5c8fQmxr/faI6m1KOs37ZlF4L\nBj7/NYsDJ8pb3N5gtGCxOpKadXoTK17dyU/7Ws9kP9v9141g7iTHtsfTV8+Bbr3fKrs3KOQK7h99\nO5dETeCLzO84VHGUd4983O5zwgK03HHVkGbBAICkbBkQSJKERq2ksrb1VuTtifhPF7oAACAASURB\nVB7gyejY9gOx9Qfe5OHtf+/xDqp9aVxCIDfPHkxdg5kT+TV4nCo2VdokOftcLt5wqQ+oghzb5Uyl\npa3ef2aGoO2o2tlKq+oprC2j2ljT2EjoQnO6TXJa2SGMNhOHyo+wKHE+NruNg+VHeHv3B8R4D+Km\n+OvRKHsjDdA5Xv8qnawiHc/eM5E5UZeyKfsH9pceYoT/xTf1OTJgGCuS7iPAzY+Ht/+dQLcAJoT0\nTu0Au91OXmkdx/NrGBHth81u581vjhAd6smmXTnERXjzxznxeGhULJ03DO9zdPI7zdvdhXqpkh9y\nfmdm+FTmx1yJWn5+FyRyBrPNsc03S9f6hU9TaZkV/PB7HldNjGycvfOcPIW6fSn4XjW38XEeGlVj\ncNWeX/YXkFlYw21XdLwIlc1uo6S+jBBN4AVXnbAzbHY7X2zP5uudOSycEc2UIEd3yf1lB7HZbR2q\nnCkCAidS+jui1KbdDJuyVFYi9/BA6si+nW7af7yMEwU1pGVWYLZYWXLVIjzUF+YMgatCzTWD5uCj\n9ubNw+9S2lDB2+kbMVpNaJVuGKxGDpan8+gnn2IrjWDC0CAWzuh4uc6+cu/8YXyc8Q2/FPzKpeFT\n2ZT9A2UNLa9iLxbhHo719RBtMPm1hRjMJiprzAT5uCLrwSJdkiRxw6WxeJ2qe2Cz2UmI9EZCYsqI\nkGZdF+MjHbN3FquNzTlb0Kq0zeopnO14VRafZ27CR+1NkCagzcddTP44ZDErd/wDg9WIwWJErWi7\nnoS/l5qZiaGE+J357JG7aQj/6yNdem2FXEZ8xJkLKqPZykufpBEX7s2VbSSo1hh1WGyWTjf6udCY\nzTbsdkfr6cvHhmO321HKFARrgjpcRlsEBE4kO1V5sT79MEX/eZWg2+5AkjsSYGwWC+bKClzCemeK\n1MddjUmeQ9KkOq6InoZCfmHvub00YhoAHx37gipDFceqTgA0a7EbLMWgCdc0+8A4nx2ryuSXwm0A\njA0azVPJj6KSX5gJdp0R6OZPji6P/3yXQl5lOUSlMDN8CpdH9kyjL7vdjk+Tq36FXMaYuAD2HCnF\n11PNmLgA3ttyjMuSwvDzcuXt747ya1ohQy7JIUuXxQj/IXi5eDY73i+phWzalUPsOEdl0vO5kZGz\nqRVqkkPGcaTyGHqzvt2AoKMtiQ9nVfDbgQLGDQkksJ3yyJOGB5NTXMu+Y2WMjvVHLpOYPT4ClaLt\nL7wKg2Nmtr18h4uBi0rO/KmDGv8tSRLPTF7dqVkRkUPQQ2r3/EZd6j7sVit2i4XdN9wMVqvT8wd2\nHioir7Suxe0RQe7sNH/I9wWbKarvemnf842PqzeVhjNFnQLc/Ah3D+WvY/7CsHF6Cvy/wD/o/C9J\narPZyap2VE67Y+hNeKjc8XRx77EmQOeTAFfHldqMCV6MHGug3lLPl1nfUWXomWJdz314gDXvpGC2\nWCks19NgtGC3w7e7c4kN9cJut2Ox2tl+0PHlvmB6NK89NJ1430FY7VZeP7gBi80CwO6iFB7c9igx\ng2QsXzQSu8KRKe/djwICgGtjrmTluGUdzl4/F4VcwmqzY7W2v8Z/NKeK1W/t5Yvt2djsdoor6/H3\ncm0zERGgsjEg6B/nqKbOyH++Oswfn/6JA8erOpVIKQKCJhqMFqrrOp/U0lTQnXc3Lh0U/fsVCv71\nPDW/bsNmMAAg0zh3jbu8xsAnWzOx2mycKKjhWF415TUNvPHd/sbHFNZdPAGBn9oHq93aOAUW4OrP\nijH3EeoeQrAmkGpjDdvyd2Kz2zlRUNPHo21dWXUDv2eU8nmKo3lRqHtIH4+od52uwFhQV0TpqSWS\nhbHzcJF3v5Rxa/48byjDBvpy17NbeeSN3WxNLeS9Lce586oEfDxcePHjNArK6rhm8kAaLA28d/wD\ndhXvadxWd1KXyxO71536OQ+j1cR/93zDgRMV6Mw6ZJIMD9WFXUCqp9Q1mHnhowN8uaP9ZNnBET7M\nmzKw2dJCa2r0JjRqBbfMjkMmSew4WMSz7+9vN5Cw2Ky4q7T4qHsnmbuvFVfWU1bVwJJZgztdxVUs\nGZxSVKHnH2+ncEliKPOmDOzycTzGjkcTP4TMB+4FoP7wISw1Z76YPCc7dzvZ1cmORByzxcrrXx2m\nrNqAv5ea2AQTOC5qKNRfPAHBdbFXszhuPjVGHd9k/9BsfXeobxxquZpdeQfYtskbD42ax28d02Lf\ncl/LLKzhm105uIXVg0x10U9lni3OJwZPlTteLl4U6kqxG11pKByAPdDO1vydpJYd4rahNzil3XOl\nzoC3uwuzxoUzY3QoRRV69AYLSoUMrasSSZK4YkIEEYGOL/QPMj5jX2ka+0rTuN7vXhJ8BlOkL2He\noDkAqE7VriyVHcPH/xL0xXr8XX3P61bHPanB0oCrou3aJi5KOdNGDsDfSU2fRsX4EezrRvip87Vw\nRsw584UmhoxhYsgYp7z+hWBwuDcrl3QtYVcEBKcE+bjx4v2TkDshuUmmbV4a2JSfh2bQIEJWrOyR\nDocnCmrYebCIO68agtZViR3H+7mmYTj7StMY5hfv9NfsK6evxNQKNX8cekOz++QyOZHukRytPsr9\nf4gnNjgQi9VGvcGCm7rvf9WP5VXzydZMFs2M4YnbxvG37T+gVfW/LxMvF0+emvQoeaU66uokXCVv\nLhsTRm5tPh8e+xyAT49/zZKE7jUsstntPPNBKp4aFQ/fMBqFXNbq1HJM6Jmp5ONVmY0/78rI4f6r\nb8bVxfG782taIaMDJrC3bA81Jh0qbQNDfOLwdOmfVfNOVGfzwr5XmRE+mWujr2z1MUqFjJEx575K\n/XJbJlU1DcweF97umrdKKSfQ242UjFK0rkoGh/evYLqzDCYLCrmsw23G+/5T8jwhSRJyJ21Jae0X\nWuXj7fRgICWjlGqjjhpZPiH+UXhqVchcDHyd9T0TZWOJ9opqTMbrL8I9gzlafRRJreelT9LYf7yc\nycODuXVO3wdFQT5ujB8ShMHoyHF4atIjF2wLVmcIC/Dg1kF3ERXkjiRJjdtLAa4ceFm3jy+TJNbc\nOb5D3fnAkSwY6j6AmoqjBLj6M3/mgMZgAKCixkBGbjXzEq/grSPvU22s4ZroORd1sZv27Cnehx07\nP+ZuY+7A2V1uFnTgRDm5JbUoZa1/dp7NaLay81BxY6nysAAtbuqLPxm3s37Ym8dHv5xg5U1JRAR1\nbEmrf/4mt6LWVMfvxaloJR9GhcR1OKLqKJWP89evXJRyfsj6nlqXk4zyH8ZMz5t498jX7C5OYXdx\nCs9MXn3RNVk5l8BTW4sqDVVcNmYgI6L9mDLi/Fij99ComD5qAKnZBRwpbGBwcNBF1XGtK8bGBzra\ngtcZScs80+TMmcsoLqqO/R9LksQ9I/6I3lzP11mbCXDz44MfHX3mK2oM3Dw7Dnc3JVo3Oc9O+Xu/\nSABtzyj/Yewo3A1Ati6XaK/W6whs2JxBpc7A/QtGtHp/YbmeonI99107rEOv66FRce/84WTkVvHx\n1kwuSQxlfMLF1V3SGZKHBTFlZEinlkxFQHCKzlTLxye+RF4dTujUiA5tlWlP6EMr0O3aiW7Hr4Bj\nhsDZhg70xVZQCmY4WJ6OxWYhr64QgFXjl/e7YABgdMBwRgcMRyVXkVZ2mM+z32dQ3Z8ZoA3u66E1\n+jx9K2WuqfxJdStDL6LlnK7adbiYt7/LwA4kDVvAdVOdU0Oips6IJJNwP5Ur0FEapRsLB88DICyg\njtp6E55aFzw1Kt769iil1Q2suXO8U8Z4IYv3jeWWhEW8lf4++XWFbQYEY+MD2v3/nz0+giVdaEg1\nONyblTe1vVauM9Xy5O51TAgew7zoKzp17ItBV2ZNREBwSpBbADJJRkSEDJVCTmZBTbtbWc7FLS4e\nt7j4xoCgJ3IH7HY744IS+SnvVyx2K4X6Yor0JYS7D7joi3C0RSV3NFE5WJ7Oawf/B0BhdRWBroFO\nn/XpjKxCHe9tS8XmnY3ZxfHB19+SCdsyJi6A8QlBVNYa8PFQk1Wo42R9GaNiuvc7vCUln1/2F/DY\nLWPw9+pacDxhaBDJw84Ek8sWjqTBaLmoK951Rqh7COOCEgl0bftc9cQ6/8/H0siuLGJYZCBxPtHU\nm+sJ1ARgsBgp1BeRVZNDsCYIvbm+3+XoNGW327Ha7CKHoLPkMjneLp6UN1TyzAf7GRMX0K2AoPG4\nnp5Ya2qQuajO/eAOMpmtPPl2ComD/Zk/6SpCtMGklKSSUXkCi82CztSyLkF/Y7XbGn9+97MKIm40\nENBOwZOeFuTjhmvUMbL0xxpv6y/7os9FqXBMafp5umK12di0K4cgX7duBwTzpw5qVqilK85u3Qs0\nyyvo74I1gd1K/iyvaSAjt5qxwyQ6ej2bXpHBx/nvAKAqmcK+0gOklR9m7eTHeTblZUrrHVtZI9wd\nPRTOp9nB3lRbb2LFq7sYGe3HnVcP6dBzxG92Ez5qb45XZ/HCHWNQOilRKPTBFVRv2UzQrMup1LXf\nkaujFHIZt10Rj9Xm2Hs7ITiJCcFJGK0mivQlTAmd4JTXuZCFuw9o/PmFeyc7/fit9XlvS2ZBDXqD\nmVJTIe4qLRqFGzpTLep+vgbdmnUfpNJgsrJ0/lDMVjPKflC58WLwc952KhoquS726hb3bTtQyM5D\nxdw8a3CLpdgGo5XD2ZWEBHoQFdCxZdqms59HSk+SGBUJQI4uD6PlTB2ZSM8wcmrz+m3grXVV8uw9\nEzsVwPbfuZRWnK66lVdVyutfpZOWWU6lztCtY7qEhBC45FbkLs4rumI0WwnycWvMsm18LbmKJQkL\nm5Xz7a981N7ckrCIv419AIB6g4XMbhYqajBa+GRrJpt+y+HRN3Z3+HejrLqBb38/Rp25jiiPCCqN\n1f2usl1HRQV7EBVj5MGtj/LE7nUcKDvc5WMVlOupN1g69NjM6pN8kfltj1VLvNjtLz3IL/k7sDWZ\nmTsteoAn10yKwkvb8jMwLEDLnVcPYeyQjicF+rn6MDHYUVdg+uBhRHlEAJBdk8N9o+4CHLMChlPB\nQX8tGiVJEm7qzuXPiICgiVBtCBHuYbgqVQwO9+KFj/fzzPv7z6uWmYdPVrJuYypma8s/PKG5MUGj\nGKANZt+xMpa+sI2f93esrW1biivrMZqtqFVypo0agKKd+ulNjR8SxKLZjiBNq9Tg7+pLiKZ/TmOe\ny4Lp0UyIjcRkM1NhqOTzzG8wW82dPo7ZYuW1Lw7z32/SO/T4zTk/8X3Ozxd1c6me5KHSYsdObSvL\nlSF+GuIivLu91FJaX84POb9gsppZEHsNS+IXMiNsMoO8IpFJMnYU7ibQzZ8VSffxwOg/NY6lvwYE\nXSGWDJpIDhlHmPsAgj38OOy9Fc9xW7l1xK19nkC042ARBeV6hkT6kJ5TSWSQO05MSbio2e12Xv58\nP55Rhdwwq+2udeeSW1KLp0bFH2ZE81P+r+SfcOXTV7N45k8T0bq2Pq1tMlv5csdJRkT7YlDrAEfv\nhRvir+vyOPoDS/2ZBMDrY6/p0rKBUiHn77eNxdaBYN5ut3OyJhc/tQ+x3tGdfi3hTIJsWUNFpwo1\n7U4vwWazc/X09r+07XY7L+x7lRqTjh/ztvH0pMcYF5wIOL7wh/klcKDsEFXG6saumn8acSsVDVWN\nicbCuYkZgiZUcmXj1pnPT2zCZDPx5dGf+fDnEx36YHG27CIdG77PYN+xMn47XMyOg0VszUgnJLaC\nB7Y+wucnNvX6mC40RfoSXJO2YPJP56NjX3T5ONvTiljzToojY1em4KTrzyxfPJyf9+W32TOhtt5M\nTkktGzYfw83qzz0j/sgI/6FdHkN/ER/hy0jfUSgbAvCXh3brWB3J8yhrKEdvqSfSUyy1dVWI1jHl\nn1mdzesHN7RYOlj/+SHue/HXFrOtlToDxzuwlFdn1lNjcgTVCT6DWxw/3D0UmSRrTCgEkEky/N18\nETpOzBC0IqUkFTuOX1wPKYDy6oZeH8PJYh0ySSLQy5WJQ4IID3THbDfx8PZ3+CTLUXlNq+p+rfeL\nXdPZnUDZQNJPVpIQ2fkiUYsvjWXxpbGAY+qyvKGCo9XpGMyBbbZe9fVUc+NlsXy94yTFpRaSh8V1\n7U30Q7OCr8JwIovCijq+zPuMMUGjGOaX0OHn7z9WRligFj/Pc283LNKXAo4lQ6FrTmfyf5n1HQAF\ndcWENWnateiSGFyULf9OZo+PaPe4WTU5KGUKTKeWjS4Jm8K1MS3LJE8Lncgl4VOclgzeX4kZglZU\nGx2R6KyIGYzzm8jY+MAOZ5Q7g9VmY8PmY2QV1jBzTCjVimx05mrMNjP+Tcq7BrkF9NqYLlRN/78O\npir4MSWfzXtyqartXFfLg+XpvHX4fXJ1+cT7OArnfFP4BdPGepFZUMPhk5WtPk+hNnLLnMHN9rIL\n5xYWoOX2KxMIDXIhpfQAH2V83eHnWm12dh4q5tNtWa3eb7PbePb3l/nzT/+PamNNY3tcZ7Xy7Y+C\n3AK4LuZqpodOAuBY1Ylm93u7u7Sa4NZgbDvp86Qul3Upr/D03hf5vSQVcGxzbI1aoRbBgBOI/8FW\nTAtNJkgTQLxPbJ8UtZDLHL3WUzOLeWzn01QZq5GQ+Nf0NTw6/iGya3JJLTvIYB/nVHS7mClkCv40\n/FY0Sg1RnuHsOVJCRl41lk4kZf6Yks8+4y5OGjIYFTCcgZ5nrmqMejVbU7O446qWV68vb/mBI7If\nSA4Zx+K4+U55P/2JSinjSI4Ru0VJlanju33kMok/t1MG96Quj2xdLgBvHX6fm+Kvx0Pl3uy8Cp2j\nlCuZHjaJ0voyfs7f3qGW61/vPElJZT1TRobg798yhyCgSbEjP1cfrh44i7FBo506bqE5ERC0Qi6T\nM8T3zPTuu98fo7LWwK1z4pEk0PRCIw21SoHGX0dVkWMblB07VYZqfF19iPIMJ0qsd3bY6fLAVYZq\ntuo/4orES/H3csVmc1TxUp5jt4DRbKXMUIqLXMUwv3hkkow5kTPxc/Ul1F/LvdcngL3lDFKEdwBH\namBH4W6CNYFMD5vUI+/vYiUhsT2tmAC/EMpsOeTVFjabhu6qvNqCxuPfM+KPqOQqMTvgJD5qb8da\n/lm7NX47XMy7PxzjpssHMzbecZV/aVIYmYU1yGStz742Lb0+KmCYqOzZC0RAcA7VxhqsvicYPnAA\nZdUNvPzpQdbcOR5VJxpGdERdg5mTRTqKKutRymUoFTJqtI4PrlkRM4jwCBMfWt2kM9VyUpfLKwf+\ni+LQFdTWW7ntivhzTudfOnYA326tIUIT2jhjdMWpbnwl9WWsTfkXAW7+3BZ7O1pXFWqV48/qqsQR\nfPfTu4Cjb7zQOTKZxH3XDedguYJX095ie8EuYr0H4aP2JqqNq/nfj5ay/umfuGV2HJOGBzcu9Vls\nFmSSDJkko1DvuHr969i/iAx0J1PIFPi4eDVu38yuySXQzY8R0X4kRPk025HjopKfM5/nqoGXc6wq\nEy+X7leNFc5N/vjjjz/e14PoS/X17VcPLGuoZGPWB3hrNcR7D2aAn4YgHzfknayLr9G4tPlah7Ir\nWP/ZISKDPcgpqeOL7dnoDRYWThhNnE8MowKGE+qEK6P+zsvFk2pDDXl1BYwNHcqD105otzz16XP2\n+YlvyKrJYZhfQotmRCariR9yf6HGpGPzLzp+2FlF8tDgxj3XSpmCjKoTXBt9Zae2YwlneKi0fJ/z\nC8V15fxemopMkrWaYLjvWBnf7XEsBVTWGJg0PBhJkiipL+Pvvz1LWUMFw/2HMMR3MGODRhHg6tev\n69z3pEiPMDxU7jy193nyagtIDh2Di1Le5hbupp+PRquJ/LoCPFUexHgPZFxwYp9v/b6YaDRtF8kT\nMwTnEOjmj4REZnkBV4bJGRnt5/TZgSGRPtxwWSxFVdXkeH7FqMu9uG3Ijbgp1cSJPAGniveNZWfR\nHoLCjB1a+tmeVkR6VSESEpdFTGtxv4/am9EBw9lXmsZlUz0IMsfw5qYjRAQ61kQnDx9L8uRxaJR9\n10fhQueqcMXHHENxvhJVVDoVhqpWH+froWZUjD9zJg0Cy5lktQOlh2iwNLCraC+zIy/B19Wn3zb/\n6g3TwyZht9tZ+vMK4MyWRHDUE5AkCb3BzEPrdzIhIZAls5rvvnnv6Mf8XpJKvE8sS0fe3qtj7+9E\neHwOKrkSL5UXhbUlbNicwZNvp/Dyp2lOO/72tCLe3HSEuHAvPINrKK4v5WjVMX4t3Om01xDOCHd3\n7GvPqy3AbrdTe44ZIg+NkjjbJayb9FSba5jXRju2QelsldjsNkrdd+ISWMDu9GIUcrkIBpxgxZRb\nuHuSo4Xtkcpj1Jvrya7J4Wjl8cbHRAS5M2d8BP7ezbcaKuRnrnsOlHe9FLLQcU2v6D1dPDCarPzl\nX7/y0icHAXBzUbDunmTmTh7Y7HlVhmp+L0klSBPIbUNv7NUxCyIg6JBg9wAklYlrLxnAkORCjni9\nwyd7fu/01rXWKOQSBqMVu/1MshM49vNabdZuH19ozlftjavClbKGcp7/6ACPvLEbq63tHQfDB/mx\nYHo0Lqq2Z4W8XDxxkauoM9URFN5Anfok3xV9zTVXq/H1FA2MnEHrqiRx8Jmr+t3F+3g25RVeSn29\ncdtgW2aETeax8csBRzAh9I45kTMBRyGh73K/Z9i0fP58raMwl6POvgJPTfMcjszqbACSg8fgKpp/\n9TqxZNABQW4BpFdksLVoK9sKdwGwU/cdkywdL5TSlvgoDwID5CjkMmZHXcLIgKHsK0nDQ+WOXObc\npQnB8UH06LgHAXjJ+gbjh0cgl7UeF9vtdkxm6zmXiCRJ4qnkR1Ar1Dzx27ONt793bCOxPpGiWpoT\nXRt+PVvyf2KIdwLbXHdS2lBOetkJhngNZ+NPxxk20JdrZrTcwhbo5s8tCYvaTEYUnG9O1KVMDUtG\no3Bjd3EKNSYd1xhn4evq3bh0cLbTuxOC2qg3IPQsMUPQAcP8Erhq4CyG+5/pKX1JVDJajdRqd6+O\nKq2q54MTH/HswWfQmWpxVbgy0DOS62Kv5rLI6c4YutAKTxcPtEoNpQ1l5NcVtbg/I7cKg8nCD3ty\nef2rdHJLas95zNOtjP849IbGpitKmRKlXMTczlRb5EPJb0k8+moaswc4Wu3uL8jkofU7gPa3BI8J\nGoWf2KnTayRJQqvUIEkSE0PGArCn4CANRgub9+Sx9PltpJ9V0KusoQIAf1e/Xh+vAJL9fGrl1wfK\nys79YX+a3W7nh9xfiPaK4ue95aTYP8FHEcCl3tczdeSAdp/r7+/e7LUsVhsrPvgEQ/BewFE29a9j\n/9K1NyF0yf0//xWL3cqA2qnEeccTPcCD4YP8+GJ7Nnmlddx17XA278zm0qSwdpcMWmO32zFajY2B\nguAcNrud43nV2Owgk9t46dhaBnpGcN/IuwFQyGUt/taEvlesL+GJ3euwVQaxMHohU0aEUG+woFLI\nUCnljecsv7aQvLpCxgaOEjOkPaS1IlCniRmCTpAkicsipjPQM5LbZiYxyXcGVdYSvt6f1m4JzrP9\ndriYlz89SFC0IxqO8RrI9bHX9NSwhTaMDHBUszN4H+ObnSc5nu9oshIV7M6+48W8uvNjKrx+o8bS\n/hp1ayRJEsFAD5BJEoPDvVGr5LzySTrWeg05NYXIZI5goKm9xfvZUbC7sQ6+0HcC3PxRyhTIfIqJ\nClcikyS0rsoWy3Gh7iFMCE4SwUAf6fX5TIvFwt/+9jcKCgowm83cfffdREdH8/DDDyOTyYiJiWHV\nqlUAfPjhh2zcuBGlUsndd9/NtGnTMBqNLF++nIqKCrRaLU8//TTe3t6kpqby1FNPoVAomDhxIkuX\nLu3x9xIR6MGOahvDhiioqjUil0k0mKwtEmWaKqrQEx7ojsli5auaYvxcffnL6Lt7fKxCSwti5vJ7\nSSpKlZX1D05Fp3fsOBg60Jcps6vZW74XiqHBYuDu4bf07WCFZqKCPXjh3kls3O7O4OBAQMJis9Bg\nMeCP4wrop7xfKawramyTK/QdmSRj8oAJ7CtNQ+3imOk5XTTKYDGgN4kA4HzQ6wHBl19+ibe3N2vX\nrkWn0zF37lzi4uJYtmwZSUlJrFq1ii1btjBy5Eg2bNjAZ599hsFgYNGiRSQnJ/P+++8TGxvL0qVL\n2bRpE+vXr2flypU8/vjjvPzyy4SGhnLnnXdy9OhR4uJ6trtc8Kn9tRpvAzKZxF9e2s6sceFcnRzV\n5nM2bM7geH4Nry2fRpLl/1FlPHfrT6FnaFUanpm8GleFGkmSKK6s579fp3NVchRZdWeaswz3G9LO\nUYS+IpNJzB07lNVv7WHT8e0UqR3Lb2/MXYvJaqKwrogQbTAK0fTmvDA/5ip8rIN48b0TFFccItjX\njduvD+HZlJdRyZWsm/KEKBTVx3r9L2X27NnMmjULAKvVilwuJz09naSkJACmTJnCjh07kMlkJCYm\nolAo0Gq1REZGcvToUVJSUrjjjjsaH/vvf/+buro6zGYzoaGOPeaTJk1i586dPR8QaBzdBtPKDjNv\n0JU8v3TSOdea40cYmDbVF5kk4aZ0w03sUe9Tp+ulGyxGqsij2G8zBxuGolFqiPAJ5bqoa/B0aXvN\nTehbbmoF/7x7IpuyfuSbk47b0suOc7ggE4vdSoLv4D4dn9DcmIgYBnkbcNEY0RuNBGscyYMmq5mU\nkgMkBY4UVQn7UK8HBK6ujg/guro67r//fh544AH++c9/Nt6v0Wioq6tDr9fj7n7mg9jNza3xdq1W\n2/jY2traZredvj0/P79D42kvweLc3HFXaagyVhMQ4I4kSW1upwFw91bxXcnnUAJl9hncMmpBN15b\ncKZ/7fqI7bl7QQWS2syzU1f29ZCETpimTOKbk5sB2Jazh98LDgAwf8RleKpFQHe+8AeigOd3vsGu\nvBSemrmCBybezvM73+Ct9PeZGDMSL3G++kyfzKUVFRWxdOlSbrzxRq64WClRBQAACrlJREFU4gqe\neeaZxvv0ej0eHh5otVrq6upavV2v1zfe5u7u3hhEnP3YjuhuNvIj4x5CQqK8vI4N6R+SUZnJXbFL\nCQto/kvt7+/OZ7/tbvy30WARmdDnkTlhlzsCAkCDI+NZZKtfONzw5KnkR/BQuVNiL+T3ggMsjL0G\nU61EWa04h+eTz09sYldeCgBaixcy2Zna+mZxvnrcebXLoLy8nNtuu43ly5czb948AOLj49m71/Fh\nvG3bNhITExk2bBgpKSmYTCZqa2vJysoiJiaGUaNGsXXrVgC2bt1KUlISWq0WlUpFXl4edrud7du3\nk5jYO4lEWqWmsTStrsFAlamKfbmZrT72YFEWAGMDR3Nl1OW9Mj6hYzxdPLguxrGvfaT/0D4ejdAV\nni4eSJLEsMA4XpmxlimhE/t6SEIrGvRnvnbkMjnuKi1/nfJnVo5d1oejEqAPZghee+01dDod69ev\n55VXXkGSJFauXMmTTz6J2Wxm0KBBzJo1C0mSuOmmm1i8eDF2u51ly5ahUqlYtGgRK1asYPHixahU\nKtatWwfA6tWreeihh7DZbCQnJzN8+PDefmtMCB1Bes0hJO9iGowWKnQGfD3UqFVyDEYL1yWO51C5\nFxNDxqKSn7uxjtC7podNYkJwktguKAg9aNLA4Wyv+IkpIcmNt40KHipm484DojCRE38JDRYjD257\nFABbeSjGrARuuDQOuVziQGYF100dxAA/jdNeT+hZYsngwiTO2/mvylDdrDy7OGe9p70lA7Efx4nU\nChcGe0eTUXWCWyfMpCpSi0IuMXXkAAJ8tXi4iVkBQRAEb7VXXw9BaIUICJzsxvgFFOlLSfCJpT6o\ngZ2Fe/j0xH5uSLyahpqu9z0QBEEQhJ4kAgIn81F746P2BiC/tpDPMzcBUGGs4o4hN/Xl0ARBEASh\nTaIsVA8a7BPd+PPpqoaCIAiCcD4SAUEPG+aXAEB8YGTfDkQQBEEQ2iGWDHrYLQmLyKg6wbjQUZSX\n1537CYIgCILQB8QMQQ9TK1wY4T9E1OcWBEEQzmsiIBAEQRAEQQQEgiAIgiCIgEAQBEEQBERAIAiC\nIAgCIiAQBEEQBAEREAiCIAiCgAgIBEEQBEFABASCIAiCICACAkEQBEEQEAGBIAiCIAiIgEAQBEEQ\nBERAIAiCIAgCIiAQBEEQBAEREAiCIAiCgAgIBEEQBEFABASCIAiCICACAkEQBEEQEAGBIAiCIAiI\ngEAQBEEQBERAIAiCIAgCIiAQBEEQBAEREAiCIAiCgAgIBEEQBEEAFH09AGey2+08/vjjZGRkoFKp\n+Mc//kFYWFhfD0sQBEEQznsX1QzBli1bMJlMfPDBBzz44IOsWbOmr4ckCIIgCBeEiyogSElJYfLk\nyQCMGDGCQ4cO9fGIBEEQBOHCcFEFBHV1dbi7uzf+W6FQYLPZ+nBEgiAIgnBhuKhyCLRaLXq9vvHf\nNpsNmaz9mMff373d+52pN19LcA5xzi5M4rxdeMQ563sX1QzB6NGj2bp1KwCpqanExsb28YgEQRAE\n4cIg2e12e18Pwlma7jIAWLNmDVFRUX08KkEQBEE4/11UAYEgCIIgCF1zUS0ZCIIgCILQNSIgEARB\nEARBBASCIAiCIIiAQBAEQRAELrI6BL3NYrHwt7/9jYKCAsxmM3fffTfR0dE8/PDDyGQyYmJiWLVq\nVePjKysrWbRoEV999RUqlYqGhgYefPBBdDodKpWKp59+moCAgD58Rxe/7p6z0zIzM1m4cCE7d+5s\ndrvQM5xx3qZMmUJkZCQAo0aN4oEHHuiLt9JvdPec2Ww21qxZw+HDhzGZTNx7771MnTq1D9/RxU8E\nBN3w5Zdf4u3tzdq1a9HpdMydO5e4uDiWLVtGUlISq1atYsuWLcycOZPt27ezbt06KioqGp//4Ycf\nMnToUO655x4+++wzXn/9dVauXNmH7+ji191zBo6KmGvXrsXFxaWP3kX/093zlpuby5AhQ/j3v//d\nh++if+nuOfviiy+wWq289957lJSUsHnz5j58N/2DWDLohtmzZ3P//fcDYLVakcvlpKenk5SUBDiu\nSHbt2gWAXC7nrbfewtPTs/H5N998M3/6058AKCwsbHaf0DO6e84AHnvsMZYtW4Zare7dwfdj3T1v\nhw4doqSkhCVLlnDXXXeRnZ3d+2+in+nuOdu+fTsBAQHcddddPPbYY0yfPr3330Q/IwKCbnB1dcXN\nzY26ujruv/9+HnjgAZqWddBoNNTW1gIwYcIEPD09ObvsgyRJ3Hzzzbz77rvMnDmzV8ffH3X3nL38\n8stMmzaNwYMHtziXQs/p7nk7/cXy9ttvc+edd7J8+fJefw/9TXfPWVVVFbm5ubz22mvcfvvt/PWv\nf+3199DfiICgm4qKirj55puZN28eV1xxRbPeCXq9Hg8Pj2aPlySpxTH+97//8c4773Dvvff2+HiF\n7p2zL7/8ko8//pibbrqJ8vJybrvttl4bd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "daily = data.resample('D').sum()\n", + "daily.rolling(30, center=True).sum().plot(style=[':', '--', '-'])\n", + "plt.ylabel('mean hourly count');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The jaggedness of the result is due to the hard cutoff of the window.\n", + "We can get a smoother version of a rolling mean using a window function–for example, a Gaussian window.\n", + "The following code specifies both the width of the window (we chose 50 days) and the width of the Gaussian within the window (we chose 10 days):" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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eXYN18pR+zeeKoEBbKwQCGLJz4tYGY1YW9uklOLdspnPfXqwTJ8WtLamg/b1N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\nGbuLW6hrOVa7+lntV+w+ut/nlZ5GJSMqRINEIiAIAumhCwhWTr6+NBC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2N+1BQGB17BkB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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "daily.rolling(50, center=True,\n", + " win_type='gaussian').sum(std=10).plot(style=[':', '--', '-']);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Digging into the data\n", + "\n", + "While these smoothed data views are useful to get an idea of the general trend in the data, they hide much of the interesting structure.\n", + "For example, we might want to look at the average traffic as a function of the time of day.\n", + "We can do this using the GroupBy functionality discussed in [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb):" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0n1RC80xPyCJy3iTd0BUkG7uSz7AJ+e677+buu+8+7fH169ef9tjy5ctZvny5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "by_time = data.groupby(data.index.time).mean()\n", + "hourly_ticks = 4 * 60 * 60 * np.arange(6)\n", + "by_time.plot(xticks=hourly_ticks, style=[':', '--', '-']);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The hourly traffic is a strongly bimodal distribution, with peaks around 8:00 in the morning and 5:00 in the evening.\n", + "This is likely evidence of a strong component of commuter traffic crossing the bridge.\n", + "This is further evidenced by the differences between the western sidewalk (generally used going toward downtown Seattle), which peaks more strongly in the morning, and the eastern sidewalk (generally used going away from downtown Seattle), which peaks more strongly in the evening.\n", + "\n", + "We also might be curious about how things change based on the day of the week. Again, we can do this with a simple groupby:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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kZWVBoVBAr9cjOTkZ+fn53Vc1EVEvY5w8BZq0dFj37YXtUF6wy6EQpWhrg3nz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\nw5ICXDSeKAAdvuXr5z//eYvXVqxY0al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IycmhsbERq9VKVlYWkZGRbNq0CR8fH6KiosjL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\n8BD/A/9r7TmuhSCKAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "by_weekday = data.groupby(data.index.dayofweek).mean()\n", + "by_weekday.index = ['Mon', 'Tues', 'Wed', 'Thurs', 'Fri', 'Sat', 'Sun']\n", + "by_weekday.plot(style=[':', '--', '-']);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This shows a strong distinction between weekday and weekend totals, with around twice as many average riders crossing the bridge on Monday through Friday than on Saturday and Sunday.\n", + "\n", + "With this in mind, let's do a compound GroupBy and look at the hourly trend on weekdays versus weekends.\n", + "We'll start by grouping by both a flag marking the weekend, and the time of day:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "weekend = np.where(data.index.weekday < 5, 'Weekday', 'Weekend')\n", + "by_time = data.groupby([weekend, data.index.time]).mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll use some of the Matplotlib tools described in [Multiple Subplots](04.08-Multiple-Subplots.ipynb) to plot two panels side by side:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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L0xFCCBFjIvU6paiqtvfwKisbtTy8JrKybHLecSIezxk6ft6uygr23/1zbOdMpMdNtwBQ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\nCAt7cXHruiB5eYH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Ht2eWL5+xzOew42tpCVvxv58pJxcAV7kkx0KI6Ne05XOcB0qxjZtA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fUE102J7+midaqcohqWr81i8vBwxg85Mz5+YvhYthTsZE/xXvaWHGCYve3BsSRJhN5+FzmFhVSu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\nRhAEQRAEQRCEPun/A1rsNddykhZ+AAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "fig, ax = plt.subplots(1, 2, figsize=(14, 5))\n", + "by_time.ix['Weekday'].plot(ax=ax[0], title='Weekdays',\n", + " xticks=hourly_ticks, style=[':', '--', '-'])\n", + "by_time.ix['Weekend'].plot(ax=ax[1], title='Weekends',\n", + " xticks=hourly_ticks, style=[':', '--', '-']);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is very interesting: we see a bimodal commute pattern during the work week, and a unimodal recreational pattern during the weekends.\n", + "It would be interesting to dig through this data in more detail, and examine the effect of weather, temperature, time of year, and other factors on people's commuting patterns; for further discussion, see my blog post [\"Is Seattle Really Seeing an Uptick In Cycling?\"](https://jakevdp.github.io/blog/2014/06/10/is-seattle-really-seeing-an-uptick-in-cycling/), which uses a subset of this data.\n", + "We will also revisit this dataset in the context of modeling in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Vectorized String Operations](03.10-Working-With-Strings.ipynb) | [Contents](Index.ipynb) | [High-Performance Pandas: eval() and query()](03.12-Performance-Eval-and-Query.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/code_listings/03.12-Performance-Eval-and-Query.ipynb b/notebooks_v1/03.12-Performance-Eval-and-Query.ipynb similarity index 57% rename from code_listings/03.12-Performance-Eval-and-Query.ipynb rename to notebooks_v1/03.12-Performance-Eval-and-Query.ipynb index 77c09bfd6..b6e2a142b 100644 --- a/code_listings/03.12-Performance-Eval-and-Query.ipynb +++ b/notebooks_v1/03.12-Performance-Eval-and-Query.ipynb @@ -4,7 +4,50 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# High-Performance Pandas: ``eval()`` and ``query()``" + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Working with Time Series](03.11-Working-with-Time-Series.ipynb) | [Contents](Index.ipynb) | [Further Resources](03.13-Further-Resources.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# High-Performance Pandas: eval() and query()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we've already seen in previous sections, the power of the PyData stack is built upon the ability of NumPy and Pandas to push basic operations into C via an intuitive syntax: examples are vectorized/broadcasted operations in NumPy, and grouping-type operations in Pandas.\n", + "While these abstractions are efficient and effective for many common use cases, they often rely on the creation of temporary intermediate objects, which can cause undue overhead in computational time and memory use.\n", + "\n", + "As of version 0.13 (released January 2014), Pandas includes some experimental tools that allow you to directly access C-speed operations without costly allocation of intermediate arrays.\n", + "These are the ``eval()`` and ``query()`` functions, which rely on the [Numexpr](https://github.com/pydata/numexpr) package.\n", + "In this notebook we will walk through their use and give some rules-of-thumb about when you might think about using them." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivating ``query()`` and ``eval()``: Compound Expressions\n", + "\n", + "We've seen previously that NumPy and Pandas support fast vectorized operations; for example, when adding the elements of two arrays:" ] }, { @@ -25,11 +68,18 @@ "source": [ "import numpy as np\n", "rng = np.random.RandomState(42)\n", - "x = rng.rand(1E6)\n", - "y = rng.rand(1E6)\n", + "x = rng.rand(1000000)\n", + "y = rng.rand(1000000)\n", "%timeit x + y" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As discussed in [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb), this is much faster than doing the addition via a Python loop or comprehension:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -49,6 +99,14 @@ "%timeit np.fromiter((xi + yi for xi, yi in zip(x, y)), dtype=x.dtype, count=len(x))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this abstraction can become less efficient when computing compound expressions.\n", + "For example, consider the following expression:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -60,6 +118,13 @@ "mask = (x > 0.5) & (y < 0.5)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because NumPy evaluates each subexpression, this is roughly equivalent to the following:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -73,6 +138,15 @@ "mask = tmp1 & tmp2" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In other words, *every intermediate step is explicitly allocated in memory*. If the ``x`` and ``y`` arrays are very large, this can lead to significant memory and computational overhead.\n", + "The Numexpr library gives you the ability to compute this type of compound expression element by element, without the need to allocate full intermediate arrays.\n", + "The [Numexpr documentation](https://github.com/pydata/numexpr) has more details, but for the time being it is sufficient to say that the library accepts a *string* giving the NumPy-style expression you'd like to compute:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -97,6 +171,24 @@ "np.allclose(mask, mask_numexpr)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The benefit here is that Numexpr evaluates the expression in a way that does not use full-sized temporary arrays, and thus can be much more efficient than NumPy, especially for large arrays.\n", + "The Pandas ``eval()`` and ``query()`` tools that we will discuss here are conceptually similar, and depend on the Numexpr package." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ``pandas.eval()`` for Efficient Operations\n", + "\n", + "The ``eval()`` function in Pandas uses string expressions to efficiently compute operations using ``DataFrame``s.\n", + "For example, consider the following ``DataFrame``s:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -112,6 +204,13 @@ " for i in range(4))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To compute the sum of all four ``DataFrame``s using the typical Pandas approach, we can just write the sum:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -131,6 +230,13 @@ "%timeit df1 + df2 + df3 + df4" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The same result can be computed via ``pd.eval`` by constructing the expression as a string:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -150,6 +256,13 @@ "%timeit pd.eval('df1 + df2 + df3 + df4')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``eval()`` version of this expression is about 50% faster (and uses much less memory), while giving the same result:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -173,6 +286,16 @@ " pd.eval('df1 + df2 + df3 + df4'))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Operations supported by ``pd.eval()``\n", + "\n", + "As of Pandas v0.16, ``pd.eval()`` supports a wide range of operations.\n", + "To demonstrate these, we'll use the following integer ``DataFrame``s:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -185,6 +308,14 @@ " for i in range(5))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Arithmetic operators\n", + "``pd.eval()`` supports all arithmetic operators. For example:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -209,6 +340,14 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Comparison operators\n", + "``pd.eval()`` supports all comparison operators, including chained expressions:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -233,6 +372,14 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Bitwise operators\n", + "``pd.eval()`` supports the ``&`` and ``|`` bitwise operators:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -257,6 +404,13 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, it supports the use of the literal ``and`` and ``or`` in Boolean expressions:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -280,6 +434,15 @@ "np.allclose(result1, result3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Object attributes and indices\n", + "\n", + "``pd.eval()`` supports access to object attributes via the ``obj.attr`` syntax, and indexes via the ``obj[index]`` syntax:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -304,6 +467,26 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Other operations\n", + "Other operations such as function calls, conditional statements, loops, and other more involved constructs are currently *not* implemented in ``pd.eval()``.\n", + "If you'd like to execute these more complicated types of expressions, you can use the Numexpr library itself." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ``DataFrame.eval()`` for Column-Wise Operations\n", + "\n", + "Just as Pandas has a top-level ``pd.eval()`` function, ``DataFrame``s have an ``eval()`` method that works in similar ways.\n", + "The benefit of the ``eval()`` method is that columns can be referred to *by name*.\n", + "We'll use this labeled array as an example:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -378,6 +561,13 @@ "df.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using ``pd.eval()`` as above, we can compute expressions with the three columns like this:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -402,6 +592,13 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``DataFrame.eval()`` method allows much more succinct evaluation of expressions with the columns:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -425,6 +622,23 @@ "np.allclose(result1, result3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice here that we treat *column names as variables* within the evaluated expression, and the result is what we would wish." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Assignment in DataFrame.eval()\n", + "\n", + "In addition to the options just discussed, ``DataFrame.eval()`` also allows assignment to any column.\n", + "Let's use the ``DataFrame`` from before, which has columns ``'A'``, ``'B'``, and ``'C'``:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -498,6 +712,13 @@ "df.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use ``df.eval()`` to create a new column ``'D'`` and assign to it a value computed from the other columns:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -578,6 +799,13 @@ "df.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the same way, any existing column can be modified:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -658,6 +886,16 @@ "df.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Local variables in DataFrame.eval()\n", + "\n", + "The ``DataFrame.eval()`` method supports an additional syntax that lets it work with local Python variables.\n", + "Consider the following:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -683,6 +921,24 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``@`` character here marks a *variable name* rather than a *column name*, and lets you efficiently evaluate expressions involving the two \"namespaces\": the namespace of columns, and the namespace of Python objects.\n", + "Notice that this ``@`` character is only supported by the ``DataFrame.eval()`` *method*, not by the ``pandas.eval()`` *function*, because the ``pandas.eval()`` function only has access to the one (Python) namespace." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## DataFrame.query() Method\n", + "\n", + "The ``DataFrame`` has another method based on evaluated strings, called the ``query()`` method.\n", + "Consider the following:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -707,6 +963,15 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the example used in our discussion of ``DataFrame.eval()``, this is an expression involving columns of the ``DataFrame``.\n", + "It cannot be expressed using the ``DataFrame.eval()`` syntax, however!\n", + "Instead, for this type of filtering operation, you can use the ``query()`` method:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -730,6 +995,14 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition to being a more efficient computation, compared to the masking expression this is much easier to read and understand.\n", + "Note that the ``query()`` method also accepts the ``@`` flag to mark local variables:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -755,6 +1028,17 @@ "np.allclose(result1, result2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Performance: When to Use These Functions\n", + "\n", + "When considering whether to use these functions, there are two considerations: *computation time* and *memory use*.\n", + "Memory use is the most predictable aspect. As already mentioned, every compound expression involving NumPy arrays or Pandas ``DataFrame``s will result in implicit creation of temporary arrays:\n", + "For example, this:" + ] + }, { "cell_type": "code", "execution_count": 26, @@ -766,6 +1050,13 @@ "x = df[(df.A < 0.5) & (df.B < 0.5)]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Is roughly equivalent to this:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -780,6 +1071,14 @@ "x = df[tmp3]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If the size of the temporary ``DataFrame``s is significant compared to your available system memory (typically several gigabytes) then it's a good idea to use an ``eval()`` or ``query()`` expression.\n", + "You can check the approximate size of your array in bytes using this:" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -801,9 +1100,33 @@ "source": [ "df.values.nbytes" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On the performance side, ``eval()`` can be faster even when you are not maxing-out your system memory.\n", + "The issue is how your temporary ``DataFrame``s compare to the size of the L1 or L2 CPU cache on your system (typically a few megabytes in 2016); if they are much bigger, then ``eval()`` can avoid some potentially slow movement of values between the different memory caches.\n", + "In practice, I find that the difference in computation time between the traditional methods and the ``eval``/``query`` method is usually not significant–if anything, the traditional method is faster for smaller arrays!\n", + "The benefit of ``eval``/``query`` is mainly in the saved memory, and the sometimes cleaner syntax they offer.\n", + "\n", + "We've covered most of the details of ``eval()`` and ``query()`` here; for more information on these, you can refer to the Pandas documentation.\n", + "In particular, different parsers and engines can be specified for running these queries; for details on this, see the discussion within the [\"Enhancing Performance\" section](http://pandas.pydata.org/pandas-docs/dev/enhancingperf.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Working with Time Series](03.11-Working-with-Time-Series.ipynb) | [Contents](Index.ipynb) | [Further Resources](03.13-Further-Resources.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/notebooks_v1/03.13-Further-Resources.ipynb b/notebooks_v1/03.13-Further-Resources.ipynb new file mode 100644 index 000000000..16c8a8ebd --- /dev/null +++ b/notebooks_v1/03.13-Further-Resources.ipynb @@ -0,0 +1,96 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [High-Performance Pandas: eval() and query()](03.12-Performance-Eval-and-Query.ipynb) | [Contents](Index.ipynb) | [Visualization with Matplotlib](04.00-Introduction-To-Matplotlib.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Further Resources" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In this chapter, we've covered many of the basics of using Pandas effectively for data analysis.\n", + "Still, much has been omitted from our discussion.\n", + "To learn more about Pandas, I recommend the following resources:\n", + "\n", + "- [Pandas online documentation](http://pandas.pydata.org/): This is the go-to source for complete documentation of the package. While the examples in the documentation tend to be small generated datasets, the description of the options is complete and generally very useful for understanding the use of various functions.\n", + "\n", + "- [*Python for Data Analysis*](http://shop.oreilly.com/product/0636920023784.do) Written by Wes McKinney (the original creator of Pandas), this book contains much more detail on the Pandas package than we had room for in this chapter. In particular, he takes a deep dive into tools for time series, which were his bread and butter as a financial consultant. The book also has many entertaining examples of applying Pandas to gain insight from real-world datasets. Keep in mind, though, that the book is now several years old, and the Pandas package has quite a few new features that this book does not cover (but be on the lookout for a new edition in 2017).\n", + "\n", + "- [Stack Overflow](http://stackoverflow.com/questions/tagged/pandas): Pandas has so many users that any question you have has likely been asked and answered on Stack Overflow. Using Pandas is a case where some Google-Fu is your best friend. Simply go to your favorite search engine and type in the question, problem, or error you're coming across–more than likely you'll find your answer on a Stack Overflow page.\n", + "\n", + "- [Pandas on PyVideo](http://pyvideo.org/search?q=pandas): From PyCon to SciPy to PyData, many conferences have featured tutorials from Pandas developers and power users. The PyCon tutorials in particular tend to be given by very well-vetted presenters.\n", + "\n", + "Using these resources, combined with the walk-through given in this chapter, my hope is that you'll be poised to use Pandas to tackle any data analysis problem you come across!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [High-Performance Pandas: eval() and query()](03.12-Performance-Eval-and-Query.ipynb) | [Contents](Index.ipynb) | [Visualization with Matplotlib](04.00-Introduction-To-Matplotlib.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/code_listings/04.00-Introduction-To-Matplotlib.ipynb b/notebooks_v1/04.00-Introduction-To-Matplotlib.ipynb similarity index 84% rename from code_listings/04.00-Introduction-To-Matplotlib.ipynb rename to notebooks_v1/04.00-Introduction-To-Matplotlib.ipynb index 93315acc2..ebf07e3bd 100644 --- a/code_listings/04.00-Introduction-To-Matplotlib.ipynb +++ b/notebooks_v1/04.00-Introduction-To-Matplotlib.ipynb @@ -4,7 +4,71 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Introduction to Matplotlib" + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Further Resources](03.13-Further-Resources.ipynb) | [Contents](Index.ipynb) | [Simple Line Plots](04.01-Simple-Line-Plots.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Visualization with Matplotlib" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll now take an in-depth look at the Matplotlib package for visualization in Python.\n", + "Matplotlib is a multi-platform data visualization library built on NumPy arrays, and designed to work with the broader SciPy stack.\n", + "It was conceived by John Hunter in 2002, originally as a patch to IPython for enabling interactive MATLAB-style plotting via gnuplot from the IPython command line.\n", + "IPython's creator, Fernando Perez, was at the time scrambling to finish his PhD, and let John know he wouldn’t have time to review the patch for several months.\n", + "John took this as a cue to set out on his own, and the Matplotlib package was born, with version 0.1 released in 2003.\n", + "It received an early boost when it was adopted as the plotting package of choice of the Space Telescope Science Institute (the folks behind the Hubble Telescope), which financially supported Matplotlib’s development and greatly expanded its capabilities.\n", + "\n", + "One of Matplotlib’s most important features is its ability to play well with many operating systems and graphics backends.\n", + "Matplotlib supports dozens of backends and output types, which means you can count on it to work regardless of which operating system you are using or which output format you wish.\n", + "This cross-platform, everything-to-everyone approach has been one of the great strengths of Matplotlib.\n", + "It has led to a large user base, which in turn has led to an active developer base and Matplotlib’s powerful tools and ubiquity within the scientific Python world.\n", + "\n", + "In recent years, however, the interface and style of Matplotlib have begun to show their age.\n", + "Newer tools like ggplot and ggvis in the R language, along with web visualization toolkits based on D3js and HTML5 canvas, often make Matplotlib feel clunky and old-fashioned.\n", + "Still, I'm of the opinion that we cannot ignore Matplotlib's strength as a well-tested, cross-platform graphics engine.\n", + "Recent Matplotlib versions make it relatively easy to set new global plotting styles (see [Customizing Matplotlib: Configurations and Style Sheets](04.11-Settings-and-Stylesheets.ipynb)), and people have been developing new packages that build on its powerful internals to drive Matplotlib via cleaner, more modern APIs—for example, Seaborn (discussed in [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)), [ggpy](http://yhat.github.io/ggpy/), [HoloViews](http://holoviews.org/), [Altair](http://altair-viz.github.io/), and even Pandas itself can be used as wrappers around Matplotlib's API.\n", + "Even with wrappers like these, it is still often useful to dive into Matplotlib's syntax to adjust the final plot output.\n", + "For this reason, I believe that Matplotlib itself will remain a vital piece of the data visualization stack, even if new tools mean the community gradually moves away from using the Matplotlib API directly." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## General Matplotlib Tips\n", + "\n", + "Before we dive into the details of creating visualizations with Matplotlib, there are a few useful things you should know about using the package." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Importing Matplotlib\n", + "\n", + "Just as we use the ``np`` shorthand for NumPy and the ``pd`` shorthand for Pandas, we will use some standard shorthands for Matplotlib imports:" ] }, { @@ -19,6 +83,23 @@ "import matplotlib.pyplot as plt" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``plt`` interface is what we will use most often, as we shall see throughout this chapter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setting Styles\n", + "\n", + "We will use the ``plt.style`` directive to choose appropriate aesthetic styles for our figures.\n", + "Here we will set the ``classic`` style, which ensures that the plots we create use the classic Matplotlib style:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -30,6 +111,106 @@ "plt.style.use('classic')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Throughout this section, we will adjust this style as needed.\n", + "Note that the stylesheets used here are supported as of Matplotlib version 1.5; if you are using an earlier version of Matplotlib, only the default style is available.\n", + "For more information on stylesheets, see [Customizing Matplotlib: Configurations and Style Sheets](04.11-Settings-and-Stylesheets.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ``show()`` or No ``show()``? How to Display Your Plots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A visualization you can't see won't be of much use, but just how you view your Matplotlib plots depends on the context.\n", + "The best use of Matplotlib differs depending on how you are using it; roughly, the three applicable contexts are using Matplotlib in a script, in an IPython terminal, or in an IPython notebook." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Plotting from a script\n", + "\n", + "If you are using Matplotlib from within a script, the function ``plt.show()`` is your friend.\n", + "``plt.show()`` starts an event loop, looks for all currently active figure objects, and opens one or more interactive windows that display your figure or figures.\n", + "\n", + "So, for example, you may have a file called *myplot.py* containing the following:\n", + "\n", + "```python\n", + "# ------- file: myplot.py ------\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "x = np.linspace(0, 10, 100)\n", + "\n", + "plt.plot(x, np.sin(x))\n", + "plt.plot(x, np.cos(x))\n", + "\n", + "plt.show()\n", + "```\n", + "\n", + "You can then run this script from the command-line prompt, which will result in a window opening with your figure displayed:\n", + "\n", + "```\n", + "$ python myplot.py\n", + "```\n", + "\n", + "The ``plt.show()`` command does a lot under the hood, as it must interact with your system's interactive graphical backend.\n", + "The details of this operation can vary greatly from system to system and even installation to installation, but matplotlib does its best to hide all these details from you.\n", + "\n", + "One thing to be aware of: the ``plt.show()`` command should be used *only once* per Python session, and is most often seen at the very end of the script.\n", + "Multiple ``show()`` commands can lead to unpredictable backend-dependent behavior, and should mostly be avoided." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Plotting from an IPython shell\n", + "\n", + "It can be very convenient to use Matplotlib interactively within an IPython shell (see [IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb)).\n", + "IPython is built to work well with Matplotlib if you specify Matplotlib mode.\n", + "To enable this mode, you can use the ``%matplotlib`` magic command after starting ``ipython``:\n", + "\n", + "```ipython\n", + "In [1]: %matplotlib\n", + "Using matplotlib backend: TkAgg\n", + "\n", + "In [2]: import matplotlib.pyplot as plt\n", + "```\n", + "\n", + "At this point, any ``plt`` plot command will cause a figure window to open, and further commands can be run to update the plot.\n", + "Some changes (such as modifying properties of lines that are already drawn) will not draw automatically: to force an update, use ``plt.draw()``.\n", + "Using ``plt.show()`` in Matplotlib mode is not required." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Plotting from an IPython notebook\n", + "\n", + "The IPython notebook is a browser-based interactive data analysis tool that can combine narrative, code, graphics, HTML elements, and much more into a single executable document (see [IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb)).\n", + "\n", + "Plotting interactively within an IPython notebook can be done with the ``%matplotlib`` command, and works in a similar way to the IPython shell.\n", + "In the IPython notebook, you also have the option of embedding graphics directly in the notebook, with two possible options:\n", + "\n", + "- ``%matplotlib notebook`` will lead to *interactive* plots embedded within the notebook\n", + "- ``%matplotlib inline`` will lead to *static* images of your plot embedded in the notebook\n", + "\n", + "For this book, we will generally opt for ``%matplotlib inline``:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -41,6 +222,13 @@ "%matplotlib inline" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After running this command (it needs to be done only once per kernel/session), any cell within the notebook that creates a plot will embed a PNG image of the resulting graphic:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -68,6 +256,17 @@ "plt.plot(x, np.cos(x), '--');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Saving Figures to File\n", + "\n", + "One nice feature of Matplotlib is the ability to save figures in a wide variety of formats.\n", + "Saving a figure can be done using the ``savefig()`` command.\n", + "For example, to save the previous figure as a PNG file, you can run this:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -79,6 +278,13 @@ "fig.savefig('my_figure.png')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have a file called ``my_figure.png`` in the current working directory:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -98,6 +304,13 @@ "!ls -lh my_figure.png" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To confirm that it contains what we think it contains, let's use the IPython ``Image`` object to display the contents of this file:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -122,6 +335,15 @@ "Image('my_figure.png')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In ``savefig()``, the file format is inferred from the extension of the given filename.\n", + "Depending on what backends you have installed, many different file formats are available.\n", + "The list of supported file types can be found for your system by using the following method of the figure canvas object:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -156,6 +378,33 @@ "fig.canvas.get_supported_filetypes()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that when saving your figure, it's not necessary to use ``plt.show()`` or related commands discussed earlier." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Two Interfaces for the Price of One\n", + "\n", + "A potentially confusing feature of Matplotlib is its dual interfaces: a convenient MATLAB-style state-based interface, and a more powerful object-oriented interface. We'll quickly highlight the differences between the two here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### MATLAB-style Interface\n", + "\n", + "Matplotlib was originally written as a Python alternative for MATLAB users, and much of its syntax reflects that fact.\n", + "The MATLAB-style tools are contained in the pyplot (``plt``) interface.\n", + "For example, the following code will probably look quite familiar to MATLAB users:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -177,15 +426,39 @@ "source": [ "plt.figure() # create a plot figure\n", "\n", - "# create the first of 2 panels & set current axis\n", + "# create the first of two panels and set current axis\n", "plt.subplot(2, 1, 1) # (rows, columns, panel number)\n", "plt.plot(x, np.sin(x))\n", "\n", - "# create the second panel & set current axis\n", + "# create the second panel and set current axis\n", "plt.subplot(2, 1, 2)\n", "plt.plot(x, np.cos(x));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is important to note that this interface is *stateful*: it keeps track of the \"current\" figure and axes, which are where all ``plt`` commands are applied.\n", + "You can get a reference to these using the ``plt.gcf()`` (get current figure) and ``plt.gca()`` (get current axes) routines.\n", + "\n", + "While this stateful interface is fast and convenient for simple plots, it is easy to run into problems.\n", + "For example, once the second panel is created, how can we go back and add something to the first?\n", + "This is possible within the MATLAB-style interface, but a bit clunky.\n", + "Fortunately, there is a better way." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Object-oriented interface\n", + "\n", + "The object-oriented interface is available for these more complicated situations, and for when you want more control over your figure.\n", + "Rather than depending on some notion of an \"active\" figure or axes, in the object-oriented interface the plotting functions are *methods* of explicit ``Figure`` and ``Axes`` objects.\n", + "To re-create the previous plot using this style of plotting, you might do the following:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -213,9 +486,29 @@ "ax[0].plot(x, np.sin(x))\n", "ax[1].plot(x, np.cos(x));" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more simple plots, the choice of which style to use is largely a matter of preference, but the object-oriented approach can become a necessity as plots become more complicated.\n", + "Throughout this chapter, we will switch between the MATLAB-style and object-oriented interfaces, depending on what is most convenient.\n", + "In most cases, the difference is as small as switching ``plt.plot()`` to ``ax.plot()``, but there are a few gotchas that we will highlight as they come up in the following sections." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Further Resources](03.13-Further-Resources.ipynb) | [Contents](Index.ipynb) | [Simple Line Plots](04.01-Simple-Line-Plots.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.01-Simple-Line-Plots.ipynb b/notebooks_v1/04.01-Simple-Line-Plots.ipynb similarity index 96% rename from code_listings/04.01-Simple-Line-Plots.ipynb rename to notebooks_v1/04.01-Simple-Line-Plots.ipynb index c8dc2b023..03acda4e3 100644 --- a/code_listings/04.01-Simple-Line-Plots.ipynb +++ b/notebooks_v1/04.01-Simple-Line-Plots.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Visualization with Matplotlib](04.00-Introduction-To-Matplotlib.ipynb) | [Contents](Index.ipynb) | [Simple Scatter Plots](04.02-Simple-Scatter-Plots.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,15 @@ "# Simple Line Plots" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Perhaps the simplest of all plots is the visualization of a single function $y = f(x)$.\n", + "Here we will take a first look at creating a simple plot of this type.\n", + "As with all the following sections, we'll start by setting up the notebook for plotting and importing the packages we will use:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -21,6 +52,14 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For all Matplotlib plots, we start by creating a figure and an axes.\n", + "In their simplest form, a figure and axes can be created as follows:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -44,6 +83,17 @@ "ax = plt.axes()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In Matplotlib, the *figure* (an instance of the class ``plt.Figure``) can be thought of as a single container that contains all the objects representing axes, graphics, text, and labels.\n", + "The *axes* (an instance of the class ``plt.Axes``) is what we see above: a bounding box with ticks and labels, which will eventually contain the plot elements that make up our visualization.\n", + "Throughout this book, we'll commonly use the variable name ``fig`` to refer to a figure instance, and ``ax`` to refer to an axes instance or group of axes instances.\n", + "\n", + "Once we have created an axes, we can use the ``ax.plot`` function to plot some data. Let's start with a simple sinusoid:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -70,6 +120,14 @@ "ax.plot(x, np.sin(x));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, we can use the pylab interface and let the figure and axes be created for us in the background\n", + "(see [Two Interfaces for the Price of One](04.00-Introduction-To-Matplotlib.ipynb#Two-Interfaces-for-the-Price-of-One) for a discussion of these two interfaces):" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -92,6 +150,13 @@ "plt.plot(x, np.sin(x));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we want to create a single figure with multiple lines, we can simply call the ``plot`` function multiple times:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -115,6 +180,31 @@ "plt.plot(x, np.cos(x));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's all there is to plotting simple functions in Matplotlib!\n", + "We'll now dive into some more details about how to control the appearance of the axes and lines." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adjusting the Plot: Line Colors and Styles" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first adjustment you might wish to make to a plot is to control the line colors and styles.\n", + "The ``plt.plot()`` function takes additional arguments that can be used to specify these.\n", + "To adjust the color, you can use the ``color`` keyword, which accepts a string argument representing virtually any imaginable color.\n", + "The color can be specified in a variety of ways:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -135,11 +225,20 @@ ], "source": [ "plt.plot(x, np.sin(x - 0), color='blue') # specify color by name\n", - "plt.plot(x, np.sin(x - 1), color='g') # short color code (options: rgbcmyk)\n", - "plt.plot(x, np.sin(x - 2), color='0.75') # Greyscale between 0 and 1\n", - "plt.plot(x, np.sin(x - 3), color='#FFDD44') # Hex color code (RRGGBB from 00 to FF)\n", - "plt.plot(x, np.sin(x - 4), color=(1.0,0.2,0.3)) # RGB tuple, values between 0 and 1\n", - "plt.plot(x, np.sin(x - 5), color='chartreuse'); # all html color names are supported" + "plt.plot(x, np.sin(x - 1), color='g') # short color code (rgbcmyk)\n", + "plt.plot(x, np.sin(x - 2), color='0.75') # Grayscale between 0 and 1\n", + "plt.plot(x, np.sin(x - 3), color='#FFDD44') # Hex code (RRGGBB from 00 to FF)\n", + "plt.plot(x, np.sin(x - 4), color=(1.0,0.2,0.3)) # RGB tuple, values 0 to 1\n", + "plt.plot(x, np.sin(x - 5), color='chartreuse'); # all HTML color names supported" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If no color is specified, Matplotlib will automatically cycle through a set of default colors for multiple lines.\n", + "\n", + "Similarly, the line style can be adjusted using the ``linestyle`` keyword:" ] }, { @@ -173,6 +272,13 @@ "plt.plot(x, x + 7, linestyle=':'); # dotted" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you would like to be extremely terse, these ``linestyle`` and ``color`` codes can be combined into a single non-keyword argument to the ``plt.plot()`` function:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -198,6 +304,25 @@ "plt.plot(x, x + 3, ':r'); # dotted red" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These single-character color codes reflect the standard abbreviations in the RGB (Red/Green/Blue) and CMYK (Cyan/Magenta/Yellow/blacK) color systems, commonly used for digital color graphics.\n", + "\n", + "There are many other keyword arguments that can be used to fine-tune the appearance of the plot; for more details, I'd suggest viewing the docstring of the ``plt.plot()`` function using IPython's help tools (See [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adjusting the Plot: Axes Limits\n", + "\n", + "Matplotlib does a decent job of choosing default axes limits for your plot, but sometimes it's nice to have finer control.\n", + "The most basic way to adjust axis limits is to use the ``plt.xlim()`` and ``plt.ylim()`` methods:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -223,6 +348,13 @@ "plt.ylim(-1.5, 1.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If for some reason you'd like either axis to be displayed in reverse, you can simply reverse the order of the arguments:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -248,6 +380,14 @@ "plt.ylim(1.2, -1.2);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A useful related method is ``plt.axis()`` (note here the potential confusion between *axes* with an *e*, and *axis* with an *i*).\n", + "The ``plt.axis()`` method allows you to set the ``x`` and ``y`` limits with a single call, by passing a list which specifies ``[xmin, xmax, ymin, ymax]``:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -271,6 +411,13 @@ "plt.axis([-1, 11, -1.5, 1.5]);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``plt.axis()`` method goes even beyond this, allowing you to do things like automatically tighten the bounds around the current plot:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -294,6 +441,13 @@ "plt.axis('tight');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It allows even higher-level specifications, such as ensuring an equal aspect ratio so that on your screen, one unit in ``x`` is equal to one unit in ``y``:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -317,6 +471,24 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on axis limits and the other capabilities of the ``plt.axis`` method, refer to the ``plt.axis`` docstring." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Labeling Plots\n", + "\n", + "As the last piece of this section, we'll briefly look at the labeling of plots: titles, axis labels, and simple legends.\n", + "\n", + "Titles and axis labels are the simplest such labels—there are methods that can be used to quickly set them:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -342,6 +514,24 @@ "plt.ylabel(\"sin(x)\");" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The position, size, and style of these labels can be adjusted using optional arguments to the function.\n", + "For more information, see the Matplotlib documentation and the docstrings of each of these functions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When multiple lines are being shown within a single axes, it can be useful to create a plot legend that labels each line type.\n", + "Again, Matplotlib has a built-in way of quickly creating such a legend.\n", + "It is done via the (you guessed it) ``plt.legend()`` method.\n", + "Though there are several valid ways of using this, I find it easiest to specify the label of each line using the ``label`` keyword of the plot function:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -368,6 +558,33 @@ "plt.legend();" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, the ``plt.legend()`` function keeps track of the line style and color, and matches these with the correct label.\n", + "More information on specifying and formatting plot legends can be found in the ``plt.legend`` docstring; additionally, we will cover some more advanced legend options in [Customizing Plot Legends](04.06-Customizing-Legends.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aside: Matplotlib Gotchas\n", + "\n", + "While most ``plt`` functions translate directly to ``ax`` methods (such as ``plt.plot()`` → ``ax.plot()``, ``plt.legend()`` → ``ax.legend()``, etc.), this is not the case for all commands.\n", + "In particular, functions to set limits, labels, and titles are slightly modified.\n", + "For transitioning between MATLAB-style functions and object-oriented methods, make the following changes:\n", + "\n", + "- ``plt.xlabel()`` → ``ax.set_xlabel()``\n", + "- ``plt.ylabel()`` → ``ax.set_ylabel()``\n", + "- ``plt.xlim()`` → ``ax.set_xlim()``\n", + "- ``plt.ylim()`` → ``ax.set_ylim()``\n", + "- ``plt.title()`` → ``ax.set_title()``\n", + "\n", + "In the object-oriented interface to plotting, rather than calling these functions individually, it is often more convenient to use the ``ax.set()`` method to set all these properties at once:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -393,9 +610,20 @@ " xlabel='x', ylabel='sin(x)',\n", " title='A Simple Plot');" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Visualization with Matplotlib](04.00-Introduction-To-Matplotlib.ipynb) | [Contents](Index.ipynb) | [Simple Scatter Plots](04.02-Simple-Scatter-Plots.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.02-Simple-Scatter-Plots.ipynb b/notebooks_v1/04.02-Simple-Scatter-Plots.ipynb similarity index 96% rename from code_listings/04.02-Simple-Scatter-Plots.ipynb rename to notebooks_v1/04.02-Simple-Scatter-Plots.ipynb index 4e7dee086..eaf6c4249 100644 --- a/code_listings/04.02-Simple-Scatter-Plots.ipynb +++ b/notebooks_v1/04.02-Simple-Scatter-Plots.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Simple Line Plots](04.01-Simple-Line-Plots.ipynb) | [Contents](Index.ipynb) | [Visualizing Errors](04.03-Errorbars.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,15 @@ "# Simple Scatter Plots" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another commonly used plot type is the simple scatter plot, a close cousin of the line plot.\n", + "Instead of points being joined by line segments, here the points are represented individually with a dot, circle, or other shape.\n", + "We’ll start by setting up the notebook for plotting and importing the functions we will use:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -21,6 +52,16 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Scatter Plots with ``plt.plot``\n", + "\n", + "In the previous section we looked at ``plt.plot``/``ax.plot`` to produce line plots.\n", + "It turns out that this same function can produce scatter plots as well:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -46,6 +87,13 @@ "plt.plot(x, y, 'o', color='black');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The third argument in the function call is a character that represents the type of symbol used for the plotting. Just as you can specify options such as ``'-'``, ``'--'`` to control the line style, the marker style has its own set of short string codes. The full list of available symbols can be seen in the documentation of ``plt.plot``, or in Matplotlib's online documentation. Most of the possibilities are fairly intuitive, and we'll show a number of the more common ones here:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -73,6 +121,13 @@ "plt.xlim(0, 1.8);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For even more possibilities, these character codes can be used together with line and color codes to plot points along with a line connecting them:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -95,6 +150,13 @@ "plt.plot(x, y, '-ok');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Additional keyword arguments to ``plt.plot`` specify a wide range of properties of the lines and markers:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -122,6 +184,23 @@ "plt.ylim(-1.2, 1.2);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This type of flexibility in the ``plt.plot`` function allows for a wide variety of possible visualization options.\n", + "For a full description of the options available, refer to the ``plt.plot`` documentation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Scatter Plots with ``plt.scatter``\n", + "\n", + "A second, more powerful method of creating scatter plots is the ``plt.scatter`` function, which can be used very similarly to the ``plt.plot`` function:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -144,6 +223,16 @@ "plt.scatter(x, y, marker='o');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The primary difference of ``plt.scatter`` from ``plt.plot`` is that it can be used to create scatter plots where the properties of each individual point (size, face color, edge color, etc.) can be individually controlled or mapped to data.\n", + "\n", + "Let's show this by creating a random scatter plot with points of many colors and sizes.\n", + "In order to better see the overlapping results, we'll also use the ``alpha`` keyword to adjust the transparency level:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -174,6 +263,16 @@ "plt.colorbar(); # show color scale" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the color argument is automatically mapped to a color scale (shown here by the ``colorbar()`` command), and that the size argument is given in pixels.\n", + "In this way, the color and size of points can be used to convey information in the visualization, in order to visualize multidimensional data.\n", + "\n", + "For example, we might use the Iris data from Scikit-Learn, where each sample is one of three types of flowers that has had the size of its petals and sepals carefully measured:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -202,6 +301,37 @@ "plt.xlabel(iris.feature_names[0])\n", "plt.ylabel(iris.feature_names[1]);" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that this scatter plot has given us the ability to simultaneously explore four different dimensions of the data:\n", + "the (x, y) location of each point corresponds to the sepal length and width, the size of the point is related to the petal width, and the color is related to the particular species of flower.\n", + "Multicolor and multifeature scatter plots like this can be useful for both exploration and presentation of data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ``plot`` Versus ``scatter``: A Note on Efficiency\n", + "\n", + "Aside from the different features available in ``plt.plot`` and ``plt.scatter``, why might you choose to use one over the other? While it doesn't matter as much for small amounts of data, as datasets get larger than a few thousand points, ``plt.plot`` can be noticeably more efficient than ``plt.scatter``.\n", + "The reason is that ``plt.scatter`` has the capability to render a different size and/or color for each point, so the renderer must do the extra work of constructing each point individually.\n", + "In ``plt.plot``, on the other hand, the points are always essentially clones of each other, so the work of determining the appearance of the points is done only once for the entire set of data.\n", + "For large datasets, the difference between these two can lead to vastly different performance, and for this reason, ``plt.plot`` should be preferred over ``plt.scatter`` for large datasets." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Simple Line Plots](04.01-Simple-Line-Plots.ipynb) | [Contents](Index.ipynb) | [Visualizing Errors](04.03-Errorbars.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { diff --git a/code_listings/04.03-Errorbars.ipynb b/notebooks_v1/04.03-Errorbars.ipynb similarity index 85% rename from code_listings/04.03-Errorbars.ipynb rename to notebooks_v1/04.03-Errorbars.ipynb index 4c55851c1..094ae9c89 100644 --- a/code_listings/04.03-Errorbars.ipynb +++ b/notebooks_v1/04.03-Errorbars.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Simple Scatter Plots](04.02-Simple-Scatter-Plots.ipynb) | [Contents](Index.ipynb) | [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,28 @@ "# Visualizing Errors" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For any scientific measurement, accurate accounting for errors is nearly as important, if not more important, than accurate reporting of the number itself.\n", + "For example, imagine that I am using some astrophysical observations to estimate the Hubble Constant, the local measurement of the expansion rate of the Universe.\n", + "I know that the current literature suggests a value of around 71 (km/s)/Mpc, and I measure a value of 74 (km/s)/Mpc with my method. Are the values consistent? The only correct answer, given this information, is this: there is no way to know.\n", + "\n", + "Suppose I augment this information with reported uncertainties: the current literature suggests a value of around 71 $\\pm$ 2.5 (km/s)/Mpc, and my method has measured a value of 74 $\\pm$ 5 (km/s)/Mpc. Now are the values consistent? That is a question that can be quantitatively answered.\n", + "\n", + "In visualization of data and results, showing these errors effectively can make a plot convey much more complete information." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Basic Errorbars\n", + "\n", + "A basic errorbar can be created with a single Matplotlib function call:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -47,6 +91,17 @@ "plt.errorbar(x, y, yerr=dy, fmt='.k');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the ``fmt`` is a format code controlling the appearance of lines and points, and has the same syntax as the shorthand used in ``plt.plot``, outlined in [Simple Line Plots](04.01-Simple-Line-Plots.ipynb) and [Simple Scatter Plots](04.02-Simple-Scatter-Plots.ipynb).\n", + "\n", + "In addition to these basic options, the ``errorbar`` function has many options to fine-tune the outputs.\n", + "Using these additional options you can easily customize the aesthetics of your errorbar plot.\n", + "I often find it helpful, especially in crowded plots, to make the errorbars lighter than the points themselves:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -70,6 +125,28 @@ " ecolor='lightgray', elinewidth=3, capsize=0);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition to these options, you can also specify horizontal errorbars (``xerr``), one-sided errorbars, and many other variants.\n", + "For more information on the options available, refer to the docstring of ``plt.errorbar``." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Continuous Errors\n", + "\n", + "In some situations it is desirable to show errorbars on continuous quantities.\n", + "Though Matplotlib does not have a built-in convenience routine for this type of application, it's relatively easy to combine primitives like ``plt.plot`` and ``plt.fill_between`` for a useful result.\n", + "\n", + "Here we'll perform a simple *Gaussian process regression*, using the Scikit-Learn API (see [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) for details).\n", + "This is a method of fitting a very flexible non-parametric function to data with a continuous measure of the uncertainty.\n", + "We won't delve into the details of Gaussian process regression at this point, but will focus instead on how you might visualize such a continuous error measurement:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -95,6 +172,15 @@ "dyfit = 2 * np.sqrt(MSE) # 2*sigma ~ 95% confidence region" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have ``xfit``, ``yfit``, and ``dyfit``, which sample the continuous fit to our data.\n", + "We could pass these to the ``plt.errorbar`` function as above, but we don't really want to plot 1,000 points with 1,000 errorbars.\n", + "Instead, we can use the ``plt.fill_between`` function with a light color to visualize this continuous error:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -122,9 +208,34 @@ " color='gray', alpha=0.2)\n", "plt.xlim(0, 10);" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note what we've done here with the ``fill_between`` function: we pass an x value, then the lower y-bound, then the upper y-bound, and the result is that the area between these regions is filled.\n", + "\n", + "The resulting figure gives a very intuitive view into what the Gaussian process regression algorithm is doing: in regions near a measured data point, the model is strongly constrained and this is reflected in the small model errors.\n", + "In regions far from a measured data point, the model is not strongly constrained, and the model errors increase.\n", + "\n", + "For more information on the options available in ``plt.fill_between()`` (and the closely related ``plt.fill()`` function), see the function docstring or the Matplotlib documentation.\n", + "\n", + "Finally, if this seems a bit too low level for your taste, refer to [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb), where we discuss the Seaborn package, which has a more streamlined API for visualizing this type of continuous errorbar." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Simple Scatter Plots](04.02-Simple-Scatter-Plots.ipynb) | [Contents](Index.ipynb) | [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.04-Density-and-Contour-Plots.ipynb b/notebooks_v1/04.04-Density-and-Contour-Plots.ipynb similarity index 98% rename from code_listings/04.04-Density-and-Contour-Plots.ipynb rename to notebooks_v1/04.04-Density-and-Contour-Plots.ipynb index bf5dea560..3fea071b4 100644 --- a/code_listings/04.04-Density-and-Contour-Plots.ipynb +++ b/notebooks_v1/04.04-Density-and-Contour-Plots.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Visualizing Errors](04.03-Errorbars.ipynb) | [Contents](Index.ipynb) | [Histograms, Binnings, and Density](04.05-Histograms-and-Binnings.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,15 @@ "# Density and Contour Plots" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes it is useful to display three-dimensional data in two dimensions using contours or color-coded regions.\n", + "There are three Matplotlib functions that can be helpful for this task: ``plt.contour`` for contour plots, ``plt.contourf`` for filled contour plots, and ``plt.imshow`` for showing images.\n", + "This section looks at several examples of using these. We'll start by setting up the notebook for plotting and importing the functions we will use: " + ] + }, { "cell_type": "code", "execution_count": 1, @@ -21,6 +52,20 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Visualizing a Three-Dimensional Function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll start by demonstrating a contour plot using a function $z = f(x, y)$, using the following particular choice for $f$ (we've seen this before in [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb), when we used it as a motivating example for array broadcasting):" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -33,6 +78,16 @@ " return np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A contour plot can be created with the ``plt.contour`` function.\n", + "It takes three arguments: a grid of *x* values, a grid of *y* values, and a grid of *z* values.\n", + "The *x* and *y* values represent positions on the plot, and the *z* values will be represented by the contour levels.\n", + "Perhaps the most straightforward way to prepare such data is to use the ``np.meshgrid`` function, which builds two-dimensional grids from one-dimensional arrays:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -48,6 +103,13 @@ "Z = f(X, Y)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's look at this with a standard line-only contour plot:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -70,6 +132,15 @@ "plt.contour(X, Y, Z, colors='black');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that by default when a single color is used, negative values are represented by dashed lines, and positive values by solid lines.\n", + "Alternatively, the lines can be color-coded by specifying a colormap with the ``cmap`` argument.\n", + "Here, we'll also specify that we want more lines to be drawn—20 equally spaced intervals within the data range:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -92,6 +163,22 @@ "plt.contour(X, Y, Z, 20, cmap='RdGy');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we chose the ``RdGy`` (short for *Red-Gray*) colormap, which is a good choice for centered data.\n", + "Matplotlib has a wide range of colormaps available, which you can easily browse in IPython by doing a tab completion on the ``plt.cm`` module:\n", + "```\n", + "plt.cm.\n", + "```\n", + "\n", + "Our plot is looking nicer, but the spaces between the lines may be a bit distracting.\n", + "We can change this by switching to a filled contour plot using the ``plt.contourf()`` function (notice the ``f`` at the end), which uses largely the same syntax as ``plt.contour()``.\n", + "\n", + "Additionally, we'll add a ``plt.colorbar()`` command, which automatically creates an additional axis with labeled color information for the plot:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -115,6 +202,19 @@ "plt.colorbar();" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The colorbar makes it clear that the black regions are \"peaks,\" while the red regions are \"valleys.\"\n", + "\n", + "One potential issue with this plot is that it is a bit \"splotchy.\" That is, the color steps are discrete rather than continuous, which is not always what is desired.\n", + "This could be remedied by setting the number of contours to a very high number, but this results in a rather inefficient plot: Matplotlib must render a new polygon for each step in the level.\n", + "A better way to handle this is to use the ``plt.imshow()`` function, which interprets a two-dimensional grid of data as an image.\n", + "\n", + "The following code shows this:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -140,6 +240,25 @@ "plt.axis(aspect='image');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a few potential gotchas with ``imshow()``, however:\n", + "\n", + "- ``plt.imshow()`` doesn't accept an *x* and *y* grid, so you must manually specify the *extent* [*xmin*, *xmax*, *ymin*, *ymax*] of the image on the plot.\n", + "- ``plt.imshow()`` by default follows the standard image array definition where the origin is in the upper left, not in the lower left as in most contour plots. This must be changed when showing gridded data.\n", + "- ``plt.imshow()`` will automatically adjust the axis aspect ratio to match the input data; this can be changed by setting, for example, ``plt.axis(aspect='image')`` to make *x* and *y* units match." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, it can sometimes be useful to combine contour plots and image plots.\n", + "For example, here we'll use a partially transparent background image (with transparency set via the ``alpha`` parameter) and overplot contours with labels on the contours themselves (using the ``plt.clabel()`` function):" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -166,9 +285,29 @@ " cmap='RdGy', alpha=0.5)\n", "plt.colorbar();" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The combination of these three functions—``plt.contour``, ``plt.contourf``, and ``plt.imshow``—gives nearly limitless possibilities for displaying this sort of three-dimensional data within a two-dimensional plot.\n", + "For more information on the options available in these functions, refer to their docstrings.\n", + "If you are interested in three-dimensional visualizations of this type of data, see [Three-dimensional Plotting in Matplotlib](04.12-Three-Dimensional-Plotting.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Visualizing Errors](04.03-Errorbars.ipynb) | [Contents](Index.ipynb) | [Histograms, Binnings, and Density](04.05-Histograms-and-Binnings.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.05-Histograms-and-Binnings.ipynb b/notebooks_v1/04.05-Histograms-and-Binnings.ipynb similarity index 94% rename from code_listings/04.05-Histograms-and-Binnings.ipynb rename to notebooks_v1/04.05-Histograms-and-Binnings.ipynb index d05fab4b7..1873ff7c5 100644 --- a/code_listings/04.05-Histograms-and-Binnings.ipynb +++ b/notebooks_v1/04.05-Histograms-and-Binnings.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb) | [Contents](Index.ipynb) | [Customizing Plot Legends](04.06-Customizing-Legends.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,14 @@ "# Histograms, Binnings, and Density" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A simple histogram can be a great first step in understanding a dataset.\n", + "Earlier, we saw a preview of Matplotlib's histogram function (see [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb)), which creates a basic histogram in one line, once the normal boiler-plate imports are done:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -45,6 +75,14 @@ "plt.hist(data);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``hist()`` function has many options to tune both the calculation and the display; \n", + "here's an example of a more customized histogram:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -69,6 +107,14 @@ " edgecolor='none');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``plt.hist`` docstring has more information on other customization options available.\n", + "I find this combination of ``histtype='stepfilled'`` along with some transparency ``alpha`` to be very useful when comparing histograms of several distributions:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -99,6 +145,13 @@ "plt.hist(x3, **kwargs);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you would like to simply compute the histogram (that is, count the number of points in a given bin) and not display it, the ``np.histogram()`` function is available:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -119,6 +172,17 @@ "print(counts)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Two-Dimensional Histograms and Binnings\n", + "\n", + "Just as we create histograms in one dimension by dividing the number-line into bins, we can also create histograms in two-dimensions by dividing points among two-dimensional bins.\n", + "We'll take a brief look at several ways to do this here.\n", + "We'll start by defining some data—an ``x`` and ``y`` array drawn from a multivariate Gaussian distribution:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -132,6 +196,15 @@ "x, y = np.random.multivariate_normal(mean, cov, 10000).T" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ``plt.hist2d``: Two-dimensional histogram\n", + "\n", + "One straightforward way to plot a two-dimensional histogram is to use Matplotlib's ``plt.hist2d`` function:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -156,6 +229,14 @@ "cb.set_label('counts in bin')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as with ``plt.hist``, ``plt.hist2d`` has a number of extra options to fine-tune the plot and the binning, which are nicely outlined in the function docstring.\n", + "Further, just as ``plt.hist`` has a counterpart in ``np.histogram``, ``plt.hist2d`` has a counterpart in ``np.histogram2d``, which can be used as follows:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -167,6 +248,24 @@ "counts, xedges, yedges = np.histogram2d(x, y, bins=30)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the generalization of this histogram binning in dimensions higher than two, see the ``np.histogramdd`` function." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ``plt.hexbin``: Hexagonal binnings\n", + "\n", + "The two-dimensional histogram creates a tesselation of squares across the axes.\n", + "Another natural shape for such a tesselation is the regular hexagon.\n", + "For this purpose, Matplotlib provides the ``plt.hexbin`` routine, which will represents a two-dimensional dataset binned within a grid of hexagons:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -190,6 +289,25 @@ "cb = plt.colorbar(label='count in bin')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``plt.hexbin`` has a number of interesting options, including the ability to specify weights for each point, and to change the output in each bin to any NumPy aggregate (mean of weights, standard deviation of weights, etc.)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Kernel density estimation\n", + "\n", + "Another common method of evaluating densities in multiple dimensions is *kernel density estimation* (KDE).\n", + "This will be discussed more fully in [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb), but for now we'll simply mention that KDE can be thought of as a way to \"smear out\" the points in space and add up the result to obtain a smooth function.\n", + "One extremely quick and simple KDE implementation exists in the ``scipy.stats`` package.\n", + "Here is a quick example of using the KDE on this data:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -229,9 +347,32 @@ "cb = plt.colorbar()\n", "cb.set_label(\"density\")" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "KDE has a smoothing length that effectively slides the knob between detail and smoothness (one example of the ubiquitous bias–variance trade-off).\n", + "The literature on choosing an appropriate smoothing length is vast: ``gaussian_kde`` uses a rule-of-thumb to attempt to find a nearly optimal smoothing length for the input data.\n", + "\n", + "Other KDE implementations are available within the SciPy ecosystem, each with its own strengths and weaknesses; see, for example, ``sklearn.neighbors.KernelDensity`` and ``statsmodels.nonparametric.kernel_density.KDEMultivariate``.\n", + "For visualizations based on KDE, using Matplotlib tends to be overly verbose.\n", + "The Seaborn library, discussed in [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb), provides a much more terse API for creating KDE-based visualizations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb) | [Contents](Index.ipynb) | [Customizing Plot Legends](04.06-Customizing-Legends.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.06-Customizing-Legends.ipynb b/notebooks_v1/04.06-Customizing-Legends.ipynb similarity index 96% rename from code_listings/04.06-Customizing-Legends.ipynb rename to notebooks_v1/04.06-Customizing-Legends.ipynb index dc15f1056..ada12a045 100644 --- a/code_listings/04.06-Customizing-Legends.ipynb +++ b/notebooks_v1/04.06-Customizing-Legends.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Histograms, Binnings, and Density](04.05-Histograms-and-Binnings.ipynb) | [Contents](Index.ipynb) | [Customizing Colorbars](04.07-Customizing-Colorbars.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,16 @@ "# Customizing Plot Legends" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot legends give meaning to a visualization, assigning meaning to the various plot elements.\n", + "We previously saw how to create a simple legend; here we'll take a look at customizing the placement and aesthetics of the legend in Matplotlib.\n", + "\n", + "The simplest legend can be created with the ``plt.legend()`` command, which automatically creates a legend for any labeled plot elements:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -58,6 +90,14 @@ "leg = ax.legend();" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But there are many ways we might want to customize such a legend.\n", + "For example, we can specify the location and turn off the frame:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -82,6 +122,13 @@ "fig" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use the ``ncol`` command to specify the number of columns in the legend:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -106,6 +153,13 @@ "fig" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use a rounded box (``fancybox``) or add a shadow, change the transparency (alpha value) of the frame, or change the padding around the text:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -130,6 +184,25 @@ "fig" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on available legend options, see the ``plt.legend`` docstring." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choosing Elements for the Legend\n", + "\n", + "As we have already seen, the legend includes all labeled elements by default.\n", + "If this is not what is desired, we can fine-tune which elements and labels appear in the legend by using the objects returned by plot commands.\n", + "The ``plt.plot()`` command is able to create multiple lines at once, and returns a list of created line instances.\n", + "Passing any of these to ``plt.legend()`` will tell it which to identify, along with the labels we'd like to specify:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -156,6 +229,13 @@ "plt.legend(lines[:2], ['first', 'second']);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I generally find in practice that it is clearer to use the first method, applying labels to the plot elements you'd like to show on the legend:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -181,6 +261,25 @@ "plt.legend(framealpha=1, frameon=True);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that by default, the legend ignores all elements without a ``label`` attribute set." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Legend for Size of Points\n", + "\n", + "Sometimes the legend defaults are not sufficient for the given visualization.\n", + "For example, perhaps you're be using the size of points to mark certain features of the data, and want to create a legend reflecting this.\n", + "Here is an example where we'll use the size of points to indicate populations of California cities.\n", + "We'd like a legend that specifies the scale of the sizes of the points, and we'll accomplish this by plotting some labeled data with no entries:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -207,7 +306,7 @@ "lat, lon = cities['latd'], cities['longd']\n", "population, area = cities['population_total'], cities['area_total_km2']\n", "\n", - "# Scatter the points, using size & color & no label\n", + "# Scatter the points, using size and color but no label\n", "plt.scatter(lon, lat, label=None,\n", " c=np.log10(population), cmap='viridis',\n", " s=area, linewidth=0, alpha=0.5)\n", @@ -218,7 +317,7 @@ "plt.clim(3, 7)\n", "\n", "# Here we create a legend:\n", - "# we'll plot empty lists with the desired size & label\n", + "# we'll plot empty lists with the desired size and label\n", "for area in [100, 300, 500]:\n", " plt.scatter([], [], c='k', alpha=0.3, s=area,\n", " label=str(area) + ' km$^2$')\n", @@ -227,6 +326,33 @@ "plt.title('California Cities: Area and Population');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The legend will always reference some object that is on the plot, so if we'd like to display a particular shape we need to plot it.\n", + "In this case, the objects we want (gray circles) are not on the plot, so we fake them by plotting empty lists.\n", + "Notice too that the legend only lists plot elements that have a label specified.\n", + "\n", + "By plotting empty lists, we create labeled plot objects which are picked up by the legend, and now our legend tells us some useful information.\n", + "This strategy can be useful for creating more sophisticated visualizations.\n", + "\n", + "Finally, note that for geographic data like this, it would be clearer if we could show state boundaries or other map-specific elements.\n", + "For this, an excellent choice of tool is Matplotlib's Basemap addon toolkit, which we'll explore in [Geographic Data with Basemap](04.13-Geographic-Data-With-Basemap.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multiple Legends\n", + "\n", + "Sometimes when designing a plot you'd like to add multiple legends to the same axes.\n", + "Unfortunately, Matplotlib does not make this easy: via the standard ``legend`` interface, it is only possible to create a single legend for the entire plot.\n", + "If you try to create a second legend using ``plt.legend()`` or ``ax.legend()``, it will simply override the first one.\n", + "We can work around this by creating a new legend artist from scratch, and then using the lower-level ``ax.add_artist()`` method to manually add the second artist to the plot:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -267,9 +393,28 @@ " loc='lower right', frameon=False)\n", "ax.add_artist(leg);" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a peek into the low-level artist objects that comprise any Matplotlib plot.\n", + "If you examine the source code of ``ax.legend()`` (recall that you can do this with within the IPython notebook using ``ax.legend??``) you'll see that the function simply consists of some logic to create a suitable ``Legend`` artist, which is then saved in the ``legend_`` attribute and added to the figure when the plot is drawn." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Histograms, Binnings, and Density](04.05-Histograms-and-Binnings.ipynb) | [Contents](Index.ipynb) | [Customizing Colorbars](04.07-Customizing-Colorbars.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.07-Customizing-Colorbars.ipynb b/notebooks_v1/04.07-Customizing-Colorbars.ipynb similarity index 97% rename from code_listings/04.07-Customizing-Colorbars.ipynb rename to notebooks_v1/04.07-Customizing-Colorbars.ipynb index 20c96d408..6620f4a49 100644 --- a/code_listings/04.07-Customizing-Colorbars.ipynb +++ b/notebooks_v1/04.07-Customizing-Colorbars.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Customizing Plot Legends](04.06-Customizing-Legends.ipynb) | [Contents](Index.ipynb) | [Multiple Subplots](04.08-Multiple-Subplots.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,17 @@ "# Customizing Colorbars" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot legends identify discrete labels of discrete points.\n", + "For continuous labels based on the color of points, lines, or regions, a labeled colorbar can be a great tool.\n", + "In Matplotlib, a colorbar is a separate axes that can provide a key for the meaning of colors in a plot.\n", + "Because the book is printed in black-and-white, this section has an accompanying online supplement where you can view the figures in full color (https://github.com/jakevdp/PythonDataScienceHandbook).\n", + "We'll start by setting up the notebook for plotting and importing the functions we will use:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -31,6 +64,13 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we have seen several times throughout this section, the simplest colorbar can be created with the ``plt.colorbar`` function:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -57,6 +97,22 @@ "plt.colorbar();" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll now discuss a few ideas for customizing these colorbars and using them effectively in various situations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Customizing Colorbars\n", + "\n", + "The colormap can be specified using the ``cmap`` argument to the plotting function that is creating the visualization:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -79,6 +135,40 @@ "plt.imshow(I, cmap='gray');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All the available colormaps are in the ``plt.cm`` namespace; using IPython's tab-completion will give you a full list of built-in possibilities:\n", + "```\n", + "plt.cm.\n", + "```\n", + "But being *able* to choose a colormap is just the first step: more important is how to *decide* among the possibilities!\n", + "The choice turns out to be much more subtle than you might initially expect." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Choosing the Colormap\n", + "\n", + "A full treatment of color choice within visualization is beyond the scope of this book, but for entertaining reading on this subject and others, see the article [\"Ten Simple Rules for Better Figures\"](http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003833).\n", + "Matplotlib's online documentation also has an [interesting discussion](http://Matplotlib.org/1.4.1/users/colormaps.html) of colormap choice.\n", + "\n", + "Broadly, you should be aware of three different categories of colormaps:\n", + "\n", + "- *Sequential colormaps*: These are made up of one continuous sequence of colors (e.g., ``binary`` or ``viridis``).\n", + "- *Divergent colormaps*: These usually contain two distinct colors, which show positive and negative deviations from a mean (e.g., ``RdBu`` or ``PuOr``).\n", + "- *Qualitative colormaps*: these mix colors with no particular sequence (e.g., ``rainbow`` or ``jet``).\n", + "\n", + "The ``jet`` colormap, which was the default in Matplotlib prior to version 2.0, is an example of a qualitative colormap.\n", + "Its status as the default was quite unfortunate, because qualitative maps are often a poor choice for representing quantitative data.\n", + "Among the problems is the fact that qualitative maps usually do not display any uniform progression in brightness as the scale increases.\n", + "\n", + "We can see this by converting the ``jet`` colorbar into black and white:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -90,11 +180,11 @@ "from matplotlib.colors import LinearSegmentedColormap\n", "\n", "def grayscale_cmap(cmap):\n", - " \"\"\"Return a greyscale version of the given colormap\"\"\"\n", + " \"\"\"Return a grayscale version of the given colormap\"\"\"\n", " cmap = plt.cm.get_cmap(cmap)\n", " colors = cmap(np.arange(cmap.N))\n", " \n", - " # convert RGBA to perceived greyscale luminance\n", + " # convert RGBA to perceived grayscale luminance\n", " # cf. http://alienryderflex.com/hsp.html\n", " RGB_weight = [0.299, 0.587, 0.114]\n", " luminance = np.sqrt(np.dot(colors[:, :3] ** 2, RGB_weight))\n", @@ -104,7 +194,7 @@ " \n", "\n", "def view_colormap(cmap):\n", - " \"\"\"Plot a colormap with its greyscale equivalent\"\"\"\n", + " \"\"\"Plot a colormap with its grayscale equivalent\"\"\"\n", " cmap = plt.cm.get_cmap(cmap)\n", " colors = cmap(np.arange(cmap.N))\n", " \n", @@ -139,6 +229,16 @@ "view_colormap('jet')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the bright stripes in the grayscale image.\n", + "Even in full color, this uneven brightness means that the eye will be drawn to certain portions of the color range, which will potentially emphasize unimportant parts of the dataset.\n", + "It's better to use a colormap such as ``viridis`` (the default as of Matplotlib 2.0), which is specifically constructed to have an even brightness variation across the range.\n", + "Thus it not only plays well with our color perception, but also will translate well to grayscale printing:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -161,6 +261,13 @@ "view_colormap('viridis')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you favor rainbow schemes, another good option for continuous data is the ``cubehelix`` colormap:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -183,6 +290,13 @@ "view_colormap('cubehelix')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For other situations, such as showing positive and negative deviations from some mean, dual-color colorbars such as ``RdBu`` (*Red-Blue*) can be useful. However, as you can see in the following figure, it's important to note that the positive-negative information will be lost upon translation to grayscale!" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -205,6 +319,27 @@ "view_colormap('RdBu')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll see examples of using some of these color maps as we continue.\n", + "\n", + "There are a large number of colormaps available in Matplotlib; to see a list of them, you can use IPython to explore the ``plt.cm`` submodule. For a more principled approach to colors in Python, you can refer to the tools and documentation within the Seaborn library (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Color limits and extensions\n", + "\n", + "Matplotlib allows for a large range of colorbar customization.\n", + "The colorbar itself is simply an instance of ``plt.Axes``, so all of the axes and tick formatting tricks we've learned are applicable.\n", + "The colorbar has some interesting flexibility: for example, we can narrow the color limits and indicate the out-of-bounds values with a triangular arrow at the top and bottom by setting the ``extend`` property.\n", + "This might come in handy, for example, if displaying an image that is subject to noise:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -240,6 +375,25 @@ "plt.clim(-1, 1);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that in the left panel, the default color limits respond to the noisy pixels, and the range of the noise completely washes-out the pattern we are interested in.\n", + "In the right panel, we manually set the color limits, and add extensions to indicate values which are above or below those limits.\n", + "The result is a much more useful visualization of our data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Discrete Color Bars\n", + "\n", + "Colormaps are by default continuous, but sometimes you'd like to represent discrete values.\n", + "The easiest way to do this is to use the ``plt.cm.get_cmap()`` function, and pass the name of a suitable colormap along with the number of desired bins:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -264,6 +418,25 @@ "plt.clim(-1, 1);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The discrete version of a colormap can be used just like any other colormap." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Handwritten Digits\n", + "\n", + "For an example of where this might be useful, let's look at an interesting visualization of some hand written digits data.\n", + "This data is included in Scikit-Learn, and consists of nearly 2,000 $8 \\times 8$ thumbnails showing various hand-written digits.\n", + "\n", + "For now, let's start by downloading the digits data and visualizing several of the example images with ``plt.imshow()``:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -293,6 +466,18 @@ " axi.set(xticks=[], yticks=[])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because each digit is defined by the hue of its 64 pixels, we can consider each digit to be a point lying in 64-dimensional space: each dimension represents the brightness of one pixel.\n", + "But visualizing relationships in such high-dimensional spaces can be extremely difficult.\n", + "One way to approach this is to use a *dimensionality reduction* technique such as manifold learning to reduce the dimensionality of the data while maintaining the relationships of interest.\n", + "Dimensionality reduction is an example of unsupervised machine learning, and we will discuss it in more detail in [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb).\n", + "\n", + "Deferring the discussion of these details, let's take a look at a two-dimensional manifold learning projection of this digits data (see [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) for details):" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -307,6 +492,13 @@ "projection = iso.fit_transform(digits.data)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use our discrete colormap to view the results, setting the ``ticks`` and ``clim`` to improve the aesthetics of the resulting colorbar:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -332,9 +524,31 @@ "plt.colorbar(ticks=range(6), label='digit value')\n", "plt.clim(-0.5, 5.5)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The projection also gives us some interesting insights on the relationships within the dataset: for example, the ranges of 5 and 3 nearly overlap in this projection, indicating that some hand written fives and threes are difficult to distinguish, and therefore more likely to be confused by an automated classification algorithm.\n", + "Other values, like 0 and 1, are more distantly separated, and therefore much less likely to be confused.\n", + "This observation agrees with our intuition, because 5 and 3 look much more similar than do 0 and 1.\n", + "\n", + "We'll return to manifold learning and to digit classification in [Chapter 5](05.00-Machine-Learning.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Customizing Plot Legends](04.06-Customizing-Legends.ipynb) | [Contents](Index.ipynb) | [Multiple Subplots](04.08-Multiple-Subplots.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.08-Multiple-Subplots.ipynb b/notebooks_v1/04.08-Multiple-Subplots.ipynb similarity index 94% rename from code_listings/04.08-Multiple-Subplots.ipynb rename to notebooks_v1/04.08-Multiple-Subplots.ipynb index 1516a2429..e06195cfc 100644 --- a/code_listings/04.08-Multiple-Subplots.ipynb +++ b/notebooks_v1/04.08-Multiple-Subplots.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Customizing Colorbars](04.07-Customizing-Colorbars.ipynb) | [Contents](Index.ipynb) | [Text and Annotation](04.09-Text-and-Annotation.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,16 @@ "# Multiple Subplots" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes it is helpful to compare different views of data side by side.\n", + "To this end, Matplotlib has the concept of *subplots*: groups of smaller axes that can exist together within a single figure.\n", + "These subplots might be insets, grids of plots, or other more complicated layouts.\n", + "In this section we'll explore four routines for creating subplots in Matplotlib." + ] + }, { "cell_type": "code", "execution_count": 1, @@ -21,6 +53,20 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ``plt.axes``: Subplots by Hand\n", + "\n", + "The most basic method of creating an axes is to use the ``plt.axes`` function.\n", + "As we've seen previously, by default this creates a standard axes object that fills the entire figure.\n", + "``plt.axes`` also takes an optional argument that is a list of four numbers in the figure coordinate system.\n", + "These numbers represent ``[left, bottom, width, height]`` in the figure coordinate system, which ranges from 0 at the bottom left of the figure to 1 at the top right of the figure.\n", + "\n", + "For example, we might create an inset axes at the top-right corner of another axes by setting the *x* and *y* position to 0.65 (that is, starting at 65% of the width and 65% of the height of the figure) and the *x* and *y* extents to 0.2 (that is, the size of the axes is 20% of the width and 20% of the height of the figure):" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -44,6 +90,13 @@ "ax2 = plt.axes([0.65, 0.65, 0.2, 0.2])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The equivalent of this command within the object-oriented interface is ``fig.add_axes()``. Let's use this to create two vertically stacked axes:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -74,6 +127,24 @@ "ax2.plot(np.cos(x));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have two axes (the top with no tick labels) that are just touching: the bottom of the upper panel (at position 0.5) matches the top of the lower panel (at position 0.1 + 0.4)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ``plt.subplot``: Simple Grids of Subplots\n", + "\n", + "Aligned columns or rows of subplots are a common-enough need that Matplotlib has several convenience routines that make them easy to create.\n", + "The lowest level of these is ``plt.subplot()``, which creates a single subplot within a grid.\n", + "As you can see, this command takes three integer arguments—the number of rows, the number of columns, and the index of the plot to be created in this scheme, which runs from the upper left to the bottom right:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -99,6 +170,14 @@ " fontsize=18, ha='center')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The command ``plt.subplots_adjust`` can be used to adjust the spacing between these plots.\n", + "The following code uses the equivalent object-oriented command, ``fig.add_subplot()``:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -126,6 +205,26 @@ " fontsize=18, ha='center')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We've used the ``hspace`` and ``wspace`` arguments of ``plt.subplots_adjust``, which specify the spacing along the height and width of the figure, in units of the subplot size (in this case, the space is 40% of the subplot width and height)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ``plt.subplots``: The Whole Grid in One Go\n", + "\n", + "The approach just described can become quite tedious when creating a large grid of subplots, especially if you'd like to hide the x- and y-axis labels on the inner plots.\n", + "For this purpose, ``plt.subplots()`` is the easier tool to use (note the ``s`` at the end of ``subplots``). Rather than creating a single subplot, this function creates a full grid of subplots in a single line, returning them in a NumPy array.\n", + "The arguments are the number of rows and number of columns, along with optional keywords ``sharex`` and ``sharey``, which allow you to specify the relationships between different axes.\n", + "\n", + "Here we'll create a $2 \\times 3$ grid of subplots, where all axes in the same row share their y-axis scale, and all axes in the same column share their x-axis scale:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -148,6 +247,14 @@ "fig, ax = plt.subplots(2, 3, sharex='col', sharey='row')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that by specifying ``sharex`` and ``sharey``, we've automatically removed inner labels on the grid to make the plot cleaner.\n", + "The resulting grid of axes instances is returned within a NumPy array, allowing for convenient specification of the desired axes using standard array indexing notation:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -168,7 +275,7 @@ } ], "source": [ - "# axes are in a 2D array, indexed by [row, col]\n", + "# axes are in a two-dimensional array, indexed by [row, col]\n", "for i in range(2):\n", " for j in range(3):\n", " ax[i, j].text(0.5, 0.5, str((i, j)),\n", @@ -176,6 +283,24 @@ "fig" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In comparison to ``plt.subplot()``, ``plt.subplots()`` is more consistent with Python's conventional 0-based indexing." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ``plt.GridSpec``: More Complicated Arrangements\n", + "\n", + "To go beyond a regular grid to subplots that span multiple rows and columns, ``plt.GridSpec()`` is the best tool.\n", + "The ``plt.GridSpec()`` object does not create a plot by itself; it is simply a convenient interface that is recognized by the ``plt.subplot()`` command.\n", + "For example, a gridspec for a grid of two rows and three columns with some specified width and height space looks like this:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -187,6 +312,13 @@ "grid = plt.GridSpec(2, 3, wspace=0.4, hspace=0.3)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From this we can specify subplot locations and extents using the familiary Python slicing syntax:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -212,6 +344,14 @@ "plt.subplot(grid[1, 2]);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This type of flexible grid alignment has a wide range of uses.\n", + "I most often use it when creating multi-axes histogram plots like the ones shown here:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -255,9 +395,27 @@ " orientation='horizontal', color='gray')\n", "y_hist.invert_xaxis()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This type of distribution plotted alongside its margins is common enough that it has its own plotting API in the Seaborn package; see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb) for more details." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Customizing Colorbars](04.07-Customizing-Colorbars.ipynb) | [Contents](Index.ipynb) | [Text and Annotation](04.09-Text-and-Annotation.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/notebooks_v1/04.09-Text-and-Annotation.ipynb b/notebooks_v1/04.09-Text-and-Annotation.ipynb new file mode 100644 index 000000000..621eeaed3 --- /dev/null +++ b/notebooks_v1/04.09-Text-and-Annotation.ipynb @@ -0,0 +1,446 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Multiple Subplots](04.08-Multiple-Subplots.ipynb) | [Contents](Index.ipynb) | [Customizing Ticks](04.10-Customizing-Ticks.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Text and Annotation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Creating a good visualization involves guiding the reader so that the figure tells a story.\n", + "In some cases, this story can be told in an entirely visual manner, without the need for added text, but in others, small textual cues and labels are necessary.\n", + "Perhaps the most basic types of annotations you will use are axes labels and titles, but the options go beyond this.\n", + "Let's take a look at some data and how we might visualize and annotate it to help convey interesting information. We'll start by setting up the notebook for plotting and importing the functions we will use:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "plt.style.use('seaborn-whitegrid')\n", + "import numpy as np\n", + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Effect of Holidays on US Births\n", + "\n", + "Let's return to some data we worked with earler, in [\"Example: Birthrate Data\"](03.09-Pivot-Tables.ipynb#Example:-Birthrate-Data), where we generated a plot of average births over the course of the calendar year; as already mentioned, that this data can be downloaded at https://raw.githubusercontent.com/jakevdp/data-CDCbirths/master/births.csv.\n", + "\n", + "We'll start with the same cleaning procedure we used there, and plot the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "births = pd.read_csv('data/births.csv')\n", + "\n", + "quartiles = np.percentile(births['births'], [25, 50, 75])\n", + "mu, sig = quartiles[1], 0.74 * (quartiles[2] - quartiles[0])\n", + "births = births.query('(births > @mu - 5 * @sig) & (births < @mu + 5 * @sig)')\n", + "\n", + "births['day'] = births['day'].astype(int)\n", + "\n", + "births.index = pd.to_datetime(10000 * births.year +\n", + " 100 * births.month +\n", + " births.day, format='%Y%m%d')\n", + "births_by_date = births.pivot_table('births',\n", + " [births.index.month, births.index.day])\n", + "births_by_date.index = [pd.datetime(2012, month, day)\n", + " for (month, day) in births_by_date.index]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Gj1hIRUVRuTIpD64Ykwn47DPgr38Fhg2jiHFFhfJr/fILRWVGjaJkPzmuXgXOnDE32xg8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\narD2Gbudx5itFAzDMAzDMIwapIQxR4wZhmEYhmGYBoe1lYI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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(12, 4))\n", + "births_by_date.plot(ax=ax);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we're communicating data like this, it is often useful to annotate certain features of the plot to draw the reader's attention.\n", + "This can be done manually with the ``plt.text``/``ax.text`` command, which will place text at a particular x/y value:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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GIcaRI0DXrkCvXsD+/brXvXGDBJ9Qbq1pU5p4wZDjpKZSZDs4mDzYq1eT3YOm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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(12, 4))\n", + "births_by_date.plot(ax=ax)\n", + "\n", + "# Add labels to the plot\n", + "style = dict(size=10, color='gray')\n", + "\n", + "ax.text('2012-1-1', 3950, \"New Year's Day\", **style)\n", + "ax.text('2012-7-4', 4250, \"Independence Day\", ha='center', **style)\n", + "ax.text('2012-9-4', 4850, \"Labor Day\", ha='center', **style)\n", + "ax.text('2012-10-31', 4600, \"Halloween\", ha='right', **style)\n", + "ax.text('2012-11-25', 4450, \"Thanksgiving\", ha='center', **style)\n", + "ax.text('2012-12-25', 3850, \"Christmas \", ha='right', **style)\n", + "\n", + "# Label the axes\n", + "ax.set(title='USA births by day of year (1969-1988)',\n", + " ylabel='average daily births')\n", + "\n", + "# Format the x axis with centered month labels\n", + "ax.xaxis.set_major_locator(mpl.dates.MonthLocator())\n", + "ax.xaxis.set_minor_locator(mpl.dates.MonthLocator(bymonthday=15))\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.xaxis.set_minor_formatter(mpl.dates.DateFormatter('%h'));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ``ax.text`` method takes an x position, a y position, a string, and then optional keywords specifying the color, size, style, alignment, and other properties of the text.\n", + "Here we used ``ha='right'`` and ``ha='center'``, where ``ha`` is short for *horizonal alignment*.\n", + "See the docstring of ``plt.text()`` and of ``mpl.text.Text()`` for more information on available options." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Transforms and Text Position\n", + "\n", + "In the previous example, we have anchored our text annotations to data locations. Sometimes it's preferable to anchor the text to a position on the axes or figure, independent of the data. In Matplotlib, this is done by modifying the *transform*.\n", + "\n", + "Any graphics display framework needs some scheme for translating between coordinate systems.\n", + "For example, a data point at $(x, y) = (1, 1)$ needs to somehow be represented at a certain location on the figure, which in turn needs to be represented in pixels on the screen.\n", + "Mathematically, such coordinate transformations are relatively straightforward, and Matplotlib has a well-developed set of tools that it uses internally to perform them (these tools can be explored in the ``matplotlib.transforms`` submodule).\n", + "\n", + "The average user rarely needs to worry about the details of these transforms, but it is helpful knowledge to have when considering the placement of text on a figure. There are three pre-defined transforms that can be useful in this situation:\n", + "\n", + "- ``ax.transData``: Transform associated with data coordinates\n", + "- ``ax.transAxes``: Transform associated with the axes (in units of axes dimensions)\n", + "- ``fig.transFigure``: Transform associated with the figure (in units of figure dimensions)\n", + "\n", + "Here let's look at an example of drawing text at various locations using these transforms:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(facecolor='lightgray')\n", + "ax.axis([0, 10, 0, 10])\n", + "\n", + "# transform=ax.transData is the default, but we'll specify it anyway\n", + "ax.text(1, 5, \". Data: (1, 5)\", transform=ax.transData)\n", + "ax.text(0.5, 0.1, \". Axes: (0.5, 0.1)\", transform=ax.transAxes)\n", + "ax.text(0.2, 0.2, \". Figure: (0.2, 0.2)\", transform=fig.transFigure);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that by default, the text is aligned above and to the left of the specified coordinates: here the \".\" at the beginning of each string will approximately mark the given coordinate location.\n", + "\n", + "The ``transData`` coordinates give the usual data coordinates associated with the x- and y-axis labels.\n", + "The ``transAxes`` coordinates give the location from the bottom-left corner of the axes (here the white box), as a fraction of the axes size.\n", + "The ``transFigure`` coordinates are similar, but specify the position from the bottom-left of the figure (here the gray box), as a fraction of the figure size.\n", + "\n", + "Notice now that if we change the axes limits, it is only the ``transData`` coordinates that will be affected, while the others remain stationary:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.set_xlim(0, 2)\n", + "ax.set_ylim(-6, 6)\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This behavior can be seen more clearly by changing the axes limits interactively: if you are executing this code in a notebook, you can make that happen by changing ``%matplotlib inline`` to ``%matplotlib notebook`` and using each plot's menu to interact with the plot." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Arrows and Annotation\n", + "\n", + "Along with tick marks and text, another useful annotation mark is the simple arrow.\n", + "\n", + "Drawing arrows in Matplotlib is often much harder than you'd bargain for.\n", + "While there is a ``plt.arrow()`` function available, I wouldn't suggest using it: the arrows it creates are SVG objects that will be subject to the varying aspect ratio of your plots, and the result is rarely what the user intended.\n", + "Instead, I'd suggest using the ``plt.annotate()`` function.\n", + "This function creates some text and an arrow, and the arrows can be very flexibly specified.\n", + "\n", + "Here we'll use ``annotate`` with several of its options:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "x = np.linspace(0, 20, 1000)\n", + "ax.plot(x, np.cos(x))\n", + "ax.axis('equal')\n", + "\n", + "ax.annotate('local maximum', xy=(6.28, 1), xytext=(10, 4),\n", + " arrowprops=dict(facecolor='black', shrink=0.05))\n", + "\n", + "ax.annotate('local minimum', xy=(5 * np.pi, -1), xytext=(2, -6),\n", + " arrowprops=dict(arrowstyle=\"->\",\n", + " connectionstyle=\"angle3,angleA=0,angleB=-90\"));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The arrow style is controlled through the ``arrowprops`` dictionary, which has numerous options available.\n", + "These options are fairly well-documented in Matplotlib's online documentation, so rather than repeating them here it is probably more useful to quickly show some of the possibilities.\n", + "Let's demonstrate several of the possible options using the birthrate plot from before:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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UgRkI573atdOIjpaUa+5JhKG44AI5P/9c0rnJlVdKZPXkSflp0yb0NrfeKvmv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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(12, 4))\n", + "births_by_date.plot(ax=ax)\n", + "\n", + "# Add labels to the plot\n", + "ax.annotate(\"New Year's Day\", xy=('2012-1-1', 4100), xycoords='data',\n", + " xytext=(50, -30), textcoords='offset points',\n", + " arrowprops=dict(arrowstyle=\"->\",\n", + " connectionstyle=\"arc3,rad=-0.2\"))\n", + "\n", + "ax.annotate(\"Independence Day\", xy=('2012-7-4', 4250), xycoords='data',\n", + " bbox=dict(boxstyle=\"round\", fc=\"none\", ec=\"gray\"),\n", + " xytext=(10, -40), textcoords='offset points', ha='center',\n", + " arrowprops=dict(arrowstyle=\"->\"))\n", + "\n", + "ax.annotate('Labor Day', xy=('2012-9-4', 4850), xycoords='data', ha='center',\n", + " xytext=(0, -20), textcoords='offset points')\n", + "ax.annotate('', xy=('2012-9-1', 4850), xytext=('2012-9-7', 4850),\n", + " xycoords='data', textcoords='data',\n", + " arrowprops={'arrowstyle': '|-|,widthA=0.2,widthB=0.2', })\n", + "\n", + "ax.annotate('Halloween', xy=('2012-10-31', 4600), xycoords='data',\n", + " xytext=(-80, -40), textcoords='offset points',\n", + " arrowprops=dict(arrowstyle=\"fancy\",\n", + " fc=\"0.6\", ec=\"none\",\n", + " connectionstyle=\"angle3,angleA=0,angleB=-90\"))\n", + "\n", + "ax.annotate('Thanksgiving', xy=('2012-11-25', 4500), xycoords='data',\n", + " xytext=(-120, -60), textcoords='offset points',\n", + " bbox=dict(boxstyle=\"round4,pad=.5\", fc=\"0.9\"),\n", + " arrowprops=dict(arrowstyle=\"->\",\n", + " connectionstyle=\"angle,angleA=0,angleB=80,rad=20\"))\n", + "\n", + "\n", + "ax.annotate('Christmas', xy=('2012-12-25', 3850), xycoords='data',\n", + " xytext=(-30, 0), textcoords='offset points',\n", + " size=13, ha='right', va=\"center\",\n", + " bbox=dict(boxstyle=\"round\", alpha=0.1),\n", + " arrowprops=dict(arrowstyle=\"wedge,tail_width=0.5\", alpha=0.1));\n", + "\n", + "# Label the axes\n", + "ax.set(title='USA births by day of year (1969-1988)',\n", + " ylabel='average daily births')\n", + "\n", + "# Format the x axis with centered month labels\n", + "ax.xaxis.set_major_locator(mpl.dates.MonthLocator())\n", + "ax.xaxis.set_minor_locator(mpl.dates.MonthLocator(bymonthday=15))\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())\n", + "ax.xaxis.set_minor_formatter(mpl.dates.DateFormatter('%h'));\n", + "\n", + "ax.set_ylim(3600, 5400);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You'll notice that the specifications of the arrows and text boxes are very detailed: this gives you the power to create nearly any arrow style you wish.\n", + "Unfortunately, it also means that these sorts of features often must be manually tweaked, a process that can be very time consuming when producing publication-quality graphics!\n", + "Finally, I'll note that the preceding mix of styles is by no means best practice for presenting data, but rather included as a demonstration of some of the available options.\n", + "\n", + "More discussion and examples of available arrow and annotation styles can be found in the Matplotlib gallery, in particular the [Annotation Demo](http://matplotlib.org/examples/pylab_examples/annotation_demo2.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Multiple Subplots](04.08-Multiple-Subplots.ipynb) | [Contents](Index.ipynb) | [Customizing Ticks](04.10-Customizing-Ticks.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/04.10-Customizing-Ticks.ipynb b/notebooks_v1/04.10-Customizing-Ticks.ipynb new file mode 100644 index 000000000..b3b6a820c --- /dev/null +++ b/notebooks_v1/04.10-Customizing-Ticks.ipynb @@ -0,0 +1,508 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Text and Annotation](04.09-Text-and-Annotation.ipynb) | [Contents](Index.ipynb) | [Customizing Matplotlib: Configurations and Stylesheets](04.11-Settings-and-Stylesheets.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Customizing Ticks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matplotlib's default tick locators and formatters are designed to be generally sufficient in many common situations, but are in no way optimal for every plot. This section will give several examples of adjusting the tick locations and formatting for the particular plot type you're interested in.\n", + "\n", + "Before we go into examples, it will be best for us to understand further the object hierarchy of Matplotlib plots.\n", + "Matplotlib aims to have a Python object representing everything that appears on the plot: for example, recall that the ``figure`` is the bounding box within which plot elements appear.\n", + "Each Matplotlib object can also act as a container of sub-objects: for example, each ``figure`` can contain one or more ``axes`` objects, each of which in turn contain other objects representing plot contents.\n", + "\n", + "The tick marks are no exception. Each ``axes`` has attributes ``xaxis`` and ``yaxis``, which in turn have attributes that contain all the properties of the lines, ticks, and labels that make up the axes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Major and Minor Ticks\n", + "\n", + "Within each axis, there is the concept of a *major* tick mark, and a *minor* tick mark. As the names would imply, major ticks are usually bigger or more pronounced, while minor ticks are usually smaller. By default, Matplotlib rarely makes use of minor ticks, but one place you can see them is within logarithmic plots:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.style.use('classic')\n", + "%matplotlib inline\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes(xscale='log', yscale='log')\n", + "ax.grid();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see here that each major tick shows a large tickmark and a label, while each minor tick shows a smaller tickmark with no label.\n", + "\n", + "These tick properties—locations and labels—that is, can be customized by setting the ``formatter`` and ``locator`` objects of each axis. Let's examine these for the x axis of the just shown plot:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n" + ] + } + ], + "source": [ + "print(ax.xaxis.get_major_locator())\n", + "print(ax.xaxis.get_minor_locator())" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n" + ] + } + ], + "source": [ + "print(ax.xaxis.get_major_formatter())\n", + "print(ax.xaxis.get_minor_formatter())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that both major and minor tick labels have their locations specified by a ``LogLocator`` (which makes sense for a logarithmic plot). Minor ticks, though, have their labels formatted by a ``NullFormatter``: this says that no labels will be shown.\n", + "\n", + "We'll now show a few examples of setting these locators and formatters for various plots." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hiding Ticks or Labels\n", + "\n", + "Perhaps the most common tick/label formatting operation is the act of hiding ticks or labels.\n", + "This can be done using ``plt.NullLocator()`` and ``plt.NullFormatter()``, as shown here:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ax = plt.axes()\n", + "ax.plot(np.random.rand(50))\n", + "\n", + "ax.yaxis.set_major_locator(plt.NullLocator())\n", + "ax.xaxis.set_major_formatter(plt.NullFormatter())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that we've removed the labels (but kept the ticks/gridlines) from the x axis, and removed the ticks (and thus the labels as well) from the y axis.\n", + "Having no ticks at all can be useful in many situations—for example, when you want to show a grid of images.\n", + "For instance, consider the following figure, which includes images of different faces, an example often used in supervised machine learning problems (see, for example, [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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kZU5WRrArBJoix2R2b4whkJcZKFivXoyPmKJi6jz5ENi0LZtdLVjBMIBSFFUuLe5dS9u0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S5tk+s6TG9msoyqhbSOmtQ7slGsNWtEccij/hHttgzQ6+06vVMBeXbPJKFOb2dKGdY1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MqlqjPZxx+/Ye21dbdpiW2NxumI91QpzXu+5LBO9hvwf0/t6g1O7PaQiv5E2qDZVF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\ns7I4JVpHKCj4E5+mEf/76nxFlqQMp0OSKCFYhh3CGQQ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eh6YqKK6La1usNiGb+YY8zdFN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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(5, 5, figsize=(5, 5))\n", + "fig.subplots_adjust(hspace=0, wspace=0)\n", + "\n", + "# Get some face data from scikit-learn\n", + "from sklearn.datasets import fetch_olivetti_faces\n", + "faces = fetch_olivetti_faces().images\n", + "\n", + "for i in range(5):\n", + " for j in range(5):\n", + " ax[i, j].xaxis.set_major_locator(plt.NullLocator())\n", + " ax[i, j].yaxis.set_major_locator(plt.NullLocator())\n", + " ax[i, j].imshow(faces[10 * i + j], cmap=\"bone\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that each image has its own axes, and we've set the locators to null because the tick values (pixel number in this case) do not convey relevant information for this particular visualization." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reducing or Increasing the Number of Ticks\n", + "\n", + "One common problem with the default settings is that smaller subplots can end up with crowded labels.\n", + "We can see this in the plot grid shown here:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(4, 4, sharex=True, sharey=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Particularly for the x ticks, the numbers nearly overlap and make them quite difficult to decipher.\n", + "We can fix this with the ``plt.MaxNLocator()``, which allows us to specify the maximum number of ticks that will be displayed.\n", + "Given this maximum number, Matplotlib will use internal logic to choose the particular tick locations:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# For every axis, set the x and y major locator\n", + "for axi in ax.flat:\n", + " axi.xaxis.set_major_locator(plt.MaxNLocator(3))\n", + " axi.yaxis.set_major_locator(plt.MaxNLocator(3))\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This makes things much cleaner. If you want even more control over the locations of regularly-spaced ticks, you might also use ``plt.MultipleLocator``, which we'll discuss in the following section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fancy Tick Formats\n", + "\n", + "Matplotlib's default tick formatting can leave a lot to be desired: it works well as a broad default, but sometimes you'd like do do something more.\n", + "Consider this plot of a sine and a cosine:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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P/p2v/WhhrPPc9OwJrFtnHE4gJgbo2BE4eTL/+1I1ef/2G/D668a+x35+sh9p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\nTn1sgejMg5O3hrT1aYtDbx0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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot a sine and cosine curve\n", + "fig, ax = plt.subplots()\n", + "x = np.linspace(0, 3 * np.pi, 1000)\n", + "ax.plot(x, np.sin(x), lw=3, label='Sine')\n", + "ax.plot(x, np.cos(x), lw=3, label='Cosine')\n", + "\n", + "# Set up grid, legend, and limits\n", + "ax.grid(True)\n", + "ax.legend(frameon=False)\n", + "ax.axis('equal')\n", + "ax.set_xlim(0, 3 * np.pi);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a couple changes we might like to make. First, it's more natural for this data to space the ticks and grid lines in multiples of $\\pi$. We can do this by setting a ``MultipleLocator``, which locates ticks at a multiple of the number you provide. For good measure, we'll add both major and minor ticks in multiples of $\\pi/4$:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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dvniYVlGtnIbeT/kxoccErzP06em3di20b59s6ENDjeFxl6EHqFOqDssGLKN8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\ntNZ3/AOqpvj/RWBKBm21L/PZZ5+5W4Q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+ "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))\n", + "ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But now these tick labels look a little bit silly: we can see that they are multiples of $\\pi$, but the decimal representation does not immediately convey this.\n", + "To fix this, we can change the tick formatter. There's no built-in formatter for what we want to do, so we'll instead use ``plt.FuncFormatter``, which accepts a user-defined function giving fine-grained control over the tick outputs:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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9MvWxK3wXKnhWAAAkpycjbGkYVp5bmeNjHOm92bMnsH69aQiGe/eADh2AU6eU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\nVLsJNqXl+LQcG8DxFUbW9orpQ0SBRBR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+ "text/plain": [ + "" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def format_func(value, tick_number):\n", + " # find number of multiples of pi/2\n", + " N = int(np.round(2 * value / np.pi))\n", + " if N == 0:\n", + " return \"0\"\n", + " elif N == 1:\n", + " return r\"$\\pi/2$\"\n", + " elif N == 2:\n", + " return r\"$\\pi$\"\n", + " elif N % 2 > 0:\n", + " return r\"${0}\\pi/2$\".format(N)\n", + " else:\n", + " return r\"${0}\\pi$\".format(N // 2)\n", + "\n", + "ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is much better! Notice that we've made use of Matplotlib's LaTeX support, specified by enclosing the string within dollar signs. This is very convenient for display of mathematical symbols and formulae: in this case, ``\"$\\pi$\"`` is rendered as the Greek character $\\pi$.\n", + "\n", + "The ``plt.FuncFormatter()`` offers extremely fine-grained control over the appearance of your plot ticks, and comes in very handy when preparing plots for presentation or publication." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary of Formatters and Locators\n", + "\n", + "We've mentioned a couple of the available formatters and locators.\n", + "We'll conclude this section by briefly listing all the built-in locator and formatter options. For more information on any of these, refer to the docstrings or to the Matplotlib online documentaion.\n", + "Each of the following is available in the ``plt`` namespace:\n", + "\n", + "Locator class | Description\n", + "---------------------|-------------\n", + "``NullLocator`` | No ticks\n", + "``FixedLocator`` | Tick locations are fixed\n", + "``IndexLocator`` | Locator for index plots (e.g., where x = range(len(y)))\n", + "``LinearLocator`` | Evenly spaced ticks from min to max\n", + "``LogLocator`` | Logarithmically ticks from min to max\n", + "``MultipleLocator`` | Ticks and range are a multiple of base\n", + "``MaxNLocator`` | Finds up to a max number of ticks at nice locations\n", + "``AutoLocator`` | (Default.) MaxNLocator with simple defaults.\n", + "``AutoMinorLocator`` | Locator for minor ticks\n", + "\n", + "Formatter Class | Description\n", + "----------------------|---------------\n", + "``NullFormatter`` | No labels on the ticks\n", + "``IndexFormatter`` | Set the strings from a list of labels\n", + "``FixedFormatter`` | Set the strings manually for the labels\n", + "``FuncFormatter`` | User-defined function sets the labels\n", + "``FormatStrFormatter``| Use a format string for each value\n", + "``ScalarFormatter`` | (Default.) Formatter for scalar values\n", + "``LogFormatter`` | Default formatter for log axes\n", + "\n", + "We'll see further examples of these through the remainder of the book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Text and Annotation](04.09-Text-and-Annotation.ipynb) | [Contents](Index.ipynb) | [Customizing Matplotlib: Configurations and Stylesheets](04.11-Settings-and-Stylesheets.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/code_listings/04.11-Settings-and-Stylesheets.ipynb b/notebooks_v1/04.11-Settings-and-Stylesheets.ipynb similarity index 97% rename from code_listings/04.11-Settings-and-Stylesheets.ipynb rename to notebooks_v1/04.11-Settings-and-Stylesheets.ipynb index 02ef1c595..bc8b6bcde 100644 --- a/code_listings/04.11-Settings-and-Stylesheets.ipynb +++ b/notebooks_v1/04.11-Settings-and-Stylesheets.ipynb @@ -4,7 +4,50 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Customizing Matplotlib: Configurations and Style Sheets" + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Customizing Ticks](04.10-Customizing-Ticks.ipynb) | [Contents](Index.ipynb) | [Three-Dimensional Plotting in Matplotlib](04.12-Three-Dimensional-Plotting.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Customizing Matplotlib: Configurations and Stylesheets" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matplotlib's default plot settings are often the subject of complaint among its users.\n", + "While much is slated to change in the 2.0 Matplotlib release in late 2016, the ability to customize default settings helps bring the package inline with your own aesthetic preferences.\n", + "\n", + "Here we'll walk through some of Matplotlib's runtime configuration (rc) options, and take a look at the newer *stylesheets* feature, which contains some nice sets of default configurations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot Customization by Hand\n", + "\n", + "Through this chapter, we've seen how it is possible to tweak individual plot settings to end up with something that looks a little bit nicer than the default.\n", + "It's possible to do these customizations for each individual plot.\n", + "For example, here is a fairly drab default histogram:" ] }, { @@ -45,6 +88,13 @@ "plt.hist(x);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can adjust this by hand to make it a much more visually pleasing plot:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -90,6 +140,29 @@ "ax.hist(x, edgecolor='#E6E6E6', color='#EE6666');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks better, and you may recognize the look as inspired by the look of the R language's ggplot visualization package.\n", + "But this took a whole lot of effort!\n", + "We definitely do not want to have to do all that tweaking each time we create a plot.\n", + "Fortunately, there is a way to adjust these defaults once in a way that will work for all plots." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Changing the Defaults: ``rcParams``\n", + "\n", + "Each time Matplotlib loads, it defines a runtime configuration (rc) containing the default styles for every plot element you create.\n", + "This configuration can be adjusted at any time using the ``plt.rc`` convenience routine.\n", + "Let's see what it looks like to modify the rc parameters so that our default plot will look similar to what we did before.\n", + "\n", + "We'll start by saving a copy of the current ``rcParams`` dictionary, so we can easily reset these changes in the current session:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -101,6 +174,13 @@ "IPython_default = plt.rcParams.copy()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can use the ``plt.rc`` function to change some of these settings:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -122,6 +202,13 @@ "plt.rc('lines', linewidth=2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With these settings defined, we can now create a plot and see our settings in action:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -144,6 +231,13 @@ "plt.hist(x);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what simple line plots look like with these rc parameters:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -167,6 +261,28 @@ " plt.plot(np.random.rand(10))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I find this much more aesthetically pleasing than the default styling.\n", + "If you disagree with my aesthetic sense, the good news is that you can adjust the rc parameters to suit your own tastes!\n", + "These settings can be saved in a *.matplotlibrc* file, which you can read about in the [Matplotlib documentation](http://Matplotlib.org/users/customizing.html).\n", + "That said, I prefer to customize Matplotlib using its stylesheets instead." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Stylesheets\n", + "\n", + "The version 1.4 release of Matplotlib in August 2014 added a very convenient ``style`` module, which includes a number of new default stylesheets, as well as the ability to create and package your own styles. These stylesheets are formatted similarly to the *.matplotlibrc* files mentioned earlier, but must be named with a *.mplstyle* extension.\n", + "\n", + "Even if you don't create your own style, the stylesheets included by default are extremely useful.\n", + "The available styles are listed in ``plt.style.available``—here I'll list only the first five for brevity:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -193,6 +309,32 @@ "plt.style.available[:5]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The basic way to switch to a stylesheet is to call\n", + "\n", + "``` python\n", + "plt.style.use('stylename')\n", + "```\n", + "\n", + "But keep in mind that this will change the style for the rest of the session!\n", + "Alternatively, you can use the style context manager, which sets a style temporarily:\n", + "\n", + "``` python\n", + "with plt.style.context('stylename'):\n", + " make_a_plot()\n", + "```\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's create a function that will make two basic types of plot:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -210,6 +352,23 @@ " ax[1].legend(['a', 'b', 'c'], loc='lower left')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use this to explore how these plots look using the various built-in styles." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Default style\n", + "\n", + "The default style is what we've been seeing so far throughout the book; we'll start with that.\n", + "First, let's reset our runtime configuration to the notebook default:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -222,6 +381,13 @@ "plt.rcParams.update(IPython_default);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's see how it looks:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -244,6 +410,16 @@ "hist_and_lines()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### FiveThiryEight style\n", + "\n", + "The ``fivethirtyeight`` style mimics the graphics found on the popular [FiveThirtyEight website](https://fivethirtyeight.com).\n", + "As you can see here, it is typified by bold colors, thick lines, and transparent axes:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -267,6 +443,16 @@ " hist_and_lines()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ggplot\n", + "\n", + "The ``ggplot`` package in the R language is a very popular visualization tool.\n", + "Matplotlib's ``ggplot`` style mimics the default styles from that package:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -290,6 +476,16 @@ " hist_and_lines()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### *Bayesian Methods for Hackers( style\n", + "\n", + "There is a very nice short online book called [*Probabilistic Programming and Bayesian Methods for Hackers*](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/); it features figures created with Matplotlib, and uses a nice set of rc parameters to create a consistent and visually-appealing style throughout the book.\n", + "This style is reproduced in the ``bmh`` stylesheet:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -313,6 +509,16 @@ " hist_and_lines()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dark background\n", + "\n", + "For figures used within presentations, it is often useful to have a dark rather than light background.\n", + "The ``dark_background`` style provides this:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -336,6 +542,16 @@ " hist_and_lines()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Grayscale\n", + "\n", + "Sometimes you might find yourself preparing figures for a print publication that does not accept color figures.\n", + "For this, the ``grayscale`` style, shown here, can be very useful:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -359,6 +575,17 @@ " hist_and_lines()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Seaborn style\n", + "\n", + "Matplotlib also has stylesheets inspired by the Seaborn library (discussed more fully in [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)).\n", + "As we will see, these styles are loaded automatically when Seaborn is imported into a notebook.\n", + "I've found these settings to be very nice, and tend to use them as defaults in my own data exploration." + ] + }, { "cell_type": "code", "execution_count": 17, @@ -381,9 +608,28 @@ "import seaborn\n", "hist_and_lines()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With all of these built-in options for various plot styles, Matplotlib becomes much more useful for both interactive visualization and creation of figures for publication.\n", + "Throughout this book, I will generally use one or more of these style conventions when creating plots." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Customizing Ticks](04.10-Customizing-Ticks.ipynb) | [Contents](Index.ipynb) | [Three-Dimensional Plotting in Matplotlib](04.12-Three-Dimensional-Plotting.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.12-Three-Dimensional-Plotting.ipynb b/notebooks_v1/04.12-Three-Dimensional-Plotting.ipynb similarity index 98% rename from code_listings/04.12-Three-Dimensional-Plotting.ipynb rename to notebooks_v1/04.12-Three-Dimensional-Plotting.ipynb index 2eb8a1f64..ffdc3d875 100644 --- a/code_listings/04.12-Three-Dimensional-Plotting.ipynb +++ b/notebooks_v1/04.12-Three-Dimensional-Plotting.ipynb @@ -4,7 +4,38 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Three-dimensional Plotting in Matplotlib" + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Customizing Matplotlib: Configurations and Stylesheets](04.11-Settings-and-Stylesheets.ipynb) | [Contents](Index.ipynb) | [Geographic Data with Basemap](04.13-Geographic-Data-With-Basemap.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Three-Dimensional Plotting in Matplotlib" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matplotlib was initially designed with only two-dimensional plotting in mind.\n", + "Around the time of the 1.0 release, some three-dimensional plotting utilities were built on top of Matplotlib's two-dimensional display, and the result is a convenient (if somewhat limited) set of tools for three-dimensional data visualization.\n", + "three-dimensional plots are enabled by importing the ``mplot3d`` toolkit, included with the main Matplotlib installation:" ] }, { @@ -18,6 +49,13 @@ "from mpl_toolkits import mplot3d" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once this submodule is imported, a three-dimensional axes can be created by passing the keyword ``projection='3d'`` to any of the normal axes creation routines:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -54,6 +92,26 @@ "ax = plt.axes(projection='3d')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this three-dimensional axes enabled, we can now plot a variety of three-dimensional plot types. \n", + "Three-dimensional plotting is one of the functionalities that benefits immensely from viewing figures interactively rather than statically in the notebook; recall that to use interactive figures, you can use ``%matplotlib notebook`` rather than ``%matplotlib inline`` when running this code." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Three-dimensional Points and Lines\n", + "\n", + "The most basic three-dimensional plot is a line or collection of scatter plot created from sets of (x, y, z) triples.\n", + "In analogy with the more common two-dimensional plots discussed earlier, these can be created using the ``ax.plot3D`` and ``ax.scatter3D`` functions.\n", + "The call signature for these is nearly identical to that of their two-dimensional counterparts, so you can refer to [Simple Line Plots](04.01-Simple-Line-Plots.ipynb) and [Simple Scatter Plots](04.02-Simple-Scatter-Plots.ipynb) for more information on controlling the output.\n", + "Here we'll plot a trigonometric spiral, along with some points drawn randomly near the line:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -75,19 +133,38 @@ "source": [ "ax = plt.axes(projection='3d')\n", "\n", - "# Data for a 3D line\n", + "# Data for a three-dimensional line\n", "zline = np.linspace(0, 15, 1000)\n", "xline = np.sin(zline)\n", "yline = np.cos(zline)\n", "ax.plot3D(xline, yline, zline, 'gray')\n", "\n", - "# Data for 3D scattered points\n", + "# Data for three-dimensional scattered points\n", "zdata = 15 * np.random.random(100)\n", "xdata = np.sin(zdata) + 0.1 * np.random.randn(100)\n", "ydata = np.cos(zdata) + 0.1 * np.random.randn(100)\n", "ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Greens');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that by default, the scatter points have their transparency adjusted to give a sense of depth on the page.\n", + "While the three-dimensional effect is sometimes difficult to see within a static image, an interactive view can lead to some nice intuition about the layout of the points." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Three-dimensional Contour Plots\n", + "\n", + "Analogous to the contour plots we explored in [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb), ``mplot3d`` contains tools to create three-dimensional relief plots using the same inputs.\n", + "Like two-dimensional ``ax.contour`` plots, ``ax.contour3D`` requires all the input data to be in the form of two-dimensional regular grids, with the Z data evaluated at each point.\n", + "Here we'll show a three-dimensional contour diagram of a three-dimensional sinusoidal function:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -133,6 +210,13 @@ "ax.set_zlabel('z');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes the default viewing angle is not optimal, in which case we can use the ``view_init`` method to set the elevation and azimuthal angles. In the following example, we'll use an elevation of 60 degrees (that is, 60 degrees above the x-y plane) and an azimuth of 35 degrees (that is, rotated 35 degrees counter-clockwise about the z-axis):" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -157,6 +241,24 @@ "fig" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, note that this type of rotation can be accomplished interactively by clicking and dragging when using one of Matplotlib's interactive backends." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Wireframes and Surface Plots\n", + "\n", + "Two other types of three-dimensional plots that work on gridded data are wireframes and surface plots.\n", + "These take a grid of values and project it onto the specified three-dimensional surface, and can make the resulting three-dimensional forms quite easy to visualize.\n", + "Here's an example of using a wireframe:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -182,6 +284,14 @@ "ax.set_title('wireframe');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A surface plot is like a wireframe plot, but each face of the wireframe is a filled polygon.\n", + "Adding a colormap to the filled polygons can aid perception of the topology of the surface being visualized:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -207,6 +317,14 @@ "ax.set_title('surface');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that though the grid of values for a surface plot needs to be two-dimensional, it need not be rectilinear.\n", + "Here is an example of creating a partial polar grid, which when used with the ``surface3D`` plot can give us a slice into the function we're visualizing:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -239,6 +357,17 @@ " cmap='viridis', edgecolor='none');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Surface Triangulations\n", + "\n", + "For some applications, the evenly sampled grids required by the above routines is overly restrictive and inconvenient.\n", + "In these situations, the triangulation-based plots can be very useful.\n", + "What if rather than an even draw from a Cartesian or a polar grid, we instead have a set of random draws?" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -254,6 +383,13 @@ "z = f(x, y)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We could create a scatter plot of the points to get an idea of the surface we're sampling from:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -277,6 +413,14 @@ "ax.scatter(x, y, z, c=z, cmap='viridis', linewidth=0.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This leaves a lot to be desired.\n", + "The function that will help us in this case is ``ax.plot_trisurf``, which creates a surface by first finding a set of triangles formed between adjacent points (remember that x, y, and z here are one-dimensional arrays):" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -301,6 +445,26 @@ " cmap='viridis', edgecolor='none');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is certainly not as clean as when it is plotted with a grid, but the flexibility of such a triangulation allows for some really interesting three-dimensional plots.\n", + "For example, it is actually possible to plot a three-dimensional Möbius strip using this, as we'll see next." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example: Visualizing a Möbius strip\n", + "\n", + "A Möbius strip is similar to a strip of paper glued into a loop with a half-twist.\n", + "Topologically, it's quite interesting because despite appearances it has only a single side!\n", + "Here we will visualize such an object using Matplotlib's three-dimensional tools.\n", + "The key to creating the Möbius strip is to think about it's parametrization: it's a two-dimensional strip, so we need two intrinsic dimensions. Let's call them $\\theta$, which ranges from $0$ to $2\\pi$ around the loop, and $w$ which ranges from -1 to 1 across the width of the strip:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -314,6 +478,15 @@ "w, theta = np.meshgrid(w, theta)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now from this parametrization, we must determine the *(x, y, z)* positions of the embedded strip.\n", + "\n", + "Thinking about it, we might realize that there are two rotations happening: one is the position of the loop about its center (what we've called $\\theta$), while the other is the twisting of the strip about its axis (we'll call this $\\phi$). For a Möbius strip, we must have the strip makes half a twist during a full loop, or $\\Delta\\phi = \\Delta\\theta/2$." + ] + }, { "cell_type": "code", "execution_count": 15, @@ -325,6 +498,14 @@ "phi = 0.5 * theta" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we use our recollection of trigonometry to derive the three-dimensional embedding.\n", + "We'll define $r$, the distance of each point from the center, and use this to find the embedded $(x, y, z)$ coordinates:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -341,6 +522,14 @@ "z = np.ravel(w * np.sin(phi))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, to plot the object, we must make sure the triangulation is correct. The best way to do this is to define the triangulation *within the underlying parametrization*, and then let Matplotlib project this triangulation into the three-dimensional space of the Möbius strip.\n", + "This can be accomplished as follows:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -370,9 +559,27 @@ "\n", "ax.set_xlim(-1, 1); ax.set_ylim(-1, 1); ax.set_zlim(-1, 1);" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Combining all of these techniques, it is possible to create and display a wide variety of three-dimensional objects and patterns in Matplotlib." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Customizing Matplotlib: Configurations and Stylesheets](04.11-Settings-and-Stylesheets.ipynb) | [Contents](Index.ipynb) | [Geographic Data with Basemap](04.13-Geographic-Data-With-Basemap.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/04.13-Geographic-Data-With-Basemap.ipynb b/notebooks_v1/04.13-Geographic-Data-With-Basemap.ipynb similarity index 99% rename from code_listings/04.13-Geographic-Data-With-Basemap.ipynb rename to notebooks_v1/04.13-Geographic-Data-With-Basemap.ipynb index 45a8992f5..b724893ad 100644 --- a/code_listings/04.13-Geographic-Data-With-Basemap.ipynb +++ b/notebooks_v1/04.13-Geographic-Data-With-Basemap.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Three-Dimensional Plotting in Matplotlib](04.12-Three-Dimensional-Plotting.ipynb) | [Contents](Index.ipynb) | [Visualization with Seaborn](04.14-Visualization-With-Seaborn.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,26 @@ "# Geographic Data with Basemap" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One common type of visualization in data science is that of geographic data.\n", + "Matplotlib's main tool for this type of visualization is the Basemap toolkit, which is one of several Matplotlib toolkits which lives under the ``mpl_toolkits`` namespace.\n", + "Admittedly, Basemap feels a bit clunky to use, and often even simple visualizations take much longer to render than you might hope.\n", + "More modern solutions such as leaflet or the Google Maps API may be a better choice for more intensive map visualizations.\n", + "Still, Basemap is a useful tool for Python users to have in their virtual toolbelts.\n", + "In this section, we'll show several examples of the type of map visualization that is possible with this toolkit.\n", + "\n", + "Installation of Basemap is straightforward; if you're using conda you can type this and the package will be downloaded:\n", + "\n", + "```\n", + "$ conda install basemap\n", + "```\n", + "\n", + "We add just a single new import to our standard boilerplate:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -21,6 +63,13 @@ "from mpl_toolkits.basemap import Basemap" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once you have the Basemap toolkit installed and imported, geographic plots are just a few lines away (the graphics in the following also requires the ``PIL`` package in Python 2, or the ``pillow`` package in Python 3):" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -45,6 +94,17 @@ "m.bluemarble(scale=0.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The meaning of the arguments to ``Basemap`` will be discussed momentarily.\n", + "\n", + "The useful thing is that the globe shown here is not a mere image; it is a fully-functioning Matplotlib axes that understands spherical coordinates and which allows us to easily overplot data on the map!\n", + "For example, we can use a different map projection, zoom-in to North America and plot the location of Seattle.\n", + "We'll use an etopo image (which shows topographical features both on land and under the ocean) as the map background:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -76,6 +136,32 @@ "plt.text(x, y, ' Seattle', fontsize=12);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives you a brief glimpse into the sort of geographic visualizations that are possible with just a few lines of Python.\n", + "We'll now discuss the features of Basemap in more depth, and provide several examples of visualizing map data.\n", + "Using these brief examples as building blocks, you should be able to create nearly any map visualization that you desire." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Map Projections\n", + "\n", + "The first thing to decide when using maps is what projection to use.\n", + "You're probably familiar with the fact that it is impossible to project a spherical map, such as that of the Earth, onto a flat surface without somehow distorting it or breaking its continuity.\n", + "These projections have been developed over the course of human history, and there are a lot of choices!\n", + "Depending on the intended use of the map projection, there are certain map features (e.g., direction, area, distance, shape, or other considerations) that are useful to maintain.\n", + "\n", + "The Basemap package implements several dozen such projections, all referenced by a short format code.\n", + "Here we'll briefly demonstrate some of the more common ones.\n", + "\n", + "We'll start by defining a convenience routine to draw our world map along with the longitude and latitude lines:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -104,6 +190,19 @@ " line.set(linestyle='-', alpha=0.3, color='w')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Cylindrical projections\n", + "\n", + "The simplest of map projections are cylindrical projections, in which lines of constant latitude and longitude are mapped to horizontal and vertical lines, respectively.\n", + "This type of mapping represents equatorial regions quite well, but results in extreme distortions near the poles.\n", + "The spacing of latitude lines varies between different cylindrical projections, leading to different conservation properties, and different distortion near the poles.\n", + "In the following figure we show an example of the *equidistant cylindrical projection*, which chooses a latitude scaling that preserves distances along meridians.\n", + "Other cylindrical projections are the Mercator (``projection='merc'``) and the cylindrical equal area (``projection='cea'``) projections." + ] + }, { "cell_type": "code", "execution_count": 5, @@ -130,6 +229,25 @@ "draw_map(m)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The additional arguments to Basemap for this view specify the latitude (``lat``) and longitude (``lon``) of the lower-left corner (``llcrnr``) and upper-right corner (``urcrnr``) for the desired map, in units of degrees." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Pseudo-cylindrical projections\n", + "\n", + "Pseudo-cylindrical projections relax the requirement that meridians (lines of constant longitude) remain vertical; this can give better properties near the poles of the projection.\n", + "The Mollweide projection (``projection='moll'``) is one common example of this, in which all meridians are elliptical arcs.\n", + "It is constructed so as to preserve area across the map: though there are distortions near the poles, the area of small patches reflects the true area.\n", + "Other pseudo-cylindrical projections are the sinusoidal (``projection='sinu'``) and Robinson (``projection='robin'``) projections." + ] + }, { "cell_type": "code", "execution_count": 6, @@ -155,6 +273,27 @@ "draw_map(m)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The extra arguments to Basemap here refer to the central latitude (``lat_0``) and longitude (``lon_0``) for the desired map." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Perspective projections\n", + "\n", + "Perspective projections are constructed using a particular choice of perspective point, similar to if you photographed the Earth from a particular point in space (a point which, for some projections, technically lies within the Earth!).\n", + "One common example is the orthographic projection (``projection='ortho'``), which shows one side of the globe as seen from a viewer at a very long distance. As such, it can show only half the globe at a time.\n", + "Other perspective-based projections include the gnomonic projection (``projection='gnom'``) and stereographic projection (``projection='stere'``).\n", + "These are often the most useful for showing small portions of the map.\n", + "\n", + "Here is an example of the orthographic projection:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -180,6 +319,20 @@ "draw_map(m);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conic projections\n", + "\n", + "A Conic projection projects the map onto a single cone, which is then unrolled.\n", + "This can lead to very good local properties, but regions far from the focus point of the cone may become very distorted.\n", + "One example of this is the Lambert Conformal Conic projection (``projection='lcc'``), which we saw earlier in the map of North America.\n", + "It projects the map onto a cone arranged in such a way that two standard parallels (specified in Basemap by ``lat_1`` and ``lat_2``) have well-represented distances, with scale decreasing between them and increasing outside of them.\n", + "Other useful conic projections are the equidistant conic projection (``projection='eqdc'``) and the Albers equal-area projection (``projection='aea'``).\n", + "Conic projections, like perspective projections, tend to be good choices for representing small to medium patches of the globe." + ] + }, { "cell_type": "code", "execution_count": 8, @@ -206,6 +359,60 @@ "draw_map(m)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Other projections\n", + "\n", + "If you're going to do much with map-based visualizations, I encourage you to read up on other available projections, along with their properties, advantages, and disadvantages.\n", + "Most likely, they are available in the [Basemap package](http://matplotlib.org/basemap/users/mapsetup.html).\n", + "If you dig deep enough into this topic, you'll find an incredible subculture of geo-viz geeks who will be ready to argue fervently in support of their favorite projection for any given application! " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Drawing a Map Background\n", + "\n", + "Earlier we saw the ``bluemarble()`` and ``shadedrelief()`` methods for projecting global images on the map, as well as the ``drawparallels()`` and ``drawmeridians()`` methods for drawing lines of constant latitude and longitude.\n", + "The Basemap package contains a range of useful functions for drawing borders of physical features like continents, oceans, lakes, and rivers, as well as political boundaries such as countries and US states and counties.\n", + "The following are some of the available drawing functions that you may wish to explore using IPython's help features:\n", + "\n", + "- **Physical boundaries and bodies of water**\n", + " - ``drawcoastlines()``: Draw continental coast lines\n", + " - ``drawlsmask()``: Draw a mask between the land and sea, for use with projecting images on one or the other\n", + " - ``drawmapboundary()``: Draw the map boundary, including the fill color for oceans.\n", + " - ``drawrivers()``: Draw rivers on the map\n", + " - ``fillcontinents()``: Fill the continents with a given color; optionally fill lakes with another color\n", + "\n", + "- **Political boundaries**\n", + " - ``drawcountries()``: Draw country boundaries\n", + " - ``drawstates()``: Draw US state boundaries\n", + " - ``drawcounties()``: Draw US county boundaries\n", + "\n", + "- **Map features**\n", + " - ``drawgreatcircle()``: Draw a great circle between two points\n", + " - ``drawparallels()``: Draw lines of constant latitude\n", + " - ``drawmeridians()``: Draw lines of constant longitude\n", + " - ``drawmapscale()``: Draw a linear scale on the map\n", + "\n", + "- **Whole-globe images**\n", + " - ``bluemarble()``: Project NASA's blue marble image onto the map\n", + " - ``shadedrelief()``: Project a shaded relief image onto the map\n", + " - ``etopo()``: Draw an etopo relief image onto the map\n", + " - ``warpimage()``: Project a user-provided image onto the map\n", + "\n", + "For the boundary-based features, you must set the desired resolution when creating a Basemap image.\n", + "The ``resolution`` argument of the ``Basemap`` class sets the level of detail in boundaries, either ``'c'`` (crude), ``'l'`` (low), ``'i'`` (intermediate), ``'h'`` (high), ``'f'`` (full), or ``None`` if no boundaries will be used.\n", + "This choice is important: setting high-resolution boundaries on a global map, for example, can be *very* slow.\n", + "\n", + "Here's an example of drawing land/sea boundaries, and the effect of the resolution parameter.\n", + "We'll create both a low- and high-resolution map of Scotland's beautiful Isle of Skye.\n", + "It's located at 57.3°N, 6.2°W, and a map of 90,000 × 120,000 kilometers shows it well:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -236,6 +443,54 @@ " ax[i].set_title(\"resolution='{0}'\".format(res));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the low-resolution coastlines are not suitable for this level of zoom, while high-resolution works just fine.\n", + "The low level would work just fine for a global view, however, and would be *much* faster than loading the high-resolution border data for the entire globe!\n", + "It might require some experimentation to find the correct resolution parameter for a given view: the best route is to start with a fast, low-resolution plot and increase the resolution as needed." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plotting Data on Maps\n", + "\n", + "Perhaps the most useful piece of the Basemap toolkit is the ability to over-plot a variety of data onto a map background.\n", + "For simple plotting and text, any ``plt`` function works on the map; you can use the ``Basemap`` instance to project latitude and longitude coordinates to ``(x, y)`` coordinates for plotting with ``plt``, as we saw earlier in the Seattle example.\n", + "\n", + "In addition to this, there are many map-specific functions available as methods of the ``Basemap`` instance.\n", + "These work very similarly to their standard Matplotlib counterparts, but have an additional Boolean argument ``latlon``, which if set to ``True`` allows you to pass raw latitudes and longitudes to the method, rather than projected ``(x, y)`` coordinates.\n", + "\n", + "Some of these map-specific methods are:\n", + "\n", + "- ``contour()``/``contourf()`` : Draw contour lines or filled contours\n", + "- ``imshow()``: Draw an image\n", + "- ``pcolor()``/``pcolormesh()`` : Draw a pseudocolor plot for irregular/regular meshes\n", + "- ``plot()``: Draw lines and/or markers.\n", + "- ``scatter()``: Draw points with markers.\n", + "- ``quiver()``: Draw vectors.\n", + "- ``barbs()``: Draw wind barbs.\n", + "- ``drawgreatcircle()``: Draw a great circle.\n", + "\n", + "We'll see some examples of a few of these as we continue.\n", + "For more information on these functions, including several example plots, see the [online Basemap documentation](http://matplotlib.org/basemap/)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: California Cities\n", + "\n", + "Recall that in [Customizing Plot Legends](04.06-Customizing-Legends.ipynb), we demonstrated the use of size and color in a scatter plot to convey information about the location, size, and population of California cities.\n", + "Here, we'll create this plot again, but using Basemap to put the data in context.\n", + "\n", + "We start with loading the data, as we did before:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -254,6 +509,13 @@ "area = cities['area_total_km2'].values" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we set up the map projection, scatter the data, and then create a colorbar and legend:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -301,6 +563,25 @@ " labelspacing=1, loc='lower left');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This shows us roughly where larger populations of people have settled in California: they are clustered near the coast in the Los Angeles and San Francisco areas, stretched along the highways in the flat central valley, and avoiding almost completely the mountainous regions along the borders of the state." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Surface Temperature Data\n", + "\n", + "As an example of visualizing some more continuous geographic data, let's consider the \"polar vortex\" that hit the eastern half of the United States in January of 2014.\n", + "A great source for any sort of climatic data is [NASA's Goddard Institute for Space Studies](http://data.giss.nasa.gov/).\n", + "Here we'll use the GIS 250 temperature data, which we can download using shell commands (these commands may have to be modified on Windows machines).\n", + "The data used here was downloaded on 6/12/2016, and the file size is approximately 9MB:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -313,6 +594,20 @@ "# !gunzip gistemp250.nc.gz" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The data comes in NetCDF format, which can be read in Python by the ``netCDF4`` library.\n", + "You can install this library as shown here\n", + "\n", + "```\n", + "$ conda install netcdf4\n", + "```\n", + "\n", + "We read the data as follows:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -325,6 +620,13 @@ "data = Dataset('gistemp250.nc')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The file contains many global temperature readings on a variety of dates; we need to select the index of the date we're interested in—in this case, January 15, 2014:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -339,6 +641,13 @@ " data.variables['time'])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can load the latitude and longitude data, as well as the temperature anomaly for this index:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -353,6 +662,16 @@ "temp_anomaly = data.variables['tempanomaly'][timeindex]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we'll use the ``pcolormesh()`` method to draw a color mesh of the data.\n", + "We'll look at North America, and use a shaded relief map in the background.\n", + "Note that for this data we specifically chose a divergent colormap, which has a neutral color at zero and two contrasting colors at negative and positive values.\n", + "We'll also lightly draw the coastlines over the colors for reference:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -385,6 +704,25 @@ "plt.title('January 2014 Temperature Anomaly')\n", "plt.colorbar(label='temperature anomaly (°C)');" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The data paints a picture of the localized, extreme temperature anomalies that happened during that month.\n", + "The eastern half of the United States was much colder than normal, while the western half and Alaska were much warmer.\n", + "Regions with no recorded temperature show the map background." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Three-Dimensional Plotting in Matplotlib](04.12-Three-Dimensional-Plotting.ipynb) | [Contents](Index.ipynb) | [Visualization with Seaborn](04.14-Visualization-With-Seaborn.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { diff --git a/code_listings/04.14-Visualization-With-Seaborn.ipynb b/notebooks_v1/04.14-Visualization-With-Seaborn.ipynb similarity index 98% rename from code_listings/04.14-Visualization-With-Seaborn.ipynb rename to notebooks_v1/04.14-Visualization-With-Seaborn.ipynb index 3add9c5e5..21817be21 100644 --- a/code_listings/04.14-Visualization-With-Seaborn.ipynb +++ b/notebooks_v1/04.14-Visualization-With-Seaborn.ipynb @@ -4,7 +4,57 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Visualization With Seaborn" + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Geographic Data with Basemap](04.13-Geographic-Data-With-Basemap.ipynb) | [Contents](Index.ipynb) | [Further Resources](04.15-Further-Resources.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Visualization with Seaborn" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Matplotlib has proven to be an incredibly useful and popular visualization tool, but even avid users will admit it often leaves much to be desired.\n", + "There are several valid complaints about Matplotlib that often come up:\n", + "\n", + "- Prior to version 2.0, Matplotlib's defaults are not exactly the best choices. It was based off of MATLAB circa 1999, and this often shows.\n", + "- Matplotlib's API is relatively low level. Doing sophisticated statistical visualization is possible, but often requires a *lot* of boilerplate code.\n", + "- Matplotlib predated Pandas by more than a decade, and thus is not designed for use with Pandas ``DataFrame``s. In order to visualize data from a Pandas ``DataFrame``, you must extract each ``Series`` and often concatenate them together into the right format. It would be nicer to have a plotting library that can intelligently use the ``DataFrame`` labels in a plot.\n", + "\n", + "An answer to these problems is [Seaborn](http://seaborn.pydata.org/). Seaborn provides an API on top of Matplotlib that offers sane choices for plot style and color defaults, defines simple high-level functions for common statistical plot types, and integrates with the functionality provided by Pandas ``DataFrame``s.\n", + "\n", + "To be fair, the Matplotlib team is addressing this: it has recently added the ``plt.style`` tools discussed in [Customizing Matplotlib: Configurations and Style Sheets](04.11-Settings-and-Stylesheets.ipynb), and is starting to handle Pandas data more seamlessly.\n", + "The 2.0 release of the library will include a new default stylesheet that will improve on the current status quo.\n", + "But for all the reasons just discussed, Seaborn remains an extremely useful addon." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Seaborn Versus Matplotlib\n", + "\n", + "Here is an example of a simple random-walk plot in Matplotlib, using its classic plot formatting and colors.\n", + "We start with the typical imports:" ] }, { @@ -22,6 +72,13 @@ "import pandas as pd" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we create some random walk data:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -36,6 +93,13 @@ "y = np.cumsum(rng.randn(500, 6), 0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And do a simple plot:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -55,11 +119,23 @@ } ], "source": [ - "# Plot the data with matplotlib defaults\n", + "# Plot the data with Matplotlib defaults\n", "plt.plot(x, y)\n", "plt.legend('ABCDEF', ncol=2, loc='upper left');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Although the result contains all the information we'd like it to convey, it does so in a way that is not all that aesthetically pleasing, and even looks a bit old-fashioned in the context of 21st-century data visualization.\n", + "\n", + "Now let's take a look at how it works with Seaborn.\n", + "As we will see, Seaborn has many of its own high-level plotting routines, but it can also overwrite Matplotlib's default parameters and in turn get even simple Matplotlib scripts to produce vastly superior output.\n", + "We can set the style by calling Seaborn's ``set()`` method.\n", + "By convention, Seaborn is imported as ``sns``:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -72,6 +148,13 @@ "sns.set()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's rerun the same two lines as before:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -96,6 +179,34 @@ "plt.legend('ABCDEF', ncol=2, loc='upper left');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ah, much better!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exploring Seaborn Plots\n", + "\n", + "The main idea of Seaborn is that it provides high-level commands to create a variety of plot types useful for statistical data exploration, and even some statistical model fitting.\n", + "\n", + "Let's take a look at a few of the datasets and plot types available in Seaborn. Note that all of the following *could* be done using raw Matplotlib commands (this is, in fact, what Seaborn does under the hood) but the Seaborn API is much more convenient." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Histograms, KDE, and densities\n", + "\n", + "Often in statistical data visualization, all you want is to plot histograms and joint distributions of variables.\n", + "We have seen that this is relatively straightforward in Matplotlib:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -122,6 +233,13 @@ " plt.hist(data[col], normed=True, alpha=0.5)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Rather than a histogram, we can get a smooth estimate of the distribution using a kernel density estimation, which Seaborn does with ``sns.kdeplot``:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -145,6 +263,13 @@ " sns.kdeplot(data[col], shade=True)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Histograms and KDE can be combined using ``distplot``:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -168,6 +293,13 @@ "sns.distplot(data['y']);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we pass the full two-dimensional dataset to ``kdeplot``, we will get a two-dimensional visualization of the data:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -190,6 +322,14 @@ "sns.kdeplot(data);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see the joint distribution and the marginal distributions together using ``sns.jointplot``.\n", + "For this plot, we'll set the style to a white background:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -213,6 +353,13 @@ " sns.jointplot(\"x\", \"y\", data, kind='kde');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are other parameters that can be passed to ``jointplot``—for example, we can use a hexagonally based histogram instead:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -236,6 +383,17 @@ " sns.jointplot(\"x\", \"y\", data, kind='hex')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Pair plots\n", + "\n", + "When you generalize joint plots to datasets of larger dimensions, you end up with *pair plots*. This is very useful for exploring correlations between multidimensional data, when you'd like to plot all pairs of values against each other.\n", + "\n", + "We'll demo this with the well-known Iris dataset, which lists measurements of petals and sepals of three iris species:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -322,6 +480,13 @@ "iris.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualizing the multidimensional relationships among the samples is as easy as calling ``sns.pairplot``:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -344,6 +509,16 @@ "sns.pairplot(iris, hue='species', size=2.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Faceted histograms\n", + "\n", + "Sometimes the best way to view data is via histograms of subsets. Seaborn's ``FacetGrid`` makes this extremely simple.\n", + "We'll take a look at some data that shows the amount that restaurant staff receive in tips based on various indicator data:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -467,6 +642,15 @@ "grid.map(plt.hist, \"tip_pct\", bins=np.linspace(0, 40, 15));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Factor plots\n", + "\n", + "Factor plots can be useful for this kind of visualization as well. This allows you to view the distribution of a parameter within bins defined by any other parameter:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -491,6 +675,15 @@ " g.set_axis_labels(\"Day\", \"Total Bill\");" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Joint distributions\n", + "\n", + "Similar to the pairplot we saw earlier, we can use ``sns.jointplot`` to show the joint distribution between different datasets, along with the associated marginal distributions:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -514,6 +707,13 @@ " sns.jointplot(\"total_bill\", \"tip\", data=tips, kind='hex')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The joint plot can even do some automatic kernel density estimation and regression:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -536,6 +736,15 @@ "sns.jointplot(\"total_bill\", \"tip\", data=tips, kind='reg');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Bar plots\n", + "\n", + "Time series can be plotted using ``sns.factorplot``. In the following example, we'll use the Planets data that we first saw in [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb):" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -653,6 +862,13 @@ " g.set_xticklabels(step=5)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can learn more by looking at the *method* of discovery of each of these planets:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -678,6 +894,27 @@ " g.set_ylabels('Number of Planets Discovered')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For more information on plotting with Seaborn, see the [Seaborn documentation](http://seaborn.pydata.org/), a [tutorial](http://seaborn.pydata.org/\n", + "tutorial.htm), and the [Seaborn gallery](http://seaborn.pydata.org/examples/index.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Exploring Marathon Finishing Times\n", + "\n", + "Here we'll look at using Seaborn to help visualize and understand finishing results from a marathon.\n", + "I've scraped the data from sources on the Web, aggregated it and removed any identifying information, and put it on GitHub where it can be downloaded\n", + "(if you are interested in using Python for web scraping, I would recommend [*Web Scraping with Python*](http://shop.oreilly.com/product/0636920034391.do) by Ryan Mitchell).\n", + "We will start by downloading the data from\n", + "the Web, and loading it into Pandas:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -769,6 +1006,13 @@ "data.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By default, Pandas loaded the time columns as Python strings (type ``object``); we can see this by looking at the ``dtypes`` attribute of the DataFrame:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -795,6 +1039,13 @@ "data.dtypes" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's fix this by providing a converter for the times:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -871,9 +1122,11 @@ } ], "source": [ + "import datetime\n", + "\n", "def convert_time(s):\n", " h, m, s = map(int, s.split(':'))\n", - " return pd.datetools.timedelta(hours=h, minutes=m, seconds=s)\n", + " return datetime.timedelta(hours=h, minutes=m, seconds=s)\n", "\n", "data = pd.read_csv('marathon-data.csv',\n", " converters={'split':convert_time, 'final':convert_time})\n", @@ -906,6 +1159,13 @@ "data.dtypes" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks much better. For the purpose of our Seaborn plotting utilities, let's next add columns that give the times in seconds:" + ] + }, { "cell_type": "code", "execution_count": 27, @@ -999,6 +1259,13 @@ "data.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get an idea of what the data looks like, we can plot a ``jointplot`` over the data:" + ] + }, { "cell_type": "code", "execution_count": 28, @@ -1024,6 +1291,16 @@ " np.linspace(8000, 32000), ':k')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The dotted line shows where someone's time would lie if they ran the marathon at a perfectly steady pace. The fact that the distribution lies above this indicates (as you might expect) that most people slow down over the course of the marathon.\n", + "If you have run competitively, you'll know that those who do the opposite—run faster during the second half of the race—are said to have \"negative-split\" the race.\n", + "\n", + "Let's create another column in the data, the split fraction, which measures the degree to which each runner negative-splits or positive-splits the race:" + ] + }, { "cell_type": "code", "execution_count": 29, @@ -1122,6 +1399,14 @@ "data.head()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Where this split difference is less than zero, the person negative-split the race by that fraction.\n", + "Let's do a distribution plot of this split fraction:" + ] + }, { "cell_type": "code", "execution_count": 30, @@ -1167,6 +1452,15 @@ "sum(data.split_frac < 0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Out of nearly 40,000 participants, there were only 250 people who negative-split their marathon.\n", + "\n", + "Let's see whether there is any correlation between this split fraction and other variables. We'll do this using a ``pairgrid``, which draws plots of all these correlations:" + ] + }, { "cell_type": "code", "execution_count": 32, @@ -1192,6 +1486,16 @@ "g.add_legend();" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It looks like the split fraction does not correlate particularly with age, but does correlate with the final time: faster runners tend to have closer to even splits on their marathon time.\n", + "(We see here that Seaborn is no panacea for Matplotlib's ills when it comes to plot styles: in particular, the x-axis labels overlap. Because the output is a simple Matplotlib plot, however, the methods in [Customizing Ticks](04.10-Customizing-Ticks.ipynb) can be used to adjust such things if desired.)\n", + "\n", + "The difference between men and women here is interesting. Let's look at the histogram of split fractions for these two groups:" + ] + }, { "cell_type": "code", "execution_count": 33, @@ -1216,6 +1520,16 @@ "plt.xlabel('split_frac');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The interesting thing here is that there are many more men than women who are running close to an even split!\n", + "This almost looks like some kind of bimodal distribution among the men and women. Let's see if we can suss-out what's going on by looking at the distributions as a function of age.\n", + "\n", + "A nice way to compare distributions is to use a *violin plot*" + ] + }, { "cell_type": "code", "execution_count": 34, @@ -1235,7 +1549,17 @@ } ], "source": [ - "sns.violinplot(\"gender\", \"split_frac\", data=data, palette=[\"lightblue\", \"lightpink\"]);" + "sns.violinplot(\"gender\", \"split_frac\", data=data,\n", + " palette=[\"lightblue\", \"lightpink\"]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is yet another way to compare the distributions between men and women.\n", + "\n", + "Let's look a little deeper, and compare these violin plots as a function of age. We'll start by creating a new column in the array that specifies the decade of age that each person is in:" ] }, { @@ -1366,7 +1690,17 @@ "\n", "with sns.axes_style(style=None):\n", " sns.violinplot(\"age_dec\", \"split_frac\", hue=\"gender\", data=data,\n", - " split=True, inner=\"quartile\", palette=[\"lightblue\", \"lightpink\"]);" + " split=True, inner=\"quartile\",\n", + " palette=[\"lightblue\", \"lightpink\"]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at this, we can see where the distributions of men and women differ: the split distributions of men in their 20s to 50s show a pronounced over-density toward lower splits when compared to women of the same age (or of any age, for that matter).\n", + "\n", + "Also surprisingly, the 80-year-old women seem to outperform *everyone* in terms of their split time. This is probably due to the fact that we're estimating the distribution from small numbers, as there are only a handful of runners in that range:" ] }, { @@ -1391,6 +1725,13 @@ "(data.age > 80).sum()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Back to the men with negative splits: who are these runners? Does this split fraction correlate with finishing quickly? We can plot this very easily. We'll use ``regplot``, which will automatically fit a linear regression to the data:" + ] + }, { "cell_type": "code", "execution_count": 37, @@ -1414,9 +1755,27 @@ " markers=\".\", scatter_kws=dict(color='c'))\n", "g.map(plt.axhline, y=0.1, color=\"k\", ls=\":\");" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Apparently the people with fast splits are the elite runners who are finishing within ~15,000 seconds, or about 4 hours. People slower than that are much less likely to have a fast second split." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Geographic Data with Basemap](04.13-Geographic-Data-With-Basemap.ipynb) | [Contents](Index.ipynb) | [Further Resources](04.15-Further-Resources.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/notebooks_v1/04.15-Further-Resources.ipynb b/notebooks_v1/04.15-Further-Resources.ipynb new file mode 100644 index 000000000..4aed29225 --- /dev/null +++ b/notebooks_v1/04.15-Further-Resources.ipynb @@ -0,0 +1,97 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Visualization with Seaborn](04.14-Visualization-With-Seaborn.ipynb) | [Contents](Index.ipynb) | [Machine Learning](05.00-Machine-Learning.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Further Resources" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Matplotlib Resources\n", + "\n", + "A single chapter in a book can never hope to cover all the available features and plot types available in Matplotlib.\n", + "As with other packages we've seen, liberal use of IPython's tab-completion and help functions (see [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)) can be very helpful when exploring Matplotlib's API.\n", + "In addition, Matplotlib’s [online documentation](http://matplotlib.org/) can be a helpful reference.\n", + "See in particular the [Matplotlib gallery](http://matplotlib.org/gallery.html) linked on that page: it shows thumbnails of hundreds of different plot types, each one linked to a page with the Python code snippet used to generate it.\n", + "In this way, you can visually inspect and learn about a wide range of different plotting styles and visualization techniques.\n", + "\n", + "For a book-length treatment of Matplotlib, I would recommend [*Interactive Applications Using Matplotlib*](https://www.packtpub.com/application-development/interactive-applications-using-matplotlib), written by Matplotlib core developer Ben Root." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Other Python Graphics Libraries\n", + "\n", + "Although Matplotlib is the most prominent Python visualization library, there are other more modern tools that are worth exploring as well.\n", + "I'll mention a few of them briefly here:\n", + "\n", + "- [Bokeh](http://bokeh.pydata.org) is a JavaScript visualization library with a Python frontend that creates highly interactive visualizations capable of handling very large and/or streaming datasets. The Python front-end outputs a JSON data structure that can be interpreted by the Bokeh JS engine.\n", + "- [Plotly](http://plot.ly) is the eponymous open source product of the Plotly company, and is similar in spirit to Bokeh. Because Plotly is the main product of a startup, it is receiving a high level of development effort. Use of the library is entirely free.\n", + "- [Vispy](http://vispy.org/) is an actively developed project focused on dynamic visualizations of very large datasets. Because it is built to target OpenGL and make use of efficient graphics processors in your computer, it is able to render some quite large and stunning visualizations.\n", + "- [Vega](https://vega.github.io/) and [Vega-Lite](https://vega.github.io/vega-lite) are declarative graphics representations, and are the product of years of research into the fundamental language of data visualization. The reference rendering implementation is JavaScript, but the API is language agnostic. There is a Python API under development in the [Altair](https://altair-viz.github.io/) package. Though as of summer 2016 it's not yet fully mature, I'm quite excited for the possibilities of this project to provide a common reference point for visualization in Python and other languages.\n", + "\n", + "The visualization space in the Python community is very dynamic, and I fully expect this list to be out of date as soon as it is published.\n", + "Keep an eye out for what's coming in the future!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Visualization with Seaborn](04.14-Visualization-With-Seaborn.ipynb) | [Contents](Index.ipynb) | [Machine Learning](05.00-Machine-Learning.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/05.00-Machine-Learning.ipynb b/notebooks_v1/05.00-Machine-Learning.ipynb new file mode 100644 index 000000000..caff9877c --- /dev/null +++ b/notebooks_v1/05.00-Machine-Learning.ipynb @@ -0,0 +1,91 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Further Resources](04.15-Further-Resources.ipynb) | [Contents](Index.ipynb) | [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Machine Learning" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In many ways, machine learning is the primary means by which data science manifests itself to the broader world.\n", + "Machine learning is where these computational and algorithmic skills of data science meet the statistical thinking of data science, and the result is a collection of approaches to inference and data exploration that are not about effective theory so much as effective computation.\n", + "\n", + "The term \"machine learning\" is sometimes thrown around as if it is some kind of magic pill: *apply machine learning to your data, and all your problems will be solved!*\n", + "As you might expect, the reality is rarely this simple.\n", + "While these methods can be incredibly powerful, to be effective they must be approached with a firm grasp of the strengths and weaknesses of each method, as well as a grasp of general concepts such as bias and variance, overfitting and underfitting, and more.\n", + "\n", + "This chapter will dive into practical aspects of machine learning, primarily using Python's [Scikit-Learn](http://scikit-learn.org) package.\n", + "This is not meant to be a comprehensive introduction to the field of machine learning; that is a large subject and necessitates a more technical approach than we take here.\n", + "Nor is it meant to be a comprehensive manual for the use of the Scikit-Learn package (for this, you can refer to the resources listed in [Further Machine Learning Resources](05.15-Learning-More.ipynb)).\n", + "Rather, the goals of this chapter are:\n", + "\n", + "- To introduce the fundamental vocabulary and concepts of machine learning.\n", + "- To introduce the Scikit-Learn API and show some examples of its use.\n", + "- To take a deeper dive into the details of several of the most important machine learning approaches, and develop an intuition into how they work and when and where they are applicable.\n", + "\n", + "Much of this material is drawn from the Scikit-Learn tutorials and workshops I have given on several occasions at PyCon, SciPy, PyData, and other conferences.\n", + "Any clarity in the following pages is likely due to the many workshop participants and co-instructors who have given me valuable feedback on this material over the years!\n", + "\n", + "Finally, if you are seeking a more comprehensive or technical treatment of any of these subjects, I've listed several resources and references in [Further Machine Learning Resources](05.15-Learning-More.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [Further Resources](04.15-Further-Resources.ipynb) | [Contents](Index.ipynb) | [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/05.01-What-Is-Machine-Learning.ipynb b/notebooks_v1/05.01-What-Is-Machine-Learning.ipynb new file mode 100644 index 000000000..1dd061dae --- /dev/null +++ b/notebooks_v1/05.01-What-Is-Machine-Learning.ipynb @@ -0,0 +1,512 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Machine Learning](05.00-Machine-Learning.ipynb) | [Contents](Index.ipynb) | [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# What Is Machine Learning?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Before we take a look at the details of various machine learning methods, let's start by looking at what machine learning is, and what it isn't.\n", + "Machine learning is often categorized as a subfield of artificial intelligence, but I find that categorization can often be misleading at first brush.\n", + "The study of machine learning certainly arose from research in this context, but in the data science application of machine learning methods, it's more helpful to think of machine learning as a means of *building models of data*.\n", + "\n", + "Fundamentally, machine learning involves building mathematical models to help understand data.\n", + "\"Learning\" enters the fray when we give these models *tunable parameters* that can be adapted to observed data; in this way the program can be considered to be \"learning\" from the data.\n", + "Once these models have been fit to previously seen data, they can be used to predict and understand aspects of newly observed data.\n", + "I'll leave to the reader the more philosophical digression regarding the extent to which this type of mathematical, model-based \"learning\" is similar to the \"learning\" exhibited by the human brain.\n", + "\n", + "Understanding the problem setting in machine learning is essential to using these tools effectively, and so we will start with some broad categorizations of the types of approaches we'll discuss here." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Categories of Machine Learning\n", + "\n", + "At the most fundamental level, machine learning can be categorized into two main types: supervised learning and unsupervised learning.\n", + "\n", + "*Supervised learning* involves somehow modeling the relationship between measured features of data and some label associated with the data; once this model is determined, it can be used to apply labels to new, unknown data.\n", + "This is further subdivided into *classification* tasks and *regression* tasks: in classification, the labels are discrete categories, while in regression, the labels are continuous quantities.\n", + "We will see examples of both types of supervised learning in the following section.\n", + "\n", + "*Unsupervised learning* involves modeling the features of a dataset without reference to any label, and is often described as \"letting the dataset speak for itself.\"\n", + "These models include tasks such as *clustering* and *dimensionality reduction.*\n", + "Clustering algorithms identify distinct groups of data, while dimensionality reduction algorithms search for more succinct representations of the data.\n", + "We will see examples of both types of unsupervised learning in the following section.\n", + "\n", + "In addition, there are so-called *semi-supervised learning* methods, which falls somewhere between supervised learning and unsupervised learning.\n", + "Semi-supervised learning methods are often useful when only incomplete labels are available." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Qualitative Examples of Machine Learning Applications\n", + "\n", + "To make these ideas more concrete, let's take a look at a few very simple examples of a machine learning task.\n", + "These examples are meant to give an intuitive, non-quantitative overview of the types of machine learning tasks we will be looking at in this chapter.\n", + "In later sections, we will go into more depth regarding the particular models and how they are used.\n", + "For a preview of these more technical aspects, you can find the Python source that generates the following figures in the [Appendix: Figure Code](06.00-Figure-Code.ipynb).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Classification: Predicting discrete labels\n", + "\n", + "We will first take a look at a simple *classification* task, in which you are given a set of labeled points and want to use these to classify some unlabeled points.\n", + "\n", + "Imagine that we have the data shown in this figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-classification-1.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Classification-Example-Figure-1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here we have two-dimensional data: that is, we have two *features* for each point, represented by the *(x,y)* positions of the points on the plane.\n", + "In addition, we have one of two *class labels* for each point, here represented by the colors of the points.\n", + "From these features and labels, we would like to create a model that will let us decide whether a new point should be labeled \"blue\" or \"red.\"\n", + "\n", + "There are a number of possible models for such a classification task, but here we will use an extremely simple one. We will make the assumption that the two groups can be separated by drawing a straight line through the plane between them, such that points on each side of the line fall in the same group.\n", + "Here the *model* is a quantitative version of the statement \"a straight line separates the classes\", while the *model parameters* are the particular numbers describing the location and orientation of that line for our data.\n", + "The optimal values for these model parameters are learned from the data (this is the \"learning\" in machine learning), which is often called *training the model*.\n", + "\n", + "The following figure shows a visual representation of what the trained model looks like for this data:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-classification-2.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Classification-Example-Figure-2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now that this model has been trained, it can be generalized to new, unlabeled data.\n", + "In other words, we can take a new set of data, draw this model line through it, and assign labels to the new points based on this model.\n", + "This stage is usually called *prediction*. See the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-classification-3.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Classification-Example-Figure-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This is the basic idea of a classification task in machine learning, where \"classification\" indicates that the data has discrete class labels.\n", + "At first glance this may look fairly trivial: it would be relatively easy to simply look at this data and draw such a discriminatory line to accomplish this classification.\n", + "A benefit of the machine learning approach, however, is that it can generalize to much larger datasets in many more dimensions.\n", + "\n", + "For example, this is similar to the task of automated spam detection for email; in this case, we might use the following features and labels:\n", + "\n", + "- *feature 1*, *feature 2*, etc. $\\to$ normalized counts of important words or phrases (\"Viagra\", \"Nigerian prince\", etc.)\n", + "- *label* $\\to$ \"spam\" or \"not spam\"\n", + "\n", + "For the training set, these labels might be determined by individual inspection of a small representative sample of emails; for the remaining emails, the label would be determined using the model.\n", + "For a suitably trained classification algorithm with enough well-constructed features (typically thousands or millions of words or phrases), this type of approach can be very effective.\n", + "We will see an example of such text-based classification in [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb).\n", + "\n", + "Some important classification algorithms that we will discuss in more detail are Gaussian naive Bayes (see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)), support vector machines (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)), and random forest classification (see [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Regression: Predicting continuous labels\n", + "\n", + "In contrast with the discrete labels of a classification algorithm, we will next look at a simple *regression* task in which the labels are continuous quantities.\n", + "\n", + "Consider the data shown in the following figure, which consists of a set of points each with a continuous label:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-regression-1.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Regression-Example-Figure-1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As with the classification example, we have two-dimensional data: that is, there are two features describing each data point.\n", + "The color of each point represents the continuous label for that point.\n", + "\n", + "There are a number of possible regression models we might use for this type of data, but here we will use a simple linear regression to predict the points.\n", + "This simple linear regression model assumes that if we treat the label as a third spatial dimension, we can fit a plane to the data.\n", + "This is a higher-level generalization of the well-known problem of fitting a line to data with two coordinates.\n", + "\n", + "We can visualize this setup as shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-regression-2.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Regression-Example-Figure-2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that the *feature 1-feature 2* plane here is the same as in the two-dimensional plot from before; in this case, however, we have represented the labels by both color and three-dimensional axis position.\n", + "From this view, it seems reasonable that fitting a plane through this three-dimensional data would allow us to predict the expected label for any set of input parameters.\n", + "Returning to the two-dimensional projection, when we fit such a plane we get the result shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-regression-3.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Regression-Example-Figure-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This plane of fit gives us what we need to predict labels for new points.\n", + "Visually, we find the results shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-regression-4.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Regression-Example-Figure-4)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As with the classification example, this may seem rather trivial in a low number of dimensions.\n", + "But the power of these methods is that they can be straightforwardly applied and evaluated in the case of data with many, many features.\n", + "\n", + "For example, this is similar to the task of computing the distance to galaxies observed through a telescope—in this case, we might use the following features and labels:\n", + "\n", + "- *feature 1*, *feature 2*, etc. $\\to$ brightness of each galaxy at one of several wave lengths or colors\n", + "- *label* $\\to$ distance or redshift of the galaxy\n", + "\n", + "The distances for a small number of these galaxies might be determined through an independent set of (typically more expensive) observations.\n", + "Distances to remaining galaxies could then be estimated using a suitable regression model, without the need to employ the more expensive observation across the entire set.\n", + "In astronomy circles, this is known as the \"photometric redshift\" problem.\n", + "\n", + "Some important regression algorithms that we will discuss are linear regression (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)), support vector machines (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)), and random forest regression (see [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Clustering: Inferring labels on unlabeled data\n", + "\n", + "The classification and regression illustrations we just looked at are examples of supervised learning algorithms, in which we are trying to build a model that will predict labels for new data.\n", + "Unsupervised learning involves models that describe data without reference to any known labels.\n", + "\n", + "One common case of unsupervised learning is \"clustering,\" in which data is automatically assigned to some number of discrete groups.\n", + "For example, we might have some two-dimensional data like that shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-clustering-1.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Clustering-Example-Figure-2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By eye, it is clear that each of these points is part of a distinct group.\n", + "Given this input, a clustering model will use the intrinsic structure of the data to determine which points are related.\n", + "Using the very fast and intuitive *k*-means algorithm (see [In Depth: K-Means Clustering](05.11-K-Means.ipynb)), we find the clusters shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-clustering-2.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Clustering-Example-Figure-2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "*k*-means fits a model consisting of *k* cluster centers; the optimal centers are assumed to be those that minimize the distance of each point from its assigned center.\n", + "Again, this might seem like a trivial exercise in two dimensions, but as our data becomes larger and more complex, such clustering algorithms can be employed to extract useful information from the dataset.\n", + "\n", + "We will discuss the *k*-means algorithm in more depth in [In Depth: K-Means Clustering](05.11-K-Means.ipynb).\n", + "Other important clustering algorithms include Gaussian mixture models (See [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb)) and spectral clustering (See [Scikit-Learn's clustering documentation](http://scikit-learn.org/stable/modules/clustering.html))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Dimensionality reduction: Inferring structure of unlabeled data\n", + "\n", + "Dimensionality reduction is another example of an unsupervised algorithm, in which labels or other information are inferred from the structure of the dataset itself.\n", + "Dimensionality reduction is a bit more abstract than the examples we looked at before, but generally it seeks to pull out some low-dimensional representation of data that in some way preserves relevant qualities of the full dataset.\n", + "Different dimensionality reduction routines measure these relevant qualities in different ways, as we will see in [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb).\n", + "\n", + "As an example of this, consider the data shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-dimesionality-1.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Dimensionality-Reduction-Example-Figure-1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Visually, it is clear that there is some structure in this data: it is drawn from a one-dimensional line that is arranged in a spiral within this two-dimensional space.\n", + "In a sense, you could say that this data is \"intrinsically\" only one dimensional, though this one-dimensional data is embedded in higher-dimensional space.\n", + "A suitable dimensionality reduction model in this case would be sensitive to this nonlinear embedded structure, and be able to pull out this lower-dimensionality representation.\n", + "\n", + "The following figure shows a visualization of the results of the Isomap algorithm, a manifold learning algorithm that does exactly this:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.01-dimesionality-2.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Dimensionality-Reduction-Example-Figure-2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that the colors (which represent the extracted one-dimensional latent variable) change uniformly along the spiral, which indicates that the algorithm did in fact detect the structure we saw by eye.\n", + "As with the previous examples, the power of dimensionality reduction algorithms becomes clearer in higher-dimensional cases.\n", + "For example, we might wish to visualize important relationships within a dataset that has 100 or 1,000 features.\n", + "Visualizing 1,000-dimensional data is a challenge, and one way we can make this more manageable is to use a dimensionality reduction technique to reduce the data to two or three dimensions.\n", + "\n", + "Some important dimensionality reduction algorithms that we will discuss are principal component analysis (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)) and various manifold learning algorithms, including Isomap and locally linear embedding (See [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Summary\n", + "\n", + "Here we have seen a few simple examples of some of the basic types of machine learning approaches.\n", + "Needless to say, there are a number of important practical details that we have glossed over, but I hope this section was enough to give you a basic idea of what types of problems machine learning approaches can solve.\n", + "\n", + "In short, we saw the following:\n", + "\n", + "- *Supervised learning*: Models that can predict labels based on labeled training data\n", + "\n", + " - *Classification*: Models that predict labels as two or more discrete categories\n", + " - *Regression*: Models that predict continuous labels\n", + " \n", + "- *Unsupervised learning*: Models that identify structure in unlabeled data\n", + "\n", + " - *Clustering*: Models that detect and identify distinct groups in the data\n", + " - *Dimensionality reduction*: Models that detect and identify lower-dimensional structure in higher-dimensional data\n", + " \n", + "In the following sections we will go into much greater depth within these categories, and see some more interesting examples of where these concepts can be useful.\n", + "\n", + "All of the figures in the preceding discussion are generated based on actual machine learning computations; the code behind them can be found in [Appendix: Figure Code](06.00-Figure-Code.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Machine Learning](05.00-Machine-Learning.ipynb) | [Contents](Index.ipynb) | [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/code_listings/05.02-Introducing-Scikit-Learn.ipynb b/notebooks_v1/05.02-Introducing-Scikit-Learn.ipynb similarity index 81% rename from code_listings/05.02-Introducing-Scikit-Learn.ipynb rename to notebooks_v1/05.02-Introducing-Scikit-Learn.ipynb index 89364ff0e..8d3ecb877 100644 --- a/code_listings/05.02-Introducing-Scikit-Learn.ipynb +++ b/notebooks_v1/05.02-Introducing-Scikit-Learn.ipynb @@ -1,5 +1,33 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb) | [Contents](Index.ipynb) | [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,11 +35,65 @@ "# Introducing Scikit-Learn" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "There are several Python libraries which provide solid implementations of a range of machine learning algorithms.\n", + "One of the best known is [Scikit-Learn](http://scikit-learn.org), a package that provides efficient versions of a large number of common algorithms.\n", + "Scikit-Learn is characterized by a clean, uniform, and streamlined API, as well as by very useful and complete online documentation.\n", + "A benefit of this uniformity is that once you understand the basic use and syntax of Scikit-Learn for one type of model, switching to a new model or algorithm is very straightforward.\n", + "\n", + "This section provides an overview of the Scikit-Learn API; a solid understanding of these API elements will form the foundation for understanding the deeper practical discussion of machine learning algorithms and approaches in the following chapters.\n", + "\n", + "We will start by covering *data representation* in Scikit-Learn, followed by covering the *Estimator* API, and finally go through a more interesting example of using these tools for exploring a set of images of hand-written digits." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Data Representation in Scikit-Learn" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Machine learning is about creating models from data: for that reason, we'll start by discussing how data can be represented in order to be understood by the computer.\n", + "The best way to think about data within Scikit-Learn is in terms of tables of data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Data as table\n", + "\n", + "A basic table is a two-dimensional grid of data, in which the rows represent individual elements of the dataset, and the columns represent quantities related to each of these elements.\n", + "For example, consider the [Iris dataset](https://en.wikipedia.org/wiki/Iris_flower_data_set), famously analyzed by Ronald Fisher in 1936.\n", + "We can download this dataset in the form of a Pandas ``DataFrame`` using the [seaborn](http://seaborn.pydata.org/) library:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -94,11 +176,67 @@ "iris.head()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here each row of the data refers to a single observed flower, and the number of rows is the total number of flowers in the dataset.\n", + "In general, we will refer to the rows of the matrix as *samples*, and the number of rows as ``n_samples``.\n", + "\n", + "Likewise, each column of the data refers to a particular quantitative piece of information that describes each sample.\n", + "In general, we will refer to the columns of the matrix as *features*, and the number of columns as ``n_features``." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Features matrix\n", + "\n", + "This table layout makes clear that the information can be thought of as a two-dimensional numerical array or matrix, which we will call the *features matrix*.\n", + "By convention, this features matrix is often stored in a variable named ``X``.\n", + "The features matrix is assumed to be two-dimensional, with shape ``[n_samples, n_features]``, and is most often contained in a NumPy array or a Pandas ``DataFrame``, though some Scikit-Learn models also accept SciPy sparse matrices.\n", + "\n", + "The samples (i.e., rows) always refer to the individual objects described by the dataset.\n", + "For example, the sample might be a flower, a person, a document, an image, a sound file, a video, an astronomical object, or anything else you can describe with a set of quantitative measurements.\n", + "\n", + "The features (i.e., columns) always refer to the distinct observations that describe each sample in a quantitative manner.\n", + "Features are generally real-valued, but may be Boolean or discrete-valued in some cases." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### Target array\n", + "\n", + "In addition to the feature matrix ``X``, we also generally work with a *label* or *target* array, which by convention we will usually call ``y``.\n", + "The target array is usually one dimensional, with length ``n_samples``, and is generally contained in a NumPy array or Pandas ``Series``.\n", + "The target array may have continuous numerical values, or discrete classes/labels.\n", + "While some Scikit-Learn estimators do handle multiple target values in the form of a two-dimensional, ``[n_samples, n_targets]`` target array, we will primarily be working with the common case of a one-dimensional target array.\n", + "\n", + "Often one point of confusion is how the target array differs from the other features columns. The distinguishing feature of the target array is that it is usually the quantity we want to *predict from the data*: in statistical terms, it is the dependent variable.\n", + "For example, in the preceding data we may wish to construct a model that can predict the species of flower based on the other measurements; in this case, the ``species`` column would be considered the target array.\n", + "\n", + "With this target array in mind, we can use Seaborn (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)) to conveniently visualize the data:" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -118,11 +256,23 @@ "sns.pairplot(iris, hue='species', size=1.5);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For use in Scikit-Learn, we will extract the features matrix and target array from the ``DataFrame``, which we can do using some of the Pandas ``DataFrame`` operations discussed in the [Chapter 3](03.00-Introduction-to-Pandas.ipynb):" + ] + }, { "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -145,7 +295,9 @@ "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -164,11 +316,116 @@ "y_iris.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "To summarize, the expected layout of features and target values is visualized in the following diagram:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.02-samples-features.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Features-and-Labels-Grid)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this data properly formatted, we can move on to consider the *estimator* API of Scikit-Learn:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Scikit-Learn's Estimator API" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The Scikit-Learn API is designed with the following guiding principles in mind, as outlined in the [Scikit-Learn API paper](http://arxiv.org/abs/1309.0238):\n", + "\n", + "- *Consistency*: All objects share a common interface drawn from a limited set of methods, with consistent documentation.\n", + "\n", + "- *Inspection*: All specified parameter values are exposed as public attributes.\n", + "\n", + "- *Limited object hierarchy*: Only algorithms are represented by Python classes; datasets are represented\n", + " in standard formats (NumPy arrays, Pandas ``DataFrame``s, SciPy sparse matrices) and parameter\n", + " names use standard Python strings.\n", + "\n", + "- *Composition*: Many machine learning tasks can be expressed as sequences of more fundamental algorithms,\n", + " and Scikit-Learn makes use of this wherever possible.\n", + "\n", + "- *Sensible defaults*: When models require user-specified parameters, the library defines an appropriate default value.\n", + "\n", + "In practice, these principles make Scikit-Learn very easy to use, once the basic principles are understood.\n", + "Every machine learning algorithm in Scikit-Learn is implemented via the Estimator API, which provides a consistent interface for a wide range of machine learning applications." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Basics of the API\n", + "\n", + "Most commonly, the steps in using the Scikit-Learn estimator API are as follows\n", + "(we will step through a handful of detailed examples in the sections that follow).\n", + "\n", + "1. Choose a class of model by importing the appropriate estimator class from Scikit-Learn.\n", + "2. Choose model hyperparameters by instantiating this class with desired values.\n", + "3. Arrange data into a features matrix and target vector following the discussion above.\n", + "4. Fit the model to your data by calling the ``fit()`` method of the model instance.\n", + "5. Apply the Model to new data:\n", + " - For supervised learning, often we predict labels for unknown data using the ``predict()`` method.\n", + " - For unsupervised learning, we often transform or infer properties of the data using the ``transform()`` or ``predict()`` method.\n", + "\n", + "We will now step through several simple examples of applying supervised and unsupervised learning methods." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Supervised learning example: Simple linear regression\n", + "\n", + "As an example of this process, let's consider a simple linear regression—that is, the common case of fitting a line to $(x, y)$ data.\n", + "We will use the following simple data for our regression example:" + ] + }, { "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -192,22 +449,87 @@ "plt.scatter(x, y);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this data in place, we can use the recipe outlined earlier. Let's walk through the process: " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 1. Choose a class of model\n", + "\n", + "In Scikit-Learn, every class of model is represented by a Python class.\n", + "So, for example, if we would like to compute a simple linear regression model, we can import the linear regression class:" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ "from sklearn.linear_model import LinearRegression" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Note that other more general linear regression models exist as well; you can read more about them in the [``sklearn.linear_model`` module documentation](http://Scikit-Learn.org/stable/modules/linear_model.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 2. Choose model hyperparameters\n", + "\n", + "An important point is that *a class of model is not the same as an instance of a model*.\n", + "\n", + "Once we have decided on our model class, there are still some options open to us.\n", + "Depending on the model class we are working with, we might need to answer one or more questions like the following:\n", + "\n", + "- Would we like to fit for the offset (i.e., *y*-intercept)?\n", + "- Would we like the model to be normalized?\n", + "- Would we like to preprocess our features to add model flexibility?\n", + "- What degree of regularization would we like to use in our model?\n", + "- How many model components would we like to use?\n", + "\n", + "These are examples of the important choices that must be made *once the model class is selected*.\n", + "These choices are often represented as *hyperparameters*, or parameters that must be set before the model is fit to data.\n", + "In Scikit-Learn, hyperparameters are chosen by passing values at model instantiation.\n", + "We will explore how you can quantitatively motivate the choice of hyperparameters in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb).\n", + "\n", + "For our linear regression example, we can instantiate the ``LinearRegression`` class and specify that we would like to fit the intercept using the ``fit_intercept`` hyperparameter:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -226,11 +548,38 @@ "model" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Keep in mind that when the model is instantiated, the only action is the storing of these hyperparameter values.\n", + "In particular, we have not yet applied the model to any data: the Scikit-Learn API makes very clear the distinction between *choice of model* and *application of model to data*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 3. Arrange data into a features matrix and target vector\n", + "\n", + "Previously we detailed the Scikit-Learn data representation, which requires a two-dimensional features matrix and a one-dimensional target array.\n", + "Here our target variable ``y`` is already in the correct form (a length-``n_samples`` array), but we need to massage the data ``x`` to make it a matrix of size ``[n_samples, n_features]``.\n", + "In this case, this amounts to a simple reshaping of the one-dimensional array:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -249,11 +598,26 @@ "X.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 4. Fit the model to your data\n", + "\n", + "Now it is time to apply our model to data.\n", + "This can be done with the ``fit()`` method of the model:" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -271,11 +635,24 @@ "model.fit(X, y)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This ``fit()`` command causes a number of model-dependent internal computations to take place, and the results of these computations are stored in model-specific attributes that the user can explore.\n", + "In Scikit-Learn, by convention all model parameters that were learned during the ``fit()`` process have trailing underscores; for example in this linear model, we have the following:" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -297,7 +674,9 @@ "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -315,22 +694,66 @@ "model.intercept_" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "These two parameters represent the slope and intercept of the simple linear fit to the data.\n", + "Comparing to the data definition, we see that they are very close to the input slope of 2 and intercept of -1.\n", + "\n", + "One question that frequently comes up regards the uncertainty in such internal model parameters.\n", + "In general, Scikit-Learn does not provide tools to draw conclusions from internal model parameters themselves: interpreting model parameters is much more a *statistical modeling* question than a *machine learning* question.\n", + "Machine learning rather focuses on what the model *predicts*.\n", + "If you would like to dive into the meaning of fit parameters within the model, other tools are available, including the [Statsmodels Python package](http://statsmodels.sourceforge.net/)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "#### 5. Predict labels for unknown data\n", + "\n", + "Once the model is trained, the main task of supervised machine learning is to evaluate it based on what it says about new data that was not part of the training set.\n", + "In Scikit-Learn, this can be done using the ``predict()`` method.\n", + "For the sake of this example, our \"new data\" will be a grid of *x* values, and we will ask what *y* values the model predicts:" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ "xfit = np.linspace(-1, 11)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As before, we need to coerce these *x* values into a ``[n_samples, n_features]`` features matrix, after which we can feed it to the model:" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -338,11 +761,23 @@ "yfit = model.predict(Xfit)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, let's visualize the results by plotting first the raw data, and then this model fit:" + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -361,11 +796,42 @@ "plt.plot(xfit, yfit);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Typically the efficacy of the model is evaluated by comparing its results to some known baseline, as we will see in the next example" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Supervised learning example: Iris classification\n", + "\n", + "Let's take a look at another example of this process, using the Iris dataset we discussed earlier.\n", + "Our question will be this: given a model trained on a portion of the Iris data, how well can we predict the remaining labels?\n", + "\n", + "For this task, we will use an extremely simple generative model known as Gaussian naive Bayes, which proceeds by assuming each class is drawn from an axis-aligned Gaussian distribution (see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) for more details).\n", + "Because it is so fast and has no hyperparameters to choose, Gaussian naive Bayes is often a good model to use as a baseline classification, before exploring whether improvements can be found through more sophisticated models.\n", + "\n", + "We would like to evaluate the model on data it has not seen before, and so we will split the data into a *training set* and a *testing set*.\n", + "This could be done by hand, but it is more convenient to use the ``train_test_split`` utility function:" + ] + }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -374,11 +840,23 @@ " random_state=1)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With the data arranged, we can follow our recipe to predict the labels:" + ] + }, { "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -388,11 +866,23 @@ "y_model = model.predict(Xtest) # 4. predict on new data" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we can use the ``accuracy_score`` utility to see the fraction of predicted labels that match their true value:" + ] + }, { "cell_type": "code", "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -411,11 +901,44 @@ "accuracy_score(ytest, y_model)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With an accuracy topping 97%, we see that even this very naive classification algorithm is effective for this particular dataset!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Unsupervised learning example: Iris dimensionality\n", + "\n", + "As an example of an unsupervised learning problem, let's take a look at reducing the dimensionality of the Iris data so as to more easily visualize it.\n", + "Recall that the Iris data is four dimensional: there are four features recorded for each sample.\n", + "\n", + "The task of dimensionality reduction is to ask whether there is a suitable lower-dimensional representation that retains the essential features of the data.\n", + "Often dimensionality reduction is used as an aid to visualizing data: after all, it is much easier to plot data in two dimensions than in four dimensions or higher!\n", + "\n", + "Here we will use principal component analysis (PCA; see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), which is a fast linear dimensionality reduction technique.\n", + "We will ask the model to return two components—that is, a two-dimensional representation of the data.\n", + "\n", + "Following the sequence of steps outlined earlier, we have:" + ] + }, { "cell_type": "code", "execution_count": 18, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -425,11 +948,23 @@ "X_2D = model.transform(X_iris) # 4. Transform the data to two dimensions" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now let's plot the results. A quick way to do this is to insert the results into the original Iris ``DataFrame``, and use Seaborn's ``lmplot`` to show the results:" + ] + }, { "cell_type": "code", "execution_count": 19, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -449,11 +984,41 @@ "sns.lmplot(\"PCA1\", \"PCA2\", hue='species', data=iris, fit_reg=False);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that in the two-dimensional representation, the species are fairly well separated, even though the PCA algorithm had no knowledge of the species labels!\n", + "This indicates to us that a relatively straightforward classification will probably be effective on the dataset, as we saw before." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Unsupervised learning: Iris clustering\n", + "\n", + "Let's next look at applying clustering to the Iris data.\n", + "A clustering algorithm attempts to find distinct groups of data without reference to any labels.\n", + "Here we will use a powerful clustering method called a Gaussian mixture model (GMM), discussed in more detail in [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb).\n", + "A GMM attempts to model the data as a collection of Gaussian blobs.\n", + "\n", + "We can fit the Gaussian mixture model as follows:" + ] + }, { "cell_type": "code", "execution_count": 20, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -464,11 +1029,23 @@ "y_gmm = model.predict(X_iris) # 4. Determine cluster labels" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As before, we will add the cluster label to the Iris ``DataFrame`` and use Seaborn to plot the results:" + ] + }, { "cell_type": "code", "execution_count": 21, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -484,14 +1061,62 @@ ], "source": [ "iris['cluster'] = y_gmm\n", - "sns.lmplot(\"PCA1\", \"PCA2\", data=iris, hue='species', col='cluster', fit_reg=False);" + "sns.lmplot(\"PCA1\", \"PCA2\", data=iris, hue='species',\n", + " col='cluster', fit_reg=False);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By splitting the data by cluster number, we see exactly how well the GMM algorithm has recovered the underlying label: the *setosa* species is separated perfectly within cluster 0, while there remains a small amount of mixing between *versicolor* and *virginica*.\n", + "This means that even without an expert to tell us the species labels of the individual flowers, the measurements of these flowers are distinct enough that we could *automatically* identify the presence of these different groups of species with a simple clustering algorithm!\n", + "This sort of algorithm might further give experts in the field clues as to the relationship between the samples they are observing." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Application: Exploring Hand-written Digits" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "To demonstrate these principles on a more interesting problem, let's consider one piece of the optical character recognition problem: the identification of hand-written digits.\n", + "In the wild, this problem involves both locating and identifying characters in an image. Here we'll take a shortcut and use Scikit-Learn's set of pre-formatted digits, which is built into the library." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Loading and visualizing the digits data\n", + "\n", + "We'll use Scikit-Learn's data access interface and take a look at this data:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -511,11 +1136,24 @@ "digits.images.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The images data is a three-dimensional array: 1,797 samples each consisting of an 8 × 8 grid of pixels.\n", + "Let's visualize the first hundred of these:" + ] + }, { "cell_type": "code", "execution_count": 23, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -542,11 +1180,26 @@ " transform=ax.transAxes, color='green')" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In order to work with this data within Scikit-Learn, we need a two-dimensional, ``[n_samples, n_features]`` representation.\n", + "We can accomplish this by treating each pixel in the image as a feature: that is, by flattening out the pixel arrays so that we have a length-64 array of pixel values representing each digit.\n", + "Additionally, we need the target array, which gives the previously determined label for each digit.\n", + "These two quantities are built into the digits dataset under the ``data`` and ``target`` attributes, respectively:" + ] + }, { "cell_type": "code", "execution_count": 24, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -569,7 +1222,9 @@ "cell_type": "code", "execution_count": 25, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -588,11 +1243,37 @@ "y.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see here that there are 1,797 samples and 64 features." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Unsupervised learning: Dimensionality reduction\n", + "\n", + "We'd like to visualize our points within the 64-dimensional parameter space, but it's difficult to effectively visualize points in such a high-dimensional space.\n", + "Instead we'll reduce the dimensions to 2, using an unsupervised method.\n", + "Here, we'll make use of a manifold learning algorithm called *Isomap* (see [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb)), and transform the data to two dimensions:" + ] + }, { "cell_type": "code", "execution_count": 26, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -614,11 +1295,24 @@ "data_projected.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that the projected data is now two-dimensional.\n", + "Let's plot this data to see if we can learn anything from its structure:" + ] + }, { "cell_type": "code", "execution_count": 27, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -640,11 +1334,41 @@ "plt.clim(-0.5, 9.5);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This plot gives us some good intuition into how well various numbers are separated in the larger 64-dimensional space. For example, zeros (in black) and ones (in purple) have very little overlap in parameter space.\n", + "Intuitively, this makes sense: a zero is empty in the middle of the image, while a one will generally have ink in the middle.\n", + "On the other hand, there seems to be a more or less continuous spectrum between ones and fours: we can understand this by realizing that some people draw ones with \"hats\" on them, which cause them to look similar to fours.\n", + "\n", + "Overall, however, the different groups appear to be fairly well separated in the parameter space: this tells us that even a very straightforward supervised classification algorithm should perform suitably on this data.\n", + "Let's give it a try." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Classification on digits\n", + "\n", + "Let's apply a classification algorithm to the digits.\n", + "As with the Iris data previously, we will split the data into a training and testing set, and fit a Gaussian naive Bayes model:" + ] + }, { "cell_type": "code", "execution_count": 28, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -655,7 +1379,9 @@ "cell_type": "code", "execution_count": 29, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -665,11 +1391,23 @@ "y_model = model.predict(Xtest)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now that we have predicted our model, we can gauge its accuracy by comparing the true values of the test set to the predictions:" + ] + }, { "cell_type": "code", "execution_count": 30, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -688,11 +1426,24 @@ "accuracy_score(ytest, y_model)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With even this extremely simple model, we find about 80% accuracy for classification of the digits!\n", + "However, this single number doesn't tell us *where* we've gone wrong—one nice way to do this is to use the *confusion matrix*, which we can compute with Scikit-Learn and plot with Seaborn:" + ] + }, { "cell_type": "code", "execution_count": 31, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -716,18 +1467,32 @@ "plt.ylabel('true value');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This shows us where the mis-labeled points tend to be: for example, a large number of twos here are mis-classified as either ones or eights.\n", + "Another way to gain intuition into the characteristics of the model is to plot the inputs again, with their predicted labels.\n", + "We'll use green for correct labels, and red for incorrect labels:" + ] + }, { "cell_type": "code", "execution_count": 32, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { - "image/png": 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srCxDm53JgSrhbcNxQ/sbfnS+q85DKYFJGr+6pQrN0PrnR25qLvan\n70deWh7+NvlvCA4KRl5aHjqGdPTojzeFkooSHC06ioGdBzodipbRMaNxsuQkPr/4OQAg9+tc+MEP\nnUM6N/BO58R1ikPOyRwUVxYDAP7x7T8QGRyJNkFtHI5M7eylsxiSNQSXvr8EAFiYsxD3/+x+h6Ny\nr/48zJmcg3VJ6xAcGIycyTno0KqD06EpnSs7h/v+eh+KyosAAGv3r0WfDn3gCjb+Y5oab0T3Ecg9\nk4tjRccAAK8deA1juo1xOKqfnkYVX69/TMMXHC06isjWkQjwD3A6FC0dQjpg430bMePdGSi/Wo7m\nAc2xcuhKr/6pcGj0UMwZOAezds5CkH8QWge2xn/0/g+nw3LrprY34amEp3DbqttQi1okdE7Ai2Ne\ndDosU/z8vP88TOiSgN8P+j0SX0tEkH8QIltHYuO95jcjcIqvXOvatWqHNUlrMGn9JHxf9T26hnbF\nipErnA5Lm6/0s+kJMyosCt899Z0dsdgiPjIeh2ccdjoMUxK6JCD7TuPPf94svX86el3u5XQYpkzv\nPx3T+093OoxG6dKmC06ln3I6DC1p8WlIi09zOoxGWZ202ukQtI2KGYVRMaO8ZqciM3yln7kiTERE\npMGv1heefiYiInIY7zCJiIg0cMIkIiLSwAmTiIhIQ6MeK7meqpK97kPT0oPAnj5g2ljS7g7Sg7JN\n+fB3Y0j9Jx2b3bsQqOj2s1S4wO5CF1JsALBs2bJGf6ZU9ACwrv/NxCw9JC+938pCF1LmpmrHHmk3\nEKeuB2bo7s4kHbfdRRhUhVqk80uKT/fctJIq21eKT2qTrhOeXqN5h0lERKSBEyYREZEGTphEREQa\nLFnDVP3WLP1uLq1FSDvZFxcXi59p1Tqhah1MWvORCsZ703ql1M85OTla77V7DVPVz9Kag7SWbffa\njjR2pTU0AEhJMe7WIx2HVHBe2v0dsK7/VetJugXjp0yZYmizew1TKkIOyNcDSVRUlKHNzHizmrTO\nt2nTJkObFZs0mGWmYLzUV9J12+6KQlJ/AvK4kWKRrh1m+kHCO0wiIiINnDCJiIg0cMIkIiLSwAmT\niIhIAydMIiIiDbZW+tGtkCOxOwtVFbOUeScdh/R+VQaWVRUxVFlputmMTmT2qiq06FZukfpelXHa\nmH7WrUalopvFa3c2smoMSGMyNDTU0KbKSLSKmepMSUlJhjbd77Yp9oJUHYvuWLC7apF0fmRlZYmv\nXbNmjaFNGktWZkxLpHGq6ueZM2ca2nSrmKmOQzeLmneYREREGjhhEhERaeCESUREpIETJhERkQZL\nkn5UC6mzZs0ytEmL8jt27LAiDCVp8VhVlks6FikJRCp5pUqqaUxChfQ3Vf2sWwbP7qQfqZ9VZeY8\nSbaxssyZlCChill6rW4yiyohTPW3rCIly0h9b3fpOE/HnnQcTbE1nXTOqRJopGSlwsJCQ5vd56GZ\nxCfdc05KqlGN6caUn5P6RJXoJX2+9H4pZtX5qpvUxDtMIiIiDZwwiYiINHDCJCIi0sAJk4iISIMl\nST/S4qqKtDhrd+ULM4kV0iK47vF5utfaD0mL06pkAWnPQ2kR2+5+lkj7iwJytRlVItb1VN9nY6qR\nSJ8l7WepIh2HlPxh5dgwQ0qMkcaWNDZUFZUakyAkxSH1k+rvSuegFLPVCTVSwp4qiU+KW0oOtDvB\nSvp+pQpmgH7ilN0VlKQ+USUk6X7HUtKQpxWteIdJRESkgRMmERGRBk6YREREGjhhEhERafCrra2t\n9fRDVIvY0kK9lGQhLTybSSRqDNXnq5JUrictopvZFspK0oK8y+UytEnb4uhuSdQUpHEkjRertktT\nUX2P0dHRhralS5ca2uweu3aQzkFVooeZrboaQ/rOJ0yYYGjztr6Xkn769u1raFuwYIGhzcqkMCkO\nVcKfNNalpBozVa6s+g5UyT1SLNK1w8yWYbpjmneYREREGjhhEhERaeCESUREpIETJhERkQZOmERE\nRBpMlcbL/iIbT2x5AgF+AQgJDMGcm+agU3An5eulbEYpA04qV2RVptWB8wfw6NZHUVpRikD/QKy4\nawXiOsUps0OlzCypVJpdpc7eKHgDS3YvgR/8AAAlFSU4c+kMTs86jXat2onv0S1bZVcWb2Nilr5f\nKdPN7oxYAJiyaQr6tO+D2bfPBmCufFZjyvF5YsvhLZj34TxUVlfilg634NVxryKkWYip7D/djEcr\n+t7d2NiyYYv4nilTpmh9tp1jQ3XdcEf3/LLrPFy7fy0Wf7wY/n7+aBnUEstGLUO/yH4A1Bmn0viV\nMqal652VGfbXn4Oq2AD5e5euHQUFBYa2NWvWNDpGwMQdZsXVCiRnJ+M/ev8HXu73Mga2HYg/Hf2T\nR3/cbuVV5Ri5diSevONJ5KXlYf7g+Xjg7QecDsut5Nhk5KflIy8tD3se2oOOIR2ROSZTOfF4A1+M\nGQAOfXsIw14fhg2fb3A6FC3fXvkWU9+Ziux7s/HFI18gOiwac9+f63RYbvni2PDF68bhi4cx94O5\n2J68HXlpefjdoN9h4vqJTofVIF87B7XvMKtrqgEAZVfLAADl1eVo7t/cnqgssv3YdsSEx2BkzEgA\nwNgeYxHtMj5L560W/XMROoR0QGpcqtOhaPOlmDP3ZGLqrVMRFSoXpvY2249tx4AbBqCbqxsAID0+\nHbErYpF5Z6bDkenxlbHhi9eN5gHNsWrsKrRv1R4A0C+yH86XncfVmqsI9Ldkjw1b+No5qN2TrZq1\nwvI7l+PfN/07QoNCUYMaZNyaYWdsHjt88XDdCfpOKgrOF8DVwoXnhj/ndFhaLl65iCWfLMFn0+Qd\nI7yRr8WcMaZu/H5w4gOHI9HzVelX6Nym87X/vrHNjbhUeQlllWUORqXHl8aGL143osKiEBX2r0ln\n9rbZSOqZ5NWTJeB756B2bx68cBDP7noWrw94HR1bdMTbZ97GHz7/A1bFr7IzPo9U1VThvSPvYeeD\nOxEfGY93vnwHY/48BqceO4WggCCnw3Pr5X0vY3zP8egS2sXpULT5Ysy+pKa2RmwP8Ato4kjM86Wx\n4cvXjStVV5CyMQVnvjuDrQ9sdTqcnxztCXPb0W1I6JKAUT8fBQC4JfYWvJTxEqJ6RikX36VFW2lx\n1q7ybJGtI9EzoifiI+MBAON6jEPqO6k4XnwcPSJ6iO/RTaCxe2/JdZ+vQ8ZovTt43ZjtTqAxE7OU\n+KC7N5/dVPttpqSkGNqs3n/RnS6hXZB7Jvfaf5/+7jRcLVwIDgpWnkO6ZcSkJCwrE9uksaH6fKns\npJSIZdc52JjrBiCfX9Kx2BX3qdJTGPfWOPRu3xs7H9yJZgHNrv3/VIls0ncgjQVpfNl9vqrGtJSg\nJl0DpRKEnibpaSf9xHWKQ87JHHxz5RsAwOajm9E1tCtcLYw1S73F6JjROFlyEvnn8gEAuwp3wd/P\n3+vXI0oqSnC06CgGdh7odCjafDFmXzOi+wjknsnFsaJjAICV+1YiqYe8CbM38bWx4YvXjeLyYiS+\nlohJvSbhzYlv/miyJOto32EOjR6KOQPnYOxfx6JZQDO4mrvw5tg37YzNYx1COmDjfRuRviUdl6su\no0VgC2Tfm+31g+lo0VFEto5EgL/3/9RWzxdjrlf/yIO3a9eqHdYkrcGk9ZNQVVOF7q7ueH3C606H\n1SBfGxu+eN1Y/ulynP7uNLIPZePtQ28DqBvXf//13+EK9t6bmnq+cg6aWhFO75+O+//P/XbFYouE\nLgnYnbrb6TBMiY+Mx+EZh50OwxRfjLne6qTVToegbVTMKIyKGeV0GKb44tjwtevGvEHzMG/QPKfD\naDRfOQdZ6YeIiEiDJfthEhER/dTxDpOIiEgDJ0wiIiINnDCJiIg02Fo3SXoAXHeXCtWDttJrrSQ9\n6C09aCw9tGtmB5TGkGID5D7NycnR+kxV9X6rduEws4uGtCtMdna2oc2pAgfSw9G6xSBUxRCsKiah\n2gFDGrvScUjnm7cUkgD0j0M13pqiwIQUj1QYQPquVOPDbtJ5rrubjZV9KvWdascqqa+k8SGNaU9j\n5h0mERGRBk6YREREGjhhEhERabDkOUzV2p1uYV/pt2bVGqbdRc+ldRvpd++srCxD244dO8TPtCpm\n1bqi9Pu/9DdnzZplaEtKkmuRWrWmolqHWLZsmaFNKpYsrad403qP1PdmCstbVeBcNTakcSoJDQ01\ntKnWRe1eD5T6RFrflmJWrfPbnfsAyOvRBQUFWu+18nF4aUyauXZIY1V1HlvF0/Ncer+ZNW5dvMMk\nIiLSwAmTiIhIAydMIiIiDZwwiYiINHDCJCIi0mBJpR9V1pxu5pKUDWVVBRSzdKugSDGrsgqtosoc\nlkixSNnMdmc8qjKEdauiSONA1c92Z0JKsUjZg3aPXem8UmXDpqSkaH2m9H5VxqndWd+6mb1SPzdF\nNqyKdC4tXbrU0KZ6qsAq0rm1adMm8bWJiYmGNrszYiXSd6k6j6Rrr3RtlPpBagP0r4O8wyQiItLA\nCZOIiEgDJ0wiIiINnDCJiIg0WJL042nZJSeSUVSkWFTJD9ezMuFAd2EbkBfHpb4vLCw0tNm9wG+m\nJJxUtsruRCozpL6SxosUs5X9bKZPdBPF7O576fN1k3tUVAkcTpGOUbom2H3OmfnenLrOekI3wUe6\nbnN7LyIioibACZOIiEgDJ0wiIiINnDCJiIg0WJL0o1p8l5KBpCohdu9xaYa0UKyb7GHlcUgJBKpq\nHap2HaqkELurkUh9NXToUEObtEemlclVUj+r9syT2nX38XMquUL6fqXzUupTu5NqpCo4gJzEJo0N\nJyrSAOp9GqVzxomkHzOkMS0l5HnTdVvqP0/3udTFO0wiIiINnDCJiIg0cMIkIiLSwAmTiIhIg+mk\nH2lB+JlnnhFfGxsba2hTLZjbSVoQVlWgKS0tNbTNnDnT0KaqbmQVqZ9VMUt9umzZMkPbmjVrDG1O\nHAcgJ6NERUUZ2uzeKkuqiqIazxKpT+1OhpA+PzQ0VHytbiKKlOBjZaKSmaQR3WSjpqgCJfXfrFmz\ntN8vjQ9vIl3vpOuJdE6ojs3ua4o0bqTrhHTtMbNFooR3mERERBo4YRIREWnghElERKSBEyYREZEG\nTphEREQa/Gpra2u1X/3ii/ju//5f1Pr743LHjvhs+nRUtmmjLPUk7b+YlJRkaNPN5GuMA+cP4NGt\nj6K0ohSB/oFYcdcKxHWKU2ZfFhQUGNqkDEQpE0yVHWYm0/ONgjewZPcS+MEPAFBSUYIzl87g9KzT\naNeqnfgeKXtWKtlmZ1ZhRm4GMvdmomVQS/Rq1wuZYzIR1iIMfn5+4uuzs7MNbdI4krLarMpC3XJ4\nC+Z9OA+V1ZW4pcMteHXcqwhpFqLsJ93sPyk7TzWezY5zVcyqDGrdsonSGLeqNN7j2x7HX774C9oG\ntwUA9IjogbcmvaV8vfR3XS6XoU0qm6jKyjYtOxt4+mlcKi/H1ZAQfDlnDio6dQKgzvSXsvGl64l0\nDVRdQ82MddW1DlCXupQyfqWShbp7UALmrjMv7nkRKz5dAX8/f3QP745Xxr6CiJYRANT7EEt/V4pP\n2m+1uLhY/EzdjHD9O8y8PGDJEuQ89xx2vPACLnfsiF5//rP2251QXlWOkWtH4sk7nkReWh7mD56P\nB95+wOmw3EqOTUZ+Wj7y0vKw56E96BjSEZljMpWTpTfYcWIHnv/4eexI2YG8tDyMjhmNh959yOmw\n3Pr2yreY+s5UZN+bjS8e+QLRYdGY+/5cp8NyyxdjBoBPTn+CdXevQ15aHvLS8txOll6hogJITgY2\nbsS+l1/GxYED8X/+9Ceno3LLF691eefysOSTJdiduhv70/cjxhWD+R/Odzost/QnzLg44MgRVAcH\nw7+yEi2KilDZurWNoXlu+7HtiAmPwciYkQCAsT3GYv096x2OSt+ify5Ch5AOSI1LdToUt/LO5WF4\nt+Ho1LruX+ATe03Eu1++i6s1Vx2OTG37se0YcMMAdHN1AwCkx6fjzQNvOhyVe74Yc2V1JfK/zsfi\njxfj1hW34u71d+Or0q+cDsu96uq6//u/dzIB5eWobt7cwYAa5ovXurhOcTgy4whCmoWg4moFzlw6\ng7Yt2zodllvm1jADAtAxNxcjH3oIbf/nf1D4b/9mU1jWOHzxcN2E804q+r/SHyPeGIGq6iqnw9Jy\n8cpFLPlkCZaNMhYg8DYDbhiAD098eO1CuDp/NapqqnDxykWHI1P7qvQrdG7T+dp/39jmRlyqvISy\nyjIHo3LPF2M+e+kshkUPw6Lhi/DZtM/w8xt/jqT/Nv4k6VVatQKWLwduvx2333MPIjduxPGHH3Y6\nKrd89VoX4B+ATYc2ofPSzvjHqX9gyq1TnA7JLdNJP1/fdhvey8rCl/feiztMVERxQlVNFd478h6m\nxU/D3of24jcDfoMxfx7jEwPp5X0vY3zP8egS2sXpUBo0KGoQFiQuwPh14zHglQEI9A9EeHA4mgU0\nczo0pZraGrE9wC+giSPR54sxdw3ris2TNyMmPAYA8MTAJ3Cs+BgKS4z5DV7j4EHg2WeBQ4fwyYYN\nOPWrX+Fnf/iD01G55cvXuqSeSfhmzjdYkLgAI9aOcDoct/RL4x07Bnz99b+SC8aNA1auxPjERIxX\nLPJKC7FSm5SwoCphZCaBJrJ1JHpG9ER8ZDwAYFyPcUh9JxXHi48rF5SlhXtpkV9qUyVwNKa827rP\n1yFjdEaDsQFyYoeUVGOXssoyDI4ajCl96/51eOHyBczfMR+uYJeyfNaECRMMbYmJiYY2u0rjdQnt\ngtwzudf++/R3p+Fq4UJwULDye5S+c919PVXfh5mkH3cxm9m/VErKsGv/0wPnD6DgfAEeuOVf62m1\ntbUICghSvkdKwJDGhm17IG7bBiQkAF27YkjXrsDgwcBLL2HILbcA4eGmEnF09270tAyhu2tdj4ge\npvbg1E2c8rTM3LGiY/i67Gvc0eUOAMDUvlMxbfM0FJcXwxXsUibZ6SZmpqSkGNo87Wf9O8xz54D7\n7gOKiur+e+1aoE8fQMhe8xajY0bjZMlJ5J/LBwDsKtwFfz9/RLuiHY7MvZKKEhwtOoqBnQc6HYqW\ns5fOYkjWEFz6/hIAYGHOQtz/s/sdjsq9Ed1HIPdMLo4VHQMArNy3Ekk9vPunQl+M2d/PHzO3zrx2\nR/nS3pcQ2zEWka0jHY7Mjbg4ICcHuHCh7r+zs4Fu3YDwcGfjcsMXr3Xnys7hvr/eh6Lyujll7f61\n6NOhD1zB3jun6N9hJiQAv/89kJgIBAUBkZGAA4XUzegQ0gEb79uI9C3puFx1GS0CWyD73myv/qkQ\nAIKIXQgAACAASURBVI4WHUVk60gE+HvvT20/dFPbm/BUwlO4bdVtqEUtEjon4MUxLzodllvtWrXD\nmqQ1mLR+EqpqqtDd1R2vT3jd6bDc8sWYe7fvjYzRGbjrrbtQU1uDG9vc6P1ZskOHAnPmAEOGAM2b\n102Umo/nOMUXr3UJXRLw+0G/R+JriQjyD0Jk60hsvNe75xRzu5WkpdX9z4ckdEnA7tTdTodhSnxk\nPA7POOx0GKZM7z8d0/tPdzoMU0bFjMKomFFOh2GKL8Y8uc9kTO4z2ekwzElPr/ufD/HFa11afBrS\n4n1nTmGlHyIiIg3mKv0QERH9f4p3mERERBo4YRIREWnghElERKTBXJasguoBU+lBb+nBUTt3pFBR\nPXQrPcAtPSgrPZCvu5tFY6kecpd2hYmKijK0SQ8kWxmzVAyib9++2u+XYpYeuFbF7OlDyQ2RxsyU\nKcZSXjt27DC02T2eVaT+093twSnS9yvFrNo1xG6qvyv1tZ07BFlBt6CBXYUt3FGNSd2dU8xcO3Tx\nDpOIiEgDJ0wiIiINnDCJiIg0WPIcpqoIsm6RZ2mN8MSJE+Jnmt2hHjC3tiato0m/j5eWlhraPN3N\nuyGqdQTp+KTdxiX5+flie2OKnkv9pFvIGZDXJqR+ltYIAevWCVU7yUufL41xqc3u9VXV2Jg1a5ah\nbenSpYY2M8W5raL6m8uWGbe0cyJnQEU1zqRzxom1P4lqswnpOjhz5kxDm93HoZsfAMjxSceXk5Nj\naPN0XuEdJhERkQZOmERERBo4YRIREWnghElERKSBEyYREZEGSyr9qLLGpMwlKSNWynpqTDasipS9\nlp2dLb52/PjxhjYp0/OZZ54xtKmyK63KkFRlFUqVR3SzZK3sZ+k4Vdl1UruUEZuYmGhoa0wGr4r0\nnamyL6WxK40juzNiJaqqKLGxsYY2p7JLr+eLMQPqjFNvzoiVrmsAkJKSYmiTjkPK/Lby2qG6duqS\njlkaR57GzDtMIiIiDZwwiYiINHDCJCIi0sAJk4iISIMlST8qugusViZx6FItgnvC04XrxtLtvwUL\nFhjanEhQAfS3PZISQ6yMWUpw2LRpk/haKUFCGkdSgooqMc6qZBZVf0oJa05959dTxeHE9UBFtywm\n4D1xS2Na2gIQkMev9H5pHKnGXGPGl5TQqCq5qltC044kLN5hEhERaeCESUREpIETJhERkQZOmERE\nRBos2Q/TDCnJQVo8Vi34NoZUBUKVhKFa0NchVSwCnKkAIh2flMCg6me7E0N0vxMp2cDKvRulvynt\nowfISVNSn0r7OUoVi4DGjXPpPUOHDhVfGxoaamiTklOk5A8r+1nqJ1VSoBSf9D1J1xIrq88Actwu\nl0t8rbTXolSFS/f4Gku6nqq+S2ksSddAqWqOU9cOqa+k711VScoTvMMkIiLSwAmTiIhIAydMIiIi\nDZwwiYiINDR50o/uIvqOHTvE9zdmcVxaeJeSSQA5PqlKRlJSkvZnOlEBRDcxZOnSpeL7rUz40CX9\nTWnh3sqKSlKChOr78iQhzMp+lmKOjo4WXyslG0njVEpMUyVvWJVMoTqXVUlXOqRqTIC54/shKTmt\nb9++5gNrgFMJg9Lnz5o1y9CWn59vaLP7uqbaRk3qf2m+sDKRqh7vMImIiDRwwiQiItLACZOIiEgD\nJ0wiIiINnDCJiIg0mNoPc8vhLZj7/lxUVVehd0Rv/Gn4nxDSLESZHapbnk2iypAym/m0dv9aLP56\nMfz9/NEyqCWWjVqGfpH9lPth6sZs5z6NL+55ESs+XQF/P390D++OV8a+goiWEWK2LyBnxKpea6eS\nkhJsObYF6dvTcSr9FABzWaBZWVlar1ONjcZk7XXt2hVTNk1Bn/Z9MPv22QDUY1Q381jKoLYq6zgj\nNwOZezPRMqglerXrhcwxmQhrESaW7QP0s4yl0mKWjaHsbODpp4GAAMDlAlatAqKjleeglCWrKi14\nPdUYMrNHKQAcOH8Aj259FKUVpQj0D8SKu1YgrlMcALncoIrUh9J3IpVTBExmySr62R3pmqVbTtES\nbmI2U+bQ6pKIKtp3mN9e+RZT35mKtXetRe6vc9GlTRc8/dHTNobmucMXD2PuB3OxPXk78tLy8LtB\nv8PE9ROdDsutvHN5WPLJEuxO3Y396fsR44rB/A/nOx2WlmPFx/CHf/zB6TC0Hfr2EIa9PgwbPt/g\ndChadpzYgec/fh47UnYgLy0Po2NG46F3H3I6LPcqKoDkZGDjRiAvDxg7Fpgxw+mo3CqvKsfItSPx\n5B1PIi8tD/MHz8cDbz/gdFju+WA/+2LM2hPm9mPbMeCGAega2hUAMPWWqdhwyLsvNM0DmmPV2FVo\n36o9AKBfZD+cLzuPqzVXHY5MLa5THI7MOIKQZiGouFqBM5fOoG3Ltk6H1aArVVcwbfs0/HHwH50O\nRVvmnkxMvXUqftn7l06HoiXvXB6GdxuOTq07AQAm9pqId79816vHM6qr6/5v/V1tWRkQHOxcPBq2\nH9uOmPAYjIwZCQAY22Ms1t+z3uGoGuCD/eyLMWv/JPtV6Vfo3Kbztf++IeQGlFWVoayyzJbArBAV\nFoWosKhr/z1722wk9UxCoL+pX6KbXIB/ADYd2oTUd1PRIrAFFg5d6HRIDZq2eRqm9pmKmyNudjoU\nbRljMgAAH5z4wOFI9Ay4YQAy9mTUnYuhnbE6fzWqaqpw8cpFp0NTa9UKWL4cuP12ICKi7iL50UdO\nR+XW4YuH0SGkA1LfSUXB+QK4Wrjw3PDnnA7LPR/sZ1+MWfsOs6a2RmwP8A+wLBi7XKm6gns23IPj\nxcfxythXnA5HS1LPJHwz5xssSFyAEWtHOB2OWy/tfQlB/kG4/+b7nQ7lJ21Q1CAsSFyA8evGY8Ar\nAxDoH4jw4HA0C2jmdGhqBw8Czz4LHDoEnD4NzJsHTPTuZZGqmiq8d+Q9TIufhr0P7cVvBvwGY/48\nBlXVVU6HpuaD/eyLMWvfanUJ7YLcM7nXFokLSwrhauFCp4hOyuQAKTlDapOSJFQJAWadKj2FcW+N\nQ+/2vbHzwZ3XLi6qvdykhAOprJlde74dKzqGr8u+xh1d7gAATO07FdM2T0NxebEyuaqgoEDrs6Wy\nYVIyhFlZBVkorypHwhsJqKyuxJWqK0h4IwFrhq9RJuhIMUuJHVKyjBOlBgF1stH1VN+Tp8oqyzA4\najCm9J0CALhw+QLm75gPV7BL+TelZAgpkUQqt2fJObhtG5CQANTH8cgjwKxZQFGRMhFKikVKlJHG\nQXZ2tviZZpIFI1tHomdET8RHxgMAxvUYh9R3UnG8+Dh6RPRQXu+kc0lKCpPGuap0ojY3/YzwcOXb\npPEhlYCUjtnj8dFAzKp+luYLr0v6GdF9BHLP5OJY0TEAwMp9K5HUwxi4NykuL0bia4mY1GsS3pz4\npnf/S/x/nSs7h/v+eh+KyosA1GX59unQB65gedNab5Cbmov96fuxeexmrB6+Gi0CWmDz2M1oF9zO\n6dB+Us5eOoshWUNw6ftLAICFOQtx/8+8/K4+Lg7IyQEuXKj77+xsoFs3txdxp42OGY2TJSeRf66u\nfuquwl3w9/NHtMt9xqmjfLCffTFm7TvMdq3aYU3SGkxaPwlVNVXo7uqO1ye8bmdsHlv+6XKc/u40\nsg9l4+1DbwMA/OCHv//67w5HppbQJQG/H/R7JL6WiCD/IES2jsTGe5v+ERFP+Pn5OR2CKX7wjXhv\nansTnkp4Cretug21qEVC5wS8OOZFp8Nyb+hQYM4cYMgQoHnzuovhpk1OR+VWh5AO2HjfRqRvScfl\nqstoEdgC2fdme/c/uH2wn30xZlPZL6NiRmFUzCi7YrHcvEHzMG/QPKfDMC0tPg1p8WlOh9EoN4bc\niAOTDzgdhimrk1Y7HYK26f2nY3r/6U6HYU56et3/fEhClwTsTt3tdBjm+GA/+1rMrPRDRESkocn3\nwyQiIvJFvMMkIiLSwAmTiIhIAydMIiIiDU1eI056wFR6gNmq3R0AeXcG1YPM0kPTug/Kq2K2qgiD\nahcN6VikmKWHv60kxac6dum10gP1ZnensYKZwgjS8UkPsDfVg9U6pHEqFfLQLdSgQ/os6VwD5Pik\nQiHS66woxGElaXyY2V3IqvGv6hfpO5DGqt3XDomquIx0LNI5a8eOTbzDJCIi0sAJk4iISAMnTCIi\nIg22Pocp/a4sFd2eOXOmoc3UTuMNkH4Ll4oiA1DuXH896Xd+K9dPpOOfNWuWR58pFXi2cq3YTD/r\nys/PN7RZWXxdWueYMGGCR58pFddWrcfYTVqjio7Wq4laXFwstjdm4wFpnC1btkx8rdR/0vkmHZtT\n/QzI67R9+/bVeq90zEDjjseTOFR27NhhaLMyv0CK2cznSwXj7ZhXeIdJRESkgRMmERGRBk6YRERE\nGjhhEhERaeCESUREpMGSSj+q7FApI1ZidxUUKQMrNjZWfO3TTz9tayy6VFV9JNKxSJmk0rFZmSVr\nBymrzcqqI1ImXmhoqPhaqU+dzMrUIY19KXtQ6tPGZMOqmMlslr5z3eo/TpIyrqOiogxthYWFtsYh\njUnVmNatOiT1v5WVoKS/qZoXpL+rm2Wrur7rjiXeYRIREWnghElERKSBEyYREZEGTphEREQaTCf9\nSAvyWVlZ4mulMnPPPPOMoc2q7a9UpAQa1dZCUnKC9FpvSqDR3cZGep1q4b4x5eekRfY1a9aIr50y\nZYqhTUqQkMaWlUk/0mK/6th1tySTkuCcSlDRPbfs2AqpoThUZcqk9pycHEObamw5RRo30jkhjWkr\ny2pK41Q1pqV23a0BVYmJVo11M58jxSxdj1XjXLf/eYdJRESkgRMmERGRBk6YREREGjhhEhERaTCd\n9CMtjqoqMuhWq5GqTVi5CC4t/qpilhaapcQY3WoYjSUtYquqdUik4zNTqcaqPSdV36Pu9+vn52do\nU8Vs1f58qs+REtakPUqlseFURSBp7Ep9b3eFKzPJVVJSTEpKiqHNymuEinQNUyWdSd/xpk2bDG1S\nZa6mOBZPSNc2VdKWt1RLk6iSPXXxDpOIiEgDJ0wiIiINnDCJiIg0cMIkIiLSYDrpR1q8V1UT8Zat\nj6SYzSyyS4vbdlduMZPAIvWz9H6pWopq4d5bSAkSqupEViX9qJIWpM+XEnyWLVtmaLOyopL0nUnJ\nRypJSUmGNrurVEnJM3ZXF7KCNBak71dFql5l93VRGlOe9rXdW9uZiVkaS01VSYt3mERERBo4YRIR\nEWnghElERKSBEyYREZEGTphEREQaTGXJZn+RjadznkaAXwBcwS6sGrsK0a5o5etV5eea0ot7XsSK\nT1fA388f3cO745WxryCiZYSyRJKU8StlZamyHq3w+LbH8Zcv/oK2wW0BAD0ieuCtSW8ps0DNlP67\nnlUl8IC6fnpk+yO4OeJmPBL3yLU21WuvJ2Xd2dn3a/evxeKPF8Pfzx8tg1pi2ahl6BfZz1TMUiaf\nVMLQynPhscceA6ZMAfr0AWbPBqDOWJT6SirXJmXeqsab2TGj6ufS0lLx9YmJiYY2u/dFVZl/4gQq\nYmLwTXLytTZVRqYUT2FhoaFNyry1Ils9IzcDmXsz0TKoJXq164XMMZkIa1EXqyoLWopFapOOzdMx\n/UbBG1iyewn84IfKykp8V/kdzl85j4/v+RhtW7Q1tWexFIs09j3tZ+07zIqrFUjOTsbGezciLy0P\nY28aixnvzfDoj9st71welnyyBLtTd2N/+n7EuGIw/8P5TofVoE9Of4J1d69DXloe8tLy8Nakt5wO\nqUGHvj2EpL8mYdNR48XYGx2+eBhzP5iL7cnbkZeWh98N+h0mrp/odFgNO3QIGDYM2LDB6Ui0+Ho/\nh73/vtORaNlxYgee//h57EjZgby0PIyOGY2H3n3I6bDcSo5NRn5aPvLS8rDxzo1oF9wOz9z2DNq2\naOt0aErad5jVNdUAgJKKun9ll1WWITgo2J6oLBLXKQ5HZhxBgH8AKq5W4MylM+jm6uZ0WG5VVlci\n/+t8LP54MY4WHUVMeAyWjlyKzqGdnQ7Nrcw9mfhV71+hcxvvjrNe84DmWDV2Fdq3ag8A6BfZD+fL\nzuNqzVWHI2tAZiYwdSogPN/njXy9n0tat3Y6Ei155/IwvNtwdGrdCQAwsddEpL6Tiqs1VxHob/px\n+ya3/MByRLSIwH033ed0KG5p92SrZq2w/M7luP3V2xHRMgLVtdX4aOpHdsZmiQD/AGw6tAmp76ai\nRWALLBy60OmQ3Dp76SyGRQ/DouGLEBMeg8UfL0bSfychLy3P6dDcyhiTgZKSEuScMhZH8EZRYVGI\nCvvXpDN722wk9Uzy/otLRkbd//3gA2fj0OTz/bx+vbNxaBpwwwBk7MnAV6VfoXNoZ6zOX42qmipc\nvHIRHUI6OB2eWxevXMSr//Mqtozd4nQoDdL+SfbghYN4dtezOPSbQzg9+zTmJczDxHU+8NMKgKSe\nSfhmzjdYkLgAI9aOcDoct7qGdcXmyZsREx4DAHhi4BM4VnwMhSXGtRDy3JWqK7hnwz04Xnwcr4x9\nxelwfrLYz/YaFDUICxIXYPy68RjwygAE+gciPDgczQKaOR1ag17e9zJGdBmBG0JucDqUBmn/M2/b\n0W1I6JKArmFdAQCPDHgEs7bNQlF5EcKDw8X3SAux0oK+lDhhxf5wx4qO4euyr9GqqBUAIM4vDoUl\nhdi1Zxd+/ctfi++REh2asjTegfMHUHC+AA/c8sC1ttraWgQFBCmTHKR+lhJUFixYYFWYopKSElRW\nVqK8vPza31d9j1KZPqmMmHRsVpVxO1V6CuPeGofe7Xtj54M7r11cVJ8vJZ5I1qxZY2izu3SXmdJn\n0vFJiR6q785s4oSqn/Pz88XX65Y4lI5ZVaazsdqGhwM33IAbfpBookp6kvpV6kMzpRN1y8+VVZZh\ncNRgTOk7BQBw4fIFzN/x/9q7+6Aor3sP4F8WUBFQwReEKKJxjI7hEikm0Qu+1DQmRIvaNCVMqRfG\nStBrvJra3thkonE6YxtLEpGYplyVCa2XSVrUGBNT0xRvjcE0WF/SUsWqCUL0RkRFJfKy94+9mDb7\nO8t52Ofx7Drfz0ynk2dw+e2zZ5/D7vk+v/M0YiJilLUB8jmUnp+/7UV9qfi4AsUPFiNpRNI/HVdd\n7+bOnet1TLre6b4eVmh/wkyNT0XVqSqcu3IOgCcxOypmlHKyDASNLY3I/k02Ll73pPHe/PRNjO43\nGv169TNcmZorxIWlby+98YnypQ9fQsrQFCREJxiu7NZy4doFTN0yFd8a9y38at6vguIv8WDE83xz\nNFxuwLSyabj8xWUAwJqqNXj0zkcNV9W95tZm1DXVYfLwyaZL0aL9CXP6yOlYMXkFpm2Zht5hvREb\nEYvt2YGdiExPTMdTGU9hwd4FCHOFYXCfwSi6u8h0WT6NHzIexQ8WY9bWWeh0d2JYv2FBkZLtEhIS\nYroELRv/tBH1l+pRWVuJ39b+FgAQghC8+713DVemief55giS8zxm4Bg8mf4k7im9B264kT48HRsy\nN5guq1t1TXVIiE5AqCvUdClaLK28F04sROHEQqdqcURBWgHuCbvHdBmW5CTnICc5x3QZPfKzf/2Z\n6RK0rMxYiZUZK02X0XObNpmuQIuv83waQbAuHyTnGQAWTVyERRMXmS7DkrSENBxbcsx0GdrY6YeI\niEhDiNvtdpsugoiIKNDxEyYREZEGTphEREQaOGESERFpcLQ/lXQzqe5Nsaobdu26AVx1o7B047O0\n44B0k72qu77TpJtxpRuSpXNq524l0vNX3Uiu+7PSc9O9sV2HNEZVjy/VLI2jQNilp4v0/GJiYryO\nVVZWeh2zuwnAV6neL9LYlRorSOfZ6euGL9KN8lKTgvfee8/rmJ1j2grp/aW7K4/TVNemQ4cOeR2T\ndgiSavb3PPMTJhERkQZOmERERBo4YRIREWlw9D5M3fUTiaoxs11rbv4+jvQ9+smTJ8WftWtNS9X0\netmyZV7HsrKyvI6ZWIdQ/U5pTUlaA9JdNwR6dp6lBs9WmrtLa0D+7upuJ+n8S82rTYwX1eslHZfe\nr1Y2bZDWQHVI1zDVY0nrlSkpKV7HpLqdXvdWvWcmTJjgdWz+/Plex1SN0J2keh9K1w7pnErXaH/n\nFX7CJCIi0sAJk4iISAMnTCIiIg2cMImIiDRwwiQiItJgudOPlEZSJahUXTd02NmBRmKlI4huetPp\npJvqPEtdLkyk2iRWusVI509Kuqk6xPTk/EvpQVU6T/q9/ozxmyGQErtfpTp3uq+jKvlpJ+k6JHX+\nAuTuX9L4N9EJykriOVCuHVbGru7zU405pmSJiIhsxAmTiIhIAydMIiIiDZwwiYiINFgO/VjZiuvi\nxYtajymFVpymam8lBQmkY9JzU7XlsmsRXRV2kbasuRnbGdlt+/btXsemTp3qdczOrZCkx1KFMqQw\nkInzLIUhVKGHqqoqrcc0sb2Uv+EXqW2dP48pPZ50THW9kl4XqQ2h9JhOh7NU12gpqBTopPMnhQOl\na4eVtpcSfsIkIiLSwAmTiIhIAydMIiIiDZwwiYiINFgO/UjhAGkRFpCDNatXr9b6OTtJC97S3nVW\nSPsH+rug3B1ViEoKA0nnNFBCKyrS3oFO1yd1YlF1kJECNJs3b7a9pu5IXUlU70GJ9Dyc7qyluy+n\nv/wZL9K/lQJ7qrp1n4+J95wqMCh1LZLqk0JJqpCj06T6pCCWEx2V+AmTiIhIAydMIiIiDZwwiYiI\nNHDCJCIi0hDidrvdTj24tChcVlbmdezgwYNex0xt7yWFE6Rj0r93etseVVjAn45Kqg4jJhb0paCS\ndO7t3NZJenwrz10KUwRSkEoKekmBt5MnT3ods3M8S+dJ9TpKPyuFb6Sgk79bhulQBWikAJnUgebC\nhQtex5weM6pOTlIATOqQI71WgX7tkOqzEo6T8BMmERGRBk6YREREGjhhEhERaeCESUREpIETJhER\nkQbLrfGs0E2mSQksp1OyqtqkNJ6U+nI6ESuRUniAnDyW9rmT2mCp2hJa2Seyi5RAU+3TqJuEdPo8\nSzWrUsdSylj1mnyVKgWpOj928TcVaBfpdVS9tlLN0jg1MV58/Q7d320iRa0ap1JKVnoeuq8JYF9K\nVpWi1k3sSu9jVbJXt61pzybMvDwgORlYvrxH//xm2nBgA17+08twhbhwe+zt+OXsX2JQ30Gmy/Lp\nyNkjePztx3Gx9SLCXGF4edbLSI1PNV2WT28eexM/+t2P0NbRhvGDxmP9fesR1SvKdFk+PbH7CZTV\nlyEyNBIAEB8Wj8cGP2a4Kt+CbTy/euhVFH1QhBCEAACaW5tx5vIZ1C+rx+DIwYarU3ti9xN4/a+v\nY2DEQADAHYPuwNZvbTVclZ687XlIHpKM5ZMC//qMykpg1SogNBSIiQFKS4GRI01XpWRtwqytBRYv\nBqqrPRNmgKtprEHR/iIcLjyMqF5RWPHOCjz9+6excdZG06UpXWu7hpnlM7E5azNmjp6JN/72Br77\n2+/iL4v/Yro0pc+vfo78HfnY/e3dSOqfhFV/XIVV+1Zh3fR1pkvzaX/9fhQOLsTtvW83XYqWYBzP\nuSm5yE3JBQC0d7ZjyuYpWJmxMqAnS8AzNioersC9w+41XYq22s9rsXjXYlTXVyN5SOBfn9HaCuTm\nAkeOeCbJF14AliwBdu40XZmStQmzpATIzweEr/sCUWp8Ko4vOY5QVyha21tx5vIZjIoZZbosn945\n8Q5Gx47GzNEzAQCz75iNkTGB+xcX4Kn57tvuRlL/JABA/r/kI+NXGQE9YV7vuI6Dnx1EW682nG07\ni7jwOGTHZGNg2EDTpSkF43j+R2v/uBZxUXFYkLrAdCk+dY2Nde+vQ11THUbHjsbzM5/H8P7DTZfm\nU8mBEuTflY8R/YPj+oyODs//d33d29ICRESYq0eDtQmzuNjz/3v2OFCKM0Jdodheux0L3liAPmF9\nsGb6GtMl+XTs/DHPRWXHAhw6ewgxfWLw0/t+arosnz69+CmG9/vyYnJb1G1oaWtBy/UWg1X51nC5\nATNGzkDGlQzEhcfhrYtvYf3/rsfqeO/t5wJJsI3nLuevnkfR/iL8+TH7ujQ5pWtsrL1vLUbHjsa6\n99ch67+zUFNQY7o0n4ozPdfnPSeD5PocGQls3AhMmgQMGuSZQPftM12VT46GfqTFXynkIC24qlo5\n9WRRP2tsFrLGZqG0phT3l9+PE4+fULa3kh7f6f06/1FbZxveOv4W/vBvf0BaQhp2/G0HMn+diU/+\n4xPlgrXuPn4SVbjKynnudHcC+DIY0NHp+cux5VKLsg7p/Eu16D4Pq5IGJGFnzs4bNc/BHCRuTETq\n11PFvU4BuWYpNCGR2o31lDSeVaT3lhSakI7ZGaB55aNXMGfsHCT2T+z2Z6XrhnRMN3BlVdfY6PKD\nyT/Amr1rcLr5NEYMCJJPb1+hCrVIY1q37aff5//oUeDZZz1LfUlJng9k8+YB/z8WVXOAbitQ6X3s\nbyDplr6t5ETTCez75Mu/WPIn5ON082lcuObdyzFQJEQnYOygsUhLSAMAfPOOb6KjswN/v/B3w5Wp\nJfZPRMPlhhv/3Xi1Ef179UefsD4Gq/LtyNkjKD9c7nU83BVuoBo9wTieu1R8XIG8u/JMl6FFGhtu\ntxvhoYE7NoLS7t1AerpnsgQ8+ZijR4GmJqNl+XJLT5iNLY3I/k02mq55XoDyw+VIjktGTESM4crU\nHhz9IE41n8LBRk9D+r2n98IV4grodcz7b78f1WeqcfqS57aVrce24hvDv2G4Kt9cIS4sfXspPrn0\nCQCg9FApxg8aj/ioeMOVqQXjeAY8ydi6pjpMHj7ZdClausbG6WbPeH7pw5eQMjQFCdEJhiu7xaSm\nAlVVwLlznv+urARGjQJiY83W5UPPvpINCbG5DGekJ6bjqYynMHXLVIS7wpEQnYBt33H2vjd/TDmW\nWAAAC+FJREFUxUXFYVv2NhS+WYgrbVfQJ6wPKr9TiV6hvXAVV02XJxocORibszajcFch2jvbkRid\niKKMItNl+TR+yHgUP1iM7B3ZcLvdSIhKQOkDpabL8ikYxzMA1DXVISE6AaGuUNOlaOkaG7O2zkKn\nuxPD+g0LmltKANy4hSfgTZ8OrFgBTJsG9O7tmSi3bzddlU89mzA3bbK5DOcUpBWgIK3AdBmWpCem\n44MFH5guw5IHRj+Asd8ca7oMS3KSc5A5PNN0GZYE43hOS0jDsSXHTJdhSU5yDnKSc0yX0SObsoLn\n+ozCQs//goSj+2ESERHdKm7pNUwiIiK7cMIkIiLSwAmTiIhIg6ONC6QO99LNrtINqqobbXvS6V+6\nEVd1A6u0o4dEuhFdtfOEXbsTqM6J9Pykcy81PnDq5u/uSL93u5CQq6ys1Pq3dlLtkiCdf6lxwfz5\n872OOdWAoTu65/mZZ57xOmZnww4ru128+OKLXsd0d4oxdZ4BedxINUo/Z+cOJrpNQQD9JgApKSle\nx1TXO7saXqh22tHd+Ub1PvYHP2ESERFp4IRJRESkgRMmERGRBkfXMKXvkKU1H+mY7g7YOqzs9i79\nXmntT6pZ9Z1+Txr+SuuS0toOIK+ZSed+7ty5XsdM3YZrYtd5ibTeo1ojlcaMtJatauzvJNXanbRe\nKa1HOb0uLL03VONZWk+VxsuyZcu8jqmuG6o1PDtJ73M7G9jrks6VlTEtjaVDhw5p/Rzg/GYV0rqr\nVJ805vwd5/yESUREpIETJhERkQZOmERERBo4YRIREWnghElERKTBlpSsqiODbtI1KyvL65idKUop\nCSalUAE5WSV1/5GSqT1Jw6pI3Y+kdCMg16x7/lSvnV3nX3Wey8rKbHl8f0lpYuncA3IqUHrNVefU\nSVaSuVJS0OkUqXSeVKly6TxL70HpunEzUqlSah6Qk5pSpyornXh6QnrvWumAtHr1aq9jUqclO+9k\nkPjbtcmJ5Dc/YRIREWnghElERKSBEyYREZEGTphEREQaLId+pECDKuwiLYLrPqYpumGXm9Fq66tU\n29VIx6WwjdRKTBUW6cnz091KygqnQxxSzaqwgDROpfMs/XvVebbr+akCNBI7w2m6pHOnOidSwGfz\n5s1ex27G85DeW6rWb1IISTJhwgSvYydPnhR/1kRrPYkU8HG6vaWV0I8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x0a8+sjs0JX/sZ+01zLr6OgBAdUM1AKCmvgbBjmBrorLAor8uQnR4NNKT0u0O\nxa2mfq66UgUAuFR3CaEBoXaGpKW6thppeWlYOmqp3aEY5i9j43LdZRR/W4zFHy9G35V98atNv8KJ\nyhN2h9UsfxsbRaeLMKL7CHRu2/irzsTeE/H212/jSv0VmyNTCw0MxZpxa9CpTScAwM/b/xzfX/re\np2P2x37WvsNsE9IGK25fgembp6NtYFvUox5Z0VlWxmaac9XnsOSTJfh8prXVeczQ1M//kv8viAiO\nQD3qkdM3x+6wmjVzy0xk9s9En06+/RPQtfxpbJy6cArD44dj0YhFSIhKwOKPFyP1z6koyiiyOzS3\n/G1sDOwyEDl7cnCi8gS6RnTF2uK1qK2vxbnqc4gOj7Y7PFFcZBziIv++zvtvn/4bfhn7SwQFGE5T\naTH+2M/avfnF2S/w9K6ncXD2QXSL7Iacwhy8WPwiPp/xuXLBWlq0rax0Xb+Qkj3MXNBf/dlqjO81\nHrERsVfbVAv3RhbMrdDUz6UPlV7t5/8o/g98PvNzLF0q/wtdWvCW+llKnDCj9Nbze59HcEAwpvad\niqMVR7XeI8VnR4KPNDZUyQYpKSkubbpJHWboFtkNW6Zsufrfjw16DM/segbHKuREBkAufSZRlaL0\nlidjQ+p/KXnMqv0YB8cNRnZKNsZvHI9ARyCm95uOqLAohASGAJD3swTk/X91paamevzen6qurcb9\nO+/HmeozeGnES82+Xio5KLUZcf78eZc26Vg118+qOUDqf2l8SEl6qn7WHUvaP8luPbQVybHJ6BbZ\nDQAwa+AsfHH2C5RfKtf9CNts/HIjpvWV61b6Gn/s5/Ul67H31F4krUrC7X+6HdW11UhalYRvq761\nO7Rm+dPY2H9mPzbs2/A/2hoaGhAc6LtLI/44NqouV2FI3BB89q+fYc+MPZjYeyIAwBnmtDky945X\nHsegFwchJCAEr416DW1D2todklv+2M/aE2ZS5yQUHC3A2YtnATRmcnZ3dkdUWJRlwZmhoqYCh8oP\nYVDXQXaHosUf+7kwvRD7MvehKKMI7055F2HBYSjKKMJ14dfZHZpb/jY2AhwBmP3+7Kt3lM/vfR6J\n1yUipm2MzZGp+ePYOHXhFIauH4oLP14AADxT8Ax+/fNf2xyVe+cvnUfKSymY1HsS/jDkD1fv0nyZ\nP/az9k+yw+KHYe6guRj60lCEBoUiKiwK+ZPzrYzNFIfKDyGmbQwCAwLtDkWLv/bzTzU9quHr/G1s\n3NjpRuQjQvsyAAAgAElEQVSMycEdr92B+oZ6XN/uer95pKSJP4yNG9rfgCeSn8Av1vwCDWhActdk\nLB+73O6w3Frx6QqU/VCGvAN5+PO+PwNo7OtXR76KiNAIm6OT+WM/G1oRzhyQicwBmVbFYon+Mf1R\n+mCp3WEY4o/93CQuMg4/PPGD3WFo8cexMaXPFEzpM8XuMDziT2Pj/gH34/4B99sdhraswVnIGtyY\nhKlbHMYX+Fs/G94Pk4iI6H8j1pIlIiLSwAmTiIhIAydMIiIiDZwwiYiINFhaN0mq3CJVVFBtMWUl\nVbUOqV3aEiY7O9ulTVUhxiyq7DepEtHmzZtd2qyqjOKOqkqSVCFHGgdStQ/VsTOL6jguXLjQpU2q\nkCN9t5asCPRTUhUuadsjqfKVmVt+SWNX1c9S9Snd8WLHGG8ixS2NValfVVVtzKp+JV0PAPn8lPpa\nis/q650R0liQjoe3cw3vMImIiDRwwiQiItLACZOIiEiDKWuYqt+y8/NdS7rl5eWZ8Se95u06mPRb\nuNW/6at2FpHWqexcy/kpVRzSmpnu+ra0MwHg2ZqbtLamWu+Rxq70Wmkc2FV9RXc3GqnvVO/1ZCch\nqZ9U/SwdX2n9WBpDZu5ypKKKW3dnGInVcauuTdKuQdJYkL6zan3VjvV66fupdtHyBu8wiYiINHDC\nJCIi0sAJk4iISAMnTCIiIg2cMImIiDQYzpKVMtOkDDYAmDp1qkublAkpZVupMtHMYiRrUaqGYUfW\no5HqRL5ClUmnWwFFGi9WV6BRZddJmYxSJqlUGcouUvaglIUqfedhw4aJn1lcXOzS1lxmpHQOqapA\nSed+RITrJsh2VU/ytlrM7NmzXdrMqugDyP1XUlKiHYt0brZUFqoOady01DnHO0wiIiINnDCJiIg0\ncMIkIiLSwAmTiIhIg+GkH2nxNzExUXytblkzqYSe1XRLhqleKy3SqxKBzEpSUS3c25X8oEMVm3TM\npSQxq7d+kxJ5VMdLeq00DlTng5VUSXLSmJSSJqQxLiXaAJ6NNyOlGqVrhBRzS5R/lPrF2+uVmQk+\nEqlfVGNSt5ynbsKb6rWeUCUzrl+/Xuv9qvHrDd5hEhERaeCESUREpIETJhERkQZOmERERBoMJ/0Y\nqe5gZA+8a6kWoz3Zc1JaPJ4zZ47hz/mpZcuWubSpkkVU+ze6Y6TSkdPp1HqdlFSjWlg3K6FCleAg\nJSHYldhxLVUyg1TlSkqAkV5nZkKYNDZUVXOk/Q7j4+O1/k52drahuIxSXUukmHWTv1TXB0/HkXR8\n4+LixNdK1WakSjotsWfntVTnoW6/SOeEmd9DOmdUx3Lp0qVar7UiuYp3mERERBo4YRIREWnghElE\nRKSBEyYREZEGw0k/UpKIKqlFapcWxlNTU13azFywlRa2U1JSxNcWFBS4tEnxSUkIZiaoSMkGqsoV\n0jGR+k86HqqkH0+Sq4zQrZ5kpCKT1XQr3Fi97ZF0HI1U35ESkKTzUpVIZBbV+XL+/HmXNinRSeoH\n1Wd6Op6lZBQjx9eOKlzS31QdS91+kfrBzGu0FLORfpaux1ach7zDJCIi0sAJk4iISAMnTCIiIg2c\nMImIiDRwwiQiItJgOEv2aKujmLp5Kiof/3v5KlUmo5SZJWUuGSkDZ8QrJa9gye4lcMDR+LdrKnDy\nwkmUzSlTlnWSyoZJmWRWlmzbf2Y/Hip4CJU1lQgKCMLKO1YiqXOSMitN6n/dMnNmZZLlfZWH+R/O\nR6AjEJGhkfjjiD8iLiJOWfpN+ruq8nFWySnMQe7eXLQObo3eHXsjd2wuIltFKsezlMkn9an0Pcwc\nL0ePHsXmA5tdzkNdunuAmrWP6/I9y5HzSQ4cDgfiwuPw74P+HVGtopTl7rwpuWb2ebm+cj36dOqD\nR2595GqbKuNUKpfZkmP6ndJ3kPVhFi7XXcZN0TfhxTtfRHhIOADvy3ZK54SZGcDT8qe59LMRUj9b\nUYLQ0B3mwXMHMfeDuWhoaDA9ECukJaahOKMYRRlF2DNjD64Lvw65Y3PRsU1Hu0NTulR7CaM2jMLj\ntz2OoowizB8yH/e+ea/dYblVc6UGaXlpePWOV1EwpQCju4/G/9n5f+wOy60dR3bguY+fw46pO1CU\nUYQxCWMw4+0ZdoelxZ/Ow6LTRVjyyRK8OfZNvH/n+4hrF4clxUvsDqtZB74/gOEvD8frX75udyha\nvq/+HtPfmo68e/Lw1ayvEB8Zj3kfzLM7rGb5Wz9rT5jVtdVIy0vD0lGuhW/9waK/LkJ0eDTSk9Lt\nDsWtbYe3ISEqAaMSRgEAxvUch013bbI5Kvfq6usAAJU/Nt7tXKy9iLCgMDtDalbR6SKM6D4Cndt2\nBgBM7D0Rb3/9Nq7UX7E5Mvf87TxM6pyEgw8eRJvgNvix7kecqT6DyNCWL6hvVO6eXEzvOx1333i3\n3aFo2XZ4GwZ2GYjuzu4AgMz+mXh1/6s2R9U8f+tn7Z9kZ26Zicz+mejTqY+V8VjiXPU5LPlkCT6f\n6frwra8pPVfaOLG/lY6SMyVwtnLi2RHP2h2WW21C2mDF7SswctNItA9rj7r6Orx/9/t2h+XWwC4D\nkbMnBycqT6BrRFesLV6L2vpanKs+Z3dobvnjeRgYEIhtx7fhiY+fQGhgKB7p69nPbi0pZ2wOAGD7\nke02R6LnROUJdG3X9ep/X9/uely4fAFVl6uu/izri/ytn7XuMJ/f+zyCA4Ixte9UNMD3fwa61urP\nVmN8r/GIjYi1O5Rm1dbX4r2D72Fm/5nYO2MvHhj4AMb+aSxq62rtDk3pi7Nf4OldT2PPb/fgy3/5\nEo8MeARpW9LsDsutwXGDkZ2SjfEbx2PgCwMRFBCEqLAohASG2B2akj+fhyNjR+KzyZ/hocSH8NsP\nfmt3OP9w6hvqxfZAR2ALR/KPTesOc33JelyqvYSkVUn4se5HVNdWI2lVEt79zbu4Lvw65fukxA47\nSkVt/HIjcsbk/I82VWKHtE9jS8Yc0zYGvTr0Qv+Y/gCAO3veifS30vHN+W+UZaykJASHw+HSJpXW\nMyMpYeuhrUiOTcZNsTcBAB5LeQxZu7JQH1qvTCqSFuRVZfqsUHW5CkPihmBav2kAgLMXz2L+jvlw\nhjmVfSIlXUl7N0r7jpqRjOLJeSh9F6n8Y15entfxSQ6XH8a3Vd+iC7oAAO7+2d14cveTqPyxUpns\nt3DhQpc2aexK496TvWeNUo1TKxOnmhMbEYvCk4VX/7vshzI4WzkRFty4NGLk2tGSiZlm0S376e01\nRusOszC9EPsy96EoowjvTnkXYcFhKMoocjtZ+oqKmgocKj+EQV0H2R2KljEJY3C04iiKTxcDAHYd\n24UARwDinXqb/tohqXMSCo4W4OzFswAaM2a7O7sjKizK5sjUTl04haHrh+LCjxcAAM8UPINf//zX\nNkflnj+eh6erTmPyf05GxY+NF+G8b/LQ09kTEaFyXWTyzMgeI1F4shCHyw8DAFZ9tgqpPV1rYJN3\nDD9WAuDqYxr+4FD5IcS0jUFggH/8NBEdHo3Nkzcj851MXKy9iFZBrZB3T55P/1Q4LH4Y5g6ai6Ev\nDUVoUCiiwqKQPznf7rDcuqH9DXgi+Qn8Ys0v0IAGJHdNxvKxy+0OyxB/OA+TY5Px5OAnMfn9yQgK\nCEJ062isGrbK7rC0+UMfA0DHNh2xLnUdJm2ahNr6WvRw9sDLE162Oyxt/tLPhifMuMg4/PDED1bE\nYon+Mf1R+mCp3WEYkhybjN3pu+0Ow5DMAZnIHJBpdxiG3D/gftw/4H67w/CIP52HGf0zMKrDKLvD\n8Mja1LV2h6BtdMJojE4YbXcYHvGXfmalHyIiIg2OBn94+pmIiMhmvMMkIiLSwAmTiIhIAydMIiIi\nDR49VnIt1YPe0s4fcXFxLm1SEQGrH/g18nD655+3fEk96eFh1W4l0oPoEunhb7N2K1FR9Z30wHRJ\nSYlLW2qq67Nkdj1ELfWV9MD0+vXrXdqys7PFz1Q9UG4WKT6p/6Q4VLtymEV1DkpFLY4dO+bSJvWp\n1f0JqOOW+lp6rfTwvJk7a0h/U3XtkM45qfCGamcZO0j9N2fOHK33Ll0q12DWLXjBO0wiIiINnDCJ\niIg0cMIkIiLSYHgNU1rHMbLWIa1FSOsOVv9mrorZ7B3bPSV9f9V6o/S7vPRaqai11VRrJ9IatbS+\nnZ/vWmJP1Q+eHDvps1QFmqV2qfi67t8xk2o8S2vI0tiS1nBU62pm5Reo1gKlz5euG3bkFgDqvpZy\nCaTNHKRzwszxodpYQiKtV0pr8L6+hqnL2400eIdJRESkgRMmERGRBk6YREREGjhhEhERaeCESURE\npMFwlqyUmaaqNJOSkqL1mapsObNIn6+K+ciRI5bGokvKWjSS2StlHktZqFZTVV6RvouU/Sa938xM\nZt1KPYCc8ShldEqZvWbGLI1nVWak7rklZQ+qPtOsCkCqLFzp7zocrhsMW515rKK6dsyePdulTRq/\nVl/vpOOjOma+cp0wUp1IypiWSPOPtxWVeIdJRESkgRMmERGRBk6YREREGjhhEhERaTCc9CMlB0jb\nRgFyooOUELFu3TqjYRgiLSirFralElDS95AWpK3ekkxVnkpauNct2aZaWDdrCy0jCSLS3zRz2yOJ\nlGikilmKRff72bV9ky4pPquTU1R0S955W+ZMh5Eyc1I8Upt0rFTJcWYli6kSpKRrirdjyRPSuS9t\nPWY33mESERFp4IRJRESkgRMmERGRBk6YREREGgwn/UiL0Kr9yaZNm+bSJlVLMatyiIq0cK9aBNd9\nrbRIr0pW8CQZSPosVWKAlFggvV9aWLc6UUkVs+4iv5ScpUrE8CSxRhrPRj5HNzHGzKQfaTx6mxwi\nfQ+rqxOpzhfdhDPp/Ub22PT0b6hI1zvJsmXLXNpUCUxmXRtV56G3rzWLVHFLagPkPpGqc1mRMMg7\nTCIiIg2cMImIiDRwwiQiItLACZOIiEiD4aQfiWphXErY0E2gMXPhWXcrKUBOONBNdFItUntSNUdK\nAlAlNOhWDrG6ao70PRcuXKj9fmm8WJ2U5I+ksaGqAqWbICS9zsxKOvHx8aZ9VhPpfDB7yy/p2jFn\nzhzxtdL4lY7LsGHDXNrMrKok9YHqGiRds3STvVR9bWaymJG/ey3pO3s7r/AOk4iISAMnTCIiIg2c\nMImIiDRwwiQiItLACZOIiEiDoSzZvK/ysKBgAQIdgXCGObFm3BrEO+OVWUtShqOUdSZlapmVJbv/\nzH48VPAQKmsqERQQhJV3rERS5yRl9qWU/aqblWhGFuorJa9gye4lcMABAKioqcDJCydRNqcMFysu\niu8pKCjQis8q7mIuLi4W39OvXz+XNimrrSX2PJyWPw19OvXBI7c+YtnfUGWSG/1+75S+g6wPs3C5\n7jJuir4JL975IsJDwpV7GOqeb1K5QTPKsjWNjZ8t/hkAoOpKFb7/8XtsumUTIkPkbErp70rnq5G9\nKo3af2Y/Hnrf9boBACkpKeJ7pPNQlTl/LTP6esO+DVj88WJUX6xGaEAoHkh4AD3b9gQAHDt2THyP\n1K/SNVA6N1WZvZ5k/Bo5B3WzcKVSm96WTtS+w6y5UoO0vDRsvmczijKKMO6GcXjwvQd1326LS7WX\nMGrDKDx+2+MoyijC/CHzce+b99odlltpiWkozihGUUYR9szYg+vCr0Pu2Fx0bNPR7tCU/DFmADjw\n/QEMf3k4Xv/ydbtD0fJ99feY/tZ05N2Th69mfYX4yHjM+2Ce3WG51TQ2Vt+8GiuSViAqJAqzfzZb\nOVn6An+8bpSeK8W87fOwLW0bVt+8GvfG3ovsL7PtDqtZ/nYOat9h1tXXAWi8ewCAqstVCAsOsyYq\nk2w7vA0JUQkYlTAKADCu5zjEO81/Hswqi/66CNHh0UhPSrc7FG3+FHPunlxM7zsdcRGuz8/5om2H\nt2Fgl4Ho7uwOAMjsn4nElYnIvT3X5sj0/On4n+AMduL2zrfbHYpb/njdCA0MxZpxa9CpTSf8DX/D\nDW1vQPnlctQ11CHQEWh3eEr+dg5qT5htQtpgxe0rcOuLt6JD6w6oa6jDR9M/sjI2r5WeK228eL+V\njpIzJXC2cuLZEc/aHZaWc9XnsOSTJfh8pv5uCXbzt5hzxuYAALYf2W5zJHpOVJ5A13Zdr/739e2u\nx4XLF1B1ucrGqPRU1lbi9bLX8cLNL9gdSrP88boRFxmHuMi/TzrPH34et3W4zacnS8D/zkHtn2S/\nOPsFnt71NA48cABlj5QhKzkLEzdOtDI2r9XW1+K9g+9hZv+Z2DtjLx4Y+ADG/mksautq7Q6tWas/\nW43xvcYjNiLW7lC0+WPM/qS+oV5s9/WLIgBsOb0Ft3W4DdGtou0OpVn+fN2orq3Ggi8X4HTNaTx2\nw2N2h/MPR/sOc+uhrUiOTUa3yG4AgFkDZ2HO1jkov1SuTNCREhGkPeNUi+jeimkbg14deqF/TH8A\nwJ0970T6W+n45vw3ylJRUsxSebfU1FSXNjPL+W38ciNyxuQ0GxsAzJ4926XNjpJyUsyqfpb2RW2J\nBB+zSf0sJX+oElSMfOfYiFgUniy8+t9lP5TB2cqJsOAw5diQ+l8qzSadg2Yej73Ve5EzJgeD4wZf\nbVMlYEgJKrrJM2Zwd93o2aGnMqFOOv+lfRqXLl3q0mbG+Xq88jjufO1OxLSKwbpb1yE4IPjq/y8i\nIkJ8z4QJE7Q+e+rUqS5tnpT8NINu0o8V84r2HWZS5yQUHC3A2YtnATRmzHZ3dkdUWJTpQZllTMIY\nHK04iuLTjZmau47tQoAjwOfXIypqKnCo/BAGdR1kdyja/DFmfzOyx0gUnizE4fLDAIBVn61Cak/X\nf7j5Gn8bG/543Th/6TxSXkrBpN6T8Pubf/8/Jksyj/Yd5rD4YZg7aC6GvjQUoUGhiAqLQv7kfCtj\n81p0eDQ2T96MzHcycbH2IloFtULePXkICQyxOzS3DpUfQkzbGAQG+P5PbU38MeYmTY/D+LqObTpi\nXeo6TNo0CbX1tejh7IGXJ7xsd1jN8rex4Y/XjRWfrkDZD2XIO5CHVy+9CqBxXK8atArtQtrZHF3z\n/OUcNPQcZuaATGQOyLQqFkskxyZjd/puu8MwpH9Mf5Q+WGp3GIb4Y8xN1qautTsEbaMTRmN0wmi7\nwzDEH8eGv103sgZnIWtwFgD1M7++zF/OQVb6ISIi0uBoaGhosDsIIiIiX8c7TCIiIg2cMImIiDRw\nwiQiItJgKEsWgLgziepBXunBVt332/UQu7RrgBSzHQ/tqh5+lx5alx7ulR6OVj0EbNb3k3Y+ULVL\nu71I48Dqh9hVWYbS35XiU31nK6nOQSlmaRxIx9vq4heq8SwVAJCKQUikgiKAfEw8/X5GdmeSzi9p\nfOk+jO8pVZEIVcGLa0nHysyYpT5VnedSMQiJNBa8va7xDpOIiEgDJ0wiIiINnDCJiIg0GF7DlNZK\njKyfSG3S7+ie7NptBit3cfeWkQoe0vqCtA4kFVX2lLQ+MGfOHPG1cXGu+99JaxPS8bB6DdPI50vj\nVFrXNLP6ipH1Hunckt4vrR9bfQ6q1s+ktcDsbNfNkKU+VeU+eLreJvWBKu7KykqtNt0xYyYj6+rS\nGrLVa6xGrrvSWJDen5/vWrpV9Xek8S/hHSYREZEGTphEREQaOGESERFp4IRJRESkgRMmERGRBsNZ\nslK2lCrDS6qaI2VrlZSUGA3Da6psqWPHjrm0FRcXWxyNHlWmpW5W27Rp07Te6ykp+09VeUXKqJUy\nPXWrRQGeZfJJMav6WWqXMjqljDtVhRHdSis/JX1/KRsT0K/043Q6Xdq8zSj8KW8zbhcuXOjSJmVL\nmjmeAfmYe3u9Uo1fKxmpquTJmPSW9DdVcUj9J40vqc2TsftTvMMkIiLSwAmTiIhIAydMIiIiDZww\niYiINBhO+pEWYlVll6RkIN3FfzMTOyRGkhCk7yctllu9HZKR5CrpOKWkpLi0mRmzka2upHbpmEhJ\nWEa2OWuO9DdVZeZ0+0o6HqpEIrNilo4tIB8T6dySShWaSTpmqkQlSWJiokublAgk9T3g+Ti3oiSc\nHVsXqq53dm2j6A0pgU4qq7ljxw7T/zbvMImIiDRwwiQiItLACZOIiEgDJ0wiIiINplT6USU0SAv9\n0iKzkUQisyp5qPbwlOgmhqgSDsyqnKFKXJD6Str7UkoMMTO5SqqiofruusdRitnMBBppjHqb6CEd\nJ6v3ljSS1CJ9P2kcmJnwIn2+qgqU7t6N8fHxLm2qhDDVudkcaUwvXbpUfK2096uUrGT13pJGeLP3\npbfJcZ7SrZRkRUUl3mESERFp4IRJRESkgRMmERGRBk6YREREGgwn/Rjh7VYqVlItbEsL+tL3kN6v\n+r5mJaNMmDDB8Of8lJR4YnVFJW+Tt6T3m7mYb0UChlSJxOpECKuTirwlJYiokkYkUp9GRES4tLXE\nNcfIsbT6uOtSVVWSziUpZinRTpVIpUq8Mov0d6XxIV0vVdV/dMcN7zCJiIg0cMIkIiLSwAmTiIhI\nAydMIiIiDZwwiYiINBjLkl2+HFi5EggIAHr0AF54AejQQZlhJGVgSdmRVmb47T+zHw+9/xAqayoR\nFBCElXesRFLnJGXmqpSVKWXzWVFSDQBeKXkFS3YvgQMOAEBFTQVOXjiJsjllaGhoEN8j/V0pk8yb\nMljNySnMQe7eXLQObo3eHXsjd2wuIltFKrMEpRKJUixS9punZc6u9U7pO3i+4Xlcqb+Cn7X7GbL7\nZaN1UGvl50sxS9mDy5Ytc2k7cuSI1/ECjTHP+3IeautqcWOHG/HHEX9EeEi4MnNYGrvS+SZlUZo1\nNh7d+ije+OoNtA9rDwDo2aEnXpv0mjJLVndfVekcNi0rNS8PWLAACAwEnE5gzRrgv0vxGemXliyD\n13StK79YjqCAICz55yVI7NRYms/IfqfScZHGuZEsZ5Xle5Zj5acrEeAIQI+oHnhh3Avo0LoDAPW8\nILVLY0YqD+ot/TvMoiJgyRJg925g3z4gIQGYP9/0gMx0qfYSRm0YhcdvexxFGUWYP2Q+7n3zXrvD\ncistMQ3FGcUoyijCnhl7cF34dcgdm4uObTraHZrSjiM78NzHz2HH1B0oyijCmIQxmPH2DLvDcuv7\n6u8x/a3pWDJwCd4c/iZiWsdg2ZeuE50vaYp5wx0bUPjbQsS2i8WCjxbYHVazPin7BBt/tRFFGUUo\nyijCa5Neszsk92pqgLQ0YPPmxuveuHHAgw/aHZVbP73WFUwpwGMDH0PG1gy7w3Kr6HQRlnyyBLvT\nd2Nf5j4kOBMw/0PfnlP0J8ykJODgQSA8vHFAnTwJtG9vYWje23Z4GxKiEjAqYRQAYFzPcdh01yab\no9K36K+LEB0ejfSkdLtDcavodBFGdB+Bzm07AwAm9p6It79+G1fqr9gcmdq2w9swsMtAXN/megDA\nXfF34d2yd22Oyr2mmLtFdAMATL9pOl4/8Lq9QTXjct1lFH9bjMUfL0bflX3xq02/wonKE3aH5V5d\nXeP/bbprr6oCwsLsi0fDtde6Md3HYO2YtTZH5V5S5yQcfPAgwkPCUXOlBicvnET71r49pxhbwwwM\nBPLzga5dgb/8BZg2zaKwzFF6rrRxwnkrHQNeGICRr4xEbV2t3WFpOVd9Dks+WYJlo337rgcABnYZ\niA+PfHj1Qri2eC1q62txrvqczZGpnag8ga7tul797+iwaFRfqUb1lWobo3Lv2pi7hHdBVW0Vqi5X\n2RiVe6cunMLw+OFYNGIRPp/5OW65/hak/lnepcRntGkDrFgB3HorcP31QG4u8Oyzdkfl1k+vdf/8\n2j9jYt5En/4Ha5PAgEDkH8hH16Vd8Zfjf8G0vr49pxhP+klNBb77DsjOBkaOtCAk89TW1+K9g+9h\nZv+Z2DtjLx4Y+ADG/mmsX0yaqz9bjfG9xiM2ItbuUJo1OG4wslOyMX7jeAx8YSCCAoIQFRaFkMAQ\nu0NTqm+oF9sDHL6bB6eKOTAgsIUj0dctshu2TNmChKgEAMBjgx7D4fOHcazimM2RufHFF8DTTwMH\nDgBlZUBWFjBxot1RufXTa92Hv/4Q6YnpuDv/br+41qX2SsV3c79Ddko2Rm7w7TlFP+nn8GHg22+B\n225r/O/p04GZM4Hz55WLv9JCvVSuSNoXz4wF5Zi2MejVoRf6x/QHANzZ806kv5WOb85/o0zskBa3\nHQ6HS5tUlsvIHpvN2fjlRuSMyfkfbVICjIrUf1YlIFRdrsKQuCGY1q/xX4dnL57F/B3z4QxzKpOr\ndMtnScdJd79Ed2IjYlF4svBqssCximNwhjlxy823KMfesGHDXNqkcZCXl+fSZkYySlPMTcfxWMUx\nOFs50blDZ0MlCKWkCati3n9mP0rOlODem/6eO9DQ0IDgwGDl5+smp5kxDkRbtwLJyUBTfLNmAXPm\nAOXlQFSUoX6xYk9GybXXuilJU/Dwfz2M8oZy9Izsqbx2SH3tdDpd2qRxbuR6JDlcfhjfVn2L22Jv\nQ0VFBSbGT8TMLTNx9NujiGwVKSbyAPJYkF4rlcHztnSi/j+nT58GJk9uHDQAsGED0KdPYwaZjxqT\nMAZHK46i+HQxAGDXsV0IcAQg3um68awvqaipwKHyQxjUdZDdoWg5deEUhq4figs/XgAAPFPwDH79\n81/bHJV7I3uMROHJQhwuPwwAWPXZKqT29O2fCv0x5gBHAGa/P/vqHeXze59H4nWJiGkbY3NkbiQl\nAQUFwNmzjf+dlwd07w5ERdkblxv+eK07XXUak/9zMsovNc4pmw5swj91+CdEtvKdDbavpX+HmZwM\nPPkkkJICBAcDMTGNWWQ+LDo8Gpsnb0bmO5m4WHsRrYJaIe+ePJ/+qRAADpUfQkzbGJ/+qe2nbmh/\nA55IfgK/WPMLNKAByV2TsXzscrvDcqtjm45Yl7oOkzZNQm19LXo4e+DlCS/bHZZb/hjzjZ1uRM6Y\nHFAceGEAACAASURBVNzx2h2ob6jH9e2u9/0s2WHDgLlzgaFDgdDQxokyP9/uqNzyx2tdcmwynhz8\nJFJeSkFAQwCua3MdNtyxwe6w3DL2HGZGRuP//EhybDJ2p++2OwxD+sf0R+mDpXaHYcj9A+7H/QPu\ntzsMQ0YnjMbohNF2h2GIP8Y8pc8UTOkzxe4wjMnMbPyfH/HHa11G/wxk9M9osZ+uveW7GQ5EREQ+\nxNGgKh9DREREV/EOk4iISAMnTCIiIg2cMImIiDQYy5JVkB72B+SHYqUH2c3afcIIVSV86cFW3Z0/\nrPbNN9+I7c8KZbs++OADl7a7777bpW3RokXeB+YBqf+kwg9W7mSjonogXmqXCjCYtmOGgtQnqmIL\n0mul+KTvZvX3UBWvkMaG7s4T0sPqgPcPrP+UKqNTuk5I10bp+1l9DVRdo6VxI7WpCpBYSTU+pAIi\nkuzsbJc2b6/bvMMkIiLSwAmTiIhIAydMIiIiDaY8h6n6/V36DfrYMdddCqTd6M1cP5F+v1f9Ji+t\ndaxfv96l7fz58y5tZhY3lz6/e/fu4mv79+/v0nbzzTe7tK1atUrr75hJVaBZtwi/twWePaFaN42P\nd63LuW7dOpc2q9ejpPVGI8W1ddeorF6nV627Sue+VFxb6mfVdUO32L8OI2trcXFxLm3SWr3Va6yq\nfpGuWdI12o5xrtrMYprmtpJSwXjVua177eYdJhERkQZOmERERBo4YRIREWnghElERKSBEyYREZEG\nw5V+pIxTVYaelJEkZVZJ2XJmZkcaqawhtUuxmJkRK3n88ce1XytV9XE6nS5tUkUgM0nZeap+1s0e\nlNrsqAwFyFl3qgoqVpLGnqr6jNQutUlj3OosWVVFJV1S5mxLHA8j/WJHJSjpWFZWVoqvlcaCdM7p\nZqYC5p2f3vaTND68vW7zDpOIiEgDJ0wiIiINnDCJiIg0cMIkIiLSYDjpR1oklhZXAXmBVVrol0qO\nqUoYebIQbOQ9UsxWL9JLpDJ28+bNE1+7fft2lzbpOP3rv/6r94G5ISULqJINdLfykpINVGPD6iQV\n6bvYkfQjJVWozkHdLfakPlUl3tmx1ZPUz/n5+S5tUgk3b0j9orvVGKCf5GhmnxpJbJH+ru6Ytvq6\n6G2CjhXnJu8wiYiINHDCJCIi0sAJk4iISAMnTCIiIg2mVPoxQlooTklJcWlT7YXmSWKH9B5V4oiU\n6KBKqGhpqv0wpaSfpKQklzZpj8zXX3/d0N9yR1VtRiKNI9X+iNeyq9KPREoAkcaQ1YkyqjGqWzFL\nOkdU57rV30W3YlRL7NHobcUxaXxIbcXFxeL7Pbn2SMcnOztbfK10HZSu0dIemWbu4Snxtu+9rSQl\n4R0mERGRBk6YREREGjhhEhERaeCESUREpMHR0NDQYOQN0nY1qoV2aUFZWtCXFplVCSBWV3OR/q6R\n+HxZRkaG9mulSkOeMJK8JSUWpKamurSZufWbEVISjG6SiR0VgYyQ4lOda2b1vypJTEpakRJMrL4W\nAHK/qJJdpLEufRcj1cTMGjdGEvKk72EkcdKTCj1SfKp+Likp0frMHTt2aH+mLt5hEhERaeCESURE\npIETJhERkQZOmERERBo4YRIREWkwVBrvndJ38Ni+x1BbX4tezl54dtCzaBPcRpmBJWV+6WZrmZWF\numHfBiz+eDECHAFoHdway0Yvw80xriXimuiWNZOyhVUZbVJmlruSV8v3LMfKT1ciwBGAHlE98MK4\nF9ChdQc4nU7x9VL76tWrXdrOnz+v1eaNzQc2Y+rmqah8vHHvSCOlyqS9L1siG3la/jT06dQHj9z6\nCAB1Zq/ULo1nI2XEjO6NmFOYg9y9uWgd3Bq9O/ZG7thcRLaKNLR/rBSz9N283Y/wqrw8YMECIDAQ\ncDqBNWuA+Hhltq1UOk46X6wsQbj/zH489P5DqKypRFBAEFbesRJJnRvLTaqO5YQJE1za4uLiXNqk\nfVVNKb+p6GdAXSZONW6uJcWsupYbGjf/HXPI5cuoa9cOJ556Cpe7dAGgnw0LABERES5tVuzXqX2H\n+X3195j+1nSsGrYK28dvR9fwrlj02SLTAzJT6blSzNs+D9vStqEoowi/G/w7TNw00e6w3Co6XYQl\nnyzB7vTd2Je5DwnOBMz/cL7dYWk5eO4g5n4wFwafVLLNge8PYPjLw/H6l3I9XV+z48gOPPfxc9gx\ndQeKMoowJmEMZrw9w+6w3KupAdLSgM2bgaIiYNw44MEH7Y7KrUu1lzBqwyg8ftvjKMoowvwh83Hv\nm/faHZZ7ftjPP4259LXX8MOQIejy7LN2R+WW9oS57fA2DOwyELFtYwEAv+n5G+R/47rjuS8JDQzF\nmnFr0KlNJwDAzTE340zVGVypv2JzZGpJnZNw8MGDCA8JR82VGpy8cBLtW7e3O6xmVddWIy0vDUtH\nLbU7FG25e3Ixve903H3j3XaHoqXodBFGdB+Bzm07AwAm9p6It79+26fHM+rqGv9v091IVRUQFmZf\nPBq2Hd6GhKgEjEoYBQAY13McNt21yeaomuGH/XxtzAHV1WgIDbUxoOZp/yR7ovIEurbrevW/O7fu\njItXLuJi7UVLAjNDXGQc4iL//pPII1sfQWqvVAQFGN6kpUUFBgQi/0A+0t9OR6ugVnhm2DN2h9Ss\nmVtmIrN/Jvp06mN3KNpyxuYAALYfcd3txRcN7DIQOXtyGs/FiK5YW7wWtfW1OFd9zu7Q1Nq0AVas\nAG69FejQofEi+dFHdkflVum5UkSHRyP9rXSUnCmBs5UTz47w7Tsff+znn8b8TxERcNTX46CwA40v\n0b7DrG+oF9sDHYGmBWOV6tpq3PX6Xfjm/Dd4YdwLdoejJbVXKr6b+x2yU7IxcsNIu8Nx6/m9zyM4\nIBhT+05FA/zj51h/NDhuMLJTsjF+43gMfGEgggKCEBUWhZDAELtDU/viC+Dpp4EDB4CyMiArC5jo\n28sitfW1eO/ge5jZfyb2ztiLBwY+gLF/Govaulq7Q1Pzw37+acx/27oVZ6ZPR/yjj9odlVvat1qx\nEbEoPFl4dSH1WMUxOFs50Suhl9d7V0oL0mYlHByvPI47X7sTN3a6ETvv23n14mKkVNSyZcu02hIT\nE8X3S39Ltch/uPwwvq36FrfF3gYAmN5vOmZumYnzl86L+14CwLPC7/533XWXVhybNnn/U9P6kvW4\nVHsJSauS8GPdj6iurUbSqiS8+5t3cV34deJ7pKQpaeHe6j33JKqxJyWj6FK9V0oUU43NqstVGBI3\nBBPiG5NLvqv+Dk82PAnHjw7leJKSNSRScop0jAzbuhVITgaaEjBmzQLmzAHKy5UxS/vj6sZiRtJP\nTNsY9OrQC/1j+gMA7ux5J9LfSsc3579Bzw49lclK0liVjqUUo9dl/tz0M6KilMl3UixSzEuXui61\neJ1U85OY+wLATTcB/+//oW9sLBAVJe53CqiT8lqC9h3myB4jUXiyEIfLDwMAVn22Cqk9Xet8+pLz\nl84j5aUUTOo9Ca9OfNW3/yX+305Xncbk/5yM8kvlABqzfPtE94EzTM6Q9QWF6YXYl7kPRRlFeHfK\nuwgLDkNRRpFysiTPnLpwCkPXD8WFyxcAAM/teQ6Tbphkc1TNSEoCCgqAs2cb/zsvD+jeHYiKsjcu\nN8YkjMHRiqMoPt24qfOuY7sQ4AhAvDPe5sjc8MN+9seYte8wO7bpiHWp6zBp0yTU1teih7MHXp7w\nspWxeW3FpytQ9kMZ8g7k4c0DbwIAHHDgv377X3DAYXN0suTYZDw5+EmkvJSC4IBgxLSNweZ77Ck2\n7ilf7VsVf4n3hvY34InkJ/DLjb9EQ0MDbom5Bf8x9D/sDsu9YcOAuXOBoUOB0NDGi2G+bycLRodH\nY/Pkzch8JxMXay+iVVAr5N2T59v/4PbDfvbHmA1lv4xOGI3RCaOtisV0WYOzkDU4S/z/Vfyo/5Ns\nS8von4GM/vo7i/iSuMg4/PDED3aHYcja1LV2h6Dt/gH3Y8rPptgdhjGZmY3/8yPJscnYnb7b7jCM\n8cN+9reYWemHiIhIg+H9MImIiP434h0mERGRBk6YREREGjhhEhERaTClRpzqAWSp2vzs2bNd2qSH\nZ61+YF21s4i0e4T00Ln0oLdu5X8d0sPRqoePvdnpQPXAtNX9r1vMQSoioHqI3ZNiF9I4UH13qQiA\n9HC1kR1azKIae/Hxrs8OTp061aXNyuIhgByfkWILUlEL6dhZsUPFtVR9LV3HpHhUhQ+sZGQHHun7\nSa+z+hqh2qlIOu6q67nu63THDe8wiYiINHDCJCIi0sAJk4iISIMpa5iq3/Sl9UqJ9Nu/6jPtWKeS\n1k+sJq1zeLumJK0ZqX7Tt6Po+bFjx7TaVGPDk7VcI0WvpaLg0jqLHWuYRtbF1q9f79Im9akpxdf/\nm7QGphrPUp9K75favC5irkG1tqa7oYP0fmkN2VPSsTSyHigdF2mNz8gGFs2RPku17irFJ12v8oUy\ne6rzRNU/1+IdJhERkQZOmERERBo4YRIREWnghElERKSBEyYREZEGU7JkjWRUSpl30vvNrDIiUWVU\nSllUUoaY1ZmQRiqj2FE5RCLFocp08yYD05vKRtfyNjtRqqSjO8bN5O3n61ZK8ZR0Pqv6Xjq+Cxcu\n1HpdS1CNXSlDV/reqnPCSqrrqXRtk8aC9PSAKlvdk2pLUnxGqvJIsUhZst6OGd5hEhERaeCESURE\npIETJhERkQZOmERERBpMSfpRJcBMmDDBpU3aFsvqRXBpoVe1cC+VSJIWvK1mpOSa1O4riQWqftbt\nU6vLErbEdlAtwUiSnNVb00l0S48BcgJTYmKiS5tUUrMlqL6LNJbMLC+oS4pDNT6kRD3p+0ljRvXd\nrE6IlP6udL2Trh3enu+8wyQiItLACZOIiEgDJ0wiIiINnDCJiIg0WLofpsSOqj5G6O7xJlUeUfFk\njz4poUG1yN6vXz+XNmnh3urKKNKxVfWn1CdSn7bE/oa6dCsq2VGBRpXkJSU+SHuMSu+3OnlDdWyl\nCi9WJyUZoYpbGuvSeWgkAcosqrGru8+odEysrg6lSuoqKSnx+DNV1aV0K37xDpOIiEgDJ0wiIiIN\nnDCJiIg0cMIkIiLSYErSj2rBdOrUqS5t69evd2mTFtHtqsAixSItPtuRjKJKJpESO3STl+yim8Rh\n9bZYRuhWE5GSIVTHzqyEN1VSh5RgIo0N6Rw2M+lH928C+ttk+RppfEgJVnYk/aiup7rXMV/ZQlBF\nmmuk8eXtOOIdJhERkQZOmERERBo4YRIREWnghElERKSBEyYREZEGQ1myeV/lYUHBAgQ6AuEMc2LN\nuDWId8aLmWCAnGUnZVvp7snmieV7lmPlpysR4AhAj6geeGHcC+jQuoMyS1P370rvN6sk2qNbH8Wm\nLzchqlUUACDBmYAXx7yoLH9mx36dKtPyp6FPpz545NZH3L5ONwvaSMapURv2bcCzf3kWAY4AhAWF\nYVHKIvSN7qscA/n5+VqfO2zYMJe21NRU8bUeZx9Omwb06QM80tjPquw/3XHqTbmx5mzYtwELti1A\ngCMAoQGheCDhAfRs21M5bqWYdbM5VZm9HmfdX9PPgDoDXTqWKSkpLm1G9siUjpXqWOcU5iB3by5a\nB7dG7469kTs2F5GtIpWxAfITALrXaG8zZ18peQVLdi+BAw4AQEVNBU5eOImyOWXo2Kaj8jycNm2a\nS5sVGbES7Qmz5koN0vLSsD9zP+Kd8fjD7j/gwfcexJYpW0wPyixFp4uw5JMl2Je5D+Eh4Zi7bS7m\nfzgfK+5YYXdobn1S9gnWjlmLAZ0H2B2KtgPfH8Csd2ehsKwQfTr1sTucZpWeK8W87fOwc/JOdGzd\nER8c/QBp76Rh//T9dofm3oEDwKxZQGFh44XcxzX18/KblsMZ4kThuUJkf5mNP9/yZ7tDc8/P+nnH\nkR147uPnUJheiM5tO2PDvg2Y8fYMvH7X63aHppSWmIa0xDQAwJX6KxiybgiyBmehY5uONkempj1h\n1tXXAWj8VwAAVF2uQlhwmDVRmSSpcxIOPngQgQGBqLlSg5MXTqK7s7vdYbl1ue4yir8txvKi5fim\n4ht0j+yO/zvk/+L6ttfbHZpbuXtyMb3vdMRFuO7M7otCA0OxZtwadGzdeHL27dQX31V/hyv1V2yO\nrBm5ucD06UCcf/Vz2MnGa8UNbW9A+eVy1DXU2RxZM/ysn4tOF2FE9xHo3LYzAGBi74lIfysdV+qv\nICjAlMftLbXor4sQHR6N9KR0u0NxS7sn24S0wYrbV+DWF29Fh9YdUNdQh4+mf2RlbKYIDAhE/oF8\npL+djlZBrfDMsGfsDsmtUxdOYXj8cGQPykb3yO7I+SwHv3n7NyiYUmB3aG7ljM0BAGw/st3mSPTE\nRcYhLjLu6s9rv9v1O4ztPtb3Ly45jf2M7f7VzztP7gQAPH/4edzW4TYEOgLtDaw5ftbPA7sMRM6e\nHJyoPIGuEV2xtngtautrca76HKLDo+0Oz61z1eew5JMl+HymtbufmEE76eeLs1/g6V1P48ADB1D2\nSBmykrMwceNEK2MzTWqvVHw39ztkp2Rj5IaRdofjVrfIbtgyZQu6RzbeCT9484M4UnkEx384bnNk\n/5iqa6tx3zv34egPR/GH4Xpb/JBxNXU1WPDlApyuOY3HbnjM7nD+4QyOG4zslGyM3zgeA18YiKCA\nIESFRSEkMMTu0Jq1+rPVGN9rPGIjYu0OpVna/5zeemgrkmOT0S2yGwBg1sBZmLN1DsovlSsTGqTk\nB4lV5c8Olx/Gt1Xf4rbY2wAA0/tNx8wtM3H+0nnlwr1uYsfs2bNd2lT7txmx/8x+lJwpwfXlf/8J\ntq6uDqVflSoTH6TEAl8qKSfRTQiTFv5V381oYsfxyuP/v717j46quvcA/s0LCCRAwiMw5ZEABSxN\ngTRopYEEYSGgNmIFMZRyyYrGwEUuWFaVBQuR1QW0GqQhgoELUlEvahsiKILeIj4KQQny0hQSJAiB\nsiQkBkJKQub+gaGW+e3JPpNz2DPc7+cfFnvN4zf77Dk7Z/bv/Dbu2nAXYtvE4nf9fofjXx4HIJdv\nBICews9z0ntK8dkxNrxRlZnT7WeptJhdTladxJwjc9C3fV/k/Tzv+klcKisIACtWrPD5vVSJKE7v\n3ah6DymxSfe8CADLly/3aJO+ExevXMTwnsMxbfC1hJhzl85hwc4FiAqPAqAuRambVCQlHNqVfLfp\nyCbkjM3xaFcdS+nce7NKJ2pfYSZ0TcCuE7tw7tI5ANcyZnt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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -739,15 +1504,66 @@ " subplot_kw={'xticks':[], 'yticks':[]},\n", " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", "\n", + "test_images = Xtest.reshape(-1, 8, 8)\n", + "\n", "for i, ax in enumerate(axes.flat):\n", - " ax.imshow(digits.images[i], cmap='binary', interpolation='nearest')\n", + " ax.imshow(test_images[i], cmap='binary', interpolation='nearest')\n", " ax.text(0.05, 0.05, str(y_model[i]),\n", " transform=ax.transAxes,\n", " color='green' if (ytest[i] == y_model[i]) else 'red')" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Examining this subset of the data, we can gain insight regarding where the algorithm might be not performing optimally.\n", + "To go beyond our 80% classification rate, we might move to a more sophisticated algorithm such as support vector machines (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)), random forests (see [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb)) or another classification approach." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Summary" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In this section we have covered the essential features of the Scikit-Learn data representation, and the estimator API.\n", + "Regardless of the type of estimator, the same import/instantiate/fit/predict pattern holds.\n", + "Armed with this information about the estimator API, you can explore the Scikit-Learn documentation and begin trying out various models on your data.\n", + "\n", + "In the next section, we will explore perhaps the most important topic in machine learning: how to select and validate your model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb) | [Contents](Index.ipynb) | [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.03-Hyperparameters-and-Model-Validation.ipynb b/notebooks_v1/05.03-Hyperparameters-and-Model-Validation.ipynb similarity index 86% rename from code_listings/05.03-Hyperparameters-and-Model-Validation.ipynb rename to notebooks_v1/05.03-Hyperparameters-and-Model-Validation.ipynb index 2b6f59e7e..3edcada26 100644 --- a/code_listings/05.03-Hyperparameters-and-Model-Validation.ipynb +++ b/notebooks_v1/05.03-Hyperparameters-and-Model-Validation.ipynb @@ -3,17 +3,94 @@ { "cell_type": "markdown", "metadata": { - "collapsed": true + "deletable": true, + "editable": true }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) | [Contents](Index.ipynb) | [Feature Engineering](05.04-Feature-Engineering.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, "source": [ "# Hyperparameters and Model Validation" ] }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "source": [ + "In the previous section, we saw the basic recipe for applying a supervised machine learning model:\n", + "\n", + "1. Choose a class of model\n", + "2. Choose model hyperparameters\n", + "3. Fit the model to the training data\n", + "4. Use the model to predict labels for new data\n", + "\n", + "The first two pieces of this—the choice of model and choice of hyperparameters—are perhaps the most important part of using these tools and techniques effectively.\n", + "In order to make an informed choice, we need a way to *validate* that our model and our hyperparameters are a good fit to the data.\n", + "While this may sound simple, there are some pitfalls that you must avoid to do this effectively." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Thinking about Model Validation\n", + "\n", + "In principle, model validation is very simple: after choosing a model and its hyperparameters, we can estimate how effective it is by applying it to some of the training data and comparing the prediction to the known value.\n", + "\n", + "The following sections first show a naive approach to model validation and why it\n", + "fails, before exploring the use of holdout sets and cross-validation for more robust\n", + "model evaluation." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Model validation the wrong way\n", + "\n", + "Let's demonstrate the naive approach to validation using the Iris data, which we saw in the previous section.\n", + "We will start by loading the data:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -23,11 +100,24 @@ "y = iris.target" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next we choose a model and hyperparameters. Here we'll use a *k*-neighbors classifier with ``n_neighbors=1``.\n", + "This is a very simple and intuitive model that says \"the label of an unknown point is the same as the label of its closest training point:\"" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -35,11 +125,23 @@ "model = KNeighborsClassifier(n_neighbors=1)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Then we train the model, and use it to predict labels for data we already know:" + ] + }, { "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -47,11 +149,23 @@ "y_model = model.predict(X)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we compute the fraction of correctly labeled points:" + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -70,11 +184,42 @@ "accuracy_score(y, y_model)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see an accuracy score of 1.0, which indicates that 100% of points were correctly labeled by our model!\n", + "But is this truly measuring the expected accuracy? Have we really come upon a model that we expect to be correct 100% of the time?\n", + "\n", + "As you may have gathered, the answer is no.\n", + "In fact, this approach contains a fundamental flaw: *it trains and evaluates the model on the same data*.\n", + "Furthermore, the nearest neighbor model is an *instance-based* estimator that simply stores the training data, and predicts labels by comparing new data to these stored points: except in contrived cases, it will get 100% accuracy *every time!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Model validation the right way: Holdout sets\n", + "\n", + "So what can be done?\n", + "A better sense of a model's performance can be found using what's known as a *holdout set*: that is, we hold back some subset of the data from the training of the model, and then use this holdout set to check the model performance.\n", + "This splitting can be done using the ``train_test_split`` utility in Scikit-Learn:" + ] + }, { "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -102,11 +247,47 @@ "accuracy_score(y2, y2_model)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see here a more reasonable result: the nearest-neighbor classifier is about 90% accurate on this hold-out set.\n", + "The hold-out set is similar to unknown data, because the model has not \"seen\" it before." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Model validation via cross-validation\n", + "\n", + "One disadvantage of using a holdout set for model validation is that we have lost a portion of our data to the model training.\n", + "In the above case, half the dataset does not contribute to the training of the model!\n", + "This is not optimal, and can cause problems – especially if the initial set of training data is small.\n", + "\n", + "One way to address this is to use *cross-validation*; that is, to do a sequence of fits where each subset of the data is used both as a training set and as a validation set.\n", + "Visually, it might look something like this:\n", + "\n", + "![](figures/05.03-2-fold-CV.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#2-Fold-Cross-Validation)\n", + "\n", + "Here we do two validation trials, alternately using each half of the data as a holdout set.\n", + "Using the split data from before, we could implement it like this:" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -126,11 +307,32 @@ "accuracy_score(y1, y1_model), accuracy_score(y2, y2_model)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "What comes out are two accuracy scores, which we could combine (by, say, taking the mean) to get a better measure of the global model performance.\n", + "This particular form of cross-validation is a *two-fold cross-validation*—that is, one in which we have split the data into two sets and used each in turn as a validation set.\n", + "\n", + "We could expand on this idea to use even more trials, and more folds in the data—for example, here is a visual depiction of five-fold cross-validation:\n", + "\n", + "![](figures/05.03-5-fold-CV.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#5-Fold-Cross-Validation)\n", + "\n", + "Here we split the data into five groups, and use each of them in turn to evaluate the model fit on the other 4/5 of the data.\n", + "This would be rather tedious to do by hand, and so we can use Scikit-Learn's ``cross_val_score`` convenience routine to do it succinctly:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -149,11 +351,27 @@ "cross_val_score(model, X, y, cv=5)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Repeating the validation across different subsets of the data gives us an even better idea of the performance of the algorithm.\n", + "\n", + "Scikit-Learn implements a number of useful cross-validation schemes that are useful in particular situations; these are implemented via iterators in the ``cross_validation`` module.\n", + "For example, we might wish to go to the extreme case in which our number of folds is equal to the number of data points: that is, we train on all points but one in each trial.\n", + "This type of cross-validation is known as *leave-one-out* cross validation, and can be used as follows:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -184,11 +402,24 @@ "scores" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Because we have 150 samples, the leave one out cross-validation yields scores for 150 trials, and the score indicates either successful (1.0) or unsuccessful (0.0) prediction.\n", + "Taking the mean of these gives an estimate of the error rate:" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -206,11 +437,146 @@ "scores.mean()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Other cross-validation schemes can be used similarly.\n", + "For a description of what is available in Scikit-Learn, use IPython to explore the ``sklearn.cross_validation`` submodule, or take a look at Scikit-Learn's online [cross-validation documentation](http://scikit-learn.org/stable/modules/cross_validation.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Selecting the Best Model\n", + "\n", + "Now that we've seen the basics of validation and cross-validation, we will go into a litte more depth regarding model selection and selection of hyperparameters.\n", + "These issues are some of the most important aspects of the practice of machine learning, and I find that this information is often glossed over in introductory machine learning tutorials.\n", + "\n", + "Of core importance is the following question: *if our estimator is underperforming, how should we move forward?*\n", + "There are several possible answers:\n", + "\n", + "- Use a more complicated/more flexible model\n", + "- Use a less complicated/less flexible model\n", + "- Gather more training samples\n", + "- Gather more data to add features to each sample\n", + "\n", + "The answer to this question is often counter-intuitive.\n", + "In particular, sometimes using a more complicated model will give worse results, and adding more training samples may not improve your results!\n", + "The ability to determine what steps will improve your model is what separates the successful machine learning practitioners from the unsuccessful." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The Bias-variance trade-off\n", + "\n", + "Fundamentally, the question of \"the best model\" is about finding a sweet spot in the tradeoff between *bias* and *variance*.\n", + "Consider the following figure, which presents two regression fits to the same dataset:\n", + "\n", + "![](figures/05.03-bias-variance.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff)\n", + "\n", + "It is clear that neither of these models is a particularly good fit to the data, but they fail in different ways.\n", + "\n", + "The model on the left attempts to find a straight-line fit through the data.\n", + "Because the data are intrinsically more complicated than a straight line, the straight-line model will never be able to describe this dataset well.\n", + "Such a model is said to *underfit* the data: that is, it does not have enough model flexibility to suitably account for all the features in the data; another way of saying this is that the model has high *bias*.\n", + "\n", + "The model on the right attempts to fit a high-order polynomial through the data.\n", + "Here the model fit has enough flexibility to nearly perfectly account for the fine features in the data, but even though it very accurately describes the training data, its precise form seems to be more reflective of the particular noise properties of the data rather than the intrinsic properties of whatever process generated that data.\n", + "Such a model is said to *overfit* the data: that is, it has so much model flexibility that the model ends up accounting for random errors as well as the underlying data distribution; another way of saying this is that the model has high *variance*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "To look at this in another light, consider what happens if we use these two models to predict the y-value for some new data.\n", + "In the following diagrams, the red/lighter points indicate data that is omitted from the training set:\n", + "\n", + "![](figures/05.03-bias-variance-2.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff-Metrics)\n", + "\n", + "The score here is the $R^2$ score, or [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), which measures how well a model performs relative to a simple mean of the target values. $R^2=1$ indicates a perfect match, $R^2=0$ indicates the model does no better than simply taking the mean of the data, and negative values mean even worse models.\n", + "From the scores associated with these two models, we can make an observation that holds more generally:\n", + "\n", + "- For high-bias models, the performance of the model on the validation set is similar to the performance on the training set.\n", + "- For high-variance models, the performance of the model on the validation set is far worse than the performance on the training set." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "If we imagine that we have some ability to tune the model complexity, we would expect the training score and validation score to behave as illustrated in the following figure:\n", + "\n", + "![](figures/05.03-validation-curve.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Validation-Curve)\n", + "\n", + "The diagram shown here is often called a *validation curve*, and we see the following essential features:\n", + "\n", + "- The training score is everywhere higher than the validation score. This is generally the case: the model will be a better fit to data it has seen than to data it has not seen.\n", + "- For very low model complexity (a high-bias model), the training data is under-fit, which means that the model is a poor predictor both for the training data and for any previously unseen data.\n", + "- For very high model complexity (a high-variance model), the training data is over-fit, which means that the model predicts the training data very well, but fails for any previously unseen data.\n", + "- For some intermediate value, the validation curve has a maximum. This level of complexity indicates a suitable trade-off between bias and variance.\n", + "\n", + "The means of tuning the model complexity varies from model to model; when we discuss individual models in depth in later sections, we will see how each model allows for such tuning." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "source": [ + "### Validation curves in Scikit-Learn\n", + "\n", + "Let's look at an example of using cross-validation to compute the validation curve for a class of models.\n", + "Here we will use a *polynomial regression* model: this is a generalized linear model in which the degree of the polynomial is a tunable parameter.\n", + "For example, a degree-1 polynomial fits a straight line to the data; for model parameters $a$ and $b$:\n", + "\n", + "$$\n", + "y = ax + b\n", + "$$\n", + "\n", + "A degree-3 polynomial fits a cubic curve to the data; for model parameters $a, b, c, d$:\n", + "\n", + "$$\n", + "y = ax^3 + bx^2 + cx + d\n", + "$$\n", + "\n", + "We can generalize this to any number of polynomial features.\n", + "In Scikit-Learn, we can implement this with a simple linear regression combined with the polynomial preprocessor.\n", + "We will use a *pipeline* to string these operations together (we will discuss polynomial features and pipelines more fully in [Feature Engineering](05.04-Feature-Engineering.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -223,11 +589,24 @@ " LinearRegression(**kwargs))" ] }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "source": [ + "Now let's create some data to which we will fit our model:" + ] + }, { "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -245,11 +624,23 @@ "X, y = make_data(40)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can now visualize our data, along with polynomial fits of several degrees:" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -280,11 +671,27 @@ "plt.legend(loc='best');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The knob controlling model complexity in this case is the degree of the polynomial, which can be any non-negative integer.\n", + "A useful question to answer is this: what degree of polynomial provides a suitable trade-off between bias (under-fitting) and variance (over-fitting)?\n", + "\n", + "We can make progress in this by visualizing the validation curve for this particular data and model; this can be done straightforwardly using the ``validation_curve`` convenience routine provided by Scikit-Learn.\n", + "Given a model, data, parameter name, and a range to explore, this function will automatically compute both the training score and validation score across the range:" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -312,11 +719,25 @@ "plt.ylabel('score');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This shows precisely the qualitative behavior we expect: the training score is everywhere higher than the validation score; the training score is monotonically improving with increased model complexity; and the validation score reaches a maximum before dropping off as the model becomes over-fit.\n", + "\n", + "From the validation curve, we can read-off that the optimal trade-off between bias and variance is found for a third-order polynomial; we can compute and display this fit over the original data as follows:" + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -338,11 +759,36 @@ "plt.axis(lim);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that finding this optimal model did not actually require us to compute the training score, but examining the relationship between the training score and validation score can give us useful insight into the performance of the model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Learning Curves\n", + "\n", + "One important aspect of model complexity is that the optimal model will generally depend on the size of your training data.\n", + "For example, let's generate a new dataset with a factor of five more points:" + ] + }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -361,11 +807,23 @@ "plt.scatter(X2.ravel(), y2);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We will duplicate the preceding code to plot the validation curve for this larger dataset; for reference let's over-plot the previous results as well:" + ] + }, { "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -394,11 +852,71 @@ "plt.ylabel('score');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The solid lines show the new results, while the fainter dashed lines show the results of the previous smaller dataset.\n", + "It is clear from the validation curve that the larger dataset can support a much more complicated model: the peak here is probably around a degree of 6, but even a degree-20 model is not seriously over-fitting the data—the validation and training scores remain very close.\n", + "\n", + "Thus we see that the behavior of the validation curve has not one but two important inputs: the model complexity and the number of training points.\n", + "It is often useful to to explore the behavior of the model as a function of the number of training points, which we can do by using increasingly larger subsets of the data to fit our model.\n", + "A plot of the training/validation score with respect to the size of the training set is known as a *learning curve.*\n", + "\n", + "The general behavior we would expect from a learning curve is this:\n", + "\n", + "- A model of a given complexity will *overfit* a small dataset: this means the training score will be relatively high, while the validation score will be relatively low.\n", + "- A model of a given complexity will *underfit* a large dataset: this means that the training score will decrease, but the validation score will increase.\n", + "- A model will never, except by chance, give a better score to the validation set than the training set: this means the curves should keep getting closer together but never cross.\n", + "\n", + "With these features in mind, we would expect a learning curve to look qualitatively like that shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.03-learning-curve.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Learning-Curve)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The notable feature of the learning curve is the convergence to a particular score as the number of training samples grows.\n", + "In particular, once you have enough points that a particular model has converged, *adding more training data will not help you!*\n", + "The only way to increase model performance in this case is to use another (often more complex) model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Learning curves in Scikit-Learn\n", + "\n", + "Scikit-Learn offers a convenient utility for computing such learning curves from your models; here we will compute a learning curve for our original dataset with a second-order polynomial model and a ninth-order polynomial:" + ] + }, { "cell_type": "code", "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -419,12 +937,14 @@ "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", "\n", "for i, degree in enumerate([2, 9]):\n", - " N, train_lc, val_lc = learning_curve(PolynomialRegression(degree), X, y, cv=7,\n", + " N, train_lc, val_lc = learning_curve(PolynomialRegression(degree),\n", + " X, y, cv=7,\n", " train_sizes=np.linspace(0.3, 1, 25))\n", "\n", " ax[i].plot(N, np.mean(train_lc, 1), color='blue', label='training score')\n", " ax[i].plot(N, np.mean(val_lc, 1), color='red', label='validation score')\n", - " ax[i].hlines(np.mean([train_lc[-1], val_lc[-1]]), N[0], N[-1], color='gray', linestyle='dashed')\n", + " ax[i].hlines(np.mean([train_lc[-1], val_lc[-1]]), N[0], N[-1],\n", + " color='gray', linestyle='dashed')\n", "\n", " ax[i].set_ylim(0, 1)\n", " ax[i].set_xlim(N[0], N[-1])\n", @@ -434,11 +954,50 @@ " ax[i].legend(loc='best')" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This is a valuable diagnostic, because it gives us a visual depiction of how our model responds to increasing training data.\n", + "In particular, when your learning curve has already converged (i.e., when the training and validation curves are already close to each other) *adding more training data will not significantly improve the fit!*\n", + "This situation is seen in the left panel, with the learning curve for the degree-2 model.\n", + "\n", + "The only way to increase the converged score is to use a different (usually more complicated) model.\n", + "We see this in the right panel: by moving to a much more complicated model, we increase the score of convergence (indicated by the dashed line), but at the expense of higher model variance (indicated by the difference between the training and validation scores).\n", + "If we were to add even more data points, the learning curve for the more complicated model would eventually converge.\n", + "\n", + "Plotting a learning curve for your particular choice of model and dataset can help you to make this type of decision about how to move forward in improving your analysis." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Validation in Practice: Grid Search\n", + "\n", + "The preceding discussion is meant to give you some intuition into the trade-off between bias and variance, and its dependence on model complexity and training set size.\n", + "In practice, models generally have more than one knob to turn, and thus plots of validation and learning curves change from lines to multi-dimensional surfaces.\n", + "In these cases, such visualizations are difficult and we would rather simply find the particular model that maximizes the validation score.\n", + "\n", + "Scikit-Learn provides automated tools to do this in the grid search module.\n", + "Here is an example of using grid search to find the optimal polynomial model.\n", + "We will explore a three-dimensional grid of model features; namely the polynomial degree, the flag telling us whether to fit the intercept, and the flag telling us whether to normalize the problem.\n", + "This can be set up using Scikit-Learn's ``GridSearchCV`` meta-estimator:" + ] + }, { "cell_type": "code", "execution_count": 18, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -451,22 +1010,47 @@ "grid = GridSearchCV(PolynomialRegression(), param_grid, cv=7)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that like a normal estimator, this has not yet been applied to any data.\n", + "Calling the ``fit()`` method will fit the model at each grid point, keeping track of the scores along the way:" + ] + }, { "cell_type": "code", "execution_count": 19, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ "grid.fit(X, y);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now that this is fit, we can ask for the best parameters as follows:" + ] + }, { "cell_type": "code", "execution_count": 20, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -486,11 +1070,23 @@ "grid.best_params_" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, if we wish, we can use the best model and show the fit to our data using code from before:" + ] + }, { "cell_type": "code", "execution_count": 21, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -513,9 +1109,50 @@ "plt.plot(X_test.ravel(), y_test, hold=True);\n", "plt.axis(lim);" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The grid search provides many more options, including the ability to specify a custom scoring function, to parallelize the computations, to do randomized searches, and more.\n", + "For information, see the examples in [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) and [Feature Engineering: Working with Images](05.14-Image-Features.ipynb), or refer to Scikit-Learn's [grid search documentation](http://Scikit-Learn.org/stable/modules/grid_search.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Summary\n", + "\n", + "In this section, we have begun to explore the concept of model validation and hyperparameter optimization, focusing on intuitive aspects of the bias–variance trade-off and how it comes into play when fitting models to data.\n", + "In particular, we found that the use of a validation set or cross-validation approach is *vital* when tuning parameters in order to avoid over-fitting for more complex/flexible models.\n", + "\n", + "In later sections, we will discuss the details of particularly useful models, and throughout will talk about what tuning is available for these models and how these free parameters affect model complexity.\n", + "Keep the lessons of this section in mind as you read on and learn about these machine learning approaches!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) | [Contents](Index.ipynb) | [Feature Engineering](05.04-Feature-Engineering.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.04-Feature-Engineering.ipynb b/notebooks_v1/05.04-Feature-Engineering.ipynb similarity index 66% rename from code_listings/05.04-Feature-Engineering.ipynb rename to notebooks_v1/05.04-Feature-Engineering.ipynb index 976b542d6..7315fb277 100644 --- a/code_listings/05.04-Feature-Engineering.ipynb +++ b/notebooks_v1/05.04-Feature-Engineering.ipynb @@ -1,5 +1,33 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) | [Contents](Index.ipynb) | [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,11 +35,43 @@ "# Feature Engineering" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The previous sections outline the fundamental ideas of machine learning, but all of the examples assume that you have numerical data in a tidy, ``[n_samples, n_features]`` format.\n", + "In the real world, data rarely comes in such a form.\n", + "With this in mind, one of the more important steps in using machine learning in practice is *feature engineering*: that is, taking whatever information you have about your problem and turning it into numbers that you can use to build your feature matrix.\n", + "\n", + "In this section, we will cover a few common examples of feature engineering tasks: features for representing *categorical data*, features for representing *text*, and features for representing *images*.\n", + "Additionally, we will discuss *derived features* for increasing model complexity and *imputation* of missing data.\n", + "Often this process is known as *vectorization*, as it involves converting arbitrary data into well-behaved vectors." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Categorical Features\n", + "\n", + "One common type of non-numerical data is *categorical* data.\n", + "For example, imagine you are exploring some data on housing prices, and along with numerical features like \"price\" and \"rooms\", you also have \"neighborhood\" information.\n", + "For example, your data might look something like this:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -23,22 +83,50 @@ "]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "You might be tempted to encode this data with a straightforward numerical mapping:" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ "{'Queen Anne': 1, 'Fremont': 2, 'Wallingford': 3};" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "It turns out that this is not generally a useful approach in Scikit-Learn: the package's models make the fundamental assumption that numerical features reflect algebraic quantities.\n", + "Thus such a mapping would imply, for example, that *Queen Anne < Fremont < Wallingford*, or even that *Wallingford - Queen Anne = Fremont*, which (niche demographic jokes aside) does not make much sense.\n", + "\n", + "In this case, one proven technique is to use *one-hot encoding*, which effectively creates extra columns indicating the presence or absence of a category with a value of 1 or 0, respectively.\n", + "When your data comes as a list of dictionaries, Scikit-Learn's ``DictVectorizer`` will do this for you:" + ] + }, { "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -61,11 +149,26 @@ "vec.fit_transform(data)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that the 'neighborhood' column has been expanded into three separate columns, representing the three neighborhood labels, and that each row has a 1 in the column associated with its neighborhood.\n", + "With these categorical features thus encoded, you can proceed as normal with fitting a Scikit-Learn model.\n", + "\n", + "To see the meaning of each column, you can inspect the feature names:" + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -87,11 +190,24 @@ "vec.get_feature_names()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "There is one clear disadvantage of this approach: if your category has many possible values, this can *greatly* increase the size of your dataset.\n", + "However, because the encoded data contains mostly zeros, a sparse output can be a very efficient solution:" + ] + }, { "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -111,11 +227,39 @@ "vec.fit_transform(data)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Many (though not yet all) of the Scikit-Learn estimators accept such sparse inputs when fitting and evaluating models. ``sklearn.preprocessing.OneHotEncoder`` and ``sklearn.feature_extraction.FeatureHasher`` are two additional tools that Scikit-Learn includes to support this type of encoding." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Text Features\n", + "\n", + "Another common need in feature engineering is to convert text to a set of representative numerical values.\n", + "For example, most automatic mining of social media data relies on some form of encoding the text as numbers.\n", + "One of the simplest methods of encoding data is by *word counts*: you take each snippet of text, count the occurrences of each word within it, and put the results in a table.\n", + "\n", + "For example, consider the following set of three phrases:" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -124,11 +268,24 @@ " 'horizon problem']" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For a vectorization of this data based on word count, we could construct a column representing the word \"problem,\" the word \"evil,\" the word \"horizon,\" and so on.\n", + "While doing this by hand would be possible, the tedium can be avoided by using Scikit-Learn's ``CountVectorizer``:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -151,11 +308,23 @@ "X" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result is a sparse matrix recording the number of times each word appears; it is easier to inspect if we convert this to a ``DataFrame`` with labeled columns:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -219,11 +388,25 @@ "pd.DataFrame(X.toarray(), columns=vec.get_feature_names())" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "There are some issues with this approach, however: the raw word counts lead to features which put too much weight on words that appear very frequently, and this can be sub-optimal in some classification algorithms.\n", + "One approach to fix this is known as *term frequency-inverse document frequency* (*TF–IDF*) which weights the word counts by a measure of how often they appear in the documents.\n", + "The syntax for computing these features is similar to the previous example:" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -289,11 +472,57 @@ "pd.DataFrame(X.toarray(), columns=vec.get_feature_names())" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For an example of using TF-IDF in a classification problem, see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Image Features\n", + "\n", + "Another common need is to suitably encode *images* for machine learning analysis.\n", + "The simplest approach is what we used for the digits data in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb): simply using the pixel values themselves.\n", + "But depending on the application, such approaches may not be optimal.\n", + "\n", + "A comprehensive summary of feature extraction techniques for images is well beyond the scope of this section, but you can find excellent implementations of many of the standard approaches in the [Scikit-Image project](http://scikit-image.org).\n", + "For one example of using Scikit-Learn and Scikit-Image together, see [Feature Engineering: Working with Images](05.14-Image-Features.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Derived Features\n", + "\n", + "Another useful type of feature is one that is mathematically derived from some input features.\n", + "We saw an example of this in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) when we constructed *polynomial features* from our input data.\n", + "We saw that we could convert a linear regression into a polynomial regression not by changing the model, but by transforming the input!\n", + "This is sometimes known as *basis function regression*, and is explored further in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb).\n", + "\n", + "For example, this data clearly cannot be well described by a straight line:" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -317,11 +546,23 @@ "plt.scatter(x, y);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Still, we can fit a line to the data using ``LinearRegression`` and get the optimal result:" + ] + }, { "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -344,11 +585,26 @@ "plt.plot(x, yfit);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "It's clear that we need a more sophisticated model to describe the relationship between $x$ and $y$.\n", + "\n", + "One approach to this is to transform the data, adding extra columns of features to drive more flexibility in the model.\n", + "For example, we can add polynomial features to the data this way:" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -370,11 +626,24 @@ "print(X2)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The derived feature matrix has one column representing $x$, and a second column representing $x^2$, and a third column representing $x^3$.\n", + "Computing a linear regression on this expanded input gives a much closer fit to our data:" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -395,11 +664,39 @@ "plt.plot(x, yfit);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This idea of improving a model not by changing the model, but by transforming the inputs, is fundamental to many of the more powerful machine learning methods.\n", + "We explore this idea further in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) in the context of *basis function regression*.\n", + "More generally, this is one motivational path to the powerful set of techniques known as *kernel methods*, which we will explore in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Imputation of Missing Data\n", + "\n", + "Another common need in feature engineering is handling of missing data.\n", + "We discussed the handling of missing data in ``DataFrame``s in [Handling Missing Data](03.04-Missing-Values.ipynb), and saw that often the ``NaN`` value is used to mark missing values.\n", + "For example, we might have a dataset that looks like this:" + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -412,11 +709,27 @@ "y = np.array([14, 16, -1, 8, -5])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "When applying a typical machine learning model to such data, we will need to first replace such missing data with some appropriate fill value.\n", + "This is known as *imputation* of missing values, and strategies range from simple (e.g., replacing missing values with the mean of the column) to sophisticated (e.g., using matrix completion or a robust model to handle such data).\n", + "\n", + "The sophisticated approaches tend to be very application-specific, and we won't dive into them here.\n", + "For a baseline imputation approach, using the mean, median, or most frequent value, Scikit-Learn provides the ``Imputer`` class:" + ] + }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -441,11 +754,23 @@ "X2" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that in the resulting data, the two missing values have been replaced with the mean of the remaining values in the column. This imputed data can then be fed directly into, for example, a ``LinearRegression`` estimator:" + ] + }, { "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -464,11 +789,32 @@ "model.predict(X2)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Feature Pipelines\n", + "\n", + "With any of the preceding examples, it can quickly become tedious to do the transformations by hand, especially if you wish to string together multiple steps.\n", + "For example, we might want a processing pipeline that looks something like this:\n", + "\n", + "1. Impute missing values using the mean\n", + "2. Transform features to quadratic\n", + "3. Fit a linear regression\n", + "\n", + "To streamline this type of processing pipeline, Scikit-Learn provides a ``Pipeline`` object, which can be used as follows:" + ] + }, { "cell_type": "code", "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -479,11 +825,23 @@ " LinearRegression())" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This pipeline looks and acts like a standard Scikit-Learn object, and will apply all the specified steps to any input data." + ] + }, { "cell_type": "code", "execution_count": 18, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -500,9 +858,36 @@ "print(y)\n", "print(model.predict(X))" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "All the steps of the model are applied automatically.\n", + "Notice that for the simplicity of this demonstration, we've applied the model to the data it was trained on; this is why it was able to perfectly predict the result (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for further discussion of this).\n", + "\n", + "For some examples of Scikit-Learn pipelines in action, see the following section on naive Bayes classification, as well as [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), and [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) | [Contents](Index.ipynb) | [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.05-Naive-Bayes.ipynb b/notebooks_v1/05.05-Naive-Bayes.ipynb similarity index 93% rename from code_listings/05.05-Naive-Bayes.ipynb rename to notebooks_v1/05.05-Naive-Bayes.ipynb index de0cb8644..f5d492a42 100644 --- a/code_listings/05.05-Naive-Bayes.ipynb +++ b/notebooks_v1/05.05-Naive-Bayes.ipynb @@ -1,5 +1,33 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Feature Engineering](05.04-Feature-Engineering.ipynb) | [Contents](Index.ipynb) | [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,11 +35,63 @@ "# In Depth: Naive Bayes Classification" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The previous four sections have given a general overview of the concepts of machine learning.\n", + "In this section and the ones that follow, we will be taking a closer look at several specific algorithms for supervised and unsupervised learning, starting here with naive Bayes classification.\n", + "\n", + "Naive Bayes models are a group of extremely fast and simple classification algorithms that are often suitable for very high-dimensional datasets.\n", + "Because they are so fast and have so few tunable parameters, they end up being very useful as a quick-and-dirty baseline for a classification problem.\n", + "This section will focus on an intuitive explanation of how naive Bayes classifiers work, followed by a couple examples of them in action on some datasets." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Bayesian Classification\n", + "\n", + "Naive Bayes classifiers are built on Bayesian classification methods.\n", + "These rely on Bayes's theorem, which is an equation describing the relationship of conditional probabilities of statistical quantities.\n", + "In Bayesian classification, we're interested in finding the probability of a label given some observed features, which we can write as $P(L~|~{\\rm features})$.\n", + "Bayes's theorem tells us how to express this in terms of quantities we can compute more directly:\n", + "\n", + "$$\n", + "P(L~|~{\\rm features}) = \\frac{P({\\rm features}~|~L)P(L)}{P({\\rm features})}\n", + "$$\n", + "\n", + "If we are trying to decide between two labels—let's call them $L_1$ and $L_2$—then one way to make this decision is to compute the ratio of the posterior probabilities for each label:\n", + "\n", + "$$\n", + "\\frac{P(L_1~|~{\\rm features})}{P(L_2~|~{\\rm features})} = \\frac{P({\\rm features}~|~L_1)}{P({\\rm features}~|~L_2)}\\frac{P(L_1)}{P(L_2)}\n", + "$$\n", + "\n", + "All we need now is some model by which we can compute $P({\\rm features}~|~L_i)$ for each label.\n", + "Such a model is called a *generative model* because it specifies the hypothetical random process that generates the data.\n", + "Specifying this generative model for each label is the main piece of the training of such a Bayesian classifier.\n", + "The general version of such a training step is a very difficult task, but we can make it simpler through the use of some simplifying assumptions about the form of this model.\n", + "\n", + "This is where the \"naive\" in \"naive Bayes\" comes in: if we make very naive assumptions about the generative model for each label, we can find a rough approximation of the generative model for each class, and then proceed with the Bayesian classification.\n", + "Different types of naive Bayes classifiers rest on different naive assumptions about the data, and we will examine a few of these in the following sections.\n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -21,11 +101,27 @@ "import seaborn as sns; sns.set()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Gaussian Naive Bayes\n", + "\n", + "Perhaps the easiest naive Bayes classifier to understand is Gaussian naive Bayes.\n", + "In this classifier, the assumption is that *data from each label is drawn from a simple Gaussian distribution*.\n", + "Imagine that you have the following data:" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -45,11 +141,50 @@ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "One extremely fast way to create a simple model is to assume that the data is described by a Gaussian distribution with no covariance between dimensions.\n", + "This model can be fit by simply finding the mean and standard deviation of the points within each label, which is all you need to define such a distribution.\n", + "The result of this naive Gaussian assumption is shown in the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![(run code in Appendix to generate image)](figures/05.05-gaussian-NB.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Gaussian-Naive-Bayes)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "source": [ + "The ellipses here represent the Gaussian generative model for each label, with larger probability toward the center of the ellipses.\n", + "With this generative model in place for each class, we have a simple recipe to compute the likelihood $P({\\rm features}~|~L_1)$ for any data point, and thus we can quickly compute the posterior ratio and determine which label is the most probable for a given point.\n", + "\n", + "This procedure is implemented in Scikit-Learn's ``sklearn.naive_bayes.GaussianNB`` estimator:" + ] + }, { "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -58,11 +193,23 @@ "model.fit(X, y);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now let's generate some new data and predict the label:" + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -71,11 +218,23 @@ "ynew = model.predict(Xnew)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now we can plot this new data to get an idea of where the decision boundary is:" + ] + }, { "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -96,11 +255,25 @@ "plt.axis(lim);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see a slightly curved boundary in the classifications—in general, the boundary in Gaussian naive Bayes is quadratic.\n", + "\n", + "A nice piece of this Bayesian formalism is that it naturally allows for probabilistic classification, which we can compute using the ``predict_proba`` method:" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -126,11 +299,58 @@ "yprob[-8:].round(2)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The columns give the posterior probabilities of the first and second label, respectively.\n", + "If you are looking for estimates of uncertainty in your classification, Bayesian approaches like this can be a useful approach.\n", + "\n", + "Of course, the final classification will only be as good as the model assumptions that lead to it, which is why Gaussian naive Bayes often does not produce very good results.\n", + "Still, in many cases—especially as the number of features becomes large—this assumption is not detrimental enough to prevent Gaussian naive Bayes from being a useful method." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Multinomial Naive Bayes\n", + "\n", + "The Gaussian assumption just described is by no means the only simple assumption that could be used to specify the generative distribution for each label.\n", + "Another useful example is multinomial naive Bayes, where the features are assumed to be generated from a simple multinomial distribution.\n", + "The multinomial distribution describes the probability of observing counts among a number of categories, and thus multinomial naive Bayes is most appropriate for features that represent counts or count rates.\n", + "\n", + "The idea is precisely the same as before, except that instead of modeling the data distribution with the best-fit Gaussian, we model the data distribuiton with a best-fit multinomial distribution." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Example: Classifying Text\n", + "\n", + "One place where multinomial naive Bayes is often used is in text classification, where the features are related to word counts or frequencies within the documents to be classified.\n", + "We discussed the extraction of such features from text in [Feature Engineering](05.04-Feature-Engineering.ipynb); here we will use the sparse word count features from the 20 Newsgroups corpus to show how we might classify these short documents into categories.\n", + "\n", + "Let's download the data and take a look at the target names:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -170,24 +390,49 @@ "data.target_names" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "For simplicity here, we will select just a few of these categories, and download the training and testing set:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ - "categories = ['talk.religion.misc', 'soc.religion.christian', 'sci.space', 'comp.graphics']\n", + "categories = ['talk.religion.misc', 'soc.religion.christian',\n", + " 'sci.space', 'comp.graphics']\n", "train = fetch_20newsgroups(subset='train', categories=categories)\n", "test = fetch_20newsgroups(subset='test', categories=categories)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here is a representative entry from the data:" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -219,11 +464,24 @@ "print(train.data[5])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In order to use this data for machine learning, we need to be able to convert the content of each string into a vector of numbers.\n", + "For this we will use the TF-IDF vectorizer (discussed in [Feature Engineering](05.04-Feature-Engineering.ipynb)), and create a pipeline that attaches it to a multinomial naive Bayes classifier:" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -234,11 +492,23 @@ "model = make_pipeline(TfidfVectorizer(), MultinomialNB())" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this pipeline, we can apply the model to the training data, and predict labels for the test data:" + ] + }, { "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -246,11 +516,24 @@ "labels = model.predict(test.data)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now that we have predicted the labels for the test data, we can evaluate them to learn about the performance of the estimator.\n", + "For example, here is the confusion matrix between the true and predicted labels for the test data:" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -273,11 +556,27 @@ "plt.ylabel('predicted label');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Evidently, even this very simple classifier can successfully separate space talk from computer talk, but it gets confused between talk about religion and talk about Christianity.\n", + "This is perhaps an expected area of confusion!\n", + "\n", + "The very cool thing here is that we now have the tools to determine the category for *any* string, using the ``predict()`` method of this pipeline.\n", + "Here's a quick utility function that will return the prediction for a single string:" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -286,11 +585,23 @@ " return train.target_names[pred[0]]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Let's try it out:" + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -312,7 +623,9 @@ "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -334,7 +647,9 @@ "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -351,9 +666,66 @@ "source": [ "predict_category('determining the screen resolution')" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Remember that this is nothing more sophisticated than a simple probability model for the (weighted) frequency of each word in the string; nevertheless, the result is striking.\n", + "Even a very naive algorithm, when used carefully and trained on a large set of high-dimensional data, can be surprisingly effective." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## When to Use Naive Bayes\n", + "\n", + "Because naive Bayesian classifiers make such stringent assumptions about data, they will generally not perform as well as a more complicated model.\n", + "That said, they have several advantages:\n", + "\n", + "- They are extremely fast for both training and prediction\n", + "- They provide straightforward probabilistic prediction\n", + "- They are often very easily interpretable\n", + "- They have very few (if any) tunable parameters\n", + "\n", + "These advantages mean a naive Bayesian classifier is often a good choice as an initial baseline classification.\n", + "If it performs suitably, then congratulations: you have a very fast, very interpretable classifier for your problem.\n", + "If it does not perform well, then you can begin exploring more sophisticated models, with some baseline knowledge of how well they should perform.\n", + "\n", + "Naive Bayes classifiers tend to perform especially well in one of the following situations:\n", + "\n", + "- When the naive assumptions actually match the data (very rare in practice)\n", + "- For very well-separated categories, when model complexity is less important\n", + "- For very high-dimensional data, when model complexity is less important\n", + "\n", + "The last two points seem distinct, but they actually are related: as the dimension of a dataset grows, it is much less likely for any two points to be found close together (after all, they must be close in *every single dimension* to be close overall).\n", + "This means that clusters in high dimensions tend to be more separated, on average, than clusters in low dimensions, assuming the new dimensions actually add information.\n", + "For this reason, simplistic classifiers like naive Bayes tend to work as well or better than more complicated classifiers as the dimensionality grows: once you have enough data, even a simple model can be very powerful." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Feature Engineering](05.04-Feature-Engineering.ipynb) | [Contents](Index.ipynb) | [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.06-Linear-Regression.ipynb b/notebooks_v1/05.06-Linear-Regression.ipynb similarity index 66% rename from code_listings/05.06-Linear-Regression.ipynb rename to notebooks_v1/05.06-Linear-Regression.ipynb index 06e6faf53..ccecf6292 100644 --- a/code_listings/05.06-Linear-Regression.ipynb +++ b/notebooks_v1/05.06-Linear-Regression.ipynb @@ -1,5 +1,33 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) | [Contents](Index.ipynb) | [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,11 +35,29 @@ "# In Depth: Linear Regression" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Just as naive Bayes (discussed earlier in [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)) is a good starting point for classification tasks, linear regression models are a good starting point for regression tasks.\n", + "Such models are popular because they can be fit very quickly, and are very interpretable.\n", + "You are probably familiar with the simplest form of a linear regression model (i.e., fitting a straight line to data) but such models can be extended to model more complicated data behavior.\n", + "\n", + "In this section we will start with a quick intuitive walk-through of the mathematics behind this well-known problem, before seeing how before moving on to see how linear models can be generalized to account for more complicated patterns in data.\n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -21,18 +67,39 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Simple Linear Regression\n", + "\n", + "We will start with the most familiar linear regression, a straight-line fit to data.\n", + "A straight-line fit is a model of the form\n", + "$$\n", + "y = ax + b\n", + "$$\n", + "where $a$ is commonly known as the *slope*, and $b$ is commonly known as the *intercept*.\n", + "\n", + "Consider the following data, which is scattered about a line with a slope of 2 and an intercept of -5:" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -46,18 +113,30 @@ "plt.scatter(x, y);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can use Scikit-Learn's ``LinearRegression`` estimator to fit this data and construct the best-fit line:" + ] + }, { "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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G4PcuFbCllbV6a2WetuScUHCQXT+/pbfGD+2h4KCGm2i09tL12VXogX6PFs1DUAPwew0F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\n0gcagDUR1PBL3x4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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -77,11 +156,24 @@ "plt.plot(xfit, yfit);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The slope and intercept of the data are contained in the model's fit parameters, which in Scikit-Learn are always marked by a trailing underscore.\n", + "Here the relevant parameters are ``coef_`` and ``intercept_``:" + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -98,11 +190,40 @@ "print(\"Model intercept:\", model.intercept_)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that the results are very close to the inputs, as we might hope." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The ``LinearRegression`` estimator is much more capable than this, however—in addition to simple straight-line fits, it can also handle multidimensional linear models of the form\n", + "$$\n", + "y = a_0 + a_1 x_1 + a_2 x_2 + \\cdots\n", + "$$\n", + "where there are multiple $x$ values.\n", + "Geometrically, this is akin to fitting a plane to points in three dimensions, or fitting a hyper-plane to points in higher dimensions.\n", + "\n", + "The multidimensional nature of such regressions makes them more difficult to visualize, but we can see one of these fits in action by building some example data, using NumPy's matrix multiplication operator:" + ] + }, { "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -124,11 +245,64 @@ "print(model.coef_)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here the $y$ data is constructed from three random $x$ values, and the linear regression recovers the coefficients used to construct the data.\n", + "\n", + "In this way, we can use the single ``LinearRegression`` estimator to fit lines, planes, or hyperplanes to our data.\n", + "It still appears that this approach would be limited to strictly linear relationships between variables, but it turns out we can relax this as well." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Basis Function Regression\n", + "\n", + "One trick you can use to adapt linear regression to nonlinear relationships between variables is to transform the data according to *basis functions*.\n", + "We have seen one version of this before, in the ``PolynomialRegression`` pipeline used in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) and [Feature Engineering](05.04-Feature-Engineering.ipynb).\n", + "The idea is to take our multidimensional linear model:\n", + "$$\n", + "y = a_0 + a_1 x_1 + a_2 x_2 + a_3 x_3 + \\cdots\n", + "$$\n", + "and build the $x_1, x_2, x_3,$ and so on, from our single-dimensional input $x$.\n", + "That is, we let $x_n = f_n(x)$, where $f_n()$ is some function that transforms our data.\n", + "\n", + "For example, if $f_n(x) = x^n$, our model becomes a polynomial regression:\n", + "$$\n", + "y = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \\cdots\n", + "$$\n", + "Notice that this is *still a linear model*—the linearity refers to the fact that the coefficients $a_n$ never multiply or divide each other.\n", + "What we have effectively done is taken our one-dimensional $x$ values and projected them into a higher dimension, so that a linear fit can fit more complicated relationships between $x$ and $y$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Polynomial basis functions\n", + "\n", + "This polynomial projection is useful enough that it is built into Scikit-Learn, using the ``PolynomialFeatures`` transformer:" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -151,11 +325,27 @@ "poly.fit_transform(x[:, None])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see here that the transformer has converted our one-dimensional array into a three-dimensional array by taking the exponent of each value.\n", + "This new, higher-dimensional data representation can then be plugged into a linear regression.\n", + "\n", + "As we saw in [Feature Engineering](05.04-Feature-Engineering.ipynb), the cleanest way to accomplish this is to use a pipeline.\n", + "Let's make a 7th-degree polynomial model in this way:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -164,18 +354,31 @@ " LinearRegression())" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this transform in place, we can use the linear model to fit much more complicated relationships between $x$ and $y$. \n", + "For example, here is a sine wave with noise:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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1DePbnHtRUHAfsrLSsWNHttSh0U0wactYXmkzVEqWxm8lUOMJYdCIoMhWeHgP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\nILz+aSlaOwewacU0q2e9nb1D+O93zuB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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -194,18 +397,66 @@ "plt.plot(xfit, yfit);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Our linear model, through the use of 7th-order polynomial basis functions, can provide an excellent fit to this non-linear data!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Gaussian basis functions\n", + "\n", + "Of course, other basis functions are possible.\n", + "For example, one useful pattern is to fit a model that is not a sum of polynomial bases, but a sum of Gaussian bases.\n", + "The result might look something like the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.06-gaussian-basis.png)\n", + "[figure source in Appendix](#Gaussian-Basis)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The shaded regions in the plot are the scaled basis functions, and when added together they reproduce the smooth curve through the data.\n", + "These Gaussian basis functions are not built into Scikit-Learn, but we can write a custom transformer that will create them, as shown here and illustrated in the following figure (Scikit-Learn transformers are implemented as Python classes; reading Scikit-Learn's source is a good way to see how they can be created):" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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PRUbePGR+5cqVWLly5egqG6Gqeg8ERnWjMi8EgMJh1uzZsgfn6HEkuwp7ThTj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\ngM4Frs4WfU0RjZqrsxLJMb4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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -216,7 +467,7 @@ "from sklearn.base import BaseEstimator, TransformerMixin\n", "\n", "class GaussianFeatures(BaseEstimator, TransformerMixin):\n", - " \"\"\"Uniformly-spaced Gaussian Features for 1D input\"\"\"\n", + " \"\"\"Uniformly spaced Gaussian features for one-dimensional input\"\"\"\n", " \n", " def __init__(self, N, width_factor=2.0):\n", " self.N = N\n", @@ -247,18 +498,43 @@ "plt.xlim(0, 10);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We put this example here just to make clear that there is nothing magic about polynomial basis functions: if you have some sort of intuition into the generating process of your data that makes you think one basis or another might be appropriate, you can use them as well." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Regularization\n", + "\n", + "The introduction of basis functions into our linear regression makes the model much more flexible, but it also can very quickly lead to over-fitting (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for a discussion of this).\n", + "For example, if we choose too many Gaussian basis functions, we end up with results that don't look so good:" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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wFKgaZwvjLLtep+Urd87jK3fOi8LIUo9GUbhhQQ4vfNDM17/zATb/ANXVq1Oi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\nMB8d7ZjStXoHRsm2GtFq4uNXtqnRykBHFhk5DnQ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -277,18 +553,31 @@ "plt.ylim(-1.5, 1.5);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With the data projected to the 30-dimensional basis, the model has far too much flexibility and goes to extreme values between locations where it is constrained by data.\n", + "We can see the reason for this if we plot the coefficients of the Gaussian bases with respect to their locations:" + ] + }, { "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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ObJyqyoA+BiYO68OgaBP9woMJMQScUzHybD39i6rz9+OWq4aw4f0M3th2jN8ljZGEyh7k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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -316,18 +605,51 @@ "basis_plot(model)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The lower panel of this figure shows the amplitude of the basis function at each location.\n", + "This is typical over-fitting behavior when basis functions overlap: the coefficients of adjacent basis functions blow up and cancel each other out.\n", + "We know that such behavior is problematic, and it would be nice if we could limit such spikes expliticly in the model by penalizing large values of the model parameters.\n", + "Such a penalty is known as *regularization*, and comes in several forms." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Ridge regression ($L_2$ Regularization)\n", + "\n", + "Perhaps the most common form of regularization is known as *ridge regression* or $L_2$ *regularization*, sometimes also called *Tikhonov regularization*.\n", + "This proceeds by penalizing the sum of squares (2-norms) of the model coefficients; in this case, the penalty on the model fit would be \n", + "$$\n", + "P = \\alpha\\sum_{n=1}^N \\theta_n^2\n", + "$$\n", + "where $\\alpha$ is a free parameter that controls the strength of the penalty.\n", + "This type of penalized model is built into Scikit-Learn with the ``Ridge`` estimator:" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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4aejX3YcHpoXJ3O2twJIlY4G6sbWeFaX4+3YgLuUclZU1JH6XQVYrXgxDtA4J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\nlqlDEq1Ar9fzWeLlIjv3dpeJu8Igwsz4Pn6T1uEHBwezY8c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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -340,18 +662,50 @@ "basis_plot(model, title='Ridge Regression')" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The $\\alpha$ parameter is essentially a knob controlling the complexity of the resulting model.\n", + "In the limit $\\alpha \\to 0$, we recover the standard linear regression result; in the limit $\\alpha \\to \\infty$, all model responses will be suppressed.\n", + "One advantage of ridge regression in particular is that it can be computed very efficiently—at hardly more computational cost than the original linear regression model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Lasso regression ($L_1$ regularization)\n", + "\n", + "Another very common type of regularization is known as lasso, and involves penalizing the sum of absolute values (1-norms) of regression coefficients:\n", + "$$\n", + "P = \\alpha\\sum_{n=1}^N |\\theta_n|\n", + "$$\n", + "Though this is conceptually very similar to ridge regression, the results can differ surprisingly: for example, due to geometric reasons lasso regression tends to favor *sparse models* where possible: that is, it preferentially sets model coefficients to exactly zero.\n", + "\n", + "We can see this behavior in duplicating the ridge regression figure, but using L1-normalized coefficients:" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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1lctWXOVzvGHXCT7acISwAC+eTRjhULMupGivA0ZjJT4B1dwweyu+QSZUFQ3c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\nfP7553z44Yd9HvPy8kIu7y3J6OzsjELRd97CxsZGW3p306ZNTJ48meB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C0JdVJ94RhNHO\nEMljNImrzKGiokJb1jo6Opro6Giz9UUQRjoR8AXBijU0NPDYY49RXV1NXFwca9euxc7Oju3bt7Nr\n1y7a29uRSqW88847jB8/nk2bNpGVlYVUKmXevHn85je/YfPmzQA88cQTvPLKK1y4cAGAZcuW8cAD\nD9y07S+++IKtW7cikUiIiopi7dq1ODo6snv3bv7yl78glUqJjo7m97//PXV1dbz66qsoFApqamr4\nxS9+wYsvvsibb75JeXk5GzZs4I477uDPf/4z27Zto6ioiLVr19LU1ISTkxOvvfYa0dHRrFmzBrlc\nzpkzZ6iuruY3v/kNv/zlL01yrgXB2okhfUGwYuXl5axbt47du3ejUChIS0tDoVCwd+9etm/fzu7d\nu5k3bx4fffQRly9f5sCBA3z11VekpaVRUlLSp7BJTk4OTU1N7Ny5k7/97W+cOHHipu2eP3+e999/\nnx07drBr1y4cHR3ZvHkz1dXVvPXWW/z9739n9+7dqFQqfvrpJ7755ht+8YtfkJaWxq5du9ixYweN\njY3aQK4ZyteMWLz88susXLmSXbt2sWbNGp599lltHfDq6mo++ugj3nvvPTZt2mTEsysII4u4wxcE\nKzZt2jQCAwMBuOeee/jyyy9ZsWIFf/jDH9izZw/FxcUcOHCAyMhIfH19cXBwYNmyZcydO5fnn3++\nT02ECRMmUFxczKOPPsqcOXNYtWrVTds9duwYt99+u7ZC19KlS3nllVeIiYlh6tSp+Pj4APQJyEeO\nHOFvf/sbhYWFKJVK2tvb+z12W1sbpaWlzJ8/H4DY2Fjc3d0pKioCYPbs2QBERETQ3Nys76kThFFH\n3OELghWzsbHRfq1Wq7G1taWqqooHH3yQlpYWkpOTue+++1Cr1djY2PDpp5/y/PPP09jYyNKlSykp\nKdG+3t3dnd27d5OamkpRURH33nsvCoWi33ZVKhXXl+Ho6enBzs6uz+NXrlzhypUrvPXWW2zfvp2A\ngACefPJJ3N3db3j9QMdWqVT09PQAIJPJhnaSBEEARMAXBKuWnZ1NVVUVKpWKr776ilmzZnH69GmC\ng4NZuXIlMTEx7N+/H5VKxdmzZ3n44YeZNm0aL7/8MhMmTNDeNQPs3buXVatWMWfOHF599VWcnZ2p\nrKzst93ExEQyMjK0d9iffvopM2bMIDo6mlOnTlFfXw/0VrD88ccfycrK4tFHH2XhwoVcvnyZmpoa\nenp6sLGx0QZyDblcTlBQEOnp6UBv6eu6ujomTJhwQz9E7S9B0J0Y0hcEKzZhwgReeeUVamtrmT59\nOkuWLKG9vZ2PP/6Yu+++G5lMRkxMDIWFhURGRhIXF8fdd9+No6MjUVFRJCcnk5eXB8CcOXP4/vvv\nta9buHBhv0EWYOLEifzHf/wHy5cvp6enh6ioKNavX4+TkxOvvvoqjzzyCCqViltuuYUlS5bg5OTE\nqlWrcHV1xcvLi+joaMrLy4mMjKS5uZnVq1dz//33a4//9ttvs27dOv74xz8ik8nYsmULtrY3flyJ\nEreCoDtRHlcQBEEQRgExpC8IgiAIo4AI+IIgCIIwCoiALwiCIAijgAj4giAIgjAKiIAvCIIgCKOA\nCPiCIAiCMAqIgC8IgiAIo4AI+IIgCIIwCvx/LtUSu+NQwFoAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -364,37 +718,118 @@ "basis_plot(model, title='Lasso Regression')" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With the lasso regression penalty, the majority of the coefficients are exactly zero, with the functional behavior being modeled by a small subset of the available basis functions.\n", + "As with ridge regularization, the $\\alpha$ parameter tunes the strength of the penalty, and should be determined via, for example, cross-validation (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for a discussion of this)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: Predicting Bicycle Traffic" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "source": [ + "As an example, let's take a look at whether we can predict the number of bicycle trips across Seattle's Fremont Bridge based on weather, season, and other factors.\n", + "We have seen this data already in [Working With Time Series](03.11-Working-with-Time-Series.ipynb).\n", + "\n", + "In this section, we will join the bike data with another dataset, and try to determine the extent to which weather and seasonal factors—temperature, precipitation, and daylight hours—affect the volume of bicycle traffic through this corridor.\n", + "Fortunately, the NOAA makes available their daily [weather station data](http://www.ncdc.noaa.gov/cdo-web/search?datasetid=GHCND) (I used station ID USW00024233) and we can easily use Pandas to join the two data sources.\n", + "We will perform a simple linear regression to relate weather and other information to bicycle counts, in order to estimate how a change in any one of these parameters affects the number of riders on a given day.\n", + "\n", + "In particular, this is an example of how the tools of Scikit-Learn can be used in a statistical modeling framework, in which the parameters of the model are assumed to have interpretable meaning.\n", + "As discussed previously, this is not a standard approach within machine learning, but such interpretation is possible for some models.\n", + "\n", + "Let's start by loading the two datasets, indexing by date:" + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ - "import pandas as pd\n", - "counts = pd.read_csv('fremont_hourly.csv', index_col='Date', parse_dates=True)\n", - "weather = pd.read_csv('599021.csv', index_col='DATE', parse_dates=True)" + "# !curl -o FremontBridge.csv https://data.seattle.gov/api/views/65db-xm6k/rows.csv?accessType=DOWNLOAD" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "counts = pd.read_csv('FremontBridge.csv', index_col='Date', parse_dates=True)\n", + "weather = pd.read_csv('data/BicycleWeather.csv', index_col='DATE', parse_dates=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next we will compute the total daily bicycle traffic, and put this in its own dataframe:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ - "daily = counts.resample('d', how='sum')\n", + "daily = counts.resample('d').sum()\n", "daily['Total'] = daily.sum(axis=1)\n", "daily = daily[['Total']] # remove other columns" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We saw previously that the patterns of use generally vary from day to day; let's account for this in our data by adding binary columns that indicate the day of the week:" + ] + }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -403,11 +838,23 @@ " daily[days[i]] = (daily.index.dayofweek == i).astype(float)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Similarly, we might expect riders to behave differently on holidays; let's add an indicator of this as well:" + ] + }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -418,18 +865,40 @@ "daily['holiday'].fillna(0, inplace=True)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We also might suspect that the hours of daylight would affect how many people ride; let's use the standard astronomical calculation to add this information:" + ] + }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { - "image/png": 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qbp2nVWp+zs5NL8FmMcLIcar7GjpstUHd6fEF1bW9VWp+xl44FwcABLvtqvwa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\nL19cQHghh93b/aK973rPTiZfxuR8CjsHuzBIx0p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"text/plain": [ - "" + "(8, 17)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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bA7KOZTzixaW5DKpgMKjweZN7zgBOa0GvQrSWI621w7MXFwEoQGvDXlycW0YV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\nIiLJ2HyJiIgkY/MlIiKS7C94s4p0653Y7QAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" ] }, "metadata": {}, @@ -445,14 +914,28 @@ " return 24. * np.degrees(np.arccos(1 - np.clip(m, 0, 2))) / 180.\n", "\n", "daily['daylight_hrs'] = list(map(hours_of_daylight, daily.index))\n", - "daily[['daylight_hrs']].plot();" + "daily[['daylight_hrs']].plot()\n", + "plt.ylim(8, 17)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can also add the average temperature and total precipitation to the data.\n", + "In addition to the inches of precipitation, let's add a flag that indicates whether a day is dry (has zero precipitation):" ] }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 20, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -468,22 +951,47 @@ "daily = daily.join(weather[['PRCP', 'Temp (C)', 'dry day']])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, let's add a counter that increases from day 1, and measures how many years have passed.\n", + "This will let us measure any observed annual increase or decrease in daily crossings:" + ] + }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ "daily['annual'] = (daily.index - daily.index[0]).days / 365." ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now our data is in order, and we can take a look at it:" + ] + }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 22, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -530,87 +1038,87 @@ " \n", " \n", " 2012-10-03\n", - " 3521\n", - " 0\n", - " 0\n", - " 1\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", + " 3521.0\n", + " 0.0\n", + " 0.0\n", + " 1.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", " 11.277359\n", - " 0\n", + " 0.0\n", " 13.35\n", - " 1\n", + " 1.0\n", " 0.000000\n", " \n", " \n", " 2012-10-04\n", - " 3475\n", - " 0\n", - " 0\n", - " 0\n", - " 1\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", + " 3475.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 1.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", " 11.219142\n", - " 0\n", + " 0.0\n", " 13.60\n", - " 1\n", + " 1.0\n", " 0.002740\n", " \n", " \n", " 2012-10-05\n", - " 3148\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", - " 1\n", - " 0\n", - " 0\n", - " 0\n", + " 3148.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 1.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", " 11.161038\n", - " 0\n", + " 0.0\n", " 15.30\n", - " 1\n", + " 1.0\n", " 0.005479\n", " \n", " \n", " 2012-10-06\n", - " 2006\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", - " 1\n", - " 0\n", - " 0\n", + " 2006.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 1.0\n", + " 0.0\n", + " 0.0\n", " 11.103056\n", - " 0\n", + " 0.0\n", " 15.85\n", - " 1\n", + " 1.0\n", " 0.008219\n", " \n", " \n", " 2012-10-07\n", - " 2142\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", - " 0\n", - " 1\n", - " 0\n", + " 2142.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 1.0\n", + " 0.0\n", " 11.045208\n", - " 0\n", + " 0.0\n", " 15.85\n", - " 1\n", + " 1.0\n", " 0.010959\n", " \n", " \n", @@ -618,24 +1126,24 @@ "" ], "text/plain": [ - " Total Mon Tue Wed Thu Fri Sat Sun holiday daylight_hrs \\\n", - "Date \n", - "2012-10-03 3521 0 0 1 0 0 0 0 0 11.277359 \n", - "2012-10-04 3475 0 0 0 1 0 0 0 0 11.219142 \n", - "2012-10-05 3148 0 0 0 0 1 0 0 0 11.161038 \n", - "2012-10-06 2006 0 0 0 0 0 1 0 0 11.103056 \n", - "2012-10-07 2142 0 0 0 0 0 0 1 0 11.045208 \n", + " Total Mon Tue Wed Thu Fri Sat Sun holiday daylight_hrs \\\n", + "Date \n", + "2012-10-03 3521.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 11.277359 \n", + "2012-10-04 3475.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 11.219142 \n", + "2012-10-05 3148.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 11.161038 \n", + "2012-10-06 2006.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 11.103056 \n", + "2012-10-07 2142.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 11.045208 \n", "\n", " PRCP Temp (C) dry day annual \n", "Date \n", - "2012-10-03 0 13.35 1 0.000000 \n", - "2012-10-04 0 13.60 1 0.002740 \n", - "2012-10-05 0 15.30 1 0.005479 \n", - "2012-10-06 0 15.85 1 0.008219 \n", - "2012-10-07 0 15.85 1 0.010959 " + "2012-10-03 0.0 13.35 1.0 0.000000 \n", + "2012-10-04 0.0 13.60 1.0 0.002740 \n", + "2012-10-05 0.0 15.30 1.0 0.005479 \n", + "2012-10-06 0.0 15.85 1.0 0.008219 \n", + "2012-10-07 0.0 15.85 1.0 0.010959 " ] }, - "execution_count": 21, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -644,16 +1152,32 @@ "daily.head()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this in place, we can choose the columns to use, and fit a linear regression model to our data.\n", + "We will set ``fit_intercept = False``, because the daily flags essentially operate as their own day-specific intercepts:" + ] + }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 23, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ - "column_names = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun',\n", - " 'holiday', 'daylight_hrs', 'PRCP', 'dry day', 'Temp (C)', 'annual']\n", + "# Drop any rows with null values\n", + "daily.dropna(axis=0, how='any', inplace=True)\n", + "\n", + "column_names = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun', 'holiday',\n", + " 'daylight_hrs', 'PRCP', 'dry day', 'Temp (C)', 'annual']\n", "X = daily[column_names]\n", "y = daily['Total']\n", "\n", @@ -662,18 +1186,30 @@ "daily['predicted'] = model.predict(X)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we can compare the total and predicted bicycle traffic visually:" + ] + }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 24, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { - "image/png": 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do3UFrusaLCKI6wDhK3N5+0OuWMJZYkqDLyd+8EKfv+260KPvR5Q5w7Zjtx1C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\ngg==\n", 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Ts2UcfWNIWkbXtchrilAauGIpoAS4QqFYcGqZ0IPUSqU6nHU05VzJlJaZKVRgE4LmdHSm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PYvuUgHUicN17a0JmvgILXslElv1eskpB38jF4CBgN3HImFTo3V3snk2m9ph8BOtYkj8j04It/D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\nknkuDQ357TeRqvGYqPYwzqjcGGPWMm6j0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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -684,33 +1220,47 @@ "daily[['Total', 'predicted']].plot(alpha=0.5);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "It is evident that we have missed some key features, especially during the summer time.\n", + "Either our features are not complete (i.e., people decide whether to ride to work based on more than just these) or there are some nonlinear relationships that we have failed to take into account (e.g., perhaps people ride less at both high and low temperatures).\n", + "Nevertheless, our rough approximation is enough to give us some insights, and we can take a look at the coefficients of the linear model to estimate how much each feature contributes to the daily bicycle count:" + ] + }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 25, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "text/plain": [ - "Mon 503.797330\n", - "Tue 612.088879\n", - "Wed 591.611292\n", - "Thu 481.250377\n", - "Fri 176.838999\n", - "Sat -1104.321406\n", - "Sun -1134.610322\n", - "holiday -1187.212688\n", - "daylight_hrs 128.873251\n", - "PRCP -665.185105\n", - "dry day 546.185613\n", - "Temp (C) 65.194390\n", - "annual 27.865349\n", + "Mon 504.882756\n", + "Tue 610.233936\n", + "Wed 592.673642\n", + "Thu 482.358115\n", + "Fri 177.980345\n", + "Sat -1103.301710\n", + "Sun -1133.567246\n", + "holiday -1187.401381\n", + "daylight_hrs 128.851511\n", + "PRCP -664.834882\n", + "dry day 547.698592\n", + "Temp (C) 65.162791\n", + "annual 26.942713\n", "dtype: float64" ] }, - "execution_count": 24, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -720,11 +1270,24 @@ "params" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "These numbers are difficult to interpret without some measure of their uncertainty.\n", + "We can compute these uncertainties quickly using bootstrap resamplings of the data:" + ] + }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 26, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -734,11 +1297,23 @@ " for i in range(1000)], 0)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With these errors estimated, let's again look at the results:" + ] + }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 27, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -746,19 +1321,19 @@ "output_type": "stream", "text": [ " effect error\n", - "Mon 504 85\n", - "Tue 612 82\n", - "Wed 592 82\n", - "Thu 481 85\n", - "Fri 177 81\n", - "Sat -1104 79\n", - "Sun -1135 82\n", - "holiday -1187 164\n", - "daylight_hrs 129 9\n", - "PRCP -665 62\n", - "dry day 546 33\n", - "Temp (C) 65 4\n", - "annual 28 18\n" + "Mon 505.0 86.0\n", + "Tue 610.0 83.0\n", + "Wed 593.0 83.0\n", + "Thu 482.0 85.0\n", + "Fri 178.0 81.0\n", + "Sat -1103.0 80.0\n", + "Sun -1134.0 83.0\n", + "holiday -1187.0 163.0\n", + "daylight_hrs 129.0 9.0\n", + "PRCP -665.0 62.0\n", + "dry day 548.0 33.0\n", + "Temp (C) 65.0 4.0\n", + "annual 27.0 18.0\n" ] } ], @@ -766,9 +1341,39 @@ "print(pd.DataFrame({'effect': params.round(0),\n", " 'error': err.round(0)}))" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We first see that there is a relatively stable trend in the weekly baseline: there are many more riders on weekdays than on weekends and holidays.\n", + "We see that for each additional hour of daylight, 129 ± 9 more people choose to ride; a temperature increase of one degree Celsius encourages 65 ± 4 people to grab their bicycle; a dry day means an average of 548 ± 33 more riders, and each inch of precipitation means 665 ± 62 more people leave their bike at home.\n", + "Once all these effects are accounted for, we see a modest increase of 27 ± 18 new daily riders each year.\n", + "\n", + "Our model is almost certainly missing some relevant information. For example, nonlinear effects (such as effects of precipitation *and* cold temperature) and nonlinear trends within each variable (such as disinclination to ride at very cold and very hot temperatures) cannot be accounted for in this model.\n", + "Additionally, we have thrown away some of the finer-grained information (such as the difference between a rainy morning and a rainy afternoon), and we have ignored correlations between days (such as the possible effect of a rainy Tuesday on Wednesday's numbers, or the effect of an unexpected sunny day after a streak of rainy days).\n", + "These are all potentially interesting effects, and you now have the tools to begin exploring them if you wish!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) | [Contents](Index.ipynb) | [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.07-Support-Vector-Machines.ipynb b/notebooks_v1/05.07-Support-Vector-Machines.ipynb similarity index 98% rename from code_listings/05.07-Support-Vector-Machines.ipynb rename to notebooks_v1/05.07-Support-Vector-Machines.ipynb index 8c94a05a6..31cf9508b 100644 --- a/code_listings/05.07-Support-Vector-Machines.ipynb +++ b/notebooks_v1/05.07-Support-Vector-Machines.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) | [Contents](Index.ipynb) | [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,16 @@ "# In-Depth: Support Vector Machines" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Support vector machines (SVMs) are a particularly powerful and flexible class of supervised algorithms for both classification and regression.\n", + "In this section, we will develop the intuition behind support vector machines and their use in classification problems.\n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -24,6 +56,23 @@ "import seaborn as sns; sns.set()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivating Support Vector Machines" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As part of our disussion of Bayesian classification (see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)), we learned a simple model describing the distribution of each underlying class, and used these generative models to probabilistically determine labels for new points.\n", + "That was an example of *generative classification*; here we will consider instead *discriminative classification*: rather than modeling each class, we simply find a line or curve (in two dimensions) or manifold (in multiple dimensions) that divides the classes from each other.\n", + "\n", + "As an example of this, consider the simple case of a classification task, in which the two classes of points are well separated:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -49,6 +98,17 @@ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A linear discriminative classifier would attempt to draw a straight line separating the two sets of data, and thereby create a model for classification.\n", + "For two dimensional data like that shown here, this is a task we could do by hand.\n", + "But immediately we see a problem: there is more than one possible dividing line that can perfectly discriminate between the two classes!\n", + "\n", + "We can draw them as follows:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -78,6 +138,26 @@ "plt.xlim(-1, 3.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are three *very* different separators which, nevertheless, perfectly discriminate between these samples.\n", + "Depending on which you choose, a new data point (e.g., the one marked by the \"X\" in this plot) will be assigned a different label!\n", + "Evidently our simple intuition of \"drawing a line between classes\" is not enough, and we need to think a bit deeper." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Support Vector Machines: Maximizing the *Margin*\n", + "\n", + "Support vector machines offer one way to improve on this.\n", + "The intuition is this: rather than simply drawing a zero-width line between the classes, we can draw around each line a *margin* of some width, up to the nearest point.\n", + "Here is an example of how this might look:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -103,11 +183,30 @@ "for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:\n", " yfit = m * xfit + b\n", " plt.plot(xfit, yfit, '-k')\n", - " plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none', color='#AAAAAA', alpha=0.4)\n", + " plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none',\n", + " color='#AAAAAA', alpha=0.4)\n", "\n", "plt.xlim(-1, 3.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In support vector machines, the line that maximizes this margin is the one we will choose as the optimal model.\n", + "Support vector machines are an example of such a *maximum margin* estimator." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Fitting a support vector machine\n", + "\n", + "Let's see the result of an actual fit to this data: we will use Scikit-Learn's support vector classifier to train an SVM model on this data.\n", + "For the time being, we will use a linear kernel and set the ``C`` parameter to a very large number (we'll discuss the meaning of these in more depth momentarily)." + ] + }, { "cell_type": "code", "execution_count": 5, @@ -130,11 +229,18 @@ } ], "source": [ - "from sklearn.svm import SVC # \"Support Vector Classifier\"\n", + "from sklearn.svm import SVC # \"Support vector classifier\"\n", "model = SVC(kernel='linear', C=1E10)\n", "model.fit(X, y)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To better visualize what's happening here, let's create a quick convenience function that will plot SVM decision boundaries for us:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -157,7 +263,7 @@ " xy = np.vstack([X.ravel(), Y.ravel()]).T\n", " P = model.decision_function(xy).reshape(X.shape)\n", " \n", - " # plot decision boundary & margins\n", + " # plot decision boundary and margins\n", " ax.contour(X, Y, P, colors='k',\n", " levels=[-1, 0, 1], alpha=0.5,\n", " linestyles=['--', '-', '--'])\n", @@ -194,6 +300,16 @@ "plot_svc_decision_function(model);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is the dividing line that maximizes the margin between the two sets of points.\n", + "Notice that a few of the training points just touch the margin: they are indicated by the black circles in this figure.\n", + "These points are the pivotal elements of this fit, and are known as the *support vectors*, and give the algorithm its name.\n", + "In Scikit-Learn, the identity of these points are stored in the ``support_vectors_`` attribute of the classifier:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -218,6 +334,16 @@ "model.support_vectors_" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A key to this classifier's success is that for the fit, only the position of the support vectors matter; any points further from the margin which are on the correct side do not modify the fit!\n", + "Technically, this is because these points do not contribute to the loss function used to fit the model, so their position and number do not matter so long as they do not cross the margin.\n", + "\n", + "We can see this, for example, if we plot the model learned from the first 60 points and first 120 points of this dataset:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -258,6 +384,22 @@ " axi.set_title('N = {0}'.format(N))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the left panel, we see the model and the support vectors for 60 training points.\n", + "In the right panel, we have doubled the number of training points, but the model has not changed: the three support vectors from the left panel are still the support vectors from the right panel.\n", + "This insensitivity to the exact behavior of distant points is one of the strengths of the SVM model." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are running this notebook live, you can use IPython's interactive widgets to view this feature of the SVM model interactively:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -281,6 +423,20 @@ "interact(plot_svm, N=[10, 200], ax=fixed(None));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Beyond linear boundaries: Kernel SVM\n", + "\n", + "Where SVM becomes extremely powerful is when it is combined with *kernels*.\n", + "We have seen a version of kernels before, in the basis function regressions of [In Depth: Linear Regression](05.06-Linear-Regression.ipynb).\n", + "There we projected our data into higher-dimensional space defined by polynomials and Gaussian basis functions, and thereby were able to fit for nonlinear relationships with a linear classifier.\n", + "\n", + "In SVM models, we can use a version of the same idea.\n", + "To motivate the need for kernels, let's look at some data that is not linearly separable:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -309,6 +465,15 @@ "plot_svc_decision_function(clf, plot_support=False);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is clear that no linear discrimination will *ever* be able to separate this data.\n", + "But we can draw a lesson from the basis function regressions in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), and think about how we might project the data into a higher dimension such that a linear separator *would* be sufficient.\n", + "For example, one simple projection we could use would be to compute a *radial basis function* centered on the middle clump:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -320,6 +485,13 @@ "r = np.exp(-(X ** 2).sum(1))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can visualize this extra data dimension using a three-dimensional plot—if you are running this notebook live, you will be able to use the sliders to rotate the plot:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -353,6 +525,25 @@ " X=fixed(X), y=fixed(y));" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that with this additional dimension, the data becomes trivially linearly separable, by drawing a separating plane at, say, *r*=0.7.\n", + "\n", + "Here we had to choose and carefully tune our projection: if we had not centered our radial basis function in the right location, we would not have seen such clean, linearly separable results.\n", + "In general, the need to make such a choice is a problem: we would like to somehow automatically find the best basis functions to use.\n", + "\n", + "One strategy to this end is to compute a basis function centered at *every* point in the dataset, and let the SVM algorithm sift through the results.\n", + "This type of basis function transformation is known as a *kernel transformation*, as it is based on a similarity relationship (or kernel) between each pair of points.\n", + "\n", + "A potential problem with this strategy—projecting $N$ points into $N$ dimensions—is that it might become very computationally intensive as $N$ grows large.\n", + "However, because of a neat little procedure known as the [*kernel trick*](https://en.wikipedia.org/wiki/Kernel_trick), a fit on kernel-transformed data can be done implicitly—that is, without ever building the full $N$-dimensional representation of the kernel projection!\n", + "This kernel trick is built into the SVM, and is one of the reasons the method is so powerful.\n", + "\n", + "In Scikit-Learn, we can apply kernelized SVM simply by changing our linear kernel to an RBF (radial basis function) kernel, using the ``kernel`` model hyperparameter:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -404,6 +595,25 @@ " s=300, lw=1, facecolors='none');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using this kernelized support vector machine, we learn a suitable nonlinear decision boundary.\n", + "This kernel transformation strategy is used often in machine learning to turn fast linear methods into fast nonlinear methods, especially for models in which the kernel trick can be used." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Tuning the SVM: Softening Margins\n", + "\n", + "Our discussion thus far has centered around very clean datasets, in which a perfect decision boundary exists.\n", + "But what if your data has some amount of overlap?\n", + "For example, you may have data like this:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -428,6 +638,18 @@ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To handle this case, the SVM implementation has a bit of a fudge-factor which \"softens\" the margin: that is, it allows some of the points to creep into the margin if that allows a better fit.\n", + "The hardness of the margin is controlled by a tuning parameter, most often known as $C$.\n", + "For very large $C$, the margin is hard, and points cannot lie in it.\n", + "For smaller $C$, the margin is softer, and can grow to encompass some points.\n", + "\n", + "The plot shown below gives a visual picture of how a changing $C$ parameter affects the final fit, via the softening of the margin:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -463,6 +685,24 @@ " axi.set_title('C = {0:.1f}'.format(C), size=14)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The optimal value of the $C$ parameter will depend on your dataset, and should be tuned using cross-validation or a similar procedure (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Face Recognition\n", + "\n", + "As an example of support vector machines in action, let's take a look at the facial recognition problem.\n", + "We will use the Labeled Faces in the Wild dataset, which consists of several thousand collated photos of various public figures.\n", + "A fetcher for the dataset is built into Scikit-Learn:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -487,6 +727,13 @@ "print(faces.images.shape)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot a few of these faces to see what we're working with:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -513,6 +760,15 @@ " xlabel=faces.target_names[faces.target[i]])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each image contains [62×47] or nearly 3,000 pixels.\n", + "We could proceed by simply using each pixel value as a feature, but often it is more effective to use some sort of preprocessor to extract more meaningful features; here we will use a principal component analysis (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)) to extract 150 fundamental components to feed into our support vector machine classifier.\n", + "We can do this most straightforwardly by packaging the preprocessor and the classifier into a single pipeline:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -530,6 +786,13 @@ "model = make_pipeline(pca, svc)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the sake of testing our classifier output, we will split the data into a training and testing set:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -543,6 +806,14 @@ " random_state=42)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can use a grid search cross-validation to explore combinations of parameters.\n", + "Here we will adjust ``C`` (which controls the margin hardness) and ``gamma`` (which controls the size of the radial basis function kernel), and determine the best model:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -570,6 +841,15 @@ "print(grid.best_params_)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The optimal values fall toward the middle of our grid; if they fell at the edges, we would want to expand the grid to make sure we have found the true optimum.\n", + "\n", + "Now with this cross-validated model, we can predict the labels for the test data, which the model has not yet seen:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -582,6 +862,13 @@ "yfit = model.predict(Xtest)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's take a look at a few of the test images along with their predicted values:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -610,6 +897,15 @@ "fig.suptitle('Predicted Names; Incorrect Labels in Red', size=14);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Out of this small sample, our optimal estimator mislabeled only a single face (Bush’s\n", + "face in the bottom row was mislabeled as Blair).\n", + "We can get a better sense of our estimator's performance using the classification report, which lists recovery statistics label by label:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -643,6 +939,13 @@ " target_names=faces.target_names))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We might also display the confusion matrix between these classes:" + ] + }, { "cell_type": "code", "execution_count": 26, @@ -670,9 +973,54 @@ "plt.xlabel('true label')\n", "plt.ylabel('predicted label');" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This helps us get a sense of which labels are likely to be confused by the estimator.\n", + "\n", + "For a real-world facial recognition task, in which the photos do not come pre-cropped into nice grids, the only difference in the facial classification scheme is the feature selection: you would need to use a more sophisticated algorithm to find the faces, and extract features that are independent of the pixellation.\n", + "For this kind of application, one good option is to make use of [OpenCV](http://opencv.org), which, among other things, includes pre-trained implementations of state-of-the-art feature extraction tools for images in general and faces in particular." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Support Vector Machine Summary\n", + "\n", + "We have seen here a brief intuitive introduction to the principals behind support vector machines.\n", + "These methods are a powerful classification method for a number of reasons:\n", + "\n", + "- Their dependence on relatively few support vectors means that they are very compact models, and take up very little memory.\n", + "- Once the model is trained, the prediction phase is very fast.\n", + "- Because they are affected only by points near the margin, they work well with high-dimensional data—even data with more dimensions than samples, which is a challenging regime for other algorithms.\n", + "- Their integration with kernel methods makes them very versatile, able to adapt to many types of data.\n", + "\n", + "However, SVMs have several disadvantages as well:\n", + "\n", + "- The scaling with the number of samples $N$ is $\\mathcal{O}[N^3]$ at worst, or $\\mathcal{O}[N^2]$ for efficient implementations. For large numbers of training samples, this computational cost can be prohibitive.\n", + "- The results are strongly dependent on a suitable choice for the softening parameter $C$. This must be carefully chosen via cross-validation, which can be expensive as datasets grow in size.\n", + "- The results do not have a direct probabilistic interpretation. This can be estimated via an internal cross-validation (see the ``probability`` parameter of ``SVC``), but this extra estimation is costly.\n", + "\n", + "With those traits in mind, I generally only turn to SVMs once other simpler, faster, and less tuning-intensive methods have been shown to be insufficient for my needs.\n", + "Nevertheless, if you have the CPU cycles to commit to training and cross-validating an SVM on your data, the method can lead to excellent results." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) | [Contents](Index.ipynb) | [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.08-Random-Forests.ipynb b/notebooks_v1/05.08-Random-Forests.ipynb similarity index 96% rename from code_listings/05.08-Random-Forests.ipynb rename to notebooks_v1/05.08-Random-Forests.ipynb index 97f148a15..f567f238e 100644 --- a/code_listings/05.08-Random-Forests.ipynb +++ b/notebooks_v1/05.08-Random-Forests.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) | [Contents](Index.ipynb) | [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,18 @@ "# In-Depth: Decision Trees and Random Forests" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Previously we have looked in depth at a simple generative classifier (naive Bayes; see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)) and a powerful discriminative classifier (support vector machines; see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n", + "Here we'll take a look at motivating another powerful algorithm—a non-parametric algorithm called *random forests*.\n", + "Random forests are an example of an *ensemble* method, meaning that it relies on aggregating the results of an ensemble of simpler estimators.\n", + "The somewhat surprising result with such ensemble methods is that the sum can be greater than the parts: that is, a majority vote among a number of estimators can end up being better than any of the individual estimators doing the voting!\n", + "We will see examples of this in the following sections.\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -21,6 +55,53 @@ "import seaborn as sns; sns.set()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivating Random Forests: Decision Trees" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Random forests are an example of an *ensemble learner* built on decision trees.\n", + "For this reason we'll start by discussing decision trees themselves.\n", + "\n", + "Decision trees are extremely intuitive ways to classify or label objects: you simply ask a series of questions designed to zero-in on the classification.\n", + "For example, if you wanted to build a decision tree to classify an animal you come across while on a hike, you might construct the one shown here:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "![](figures/05.08-decision-tree.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Decision-Tree-Example)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The binary splitting makes this extremely efficient: in a well-constructed tree, each question will cut the number of options by approximately half, very quickly narrowing the options even among a large number of classes.\n", + "The trick, of course, comes in deciding which questions to ask at each step.\n", + "In machine learning implementations of decision trees, the questions generally take the form of axis-aligned splits in the data: that is, each node in the tree splits the data into two groups using a cutoff value within one of the features.\n", + "Let's now look at an example of this." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Creating a decision tree\n", + "\n", + "Consider the following two-dimensional data, which has one of four class labels:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -47,6 +128,37 @@ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='rainbow');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A simple decision tree built on this data will iteratively split the data along one or the other axis according to some quantitative criterion, and at each level assign the label of the new region according to a majority vote of points within it.\n", + "This figure presents a visualization of the first four levels of a decision tree classifier for this data:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](figures/05.08-decision-tree-levels.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Decision-Tree-Levels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that after the first split, every point in the upper branch remains unchanged, so there is no need to further subdivide this branch.\n", + "Except for nodes that contain all of one color, at each level *every* region is again split along one of the two features." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This process of fitting a decision tree to our data can be done in Scikit-Learn with the ``DecisionTreeClassifier`` estimator:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -59,6 +171,13 @@ "tree = DecisionTreeClassifier().fit(X, y)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's write a quick utility function to help us visualize the output of the classifier:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -94,6 +213,13 @@ " ax.set(xlim=xlim, ylim=ylim)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can examine what the decision tree classification looks like:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -116,6 +242,13 @@ "visualize_classifier(DecisionTreeClassifier(), X, y)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you're running this notebook live, you can use the helpers script included in [The Online Appendix](06.00-Figure-Code.ipynb#Helper-Code) to bring up an interactive visualization of the decision tree building process:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -135,11 +268,53 @@ } ], "source": [ - "# helpers_05_08 is found in the Online Appendix\n", + "# helpers_05_08 is found in the online appendix\n", "import helpers_05_08\n", "helpers_05_08.plot_tree_interactive(X, y);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that as the depth increases, we tend to get very strangely shaped classification regions; for example, at a depth of five, there is a tall and skinny purple region between the yellow and blue regions.\n", + "It's clear that this is less a result of the true, intrinsic data distribution, and more a result of the particular sampling or noise properties of the data.\n", + "That is, this decision tree, even at only five levels deep, is clearly over-fitting our data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Decision trees and over-fitting\n", + "\n", + "Such over-fitting turns out to be a general property of decision trees: it is very easy to go too deep in the tree, and thus to fit details of the particular data rather than the overall properties of the distributions they are drawn from.\n", + "Another way to see this over-fitting is to look at models trained on different subsets of the data—for example, in this figure we train two different trees, each on half of the original data:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](figures/05.08-decision-tree-overfitting.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Decision-Tree-Overfitting)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is clear that in some places, the two trees produce consistent results (e.g., in the four corners), while in other places, the two trees give very different classifications (e.g., in the regions between any two clusters).\n", + "The key observation is that the inconsistencies tend to happen where the classification is less certain, and thus by using information from *both* of these trees, we might come up with a better result!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are running this notebook live, the following function will allow you to interactively display the fits of trees trained on a random subset of the data:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -159,11 +334,31 @@ } ], "source": [ - "# helpers_05_08 is found in the Online Appendix\n", + "# helpers_05_08 is found in the online appendix\n", "import helpers_05_08\n", "helpers_05_08.randomized_tree_interactive(X, y)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as using information from two trees improves our results, we might expect that using information from many trees would improve our results even further." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ensembles of Estimators: Random Forests\n", + "\n", + "This notion—that multiple overfitting estimators can be combined to reduce the effect of this overfitting—is what underlies an ensemble method called *bagging*.\n", + "Bagging makes use of an ensemble (a grab bag, perhaps) of parallel estimators, each of which over-fits the data, and averages the results to find a better classification.\n", + "An ensemble of randomized decision trees is known as a *random forest*.\n", + "\n", + "This type of bagging classification can be done manually using Scikit-Learn's ``BaggingClassifier`` meta-estimator, as shown here:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -194,6 +389,19 @@ "visualize_classifier(bag, X, y)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example, we have randomized the data by fitting each estimator with a random subset of 80% of the training points.\n", + "In practice, decision trees are more effectively randomized by injecting some stochasticity in how the splits are chosen: this way all the data contributes to the fit each time, but the results of the fit still have the desired randomness.\n", + "For example, when determining which feature to split on, the randomized tree might select from among the top several features.\n", + "You can read more technical details about these randomization strategies in the [Scikit-Learn documentation](http://scikit-learn.org/stable/modules/ensemble.html#forest) and references within.\n", + "\n", + "In Scikit-Learn, such an optimized ensemble of randomized decision trees is implemented in the ``RandomForestClassifier`` estimator, which takes care of all the randomization automatically.\n", + "All you need to do is select a number of estimators, and it will very quickly (in parallel, if desired) fit the ensemble of trees:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -219,6 +427,25 @@ "visualize_classifier(model, X, y);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that by averaging over 100 randomly perturbed models, we end up with an overall model that is much closer to our intuition about how the parameter space should be split." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Random Forest Regression\n", + "\n", + "In the previous section we considered random forests within the context of classification.\n", + "Random forests can also be made to work in the case of regression (that is, continuous rather than categorical variables). The estimator to use for this is the ``RandomForestRegressor``, and the syntax is very similar to what we saw earlier.\n", + "\n", + "Consider the following data, drawn from the combination of a fast and slow oscillation:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -252,6 +479,13 @@ "plt.errorbar(x, y, 0.3, fmt='o');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the random forest regressor, we can find the best fit curve as follows:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -284,6 +518,24 @@ "plt.plot(xfit, ytrue, '-k', alpha=0.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the true model is shown in the smooth gray curve, while the random forest model is shown by the jagged red curve.\n", + "As you can see, the non-parametric random forest model is flexible enough to fit the multi-period data, without us needing to specifying a multi-period model!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Random Forest for Classifying Digits\n", + "\n", + "Earlier we took a quick look at the hand-written digits data (see [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb)).\n", + "Let's use that again here to see how the random forest classifier can be used in this context." + ] + }, { "cell_type": "code", "execution_count": 12, @@ -308,6 +560,13 @@ "digits.keys()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To remind us what we're looking at, we'll visualize the first few data points:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -340,6 +599,13 @@ " ax.text(0, 7, str(digits.target[i]))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can quickly classify the digits using a random forest as follows:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -350,12 +616,20 @@ "source": [ "from sklearn.cross_validation import train_test_split\n", "\n", - "Xtrain, Xtest, ytrain, ytest = train_test_split(digits.data, digits.target, random_state=0)\n", + "Xtrain, Xtest, ytrain, ytest = train_test_split(digits.data, digits.target,\n", + " random_state=0)\n", "model = RandomForestClassifier(n_estimators=1000)\n", "model.fit(Xtrain, ytrain)\n", "ypred = model.predict(Xtest)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can take a look at the classification report for this classifier:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -390,6 +664,13 @@ "print(metrics.classification_report(ypred, ytest))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And for good measure, plot the confusion matrix:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -415,9 +696,43 @@ "plt.xlabel('true label')\n", "plt.ylabel('predicted label');" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find that a simple, untuned random forest results in a very accurate classification of the digits data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary of Random Forests\n", + "\n", + "This section contained a brief introduction to the concept of *ensemble estimators*, and in particular the random forest – an ensemble of randomized decision trees.\n", + "Random forests are a powerful method with several advantages:\n", + "\n", + "- Both training and prediction are very fast, because of the simplicity of the underlying decision trees. In addition, both tasks can be straightforwardly parallelized, because the individual trees are entirely independent entities.\n", + "- The multiple trees allow for a probabilistic classification: a majority vote among estimators gives an estimate of the probability (accessed in Scikit-Learn with the ``predict_proba()`` method).\n", + "- The nonparametric model is extremely flexible, and can thus perform well on tasks that are under-fit by other estimators.\n", + "\n", + "A primary disadvantage of random forests is that the results are not easily interpretable: that is, if you would like to draw conclusions about the *meaning* of the classification model, random forests may not be the best choice." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) | [Contents](Index.ipynb) | [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.09-Principal-Component-Analysis.ipynb b/notebooks_v1/05.09-Principal-Component-Analysis.ipynb similarity index 95% rename from code_listings/05.09-Principal-Component-Analysis.ipynb rename to notebooks_v1/05.09-Principal-Component-Analysis.ipynb index 51e3c1b0a..065b1f4a7 100644 --- a/code_listings/05.09-Principal-Component-Analysis.ipynb +++ b/notebooks_v1/05.09-Principal-Component-Analysis.ipynb @@ -1,5 +1,33 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) | [Contents](Index.ipynb) | [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,11 +35,30 @@ "# In Depth: Principal Component Analysis" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Up until now, we have been looking in depth at supervised learning estimators: those estimators that predict labels based on labeled training data.\n", + "Here we begin looking at several unsupervised estimators, which can highlight interesting aspects of the data without reference to any known labels.\n", + "\n", + "In this section, we explore what is perhaps one of the most broadly used of unsupervised algorithms, principal component analysis (PCA).\n", + "PCA is fundamentally a dimensionality reduction algorithm, but it can also be useful as a tool for visualization, for noise filtering, for feature extraction and engineering, and much more.\n", + "After a brief conceptual discussion of the PCA algorithm, we will see a couple examples of these further applications.\n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -21,11 +68,27 @@ "import seaborn as sns; sns.set()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Introducing Principal Component Analysis\n", + "\n", + "Principal component analysis is a fast and flexible unsupervised method for dimensionality reduction in data, which we saw briefly in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb).\n", + "Its behavior is easiest to visualize by looking at a two-dimensional dataset.\n", + "Consider the following 200 points:" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -46,11 +109,27 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By eye, it is clear that there is a nearly linear relationship between the x and y variables.\n", + "This is reminiscent of the linear regression data we explored in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), but the problem setting here is slightly different: rather than attempting to *predict* the y values from the x values, the unsupervised learning problem attempts to learn about the *relationship* between the x and y values.\n", + "\n", + "In principal component analysis, this relationship is quantified by finding a list of the *principal axes* in the data, and using those axes to describe the dataset.\n", + "Using Scikit-Learn's ``PCA`` estimator, we can compute this as follows:" + ] + }, { "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -70,11 +149,23 @@ "pca.fit(X)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The fit learns some quantities from the data, most importantly the \"components\" and \"explained variance\":" + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -94,7 +185,9 @@ "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -109,11 +202,23 @@ "print(pca.explained_variance_)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "To see what these numbers mean, let's visualize them as vectors over the input data, using the \"components\" to define the direction of the vector, and the \"explained variance\" to define the squared-length of the vector:" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -143,11 +248,63 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "These vectors represent the *principal axes* of the data, and the length of the vector is an indication of how \"important\" that axis is in describing the distribution of the data—more precisely, it is a measure of the variance of the data when projected onto that axis.\n", + "The projection of each data point onto the principal axes are the \"principal components\" of the data.\n", + "\n", + "If we plot these principal components beside the original data, we see the plots shown here:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.09-PCA-rotation.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Principal-Components-Rotation)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This transformation from data axes to principal axes is an *affine transformation*, which basically means it is composed of a translation, rotation, and uniform scaling.\n", + "\n", + "While this algorithm to find principal components may seem like just a mathematical curiosity, it turns out to have very far-reaching applications in the world of machine learning and data exploration." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### PCA as dimensionality reduction\n", + "\n", + "Using PCA for dimensionality reduction involves zeroing out one or more of the smallest principal components, resulting in a lower-dimensional projection of the data that preserves the maximal data variance.\n", + "\n", + "Here is an example of using PCA as a dimensionality reduction transform:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -167,11 +324,24 @@ "print(\"transformed shape:\", X_pca.shape)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The transformed data has been reduced to a single dimension.\n", + "To understand the effect of this dimensionality reduction, we can perform the inverse transform of this reduced data and plot it along with the original data:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -192,11 +362,42 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The light points are the original data, while the dark points are the projected version.\n", + "This makes clear what a PCA dimensionality reduction means: the information along the least important principal axis or axes is removed, leaving only the component(s) of the data with the highest variance.\n", + "The fraction of variance that is cut out (proportional to the spread of points about the line formed in this figure) is roughly a measure of how much \"information\" is discarded in this reduction of dimensionality.\n", + "\n", + "This reduced-dimension dataset is in some senses \"good enough\" to encode the most important relationships between the points: despite reducing the dimension of the data by 50%, the overall relationship between the data points are mostly preserved." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### PCA for visualization: Hand-written digits\n", + "\n", + "The usefulness of the dimensionality reduction may not be entirely apparent in only two dimensions, but becomes much more clear when looking at high-dimensional data.\n", + "To see this, let's take a quick look at the application of PCA to the digits data we saw in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb).\n", + "\n", + "We start by loading the data:" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -216,11 +417,24 @@ "digits.data.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Recall that the data consists of 8×8 pixel images, meaning that they are 64-dimensional.\n", + "To gain some intuition into the relationships between these points, we can use PCA to project them to a more manageable number of dimensions, say two:" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -239,11 +453,23 @@ "print(projected.shape)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can now plot the first two principal components of each point to learn about the data:" + ] + }, { "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -266,11 +492,131 @@ "plt.colorbar();" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Recall what these components mean: the full data is a 64-dimensional point cloud, and these points are the projection of each data point along the directions with the largest variance.\n", + "Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the digits in two dimensions, and have done this in an unsupervised manner—that is, without reference to the labels." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### What do the components mean?\n", + "\n", + "We can go a bit further here, and begin to ask what the reduced dimensions *mean*.\n", + "This meaning can be understood in terms of combinations of basis vectors.\n", + "For example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$:\n", + "\n", + "$$\n", + "x = [x_1, x_2, x_3 \\cdots x_{64}]\n", + "$$\n", + "\n", + "One way we can think about this is in terms of a pixel basis.\n", + "That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image:\n", + "\n", + "$$\n", + "{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n", + "$$\n", + "\n", + "One way we might imagine reducing the dimension of this data is to zero out all but a few of these basis vectors.\n", + "For example, if we use only the first eight pixels, we get an eight-dimensional projection of the data, but it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.09-digits-pixel-components.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Digits-Pixel-Components)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The upper row of panels shows the individual pixels, and the lower row shows the cumulative contribution of these pixels to the construction of the image.\n", + "Using only eight of the pixel-basis components, we can only construct a small portion of the 64-pixel image.\n", + "Were we to continue this sequence and use all 64 pixels, we would recover the original image." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But the pixel-wise representation is not the only choice of basis. We can also use other basis functions, which each contain some pre-defined contribution from each pixel, and write something like\n", + "\n", + "$$\n", + "image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n", + "$$\n", + "\n", + "PCA can be thought of as a process of choosing optimal basis functions, such that adding together just the first few of them is enough to suitably reconstruct the bulk of the elements in the dataset.\n", + "The principal components, which act as the low-dimensional representation of our data, are simply the coefficients that multiply each of the elements in this series.\n", + "This figure shows a similar depiction of reconstructing this digit using the mean plus the first eight PCA basis functions:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "source": [ + "![](figures/05.09-digits-pca-components.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Digits-PCA-Components)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Unlike the pixel basis, the PCA basis allows us to recover the salient features of the input image with just a mean plus eight components!\n", + "The amount of each pixel in each component is the corollary of the orientation of the vector in our two-dimensional example.\n", + "This is the sense in which PCA provides a low-dimensional representation of the data: it discovers a set of basis functions that are more efficient than the native pixel-basis of the input data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Choosing the number of components\n", + "\n", + "A vital part of using PCA in practice is the ability to estimate how many components are needed to describe the data.\n", + "This can be determined by looking at the cumulative *explained variance ratio* as a function of the number of components:" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -291,11 +637,43 @@ "plt.ylabel('cumulative explained variance');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This curve quantifies how much of the total, 64-dimensional variance is contained within the first $N$ components.\n", + "For example, we see that with the digits the first 10 components contain approximately 75% of the variance, while you need around 50 components to describe close to 100% of the variance.\n", + "\n", + "Here we see that our two-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance. Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in multiple observations." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## PCA as Noise Filtering\n", + "\n", + "PCA can also be used as a filtering approach for noisy data.\n", + "The idea is this: any components with variance much larger than the effect of the noise should be relatively unaffected by the noise.\n", + "So if you reconstruct the data using just the largest subset of principal components, you should be preferentially keeping the signal and throwing out the noise.\n", + "\n", + "Let's see how this looks with the digits data.\n", + "First we will plot several of the input noise-free data:" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -321,11 +699,23 @@ "plot_digits(digits.data)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now lets add some random noise to create a noisy dataset, and re-plot it:" + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -345,11 +735,24 @@ "plot_digits(noisy)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "It's clear by eye that the images are noisy, and contain spurious pixels.\n", + "Let's train a PCA on the noisy data, requesting that the projection preserve 50% of the variance:" + ] + }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -368,11 +771,24 @@ "pca.n_components_" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here 50% of the variance amounts to 12 principal components.\n", + "Now we compute these components, and then use the inverse of the transform to reconstruct the filtered digits:" + ] + }, { "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -392,11 +808,37 @@ "plot_digits(filtered)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This signal preserving/noise filtering property makes PCA a very useful feature selection routine—for example, rather than training a classifier on very high-dimensional data, you might instead train the classifier on the lower-dimensional representation, which will automatically serve to filter out random noise in the inputs." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: Eigenfaces\n", + "\n", + "Earlier we explored an example of using a PCA projection as a feature selector for facial recognition with a support vector machine (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n", + "Here we will take a look back and explore a bit more of what went into that.\n", + "Recall that we were using the Labeled Faces in the Wild dataset made available through Scikit-Learn:" + ] + }, { "cell_type": "code", "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -416,11 +858,25 @@ "print(faces.images.shape)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Let's take a look at the principal axes that span this dataset.\n", + "Because this is a large dataset, we will use ``RandomizedPCA``—it contains a randomized method to approximate the first $N$ principal components much more quickly than the standard ``PCA`` estimator, and thus is very useful for high-dimensional data (here, a dimensionality of nearly 3,000).\n", + "We will take a look at the first 150 components:" + ] + }, { "cell_type": "code", "execution_count": 18, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -441,11 +897,25 @@ "pca.fit(faces.data)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "In this case, it can be interesting to visualize the images associated with the first several principal components (these components are technically known as \"eigenvectors,\"\n", + "so these types of images are often called \"eigenfaces\").\n", + "As you can see in this figure, they are as creepy as they sound:" + ] + }, { "cell_type": "code", "execution_count": 19, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -467,11 +937,24 @@ " ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The results are very interesting, and give us insight into how the images vary: for example, the first few eigenfaces (from the top left) seem to be associated with the angle of lighting on the face, and later principal vectors seem to be picking out certain features, such as eyes, noses, and lips.\n", + "Let's take a look at the cumulative variance of these components to see how much of the data information the projection is preserving:" + ] + }, { "cell_type": "code", "execution_count": 20, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -491,15 +974,29 @@ "plt.ylabel('cumulative explained variance');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that these 150 components account for just over 90% of the variance.\n", + "That would lead us to believe that using these 150 components, we would recover most of the essential characteristics of the data.\n", + "To make this more concrete, we can compare the input images with the images reconstructed from these 150 components:" + ] + }, { "cell_type": "code", "execution_count": 21, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ - "# Compute the components & projected faces\n", + "# Compute the components and projected faces\n", "pca = RandomizedPCA(150).fit(faces.data)\n", "components = pca.transform(faces.data)\n", "projected = pca.inverse_transform(components)" @@ -509,7 +1006,9 @@ "cell_type": "code", "execution_count": 22, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -535,9 +1034,57 @@ "ax[0, 0].set_ylabel('full-dim\\ninput')\n", "ax[1, 0].set_ylabel('150-dim\\nreconstruction');" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The top row here shows the input images, while the bottom row shows the reconstruction of the images from just 150 of the ~3,000 initial features.\n", + "This visualization makes clear why the PCA feature selection used in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) was so successful: although it reduces the dimensionality of the data by nearly a factor of 20, the projected images contain enough information that we might, by eye, recognize the individuals in the image.\n", + "What this means is that our classification algorithm needs to be trained on 150-dimensional data rather than 3,000-dimensional data, which depending on the particular algorithm we choose, can lead to a much more efficient classification." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Principal Component Analysis Summary\n", + "\n", + "In this section we have discussed the use of principal component analysis for dimensionality reduction, for visualization of high-dimensional data, for noise filtering, and for feature selection within high-dimensional data.\n", + "Because of the versatility and interpretability of PCA, it has been shown to be effective in a wide variety of contexts and disciplines.\n", + "Given any high-dimensional dataset, I tend to start with PCA in order to visualize the relationship between points (as we did with the digits), to understand the main variance in the data (as we did with the eigenfaces), and to understand the intrinsic dimensionality (by plotting the explained variance ratio).\n", + "Certainly PCA is not useful for every high-dimensional dataset, but it offers a straightforward and efficient path to gaining insight into high-dimensional data.\n", + "\n", + "PCA's main weakness is that it tends to be highly affected by outliers in the data.\n", + "For this reason, many robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components.\n", + "Scikit-Learn contains a couple interesting variants on PCA, including ``RandomizedPCA`` and ``SparsePCA``, both also in the ``sklearn.decomposition`` submodule.\n", + "``RandomizedPCA``, which we saw earlier, uses a non-deterministic method to quickly approximate the first few principal components in very high-dimensional data, while ``SparsePCA`` introduces a regularization term (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)) that serves to enforce sparsity of the components.\n", + "\n", + "In the following sections, we will look at other unsupervised learning methods that build on some of the ideas of PCA." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) | [Contents](Index.ipynb) | [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.10-Manifold-Learning.ipynb b/notebooks_v1/05.10-Manifold-Learning.ipynb similarity index 98% rename from code_listings/05.10-Manifold-Learning.ipynb rename to notebooks_v1/05.10-Manifold-Learning.ipynb index 3bf52b05d..7ec547ba9 100644 --- a/code_listings/05.10-Manifold-Learning.ipynb +++ b/notebooks_v1/05.10-Manifold-Learning.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb) | [Contents](Index.ipynb) | [In Depth: k-Means Clustering](05.11-K-Means.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,26 @@ "# In-Depth: Manifold Learning" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have seen how principal component analysis (PCA) can be used in the dimensionality reduction task—reducing the number of features of a dataset while maintaining the essential relationships between the points.\n", + "While PCA is flexible, fast, and easily interpretable, it does not perform so well when there are *nonlinear* relationships within the data; we will see some examples of these below.\n", + "\n", + "To address this deficiency, we can turn to a class of methods known as *manifold learning*—a class of unsupervised estimators that seeks to describe datasets as low-dimensional manifolds embedded in high-dimensional spaces.\n", + "When you think of a manifold, I'd suggest imagining a sheet of paper: this is a two-dimensional object that lives in our familiar three-dimensional world, and can be bent or rolled in that two dimensions.\n", + "In the parlance of manifold learning, we can think of this sheet as a two-dimensional manifold embedded in three-dimensional space.\n", + "\n", + "Rotating, re-orienting, or stretching the piece of paper in three-dimensional space doesn't change the flat geometry of the paper: such operations are akin to linear embeddings.\n", + "If you bend, curl, or crumple the paper, it is still a two-dimensional manifold, but the embedding into the three-dimensional space is no longer linear.\n", + "Manifold learning algorithms would seek to learn about the fundamental two-dimensional nature of the paper, even as it is contorted to fill the three-dimensional space.\n", + "\n", + "Here we will demonstrate a number of manifold methods, going most deeply into a couple techniques: multidimensional scaling (MDS), locally linear embedding (LLE), and isometric mapping (IsoMap).\n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -21,6 +63,16 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Manifold Learning: \"HELLO\"\n", + "\n", + "To make these concepts more clear, let's start by generating some two-dimensional data that we can use to define a manifold.\n", + "Here is a function that will create data in the shape of the word \"HELLO\":" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -30,7 +82,7 @@ "outputs": [], "source": [ "def make_hello(N=1000, rseed=42):\n", - " # Make a plot with \"HELLO\" text; save as png\n", + " # Make a plot with \"HELLO\" text; save as PNG\n", " fig, ax = plt.subplots(figsize=(4, 1))\n", " fig.subplots_adjust(left=0, right=1, bottom=0, top=1)\n", " ax.axis('off')\n", @@ -51,6 +103,13 @@ " return X[np.argsort(X[:, 0])]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's call the function and visualize the resulting data:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -76,6 +135,24 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output is two dimensional, and consists of points drawn in the shape of the word, \"HELLO\".\n", + "This data form will help us to see visually what these algorithms are doing." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multidimensional Scaling (MDS)\n", + "\n", + "Looking at data like this, we can see that the particular choice of *x* and *y* values of the dataset are not the most fundamental description of the data: we can scale, shrink, or rotate the data, and the \"HELLO\" will still be apparent.\n", + "For example, if we use a rotation matrix to rotate the data, the *x* and *y* values change, but the data is still fundamentally the same:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -106,6 +183,16 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This tells us that the *x* and *y* values are not necessarily fundamental to the relationships in the data.\n", + "What *is* fundamental, in this case, is the *distance* between each point and the other points in the dataset.\n", + "A common way to represent this is to use a distance matrix: for $N$ points, we construct an $N \\times N$ array such that entry $(i, j)$ contains the distance between point $i$ and point $j$.\n", + "Let's use Scikit-Learn's efficient ``pairwise_distances`` function to do this for our original data:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -130,6 +217,13 @@ "D.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As promised, for our *N*=1,000 points, we obtain a 1000×1000 matrix, which can be visualized as shown here:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -153,6 +247,13 @@ "plt.colorbar();" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we similarly construct a distance matrix for our rotated and translated data, we see that it is the same:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -176,6 +277,18 @@ "np.allclose(D, D2)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This distance matrix gives us a representation of our data that is invariant to rotations and translations, but the visualization of the matrix above is not entirely intuitive.\n", + "In the representation shown in this figure, we have lost any visible sign of the interesting structure in the data: the \"HELLO\" that we saw before.\n", + "\n", + "Further, while computing this distance matrix from the (x, y) coordinates is straightforward, transforming the distances back into *x* and *y* coordinates is rather difficult.\n", + "This is exactly what the multidimensional scaling algorithm aims to do: given a distance matrix between points, it recovers a $D$-dimensional coordinate representation of the data.\n", + "Let's see how it works for our distance matrix, using the ``precomputed`` dissimilarity to specify that we are passing a distance matrix:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -202,6 +315,23 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The MDS algorithm recovers one of the possible two-dimensional coordinate representations of our data, using *only* the $N\\times N$ distance matrix describing the relationship between the data points." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## MDS as Manifold Learning\n", + "\n", + "The usefulness of this becomes more apparent when we consider the fact that distance matrices can be computed from data in *any* dimension.\n", + "So, for example, instead of simply rotating the data in the two-dimensional plane, we can project it into three dimensions using the following function (essentially a three-dimensional generalization of the rotation matrix used earlier):" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -232,6 +362,13 @@ "X3.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's visualize these points to see what we're working with:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -258,6 +395,14 @@ "ax.view_init(azim=70, elev=50)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now ask the ``MDS`` estimator to input this three-dimensional data, compute the distance matrix, and then determine the optimal two-dimensional embedding for this distance matrix.\n", + "The result recovers a representation of the original data:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -283,6 +428,25 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is essentially the goal of a manifold learning estimator: given high-dimensional embedded data, it seeks a low-dimensional representation of the data that preserves certain relationships within the data.\n", + "In the case of MDS, the quantity preserved is the distance between every pair of points." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Nonlinear Embeddings: Where MDS Fails\n", + "\n", + "Our discussion thus far has considered *linear* embeddings, which essentially consist of rotations, translations, and scalings of data into higher-dimensional spaces.\n", + "Where MDS breaks down is when the embedding is nonlinear—that is, when it goes beyond this simple set of operations.\n", + "Consider the following embedding, which takes the input and contorts it into an \"S\" shape in three dimensions:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -301,6 +465,13 @@ "XS = make_hello_s_curve(X)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is again three-dimensional data, but we can see that the embedding is much more complicated:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -326,6 +497,15 @@ " **colorize);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The fundamental relationships between the data points are still there, but this time the data has been transformed in a nonlinear way: it has been wrapped-up into the shape of an \"S.\"\n", + "\n", + "If we try a simple MDS algorithm on this data, it is not able to \"unwrap\" this nonlinear embedding, and we lose track of the fundamental relationships in the embedded manifold:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -352,6 +532,50 @@ "plt.axis('equal');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The best two-dimensional *linear* embeding does not unwrap the S-curve, but instead throws out the original y-axis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Nonlinear Manifolds: Locally Linear Embedding\n", + "\n", + "How can we move forward here? Stepping back, we can see that the source of the problem is that MDS tries to preserve distances between faraway points when constructing the embedding.\n", + "But what if we instead modified the algorithm such that it only preserves distances between nearby points?\n", + "The resulting embedding would be closer to what we want.\n", + "\n", + "Visually, we can think of it as illustrated in this figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![(LLE vs MDS linkages)](figures/05.10-LLE-vs-MDS.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#LLE-vs-MDS-Linkages)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here each faint line represents a distance that should be preserved in the embedding.\n", + "On the left is a representation of the model used by MDS: it tries to preserve the distances between each pair of points in the dataset.\n", + "On the right is a representation of the model used by a manifold learning algorithm called locally linear embedding (LLE): rather than preserving *all* distances, it instead tries to preserve only the distances between *neighboring points*: in this case, the nearest 100 neighbors of each point.\n", + "\n", + "Thinking about the left panel, we can see why MDS fails: there is no way to flatten this data while adequately preserving the length of every line drawn between the two points.\n", + "For the right panel, on the other hand, things look a bit more optimistic. We could imagine unrolling the data in a way that keeps the lengths of the lines approximately the same.\n", + "This is precisely what LLE does, through a global optimization of a cost function reflecting this logic.\n", + "\n", + "LLE comes in a number of flavors; here we will use the *modified LLE* algorithm to recover the embedded two-dimensional manifold.\n", + "In general, modified LLE does better than other flavors of the algorithm at recovering well-defined manifolds with very little distortion:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -381,6 +605,61 @@ "ax.set_ylim(0.15, -0.15);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result remains somewhat distorted compared to our original manifold, but captures the essential relationships in the data!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Some Thoughts on Manifold Methods" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Though this story and motivation is compelling, in practice manifold learning techniques tend to be finicky enough that they are rarely used for anything more than simple qualitative visualization of high-dimensional data.\n", + "\n", + "The following are some of the particular challenges of manifold learning, which all contrast poorly with PCA:\n", + "\n", + "- In manifold learning, there is no good framework for handling missing data. In contrast, there are straightforward iterative approaches for missing data in PCA.\n", + "- In manifold learning, the presence of noise in the data can \"short-circuit\" the manifold and drastically change the embedding. In contrast, PCA naturally filters noise from the most important components.\n", + "- The manifold embedding result is generally highly dependent on the number of neighbors chosen, and there is generally no solid quantitative way to choose an optimal number of neighbors. In contrast, PCA does not involve such a choice.\n", + "- In manifold learning, the globally optimal number of output dimensions is difficult to determine. In contrast, PCA lets you find the output dimension based on the explained variance.\n", + "- In manifold learning, the meaning of the embedded dimensions is not always clear. In PCA, the principal components have a very clear meaning.\n", + "- In manifold learning the computational expense of manifold methods scales as O[N^2] or O[N^3]. For PCA, there exist randomized approaches that are generally much faster (though see the [megaman](https://github.com/mmp2/megaman) package for some more scalable implementations of manifold learning).\n", + "\n", + "With all that on the table, the only clear advantage of manifold learning methods over PCA is their ability to preserve nonlinear relationships in the data; for that reason I tend to explore data with manifold methods only after first exploring them with PCA.\n", + "\n", + "Scikit-Learn implements several common variants of manifold learning beyond Isomap and LLE: the Scikit-Learn documentation has a [nice discussion and comparison of them](http://scikit-learn.org/stable/modules/manifold.html).\n", + "Based on my own experience, I would give the following recommendations:\n", + "\n", + "- For toy problems such as the S-curve we saw before, locally linear embedding (LLE) and its variants (especially *modified LLE*), perform very well. This is implemented in ``sklearn.manifold.LocallyLinearEmbedding``.\n", + "- For high-dimensional data from real-world sources, LLE often produces poor results, and isometric mapping (IsoMap) seems to generally lead to more meaningful embeddings. This is implemented in ``sklearn.manifold.Isomap``\n", + "- For data that is highly clustered, *t-distributed stochastic neighbor embedding* (t-SNE) seems to work very well, though can be very slow compared to other methods. This is implemented in ``sklearn.manifold.TSNE``.\n", + "\n", + "If you're interested in getting a feel for how these work, I'd suggest running each of the methods on the data in this section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Isomap on Faces\n", + "\n", + "One place manifold learning is often used is in understanding the relationship between high-dimensional data points.\n", + "A common case of high-dimensional data is images: for example, a set of images with 1,000 pixels each can be thought of as a collection of points in 1,000 dimensions – the brightness of each pixel in each image defines the coordinate in that dimension.\n", + "\n", + "Here let's apply Isomap on some faces data.\n", + "We will use the Labeled Faces in the Wild dataset, which we previously saw in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) and [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb).\n", + "Running this command will download the data and cache it in your home directory for later use:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -405,6 +684,16 @@ "faces.data.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have 2,370 images, each with 2,914 pixels.\n", + "In other words, the images can be thought of as data points in a 2,914-dimensional space!\n", + "\n", + "Let's quickly visualize several of these images to see what we're working with:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -429,6 +718,14 @@ " axi.imshow(faces.images[i], cmap='gray')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We would like to plot a low-dimensional embedding of the 2,914-dimensional data to learn the fundamental relationships between the images.\n", + "One useful way to start is to compute a PCA, and examine the explained variance ratio, which will give us an idea of how many linear features are required to describe the data:" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -455,6 +752,16 @@ "plt.ylabel('cumulative variance');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that for this data, nearly 100 components are required to preserve 90% of the variance: this tells us that the data is intrinsically very high dimensional—it can't be described linearly with just a few components.\n", + "\n", + "When this is the case, nonlinear manifold embeddings like LLE and Isomap can be helpful.\n", + "We can compute an Isomap embedding on these faces using the same pattern shown before:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -480,6 +787,14 @@ "proj.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output is a two-dimensional projection of all the input images.\n", + "To get a better idea of what the projection tells us, let's define a function that will output image thumbnails at the locations of the projections:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -512,6 +827,13 @@ " ax.add_artist(imagebox)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling this function now, we see the result:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -537,6 +859,27 @@ " images=faces.images[:, ::2, ::2])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is interesting: the first two Isomap dimensions seem to describe global image features: the overall darkness or lightness of the image from left to right, and the general orientation of the face from bottom to top.\n", + "This gives us a nice visual indication of some of the fundamental features in our data.\n", + "\n", + "We could then go on to classify this data (perhaps using manifold features as inputs to the classification algorithm) as we did in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: Visualizing Structure in Digits\n", + "\n", + "As another example of using manifold learning for visualization, let's take a look at the MNIST handwritten digits set.\n", + "This data is similar to the digits we saw in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb), but with many more pixels per image.\n", + "It can be downloaded from http://mldata.org/ with the Scikit-Learn utility:" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -561,6 +904,14 @@ "mnist.data.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This consists of 70,000 images, each with 784 pixels (i.e. the images are 28×28).\n", + "As before, we can take a look at the first few images:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -585,6 +936,17 @@ " axi.imshow(mnist.data[1250 * i].reshape(28, 28), cmap='gray_r')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us an idea of the variety of handwriting styles in the dataset.\n", + "\n", + "Let's compute a manifold learning projection across the data.\n", + "For speed here, we'll only use 1/30 of the data, which is about ~2000 points\n", + "(because of the relatively poor scaling of manifold learning, I find that a few thousand samples is a good number to start with for relatively quick exploration before moving to a full calculation):" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -615,6 +977,14 @@ "plt.clim(-0.5, 9.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting scatter plot shows some of the relationships between the data points, but is a bit crowded.\n", + "We can gain more insight by looking at just a single number at a time:" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -644,9 +1014,32 @@ "plot_components(data, model, images=data.reshape((-1, 28, 28)),\n", " ax=ax, thumb_frac=0.05, cmap='gray_r')" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result gives you an idea of the variety of forms that the number \"1\" can take within the dataset.\n", + "The data lies along a broad curve in the projected space, which appears to trace the orientation of the digit.\n", + "As you move up the plot, you find ones that have hats and/or bases, though these are very sparse within the dataset.\n", + "The projection lets us identify outliers that have data issues: for example, pieces of the neighboring digits that snuck into the extracted images.\n", + "\n", + "Now, this in itself may not be useful for the task of classifying digits, but it does help us get an understanding of the data, and may give us ideas about how to move forward, such as how we might want to preprocess the data before building a classification pipeline." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb) | [Contents](Index.ipynb) | [In Depth: k-Means Clustering](05.11-K-Means.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.11-K-Means.ipynb b/notebooks_v1/05.11-K-Means.ipynb similarity index 99% rename from code_listings/05.11-K-Means.ipynb rename to notebooks_v1/05.11-K-Means.ipynb index e91644c1e..8907d80cf 100644 --- a/code_listings/05.11-K-Means.ipynb +++ b/notebooks_v1/05.11-K-Means.ipynb @@ -4,7 +4,42 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# In Depth: K-Means Clustering" + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) | [Contents](Index.ipynb) | [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# In Depth: k-Means Clustering" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the previous few sections, we have explored one category of unsupervised machine learning models: dimensionality reduction.\n", + "Here we will move on to another class of unsupervised machine learning models: clustering algorithms.\n", + "Clustering algorithms seek to learn, from the properties of the data, an optimal division or discrete labeling of groups of points.\n", + "\n", + "Many clustering algorithms are available in Scikit-Learn and elsewhere, but perhaps the simplest to understand is an algorithm known as *k-means clustering*, which is implemented in ``sklearn.cluster.KMeans``.\n", + "\n", + "We begin with the standard imports:" ] }, { @@ -21,6 +56,30 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introducing k-Means" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *k*-means algorithm searches for a pre-determined number of clusters within an unlabeled multidimensional dataset.\n", + "It accomplishes this using a simple conception of what the optimal clustering looks like:\n", + "\n", + "- The \"cluster center\" is the arithmetic mean of all the points belonging to the cluster.\n", + "- Each point is closer to its own cluster center than to other cluster centers.\n", + "\n", + "Those two assumptions are the basis of the *k*-means model.\n", + "We will soon dive into exactly *how* the algorithm reaches this solution, but for now let's take a look at a simple dataset and see the *k*-means result.\n", + "\n", + "First, let's generate a two-dimensional dataset containing four distinct blobs.\n", + "To emphasize that this is an unsupervised algorithm, we will leave the labels out of the visualization" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -46,6 +105,14 @@ "plt.scatter(X[:, 0], X[:, 1], s=50);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By eye, it is relatively easy to pick out the four clusters.\n", + "The *k*-means algorithm does this automatically, and in Scikit-Learn uses the typical estimator API:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -60,6 +127,14 @@ "y_kmeans = kmeans.predict(X)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's visualize the results by plotting the data colored by these labels.\n", + "We will also plot the cluster centers as determined by the *k*-means estimator:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -85,6 +160,61 @@ "plt.scatter(centers[:, 0], centers[:, 1], c='black', s=200, alpha=0.5);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The good news is that the *k*-means algorithm (at least in this simple case) assigns the points to clusters very similarly to how we might assign them by eye.\n", + "But you might wonder how this algorithm finds these clusters so quickly! After all, the number of possible combinations of cluster assignments is exponential in the number of data points—an exhaustive search would be very, very costly.\n", + "Fortunately for us, such an exhaustive search is not necessary: instead, the typical approach to *k*-means involves an intuitive iterative approach known as *expectation–maximization*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## k-Means Algorithm: Expectation–Maximization" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Expectation–maximization (E–M) is a powerful algorithm that comes up in a variety of contexts within data science.\n", + "*k*-means is a particularly simple and easy-to-understand application of the algorithm, and we will walk through it briefly here.\n", + "In short, the expectation–maximization approach here consists of the following procedure:\n", + "\n", + "1. Guess some cluster centers\n", + "2. Repeat until converged\n", + " 1. *E-Step*: assign points to the nearest cluster center\n", + " 2. *M-Step*: set the cluster centers to the mean \n", + "\n", + "Here the \"E-step\" or \"Expectation step\" is so-named because it involves updating our expectation of which cluster each point belongs to.\n", + "The \"M-step\" or \"Maximization step\" is so-named because it involves maximizing some fitness function that defines the location of the cluster centers—in this case, that maximization is accomplished by taking a simple mean of the data in each cluster.\n", + "\n", + "The literature about this algorithm is vast, but can be summarized as follows: under typical circumstances, each repetition of the E-step and M-step will always result in a better estimate of the cluster characteristics.\n", + "\n", + "We can visualize the algorithm as shown in the following figure.\n", + "For the particular initialization shown here, the clusters converge in just three iterations.\n", + "For an interactive version of this figure, refer to the code in [the Appendix](06.00-Figure-Code.ipynb#Interactive-K-Means)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![(run code in Appendix to generate image)](figures/05.11-expectation-maximization.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Expectation-Maximization)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *k*-Means algorithm is simple enough that we can write it in a few lines of code.\n", + "The following is a very basic implementation:" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -113,14 +243,14 @@ " centers = X[i]\n", " \n", " while True:\n", - " # 2A. Assign labels based on closest center\n", + " # 2a. Assign labels based on closest center\n", " labels = pairwise_distances_argmin(X, centers)\n", " \n", - " # 2B. Find new centers from means of points\n", + " # 2b. Find new centers from means of points\n", " new_centers = np.array([X[labels == i].mean(0)\n", " for i in range(n_clusters)])\n", " \n", - " # 2C. Check for convergence\n", + " # 2c. Check for convergence\n", " if np.all(centers == new_centers):\n", " break\n", " centers = new_centers\n", @@ -132,6 +262,31 @@ " s=50, cmap='viridis');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Most well-tested implementations will do a bit more than this under the hood, but the preceding function gives the gist of the expectation–maximization approach." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Caveats of expectation–maximization\n", + "\n", + "There are a few issues to be aware of when using the expectation–maximization algorithm." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### The globally optimal result may not be achieved\n", + "First, although the E–M procedure is guaranteed to improve the result in each step, there is no assurance that it will lead to the *global* best solution.\n", + "For example, if we use a different random seed in our simple procedure, the particular starting guesses lead to poor results:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -156,6 +311,22 @@ " s=50, cmap='viridis');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the E–M approach has converged, but has not converged to a globally optimal configuration. For this reason, it is common for the algorithm to be run for multiple starting guesses, as indeed Scikit-Learn does by default (set by the ``n_init`` parameter, which defaults to 10)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### The number of clusters must be selected beforehand\n", + "Another common challenge with *k*-means is that you must tell it how many clusters you expect: it cannot learn the number of clusters from the data.\n", + "For example, if we ask the algorithm to identify six clusters, it will happily proceed and find the best six clusters:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -180,6 +351,26 @@ " s=50, cmap='viridis');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whether the result is meaningful is a question that is difficult to answer definitively; one approach that is rather intuitive, but that we won't discuss further here, is called [silhouette analysis](http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html).\n", + "\n", + "Alternatively, you might use a more complicated clustering algorithm which has a better quantitative measure of the fitness per number of clusters (e.g., Gaussian mixture models; see [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb)) or which *can* choose a suitable number of clusters (e.g., DBSCAN, mean-shift, or affinity propagation, all available in the ``sklearn.cluster`` submodule)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### k-means is limited to linear cluster boundaries\n", + "The fundamental model assumptions of *k*-means (points will be closer to their own cluster center than to others) means that the algorithm will often be ineffective if the clusters have complicated geometries.\n", + "\n", + "In particular, the boundaries between *k*-means clusters will always be linear, which means that it will fail for more complicated boundaries.\n", + "Consider the following data, along with the cluster labels found by the typical *k*-means approach:" + ] + }, { "cell_type": "code", "execution_count": 8, @@ -216,6 +407,17 @@ " s=50, cmap='viridis');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This situation is reminiscent of the discussion in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb), where we used a kernel transformation to project the data into a higher dimension where a linear separation is possible.\n", + "We might imagine using the same trick to allow *k*-means to discover non-linear boundaries.\n", + "\n", + "One version of this kernelized *k*-means is implemented in Scikit-Learn within the ``SpectralClustering`` estimator.\n", + "It uses the graph of nearest neighbors to compute a higher-dimensional representation of the data, and then assigns labels using a *k*-means algorithm:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -243,6 +445,47 @@ " s=50, cmap='viridis');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that with this kernel transform approach, the kernelized *k*-means is able to find the more complicated nonlinear boundaries between clusters." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### k-means can be slow for large numbers of samples\n", + "Because each iteration of *k*-means must access every point in the dataset, the algorithm can be relatively slow as the number of samples grows.\n", + "You might wonder if this requirement to use all data at each iteration can be relaxed; for example, you might just use a subset of the data to update the cluster centers at each step.\n", + "This is the idea behind batch-based *k*-means algorithms, one form of which is implemented in ``sklearn.cluster.MiniBatchKMeans``.\n", + "The interface for this is the same as for standard ``KMeans``; we will see an example of its use as we continue our discussion." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Examples\n", + "\n", + "Being careful about these limitations of the algorithm, we can use *k*-means to our advantage in a wide variety of situations.\n", + "We'll now take a look at a couple examples." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 1: k-means on digits\n", + "\n", + "To start, let's take a look at applying *k*-means on the same simple digits data that we saw in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) and [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb).\n", + "Here we will attempt to use *k*-means to try to identify similar digits *without using the original label information*; this might be similar to a first step in extracting meaning from a new dataset about which you don't have any *a priori* label information.\n", + "\n", + "We will start by loading the digits and then finding the ``KMeans`` clusters.\n", + "Recall that the digits consist of 1,797 samples with 64 features, where each of the 64 features is the brightness of one pixel in an 8×8 image:" + ] + }, { "cell_type": "code", "execution_count": 11, @@ -267,6 +510,13 @@ "digits.data.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The clustering can be performed as we did before:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -291,6 +541,15 @@ "kmeans.cluster_centers_.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is 10 clusters in 64 dimensions.\n", + "Notice that the cluster centers themselves are 64-dimensional points, and can themselves be interpreted as the \"typical\" digit within the cluster.\n", + "Let's see what these cluster centers look like:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -317,6 +576,16 @@ " axi.imshow(center, interpolation='nearest', cmap=plt.cm.binary)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that *even without the labels*, ``KMeans`` is able to find clusters whose centers are recognizable digits, with perhaps the exception of 1 and 8.\n", + "\n", + "Because *k*-means knows nothing about the identity of the cluster, the 0–9 labels may be permuted.\n", + "We can fix this by matching each learned cluster label with the true labels found in them:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -333,6 +602,13 @@ " labels[mask] = mode(digits.target[mask])[0]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can check how accurate our unsupervised clustering was in finding similar digits within the data:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -356,6 +632,14 @@ "accuracy_score(digits.target, labels)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With just a simple *k*-means algorithm, we discovered the correct grouping for 80% of the input digits!\n", + "Let's check the confusion matrix for this:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -384,6 +668,19 @@ "plt.ylabel('predicted label');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we might expect from the cluster centers we visualized before, the main point of confusion is between the eights and ones.\n", + "But this still shows that using *k*-means, we can essentially build a digit classifier *without reference to any known labels*!\n", + "\n", + "Just for fun, let's try to push this even farther.\n", + "We can use the t-distributed stochastic neighbor embedding (t-SNE) algorithm (mentioned in [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb)) to pre-process the data before performing *k*-means.\n", + "t-SNE is a nonlinear embedding algorithm that is particularly adept at preserving points within clusters.\n", + "Let's see how it does:" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -394,7 +691,7 @@ { "data": { "text/plain": [ - "0.80356149137451305" + "0.91930996104618812" ] }, "execution_count": 17, @@ -406,7 +703,7 @@ "from sklearn.manifold import TSNE\n", "\n", "# Project the data: this step will take several seconds\n", - "tsne = TSNE(n_components=2, init='pca', random_state=0)\n", + "tsne = TSNE(n_components=2, init='random', random_state=0)\n", "digits_proj = tsne.fit_transform(digits.data)\n", "\n", "# Compute the clusters\n", @@ -423,6 +720,27 @@ "accuracy_score(digits.target, labels)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's nearly 92% classification accuracy *without using the labels*.\n", + "This is the power of unsupervised learning when used carefully: it can extract information from the dataset that it might be difficult to do by hand or by eye." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 2: *k*-means for color compression\n", + "\n", + "One interesting application of clustering is in color compression within images.\n", + "For example, imagine you have an image with millions of colors.\n", + "In most images, a large number of the colors will be unused, and many of the pixels in the image will have similar or even identical colors.\n", + "\n", + "For example, consider the image shown in the following figure, which is from the Scikit-Learn ``datasets`` module (for this to work, you'll have to have the ``pillow`` Python package installed)." + ] + }, { "cell_type": "code", "execution_count": 18, @@ -449,6 +767,13 @@ "ax.imshow(china);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The image itself is stored in a three-dimensional array of size ``(height, width, RGB)``, containing red/blue/green contributions as integers from 0 to 255:" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -471,6 +796,14 @@ "china.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One way we can view this set of pixels is as a cloud of points in a three-dimensional color space.\n", + "We will reshape the data to ``[n_samples x n_features]``, and rescale the colors so that they lie between 0 and 1:" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -495,6 +828,13 @@ "data.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can visualize these pixels in this color space, using a subset of 10,000 pixels for efficiency:" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -545,6 +885,14 @@ "plot_pixels(data, title='Input color space: 16 million possible colors')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's reduce these 16 million colors to just 16 colors, using a *k*-means clustering across the pixel space.\n", + "Because we are dealing with a very large dataset, we will use the mini batch *k*-means, which operates on subsets of the data to compute the result much more quickly than the standard *k*-means algorithm:" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -564,6 +912,8 @@ } ], "source": [ + "import warnings; warnings.simplefilter('ignore') # Fix NumPy issues.\n", + "\n", "from sklearn.cluster import MiniBatchKMeans\n", "kmeans = MiniBatchKMeans(16)\n", "kmeans.fit(data)\n", @@ -573,6 +923,14 @@ " title=\"Reduced color space: 16 colors\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is a re-coloring of the original pixels, where each pixel is assigned the color of its closest cluster center.\n", + "Plotting these new colors in the image space rather than the pixel space shows us the effect of this:" + ] + }, { "cell_type": "code", "execution_count": 24, @@ -594,16 +952,38 @@ "source": [ "china_recolored = new_colors.reshape(china.shape)\n", "\n", - "fig, ax = plt.subplots(1, 2, figsize=(16, 6), subplot_kw=dict(xticks=[], yticks=[]))\n", + "fig, ax = plt.subplots(1, 2, figsize=(16, 6),\n", + " subplot_kw=dict(xticks=[], yticks=[]))\n", "fig.subplots_adjust(wspace=0.05)\n", "ax[0].imshow(china)\n", "ax[0].set_title('Original Image', size=16)\n", "ax[1].imshow(china_recolored)\n", "ax[1].set_title('16-color Image', size=16);" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some detail is certainly lost in the rightmost panel, but the overall image is still easily recognizable.\n", + "This image on the right achieves a compression factor of around 1 million!\n", + "While this is an interesting application of *k*-means, there are certainly better way to compress information in images.\n", + "But the example shows the power of thinking outside of the box with unsupervised methods like *k*-means." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) | [Contents](Index.ipynb) | [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.12-Gaussian-Mixtures.ipynb b/notebooks_v1/05.12-Gaussian-Mixtures.ipynb similarity index 98% rename from code_listings/05.12-Gaussian-Mixtures.ipynb rename to notebooks_v1/05.12-Gaussian-Mixtures.ipynb index 4f39437df..f5c4d7358 100644 --- a/code_listings/05.12-Gaussian-Mixtures.ipynb +++ b/notebooks_v1/05.12-Gaussian-Mixtures.ipynb @@ -1,5 +1,33 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,11 +35,27 @@ "# In Depth: Gaussian Mixture Models" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The *k*-means clustering model explored in the previous section is simple and relatively easy to understand, but its simplicity leads to practical challenges in its application.\n", + "In particular, the non-probabilistic nature of *k*-means and its use of simple distance-from-cluster-center to assign cluster membership leads to poor performance for many real-world situations.\n", + "In this section we will take a look at Gaussian mixture models (GMMs), which can be viewed as an extension of the ideas behind *k*-means, but can also be a powerful tool for estimation beyond simple clustering.\n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -21,11 +65,28 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Motivating GMM: Weaknesses of k-Means\n", + "\n", + "Let's take a look at some of the weaknesses of *k*-means and think about how we might improve the cluster model.\n", + "As we saw in the previous section, given simple, well-separated data, *k*-means finds suitable clustering results.\n", + "\n", + "For example, if we have simple blobs of data, the *k*-means algorithm can quickly label those clusters in a way that closely matches what we might do by eye:" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -40,7 +101,9 @@ "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -62,11 +125,29 @@ "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "From an intuitive standpoint, we might expect that the clustering assignment for some points is more certain than others: for example, there appears to be a very slight overlap between the two middle clusters, such that we might not have complete confidence in the cluster assigment of points between them.\n", + "Unfortunately, the *k*-means model has no intrinsic measure of probability or uncertainty of cluster assignments (although it may be possible to use a bootstrap approach to estimate this uncertainty).\n", + "For this, we must think about generalizing the model.\n", + "\n", + "One way to think about the *k*-means model is that it places a circle (or, in higher dimensions, a hyper-sphere) at the center of each cluster, with a radius defined by the most distant point in the cluster.\n", + "This radius acts as a hard cutoff for cluster assignment within the training set: any point outside this circle is not considered a member of the cluster.\n", + "We can visualize this cluster model with the following function:" + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -93,7 +174,9 @@ "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -112,11 +195,24 @@ "plot_kmeans(kmeans, X)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "An important observation for *k*-means is that these cluster models *must be circular*: *k*-means has no built-in way of accounting for oblong or elliptical clusters.\n", + "So, for example, if we take the same data and transform it, the cluster assignments end up becoming muddled:" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -138,11 +234,45 @@ "plot_kmeans(kmeans, X_stretched)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "By eye, we recognize that these transformed clusters are non-circular, and thus circular clusters would be a poor fit.\n", + "Nevertheless, *k*-means is not flexible enough to account for this, and tries to force-fit the data into four circular clusters.\n", + "This results in a mixing of cluster assignments where the resulting circles overlap: see especially the bottom-right of this plot.\n", + "One might imagine addressing this particular situation by preprocessing the data with PCA (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), but in practice there is no guarantee that such a global operation will circularize the individual data.\n", + "\n", + "These two disadvantages of *k*-means—its lack of flexibility in cluster shape and lack of probabilistic cluster assignment—mean that for many datasets (especially low-dimensional datasets) it may not perform as well as you might hope.\n", + "\n", + "You might imagine addressing these weaknesses by generalizing the *k*-means model: for example, you could measure uncertainty in cluster assignment by comparing the distances of each point to *all* cluster centers, rather than focusing on just the closest.\n", + "You might also imagine allowing the cluster boundaries to be ellipses rather than circles, so as to account for non-circular clusters.\n", + "It turns out these are two essential components of a different type of clustering model, Gaussian mixture models." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Generalizing E–M: Gaussian Mixture Models\n", + "\n", + "A Gaussian mixture model (GMM) attempts to find a mixture of multi-dimensional Gaussian probability distributions that best model any input dataset.\n", + "In the simplest case, GMMs can be used for finding clusters in the same manner as *k*-means:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -163,11 +293,24 @@ "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But because GMM contains a probabilistic model under the hood, it is also possible to find probabilistic cluster assignments—in Scikit-Learn this is done using the ``predict_proba`` method.\n", + "This returns a matrix of size ``[n_samples, n_clusters]`` which measures the probability that any point belongs to the given cluster:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -187,11 +330,23 @@ "print(probs[:5].round(3))" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We can visualize this uncertainty by, for example, making the size of each point proportional to the certainty of its prediction; looking at the following figure, we can see that it is precisely the points at the boundaries between clusters that reflect this uncertainty of cluster assignment:" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -210,11 +365,35 @@ "plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis', s=size);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Under the hood, a Gaussian mixture model is very similar to *k*-means: it uses an expectation–maximization approach which qualitatively does the following:\n", + "\n", + "1. Choose starting guesses for the location and shape\n", + "\n", + "2. Repeat until converged:\n", + "\n", + " 1. *E-step*: for each point, find weights encoding the probability of membership in each cluster\n", + " 2. *M-step*: for each cluster, update its location, normalization, and shape based on *all* data points, making use of the weights\n", + "\n", + "The result of this is that each cluster is associated not with a hard-edged sphere, but with a smooth Gaussian model.\n", + "Just as in the *k*-means expectation–maximization approach, this algorithm can sometimes miss the globally optimal solution, and thus in practice multiple random initializations are used.\n", + "\n", + "Let's create a function that will help us visualize the locations and shapes of the GMM clusters by drawing ellipses based on the GMM output:" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -252,11 +431,23 @@ " draw_ellipse(pos, covar, alpha=w * w_factor)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this in place, we can take a look at what the four-component GMM gives us for our initial data:" + ] + }, { "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -275,11 +466,23 @@ "plot_gmm(gmm, X)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Similarly, we can use the GMM approach to fit our stretched dataset; allowing for a full covariance the model will fit even very oblong, stretched-out clusters:" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -298,11 +501,67 @@ "plot_gmm(gmm, X_stretched)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This makes clear that GMM addresses the two main practical issues with *k*-means encountered before." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Choosing the covariance type\n", + "\n", + "If you look at the details of the preceding fits, you will see that the ``covariance_type`` option was set differently within each.\n", + "This hyperparameter controls the degrees of freedom in the shape of each cluster; it is essential to set this carefully for any given problem.\n", + "The default is ``covariance_type=\"diag\"``, which means that the size of the cluster along each dimension can be set independently, with the resulting ellipse constrained to align with the axes.\n", + "A slightly simpler and faster model is ``covariance_type=\"spherical\"``, which constrains the shape of the cluster such that all dimensions are equal. The resulting clustering will have similar characteristics to that of *k*-means, though it is not entirely equivalent.\n", + "A more complicated and computationally expensive model (especially as the number of dimensions grows) is to use ``covariance_type=\"full\"``, which allows each cluster to be modeled as an ellipse with arbitrary orientation.\n", + "\n", + "We can see a visual representation of these three choices for a single cluster within the following figure:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "![(Covariance Type)](figures/05.12-covariance-type.png)\n", + "[figure source in Appendix](06.00-Figure-Code.ipynb#Covariance-Type)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## GMM as *Density Estimation*\n", + "\n", + "Though GMM is often categorized as a clustering algorithm, fundamentally it is an algorithm for *density estimation*.\n", + "That is to say, the result of a GMM fit to some data is technically not a clustering model, but a generative probabilistic model describing the distribution of the data.\n", + "\n", + "As an example, consider some data generated from Scikit-Learn's ``make_moons`` function, which we saw in [In Depth: K-Means Clustering](05.11-K-Means.ipynb):" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -322,11 +581,23 @@ "plt.scatter(Xmoon[:, 0], Xmoon[:, 1]);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "If we try to fit this with a two-component GMM viewed as a clustering model, the results are not particularly useful:" + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -345,11 +616,23 @@ "plot_gmm(gmm2, Xmoon)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "But if we instead use many more components and ignore the cluster labels, we find a fit that is much closer to the input data:" + ] + }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -368,11 +651,25 @@ "plot_gmm(gmm16, Xmoon, label=False)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Here the mixture of 16 Gaussians serves not to find separated clusters of data, but rather to model the overall *distribution* of the input data.\n", + "This is a generative model of the distribution, meaning that the GMM gives us the recipe to generate new random data distributed similarly to our input.\n", + "For example, here are 400 new points drawn from this 16-component GMM fit to our original data:" + ] + }, { "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -391,11 +688,40 @@ "plt.scatter(Xnew[:, 0], Xnew[:, 1]);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "GMM is convenient as a flexible means of modeling an arbitrary multi-dimensional distribution of data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### How many components?\n", + "\n", + "The fact that GMM is a generative model gives us a natural means of determining the optimal number of components for a given dataset.\n", + "A generative model is inherently a probability distribution for the dataset, and so we can simply evaluate the *likelihood* of the data under the model, using cross-validation to avoid over-fitting.\n", + "Another means of correcting for over-fitting is to adjust the model likelihoods using some analytic criterion such as the [Akaike information criterion (AIC)](https://en.wikipedia.org/wiki/Akaike_information_criterion) or the [Bayesian information criterion (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion).\n", + "Scikit-Learn's ``GMM`` estimator actually includes built-in methods that compute both of these, and so it is very easy to operate on this approach.\n", + "\n", + "Let's look at the AIC and BIC as a function as the number of GMM components for our moon dataset:" + ] + }, { "cell_type": "code", "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -420,11 +746,42 @@ "plt.xlabel('n_components');" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The optimal number of clusters is the value that minimizes the AIC or BIC, depending on which approximation we wish to use. The AIC tells us that our choice of 16 components above was probably too many: around 8-12 components would have been a better choice.\n", + "As is typical with this sort of problem, the BIC recommends a simpler model.\n", + "\n", + "Notice the important point: this choice of number of components measures how well GMM works *as a density estimator*, not how well it works *as a clustering algorithm*.\n", + "I'd encourage you to think of GMM primarily as a density estimator, and use it for clustering only when warranted within simple datasets." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: GMM for Generating New Data\n", + "\n", + "We just saw a simple example of using GMM as a generative model of data in order to create new samples from the distribution defined by the input data.\n", + "Here we will run with this idea and generate *new handwritten digits* from the standard digits corpus that we have used before.\n", + "\n", + "To start with, let's load the digits data using Scikit-Learn's data tools:" + ] + }, { "cell_type": "code", "execution_count": 18, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -444,11 +801,23 @@ "digits.data.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next let's plot the first 100 of these to recall exactly what we're looking at:" + ] + }, { "cell_type": "code", "execution_count": 19, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -473,11 +842,25 @@ "plot_digits(digits.data)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We have nearly 1,800 digits in 64 dimensions, and we can build a GMM on top of these to generate more.\n", + "GMMs can have difficulty converging in such a high dimensional space, so we will start with an invertible dimensionality reduction algorithm on the data.\n", + "Here we will use a straightforward PCA, asking it to preserve 99% of the variance in the projected data:" + ] + }, { "cell_type": "code", "execution_count": 20, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -498,11 +881,24 @@ "data.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result is 41 dimensions, a reduction of nearly 1/3 with almost no information loss.\n", + "Given this projected data, let's use the AIC to get a gauge for the number of GMM components we should use:" + ] + }, { "cell_type": "code", "execution_count": 21, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -524,11 +920,24 @@ "plt.plot(n_components, aics);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "It appears that around 110 components minimizes the AIC; we will use this model.\n", + "Let's quickly fit this to the data and confirm that it has converged:" + ] + }, { "cell_type": "code", "execution_count": 22, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -545,11 +954,23 @@ "print(gmm.converged_)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now we can draw samples of 100 new points within this 41-dimensional projected space, using the GMM as a generative model:" + ] + }, { "cell_type": "code", "execution_count": 23, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -568,11 +989,23 @@ "data_new.shape" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we can use the inverse transform of the PCA object to construct the new digits:" + ] + }, { "cell_type": "code", "execution_count": 24, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -590,6 +1023,32 @@ "digits_new = pca.inverse_transform(data_new)\n", "plot_digits(digits_new)" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The results for the most part look like plausible digits from the dataset!\n", + "\n", + "Consider what we've done here: given a sampling of handwritten digits, we have modeled the distribution of that data in such a way that we can generate brand new samples of digits from the data: these are \"handwritten digits\" which do not individually appear in the original dataset, but rather capture the general features of the input data as modeled by the mixture model.\n", + "Such a generative model of digits can prove very useful as a component of a Bayesian generative classifier, as we shall see in the next section." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { diff --git a/code_listings/05.13-Kernel-Density-Estimation.ipynb b/notebooks_v1/05.13-Kernel-Density-Estimation.ipynb similarity index 90% rename from code_listings/05.13-Kernel-Density-Estimation.ipynb rename to notebooks_v1/05.13-Kernel-Density-Estimation.ipynb index dd8d187fc..5ddf8b59a 100644 --- a/code_listings/05.13-Kernel-Density-Estimation.ipynb +++ b/notebooks_v1/05.13-Kernel-Density-Estimation.ipynb @@ -3,17 +3,62 @@ { "cell_type": "markdown", "metadata": { - "collapsed": true + "deletable": true, + "editable": true }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb) | [Contents](Index.ipynb) | [Application: A Face Detection Pipeline](05.14-Image-Features.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, "source": [ "# In-Depth: Kernel Density Estimation" ] }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "source": [ + "In the previous section we covered Gaussian mixture models (GMM), which are a kind of hybrid between a clustering estimator and a density estimator.\n", + "Recall that a density estimator is an algorithm which takes a $D$-dimensional dataset and produces an estimate of the $D$-dimensional probability distribution which that data is drawn from.\n", + "The GMM algorithm accomplishes this by representing the density as a weighted sum of Gaussian distributions.\n", + "*Kernel density estimation* (KDE) is in some senses an algorithm which takes the mixture-of-Gaussians idea to its logical extreme: it uses a mixture consisting of one Gaussian component *per point*, resulting in an essentially non-parametric estimator of density.\n", + "In this section, we will explore the motivation and uses of KDE.\n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -23,11 +68,29 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Motivating KDE: Histograms\n", + "\n", + "As already discussed, a density estimator is an algorithm which seeks to model the probability distribution that generated a dataset.\n", + "For one dimensional data, you are probably already familiar with one simple density estimator: the histogram.\n", + "A histogram divides the data into discrete bins, counts the number of points that fall in each bin, and then visualizes the results in an intuitive manner.\n", + "\n", + "For example, let's create some data that is drawn from two normal distributions:" + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -40,11 +103,24 @@ "x = make_data(1000)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We have previously seen that the standard count-based histogram can be created with the ``plt.hist()`` function.\n", + "By specifying the ``normed`` parameter of the histogram, we end up with a normalized histogram where the height of the bins does not reflect counts, but instead reflects probability density:" + ] + }, { "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -62,11 +138,24 @@ "hist = plt.hist(x, bins=30, normed=True)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Notice that for equal binning, this normalization simply changes the scale on the y-axis, leaving the relative heights essentially the same as in a histogram built from counts.\n", + "This normalization is chosen so that the total area under the histogram is equal to 1, as we can confirm by looking at the output of the histogram function:" + ] + }, { "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -86,11 +175,25 @@ "(density * widths).sum()" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "One of the issues with using a histogram as a density estimator is that the choice of bin size and location can lead to representations that have qualitatively different features.\n", + "For example, if we look at a version of this data with only 20 points, the choice of how to draw the bins can lead to an entirely different interpretation of the data!\n", + "Consider this example:" + ] + }, { "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -102,7 +205,9 @@ "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -128,11 +233,29 @@ " markeredgewidth=1)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "On the left, the histogram makes clear that this is a bimodal distribution.\n", + "On the right, we see a unimodal distribution with a long tail.\n", + "Without seeing the preceding code, you would probably not guess that these two histograms were built from the same data: with that in mind, how can you trust the intuition that histograms confer?\n", + "And how might we improve on this?\n", + "\n", + "Stepping back, we can think of a histogram as a stack of blocks, where we stack one block within each bin on top of each point in the dataset.\n", + "Let's view this directly:" + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -169,11 +292,27 @@ "ax.set_ylim(-0.2, 8)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The problem with our two binnings stems from the fact that the height of the block stack often reflects not on the actual density of points nearby, but on coincidences of how the bins align with the data points.\n", + "This mis-alignment between points and their blocks is a potential cause of the poor histogram results seen here.\n", + "But what if, instead of stacking the blocks aligned with the *bins*, we were to stack the blocks aligned with the *points they represent*?\n", + "If we do this, the blocks won't be aligned, but we can add their contributions at each location along the x-axis to find the result.\n", + "Let's try this:" + ] + }, { "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -197,11 +336,26 @@ "plt.axis([-4, 8, -0.2, 8]);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result looks a bit messy, but is a much more robust reflection of the actual data characteristics than is the standard histogram.\n", + "Still, the rough edges are not aesthetically pleasing, nor are they reflective of any true properties of the data.\n", + "In order to smooth them out, we might decide to replace the blocks at each location with a smooth function, like a Gaussian.\n", + "Let's use a standard normal curve at each point instead of a block:" + ] + }, { "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -226,11 +380,46 @@ "plt.axis([-4, 8, -0.2, 5]);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This smoothed-out plot, with a Gaussian distribution contributed at the location of each input point, gives a much more accurate idea of the shape of the data distribution, and one which has much less variance (i.e., changes much less in response to differences in sampling).\n", + "\n", + "These last two plots are examples of kernel density estimation in one dimension: the first uses a so-called \"tophat\" kernel and the second uses a Gaussian kernel.\n", + "We'll now look at kernel density estimation in more detail." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Kernel Density Estimation in Practice\n", + "\n", + "The free parameters of kernel density estimation are the *kernel*, which specifies the shape of the distribution placed at each point, and the *kernel bandwidth*, which controls the size of the kernel at each point.\n", + "In practice, there are many kernels you might use for a kernel density estimation: in particular, the Scikit-Learn KDE implementation supports one of six kernels, which you can read about in Scikit-Learn's [Density Estimation documentation](http://scikit-learn.org/stable/modules/density.html).\n", + "\n", + "While there are several versions of kernel density estimation implemented in Python (notably in the SciPy and StatsModels packages), I prefer to use Scikit-Learn's version because of its efficiency and flexibility.\n", + "It is implemented in the ``sklearn.neighbors.KernelDensity`` estimator, which handles KDE in multiple dimensions with one of six kernels and one of a couple dozen distance metrics.\n", + "Because KDE can be fairly computationally intensive, the Scikit-Learn estimator uses a tree-based algorithm under the hood and can trade off computation time for accuracy using the ``atol`` (absolute tolerance) and ``rtol`` (relative tolerance) parameters.\n", + "The kernel bandwidth, which is a free parameter, can be determined using Scikit-Learn's standard cross validation tools as we will soon see.\n", + "\n", + "Let's first show a simple example of replicating the above plot using the Scikit-Learn ``KernelDensity`` estimator:" + ] + }, { "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -269,11 +458,42 @@ "plt.ylim(-0.02, 0.22)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The result here is normalized such that the area under the curve is equal to 1." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Selecting the bandwidth via cross-validation\n", + "\n", + "The choice of bandwidth within KDE is extremely important to finding a suitable density estimate, and is the knob that controls the bias–variance trade-off in the estimate of density: too narrow a bandwidth leads to a high-variance estimate (i.e., over-fitting), where the presence or absence of a single point makes a large difference. Too wide a bandwidth leads to a high-bias estimate (i.e., under-fitting) where the structure in the data is washed out by the wide kernel.\n", + "\n", + "There is a long history in statistics of methods to quickly estimate the best bandwidth based on rather stringent assumptions about the data: if you look up the KDE implementations in the SciPy and StatsModels packages, for example, you will see implementations based on some of these rules.\n", + "\n", + "In machine learning contexts, we've seen that such hyperparameter tuning often is done empirically via a cross-validation approach.\n", + "With this in mind, the ``KernelDensity`` estimator in Scikit-Learn is designed such that it can be used directly within the Scikit-Learn's standard grid search tools.\n", + "Here we will use ``GridSearchCV`` to optimize the bandwidth for the preceding dataset.\n", + "Because we are looking at such a small dataset, we will use leave-one-out cross-validation, which minimizes the reduction in training set size for each cross-validation trial:" + ] + }, { "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -287,11 +507,23 @@ "grid.fit(x[:, None]);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Now we can find the choice of bandwidth which maximizes the score (which in this case defaults to the log-likelihood):" + ] + }, { "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -309,11 +541,41 @@ "grid.best_params_" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "The optimal bandwidth happens to be very close to what we used in the example plot earlier, where the bandwidth was 1.0 (i.e., the default width of ``scipy.stats.norm``)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: KDE on a Sphere\n", + "\n", + "Perhaps the most common use of KDE is in graphically representing distributions of points.\n", + "For example, in the Seaborn visualization library (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)), KDE is built in and automatically used to help visualize points in one and two dimensions.\n", + "\n", + "Here we will look at a slightly more sophisticated use of KDE for visualization of distributions.\n", + "We will make use of some geographic data that can be loaded with Scikit-Learn: the geographic distributions of recorded observations of two South American mammals, *Bradypus variegatus* (the Brown-throated Sloth) and *Microryzomys minutus* (the Forest Small Rice Rat).\n", + "\n", + "With Scikit-Learn, we can fetch this data as follows:" + ] + }, { "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -328,11 +590,23 @@ " for d in data.train['species']], dtype='int')" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "With this data loaded, we can use the Basemap toolkit (mentioned previously in [Geographic Data with Basemap](04.13-Geographic-Data-With-Basemap.ipynb)) to plot the observed locations of these two species on the map of South America." + ] + }, { "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -366,11 +640,29 @@ " c=species, cmap='rainbow', latlon=True);" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Unfortunately, this doesn't give a very good idea of the density of the species, because points in the species range may overlap one another.\n", + "You may not realize it by looking at this plot, but there are over 1,600 points shown here!\n", + "\n", + "Let's use kernel density estimation to show this distribution in a more interpretable way: as a smooth indication of density on the map.\n", + "Because the coordinate system here lies on a spherical surface rather than a flat plane, we will use the ``haversine`` distance metric, which will correctly represent distances on a curved surface.\n", + "\n", + "There is a bit of boilerplate code here (one of the disadvantages of the Basemap toolkit) but the meaning of each code block should be clear:" + ] + }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -423,11 +715,56 @@ " axi.contourf(X, Y, Z, levels=levels, cmap=cmaps[i])" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Compared to the simple scatter plot we initially used, this visualization paints a much clearer picture of the geographical distribution of observations of these two species." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Example: Not-So-Naive Bayes\n", + "\n", + "This example looks at Bayesian generative classification with KDE, and demonstrates how to use the Scikit-Learn architecture to create a custom estimator.\n", + "\n", + "In [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb), we took a look at naive Bayesian classification, in which we created a simple generative model for each class, and used these models to build a fast classifier.\n", + "For Gaussian naive Bayes, the generative model is a simple axis-aligned Gaussian.\n", + "With a density estimation algorithm like KDE, we can remove the \"naive\" element and perform the same classification with a more sophisticated generative model for each class.\n", + "It's still Bayesian classification, but it's no longer naive.\n", + "\n", + "The general approach for generative classification is this:\n", + "\n", + "1. Split the training data by label.\n", + "\n", + "2. For each set, fit a KDE to obtain a generative model of the data.\n", + " This allows you for any observation $x$ and label $y$ to compute a likelihood $P(x~|~y)$.\n", + " \n", + "3. From the number of examples of each class in the training set, compute the *class prior*, $P(y)$.\n", + "\n", + "4. For an unknown point $x$, the posterior probability for each class is $P(y~|~x) \\propto P(x~|~y)P(y)$.\n", + " The class which maximizes this posterior is the label assigned to the point.\n", + "\n", + "The algorithm is straightforward and intuitive to understand; the more difficult piece is couching it within the Scikit-Learn framework in order to make use of the grid search and cross-validation architecture.\n", + "\n", + "This is the code that implements the algorithm within the Scikit-Learn framework; we will step through it following the code block:" + ] + }, { "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -435,7 +772,7 @@ "\n", "\n", "class KDEClassifier(BaseEstimator, ClassifierMixin):\n", - " \"\"\"Bayesian Generative Classification based on KDE\n", + " \"\"\"Bayesian generative classification based on KDE\n", " \n", " Parameters\n", " ----------\n", @@ -468,11 +805,140 @@ " return self.classes_[np.argmax(self.predict_proba(X), 1)]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### The anatomy of a custom estimator" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Let's step through this code and discuss the essential features:\n", + "\n", + "```python\n", + "from sklearn.base import BaseEstimator, ClassifierMixin\n", + "\n", + "class KDEClassifier(BaseEstimator, ClassifierMixin):\n", + " \"\"\"Bayesian generative classification based on KDE\n", + " \n", + " Parameters\n", + " ----------\n", + " bandwidth : float\n", + " the kernel bandwidth within each class\n", + " kernel : str\n", + " the kernel name, passed to KernelDensity\n", + " \"\"\"\n", + "```\n", + "\n", + "Each estimator in Scikit-Learn is a class, and it is most convenient for this class to inherit from the ``BaseEstimator`` class as well as the appropriate mixin, which provides standard functionality.\n", + "For example, among other things, here the ``BaseEstimator`` contains the logic necessary to clone/copy an estimator for use in a cross-validation procedure, and ``ClassifierMixin`` defines a default ``score()`` method used by such routines.\n", + "We also provide a doc string, which will be captured by IPython's help functionality (see [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb))." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next comes the class initialization method:\n", + "\n", + "```python\n", + " def __init__(self, bandwidth=1.0, kernel='gaussian'):\n", + " self.bandwidth = bandwidth\n", + " self.kernel = kernel\n", + "```\n", + "\n", + "This is the actual code that is executed when the object is instantiated with ``KDEClassifier()``.\n", + "In Scikit-Learn, it is important that *initialization contains no operations* other than assigning the passed values by name to ``self``.\n", + "This is due to the logic contained in ``BaseEstimator`` required for cloning and modifying estimators for cross-validation, grid search, and other functions.\n", + "Similarly, all arguments to ``__init__`` should be explicit: i.e. ``*args`` or ``**kwargs`` should be avoided, as they will not be correctly handled within cross-validation routines." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next comes the ``fit()`` method, where we handle training data:\n", + "\n", + "```python \n", + " def fit(self, X, y):\n", + " self.classes_ = np.sort(np.unique(y))\n", + " training_sets = [X[y == yi] for yi in self.classes_]\n", + " self.models_ = [KernelDensity(bandwidth=self.bandwidth,\n", + " kernel=self.kernel).fit(Xi)\n", + " for Xi in training_sets]\n", + " self.logpriors_ = [np.log(Xi.shape[0] / X.shape[0])\n", + " for Xi in training_sets]\n", + " return self\n", + "```\n", + "\n", + "Here we find the unique classes in the training data, train a ``KernelDensity`` model for each class, and compute the class priors based on the number of input samples.\n", + "Finally, ``fit()`` should always return ``self`` so that we can chain commands. For example:\n", + "```python\n", + "label = model.fit(X, y).predict(X)\n", + "```\n", + "Notice that each persistent result of the fit is stored with a trailing underscore (e.g., ``self.logpriors_``).\n", + "This is a convention used in Scikit-Learn so that you can quickly scan the members of an estimator (using IPython's tab completion) and see exactly which members are fit to training data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Finally, we have the logic for predicting labels on new data:\n", + "```python\n", + " def predict_proba(self, X):\n", + " logprobs = np.vstack([model.score_samples(X)\n", + " for model in self.models_]).T\n", + " result = np.exp(logprobs + self.logpriors_)\n", + " return result / result.sum(1, keepdims=True)\n", + " \n", + " def predict(self, X):\n", + " return self.classes_[np.argmax(self.predict_proba(X), 1)]\n", + "```\n", + "Because this is a probabilistic classifier, we first implement ``predict_proba()`` which returns an array of class probabilities of shape ``[n_samples, n_classes]``.\n", + "Entry ``[i, j]`` of this array is the posterior probability that sample ``i`` is a member of class ``j``, computed by multiplying the likelihood by the class prior and normalizing.\n", + "\n", + "Finally, the ``predict()`` method uses these probabilities and simply returns the class with the largest probability." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "### Using our custom estimator\n", + "\n", + "Let's try this custom estimator on a problem we have seen before: the classification of hand-written digits.\n", + "Here we will load the digits, and compute the cross-validation score for a range of candidate bandwidths using the ``GridSearchCV`` meta-estimator (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb)):" + ] + }, { "cell_type": "code", "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -488,11 +954,23 @@ "scores = [val.mean_validation_score for val in grid.grid_scores_]" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Next we can plot the cross-validation score as a function of bandwidth:" + ] + }, { "cell_type": "code", "execution_count": 18, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -523,11 +1001,23 @@ "print('accuracy =', grid.best_score_)" ] }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "We see that this not-so-naive Bayesian classifier reaches a cross-validation accuracy of just over 96%; this is compared to around 80% for the naive Bayesian classification:" + ] + }, { "cell_type": "code", "execution_count": 19, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -546,9 +1036,41 @@ "from sklearn.cross_validation import cross_val_score\n", "cross_val_score(GaussianNB(), digits.data, digits.target).mean()" ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "One benefit of such a generative classifier is interpretability of results: for each unknown sample, we not only get a probabilistic classification, but a *full model* of the distribution of points we are comparing it to!\n", + "If desired, this offers an intuitive window into the reasons for a particular classification that algorithms like SVMs and random forests tend to obscure.\n", + "\n", + "If you would like to take this further, there are some improvements that could be made to our KDE classifier model:\n", + "\n", + "- we could allow the bandwidth in each class to vary independently\n", + "- we could optimize these bandwidths not based on their prediction score, but on the likelihood of the training data under the generative model within each class (i.e. use the scores from ``KernelDensity`` itself rather than the global prediction accuracy)\n", + "\n", + "Finally, if you want some practice building your own estimator, you might tackle building a similar Bayesian classifier using Gaussian Mixture Models instead of KDE." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb) | [Contents](Index.ipynb) | [Application: A Face Detection Pipeline](05.14-Image-Features.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { + "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", diff --git a/code_listings/05.14-Image-Features.ipynb b/notebooks_v1/05.14-Image-Features.ipynb similarity index 97% rename from code_listings/05.14-Image-Features.ipynb rename to notebooks_v1/05.14-Image-Features.ipynb index a128398f9..47ddff7da 100644 --- a/code_listings/05.14-Image-Features.ipynb +++ b/notebooks_v1/05.14-Image-Features.ipynb @@ -1,5 +1,27 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) | [Contents](Index.ipynb) | [Further Machine Learning Resources](05.15-Learning-More.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -7,6 +29,24 @@ "# Application: A Face Detection Pipeline" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This chapter has explored a number of the central concepts and algorithms of machine learning.\n", + "But moving from these concepts to real-world application can be a challenge.\n", + "Real-world datasets are noisy and heterogeneous, may have missing features, and data may be in a form that is difficult to map to a clean ``[n_samples, n_features]`` matrix.\n", + "Before applying any of the methods discussed here, you must first extract these features from your data: there is no formula for how to do this that applies across all domains, and thus this is where you as a data scientist must exercise your own intuition and expertise.\n", + "\n", + "One interesting and compelling application of machine learning is to images, and we have already seen a few examples of this where pixel-level features are used for classification.\n", + "In the real world, data is rarely so uniform and simple pixels will not be suitable: this has led to a large literature on *feature extraction* methods for image data (see [Feature Engineering](05.04-Feature-Engineering.ipynb)).\n", + "\n", + "In this section, we will take a look at one such feature extraction technique, the [Histogram of Oriented Gradients](https://en.wikipedia.org/wiki/Histogram_of_oriented_gradients) (HOG), which transforms image pixels into a vector representation that is sensitive to broadly informative image features regardless of confounding factors like illumination.\n", + "We will use these features to develop a simple face detection pipeline, using machine learning algorithms and concepts we've seen throughout this chapter. \n", + "\n", + "We begin with the standard imports:" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -21,6 +61,24 @@ "import numpy as np" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## HOG Features\n", + "\n", + "The Histogram of Gradients is a straightforward feature extraction procedure that was developed in the context of identifying pedestrians within images.\n", + "HOG involves the following steps:\n", + "\n", + "1. Optionally pre-normalize images. This leads to features that resist dependence on variations in illumination.\n", + "2. Convolve the image with two filters that are sensitive to horizontal and vertical brightness gradients. These capture edge, contour, and texture information.\n", + "3. Subdivide the image into cells of a predetermined size, and compute a histogram of the gradient orientations within each cell.\n", + "4. Normalize the histograms in each cell by comparing to the block of neighboring cells. This further suppresses the effect of illumination across the image.\n", + "5. Construct a one-dimensional feature vector from the information in each cell.\n", + "\n", + "A fast HOG extractor is built into the Scikit-Image project, and we can try it out relatively quickly and visualize the oriented gradients within each cell:" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -55,6 +113,35 @@ "ax[1].set_title('visualization of HOG features');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## HOG in Action: A Simple Face Detector\n", + "\n", + "Using these HOG features, we can build up a simple facial detection algorithm with any Scikit-Learn estimator; here we will use a linear support vector machine (refer back to [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) if you need a refresher on this).\n", + "The steps are as follows:\n", + "\n", + "1. Obtain a set of image thumbnails of faces to constitute \"positive\" training samples.\n", + "2. Obtain a set of image thumbnails of non-faces to constitute \"negative\" training samples.\n", + "3. Extract HOG features from these training samples.\n", + "4. Train a linear SVM classifier on these samples.\n", + "5. For an \"unknown\" image, pass a sliding window across the image, using the model to evaluate whether that window contains a face or not.\n", + "6. If detections overlap, combine them into a single window.\n", + "\n", + "Let's go through these steps and try it out:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1. Obtain a set of positive training samples\n", + "\n", + "Let's start by finding some positive training samples that show a variety of faces.\n", + "We have one easy set of data to work with—the Labeled Faces in the Wild dataset, which can be downloaded by Scikit-Learn:" + ] + }, { "cell_type": "code", "execution_count": 3, @@ -80,6 +167,24 @@ "positive_patches.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us a sample of 13,000 face images to use for training." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2. Obtain a set of negative training samples\n", + "\n", + "Next we need a set of similarly sized thumbnails which *do not* have a face in them.\n", + "One way to do this is to take any corpus of input images, and extract thumbnails from them at a variety of scales.\n", + "Here we can use some of the images shipped with Scikit-Image, along with Scikit-Learn's ``PatchExtractor``:" + ] + }, { "cell_type": "code", "execution_count": 4, @@ -133,6 +238,14 @@ "negative_patches.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have 30,000 suitable image patches which do not contain faces.\n", + "Let's take a look at a few of them to get an idea of what they look like:" + ] + }, { "cell_type": "code", "execution_count": 6, @@ -158,6 +271,23 @@ " axi.axis('off')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our hope is that these would sufficiently cover the space of \"non-faces\" that our algorithm is likely to see." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3. Combine sets and extract HOG features\n", + "\n", + "Now that we have these positive samples and negative samples, we can combine them and compute HOG features.\n", + "This step takes a little while, because the HOG features involve a nontrivial computation for each image:" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -196,6 +326,26 @@ "X_train.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are left with 43,000 training samples in 1,215 dimensions, and we now have our data in a form that we can feed into Scikit-Learn!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4. Training a support vector machine\n", + "\n", + "Next we use the tools we have been exploring in this chapter to create a classifier of thumbnail patches.\n", + "For such a high-dimensional binary classification task, a Linear support vector machine is a good choice.\n", + "We will use Scikit-Learn's ``LinearSVC``, because in comparison to ``SVC`` it often has better scaling for large number of samples.\n", + "\n", + "First, though, let's use a simple Gaussian naive Bayes to get a quick baseline:" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -221,6 +371,14 @@ "cross_val_score(GaussianNB(), X_train, y_train)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that on our training data, even a simple naive Bayes algorithm gets us upwards of 90% accuracy.\n", + "Let's try the support vector machine, with a grid search over a few choices of the C parameter:" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -269,6 +427,13 @@ "grid.best_params_" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's take the best estimator and re-train it on the full dataset:" + ] + }, { "cell_type": "code", "execution_count": 12, @@ -295,6 +460,16 @@ "model.fit(X_train, y_train)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 5. Find faces in a new image\n", + "\n", + "Now that we have this model in place, let's grab a new image and see how the model does.\n", + "We will use one portion of the astronaut image for simplicity (see discussion of this in [Caveats and Improvements](#Caveats-and-Improvements)), and run a sliding window over it and evaluate each patch:" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -323,6 +498,13 @@ "plt.axis('off');" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, let's create a window that iterates over patches of this image, and compute HOG features for each patch:" + ] + }, { "cell_type": "code", "execution_count": 14, @@ -357,6 +539,13 @@ "patches_hog.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can take these HOG-featured patches and use our model to evaluate whether each patch contains a face:" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -380,6 +569,14 @@ "labels.sum()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that out of nearly 2,000 patches, we have found 30 detections.\n", + "Let's use the information we have about these patches to show where they lie on our test image, drawing them as rectangles:" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -410,6 +607,68 @@ " ax.add_patch(plt.Rectangle((j, i), Nj, Ni, edgecolor='red',\n", " alpha=0.3, lw=2, facecolor='none'))" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of the detected patches overlap and found the face in the image!\n", + "Not bad for a few lines of Python." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Caveats and Improvements\n", + "\n", + "If you dig a bit deeper into the preceding code and examples, you'll see that we still have a bit of work before we can claim a production-ready face detector.\n", + "There are several issues with what we've done, and several improvements that could be made. In particular:\n", + "\n", + "### Our training set, especially for negative features, is not very complete\n", + "\n", + "The central issue is that there are many face-like textures that are not in the training set, and so our current model is very prone to false positives.\n", + "You can see this if you try out the above algorithm on the *full* astronaut image: the current model leads to many false detections in other regions of the image.\n", + "\n", + "We might imagine addressing this by adding a wider variety of images to the negative training set, and this would probably yield some improvement.\n", + "Another way to address this is to use a more directed approach, such as *hard negative mining*.\n", + "In hard negative mining, we take a new set of images that our classifier has not seen, find all the patches representing false positives, and explicitly add them as negative instances in the training set before re-training the classifier.\n", + "\n", + "### Our current pipeline searches only at one scale\n", + "\n", + "As currently written, our algorithm will miss faces that are not approximately 62×47 pixels.\n", + "This can be straightforwardly addressed by using sliding windows of a variety of sizes, and re-sizing each patch using ``skimage.transform.resize`` before feeding it into the model.\n", + "In fact, the ``sliding_window()`` utility used here is already built with this in mind.\n", + "\n", + "### We should combine overlapped detection patches\n", + "\n", + "For a production-ready pipeline, we would prefer not to have 30 detections of the same face, but to somehow reduce overlapping groups of detections down to a single detection.\n", + "This could be done via an unsupervised clustering approach (MeanShift Clustering is one good candidate for this), or via a procedural approach such as *non-maximum suppression*, an algorithm common in machine vision.\n", + "\n", + "### The pipeline should be streamlined\n", + "\n", + "Once we address these issues, it would also be nice to create a more streamlined pipeline for ingesting training images and predicting sliding-window outputs.\n", + "This is where Python as a data science tool really shines: with a bit of work, we could take our prototype code and package it with a well-designed object-oriented API that give the user the ability to use this easily.\n", + "I will leave this as a proverbial \"exercise for the reader\".\n", + "\n", + "### More recent advances: Deep Learning\n", + "\n", + "Finally, I should add that HOG and other procedural feature extraction methods for images are no longer state-of-the-art techniques.\n", + "Instead, many modern object detection pipelines use variants of deep neural networks: one way to think of neural networks is that they are an estimator which determines optimal feature extraction strategies from the data, rather than relying on the intuition of the user.\n", + "An intro to these deep neural net methods is conceptually (and computationally!) beyond the scope of this section, although open tools like Google's [TensorFlow](https://www.tensorflow.org/) have recently made deep learning approaches much more accessible than they once were.\n", + "As of the writing of this book, deep learning in Python is still relatively young, and so I can't yet point to any definitive resource.\n", + "That said, the list of references in the following section should provide a useful place to start!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "< [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) | [Contents](Index.ipynb) | [Further Machine Learning Resources](05.15-Learning-More.ipynb) >\n", + "\n", + "\"Open\n" + ] } ], "metadata": { diff --git a/notebooks_v1/05.15-Learning-More.ipynb b/notebooks_v1/05.15-Learning-More.ipynb new file mode 100644 index 000000000..17d8cc77c --- /dev/null +++ b/notebooks_v1/05.15-Learning-More.ipynb @@ -0,0 +1,127 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Application: A Face Detection Pipeline](05.14-Image-Features.ipynb) | [Contents](Index.ipynb) | [Appendix: Figure Code](06.00-Figure-Code.ipynb) >\n", + "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Further Machine Learning Resources" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "This chapter has been a quick tour of machine learning in Python, primarily using the tools within the Scikit-Learn library.\n", + "As long as the chapter is, it is still too short to cover many interesting and important algorithms, approaches, and discussions.\n", + "Here I want to suggest some resources to learn more about machine learning for those who are interested." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## Machine Learning in Python\n", + "\n", + "To learn more about machine learning in Python, I'd suggest some of the following resources:\n", + "\n", + "- [The Scikit-Learn website](http://scikit-learn.org): The Scikit-Learn website has an impressive breadth of documentation and examples covering some of the models discussed here, and much, much more. If you want a brief survey of the most important and often-used machine learning algorithms, this website is a good place to start.\n", + "\n", + "- *SciPy, PyCon, and PyData tutorial videos*: Scikit-Learn and other machine learning topics are perennial favorites in the tutorial tracks of many Python-focused conference series, in particular the PyCon, SciPy, and PyData conferences. You can find the most recent ones via a simple web search.\n", + "\n", + "- [*Introduction to Machine Learning with Python*](http://shop.oreilly.com/product/0636920030515.do): Written by Andreas C. Mueller and Sarah Guido, this book includes a fuller treatment of the topics in this chapter. If you're interested in reviewing the fundamentals of Machine Learning and pushing the Scikit-Learn toolkit to its limits, this is a great resource, written by one of the most prolific developers on the Scikit-Learn team.\n", + "\n", + "- [*Python Machine Learning*](https://www.packtpub.com/big-data-and-business-intelligence/python-machine-learning): Sebastian Raschka's book focuses less on Scikit-learn itself, and more on the breadth of machine learning tools available in Python. In particular, there is some very useful discussion on how to scale Python-based machine learning approaches to large and complex datasets." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "## General Machine Learning\n", + "\n", + "Of course, machine learning is much broader than just the Python world. There are many good resources to take your knowledge further, and here I will highlight a few that I have found useful:\n", + "\n", + "- [*Machine Learning*](https://www.coursera.org/learn/machine-learning): Taught by Andrew Ng (Coursera), this is a very clearly-taught free online course which covers the basics of machine learning from an algorithmic perspective. It assumes undergraduate-level understanding of mathematics and programming, and steps through detailed considerations of some of the most important machine learning algorithms. Homework assignments, which are algorithmically graded, have you actually implement some of these models yourself.\n", + "\n", + "- [*Pattern Recognition and Machine Learning*](http://www.springer.com/us/book/9780387310732): Written by Christopher Bishop, this classic technical text covers the concepts of machine learning discussed in this chapter in detail. If you plan to go further in this subject, you should have this book on your shelf.\n", + "\n", + "- [*Machine Learning: a Probabilistic Perspective*](https://mitpress.mit.edu/books/machine-learning-0): Written by Kevin Murphy, this is an excellent graduate-level text that explores nearly all important machine learning algorithms from a ground-up, unified probabilistic perspective.\n", + "\n", + "These resources are more technical than the material presented in this book, but to really understand the fundamentals of these methods requires a deep dive into the mathematics behind them.\n", + "If you're up for the challenge and ready to bring your data science to the next level, don't hesitate to dive-in!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Application: A Face Detection Pipeline](05.14-Image-Features.ipynb) | [Contents](Index.ipynb) | [Appendix: Figure Code](06.00-Figure-Code.ipynb) >\n", + "\n", + "\"Open\n" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/figure_appendix/06.00-Figure-Code.ipynb b/notebooks_v1/06.00-Figure-Code.ipynb similarity index 91% rename from figure_appendix/06.00-Figure-Code.ipynb rename to notebooks_v1/06.00-Figure-Code.ipynb index daf5d5bd2..73940a1c1 100644 --- a/figure_appendix/06.00-Figure-Code.ipynb +++ b/notebooks_v1/06.00-Figure-Code.ipynb @@ -2,10 +2,46 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "\n", + "\n", + "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "\n", + "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, "source": [ - "# Appendix: Figure Code\n", + "\n", + "< [Further Machine Learning Resources](05.15-Learning-More.ipynb) | [Contents](Index.ipynb) |\n", "\n", + "\"Open\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Appendix: Figure Code" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ "Many of the figures used throughout this text are created in-place by code that appears in print.\n", "In a few cases, however, the required code is long enough (or not immediately relevant enough) that we instead put it here for reference." ] @@ -14,7 +50,9 @@ "cell_type": "code", "execution_count": 1, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -28,18 +66,23 @@ "cell_type": "code", "execution_count": 2, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ "import os\n", - "if not os.path.exists('fig'):\n", - " os.makedirs('fig')" + "if not os.path.exists('figures'):\n", + " os.makedirs('figures')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Broadcasting\n", "\n", @@ -50,14 +93,16 @@ "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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Ojg529uxZ1tHRwQoLCynrCbJyc3OZm5sby83NFTSLV9Z+L/OaZY05inZ1cqz/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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -251,12 +296,15 @@ "ax.set_xlim(0, 16)\n", "ax.set_ylim(0.5, 12.5)\n", "\n", - "fig.savefig('fig/02.05-broadcasting.png')" + "fig.savefig('figures/02.05-broadcasting.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Aggregation and Grouping\n", "\n", @@ -265,7 +313,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Split-Apply-Combine" ] @@ -274,14 +325,16 @@ "cell_type": "code", "execution_count": 4, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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SErZv306rVq0AuOeee0xOJSINMXfuXPbv389vfvMbBgwYoPPBpEnQHjBpdt58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\nSUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -394,12 +447,15 @@ "plt.axis('equal')\n", "plt.ylim(-1.5, 5);\n", "\n", - "fig.savefig('fig/03.08-split-apply-combine.png')" + "fig.savefig('figures/03.08-split-apply-combine.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## What Is Machine Learning?" ] @@ -408,7 +464,9 @@ "cell_type": "code", "execution_count": 5, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -423,7 +481,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Classification Example Figures\n", "\n", @@ -436,7 +497,9 @@ "cell_type": "code", "execution_count": 6, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -462,7 +525,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Classification Example Figure 1" ] @@ -471,14 +537,16 @@ "cell_type": "code", "execution_count": 7, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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IirQNaHve+eRTxIyfCa3u5h50c30trMV5WDRv7t39Yk7EWd/L/QnHWBmcNU1OIT4uHvFx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\nYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -495,12 +563,15 @@ "format_plot(ax, 'Input Data')\n", "ax.axis([-1, 4, -2, 7])\n", "\n", - "fig.savefig('fig/05.01-classification-1.png')" + "fig.savefig('figures/05.01-classification-1.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Classification Example Figure 2" ] @@ -509,14 +580,16 @@ "cell_type": "code", "execution_count": 8, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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Yza24du2qO6m2J9aIiEiMGzdRcnxNzU3s379HkljVavlkmJGRjZUrf9Lt3qj2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\nSUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -543,12 +616,15 @@ "format_plot(ax, 'Model Learned from Input Data')\n", "ax.axis([-1, 4, -2, 7])\n", "\n", - "fig.savefig('fig/05.01-classification-2.png')" + "fig.savefig('figures/05.01-classification-2.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Classification Example Figure 3" ] @@ -557,14 +633,16 @@ "cell_type": "code", "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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zFkXyipRbVKbOT/aoItvQ3bfdmrT+w2DFxSV65Nt3a8tbb6k7HJWiUS2YUaXL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\nAAAAAIBjCCIAAAAAAIBjCCIAAAAAAIBjCCIAAAAAAIBjCCI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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -586,12 +664,15 @@ "format_plot(ax[0], 'Unknown Data')\n", "format_plot(ax[1], 'Predicted Labels')\n", "\n", - "fig.savefig('fig/05.01-classification-3.png')" + "fig.savefig('figures/05.01-classification-3.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Regression Example Figures\n", "\n", @@ -604,7 +685,9 @@ "cell_type": "code", "execution_count": 10, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -629,7 +712,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Regression Example Figure 1" ] @@ -638,14 +724,16 @@ "cell_type": "code", "execution_count": 11, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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MF8/QXG3jlccfop+LEcTHT5xi3fZfCPD1ZvrE8Wi12np7FkGoS25LxFlZtdse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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -662,12 +750,15 @@ "format_plot(ax, 'Input Data')\n", "ax.axis([-4, 4, -3, 3])\n", "\n", - "fig.savefig('fig/05.01-regression-1.png')" + "fig.savefig('figures/05.01-regression-1.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Regression Example Figure 2" ] @@ -676,14 +767,16 @@ "cell_type": "code", "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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8fMrTq7wwcurewueejOM4WOUqnuuSMHWctTL6gEahUNgwqriT1B3Bw4mwqu8h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86Pi+tdU1HJYk0nEAjQ2tp6ugY4m0VRAEVHsapEU0lsFsh2xc+41rn3Ze78Obz1yj6I2bErVhIp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\nJZPJcOW6NcRTaU529LJ2/fqCY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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -726,12 +819,15 @@ "for tick in ax.w_zaxis.get_ticklines():\n", " tick.set_visible(False)\n", "\n", - "fig.savefig('fig/05.01-regression-2.png')" + "fig.savefig('figures/05.01-regression-2.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Regression Example Figure 3" ] @@ -740,14 +836,16 @@ "cell_type": "code", "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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X7oQdN7x+il3pCYhofoKBAOebj/PDt4e5ePIEui7HhCWSaMg5YolkhXD3Zjut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1w/qU1deiSEEnPMrOVLz7zsaEZtko8V3fBBMXEsc9pMt6ToXncfbKXxa5H9uaVou3kNdavXwa7a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\nAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -775,12 +873,15 @@ "format_plot(ax, 'Input Data with Linear Fit')\n", "ax.axis([-4, 4, -3, 3])\n", "\n", - "fig.savefig('fig/05.01-regression-3.png')" + "fig.savefig('figures/05.01-regression-3.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Regression Example Figure 4" ] @@ -789,14 +890,16 @@ "cell_type": "code", "execution_count": 14, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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IMkxEEBEREREREZFkmIggIiIiIiIiIskwEUFEREREREREkmEigoiIiIiIiIgkw0QEERER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\nqlgLAP3798e7776LgQMHNuvC56ZbBYuLp5gFC96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pPkkQEbU09c55ys/Px3XXXQdRFKHT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\nRK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -819,12 +922,15 @@ "format_plot(ax[0], 'Unknown Data')\n", "format_plot(ax[1], 'Predicted Labels')\n", "\n", - "fig.savefig('fig/05.01-regression-4.png')" + "fig.savefig('figures/05.01-regression-4.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Clustering Example Figures\n", "\n", @@ -837,7 +943,9 @@ "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -855,7 +963,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Clustering Example Figure 1" ] @@ -864,14 +975,16 @@ "cell_type": "code", "execution_count": 16, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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EUI3PCACqQxDDV6ZPn6FYLFbwvlgspnh8uu0xmOQFwEsYI4avRCIRtbV1TBgj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\nAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -886,12 +999,15 @@ "# format the plot\n", "format_plot(ax, 'Input Data')\n", "\n", - "fig.savefig('fig/05.01-clustering-1.png')" + "fig.savefig('figures/05.01-clustering-1.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Clustering Example Figure 2" ] @@ -900,14 +1016,16 @@ "cell_type": "code", "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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KTWvFv4sXj//pqTsac9syqhWv/fu1ig8UQlQ76axVx7WK6kLs5J/YeuyPvPOR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\nhMPhcLt/IvJtDGJq9VI3boEcEOnULqrU+DU33+3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PT0ZO7t+w9Xge7Kb2kK01iHAU4+kp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\nv9AAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -922,12 +1040,15 @@ "# format the plot\n", "format_plot(ax, 'Learned Cluster Labels')\n", "\n", - "fig.savefig('fig/05.01-clustering-2.png')" + "fig.savefig('figures/05.01-clustering-2.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Dimensionality Reduction Example Figures\n", "\n", @@ -938,7 +1059,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Dimensionality Reduction Example Figure 1" ] @@ -947,14 +1071,16 @@ "cell_type": "code", "execution_count": 18, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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Xi8V8c1IBtSTfTTy1h7T01RKkPT33uL6vsObHpQ9T0UZcBTJ7+EnS66//X8Xj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\nA532xVzn6tbEAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -975,12 +1101,15 @@ "# format the plot\n", "format_plot(ax, 'Input Data')\n", "\n", - "fig.savefig('fig/05.01-dimesionality-1.png')" + "fig.savefig('figures/05.01-dimesionality-1.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Dimensionality Reduction Example Figure 2" ] @@ -989,14 +1118,16 @@ "cell_type": "code", "execution_count": 19, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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JO26muCKb2KBr0SjRRPhGU1GbhyG4jF/97tkmu364O5nOIEQrpOzcgH2g49Je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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1019,19 +1150,25 @@ "cb.set_ticks([])\n", "cb.set_label('Latent Variable', color='gray')\n", "\n", - "fig.savefig('fig/05.01-dimesionality-2.png')" + "fig.savefig('figures/05.01-dimesionality-2.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Introducing Scikit-Learn" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Features and Labels Grid\n", "\n", @@ -1042,14 +1179,16 @@ "cell_type": "code", "execution_count": 20, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1080,19 +1219,25 @@ "\n", "ax.set_ylim(10, -2)\n", "\n", - "fig.savefig('fig/05.02-samples-features.png')" + "fig.savefig('figures/05.02-samples-features.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Hyperparameters and Model Validation" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Cross-Validation Figures" ] @@ -1101,7 +1246,9 @@ "cell_type": "code", "execution_count": 21, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -1119,7 +1266,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### 2-Fold Cross-Validation" ] @@ -1128,14 +1278,16 @@ "cell_type": "code", "execution_count": 22, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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1alSVJgMADhZhVkWrVq1KU1NTkuSBBx5IXV1d6yuT/mbDhg156qmnqjAdAHCwCbMq6tq1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\nnOjGf5sKAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1148,12 +1300,15 @@ "ax.axis('off')\n", "draw_rects(2, ax, textprop=dict(size=14))\n", "\n", - "fig.savefig('fig/05.03-2-fold-CV.png')" + "fig.savefig('figures/05.03-2-fold-CV.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### 5-Fold Cross-Validation" ] @@ -1162,14 +1317,16 @@ "cell_type": "code", "execution_count": 23, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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//76OHTumFStW6JtvvlFhYaF27dr1swGdk5Mz8vQgz54907NnzyRJzc3N2rhx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\nwACiCwAAwACiCwAAwACiCwAAwID/A+awRviS8pn9AAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1182,12 +1339,15 @@ "ax.axis('off')\n", "draw_rects(5, ax, textprop=dict(size=10))\n", "\n", - "fig.savefig('fig/05.03-5-fold-CV.png')" + "fig.savefig('figures/05.03-5-fold-CV.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Overfitting and Underfitting" ] @@ -1196,7 +1356,9 @@ "cell_type": "code", "execution_count": 24, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -1216,7 +1378,9 @@ "cell_type": "code", "execution_count": 25, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -1231,7 +1395,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Bias-Variance Tradeoff" ] @@ -1240,14 +1407,16 @@ "cell_type": "code", "execution_count": 26, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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goaEB0dHRmDlzJh5//HFs2bIFzzzzDGpqalo974mcoRDMsaFOaNeuXRg/fjxC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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1273,12 +1442,15 @@ "ax[1].axis([-0.1, 1.0, -2, 14])\n", "ax[1].set_title('High-variance model: Overfits the data', size=14)\n", "\n", - "fig.savefig('fig/05.03-bias-variance.png')" + "fig.savefig('figures/05.03-bias-variance.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Bias-Variance Tradeoff Metrics" ] @@ -1287,14 +1459,16 @@ "cell_type": "code", "execution_count": 27, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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NyMhI7r7JcvWYkEgk+Q6vlclkBQ691a9LTU2Fn58fLl26BIVCwb2GPj4+cHR0xO7du9G6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\nNQEBAADb6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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1327,12 +1501,15 @@ "ax[1].text(0.02, 0.91, \"validation score: $R^2$ = {0:.2g}\".format(model20.score(X2, y2)),\n", " ha='left', va='top', transform=ax[1].transAxes, size=14, color='red')\n", "\n", - "fig.savefig('fig/05.03-bias-variance-2.png')" + "fig.savefig('figures/05.03-bias-variance-2.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Validation Curve" ] @@ -1341,14 +1518,16 @@ "cell_type": "code", "execution_count": 28, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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pXbo08+b9QGJiEkuXLgYgJKQ633+/mH/+cyA//LCAJk2ecUr5+T6cw8LuUKNG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JDWWIjSjcvaRAQg/Z/vHQwG0dPTg5ycHGVJnGi34rI2ERFRhuHMmYiIKMOwOBMREWUYFmciIqIM\nw+JMRESUYViciYiIMgyLMxERUYZhcSYiIsowLM5EREQZ5i8j/j8f7uiIWgAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1382,12 +1561,15 @@ "\n", "ax.set_title(\"Validation Curve Schematic\", size=16)\n", "\n", - "fig.savefig('fig/05.03-validation-curve.png')" + "fig.savefig('figures/05.03-validation-curve.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "#### Learning Curve" ] @@ -1396,14 +1578,16 @@ "cell_type": "code", "execution_count": 29, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { - "image/png": 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OwPLzapSSEpw33oL1i88wr11jvM/jQY+Px/z7JuP4dlg46v59vtHeWlw8qCqm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+ "image/png": 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JZyGEEMLHSDgLIYQQPkbCWQghhPAxEs5CCCGEj5FwFkIIIXyMzwxC8tZbEBRkIiVFIzpa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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1416,11 +1600,11 @@ "y2 = 0.7 - 0.6 * np.exp(-4 * N)\n", "\n", "fig, ax = plt.subplots()\n", - "ax.plot(x, y2, lw=10, alpha=0.5, color='blue')\n", - "ax.plot(x, y1, lw=10, alpha=0.5, color='red')\n", + "ax.plot(x, y1, lw=10, alpha=0.5, color='blue')\n", + "ax.plot(x, y2, lw=10, alpha=0.5, color='red')\n", "\n", - "ax.text(0.2, 0.5, \"training score\", rotation=30, size=16, color='blue')\n", - "ax.text(0.2, 0.88, \"validation score\", rotation=-10, size=16, color='red')\n", + "ax.text(0.2, 0.88, \"training score\", rotation=-10, size=16, color='blue')\n", + "ax.text(0.2, 0.5, \"validation score\", rotation=30, size=16, color='red')\n", "\n", "ax.text(0.98, 0.45, r'Good Fit $\\longrightarrow$', size=18, rotation=90, ha='right', va='center')\n", "ax.text(0.02, 0.57, r'$\\longleftarrow$ High Variance $\\longrightarrow$', size=18, rotation=90, va='center')\n", @@ -1436,12 +1620,15 @@ "\n", "ax.set_title(\"Learning Curve Schematic\", size=16)\n", "\n", - "fig.savefig('fig/05.03-learning-curve.png')" + "fig.savefig('figures/05.03-learning-curve.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Gaussian Naive Bayes\n", "\n", @@ -1454,14 +1641,16 @@ "cell_type": "code", "execution_count": 30, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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0Tq3fv+PCwHMCFdFdMRUKvLB+o0VnB2zfriLBy/qJdCZLHzJb7PZhfkOZjh2P\nDv689xUhoLwc4nGLnTsNWlsF0ShMnz55KwOm4yN0qprxwLKgtrZvSrnqamvSpEh1B6CxUVkxlqUC\ndsrKPlpF/u0ZRM2eSZU0B4TLpcSqrExZ0p0dsLNW0OSCKRUS/yQokel2w+zZFrt29aVczZplfWSi\nufWvRzNmJJOwfbtBd7eakH327MkhzMFu2LZVUFOjhDnfD4fNkUyb9tESZoBFC+djs6KDV5hxjp1/\n+MFv0BC0t7XyzFNPsWHDB+PdlFHF5VLpR4fNUZ3DaBR21Ai2bRWEQuPdugPHZlPBYqWlkngctm0z\niKb5uk1GtOWsGROSSaipMYhEVFGFadOyf8wokUCVH+xS/+flK0vZ41Eego8iJ528lLPXvsMTa3eS\nNFR0tmFGOOWoMs5ZvnycW6cmEvn5L37J82s30xbLwUmco2fk8b1rvsq0adPHu3mjRk6OEumSEmjc\nI3o7kHn5qtJetneKp0xRgaN79gi2bTOYNcua9FXFtDhrRp3+wlxYKKmqyv5wqLY2qKsXWKYK9JpS\nMTmLQ+wrQgi++51rOPn113jltTexpOTYjx/JSScvzTg+fLC4554/8tArtWB4ETZI4ODNXSbX3/RL\n7rnz1gnRxtHE7YYZMyXhEOxpUB3JQEBQWKgCx7K5jkBpqZoitr5eCfTMmdak/g1qcdaMKpNNmGMx\n2L1blVkUBlRWSYqKxrtVo8N76z/k5rsepCsYoaK0gEs/dyFFxfte/UEIwcITTmThCScCaeffGDde\neWM9GIMVaX1dlDWvvMziJSeNQ6vGHq8XZh+qpmzc0yBob4OODjXZRHHxeLdu/ykulthskt27DWpq\nDGbMsPB6x7tVY4MWZ82oMZmEWUpobITNW1S97/x8qJhEFcwe+9cT3PrHf9KeUCHlUrby/L+v4yf/\n/V8cfvjYjBVLqdz/lqki2KXVNxyQMmCFoG/OD6FyiG329NNhDv9+kvZAGBicKGvZ3NTW7mLxkv06\nlawhP1/NKd3erlzC9XWqqEl1dfZOXVlQAIahIrl37DCorj44s9YdbLQ4a0aFgynMmVI9hskcwsqw\nQarwRjgMdbsFbieApGqaSlFJWpIhZlgcNmUpYQ69frjpJmMZ1keTQzSoh0ia9Yl4nN888HivMIOy\nfncH3dx291/4/g3/j2gi8/nE+7XJTEIyKUgmwEyqtJfUMjMJpqmGA1LsVyqVUMFBdntKrCWGDewO\nicMpcThMDA3xAAAgAElEQVTB7RK9BW3mz4CajigFfh8tLYMP55AhymYdRm1nBAC3I7P6exxDV8px\n2TPv68pQZcc5TES73ZYhbSnD92LvKPr8AvB4Jbt3CTq7YMMGqKqSaVMahyuMkqmCyXCpjKNV4CQ/\nH2bMsNixw6C2dnJa0FqcNQeMaU4ei7m5SaVHSQmVU2BK1eTLrXztlZfY3WUg0mjG5h2NxKIRsA2O\nIDJNiMcE8ZggFBbEo4KmPa2sWf0ygWAYjzuH4xYeT0lFVe8+hg1sNuVxEIayhoVhYQgQNmUZp7Ra\n9v7pWSZVZ8vqEXfTFCSTgngM0imE3Wao93LCjkLoaDU47hNLqHl8NUmj/7zcFkdW53PoER/b72uY\njTgcMHOWpLUFmhsFtTsEBYVqspmJUqVvX/D5VGpmba2yoCebQE+y247mYCOlymPOdmFOnUdXpyr0\nMK1KUl0Nze3j3bLRxxrGUpdSIiXEo4JIRBAJKSFOJvoEMWFZ1G7dwt8feYzOpIEwTBAmG3euY8UF\nS1l48knYHenLSB5IERLDUB0nJdaQTAgScdU2aUIyLohFBe3t0N5i49C5yzij2cPb696lvbsLjyfB\nvLnlXPWfX9zvNmQ7xSWQnyfZtVPQ0Q7hsGDGjPFLAwwGg9z714doaO6gorSAyz934YjKWwLk5cH0\n6X0u7sMOmzx50FqcNQdES4sgGBTk5WWvMJsm1O4QBLolXi9Mrx4fa3nr1i3c/+Cj1Da04st1ceqi\nj/Pp5eeO+vucePLJVD74FPX98mCVpeqkeuohtLf46AooizWFzS5xey2cORJnjkQ4LP721z8TsCcx\n+l2rMPDsc0+x6JRFiHSm+SggesahbXZw5vSY2IDDJnvPZd48+CCYJBYRLF12EgtPPolYsJsclxuH\nM4eGXZDjknhyLTw+iStv8s6fnA6XSwWMNTQIWltg61Yl0Ac7+nnd++/ztR/ewbZOB8KwIa0aHnr2\n3/zltmupnFo9omPk5yvrv65OsHu3YNas7LwP7c2o3oKklFx//fVs3rwZp9PJjTfeSFVV1fA7arKS\ncFi5gO12slaYEwlVtCESUT/yadPlfgUfHSjvr3+fb/7Pb9gTTrmTE6zZ8DQ1O3fz1a9+ZVTfy+nM\n4aLlp/D7B5+nK14IyVyk6aLImeDkxcsJdQsMmyTXZ+HyWLhzBwfCtbW1U1PXCrbBRZ3rOiw2vvcW\nRyw4blTbPVKEUHm/uV5Jrrfve2nIXGIRQSxiEo0KomGDWNRGRxt05Ag8Xkmu1yLXK7F9BMwWIZSo\n5eRAfZ2gZrtgxkx5UCeauPH2P7E94EL0/OaEYWNbl43v/uQu7r/9JyM+TlGRikzv7ha0tjIp5oQf\n1a/gqlWriMfj/O1vf+O9997jpptu4s477xzNt9BMENQ4s7JSpk2zsnJcNhaDmu2CeBwKi1Q09lhZ\nT6ueX82zL/2baCzB3JlT+Y/Pfw6Pp89M+cNfHu4nzIqkkcMjq9/lwgsaKS0rH5V2SAnhkGDBMcv5\nRcUJ/PbBVYQicYoLXZx17klUVpfg8iQxJ+FUHQ4HOBwSb546N8syCQcFkZCBGbXR3SXo7lLWvsst\nyfNb+PKzczx2XyguVtdlZ61gR41g5iwOSvRzbe0O3t7eDvbBvYHXNzZSX1/H1KmVIz5eVZVk0ybB\nnj2qIuH+uumDwW4ikSjFxcXjmgc/qrfUt99+m8WLFwNw1FFH8cEHk6tUnqaPujqBEGrWpWxMY4hE\noKZGRRiXlUnKpwwf6b2//OTWX/HHp9f3VtB65v1WVv/7XX536w8pKCwEYMP2BmCwT7E9mcszzzzH\n5y/7/AG1IRwSSnwCBmbPXBfHfexwriorwpdv4eqttqQugjlMUK3PX8CsqiI+bBgcDV5ZYDD3qI8f\nUHv7Y5kmxhgopGGAN0/izTNxOySxKIS6DUJBQSQsiEZstDaBL9+ivATcnuGPma3k50P1DEntDsGO\nHYIZ1RLfGFvQ4XCYuElaFYomIbSP9UdTc8Pv2mWwe7fgkEP27QddV1/P9bf+hjc2NRCJW8yp9POF\nC87gM2efuU/HGS1GVZyDwSC+fndqu92OZVkY4+En1IwZ7e3Q2SmorFRBYNlGMAg7dqgI4IqpquTh\nWLFl82YeeO49kkaf8Aph8H6j5Ne/+yPf/+43AXA6bJCuZrA0cbv3r/ailNDdJWhvM4iGlQVgs4O/\nUFmERx4JDR/sf8mQ885fTtNv/0xLzNNrYfhsIc4++8yMYtre0sRzT/yLQHeYwoI8Tjv7XPL8hXu1\nXfLkPx7kjbfep6MrREGeh48fM49zL7pkVK2Z+p07eOrxJwmGIpQU+Fh+/qepmjGFZAK6Og0CHQZd\nHQaxbhs5Lom/0CJvklrTeXmqjvXOXYKaHoHOG8MJNA47bA6HT/WwoXXwuqOr8znkkNn7fMyCAujq\nknR1CZqbVVWxkZBMJrn6uz9mXZMd8IEB7zRItt3xKP48L0uXLN7nthwooyrOXq93QG9HC/PkIxqF\n+noDw4AZMyAQGP33GC5XMpOFO1y+cXdAUlMjkFLlLxcUqIIYQ+2b7JefnMhQQDuRTP++jzz5PCE5\n2CIWQvDu5l1EEibhRJIjDq1ix1vNg4SnIjfG8UtPozXN1IsAXdHBlqtlQXeXQWebQSBoAiYerySv\nwMThkcSEcukD7GyNpD1uLJZ+KskU8biJp2QWX7jqal59/mm6AkFyc90ct+gzlFTOYNee9F+Mrevf\n5tFH/kXA8iKEQMpW1vz7fzj/sxdRdcjc3gSp1f98kJffqUHacgAn3QHYtepDWlrv4ozzL017bHu/\nXOUNGzby+GMvU33YPPIKVEm3nJyBt7v3/r2Gv//jSYJS5d9I2cGLb/yEL3zpYmYffiQYYBSCDAu6\nIzk0txrsalEpYd48C3+RicMJea7MSp1pfe4w40Fu+9D7xof4zgFI2zAR+UPkMru9UD3dYscOQU2N\nisEYNFd0hlu6kSkJmoG/bQcOvnzRmVz3238RSPZ1QH22CP956QX7rR2VlZJgUNDUpAJVR1JX/KHH\n/sU7Ddag9MKA6eIvjz6X/eK8YMECXnjhBT71qU/x7rvvcuihhw67z0hD5rOVyXR+lgWbNikX2MyZ\nKugmm84vGIS6dijsaf9IJqivKDmw8NVC39ADX54cO0dMU434/U+/zXlf/Bav74gjbE6klJS7wvzk\nGxdz5oIZI3ov04TmZvVI5oPwQ1ERlJUx5A3qqpNn7vM5DWQufPGTI9pSSsmiP/yCbunrVxHMoNPM\no3bdy/zm2xcCEI1Gue/2HT3C3A+bk121tfznadV4POl9zPX1DVz9nZu44cNmwqaDMvcLnLt4Drf/\n9PvY+pm7lmVx/K039gqzaougPZHLuhdXcdNVgyftSCRUjfXWVtW5EUJd3/JyxiUNaeaUMfrtFUNJ\nEWzdCt2dUOSHwsLhd9sfVl7xOQ6ZUcGf/v40Da0BKkry+MKFZ3LqJw+sdJvLpWJiQiGorBw+Er++\nuSXtvOQATR3d43KfG1VxPu2003j11VdZsWIFADfddNOw+7S0dI9mEyYUJSW+SXV+zc0q2KKoSJJM\nSmBszm8sLOdkEjZtEiQTkunVkpgJTW2Z960oyaWhpc8TtD+W8wknLiL3oVcJMbA6gpSSWdOn8OGu\nTsIJZaX+9Kc38vi//sW2HXV4PTmcd965lJVP4YWNTUO+b8pyDnULWvbYMJMq0jq/0CLPb7GhIQkN\n6fe9dOE0fvtiTdp1I7Gch2Koimd12zfy5vYucA6+0b28vo5r73mRvIJimutq2NYYQbgG3yxr25J8\n+84nmDb7iEHr7A6Du39+E9taDYTIRdigOe7k7udq2NT0PfwFfmprdyMMA3+ujXd3hcExuPP16gf1\n3PbPN8kr6CtCnevqX8QEQgFBR6uNRFzgcxkUl5vkF6T/DoyF5XxYVT41e4b+7TkyVBYDsGeoApZa\nV1Cs4jLWvQeHzFazr0HmCmLGMCqYbvWxnziOYz9x3KDqYQd+bxHU1QksS1JSktmj5vfkIq0kwhj8\nefhzXaN+nxuJ2I+qOAshuOGGG0bzkJoJRFubwDDU9G3Zxp49qpTklCnpSxaOFYccMpvPnT6fPz3z\nHgnRU8faMvlYmeSqKy4fsK3d4eDTn/nMkMdqamzgf//6d2rqmslx2Dj6iFmc9umL6Opw0tlqAwEF\nJSb+IqsvHSxzdc+DimkmGar2oyUFlqU6BN78QhwiTrruQY6RxF9UmvYYO7d8SG1zBGEb2BEShp3X\nX3+ThGcqhk2JrBXcg3D60rZGkrlQihDgzZfk5iUJdhlEOw2a99gIdUvKKsxJk4aVmwvV09UwUH2d\nYPah2fW7r6hQY88tLYLi4syZGJd89jP8+fGX2dY18MNzEmP5qaeMcUvToweENSMiGIR4XBXRz7Zg\nmFAI2tuUq2s/Jl06YL7xf77KrddczLkfL+O0jxXyX+fN53e3/wS/v2DEx2hqbOD//eBnPP7mHjbs\nMVm3K849j3/IT79/Dx2tBnanpHJGgsISa1TytC3TJBGPHfiB+lE163BK84ZoXLSd11c/SzIRx2Z3\nYoXbBgmklBK3DJBXmP5DbNhVMyDwrj9x6RggxCK3DBlKU3QbmD7FT/4Q79EfIcDnt5g2K4nbIwkF\nBTu32wl1T55qJr48yPermgataQK3JjJ2uwpYTSSgoyPztm63m5//90o+XiGxmyFkMkZVboSvX3As\nF3569AsBjYRJ0sfTjDXt7eqGU1SUXb1nKVWBBYCplWOXxzwci5csYfGS/R9He/Cvf2dXd9/AsTSd\niHgJ79UkWFjzDiedeeSodJrCwQD/+PO9bN1eRyxhUlacz6KTl3DUsYsO+NiGzcaJi0/kyWfXEBN9\nImqFmrBMg1dff5P1775DSbGfhKcC0bEdPCUIVz4yFkCGmnGUDD3f4cw5H8O16g1itsEuQ2El6F/K\nTAgD6fRgRFuxXOqYUkoKHGHOOufCfTovhwMqq0062gzamgwadtsoKLIoLptIk2fuP1OnSrq71ZBW\nfv74lfncH0pKJG1tgpYWg8LCzJ/HMUcfxaN//CXvrFtHa1sHi09cOGRsw8FAi7NmWEwTuroETidZ\nV1i+tVXlNBcUqrZnGDae0Gzf1dj7Wia9yGgeJKNIV4RdDa9jsx15wO8hpeSeX/6CzS0GQuSBATva\nofHhZ3E6nMydf+wBv8f8E5biLyrhH/fdQ2dEgrSQponhzsfwFBMCgt0WIrIL4S0HM4HVtQvh9GIU\nHoI0hh77K6usZvb0QtbvjiFEn4UuE2Ew7IMi4Y3cMuaUW+QXFhEOhSnw5/HJT51J2dT9q2pYUGTh\nybXYs9tOR5tBIiEoq9j3cYVIJMzTTz5F0jI5b9lZ+MYyn2kEOBzKRVy3W43hzpo1rs3ZJ5xOyM+X\ndHYKAgGGrX4mhOCYBQsOTuOGQYuzZlg6OtScxtmW05xIqPKihk3dXLIZp8OGlCYy7kd2dIMtgfB0\nI2PNfPiuCzOZxHaAZdrWv/EqWxvjCLt7wPIIHp5+7B+seeklWlo7cbmczJ5VzamfXoFtPwZYp8+e\nhyuvGMPpRlpJ6N6D8PRZxEIYCH81VucODP8MhLvP/V9eOthy3r7xPV576QVa2jpx2gRlRoAcj5/G\nzhiFPif+IhubmssG7SeSEY5bfDpHHrcYt3N0xmpyXFA1I8me3TaCAUEyYcM7mxFX0Hv00ce496Fn\nqA/lgBD86eEXuOTsxXzxPw6sCM2BUlQEnR0Q6ILOzpFlOkwUSkuVODc3q9SqbEGLs2ZYUi7t0RTn\nTBHZw01alClYp/+6+nqBmZRMrVTj5FL2zdmcjmS6POd+y5IZ5mTONLcu0BuRnY6uYSKjO8JJZs2Y\nybtbOpGBdkReIcLVjjCcQCW14SR3/up2Lv7yykH7BkPp86NTtLeHe19v2rAZuZcwA1jhFurCAhE1\nAR8EoX7dbpobf8myi64YfNDE0GPVlgVWQmJYLmTSg9XdjMg9DJk06AnFAqGepeXGMu0Iw0QISR4B\n5i84l85+U4XtrtnEv556hrDwAV5IgLRcnD3Dx7nHLsPj84OUmPffxdbmGMKufLLCjPKxGX6mzjya\n9tYgLk/mqYyiuUNbwPHk4O9yTjF077HT2GYQi9uomJbEmcYdbPW73Nu3bOb2+5+m28rtrTXdHMvl\nN/94leoZ01l4wokD9s00D7ghMgceZBreETL9yimVks2bBLvrhKo/nqY/MxEnD3G7wedTrvlQ6OBP\n7rG/aHHWZCQSUQ+fb/DkBxOZYLfq6bvdqtefzSTisODYS1n/zt1sjkQR7haE6OsoCMPO+o21RMNB\nXJ79H3fw5eUjrd2D00niIYS/esAiYdjZ1tBFc0MtpRUD1wFICyJhO4mYjWTCwDIFpmmojpdlUZp/\nJA3t7ZC0IF5Euig2J4JiWwGJpIU/z8GRC47C460kHLRwuZMYNnj7zdd6hLl/22w8t76N86bVU52v\nPvzzPv8VNr/7Ojt27EAIwexDj2HughNGpdpYe/MeouEw5dNm9BbOEAJKKpI4nDaSQTt1O+yUV5l4\ncofu4D3x5LN0W4OVI4qbp1etGSTOB5ucHCgvlzQ3CRoaRFZNdlNaqsS5uVnNvpUNaHHWZCQQGH2r\n+WDQ0jL+QWCjRcseO0jBuRcu5tbfbUSIwT/bjrBFW9Meps7Y95KHKY5ZdCpvrH2T1sTICi4kbD52\nbF4/QJylBeGAg1DAidl/ykmbxO6wMGwWNmFy3MnHEIk/xPY9ARKxRoRvKiBACvWMoLLYwelnnUUy\naWAmDExTEAqocw+Qg9Nt0tqeAAb3GuPCzc6arVQfpsbiDcPGUQuXctTC/bw4adi9fQuPPfQQtQ0B\nkhZUlbg59dQlLDr1jN5t/MUmtvwkzQ12mupsTJ+dHDKaPhge2uMQCKer7XrwKSlVru32NlV8JVs6\n7F6v6qgHAgLTzI6MEy3OmoxEeqo7jmPQ4n4RCoEzh6xxYQ1FNALRsMCdKymdWk5+jiSQpp+U7zYo\nLD2wmavsDifnnH8BTz32CI3dBtLmxCO7sZw20smGTMbw+lSwkpQQ6bYT7HJixhIIAbl5cdy5SewO\na2AHyVIu4uUrzqOxbgevPP84u7vqsXL8PceS+EUXJ51yLvlFfe9sWZC0ckjEbERCdmIRG7ZkFdJM\ngKN9gDdBWiZu92AX/WgRi4S57557aYl5waGuwe4A/O2RF/AXFDDvmL7gOV++JB4z6Wi10d1pkD9E\n1HDllCLku80DgtlAXY+qspGn3Y0lQoC/QNK4RxAKZdfYs9criUQE0Wh23Bd0nrMmI5GIKjzizDwk\nN6GIRlWEebZ1KNLR0aa6+PmFJt48P0fNrULKgTd3aZkccVgV7twDLzFYPfsIrvrG97hg2SLOOH42\nX/7KVzjyqI8hrcFjriWuGHOOPoFwwE5LvZuu9hwsS4ly6dQgeQVxHE4ro+eivHIGF/7Hf3H+sqUc\nUW5nZgF8fHouK1ZcTGnF9AHbGgY4cyxy8xIUT4lQVB6hsrIIGXdBdCoy2SfGs/wJjl44srKi+8Mr\nzzxBc2Sw+EekmzUvvTJoeX6Bug6d7caQMRUXXHghM/2DYwSqvFEuXnHBAbd5tEgJWyiYXS6pVApY\nNJod7daWs2ZITFMVHvH5ssulHQyqZ683u9q9N4k4BAMCZ47E03MuX1y5EnnHHby7aTfdMQNfjmTe\n3Kl87ktfHrX3NQyDQ488rvf/pWd/lkDn79jeGCRp8yLNOMXOCJ887Rw6W73EozaEkOTmJcjNS2CT\nmYPQ0jF91uFMn3U4Q1UQ25tIKIBlJll67scJ/e0xaursmLIUKxGgwL2LW7/3Ff7dNHaWc3tHJ8JI\n7xvtCAye6tDugDy/RVeHQahb9M4p3R+P18sPr/smf/jj/WzYWodlSebNruKLl36J8ikVo34O+4vH\noyzofZzRcdzJyZGA6J30ZaKjxVkzJCmX9hh6B8eEYE+FpmzLyd6blJXV3w3qzHHxlW98k2BXB/W7\navGVVuLNG1vfos3u4PzLv0rdjk3s3LoJry+PGYedSKAjl3jUwOVJklcYx2bvEZxh5oI+EBrraljz\n4ioa2rqxJJT53Rx73Al84sQCNq9vxm6r5NCPXcJxxyzg30++MWbtKPDnIa3GtALtz0vvM/UXmXR1\nGHS22fDmpY/Qr6is4v99/9rerIM858Qb1DUMJdChkOrAZ8P4LfRN/hKdGMP3w6LFWTMk4Z45gN3u\ng2uBDvdumVKtpFSWs8OZfqagzPsOXtl/WaYJN9KlYfUn06QZ0eTgdaYJLa0GwrBweJLsNScADk8+\n1XOOoiscJ5phEoroMGlasWh6MyIeGXwHKy2vprS8mkjIRmedRMowvvwYXm8c4qgHQGKYu18aF3kv\nGXzgkXCQx//5MJ0UgkONwdaH4ZnnX+D8M09l6VlHEe520N2ZZOdOaN5hUlAcxbCpzyYmh+6tiQyT\nOQDYbQNHAI87+VOsfeNdWuMDhxJcIsKxJ55ONNF3jtFEj3oJsLuTBLoNOrskLo8k7sicgpfM8IXN\nlL03zNcxc7risLmMkOuBUBDCQYmvX2GP4XbNFB3v3Guik73/j0f33SPTH7tdPWIxwfB3mfFHjzlr\nhiTckwKbTZZzJKKEzZc9M1mmJdBpYFkCf2HmMduDiZTQ3eGks0WZIAXFEbz5B3bD3Bfeeet1OuRg\nL0HYyOfVV1ax/q2XicV2UzwlRH4+xKN22pvdA6LGR4scdy4XXXIJMwpMbIkuiAeo8Eb5zNmLOWLB\n0JXU/D1ekM727L715vYMs4RCE+TLOUJcLkk8nh2VArXlrBmSVDBYNtXSDfZUd8zm8WYpoavdUIU3\nCiy6J4AbTkroaHYRi9iwOyQFRSHsw1h9o01XKDI4kjkZRQbqqYkWsv3NHeSsXc/Mch8/vPIEcn1x\nQt1O2hs9FJaHR90SmXbIHK6+5lrCXY3EIhGmzjgEYxgfr8sjcbok4W6DRNyELA1a7A0Ky7pxZ+VZ\ni0YnfsCoFmfNkCQSfeM02UI0lnLFj3NDDoBkApIJQa7PmjDjecmEQSxiw7BJiqaEMeIH3/TIdTmR\nMjbANSoD9YiCmSAEAogb+WxsNrnmupvJm3EiyaRBLKLSrhxjFINQOnXaPm3v9Vm0R23EsiRqOB02\nmwpyix08x8mokMrLTmYe7ZkQZLdvRTOm2GzKRZxNpOJnkmMYlDTW2B0ghCQemzg3b4fTIsdtYpmC\nWHh8+vQLFhyH1+qb+09GuxDugkHjmMKw8cy/N5KIJYnHVIfC7Zk4d+N4XLXXmZO93h0AMwmOLDPv\nUu7s0ZhWdazJgiZqxguHIzt6mP1J3fCyrUffHyHA5ZYk4mJCdY7yCmMIQ407j8eYnS+/gNOXnECp\nvQviQaxIOzjTBxe0BuK0t1hIS+DNizFMqemDSjTcUzsgi4aL9iaRUEMdjiyqfwB997MDnCPmoJAF\nTdSMF3a7qqiTTekSKcs5niURmUPhcksiYYhFxEhTf8ccu0PizY/T3eGku9NFfuHBHwyfdegRzDxk\nLnW7ttHd2cbqNz8kyuDqWdNLCzCTfhwOC49v4rhRzKQasnBnqLGdDcR7Or/ZUr4zhRZnzaQg9cNL\nJLJInHuskfjEuR8PYtfOWl568WVcrhzOWrYMbIMH9nN60teiEYExgQJXcvMSRIJ2wkEH7twEzpyD\nb9oLw6Cq+lAAdtbV8UFTcsBkHcKMcsZxy2lK2PD6IxMm2h3oHWd2ebIgXDgDKZFzOLKrk5HyRGlx\n1mQ14xU8Mey9NMMGDodyC8f3pwpQuuOKzKtTDJMmiyEEUkpu+/kveebfWwnJXEDy0OOvcPGFZ7H0\njDMGbO/NBZuAZMzA7Rv64HbbvuXn7s1Qc0Ab9qFNIn+pResuJ4GAnaLy8L6LX8Y852H2tQ30o55+\n7ufIee4xanbvIRyHPI+DWbOO5oJzP8vvn30Ht98GqJ6l3T50D9O217pQsIsX/vUP6hqakFJSPW0K\npy+/gPzCwVOc2YcZwLT3+3IkogY2Q5DrUcttw3xxMh05067DXcaM64f7QIVQnV8hVGd4lDo/A/KY\nfTkHnNecjmRSZI2hocVZMySp+3ZiAluheyOEGgeLT8Ax54cf+juPvLoDbN6e+5+gOeblj399giPn\nH0Vxv4kr7A71iEYEEy3wPMdt4c61iIQchLsd5OaN3Rekftd23nzzDZo7AjhsBpXlJZx06jk4Xeqq\n2Gx2ln7qfE42TeJSIvDS0ZKL0ynwF++b272zrYl/v/Asga4AO7ZtIeSahhDKFbNnYzu7dt3Gymu+\ngzt3/8O+YxEltzkHubDPaJPIYrd2NljNoAPCNBlIuawSiQnkFxwBOU71I5xIhQa2bd3C7+7937Qu\n7M6kl6f+9cSg5W6PxEzupxdgjMkriGEYkmCXk0jIjhyDa91Yv5N/PbuabZ12AqKQNsvPu/UxHnno\nT8i9PlwhbEjLT1ebGgOYOROGKH2dli0fvM3v77yL1z5sZv2GrYRyKgdEgQshqA+5eenpf+73+ViW\n6mw5nNkxZWEm4j33hGyaEEdK5da227OjY6TFWTMkqeIj2VZoIJWb3dk5vu1IIaXkttt/TyiZvssu\nhCCSxoXn8VpEImEevX81Tzz0Nzpam8e6qSPGsIGvIIZlCTpbXTTVeWlvchMKOEjER+e28vbbawmK\ngRXBhDDY3e1g8wdvIS2Ihu10tLpoqvfS2ZqDaQp8/vg+1VWXUvLCM8/QLX29gpyuZrYQBnv2tOzX\nuUgJTfU2pFSfazosy+LVF1fz6EMP0tzYsF/vczAwTejuBps9e6xQ6Kt4mC0diiy6tJqDjculinl0\ndwuSSZk1P8TiEklrq6C5WVBYOP695PXvv8uGujBDmpdmjEMOqR60eM1Lj/LX/11PR6QYbFGeXPUT\nli4+ivMv/Y+xbfAI8XiTOJxhomE7sbCdWNRGLGoDU2AYkhyXidOVxJljYrNZ+5zO1N4VApTKSinA\ncmgF7fMAACAASURBVIJ0glVEzRYTf4FXLQfsdguXP4E7N4F9H4OUGndto6EjAc6eXl2GAtFO577/\nCKSE5gYb4aCBO9eiqLTvexCNhPnTH+5l7bqNNDa1Ek9Y4Cnhz4+uYcmCmfz3d76JMcGScltbVNhA\n+RQ5oYLthqOrSzXW7x//e8JIyJLbrWa88Psle/YIAgEoLBzv1owMpxP8BdDRDl1dkJ8/vu1pbGwi\ngRPhLsLqrsfwTe1dJ6VkbpnkpFNPH7BP7fat/PkfqwkKL8IeA9NDd7yaJ1/awLTpL/KJxScf5LPo\no6utie3r36SguIxps47A57fw+ePs2raFd9/+kFDIwOXI59BDj6SwpG8c3TAkNrvEJpIYNgub3cJm\nkyrhzRJIVPKblAJpCWyyFBnL7RHlvluVlBaG4cZuV4VRXJ4EDqfVJ677iGUl6R/VJJy5yFgXImfg\nF8cwwxw5f9E+H7+l0UYwYOByS8orzV5BsyyLH9zwI97ZbSGEF7xeDMDq2kVAFPHEG/VU3fdnLr98\nYnTGQFnNzS0Cmx1KSsa7NSNHSujoUPnl2VJ3X4uzJiN5eSlxnhhW6EgpKZF0tAtamgX5+ePb7uOP\nX0jJ7x+lNeEDLKzOWhAGSEmBy+T6/7kb216DkM8+9RwhqQLHpLMFYuWQ9JJgCm+sfWtcxLmtaTdP\n/u1umrsTJDyV2KwtTMl9idPOPJfG+l28uHYdMaPnzhfvpOHNTZx8/BIqpx2BmTQwTUEyYZAwM9x2\n+lli5UWzqe9oBpsBRhSMOBhxvLKJxaetINcXHpXzmjL9UMryDZp6pkgVnmKsrp3IZAzhUQrkkkEW\nHjObj31i38S5vcmGjBrkuCTlVckBlaleXb2Kd3fGELaB1UiM/GlYnbUIfzVr3vyQyy8/kLMbXVqa\nBZYJUypkVlTZShEKqTiUwsLssfa1OGsy4nIpS7S7W6UCZcsX2+2GvDwIBNTUdgcQYHvA5OXnc9qJ\n83jwhc1YOfm9FplbRLj686fjSdO4cL8xaCEkMqcZomWQzKOrY3AUcqCjjReffoJAIITf7+XkM8/p\nnefZsixeW/U4W7duxzQtppQVc9KZy0fcfjOZ5Mm/38vm2kbMnCngCEJnLZa3nIaYl6efeISEBTFj\noKUZsbt578OXOOLoWQOWWwkL0xSYpoGVNECo75UQEgz1LAQsKjuMhNzA5voWYrZ8kCb5IsCSExeS\n6xs9d4hh2Fi0ZAlPPvMikR43upE/HVe8hZnlUFw+lYUnnUTp1On7dNyOVhuBThuFeZIpVclBQWBb\ntm5H2oYoE9YzBtAVHJ0OyGiQTEJLi4rQLi4e79bsGx0d6sZVUJA9BoYWZ82w5OWpMdxgcPRcQpnm\ndZXDVPYSGVb3P25pmepUtLQKvD61U6bevi1Nwmb/PFSZIcLWmWkl8PX/s5Lykr+x+rV1dATCVJT4\nOfeM0znt9NMJJQYnkh9aPYXn1+3pLa4hhIl0NSGjpRTnVZHoclJSrqaT3PDu29x99wO0xnMRQiBl\nK+vW3cxVX7mc8urD+MMvb+Gtbd0Im8p72dbcRG3tr1h52mzy/ekTtaKuvhyZJ/72RzY0xBCuYnWF\ncnyIHB9W+3YomMme9iAix49IE2jT3BUnLsBX0OcDlRlDuwd+Budc9v/Ze+/4yK767v997p3eNOp1\ntdpd77obV2wMxjZuj3HBNs2Y0HkwJCEJSUjgFwI81JA8kADhBwRIgAAGx5hmMGCK12Aw67Lu7HqL\nVr3MSNP73HueP86M6mgk7UqrGe19v17zkqafafdzvv12Lp4YZt8Tj+B0OTn74pfgcFZes31Bo2d/\n43wBdziXPtxdcvXV9Pb18Lvd9xNPZAgGvLzwilfSs20nAF7X0jVDAdfix41OaZgpnUa/5NSTwVah\nCXWDx1Ha8Fb4LZTi3ls7m3EtUZ9drcZ92frpKr+/pe46FRIgob196Wzzar9r2Jhmd1KqeLPNNjtN\nqx6wxNliWRoalDjH4wK/v352nj6fGgsXj6kRcRs5YUsIwW23vYbbbnvNim5/88tv5le/eZj9U/ps\nBrEw6Awe4eprX0t0WkNKcAQld935PaYKvhmvhhAakzkvd337Li6/6gr2Howg9FlBE0IwlHDxic9+\nhd4X3Vx1HaZp8tzBAYS22LoX3jbITCN0F2IJwRVCounHdphpbu/hhVf3AKAt01TlWNi66zS27jrt\nmB8nFtGYmtSx2SRdW4sVhRng2uuv5We//Rfi5vz3VhZzoOn4tAwvv/7GY17PWlAsQjisau+bF/dh\nqWkSCRUrb2mpH88fWKVUFivA61UWZywmqiWy1iRt7WrBExN19KsEnC43H/vwe7moT8OZHkLEj+DN\n9HPGrhZOPcuH06lE4MmHhjg0mqn4GAeHozz20O8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Rd/zgZyTNxYmA00UPX7/zR3z8HzdG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nwpV/imzXt4a1E1N195ad+LLAtXRztISaSkJGW1W5y4eDGlxSW8u/U9SmfOYPt77yHCMar/tpEP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\nAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1498,12 +1687,15 @@ " \n", "ax.set(xlim=xlim, ylim=ylim)\n", "\n", - "fig.savefig('fig/05.05-gaussian-NB.png')" + "fig.savefig('figures/05.05-gaussian-NB.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Linear Regression\n", "\n", @@ -1516,14 +1708,16 @@ "cell_type": "code", "execution_count": 31, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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KvLzxGA6XT+uQYsLpCxa+OHKRfrkp3DEir1s/2+fz0thYj9ncRCAQ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\nrm0QwiKjyxaJO6+GQimFoihot0dNgElZlpg5vlwbFKVsg223O6jVxo9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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1585,13 +1779,15 @@ "ax.set_xlim(0, 10)\n", "ax.set_ylim(yfit.min(), 1.5)\n", "\n", - "fig.savefig('fig/05.06-gaussian-basis.png')" + "fig.savefig('figures/05.06-gaussian-basis.png')" ] }, { "cell_type": "markdown", "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "source": [ "## Random Forests" @@ -1599,7 +1795,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Helper Code\n", "\n", @@ -1610,7 +1809,9 @@ "cell_type": "code", "execution_count": 32, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -1710,7 +1911,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Decision Tree Example" ] @@ -1719,14 +1923,16 @@ "cell_type": "code", "execution_count": 33, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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oUWG4RCJh27dvZzzPMwsLC3b9+nW5ZYhEItanTx+Za11MTAzr1asX43merVq1Si6G+qRB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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1769,12 +1975,15 @@ "ax.plot([0.8, 0.88, 1.0], [0.0, 0.3, 0.0], '--k')\n", "ax.axis([0, 1, 0, 1])\n", "\n", - "fig.savefig('fig/05.08-decision-tree.png')" + "fig.savefig('figures/05.08-decision-tree.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Decision Tree Levels" ] @@ -1783,14 +1992,16 @@ "cell_type": "code", "execution_count": 34, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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AsUahy7F4lrOxUWAnXev3eYShZ9gkclKOfspra252ve19ZlEbHx/YRUTUhEHN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\nNzE1JBv/UXcsZR5g4MTZDhLWvMLR00b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9nCr3oaHZg/VLmwnPFLHOkXnpVSNPrlITGKCi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8LK7JXIn5XTb9CvN4unM5DzP+IS7V5lBHIZOJ1XRrXf17f1FrtRUanU1v6V9774DrnUglw1hP79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fSBfyO8/uFWnPY8pD8HVewZbDl6gon5Rbxx8AiaxKyY/SWtCVGti0nxBVCY4ujt7SYlOY0+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\npEfz+akqiErD4PTf5KwoC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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1814,12 +2025,15 @@ " visualize_tree(model, X, y, ax=axi)\n", " axi.set_title('depth = {0}'.format(depth))\n", "\n", - "fig.savefig('fig/05.08-decision-tree-levels.png')" + "fig.savefig('figures/05.08-decision-tree-levels.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Decision Tree Overfitting" ] @@ -1828,14 +2042,16 @@ "cell_type": "code", "execution_count": 35, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { - "image/png": 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KLGazhLcPJ2Hl1m/JnIyI6OkNd2/BkQ/jQGnhUWzP0ve/9vUWEeBSCF23ftxOCyAiIhqr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\n/vwHMCjhMA4fPQ2NRsScxx5DA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j1VdgMZslvH0kCau2fUfmZERET+9x9xYc+TAOlBUdw45Mff9rX28RAS5F0HXrx+20ACIi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\nbqSlpSI+2ooHn30Ek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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1850,19 +2066,25 @@ "visualize_tree(model, X[::2], y[::2], boundaries=False, ax=ax[0])\n", "visualize_tree(model, X[1::2], y[1::2], boundaries=False, ax=ax[1])\n", "\n", - "fig.savefig('fig/05.08-decision-tree-overfitting.png')" + "fig.savefig('figures/05.08-decision-tree-overfitting.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Principal Component Analysis" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Principal Components Rotation" ] @@ -1871,7 +2093,9 @@ "cell_type": "code", "execution_count": 36, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -1882,7 +2106,9 @@ "cell_type": "code", "execution_count": 37, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -1898,14 +2124,16 @@ "cell_type": "code", "execution_count": 38, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { - "image/png": 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AuHDhAh588EEsW7YMd9xxh/v+hIQEtLS0uG+bTCYkJfX9nzQ9PbHP51Dv2If+Yx8GBvvR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\noCcuzqOWFvmuFpSQ4JVk04QJ2ZKklpbebdOz7fbsKVdm5ll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xEQVCuBWMZJ2IwHL9XsxmFQQhHpcu1SI9PYn9TNQGAxtEREQBcv78OWzYsB46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\nNmAZ8c5GJyrD3NeuHwcOtMRc+dC9yiGv23Nd701tbZMikXx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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1936,14 +2164,18 @@ "draw_vector([0, 0], [3, 0], ax=ax[1])\n", "ax[1].axis('equal')\n", "ax[1].set(xlabel='component 1', ylabel='component 2',\n", - " title='principal components')\n", + " title='principal components',\n", + " xlim=(-5, 5), ylim=(-3, 3.1))\n", "\n", - "fig.savefig('fig/05.09-PCA-rotation.png')" + "fig.savefig('figures/05.09-PCA-rotation.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Digits Pixel Components" ] @@ -1952,7 +2184,9 @@ "cell_type": "code", "execution_count": 39, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -2004,14 +2238,16 @@ "cell_type": "code", "execution_count": 40, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2027,12 +2263,15 @@ "fig = plot_pca_components(digits.data[10],\n", " show_mean=False)\n", "\n", - "fig.savefig('fig/05.09-digits-pixel-components.png')" + "fig.savefig('figures/05.09-digits-pixel-components.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Digits PCA Components" ] @@ -2041,14 +2280,16 @@ "cell_type": "code", "execution_count": 41, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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89thjAIDXX38d/fr1g7+/v+b7nd3n3MVV+cjNzcXzzz+P+Ph4VKtWDb169UJU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\nOrVm8k5PT8f06dPtPicRcUB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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2062,19 +2303,25 @@ "fig = plot_pca_components(digits.data[10], Xproj[10],\n", " pca.mean_, pca.components_)\n", "\n", - "fig.savefig('fig/05.09-digits-pca-components.png')" + "fig.savefig('figures/05.09-digits-pca-components.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Manifold Learning" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### LLE vs MDS Linkages" ] @@ -2083,7 +2330,9 @@ "cell_type": "code", "execution_count": 42, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -2113,7 +2362,9 @@ "cell_type": "code", "execution_count": 43, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -2133,14 +2384,16 @@ "cell_type": "code", "execution_count": 44, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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p527nPX1+6V/2VnjM9Caw2WztvgOampqyvxCKyL5P+act5Z/2lH9kT1P+ka5S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iFr88UXsZaW6Lsul5eX6R88iHT2LHsyGdbPnGFPGNKs10nU69TOniX8hV9AH2fgvKtwy6Fj\nlOf+bzqdDncbBl/7o/+Lgpbi3EaDOxameHmlQqPv0+pGarq2HVKcSDExMUEikeDw4cOUSqV3+mnc\ncHi3vn+O8cYxnvxvUlwr/FEoHt4uvB2PdXVY8s7H3EkOXIsoCIKAl77yFZTnnuMvKhUs02SYTLLo\nOBSGQ54A7gKOEVnQAiKi5wARkXSCaLVtg2iIKgN/QSTz9oAPAOeIhqssEYn0iq4jGwb2YIDjeRwh\nGtKqwC5J4qSqMuG67NqxnQeDgKDZJEil4jBmx3HiwdiyLDIjRY4IgxbSa2Epu+z7zA0GHPF9CqPH\nuwV4CPh7IvLKAj4CpIkGxcc0DbVYjMkMz7Y55nmYo+DpWySJNVVFTyRQXRcdSKsqc0FAMgxJdLtI\n+TwvGAb1kU1MZPB0u93YniaGWpH7k0ql4qHXMIz4GHe73fj47iSNhPXMtu0rgqzhVfJEhGCLNjJx\nrlzrvPhhK7eKosSKH9EsJ84jcTxEq1qr1YqzmMQ2J5NJVFVFkiQ6nU6kdtO0WK0k9rOmaWxsbNDr\n9WJbmmhXSyaTTExMxDYLz/PodDqx5S2ZTMbboqpq3JYnAhz7IxLPNE2Ko+F4qxPQtX3qXYeXLtY4\ns9bkhYsB/+fn78LUFX7/786hH/p5JicnkWWZycnJN/3h683iZho6xiqtMca4vhjPPz96/gE48dd/\njfzMM3xhe5td8/NcXl5mkojEgVc/IPSI5heZiBQSC2Y+EXEEEdHkA87oqz66LUCBaFbqahpeLkdY\nqeASzVQGMAsc1DQGySTVWo0wCFgCMr6P3uvx/NNPM1ku47puvOAnFMmqqiK//HJ8fdZ1HV3XURQF\n0zQj25mu49s2xUaDYaNBOwzRTpzgqeVlUkePIgUBpWKR+ySJYjJJz/MY3Hkn07feiuM4dDodGrUa\n8smT+IqC57qozSbnl5YIm01W6nU2fZ8t08Tu97l9926ynQ7PLS8z/4lPMH/8+Js6vmO89RAzci6X\nwzRNrHwZk2VKhQwD26PnhrQ7r567lgu3P/CzDAYDjh07xoEDB952i9p4/hnj3YQxcXSD4UfJkYMg\niOvQ4crwxx9WMf5uwut9U7m6She4ZsilUKaIpi1xX4BLTz7J0a9/nUlJIshmecR1mbrrLgaNBj84\ncYL7fZ8fABWi5rQe0cB0mEjOrQIXiYaeh0c/Ozn6PmsY3Oa63BcEbBGRS19TFB7P5yl0u/xAkmjK\nMvcHAb4k0VEUuqrKiq4zBFZdlwlgZfS4qmkim2acHdTtdmm32/Hxbjab8UqcyHIQx1uWZZYkCScM\nSQcBDtFQpwKLRIRRcvS1PdpvaWDBdXl6JM9WVRVDlglkGWe0j5c8j163S6Cq6JJEYzCgDZRlGYIA\n1fO4rdtFMwye9n2ao8p7Qbg0m83YqjYcDikUCqRSKZLJZGyT832fcNQOJ1rEdpJDpmliWRZhGF6z\njU0obXaGoYtzQFTei78bhmGs1BLnyE51UiqVilvFarVanDck1EKDwYBqtcpwOIzVQdlsNm5mazQa\nca6Sruvk8/lYZaQoCoqiUKvVaDabJBIJUqkU3W6XMAyZnp6+wqIn7HWCbBOqJdu2GQwGseJJ5F/p\nuh6Hl9dqNVzXjRtC1nopfv3fPcMn7priU/fMcW6jzdxEksdPb3N0b5Ff/8Qx/uRkDV3XSaVSTE5O\nvuZr83piPHSMMcZ7F+P5J8JbMf+c/t73OPLQQ+QliSldp5tKEc7O8ujly0BE9hhEAdg2r6qLJnj1\ng4PLq2rsBDBIpynmcqSSSdqnT1Mf3W8BGJomk7fcgt/v03VdnGaTBJFKqSRJ5HfvJnfrrYRbW+Sf\nfZYhMGFZTORydA8fZmr37ti2rShKvEDS7/dj1a3ruvT7/TgPUeT+DYdDasvLKJubuL0euqridTo0\n19cZnj4dqXIHA/4N0SLhR44dQ37sMWaOH2dycpJ8Po9v26R6PZKJBIHn4WazNNptsrkcW9Uqrizz\n5KlTTCUSrK6vk1cUCoMB7hNPsBKGzL///dc8zlcf8/E17vpiZzSDLMt88Oc+z7//V6dptVe5e98U\nz56vYZk2F7ej2//iA7dyYek09z7wMe644w5SqdRr/PXri/G5Mca7AWPi6CaBCNjt9XqEYfhDwx/f\nrHf+x922t/INT9ieXNeNVR2iSeqHYWewpvjqLC2RtW3aly6h2TZ7ZJlvPPAA/8R1KeVyPF2vsxiG\n9CEOhpSBJ4nCrreISCSIZNoakR0NoGXb/C4RsVQAHlcUHldVPtFo8P5R29njus5DisLhMCSlKKiy\nTBW4pKr8mSxzu++jhCF/r6rYioIxGopFKLMYoMQKnKicF0qanStwQRCwKcuclmUO+T5aGNIEyiNl\nkkdEgJlAjYg4EpoS0ZKm6zprvs+BEVmy7rqcmZhAU1VC2+Zotcr5Xo+pEXF0OQxRbJtA05iSZZZk\nGd/zmE6laOo6suMwNRzSBZZ5tS2tXq+ztbUVt7V5noccBJTCENlxWIf4/Ba5QkK1JBQ9YjgQ54th\nGPFXQbCIcOpEIoE9krgPh8P4Q8e1FEkikyiZTNJqteJjILZHEEqCDNra2iKdTmPbNs1mE1VV4zay\nXC5HOp2OCSdBBjF6frIskxqpzNrtNqZpout6TBjquk4ul7si90iEYLuui6Io5PN5ANrtiBL0fZ9c\nLhcHh7uuS6vVomeZfOS2Mn///GVkSeIn7pghCEK+9vRlfu7+HNqo1W5+fn4cCHkdcDOtKI4xxtuN\n8fzzxucfe2mJrOty4aWX+E63iyVJVBcX2dfrUW02MYgU1gKCouoRzUEQKalloATMJJP4CwuUFxbY\n2tqiNTlJvlJhRtfJLyyQ2L+f5okTzKkqbi7HYHYWQ9e5VdM4NjNDxjCo3HUXyuwsL/zu77Kr1WJf\nOk3lttu4+1d+BWe08CRII6GoFuQQRGoSoTDeSRq1Wi0GgwFb3/sexqVL+EDdcagNh/R1HV9R2N7c\npOJ5DIBnzp+nCyRWVuLG0nQ6jTkcsjuRIJdMEqoq6v79NJNJwnIZ+exZhhMT1Ot1OvU6S/k84Zkz\nGK5LYmWFo70e01NTmP0+smkS9vtojQZeMknh9tuvGdQujlW/3WbrxAm8IGDh3nvjgO6dt7n6+9f6\n3eu9j3i93CzXJ7GwChFxJBRss7vm+extAb/95ScI/IBiMsFFBphA3/OBkCNHjjA/P/+Obv/Nipvl\n/HqvYEwc3YC4+kW2c7UFoiBj0zRvaHb6Wm8kQlXS7/cJwxBN00gmk/GK0xuFtW8faysrHLBtQuBc\nEDBvWfztRz6C8cIL7A5D5okGo8eIBqcDwIIk8d0w5CHgFFFmkQX8R6Kg6weJgiK/qih8OZ2OPuj7\nPqUg4H0AsowsSXxQkvh3kkSgKGRlmdPAhqIgBwF/p+uckGV8oJVIMDMiIjzPwzRN0ul0fMwty4oH\nKrGyKGTa4twQipRzts1DjQa3hSF9VaXX65HLZKhWKmwAhixzuywj+T6DMKQCnPP9qNUkDDmXSLBt\n2ySBhmWRUBQCRaGk6xQtC1fXOdfrcXsQsFdRqPk+R3s9TmgaeB4fAnYNh6TDkC7REBoClqrySq3G\noN1mSpJIhiHOSEljahof6nQ4TGSpewz43khBI4glEYbted41B2ix2izsW0JlJJrZxErl1a8ZEYyZ\nTCaxLItsNhvnCuVyOWq1GpVKBcdx4r8NEVFjWRaDwYB+v082myWbzSJJUqw0cl2XarUaE0ciu0io\nkgRxJstyvB1bW1uYpolhGPEALeT62Ww2qjoeZURBZOkzTRPP88hms7GiC+Dll1+mXq9HJKSv8eKl\nGqWsyWfu38Mrqy02GwMmMjr/8ssnuO8X/3v27NkTW97GGGOMMd4JjOeft2b+MRcWWF1eZs73mQlD\nzgB5XefyoUOojz3G+jXukyKynIVAzzBQbBsNWMjnCaanyWsa8pNP4to2s+UyE3ffTblcRtd1Vs+c\n4dbRtShtGBR0nfahQ2QB2zB4JZ/nlsOH6ff7/Oxv/zbrL7yAa1ncdtdd8XUwnU4DxCUXvu/HhNLO\nr47jxNdiwzDia+/c7CyXH36YYq1GulRia3ub6XKZjVaLSqVC0nW5dXRttqemOJfJMMxmqVQq1Ot1\nut0uJxoNpFaLRDaL/tJLGIaB12yS8Ty0IKBt2yiDAWGvx8D30SsVnD17+P7FiwSVCruTSWYUhYOl\nEh/72MeQGg1Wez1mP/hBes0mw9VVAlVl6tChqKyk3abyp3/KLfU6siTx4lNPsfDP/hnGVddicc5c\nj/Pe87wrMrSuJ1n1497/tSBU24Kk63Q6tNttstk0FzZbzE5myJoK33h6FYBiCr793Cq/9Kuf4t57\n7x0vmo0xBmPi6IbG1eGPQs2gKMo1b/9mWzd2Pt47hZ2rbBDJsg3D+LEukgc//GH+v7k5mpcu4UkS\nuakptK0twtVVZhyHjxC1hJwhUhmliYamJ0cqpIDIgtYisqh1gV8hUh5NAZ/2fX672YwfbxiGBIqC\nqapIskygqtiaxhOmGa+YmoaBrutMT09TKBSoVqtMaVpMUnQ6nbg+VhBFIlBaSLNFro4gDxKJBBMT\nEzFR0u52+e5wSOi6UK/zEd8nn83S6Pd50fdRXBfHdUl5Hvf6Psuj/BwxqDV1nY4so0pRA5uu61Q9\nj0CSkICGrvOk4zBJlPuE5zHpeVSIlFvD4ZApolXK54jehPKehwrc47rMjnIJXvF9NlIpCmHI7UEQ\nh3jfJ0mcU1Xqo4t/v9+nCByWJAzT5HQYsjHaF1fDtu04D0ioqETbmiCg0ul03LzmOA6WZWGaZmyh\nC4KAfr+P4zgMBoOowWXHa0NVVcIwpNfrxT8LgiC2ntXr9ZgYEiSRIHssy4pXhzVNYzgc0ul0Youf\nUJCVSiV836fdbtPr9bAsC9d16Xa77Nq1C9d1qVQq5HI5qtUquq5TLBbZt28f09PTLC8vk06nOXPm\nDBcuXODkSpvnLtR44FCJP/3WWQq5BEldRVcU9hYVnEGPQqFwxT59q4e69zLG+2iMMd4YxvPPjz//\n/PXcHLO2zctBgJNMone7aNvbzAGbO24rEZFG00TX64yqoqbT+IaBKUlIs7NkcjmSFy6w2etxOJ1m\nu14neegQhUIBx3H+f/bePEiS+77u/OSddV99H9M994EZDG6A4A1RIG2K8pqCKK+usFZahxzejZAt\nhuQNxob/UvgP78raQ7K9llchr26LskWTFA9DxEECIEBcc2HumZ7unuruuqsyK7Oy8tg/qn4/DihA\nwjEAOFS9iInp6emuIyur6tX7vu972NksapLQGw5JmyblTIbS4cO876Mfpdvt4m1s4HkeCwsLTE1N\nER8/jmmaspU0nU7LTCfhFhaFD6KoQbx3inOj2+3iOA6WZeH7PsVikaWf/3nCIMB3XaxXXsG5cIED\nc3N88MgRrqoqe1wXH8im0+z2PIY//MOkMhkZot1qtWi327RaLSlWtbe2yNbrKMB0schV30f1fYqK\nQh8Iez3yY/fvK9vbPFWr0fN9dv7zf6ZkGOxdWuKuhx5it++zd2qKgm1z4YUXWPnIR9g+eZLFa9fY\n0TQqqRTHPI+rZ85w4IMfBEbn5fapU6gXLkCSEO7bx9yxY/L/BN7s1+K8Eyv+r+VEEj/z/YTv5SLi\n9vm+LzMeRZturVZjOBzy/o//OP/+X3yZ6ZzNTq1NNKY5bQfmZhT27F6RvPv1rue1vn6tf0/wVzE5\nRrcWJsLRLYYbG8HEpEmEP4qGp+8X3KzbInb5ReDvX0cO3yzmPvlJjn7961iqSrPR4MyVKxz2PI5E\nEY8BJUZOozvGf3cYEYp54A7P4/bxG+gPAV9kFIidYxQ+fePbqa7rmKUSXx8M+JSqopsmj6ZSZPN5\ncuM3Mc/zZMBxOp2WxMT3fZrNpszfEbZp13Xp9/s4jiMdJ+INEUbniHAKbW1tSRKQJAnZbHa0omaa\nPGnbZIZDNlSVXJJQCAJM08T3fbZ7PWxVxRoHN+u6ThRFMt/HNE36/T5dVeUbQcDiYMAgjlkADioK\nPUakczejMHEBn1GukgKoisJA15kdDikDiqqS1TQeCkNOKwr9fB7bddEti8T3scbZSWu5HJdVlYyu\n88O2jcloMpYJQx4zDNqvIRxpmjZqTwkCstmsJJPZbJadnR3pRrJtW7qYRM7Rjb8ThiHtdpvhcEgm\nk3nVNO61BKt+v4/ruq8K8hYClqqq5PN5OTkXa27dblc+5mLtIp1OMz8/j6ZpVKtVuYJXq9VIp9MU\ni0VarRae58nzKY5jyuUyg8GA9fV1NjY28H2fQqHA0aNHKRQKnDt3jt99bJ3BMOLYSomMqfHho3PY\nls5Hb0/4jce/xuATn3wzT63XxFudLAryd2OO1c2cZr6XuDF7a4IJJnh9TPjPzeU/C5/6FHu/8AWW\nooj/traG12yyOhiQAp4d/4wNLDEKvz40NcVWv890Os0Jx6EAlG2b+WaTb1+6RNnzmALqvR5qPk+5\nXKbf76NpGsfuvpvTzSb5Wo1KJsPg4EHuvvdePM9jZ2cH13VZXl6WjbHC3aHrOuVyWa6hC4etcByL\n1TTxHiG+J35ubm5OHi/hNGk0GniDAeX9+0nm50miiHjvXhbabaYuXBgVShgGmq4TTE1hjAd0hUKB\nmZkZwjCUWVqi0bR27hzKzg5BHBM7DqtRRM/3CeKYtmGQ3b2bQysrDKOI3vY2zWqVx69dYz2KOHXt\nGhf+6I8o6DqFdJqpVIpKkpB+9FG0VIq929tUMhkynoff60GzSbdaZf/HP06v0SB/+jRZ08QyTfqX\nL9OZnaU8P/+2z48oivA8b5RxOc6m/OvwvcLTWxGr3q7Y9XqillhLE7yr0+nQbDZZWlrC8weUb/s4\nF574Aww7xXRZw2hHbPbhw8fm6F16At//sb/x/v9NmPCfv4oJ/7n1MBGObjGIF8VerweMbLipVOoN\nWyjfix3/t3pdNzo74OZM2b4Xd//cz/FMNot69SqXTp3iJ8tlNppNLm9vc18UETFaOyszCr2eUlV0\nTeOZJCF1w+UYwOMuVRUAACAASURBVIOMxKIyI5L1F8DU1JT84F8ul6kGAb8Tx6Cq7LRaJLUaiqLI\nxjHDMEYtaJubUrAYDodks1npIBJV7CI42rIsua7W6/XwPE86ZDzPI5PJyAYvTdNeJfzYto2jaZjT\n02Qch1q9zpnBgOOKgppKcS2fZ46R4CKygSzLotVqyQr6IAhGBENVuZQkoCjsCQLuZvQCI4Iz7wFW\nGGUpXQC+yiiku5sknB6HgSdA0O+z1zSxkoRsq8XlKOIJReGHdJ2C7/MKsBfY3+vxR0DfNFGGQ7ww\nJE4S0knCnjima5pcCgJuPOPVwYB8u41ZKtEY5x/Ytk2325XPDdu2ZeuZaGcROUKapsngbvFBJY5j\nmbcgr+eGQG6xJiiEnHw+LzMaBCETQY2Kokiy7bquDNHWdR3f9zFNk2q1Kh1qg8GAJEkwTZNer0e/\n38eyLPr9PuVyWZLo9fV1oijCNE257ri9vY2u63Q6nZEbTVP4wOEZ9sznubrdI23rxAmgqKxWjFfl\nKtwMgvhWJpWvFYB+M/BuWO/F/RXirRCEVVXFMAzZNGgYxtt+jXMch89+9rPSpfDP//k/54477nhb\nlznBBO81Jvzn5vOfb0QR8bVrnA8C7up2+U6jgdPrsQ+4yojb6Ixapmq9HpVcjpauM2/bo1y+4ZBL\n3S49zyPPKEg7AZxxrp5hGBw5coRqtcrsnXcyHAzI7d3L0ePHsSyLdrtNJpPBtm3m5+clZxLvS2IF\n+8bMQ/G+B8iCClEa4TiOLIbI5XKUSiV835eFIoL/TE9PUy6XSaVSlEolkiShXq9z9epV9igKnSCg\ntns3K6WSdNyIwdxwOMTzPBzHIZ/P4/s++Xxefgi2vvENls+cYWhZnGu1iB2HnRdfZNDrsZxOs22a\nxCsrPHLPPbhA3bI4e+oU3WvXCIKAxtYWNd/Harexs1muWBYHOx20TocOUHj5ZU6/8go8/ji7Dh3i\nQKeDqetU8nkMz6PeatE9cICZu+7CTqXkbW9ubDDY3IRMhrnbbrvp5/b3o9tGDPp0XZfucRGiXyqV\nmJmZ4ZlnniGTTXHbapm1zQYJOj/xwQK//tUmn7l/mW56wn/e6Nev938T/vODg4lwdAvB9325y/56\n4Y/fj3grZC0Mw3dsynYjdF3n+COPjEjav/k3qE8/zXw2iz83xx9ubDCMY7LAMrCiqnwpk2F7ZYVG\nr8dD/T6zSUKdUQVtilFmz3OKQggkYzHIdV0Z1qjrunTthGFINpuVkzRd12UejbBAC1EARoKROJai\nUl1UzOdyOcIwlOtXuVyOVColp2GFQkEGSYsw7W63K4+rEDcM02RtcZHNIEAzTRTbJtXr4fu+/FmR\ncyPEC1VVJVkTItJJ4D8yyoRaYeTW+ruManqfYUQsLwGd8e03VZUok+Fat8sHgoC9QTASnDodssC/\n1nWeAh4KQ44ycnXBSKx7JQgwAVvXiVSVJcDQNCzDYNG2eUlR6HQ6ZICHgIzrkgFeNE2uaZpsLhNh\n0+LYWJZFqVSSbqM4jrl+/fpIFIoiVhUFLwy5ckNIuYBYTRPuL5GjNBwOabVaUswT4lQ+n5dTVCFm\nzc3NyRW2Xq83WjPsdmWgtxCyhJvIcRy5XlepVFheXpY/l81mabVapFIparWaPE/EGoDv+6RtGxSF\nY6slnjm7Q38QEiegmhmMfOlVxOlm4o2QMN/3SZLkVRlL79Q085223gsn20/+5E9y/fp3k0Tuvvtu\n+bVhGOzatYvPf/7zUjB+M/id3/kdHnzwQX72Z3+WK1eu8Mu//Mv82Z/92du/8RNM8B5hwn9uPv8J\nw5Djn/40nudxPQwJvvEN5m0bN53mQr+PzkgI6jBaU2uXSvjLy5iWhf/CC8Sex8CyGIQhxfFlXmG0\nqn9odpalpSUpBBmGQT6fZ35+nl27djEYDGQBhHAuZ7NZuVYmmj/Fz4nBijgeQiwUa3yO40i38NTU\nFDAaAu3s7NBqteSgJ4oiSqUSmUxGupkURcHzPAqFApWf/3nq166Rsm3uWViQXE1wMsHXRMvoYDCQ\nK5O9Xo9ms0nxzjs51W5T6PWYHgyY37ULo9nESaXoVSoslkqEBw+SX10lNRyScl0yhQJXbZvmiRPE\n/T4+UAgCjOGQaqHAyVSKbBAwG0XkkwQ1DLl84gSb6+ucaLVYnp2lmM/Tr1ap7N1L78oVTjzzDKsf\n/zjpdBp3Z4fiyZNUxkUXl7a22PWhD8njKv5+I+g2GvTOnCFRFEq3304mn7+p5+U7ARHjYBgGzWYT\n13XZt28fFy9eHImSYYLvDVmdybE8nabqpPlHD5f4wP238fW1zIT/3CRM+M+tj4lwdAvhxgDEfD7/\npoPa3q6K+27s+IvrEB+430jQpfi/N9teUt3cJBgOqYyJzcrf//s8evEih65coVYu01EUHmm1mI0i\nrikKTVUlf+AAuaNH+dEvf5lUHLPBqIXs9zSN9wHvSxLmFYULisIzliVt1Dc6V3zfl+HMwnmSz+dl\ne4fv+/LFWxCUYrGIoijyQ74gL+LyxRuLoiivIpliNUrk0wjXyczMDPV6nWw2+6qg5iiKSKfT5HI5\nKTaIx2Nra0vaw4VzCUbiWz6fl1O+bDaL67q8GIacAH6c0Vqaxmh6WQAWGIlJJ8OQq0kyCpLu9fCG\nQ4Lxzx0HrjMirXYYcoVRy8v7xo9fD9gPmIqCZhhkVJU1TSOlaWTHQdX7NY3z4yay5SQhM/5d13WZ\nGw65NBZlACnEeZ4nxTchqiVhCM0miW0zVFU+6HkcVVVUw+CErvOt8dQ7SRKZueF5nnR5iesQLWqq\nqlIsFuU5niQJ5XJZTk0LhQK9Xg9VVZmdnWVjY4NOp8Pu3btl9lGxWJR2/BvXNkSLjGEYTE9Ps2fP\nHvl4qarK0tKSPJ+GwyEXLlwgl8uRz+d56nKLPfNtPv3gKr//2GWmZuYgV2L/R/7BG35evVm8kSml\nyK0QWRbvFm6m9f57gzl/6qd+itOnTzMYDDhx4gRHjx6VTXdBEDA7O/uWPxj/3M/9nCS6Ih9rgglu\nZUz4z2vj7fCfZrNJsVzG8zx2fexjfPv0aSrVKmEuhzUYcCiK6I5/3tQ0tHwezTDYfv55Bp7HNqAM\nBszu2sW+KGL++nU6SULGtpm65x4AOp2ODLa2bZvp6WnpGJqbm8O2bVzXlc5fVVXle6RwOotVRJEL\nKIQ1EYQdRZG8bHE5YgVODGJgJDiWy2UpIpXLZWC0Sn7jOtb83r3yOIlh3/d+aBetbeK2OI5DKpWi\nUqnguqNMwNMvvYT7wgtoUUSv00EDnGaT1eGQWhCg2jZTBw+OBkaOg62q6FFEWddJRxEdz8NJpSil\n06SXlmh2Ori+z6XBAHscMF5QVXIrK+xsb3Op22VXsYjqODiui1qt0pyeJpfL0Tl1innPQ9U00oZB\nsL7OYH6eVColj60YDGqaJle6giDA7XRwNjfJTk+TLZdp/vEfU9neJlZVapcvo3/mM38lrPv7BeKx\nEu784XDIzs6OdH5fv36d6elpDh67g//46J9Q0VxWZks8c67GL/539/HVy+aE/7zGvyf8528vJsLR\nLYRMJiOnHt8PFtCbDRE2DEii8U5M2ZIk4fF/9a/Y//WvYycJT959N+//3OfIFQrs/dznOHfuHC89\n+SS7v/IVTnseT/Z6bBeLnLdtdn3iE1SfeopDcUydUUZPCWhFEX+Wy7GpaczHMWcti3XLIur1MAxD\n2i+FQyeVSjE3N0e/Pyq5FVbiWq0mW9DEVC2fz0uRwXEc4jiWxLnb7UrRIBhnE4nq9l6vJ3N5Wq0W\nuq6zs7Mjp3tifUrkJwmRSfxep9Oh3W7LnCWxrgWjN4EoijAM41XCmPj6VW4b32de1+kMBqSDgPnx\nB4Ay8BHgi1FEs9fjYeB+RoLRBUaupDqjgHJX18mn01zSdU66LpkkwdU0DoYh8XCIAoS6jpdKYcSx\nbBxzGU0vKpUKQb3+qvOgFwS4N0xXTNNkMBjQ6/XI2jYHBgOywyHrvs+PhSG745hav88XgYcUhdLY\nKVWOY17WddK5HAeiCHSd0/0+28Mh6nDI3mwW17ZpjcUlIfg5jkMul5NTUiHaKYrC9vY2mqaRzWZZ\nX1+n3W4TRRGNRoPBYEBpHLQpzidBfIvFohQfBVHP5XLous78/Dxnz57FMAwZnG3bNnv37kXTNHbv\n3s3c3Bx/8uyjDPtd7vvYL/LQJ37kHXkOvlm82Q9FNws303ovQl3Fh5af+ImfAEYfrH7xF3+Rf/tv\n/+1butw//dM/5Xd/93df9b1/+S//JUePHqVWq/Erv/IrfO5zn3vLt3uCCb4fMOE/Nwc38p/A8/jq\nbbdx1z/+x+iWxeFf+AWuX7sGL7/Mwl/+Ja1mkwEjp7A3N8fSvn3QbrOq63xxfHkfAXbdcQdLR47w\n9Be+gO15zNxxBwc+9SlOnDjB3NycdNROTU3R6/VwXZf9+/eTTqdxHEeKFcK1Oz09TRRF5HI5KRDe\n2JYmBljChSHW+KIoolar0el05HBNxAAIh5E4d24UjUzTfFOOEhErIG5bLpdjampK8o7hcCjFo/Pb\n20Sui1+r4ToOVzY32bYsFgsF0prG2Y0N1FyOwYkTFKtV8lHERWCg65AkZNNp/HGbnLW8jH/1KhpQ\nC0Oieh09jslYFnOFAkY+TyWTIVEUSBKacUwlCEbrc6kU1mCAFwR0goCOpo0ua+xgFkMogCgIcE+c\nwIxjdoKA0osvshJFbBoG55aXuXtjg2YcM2XbpGs1qnffTXlujtZTT6GHIcrevSzcfjutrS16586R\nmCaL9977rgsfAiKf0zAMGo0Gvu+ztLTESy+9RC6XYzAYoCgK9378Z/jSf/kTrlc3+bF/8Iv8g1/9\nX96z23wjJvzn9THhP+8+3vtnxARvGEJceLt4t16E3uh1JEkiV6oExM76272+G6dxAmeeeYb7H32U\n8vgNYeb55/nW177GwQ9/GEVRmFlcpHTyJB8yDDJ799IfiwUbU1OUHIcrrRYuUMnlmHMcfEXhn9o2\njy4sMFhYYE1RSPp97HpdCkOmaco3IF3XSaVSsrFLURQcxyGKIrLZLKVSiUKhwMLCgiSSvu8zGAyk\n2CRWkNrttlyzmpubY//+/TLHRrSKCMGn3++zsLBAkiS0Wi0URSEIAizLwnVdut2udKx4nodlWXIa\nKEitmE6JFq90Ok2SJPR6PRRFkYKWuK+u6/JiNksnCDiXy9EIAu4Y7x2LR7fISHxbYNRMlzCyuvc0\njaqq8rxlMczlsMKQWNP4yzhmdxAQA21dJxvHDIKAKAhoOA4XLIuyZTHUNJ4dC1yZVAovlcLyPHYx\nEqZe5rtB1oIEipWwD9k2B+MY3/N4OAgoMFq5OwiEgJkko+sMQ0xVJdQ0HlQUHkwSNOAe2+Y/uC4f\nAmYdB0PXec5xODsmr8JeH4YhhUIBTdPY2NggjmOmpqbkOqE4d4Xlvlgssm/fPgqFAqVSCdd1mZ+f\nx7Is1tbWCIKAnZ0dms2mfJxffvll0uk0hUJButn27NkjBaOrV68ShqE8R4/c8xHC4YAPP/Tw94Vo\n9IMOsXL4VvHII4/wyCOP/JXvnzt3js9+9rP86q/+KveMp/8TTHCrYsJ/3vz1/XX8J5UkXPA8Dn/n\nO7z86KMcGa8ttdtt1CtXuNOyWMtmSVyXqqIwfegQSZLghCFpRu/RGeABoPvyy6xHEbsfeIBdu3ax\ne/duzp8/T6vVolgssrCwgK7rclV7cXGRmZkZHMdhdnYWXddl46gYkgnxRVEUeTxuHMCFYUgqlZKO\n3U6ng+u60sHtOI5cfxMr6EJsqlQq0qktnMZvBiLXMIoimVEojrO4fZqmsbKyQvYf/kP0ixdJPvpR\nXr5yhcrTT/PU5ia/cfo0+unT5DIZLMtiVtMwg4D8eHVe0bRRyYqmMZdOo8QxmmVRz+fRXZfEMCCO\nsVWVTrfLZqOBA3wrDJnOZJgqFsns20f3yhUuXbyIOhxy8eRJimFIJ5cjd999qGN+2Ol0AOQA8Ppj\nj7GaJLhRRPPpp2m4Ls0wxDYMLrz0EuWVFbzhkIJpMpvNUl9bo/61rzF79SrGcEjw3HOc6/UonzrF\n3vFA8dy1a+z9zGfedQFERCqIGIitrS1KpRKbm5sMBgNs28YwDFqtFpubm+TLs8wt7OK//+mf/b4Q\njX7QMeE/tx4mz4pbFO+mAv1OXo8gB/HYJSJyV97J6/TabTJxjNfvY9o2tqYR93oySHgwGBAFgcwP\n0lQVd2sLzbJ47rnnaA0G/DvL4kd6PULbxsnluCdJcDodvl4uywp1z/NkS1ahUCCbzVIoFGSgp+u6\n5HI51tfXpYCTTqdZWlqiUqmQTqc5ffq0DGAUBCVJEmq1mpySiPwkMTUSgXBJkkjxQWQHiNyEKIqo\nVqvyzVTTNJmhFI6r7H3flxk74nKFm0iENos1t1Kp9Cqbueu65PP50eUBF9PpkQimaRRMk6OWRQK4\nQUAjDFk2TTKqylBReLbfR08STiUJZ0yTRiqFNl6P03WdMJ/nzDgvKBVF3GYYqIMB5cGAB3UdJY45\n6Tg8bRikBwM+1u0yn8lgA13DYGM45D7gMKM1uP8EDBWFTrdLFMfMzs4y67rYnsfuKGKJUc5DmtFz\nYTZJeBa4DQjjmNNxzHanw0FgdnyOFRnlL+0a/+4wDLndMHgljokZCVXCZeR5njz/8/k8x44do16v\ns7OzQzabJYoitre3mZ+f58CBA3KKWiqVePDBB5mamuL8+fOsra1RKBTY3t6WIlCz2WR9fR1VVVle\nXuZDH/qQbNoTAdowmgZtX3qJzec3uGtZ44O3rfD475/igR/7ZYql8jv2XJxg9CHkZhPUixcv8ku/\n9Ev8xm/8BgcPHryplz3BBO81JvznrUPwH6fXoxUE7EqlKI1bw4QQUk6lyGoaq7kcvShiy/PoNRrs\nO3KEra0tttNp7F6PBPiWZfEJy+LZM2dYWl1lOBzKsgkxXJqenmZjYwPHcThw4ADLy8vSaVsul2VD\nrBioANJBLRxFYrXf8zz5XgnQ7XZlS6nIvnJdl16vx8zMDNlsVnIhIRoJnpdKpd7Uh9YkSUZttONB\ni1gjFN8X90Fcruu6zO/ahX3gAL7vc3xnh7KmcWx7m//xAx/g25cvczmbpbWzg93roSsKUa+H2+3S\nn54mPzuLXiwSjF1DpmmyuLoqM53CVIpOt4ui6ySuy6xtExgGDc+jaVkMn3kG3fMoGAaK53FgdRWj\nWCQ6d47tK1foZLMM77iD3OwsmUIBO5cbOcKuXuXK1hZBt0tw/Tp+kpCzLKZSKQZxzItBQNLrMYhj\nzCRhZmMD5ctfJu/7FCyLkmny+KlTfGB5mevFIgfn5pje2qLTblMcu6XfLYRhKJ3wotgkm81y9uxZ\ncrkcyjgD8ytf+GNefPYZyvaQTz58Jyf/4t9Q+IlfmfCfdxgT/nPrYSIc3WJ4O4TivbJ3v1Y2wPdO\n2WzbJpVKvSpg+J2Cncvx51eu8GOOg28YPH7oEHs++EFJdPr9PlsHDnD1zBkORRHV9XUWfZ/Pvvgi\nX04SfNvmO5UKzxeLHE4S7DgmGIstIohYBDoqisLMzAx79uyRJEOsGZmmyc7OjmwVMU2T1dVVbNvm\n+vXreJ4nXUkzMzMEQYDjOLTbbVmxLsiEWBMTgdciG6HZbNLv92k0GnQ6HSkcOY4jc29EQwhAoVCg\nPBa/xKqT53lEUSQJmghWNk3zVRXyhUJBEsZMJiPJvZjqTE1NYRgGm70eQb1OWlHYyGbxej2uAPuS\nhN2GQb9U4guOgztuM0mZpgx+FtNBYXmNgJOKQj5J2BNF2KkUmqpy+3DIS4zykCpA6Lrcrig8ryjs\nZSTqnGK0FncUaAUBF4E/Bmq1GltxzEcVBVPXMaOIYZLgqyqoKu0wJGKUbXUWeJqRlT/DSDDyGYlM\nR4F7NI0zUUQnk6EeReSShJkooqmq2LOzMli80+nIyerpF5+hVCrJEEeA2dlZCoUChmGQzWaZm5vj\n4MGD0nnW6XSkO8z3fdkeIqatjUaDRqPBpUuXePDBB2m1WjKTStd1WleeZ07Z5vjeAvvnszx74gIf\nvvcIzzz2X/jo3/8f3vHn5N8GiNfB730dfrsTt9fCr//6rxMEAb/2a79Gkoya/H7zN3/zpl7HBBO8\n25jwn7cPwX/+TrfL7jjmW3v2cOTwYemgMQwD7dgx/FqNpSDguueRAcKXXuLll16iqWnkdu3Cmp5m\nwfMoKwrVXg/GPERkyAjnz+7du2m32zSbTVZXV7n77rvZ3t7G8zyKxSKdTgfHcVBVVa6jidUzMaSC\nkUAEoyGYoihypV44uEWOjfj+4uKiDNYVGZCVSkVmE4mmtjcCkfUzHA5ljIAY2nmeJ/nTjStzgjf1\nej0pNtm2zdTHPsbmU0+xlM1y9M47+eEjR/Ach7U//3MygwHOYMDmzAxzBw/KzKEwDOXl3TgQrFar\nI75y+TKLts0wDBkAhu/TNU2o1yEI2Oh2GYYhF06ckI7uGHg/0DtzhmyxiFcsYtx5J7npabZrNabH\n+ZaarmP6PhldpxUEdA2DbruNNRxi79pFc2YGrdWiu7GB1e+jW9ZomKfrNNptLmsaw/e9j6Gm4T/x\nBNnBgPzKCnvvvvuvCAZBELB24SSgsHrg2E0JvxeiW5IkVKtVpqenOXfu3KhJVtdRVZUv/sl/4OLz\nTzKfTrh9dRqn1ebvPahO+M9NxIT//OBgIhxN8IZxs8Ihb5yyiVaNm6E4v9EpZPdP/oSHFxZ4utEA\noF+pUJyelrWdvV6PzOoqzYcf5g8//3nud13mT57kYJIwDZx0HFbCkN8vl3kgjjmkabQ0jVempshm\ns1SrVZkZVKlUKBQK5HI5abdutVpsbGzI9bNdu3YxMzNDqVTCtm05mVNVVYo6ovUsCAK5cjQ9PS0D\nDOfn55mZmcF1XXZ2drAsiziOqdVqkmilUil0XaderxPH8aseB8uy6HQ6Mj9J2K0VRSGbzUq3j5hI\n9vt9tra2XhX6DEjnVCaTkQJWrVbDdV0ZUJeamaE6dj3FcUw2GTWJPWGavBBFaNkszTjGHotshmGQ\nTqdfVScv7oOstlcUNF0nHA5JNI2BqmLaNlOahun7BMMhzSRBTRLSjNrvYmA3I2FpANwBbAD/NY45\nC1zSNPK6TsswWBkMeFJRyEQRJUVhWtPohiEtYAc4Nj63LEaNb1cAM5fjQpKw4vs8EYacURR+3HXJ\nJgmepvEX1Sr9clk6tlqtFrsyfR7aW6FQSHjmfI2mr7G4uMj8/LzMKxIrZiKT6cqVK5w8eVKS9kKh\nwL59+8hms8RxzLVr1zDH4tuJEyfodDocP36cIAjo9XpomkZj4zwfuG+Bh25fwDQ09sxl+dKLVzD2\n7Hnbz8sJ/npEUXTTJ26/9Vu/dVMvb4IJ/rbjB43//FkcEyUJ1uwsc4uL8n06m82ydPAgg7k5Tn7t\na5Qch121GmcYOWoLUUS8vo6+sgJhiB/HXAsCegsLMrdPNIjefvvt5HI5nnzySebm5jh8+LBsH9N1\nXTaxZrNZVFXFtm25Ci/yE0WTqOAhwlEt6tXF4yLW1HRdZ3p6WgpDjuMAjHIOx0HaIiLgjUCIWeL6\nREC3WOkXLifLsqSg1el0pAMql8sRxzGO45DNZgmiiNs+9Smmp6dZDUPW1taYnp5m6Z/8E66dOUPB\nNNk/dhklSUK325WOcuEyF42Cx48fJ5VKcf655wi//W2cfp9CKoWnKPh33831r3yFYRDQ7HRoVqvs\nDAZseR4Xxvft0vhvvd2m1G4TXr1KZd8+wm6XTK8HQYBmWWQUhZeDgLSikDcMSoCWzxNoGgv79rFz\n4gTWcEjcatEAXlZVUsePczaKKLkuL129SqdSYeXzn6fteUSWxTN33MHBD3yAcrlMqVQilUpx7cWv\ncnw5DcDLz1xh/wM/+rbEI9GIa1kWtVpNDjo7nQ6lUgld13nllVd44dlvMpNVObZS4aHjizx4eJ5v\nnJrwn3cDE/5z62EiHN2ieDsk5r0KWhONU6KOUUzZXuu2vJn792bviz4YUDIMPjg3B8Bj4/WvOI5l\nALFlWey7/XbUy5dZPnsW3zCoBAEDoGgYzFkWX5ya4stzc3y1XqerqniWhTMOmk6n03L3vlgsMjc3\nRxzHZDIZNjc3ieNYupFEXW2/36dardLv9ykUCjLXRhAsMTWbm5uT7QSO4+D7Pmtra9TrdUmMcrmc\nPIaiBU24TDzPI51OSzFGrKSJzCMhVokWh62tLYbDIY7jyMwBMR3MZrNMTU3JqWChUJDuGbGyJtbf\nALliJUQzEdq8tbU1yvupVEYiVTZLvV6X63xiZUusxAmnle/7uK5LJ0l4Stc5HAS4gwHfVlV8VeWs\novB+XYfhkGeBc+M/HqNGthwj19BuRi+Gc+P7YJfLdD2PlGliDoc86bq8MhiwNwwxFQVbUYgYBXwD\n7GNEqgPABDRVZRBFKKrKqWyWp8pljtXr3BeGVJIED7jmOPwXz5M1sVN5m/cfnmEwCNjZqfH+IwtY\ntRw9P6bf77O8vEyn02F9fZ0oitjc3KRYLOK6rnQjweiNuFKp4HkeuVyOPXv2MDs7i+d5XLx4kTNn\nzrC+vs79999P4PdxXvkL7tlToNcfcvJqi7v2VVAUlVrX546D97+p59YEbx7vxMRtggl+kDHhP9/F\nW+U/D0xN0Y9jLhoG+Xxe8gtRwFCcm+PQ8eO4ly6RZuSobTAatOSBpqahHzvGzs4OdqFAplAgjmOa\nzeZo3a1cZmZmhmq1Kl3IqqpSr9dlxlC322Vubo5isYjjODiOIwOwPc8braOnUmQyGQaDAcPhUApL\nN6Jer0uuJVzfmqbJ7J5KpSLdXW9UNArDUDrHhWAUhiGO40juksvlME1TurhF5mSlUiGVSuE4Dtvb\n20RRJJtsRVi4OV4PnJ6eptPpkMlkOPr+92NZFo7jyEa4paWlUdHHWBhrNpt0u12Zk5nNZpk9cIB6\nr0elWmXbBJYYfgAAIABJREFUcXAXF9mzusrMRz7CbWM+ttZsclnXqV64wPlTp9hstagCNUa5jTVG\nzbepfh/FMPDG0QiBouDoOpFp0nUceo7DRc+jmEphN5tkgN7ZsyQ7O3JwdjGOiatVdheLXDAMyGSI\nTp/m8tWraEFArGnUzpzhW+fPS2d9fWcLt77B2bUazst/xO1LKc5eOMO+I8ff1Pn9vY+h4Pbb29sU\ni0XOnDlDOp1G13We/84zfPH/+z9ZLmrUuxG5lMnRXWUyaWvCf94lTPjPrYeJcDTB34i3SrJu/D3x\nhiumbGJicjPxRglh8sEPsnXxInNAI0kI3v9++ftxHFOv12WY4p4f+RG+9tu/zScUha6icEpVuVPT\n+FI+Ty6bJW+a9HbtYthqocbxq9o1BoOBtH8Ph0M6nQ4vvPACAIuLi7Litd1uo+s6m5ubFAoF5ufn\npUgiyI+ojhU5R61Wi3a7LQmMruuUSiWmp6elI8fzPHRdl84S0aRWLBbJ5XLkcjn6/T4zMzPyckWY\nt23bbG1tyWmbmHSl02mCICCVSknRSAhPlUqFbDZLNptle3tbBm2rqoqqqnJlzbIs9uzZg+d5DAYD\nFhcXSafTUlATpFlcl7gPNxIzYeE2DEO6uapxzHoYsr29TRJFpMOQc4aBOyasl1yXBaBs2zzq+3SB\nV4BPAAaj6dtaJsP8/DyqpnFydpZeELDdbHJG10l7HgvdLncMh4RJwguMnEUAPeAAI1IdA9txzJ7h\nkMPZLE+bJiuFArPNJiuqSjGK0JOEe3SV4scO4g+GPHFqG28QsDKTo5g1UY0UvcgiSUbHodlscuHC\nBba3t8lkMuTzeWzbpj4OYBeuMSEmiuMjbNrz8/Nks1kqlQpTU1N885vf5L99/avcVupzYKnAw3ct\nsVhJc3qtzSvXWvT8mGT5I+w/JLxUE7xTeCcmbhNMMMHNwQ8q/zmYzXIxCOgeP8729jbNZpNyuYzj\nOJimSbPZZO6uu3jq936PGWANaAPzQCuTIVFVtra2mF1aQlEUyTtM0+TIkSNkMhlarRaapjE3N0cm\nkxmJTLbN9PQ07XZblmmIIZUoqICR0yeXy8l1L+FCEmtHqqri+z6O48j1Mdd1qVQqrwp8LpVKUgCy\n30BlvMg/EqUUwsnb7XblqlqxWMQwDHzfp9VqSXeQyLIcDoc0m81R0LiqMj09LS9fRBWIAVyhUAC+\n25ibTqcpFosUCgXa7Ta1Wg3DMCiVSqiqyu7du2k2m+zs7MhA8XQ6zcy992IYBjNjR3ir1SJcXOSp\nJKFgmljHjpG/dInAcehfucKhJMFrtxFHxACScpn9R4+STqfxez38nR06nkdxYYFWrYbf7zMVRfSC\nAF/TiJKEVBzTHQ5RAZtR0UkXKLdaHFQULto25UKB1nBI1vPwXZcysNFq0Ziyqbe7XNvu0Gh15DH6\n3d/+f/j0Z34SxX57goJoA240GiiKQrValRlUF8+f5T/9u3/FrtkUaV1l93yR21YrtLyQa+frE/7z\nLmHCf249TB6tWwy34o6/7/sEQQAgA6Dfyzrd+3/6pzk5M8OZs2ex9uzh/Z/8pMzmcV2X7cuXWXjl\nFfp/8Adszs6ytn8/3+x22fB9DigKXwGeNwz+xeXLhOfO8XuGwfDuu+U6kCBGtVoNgHw+z87ODp1O\nh1QqxW233Ybv+zSbTSn8CFFHkI4bnURRFFEoFKjVajIDwbZtut2uDNHe2tqiVqvJppAwDKV7KJVK\nyeMu1r6WlpYkSRMupV6vJ9fHxG0Rtm8YVQR3Oh22t7fltFQEPIssI2ElFwHg6XSaTCYj3VQ3WrZF\nm9z29rYU2drttnTRBEEgHUW5XI5KpUKz2ZRrdu12W67/idW4ZrPJ9PS0JJ+GYVDXNALTZMX3+VQU\nseL77AOqjASf54GOqnIynaY6M4OqqhiGQbXX4+pgwNxgwAejiIrjkDNNThoG9mDAhTDk5fE59RTw\nHUa5RnVANwwapsk1XWe/otBqt1nL53E8j4phsBXH7M7qeOGQwoFZlmcLfOvMDl6ocNfyLKqq8IdP\nXKMXzGFZIcVikUwmw8z49lUqFZmlYFkW6+vr2LZNv9+n2+1y5coVLMuSomIqlZLZVKVSiR/90R/l\npf/2+xxdKfEzD+2j0R3w+KkqHz46z6/96Rnu/bu/wGc+/dPv1lPybzWiKJpM3CaY4A1gwn/ePm7k\nP+bu3Xz0nnvodrvU63Xq9Tpba2ts/OEfojab1KencRcXifp9ojCkzKiR1FBVVi9c4EIUUW80yI7z\neBqNhsxr7Ha7HDlyZNRUlc+zuLjI+vo69957LzByAQkXdBAEcq0siiLK5bJ08WSzWekQEeKYWAkT\n7mpFUeh2uzJHsd1uy8sRwyexKv96EE1pIkhZhHGLVTHLsqR40+/3abfbADIIW9M0FEWRzqA4juV6\nnGEYbG1tUalU5GMv/rZtW7qhRLttpVIBoFgsks1m6ff7OI4jc47m5ubI5XI0m02G4+bYKIqka6tQ\nKMgA8u10mnq9TvvZZ9lz/Tpbp09zZ7PJxX4fjVGbbQL083kK+/fLgVx5ZYXKXXexdvo0qUYDvdlE\nKZUIgwC93ydtWaizs7TbbbqKwvUbjuVRYHMwYL1eZ6ZYpPrYYzSDgKHrYjJyJfWAzpVrRIaBFg+Z\nKRc5tGjzSz/+IB++5xBffuYEn/z5T7/l81zwREVR2N7eJpfLyYyjXq/HH/37/43dcxn2zGc5v9Hh\neCnFQ3csTfjPu4wJ/7n1MBGOJnjDeLP2cBHgJ0jBG5myvVuE6tjDD8PDD8t/i/wex3GYffZZPj2+\nvYfW1rhg21wrFPh4Ps+OrvNCqcTPXryIpWkQhvxMFPH/BgHJzIzcvRdihuM4nDx5kiRJWF1d5fbb\nbwdGE8ipqSna7TaGYbB3715SqZRsY7t+/fqo3WI8Qcvn8zLXBpBCj+/7NBoN2ZAmJnzC9eS67qsc\nScJBJCrYhbBjmqac/onQx1wuJ0mIyBVIpVKsrKxICzDA1NQUURTRarUk8RM2bpHTdGNopBDMNE2T\nrV+GYUgHkrDyZ7NZSarEap6qqszOzsqQccMw6Ha7+L6PoigyU6rdbksBSxCIfbZN0XXZyyjMugiU\nVZVLqsr5JOFxwxjdjnGNb5IkLKoqf8fzKMcxu8KQahTRzOfRTZP9vs8vAReShCdVlZejiK6mMZtK\nMdft8tBwSKnXo6XrrLgunXyehqKgWRZqOMAo55hN22RyFgoKe+bzZHNZHjuxRSqdJlMoU47K9Pt9\n9u7dS7vd5vDhw3IFoNls0hoHWGYyGVkxu7OzI0O0YfQ8FMHohmFw/fp1IOHgnM3/9CNHQIGFSpph\nHHOh2uXoQz/Fxyek6V3DZOI2wQTf//hB5T+NRgNVVVlaWqJWq7H5hS9woF7n0mDAoUaDrWwWZ36e\n97kuZx2H85rGA/0+oaYxjCJSjQY7166Rm56Wwli9Xmd2dlYOM/bv34+u61QqFWq1mixvEG7aWq0m\nxRoxNDNNk0wmI51Iwmk8GAxwHIdUKiVd00EQSEd2s9l8lWgknLivB5GDc2NTWhAENBoNkiQhlUpR\nKBSkiDQcDrEsi3w+TxRFkmPZti3X8jVNo1AoyAwkkXmUy+Vky5cI5lZVVa4sikwjkZmUSqXwPE+u\n/vX7fXZ2drh69SqlUkmusYkA7kwmA4xytEQcQKFQYGZmhheffZZvnjpFs17H6/dpAQ9ms/TTaRqA\nvbqKNl7JE+LY1pUrZNfX0XyfuxyHbaB08CDbjsPWzg7O2hrX2m3cMS+F0YdKnfEa/3BIUKvRqdWI\nx9EQAaOhnQf4/QGLS3nuPLiLYaRw1+Elrgc5rnlZ9u9fkEUfbzTE/EYIsXZnZ4c4jrl69arM52w0\nGpStkAePzHJmrcU/fGgfM1OFCf95DzDhP7ceJo/WLYQbScXb3fF/J5GMw47FC7f4EPteTtn+JoiG\nsUajQW4wwByTAt/zsKKI6o//OH/gOPjdLoUvfYmlVouhYZBkswRhSBwEROOsGrFiVq/XWV9fJ0kS\nVlZWyGQytNttWXXved5oP312Fk3TqFar9Ho92bIlspGWxlbwVqtFq9UiiiJ5Ofl8nmw2S6FQwLIs\nWbUuRBixYqbruswJEPkAwl4tJnjw3TykXC4nXU5ionfx4kVgNCHrdDqyhW4wGGBZlrRci+YPsfsP\n0Gw2sW2b7e1t2RCytLTE4uIi169fl+0pzWYTx3Hk/RCXI0I3M5kMjUZDEkEh0onVOgERJt5utykU\nChw8eJB4fZ3scIgNo+yhKKIUhgyjiI/qOnc5Dv/Rdfn2+H5ZlkVKUZiJY+5PEoZJQo7RepszGJAH\nzCRhWdMYGgZPmeZowtXvM1RVdsUx+TjG9X1MTeOeMEQ1TV5WFFKlCitliwO3z1GZyXB6rcGhBZvb\nd2W4UjPwhgpPna+z5fdlPsTy8jJhGEr3Vr1el+duOp2WRDGKIrnOpus6zWZzVOO7uEgYhuzatYvh\nxnMctOfJpQ0SoNcfYuka/3WtxP/8v/7CO/58e7MQqwm3Ml7vdXey4z/BBH8zJvzn5kOs55um+d1i\ni8EAS9cpRxFt1yUyTfY88gitahX90iWi557DZZSLk2b0IWIwHGKOhQvTNMnlcqOw42vXZJiz7/ss\nLi7SarXk6pmqqtK5I1bMRAh1q9WSr/lirUu4f0qlkhSJkiSRQlRznDFZHpdOiBbW17vvNzalpdNp\nBoOBbG8TQp/v+9RqNTRNk3lLcTzKHYyiSOYVifxITdNeVTAixKWZmRnJr4RLW8CyLFkTL26DWGkT\n2VCdTodCocDCwgKZTIZer0ev1xu14I3LS0RYuGjALRaLRFHE9vY2NUarZAVgG+gDTpJgBQGHFYX+\nxYtUV1YwpqaYnZ3FNE3OX71Ku1pl3XVZY7SGv3XtGh3HIbIsgsGAomGMnF+VChVdR+10qPk+Q0bO\nooDRoE4fDukCQ6CSzTKleOy6d4U9u6bYqbeItBR3LVscPLxKeW6Gk9salmXJTM43+/wRsQvC7T8Y\nDGQu5tYr36ScM9hqePzofUvcd2iB6y1/wn/eQUz4zw8OJsLRBDcVwrUTRZH8nqihfzN4K+Tur7uO\n17u8G6eCW1tbVKtVuvPzDD2PuN+n5rq0b7uNxcVFNjY2KH/xi/xwFPGsZfGJKMJ3HP4on6dqWaQd\nh1KphOu6vPLKK1SrVdmsNj09zezsLI1Gg/X1deI4ZnV1lampKbrdLp7nSbu1qqqsrKygqqoMvRYu\nICHqFItFZmdnabVapFIpKUQJsUYETGYyGebm5tja2sL3fWzbZmbsjBJNHbquS0uvEJVc15X7/d1u\nl52dHQDZOifEiVwuJyd0whFVrVZlLhIgRa0oipienmZzcxPTNGm32+RyOQzDYDgcyrwksesvfl+8\nsRiGQaFQkAHbqqrieZ78+ampKemScl2XMAxxXVdavA+6Lj1FYStJCCwLK5tlq9nkAVWlFMcMw5BP\nBAE1RjkOyWBAHVgGypqGAjyTJDzh+2iKwj3j+uEkjskMh2wnCX8eRXw8ivgRRaGhqmwpCptRhKHr\n5LJZrEqFrutyIqOjHJtiVVe5ut3lgUOzXNpyuXy9w7X6gKeueGx0FDRtdL/ElHV1dVWSxHw+T6fT\nwbIseV9vFCTF91zXZffu3SNSn/g0Lz1Np77Bh++b5tnzNe47MA0k/Olzdf7Z//E735cfcH5Q8FrH\ndjJxm2CCHwzcavxHvJ9blsXW1tao9GJlBbXR4L5cjucch+yePWxtbbGwuEj9iSfYzahgYh+jXJwN\nw0Adr4HZti3zf+I45ty5cxw4cIBWqyUDoy3LolqtyjV9MRgyTRPTNEfZPOMhnFibF05k27Ypl8ty\nkKZpmuQ5nU5HikqC27zeB9Ibm9KEq0e4grLZrBy+dbtdORRLbmiCjeNY8hFRbHKjACW4iaqquK4r\nMyF935fta9/72JnjwVOhUJCcUAyE0uk0cRyztbVFuVxmaWmJwWAgG3jFcW00GgRBQLFYJJ/P02g0\nZN5l6Lp0XZftXo+5TIYPHz3K5bU18v0+A0UhmyRktra47Dicefxxiuk0VjaL6boUAIVRzlWz1UK3\nbaYBooi0rhPoOkuHD7O0tET/5ZfRL1xgEIY4gD8+T0zfZ+/MDK6qMsynSRSHtjfg6tUNju6bI2Xl\n6Lo+Zy5uMJM6wp477icMQxnl8GbEI7G6V6vV6Pf7bG9vU6lUePE7T1O7epK1y5dYKOjMr6T4oTtX\n8MN4wn/eBUz4zw8GJo/WLYb3Ysf/DQUujqdsnucBYJqmDC98p/HX3b7X+78kSXjsX/9r0l/5Cr1u\nl53BgPsB2m0KwP8NeIUC3H8/9/3Mz/Ctb32LS5cu8bCiUMhkuKtc5mv1Ol8NQ07t3k3YbJJKpwnD\nkJMnTxKGIdPT0zSbTdmS1u/3uXz5Mq7rsrq6yvz8vJzAXb16lWvXrkkCJYQfYbkuFouSZIlsH9d1\n6XQ60pasKIqsbBWTOyEKlctlwjCU4d2CWAmLtJhoiUmVsFPX63WuX79OOp2WLWmlUolsNovruqTT\naekEErvxovlDBHGnUimZpySmhMKGLUK1O50OnudRqVSk00hYpj3Pk+tygCSSghw5jiOJqLB7C2dS\nLpcbuaMaDf6eaWJqGtcNg1hR+EIUcV8uR348mdLCkAXgHzHa0deAJ4BvAkkUESoKGSCOIqqpFB9K\nEizLohfHXDdN9HEA6reiiD2Mco5M0+SiYXBkbKOP45hzlsWx9y9y/Og0K7M5UmpItz9EVXXuOVDk\n7NY6Sn4Xc6kh6+vrcmo7GAxYWFiQVce9Xo84jmm32yMBazxpFGGcuq4TxzF33HEHlmVRXzvDB6Yu\nc8dDZZq9Jf6vL53lMx/az1+8cJ0nL3j80//985PJz3uAycRtggneGCb856/i7fAf48tf5kK9ThRF\nzCYJLyQJzX6fDcfBXF3lyCOP8Hc+8hG+8Y1vjBpVo4iKrrMehlxglI0zc9tt0i0j1rXEmj0gj0MU\nRfJr13VpNBocOHCAxcVFqtUqrutKniMKHjRNo91uY5omxWKRdDotW19vFI1udNiIgOnXcmgIh7Sm\nfdfN0u12pSssDEMpIFmWhW3brxKKBPcQQzZxecmYCwiRMAxDoiiSAlWlUpHrdiIO4HshhCOxLid4\nnIgg0HWdqakpGdQNMD8/z3A4xHVduaIuqufF7crn81x66SWWGw2M+Xny09Okw5D+3r0sKAr6+fNs\n9vts+j5Bt0samGHkKPNsmxowYBSMbgNRkpDOZEi6XZTxfSrNzJBKpWg2m2zGMYlpkoQhfcBQFPbP\nzlKwbUqpFJczGSKzz5RlsHchB/GAetdjfjrNvYcXeeG6yr67PiqPtcjA8TzvdVsIvxe+7zMcDqlW\nq2xsbBCGIU8/9hccNS+ze1pB6+gM4oQP3bmHR0/tTPjPe4gJ/7n1MBGOJnjbEFbcMAylLdk0TUmi\n3mlruMCbqdl96Wtf4/4//mOmgP61a+yEIc1cjn/WaPBNVeUh4C8bDV4cDnl8MMA4coRDhw5xbWcH\n/5VXSLdaLPX7DBWFwcYGxuKiFFlSqZTMAFLbbR6IY4ynn+YFy2IwdhqJCtatrS3W1tbY2tqSq2aA\nzDQSIYuirn44HEq3kgiuVhRF2pFFkPS+fftkzpIgcv1+XwZYClFKTNEEmREB4Y1GQ7a2iTBGEZIt\nLNwim0i0VBSLRSkWicc+DEMAGbYtJrEbGxvya9FiIsQ2MT0UriOxSlcqlTBNk0ql8t3jq6qYpsn8\n/Lz8PVEp7DiOXM8zfR9dVUeuKE1j4HmsKwpBNstKu83R4ZBukrAMHGZEkvKKwmKSsAlcVFVmFIXr\nisKJbJaPDQb4cQw7OzyrKCTpNMHYvbYF/BZQGQ7xDYNsscADccyeKGJD0wgOH+bD969QbzUxWx7T\naYVHT2zx8fv30ep5nKslOIEjsx0GgwHnzp1jeXmZ73znO8zPz8sWGl3X2dnZYXl5mWw2K8ljLpej\n1+sxNzcnG1n6L73MXQ+sAjBVsDm6nOfFepb/n733DJLkPs88f1mZWd679r7HW4yDJTxAACRB0EGk\nQIVW4ooyR+0Jq5V0u3sbIcVdiNrQXexp9zZEabUSSVEkdSRBggaO8MCAwBiMx0yP6Z72Xd5XZVWl\nuQ/V+WcDAkEAhBuwnoiOsWWzqvKp932MK7aO3//cb+PxeH6xN2AXbwrdjVsXXVy6uJT5j6Pdxj87\nS0iSeNLp5PZ6nSN07ExLU1Pk221Ul4tkMkkmk0GLRvGnUgSBRToWpFC5zObLLkOWZXRdZ2VlRbTF\n0mgQmZ4m7/PRuv12KpWKGIDYtfbBYBCv10u1WhVKo7V2P6/XSywWw+12o2mayAdqtVq43W4ajQaa\npgl72KsNF3Rdf5ltX9M0oSbyeDxiEeN0OoXiyOFwoCjKy5rcbBWRfV9sDrOWuwFiaKNpmigJsb8g\nm6b5qsdJkiTUVduXfbt2fpPNBbxeL8VikVarJfIu2+02rVaL4eFhSqUS8/Pz1Go1oQrP5/NUymUa\nq0PMqNuNB6j29kI4TGNxkUnT5LymUQX8wFk6SqG8pqEAPjpDIyfgHBwkvhqFkLMsqoBreZniamSB\n2+Oh3tuLYllEw2H6+nqpzc3jlWXmPR6MUJCwaZKv11BzNcYSHizD5KZdE2SKDbJGP/l8Hp/PJ4Z5\n9nvLfj5/HhqNBul0muXlZaF2a60cQxkJMpOu8PGrxqm2DI4XgrhiG7r8511El/9ceugerUsU74bH\n/5WXsyyLZrMpvMROp/NNB9nZeKdkotWFBeL2bZomo5bFyWqV3YBqmijATcDJTIZPnjnDmTvu4MCx\nY8w0m8SqVbZqGn7gTsvi9sVF/msigScU6mzPFheZPX0ao9Xif9M09rRaKMUiflnmyfXrAZiZmSGd\nTpPJZMSwxev1Crm27a23CdFa9Y1t+7I3bzahcLlc9Pb2MjY2RiQSoVqtiuYy25LX09NDpVIRgxib\nqNn+/FqthmVZogZ3aGhIEJChoSHhqw8EAvT19VEsFrEsi1KpJGrf6/V6ZzspSSLnwbbAuVwuhoaG\nqNVqghwEAgGx4bOJn6ZpOBwO0SjndDrFfbfzjuzsJTt4NBAIiLa1VqtFIpEQRMyvaaQ1jctkmWi1\nyrQsc6PTyVKhwAPtNk9ZFtdIEgFJ4nogYFksA6bDwfOmyZWmiaSqTEsS11errDNNYrrONjr1s1fq\nOl91uzliGJ3HD8helQ/v7eGqzf3M5dt8/0SesXUb2b1jKy+eO8/1OwYo19s8emYWNdDDM1NVTqYM\nkpO70ebmKJVKQvq+vLzM3NycCMIcHx9nbGyMxcVFms2mUJKVSiX6+/sFCff5fLRbTUrL56jWGy97\nD+imxfYP/z7j4+Nv51uti5+D7satiy7eGLr85xeDzX8quk7NMIg4HCzV64ToBBfPAOuB56enmbjv\nPmY+9KEOFxkZYeH0afx0BgsmYE1Ps/3Tn8YXjfLYY4+RyWQo5nKossz62VkGPB6isszRs2dZf++9\njIyMiHN6Op0W5257oWXb3RVFIZlMEgqFhF1JURQkSaJer4vhka1UUlX1X9gC7aWUPQhqNBroui4a\nRu1hkj0wAsTQZu1xtDONbCWZzW8AYfe3YavF18YFyLIsBkCvlVfjdDqFkrtSqQiljb0gzGazomHO\nVoTbaqnFxUUsyxIqpHa7zezsLHNzc0yfOYOyvMxYs0kPUPB4MA4coBkM0hwdZeHiRQxFYTqbRQJq\n/NRi5lBVou02tdW/dy0sMG+a1OgMmQzAUSpR03WMWAzTNAlGo+SyaeqL03jNIqZTYdmfxOcPEfD7\nkLUqv3rNVoKRKNnMCh5/gBMpi6raywc/+Zs0Gg0ajQb1el0cW5tL2sqjnwV7CHju3Dmmp6fxeNxM\nn36R+ZUi43EXn7p6nJ2TSb793GyX/7wH0OU/lx66g6Mu3hReuWWzBxeXCoavuoqjX/86O6tVDI+H\npyoV1jWbXKRzsoROCHK/00lPpcKXfvQjZkoleufmuE2SmAQcwAU65Cl64QJZt5v6xYt8emmJiVqN\nM0B0VbZsWhZXVqv888WL1Ot1IWsPh8PCihYMBoXf3j5J2tstO9/I5/MRDodFILVdde90OjFNky1b\ntjA6OorL5RJDp5mZGZaXl9E0TQwifD4fkiRRLBYplUpCDjw4OAhAsVhk48aNQglUrVZF04Ztp0sm\nk+KyHo+HVqvF/Py8UEpFo9GXtXzY1wUwMDAA8DKiY+cpRSIRcTuJRIJarUZfXx99fX3UajWmpqaI\nx+OCvJmmKaTxtVpNZD0FAgEAtjudfNLrxVuvEzMMzgEew+B3ymUeVxSSXi+GrpN2OPA7HMw2m5QM\ngyVZ5lGnE49l0dNokGy3uQM4IElsdTg4sdr05rQs+tptrm+1qK2GX+8Yi/Ann9zOuv4Az5xKM5l0\ncvlEiIqew7vyNIbq5MQZjbmKi8DINUjBMNlCkdHLwiLM+vjx4yiKQigUEsOjCxcukMlk8Hg8jI6O\nCnJlbxar1SqqqpLJZJiYmKBaKRMrHeJXLw/zQNrPN5+a5vrtvZxfKnN0QedDo6Nv91uti5+D7sat\niy4uLbxv+A9weSTC/lKJa4E0MA6M0rFoN4CpQoHDhw6Rr1TQV9VGTjq8B+BuoPzcc2z83d/F1Wwy\nf+gQXjo1733RKCeaTbb4/VxVq5FbtbG3222SySSRSISLFy+KttBUKiXyjAYHBwkEApimSa1WEyHR\nhUIB0zRRFIVKpSIyFN1ut3h8tlrZVgTZym17AWfbwGwbvaqqomjjlbDLTNxud6cwZXWpZYdyrx0C\n2cNEu8nV7XaL14VhGLjdbpEn+Wqwh1j2c2A/tlwuh9frfZlVr91uEwgEyGazFItF3G43fr8fn8+H\nx+NhcXGRSqXC8ccfZ2hpCVnTaObz7KfDceMLCyyFw/T39OButVjUdUKBAGalgpvOl8NKT08nx8gw\naBcHjvMTAAAgAElEQVQKNICiaeKmE65t0hkwOQGtVsOUZTS3m5lzZzGtzlDpYrrEvk2DeJwVgk4/\n673L9I4mMYwWVdPLnk/8IUgq5XKJ3v5BsbhstVoirzIUColGOvv5W3u816LRaDA3N8fJkyfBMlk4\n/AS9vhYDYR8up5OBZJAXzma7/Oc9gi7/ufTQPVqXGN6N4LZXtpms3bKpqipO6K91uTeKt1vePbJp\nE2f+7M945L77yKbT1J59lnq9zvOaxlbgH4GcLHOXLPOoqtK7cSOpEycoWBZNy6IJeCSJgmV15Nrh\nMLENG5h8+mmudjioADcCM5bFSKPBiiSxoChEenuRVvNo1q1bx/DwMH6/n0qlwtLSEoVCgVar9TKf\nvMfjESfJiYkJenp6xLYtnU5TKBREK9n58+eFAqVYLBIOh9E0TWzvisUi2WyWlZUVIQO3pdmWZbG0\ntEQul0NRFEqlkgjXti1ygUAATdMoFArU63U8Ho/YoK0NBrW3evaxLJVK4rK2daparVIoFMT90zQN\nXdfJZDK0Wi3RPGLftq2ucjqdpFIp6vW6qPS1VUp284k9vMpms+zJ5fDrOluBHjpNH/amLG4YOFQV\nn9/PAaDodHJSUXhBlikqCvlCgdtTKS6jE5Jt0FEj1S2LCNA2TUqWxT5JYkWWuRf4f4J+Pnfreobi\nPkJeF7ftHuCJUwUGoxafurKP8d4AmZLGt36yiNsb4+TUBcLhMIlEArfbTW9vL5FIRGzN7NeK3++n\nWq2STqc5cOCAyKiyQ7Cnz51BbZdYmr3A4Ni6jnpLz/Grl4dxSBIfuWodPz58kT//4QqJgXH++L9+\n5ZJv6ng/oLtx66KL14cu/3lr8Gr8J9Fqsb9aZRcdq5LqdvMHvb3s93i44ZZbuO+736Wm67iABPAh\n4EfADwD5/HnM55/HOT2NQkextB1o5PPcLsuUdJ2TLhf9bjexWIxiscjCwgLJZJJAIMDs7KxonbX5\nhp2XKEkSoVAIVVWpVCq0222RyRiJRIQ10H7e7Fwhe3hkW8Ns1bWt0LGVRa/12bu2NXbtMg941bBm\n+/ZsJbdztUDD5jK25e3nBZnX63Wi0ajgSzYPsl9/9uO8cOECfr+fwcFBkdlk5x0tLi6Sy+UYWm3I\nW6nXMemohtrAErBSLHK21cLlcLCo653Myr4+/KOjOLxe9GqVmRdeYIlOzlFlzf1U6ORAeoAgnbyr\ndrlMaTV/aS16wl6G+n1cPdZitCfMUqHCUqHO7o3bGBnfgKZp9A8OCWWRrSgLBAI0Gg0ymQyVSoV4\nvOMTsDM91w5r52YuMDN1lGoTjr90lkajQT49Q0Kq0h+N8q9u2cLFdJm/eCDd5T/vIXT5z6WH7uDo\nlwi/KOmyLItqtfqyBi6n0/mutxC82dvfeM01cM017P/2t/mVM2cwWi3GL17E43bzv4+OsjUQ4Nte\nL9a11xKdm+Pmw4dJFYt8ye3mLlXF0nXmVRUtFIKdOztZOobRIQt0Nm6HgClJomZZfD8apbyq3LGz\nZ+xAbF3XxQnT6XQSDAZRVZVwOCxIk+1zT6VSlEolCoWCaBnRNE1YtOzAaJtoLC8vi0BqTdOIxWIM\nDg6KoYMkSVQqFfL5PIVCgVAoBHQaUuwTt01cotEo1WpVnLDb7TYLCwt4vV4SiYQYZthbMMuyROta\nuVxGURRqtRrNZlNs/2wlld2csbi4iKIoYrskyzJLS0ticAQdq5/dHjIxMUGxWERRFBEcrqoqxWKx\nkxEQChGo13EBjVYLDegFDgI+WUZTVdqGwUIyycKqWkvN5fDV6zRbLZyKQlzXcdMhSitAj6JwQZKY\nVhQ21Os8pKoMh0KoksQut8Q1WwdwKRZhvwtDUlDUGlg1eiIdiXUi5GY07uJCqUNMc7kc5XKZlZUV\nsUk0DIOxsTHS6TT5fJ6BgQFM0+TUqVPMz8/zyCOPsHPnTtrtNmeOH+L28Qa7rlzHYr7JV589iBG4\nHE88jEQRVt8jG4YTBK77TbbuuOzNvdm6eNP4WRaF7satiy7efnT5z8vxL/iPrjMYDOKVZb5zxRUM\nWhYngJ7rr2f+0CEqJ06QB5xuN5s1jU3ACFD2+Wjt2cPKygr5RoMrgfvpqJUO0lnO+BsNVjZvpl+S\nSKfTYhCTzWbxeDykUin6+vqIxWLCjlYqlYjH4/j9frEIsgsh6vW6KOlQVRXLssSQp9VqiaWbPYCz\n1UU2N3g9n7e2QtpWACmKIpTZr6Z2sdVINleyyz/sPEn7Nl/LqmZnONk5kfbgKBAICPuey+WiUCiI\nMPBYLIbX66VcLmMYBsVikbm5OV566SXC4TCS10u71aJHlknRWX65gRzgBZyKgktVWbdlC7GREZEp\nlE6nqVartOio69cOjcJ0hk/QGRhd+BnPYRD43bt3slyWuDC3TKuk4lQlLt+YwGhZnLu4RHRhQUQn\n2Iorp9OJYRiC88myTKVSYW5ujmAwKNpz7f9/+tgBpLP3c0Ovwv/9w+d54OAiPb1D1OsN7ri6lw/v\nGyMccONyu7r8511Cl/+8f9A9Wpco3kmPv/3/7Xr019qyXYrYfMMNPPXlL3NjKsWGDRv4SSjE//qX\nf0kwmaRWq3HuwAF2ffObyI0GNV1nut3mP+/aRbzVIgTo4+MMTEwQDAap6DrGkSP0OhwU83lCQMjt\nJu5y4Y1G+UirxWgqRXNmhqrTyfGhIfwTE/j9ftFUll1tOWm1WoKs2jaytUOmUChEIpEgFAoJK1kq\nlQIQ7WuZTIZsNovT6WRgYIBgMNgJCly9btuG1m63yWazIhw7mUwKWTh0jnk+nwcQGUv25swOMLRJ\nFXQCtG2CbecWGYYhPPqmaYptYT6fFwOldrtDR+yhlb3VS6fTOJ1OcT22xz8ajQo5t934lkgkREj0\njcEgO0oljjSbpE0TRVXp13XudzjweL2k3G7CY2MsJRKEQyHmDx9my9ISOySJ6cFB2pdfTrJa5alM\nhiHLwpAkvA4HTykKk6EQartNyDSZlCQ8fj8ORaFvxM+5dJMbt/dSazR56PACT8662BB20tZNWg4d\np6pQ1nQy1hDBYEBsKu1taT6f5+LFi8iyTCAQYGZmhosXL3LDDTeQSCR46qmnWFhY4OGHH2bLli1s\nidbZOz6CobdZ3+Pi4zv9XLO9wteOVfnHAzU+s8dLvWnwRCrJxz+68x1/j3Xxs7H2fdNFF138fHT5\nz1uHtfxnj6qyPxjkznvvJbmaRXj4sccYefRRakAL+ISioP7RH2GVSsQqFSa3biU+NES1WuVAsUjk\n4EE+U6lQaDYpAU8AG1wuyprGof/yX2i99BJWq4UaCqHcdBPbP/Qhenp6KJfLDA8Pk06nhTXMttTb\n7aH2MMe29tutsfV6nWazKdQ4xuoCz+Vy4fV6xbDojTTk2dY2u+nMDqS21U2vhKZp4rbtDCWHwyEU\nSHbOo22zWwvTNIUFzlZPt9ttEYZtt6XZJSkDAwMMDw+LRrVKpSLudyqV4ujRozgcDs4+9hjGhQsc\nz+fpbbfx+f0MVKukZZnJeJzlVgt3LIZvcJCebds4eegQ0wcP4tR1HNEoZiyGDlRX76dKZ2hUBSQ6\nNjU7OdENuOhY2DYPerh57yQOh8SFpRqO5GbikoMrN4eIqRCNeDl7dAnTCHPw4EEcDgeRSASXy0Ug\nECAYDApe5/V6aTabeL1eCoUC6XSaXC5HNBrFNE1CoRDZqWe4ecjFMy9OcfTcHK5WgXBbYmxogqY7\nid/notzQu/znPYgu/7n00B0cdfGasC1CNmwv/xvZcr0RovZubO8isRhDf/VXPPTVr+IwTfo+8Qkm\ndv705JJ69lnGFIXU6nBiE+BuNAjs3k04GhWbL6fTifuOO3h4ZITco48yXCjwa4ZBo17nm8BoJsO/\nKZdJtNsULYsZXWfTwgKntm4lvHevsItduHCBmZkZDMMgGAzidrsJrQZv241nvb299PT0CDWQLemu\n1+ssLS2JkOt4PC7un235smXTa7OWZmdnCQaD4vZcLpfIArA/1Ov1Oo1Gg1wu1wmc9vuRJIloNMrs\n7KzIHkgmk6I9xL5crVZDURTh0bfb3drtNisrK2iaJqxltr/dzgOwW1Lm5ubwer1Eo1Gi0SiNRkMQ\nLl3XRdZPvV7HNE36LItPl8vIhoHp93Nc03gmFsMlSfgdDjRVpTY+3gmubLfRzp7ldxcWuNE0sSyL\n4zMz/E/T5HwkwpZGA3e1is+ymFYUcrLMhGEQiURwxGIsVCpYySTp3l7W7e1h27iPZ88tIWGRtWKM\nbV7HwsI0D7y4wmVjQU7OFnlqTmVi+xi1Wk3Y9eCn7xc7bFXXdfL5PPl8nkB7hSu2DnPHvjGO9vXx\nxJNPcuTIEa4d3opHHsR0OHCrDvIVDbdL4daRCmdin+L7uWUC4Sgf+61b3vUN+RuF/Xxcavf79aK7\nceuii/cmfmn5z9atAIRCIc6123zQ7eYfgOeBdLtN8cgRLr/pJjaOjxMOh4V1Pvrrv86xkRFWHnyQ\n+uwstwJ54GCtRu3ZZ5ksl9lIp7WtXq/TuO8+zrpceO+8k2AwyOLiouANdj4RQLlcplQqiebV2GoI\nc6lUol6vU6/XxcDG7XYTDodxu93C5vV6YdvE7MvYTWetVktY4F8NttpJVVUajQZutxun0ynaX+2M\nSvs21g4dbWXN2uBtW12ey+WQZZl8Pi+iAmxrvrnKUyqVCuVyGafTyfz8PEeOHEGWZTLnz+M7exYZ\nmBwYYKpSYWZ4mHqlQsDlouV0khwfR2s0kFwunn/uOaqHD+OlY0vL5/NU83kcQJTOkKgOZFbvt5+f\nDpIkIBYM4orFiA742TUWp9luEfC6GQj4uez6j1EtpKlMP04irHJ4toIydAW7r7lZ8NBqtUqpVGJ5\neVk8l3auUygUwu12c/yp7+KxKqyULYa2fYBwJEoikeDF559isxTnG4+c5PxCAY9T5vMf3MzoQIxz\nybu7/Oc9jC7/ufTQPVqXEGz1xjsF28u/9ovszwqkey/gF9lCDkxMMPBnf/bq/7Z3Ly997Wts7euj\nr7eXgz4f/+GLX6SqaeTSaSLJpCAHhmEQueYaRp54golwmIeyWVTgWKvFnZKEYprIQFKSOA34TBPv\n9DT59etRFAWn00k0GiWbzVKpVMjlcqLBrFQq0Ww22bBhg9heGYZBPp8XuUW5XI5YLEZ/fz+appHJ\nZCiVSiQSCSH/tS1hdhh1KpUSQdajo6NCaq2qqrCLGYZBOBymUqngcrnE9k/TNEGmnU4nPp+Pnp4e\nQaBisRiSJLG8vEyxWMQwDBKJBJFIhHa7zeLioiAL9mbQbpUrFotUq1WCwaDITbItbrZ0fXFxUdjw\ndF0nWa+jtFoUDYOQYWA2GmitFg5ZZtLp5LHBQdw9PaRrNbKnT3P7k0+yXlE4FQwyFYmwZZW0yg4H\n2yWJnlqNR/1+MpbFjXRqafubTbYEAjzocrFHUci53cxffz1je/Zw+cgIKzMvUTVXuGrXFk4vFIgH\nBhgMJkgkEpyan+e7D54ik6uzbt06HA4H/f39IiPK3jZWKhUhUZckiaGhIcaj8EcfmaAn4sEhSfyf\n31kkEomwsUfhrssHmUlV2DUR4/D5HEu5Kg1NR9MtgqEwO3btEa0xXby30PX4d9HFz0eX/7w23i7+\nM7R3LwvhME9u2cLFYpFvKgqVHTs4fvw40+fOMblhA4qiEIvFiMfjXHfXXShPPYUeCvFiqUQMUAMB\n1q82cx2j88WjDfTW6wTOnGF5714ymQxer1e0vdZqNaBzHFKpFO12m4GBAcFDisWiKMjwer2Ew2EC\ngYAYurxR2BY46DyXa9trX6stz1Zp25lMth1OlmWhxF77xXhtxtHaDCX7tiRJolwui3DocrlMNBoV\ntr1CoUC5XBb19JVKhVKpxPT0ND95+GG8isLApk2EnU6SPh/FcpkThQJlXQe/n7GNG9F1ncXpaVa+\n/31ajQZVrxfD48FLR02Up2NBawGRaJRKPi+saawePx0YUlX6IxGc27bRPzrKxMQEfsVgQzDH+v4I\ni4UmC/J6kv3DuNevx9p3NfMXp9l93QjJZFI0oK3lpnabsKZpghs2Gg0OPPlDtiVN+uIBEi4Hzzww\nz+Dmq3nmoW9xeW+D//d753joxRQjMZUrNyXZt2WQxYLW5T/vcXT5z6WH7uDolwivl3TZJ1A7DNDt\ndgvv9ttxe28n7Pvwi5Cq8W3bOPEf/gOPfve7WA4HsV/5FTL79zPy9a+zud3muZ07ufwv/1IEWuu6\nzlQgwHCrxdZVebTmcjEdi7GnVMIql2mu1pmaioJ7fJzhzZvRNI1arSYIqu3btwMRo9Eoe/bsQZZl\nZmdnWVhYEGHafr+fvr4+HA4H0WhnCwOIcGxVVYnFYiQSCQzDEGSj2WwSi8Xo6ekhFosJhZEkScIi\nV6vVKJfLyLJMu91G13Wx/fP5fNRqNbEVs7dh0WhUNKHY9bKmaQrffybT2Vv5fD76+vpIpVIEAgFC\noRB+v1/kPem6LixplUqFlZUVAoEAw8PDQl20sLBANBrlZkni8/U6tXKZF2WZf/b5eEnT2OzxEAwE\neMHvp298nHK5jGma3KxpXL26kRw1DKqNBilZptcwcLRaLFoWjnKZK6tVfkNVmXQ6ecQw8AeD+P1+\ntPFxntu+nUgkwnBPD5ZlcebMGSRJ5kdnFRwvFQklBokne4XU2h6qzczMMDMzA8DWrVtF2KdNJEul\nkshqWFyY57oxiXuu3kal3uTkXIFd41Fu2RbmM1f18sKZDPvWJ8iWNZ44vszp+RKSw8Fcts7h2gg3\nT65728NWu3jz6G7cuuji7UeX/7w5vJL/XP2RjzC9fz8Djz1GUNM4sWkTI/fcg6ZpLCwsdNQwssyW\nep3ddBq3flypUEokWF+t0qAzkDhNJxvHymSoHj6M0+kkFAoRi8XweDyCMywsLFCpVFi/fj0Oh4Pp\n6WmRBRmJRIQa5Rf58qnrulCWybKMy+USKu5XC8FeC7u9zb59OxR77XWvDXG2B0eapmEYxsuCt+2B\nSbVapVKpoCgKAwMDgk/ZHKFcLpPJZEREQSaT4blvfIPd9TpJt5uL6TTLExO8lM1Cq4Uiy7S9XgJ+\nP9PT09RqNQonTuBbHebJ1Sor1SouOl8KfXTURC6gnc8jw8sGRx90u/Hu28fg7t2Ypkl/fz8TExP0\n9/cTCoVYWZzjcGaR+NAIg04PhUKBSqVCOBxmZHwSp9MpYhfWtszZeZdut1tYEjPpFRaPPMDVg00y\nxQYvnMiQCHk4fmaJE4ef56WZFIcdsFSGLf0SH71mK6rLxUJe6/KfSwBd/nPpoXu0LlG8XR7/Vqsl\nbE6Koog6dU3T3vTtvRm81z7ot918M9x8MwDzFy8ydu+9bLIsUBQ+ceIEj3z721z7O78jNkwn7riD\nuQMH2KIovCjLbEsmqWzZwv56He3kSeZzOXokiZhlIVUqjI6OIssy9XqddDrNyv33M3L8OCVVZW7n\nTjGEOXbsGIVCQXjtJyYmBBGxpb4Oh0PkGBUKBZFr1NfXR7PZFOHU9rBmy5Yt9PT0CHJs1wzncjnS\n6TS6rgOIX8PhMO12G7/fL+xkXq+XCxcuvEwxZIc75nI5QQI2bNiAy+Uim81y7tw5crmceGz1ep3x\n8XHh1R8aGhIDpEajIchVJpMhGAwC4JRldug68VyOG1SVusOBCezUdZ7Rdfbv3k2h3aYpSRQmJgTR\nzOfzxJ1OvKs2P8uy6I3H+U5/PzOHDpGQJAo+H59SVebrdXpHRqjkcnykWuXHbjcz4TCBvXsZGBkR\nNkCb9LhcLhFkbbfLBYNBMTyyW1Y0TWNqagqn08lll12GZVnClre8vEw0GqXdbrMuDr97yzB+t4PA\nQIByvY1blfE5VfZMxrlqU5LHji3x4X3DDCUDXExVmauESY/ew517r6TRaLzn3k9d/BRdj38XXbwx\ndPnPO4tX8h/vv//31GQZyevluuVlHpmfZ+tddwlbtXn55SyePEkfnYa2y+JxjgwPU4vFyE1NMd9u\no9IZTuQqFZaXl9F1XTSd5c+cIVatsvTlL+O49lr2XX89c3NzHUV3JMLY2BiBQOAt+dxstVpiaGTb\n2xqNhgiifi2Ypkm1WsXj8VCr1fB4PCiK8rL79cpgbEDY4WzltJ3TVKlUqFarYmDk8XjI5/OkUilk\nWSabzdJqtVhaWhLZR/kDBzh76hSjc3M0AgH2F4vk2m3OpdOofj9qrYakKBCJMHP8uLgPWrstBkJV\nOl8GDZcLpdlEBsp0ykA0IE6nkfYKgFgMdXiY1vr1qKrKunXr6O/vZ2BgQDxf/UOj9A+NiqWnpmm0\nWi0cDgeSJAl1vc2JnE6naL+zh0mNRoN6vc65F59hQ1ijWoFkUGWlUMPQW4R8KmG/h5ivj7qm8ZfX\nDPKZ2/by9w9PMdXlP5cMuvzn0kN3cHSJ4e3aYr1yy2ZXwEuSJLzmb/bD9+3+0H6nN3v1cpm+dhtW\nyYAsSThWs4ZUVUVVVT7wa7/Gw3/91xTKZTZGo8Tcbs7t2cOVv/3bPP+Vr3D3177W8aibJvnz53n4\n+ecZ3bYNj8dD/fBhvjA/T6rRwKFpPHDqFAd9PmZnZ8WwKB6PE41GxXar3W7T09MjqmpDoRC6rlMs\nFolEIvT09BCPx6lWq6RSKc6fP4/P52N4eJhWq0WpVCIYDIrhRbFYJBAIiBO4rT6yT/DhcBhZlgmH\nw0BnmKNpGufPn6dUKokMIkBszuw6XVmW6evrw+Vy8eKLL7K8vIzT6WRlZYVyuYzP5xMy5kajQTab\nRWs0CNIJYiwWiywtLeFyubh9eZlfpdPcsmwYHcKjKJiKAm43LZ+PhXiceDxOcpWo2ORzaWQEeWEB\nF7DYbrPU08P6667DBK5YHaItz84SXc1mqlkWFxWFJ8bHGbzlFkb6+pAkSYRmKoqCoijCtuhyuUQT\ni51FFQqFCAQCwhoIcPjwYdxuN729vbRaLaHq8nq91Go1ehNRAh4Zr0uhpuk4HBL/8OhZPnn1BE6X\nC6/XzbGLZ/A4FRbzdU5kFP7sS//0vglvfT/gtXIKusSpiy5eH7r851/i3eA/A4aBV1UpGAYhRSHk\ncODz+ZBlGVVV2fuhD3Ho/vvxV6tsDIVQXC4i69ez8fbbOfKjH3H1Y4+ht9tULIt8pcJFScL0+0mn\n05w7dgy5VGIBGMzlKMzO4o5GmZycZGxsjFgshsvleks+M+1Fmp2/CJ2hjm03+3mo1WrCZm7nKa1V\nG9nDEPtcbCubbPt9u90WdrNisYjD4SCZTIpsw1wuR6VS4czp06RmZ3G43QQjEaKrz8f+//gfyR87\nRn+zyRmgXKlQBmpAY7VYo+50YlkWrVRKDLYURaHmclFvNrHoZE5J4+P4QyGyp0/j1TQCdLKNQsCe\n/n68ioKj2eTY+vVsuukmtmzdSjKZRNd1QqGQWGbaP3YYua7ruN1uisUiPp9PBJrbxS/2e8/OwrSb\n8WRZ7vCndoOeuMq2wRjlmk69ZXB4Os+teyfZOBhj61CIv33oJMmeOF997FyX/7wH0eU/7y90B0dd\nvGzLJsuyqD/t4tUxvmkTP96+nY+dOoUsSfwkHGbkjjvEv1uWxbNf/CITzSatRoPTKyssfvCD3Pb5\nz3dOZqtZDaqqIgEuRWFsYoLBoSEKhQL1EydQm00ky0I3DDY2m5yPRNi3bx+KotBoNETjhB3maLdw\n1Ot1qtUqi4uLFAoFUe8ei8VYWVlhenqa6elpotEoY2NjuN1uDMMglUoxNTUlyAwg1DKmaYoTfiAQ\nEOGVhUJBhGhHIhEAstks8XiccDjM/Pw8jUYDWZbp6ekRrXHVahXDMKhWq+RyOdGaYg9dPB4P7Xab\narXaCc0uFPi1Wo2bVJVZr5e/bjZZt7xMVJa5wTDYQacu1gG8CPTrOt9TVfTJSdaNjoqw7XK5LFpL\nnE4nVjLJDxoNLJeLKQBJYofPx3I4jJlK0arXkT0eDkgSg6dP4zQM7g952XvTJIazxMT41QRDIaDz\nHmo2m0IZZW/ZbOIoyzKyLFMsFsXGbXh4WGwsn3zySW6++WbcbidycZqxgIZutdmzZw+K2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trp0iFAKICYr5kkngikajRmXU6XQayyKnG+byxTw3gZW7mYuu/yI0JapQWYVY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\nERERUUJsOCIiIiIiIiIiooT+P2wTBDSvVgX3AAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2173,13 +2426,15 @@ " axi.view_init(elev=10, azim=-80)\n", " axi.set_title(title, size=18)\n", "\n", - "fig.savefig('fig/05.10-LLE-vs-MDS.png')" + "fig.savefig('figures/05.10-LLE-vs-MDS.png')" ] }, { "cell_type": "markdown", "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "source": [ "## K-Means" @@ -2188,7 +2443,9 @@ { "cell_type": "markdown", "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "source": [ "### Expectation-Maximization\n", @@ -2202,14 +2459,16 @@ "cell_type": "code", "execution_count": 45, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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9l1dffZWysjJWrFjBkiVLAA4qn8FNN93EVVddxd13382FF17IihUrWL58eW6/\nKIrccMMNPPjgg/h8Pr7xjW+wdetWFixYwPnnnz9sEsYjyU4F/6OPPmLEiBFDEjBOmTKF5557jqVL\nlzJ+/Hg2bNjAokWLEEXxgO7bbbfdRmdnJ0888QR1dXWDFI6qqiqmTJnCsmXLWLhwISeeeCI7duxg\n4cKFQ9r3eDx88sknzJgxY0gYxiWXXMJ///d/c/XVV3PzzTfjdrv53e9+R19f36DymMcKDc1tSOqu\nVbF0KkU6ncHpctLQ2sn0SQMu8Lqu09MbpLW+joyrGJs8MPR58/LoC7eSMiS0zwwCo0dUUNfWTSwW\np3ZHlHQ6i6rIOFSVcDxFRVEZsZRGFpFYKITkzCJhI5mIk9QjpNIpbB4b2+sNOoJRbKoPweym0Otk\nRNVAgknR7qAn0EtZackXuv5YLDbkpQYDBs09Q48mTpzIWWedxQ033MCtt97KzJkz6e/v5+2332br\n1q25UCqXy0UgEKCtrY3KykouvfRS7r//fn7xi19QVFTE448/zvbt26muriYQCAAwb948fvnLXxKN\nRnn66af5wQ9+8IWu63DR0NqJ4tx1X+KJOIamozqdNLW2M6Z6oJRVOp1G0zQ2btiAs6Q6d7zX5yUW\n6CeR1jAMA1EUGV1ZRu+WZqL9fXT0hsmmU7hdTgzDIG2a2POKSScihKNxIn3dOPIK0bIayUSMbCpN\nNp1kbLGLFR+vJYuNTU2dyOiUFvgo+WyyFEtlDslKmCUvB0dzZy+yMnBfTNMkFosiiiJZUaQ/HMkl\ngI1GYxhahg2bt+Er2+UN4FIdhNMmsfjAqpZkkxhRUsjKdZto2L6FlAamYTC2ZgKaYMO0KeDwkEkm\niQSjRPt6sPuKSOsm8WiYTCZDMBPHP7KIFWvW43C52bijFYcNqkqL8Pl8AEQSX7wijiUrFhYHz4Es\nLAkIR7Ss7VeZiRMnIooijz76KN///vcJBoM8//zz9PX1HXDOBhjIqXDFFVewePFi6uvrueiii3A6\nnXz88cf87ne/44QTTuCaa67JHb/773766afz4osvct9993HBBRewcuXKQbqP3+9n5MiR/OpXvyKR\nSFBWVsbf//53Ojs7cwnYvV4vqVSK5cuXM3Xq1FwZz6uuuoobbriBsrIy3nrrLV566SXuv//+Q3Dn\ndnHddddxxRVXcO+993Leeefx6aef5vI1fF7vBsvYcIiRJOmABpsj4T61NyH54Q9/yP/8z/+wePFi\nLr74Yu550V31AAAgAElEQVS8807S6TTz5s0DYPTo0SxYsIB58+axbt06Lr744r22t/u2k08+maef\nfpqnnnqKv/71r0yZMoX//M//HPRgXHbZZaiqypIlS3j55ZcpKiriiiuu4Mc//vE++z1cOZzP8xDs\n7zu773e73Vx99dW88MILfPrpp7z22muD9l999dX09vaycOFC0uk0I0eO5Gc/+xmvv/4669at2+85\n/vGPfyAIAjfeeOOQY+bNm8d3v/tdmpubWbZsGb/5zW+orKzkyiuvpKGhYZDV9qabbuKpp57i448/\nZsWKFYPO4XK5WLp0KY888ggPPPAAmqYxffp0li5dOmz1ioO5V0eCWDKNKEpkMmnqGlro6Y8g21VU\nu0SJU2L6pPE0trRR1x7A5nCREBRaWlopKsjHl+cD08RBBsXhoi8UweN2gQBCKoxit5NJplE8PjRd\npz+RJZXR2NHaAbqGt6gctaiCZLCLWLAH06biLijB51TJLymmO5HFLttQnE4A+tMaQlsbVZWV6JqG\nw3HgL7698fDDD/Pwww8P2f6jH/0oV6lld37961/z7LPP8uyzz3Lfffdht9uZNWsWL774IiUlA4aP\nc845h5deeomLLrqI5cuXc9ddd/Hoo49y6623kk6nOeGEE1iyZMmguL8LL7yQa6+9FsMw+P73v3/U\nGq4SaQ1kmVg0yvamFsKJLA6HA1UWyZR4GVM9go1b6+gMJbA7XcQ0iY6GRirLSnGoKjabDSndj6+o\njEBfiJKiAlwuFT0WwGa3YyRB8eaTTCcxsJHKGGzasg1BFMgrrsRZVEUi2Eki0I2WV4LT46W4wIfg\n8tKXiFNa6MWhDshLRyiBTeqjoKAAURAOieu4JS8HRyKjoSoQ6O2lobWDRNZEVRw47SJ5doMTpk5m\nzcYthNMmumESyeiEmpqprCzHZpNxOVUivY3IpRVkMhk+XbuWdz5cQ3sc7IXjc96Ca7c0IGlJVNVJ\nJJZEEEX8xeU4CirI9vfQ39NFtqQK1aFSVVJMTHCSSvZTXO7Llcysb+9hoqLgcDiwSZasWFh82QiC\ngMthZ38agJZJke8/NsNWDzUHO6/c3/HV1dU88sgjLFiwgGuuuYbCwkLOPPPMnGEzEAhQVFQ0rA6x\nJ3fccQeTJ0/mpZde4uc//zmJRIKqqiquv/565s6dOyhXwu5tnXbaafzkJz/hxRdf5LXXXmP27Nk8\n/PDDuVw3MFCJ59FHH+Wxxx4jHA4zatQoHnvssVyliQsuuIDXXnuNW265hVtuuYUrrriCJUuW5L4T\ni8UYOXIk8+bNy+lk+7pnu/dvf7rbnDlzeOSRR1i4cCGvvfYaEydO5Pbbb2fevHnD5s87EARzL5px\nW1sb3/jGN1i+fDmVlZXDHWIxDKFQiObm5mFrm+4kmUxSXV19zMbIW1jsycGOF4dqfKmtayCQNPnH\nh6vo121IsoJpGAh6lvI8lVMmj6Q/LaB8psDV1tWjS056erpR0EjpBg6Hi5bWVoJ93ZQVFpCIhimt\nHMmW+kZSNg+SZCej6QR7u1EEE8lXhKwl8RSUgGhDEXXsWoJRI6owTANFNElkDUpKSmlra6WsrBS7\nMhBWoyUiTJswDiET54xZ0/Z1accE7e3tfPOb3+T//u//ho3v3htHSl4+3rCFSFbg/z5YRVZyIcl2\ndF3DZuqMLXEzbVQ5ccGB9FmM5tpN2xEdTnq7u1AkyBoCkk1mR309WipOfp6XVDxKWVU167Y2gOoD\n0UYinSbS14MiidjzirCbGg5fPqIo4ZHBSISpGT+ORCqBKkFWVCjMz6ehoZ4xY8fmXvxSNsGEcaNx\ni1lmTN63MfBY4MuQl0M5d/n76vWEYik+XL8NU3EjSTb0bBZZ0JkxqoiqUj9pyY0gCCTiMba2BjAQ\nifT1IACS3U4mq7F12zY6mnYQUcuRfcV7PV8y0IqsxRk5pgbZ7QMMPDYTm5ZmzJjRxKIRVJuIpLpx\nupy0tbYyarfKQi4hS1VFGSPyHIwbPfILXfuR5vPKCljz10OBdQ8/H3UNTbSGM/tcUHSSYdbUCV9i\nrywsDpx33nmHkSNHMm7cuNy2ZcuWcf/997Nq1aohOXZg/+OFlbPhEOP3+/fp3WCaJpIkWYYGC4tD\nwOiqcmo3bqAxECUYTRDoC9IfiZI1BRJZg0+3NOUMDQAuRQEBFMVOwpCwO1S2N7WSkFzkV4yjT3eQ\nzRtJU28c0xRJayZZXSOZjGNz5ZNVvET7AgR7A6Bn0VIxEuEgXl8eiVSKPFXGFEQSukRzVy+S4iTU\n04XxWT6UVEajYVstTlkk1B8edC2aptHZ1U0w1M+xxNFcoWRPKksKWbFyNYG4TjASI9AXJB6Po5mQ\n0gU21LfmDA0ATocNm802kJDP7kTTDepaOjDdRbjLxxAR3CS9FbQGE2i6RtoAXddIJ5PYfcVkbU5C\nfQGC3e2Iho6WjBMNBvCXlJFMxilwO0lpEE0bNHf2YJMV4v29mMbAPe2PRGlrqEOxSUNCsVKpFO2d\nXcRicY4ljiV5Kcv38OHqT+nPmARDYXqDIZKZNIg2+tMmtQ2dOcOQ6nQhGQMeS9FEGk9+If39ERo7\ng/QEw0RcI/ZpaABQi6rIyB5atq/HzKbJJuOkwn34isvR0gmK/V4iaY3eWJrOnhCmrpFNJeGze9oT\n6CXU1YogkMvBtJNoNEZHVzfpdPrw3KzDwLEkKxYWAGNHjcRhpPcaJqElokweN+qA2opEo9Q3tbCj\nsZlE4vOVZLewOFjee+89rrrqKl5//XXWrFnDSy+9xBNPPMG//Mu/DGtoOBCsMIrDwMSJE6mtrUXX\n9UEeDslkEkmSDrjMSygUIhAI5GJ1i4qKjrkKDRYWhxOHw0FHVxem7AZJAgQ0UyedSOAsK6Sts4Xj\nTDOnEFSUl9K/vZ7Orm7i6SzJjE4woWNmOvE4VbwFxYQCnaSSaYK9fTgLHcQSKURBQJfAtKkYcgZZ\nEohH+impqMArqpTmOdFNyAoSmp5Fy2Zwuj3ohoHXIVOe76Kzu5dIqJcZp84hIcqs2daC3ykxY/IE\ntu5opK0vgig70DUNRWxm2nGjyNtHremjhaMxvGZvFObn0d7di+EsBlECTNK6jpJJYUqF9PaF2L0g\nWWVZMdsa2+kO9GGINsLxFOFEFtmM4PZ4kRUHqViCtq4W0oYNu5ghk8lgAgIipuKBTAZJ9ZBNRMgv\nLqHI5sDnUTG0NBlTJKtlEaQBr5xUNkuB143HbaOts4dsOkXlqGn0ZaB93XaqS3yMqx7Bp7Xb6I1m\nsCkOtOYevIrIjEnjhy2ZdbRxLMmL16USCMcRfG5Eu4JhGCTTGnkOnUgihUPYpVAIgkB5sZ+6tm4C\nkSjR+ma6QhHiyQydPX24qwfnz9HTSdKRIIo3H0nZNU9wFlYQrutEMnTy/D6K7U4K/G7i4T6SmoGu\nadgcNhAENEGissBDWtNpbutElSWKKkfRGs7Q0LmRyaMr8Pu8rK2tI541kewKemMnxV4n0yaOO+p/\ni6O9fxYWeyIIArOnT6K2roGuUARDtCOIAmY2Q4HHwcRpNajqvpPIR6IxNtU1EcuaucWS+q468lSJ\naTVjDknZdwuLvfHTn/6Uxx9/nCeeeIK+vj6Ki4u57LLLuO666z53m5ax4TAgSRJTpkyhv7+fnp6e\nnLHgQEMndF0fZKwQRRHTNGlubqatrY2JEydaJXMsLBiobe/yl5CfMNARMA1wOBQEAUKhMA5pcKya\nzWZj7MhK1m6qI5o1iMTT6JIdlzefvlCI/lgzmCbRZBJcfnQTsNnRENDSKWTFgSQKuL1FxBNRov39\niDJE7TZqG1tx5RXjUB1k4jFi8ThepwOlogRFlskYMH7MqFycn111Es5qvPfRagyHF7tzIJml7bP9\nn9TWc9aJ047qMm8VFRWDssUf7WxvbMFfVIJb9pDOZBFEcCgKhqETSyRRhMErqW6XmwKPg3gqS1pL\n0B9NIaouRLuPzp5enE4XqUScFE4MG8iiDcMmkM2kCG/9BFG2Yxo6ScVBb3sjFeXluMaPItbaQlco\nhjO/EFWWScSCeDwevC4HCc2kUJZBsjNh/Bj4THwdLjctvTG6uj/BUPNwuAYMCzabjQywdvN2Zk+f\nzNHMsSYvG+uaKasow5BdpNJZbJKE3S6TyaTJaDpe++DVy6LCQrZtq0MzRLp7e4lnJYIdTahlu9xR\nDV2j7cNXiDRtJpuIIDu9eKsnUXnKdxClgSmZo2Q09VvWM3biVIoKnXzyyccYNicOdwKbKJAKtZCf\nl4fP6SAYTeByKjicLmpGVQADyZcVt5dNDe0oUjuoXpTPwottNg/BjE5tXQOTxh9dSZh351iTFQuL\nnYiiyOTjxjLRMOgPh9F0Hb/PNyjGf2/E4nE+rq3HprpRdtPQHC4XKeCjdVs49YRJx4Rh2eLYRFVV\n7rnnHu65555D1ubRO4v9CpCXl8f48eOZMGEC48ePP+DQidraWmRZHpL3QVVVZFmmtrb2cHTXwuKY\nozcUoaioAJuZRbHbUdUBQ0MylaKju5ux5QVk4rtKYJqmSXd3L4lUGrvLh2Czowk2+qMJwrE4oUiU\nvlAQXVLQsjqappFJJVDsDmx2BZuRgUwKDUBRSaXihLOwvbkNhysPxeVBsCmIqgtN08gmwoiSxNat\nW8hzyoysGhzLZrPZ2NbSg00eZuJgd9La3nl4b+DXjEg8RVlJEVoqiqoqOD7LTp1KpWluaOCECSPJ\npHbVwzYMg3A0QTKRwOEtxLTJZE2JYDhGPKPT3dNFJJEgresg2Ekl4vTWrSMW6MQ3djreUVPxjZmO\ns3ICnrGz6NVV3v3nKnbs2IHLX4TicGPYHNgUlUQsiqilSaU02lpbKct3U1RYOKj/NrvCttaeYQ1Q\n4bRBPJ4Yst3i82MIEnluN1omhVN1YLfLGIZBKpOlrXEHMyaMRtN2lZ7UdZ2MDol4DLvLj4FIIpUZ\n5LnQ9uEr9NWuIJuIAJBNROirXUHbh6/kjlG8+cTjcbK6TmNflEzWxOH1IztcmLID2a7QF+hClW1E\n43FCgR5GlRfidO4KGQNIagYtPYPDtWBgQaQrFB2y3cLC4tAhiiL5fj/FhYU5Q0MqlWJbfSObtzfQ\n2NI2JNxiS0MrNnXvruqS08v2hpbD2m8Li0ON5dnwJbO/0IhQKIRhGHt1HxQEAV3X6e/vt/I+WHzt\nEUWR0kI/4ViKnmA/sXSW/miMTDoLyTBBrZpUWxsjq8qobWynuTNAfWMzYVQygT5km4xgmCRTKUTF\nRSre/1mpO4GspiFLNoxUCtnIgGDgcMg4ZS82RSEVT6EnojjcHrz5VaSzWYx0jFgqjWmaFOc5qSgs\npNwjU1Y5FsM5fAhUao/Y6p3YbAOJBi0OHZI0IC+prEFPqJ94KkN/NEkmncYlpKjrjuKT+skvKmZL\nQxstXb1sb2omjkqkL4QoSmiGSSaTQbCrA94uNidgkErEiHc34R45CdkxfMZmuycfuyefrq46XH09\nuPL8pLMaGDqjK0ooyXNQXeykvKiSjM055PvZbJbsXqom22Q70VgMl2vo9yw+H4rdTnmRH1MUCYaj\nRBNpIrEk6XSKCp+dtTvaKXTZEGUH25s7aQ8E2dLQTEpyIYsZRIxBmen1dJJI0+ZhzxVp2ox+0rdz\nhglBFJCNDKImUDZqHKlEjGS4j7RuIKEzadwY/KrImPICFNU5qATwTlKpFMJwhkwgqxm58q0WFhaH\nF8Mw+LR2O33RNMpnFWT0eIL6jg1Ul+QzdtQIstkswVgKh2vfHhDd4RiTdgsP3ZNsdsAAeiCeFBYW\nXwaWseFL4kBDIwKBwH7jsVRVpaenZ1hjg5XnweLrRHVFKW19OxhTWYyq2NnW1IokiKiqk6oRJRh2\nN6FMho3vfkjVyFGg+jBkJ1pWIpvRyaYzpJKJAcOCy4+pa2TiGmqeA4e3gGwsCIZJFgFZEnGaGjav\nD5tdocxXjEsuJWuaePP8NLW0IjvdeP1eNE0jlk7R2hXkhFFljB89ko3NAeRh6jznuYZ/3rPZDD53\nweG+hV8rSvxeopqAaRg47BJbG1sRTROXS2XiqLFodg8t0QibV36CM78Ym6cQwxZA02UysdiA10y8\nDx0Bm+rC0DXSyTDOvBISPa24qmqGGBqGi823l45j69ZPmPONC3CIItlshkAkQToe4RszJuJQZLri\nQ43OkiThcQz/2tYzafJ8R3+Oj2OJQq8TUXEhiiKyBNFYAlEU8HtUxk+cSEaSWN/ciks0iOkikisP\nU+7BwE401DeQVyGbybWXjgRzHg17kk1ESEeDOJWBUIg8r5vK6tEko2EcikxHR5T84lJUIJGM094b\nJq3oXHT6THpCYRLD5FJ02GWkvRgzHbJkGRosLL4kVq/fTFJw5AwNMDCeS04PTb0xoIX8PA+Cbf/h\nEVl9IAHs7sYE0zT58OO11LUGSOkmdpvIyNJCKov9jB9dbT3rFkcUy9hwgHxRJX5naMSecVaqqmKa\nJrW1tUyZMgVd1w9oUNB1fcj/q1atIhwOY7fbEUURr9dLIpGw8jxYfGVxuZyMKc2jvjPEuBFl9IWj\nGGICVTYpLSunt7eX3mCY9rDJ9rXbKCgoRHV76Wptx1T9CIKCKivYNZ1oKEA22ofN4SKbiCLa7Kie\nfDKRXqK97XjsMmJJMal0FoehYffYcao+HKqT3v5+7KoLuygQDPZiCBKyJGCk03T29lGQ78fV1kVq\nj5XEbCLGydNqaO6LY3cMDpuS9TRlJUVf9i39SjOyqoJgeBuG140oigQiCWQliddpx+X20tnZTXdv\nkEB/AluwHZ/Xi9PppLerD8mTj2DouHwKmqYR7u3EyCSR7CpaMoKWTeNx7lL29xebr5QfR9u29biL\nq9AFCadig1SS1o5OzjvzFNo/2YTNOdh4IGTinDBhDN2JLDbbrommYRgUeBQrcdghZtL40Xy0diNl\nxfmYpkkolkFNpSnK86AbOu1dATp7+gmGIrjz/DjtEk6Xh1BPH7KnEMHIIom7DEaKNx/Z6R3W4CA7\nvSiefABM08CrKhjpBH6vi0A0hi8/n0wyTjieAEHCJoqEklH6QiHGjqhkzZZm7M5dhi7DMCjxOREE\ngeQeq6DZTIbRxfmH8c5ZWHx16AuFaOvqJaPpyJJEZWkBhflDn594PEFjeyeZjIZNkqgoLaDA76ez\nu4eobsNuH35uLysKDV19FPq9GMZeXNd2xxw8j4hEo/zPG8tJ2DzYFQ/IkDJNVm1tY+32Fgo/3cKs\nKccxdmTFkPBsC4svA8vYsB8ONlnjcEYJ4IBDI/ZVNnN3dj+nruu88cYb2O12lM9WTnf2MZVKUVhY\nSGtrK3PmzLG8HCy+cowdNYLykiI2bqnDSMaoKPLj9ngJBkNEMyZZA0ybgmEKCLKDZCiIIsvEUkkQ\nBExTw8hmMbQMzoJK7A4HhmEOeCcEe3A53SQj3eR5FY4r99PY3o3XnY/H46XMJ4Pqpqu7E0lyIQom\neXn5pDNpCt0qBV6FmOBk7ebtnHT8JLbsaKQ3HEfTDbwuhXETBypOONUu6tt7SGRNRAz8LoVp0yZY\n2dgPA9MnH0dfKMSqTzchaUkqSwtQVSedXd2kBRlEibQGituNIdrRDQ2baJJNxjBMMLIZwEQSRJT8\nCmS7TLS7DbV45KDz7IzN38nO2HyAEaf/GzbVTaCjmYrjpqFl0hR5nZQWVNIR06lvbuXkaRPY2tBC\nKDZQ8izfozJh+iQURcG2o4H23ggZQ0ASDErz3Ew+bjwWhxZJkjht1vF0dPUQ6upAyCSorqhAtttp\nam1HtDsRRBtpU8AtyWiSjJlNI2GiJaPohoFdUUn0deAsKEdSVLzVkwbJxU681ZNyni+ZniYmzqxh\nfEUhadFOc8cWXHkFpHQdvz8fwdTwO2RGVk1hXUM3ZcXFzJwwkh0tHUTiaWySSGmem+PGTMQ0TTZs\n3UFvJIlmCigSVBf7GV1d9WXfTguLYwpd1/l4Qy2RrIDiUAERNAjs6MQptXPStAnYbDZM02Td5u0E\nYmkUpwuwgQHddR04pTYEDOz2fZcMlFU3ff2RQRVu9obPac/pAJlMhlff+YC0w4/9swSzmpaloyuA\nJtgQBZE0IO1ooyMUp9zvZErNuH20bmFx6LGMDfvhYDwS9maU6OjooLq6ep/n2RkaUVRURHNz8z6t\nj8lkclB7K1euxGaz5QwNhmHQ3d2NIAjYbDaCwSBer5eNGzfi9/stLweLrxxOp8rM4yexoaGNjDKw\nGhxNpJBkB7JdRkvGsSkDq77OvHwi8Rg+j494JALiQDUCtWwEyXSadKQf2elGwEDQ0mjxNHl5RRiK\ngq+glAnufMLhMEUFeSgOEb9HpVNViKZT9EUS2BQVv9NOgVehqKgYsilCCY10Or3X7O+V5aVUlpeS\nTqex2WzW83mYKfD7mXPCVHb0xJBUJ4amkcjoyIodQRAQBNA1DUEQMHQTjy8PTVKIhkLITjdaMkpe\nSSXxWIR0IkY2FcNVuUvZP9DY/IwOejJGoVelKM+Fx+vFJmh0BqPUjHUwfdLwBoSasaM5bsxA7ghZ\nli0X2cNMeWkxJ0wcS2ski2y3E4tGMcUBzxLD0HOLBJIooWlZ8gqKyBgCsXCI/IrRtG/7FGdBOQCV\np3wHYFiPFxhYKPCKGUaNm0CBR6Y/msQtG+iJIFndhl3PUFLgo7jAj92uoCgCrV0BTpw2kVlTfMP2\nf/qk4zAMg2w2i91ut4yYFhYHwJqNW0mJKopj8PNidzjImiar1m/hlBlTWF+7nVBW+MzQMPg4Dajd\ntImJkwdXCtJ1nZ6eABldQxQESooKSaZFKgrzaO1PIdmGV8+0TIaxFbs8Huub24hkBCR14HjTMGnr\n7EG0O3MKXiSZpj8qMqKygkDCYNO2eiYfd/RWorH46mEZG/bBwSRrbG1t3atRwm6309jYyNixYwft\ni0QihEIhzM9cHH0+H+PHj6etrS23bU9M00SSpFy+hlAoRCgUGpSFuru7G1mWc9/f6SmRSqVy1Sym\nTJny+W+MhcVRiCRJTBhZwurGIIrqRNMNZBnsigOHpCMrMgYg2+y4nW7S2RQ20cRhF9GQkWQJSXQQ\n093Y7A4cIqgFBaSCHSheHw6Ph1giSXlZCapTJdDTjeC1M3VUOdP/5Qw+XL+NllASv78ASbYNPH+m\nidfpQJRtxBKJ/bowKsPkdLA4PPjzfJS4JHo0nUw2AzvLDjoUFNFEkQfGT7vLg92E3kAPit2G0y6Q\nNGRkh4yuKWRNJ6ng4KohBxqbb7fLzJoyPlfuVNc0/PluUhltr++AnQiCYMnLl0j1iEpcq9ajAelM\nBumzMBZVEnDKIrI08FvJihOfz0drcwOqw4kqmhSXVxNqqcU9YiKiZGPE6f+GftK3SUeDKJ5duTxM\n00QK1HHq6afT3dlOvq2IkyaOoqbCx5q6DlDc2BU70meymk0lKSmvJJXNDtvn3RFF0ZIXC4sDpD8c\nIZI2sKt7n/8ndJHWtna6Iykcrr17LhiySl9fHwUFAzmYWtvaCEQS2BxuRHHAMyKwo5VYnsy/nnMm\n0c3b6UtnhugTyUQcKR0jmVTpDQYpzM+no7eflG7y/7P3pjGSpPl93hN3RN5n3Xf1Nd0997G7s+Ry\nScpLSqIs0vZ+sGHJhCFYggHbkKEPAmzZhu0PMiDIlmH7gyQIMEzKMAyaNC3ZJJfa5R4zu3MfPX1W\nddddmVl5Z0Zm3BH+kFXZlV1V3T3XcnomH2AwqMyIyIjozDfe93/8frLrIooi3a4J8gO/c1GiY3lY\n/R7xRJJSs8sl30c+I6AxZsxnzfib9hAeV6xxfX19ZHH/IJIkIQgCnU6HVCpFEARsbGwgCMLI8RuN\nBteuXePixYvcvn17WCVxRK1Wo91us7CwwJ07dygWi1SrVVzXxTRNYFD1AIwMUrIs0+/3SSaTj3Sz\nGAtMjnmS+YVXXqTW/AFb9RaBbSJEPq7tkI7H6Nh9bNtCVnUUAmRdYaKY4/z8NNt7ewRSjHazjmt6\nRF5ApjiFIApYvoeiqGiKgh8MxNYSiTjx+DJFqc83XxhkLGRZ5vf+7F1k9TDjGfjIoc/c4gKu1SOT\nGov3fdH4N379l/ndP/wTGl6E12kQaRoEIUkFHMvEsm0USSLy+mTTKTKZNBcWZri1do9Ii9HEodTq\nIYTeSHDgcXvzZYFhoMFzXTK6RD6XAac3zj5/wZAkid/61Vf5v/7V60iBS7/dRxQENF1DaTexzSaW\nqKNpCn6/xWQxz2QuRyETY+ugRaOa5fq1N4gvXEXW40iaMRSDBPD6XRL9fX7jr/xFMrkC/W6TX3jh\nMiuLC4Nqxdr3KLvSsUCDzUwuiaIqxMaFLWPGfKbslA5QjYc7+6i6ztvX75CbXnjodvl0ilqzTT6f\nZ2d3l7oVoh7T4xEEAUGSMTITvP3hDV557ir75QN2KjVM24Uoolw+QNV1itOz7JkBG7USuPd459p1\nds0QJZZCiCJarSbxZHokASmKEn5wX6hW1uNs7eyxujza+heGIVs7e9S7PcIIYqrM6sJY52HMp2cc\nbHgIjyvWWKvVWF5ePvP9VCqF4zg0m01SqRQbGxvouj4ymXRdl8nJSRRF4fbt2zz99NO0Wi0ODg7w\nPI+trS0SiQSrq4PSpyiK2NjY4M0330SWZdLp9PA4giDQbDbJZDLDzzheoXGam8XH1aYYM+aLyl/9\nzrfZ2t3ng5trvHZji0IhRy53jkajQbnWxGrWeOn589zd3qU4N0s6ncJxLEwn4ML8JQq7GQ6aHfwo\nwvd80vkiBD6NRoOklEFRagiEiEQsLt53i1hdXuRXOl2ubTcQRZFEKk4hmyUIAyaSxtiG6guIoij8\ntd/8ddY3t3n93Ygb+20KxQIXVlfYL5epNdtEvRYvPHOOmxu7LKwsYBg6xXyGQJB4ZuVF3rt9jwNd\nZKu8RWxyCeCxe/NXJxIkpMHYnM3nSCUTeK7L6uRYvO+LyESxwG//5ndY39zlj197mwMLctkMqyuL\n7OxWysMAACAASURBVO5XaLXaxKOA1aVF7uwccOHcIoIo0un2mTy/zNdeuMof/dH3qFfW8Th8nkYR\nsgipuMEv/ep3sJwQr1ojtHtkkklgUJXwb/6lX+X3/viH2ESIosDE1DS6ruFaPZ6++PDFzpgxYz4e\nrh/wOEskxz3d7eU4kxN5atUKvudRbfdR4w8kHqKIuCJixAzatk2t0WBmaoKZqYmBy8Q715hZWhlZ\njwTAnVKTA0cmCCzi6mEbtaTSsX28oEM6OficMAxQxBDjsM1DFEUcf1SIslZv8N6dTSQ9gSQN5iqW\nA3vv32GxmOTSuZVHXueYMWfxpQk2fB4Z+ccVa3xUQCKRSFCv1wnDkE6nc9gTfD/QEEURoigSjw8G\nguOVB5lMhmvXrrGysnIi01Wr1cjlctTrdWzbHlZJHAnWtFqt4T1wXXfkfjzoZvG42hRjxnzREQSB\npflZZFmi40U0ujaebZM0NOITCYKsjhA4/Iff/Yv89MYmAS7np3PU2yZyLMZMMY/dM3FR0WMRXiDT\n7DkIkUet3aFjDXQVpvMpDkyLdz+6xfNXLiIIAi8+c4VYbIP9ehs/FHH6HaYzCa6OBZm+sEiSxMXV\nZVzPB3WHVt/BtS2K6ThpOSAqxElqAr/9l3+JaztVwsjl0lyBVt9FM3SmcimE0KW0szNy3Ef15gu9\nOn/nP/63kXSDWscmYqDfsDSRZXlh7ud9G8Y8Jrquc/XSOZqdLjd2qvTckMD1mM0nySsBERHnZ/M8\nc36OrXqfIPC4vFDADERUI8Gzzz1Lx3Lxg4hUwqB8UMPxQgxdZW1jG82IoSkyKxMp3rqxzrMXlpma\nKCDLMn/521/no7VNWn2X0PcQ3ICry9PkTqlSHDPmq4DjOKxt7lJtm7h+gCyK5JIxVhemSR0G6z4J\nmiJjOo/eTlUevYwSRZHLK7Nsbd5D1kfPKfR95Mjn3MogYKjqOjul2tDtYnt3H0dQkR9YZ2zuVpC0\nGKl0mna7RRSGCKKIOPhALNdHdxw0TSMKfGancsO1ShRFyMeSh/2+xftrO6jxk5ovejzBbstB29ph\neXEsKjvmk/HEBxs+z4z8cbHGB/UVstksqVQKy7LInWKB8yDz8/NsbGxQLpeHQQUYBAFEUSSbzbK/\nv094aI3n+z4vvfTSmboRpmkShiGJRIJ+v49pmiP9mEfbO46DKIrouk7qWBn3gw4aj6tNcVrrxZgx\nX0RanR4L8wvMhSGObVOuHNAU0xi5GHgOGw2LpCIQz+bRYnHmgoDd3V3iCYEgZ+BJCrF4iv1SGT9U\nKBZnqbc6xHWNbDaL1aoxN3OZpiuwvrHN+ZVFBEHg8vkVLq2GuK47tKEd88WnZ7usLC8SBAGObbO5\nu4+QmUBRVVwh4KDnk1Yi4oVpVFXFdR22N7d5di7NNauJeHmFd7f2kbMDIcCH9uaHIS9Myrzy0gvA\n4DnmeR6apo3bJ54QnBAunV/F9zz6/R73dkrEirNIskzdg4wTklIFkvkZZFmm1+uxs7XNc3Np7uw3\niSVTSIpCu1Ejk82jqQqdnsX01ASiIBCGFnoqx4frOxRyGWRZJhGP8/XnruB5HmEYjjUYxnylMXs9\n3ri2hhxLIuoJjpqSOwG8cX2DqyvTTE98MvvohZkJ9m9sohkxzJ5JuVLHtB3CEBRFJBPXKWQyvHT1\nAjd36ujx+JnH8n2PC4uzZJIJbu036PQcgjBCkQTy2STJeIzdUgXLHWivJESfp1YX0HWd/VoTWRlt\nY+j1LJxwsIDLpVM0UxnMZplEdgpNlbGCEEmS6Vk2siyRFD0W5u+3bLl9k+XLV4Z/r2/tosTO1pxQ\nVJXNSoOlhbnx82nMJ+KJDzZ8nhn5bDbL1tYWa2trwwX7EdVqlUqlwtzcHKurq490kHAch1dffZU7\nd+7Q6/WGQYVCoUCj0aBerw9VoqMoYn9/n2vXriHL8qm6EZ1OZ3jNuq4jiiKWZSGK4nCRI8syrVYL\nwzB47rnnhvs+6GbxuNoUD7ZejBnzRUZVJCLbRxRFPM+n6UTDHkxZGlhZSZMzTOggSBCEAk+9cpXp\nyQl+8OYHOJFEo9Ek8lzmjRgbWzuAjO/ahI7JwtwMzU6X6akJSo0O549VGT44Xoz54qPKMk44CMQ2\nWm18OYZyGJSVRBHjUPNmJW9g2h6iqvLir36dZCJO4a3reEFE/E++x0/WS0iZ6eFxH+zNDwOfGXub\n//G//+/ubyNJ4za1JwxVlokYaG6U603kxKByMAxDFFkjkc3jmm1WCnHapkUhn+Dbz/4qtWaTlQOT\nVqvFfvmA55+5SqfbZWO3TCQqBFYPw1BJZQbHU+NJNrb3OL9yv7963JI1Zgy8d+Mucuz06gU1Fufa\n+i6FbOYT/V5SySRZXWTz4IDdehfViCPH7gf3Wm5IZ2ODX37xEtVWl44fnplYUAKHuekp2t0+s1OT\nzB57r1ypcmOzhKLrIA7m9F3f54fv3eLiXBHbCxEfeDS0u13kw7YJSZZYmJ2mXS0RhDaaBK12G0WL\n0e+1WMlpvPL880MxyCAImM7ER+5JrdNHMh5uzemLKtV6nYlC4XFv4ZgxQ57oYMPPIyMvCAKKopxo\npxBFcSj8mM1mH9tBIpPJDPUVALa2tpAk6YQqrK7rKIrChx9+SLFYHAYnUqkUiURi5LqLxSK7u7tM\nTk7iui7r6+sEQTCs9nj11VdHyqeOu1nA42tTPNh6MWbMF5nl+Vk23/oILZGi1myh6oNgYBj4ZFOD\nLIQsK1i+yyuXR22gEoaGGCnMzhrUTQdRM5iadGhbPhMZg0wmB8fGBD98tDf2mC82C9NF3ru7j6ob\ntHsWojr4jniOzcT8JAB6IoHthTz71GhbjKEIGIkkv/VX/3XCf/k9rq/dpeGrqNn7QYfAc9C7+zy1\nUOBv/Ad/Y0TAa8yTx1QuyU7LQZIkun0XLXFYteLaTBQG/+6iFkNVZJ67fP/7MimJ3Nw+IJ/P4wcR\nB6ZHPJHAshxCYGVxHlGS8KweMJiDuONn75gxI1RrdRxkHhZGUONJ7m7vcmn1bE21h3H53BJv3vhX\niMroQtxzXWIynL9yhXdvrPG1Zy/zzrWbtOxoOM+AQeWyGjq88sxTCILA3FSR0q2tYdKj0WhRaVuD\nQMMhQeBTSMTR40nu7NW5t76OmMgSRiBLIoXMyeCKpqk8tbqArOq0uibz2RjlgyoT88u88tz9CgbH\n6lOIK1y9dHFkfz8IeVSoW1EU+n37cW/dmDEjPNHBhs87I99sNgFYWlqi1+vRbreHi/6JiQni8TiW\nZdFqtbh8+fJIO8cRlmUhSRKXL18GRlszjlohHgw02LZNPp9ne3ubTqeDruskEomBPU61Sr1eH8mC\nCYLA9PQ0hUKBdrvN1atXKZfLJBIJstnsMJDw4LkcXePu7u4weHHUHnIa48zbmCcJRVF45tw8H93d\nwfN9kFU82yaf1Jgs3hd2DIKTgYLzizO8dWMTNRYnritYERi6Sr9vkckM8hKeY1OYHfTW+3aPn775\nLp4gESGQNDTOL82STDw8WzDmi0Mhn2O5Y3Kv3CAMQwgjAtdmtpAmFrs/poenBJaWZya4vd9A1XSe\nefoKV59/gQ/efoONrW1U3UAUBTJJhb/+N/8Wkizj9Rr86KdvEUqDtol80uDCysKJCr0xX1zOLy/S\nu36HcnvgBBX6PpHvsjw7MUwESLKM647aUmqaxmwuwUHPp5jPUWpuIWsGIiGFQgHx8DmbOMyiWlaP\nju3yo581iSQFSRQpZuJcWFkalzSP+cpSqbdQHtFGJAgCrW7/E3/Gxm6Jq1eu0OtZ1JotvCBEFkUK\nswUS8UHAoNMPMXs9Xn72Cs1Wm+3SAY7nI4si0/N5picnhsfLpFPEFTgaEcqNDpKqYvX6dMweYRQR\n2l3Ovfwcvb7F+naFWqvHZGoQ7A6A7VqX0OkRiSrq4VrD7ZsU5xZRFJWJQg5YIIoirGYFPbTpmCa6\novDKpVUyh8lO3/dZ39ym0jS5traBrBkkDY3piSKx+MlAuOe6xONjZ7oxn4wnOtjweWfkjwcz4vH4\niNbCEceDGccdJI6EKpeWlkYCHcerII63QhzpLkRRRL/fx7IsMpkMU1NTHBwckDhctKiqShRFQ40G\nVVWxbZtisThyjouLi1QqFXzfZ2NjA1EUyeVyLC4uIknSiNZFLpejWq2iKArVapWDgwOWl5dHggsP\ntl6MGfMkMDVRYKKQI/7O+2zU+0zMzKKo93MhURSRjp8MWGZSKV56apH1rX2mUgZ3tnaZzmZJqQPR\n2NDzmMjEsWyLD2/cIgRkI0XkO0xmk8zOTPPG9bu8/NQK6dQnF6ka8/Pl3PICi3PT+FaXXqRSyE+O\nPGM816U4dbKMdGF2GlmS2Nw/YCqpslWu8otfe4Erl59CjqXwHJvFySytdpvNnT1ERUPSYoiBx/xU\nHrQYr713nW+99Mw4qPuEIAgCz1+9SK/Xx2zXkWIJ8tkMHFv/O32TucuLJ/a9evEcdze22au1KGgR\ndbPBM+dmafQ8iCICx2J+aZbNrR0ODg5Q4mkiSUYJPVYWZnA7Hu0PrvPKc1d/jlc8ZswXh0G18aOD\nbeGjNd4H24XhYQIwIplMIEkSLdMGxSAeH/x3Gnoszn6lOmi7yKTJZk6KLB7nhcvn+b//9Cc0nYjN\nvRq27yMbCSRRwrdNZqdmuLm5z0GlwvzyKnosiWW2MRKD4zqOQ7drUatsMre4QDKVJqXLKMpooLrX\n7WKoKh3bI9KSWFHE2zfvMZVNsjQ7zZsf3UE0kghanIniBB1fwALubO+zMJk7oUWn4lHM5xkz5pPw\nRAcbTnOLOE3I8Xjbwlmc5mbxSYIZR60SD2N6epo333yTSqVCPB7HNE10XScIAsIwZGJignq9jmma\n5HI5Wq0W1WoVSZIIw4HwnO/7uK5LsVhEVdUT1Qi+79NsNllcXByptDgSzgyCAF3Xh8GOer1OFEXo\nuj601Tx37hxweuvFmDFPCqIo8rUXn8N/5xrBA8rRkd3lwpXTNV2y6TQvPzMYO77jv8D65jbNbp+d\nvTJKTENTJe5tbTMzNUmlYyOrKmgaVdNBq9UoFAqsbe/x0tVLn/s1jvnsUBSFX/7Gy7z2wc2R8T8M\nQxKSz9QZgmNHVmUwUPe+u71Ho9OlVKkSKyTxrA61js1EsUjXlxBEAdDZLNWJxWKoWoL1zW0ufsKS\n3zF/PsTjMb79ted5f31vZO3juS7zhdSZ/eKrywusLg8U6OvNJjulKgeNJo1Wl+RkmmppBz9SyBUn\nsIfF4jprW3s8+9R52o5ArdEYqtaPGfNVImFoVA+rdY9otVoc1JuYlkcURaiKxHxaG87rTyMMQ26s\nbVBpdvEYtEaLkU8haeD5PuJjyD08bkBje6/E7e0yhZl5rJ1tdkv7iEYSudtjeiLH/MIcoiTRbLYJ\n9Azl/f3BefdNdvcr9BwXPZYmlkggpwvsV1toBxW+8fyVkc/pmV2qlRLL5y8+0B6hU7VCfvKHf8LF\ny1eHlVHTEwVam7uIqoFsJNgs1Uglk8iHY5dn25yf+WRCm2PGwBMebDjekhAEARsbGwiCMNJasbe3\nh+d5rK6unjrYPMzNYn9/n+Xl5UcGHB43E3X8s1ZXV7Ftm83NTSRJotfrsbCwQDKZpNFoEIvFaLfb\nrK+vUywW6ff71Ot1NE3DMAxSqcEkplarkclkRgZTy7LY2tri/PnzJ87NMAy63S47Ozsj7RTz8/Ps\n7OwQhuFQqLLT6aAoyonWizFjnjREUeTVF65y+94W9U6fMIzIJQ0uXroy0sYUhiF37m1SbQ+2ySZ0\nLq4soGna0Gf6G88Psolr97Yw0ln2y9VBoOEQWdWotTqDtqbeuMfxScQwdF595hJrm7u0ehaSKDKV\niXN+eXRSZ1k2a5s7NE0bSRQopGNcWFkiFjN4+tK5kW3f+egWhWmFta3dw0DDADWepHxQY2lhjpZp\n/Vyub8xnSzGf40VJ5O5Omb7toikSS1NZFudmRrZrttvc3SnRs1xUWWIqn2Z5YY58Nkv+AavuH731\nIZEW56O1TTgWsBDUGLVajWKxSLnWHAcbxnwlWZyf5W7pA6TYING2t1/ioOugqDpyTBsIQ7sOSirH\nT965xjdfuHqiZTkMQ15/9yM82UCOJUcWRJ0A1ja2WL1w6cR+x/F9j3Ti0e0F+5UDbu/VUOOD81VV\nhWx+gnh6sK/nu4RRhAj0HZcwgo1Kg0xM49zyIl6zRyQbtLomvX6PYi5DMZMgm5lnY6+C73tkkini\nqkhodVg+f/HU8+j3Lfpyir1SifnZQUuooiqszk1xb7dEJKkosSSlSoW52VncvsnqVO7EWDZmzMfh\niQ42HG9J2NjYIAxDer0enU4HGLQ+xGIxcrncma4UD3OzKBQKrK2tcfHiyR/tUQWFbdvMzMzQbDbJ\nZh8+4Dz4WZlMZmiNF0UR29vbLCwsEIYhnU4HURQRRRFZlocVD5Zl4fs+jUaD2dlZXnrpJUzTZHNz\nc9j6kMlkEAThzCBIt9tF0zQ6nc6wIkIURRYXF4faFJqm0Wq1ePnll8cVDWO+FEiSxOXjlhEPEEXR\ncOIhHlpNNT34yXs3+MUXrpwYIxxv4HQhiQJEIRzrn/aCQarjQW/sj8OHH13np2+/jx+EFLNpfvM3\nfn3c0/9zJBYzePby+TPfdxyH1z+4iRxLgRYjAEpmQOO963zjhasn+uk9PwQRJEGEBzJh3mF13LiF\n4skll8mQe8izst5o8u6dHdRYHDQFF7hb7dKz7nL14uqJ7d0gRAFEQeS4Sogky9iOSxRFyOPvy5iv\nKKIocnF+ilt7NWzH5+5elb4f4rgBkQBCGDKZ0jH0eSJR4P2ba7z09FMjx7izsTV43p/xnJ6YnuHu\n5g4Xz41Wm1mWRalSxbRdQrdPTDhPEARoqoLZ6yPLErPTU8Mghed5vPfRbf70tbe4V6pT7/Ro912C\nMEKIAlRJIKZKXLlylUuXLhKEEY2OiRbPELhNGs0G8XSBxOEzJQxDDFVksphlYXaKMJwh6LX4hRcu\nIkkSP3j7+pn3rdE20fRDIcljr8djBk+fX6HebNHp9Qlti+mExOqVk0GaMWM+Lk/8N+jy5cu89tpr\n7O7ukkwmhyWLvu/TarUoFotEUXSqK8Wj3CzS6TS7u7uYpjnUTDheQaFpGrquk0wm2draGgYTWq0W\nYTgQe1pdHUwi7t69S6lUQtM0stks8Xh8GCAxDGPonFGv12k2myQSCWRZRlVVTNPEMIxhVcPR9R0N\nkInEoL9senqaTCbDnTt3HiqcGYYhuq7TbDZPtF8c130Iw3AcaBjzlWF3v4wjqCcCBHIsxdrmLlcu\njAYq4oZGpddjopCnvLaFYtwXVdJkcRAgTJ/tvX0aURTxO//nH/DHP/2AmzWPMJ4fjA3eHv/4//kx\nX7s4x9/6a//WMCMx5s+PtY2dQaDhGKIo0g9kSpXqsKXiCF2VcXzIpxN0Kq1hNUwUReiKhOe6zMyN\ne2K/rKxt7w8CDcdQFJW9hsk52z7xzNYVmQBIJTSa/XBYDeN7Lol0AqdvsnRx3KI15qvL/Ow0kiTx\nv/7+H1H3dDQjhqQGEAakUzqJdIrrd7e4tDxP3XVwHAftmKhkpdFB1M4Wcc5mc5T2Sniui3I4Xtfq\ndbYrTdRYgkiMWFhYZLdu8rMbm7Q6HYrFCWzHI3TfICnDRD7LD15/gx9f30IoLCPKBUgVUFKMOGn0\nAp8fv/0hG/fWKc7Mo6an8F2bXCKJZXtIxv3xQRRFOr1BNd3R376s43oetmkiqg8TzhxEut0gHAre\nDxEgn8uQz2WQfWvc0jfmM+OTp92+IEiShGmazM/PD8UTBUEgnU4zOzuLoijs7OwMhRyP8zhuFpcu\nXaJSqWBZg/LWjY0NdF1HFEWCIGB+fp4gCNjZ2WFtbY0bN24MgwTlcpnf/d3f5c/+7M9ot9vE43Fk\nWaZarfKTn/wEXdeZmpoiCAJ83x9aaSqKwr1796jX6wiCMGyfOM6DWhXHr+9RgpjHbTAfdW/HjPmq\nUG93hz2KD9IyTypaL87NILh9JFlifjKHZ/UhivDtPrl0Ei2weerc4z+swzDkb/+Xf59/+P9d54ad\nJkoU7qvaKxoNfYb/dzPg3/97/4i33/3gk13kmM+M1hktMoqiUm22T7y+ujCD2++RTqfIxVU81wHA\n73fJpRJMJuQTAYoxXx7O+r7o8QT75YMTry/PFPFsm9nJCVQ8Am+gYS/7NoYic3Gu+Mj5y5gxX3Y0\nTUGNp5mfzJPSRIopg6WZyYFQoyAgqAabu/tosQR7x35nvu9j+48WW1hZXSGBg9fv0O122a40EWUV\n0XdYnMzi2DZ7TZMD06Mnxik3OhjJFK6oc7Pu8A/+6e/w410Paeoionx2ZaIoyRizF6mIed5+4w3u\n3fkI17ExTZNe/xRHjSg8XkyJrOm0Ot1BJdQDIhKBH7BbqrC+tcdBrUGr1R6x7j4NQ30MsYoxYx6T\nJ76yodlsEgQBgiDg+z4wmLQf2ZMJgjBsrzgulAiP52YhSRLLy8tMT0+zvr4OMGJ9CbC+vo5pmsRi\nMXzfp9/vDzUXisUi7Xabfr/P9PTAe9vzPAzDoNlsMjk5STabxXEc+v0+3W4XURTJZDIYhoGqqjiO\nQ6lUYnJycthycSTm+OD1HJ3zg4EE0zTpdDqEYYht23ie91Cf97H7xJivGtJDxgJZOvmeKIp8/ZlL\nXLtzj7gisDKVodtuMjOb4fL5ZSbPEBI8i//s7/8P/Nk+iPrZ1RCCIFDXpvm7/9Pv8k/+iwzLSyeV\n7sf8fJBEgbPCuqd9l5KJBM+fn+PW5j7FdJyEKmCZJisXZ3nq3BLpMyyHx3w5OGt8CYIAWTmpdD87\nPYkfBGzsV5mfyGF224Run6eeXubCytI40DBmDHBnY4d6q4MrOkOhRk3tkkkmhhXJphPieR5RNLrY\nf1TCDQbP3Evnlkmlknz/tTeZLWSIxwwSiThBEHBvr0zbCggEBUmAvuPg2Bb1Tp83fvRnOIWnkKTH\nX2rJWoz4uZcorb/F5NQURmqKvf19nEDEiMeJGTpRFJJJGCPClL7voWsquWwGwd+CwwRlqVKl3Oii\n6AYIEloyy972LmLgcHF5fmjheRzHtrh6frR60nEcumYPXVOH93XMmMfliQ82lMtlDg4OMAxjRPW5\n0+nQbreZnJxEVVXa7faJH8hpi/LTONJBSKVSJJNJOp0OtVqNarU6tKyUZXlYlWCaA99tQRAGPd2H\n1Rf2Yalkt9tF13Vc1x22aGiaRr/fJ5vN4rouoihSqVSGLRaiKHLv3j1yuRyKorCwsHAiUHJUiXBc\nODMMwxPCj4ZhsLOzQ7FYPFlGxenuE6e5dTxKo+LT7DdmzM+buakipdvbaMbow9f3PCYKp9tXxmIG\nX3vuCr7vD39jDyMMQ/ZKFYIgYHZ6cjhmvfXOu/zJ9RJialSEKXAsnE4DLZVD0u4vSBraNP/z//Z7\n/IO/959+kksd8xkwkU2y2bBO9LPa/R4Ly6dXtBTyOX4hn8M7zFKf5VRwhOd51Gu7iJJMoTCLKA7a\ncxqNCgC53OQw+Dzuq/1ik0/G6IYnXw+dHnPT506+waB6anFuBsdxkGX5kdWG/X6PTruCqsXJ5SYB\nDjWeyiiKRjZbxPM8JEl6LKetMWO+yPT7Fj+7dpdAVJC02NB5IQQO2n08zyObzaLoOqVSiZfOvTjc\nV5ZlYqr8oHzOCcTQJZVKIooiih5Di3xKB1W8/Qq1Rh0vkjG9COXw+SxrMbZ3S9y5dRM7Nf+xAg1H\nCKJEbPl5brz5E6yrL+O4Dl3bZ1JSB+3gCZ254gLqsTFfCgbWlIIgMJlJUHdCao0WBx17pMVTEAWy\nyRi+I3B3t8KlpVk07f68JfB9JuLKULC20Wyxtr1Ps+ciKipR4GNIsDCVZ2n+7HZO3/e5u7VDrd0j\nCCMUSWC6kGVhdno89nwFeeJnJ+vr6+Tzebrd7sjETVEUoiiiUqkwPT1Nv99nYmK0RPX4ovwsjmf4\nXddla2trxPHCcRxM08TzvGHlAQwqCY7O5yiw0Gq1mJqaot/v0+v1AGg0GszNzQ0rM44moaIokkql\nsG0bQRDY398fWngahkGpVOKpp5469TyPC2fu7OwgSdLIRDSKImZnZxEE4YQApnVoJXTkPvEwt47d\n3V0uX778sV0+HrbfmDF/XmQzaRaLSTYPOuiHvdWubZM1RJYW5h667+Ms9PbLB9zY3ENQY0iSxJ29\n62QNiZ4b8E//9z8gTE4PnfPCwGf3td+ns3kdr99BiaVILV1h7pu/hXg4efnZnT16vd6wwuphtNs1\neu3bCHQAiVCYYGrm6fFv8FOwsjhPo3OTlu2jHj4PrJ7JymSaVPL04NQRjwoyAJRLtxCDDSbyKkEQ\nUtm9Sd/NEVMb5LPQM3t89M4msXiWVKqAF2TwwgyaYgEBgpRnYnKVbreF1W+TSk8Qiz2ehkituoVr\nbSJEPSJUBGWWqelLZ+objXk0Vy8s89P3b+BLOvLh/MTtd3l6de6Rk+8H2ygfJIoi9nbeIaZWmcxq\n2LbH7qaC6ydJ6DVyWZmDgyo76wdkclNoagrHz4GQQJFNQEJWJykU52k0Kvi+Qy4381jf0yiKKJdu\nEXl7CLhEQhzVWKJQHFddjfl8ef/WXeR4imTYo2X7SMeew7Ks0DQdYrqNZujoQjBorTjGbD41CBif\n8T0Pw5DJdGI4f711dxNLTqCoOpEcUe/5mF5ArXrA7HSRRDKDAJjdLtvVFurU6dWNZmmD5vq7BK6F\npOpkz71IYno0QC0pGk68gKbrqPEErXoVu33A/NIqoiiyvbPD08uvAIMAwWwxPRyfr15c5bV3PqRc\nbyFpo8mTwPOYzsbIpqcoVZts7+5zfnVpUBnuWswWUkPnrYNanQ/W91BjcYzE0RikEQHr5Ta24wy3\nPU670+WtG+tIegJRHqyvBoK4JlulD/nGc5fHYtdfMZ7oYEOz2USWZeLxOO12e6jXcIQgCAiCqHG5\nOwAAIABJREFUQK/XO5Gph9FF+WmTqAcz/Nvb2+i6PtzWtm06nc4wQLCzs8Pi4ugD1rIsLMui3+/T\nbrcplUqYpjk8ZjKZpNVq0e/3kWV56CTRarVoNpusrKwgSRLtdhvbtocVAkEQ0Gg0SCaTp1YiXL58\nmT/90z9la2tr2C5xJKAZRdHQCrRSqdDtdonH40iSxNLS0shxHubWEUXRJ3L5eNh+Y8b8eXJxZYnZ\niR5b+xWiKGJqbvozsZazLItrG/vo8ful8ooR50cf3mBlcZ7tahcheb/iZ/e136d+46fDv71+Z/j3\nwre+C4BpTPFf/8P/hf/q7/xHGMbZJdWdTh2//zbTEyowmDBEUZ3d7ddZWP7FT31tX1UEQeDlZy5T\nqzco15oIgsDiyjkSiY8nCnoa9foeSX2TmDH495JliUSsh939Y3KTLxKGYFvrXL2k0O9XEZQc9fp1\nDLlFJvUMqqrRbGzwoz/5xywtFUjEYlR3U0jaU8zMv/TQxW31YJOYcov8hAoMvleet8P+rsPs/HOf\n+tq+qqiqyrdefpbd/TLtnoUsiaxevvpYC/pHUd6/wVS+iSQNvi+6rqBKFSL3HQqFF2i32sTUPa5e\nUmi2dklmnqa0/zM0NWSi8CwCAjvb7/LDd+5y6dIkkqSzt5FHiz/D9OzDba/3dt5nMldDliUG35eA\nXv8mtSrjgMOYz41Ot4vpDcR1hVyO7s4OoRhDFO8H0GVVo9HpkHFMXvmlF04cY2VpgUb3Bh2PEwGH\nMAxRvD5XnhnMU6/fuUsgx1BUjWq9iWm7mG6IiwxGms39GpNZl1wuy73bN1CKJxfhoeey+f1/Tmf7\nJlHgDV+v33qL1MJTLP3Kv4Oo3J8zG1Or7N69yZWXfxFN1zEr2wO9uDAgnUqzX6kxlc8wkVC4uLIE\nDCoK9soVFCGkXtmj74EXhEiiwEQ2xeLcNFOTAx+KQj5Ps7LHfFpFU+NMT54f0XS7cW8XNXZ6y4Si\naWzVTGYmuyPB9TAMefvGOkrsZFugLMsgJ3n7o9u8+sJ4/v9V4okONlSrVSYmJqhWq8zMzLC/v48o\niiO9jEEQsLe3x3e/+91Tj3H58uWRDPwRD2b4m80mmUyGTqeDoihUq9Vh+epRdvDIgvPSpUuYpkmz\nOZiAqqqKoig0Go1hhsL3fXRdx/O8of2lbdtD3QlN0ygUCsM2j2Qyieu61Go10uk0U1NT+L5PrVYj\nlUqNnGe5XGZ9fX1ox3mk5dBqtYjFYly5cmV4zpOTkwiCwIULF07cm0e5dRw5aHxcl4+z9hsz5otA\nIhE/4Tzxabm3U0KPj2a7Dw6qqMks9XYX03bh8O3Asehsnm5d1dm8TvC130DSDERJ5s72Hu/eWOOb\nL5794Dbbd5kuDsRz6/UGvu+QTudJGT1uXn+NTLZILr/4yOzpmNMp5HMU8p8+IHUc19ohVxgN1Hba\nZRYX4jQ7ZWw7YKo4eHzHYgqbO+tMFgIMQ6PZKaHpGczW6/ziKyKVeptkQsZz7+HYPUp76plBgyiK\n8Oy7xFIqQRBQq9WAiHy+iGutsbUhoRsJCsWFcVXMJ0AQBOZnp0cs5z4TgtKJfw/PrTFREDC7Tfq9\nCtMTg8VUJiWyvnGNc0sSgR/R6dQIPBtVfJ+Xn5VwfAtdD+j3KviWQ/UgRnFi6dSPtW0bXS4hyzq2\n7dBqNZAkmUKhwPb6W3iehaImyednxlUxYz5TSgc1NCNGIe2y0xiIxFfKZcx+H0kdVNN6rk3k97l6\n4RJLiyd/dYIg8NLTl7m3uc1erU3fG/Q56bLAVDbBxdWnh2LwpaZJIZPko80ynb5DEIZIIghBiEiI\nnsjQ6poIUYDphQinjI+b3//ntDc+PPF6FHi0Nz5k8/uw8mu/PXJ+PWewJjA0HSGdw2vsk07FySfy\nmM0DXvj6ZfKH8/wPb61T61r03YD3rq/RDuOoushMJoluGASeS9fsMTlxP8FqxBKsnHJv9ssHBLL2\n0EWiHotzb6fEc5fvz222dvYQtIcH3HseNFvtE5UmY768PNHBhiAISCQS1Ot1RFFkfn5+KIR4RCqV\nIpfLkc+fbikmSRJPP/00rVaLg4ODYeXAgxn+arVKPp/HNE22t7dxXRcYtFEEQYAsyxiGQbvdptvt\n4jjOsH3Btm3q9Tq5XI54PI7v+2xubjI5OUksFiORSGDbNvl8nlgshqZplMtlFhYWcBwH2x6oWB99\nfiwWY29vDxgERY4CDdeuXRsGV2KxGJZlHYriRCPikhsbG5w7d79H9Cz3isdx6zhywXjwXn2S/caM\n+bLiBwEPmv+4vocoyQShO/K602ng9Tuchtfv4HQbxLRBr2Sjb/GHP/ghhmjzwvMvA9Dv9/n+9/4Z\nobdHFAV02nVeeOFl0skexTwoisTt2x8giD6TU8+SydrUa+uE0nkmp85/9hc/5mMj4J58TfAO/+8j\nCO7I4s11GhhG4fAvm1ZjjXw2BERqB7vIYot0EsrlNe5ubiIrBSanTrYGeZ6HpthUq21Cf5dCTh5k\nuK69QTppkM5AIp7hYO82evI5stmpz+Pyx3xcIpejKpQjBDwURca0HQQcjsYfQRQhbCAIBWRFwu+Z\nmN27zE0pRGHE2t01FubjFDIh2zsbbGzsEHv1b5/artVuVyhkVPb3NtDkOpN5Favv8P47PyabzVBM\npwmCiL2tW+QmvkbsjCzpmDEflyOthVwuQ6Nr0vdDpqanCcMQs9MmCAJi2Ryiq/KN56+ceRxBEFhd\nXmR1mTO1dHb2Ssh6nLBjsbG9C0YCSVTwvZB6rYyg6OixJK7noShJeo7Pg6F7s7RBZ/vmQ6+ps30T\ns7xJYmpp+FooyOD1kRSNiVySuWwcLZHE8UJcJ+L9WxtMFxrUmh1CLQmyyr2NLRK5AmarB6JEud5m\npiihGzr9wGdze5flwwCDIp8eNG52TWT50VVXPXv0WVVtm0jSw1skVCPGXqU2DjZ8hXiigw1HAo/z\n8/NDEcRE4r4C7ZHQ4vz8o/MImUzmoQvfowV5r9ej0+kM2wEEQaDT6QwDH+l0elih0Ov1EEVxmOkX\nRZF+v48gCExNTWHb9lDwUVXVQ+GvBplMZqgvoWnaMOPoOPd9go+u6UgHYWtri/Pnzw81Ho5EJR/U\nrjh6r9PpkDpUPz8rQ/U4bh3H782n3W/MmC8rCV2lbjsjv7W4YdBo9IhpMilN4ii8oKVyKLHUqQEH\nJZZCSw6y6J7VpViIoyVlPlr/KXJU5vpH3yep/Ixf+UYVXb9fDvn62z/gnb0czz7zTebnisxNWaiq\nQKnRIJtboJDX6Zp3abdzpNOnB2bH/PwIozgwap8ZRRpBYCGIMQZTbZcoDPF9jzAYPMotq0urYeHa\n+2SMgGotJJ3yScZV8DsszopoaoXa3u/guX+B2fkXR4IWrWaJ7Y2PSOl7JFMpIEe1Wufy+Qiz18Zz\nfaSUxNSERPngPYLUd8YVDl8AIiEOD3ijRGj0rT6GkcKxG0BAEAQ4rosoakCE2W1wUCkR08o4FnR7\nDsW8jKb0kYU+CzOQzZbYuP3PKM78GpNT9ysgwzCk3Tpg7+6PyKW7KLE0oNJoHPDcFZnd/ToREaoq\nMzsFe+V3iS196+d5W8Z8iSlk0uzUS6i6zrmFOXYrFRqdPgES8USS0PdJ6DLnF+ZJpx6uoXPEWS1N\nnu9Ta7S4sVVmam6Ber1Bs9MmEhWUeIZuu41pmsQVgSBwCZWTDg/N9XdHWidOIwo8mmvvjAQbhFgG\nXItkKoEqKXRcKGoJNA0ESUKKpXh3bZd2z+XKhST75QOUWBJVEJAaXRAlZM2g1mwxZ0whSTLNXoeF\nw8RqIXW2K90nIQyjB/MqpxKEp6jljvnS8kRLghaLRSzLQhRFFhcXmZiYQBCEYRBgYmKCiYkJDMPg\nzp073Lx5kzt37tBsNj/2Z0mSxM7ODr7vMz09jeu69Ho9wjAknU5jGAb9fp9yuczm5iaNRmOoqyCK\nIoIg0O12iaKIIAiGwYlUKoXjOERRRKfTQdd15ufnTwjORVFEo9EgnU6PVA2IoojneciyzO7uLs1m\nc/j+kRXnUYChf+jVq+v68B5YlnVCOPP4NT/uvfks9hsz5svK8uI8OL2R13K5HJHZJJ3QmM4YhMGg\nXFLSDFJLp2diUktXhq4UYnOT2YVpHLtHLGnw0x/+N3z3L/wL/tIv14eBBhhkbr75ssy/+5sd6uV/\nyes/fYd4XMZxI+Kx+9slEypmZxPXdR/LpWfM50cqe456Y3Rimi/McmvNIwxUyuUm77/3Flv3fsad\n2+8hyzab965j9/aYLCbIZjWCwCbwKgRBBGEHPwhoNC0cV2JpTkQTNqiU7w6Pv7v9Lin9Frlkj3NL\nAsVsl73dTQK/iySJCKKOKHSH208UFMqlu8MqvzF/fmixFcze6L+DYUyyX5Zpt3tsbde4eeMNdjbf\n4N7aDXzPZH/vJla/wdxMEkOTIOxh9w+ICFHkPrbt0+5aIKgUs30U1uh0BvOGIAjY3fwxK3MtskmT\nhZmIVKzO5sY2qmJBFJFKJel2Dobnk0qYNBr1YavomDGfhkI+hyYcBtgEmJua5Jnzy5yfybNYTHF1\nZZbFqQK5VJy3rt3kx+98xOvvXefW3Y1HfgejKBrqrVmWhW1ZbOyUiASJKAoJgFQqja6IGIrERDFH\nLhnHs/u898ZPiTjZMhS41mNd14ntBAHfdZFCH8cNSWXvJ0XjmoIgCLR7NpFisL1bpms5wwByOmkQ\nhoN75AaDhCWArCeoVmt4lsm5xdPFrydzGdzDquqHkY6NVlSpZ1RKHCeKIgzt02vVjHlyeKIrGx4U\neIzH4yOlfkEQsLa2BvCxHBGO2zUeuUa0Wi329vaQZRnLsjAMYyi8CANNhe3tbdrtNpIkoSgKqVQK\nXdexLAvTNIcBg1QqRSwWGw5oMzMzZDIZms3mQKHadYnFYrTbbWRZxvM8bNsmFosNqxFgULkxMTFB\nrVbDMAxc18W27eE2uq7T6XSIomhoyXl0zsf1Js6q6Pi4bh2fdr8xY76siKLIN559io/WNmh0LcIo\nQhcjVmYKfO+Hr9NTMvTu3SS5NNBemPvmbwGc6kYBEPoeczmbqVyDnBZy+2e/w9/9m+Yj+6K//arI\nH//gA17/GczOTeL7d3E9BcOYpG816XRsDKWM42oIyjxT0xcferwxnw+JRJowfInSwS1EWkSItDoi\nyAu8994fMlss4/kW9abG6soi9WaHvXIT18tz4WKMXi9Bvdng4MBjYbaHaQYkjAhZilBVj3Jpja7V\nRNF2Cf2vE0R5cokKmqaRzEzR6ZkYmsvctMS1G1UsS0fTDFzvNrYdYRgFer0yPeseujSL48XRYufI\nFx7u2jLm8yFfmKdeg9LBPSTBJIxkag0d14lTKf0BE5kqPcvFtuKsriyyW+qyuVFlYXGV4mQC0zS4\nvV4iZkgk5CaddkAyIWA74DptWp02RsLH8XfJFl7E9RTmpzxEUUKPT9IxS8QMSCf61BomrZZMIpGk\nZ1/H6ttoWhrT3CWkSWBl8IIMyexlksmxDfaYT87Vcwu8e3sL5ag9R2Ao0Ou5DpW9TZhfGVQOSyGt\nXo+q2WSr3ODFS8sntHbCMOTG2gYHLZODVpdKvYXn+bi2yX7bxUei74XI6mBuGzu0lIwA1/NIxXSM\n5YvcWb934lwl9ez58MO2i+wu83NX8QUZNfTR9MH7oe9TzA3m+o4foGkCrX6fKAiHC7t0KnkoGFkj\nQCBw+hQLeRKJOLZp8sLLl4nFTj+vYiGPtrH7UGtQp9dl9fzoHGFhpsh766WhQ9NpuH2TlStXH34j\nxnypeKKDDfBwgcetrS3OnTuHLMtDLYejdoZkMnnCEeG4XaOmacPWjDAMKZVKIy0RyQeszUxzMNGf\nnZ0liiKy2SypVArTNDFNc1jdcHSOjuPguu7Q3jIWi3FwcMDVq1eRZZl2u02z2SQIAlKpFIIg4Lru\nsEUkiiJEUSQej1OtVoGB2nW9Xh8JSBSLRba3t7Gs+9HSRCIxEALzvKHew2l8XLeOT7vfmDFPOmEY\nUqpWEEWRyXxxpJ3IMHRefuapYaDvh299yDt3tqiHOmI8RiFfp9MooeWmESWZhW99l+Brv4HTbaAl\nc8OKhigMEEuv89J3FtGDDo3de/x7v9VBEEYDp+1OwMa2x/KCQjp1/71f+2WZ/+MPd3j164uYfZlE\nymPj3mskEgkmJ8+TzRyNUZtUyuJYx+FzxPM8yvUqMU0nnx2d+KZSeVKpbxKG4aD6LfxT1m7+kJeu\n9iEKkaU4fqBx0HBR1CS53ASdLrz5TglddQgCDVDZL5VYmE9ROhAIohTxWBNd8ek7GrIU4/Uf/WOc\n3gfEdG8gVOxqyMoU3/j6MyTiAgf1Mt++mESWRcy+RiLZ58bN7zM1OUU29zTxuAGEdLof0WqpZDKn\nV8qN+fT0+z263RrxeJZEYlTtPV+YB+YJw5BW64B8+CPu3v4Rz15yAAFRTGJZKge1AEkWmJ1f4d5m\nn0p1D9d1+OCDGjGthqZ6aKpEzxIJoizfelVAEiLixixZA3L5DteufUg0Oai+UtU0qbSKZZmIis1u\nqc63v5knCEPSgYEsNVhbe4fpmUUyhYnDBI9DpfoGivLtR+o7jRlzFrlshhefErizuUer5yFpKoEf\noAkBZrPB7PIFiODe9h6dvgtHFcO+z+Zemb/+V35lOCcPw5DX3rmGr8Ro9D0qXRc5kUUGGnseUeQg\niCJN0ySZkNCPOa31LQvPcVBEmWQmjxTdOXGu2XMvUL/15kNbKQRJIXv+xZHXYmLA1Mwst+/cYeUw\nQee7LoWERi43mEOLh5UUoSATeNZwYdfpdGibfRLpDKZlIcoCPdvB65t865uXyWUfPgd/9uIKb924\nixI72Ybi2n0uzBVPJBULuRwZvUz3sE3jQTzXZWEi/Vh24WO+PDzx/9pnCTweWUiKosjW1hZhGKKq\n6rDNolar4bouMzMzQ/HI43aNt27dGpYTHy0YjsQej1oSjqoout0upmliGAaKoiBJErZto2na8P9H\n+ySTyaHNpaIoNJvN4XlduHABwzAIgoCZmRmmpqbY2dmh3+/T6/WGtpoPalEcX9DH4/GBQrSuE4Yh\nlUplqPvQ7/cRRXHo3nFWZcdxHtet47Pab8yYJ5XN8i532yXEpA5+xM0721zMzTM7MSqiJwgCWzu7\nXL+3y9ZBBz2Rx+qazJy7inD3BrXtm8TnLiKIIpJmDMUgAbxuA7F2nd/4tsHLKxXSCXj3zdvMTN7/\nHbtuxH/ynx/wL77XY78cMDMl8Rv/Wpx/9N9OoKqDsSIea9Fo2sRTC7iOSzHnsltpcmFq+v9n782C\nJEvP87zn7GvumbVkrV3V1dt0zwoMgAHBwUIABsQFIdq0BVmU7HDYJsMh3unKsi8sRyh047AiHIxw\nBB0SJUoRNEmRJikuoLARA2D2nu6eXqq6qytrr9z3k2f3RXZndXVVz/QAGBIzk89dZZ3KOll1zn/+\n//2/9/1G76NpClGrRByfHifJvw9c21hjz2uiJk2Cto+8v87Ts2dIJY4uIgVB4GDvJv3mGyzMNIfW\nl0hCEgX8YADBgK5Tww9iTCNFKuGimzmy2SWuvX2D2O9T2vKYmTYQhBaDgcvANXnttZeYne7ytc+B\nKD74/3UIwwbffOkWTvAE587mcAYRghBjWFna7RYrpwTWSj2emDo812RCZa9yZyw2vA+EYcju1mvY\nRo18QqXb89iqJpksPn9iv/pa5Tpe+2WW53wUNUaTFCCGuE+lvg2xQKenoasC25ttJDb5b38FVFUB\nDsubXbfNn32zghdmefqpVZLicM6Rywi0Wntks7Po5hTd3hq2laDddlmcz+G6AV6gkEwnqNfKnDkt\nsb4dk3tgnJosqOzXbjM9M97hHPOjk0ml+MRTw6y0dreLKivousZ33rwJMVy/UwJFR9YfWBTLCn6k\n8Xt//i3+3i98CVmWub62TqhaEMWsbe3T90IGfguIadabqHYKqd8kcrr0RIU48AmCkMBzcLptCsUF\nmrV9dE3HkGOihzbb7OlTJOfPn9iN4j7J+fNH8hoAikkFy28ylTZRhBgNn9nJNOnU4dhr6cowUlgQ\nSBgabhQxcByqrT6yNqy+SBgai9MTCKJA0G9T6YY0Wi0yqUeHNKaSCV548iyrG1tUWj2iWCSOQ7K2\nzvmlIhP5k/OdPnbpPFdurHHQ6qCa9qgDXTjosTCZ4czS4ok/N+bDywdebLjPwwGPq6ur6LpOqVQa\ndYV4kPvtKF9++WW++tWvjioW4jjm5s2boxDI++JEr9fD8zwKhQKtVotarUa9XkeSJIIgIJ/Pj6oH\nLMui2+2OukhomobneSiKQrPZHLXntG0bz/MolUosLS3xpS8Nw7buCycAi4uLqKrK2traqDpiYmLi\niF0kk8mMOkCkUin6/f4oFFJRhp6uIAgoFotomoZlWSwsLByr7DiJx+3W8ZP6uTFjPojUmw1u98to\nmQfS1rMK11vbpCwb2xq+vls5YLW6yfdev8wrr6wycFTsdEysyMSKhCGaJDs13Gsv4+sqsWogKAqS\nEJJWY56eE3juhTayFFDe9xDyOtNZBzicSP3G/1zm//43h+GSu/vh6Ovf/BeTAHzxM/D7f9XmK19S\n6XTapBMmhUIK3z+6G6EqLkEQPDI4a8yPxp2dEmXZQb9X/qsaGhgab2zf4sWzz40E7oP9Vfqdm5R3\nvoHff5ue5pGyU6hKhCzF3FqrI+CimxkEQUGIysRxkXTCYe32Oq3WAWLsELgd9gQZ29IxDI3vfK/E\nz38xojh18hRAkgS++LMx66W3+P6ry3z+5748zAeKA9otFzGTPHFXTIj7798f7SPM3s6bzEx2EYRh\nFUAyoZNMeOzsvc7swqeAe1VVO1dwe6tUdv4U/E28XoCmWkh2jNPz2diuI0sgK2liOeDq69t87gWX\npYWTrwNNE/naVwxurrX51neu87nPTRPHEb2+hKZ1ATDNJL14mUZzl0qlSSY7RaVtYegKjaZPp+uj\n6VlSqRNC+uLe8dfGjPkR0HV9VCVze72EZtps7eyDosMJYrkgirRdiR++cYWFmSnWd8qk8pNcubFK\npeujKArivfwBWdXp9AfgRkwXcmxs7eBqJrZlops2gahSr1URAp9MKsG5Cxd5c7WE/lDL2MXPf52N\nbw67TjxY4SBICsn58yx+/utHjo86Vf67r3+ZL3/hc/zwyk3QTu7mMpFLc3e/CcQsLS1w/fY69baD\nrA7D5eP4Xr6DKNBq1LGlkGa3x831LT71zDt3hDBNg6cvnCGOY4IgQJKkdw2AFwSBpy6cwfd9NrZ2\nCKIIXTVZmD39WOHxYz58fGjEhocJw5B+v08URY8s1xEEgVarxWuvvUa1WkXTNFqtFoPB4FhpUDKZ\npN/vc3BwgGmaWJaFpmnYtj0SIvb29lhcXBxlMpRKJTRNG4kdruui6zqVSgVBECiXy6PWlF/4whdG\nk/x0Ok0cx6PcCM/zOH36NK1W68QchGQySblcxnVdJicnmZyc5O2338Z1XVRVPWJnqNfr2LZNqVTC\n8zwSicRjZSe8W7eOn/TPjRnzQWKjtoeWOH5v6imLu+UdLp06S6VR43pnh/WtXcRAQU8kkBIG7VoN\nTbTpVzaQKxFJsljmJJYc0Rw0mCieQsq5nJsvsVTssZjvkUmEOL0utcoAJXnoqmy1Q/7kGydP4P/k\nGz3+eTsklZTQNBHbzpMtPIuZ6BN5N/D7EZJ0dCLgB9I4yPV9YLdXR0mfUD6e0tk+2GN+eoaD/TVM\nZQ1ZX8OYjQgHOrIY4Q7adLsx7bbDylKE78tEcUy1oVBr9JmZHvDWtS0srU026ZNP+5i6QmnLp93u\nsHanxmc+IVKcOrojfpLtZmlBotoo0R9kWDm9CICo7GMa+3QHJ1jkeOeWZ2PeO0EQoIoVBOHhZnpg\nao1RhtTu1uskrS0SSglTFIk8Dc/3kYQBpS0XIpfzpwUGnkivH/DqWw5PXXBYWnj36+DcikK92abb\nXmNxYRpDjbm2KvFCdihOWlYaWbYI5QyzC9NHT1K8g2X16PRPGEeEsYVizE+e4F4oYrM3QNROziRo\nNlvUygc4rkfTg5u7TYSdOlvlGkby6I59IpWmu7eH44W0uz3mls8SuAM0TSUIAtwgQhJ1xFgkDgNm\n5+fZWl+jE4YIDzw/RUVl6cv/iO7+Bo211wk9B0k1yKw8d6yiIY4jli0fa+oU33njBu1mDSsjHsmK\nu086naHQc+j2+iiqwumFIuvfewPRTCIpGnIcoCkat1dXsW2LVHGGg17IxvYquiLz1IUzjyUgvNdN\nB0VRWBlXMYzhA96N4p2QJIl2u31iiSEwymFwHIdOp4MgCDiOQ6vVolKpED3UlsWyLIIgoNvtIkkS\nuVxuZH+AYfXC/S4VQRCQTCbJZrN0Oh12dnY4ODgY2SGSySSJRALbtpmYmGBhYYH19XVqtRphGHL1\n6lVKpdLIwhHHMa1Wi1Kp9MgU3cXFxZG9QpIkUqkU+XyeXq+H4zikUqlha557IomiKFiWxY0bN7h6\n9eq4DeWYMT8GXvzo+8eNh/fsRm2P7sAhcmLSqSSWoUHko1oiTuUAqREQhSGR6+I2KqhuSCbScbb2\nkDdfRalU6W3ewdYidF1kZkphbk6l3z8cq+5u+uzun3wuu/shpa3hbkocxwjiUITVdZP+QMcNbBTl\nUJiNooiQ6fFOxPuAF508jsuyTN8fVsSFbglvUCaTljCMHBEquq7SbId0Oz6ZNLhuSLcfUNr20Q0d\nQVTY3m3QbW8gxG363Sq6JqCoIsunNCYLCtu7HufPHD4XPS/m1/7JARdfLPHcF7e4+GKJX/snB3je\nUMR6/umYy2/85ej4ZHKCRjMg5qjdYzDwUfR3bzM95r3heR6aevI9bRoijtMZCg5qFX+wj20pSEqK\nQSAymTfZ2nWJw5BkArq9gEbDo9YQadQ7fOypx78OXvi4xpUr19na+Ab1ymVkUaLaXmYEQ/D9AAAg\nAElEQVS/arNfTdL1L7J4+ov0+u6RczTMKWq1Pop6dAHXaLokUqd+wn+tMWPA1HWcfp8gPtn+V63W\naPQ8FMNCUs3hpqSi0BqEdL2ITrdz5HhBEMimU/TbTWTNJI4jdF0jl04ymc9iqQLTk3kSqSzNegND\nkfnUC5+me/fNE3+/PbXI3Gd+mcUv/NfMfeaXjwkNAFZrg//mH/w9ZFlGsxLkiwvcXrs96ir3MMWs\nzS98+ilMwcPvdShO5plJ6kzrAVOWyKDdYml5mani0JYpiiKKmaLSj3jlrbfHHajGvK98aCsbCoUC\na2trj+yIcHBwQBRF5PN5oigaZSqYponnedTrdfL5/JGfsW2bZrNJv99H1/VRZQMMAyLn5+fZ3d2l\n3W7j+z5RFJHNZvF9nyAI6HQ6eJ7H1NTUqKIhCAI0TSOVSvHyyy8zNzc3yo14EMMwWFlZYW1tjYWF\nhRNzEH7+53+eTqczsi0kEglmZ2exLIvbt2+Ty+WOea/v20kex1IxZsyHlW6/x+peiVbQRxREcorN\n+fnlx97VtySVJsf7RsdxjC0Pd+/6kUev3UOShtUCs4UMYVAhCsDrO/jVDrZs0mkcIMQSB7UWYizg\nRiFnvxhioaD7OnevDZhcclma9UlaIvXm4STh1LxCcUo6UXAoTkkszA13Jl65LHLp4pMABEFI110h\niETanQGWqdBqBzh+geLseEw4iWqzznp1h17ooYgSk3qKlbnHXziZksZJcoM38MhY+aF1RXYRGFrz\nEok0vjvNQW2HdDJkvdSh7/rksjq9XsSpRZNup0bKHnBw0Of0KQNdlchlRLpdj2ZHJJuCWt1ncfbo\nY/9xbDcKN3AcF8PQ8LyQWvcSpqHQ77uoqky9GRJLi0xNL763P+RHhM2DXbbaZbwoRBdl5lOTx7Jc\nHoWu67Rr6kPSzpBONyY9kaHZLJNOyLQbfUAmmZpGiNvc3d5FkiRcP2avHGLbKnGkkMtCNt3hvdqv\nsukAXYvRTZmYN9jdfZbzFz6BpmkjUXJ3e44g2CSVHI57QShz0H6WXFrE84ZiZ70popqXjoVcjhnz\nk2C2OMXb6zsnfs/3PFp9D1GSSdxr26jpBlJcwfECDN2g1elhmdYRoV2SZWzbxLZ1nFYN2bYJXAlD\nVShmk3TdEKKAfqtGO2GgWGkuPfMxrl25jLXwJMJjivZxHGO2S/z3X/8aiQfC3gVB4NKTlyhv30Uh\nTygMLdJC6JNLGFx85glUVaU4PcVgZYD6xi3Me+uTqzdvMzmXP/a7BCIUVaEbCmzv7TNXnD52zJgx\nPwk+tGJDJpMZ5S08vMC+rwxGUYRtD8NLkskkBwcH6LqOYRgjO8WDScntdptTp04RhiGtVgvbtgnD\nENu2cV2XSqWCLMvs7++zsrIyqiYYDAZ0Oh1kWcYwDPb395mYGIZoadqwNHJ/fx9RFEmn06PAyoeR\nJImFhQXS6TSe552Yg/CgbeG+Utlut4eD0gm+tfs5EGEY0mw2x5aHMR85+k6flzevo2ZtZIZZKPU4\n4Purb7FSmKXZ76LJCgtTM4/c5V+emuMHW2+jpo96Kv1Gj1yuwKtvvMatjVu4ikCzOWAQBURKSCpl\nkEmKbLyxQbW9T6U+QOjIxJFGRIQjdvEVj/W7MTNTk4SBQGVLoF2TCBo6guLR7Qu4boSmiaSSwzDI\nBxcN9/n5L1qjsui1rbPMX/wk+zUPSU6wsLyAKIp0ux0a/TaJTI7cOCX+RMr1KlcaJbSkiYxMDGz7\nXbq3r5OzUvR9l4RuUixMPjJYczEzydudHTTrcLEXxzFqL2RyvjAUokMZP/DotrchHvZOT6ayOG6W\ngbuFaSZQVZOE3UaRPJIJjzhyKPkRzaZDPmsRRTGyAr12hKMKXF/1+PzPHArZj2u7WZ7vcPm6wKnF\nAqqe59wTw0lps1mj7wzITU2O08Ufwe3tDUphEzWlIQMBcLO/h7M1QBQE/DikkMiQTZ/cBlIURWJp\nDs/bQlUP/8ZhGOJF0yiKgmmm6PcDHMdBERqATxTL5AtF1ta7WHoNRBvD1DG1Fmt32jx5/vC9Hvc6\nOLMkcWutyac/mcF1Oty59X+Qtf8Ojqfhudyb15i0evM49yzpVmKGi09miKKIRmOYRTU19+h7Y8yY\nHxdRFDm3MMWt7TJw9DlWb7aRVY1o0CZdXEDwh/bmlGUQVbpYlk2nP6Db7ZBMHuYZeO6AZCpNJpcn\nOZFmZW6KaqvD1l4VJwhxHA/dtPCjgGqzRU7RmV9YxAth9cpryLlZ9Mw7C4xBt86y6fKP/od/gJ1I\n4A4GSLI8GlsFQSCVyfOZZy7gOAOiOCKVTB7bFNF1nZQu4QONRp1QUk9c7NmGiiiKiKLKTrk+FhvG\nvG98qGcHzz//PN/97nePBMcA1Go1AIrFIp7njQIX77eku28zuF/BAMOJYBRFo6+LxSLZbJbV1VXC\nMCSbzeI4Dr7vH2lnORgMiOOYVCqF7/ujioX7LS3vixVxHLO3t8fU1HAwarfbNBqNkVhyv5WmYRh4\nnseZM2fe8bMXCgVKpRKGYdBoNE5sL3X/s8OwcqJcLo/FhjEfOW7vb6Fmj4oEYRhyvbrOrteiOD1F\nGPZZv7XPM8XTZFPHFwWmYfLM5GlulTdphwMQYO2tG1zZvc0/jcr0csNwpqjaw9h3mVULnLtwiYSu\nsPnKdXau3CJRLWAK90LU7s3DzdgGDza+28Lt7PDlF5PYlsGgLdBtBuztx9Q2k/zenzT5+7883AX5\nP//Z8J4+qRsFwPqmwKmljxH6+xRPvXg0MdtOYNsnBLmNGXGntoOWOuqb9TyXb5ZWeeLUCpZts+t1\nuXNzm+dPXTxx7J3OTxJGEeuNPRwhQAghp1o8eXpYSSIIAj0ngRbXUcwBmiYDEr4fc/3lDrGcZXH5\nCcr7r5FJybhOl263R6/voUoCrmfhuCFJW0TXJLpdD00V8bwQTT303T6O7ebJJyQMPaLabTM9858d\nOSadPlkYHzMkiiJKvQpq5uj40nX7/H/bN3n2wiUkSWKruUHiYIuPr1w8UdCcLp5nf08gbm6hyB5+\nIBOLMxRnh+0nLcvm6lqfnNnFMAIkUcK2TDrdDrWmgpQtcOHCRWrl75BOyDRbfRaKh/f9414HpiFg\n6iGNRo0oUnjirIYsrmInTRKJFLVmzHRxnr6zTc87w8Tk0uh9RFEkl3u8ao4xY35cTi3McWlzm8ul\nGqqVRLy3IHe6HSRZZnZuljiOySaHgu/C3AzX1u6CqpFO2nRbTbgnNsRRhBgMsO0EvtPj7BOLFHI5\nqu0u84vDLnHEMXsHZWqqSTY/SbdRI5u0OD+bxZKf46BSo7pzHS8EyUqjJrIgCATdJsKgSUYXObsw\nwy/9wt9lr1Ljzm6FWJQRohBbk5kqZEmlUoiqRqvTYSJ/vFLhyOefneTaxgHdvoOsHLeTh57L5PTh\n+O14J1v7xoz5SfChFhvy+TwrKys4jkOz2Rwt3G3bJpPJjMSF+50dzp07x5UrV9A0jXQ6PQpwDMOQ\nKIooFAr0+33S6TRzc3NsbW0xOXlUod/Y2MC2bRKJBEEQ8MILL7Czs8Pq6iqmaSLLMrqu0+l0CMNw\ntLgPwxBd12m1WvT7fQRBODJJrVQqlMtlTp069Vg7AplMhu3t7dFnfJj7eRAPdrUY5zaM+agQRRGt\nThtFkukEDnA0fG1jdxtxIoF77wEsSRJSzuat3dt8NvmxE+/BMAyxZB0FkX/9R7/LDyaaiOcSQP7w\n3QtJ4vNwtzfg9l/8MefVJdb/8DLp6tQ73tdWlKLyuso3hV1+5nkL3RC5uyHTLutMm1lee8Vlftbj\nM59QUVWB3/wXk/zz9nCRsDB3GPS2sx/x0pvP8qv/8GfwPJdqdZtCYeyzfzeCIKDd7WDqBm1/gPlQ\nEOL6wQ7WXJ72oI9l2yiqAjmFt7bW+MTKcStKHMfEUUxKNUmGEYtTM6STR1PBDUMi8mbY2nPIJDt4\nbgPHjZiYMOn1M+wfHCDhsrdXw9AjtvdcVFXgqScM9sse5WpAOqHS7Q5QZIGtfYGFeZPdA590ang9\nPK7t5qCqUlwIcZw+hnE8oGzMUVzXpef0h3ZJ42ioWhiGbDQOkAo2vu8jSRKaqTPQI25t3eX8wvKx\n9wvDkG6o0w3nkAM4XVw8JmIlExZBMMPG1jqZZJ9er44fSCSTEqnMFNvbJTTZo1ptYugxB9WQQn44\nBXzc66Bci8hkdDqdHrncNK0upFIOXhihKFmIq8TxHKah0mqvE8ePN18ZM+b94PM/80ks6yp39hsE\nUYAkwvxEGtHOEIUhBgEzk0VgKIY9dX6F1c19wsgnqUvE/RaDgYOl68wXJ6nVakxNTDA5UWBzew9B\necCmLQhoisTSwhyThRxM5UhqAssLs3zrpZfxJY10cZGYmM5uCU1qo2s6uYVTpLM55qcnuHnlTW7v\nVFAN60jVmw/c3asx4/skEwnkx7B3Tk8UcF2P7e0tkBKjjhxxFBO4DguTWZKJQxFUHN+nY95HPtRi\nA8CFCxe4fv06qqqOcg7ud2IQRZG5ucOJdiqVYn5+fhQamUgkMAxjJEh0u1183+fcuXN0u91Hdroo\nFouj7AdRFDl37hzr6+uIojgKntQ0jUxmuEN6XwSxLItSqcTFixePPaB1XSeOY+7evcvKysp7+uz3\n227e56TPDoxT58d8JLi7u8nd9gGRIROFERtbG8xJ86P8FYB26KAJNtLDGbpJjb3KAcWH/NaXb1+n\nKrtols7/829/hyunPCTr0RUCsqUjfe0Cl3/rFaZ30sfu9yD26dPFxEYWhveuhsGdN5L0ahFmQuLU\nShJvEOL1NGJ9hb/+dpnVO1V+4UsqE3mZVFLiySeG97TnxfzV90Qi8Um++MUvA6CqCmG3CYzFhkcR\nxzFv311lz28hGCpRNWB9t8TZ5FmUe1VqvW4PXxOQwhBFPrqwbEbDBeeD428Yhnz/1mWClIJsKYDA\nK+U1ltp5Ts8ujo4TaVOcXcF1F7i99iaaZGEnDOayGVbXKiTsDjeuVzi7LNHrh2RSMt1+RODHJCyB\nO5sexAKqErFflpmczGCZfV6/UuHCvcK4x7Xd7FXn+fTPTbJf38cwlo4dO2ZIEAS8efcmdRwkTcFp\ndthr1jh39szoHj+olFHSJv7AQ3pg/iCKImW3xfmH3rPb7/Fy6TpyxkRUh4HRf71xhacmlpjIDnc3\nXdclaQekUxfp9ZZYW32ZdDJNImXw7JTB7n4boiqVcoOZaYVCTubl17tcPDeUQR/3Orh2Ey6cFZnI\nC1RrHdwow7wh4veGoqymhPh+gKoqmMbgxM5eY8b8TSEIAp945hITpS12qi26ro/r9HE8h4mUzdRE\nYVRFCDA7PUm7N8BHYsISyefyyIpCFIVIkszu5iZ2Og3xyZ0ufHdAJpUeis1Ax3GIoohTczOUmh6x\nqCCIEgllkZniNFEUIkQh04UMgijQ7juohsVJyLrJ1kGdC5pEOvXO7Srvszg3w3+eTvJ73/g+oaJD\nDKapML2wiPhQ56mMPb5Px7x/fOjFBkmSuHTpEs1mcxScmM1mcV33WAAkMKpYiOOYmZkZkvcCWhzH\noVgsEkURcRyf2OnifhXB/dY0qqrSarWwLIulpSV2d3eRZRlJkhgMhonjQRAgCAKFQoHNzc0jHS4e\nRhCEI1aMx/3siUSCGzduoKpDf9Z928iDOI7zWC0wx4z5ILNb2Wfdqx2xTWSLk9zc3eDZ0xdG3V8i\nIjzHpZCZPfLzsqIw8L0jr+2U96lpAZqmc/P6Dd6yW8jWUatF0Bvg7jfRptLI1nBHUhAF7F99lurL\nrzK1WwAgiiNu8SYV9vAYoKJTiKc5yzOIgkgqzLNXKfPc9LNUN3263RYTaRtB8hmUUyiTCX7wehtn\n0EKWYgRBw/VlFDXPFz7/JdIZk2rz0BoWf/gfAT8WNzfXqege+n1ria5hTWRY297gwtJwxe77HoIi\nEjs+uZmHbGiyNAx7fEBsuLG1TpwzkB8Y542kxXqrwowzebg4ExQgQtUUpidlMumhKBRFEa6vo6st\nMikdTXZJFwR29qDbDYgIaXdCnr2oEIQyopRnqlik26sThxKa5uJ5Hqo6/P3vZrvpdCPszLO4ro+q\njasa3onX1q/jpWRMYTi+aFMa216D0s4Wi7PzAARhiCiKmLGM8tBmxf2WfQ/y9s4d1NzheCUIAno2\nwdsHdylkhqHPkiTh+8P/pyQJrCzbmMawRLrb9ej1YLFo4TsSuhaRsmWcQYzvxyjK410HjhMRhBKX\nLph0Oh1wdTRFod12iMXh4scLRGT5vsApYr/HVnljxvykEQSBpcV5lhbvdVgKQ7716lU0+/iCXRRF\nLiwvsHrrBrnUHKqmDTPNfA+FkK+++DEOKjVu7zXxI+FIPaTb67AyN0G1czg/iAQR13UxdI1CyiYQ\nZHrOAFGMUYQQy9JIJhIgQHlvj8nJSaIgQHxE/o2kWYSu8546RCUSCS6enqMXP3pt4fa6LF06/djv\nOWbMe+UjM9N8MDgR4OrVqyeGR4qiyPz8PPV6nVQqdSyEMQxDrl+/Tr/fP6LY389meOKJJ6jX66MS\nx/uVDMlkkm63CwzzGAzDGIa9pFKjqoUoikilUieeFzASMjzPO/a9d2JxcZFOp4OiKI98X0mSxnkN\nYz70bLbKqMmj5ceT2RydfoetjU0W7vWElnoBxdQExkOlyk6ry/QDu88AB906qj2cVH/7zR8inz8U\nGiI/ZPM3/5LmK7fxa12UnE36+dPM/9qXEBUJUVPwnzFgd3j8Ld5kh7ujn/cYjL4+z3MIgkDkRmiy\nRrPmQqiye1AmmTWRLIHJwhyG1eLCE6dJJRMoMuwfNHC8DJmsxX45YHJ6uHio1lwy+XHruUcRxzF7\nTgPloZ2m+Yki19Zu0KjWyeSzWLaNd7PEuaXTx8ZXzedYuXvd6yKYx3McjJRNqbLLufl7ZfTSJGG4\njSgKSOJhp5NKLWBuNosgStzdfBNJirD1mIELL3w8ye2SixcoNNs6pi4RRgqK5rMwA6WtkLlpnX//\nhx3+4a8Mz+GdbDdxHPMHf1Hk7//qz1GuScwsTP7Yf9cPK91el47kowtHF9jLk3O8fesGxcIkqqZh\naQaV8h4XF45XKCaVo7uLYRjSjBxMji/aI1ujWq9RyOWRZRkvzAM9fH+A8UAL21ZXZXEhS6cdcedu\nhCwNszt+9lNJ/uBPu/yXXxsKGe90HQD8zh/4fPZnz7B1oOP5SRbnCvi+w9s3q5w5N0UYRkRxdrQQ\n8sL8ODR0zE8VwzBEkSdPz3N1fRfVtPD9gEqtThDGqIpIxlT5la+8iKnr7OyXiaKI3PwcmfRQnMik\nUhSydbZ2dsGLQIgxVJWV03Nomk7/9voDnYZiREHEMHQytkm10ydhaqQzU2QeCIKPoojI7bO0MIet\nibTc4EjV0/1jNAIK+feee/LMhTN8/823CWTjWAWz2+9xfmES2z65omLMmJ8EH9knwX2LQRiGhGFI\nu90miiI8zyOVSvGJT3ziRFvB/WoB13Wp1+sjYaBQKIyqIGq12uj1+w/eZDKJ4zjU63VkWWZhYWH0\nnveFimw2y9zcHPV6nSiKjlQwPGh9+FGyFR78vCe1zbxw4cJ7fs8xYz5ouFGAeMLE/fTsIs5Gmebt\nXWLgE/kV2g8dFvgBQsvl9fgWvcBFk2Qm9TRhHAHDHex1pwIcJjpv/uZfUvmzy6Ov/Vp39PXiP/4K\nAOpX5+h8o4ThGlTYO/G8K+yxEvtDS0Uk0GjUcZ2QVqeJbioETQXyFTbXNE4/PYEf2tSbZZqVHoQq\n1XafrnOTS5e+hCAIHFQ8FOPJE8MLxwwJw5BAjI5dLZIocmnlPM7aAbXmDpok80LhDH3p6OPU6w8Q\n+wHfXXuTQeBjSArzqQniOOJR7tjogXydqelzbJfapBN1wkgnikIqtQBVPwVRGXfgcvGJJQKvSrVR\npTgVUakHeL5AcVJBt6aoNwJcN8IWezQaHRrNDufOpMhl8/zr3z3gV/8LcySQPGi7GX7+mH/3RwW+\n/NVfp1wTSOefG/vv34FWt4NiasdeNzSdc3PLiHtdqkGFpGLyTHKe+KHFhNPsIgzgmzdfxY8ikorO\nfHJi5LV+GFEEPzxc1hSmnmZr5/tk0zq9foRhQLkK6ewKnnMLRY6YX1wmokkQNshlRE4vGfz7/9Dl\nv/qa9cjrII5j/t0fODx1MYei6HSdNKJksL2zjyC6GJrMnbUNNnWRjz3/FI7jUW2YTM0+/ZP4s44Z\n8xNnaiKPpir8xXdfZqvWRVR1ZEnA1lVMGQ4qNc6dXmJp4WSLYS6b5eLpBSL1eKXX4myRm3c2ka0k\nqjC0TGu6RtLSEARo1w+wssP3Df2Adr1CwlCYmZ7EtgzmZqao1hrUWh167rCli67I5BMmUxNFRPG9\nBznKsszPPHeJu6Ut9uodBr6PKIhkbIPlJ04NqyvGjHkf+ciKDfcX2D/84Q+p1+sj+0I+n0dRFK5f\nv86FCxcemWOwvLw8amX5MKdOneLu3bv4vs/8/LB00rZtdnZ2SKfTnD59mna7Ta/Xo9/vjwIl+/0+\niUSCRCJBr9ej1WoRRdEx68OPMuE7yU7ycNvMMWM+7BiiQmMw4KBZxYl8FFEib6Zodtp0m3WyEwUS\ntk1PV/B2GtihzCD2kQUJ2fGJchaxpWHeK6A8CB16O2Usc4JGpYpjiaPowKA3oPnK7RPPo/nKbYLe\nANnS0eazOPYqsRviMTjxeI8BfXokSSMrMhgxTrlHwrSHVVKKiK6n8JpQqejMnc2zeV1DEzWC0MNv\nWnhSipu3B5w++yyqqTPo32V/6xZRrKDo81j2BK7bI5HIjHckGY6ZSizS6naodJv4cYiKxGQqx53N\nDWxJQzcNzHSSHgLxXgshk8SPA3RRwW87MJVAVGRMhs+JO06VQatDMmMycAZ4notl20NrXa/PdPYw\nHFAQBOYWP0G73aDc0ml2Npifn0WWJcrlLnt7B2iaSSAs0uy2eCINvhcTBB61pkBG8JC10/jOgM2t\nfeaLITOTCeyERRCZfPw5ld/5/SqaLvLVz4dY5lAYb7VDvvHXKo3uDBef/XUU+3mi0KfTuEqn7hIL\nFmZiGVHUiKKAVCo7FiGATDKFv7tLPXBoDLqERJiiRiGR5sb6GlOTk8i6hJhLMOgNUPY6iLZOGIfY\nsk6vPSCay6EIAgrDFpk3OruE3QGkE3S7XeIoxk4M23WHnQGTK4XR79c0jfmlz1Gr7bF9EJJPd5iZ\nGwbP7jZ1dvf2sK0pHMem2a5z8ZyOqkqUqyK//bseuWzMl17URvaawSDiL7/t4rgm586e4sIZiWq9\ni2p8HFVukU1LGLpEo9FHM5e5sxlzZytJNjeHojeoHfwA4oBYSJLMnCUIfERRPtJOcMyYvy1ub+4w\nOX+K6UXxWDXxdsslXlvn/Mqj82lmJzKsV7vID+X06LrOudPzbGzuoIoRjtMHYiYtCUtW+eSTn6HZ\nbLK6vkHfi8hk84iSxObGGguLiwRBQD6XIZ+7VyEZM8qViKII23g8G/XDiKLI8qkFlsfFjGP+FvhI\nzyivX79OLpc7MbshjmOuX7/OpUvHk8ThaLeHhydakiSxvLxMrVbDtu3Rwv7Tn/40u7u7+P5QrTQM\ng1QqxWAwwHEc8vk8t27dYnp6ehRAKYoiyWRyJDT8uNkKD9tJxoz5MLJT3mezVcaNfZRYYtDtIVgq\npYNdrtQ3mJ4pkkyn8IAr++vcvX2bp557hqYWUumVUWsxp2cWyEUJzswPJxzfvfUGqnW0EkCSJISs\nya3Lb3Mg9I90fnH3m/i17onn59e6eAct5KV7+QnEmNio6CcKDio6JsMxQE+o5CZzOGUPxBhRE5EF\nmXpZYWoiwOn32L3TwVSGuy6uq5DJTKCrOs29FvITClL0FtMFFRAYDLrsbv8HunWL6el56vsQMEtx\n9uKP+2/4QBDHMXd2Shw4Tfw4QvQjojDEUwSurd9kX+gyPV3EsEwGwLduvEqv2eaJpy8xkELK9S2S\nocLs5DQX0gtk0xl83+fb62+iK0cfsaqh0SHkyltXCLIagiIRN3axPIlL2QUyqeNjczKZIXnxc9Sq\n21Tq67Ram4TuPqBwZlmi3fHxBlO8db1KwpaYmZlgc6fP4tI8fmAQCgu0an0cp8vAldF6ArYt0+2p\n/MJXFnjrZp4//24dRfYQBIFYMPilr30eWZG5dqtD4LXI2NtoaQUQabX2OCh9j2S6SCqZZX9LRtZX\nKEws/k38u/7WCcOQG1vr1LwOxDHCIARZwBEiXnr7Nfy0xsz0NLKq0CXk+69+m4SiYVgFIGJv5w5T\nRoqcZfPC0iVkWaZSr9KWg+M2nIRJY2ufW9d2ETMGgiggVEOSkcYnZ86duBmSy02Ty/0i+3u32K9s\nU6vcQRTaGIbO2WWF7V0Jx5nl2s06hpHg2WdX2C+7zM9N88ff2qDXB3+wja4HPPvUMsUpHVkWKdfa\nGLrO3Y11Pv6UjWEMBVdJSZNMWlw8G7K2XaPX9pmZ7N+r6hSoVNbYXP1PTBXPICs6OyUDO32JVOqd\nW/eNGfN+UWs0aA5iVH0osD583ymKyla1zenFo+G+D3JqfpZW5xbVgYfyUGtJRZJ59vQMT184M6oe\nNs1LlLZ3uVnaY3O/ipWbxgJ8z0UI+nz6kx9ndWOX67dLZBMmjh8SxzG6IjNZyKFpKm6vzfzZC4+0\nWo8Z89PKR1ZsaDQaRFH0jmGMYRjSbDYfuTh/N2vCJz/5yWOTgVwux0svvTQaLIIgGFkwoijizp07\n1Go1FhYWhhO/OKZSqbC1tYVt2ziOg2maxHE86mYxZsyHnTAMubu3RcPtIgki04kc04WT/eN3dzeH\nIZApHQmFt9fXGBgCRVIEKYUpq8h+tUK/28PzfW7dXsWYSNFpd8kVNBRDI9JjSnvbmJnDUL5+7GNh\nEPg+u5UDwjjCVDRaTpfU3ARWGCK9cpinok2lUXL2iYKDkrNRJ4c7fO5mHbOrI2NMAj0AACAASURB\nVAsKhXj6SGbDfQpMIwsKcRwzdWYCURfIzaRpN7oQiCAKdKoG6ztlFjMekSODBp4XMvBssomhqNGv\ne3SaN1iYPZwcVcqrnFoQaLdbyLJEIS/hebsc7GtMTj1e55ufNlzX5fbeJv3QRRVk5nNTJy7kAd5a\nv0lD95FTGoQhb22sgqlwSptEmU5jezKl7U1yiTSdXo9bd9YozE7R7/WRBJHKzj5bAxen1WVy2SSb\nzlBvNZCs4WKs3+tTaQ6tdWkrwXq3zPnTK9S6LXZbVVqDDpIoozQlwlW4NHOahGUfO89cfhbfn0QS\nekwUivj+s2xvfovA3WKqELG6PsGlU9MoisgpLUO10aHTaTM5+yk21q8gxHl0rUPSipGlCBGB0raP\n73X5u794AUEQ6Pd9gjg/SlMXqCHFJTRteP34foDTu8PKkkKjWcMwpjEM6HRv0mxapNOFY+f9QaDd\n7bBR3sGNAwxRZXlq7sSqxTiO+f7qZeKsgWgadLtd1jo7iIHEQmqC3MoctV6LO2u3yRfyVA6q7FT3\nmJmZwXUG6KaBlrYo97qYmsFWeY9TxTmqnRbqvcV7q9Wi0WkhCAJJ3WIrbHHh9Fn2mzW2m2V6/oAa\nEnZVp+33eWbx3ImVSFPTZ2k2syRtD8tcptU8w075BwwGXSZzAlv7s1x6cpK+EzE3P0HfqXL+7Gmm\nF36Oty//K2wLEnaPpAVxHNHrxbgexEEDwxjeS612gG4MWwcqikSvfYeluWVEcTi+NJtNNGmHcys6\njVYVK30ay4o5qLyGaX7hkQu5MWPeTzZ3K6jvYiFUTZs7m9uce4dSgKefOMvWzh7b5Rrt/lCsNTWF\nhYkMi3MzAEeu8cW5GVqdHo3ugIHvIwCZiTTpe3kQaVvj8u0dErbF9NQkCOAFsHltlWDQZak4wXfe\nvIUkxBRSFmcW5zDNcReJMT/9fGTFhkql8q5+ZcMwKJfLjxQbfhRrQqPRwLbtE6sptra2mJ+fp1Qq\nUa/XyWazRFFErVZjMBhQq9X41Kc+RRzHlEoltre339HqMWbMh4EgCHhp9TJkDUR1eK1f7+9RW29y\ncens6LhOr8uNrTv8+eXvoacSXFheQRBFXENANTT2O00CISKVTKFrBhs315hZnCN7Zp44obDvt2lv\ntFFTNm7o4zd7CF2f5+bPDTu5hDGVSpX15h56NoEkSTT7bW5vr/O58x9jIpNjUrKp3Tsf2dJJP3/6\nSGbDfdLPnx51pfD+bJNJb5j3cpZnAI52o2B69Lprdfn1/+V/wjAN/u3/9gfkQwM3GOD7PraZIKEs\nsbNZwtL7FIsWkpwlm0uOfm8YayhSFxhObur1BvlMAMhYlkS31ySVzKGqMmFzE/jgiQ2tTptXd26h\nZiwEQWJAzGvVO6w4kyxOHXYXqTRqvHX7Jt9dv0w+n+P86bNUGzWkjIkoitze20TOmEzYeQxVp1za\nITGRYeLSKXZub3L9rWt09QihmEQQRcKrl/nD732Drz/9c/ziZ7+E23fZq5TZ81qY6QSCILB5cJdG\nv8Uzmk4qCmjgkJwYisa9Zp8wrfHK5g0+d/a5ExPHa9UNJvLDhVwQuGiqialZJAyXMIZrNzro1gLF\n6QlEdQFBN4mVn0FJ+GQyf8pEQaNRGzDwA5LpKbK5NG/dqlOuRiiqga5PkLQOfcj9fkAueyhMVSu7\nTOaH0wZJdEbPvIStsle5+4EUG3bK+1xvb6MnLUBiQMhLm1d5dmqFbOpQ0N/c2+F7b7/GWmePqdwE\nZ1fOsFevoCaHFUerOyWs6QxFU+cgAqfdIzGRIZsV2dva5+rrl/ElCIUYMRbIhRq/8eWvc6o4hybL\nuF6X9a0SHSXEsE0EEW6uX0dVNCzDRO91SBdy5O91e2i1BzgJkVfvXONTZ0/OR3C6m0zlhyKGKEZI\nkkEqbZJJCETA917pUCyeJZW2kbQFJCuLoH0SUbvDzNSrpBM65eoALw6Zm1um1hQ5qDnUWwKgYdkZ\nNG34/oEfEoQyxgNl3v3ePtMT9xdb/dHrE3mFg8ptposPN/ocM+b9x/V9EN953jzMNqph6ToJ23xk\nu8m5mWnmZqZP/N7DRFFEtdOnWDx+vDMY0HZjZiYLlA92cboGoiTTqNdxBi6ZbAbNTmHc64zUCuAH\nV2/x8QunSSaOi9Njxvw08ZEVG8J77afeiXa7Ta1WG02oCoXCidUE78Wa8CiR475tQlVVlpeXaTab\nBEHA1tYWmqZRKBRQVZXBYIBlWRiG8a5WjzFjPgzc3L6LkDOPVCGphsZer8tsu0U6mWKvWua3X/oT\nSkGTdiZEFjxuvLHNoppj8uIpojjmoN+g3WpjpG267S6BFrPfqBLEPn7XR9dtdsMW2X6MmbQJLJVY\nk/g3/+kPEQyFtzZusenW8BQRQRJRZYWCZiOaOi23Tz/weOapp/mz0mWUhSwA87/2JYATu1EARK6P\nvt0njoc+bFEQOc9zrMQ+fXqYWMNQSCAQPZ7+pQt89oufJY5j/ursd+isu5iBgazK6LpOL+rwwot/\nh+2d69iJNMoDZfydbkB66hSyfBgw67l9MonhMWEQIkuHuzAi7vv0H31/uXVQQssenXzpCZPb9V3m\nCtNIksTVtZv8/rVvsxk0CfM6m94u115aZzk9Q+r0NH4QsN2ugK+gKDKNZhNFERi0Grz53ZfwV9Jo\nn5rlyEheSNIA/mXvFX7rf/8j5qaL9NIyXhQiqwq6JJOSLdJTOcrNGj3fQXlgYebHw44TUtqgtLfN\nqZn5Y58tjrzRfXCwdw1VahAiU9oJabclnv/4UxzUNKaKTwxbm5aT5AtFTOtrXP7+98hmfey0RVrS\nkGWVKzcCvvqVX2F7602efCKP8MAzsd6IsFJP4Hkh+v1yYw5/fxyLiOLhPSkKJ+eN/DQTxzGrjW30\nzNEkdi2T4GZ5kxfuiQ1/9fr3+KuNy+zSQcyYrLfvcPVbtzlVnMdKZum7AzabBxhSHyGGRreNFonU\n7u7y1tvXEJay6J8a7nQKDG3YZT/kn37nX/Fb//F3efHFF/nOtVdxcwp+EKKqCqaoYak6U4VJur0e\ntUEH2T4MoPTjYWVmVw1pddqkEkmOMwyTC8OQ8sEVDKWLG+rcrjXoOUk++5kn2a8mmS4uEQQhYmeR\nbHaCheWvcbB7AzshkMzYqKpJHAtUNzQ+/rFzdPo7LMwdLr7iKKLWUkiklo6UeIvCg2F2h9eWIAgI\n8Qfvehnz4UB6l7n/QbnMQa2NocqEWpJgu4YubbI8M8HM9I/ekcd1XfxIOHHhtV+pI2s6sqYzLc9x\ndiaP7/uEvsvUzFAkrzQ6TBYOu1jIRoK3bq7zmY8/+SOf05gxfxN8ZMUGSZKO+KsfJAxD7t69iyAI\nGIaBKIo/sWqCR4kc7Xb7SPcJy7LIZDIEQXBEnGi1WkeCIt/N6jFmzAedxiNaBeqWybW7q1gJm//3\npT+nkoN0MY8z6CArEpGpcuvuHmolRUdw8aQIK50ktmT2Dxp4ns9yNkm93KbrO2wPdohFKLU3sNMp\nlHIfP1mhkQR9oNJTBhx0ugimgZY0USyL/VqXVDtgO1GmmCyg5xIkf+jQyQ/DH0VFYvEff4WgN8A7\naKFOpkYVDXEUs3LN52v/42/wr//l7zB4O0YShkOyLCgkObynB0qfi7+4xD/7v/5XYHjvf+Frn+UH\nf/Eqta06YeAhZBSef/Y5pqanMPIarVYX2ekCITE6op7h2ReeJvBLwNDaYZgJer09LEul01fITxwu\nWCKOJ23/tBNFEXW/j8XxhZeUNHjt+hUiBX77+3+KtJTDVvL0xQDBAt9UePv2Ok8XUxw4LURbQ5Il\nAiFmz2uheDF7V+8QPTuNlnx06apkaTifW+CN/3iV5EoRdTKFaojIdoK9UhW5r3PQqSOIItVuByfy\ngRi15eNMncIwdHreyUKPYU3Q72/S7TTRpA2mJkxAJZeZYm+vydb2FqlUkVarR7uXojg/rIgxTYtC\n8cusld5AEoe1N36YYGnleZJJm+2D5zmo19GUe5YfwaYfTLJ85kXqlZcp3rv9YnSiqIsoigRxAkE4\nfJZF8QevnLfWqBMa8okToWbocH19jbW9Df74zstYy9MkYhVPjsDU/n/23jRGsiw9z3vuvsS+ZuS+\nVFZW1tpdvQ+n2TNNkTOiDEEkvZCAJRsWCNmEYfmPIfifAdnwJtgQYECEAVuyRIGGIVsCSXFfhjPD\nme6eXqu69szKPSMyY9/j7tc/ojqrsjKrq3u6qruqKx6ggY5b90acG3nuiXPe833vR0+3uLZ2izOp\n59i3mpipGL4s0G532Au6hKUWt7c2MN9cOvazRUWCixOstvps/vH/R2ZxilqviZ5L4GsygqbSXa8Q\nTScpNat0rT7dQRM7cIcpFu0Qf2oOPWJSbzePFxvEOEHQYX39KoVUg0hEBQxsO09pb8D+fhlBCul0\nbVq9LFMziwCMjc/SaX6T25srSGKbEAE/KHDxxZdxHJ/b6xlqzRqiMIxWCIUUTjDNiZOvUqt/n2zm\nTunvUAWsYQlwMX3QrOHrUam9EV8N2WSMtWrv2PSjnd0i1Z4HksJ4IYckSUiGQQhc26niet5BisTn\nRRCEodJ4DJ2+jagNx1AhDFFVlUq9iRm/u8HpCRLtTudQ9QgrlKjW62TT6SPvOWLEk8IzKzbkcjk2\nNzePzctcX19H13Vc1yVxT+jUo4gmeJDIcb9/hCAINBqNI1EQQRAcev2wVI8RI76u7JSKWLZNTvfY\nlfso6Qz1fgchCECREGUJOR1hbfU2mfNzaD2PQibHtc3bWIKPLEus7G/hCSDpGi17gGxqBIMQXQM3\nKrBqdsmlcnR9j51SmYEBIh79So1eq0M+kcbtulTaDXACBimJn/nlX+DHv/tntOYjqIXh+CFH9AMz\nSAC/Z3P6JvyT/+IfUtws8e83f4Xf/e0/oFaq49YCFF8jJMCPOCTnY/zy3/2b/Gf/5d87JFQWZsd4\n6bUXkb95eBh3PZcLr5xFUVW2V3dwBi56RGN2aZpUOoVtJ9ne/SvGsj6JRJyNNQXb8YnE7qZMWJaL\nrB2/SHpaWdlcIxlNUCvVsPIakiYgODYBIZImI2sKbkJl9eYKiaUJ9IFM1IxyZWsFN/Dolpu0Cgrm\nfUKD17Ow95poheSBkCSIApHvnKH6l9dIxBX6/T5Wd0A+n6ZTa1FRm8MSxjkTGQ3fcTEzBjdL65ye\nmMeQjvfjSSZzbK0nsHtXmMnfFacHlkSucJ5ur0exqpDKn2Nm4XCusRmbZXHh6IK03rA5fe6v02nv\n4zhFCF1CEuQnltB1Ay/1PKX998hnRXL5cXa3SximRipz16m92XKIJk4cee+nFc/zuL59G/W0wdX2\nDn7WoIuN5IX4gCRLyFEdS2uxub2FWUiSMAwCQWCjtY2Dw9q1G8S/e9hk9bi+IidMnIsFbr19nfjL\ni9jNJh1RIhaNMjGVpVGtUgx0GgzQMjFkJNzuAH0syfX1VRbHZ0imjw/jzuVPUtzeJvDKd4SGId2+\nweTMKbZ36/TsKLH8zzCdvTvXUVWVRPIkE6eO5qtXaiJnn/8O5f1V8KtACGKGqbklJEli0D9LpXqV\nbEYjGhtnr3wVWU6RHbu7QNuv+OQnH+z0P2LE42R2aoL14iWQD4+HtmVRbvVRzSiybxONHBbcVU3n\n1naZ6YnCT7XhqOs6xgNsSrwgOKhkpQghmq5jOR7cswkpSTK24x5uk65TrjVHYsOIJ5pnVmx4UDWJ\ndrt9NwRQFA+iCD7hi0YTPEjk+CR6AsCyLHK5HPV6/cj1x0VF+L5/5NiIEV8XUmqUeugeek5ty2an\nU+Hc5CKtWgPBUBEAQZMQbAhsH1SJUBZRBQlns8r07Aw9a0Cn3YZWn25MQozppCSD9Y1NwqjEoNJG\nM3Ts7gAhqRMoIp1Om57Vpy24KOk4oeMjqBp+ALV+B1mP0dnYp3A6xaDZRRYEvvXmt2ntVbn+4Spl\ncUBYiCKIAnLD5lyY5efnX+PX/sEvI8sy8fNxVj6+zQsvXsTtBnTtFr7okUwmyWcKqGmJv/Mbv3rk\n2Z+dn6GyW8Gqegc7NK7nEi0YTEwNTdty+aPeMJqmMT3/c9Rqu3jdFkrsbzDwGoT9Oq7bp29piOoC\nY4Wnr0aWKIqkZAPnvuO1Wp2e4LGUy7G7XwRRQhAg1CRk28dzPERVRtIU5K6Iu9Vg8uQCtU6LXquD\nMLAobu0Q+2t3c8wD12frN//k2BQZUZEQVRk0CaIqhCKW7bLfqXMikqV6Y5OJsydotHqIASRVk3Q+\nQxiGbN3e4M03HhwWOzX7Gtc+ukqpskUs4hOiYZhjGIaBYZrs1RNMTs4duS43dpad3R8yMRYe9KVO\n18ZlAV3X0fVZYPbIdfF4hkjk56lWtgj8Hhh/C4cy7U4bSXLoWxH06AXi8advsptJpZEq66Brh47v\n7hWJZJJoqooT+viEyJKIF/qovoAT+kiKhJGMY+23iIgqsfks2/slfMuhcXMd/YXpg/d7WF9RMlFC\nUyWUQIzpSIrCoG+x6exxzpykvVPBnM3Qa/dQfIFcJE4kFsPTXKy9Jqn54+cisiwTS71Cv/0xpf0G\nui4TYhJPZFAUhcnxDOulWWKxo/no8fR59ivvkM8qB2Nvre5gxJ9HkiTGJ04Bp45cl83NYtsF9mvr\nEHq40iIIZdrtHr4PlpMgkXlxVF53xFeGKIq8dPYk715dQdSjB+Nhcb+CrOrgDFhcmD72WsWMsr65\nw+LC0bHyszCRSbLVtI70f/mOeOH7Hpn48VGFnudi6EcF4wcEaY8Y8cTwTI/2x1WTaDQaiKKI7/tM\nTx8/2HyRaIIHiRzxeJxKpYKiDB3n4/E4jUbj0LWO45DP54+858ggcsTXmeWpeX688hFByjiYFJT2\nSozFMkQjEYQQlBWfMAiGRn0C5GMp+tYAYRCSCzRShSn2NovUBx0SmsbUC8/x1ttvE3gOPaVDYMq4\nfQu31UPPxrAHPooq4Pku1UYHL6oMF4+iSIiHIIiIcR2vbVFu1DgfP8Fry89RbzQo9eoEukQ2k+XU\n0imMmsu5zAyu5zM/PcP4+NFdyKn5SfS/ZrB+dRtFvDuJ8QOP3GzyWJ8XQRB46fUX2dnapVaqIwgC\nucmJA6Hh0xAEgWx2CrhrmOi6Lq7rUsgZT3VZreXCHO8Vb6IkIwf3Ua5VmM6NIYkihUyeS7e3IG0O\nBSpRYiwSozsYoFoCGV8lnhtj5ePrOCLk4inGp8ZZub166HO2fvNPDpl/urXuweu5v/+LAESWJ+mt\n7BFZHEdOGHh9l61ikV+ZfInzixcolsvUgz5oEo5lo/oic9mJTx3TRVEknT2BqUVRxR10/e5WWbdn\no5lLx/79VFVlYubbVMprhH4TBBkzOkMhmzly7v1IknSf+LSMbdsEQUAy//SlT3yCIAgspabuMYgc\n0mg1OTE33HnPRZOsNYbCvyRLSIhkdYOeNUCsu4zFc+iRBFc+vAwCTE9Osn7lJmru7gL+s/WVCQa7\ndfTJDJIhEugyXgC7G9t84+KbTJ+YY3Nvl77igSJj9y0iqEw/oCrPJ0QiEdLZZYQwQcxsISt3+1a5\n6pDJnT32ulgshaq+yX51FcI+IRrJ9AlM8+HpD5qmMT6xfM+RswwGA0RRJKNpD7xuxIgvi3gsyrdf\nvsD65g6VVhcvCMEdMJ7Mksukh+YqxyCKIl3rfjn7s7M4P0Pz42t0PJDuERwSpkbL8tBDm8mJ4dij\nKtKhQtiqGBK9bwPUdR3SYw8fw0eM+Cp5psWG46pJAOTz+SMRDffzRaIJjhM5otEou7u7eJ7HwsJw\noEmlUgeGkmEYHhtpMRgMmJub+6nbMmLEk44sy3xz6eKh0pcntCxeYfgsRKIRJs00H6xtoE6kwfUx\nJBUdmVRf4tyLL1CkjTKRJKOmKG8UcWs1fDFAUCTCwMNudVAn0ihxA98PCGwLxVfxwgDBcRElDUQB\nSRbxXA+8AIKQYGDj2z4BHkEQkM/lyOdyDAYWQRhgGgZh1OLlpRc+9R4n5sdplbqcOD/H/k4Zu+8g\nKSKxVIRv/eLrD7xOEASmZ6eYnp164DmfFUVRvhal6BKxOK/PXWB1b5u+Z6GKMsuJSYTU0DRyYnyc\n+HWRzZ0SSjqG5IVokozmgu5qnHr+HDXZxhSyRHSF3Vvr2J0GYvLuotrrWTR/snrs5zd/sorXG3p2\naPkErQ83MKYz+GFA0LcJuxaiHyIrCrNTU8yEIb1+H1mS0HUds/vwbSpBHica9RkMNBqtfQTBIQxV\nGp0JTp567YHXSZJEYfzRVBjRviaLxsl8gZgZYaNSxA5cDFHlTG4O9U750fnJGd65fZWK4CBHdTRP\nQJUVlLbDTHKc9MwYXcUjphWQNYXt6ytYcsAnFqWfta/o4yl6q/uoaRuXEEmR8doWjd4AJRDQdI2l\nuQV832dgWWiqiizLGPanV9VSFAXbyzI5ZtBq7uP36wiCRxgauJxmtnD8pgrcEQ0mjxcjPi/HpayO\nGPFVIkkSiwuzLN55rSsSfdRPveaLIggCL184y/rmNrvV1oFwMZUyEctVpufvpqMVcmlu7VRRdQPP\ndZjJHI1Akn2b8bGjm5AjRjxJPNNiwyfcW03i04wj7+WLRBM8qGTmN7/5TYrFIo7jYBgG8XiccrmM\nbdtIknQk0iIMQyRJGvk1jPjaI0kSi1NzB69t2+YHW5fRE1EanRbJqTwLuxbbm/sEErTrDlHL5OUX\nXiQ/lqe52aFcrmBk4khxnZUPr6GNRyFlYvcGKLkYQddCL6Rwym20uAkByFYIvoAUCEimxmCvQeB4\nRCYzCLKC5/ioXoCxlOPP/ur7nFk6xVgmj2EMFwC+71PQjy+ZdS9jhTytUy12bpaYWxpGNlhen/nz\nMyRTo+f786JpGmdnFw9elyr7XB3soekqpXqZ6cUF7PU1KtsNBEmitWexSIJX33gdTdfZW71GpVUn\nnklCVKN4aQ1BuieNZ6+JW+se+9lurYuz3zrw6BARUFNRBEHEbTtEjQidSMhf/OgHLC0sMp4fO9it\ncgY2J+MPj0wpjC+zs9klHvFIZ08Nqw1UA7LjF0eRbj8F8WiMC9G7KQHCxgq1O6lbe506p5eXubl6\nk3qjjqoZtEt9ThvjvPjGC7iuxw+uvktLtogQwVZF/Hu8lT5PX/F7A0RZQU1GEQG70iWZTrHl1Ch9\n+C5zkzOM5fIH/WXQ6DA393CvjPz4RXZ23yaTTGEkx7Btl2pDZXL21S/wrY0Y8fUiFTXptp1PrVTn\neS6Z7MN/0x/G/Ow087PTB+sNQRBottt8eH0NX9ZQFJVoNEbKaFBrt5gZz5FOH54LOP0eF08erVo0\nYsSTxkhsuI9PM478hEcVTXBcycxMJnNIhFhYWKDRaGCa5qEBcDAYIEkSZ86c+cLtGDHiaUPTNOaM\nHJu9OnudOnrM5NSpU0yXckwl82TSaXZ3ipjxCNd2buPoAulkklKjRmV/H0WW0UWVvfUyLj6+AKKp\nMqg0EewANRnDK7aQLZ+oZiCECo3dMqImIakqftsmsLsIHZvsxARBXCUey1PsNqi5XRZSExiKStJT\nObX42YzQls6eZObENLubRQQRpuee/1pEGjwJjOfGKK5UaGBTsdrEknEunD+PXWwwPz5NMpVk9dYK\nfhhwZXcVJRMh7kTYL5Vo1ZpEYzH2S3fT2rRCEiUTPXYRqWSiqGPDyahdbqHGDfx6n6BnI3mQnsgT\nnc5TL1bYc1tUN9ssT8yD4zGjpSlkH75LJQgC03Mv0+222auXkCSNwvTMQ8s5j/hsnJqa50e3PqKj\nBXQll1QmxYvRFxCrFtMTEyQSCW7euEGj02arXSY3M0GtuM72xiZu30K8Z7/is/YVANEbhml7tQ5B\nY4Ch6mSmxkktTLG/vs2u06K21uLU7AJee8DZ9MxnijBRVZXp+TdoNMq06g1ULc7kbOGpTpcaMeJR\nMz87xca7lxHN48rIDhHdAVPjR71KflrufQaT8TjffuU5intlqs02YRjy+tkFRFFgp9Jk0O8hSDKh\n65KMKFw4PUsqcbzw4Xketze36VkuhCGZRJSZqYnRMz/iK2EkNtzHgzwVPuHLiCY4ToS4Pwpibm7u\noW1oNBpUKpWDa3K5HKnU8S7nI0Y8TQRBgCxJyFWP0u1tchN5EkaU5aVzB8ZLkXiES2s3SUznUYBc\nMs3GfhFtOoO3VSUzM4G1B41uG8F2kFQZSVFwWg0GOw0SRoSg0cbXQnpr+6iWgzCVRIiogIDseaSy\nebKJNJlEElEUifdEVEOju9/gZy/8DKnE5xsndF3nxKmRS/ujxnVdoprJ+uoNmnaNMS9HxoySP/fc\n3QW6InGztIGeHU4088k0W5Ui+kKO/nqFhHY3hU2O6CRfWTyUh/8JyVcWDyoN9K/skH71FGFvmM6R\nH8+SjWdQFYVUNsXJWIGOM6C/W+W7F1//3KHm0WicaPTBE+MRPx2O65A24ty6+gFWxMOMpilEU2TO\n3jXBHDg2W90yamz4N8tGEmyX91DmMihX76oNn7Wv9G6VMCcyaAkTt9pGU3WmZ6fJ6kkEYTg3Wc5M\nU203CHdbvHnxtc9tsphK5SE1CrkeMeI4JEniwuIMl1Z3UY/xJnH7HV48vfBYF+yCIDA5Psbk+GEv\nloW5GbrdLpbtEItGjoiMYRhS2i/T7w+o1Oq0nBAtEkcUh5FujUqXlZ2PeH5plmzm6TPzHfF0MxIb\njuE4TwX4aqMJjhMg7ucTccF1XTY3N4lGo4yNjR1Uutjc3GRnZ4czZ86MQm1HPLU4jsNbq5cIkjry\nRIy0ncfTJHTTODT5jsfi9G91SE4PJ9eaoqKIAo4ogiCweekGTlQhDAKQRIKBizDwUDQVydCw2wPG\nlqaIpuO4IuxvFekVK7Rul4lPZZnJjKPHTWaTw2fMtR1iZppkKsVANVGk0fD6JNBst3iveAs1FSFx\nYpxY1cEiIBKJHooEUEOReujzSQa8JijIuorr+tiWhaTKtFdKRE4ODT5nV+jo+AAAIABJREFUfuM7\nw/c/psIADCsQCE0b6/I2iYksk4kCsXiCxdwdfw03wDBNYvE4ltAZ5bQ/IWyXS9xo7qAno6TmCthC\nD2fgEY/HDp9o+wj3mC1qgYSeimB1Bxi6QX+9jDE/HHse1lcA3LUqkViUwfVdMtkcE7ksETXCQmHY\nX1RRxjQMZgwDue2OqjmMGPEYyGczvKZrrG4WqXV6uF6Aqkjk4hEWL5zCNL+6cToajRKNHj2+vrnN\n+l6dUNZod3pslBsIgUs23mV6ajh+yLIMcpxLKzu8oqnEjnujESMeE6Nfq2N4kKfCZ4km+Crwff+Q\nOLK7u4umaXS7XTqdDvPz80iShGEYhGHItWvXOH/+/Ffd7BEjfiqubd9GzA5zmgESsklXD9nt1sjE\nkgdCWtiyODe3xH69hRjTsS2LSDRGY7eIkotiBnH26xUcx0FUFYSugxY3EUQRQZLRNYF0Kk0iFqfZ\nayNFNWTToBCLkkinQBCIhgqFdA4AqeuRPHEnckgQCMLgmNb/dKyvrFPeruI6PtGUycLyHPHEaEf7\ns3Blbw0tPZxY6YaO4YmEKZ2t5j5nI3cnXAlRJxKPUWw2kOMGnXabhB6huL9HZDaHMUhR+eF7qGNJ\nlLiBqEjM/f1fxOtZOPst1LHEwS51GIa0//wqE2dPIAJjE5O49R4FM0ksEiEIAuKCdrBgfJSVy3zf\n59bVFRp7LcIwJJGNsnR+CVV9sPFZGIZsbW1Rq9ZIppLMzMw8k4tZ3/e5Ud9GTw+FhVw2R3GjjpyO\nslXd48T40DcpCALmMuO0HZ+61UOLR+g7A3RHpNexmPzZ81z9gx+hz2QRJPFT+wqAtVnFTMXIT0/g\ntHoUCgXsWpdzC6dQZBnPdcnrd8WO8BH2mH6/z+2ra7RqXSRZJDuR5sTywudKyXlQJOiIEU8jsWiU\ni2eXgCe/b6+ub7FZ6yEbw9+yvXoLVTcAg/rAxd3YYmHurq+DbEa4vVXk+TNLX1GLRzyLPHuzic/B\nZ4kmeBK4du0aiqKgqirdbncYYi7LB1Us1tfXWVwcmqUJgoDv+zSbzafi3kaMuJ+620Phbojj7OQU\ntzbXcFWoNGtkE2mClsVLM8tc3lujMDnO/t4eqzsleu06PdkjsAeIAfiqiGaY9HcbmCjERZ1Op4EZ\nMUmkYkRME1mSGNg20XQC3QpZWjxJf7OCno1TqpTpNNvEQ5XFibslKzUnJB57NGLApXc/prPbR5Ik\nJGQGZYcP9i5z8VvnSSQ/3aiq0+lw89IqrXIbgEQ+zvLzJ4k+I7salmXREz3urVo+X5hmpbiBLYcM\nBhaSIKL2Pb595mV+Ulkhk86wvbPDTqlJJ2jRVQJEe0Dg+6RfPUn1rVtEzk5hTA3LjckR/cDgD8Dv\n21g/WuP0z7+K1gmYnZ3B3msiz2bY2tslq8WIorAwfbeUZEo9vq765yUIAt7+3rsIfQlBkBCATtHi\n7f13+ZnvvHpEQGi32/wf//if8ZM/fJ/dDyuEtkAoB5hTKgsXZ/gPfv1X+NZ33nhmhIft/SJq8u7Y\nIooiC5kJ1msl7DtBDFavT9JTWVg4zYpXo+D7bGxtYu216Hpt+lqA1e2Qef4EpT+6ROa7FxDl4cX3\n9xUAZ7uOXrWZfuMi+r5NqjCLIav0x03WS9uczs2SUSKMTxaA4eInrT6a57ff7/Pun3+Aio6EDC6U\nV+o0qk1eeeOlh16/ubbJ9koRu2uj6ApjszmWzp58ohdnI0Z8Hp7kvuy6Lmt7dbTIUIgcDCzsAD5x\nepIUheagT6/fI3JPWki13fsKWjviWWbkJvWU02g0CILgYEBst9uHdrAEQUAQBNrt9sExwzAol8tf\neltHjHgUBPft6omiyPL8Iifj46Q6IieENG+eepFMMs1cPI/V7bPfbxJbmqBud1HTMVRVwfId5LiJ\nGDExcgmMuSyWbaPGIgiyTL/dQxRFgjCkYXfo2QMs16bcayKoErOZcWbNDMJ+jzPzJw8qUNjtPkuZ\nL16KEobPc32rcSTtSRN1Vq+uA3dyNYt7bKxtYFl3q3Lbts373/sIt+FjKhFMJYLb8HnvLz7Edd1H\n0r4nHd/34b4dWsPQuXBimQkxTrYvcy4ywc8uv0gymSQvROj2ejSxSC+OU+k1MXJxAj/AU0CJm+Te\nvIC/06T1vet03l/H3m/hVDv0rhfhnR3y6w7T37qALQb0cdlv1YnEosymC6RclbSvszR74mDn2Kl3\nWS7MPZL73d7cIegenSDLnsrtG2sH38n25g6/969/n7/9M7/O7/83P6D2zgDdiWIIEUw/Bpsat//N\nHv/df/K/8r/99//kkbTtaeDe39JPSCQSXJhbImspjFkaL2cWefnkeabGJlA6Lu1uBysqIkQ1eqqP\nkY7j2g5KJsLYm+dp/uAGjbduETjeofd1Sk2Cd7bI9xSyLy3RrjexdYGm3SWZSHAiO4W03+d0dprZ\nybsRFdT7nJyceyT3e/vaGiqHxQ9RFLFqDvt7wzmCbdtsrG1Q2i0dqtS1vrLOxkc7SI6CqUZRAo3y\nap2rH1x9JG0bMWLEp7O2tYNq3hUeLctCEg/PFVTDZL9cO3TMC+6MJSNGfEk8G9sVX2MqlQq6fney\ncNxkSdd1Go0G8fjdnVbf97+0No4Y8ShJKAbWMcflQOCb5186lPs+PzHD+vu7yJrKXrFMLBqhXu0h\nRFW0VAyrNyAcWEgRDdfzkJMafq2HWG6TzmWpDdoEjosngt8ekEqlCPsuRiFLuVVjcmGW+YZOvCtg\nhR66IDNfWCIejR3Tws/P/k4Z/QG73p1ah3qtzpW3r4EtIcsyax9tkZ/LcPq5Zf7gX/8RK2+vIyoi\nMydmmJqcRBAEVHRu31xn+dzXP4wyEomgP0BXGYskuXjq3KHx8rkTp1n78Z+imArbxT0SZox+fYAs\nK6AJOLZN2BuQen6esGsjBNC5sk00FqMwOUHipUn67S5Nycav9shPjCP1PcgZtAc9Zk8ucEafQOiG\neASYosbJ+QufqaLAZ6Gx30Q+xitEEATatQ6b61usX96kuFXin/6P/xKhpCEKx+85CIKAXDH4vX/8\np8wuzfArv/ZLj6SNTzKTuQK3Ny+jJw9HDoiiyNL4HEszd81bBUHgtcUL/NaP/i1CXKbd72IGCl7H\nRoloeCKIXkjq7CyiKNJ+6zYhEA5cDFVjfHqS8W+/RqPdwhICxL5HYj6F2LZphTYqKicWFliQMjQ6\nPUIgqZicWFp+ZJ5L7VoX8ZhpoCKrVEtVavs19m5X0WV9mJ6j3Obsq6eRZInf/a3fx2p5ROIRls8u\nEYlEkCWZ/c06S+edT03bGTHiWSIIAvbLFWzHJRGPkXpIROJnxXI8hHvGb13T8IPWkWfa9Q8LC5LA\nqHLRiC+VkdjwJfA4q0L4vn9o0PjEDPJ+7j82Mogc8bRyamyWd3dvoKbuLggcy2FCSR5rsmcmIpyN\nJ9FkFVf0iWOxubOF3/fA9YhNZAgdn6DWJZqK4zU8JiMJknqK2l6HitUkDEIiMQNdlEmaUWRlGBnR\n3qvxynO/SDadeSz3KikiQRAcPzEQBS7/6CqaYBzETRqKyd6tKn/+O79JfaWL7KtAwEdrV9g5scOr\nr7+CKIr0W/0Hfqbv+ziOg6Zpn2tC0um06HaqGGaCZDL7Oe/08bGYmuRGt4gavds3nJ7FydTRMmCC\nIBDPpMilo8NcXV2mHg7YLu7g9X3CMCAxnsPrWEiigpFPkhnIFOQYyfEc21tl2sGAwHVJZtIIfZd0\nKoMgiXQGFsmBxHPPn31saQmS9OC/V6/fZ/2jLTTZ4Hd++98ilI4KHF7o0qeLSRRZGHYqqanzz/+n\n/5tf/tW/dWxIseu6+L5/SPT+LJT3y3Q7PfKF3BOT1qNpGlNamuKgg2rc/X6cZpcLx5S7cxyHyZkZ\ndNPAciyidpPd2j7WwMb1Bki6SmQyR9DoE794CkVXiVQccmIUNRdje3MfV/TxHZtULkvQ7JMbG0OU\nJVr9LqfEJIuz80c+91EhyRKhc/y/7Zf2kW0dQxk+N7IsQyjzh//PH1PdblBbaaMpOnapzV+sfJ8X\nv/08E5MTqKJKrVpnfKJw7Ps6zvADP48YEQQBe8U9HMdhfHL8kYlzI0Y8bm6srrFbbYOiI8ky7l4L\nXdzi5Mw4hfyj/Z00TANVPOoBdP+onY0/mrS9ESM+KyOx4TFyv3Hj46gKIUnSISEhHo9TqVSO/JDf\nO0kcDAbMzc19oc8dMeKrIh6N8Y2Zs6zubdPxLFRRYj6aZ2ps/NjzP9m5VQSJdDyJ3a0T1U0wwXZs\nfMvBrXTJT4wR+gEx2WR56gSnZ0+wV69wpbiGUO/TtH3yc+OIdxZ0vu8zYUUfm9AAMDM/w8aVbQzx\ncBmuMAxxggFmGAfp7rFKpcyH71ymttVkLJ8nvBPAZCgmjY02OzM7TM1MERIcETGCIODj969S32kQ\neCGSJjK+MMaph0RA+L5Pcfsd4pEmhbROv2+zvW6SG38FXf/qKyxM5gsYqsZ6rYgVeGiizJnMLJnk\n8eW/xDtTM0VSSJpRXFfA1EzCKPiOh9MZIDYsYjNjBK0BuViaF2eWyaWzFPQdthtlxJZF2xPJTt8V\nNAbtDi/NXHis/geTCxNc2rqGrh5e+Huehxu6ROU4O7s77F2pod7jZBGEATf5kAolHCxUdHLhOKe4\niCiItK4M+NM//DO+8zd+4eCawWDAlfeu0S53IRBQozJzp2eYnvv0FKJut8tHP/6YoBeiyCqbl7aJ\nF2Jc/MZzT8Ru2+nZE8TLJYqdGm4YEBFVFqfOHMp5/gRJkiAIEEUBXdWIDGRy6Sz9iosfkZFEkUGt\njeEIJKbyWNtVJrMTvDZ9BkESyWsJSuU9JFnAkXSS43fHkt5enTe+8XOP9V4zEyn2b9aOzEP6dh/Z\nlFFk5eCY7djsbO3y1p+9Ty6ZPRgHBUHACKNcfvsq+V/KM7AGKOrRPl6v1bn54Sq95gCASNLg1MVF\n0g8pw1feK3P93ZuIvoIkStz+aIvJk2Msnz8q/owY8STx4ZWbNByQzbuRjqquEwAfr5fwff9IicvP\nQyGTpLJVRblnvl9IJ9iptpHuHAt8n/g9ZrROv8fCmccnYI4YcRwjseExcq9x4708yqoQuVyOzc3N\ngx3daDRKrVY75KBrWRa53NAxPwxDJEkamUOOeKoxDZML859tspkz4mx4LXLxFPVmn0I0hd8ecKW4\njqRKCAEUEnm6+23iksHLz79IwleJx+NEozEGSkBqziCqR7iyeYtu4KAIIgtSjH/3jb/+WO9TlmVO\nvbjIzfdW0WUTQRBwPRc5JjCVm6K1NTR68nyPm5dvEVoi1fUaoq3SbfbwXI9EfPisy4LKhz/5iJ31\nIvFclM0bW5x+5TTL55YQBIGP3rnMoOygy+bBL0PxRpmNlU1SqRSiJJGfyjAzP3OojaWdD5gcGyAI\nwwmNaWqYps/u/vtMzb7+WL+fz0o6mSKd/GzRZBklQisMSetRbCVEbAlYUpSbxV1kXUXxA9LJLO1S\nk4Ic5+LF54nbCrlslkgkQlhWOXVugna/y8r+NoPAxRRVzkRmee3cC4/3PjNpxk/lKd3cO0i/sRyL\nzEwS09ZwGj5/8cffQ+kah7a7bvIhu6wfvHawDl6f5kUUX+P//B/+BctnlpmZmyYMQ977/ofIroqp\n3lmEe3DtxzdYu7mGoRoousrkwgT5sdyhNn7044+RbIVPsj101cSqulz76DrnXjj7+L6cz8FkfpzJ\n/PHi5b3ouk40UAiAuGwgjo8jlyu0XZVWs4ys68SRMGUNr9RiIVbgxPw8MTNGPB5H0mT0iMGLC2e4\ntX6b7XIFL/SJiBqvTz/P7MSj8X55EIvLJ2jV2vTKA1RlGC0wcPosPDfN9krp4LxatcrOSolus0/Y\nEui6AzxcUvEU0p0/pN2yefsH7xCEPpVyhcJcnue+cZ5sLkO/3+fSD6+iSwYR7U5/GcAP/+AtCjN5\nhAD0qMHcqZlD6Z6u63LlresYcuRAVDUVk/JqjUhsm+m56cf6/YwY8dNSrdep9Fy0B5Q0Vg2Tm1sl\nJgr5n9qEciyf49ZmiYC7a4xMOonneRTrHRRNx7e65OdP4vs+vtXluZOzJO4v4ztixGNmJDY8Ju43\nbryfR1UVIpVKsbOzc0hcmJ6eZnt7myAIUBSFMAyJx+MMBgMkSeLMmTM/9eeNGPG0MTc+TXWlRVuX\nmDLS7HSrZNNZ5uotulpAMpcmakZolGSMWASCkGx0mFMpigLGQCSVTxCLx3gj/SowFO30lk808vjD\nvydnJsmOZdlc3cJ1XNL5FOOT4+wV96jcbqAqKhurG3RqveG4EoQoskTEiNJ0G7i+jSKpVOtVuoM2\naTODHNGp3+7xl2s/ovWdJs+9coFmsYOhDidGjutgWRYbNzYRQpHYy0kEwWerVqJebvD8q88Bw6gG\nRawcCA33EjPbdLsdoo/Iv+LL4szMIj9euUQ6EWdQtwl0k2wyzaDVxTVV0rkMqiCjBSLJTAavM6Aw\nOQmAaRiY7YDYdJxEMsn0ncWi53qM++aX4my+fG6JiZkCuxtFwhBOTS2QzqS5/vFN7Hqbfss61A4v\ndKlQOva9KpQ4GbrIgkKr2OWP/q8/4zt/500kWYaBeDCDsG2LTrfL7koJM2Zw8uwiftflWukWnbMd\nTpwaeh1UK1X8boCkHP4cURSp7tQJLz7ZZeaO49z4Au/t3GQ6O856eYdEPEEhkca3bMR4hEwmg+AG\n1Gt1EoUMYt8nXhguqHPJLJXdvaHJ7YmTLHMSGKb5nIlNPva2C4LAS6+/QKVcoVysIskSzy2cwTRN\n6vtNnIZPEASs3djEGwRY1oAgCNB1Dd1IUO/USUSG85f9YhnLG3BqeRmnEnC7tMnGtS3+vd/4JbbX\ndtCl4dgShiGWbVGv1altNrDqDjML0/S6Fh/sXubsN06RuyNQbaxsoktHQ74VWaW0sT8SG0Y8sWwW\nyw8UGj4hlHV2SntMTzxc2HwQL5xZ5J0rtxD16MHYOZbPkk4l2NncYGYuT0z2SccizE0vPhHRYyOe\nPUZiw2PifuPG4/ikKsQXjTI4c+bMkXSN2dlZqtUqrVaL2dlZBEFgbm5uFNEw4plDEAReXjrPfq1C\n2a9zIpnhev0WJy9+k4E1YLdfx1AjTJ8aY21jDa/eJzk13AV3Bjavjp8CQvYaTQJVAscnLZlcPPHl\niXaaprF09uShY4WJAmvxTfY3ynzwV5fwm8OdwO3yFslEknQuRSKexExrCIJAf6fLwskFcvlh2Oaw\nlKbJu3/yIfnJHP1Oj17QZW11i261S7/bRwpktLjKYDDAMAwkSaK526VWrZHJZnBdF1U93tXa0GU6\ndu+pExsUReGN0y+ytbdLOqoSuD6XKh7PvbJAtdWgEQwwYxHGo2nWtzaJRyaRleHq2er0+cXTr1Hp\ntmgEHVAkBNtnQk+xPHfiS7uHeDxO/MLh0qsnTs3z4/V36HTah4736eIca7k6jHDo0yPO8HdD8Q3+\n8nf+ihe+9RztdpvBYMDmyhZWx6Xd6KArGomxKHNLsyiKgqZobF3fZfbEDLIs0+10D3bQ78d3/Ce+\npv1xJGJxvnXyIuulbdKJOQbdHlcjAS+9sMxOYx9bCDGzUTJ6nFJpl1fO332O3WaXv3n2dTYb+3Ql\nD0ESke2AE8lxxrP5L+0ecvkcufzhCJS55Rkuff8Kl9+7wvoH2wSOQHfQoVjZIZ6MoGMQi8UozOTY\n3t5GViTOnD2Logx3WRVZI+wGfO/3v08un6NZb9Nqt9i6tYs/8Gk1WphmBFEFf2YcSZbRJJ2Vy2vk\nfmHYFsd2H9gfXHtkcj3iyWXgeCArn3qOrCh0eoMv9DmRiMkbL55jdXObcqOL6/nIkkghHuFn/503\nR/4mI54IRmLDY+J+48ZPO++LIkkS58+fp9lsUi6XD4woz549+8SKC2EY8nt/9Ke8dekGu9UW7b6N\nKAhk4iZT2QS//N1vceHckxFSO+LrwVgmx1hmOIntBTZ+fDgpHu8XqDRr4MDi0ss4lQ5qx0MWJBZj\n44znhovz075Pr9djv1lj32ryl6sfoAkKs4k802MTX+q9VCs1Nm9t06o3+ckP3qW23UQKZHzXZzw2\nxd7+HlftKywsLGCiIWkSWkw/MG3zA59GrU672WZnd5eNrU3kgUpxp0RcSZLKpGjU2th9G0EFRZJJ\n5dNkx1MUJgvsbe+TyWbQNI2Gfbyo2mr7JPOPz8/icSIIArPjU8zeeV3xexiZGGNjY7TbbRqdFrIo\ncebMN6DeR+146KLC+dwiyXiCOaZxHId+v89Oo0zV6fAXN98jKmksZCfJPsAv4nGxs7lDaWOf4m6R\nZqOJxN2IHJMoKvqxgoOKjskw7D0UAm5du8VGcZ3b19cZ1GwqOzUSZoJUJk1tp44QCBS3QmRRJRqP\nUJjNk0gl2N0uMjs/Q24sx/pH2+jK0R0/Lfb5DEmfJGRZ5uT0MA+60WrSjYtohs7Y+Bi1Wo2ePWA8\nFuOkniXjqEgdj4iocWLuPIZuMFWYwLIsut0uO0GFteYea80SSSXC8sQcpvHlGbqFYcjqjdvUig1u\n3rjFjXdv4TfFO2X1ZMajU1z5+DpzC3Nkcik0XcfyBkwvTNOz+uys3aDX7yILChomez/YZeHEPPX9\nNoOqRTwWx4jqNHbbNKUO+8U9PCvEjOtMnZgEK8S2bTRNI5aKUt9oHetzYsY/nyHpiBFfJp9VMn0U\n0qosyyyfmGf5EbzXiBGPg5HY8Ji437jx0857VCSTySdWXLiX//d3/4B//vs/ZNsxEfUocOe/EDaa\n8H7T5nc/+m3O5hT+wa//KufOnP6qmzzia4YuKPTu/L9hGsyYw3D3IAhYMsZYnJo7co0kSZRaVXbo\noCZ1VIauz7cGZbyix/zEzJFrHgfFnRK33r2NJuvUd9pEwhiaWiO0RRKpYfrHrD5PpVOkWN+hb7SQ\ndJl6rcL1S9cpTBWo7tfoN2069Q624+IbAlvVNcx+giAW0qy26HV7CLaMIksMug65jExtq4EgiiTu\nKQFYrhiUt2+RSBtMz2YRRRHP83GCcRTl03d2nhaMe+L+4/H4QV651Rvw0vJFUomj466qqlzavEk/\nJiJGDETABj6qrfM8fGmCw40rtyivVFFklUHF4fTiWT7YuEw0GPYVWVDIheOHPBs+Icc4sqBgY5GQ\nDHZv7SN4Mta+x+3b6yTDDIEEjUoDq20hhQrxSIxuu0fMjLO7UkJYFpCkoRhnGAb9oEdpbZ94IkYm\nMxSjHNdm7tzXIyQ+FokS7rlg6AiCQDab5RPPeave4dWTzx37u68oClfK60jZKModgacHvLVxldcX\nHl151Ifx3l+9j13zEQQBu+6RjRdY21sjk8gh3RGDBAV6/S5Wp4e92efK7Uu0dwaEbQndMRERsQUL\n2+ihRmUSZpL9jQpxKUWghDSsJnbXJQhDCpkcg94AXTW4fWWd2XNTB9EM+UKOH1XeQrRlUpkksdid\n586zOL28+KV8HyNG/DQkIgY1+9PPcQZ9JuZmP/2kESO+BozEhsfE/caNx/GsVYVwXZf/6h/+I364\n7YCRR/yUjYkwmuXKAP7T//lf8B//3HP8vf/o1768ho742rOQm+Td8gp6/LDDvN/oM790/P6A7/ts\n92toqcM+DaqhsdEoMxdOP/YQ8E6nw0dvXSahDtM8PMej0+5hD1wGTQshFDFMHVkSSSXTeKKLFpgo\nPQ3F0ynfrnPr8hqpZBIxkGg0mjhYpJ0koisjKAL9bh+341KpllEFnbAWUG2VcQcumqFSHzR481e/\niW3b/OQv34e+RK+bY/P6HpfeLrL80gni6ZNMTH19RMKZRJ7VQeVQOcQwDIk50rFCAwx3uFuyiyYe\n/g3QYiZr1d3HLjYMq5NUufXhKrnkMCS/2+kRleK4hgW9u7XeT3ER4HA1CsYPjveNFjNMUS/XCLWA\nTC+NIqggQLfdozNo02l3UESVaqtCubXHYNFCj2i4ms13/8Ofo16rc/lHV4mLSXrCgO1bO2xIG5x7\n9QwLL8wx8zXJv5dlmTElTs1zD+3Ie67LuJ564AbDemkbIX00gkHNRFkpbXFu7uQxVz06fN/n1o0V\n6tst4rEEruvSbfYZdAf4VkDVqpJKJVB1jZgZpxU0MQSNSz+5zGAFouGdKKY7Q6BJFHMQJegHvPvW\ne+SzY8SkkE67S7VewbFdZFGmfalBpbHP7MwcelQjPhtBVVW2NrZZ/WCNyew022s73PhoBT2hcOEb\n5zh//jTJ1JO/sTLi2WVxdpLdD66jR+MPPCeiCCTiD/73ESO+LozEhsfEccaN9/KsVYUIgoDf+K//\nW95rRxEfYppzLwMjz//+vRu43r/kP/+7f/sxtnDEs0QynuA5b45b1R16OBCGJEWDi7MPLkfbaDXB\nOH6n3pGH4qFpPp5w51azxdV3b9Ctdrn9/haKUSSejbGxsUFxs0TggKGZdPsduv0OqWwKGwtTNbHq\nDnoyQiQeYX1/A78X4DsBgghBEBLXU9SLTSzXRtAkPNvDdwISRoper4foK3idgOJ2kcnpKex6H9fx\nuHX5KrKjggyJZAEoDBe4RY9T579eJrSzY5OEpZDNxj6W4CMGkJEjPLd47oHXlFt1tMjxY13HO94j\n4VGxu13k9uV19jbK1Lea7BsVYrkYG+sb1HfbFFIFylaFhD/ccxcFkdO8yMnQpU8PkwiyMOzrHRrI\nskKn0yIIA9JKhvJWhZ7dxUxEqDdqaIJORIti9S0kV8GuOTRSDVIkaTVDPM/jyjvX0QQDFJien2Z6\nfljVwsiqXxuh4RPOz5/i6uYq++0mnhiiBALjRprl2YUHXtNy+ojq8WkkPf8hW6RfkJVrq+yulNhe\nKdKr9ZENiVg2xvr6bdxqiKFEsL0BrXYbsS8SSeuoksyVq1cRdw10HrxzIAoiyc4Y24Mt0ktZ6rU6\nGgayrmB1bARPpL3fpZ8aEIQ+7UYLy7JYeX/toNLJwql5Fk7N43r+jawDAAAgAElEQVQuucks2dzT\nmZ414tlB13XOzU9wbXMf1TxaujoYdHjlua+PID9ixKcxEhseI/cbN37Cs1gV4n/5zX/Key0D8acI\nqw71BL/1g+u8dP4DXn358ZaOG/HskE9nyaezuK6LKIoPTWkyNJ2webzHiuAHjy1lwPd9PvrhZVQM\nTD2CIsu0y102rm4z6PchDOm0OwgexBMJFFmh0ayhRhT6nkW/U2NrdQdN0DHCCB16WP0BalQhncgQ\nBAGdVo+B06ettlBdA1XQcEIXXTSw6CMi02g0Of3yKZLpCW5fXaNb698tewh02h3KuxV6vR5e6HL+\npbNksl+fRcHc+BSzhUlcd7hj/TB/AVVW8P3+sf1KFh9d+tz9tJotVt67jSYbRMwIbanH/kaZ6+/d\nAl/CdwMEV8aIGTR7FRJO9kAQlwXlwAwSoClU8RWPRJhC0EQSZgInsGk32ziBxa6zg2gr+FgIkogu\nmfSDDnJosFfZ58xLp4mkDN798Xtgi4dmHNVylUalRfeDDpIocuLsApFI5P7beSoRBIFzcyc5G4a4\nrouiKA+NelIFiT7Hm61KjzFianN9i9LNMppsoGs6Fg67N0vU3rpKVE6y3y/T6TTQVJ1UPInn+7Q6\nbQQtxCp5JDhc2tsLXfp0MYkeCFYAeXeajzc+YlKbw/IsFFVGkzW6YQctSFBulPjZ598gomh88PaH\nh8aWMAgp7e7RbXRZXb2N812Hk2cWj/VyGDHiSWFyfIxoxGRtu0i9M8APQjRFopCKsnj2/Kj/jnhm\nGPX0x8iDjBuftaoQa+sb/JufrCKaY8f+e7e0TmP1A3xngKTqpBZfJDo+f+gcx8jyj/7Zv+JfvXTx\nqXMrH/Fk81lFgkgkgumKxy4HEoLx2MSGrfUt5EADESRZxhd9evUBoivh2wETswWqtTq2a6EFGqHo\no6oyoSewWdokJiQQPZF+2Mf1PAQCIlocVB83dLDbHq7lEXghru0xcBsYqokiqYRKgB7VSccyOJ5D\no95gbnmG7v/P3nsFy5GmZ3pP+szy3hzv4A5MN9p3zwzH7TiSQzNkkIyhJO4GFRJDUvBGF5JCoQvd\n6Uah0N5sKIKK2F2uyJXIndWulk7cGXJnNKZ72gLd8Dg43pT3WZVWF4VTQOGcA6C7gTbofCIQAWRl\nVWUlqv78/ze/732bPe4+EdVSle2beyiSiugqdPZMLv7oCseenWNy5vFH+H1UCIKAqqoP3hGYyU9w\n8/ouUmq87cbzPHJa/IhnfXjWrm+gyUNxO5lOcuHVd3F7PpKtYPs2iXycarWMJuqkplLstbYZdG0M\nM4qMgotDR2riyz4pLQ0eJKNpBm4PR5TpN228AXiegNlrIXgKhmogOhKe5pBIJIgYUTqDFp7nkp1I\n0yy3SGh3hKeNWxu0djtIkgK2QGu7x2s7b/Lsl54iFn9yyorfz/dlKpVnr7qCFhmvhrHMAUvRDx6N\n9yC2b+6iyMNjzBTSvPvqFWRHAVNEi6gYKZ1qq4JnuRi+hqiJKKrCpWvvkXDzo7YJz/e4ylvjrTj+\nsBVHFEQEQcDpudTtKmEtim1ZKKpEPplHV3TMXgcPl8mZSRqVJkltWHXj+z7X37uB0/URRRHP8aiv\ntvnp1qu8/LUXgwVbwCeaeCzK+dMnPu7DCAj4WAlG6Y+AT4tx4/2o1+uUy+WRYJLNZkkmkw+13//+\nf/4bTCN3wHXXsy1Wf/AntNYv47v2aHv1ys+JzZxi7ivfRVTuTNRu9HT++t//Hd/62lce18cMCLgv\nT08f5+erl/BiGoqqMOhbqF2HpxeOLqf/sJid/thd9HA4hCjX8HwPz/FxbZ/5uVlMepRqO/QcCX8A\n7V6LTrODK/gonooqafTdPp7v0rU7uI5DWILBYIBngabrKIJC22+iKhpd2hTCE0TCUTzPx/MdtJDM\n5MwEYhhs2wF7uBjYXS+hSMPfqiPYJOIJJEli5b01JqYnPpMCoSRJnMvNc6F0Czk+jA3td3skHJUT\ni/MPfoEPyKBnjf4uCAKRaIRKtQ6A73oogsLC8UVagzqNdo10JouXtNkqb2H1bAw/TFLMoEoag0Ef\nH5dGo46neiBJ9MweuAJhPYLoiQwcE1GEvtglE59GVw08zwcJtJhMMpVETYk09jqElBCWZVHfaaHK\nQ/8LLazdjmE1uP7uCs9+7unHdm4+ySTjCRa6GW40dtHjEQRBwGx2mFZTo0Scx8GgNxi2twCKLGOE\ndXrVAZIoYTsOYS3CsVPHKDX3aNk1RFti0B0MWyDu+l1f5a0xk1GL/ujfp3gWgKw/Qc3fQxdDuJJN\nMT2LJMh4noePR2E+iyzLZLIpzF0LVVGpVWrYHW9UIWREhsabkq1y88oKJ84cf2znJiDgs47neZRL\na3jOLvgWCBqyOkEme9CjynVdyqVb+G4VQQDPN0imlzBup+k0m3Usq4dhxD51kdi+P2wHlCTpU5ua\n9HESiA0B98V13bFWEFEU8X2ftbU1Njc3WV4e9rjfb78fX7yJEDs4uV79wZ/QvHXhwHbftWneusDq\nD2DhG/9wtF00YvzNT976WMSGhxVbAp5swqEwXzz1HNvlPTr9HjEjRXHm8S0EAIyoQdVtIkvD4VoU\nRWYWpymXymxV1xk0TWrVBr1uD7fvEzeidN02NCTUgUHba5KW8rTsJqqgoWsKPa+DIYSRVZFu38YI\nh1AkGVcSER0RbDCECB2rTTwVR9M0jIjMieUTuK7LxFwBRVG4/votXNvDG/hICjieTWbijgme3RnG\nhUYikft9xCeWXCrDl+NJ1ve2sfo2uVTxSEPJR4UeVum07nhC6LrOzLEpbq2uUlrbBQsajRadThfF\nVQhpBm1rQNzM0bZbSL6CKEl0nDaqqKNoCh23RVJM4UsuvuATihgIAoSVEGaji+ob2LaD7dlEjAiy\nLJMsTJDJZ+jbfU4tn2E7skN1pUm1VB0JDZY7YHK6MDrWVrn1WM/NJ52FiRkmB3nWS9v4vs/01Nx9\nTaYfBUZEx7sdzeN5HolknFRS5NLFGt2eSbvVptc2abfbRKQYoipjdTrIrjyqanB8mzI7h75+mR2O\n+TayoCALCpY3wHANOq6FJ3gYYQVEKC7OE0vEsIUBL734Cq//6E2cpker3h6NJwPfZHZqERgKac1y\n87Gem4CAzzK9Xoda6WcUsv5d7YA9bPsKG7dWKEy9MqrcajbLdBtvks/evRjvUqtvsXJTIRkTiYX7\nJAwFs2+zXYtgRI+RTN6p2qrXSwzMCgB6KEsikf0IP+3hmGaPevUqgreLqng4DrikCUUXSNw2Xg54\nMIHYEHBfLl26hKIoB0pBDcPA930uXbrE2bNnj9yv1WpRc9UDX7TOzi1a65fv+96t9ct0dleJFOZG\n21a2K1y7du0jW/Q/rNgS8NlBEAQmc4UH7/iImJ2fYePKJnjDX5ERNWh1OtSbdU4tn+Lq29dRujpi\n1wJ88MBuePg2hMQIju/QF3r4nkdf6OGKwwm/YmlIUQlDM9BkjYE5wBd9onKMbr+HjAIDib3SHvFi\nhBfOPo8SU0jORplbnANAVmSuXriOJfaRdZFsLkW+cEd88fE+878PSZKYn/joDBDnTszy+sbb6Ldb\nKfSITrvaw7Ztjh8/zts/uYBuhul3HVBARsZtDMvg03KailOmL3QRPIm+0EUWJRzXwrYcQmGdkC2i\nCAqDQR9cYejTMOjiCT5mp0/f3mbyWIGFkycIp0LMPzVFIpkgkUywGlml3C4xwEQPa0xPTJK8K1VA\nlII7RpqmcWz68VW+3MvUsUluvL6KKqvIioKsSXQaPcKRMMl4induvYti66imjRvyUF0JtyVwd7B3\njw4Wh5ueWvTp0R15gUiCTNfqgijRrDdp9BqcPL/EzNIUgu5z5qXhNfX5X3iWa+9dZ3XdwRb6GFGD\nmZlFjLtMeIXgDmNAwGPB932qe68yVTz4G1MUmekJj83t15ie+zy9Xger8ybF/MFW0oG5x2RiF+QZ\nwuHhvCkakYhGHFrtd6iUbTQ9Sqv2DslYn0RquIbo9dbYXDVIZM4TiQzbDh3HoVy6Dl4HAEFKkssv\nPLZKg06nSbfxKsWMDNwdPdyj1X6Tcukk2dzcY3nvJ41AbAg4knq9jud5R5ZAC4KA67qsrq4eud87\nl64iRDIHttdvvDnWOnEYvmtTv/7GmNiwWa6xtbVFLBYjEok89kX/w4otAQGPC1EUefZL53nv9cu0\nyz3i6ShXr10hm8kSi0VZVTewNBev7RMNRTHtHqIroKDjiDYJP03N3yMupfF8H9EVKEZm6Hot8EVM\nu4fvg6wo+I6HjUdEjWJ6PUKpCKlUknDBYPKZDL/0W19H1+84z+eLefLFPLKoIPQP/v5CSeOx35kN\nGCcajXLmlZNcf2cFszkgno9y48Z1ZmdmsC2bWDhGrdNAFiV0RaNlNpF8Bc/3cQWISDEccUBYDOO4\nFho68XACV7DxXI+u3SKsxBBlCcETkUUFWVPp+k3CmRCpdBw9o3L6K8f4ha99fmxcnlucY2p2ih/9\nu5+gSweTW5KFx+dlEXA4k9MTOLbN2uVNnJ5DJB9ibX2N2YU5dja2SSYS7G6V0DV9GHXabaOi4wl3\nTFtCRFDRDxUcVHRCDM0eLX+ALmsYcoie0iKSCpMqDNtsnv/lp3nmhadH8whRFDl59gTZYoaLP7yC\npmhjr+u4DoWpj070DQj4LFEpb5DPuNxvmZiItmm1anRaaxQzB4WGXs9Ek0vE4jr1xh4+eYS7Gqpj\nUZWVtZ8TCYWYyGtwl9lsKKQRCnmUKj9DEF5hY/UCvvMm2ZSIIChooRy61mBv8wZ69GmSyUc/FjQq\nbzJZOPzzx6Iq1dolTDMfzHEegkBsCDiScrk8trA4DMMwuH79OjMzM4c+3mg0EQ5xXnct86GO4eB+\n4rCHrFymWq0yPT3sG3sci/6HFVsajcan3pMj4JNNOBzmhS8+h2VZuK5LYiLKzTfW2bq1jayI5Ody\nWI6FYA+d2xFFJASQJcDHECKYbhdV0NA0g1gygi7IaIJB12yjiBKCJzDwHWRFQldDCJJHOp0iFAlR\nKGQ4efbEkePB8nMnePuHF3B6HvVKE9/3iBejvPj55z7aExUAQDafJfv1LP3+cPFnxDR2r1dYubyC\naqjkZtPUN1s4lovveoiihOLLeJKP5EjgKcMUElHECOnEYnEG9NDFMB2zi6zI+I6H6fbRNB1ZEpGU\nGOl0Ej2qMzmV5+TZ44cnccgyS08vcO2Nm1hdh3azjSgKZGZTPPvUuY/6VAUAswuzzMzPYJomiqIg\nSSK9Sp9Wp0UkESWNjd3w6PcGOJ6Nquj4lofvDaO9ZUEh6xfHPBv2yVIcpVLUxRJzkSV82SOhx8nk\nMugxjeJUkdNPnTr0WpvOpMktpti9VqHT7NDvDZBUkZnTE8wtzD72cxMQ8FnEsfZQYvdfIkbCGrvV\nTQSvzGHLyUZ9h2JuKCBEQi7dTmtUpbCPKu6gKmng8HbUeNTh9Vf/CctLHomkDriAzWBwnVolQj53\njEbzbdrtF4lGH12Vc71eIhUfAEcb/KZTOjuVGxhTwQ3HBxHUoAUcieseHvN3L47jHPmYrkq4g96B\n7ZL6cErgvfupkjBy+JYkiY2NjbFF/6PkYcWWUqn0SN83IOAoVFXFMAzC8Qhzx2ZZfu4khZkC6UyK\nRDqGqquEIyFUXQHJQ1M0bNUiEU6haMMKncxkmrbZQhJlun4bKSJgaSZdpYkXctBCGmLYZ25qnmQy\nSWEqR24iS79jHXlciWSCWD7KTmmXgWUhSAKiL1It1T7CsxNwL7quo+s6iUycpeUFTj1zgtxUhqnp\nafSohqZrRBNRREXAkxzCWghPdYhGYwjq0KMkmonQ7reQJZWWWyMUUejKTXpqGzUkoeoSWkxhZmqW\nRCpBYSpPtpClUT3af2FiuogYEqlWK8PoWUXEGTjUbxtZBnz0CIJAKBRCURRyk1mOnzvG8rMniWdj\nzM7NIOkikioSi8cQJJGEmqYhlEfPP8F5JplHZXjNVNGZZJ4TnAeGbTqyISEbArFElMnCFOlsismZ\nCTLpDJVS5chjm1mcpud2aDVb2K6DrMqYrT6dTufxnpSAgM8ogvBw8398Z/jnEERhMPq7okg4znjl\nk+O4qHIX3zu4RgDwfY928yqp6AbR2PiiX9MU0gmTamWFZEKl3bjxcMf7kPR7JQzjwUlCgv9o1x1P\nKkFlQ8CRSJKE7/sP3O9+0VPHFxdQfvK3EBqPM0suPUP1ymv3baUQJIXksWfHtqUjd378giDgeR7d\nbpdwOEypVHqkFQau6z5UL9i+KBOYSAZ8VMwdm+G1lTeJJ+Kg+ZS3KmiGTrVUQdfDhMIGe14LQwIt\nrBAyNFoNl77UpmeFSWdS9AcDIloUTdaJZkOkJhPsrZeRzeEC1fUcFE0hEg+RyidRtKN/5xurG3R3\nBiwtLI1tX393i0w+PTzOgI+N4lyBlTfWSOfT9D2TfqWNHtGoNXZIhlNYhkW/79KTusRiEWREPN9m\nYHSx3SjpdJJ+f0AqmqUtNZmfT5Mp5Fi5uEJYjKKqGrZnI2sy4YRBOp9C1Y6Ogr38zhU0W2dxaXF8\n+2tXyX47G7h9f8xkptI01tokswne7V3GN0VkXcRsdcjFi2x1tlAVhY44wDS7GIQRBZFTPMsx36ZH\nlxDhUUWD7/v08jVO5ZaHwqes4EkuyD5aRCGdTxOJHW0i+97PL5MOZ0kfv8swzoN3X7vMy1994XGf\njoCAzxyerwKHiwD7+L4Pgg7C4Yvyu1cPA8tBUcdb5wYDC0MH+7A8cYamk2Hdph82sSznwOK/0ehS\nr+8xsA1EMYnneY/w2jG+9un3B9Rru4ADyCSSeQxDB/yhv0V1C7u/M3xc0AlH54jFgvn/PsEVPeBI\nstkspnn/dgfTNDl27NiR+xmGQS50sDQyUpwnNnPqvq8dmzk15tfg+z756J3Bpt1uU6lUuHz5Mmtr\na9Trj/au2L0lwK1Wi7W1NVZXV1lbW6PVunPn7uLFi6ytreH7/piJ5MWLFx+6QiQg4GEJh8MsPTPP\nhXcukIgmUCMSjmgRmQxRdyrsCVuEUxpSREBVFNp2k7njs5xaOE0xM4VgCMwdn2VqboLCVJZoPsxX\nv/1lnn7lHJbSpT1o4SgDElMRCsfzZAppphcnjzyevY3KoaKjrhpsrGw9zlMR8BBMzUwSm4pw6Z3L\n5HMF0Dw8xcXIa+wMtmhqVfSkihZWQPCxJYeT509xbPYk6UQGKSqxeHqBwmSW6YUpUpNJXvjiMyyd\nn8cUurT7TaQYpGbjTB2fIJwwmF08vLUOoLrTOLRkXvY1NtY2HuepCHgITp07QV/qsnlrh3whhyNY\nKFEJNS2z3r2OHeuhx2SmM/OY8QZN8U4FkywoxITESGiwfQt7rsV/+d/8AVMnC5j+8PuiJESyC2nm\nl2eJZkJH3ijo9/t0Kocvenq1/gPnKAEBAe+fcHSWTndw331q9QHJ9AK+eFQqQwTPGyoJPVMlHBqP\nu5QkiZ7poKiH34zw3DrubQFBlu/Mx2vVJjtbKxjqHkszfcLKJTqtd9hcv/jwH/ABKFoKy3LwfZ/N\nzRt0mxcoZJsUsl0K2SZm+102N67RNUU2V/+OqHqJQqZNIWNSSNcR7J+xsfrq6PN/1gkqGwKOJJlM\nsrm5ie/7h04MfX8YhzM3N8fFixcP3S+ZTHK8EGO3ZiEq46rk3Fe+y+oPhqkTd1c4CJJCbOYUc1/5\n7tj+Qn2Tb/zGy7iuy/b2NqIoouv6KP/26tWrlEollpaWKBQKH7qqIJvNsra2hqqq3Lp1C0EQxtoq\nyuUyGxsb5HI5MplMYCIZ8JFiWxbLp5ep1epMnMxT3iuzvbLLwBowLc0R0gwEBZqdBoZhEJuIUl2v\n0W13CYUMmq0GqVSKmfkZIgWdarfEbmkXParT6XXITk+w/MIpovEQs2enSKVTRx6L5zjA4d4mrhOI\nbZ8IPDj77Bmq5RozZybYWN1ib32XqxdtJmMnEQQJQfVpNpokcwnQPdqdHs7ARQ8ZtFpNEqk4k1MF\n4nMRtmqbdHs9ZEPG8gak54qce/4Mclhk+fkT961482wXDvHzlSQJe3B0W17AR4MoihhaiOXzJ2g0\nmiw8O8utq2tE1g1Wr8B0eh58H0cekGmlUbMSV65colMaptwIvoin2ITyOqfOL/Gl73yB7Ru7uIKP\nr/mImk/xeJazzy0jhUWeeuXo66Nt2+Af4ZuEwGAwCAzaAgIeMfF4mo3VNCGjdWi1gG27DNwpMrpO\nKnOMvfIu+ez4mJ/NTVAu7RGPCijaQfFZ11WuVSOcmzhibuE7qIpMu6NQnBxeMCqVOrpcJZWX2b9f\n7nk2ulJH8f4Db/38ApMzXyCTnflQVQ7p9ATb65fx7BsUMl0kadygNplUkVo1tm6+xosvPM29y+lI\nWCNktNnefIupmfEK7c8igdgQcF+Wl5fHoh/3MU0TSZJYXl6+736KovALL5znyr/5IRVlPM5LVFQW\nvvEP6eyuUr/+Bq5lIqkGyWPPjlU0APiey8mERzaTZmNjA8MwEAQB3/dpNBqYpkk6ncYwDFZWVhgM\nBh86pWJfbFlZWRm9391omoZpmtRqNbLZw/OAAxPJgMdFdbeBqqoUCnlsy6KyViekRcnFiggIKJpM\nx2wTDkcRfOiV+sSicbzwMLve7zucO32a4nSOdr/N7tUqS5PHYXLYK9lqtrn49gX+6//pDx/oXRJO\nRmh1uge2O65DMhtkUX8SaJZbaKrOxGSRWqVGVIrSkNsU4hMICqiKTL1TI5PLYHb6iAOffDFPq9Gi\n227j+xrzT50lP5VnffsWTk3gxPwpmAfXsWk0W1y6/h7/1X//B0ea6u4TSYVxmgdb9EzLpDB18nGd\ngoCHpN/vYzYGhMNhwuEwG7c2yESylP0qhfgEkiEgItFqNMgVcnSaXc4sPE3i2QRrG2uYZo/iYoFX\nvvgSxZkCFy6+TcRNcvp4Fo7DoN+n2Wyw29rht379N+57LJFIBDkk3lvVDICkC8RisYMPBAQEfGgm\nZ55je/MtdHmPVFIbzbkrVQuHaSanzwCg6waR5Its7b5OJumg3W6hE0WBVm+KvuUwN3dwjlyqOCSy\nX6VnbhK63SLR7jSwLRNJksGXsewBrlAEwPM8HKtCJLHfoufT69bxXYGQkSOV9ggbO9jOG2yvXyeR\neeGAIeXD4HkejuPgi3N4zmtIhyQnWZbDblVl+ZhFr9chFDrYBiaKIoZSot/vP3AO9aQTiA0B90WS\nJM6ePUuj0aBUKo38CObm5sYWz/fb7+zZs/Rtl//1L97EjR6Mp4kU5g6IC/cSql7lP/pHv0a73UaS\npNFktlarEQ6HEUWR0O38bUEQsG0bXdePrCrwPI8L77zG6s0fI1IHfDziFKeeZ2HxDPV6Hdd1MU2T\ndruNLMtjlQuWZSGKIuHwMNJr3zfiMPZNJAOxIeBRcveCrrRTRpN1rH4Z3/fQtRCJZAJREajvNoiE\nooiCiCc6pJMZ0uk0XbvF/KlZwqEwl354iaw+cddri8QTcUJOiDd+8iaf+8oro8darRaO45BIJEZ3\nDpZOLfDTjdfQuCM0+r6PGPaZmp36CM5GwAMRhNGCrV5uIkkKdt/C94djVDQWwxVcWtUWYSMCElj2\ngHwhDwUYiD2WTi3i+R57m2Um43eSACRZIZ1O02612N7aZnJq2HKzLwaLokg8fmfSt3h6ngs/uoQm\n3ZmAOY5DeiZBJHJ0737AR8md1X271sVxPZyBiyjKRCJhVFWj75jUyw0MLYQnu0iizInFoVgkJT3m\nj8/RajXoVE1iqTsR2Jquk9MLlK5XRnMFGPofNeoNdEMfXU8FQWD21BRrF7ZR5buuwY7FzNmpwN8j\nIOAxIYoiUzPP0u/32avdQsDFRyGTX0BRxj15IpE44fBXqFa3qXdK4HsIUpSlU1+m12uzU76B4JcR\nBQ/Xk0EqkEwfI2+E2NmWqNVeJ6RWiYQcIlEZz/O4tFpClGJMTJ6k1Vqh3++QTd+5eWj2mniuiSTl\nUI3U7eNQ2SlVmJxMsrP3Krr+lftW2d1Nq1Wl07yJRAVZ9mhVt9AUjc0dl0TURVMFHNejPzCQ1Eli\nkRqRiE29VTpUbABIJTV2a7coTty/bfxJJxAbAh6KRCLxUIvlo/b7pW9+nY3tPf78jU38ePF9vbdW\nucZ/+49+HfCpVqtEo8O+L8uyGAwGRKNR8vk7sTm6rlOv14nFYgeqCizL4i//7f+C0/sBz5y6wbc/\nJ44t2rZ2/jf+9l9naFvP8fwrv0+32yUej9PpdEgkEgiCgCiK5HI5wuEwq6urKIpCs9k8UmyAh0/2\nCAh4WNLFBFvVEpIk4brDvkBJEpEkEc0YlvzpukGjvYahhUGDidkinVoHRdTQQyGqe1XURYlwODJM\nlLoHRVYobw/7sRv1Bu/9/ApWy0YQRATVZ+bUFPNLc2iaxov/4DluvHuTRqWFIIgkC3FOnj0eLAY+\nISRzMbq7wx5c7/Z4JN826gtFhmOXJAm0220MLYSiyhTmcrTKHRRRRdU0ypUyqek4ES166HuElDDr\nN9aZnJpka32LGxdX8U0fH1CiEieeXiKbz5JKp3j6i2e4eWmVbrOHospMTOdYOD5/6OsGfLTouk4o\nacBtOwTPHfZNG4aO2a6jqsPxZTDo4/R9NNUjmU5gRFQGLRsBEckHc2DSl01S4cMr/9y+P6oMvPru\nNbZv7iE4Ip7vEkoZnHvpNKFQiLnFOVRNY/PGFmZ3gBHWWFqcY3J64tDXDQgIeHTouv5Qi2VBEMhk\nJoGh2Nzr9SiXdrGtbWRh6KnmuCqCXCSTOz66gSfLBr4Yom+ZWLaJ74NPlPmFJUqlG7hOHVeYoVz9\nOZnb3dG+7+E6HapNg3S2OFZRLdxOwSjkJPZK1x/q2KuVTUT3XYpZFW4n6uBBMiZRrdpY7hyCryKr\nCqnY8L3M7jBBR+Boo/vhwT7g8c8AgdgQ8FjYT2awbZu1tY0CMswAACAASURBVDUikQjf+eVvUMi/\nyb/4m59RC00jiPdvb3D7XRakCt/+pZfwXYelEycYDAZYloVt27RaLebn5w+9E7afo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X28d1NtxBLMvqM+63jfPV1VVSqRSnTt1+btDtcCd0AnamY4RCIfL5/EAqRafTIZlM4vf7EUWx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BIKhfY4XRzEg2pK5PN5NjY2Hjmo8Sjn3BUqHTHiXmanJtguXcQWAsOFuuu6aE6P6cnD7chE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qmqYRRQfX//7y84R4EhPDo7Tmuqy0q9iZJL7nozQcLgwdO7RfLW+sYmQOTpK047UPzVPy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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2285,12 +2544,15 @@ " ha='right', va='top', size=16)\n", "\n", "\n", - "fig.savefig('fig/05.11-expectation-maximization.png')" + "fig.savefig('figures/05.11-expectation-maximization.png')" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Interactive K-Means\n", "\n", @@ -2302,14 +2564,16 @@ "cell_type": "code", "execution_count": 46, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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SRxRCr9DwkfqM+HwkgYGBTuvyL4PBwMtvvuL0XJmyZRn0bs4Urn/nMl4+Fub0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\nOCRqVRULT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fgt0v/JW3987PBZJhyeyKdrZuPj4+viCF0nK0uPLjEbDY5fOBR6NSf/FYlY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\nAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2389,14 +2653,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "## Gaussian Mixture Models" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Covariance Type\n", "\n", @@ -2407,14 +2677,16 @@ "cell_type": "code", "execution_count": 47, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { "data": { "image/png": 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BQ/5fqhwo49urqoqqgK6rhEwTwzDQdb38WmKyI1kzu5HW224Uw6NxAq2+h5n4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\nsLaVZE8SiKIQ3wv4k3fN3mJhkpDECcn68zaBGFATD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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2461,7 +2733,20 @@ " ax[i].xaxis.set_major_formatter(plt.NullFormatter())\n", " ax[i].yaxis.set_major_formatter(plt.NullFormatter())\n", "\n", - "fig.savefig('fig/05.12-covariance-type.png')" + "fig.savefig('figures/05.12-covariance-type.png')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "\n", + "< [Further Machine Learning Resources](05.15-Learning-More.ipynb) | [Contents](Index.ipynb) |\n", + "\n", + "\"Open\n" ] } ], @@ -2482,6 +2767,18 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" + }, + "widgets": { + "state": { + "a65a11f142ca44eebc913788d256adcb": { + "views": [ + { + "cell_index": 92 + } + ] + } + }, + "version": "1.2.0" } }, "nbformat": 4, diff --git a/notebooks_v1/Index.ipynb b/notebooks_v1/Index.ipynb new file mode 100644 index 000000000..a368faa84 --- /dev/null +++ b/notebooks_v1/Index.ipynb @@ -0,0 +1,131 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Python Data Science Handbook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*Jake VanderPlas*\n", + "\n", + "![Book Cover](figures/PDSH-cover.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is the Jupyter notebook version of the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", + "The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Table of Contents\n", + "\n", + "### [Preface](00.00-Preface.ipynb)\n", + "\n", + "### [1. IPython: Beyond Normal Python](01.00-IPython-Beyond-Normal-Python.ipynb)\n", + "- [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)\n", + "- [Keyboard Shortcuts in the IPython Shell](01.02-Shell-Keyboard-Shortcuts.ipynb)\n", + "- [IPython Magic Commands](01.03-Magic-Commands.ipynb)\n", + "- [Input and Output History](01.04-Input-Output-History.ipynb)\n", + "- [IPython and Shell Commands](01.05-IPython-And-Shell-Commands.ipynb)\n", + "- [Errors and Debugging](01.06-Errors-and-Debugging.ipynb)\n", + "- [Profiling and Timing Code](01.07-Timing-and-Profiling.ipynb)\n", + "- [More IPython Resources](01.08-More-IPython-Resources.ipynb)\n", + "\n", + "### [2. Introduction to NumPy](02.00-Introduction-to-NumPy.ipynb)\n", + "- [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb)\n", + "- [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb)\n", + "- [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb)\n", + "- [Aggregations: Min, Max, and Everything In Between](02.04-Computation-on-arrays-aggregates.ipynb)\n", + "- [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb)\n", + "- [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb)\n", + "- [Fancy Indexing](02.07-Fancy-Indexing.ipynb)\n", + "- [Sorting Arrays](02.08-Sorting.ipynb)\n", + "- [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb)\n", + "\n", + "### [3. Data Manipulation with Pandas](03.00-Introduction-to-Pandas.ipynb)\n", + "- [Introducing Pandas Objects](03.01-Introducing-Pandas-Objects.ipynb)\n", + "- [Data Indexing and Selection](03.02-Data-Indexing-and-Selection.ipynb)\n", + "- [Operating on Data in Pandas](03.03-Operations-in-Pandas.ipynb)\n", + "- [Handling Missing Data](03.04-Missing-Values.ipynb)\n", + "- [Hierarchical Indexing](03.05-Hierarchical-Indexing.ipynb)\n", + "- [Combining Datasets: Concat and Append](03.06-Concat-And-Append.ipynb)\n", + "- [Combining Datasets: Merge and Join](03.07-Merge-and-Join.ipynb)\n", + "- [Aggregation and Grouping](03.08-Aggregation-and-Grouping.ipynb)\n", + "- [Pivot Tables](03.09-Pivot-Tables.ipynb)\n", + "- [Vectorized String Operations](03.10-Working-With-Strings.ipynb)\n", + "- [Working with Time Series](03.11-Working-with-Time-Series.ipynb)\n", + "- [High-Performance Pandas: eval() and query()](03.12-Performance-Eval-and-Query.ipynb)\n", + "- [Further Resources](03.13-Further-Resources.ipynb)\n", + "\n", + "### [4. Visualization with Matplotlib](04.00-Introduction-To-Matplotlib.ipynb)\n", + "- [Simple Line Plots](04.01-Simple-Line-Plots.ipynb)\n", + "- [Simple Scatter Plots](04.02-Simple-Scatter-Plots.ipynb)\n", + "- [Visualizing Errors](04.03-Errorbars.ipynb)\n", + "- [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb)\n", + "- [Histograms, Binnings, and Density](04.05-Histograms-and-Binnings.ipynb)\n", + "- [Customizing Plot Legends](04.06-Customizing-Legends.ipynb)\n", + "- [Customizing Colorbars](04.07-Customizing-Colorbars.ipynb)\n", + "- [Multiple Subplots](04.08-Multiple-Subplots.ipynb)\n", + "- [Text and Annotation](04.09-Text-and-Annotation.ipynb)\n", + "- [Customizing Ticks](04.10-Customizing-Ticks.ipynb)\n", + "- [Customizing Matplotlib: Configurations and Stylesheets](04.11-Settings-and-Stylesheets.ipynb)\n", + "- [Three-Dimensional Plotting in Matplotlib](04.12-Three-Dimensional-Plotting.ipynb)\n", + "- [Geographic Data with Basemap](04.13-Geographic-Data-With-Basemap.ipynb)\n", + "- [Visualization with Seaborn](04.14-Visualization-With-Seaborn.ipynb)\n", + "- [Further Resources](04.15-Further-Resources.ipynb)\n", + "\n", + "### [5. Machine Learning](05.00-Machine-Learning.ipynb)\n", + "- [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb)\n", + "- [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb)\n", + "- [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb)\n", + "- [Feature Engineering](05.04-Feature-Engineering.ipynb)\n", + "- [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)\n", + "- [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)\n", + "- [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)\n", + "- [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb)\n", + "- [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)\n", + "- [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb)\n", + "- [In Depth: k-Means Clustering](05.11-K-Means.ipynb)\n", + "- [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb)\n", + "- [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb)\n", + "- [Application: A Face Detection Pipeline](05.14-Image-Features.ipynb)\n", + "- [Further Machine Learning Resources](05.15-Learning-More.ipynb)\n", + "\n", + "### [Appendix: Figure Code](06.00-Figure-Code.ipynb)" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks_v1/Untitled.ipynb b/notebooks_v1/Untitled.ipynb new file mode 100644 index 000000000..363fcab7e --- /dev/null +++ b/notebooks_v1/Untitled.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git 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Washington,189 +2,John Adams,170 +3,Thomas Jefferson,189 +4,James Madison,163 +5,James Monroe,183 +6,John Quincy Adams,171 +7,Andrew Jackson,185 +8,Martin Van Buren,168 +9,William Henry Harrison,173 +10,John Tyler,183 +11,James K. 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Bush,182 +44,Barack Obama,185 diff --git a/notebooks_v1/data/state-abbrevs.csv b/notebooks_v1/data/state-abbrevs.csv new file mode 100644 index 000000000..6d4db366f --- /dev/null +++ b/notebooks_v1/data/state-abbrevs.csv @@ -0,0 +1,52 @@ +"state","abbreviation" +"Alabama","AL" +"Alaska","AK" +"Arizona","AZ" +"Arkansas","AR" +"California","CA" +"Colorado","CO" +"Connecticut","CT" +"Delaware","DE" +"District of Columbia","DC" +"Florida","FL" +"Georgia","GA" +"Hawaii","HI" +"Idaho","ID" +"Illinois","IL" +"Indiana","IN" +"Iowa","IA" +"Kansas","KS" +"Kentucky","KY" +"Louisiana","LA" +"Maine","ME" +"Montana","MT" +"Nebraska","NE" +"Nevada","NV" +"New Hampshire","NH" +"New Jersey","NJ" +"New Mexico","NM" +"New York","NY" +"North Carolina","NC" +"North Dakota","ND" +"Ohio","OH" +"Oklahoma","OK" +"Oregon","OR" +"Maryland","MD" +"Massachusetts","MA" +"Michigan","MI" +"Minnesota","MN" +"Mississippi","MS" +"Missouri","MO" +"Pennsylvania","PA" +"Rhode Island","RI" +"South Carolina","SC" +"South Dakota","SD" +"Tennessee","TN" +"Texas","TX" +"Utah","UT" +"Vermont","VT" +"Virginia","VA" +"Washington","WA" +"West Virginia","WV" +"Wisconsin","WI" +"Wyoming","WY" \ No newline at end of file diff --git a/notebooks_v1/data/state-areas.csv b/notebooks_v1/data/state-areas.csv new file mode 100644 index 000000000..322345c52 --- /dev/null +++ b/notebooks_v1/data/state-areas.csv @@ -0,0 +1,53 @@ +state,area (sq. mi) +Alabama,52423 +Alaska,656425 +Arizona,114006 +Arkansas,53182 +California,163707 +Colorado,104100 +Connecticut,5544 +Delaware,1954 +Florida,65758 +Georgia,59441 +Hawaii,10932 +Idaho,83574 +Illinois,57918 +Indiana,36420 +Iowa,56276 +Kansas,82282 +Kentucky,40411 +Louisiana,51843 +Maine,35387 +Maryland,12407 +Massachusetts,10555 +Michigan,96810 +Minnesota,86943 +Mississippi,48434 +Missouri,69709 +Montana,147046 +Nebraska,77358 +Nevada,110567 +New Hampshire,9351 +New Jersey,8722 +New Mexico,121593 +New York,54475 +North Carolina,53821 +North Dakota,70704 +Ohio,44828 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index 000000000..bbea5ad4b Binary files /dev/null and b/notebooks_v1/figures/array_vs_list.png differ diff --git a/notebooks_v1/figures/cint_vs_pyint.png b/notebooks_v1/figures/cint_vs_pyint.png new file mode 100644 index 000000000..0b976a941 Binary files /dev/null and b/notebooks_v1/figures/cint_vs_pyint.png differ diff --git a/notebooks_v1/helpers_05_08.py b/notebooks_v1/helpers_05_08.py new file mode 100644 index 000000000..0f3b15aa9 --- /dev/null +++ b/notebooks_v1/helpers_05_08.py @@ -0,0 +1,83 @@ + +import numpy as np +import matplotlib.pyplot as plt +from sklearn.tree import DecisionTreeClassifier +from ipywidgets import interact + + +def visualize_tree(estimator, X, y, boundaries=True, + xlim=None, ylim=None, ax=None): + ax = ax or plt.gca() + + # Plot the training points + ax.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap='viridis', + clim=(y.min(), y.max()), zorder=3) + ax.axis('tight') + ax.axis('off') + if xlim is None: + xlim = ax.get_xlim() + if ylim is None: + ylim = ax.get_ylim() + + # fit the estimator + estimator.fit(X, y) + xx, yy = np.meshgrid(np.linspace(*xlim, num=200), + np.linspace(*ylim, num=200)) + Z = estimator.predict(np.c_[xx.ravel(), yy.ravel()]) + + # Put the result into a color plot + n_classes = len(np.unique(y)) + Z = Z.reshape(xx.shape) + contours = ax.contourf(xx, yy, Z, alpha=0.3, + levels=np.arange(n_classes + 1) - 0.5, + cmap='viridis', clim=(y.min(), y.max()), + zorder=1) + + ax.set(xlim=xlim, ylim=ylim) + + # Plot the decision boundaries + def plot_boundaries(i, xlim, ylim): + if i >= 0: + tree = estimator.tree_ + + if tree.feature[i] == 0: + ax.plot([tree.threshold[i], tree.threshold[i]], ylim, '-k', zorder=2) + plot_boundaries(tree.children_left[i], + [xlim[0], tree.threshold[i]], ylim) + plot_boundaries(tree.children_right[i], + [tree.threshold[i], xlim[1]], ylim) + + elif tree.feature[i] == 1: + ax.plot(xlim, [tree.threshold[i], tree.threshold[i]], '-k', zorder=2) + plot_boundaries(tree.children_left[i], xlim, + [ylim[0], tree.threshold[i]]) + plot_boundaries(tree.children_right[i], xlim, + [tree.threshold[i], ylim[1]]) + + if boundaries: + plot_boundaries(0, xlim, ylim) + + +def plot_tree_interactive(X, y): + def interactive_tree(depth=5): + clf = DecisionTreeClassifier(max_depth=depth, random_state=0) + visualize_tree(clf, X, y) + + return interact(interactive_tree, depth=[1, 5]) + + +def randomized_tree_interactive(X, y): + N = int(0.75 * X.shape[0]) + + xlim = (X[:, 0].min(), X[:, 0].max()) + ylim = (X[:, 1].min(), X[:, 1].max()) + + def fit_randomized_tree(random_state=0): + clf = DecisionTreeClassifier(max_depth=15) + i = np.arange(len(y)) + rng = np.random.RandomState(random_state) + rng.shuffle(i) + visualize_tree(clf, X[i[:N]], y[i[:N]], boundaries=False, + xlim=xlim, ylim=ylim) + + interact(fit_randomized_tree, random_state=[0, 100]); \ No newline at end of file diff --git a/notebooks_v2/data.csv b/notebooks_v2/data.csv new file mode 100644 index 000000000..25cc7c115 --- /dev/null +++ b/notebooks_v2/data.csv @@ -0,0 +1,11 @@ +,a,b +0,one,1385 +1,one,1162 +2,one,2827 +3,one,2138 +4,one,1847 +5,one,1477 +6,one,883 +7,one,9071 +8,one,835 +9,one,2104 diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 000000000..fe9cdd918 --- /dev/null +++ b/requirements.txt @@ -0,0 +1,15 @@ +numpy==1.11.1 +pandas==0.18.1 +scipy==0.17.1 +scikit-learn==0.17.1 +scikit-image==0.12.3 +pillow==3.4.2 +matplotlib==1.5.1 +seaborn==0.7.0 +jupyter +notebook +line_profiler +memory_profiler +numexpr +pandas-datareader +netcdf4 diff --git a/tools/README.md b/tools/README.md new file mode 100644 index 000000000..a4cd76d77 --- /dev/null +++ b/tools/README.md @@ -0,0 +1,9 @@ +# Tools + +These are tools for managing the notebooks in this repository. + +- ``generate_contents.py``: this will generate a markdown table of contents for use in the README and in the Index.ipynb notebook + +- ``add_navigation.py``: this script adds navigation links at the top and bottom of each notebook. + +- ``add_book_info.py``: this script adds book information to the top of each notebook. \ No newline at end of file diff --git a/tools/add_book_info.py b/tools/add_book_info.py new file mode 100644 index 000000000..ae9ca2be5 --- /dev/null +++ b/tools/add_book_info.py @@ -0,0 +1,37 @@ +import os + +import nbformat +from nbformat.v4.nbbase import new_markdown_cell + +from generate_contents import iter_notebooks, NOTEBOOK_DIR + + +BOOK_COMMENT = "" + + +BOOK_INFO = BOOK_COMMENT + """ + + +*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).* + +*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*""" + + +def add_book_info(): + for nb_name in iter_notebooks(): + nb_file = os.path.join(NOTEBOOK_DIR, nb_name) + nb = nbformat.read(nb_file, as_version=4) + + is_comment = lambda cell: cell.source.startswith(BOOK_COMMENT) + + if is_comment(nb.cells[0]): + print('- amending comment for {0}'.format(nb_name)) + nb.cells[0].source = BOOK_INFO + else: + print('- inserting comment for {0}'.format(nb_name)) + nb.cells.insert(0, new_markdown_cell(BOOK_INFO)) + nbformat.write(nb, nb_file) + + +if __name__ == '__main__': + add_book_info() diff --git a/tools/add_navigation.py b/tools/add_navigation.py new file mode 100644 index 000000000..0fec360d0 --- /dev/null +++ b/tools/add_navigation.py @@ -0,0 +1,65 @@ +import os +import itertools + +from ipykernel import kernelspec as ks +import nbformat +from nbformat.v4.nbbase import new_markdown_cell + +from generate_contents import NOTEBOOK_DIR, REG, iter_notebooks, get_notebook_title + + +def prev_this_next(it): + a, b, c = itertools.tee(it,3) + next(c) + return zip(itertools.chain([None], a), b, itertools.chain(c, [None])) + + +PREV_TEMPLATE = "< [{title}]({url}) " +CONTENTS = "| [Contents](Index.ipynb) |" +NEXT_TEMPLATE = " [{title}]({url}) >" +NAV_COMMENT = "\n" + +COLAB_LINK = """ + +Open in Colab +""" + + +def iter_navbars(): + for prev_nb, nb, next_nb in prev_this_next(iter_notebooks()): + navbar = NAV_COMMENT + if prev_nb: + navbar += PREV_TEMPLATE.format(title=get_notebook_title(prev_nb), + url=prev_nb) + navbar += CONTENTS + if next_nb: + navbar += NEXT_TEMPLATE.format(title=get_notebook_title(next_nb), + url=next_nb) + + navbar += COLAB_LINK.format(notebook_filename=os.path.basename(nb)) + + yield os.path.join(NOTEBOOK_DIR, nb), navbar + + +def write_navbars(): + for nb_name, navbar in iter_navbars(): + nb = nbformat.read(nb_name, as_version=4) + nb_file = os.path.basename(nb_name) + is_comment = lambda cell: cell.source.startswith(NAV_COMMENT) + + if is_comment(nb.cells[1]): + print("- amending navbar for {0}".format(nb_file)) + nb.cells[1].source = navbar + else: + print("- inserting navbar for {0}".format(nb_file)) + nb.cells.insert(1, new_markdown_cell(source=navbar)) + + if is_comment(nb.cells[-1]): + nb.cells[-1].source = navbar + else: + nb.cells.append(new_markdown_cell(source=navbar)) + nbformat.write(nb, nb_name) + + +if __name__ == '__main__': + write_navbars() diff --git a/tools/fix_kernelspec.py b/tools/fix_kernelspec.py new file mode 100644 index 000000000..c98d5e927 --- /dev/null +++ b/tools/fix_kernelspec.py @@ -0,0 +1,19 @@ +import os + +import nbformat + +from generate_contents import iter_notebooks, NOTEBOOK_DIR + +def fix_kernelspec(): + for nb_name in iter_notebooks(): + nb_file = os.path.join(NOTEBOOK_DIR, nb_name) + nb = nbformat.read(nb_file, as_version=4) + + print("- Updating kernelspec for {0}".format(nb_name)) + nb['metadata']['kernelspec']['display_name'] = 'Python 3' + + nbformat.write(nb, nb_file) + + +if __name__ == '__main__': + fix_kernelspec() diff --git a/tools/generate_contents.py b/tools/generate_contents.py new file mode 100644 index 000000000..705677fa5 --- /dev/null +++ b/tools/generate_contents.py @@ -0,0 +1,54 @@ +import os +import re +import itertools +import nbformat + +NOTEBOOK_DIR = os.path.join(os.path.dirname(__file__), '..', 'notebooks') + +CHAPTERS = {"00": "Preface", + "01": "IPython: Beyond Normal Python", + "02": "NumPy", + "03": "Pandas", + "04": "Matplotlib", + "05": "Machine Learning"} + +REG = re.compile(r'(\d\d)\.(\d\d)-(.*)\.ipynb') + + +def iter_notebooks(): + return sorted(nb for nb in os.listdir(NOTEBOOK_DIR) if REG.match(nb)) + + +def get_notebook_title(nb_file): + nb = nbformat.read(os.path.join(NOTEBOOK_DIR, nb_file), as_version=4) + for cell in nb.cells: + if cell.source.startswith('#'): + return cell.source[1:].splitlines()[0].strip() + + +def gen_contents(directory=None): + for nb in iter_notebooks(): + if directory: + nb_url = os.path.join(directory, nb) + else: + nb_url = nb + chapter, section, title = REG.match(nb).groups() + title = get_notebook_title(nb) + if section == '00': + if chapter in ['00', '06']: + yield '\n### [{0}]({1})'.format(title, nb_url) + else: + yield '\n### [{0}. {1}]({2})'.format(int(chapter), + title, nb_url) + else: + yield "- [{0}]({1})".format(title, nb_url) + + +def print_contents(directory=None): + print('\n'.join(gen_contents(directory))) + + +if __name__ == '__main__': + print_contents() + print('\n', 70 * '#', '\n') + print_contents('http://nbviewer.jupyter.org/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/') diff --git a/website/.gitignore b/website/.gitignore new file mode 100644 index 000000000..1af125fab --- /dev/null +++ b/website/.gitignore @@ -0,0 +1,4 @@ +content/pages/*.md +output +content/figures +content/notebooks \ No newline at end of file diff --git a/website/Makefile b/website/Makefile new file mode 100644 index 000000000..b419e74ea --- /dev/null +++ b/website/Makefile @@ -0,0 +1,132 @@ +PY?=python3 +PELICAN?=pelican +PELICANOPTS= + +BASEDIR=$(CURDIR) +INPUTDIR=$(BASEDIR)/content +OUTPUTDIR=$(BASEDIR)/output +CONFFILE=$(BASEDIR)/pelicanconf.py +PUBLISHCONF=$(BASEDIR)/publishconf.py + +FTP_HOST=localhost +FTP_USER=anonymous +FTP_TARGET_DIR=/ + +SSH_HOST=localhost +SSH_PORT=22 +SSH_USER=root +SSH_TARGET_DIR=/var/www + +S3_BUCKET=my_s3_bucket + +CLOUDFILES_USERNAME=my_rackspace_username +CLOUDFILES_API_KEY=my_rackspace_api_key +CLOUDFILES_CONTAINER=my_cloudfiles_container + +DROPBOX_DIR=~/Dropbox/Public/ + +GITHUB_PAGES_REMOTE=git@github.com:jakevdp/PythonDataScienceHandbook.git +GITHUB_PAGES_BRANCH=gh-pages + +GIT_COMMIT_HASH = $(shell git rev-parse HEAD) + +DEBUG ?= 0 +ifeq ($(DEBUG), 1) + PELICANOPTS += -D +endif + +RELATIVE ?= 0 +ifeq ($(RELATIVE), 1) + PELICANOPTS += --relative-urls +endif + + +help: + @echo 'Makefile for a pelican Web site ' + @echo ' ' + @echo 'Usage: ' + @echo ' make html (re)generate the web site ' + @echo ' make clean remove the generated files ' + @echo ' make regenerate regenerate files upon modification ' + @echo ' make publish generate using production settings ' + @echo ' make serve [PORT=8000] serve site at http://localhost:8000' + @echo ' make serve-global [SERVER=0.0.0.0] serve (as root) to $(SERVER):80 ' + @echo ' make devserver [PORT=8000] start/restart develop_server.sh ' + @echo ' make stopserver stop local server ' + @echo ' make ssh_upload upload the web site via SSH ' + @echo ' make rsync_upload upload the web site via rsync+ssh ' + @echo ' make dropbox_upload upload the web site via Dropbox ' + @echo ' make ftp_upload upload the web site via FTP ' + @echo ' make s3_upload upload the web site via S3 ' + @echo ' make cf_upload upload the web site via Cloud Files' + @echo ' make github upload the web site via gh-pages ' + @echo ' ' + @echo 'Set the DEBUG variable to 1 to enable debugging, e.g. make DEBUG=1 html ' + @echo 'Set the RELATIVE variable to 1 to enable relative urls ' + @echo ' ' + +html: + $(PELICAN) $(INPUTDIR) -o $(OUTPUTDIR) -s $(CONFFILE) $(PELICANOPTS) + +clean: + [ ! -d $(OUTPUTDIR) ] || rm -rf $(OUTPUTDIR) + +regenerate: + $(PELICAN) -r $(INPUTDIR) -o $(OUTPUTDIR) -s $(CONFFILE) $(PELICANOPTS) + +serve: +ifdef PORT + cd $(OUTPUTDIR) && $(PY) -m pelican.server $(PORT) +else + cd $(OUTPUTDIR) && $(PY) -m pelican.server +endif + +serve-global: +ifdef SERVER + cd $(OUTPUTDIR) && $(PY) -m pelican.server 80 $(SERVER) +else + cd $(OUTPUTDIR) && $(PY) -m pelican.server 80 0.0.0.0 +endif + + +devserver: +ifdef PORT + $(BASEDIR)/develop_server.sh restart $(PORT) +else + $(BASEDIR)/develop_server.sh restart +endif + +stopserver: + $(BASEDIR)/develop_server.sh stop + @echo 'Stopped Pelican and SimpleHTTPServer processes running in background.' + +publish: + $(PELICAN) $(INPUTDIR) -o $(OUTPUTDIR) -s $(PUBLISHCONF) $(PELICANOPTS) + +ssh_upload: publish + scp -P $(SSH_PORT) -r $(OUTPUTDIR)/* $(SSH_USER)@$(SSH_HOST):$(SSH_TARGET_DIR) + +rsync_upload: publish + rsync -e "ssh -p $(SSH_PORT)" -P -rvzc --delete $(OUTPUTDIR)/ $(SSH_USER)@$(SSH_HOST):$(SSH_TARGET_DIR) --cvs-exclude + +dropbox_upload: publish + cp -r $(OUTPUTDIR)/* $(DROPBOX_DIR) + +ftp_upload: publish + lftp ftp://$(FTP_USER)@$(FTP_HOST) -e "mirror -R $(OUTPUTDIR) $(FTP_TARGET_DIR) ; quit" + +s3_upload: publish + s3cmd sync $(OUTPUTDIR)/ s3://$(S3_BUCKET) --acl-public --delete-removed --guess-mime-type --no-mime-magic --no-preserve + +cf_upload: publish + cd $(OUTPUTDIR) && swift -v -A https://auth.api.rackspacecloud.com/v1.0 -U $(CLOUDFILES_USERNAME) -K $(CLOUDFILES_API_KEY) upload -c $(CLOUDFILES_CONTAINER) . + +publish-to-github: publish + ghp-import -n -m "publish-to-github from $(GIT_COMMIT_HASH)" -b blog-build $(OUTPUTDIR) + git push $(GITHUB_PAGES_REMOTE) blog-build:$(GITHUB_PAGES_BRANCH) + +publish-to-github-force: publish + ghp-import -n -m "publish-to-github-force from $(GIT_COMMIT_HASH)" -b blog-build $(OUTPUTDIR) + git push -f $(GITHUB_PAGES_REMOTE) blog-build:$(GITHUB_PAGES_BRANCH) + +.PHONY: html help clean regenerate serve serve-global devserver stopserver publish ssh_upload rsync_upload dropbox_upload ftp_upload s3_upload cf_upload github diff --git a/website/README.md b/website/README.md new file mode 100644 index 000000000..d7a5e45eb --- /dev/null +++ b/website/README.md @@ -0,0 +1,45 @@ +2# Tools for creating http://jakevdp.github.io/PythonDataScienceHandbook/ + +The website is generated using the [Pelican](http://docs.getpelican.com/) static site generator. +The themes here are adapted from those used for my blog: https://github.com/jakevdp/jakevdp.github.io-source + +## Building the Website + +Clone the repository & make sure submodules are included + +``` +$ git clone https://github.com/jakevdp/PythonDataScienceHandbook.git +$ git checkout origin/website +$ git submodule update --init --recursive +$ cd website +``` + +Install the required packages: + +``` +$ conda create -n pelican-blog python=3.5 jupyter notebook +$ source activate pelican-blog +$ pip install pelican Markdown ghp-import +$ mkdir plugins +$ git submodule add git://github.com/danielfrg/pelican-ipynb.git plugins/ipynb +$ git submodule add https://github.com/getpelican/pelican-plugins.git plugins/pelican-plugins +``` + +Copy the notebook content to the right location (this script also modifies some links for the HTML): +``` +$ python copy_notebooks.py +``` + +Build the html and serve locally: + +``` +$ make html +$ make serve +$ open http://localhost:8000 +``` + +Deploy to github pages + +``` +$ make publish-to-github +``` diff --git a/website/content/favicon.ico b/website/content/favicon.ico new file mode 100644 index 000000000..91c0253f5 Binary files /dev/null and b/website/content/favicon.ico differ diff --git a/website/copy_notebooks.py b/website/copy_notebooks.py new file mode 100644 index 000000000..b60299847 --- /dev/null +++ b/website/copy_notebooks.py @@ -0,0 +1,111 @@ +""" +This script copies all notebooks from the book into the website directory, and +creates pages which wrap them and link together. +""" +import os +import nbformat +import shutil + +PAGEFILE = """title: {title} +url: +save_as: {htmlfile} +Template: {template} + +{{% notebook notebooks/{notebook_file} cells[{cells}] %}} +""" + +INTRO_TEXT = """This website contains the full text of the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook) in the form of Jupyter notebooks. + +The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). + +If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)! +""" + + +def abspath_from_here(*args): + here = os.path.dirname(__file__) + path = os.path.join(here, *args) + return os.path.abspath(path) + +NB_SOURCE_DIR = abspath_from_here('..', 'notebooks') +NB_DEST_DIR = abspath_from_here('content', 'notebooks') +PAGE_DEST_DIR = abspath_from_here('content', 'pages') + + +def copy_notebooks(): + if not os.path.exists(NB_DEST_DIR): + os.makedirs(NB_DEST_DIR) + if not os.path.exists(PAGE_DEST_DIR): + os.makedirs(PAGE_DEST_DIR) + + nblist = sorted(nb for nb in os.listdir(NB_SOURCE_DIR) + if nb.endswith('.ipynb')) + name_map = {nb: nb.rsplit('.', 1)[0].lower() + '.html' + for nb in nblist} + + figsource = abspath_from_here('..', 'notebooks', 'figures') + figdest = abspath_from_here('content', 'figures') + + if os.path.exists(figdest): + shutil.rmtree(figdest) + shutil.copytree(figsource, figdest) + + figurelist = os.listdir(abspath_from_here('content', 'figures')) + figure_map = {os.path.join('figures', fig) : os.path.join('/PythonDataScienceHandbook/figures', fig) + for fig in figurelist} + + for nb in nblist: + base, ext = os.path.splitext(nb) + print('-', nb) + + content = nbformat.read(os.path.join(NB_SOURCE_DIR, nb), + as_version=4) + + if nb == 'Index.ipynb': + # content[0] is the title + # content[1] is the cover image + # content[2] is the license + cells = '1:' + template = 'page' + title = 'Python Data Science Handbook' + content.cells[2].source = INTRO_TEXT + else: + # content[0] is the book information + # content[1] is the navigation bar + # content[2] is the title + cells = '2:' + template = 'booksection' + title = content.cells[2].source + if not title.startswith('#') or len(title.splitlines()) > 1: + raise ValueError('title not found in third cell') + title = title.lstrip('#').strip() + + # put nav below title + content.cells.insert(0, content.cells.pop(2)) + + # Replace internal URLs and figure links in notebook + for cell in content.cells: + if cell.cell_type == 'markdown': + for nbname, htmlname in name_map.items(): + if nbname in cell.source: + cell.source = cell.source.replace(nbname, htmlname) + for figname, newfigname in figure_map.items(): + if figname in cell.source: + cell.source = cell.source.replace(figname, newfigname) + if cell.source.startswith(""): + # Undo replacement of notebook link in the colab badge + cell.source = nb.join(cell.source.rsplit(name_map[nb], 1)) + + nbformat.write(content, os.path.join(NB_DEST_DIR, nb)) + + pagefile = os.path.join(PAGE_DEST_DIR, base + '.md') + htmlfile = base.lower() + '.html' + with open(pagefile, 'w') as f: + f.write(PAGEFILE.format(title=title, + htmlfile=htmlfile, + notebook_file=nb, + template=template, + cells=cells)) + +if __name__ == '__main__': + copy_notebooks() diff --git a/website/fabfile.py b/website/fabfile.py new file mode 100644 index 000000000..79e9a93ce --- /dev/null +++ b/website/fabfile.py @@ -0,0 +1,92 @@ +from fabric.api import * +import fabric.contrib.project as project +import os +import shutil +import sys +import SocketServer + +from pelican.server import ComplexHTTPRequestHandler + +# Local path configuration (can be absolute or relative to fabfile) +env.deploy_path = 'output' +DEPLOY_PATH = env.deploy_path + +# Remote server configuration +production = 'root@localhost:22' +dest_path = '/var/www' + +# Rackspace Cloud Files configuration settings +env.cloudfiles_username = 'my_rackspace_username' +env.cloudfiles_api_key = 'my_rackspace_api_key' +env.cloudfiles_container = 'my_cloudfiles_container' + +# Github Pages configuration +env.github_pages_branch = "master" + +# Port for `serve` +PORT = 8000 + +def clean(): + """Remove generated files""" + if os.path.isdir(DEPLOY_PATH): + shutil.rmtree(DEPLOY_PATH) + os.makedirs(DEPLOY_PATH) + +def build(): + """Build local version of site""" + local('pelican -s pelicanconf.py') + +def rebuild(): + """`build` with the delete switch""" + local('pelican -d -s pelicanconf.py') + +def regenerate(): + """Automatically regenerate site upon file modification""" + local('pelican -r -s pelicanconf.py') + +def serve(): + """Serve site at http://localhost:8000/""" + os.chdir(env.deploy_path) + + class AddressReuseTCPServer(SocketServer.TCPServer): + allow_reuse_address = True + + server = AddressReuseTCPServer(('', PORT), ComplexHTTPRequestHandler) + + sys.stderr.write('Serving on port {0} ...\n'.format(PORT)) + server.serve_forever() + +def reserve(): + """`build`, then `serve`""" + build() + serve() + +def preview(): + """Build production version of site""" + local('pelican -s publishconf.py') + +def cf_upload(): + """Publish to Rackspace Cloud Files""" + rebuild() + with lcd(DEPLOY_PATH): + local('swift -v -A https://auth.api.rackspacecloud.com/v1.0 ' + '-U {cloudfiles_username} ' + '-K {cloudfiles_api_key} ' + 'upload -c {cloudfiles_container} .'.format(**env)) + +@hosts(production) +def publish(): + """Publish to production via rsync""" + local('pelican -s publishconf.py') + project.rsync_project( + remote_dir=dest_path, + exclude=".DS_Store", + local_dir=DEPLOY_PATH.rstrip('/') + '/', + delete=True, + extra_opts='-c', + ) + +def gh_pages(): + """Publish to GitHub Pages""" + rebuild() + local("ghp-import -b {github_pages_branch} {deploy_path} -p".format(**env)) diff --git a/website/pelicanconf.py b/website/pelicanconf.py new file mode 100644 index 000000000..4b744f242 --- /dev/null +++ b/website/pelicanconf.py @@ -0,0 +1,70 @@ +#!/usr/bin/env python +# -*- coding: utf-8 -*- # +from __future__ import unicode_literals + +AUTHOR = 'Jake VanderPlas' +SITENAME = 'Python Data Science Handbook' +SITESUBTITLE = u'Essential Tools for Working with Data' +SITEURL = '' +SITESUBURL = 'PythonDataScienceHandbook/' +PATH = 'content' +TIMEZONE = 'America/Los_Angeles' +DEFAULT_LANG = 'en' + +# Feed generation is usually not desired when developing +FEED_ALL_ATOM = None +CATEGORY_FEED_ATOM = None +TRANSLATION_FEED_ATOM = None +AUTHOR_FEED_ATOM = None +AUTHOR_FEED_RSS = None + +# Set the article URL +ARTICLE_URL = 'blog/{date:%Y}/{date:%m}/{date:%d}/{slug}/' +ARTICLE_SAVE_AS = 'blog/{date:%Y}/{date:%m}/{date:%d}/{slug}/index.html' + +DEFAULT_PAGINATION = 10 + +# Uncomment following line if you want document-relative URLs when developing +#RELATIVE_URLS = True + +#MARKUP = ('md', 'ipynb') +#PLUGINS = ['ipynb.markup'] + +MARKUP = ['md'] +PLUGIN_PATHS = ['./plugins', './plugins/pelican-plugins'] +PLUGINS = [ + 'summary', # auto-summarizing articles + 'feed_summary', # use summaries for RSS, not full articles + 'ipynb.liquid', # for embedding notebooks + 'liquid_tags.img', # embedding images + 'liquid_tags.video', # embedding videos + 'liquid_tags.include_code', # including code blocks + 'liquid_tags.literal' +] +IGNORE_FILES = ['.ipynb_checkpoints'] + +# for liquid tags +CODE_DIR = 'downloads/code' +NOTEBOOK_DIR = 'downloads/notebooks' + +# THEME SETTINGS +THEME = './theme/' + +ABOUT_PAGE = '/pages/about.html' +TWITTER_USERNAME = 'jakevdp' +GITHUB_USERNAME = 'jakevdp' +STACKOVERFLOW_ADDRESS = 'http://stackoverflow.com/users/2937831/jakevdp' +AUTHOR_WEBSITE = 'http://vanderplas.com' +AUTHOR_BLOG = 'http://jakevdp.github.io' +AUTHOR_CV = "http://staff.washington.edu/jakevdp/media/pdfs/CV.pdf" +SHOW_ARCHIVES = True +SHOW_FEED = False # Need to address large feeds + +ENABLE_MATHJAX = True + +STATIC_PATHS = ['images', 'figures', 'videos', 'downloads', 'favicon.ico'] + +# Footer info + +LICENSE_URL = "https://github.com/jakevdp/jakevdp.github.io-source/blob/master/LICENSE" +LICENSE = "MIT" diff --git a/website/publishconf.py b/website/publishconf.py new file mode 100644 index 000000000..157ad0ccf --- /dev/null +++ b/website/publishconf.py @@ -0,0 +1,24 @@ +#!/usr/bin/env python +# -*- coding: utf-8 -*- # +from __future__ import unicode_literals + +# This file is only used if you use `make publish` or +# explicitly specify it as your config file. + +import os +import sys +sys.path.append(os.curdir) +from pelicanconf import * + +SITEURL = 'http://jakevdp.github.io/PythonDataScienceHandbook' +RELATIVE_URLS = False + +SHOW_FEED = False +FEED_ALL_ATOM = 'feeds/all.atom.xml' +CATEGORY_FEED_ATOM = 'feeds/%s.atom.xml' +FEED_USE_SUMMARY = True # from the feed_summary plugin + +DELETE_OUTPUT_DIRECTORY = True + +DISQUS_SITENAME = "pythonicperambulations" +GOOGLE_ANALYTICS = "UA-34061646-1" diff --git a/website/theme/README.md b/website/theme/README.md new file mode 100644 index 000000000..f79086600 --- /dev/null +++ b/website/theme/README.md @@ -0,0 +1,4 @@ +# Pythonic Perambulations Theme + +This theme was adapted from that at https://github.com/danielfrg/danielfrg.github.io-source; the original is released under the Apache v2.0 license. +Adaptations are contained in this directory. \ No newline at end of file diff --git a/website/theme/static/css/icons.css b/website/theme/static/css/icons.css new file mode 100644 index 000000000..329e1ad75 --- /dev/null +++ b/website/theme/static/css/icons.css @@ -0,0 +1,60 @@ +/* Copied from https://github.com/porterjamesj/crowsfoot */ + +@font-face { + font-family: 'icons'; + src: url('../font/icons.eot?79801659'); + src: url('../font/icons.eot?79801659#iefix') format('embedded-opentype'), + url('../font/icons.woff?79801659') format('woff'), + url('../font/icons.ttf?79801659') format('truetype'), + url('../font/icons.svg?79801659#icons') format('svg'); + font-weight: normal; + font-style: normal; +} +/* Chrome hack: SVG is rendered more smooth in Windozze. 100% magic, uncomment if you need it. */ +/* Note, that will break hinting! In other OS-es font will be not as sharp as it could be */ +/* +@media screen and (-webkit-min-device-pixel-ratio:0) { + @font-face { + font-family: 'icons'; + src: url('../font/icons.svg?79801659#icons') format('svg'); + } +} +*/ + + [class^="icon-"]:before, [class*=" icon-"]:before { + font-family: "icons"; + font-style: normal; + font-weight: normal; + speak: none; + + display: inline-block; + text-decoration: inherit; + width: 1em; + margin-right: .2em; + text-align: center; + /* opacity: .8; */ + + /* For safety - reset parent styles, that can break glyph codes*/ + font-variant: normal; + text-transform: none; + + /* fix buttons height, for twitter bootstrap */ + line-height: 1em; + + /* Animation center compensation - margins should be symmetric */ + /* remove if not needed */ + margin-left: .2em; + + /* you can be more comfortable with increased icons size */ + /* font-size: 120%; */ + + /* Uncomment for 3D effect */ + /* text-shadow: 1px 1px 1px rgba(127, 127, 127, 0.3); */ +} + +.icon-stackoverflow:before { content: '\e032'; } /* '' */ +.icon-twitter:before { content: '\e801'; } /* '' */ +.icon-facebook:before { content: '\e802'; } /* '' */ +.icon-rss:before { content: '\e800'; } /* '' */ +.icon-mail-alt:before { content: '\f0e0'; } /* '' */ +.icon-github:before { content: '\f113'; } /* '' */ \ No newline at end of file diff --git a/website/theme/static/font/icons.eot b/website/theme/static/font/icons.eot new file mode 100644 index 000000000..7c6b12539 Binary files /dev/null and b/website/theme/static/font/icons.eot differ diff --git a/website/theme/static/font/icons.svg b/website/theme/static/font/icons.svg new file mode 100644 index 000000000..d97088804 --- /dev/null +++ b/website/theme/static/font/icons.svg @@ -0,0 +1,17 @@ + + + +Copyright (C) 2012 by original authors @ fontello.com + + + + + + + + + + + + + \ No newline at end of file diff --git a/website/theme/static/font/icons.ttf b/website/theme/static/font/icons.ttf new file mode 100644 index 000000000..121809925 Binary files /dev/null and b/website/theme/static/font/icons.ttf differ diff --git a/website/theme/static/font/icons.woff b/website/theme/static/font/icons.woff new file mode 100644 index 000000000..e693b496e Binary files /dev/null and b/website/theme/static/font/icons.woff differ diff --git a/website/theme/templates/_includes/analytics.html b/website/theme/templates/_includes/analytics.html new file mode 100644 index 000000000..ac8137766 --- /dev/null +++ b/website/theme/templates/_includes/analytics.html @@ -0,0 +1,30 @@ +{% if GOOGLE_UNIVERSAL_ANALYTICS %} + +{% elif GOOGLE_ANALYTICS %} + +{% endif %} diff --git a/website/theme/templates/_includes/disqus_thread.html b/website/theme/templates/_includes/disqus_thread.html new file mode 100644 index 000000000..a347fa408 --- /dev/null +++ b/website/theme/templates/_includes/disqus_thread.html @@ -0,0 +1,17 @@ +{% if DISQUS_SITENAME and SITEURL and article.status != "draft" %} +
+

Comments

+
+ +
+{% endif %} diff --git a/website/theme/templates/about.html b/website/theme/templates/about.html new file mode 100644 index 000000000..98d471047 --- /dev/null +++ b/website/theme/templates/about.html @@ -0,0 +1,43 @@ +{% extends "base.html" %} +{% block title %}{{ page.title }}{% endblock %} +{% block headerimg %}{% if page.headerimg %}{{ page.headerimg }}{% else %}{{ DEFAULT_HEADER_BG }}{% endif %}{% endblock %} + +{% block content %} + +
+
+
+

{{ page.title }}

+ {% if page.date %} + + {% endif %} +
+ +
+ {{ page.content }} +
+ +
+
+{% endblock %} diff --git a/website/theme/templates/archives.html b/website/theme/templates/archives.html new file mode 100644 index 000000000..24efb6fc1 --- /dev/null +++ b/website/theme/templates/archives.html @@ -0,0 +1,28 @@ +{% extends "base.html" %} +{% block title %}Archives{% endblock %} +{% block headerimg %}{{ DEFAUT_HEADER_BG }}{% endblock %} + +{% block content %} +
+ +
+{% endblock %} diff --git a/website/theme/templates/article.html b/website/theme/templates/article.html new file mode 100644 index 000000000..f38b8660a --- /dev/null +++ b/website/theme/templates/article.html @@ -0,0 +1,43 @@ +{% extends "base.html" %} +{% block title %}{{ article.title }}{% endblock %} +{% block headerimg %}{% if article.headerimg %}{{ article.headerimg }}{% else %}{{ DEFAULT_HEADER_BG }}{% endif %}{% endblock %} + +{% block extra_head %} +{% if 'angular' in article.include %} + +{% endif %} +{% if 'jquery' in article.include %} + +{% endif %} +{% endblock %} + +{% block content %} +
+
+
+

{{ article.title }}

+ +
+ +
+ {{ article.content }} +
+ +
+
+ {% for tag in article.tags %} + {{ tag }} + {% endfor %} +
+
+
+ + {% include '_includes/disqus_thread.html' %} + +
+ + + +{% endblock %} diff --git a/website/theme/templates/base.html b/website/theme/templates/base.html new file mode 100644 index 000000000..f7eb484dd --- /dev/null +++ b/website/theme/templates/base.html @@ -0,0 +1,94 @@ + + + + + + + + + {% block title %}{% endblock %} | {{ SITENAME }} + + + + + + + + + + + + + + + {% if ENABLE_MATHJAX %} + + + {% endif %} + + {% block extra_head %}{%endblock%} + + + +
+
+
+ + {{ SITENAME }} +
+ +
+
+ +
+ {% block content %}{% endblock %} +
+ + {% include '_includes/analytics.html' %} + + diff --git a/website/theme/templates/booksection.html b/website/theme/templates/booksection.html new file mode 100644 index 000000000..6c012761f --- /dev/null +++ b/website/theme/templates/booksection.html @@ -0,0 +1,34 @@ +{% extends "base.html" %} +{% block title %}{{ page.title }}{% endblock %} +{% block headerimg %}{% if page.headerimg %}{{ page.headerimg }}{% else %}{{ DEFAULT_HEADER_BG }}{% endif %}{% endblock %} + +{% block content %} + +
+

+ +This is an excerpt from the Python Data Science Handbook by Jake VanderPlas; Jupyter notebooks are available on GitHub. +

+

+The text is released under the CC-BY-NC-ND license, and code is released under the MIT license. If you find this content useful, please consider supporting the work by buying the book! +

+
+ + +
+ +
+
+

{{ page.title }}

+ {% if page.date %} + + {% endif %} +
+ +
+ {{ page.content }} +
+ +
+
+{% endblock %} diff --git a/website/theme/templates/index.html b/website/theme/templates/index.html new file mode 100644 index 000000000..fed18ce36 --- /dev/null +++ b/website/theme/templates/index.html @@ -0,0 +1,53 @@ +{% extends "base.html" %} +{% block title %}Home{% endblock %} +{% block headerimg %}{{ DEFAULT_HEADER_BG }}{% endblock %} + +{% block content %} +
+ + {% for article in articles_page.object_list %} + +
+ {% endfor %} + + + +
+ + + +{% endblock %} diff --git a/website/theme/templates/ipynb.css b/website/theme/templates/ipynb.css new file mode 100644 index 000000000..217627202 --- /dev/null +++ b/website/theme/templates/ipynb.css @@ -0,0 +1,47 @@ +{ + max-width: 700px; +} + +.text_cell .prompt { + display: none; +} + +div.cell { + padding: 0; +} + +div.text_cell_render { + padding: 0; +} + +div.prompt { + font-size: 13px; +} + +div.input_prompt { + padding: .7em 0.2em; +} + +div.output_prompt { + padding: .4em .2em; +} + +div.input_area { + margin: .2em 0.4em; + max-width: 580px; +} + +table.dataframe { + font-family: Arial, sans-serif; + font-size: 13px; + line-height: 20px; +} + +table.dataframe th, td { + padding: 4px; + text-align: left; +} + +pre code { + background-color: inherit; +} diff --git a/website/theme/templates/main.css b/website/theme/templates/main.css new file mode 100644 index 000000000..293ec2a60 --- /dev/null +++ b/website/theme/templates/main.css @@ -0,0 +1,300 @@ +body { + margin: 0; + padding: 0; + font: 15px 'Source Sans Pro', sans-serif; + line-height: 1.6em; + color: #222; + text-rendering: optimizeLegibility; + -webkit-font-smoothing: antialiased; +} +a { + color: #007EE5; + text-decoration: none; +} +a:hover { + color: #007EE5; + text-decoration: none; +} +header.main-header { + background: none repeat scroll 0% 0% #205F29; + margin-bottom: 0px; +} +header.main-header a { + color: #fff; +} +header.main-header .container { + max-width: 1000px; +} +header.main-header .container nav a:hover { + background-color: #5C881C; +} +article { + margin: 0; +} +article header.about { + margin-bottom: 0px; + padding-bottom: 0px; +} +article header { + margin-bottom: 20px; + padding-bottom: 20px; +} +article header h1 { + margin-bottom: 2px; + font-weight: 700; + color: #000; +} +article header time { + color: #9E9E9E; + font-size: 0.85em; + float: right; +} +article header time.left { + color: #9E9E9E; + font-size: 0.85em; + float: left; +} +article div.social-links ul { + padding: 0px; +} +article div.social-links li { + display: inline; + font-size: 20px; +} +article div.social-links li a { + color: #000; + padding: 10px; +} +article div.social-links li a:hover { + color: #666; + text-decoration: none; +} +article p { + font-size: 16px; + margin-bottom: 20px; + line-height: 1.6em; +} +article p.note { + background: #f5f5f5; + border: 1px solid #ddd; + padding: 0.533em 0.733em; +} +article p.update { + background-color: #FEEFB3; + border: 1px solid #e6e68a; + padding: 0.533em 0.733em; +} +article p.alert { + background-color: #ffe2e2; + border: 1px solid #ffb2b2; + padding: 0.533em 0.733em; +} +article ul, +article ol { + margin-top: 0px; + margin-bottom: 25px; +} +article li { + font-size: 16px; + line-height: 1.6em; +} +article a:hover { + text-decoration: underline; +} +article blockquote { + border-left: 2px solid #c7c7cc; + color: #666; + margin: 30px 0; + padding: 0 0 0 25px; +} +article img { + max-width: 100%; +} +article code { + color: #333; + background-color: #EEE; + border-radius: 0; + font-size: 13px; +} +article .meta { + font-size: 11px; +} +article .meta a:hover { + text-decoration: none; +} +article .meta div { + margin-bottom: 20px; + display: block; +} +article .meta a.tag { + margin: 0 10px 10px 0; + padding: 1px 12px; + display: inline-block; + font-size: 14px; + color: rgba(0, 0, 0, 0.8); + background: rgba(0, 0, 0, 0.05); +} +article .meta a.tag:hover { + background: rgba(0, 0, 0, 0.15); +} +article .meta a.read_more, +article .meta a.comments_btn { + font-size: 14px; + font-weight: 800; + padding: 10px 20px; + color: #205F29; + background: #FFF; + border: 1px solid #205F29; +} +article .meta a.read_more:hover, +article .meta a.comments_btn:hover { + color: #FFF; + background: #5C881C; +} +.index { + max-width: 700px; +} +.index article header h2 { + font-size: 36px; + margin-bottom: 2px; + font-weight: 700; +} +.index article header h2 a { + color: #000; +} +.index article header h2 a:hover { + color: #007EE5; + text-decoration: none; +} +.index .separator { + padding: 40px 0 0 0; + margin: 0 0 40px 0; + height: 10px; + border-bottom: solid 1px #CCC; +} +.index .pagination { + display: block; + margin-bottom: 100px; +} +.index .pagination .left { + text-align: right; +} +.index .pagination .right { + text-align: left; +} +.index .pagination a { + display: inline-block; + border: 2px solid #5C881C; + margin: 0 5px; + padding: 8px 20px; + font-weight: bold; + color: #5C881C; +} +.index .pagination a:hover { + color: #FFF; + background: #5C881C; +} +.post { + max-width: 700px; +} +.post h2:before { + content: "# "; + font-weight: bold; + color: #DDD; +} +.post h3:before { + content: "## "; + font-weight: bold; + color: #DDD; +} +.post h4:before { + content: "### "; + font-weight: bold; + color: #DDD; +} +.post article .meta { + margin: 50px 0 100px; +} +.list { + max-width: 700px; +} +.list ul.double-list { + margin: 0 auto 60px; + padding: 0; + list-style-type: none; +} +.list ul.double-list li { + padding: 5px 0; +} +.list ul.double-list li h2 { + font-size: 1em; + display: inline; + font-weight: normal; +} +.list ul.double-list li span { + font-family: sans-serif; + text-transform: uppercase; + text-align: right; + float: right; + padding-top: 3px; + font-size: 12px; + color: #999; +} +.full-width-content { + padding-top: 10px; + padding-left: 0px; + padding-right: 0px; + margin-left: -20px; + margin-right: -20px; +} +.col-xs-1, +.col-sm-1, +.col-md-1, +.col-lg-1, +.col-xs-2, +.col-sm-2, +.col-md-2, +.col-lg-2, +.col-xs-3, +.col-sm-3, +.col-md-3, +.col-lg-3, +.col-xs-4, +.col-sm-4, +.col-md-4, +.col-lg-4, +.col-xs-5, +.col-sm-5, +.col-md-5, +.col-lg-5, +.col-xs-6, +.col-sm-6, +.col-md-6, +.col-lg-6, +.col-xs-7, +.col-sm-7, +.col-md-7, +.col-lg-7, +.col-xs-8, +.col-sm-8, +.col-md-8, +.col-lg-8, +.col-xs-9, +.col-sm-9, +.col-md-9, +.col-lg-9, +.col-xs-10, +.col-sm-10, +.col-md-10, +.col-lg-10, +.col-xs-11, +.col-sm-11, +.col-md-11, +.col-lg-11, +.col-xs-12, +.col-sm-12, +.col-md-12, +.col-lg-12 { + padding-right: 0px; + padding-left: 0px; +} diff --git a/website/theme/templates/main.less b/website/theme/templates/main.less new file mode 100644 index 000000000..a11ef6db5 --- /dev/null +++ b/website/theme/templates/main.less @@ -0,0 +1,316 @@ +// out: ./main.css, compress: true + +@text-color: #222; +@link-color: #007EE5; + +body { + margin: 0; + padding: 0; + font: 15px 'Source Sans Pro', sans-serif; + line-height: 1.6em; + color: @text-color; + text-rendering: optimizeLegibility; + -webkit-font-smoothing: antialiased; +} + +a { + color: @link-color; + text-decoration: none; +} + +a:hover { + color: @link-color; + text-decoration: none; +} + +header.main-header { + background: none repeat scroll 0% 0% #205F29; + margin-bottom: 0px; + + a { + color: #fff; + } + + .container { + max-width: 1000px; + + nav { + a:hover { + background-color: #5C881C; + } + } + } +} + +article { + margin: 0; + + header.about { + margin-bottom: 0px; + padding-bottom: 0px; + } + + header { + margin-bottom: 20px; + padding-bottom: 20px; + + h1 { + margin-bottom: 2px; + font-weight: 700; + color: #000; + } + + time { + color: #9E9E9E; + font-size: 0.85em; + float: right; + } + + time.left { + color: #9E9E9E; + font-size: 0.85em; + float: left; + } + } + + div.social-links { + ul { + padding: 0px; + } + li { + display: inline; + font-size: 20px; + a { + color: #000; + padding: 10px; + } + a:hover { + color: #666; + text-decoration: none; + } + } + } + + p { + font-size: 16px; + margin-bottom: 20px; + line-height: 1.6em; + } + + p.note { + background: #f5f5f5; + border: 1px solid #ddd; + padding: 0.533em 0.733em; + } + + p.update { + background-color: #FEEFB3; + border: 1px solid #e6e68a; + padding: 0.533em 0.733em; + } + + p.alert { + background-color: #ffe2e2; + border: 1px solid #ffb2b2; + padding: 0.533em 0.733em; + } + + ul, ol { + margin-top: 0px; + margin-bottom: 25px; + } + + li { + font-size: 16px; + line-height: 1.6em; + } + + a:hover { + text-decoration: underline; + } + + blockquote { + border-left: 2px solid #c7c7cc; + color: #666; + margin: 30px 0; + padding: 0 0 0 25px; + } + + img { + max-width: 100%; + } + + code { + color: #333; + background-color: #EEE; + border-radius: 0; + font-size: 13px; + } + + .meta { + font-size: 11px; + + a:hover { + text-decoration: none; + } + + div { + margin-bottom: 20px; + display: block; + } + + a.tag { + margin: 0 10px 10px 0; + padding: 1px 12px; + display: inline-block; + font-size: 14px; + color: rgba(0,0,0,0.8);; + background: rgba(0,0,0,0.05); + } + + a.tag:hover { + background: rgba(0,0,0,0.15); + } + + a.read_more, a.comments_btn { + font-size: 14px; + font-weight: 800; + padding: 10px 20px; + color: #205F29; + background: #FFF; + border: 1px solid #205F29; + } + + a.read_more:hover, a.comments_btn:hover { + color: #FFF; + background: #5C881C; + } + } +} + +.index { + max-width: 700px; + + article { + header { + h2 { + font-size: 36px; + margin-bottom: 2px; + font-weight: 700; + + a { + color: #000; + } + a:hover { + color: @link-color; + text-decoration: none; + } + } + } + } + + .separator { + padding: 40px 0 0 0; + margin: 0 0 40px 0; + height: 10px; + border-bottom: solid 1px #CCC; + } + + .pagination { + display: block; + margin-bottom: 100px; + + .left { + text-align: right; + } + + .right { + text-align: left; + } + + a { + display: inline-block; + border: 2px solid #5C881C; + margin: 0 5px; + padding: 8px 20px; + font-weight: bold; + color: #5C881C; + } + + a:hover { + color: #FFF; + background: #5C881C; + } + } +} + +.post { + max-width: 700px; + + h2:before { + content: "# "; + font-weight: bold; + color: #DDD; + } + + h3:before { + content: "## "; + font-weight: bold; + color: #DDD; + } + + h4:before { + content: "### "; + font-weight: bold; + color: #DDD; + } + + article { + .meta { + margin: 50px 0 100px; + } + } +} + +.list { + max-width: 700px; + + ul.double-list { + margin: 0 auto 60px; + padding: 0; + list-style-type: none; + + li { + padding: 5px 0; + + h2 { + font-size: 1em; + display: inline; + font-weight: normal; + } + + span { + font-family: sans-serif; + text-transform: uppercase; + text-align: right; + float: right; + padding-top: 3px; + font-size: 12px; + color: #999; + } + } + } +} + +.full-width-content { + padding-top: 10px; + padding-left: 0px; + padding-right: 0px; + margin-left: -20px; + margin-right: -20px; +} + +.col-xs-1, .col-sm-1, .col-md-1, .col-lg-1, .col-xs-2, .col-sm-2, .col-md-2, .col-lg-2, .col-xs-3, .col-sm-3, .col-md-3, .col-lg-3, .col-xs-4, .col-sm-4, .col-md-4, .col-lg-4, .col-xs-5, .col-sm-5, .col-md-5, .col-lg-5, .col-xs-6, .col-sm-6, .col-md-6, .col-lg-6, .col-xs-7, .col-sm-7, .col-md-7, .col-lg-7, .col-xs-8, .col-sm-8, .col-md-8, .col-lg-8, .col-xs-9, .col-sm-9, .col-md-9, .col-lg-9, .col-xs-10, .col-sm-10, .col-md-10, .col-lg-10, .col-xs-11, .col-sm-11, .col-md-11, .col-lg-11, .col-xs-12, .col-sm-12, .col-md-12, .col-lg-12 { + padding-right: 0px; + padding-left: 0px; +} diff --git a/website/theme/templates/page.html b/website/theme/templates/page.html new file mode 100644 index 000000000..97b1e59df --- /dev/null +++ b/website/theme/templates/page.html @@ -0,0 +1,22 @@ +{% extends "base.html" %} +{% block title %}{{ page.title }}{% endblock %} +{% block headerimg %}{% if page.headerimg %}{{ page.headerimg }}{% else %}{{ DEFAULT_HEADER_BG }}{% endif %}{% endblock %} + +{% block content %} +
+ +
+
+

{{ page.title }}

+ {% if page.date %} + + {% endif %} +
+ +
+ {{ page.content }} +
+ +
+
+{% endblock %} diff --git a/website/theme/templates/pygments.css b/website/theme/templates/pygments.css new file mode 100644 index 000000000..98db4dd5f --- /dev/null +++ b/website/theme/templates/pygments.css @@ -0,0 +1,61 @@ +.highlight .hll { background-color: #ffffcc } +.highlight .c { color: #60a0b0; font-style: italic } /* Comment */ +.highlight .err { border: 1px solid #FF0000 } /* Error */ +.highlight .k { color: #007020; font-weight: bold } /* Keyword */ +.highlight .o { color: #666666 } /* Operator */ +.highlight .cm { color: #60a0b0; font-style: italic } /* Comment.Multiline */ +.highlight .cp { color: #007020 } /* Comment.Preproc */ +.highlight .c1 { color: #60a0b0; font-style: italic } /* Comment.Single */ +.highlight .cs { color: #60a0b0; background-color: #fff0f0 } /* Comment.Special */ +.highlight .gd { color: #A00000 } /* Generic.Deleted */ +.highlight .ge { font-style: italic } /* Generic.Emph */ +.highlight .gr { color: #FF0000 } /* Generic.Error */ +.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */ +.highlight .gi { color: #00A000 } /* Generic.Inserted */ +.highlight .go { color: #808080 } /* Generic.Output */ +.highlight .gp { color: #c65d09; font-weight: bold } /* Generic.Prompt */ +.highlight .gs { font-weight: bold } /* Generic.Strong */ +.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */ +.highlight .gt { color: #0040D0 } /* Generic.Traceback */ +.highlight .kc { color: #007020; font-weight: bold } /* Keyword.Constant */ +.highlight .kd { color: #007020; font-weight: bold } /* Keyword.Declaration */ +.highlight .kn { color: #007020; font-weight: bold } /* Keyword.Namespace */ +.highlight .kp { color: #007020 } /* Keyword.Pseudo */ +.highlight .kr { color: #007020; font-weight: bold } /* Keyword.Reserved */ +.highlight .kt { color: #902000 } /* Keyword.Type */ +.highlight .m { color: #40a070 } /* Literal.Number */ +.highlight .s { color: #4070a0 } /* Literal.String */ +.highlight .na { color: #4070a0 } /* Name.Attribute */ +.highlight .nb { color: #007020 } /* Name.Builtin */ +.highlight .nc { color: #0e84b5; font-weight: bold } /* Name.Class */ +.highlight .no { color: #60add5 } /* Name.Constant */ +.highlight .nd { color: #555555; font-weight: bold } /* Name.Decorator */ +.highlight .ni { color: #d55537; font-weight: bold } /* Name.Entity */ +.highlight .ne { color: #007020 } /* Name.Exception */ +.highlight .nf { color: #06287e } /* Name.Function */ +.highlight .nl { color: #002070; font-weight: bold } /* Name.Label */ +.highlight .nn { color: #0e84b5; font-weight: bold } /* Name.Namespace */ +.highlight .nt { color: #062873; font-weight: bold } /* Name.Tag */ +.highlight .nv { color: #bb60d5 } /* Name.Variable */ +.highlight .ow { color: #007020; font-weight: bold } /* Operator.Word */ +.highlight .w { color: #bbbbbb } /* Text.Whitespace */ +.highlight .mf { color: #40a070 } /* Literal.Number.Float */ +.highlight .mh { color: #40a070 } /* Literal.Number.Hex */ +.highlight .mi { color: #40a070 } /* Literal.Number.Integer */ +.highlight .mo { color: #40a070 } /* Literal.Number.Oct */ +.highlight .sb { color: #4070a0 } /* Literal.String.Backtick */ +.highlight .sc { color: #4070a0 } /* Literal.String.Char */ +.highlight .sd { color: #4070a0; font-style: italic } /* Literal.String.Doc */ +.highlight .s2 { color: #4070a0 } /* Literal.String.Double */ +.highlight .se { color: #4070a0; font-weight: bold } /* Literal.String.Escape */ +.highlight .sh { color: #4070a0 } /* Literal.String.Heredoc */ +.highlight .si { color: #70a0d0; font-style: italic } /* Literal.String.Interpol */ +.highlight .sx { color: #c65d09 } /* Literal.String.Other */ +.highlight .sr { color: #235388 } /* Literal.String.Regex */ +.highlight .s1 { color: #4070a0 } /* Literal.String.Single */ +.highlight .ss { color: #517918 } /* Literal.String.Symbol */ +.highlight .bp { color: #007020 } /* Name.Builtin.Pseudo */ +.highlight .vc { color: #bb60d5 } /* Name.Variable.Class */ +.highlight .vg { color: #bb60d5 } /* Name.Variable.Global */ +.highlight .vi { color: #bb60d5 } /* Name.Variable.Instance */ +.highlight .il { color: #40a070 } /* Literal.Number.Integer.Long */ \ No newline at end of file diff --git a/website/theme/templates/tag.html b/website/theme/templates/tag.html new file mode 100644 index 000000000..1e83db83e --- /dev/null +++ b/website/theme/templates/tag.html @@ -0,0 +1,22 @@ +{% extends "base.html" %} +{% block title %}Archives{% endblock %} +{% block headerimg %}{{ DEFAUT_HEADER_BG }}{% endblock %} + +{% block content %} +
+ +
+{% endblock %}