diff --git a/.codespell-ignore-words b/.codespell-ignore-words new file mode 100644 index 00000000..e69de29b diff --git a/.codespellrc b/.codespellrc new file mode 100644 index 00000000..029c71ef --- /dev/null +++ b/.codespellrc @@ -0,0 +1,5 @@ +[codespell] +skip = .git,*.bib,*.ps,*.js,*.pdf,_build,*.fodp,*.fods +ignore-words = .codespell-ignore-words + + diff --git a/.github/dependabot.yml b/.github/dependabot.yml new file mode 100644 index 00000000..5d808809 --- /dev/null +++ b/.github/dependabot.yml @@ -0,0 +1,13 @@ +# Dependabot configuration +# ref: https://docs.github.com/en/code-security/supply-chain-security/keeping-your-dependencies-updated-automatically/configuration-options-for-dependency-updates +version: 2 +updates: + - package-ecosystem: "github-actions" + directory: "/" + schedule: + interval: "weekly" + + - package-ecosystem: "pip" + directory: "/" + schedule: + interval: "weekly" diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml new file mode 100644 index 00000000..9f2c4e60 --- /dev/null +++ b/.github/workflows/main.yml @@ -0,0 +1,37 @@ +name: Publish JupyterBook to GitHub Pages + +on: + push: # trigger build only when push to main + branches: + - main + +jobs: + build: + runs-on: ubuntu-latest + + steps: + - uses: actions/checkout@v5 + - name: Set up Python + uses: actions/setup-python@v6 + with: + python-version: "3.11" + cache: "pip" + - name: Install Python dependencies + run: | + sudo apt-get install python3-pip graphviz + pip install -r requirements.txt + pip install ghp-import + PATH="${PATH}:${HOME}/.local/bin" + + - name: Build book HTML + run: | + jupyter-book build ./content + + - name: Push _build/html to gh-pages + run: | + sudo chown -R $(whoami):$(whoami) . + git config --global user.email "$GITHUB_ACTOR@users.noreply.github.com" + git config --global user.name "$GITHUB_ACTOR" + git remote set-url origin "https://$GITHUB_ACTOR:${{ secrets.GITHUB_TOKEN }}@github.com/$GITHUB_REPOSITORY" + + ghp-import ./content/_build/html -f -p -n diff --git a/.gitignore b/.gitignore index 9c4d703b..0045a3f3 100644 --- a/.gitignore +++ b/.gitignore @@ -4,6 +4,19 @@ *~ .ipynb_checkpoints/ -Untitled0.ipynb +Untitled*.ipynb \#* + +syllabus.pdf +syllabus.out + +.cache + +*egg-info + +.~lock* + +*.fodp + +_build diff --git a/CHANGES b/CHANGES index 4f3ecab4..0c9edf6f 100644 --- a/CHANGES +++ b/CHANGES @@ -1,3 +1,19 @@ +-- python tutor: http://www.pythontutor.com/ + +-- show pybind11 + https://pybind11.readthedocs.io/en/stable/basics.html#compiling-the-test-cases + +-- use RISE: + https://damianavila.github.io/RISE/customize.html + +-- merge in the REU python stuff + +-- matplotlib example: mandelbrot + +-- matplotlib state vs OO interfaces + + http://pbpython.com/effective-matplotlib.html + -- git diff of jupyter notebooks: https://nbdime.readthedocs.io/en/latest/ @@ -8,6 +24,12 @@ http://mybinder.org/ http://ivory.idyll.org/blog/2016-mybinder.html +-- pandas: + + https://github.com/jakevdp/PythonDataScienceHandbook + + Star Wars API examples :) + http://nbviewer.jupyter.org/github/rasbt/pattern_classification/blob/master/data_viz/swapi_viz.ipynb -- snakify: diff --git a/lectures/01-python/NOTE b/content/01-python/NOTE similarity index 100% rename from lectures/01-python/NOTE rename to content/01-python/NOTE diff --git a/lectures/01-python/VARDEN-tests.ini b/content/01-python/VARDEN-tests.ini similarity index 100% rename from lectures/01-python/VARDEN-tests.ini rename to content/01-python/VARDEN-tests.ini diff --git a/content/01-python/basics.md b/content/01-python/basics.md new file mode 100644 index 00000000..0a3d9198 --- /dev/null +++ b/content/01-python/basics.md @@ -0,0 +1,51 @@ +# Python Basics + +The following references give helpful introductions to python: + +* The [official python tutorial](http://docs.python.org/3/tutorial/) + +* The [software carpentry python lessons](https://swcarpentry.github.io/python-novice-inflammation/) + + +## Practicing + +Some resources for practicing on your own: + +* [Code Academy python rack](http://www.codecademy.com/tracks/python): + step-by-step tutorial through the basics of the language + +* [Project Euler](https://projecteuler.net/): + a set of increasingly complex programming tasks to try out with + python + + +## Online books: + +* [Think python](https://greenteapress.com/wp/think-python-3rd-edition/) + +* [Dive into Python](https://diveintopython3.net/) + +* [SciPy Lecture Notes](http://scipy-lectures.github.io/) + +* [Google's python class](https://developers.google.com/edu/python/) + +* more resources can be found at: http://pythonbooks.revolunet.com/ + + +## Domain-specific libraries + +* Astronomy: [AstroPy](http://astropy.org) + +* Atmospheric sciences: [PyAOS](https://pyaos.github.io/) + +* Biology: [Biopython](http://biopython.org/) + +* Ocean and marine sciences: [OceanPython](http://oceanpython.org/) + +* Psychology resources: [PyschoPy](http://www.psychopy.org/) + +* Quantum physics: [QuTiP](http://qutip.org/) + +* Solar physics: [SunPy](http://sunpy.org/) + + diff --git a/content/01-python/functions-classes.md b/content/01-python/functions-classes.md new file mode 100644 index 00000000..f347a7dc --- /dev/null +++ b/content/01-python/functions-classes.md @@ -0,0 +1,5 @@ +# Functions and Classes + +Functions and classes are the building blocks of complex programs. +These allow you to organize your code into logical units that can +reused. diff --git a/content/01-python/installing.md b/content/01-python/installing.md new file mode 100644 index 00000000..8c7d3dfa --- /dev/null +++ b/content/01-python/installing.md @@ -0,0 +1,41 @@ +# Introduction + +This class will introduce the basics of the python programming +language and the libraries used for scientific computing. + +```{tip} +To get the most from this class, you should work on your own laptop. That +way you practice using python and the scientific libraries on the in the +environment you are most comfortable with. +``` + +## Getting python + +You will want to install python and the associated libraries on your +laptop that you can bring to the seminar. + +On Linux machines, you probably already have python and you can get +the needed libraries through your system package manager. + +For Mac and Windows, I recommend the free Anaconda distribution: + +https://www.anaconda.com/products/individual + +This will install everything that you need. + +```{tip} +If you have trouble getting a local install working, most of the class +material will work automatically in the cloud, either on +[binder](https://mybinder.org/) or [google +colab](https://research.google.com/colaboratory/). +``` + +If you have python successfully installed, you should be able to start +the python interpreter at the command line as: `python`. A shell will +come up, and you can try out your first program: + +``` +print("hello, world") +``` + + diff --git a/content/01-python/misc.md b/content/01-python/misc.md new file mode 100644 index 00000000..59891c0e --- /dev/null +++ b/content/01-python/misc.md @@ -0,0 +1,5 @@ +# Miscellaneous + +There are a lot of topics that we didn't cover, as well as a lot of +the python standard library that we won't address. Here we introduce +a few more concepts. diff --git a/lectures/01-python/myprofile.py b/content/01-python/myprofile.py similarity index 97% rename from lectures/01-python/myprofile.py rename to content/01-python/myprofile.py index 9ec4d463..1a5d66ec 100644 --- a/lectures/01-python/myprofile.py +++ b/content/01-python/myprofile.py @@ -22,7 +22,7 @@ enough to offset the overhead of the timer class method calls. - Multiple timers can be instanciated and nested. The stackCount + Multiple timers can be instantiated and nested. The stackCount global parameter keeps count of the level of nesting, and the timerNesting data structure stores the nesting level for each defined timer. diff --git a/lectures/01-python/paradigms.png b/content/01-python/paradigms.png similarity index 100% rename from lectures/01-python/paradigms.png rename to content/01-python/paradigms.png diff --git a/lectures/01-python/python-io.ipynb b/content/01-python/python-io.ipynb similarity index 100% rename from lectures/01-python/python-io.ipynb rename to content/01-python/python-io.ipynb diff --git a/content/01-python/python.md b/content/01-python/python.md new file mode 100644 index 00000000..60132f80 --- /dev/null +++ b/content/01-python/python.md @@ -0,0 +1,3 @@ +# python + +These notebooks introduce the core python language diff --git a/lectures/01-python/python.png b/content/01-python/python.png similarity index 100% rename from lectures/01-python/python.png rename to content/01-python/python.png diff --git a/lectures/01-python/scipy.png b/content/01-python/scipy.png similarity index 100% rename from lectures/01-python/scipy.png rename to content/01-python/scipy.png diff --git a/lectures/01-python/shopping.csv b/content/01-python/shopping.csv similarity index 100% rename from lectures/01-python/shopping.csv rename to content/01-python/shopping.csv diff --git a/lectures/01-python/shopping.fods b/content/01-python/shopping.fods similarity index 100% rename from lectures/01-python/shopping.fods rename to content/01-python/shopping.fods diff --git a/lectures/01-python/shopping_cart.py b/content/01-python/shopping_cart.py similarity index 100% rename from lectures/01-python/shopping_cart.py rename to content/01-python/shopping_cart.py diff --git a/lectures/01-python/test.txt b/content/01-python/test.txt similarity index 100% rename from lectures/01-python/test.txt rename to content/01-python/test.txt diff --git a/content/01-python/tic_tac_toe.py b/content/01-python/tic_tac_toe.py new file mode 100644 index 00000000..390bc8e1 --- /dev/null +++ b/content/01-python/tic_tac_toe.py @@ -0,0 +1,82 @@ +import sys + +board = """ + {s1:^3} | {s2:^3} | {s3:^3} +-----+-----+----- + {s4:^3} | {s5:^3} | {s6:^3} +-----+-----+----- 123 + {s7:^3} | {s8:^3} | {s9:^3} 456 + 789 +""" + + +def initialize_board(play): + for n in range(9): + play["s{}".format(n+1)] = "" + +def show_board(play): + """ display the playing board. We take a dictionary with the current state of the board + We rely on the board string to be a global variable""" + print(board.format(**play)) + + +def get_move(n, xo, play): + """ ask the current player, n, to make a move -- make sure the square was not + already played. xo is a string of the character (x or o) we will place in + the desired square """ + valid_move = False + while not valid_move: + idx = input("player {}, enter your move (1-9): ".format(n)) + if play["s{}".format(idx)] == "": + valid_move = True + else: + print("invalid: {}".format(play["s{}".format(idx)])) + + play["s{}".format(idx)] = xo + + +def check_win(play): + + # winning combinations + combos = [(1, 2, 3), (4, 5, 6), (7, 8, 9), + (1, 4, 7), (2, 5, 8), (3, 6, 9), + (1, 5, 9), (7, 5, 3)] + + winner = None + + for c in combos: + # if we are empty, then pass + if play["s{}".format(c[0])] == "": + continue + if play["s{}".format(c[0])] == play["s{}".format(c[1])] and \ + play["s{}".format(c[0])] == play["s{}".format(c[2])]: + winner = play["s{}".format(c[0])] + break + + return winner + +def play_game(): + """ play a game of tic-tac-toe """ + + # initialize the board + play = {} + initialize_board(play) + + symbols = ["x", "o"] + + for n in range(9): + show_board(play) + + player = n % 2 + + get_move(player, symbols[player], play) + + winner = check_win(play) + if winner is not None: + show_board(play) + print("winner is {}!!!".format(winner)) + sys.exit() + +if __name__ == "__main__": + play_game() + diff --git a/content/01-python/using.md b/content/01-python/using.md new file mode 100644 index 00000000..c9e2738d --- /dev/null +++ b/content/01-python/using.md @@ -0,0 +1,45 @@ +# Using These Notes + +These notes are built via [Jupyter book](https://jupyterbook.org/), as +a collection of [Jupyter](https://jupyter.org/) notebooks and markdown +pages. + +The course is on Github at: +https://github.com/sbu-python-class/python-science, and the course +website is built automatically via a Github action each time a change +is pushed. + +If you find any problems or have suggestions for improving the notes, +feel free to create an issue or pull request at the Github repo. + +## Interactive Usage + +For the Jupyter notebooks in this collection, there are a few ways to +access them to run them on your own. + +* clicking on the {octicon}`download` icon in the upper right let's + you download the raw notebook so you can run it on your local + computer. + +* clicking on the {octicon}`rocket` icon in the upper right will allow + you to run the notebook directly in the cloud. There are 2 different + compute clouds: + + * [mybinder](https://mybinder.org/) : this is an open project with + ties to the Jupyter project. It can take a few minutes for the + page to appear if it hasn't been accessed recently, but then it + will give you the standard Jupyter experience. + + * [Google colab](https://colab.research.google.com/) : this is + Google's version of an online notebook, which runs directly in + Google's cloud. This starts up almost instantly. + +````{note} +Some notebooks use [MyST Markdown](https://jupyterbook.org/en/stable/content/myst.html) to +allow for more styling. To see these styles, you need to install `jupyterlab-myst`, which +can be done via: +``` +pip install jupyterlab_myst +``` + +```` diff --git a/lectures/01-python/vector2d.py b/content/01-python/vector2d.py similarity index 100% rename from lectures/01-python/vector2d.py rename to content/01-python/vector2d.py diff --git a/content/01-python/w1-jupyter.ipynb b/content/01-python/w1-jupyter.ipynb new file mode 100644 index 00000000..5db52542 --- /dev/null +++ b/content/01-python/w1-jupyter.ipynb @@ -0,0 +1,184 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Jupyter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll be using Jupyter for all of our examples -- this allows us to run python in a web-based notebook, keeping a history of input and output, along with text and images.\n", + "\n", + "For Jupyter help, visit:\n", + "https://jupyter.readthedocs.io/en/latest/content-quickstart.html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{note}\n", + "There are several interfaces to [Jupyter](https://jupyter.org/).\n", + "\n", + "We will use *JupyterLab*, which is traditionally started at the command line via:\n", + "```\n", + "jupyter lab\n", + "```\n", + "\n", + "The older (classic) interface is *Jupyter Notebook*, which can be started via:\n", + "```\n", + "jupyter notebook\n", + "```\n", + "````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We interact with python by typing into _cells_ in the notebook. \n", + "\n", + "By default, a cell is a _code_ cell, which means that you can enter any valid python code into it and run it. \n", + "\n", + "Another important type of cell is a _markdown_ cell. This lets you put text, with different formatting (italics, bold, etc) that describes what the notebook is doing." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A \"markdown cell\" enables you to typeset LaTeX equations right in your notebook. Just put them in `$` or `$$`:\n", + "\n", + "$$\\frac{\\partial \\rho}{\\partial t} + \\nabla \\cdot (\\rho U) = 0$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{tip}\n", + "You can change the cell type via the menu at the top, or using the shortcuts:\n", + "\n", + " * ctrl-m m : mark down cell\n", + " * ctrl-m y : code cell\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some useful short-cuts:\n", + "\n", + " * shift+enter = run cell and jump to the next (creating a new cell if there is no other new one)\n", + " * ctrl+enter = run cell-in place\n", + " * alt+enter = run cell and insert a new one below" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{warning}\n", + "When you work through a notebook, everything you did in previous cells is still in memory and _known_ by python, so you can refer to functions and variables that were previously defined. Even if you go up to the top of a notebook and insert a cell, all the information done earlier in your notebook session is still defined -- it doesn't matter where physically you are in the notebook. If you want to reset things, you can use the options under the _Kernel_ menu.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + " \n", + "Create a new cell below this one. Make sure that it is a _code_ cell, and enter the following code and run it:\n", + " \n", + "```\n", + "\n", + " print(\"Hello, World\")\n", + " \n", + "```\n", + "\n", + "````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`print()` is a _function_ in python that takes arguments (in the `()`) and outputs to the screen. You can print multiple quantities at once like:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 2 3\n" + ] + } + ], + "source": [ + "print(1, 2, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the default behavior in Jupyter is to print the return value from the last statement in a cell, so we don't need to `print` if we just want the value of something like:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = 10\n", + "a" + ] + } + ], + "metadata": { + "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": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/01-python/w1-python-datatypes.ipynb b/content/01-python/w1-python-datatypes.ipynb new file mode 100644 index 00000000..a8608991 --- /dev/null +++ b/content/01-python/w1-python-datatypes.ipynb @@ -0,0 +1,1365 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Basic Python Datatypes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Python is a dynamically typed language -- this means that you don't\n", + "need to specify ahead of time what kind of data you are going to store\n", + "in a variable. Nevertheless, there are some core datatypes that we\n", + "need to become familiar with as we use the language.\n", + "\n", + "The first set of datatypes are similar to those found in other\n", + "languages (like C/C++ and Fortran): floating point numbers, integers,\n", + "and strings." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{tip}\n", + "Floating point is essential for computational science. A great\n", + "introduction to floating point and its limitations is: [What every\n", + "computer scientist should know about floating-point\n", + "arithmetic](http://dl.acm.org/citation.cfm?id=103163) by\n", + "D. Goldberg.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The next set of datatypes are containers. In python, unlike some\n", + "languages, these are built into the language and make it very easy to\n", + "do complex operations. We'll look at these later.\n", + "\n", + "\n", + "Some examples come from the python tutorial:\n", + "http://docs.python.org/3/tutorial/" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## integers" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Integers are numbers without a decimal point. They can be positive or negative. Most programming languages use a finite-amount of memory to store a single integer, but in python will expand the amount of memory as necessary to store large integers.\n", + "\n", + "The basic operators, `+`, `-`, `*`, and `/` work with integers" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "7" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "2+2+3" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "-8" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "2*-4" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "Integer division is one place where python and other programming languages differ.\n", + "In python, dividing two integers results in a float. In C/C++/Fortran, dividing two integers results in an integer, so `1/2 = 0`.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1/2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get an integer result, we can use the // operator." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1//2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Python is a _dynamically-typed language_—this means that we do not need to declare the datatype of a variable before initializing it. \n", + "\n", + "Here we'll create a variable (think of it as a descriptive label that can refer to some piece of data). The `=` operator assigns a value to a variable. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "a = 1\n", + "b = 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Functions operate on variables and return a result. Here, `print()` will output to the screen." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a + b" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a * b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that variable names are case sensitive, so a and A are different" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "A = 2048" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 2048\n" + ] + } + ], + "source": [ + "print(a, A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we initialize 3 variable all to `0`, but these are still distinct variables, so we can change one without affecting the others." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "x = y = z = 0" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0 0 0\n" + ] + } + ], + "source": [ + "print(x, y, z)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "z = 1" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "z" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Python has some built in help (and Jupyter/ipython has even more)\n", + "\n", + "try doing:\n", + "```\n", + "help(x)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "alternatively, try:\n", + "```\n", + "x?\n", + "```\n", + "\n", + "(this only works in Jupyter)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another function, `type()` returns the data type of a variable" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "int" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "In languages like Fortran and C, you specify the amount of memory an integer can take (usually 2 or 4 bytes). This puts a restriction on the largest size integer that can be represented. Python will adapt the size of the integer so you don't *overflow*\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "12345678901234567890123456789012345123456789012345678901234567890\n", + "213\n", + "\n" + ] + } + ], + "source": [ + "a = 12345678901234567890123456789012345123456789012345678901234567890\n", + "print(a)\n", + "print(a.bit_length())\n", + "print(type(a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## floating point" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "when operating with both floating point and integers, the result is promoted to a float." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3.0" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1. + 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "but note the special integer division operator" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1.//2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{important}\n", + "Not every number can be represented in floating point. Since there are infinitely many real numbers between any two bounds but we are using a finite amount of memory, on a computer we have to approximate numbers. There is an IEEE standard for floating point that pretty much all languages and processors follow. \n", + "\n", + "The means two things\n", + "\n", + "* not every real number will have an exact representation in floating point\n", + "* there is a finite precision to numbers -- below this we lose track of differences (this is usually called *roundoff* error)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the following expression, for example:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "-4.440892098500626e-16" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "0.3/0.1 - 3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's another example: The number 0.1 cannot be exactly represented on a computer. In our print, we use a format specifier (the stuff inside of the `{}`) to ask for more precision to be shown:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.10000000000000000555\n" + ] + } + ], + "source": [ + "a = 0.1\n", + "print(\"{:30.20}\".format(a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can ask python to report the limits on floating point" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import sys\n", + "sys.float_info" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that this says that we can only store numbers between 2.2250738585072014e-308 and 1.7976931348623157e+308\n", + "\n", + "We also see that the precision is 2.220446049250313e-16 (this is commonly called _machine epsilon_). To see this, consider adding a small number to 1.0. We'll use the equality operator (`==`) to test if two numbers are equal:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} Quick Exercise\n", + " \n", + "Define two variables, $a = 1$, and $e = 10^{-16}$.\n", + "\n", + "Now define a third variable, `b = a + e`\n", + "\n", + "We can use the python `==` operator to test for equality. What do you expect `b == a` to return? run it an see if it agrees with your guess.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## modules\n", + "\n", + "The core python language is extended by a standard library that provides additional functionality. These added pieces are in the form of modules that we can _import_ into our python session (or program).\n", + "\n", + "The `math` module provides functions that do the basic mathematical operations as well as provide constants (note there is a separate `cmath` module for complex numbers).\n", + "\n", + "In python, you `import` a module. The functions are then defined in a separate _namespace_—this is a separate region that defines names and variables, etc. A variable in one namespace can have the same name as a variable in a different namespace, and they don't clash. You use the \"`.`\" operator to access a member of a namespace.\n", + "\n", + "By default, when you type stuff into the python interpreter or here in the Jupyter notebook, or in a script, it is in its own default namespace, and you don't need to prefix any of the variables with a namespace indicator." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import math" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`math` provides the value of pi" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3.141592653589793" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "math.pi" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is distinct from any variable `pi` we might define here" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "pi = 3" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3 3.141592653589793\n" + ] + } + ], + "source": [ + "print(pi, math.pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note here that `pi` and `math.pi` are distinct from one another—they are in different namespaces." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### floating point operations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The same operators, `+`, `-`, `*`, `/` work are usual for floating point numbers. To raise an number to a power, we use the `**` operator (this is the same as Fortran)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "R = 2.0" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "12.566370614359172" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "math.pi * R**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "operator precedence follows that of most languages. See\n", + "\n", + "https://docs.python.org/3/reference/expressions.html#operator-precedence\n", + " \n", + "in order of precedence:\n", + "* quantites in `()`\n", + "* slicing, calls, subscripts\n", + "* exponentiation (`**`)\n", + "* `+x`, `-x`, `~x`\n", + "* `*`, `@`, `/`, `//`, `%`\n", + "* `+`, `-`\n", + "\n", + "(after this are bitwise operations and comparisons)\n", + "\n", + "Parentheses can be used to override the precedence." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} Quick Exercise\n", + "\n", + "Consider the following expressions. Using the ideas of precedence, think about what value will result, then try it out in the cell below to see if you were right.\n", + "\n", + " * `1 + 3*2**2`\n", + " * `1 + (3*2)**2`\n", + " * `2**3**2`\n", + "\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The math module provides a lot of the standard math functions we might want to use.\n", + "\n", + "For the trig functions, the expectation is that the argument to the function is in radians—you can use `math.radians()` to convert from degrees to radians, ex:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.7071067811865476" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "math.cos(math.radians(45))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that in that statement we are feeding the output of one function (`math.radians()`) into a second function, `math.cos()`\n", + "\n", + "When in doubt, as for help to discover all of the things a module provides:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on built-in function sin in module math:\n", + "\n", + "sin(x, /)\n", + " Return the sine of x (measured in radians).\n", + "\n" + ] + } + ], + "source": [ + "help(math.sin)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## strings" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "python doesn't care if you use single or double quotes for strings:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "a = \"this is my string\"\n", + "b = 'another string'" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "this is my string\n", + "another string\n" + ] + } + ], + "source": [ + "print(a)\n", + "print(b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Many of the usual mathematical operators are defined for strings as well. For example to concatenate or duplicate:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'this is my stringanother string'" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a + b" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'this is my string. another string'" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a + \". \" + b" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'this is my stringthis is my string'" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a * 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are several escape codes that are interpreted in strings. These start with a backwards-slash, `\\`. E.g., you can use `\\n` for new line" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "this is my string\n", + "\n" + ] + } + ], + "source": [ + "a = a + \"\\n\"\n", + "print(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} Quick Exercise\n", + " \n", + "The `input()` function can be used to ask the user for input.\n", + "\n", + " * Use `help(input)` to see how it works. \n", + " * Write code to ask for input and store the result in a variable. `input()` will return a string.\n", + "\n", + " * Use the `float()` function to convert a number entered as input to a floating point variable. \n", + " * Check to see if the conversion worked using the `type()` function.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\"\"\" can enclose multiline strings. This is useful for docstrings at the start of functions (more on that later...)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "c = \"\"\"\n", + "Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor \n", + "incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis \n", + "nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. \n", + "Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore \n", + "eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt \n", + "in culpa qui officia deserunt mollit anim id est laborum.\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor \n", + "incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis \n", + "nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. \n", + "Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore \n", + "eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt \n", + "in culpa qui officia deserunt mollit anim id est laborum.\n" + ] + } + ], + "source": [ + "print(c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "a raw string does not replace escape sequences (like \\n). Just put a `r` before the first quote:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'this is a raw string\\\\n'" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d = r\"this is a raw string\\n\"\n", + "d" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "slicing is used to access a portion of a string.\n", + "\n", + "slicing a string can seem a bit counterintuitive if you are coming from Fortran. The trick is to think of the index as representing the left edge of a character in the string. When we do arrays later, the same will apply.\n", + "\n", + "Also note that python (like C) uses 0-based indexing\n", + "\n", + "Negative indices count from the right." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "this is my string\n", + "is\n", + "t\n", + "this is a raw string\\n\n", + "\\\n" + ] + } + ], + "source": [ + "a = \"this is my string\"\n", + "print(a)\n", + "print(a[5:7])\n", + "print(a[0])\n", + "print(d)\n", + "print(d[-2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} Quick Exercise:\n", + "\n", + "Strings have a lot of _methods_ (functions that know how to work with a particular datatype, in this case strings). A useful method is `.find()`. For a string `a`,\n", + "`a.find(s)` will return the index of the first occurrence of `s`.\n", + "\n", + "For our string `c` above, find the first `.` (identifying the first full sentence), and print out just the first sentence in `c` using this result\n", + "\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "there are also a number of methods and functions that work with strings. Here are some examples:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "that is my string\n", + "17\n", + "this is my string\n", + "g\n" + ] + } + ], + "source": [ + "print(a.replace(\"this\", \"that\"))\n", + "print(len(a))\n", + "print(a.strip()) # Also notice that strip removes the \\n\n", + "print(a.strip()[-1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that our original string, `a`, has not changed. In python, strings are *immutable*. Operations on strings return a new string." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'this is my string'" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "str" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can format strings when we are printing to insert quantities in particular places in the string. A `{}` serves as a placeholder for a quantity and is replaced using the `.format()` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a = 1; b = 2.0; c = test\n" + ] + } + ], + "source": [ + "a = 1\n", + "b = 2.0\n", + "c = \"test\"\n", + "print(\"a = {}; b = {}; c = {}\".format(a, b, c))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "But the more modern way to do this is to use *f-strings*" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a = 1; b = 2.0; c = test\n" + ] + } + ], + "source": [ + "print(f\"a = {a}; b = {b}; c = {c}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note the `f` preceding the starting `\"`" + ] + } + ], + "metadata": { + "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": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/lectures/01-python/python-advanced-datatypes.ipynb b/content/01-python/w2-python-advanced-datatypes.ipynb similarity index 61% rename from lectures/01-python/python-advanced-datatypes.ipynb rename to content/01-python/w2-python-advanced-datatypes.ipynb index f5696b92..a34fd9ce 100644 --- a/lectures/01-python/python-advanced-datatypes.ipynb +++ b/content/01-python/w2-python-advanced-datatypes.ipynb @@ -4,25 +4,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "These notes follow the official python tutorial pretty closely: http://docs.python.org/3/tutorial/" + "# Advanced Datatypes" ] }, { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], + "cell_type": "markdown", + "metadata": {}, "source": [ - "from __future__ import print_function" + "These notes follow the official python tutorial pretty closely: http://docs.python.org/3/tutorial/" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# Lists" + "## Lists" ] }, { @@ -36,10 +32,8 @@ }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, + "execution_count": 1, + "metadata": {}, "outputs": [], "source": [ "a = [1, 2.0, \"my list\", 4]" @@ -47,21 +41,24 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, 2.0, 'my list', 4]\n" - ] + "data": { + "text/plain": [ + "[1, 2.0, 'my list', 4]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "print(a)" + "a" ] }, { @@ -73,21 +70,24 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "my list\n" - ] + "data": { + "text/plain": [ + "'my list'" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "print(a[2])" + "a[2]" ] }, { @@ -99,21 +99,24 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, 2.0, 'my list', 4, 1, 2.0, 'my list', 4]\n" - ] + "data": { + "text/plain": [ + "[1, 2.0, 'my list', 4, 1, 2.0, 'my list', 4]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "print(a*2)" + "a*2" ] }, { @@ -125,21 +128,24 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "4\n" - ] + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "print(len(a))" + "len(a)" ] }, { @@ -151,9 +157,9 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { @@ -162,7 +168,7 @@ "[1, -2.0, 'my list', 4]" ] }, - "execution_count": 7, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -172,29 +178,6 @@ "a" ] }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[-1, -2.1, -2.0, 'my list', 4]" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "a[0:1] = [-1, -2.1] # this will put two items in the spot where 1 existed before\n", - "a" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -206,9 +189,9 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { @@ -217,7 +200,7 @@ "[-1, -2.1, -2.0, 'my list', 4, 6]" ] }, - "execution_count": 9, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -229,9 +212,9 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { @@ -240,7 +223,7 @@ "6" ] }, - "execution_count": 10, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -251,9 +234,9 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { @@ -262,7 +245,7 @@ "[-1, -2.1, -2.0, 'my list', 4]" ] }, - "execution_count": 11, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -275,6 +258,35 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "````{admonition} Quick Exercise\n", + "\n", + "An operation we'll see a lot is to begin with an empty list and add elements to it. An empty list is created as:\n", + "```\n", + "\n", + " a = []\n", + " \n", + "```\n", + "\n", + " * Create an empty list\n", + " * Append the integers 1 through 5 to it. \n", + " * Now pop them out of the list one by one.\n", + " \n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### copying lists\n", + "\n", "copying may seem a little counterintuitive at first. The best way to think about this is that your list lives in memory somewhere and when you do \n", "\n", "```\n", @@ -294,22 +306,23 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[-1, -2.1, -2.0, 'my list', 4]\n", - "['changed', -2.1, -2.0, 'my list', 4]\n" + "[1, 2, 3, 4]\n", + "['changed', 2, 3, 4]\n" ] } ], "source": [ - "b = a # this is just a pointer, both a and b refer to the same list object in memory\n", + "a = [1, 2, 3, 4]\n", + "b = a # both a and b refer to the same list object in memory\n", "print(a)\n", "a[0] = \"changed\"\n", "print(b)" @@ -324,17 +337,17 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "['changed', 'two', -2.0, 'my list', 4]\n", - "['changed', -2.1, -2.0, 'my list', 4]\n" + "['changed', 'two', 3, 4]\n", + "['changed', 2, 3, 4]\n" ] } ], @@ -349,271 +362,166 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Things get a little complicated when a list contains another mutable object, like another list. Then the copy we looked at above is only a _shallow copy_. Look at this example -- the list within the list here is still the same object in memory for our two copies:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, [2, 3], 4]\n" - ] - } - ], - "source": [ - "f = [1, [2, 3], 4]\n", - "print(f)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, [2, 3], 4]\n" - ] - } - ], - "source": [ - "g = list(f)\n", - "print(g)" + "Things get a little complicated when a list contains another mutable object, like another list. Then the copy we looked at above is only a _shallow copy_." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now we are going to change an element of that list `[2, 3]` inside of our main list. We need to index `f` once to get that list, and then a second time to index that list:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, ['a', 3], 4]\n", - "[1, ['a', 3], 4]\n" - ] - } - ], - "source": [ - "f[1][0] = \"a\"\n", - "print(f)\n", - "print(g)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that the change occured in both -- since that inner list is shared in memory between the two. Note that we can still change one of the other values without it being reflected in the other list -- this was made distinct by our shallow copy:" + "When in doubt, use the `id()` function to figure out where in memory an object lies (you shouldn't worry about the what value of the numbers you get from `id` mean, but just whether they are the same as those for another object)" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 13, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[1, ['a', 3], 4]\n", - "[-1, ['a', 3], 4]\n" + "140643968865472 140643968865472 140643969109824\n" ] } ], "source": [ - "f[0] = -1\n", - "print(g)\n", - "print(f)" + "print(id(a), id(b), id(c))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Note: this is what is referred to as a shallow copy. If the original list had any special objects in it (like another list), then the new copy and the old copy will still point to that same object. There is a deep copy method when you really want everything to be unique in memory.\n", - "\n", - "When in doubt, use the `id()` function to figure out where in memory an object lies (you shouldn't worry about the what value of the numbers you get from `id` mean, but just whether they are the same as those for another object)" + "Or use the `is` operator" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 14, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "139805355371976 139805355371976 139805346440328\n" - ] + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "print(id(a), id(b), id(c))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "An operation we'll see a lot is to begin with an empty list and add elements to it:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "my_list = []\n", - "my_list.append(200.0)\n", - "my_list.append(-1.0)\n", - "my_list.append(-1.0)\n", - "my_list.append(3.14)\n", - "my_list.append(27)" + "a is b" ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 15, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { "data": { "text/plain": [ - "[200.0, -1.0, -1.0, 3.14, 27]" + "False" ] }, - "execution_count": 20, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "my_list" + "a is c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "There are lots of other methods that work on lists (remember, ask for help)" + "There are lots of other methods that work on lists (remember, ask for `help`)" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 16, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "2\n" - ] - }, { "data": { "text/plain": [ - "[-1.0, -1.0, 3.14, 27, 200.0]" + "[-1, -1, 2, 5, 9, 10, 24]" ] }, - "execution_count": 21, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ + "my_list = [10, -1, 5, 24, 2, -1, 9]\n", "my_list.sort()\n", - "print(my_list.count(-1.0))\n", "my_list" ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 17, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Help on built-in function insert:\n", - "\n", - "insert(...) method of builtins.list instance\n", - " L.insert(index, object) -- insert object before index\n", - "\n" - ] + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "help(a.insert)" + "my_list.count(-1)" ] }, { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": false - }, - "outputs": [], + "cell_type": "markdown", + "metadata": {}, "source": [ - "a.insert(3, \"my inserted element\")" + "We can also insert elements" ] }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 18, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { "data": { "text/plain": [ - "['changed', 'two', -2.0, 'my inserted element', 'my list', 4]" + "['changed', 'two', 3, 'my inserted element', 4]" ] }, - "execution_count": 24, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ + "a.insert(3, \"my inserted element\")\n", "a" ] }, @@ -626,31 +534,34 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 19, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, 2, 3, 4, 5, 6]\n" - ] + "data": { + "text/plain": [ + "[1, 2, 3, 4, 5, 6]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "b = [1,2,3]\n", - "c = [4,5,6]\n", + "b = [1, 2, 3]\n", + "c = [4, 5, 6]\n", "d = b + c\n", - "print(d)" + "d" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# Dictionaries" + "## Dictionaries" ] }, { @@ -662,10 +573,8 @@ }, { "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false - }, + "execution_count": 20, + "metadata": {}, "outputs": [], "source": [ "my_dict = {\"key1\":1, \"key2\":2, \"key3\":3}" @@ -673,21 +582,24 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 21, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "1\n" - ] + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "print(my_dict[\"key1\"])" + "my_dict[\"key1\"]" ] }, { @@ -699,65 +611,69 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 22, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'key2': 2, 'newkey': 'new', 'key1': 1, 'key3': 3}\n" - ] + "data": { + "text/plain": [ + "{'key1': 1, 'key2': 2, 'key3': 3, 'newkey': 'new'}" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ "my_dict[\"newkey\"] = \"new\"\n", - "print(my_dict)" + "my_dict" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Note that a dictionary is unordered.\n", - "\n", "You can also easily get the list of keys that are defined in a dictionary" ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 23, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "['key2', 'newkey', 'key1', 'key3']\n" - ] + "data": { + "text/plain": [ + "['key1', 'key2', 'key3', 'newkey']" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ "keys = list(my_dict.keys())\n", - "print(keys)" + "keys" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "and check easily whether a key exists in the dictionary" + "and check easily whether a key exists in the dictionary using the `in` operator" ] }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 24, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { @@ -770,128 +686,61 @@ } ], "source": [ - "print(\"key1\" in keys)\n", - "print(\"invalidKey\" in keys)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# List Comprehensions" + "print(\"key1\" in my_dict)\n", + "print(\"invalidKey\" in my_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "list comprehensions provide a compact way to initialize lists. Some examples from the tutorial" + "````{admonition} Quick Exercise\n", + "\n", + "Create a dictionary where the keys are the string names of the numbers zero to nine and the values are their numeric representation (0, 1, ... , 5)\n", + "\n", + "````" ] }, { "cell_type": "code", - "execution_count": 31, - "metadata": { - "collapsed": false - }, + "execution_count": null, + "metadata": {}, "outputs": [], - "source": [ - "squares = [x**2 for x in range(10)]" - ] + "source": [] }, { - "cell_type": "code", - "execution_count": 32, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], + "cell_type": "markdown", + "metadata": {}, "source": [ - "squares" + "## Tuples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "here we use another python type, the tuple, to combine numbers from two lists into a pair" + "tuples are immutable -- they cannot be changed, but they are useful for organizing data in some situations. We use () to indicate a tuple:" ] }, { "cell_type": "code", - "execution_count": 33, - "metadata": { - "collapsed": false - }, + "execution_count": 27, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]" + "(1, 2, 3, 4)" ] }, - "execution_count": 33, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "[(x, y) for x in [1,2,3] for y in [3,1,4] if x != y]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Tuples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "tuples are immutable -- they cannot be changed, but they are useful for organizing data in some situations. We use () to indicate a tuple:" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "a = (1, 2, 3, 4)" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(1, 2, 3, 4)\n" - ] - } - ], - "source": [ - "print(a)" + "a = (1, 2, 3, 4)\n", + "a" ] }, { @@ -903,10 +752,8 @@ }, { "cell_type": "code", - "execution_count": 36, - "metadata": { - "collapsed": false - }, + "execution_count": 28, + "metadata": {}, "outputs": [], "source": [ "w, x, y, z = a" @@ -914,40 +761,24 @@ }, { "cell_type": "code", - "execution_count": 37, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1\n" - ] - } - ], - "source": [ - "print(w)" - ] - }, - { - "cell_type": "code", - "execution_count": 38, + "execution_count": 29, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "1 2 3 4\n" - ] + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "print(w, x, y, z)" + "w" ] }, { @@ -959,9 +790,9 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 30, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { @@ -971,7 +802,7 @@ "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\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[0ma\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "Cell \u001b[0;32mIn[30], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43ma\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m2\u001b[39m\n", "\u001b[0;31mTypeError\u001b[0m: 'tuple' object does not support item assignment" ] } @@ -989,10 +820,8 @@ }, { "cell_type": "code", - "execution_count": 40, - "metadata": { - "collapsed": true - }, + "execution_count": 31, + "metadata": {}, "outputs": [], "source": [ "z = list(a)" @@ -1000,10 +829,8 @@ }, { "cell_type": "code", - "execution_count": 41, - "metadata": { - "collapsed": true - }, + "execution_count": 32, + "metadata": {}, "outputs": [], "source": [ "z[0] = \"new\"" @@ -1011,36 +838,63 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 33, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "['new', 2, 3, 4]\n" - ] + "data": { + "text/plain": [ + "['new', 2, 3, 4]" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "print(z)" + "z" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is often not clear how tuples differ from lists. The most obvious way is that they are immutable. Often we'll see tuples used to store related data that should all be interpreted together. A good example is a Cartesian point, (x, y). Here is a list of points:" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 34, "metadata": { - "collapsed": true + "tags": [] }, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "text/plain": [ + "[(1, 2), (2, 3), (3, 4)]" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "points = []\n", + "points.append((1,2))\n", + "points.append((2,3))\n", + "points.append((3,4))\n", + "points" + ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -1054,9 +908,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.2" + "version": "3.13.1" } }, "nbformat": 4, - "nbformat_minor": 0 + "nbformat_minor": 4 } diff --git a/content/01-python/w2-python-control-flow.ipynb b/content/01-python/w2-python-control-flow.ipynb new file mode 100644 index 00000000..d6652498 --- /dev/null +++ b/content/01-python/w2-python-control-flow.ipynb @@ -0,0 +1,485 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Control Flow" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These notes follow the official python tutorial pretty closely: http://docs.python.org/3/tutorial/" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To write a program, we need the ability to iterate and take action based on the values of a variable. This includes if-tests and loops.\n", + "\n", + "Python uses whitespace to denote a block of code." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## While loop\n", + "\n", + "A simple while loop—notice the indentation to denote the block that is part of the loop.\n", + "\n", + "Here we also use the compact `+=` operator: `n += 1` is the same as `n = n + 1`" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n", + "6\n", + "7\n", + "8\n", + "9\n" + ] + } + ], + "source": [ + "n = 0\n", + "while n < 10:\n", + " print(n)\n", + " n += 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This was a very simple example. But often we'll use the `range()` function in this situation. Note that `range()` can take a stride." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2\n", + "4\n", + "6\n", + "8\n" + ] + } + ], + "source": [ + "for n in range(2, 10, 2):\n", + " print(n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## if statements" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`if` allows for branching. python does not have a select/case statement like some other languages, but `if`, `elif`, and `else` can reproduce any branching functionality you might need." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "zero\n" + ] + } + ], + "source": [ + "x = 0\n", + "\n", + "if x < 0:\n", + " print(\"negative\")\n", + "elif x == 0:\n", + " print(\"zero\")\n", + "else:\n", + " print(\"positive\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Iterating over elements" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "it's easy to loop over items in a list or any _iterable_ object. The `in` operator is the key here." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "2.0\n", + "three\n", + "4\n" + ] + } + ], + "source": [ + "alist = [1, 2.0, \"three\", 4]\n", + "for a in alist:\n", + " print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t\n", + "h\n", + "i\n", + "s\n", + " \n", + "i\n", + "s\n", + " \n", + "a\n", + " \n", + "s\n", + "t\n", + "r\n", + "i\n", + "n\n", + "g\n" + ] + } + ], + "source": [ + "for c in \"this is a string\":\n", + " print(c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can combine loops and if-tests to do more complex logic, like break out of the loop when you find what you're looking for" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2\n" + ] + } + ], + "source": [ + "n = 0\n", + "for a in alist:\n", + " if a == \"three\":\n", + " break\n", + " else:\n", + " n += 1\n", + "\n", + "print(n)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(for that example, however, there is a simpler way)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alist.index(\"three\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "for dictionaries, you can also loop over the elements" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "key = key1, value = 1\n", + "key = key2, value = 2\n", + "key = key3, value = 3\n" + ] + } + ], + "source": [ + "my_dict = {\"key1\":1, \"key2\":2, \"key3\":3}\n", + "\n", + "for k, v in my_dict.items():\n", + " print(f\"key = {k}, value = {v}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "key1 1\n", + "key2 2\n", + "key3 3\n" + ] + } + ], + "source": [ + "for k in sorted(my_dict):\n", + " print(k, my_dict[k])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "sometimes we want to loop over a list element and know its index -- `enumerate()` helps here:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0 1\n", + "1 2.0\n", + "2 three\n", + "3 4\n" + ] + } + ], + "source": [ + "for n, a in enumerate(alist):\n", + " print(n, a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + " \n", + "`zip()` allows us to loop over two iterables at the same time. Consider the following two\n", + "lists:\n", + "\n", + "```\n", + "\n", + " a = [1, 2, 3, 4, 5, 6, 7, 8]\n", + " b = [\"a\", \"b\", \"c\", \"d\", \"e\", \"f\", \"g\", \"h\"]\n", + " \n", + "```\n", + "\n", + "`zip(a, b)` will act like a list with each element a tuple with one item from `a` and the corresponding element from `b`. \n", + "\n", + "Try looping over these lists together (using `zip()`) and print the corresponding elements from each list together on a single line.\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + " \n", + "\n", + "The `.split()` function on a string can split it into words (separating on spaces). \n", + "\n", + "Using `.split()`, loop over the words in the string\n", + "\n", + "`a = \"The quick brown fox jumped over the lazy dog\"`\n", + "\n", + "and print one word per line\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## List Comprehensions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "list comprehensions provide a compact way to initialize lists. Some examples from the tutorial" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "squares = [x**2 for x in range(10)]" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "squares" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + "\n", + "Use a list comprehension to create a new list from `squares` containing only the even numbers. It might be helpful to use the modulus operator, `%`\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/01-python/w2-python-exercises.ipynb b/content/01-python/w2-python-exercises.ipynb new file mode 100644 index 00000000..1651a963 --- /dev/null +++ b/content/01-python/w2-python-exercises.ipynb @@ -0,0 +1,453 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercises" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 1\n", + "\n", + "When talking about floating point, we discussed _machine epsilon_, $\\epsilon$—this is the smallest number that when added to 1 is still different from 1.\n", + "\n", + "We'll compute $\\epsilon$ here:\n", + "\n", + " * Pick an initial guess for $\\epsilon$ of `eps = 1`. \n", + "\n", + " * Create a loop that checks whether `1 + eps` is different from `1`\n", + " \n", + " * Each loop iteration, cut the value of `eps` in half\n", + " \n", + "What value of $\\epsilon$ do you find?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 2\n", + "\n", + "To iterate over the tuples, where the _i_-th tuple contains the _i_-th elements of certain sequences, we can use `zip(*sequences)` function.\n", + "\n", + "We will iterate over two lists, `names` and `age`, and print out the resulting tuples.\n", + "\n", + " * Start by initializing lists `names = [\"Mary\", \"John\", \"Sarah\"]` and `age = [21, 56, 98]`.\n", + " \n", + " * Iterate over the tuples containing a name and an age, the `zip(list1, list2)` function might be useful here.\n", + " \n", + " * Print out formatted strings of the type \"*NAME is AGE years old*\"." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 3\n", + "\n", + "The function `enumerate(sequence)` returns tuples containing indices of objects in the sequence, and the objects. \n", + "\n", + "The `random` module provides tools for working with the random numbers. In particular, `random.randint(start, end)` generates a random number not smaller than `start`, and not bigger than `end`.\n", + "\n", + " * Generate a list of 10 random numbers from 0 to 9.\n", + " \n", + " * Using the `enumerate(random_list)` function, iterate over the tuples of random numbers and their indices, and print out *\"Match: NUMBER and INDEX\"* if the random number and its index in the list match." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8\n" + ] + } + ], + "source": [ + "import random\n", + "\n", + "random_number = random.randint(0,9)\n", + "print(random_number)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 4\n", + "\n", + "The Fibbonacci sequence is a numerical sequence where each number is the sum of the 2 preceding numbers, e.g., 1, 1, 2, 3, 5, 8, 13, ...\n", + "\n", + "Create a list where the elements are the terms in the Fibbonacci sequence:\n", + "\n", + " * Start with the list `fib = [1, 1]`\n", + " \n", + " * Loop 25 times, compute the next term as the sum of the previous 2 terms and append to the list\n", + " \n", + " * After the loop is complete, print out the terms \n", + " \n", + "You may find it useful to use `fib[-1]` and `fib[-2]` to access the last to items in the list" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 5\n", + "\n", + "We can use the `input()` function to ask for input from the prompt (note: in python 2 the function was called `raw_input()`).\n", + "\n", + "Create an empty list and use a while loop to ask the user for input and append their input to the list. Keep looping until 10 items are added to the list" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 6\n", + "\n", + "Here is a list of book titles (from http://thegreatestbooks.org). Loop through the list and capitalize each word in each title. You might find the `.capitalize()` method that works on strings useful." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "titles = [\"don quixote\", \n", + " \"in search of lost time\", \n", + " \"ulysses\", \n", + " \"the odyssey\", \n", + " \"war and piece\", \n", + " \"moby dick\", \n", + " \"the divine comedy\", \n", + " \"hamlet\", \n", + " \"the adventures of huckleberry finn\", \n", + " \"the great gatsby\"]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 7\n", + "\n", + "Here's some text (the Gettysburg Address). Our goal is to count how many times each word repeats. We'll do a brute force method first, and then we'll look a ways to do it more efficiently (and compactly)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "gettysburg_address = \"\"\"\n", + "Four score and seven years ago our fathers brought forth on this continent, \n", + "a new nation, conceived in Liberty, and dedicated to the proposition that \n", + "all men are created equal.\n", + "\n", + "Now we are engaged in a great civil war, testing whether that nation, or \n", + "any nation so conceived and so dedicated, can long endure. We are met on\n", + "a great battle-field of that war. We have come to dedicate a portion of\n", + "that field, as a final resting place for those who here gave their lives\n", + "that that nation might live. It is altogether fitting and proper that we\n", + "should do this.\n", + "\n", + "But, in a larger sense, we can not dedicate -- we can not consecrate -- we\n", + "can not hallow -- this ground. The brave men, living and dead, who struggled\n", + "here, have consecrated it, far above our poor power to add or detract. The\n", + "world will little note, nor long remember what we say here, but it can never\n", + "forget what they did here. It is for us the living, rather, to be dedicated\n", + "here to the unfinished work which they who fought here have thus far so nobly\n", + "advanced. It is rather for us to be here dedicated to the great task remaining\n", + "before us -- that from these honored dead we take increased devotion to that\n", + "cause for which they gave the last full measure of devotion -- that we here\n", + "highly resolve that these dead shall not have died in vain -- that this\n", + "nation, under God, shall have a new birth of freedom -- and that government\n", + "of the people, by the people, for the people, shall not perish from the earth.\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We've already seen the `.split()` method will, by default, split by spaces, so it will split this into words, producing a list:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "ga = gettysburg_address.split()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ga" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, the next problem is that some of these still have punctuation. In particular, we see \"`.`\", \"`,`\", and \"`--`\".\n", + "\n", + "When considering a word, we can get rid of these by using the `replace()` method:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = \"end.,\"\n", + "b = a.replace(\".\", \"\").replace(\",\", \"\")\n", + "b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another problem is case—we want to count \"but\" and \"But\" as the same. Strings have a `lower()` method that can be used to convert a string:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = \"But\"\n", + "b = \"but\"\n", + "a == b" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a.lower() == b.lower()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Recall that strings are immutable, so `replace()` produces a new string on output." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## your task\n", + "\n", + "Create a dictionary that uses the unique words as keys and has as a value the number of times that word appears. \n", + "\n", + "Write a loop over the words in the string (using our split version) and do the following:\n", + " * remove any punctuation\n", + " * convert to lowercase\n", + " * test if the word is already a key in the dictionary (using the `in` operator)\n", + " - if the key exists, increment the word count for that key\n", + " - otherwise, add it to the dictionary with the appropriate count of `1`.\n", + "\n", + "At the end, print out the words and a count of how many times they appear" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# your code here\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More compact way\n", + "\n", + "We can actually do this a lot more compactly by using another list comprehensions and another python datatype called a set. A set is a group of items, where each item is unique (e.g., no repetitions)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a list comprehension that removes all the punctuation and converts to lower case:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "words = [q.lower().replace(\".\", \"\").replace(\",\", \"\") for q in ga]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and by using the `set()` function, we turn the list into a set, removing any duplicates:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "unique_words = set(words)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "now we can loop over the unique words and use the `count` method of a list to find how many there are" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "count = {}\n", + "for uw in unique_words:\n", + " count[uw] = words.count(uw)\n", + " \n", + "count" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even shorter -- we can use a dictionary comprehension, like a list comprehension" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "c = {uw: count[uw] for uw in unique_words}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "c" + ] + } + ], + "metadata": { + "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": "3.9.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/01-python/w3-python-exceptions.ipynb b/content/01-python/w3-python-exceptions.ipynb new file mode 100644 index 00000000..c5769516 --- /dev/null +++ b/content/01-python/w3-python-exceptions.ipynb @@ -0,0 +1,184 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exceptions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Python raises exceptions when it encounters an error. The idea is that you can trap these exceptions and take an appropriate action instead of causing the code to crash. The mechanism for this is `try` / `except`. Here's an example that causes an exception, `ZeroDivisionError`:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "ename": "ZeroDivisionError", + "evalue": "division by zero", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\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[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero" + ] + } + ], + "source": [ + "a = 1/0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and here we handle this " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "warning: you divided by zero\n" + ] + }, + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "try:\n", + " a = 1/0\n", + "except ZeroDivisionError:\n", + " print(\"warning: you divided by zero\")\n", + " a = 1\n", + "\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "another example—trying to access a key that doesn't exist in a dictionary:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "ename": "KeyError", + "evalue": "'d'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mdict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m\"a\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"b\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"c\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"d\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mKeyError\u001b[0m: 'd'" + ] + } + ], + "source": [ + "dict = {\"a\":1, \"b\":2, \"c\":3}\n", + "print(dict[\"d\"])\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`KeyError` is the exception that was raised. We can check for this and take the appropriate action instead" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "None\n" + ] + } + ], + "source": [ + "try:\n", + " val = dict[\"d\"]\n", + "except KeyError:\n", + " val = None\n", + "\n", + "print(val)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We haven't talked about I/O yet, but as you might expect, when you open a file, you get an object which you can then interact with. Here we try to open a file for reading that does not already exist." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "try:\n", + " f = open(\"file.txt\", \"r\")\n", + "except IOError:\n", + " print(\"error: that file does not exist\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a lot of different types of exceptions that you can catch, and you can catch multiple ones per except clause or have multiple except clauses. You probably won't be able to anticipate every failure mode in advance. In that case, when you run and your code crashes because of an exception, the python interpreter will print out the name of the exception and you can then modify your code to take the appropriate action." + ] + } + ], + "metadata": { + "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": "3.9.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/01-python/w3-python-exercises.ipynb b/content/01-python/w3-python-exercises.ipynb new file mode 100644 index 00000000..f84e4a67 --- /dev/null +++ b/content/01-python/w3-python-exercises.ipynb @@ -0,0 +1,500 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercises" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 1 (function practice)\n", + "\n", + "Let's practice functions. Here's a simple function that takes a string and returns a list of all the 4 letter words:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "def four_letter_words(message):\n", + " words = message.split()\n", + " four_letters = [w for w in words if len(w) == 4]\n", + " return four_letters" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['over', 'lazy']\n" + ] + } + ], + "source": [ + "message = \"The quick brown fox jumps over the lazy dog\"\n", + "print(four_letter_words(message))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Write a version of this function that takes a second argument, n, that is the word length we want to search for" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 2 (primes)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A prime number is divisible only by 1 and itself. We want to write a function that takes a positive integer, n, and finds all of the primes up to that number.\n", + "\n", + "A simple (although not very fast) way to find the primes is to start at 1, and build a list of primes by checking if the current number is divisible by any of the previously found primes. If it is not divisible by any earlier primes, then it is a prime.\n", + "\n", + "The modulus operator, `%` could be helpful here." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 3 (exceptions for error handling)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We want to safely convert a string into a float, int, or leave it as a string, depending on its contents. As we've already seen, python provides `float()` and `int()` functions for this:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.0 \n" + ] + } + ], + "source": [ + "a = \"2.0\"\n", + "b = float(a)\n", + "print(b, type(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But these throw exceptions if the conversion is not possible" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "could not convert string to float: 'this is a string'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[4], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m a \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mthis is a string\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m----> 2\u001b[0m b \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mfloat\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m)\u001b[49m\n", + "\u001b[0;31mValueError\u001b[0m: could not convert string to float: 'this is a string'" + ] + } + ], + "source": [ + "a = \"this is a string\"\n", + "b = float(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "invalid literal for int() with base 10: '1.2345'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[5], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m a \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m1.2345\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m----> 2\u001b[0m b \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mint\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28mprint\u001b[39m(b, \u001b[38;5;28mtype\u001b[39m(b))\n", + "\u001b[0;31mValueError\u001b[0m: invalid literal for int() with base 10: '1.2345'" + ] + } + ], + "source": [ + "a = \"1.2345\"\n", + "b = int(a)\n", + "print(b, type(b))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.2345 \n" + ] + } + ], + "source": [ + "b = float(a)\n", + "print(b, type(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that an int can be converted to a float, but if you convert a float to an int, you rise losing significant digits. A string cannot be converted to either.\n", + "\n", + "### your task\n", + "\n", + "Write a function, `convert_type(a)` that takes a string `a`, and converts it to a float if it is a number with a decimal point, an int if it is an integer, or leaves it as a string otherwise, and returns the result. You'll want to use exceptions to prevent the code from aborting." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q 4 (tic-tac-toe)\n", + "\n", + "Here we'll write a simple tic-tac-toe game that 2 players can play. First we'll create a string that represents our game board:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "board = \"\"\"\n", + " {s1:^3} | {s2:^3} | {s3:^3}\n", + "-----+-----+-----\n", + " {s4:^3} | {s5:^3} | {s6:^3}\n", + "-----+-----+----- 123\n", + " {s7:^3} | {s8:^3} | {s9:^3} 456\n", + " 789 \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This board will look a little funny if we just print it—the spacing is set to look right when we replace the `{}` with `x` or `o`" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " {s1:^3} | {s2:^3} | {s3:^3}\n", + "-----+-----+-----\n", + " {s4:^3} | {s5:^3} | {s6:^3}\n", + "-----+-----+----- 123\n", + " {s7:^3} | {s8:^3} | {s9:^3} 456\n", + " 789 \n", + "\n" + ] + } + ], + "source": [ + "print(board)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and well use a dictionary to denote the status of each square, \"x\", \"o\", or empty, \"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'s1': '',\n", + " 's2': '',\n", + " 's3': '',\n", + " 's4': '',\n", + " 's5': '',\n", + " 's6': '',\n", + " 's7': '',\n", + " 's8': '',\n", + " 's9': ''}" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "play = {}\n", + "\n", + "def initialize_board(play):\n", + " for n in range(9):\n", + " play[f\"s{n+1}\"] = \"\"\n", + "\n", + "initialize_board(play)\n", + "play" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that our `{}` placeholders in the `board` string have identifiers (the numbers in the `{}`). We can use these to match the variables we want to print to the placeholder in the string, regardless of the order in the `format()`" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'2 1'" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = \"{s1:} {s2:}\".format(s2=1, s1=2)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's an easy way to add the values of our dictionary to the appropriate squares in our game board. First note that each of the {} is labeled with a number that matches the keys in our dictionary. Python provides a way to unpack a dictionary into labeled arguments, using **\n", + "\n", + "This lets us to write a function to show the tic-tac-toe board." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " | | \n", + "-----+-----+-----\n", + " | | \n", + "-----+-----+----- 123\n", + " | | 456\n", + " 789 \n", + "\n" + ] + } + ], + "source": [ + "def show_board(play):\n", + " \"\"\" display the playing board. We take a dictionary with the current state of the board\n", + " We rely on the board string to be a global variable\"\"\"\n", + " print(board.format(**play))\n", + " \n", + "show_board(play)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we need a function that asks a player for a move:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def get_move(n, xo, play):\n", + " \"\"\" ask the current player, n, to make a move -- make sure the square was not \n", + " already played. xo is a string of the character (x or o) we will place in\n", + " the desired square \"\"\"\n", + " valid_move = False\n", + " while not valid_move:\n", + " idx = input(f\"player {n}, enter your move (1-9)\")\n", + " if play[f\"s{idx}\"] == \"\":\n", + " valid_move = True\n", + " else:\n", + " print(\"invalid move\")\n", + " \n", + " play[f\"s{idx}\"] = xo" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function get_move in module __main__:\n", + "\n", + "get_move(n, xo, play)\n", + " ask the current player, n, to make a move -- make sure the square was not \n", + " already played. xo is a string of the character (x or o) we will place in\n", + " the desired square\n", + "\n" + ] + } + ], + "source": [ + "help(get_move)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### your task\n", + "\n", + "Using the functions defined above,\n", + " * `initialize_board()`\n", + " * `show_board()`\n", + " * `get_move()`\n", + "\n", + "fill in the function `play_game()` below to complete the game, asking for the moves one at a time, alternating between player 1 and 2" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def play_game():\n", + " \"\"\" play a game of tic-tac-toe \"\"\"\n", + " \n", + " play ={}\n", + " initialize_board(play)\n", + " show_board(play)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " | | \n", + "-----+-----+-----\n", + " | | \n", + "-----+-----+----- 123\n", + " | | 456\n", + " 789 \n", + "\n" + ] + } + ], + "source": [ + "play_game()" + ] + } + ], + "metadata": { + "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": "3.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/lectures/01-python/python-functions.ipynb b/content/01-python/w3-python-functions.ipynb similarity index 57% rename from lectures/01-python/python-functions.ipynb rename to content/01-python/w3-python-functions.ipynb index d61bff7d..ee20eaf9 100644 --- a/lectures/01-python/python-functions.ipynb +++ b/content/01-python/w3-python-functions.ipynb @@ -1,21 +1,10 @@ { "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from __future__ import print_function" - ] - }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# functions" + "# Functions" ] }, { @@ -29,31 +18,36 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "A function takes arguments, listed in the `()` and returns a value. Even if you don't explictly give a return value, one will be return (e.g., `None`). \n", + "A function takes arguments, listed in the `()` and returns a value. Even if you don't explicitly give a return value, one will be return (e.g., `None`). \n", "\n", "Here's a simple example of a function that takes a single argument, `i`" ] }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def my_fun(i):\n", + " print(f\"in the function, i = {i}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "in the function, here's i: 10\n", - "in the function, here's i: 5\n" + "in the function, i = 10\n", + "in the function, i = 5\n" ] } ], "source": [ - "def my_fun(i):\n", - " print(\"in the function, here's i:\" , i)\n", - "\n", "my_fun(10)\n", "my_fun(5)" ] @@ -62,146 +56,114 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "functions are one place where _scope_ comes into play. A function has its own _namespace_. If a variable is not defined in that function, then it will look to the namespace from where it was called to see if that variable exists there. \n", - "\n", - "However, you should avoid this as much as possible (variables that persist across namespaces are called global variables)." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-----\n", - "----------\n" - ] - } - ], - "source": [ - "global_var = 10\n", - "\n", - "def print_fun(string, n):\n", - " if n < global_var:\n", - " print(string*n)\n", - " else:\n", - " print(string*global_var)\n", + "```{note}\n", + "Functions are one place where _scope_ comes into play. A function has its own _namespace_. If a variable is not defined in that function, then it will look to the namespace from where it was called to see if that variable exists there. \n", "\n", - "print_fun(\"-\", 5)\n", - "print_fun(\"-\", 20)" + "However, you should avoid this as much as possible (variables that persist across namespaces are called global variables).\n", + "```" ] }, { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [], + "cell_type": "markdown", + "metadata": {}, "source": [ - "global_var = 100" + "Functions always return a value—if one is not explicitly given, then they return `None`, otherwise, they can return values (even multiple values) of any type" ] }, { "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, + "execution_count": 2, + "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--------------------------------------------------\n" + "in the function, i = 10\n" ] } ], "source": [ - "print_fun(\"-\",50)" + "a = my_fun(10)\n", + "a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "By default, python will let you read from a global, but not update it." + "Here's a simple function that takes two numbers and returns their product." ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 3, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "in function outer = -100.0\n", - "outside, outer = 1.0\n" - ] + "data": { + "text/plain": [ + "12" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "outer = 1.0\n", + "def multiply(a, b):\n", + " return a*b\n", "\n", - "def update():\n", - " # uncomment this to allow us to access outer in the calling namespace\n", - " # global outer\n", - " outer = -100.0\n", - " print(\"in function outer = {}\".format(outer))\n", - " \n", - "update()\n", - "print(\"outside, outer = {}\".format(outer))" + "c = multiply(3, 4)\n", + "c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "functions always return a value -- if one is not explicitly given, then they return None, otherwise, they can return values (even multiple values) of any type" + "````{admonition} Quick Exercise\n", + " \n", + "\n", + "Write a simple function that takes a sentence (as a string) and returns an integer equal to the length of the longest word in the sentence. The `len()` function and the `.split()` methods will be useful here.\n", + "\n", + "````" ] }, { "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "in the function, here's i: 10\n", - "None\n" - ] - } - ], - "source": [ - "a = my_fun(10)\n", - "print(a)" - ] + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "None is a special quantity in python (analogous to `null` in some other languages). We can test on `None` -- the preferred manner is to use `is`:" + "`None` is a special quantity in python (analogous to `null` in some other languages). We can test on `None`—the preferred manner is to use `is`:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def do_nothing():\n", + " pass" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { @@ -213,135 +175,125 @@ } ], "source": [ - "def do_nothing():\n", - " pass\n", - "\n", "a = do_nothing()\n", "if a is None:\n", " print(\"we didn't do anything\")" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## More Complex Functions\n", - "\n", - "Here's a more complex example. We return a pair of variables -- in python this is done by packing them into a tuple and then unpacking on the calling end. Also note the _docstring_ here." - ] - }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 5, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "14\n", - "[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233]\n" - ] + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "def fib2(n): # return Fibonacci series up to n (from the python tutorial)\n", - " \"\"\"Return a list containing the Fibonacci series up to n.\"\"\"\n", - " result = []\n", - " a, b = 0, 1\n", - " while a < n:\n", - " result.append(a) # see below\n", - " a, b = b, a+b\n", - " return result, len(result)\n", - "\n", - "fib, n = fib2(250)\n", - "print(n)\n", - "print(fib)" + "a is None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Note that this function includes a docstring (just after the function definition). This is used by the help system" + "## Keyword arguments\n" ] }, { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Help on function fib2 in module __main__:\n", - "\n", - "fib2(n)\n", - " Return a list containing the Fibonacci series up to n.\n", - "\n" - ] - } - ], + "cell_type": "markdown", + "metadata": {}, "source": [ - "help(fib2)" + "You can have optional arguments which provide defaults. Here's a simple function that computes $\\sin(\\theta)$ where $\\theta$ can optionally be in degrees." ] }, { - "cell_type": "markdown", + "cell_type": "code", + "execution_count": 1, "metadata": {}, + "outputs": [], "source": [ - "you can have optional arguments which provide defaults" + "import math" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def my_sin(theta, in_degrees=False):\n", + " if in_degrees:\n", + " return math.sin(math.radians(theta))\n", + " return math.sin(theta)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, "metadata": { - "collapsed": false + "tags": [] }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "True\n", - "False\n" - ] + "data": { + "text/plain": [ + "(0.7071067811865475, 0.7071067811865475)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "def check_answer(val, correct_answer=\"a\"):\n", - " if val == correct_answer:\n", - " return True\n", - " else:\n", - " return False\n", - "\n", - "print(check_answer(\"a\"))\n", - "print(check_answer(\"a\", correct_answer=\"b\"))" + "my_sin(math.pi/4), my_sin(45, in_degrees=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "it is important to note that python evaluates the optional arguments once--when the function is defined. This means that if you make the default an empty object, for instance, it will persist across all calls.\n", - "\n", - "** This is one of the most common errors for beginners **\n", + "```{important}\n", + "It is important to note that python evaluates the optional arguments once—when the function is defined. This means that if you make the default an empty object, for instance, it will persist across all call.\n", "\n", + "**This leads to one of the most common errors for beginners**\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "Here's an example of trying to initialize to an empty list:" ] }, { "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": false - }, + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def f(a, L=[]):\n", + " L.append(a)\n", + " return L" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, "outputs": [ { "name": "stdout", @@ -354,10 +306,6 @@ } ], "source": [ - "def f(a, L=[]):\n", - " L.append(a)\n", - " return L\n", - "\n", "print(f(1))\n", "print(f(2))\n", "print(f(3))" @@ -369,36 +317,49 @@ "source": [ "Notice that each call does not create its own separate list. Instead a single empty list was created when the function was first processed, and this list persists in memory as the default value for the optional argument `L`. \n", "\n", - "If we want a unique list created each time (e.g., a separate place in memory), we instead do" + "If we want a unique list created each time (e.g., a separate place in memory), we instead initialize the argument's value to `None` and then check its actual value and create an empty list in the function body itself if the default value was unchanged." ] }, { "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def fnew(a, L=None):\n", + " if L is None:\n", + " L = []\n", + " L.append(a)\n", + " return L" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(fnew(1))\n", + "print(fnew(2))\n", + "print(fnew(3))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[1]\n", - "[2]\n", - "[3]\n" + "[1, 2]\n" ] } ], "source": [ - "def fnew(a, L=None):\n", - " if L is None:\n", - " L = []\n", - " L.append(a)\n", - " return L\n", - "\n", - "print(fnew(1))\n", - "print(fnew(2))\n", - "print(fnew(3))" + "L = fnew(1)\n", + "print(fnew(2, L=L))" ] }, { @@ -408,11 +369,29 @@ "Notice that the same `None` that we saw previously comes into play here. " ] }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 2]" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L" + ] + }, { "cell_type": "markdown", - "metadata": { - "collapsed": false - }, + "metadata": {}, "source": [ "## Lambdas" ] @@ -428,10 +407,8 @@ }, { "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": true - }, + "execution_count": 13, + "metadata": {}, "outputs": [], "source": [ "pairs = [(1, 'one'), (2, 'two'), (3, 'three'), (4, 'four')]\n", @@ -440,10 +417,8 @@ }, { "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, + "execution_count": 14, + "metadata": {}, "outputs": [ { "data": { @@ -451,7 +426,7 @@ "[(4, 'four'), (1, 'one'), (3, 'three'), (2, 'two')]" ] }, - "execution_count": 15, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -464,15 +439,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Here we use a lambda in a extract from a list (with the filter command)" + "Here we use a lambda in an extract from a list (with the filter function)" ] }, { "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, + "execution_count": 15, + "metadata": {}, "outputs": [ { "data": { @@ -496,7 +469,7 @@ " 9216]" ] }, - "execution_count": 16, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } @@ -504,31 +477,57 @@ "source": [ "squares = [x**2 for x in range(100)]\n", "sq = list(filter(lambda x : x%2 == 0 and x%3 == 0, squares))\n", - "sq\n" + "sq" ] }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on class filter in module builtins:\n", + "\n", + "class filter(object)\n", + " | filter(function or None, iterable) --> filter object\n", + " | \n", + " | Return an iterator yielding those items of iterable for which function(item)\n", + " | is true. If function is None, return the items that are true.\n", + " | \n", + " | Methods defined here:\n", + " | \n", + " | __getattribute__(self, name, /)\n", + " | Return getattr(self, name).\n", + " | \n", + " | __iter__(self, /)\n", + " | Implement iter(self).\n", + " | \n", + " | __next__(self, /)\n", + " | Implement next(self).\n", + " | \n", + " | __reduce__(...)\n", + " | Return state information for pickling.\n", + " | \n", + " | ----------------------------------------------------------------------\n", + " | Static methods defined here:\n", + " | \n", + " | __new__(*args, **kwargs) from builtins.type\n", + " | Create and return a new object. See help(type) for accurate signature.\n", + "\n" + ] + } + ], + "source": [ + "help(filter)" + ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -542,9 +541,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.2" + "version": "3.13.2" } }, "nbformat": 4, - "nbformat_minor": 0 + "nbformat_minor": 4 } diff --git a/content/01-python/w4-python-classes.ipynb b/content/01-python/w4-python-classes.ipynb new file mode 100644 index 00000000..6e539844 --- /dev/null +++ b/content/01-python/w4-python-classes.ipynb @@ -0,0 +1,833 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Classes" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "Classes are the fundamental concept for object oriented programming. A class defines a data type with both data and functions that can operate on the data. An object is an instance of a class. Each object will have its own namespace (separate from other instances of the class and other functions, etc. in your program).\n", + "\n", + "We use the dot operator, `.`, to access members of the class (data or functions). We've already been doing this a lot, strings, ints, lists, ... are all objects in python." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "## Naming conventions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The python community has some naming convections, defined in PEP-8:\n", + "\n", + "https://www.python.org/dev/peps/pep-0008/\n", + "\n", + "The widely adopted ones are:\n", + "\n", + "* class names start with an uppercase, and use \"camelcase\" for multiword names, e.g. `ShoppingCart`\n", + "\n", + "* variable names (including objects which are instances of a class) are lowercase and use underscores to separate words, e.g., `shopping_cart`\n", + "\n", + "* module names should be lowercase with underscores\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A simple class" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a class that holds some student info" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "class Student:\n", + " def __init__(self, name, grade=None):\n", + " self.name = name\n", + " self.grade = grade" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This has a function, `__init__()` which is called automatically when we create an instance of the class. \n", + "\n", + "The argument `self` refers to the object that we will create, and points to the memory that they object will use to store the class's contents." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mike\n", + "None\n" + ] + } + ], + "source": [ + "a = Student(\"Mike\")\n", + "print(a.name)\n", + "print(a.grade)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's create a bunch of them, stored in a list" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "students = []\n", + "students.append(Student(\"fry\", \"F-\"))\n", + "students.append(Student(\"leela\", \"A\"))\n", + "students.append(Student(\"zoidberg\", \"F\"))\n", + "students.append(Student(\"hubert\", \"C+\"))\n", + "students.append(Student(\"bender\", \"B\"))\n", + "students.append(Student(\"calculon\", \"C\"))\n", + "students.append(Student(\"amy\", \"A\"))\n", + "students.append(Student(\"hermes\", \"A\"))\n", + "students.append(Student(\"scruffy\", \"D\"))\n", + "students.append(Student(\"flexo\", \"F\"))\n", + "students.append(Student(\"morbo\", \"D\"))\n", + "students.append(Student(\"hypnotoad\", \"A+\"))\n", + "students.append(Student(\"zapp\", \"Q\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + "\n", + "Loop over the students in the `students` list and print out the name and grade of each student, one per line.\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use list comprehensions with our list of objects. For example, let's find all the students who have A's" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['leela', 'amy', 'hermes', 'hypnotoad']" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "As = [q.name for q in students if q.grade.startswith(\"A\")]\n", + "As" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Playing Cards" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a more complicated class that represents a playing card. Notice that we are using unicode to represent the suits." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "class Card:\n", + " \n", + " def __init__(self, suit=1, rank=2):\n", + " if suit < 1 or suit > 4:\n", + " print(\"invalid suit, setting to 1\")\n", + " suit = 1\n", + " \n", + " self.suit = suit\n", + " self.rank = rank\n", + " \n", + " def value(self):\n", + " \"\"\" we want things order primarily by rank then suit \"\"\"\n", + " return self.suit + (self.rank-1)*14\n", + " \n", + " # we include this to allow for comparisons with < and > between cards \n", + " def __lt__(self, other):\n", + " return self.value() < other.value()\n", + "\n", + " def __eq__(self, other):\n", + " return self.rank == other.rank and self.suit == other.suit\n", + " \n", + " def __repr__(self):\n", + " return self.__str__()\n", + " \n", + " def __str__(self):\n", + " suits = [u\"\\u2660\", # spade\n", + " u\"\\u2665\", # heart\n", + " u\"\\u2666\", # diamond\n", + " u\"\\u2663\"] # club\n", + " \n", + " r = str(self.rank)\n", + " if self.rank == 11:\n", + " r = \"J\"\n", + " elif self.rank == 12:\n", + " r = \"Q\"\n", + " elif self.rank == 13:\n", + " r = \"K\"\n", + " elif self.rank == 14:\n", + " r = \"A\"\n", + " \n", + " return r +':'+suits[self.suit-1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can create a card easily." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "c1 = Card()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can pass arguments to `__init__` in when we setup the class:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "c2 = Card(suit=2, rank=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once we have our object, we can access any of the functions in the class using the `dot` operator" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c2.value()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "invalid suit, setting to 1\n" + ] + } + ], + "source": [ + "c3 = Card(suit=0, rank=4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `__str__` method converts the object into a string that can be printed." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2:♠\n", + "2:♥\n" + ] + } + ], + "source": [ + "print(c1)\n", + "print(c2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "the value method assigns a value to the object that can be used in comparisons, and the `__lt__` method is what does the actual comparing" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "False\n", + "True\n" + ] + } + ], + "source": [ + "print(c1 > c2)\n", + "print(c1 < c2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that not every operator is defined for our class, so, for instance, we cannot add two cards together:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "ename": "TypeError", + "evalue": "unsupported operand type(s) for +: 'Card' and 'Card'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[12], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mc1\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m+\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mc2\u001b[49m\n", + "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for +: 'Card' and 'Card'" + ] + } + ], + "source": [ + "c1 + c2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + "\n", + " * Create a \"hand\" corresponding to a straight (5 cards of any suite, but in sequence of rank)\n", + " * Create another hand corresponding to a flush (5 cards all of the same suit, of any rank)\n", + " * Finally create a hand with one of the cards duplicated—this should not be allowed in a standard deck of cards. How would you check for this?\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Operators" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can define operations like `+` and `-` that work on our objects. Here's a simple example of currency—we keep track of the country and the amount" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "class Currency:\n", + " \"\"\" a simple class to hold foreign currency \"\"\"\n", + " \n", + " def __init__(self, amount, country=\"US\"):\n", + " self.amount = amount\n", + " self.country = country\n", + " \n", + " def __add__(self, other):\n", + " return Currency(self.amount + other.amount, country=self.country)\n", + "\n", + " def __sub__(self, other):\n", + " return Currency(self.amount - other.amount, country=self.country)\n", + "\n", + " def __str__(self):\n", + " return f\"{self.amount} {self.country}\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now create some monetary amounts for different countries" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "d1 = Currency(10, \"US\")\n", + "d2 = Currency(15, \"US\")\n", + "print(d2 - d1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise \n", + "\n", + "As written, our Currency class has a bug—it does not check whether the amounts are in the same country before adding. Modify the `__add__` method to first check if the countries are the same. If they are, return the new `Currency` object with the sum, otherwise, return `None`.\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Vectors Example\n", + "\n", + "Here we write a class to represent 2-d vectors. Vectors have a direction and a magnitude. We can represent them as a pair of numbers, representing the x and y lengths. We'll use a tuple internally for this\n", + "\n", + "We want our class to do all the basic operations we do with vectors: add them, multiply by a scalar, cross product, dot product, return the magnitude, etc.\n", + "\n", + "We'll use the math module to provide some basic functions we might need (like sqrt)\n", + "\n", + "This example will show us how to overload the standard operations in python. Here's a list of the builtin methods:\n", + "\n", + "https://docs.python.org/3/reference/datamodel.html\n", + "\n", + "To make it really clear what's being called when, I've added prints in each of the functions" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import math" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "class Vector:\n", + " \"\"\" a general two-dimensional vector \"\"\"\n", + " \n", + " def __init__(self, x, y):\n", + " print(\"in __init__\")\n", + " self.x = x\n", + " self.y = y\n", + " \n", + " def __str__(self):\n", + " print(\"in __str__\") \n", + " return f\"({self.x} î + {self.y} ĵ)\"\n", + " \n", + " def __repr__(self):\n", + " print(\"in __repr__\") \n", + " return f\"Vector({self.x}, {self.y})\"\n", + "\n", + " def __add__(self, other):\n", + " print(\"in __add__\") \n", + " if isinstance(other, Vector):\n", + " return Vector(self.x + other.x, self.y + other.y)\n", + " else:\n", + " # it doesn't make sense to add anything but two vectors\n", + " print(f\"we don't know how to add a {type(other)} to a Vector\")\n", + " raise NotImplementedError\n", + "\n", + " def __sub__(self, other):\n", + " print(\"in __sub__\") \n", + " if isinstance(other, Vector):\n", + " return Vector(self.x - other.x, self.y - other.y)\n", + " else:\n", + " # it doesn't make sense to add anything but two vectors\n", + " print(f\"we don't know how to add a {type(other)} to a Vector\")\n", + " raise NotImplementedError\n", + "\n", + " def __mul__(self, other):\n", + " print(\"in __mul__\") \n", + " if isinstance(other, int) or isinstance(other, float):\n", + " # scalar multiplication changes the magnitude\n", + " return Vector(other*self.x, other*self.y)\n", + " else:\n", + " print(\"we don't know how to multiply two Vectors\")\n", + " raise NotImplementedError\n", + "\n", + " def __matmul__(self, other):\n", + " print(\"in __matmul__\")\n", + " # a dot product\n", + " if isinstance(other, Vector):\n", + " return self.x*other.x + self.y*other.y\n", + " else:\n", + " print(\"matrix multiplication not defined\")\n", + " raise NotImplementedError\n", + "\n", + " def __rmul__(self, other):\n", + " print(\"in __rmul__\") \n", + " return self.__mul__(other)\n", + "\n", + " def __truediv__(self, other):\n", + " print(\"in __truediv__\") \n", + " # we only know how to multiply by a scalar\n", + " if isinstance(other, int) or isinstance(other, float):\n", + " return Vector(self.x/other, self.y/other)\n", + "\n", + " def __abs__(self):\n", + " print(\"in __abs__\") \n", + " return math.sqrt(self.x**2 + self.y**2)\n", + "\n", + " def __neg__(self):\n", + " print(\"in __neg__\") \n", + " return Vector(-self.x, -self.y)\n", + "\n", + " def cross(self, other):\n", + " # a vector cross product -- we return the magnitude, since it will\n", + " # be in the z-direction, but we are only 2-d \n", + " return abs(self.x*other.y - self.y*other.x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a basic class that provides two methods `__str__` and `__repr__` to show a representation of it. There was some discussion of this on slack. These two functions provide a readable version of our object.\n", + "\n", + "The convection is what `__str__` is human readable while `__repr__` should be a form that can be used to recreate the object (e.g., via `eval()`). See:\n", + "\n", + "http://stackoverflow.com/questions/1436703/difference-between-str-and-repr-in-python" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v = Vector(1,2)\n", + "v" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(v)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vectors have a length, and we'll use the `abs()` builtin to provide the magnitude. For a vector:\n", + "\n", + "$$\\vec{v} = \\alpha \\hat{i} + \\beta \\hat{j}$$\n", + "\n", + "we have\n", + "\n", + "$$|\\vec{v}| = \\sqrt{\\alpha^2 + \\beta^2}$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "abs(v)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at mathematical operations on vectors now. We want to be able to add and subtract two vectors as well as multiply and divide by a scalar." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u = Vector(3,5)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "w = u + v\n", + "print(w)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u - v" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It doesn't make sense to add a scalar to a vector, so we didn't implement this -- what happens?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u + 2.0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now multiplication. It makes sense to multiply by a scalar, but there are multiple ways to define multiplication of two vectors. \n", + "\n", + "Note that python provides both a `__mul__` and a `__rmul__` function to define what happens when we multiply a vector by a quantity and what happens when we multiply something else by a vector." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u*2.0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "2.0*u" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and division: `__truediv__` is the python 3 way of division `/`, while `__floordiv__` is the old python 2 way, also enabled via `//`.\n", + "\n", + "Dividing a scalar by a vector doesn't make sense:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u/5.0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "5.0/u" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Python 3.5 introduced a new matrix multiplication operator, `@` -- we'll use this to implement a dot product between two vectors:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u @ v" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a cross product, we don't have an obvious operator, so we'll use a function. For 2-d vectors, this will result in a scalar" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u.cross(v)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, negation is a separate operation:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "-u" + ] + } + ], + "metadata": { + "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": "3.12.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/01-python/w4-python-exercises.ipynb b/content/01-python/w4-python-exercises.ipynb new file mode 100644 index 00000000..9308beb6 --- /dev/null +++ b/content/01-python/w4-python-exercises.ipynb @@ -0,0 +1,426 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Practicing Classes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(w4-exercise-1)=\n", + "## Exercise 1 (shopping cart)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's write a simple shopping cart class -- this will hold items that you intend to purchase as well as the amount, etc. And allow you to add / remove items, get a subtotal, etc.\n", + "\n", + "We'll use two classes: `Item` will be a single item and `ShoppingCart` will be the collection of items you wish to purchase.\n", + "\n", + "First, our store needs an inventory -- here's what we have for sale:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "INVENTORY_TEXT = \"\"\"\n", + "apple, 0.60\n", + "banana, 0.20\n", + "grapefruit, 0.75\n", + "grapes, 1.99\n", + "kiwi, 0.50\n", + "lemon, 0.20\n", + "lime, 0.25\n", + "mango, 1.50\n", + "papaya, 2.95\n", + "pineapple, 3.50\n", + "blueberries, 1.99\n", + "blackberries, 2.50\n", + "peach, 0.50\n", + "plum, 0.33\n", + "clementine, 0.25\n", + "cantaloupe, 3.25\n", + "pear, 1.25\n", + "quince, 0.45\n", + "orange, 0.60\n", + "\"\"\"\n", + "\n", + "# this will be a global -- convention is all caps\n", + "INVENTORY = {}\n", + "for line in INVENTORY_TEXT.splitlines():\n", + " if line.strip() == \"\":\n", + " continue\n", + " item, price = line.split(\",\")\n", + " INVENTORY[item] = float(price)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "INVENTORY" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### `Item` " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the start of an item class -- we want it to hold the name and quantity. \n", + "\n", + "You should have the following features:\n", + "\n", + "* the name should be something in our inventory\n", + "\n", + "* Our shopping cart will include a list of all the items we want to buy, so we want to be able to check for duplicates. Implement the equal test, `==`, using `__eq__`\n", + "\n", + "* we'll want to consolidate dupes, so implement the `+` operator, using `__add__` so we can add items together in our shopping cart. Note, add should raise a ValueError if you try to add two `Items` that don't have the same name.\n", + "\n", + "Here's a start:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "class Item:\n", + " \"\"\" an item to buy \"\"\"\n", + " \n", + " def __init__(self, name, quantity=1):\n", + " \"\"\"keep track of an item that is in our inventory\"\"\"\n", + " if name not in INVENTORY:\n", + " raise ValueError(\"invalid item name\")\n", + " self.name = name\n", + " self.quantity = quantity\n", + " \n", + " def __repr__(self):\n", + " return f\"{self.name}: {self.quantity}\"\n", + " \n", + " def __eq__(self, other):\n", + " \"\"\"check if the items have the same name\"\"\"\n", + " return self.name == other.name\n", + " \n", + " def __add__(self, other):\n", + " \"\"\"add two items together if they are the same type\"\"\"\n", + " if self.name == other.name:\n", + " return Item(self.name, self.quantity + other.quantity)\n", + " else:\n", + " raise ValueError(\"names don't match\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are some tests your code should pass:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = Item(\"apple\", 10)\n", + "b = Item(\"banana\", 20)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "c = Item(\"apple\", 20)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "# won't work\n", + "a + b" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# will work\n", + "a += c\n", + "print(a)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "d = Item(\"dog\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# should be False\n", + "a == b" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# should be True -- they have the same name\n", + "a == c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How do they behave in a list?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "items = []\n", + "items.append(a)\n", + "items.append(b)\n", + "items" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# should be True -- they have the same name\n", + "c in items" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### `ShoppingCart`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we want to create a shopping cart. The main thing it will do is hold a list of items." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "class ShoppingCart:\n", + " \n", + " def __init__(self):\n", + " # the list of items we control\n", + " self.items = []\n", + " \n", + " def subtotal(self):\n", + " \"\"\" return a subtotal of our items \"\"\"\n", + " pass\n", + "\n", + " def add(self, name, quantity):\n", + " \"\"\" add an item to our cart -- the an item of the same name already\n", + " exists, then increment the quantity. Otherwise, add a new item\n", + " to the cart with the desired quantity.\"\"\"\n", + " pass\n", + " \n", + " def remove(self, name):\n", + " \"\"\" remove all of item name from the cart \"\"\"\n", + " pass\n", + " \n", + " def report(self):\n", + " \"\"\" print a summary of the cart \"\"\"\n", + " for item in self.items:\n", + " print(f\"{item.name} : {item.quantity}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are some tests" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sc = ShoppingCart()\n", + "sc.add(\"orange\", 19)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sc.add(\"apple\", 2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sc.report()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sc.add(\"apple\", 9)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# apple should only be listed once in the report, with a quantity of 11\n", + "sc.report()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sc.subtotal()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sc.remove(\"apple\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# apple should no longer be listed\n", + "sc.report()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 2: Poker Odds" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Use the deck of cards class from the notebook we worked through outside of class to write a _Monte Carlo_ code that plays a lot of hands of straight poker (like 100,000). Count how many of these hands has a particular poker hand (like 3-of-a-kind). The ratio of # of hands with 3-of-a-kind to total hands is an approximation to the odds of getting a 3-of-a-kind in poker.\n", + "\n", + "You'll want to copy-paste those classes into a `.py` file to allow you to import and reuse them here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 3: Tic-Tac-Toe\n", + "\n", + "Revisit the tic-tac-toe game you developed in the functions exercises but now write it as a class with methods to do each of the main steps. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/01-python/w4-python-modules.ipynb b/content/01-python/w4-python-modules.ipynb new file mode 100644 index 00000000..187eb7cc --- /dev/null +++ b/content/01-python/w4-python-modules.ipynb @@ -0,0 +1,117 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modules" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we import our own module called `myprofile` (we have it in the same directory as this notebook)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import myprofile" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have a docstring at the top -- the comments there are what appear when we ask for help" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "help(myprofile)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This module simply provides a way to time routines (python and ipython have built-in methods for this too)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "t = myprofile.Timer(\"main loop\")\n", + "t.begin()\n", + "\n", + "sum = 0.0\n", + "for n in range(1000):\n", + " sum += n**2\n", + "\n", + "\n", + "t.end()\n", + "myprofile.time_report()\n", + "\n", + "print(sum)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the file `myprofile.py`, you will see a block of code under\n", + "\n", + "```\n", + "if __name__ == \"__main__\":\n", + "```\n", + "\n", + "That code is executed if the file is run directly, either from the commandline as:\n", + "\n", + "`python myprofile.py`\n", + "\n", + "for through the `%run` magic" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%run myprofile" + ] + } + ], + "metadata": { + "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": "3.10.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/01-python/w5-python-more-examples.ipynb b/content/01-python/w5-python-more-examples.ipynb new file mode 100644 index 00000000..82a82920 --- /dev/null +++ b/content/01-python/w5-python-more-examples.ipynb @@ -0,0 +1,177 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercises" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 1: Rock-Paper-Scissors\n", + "\n", + "Implement a set of games of rock-paper-scissors against the computer. \n", + "\n", + " * Ask for input from the user (\"rock\", \"paper\", or \"scissors\") and the randomly select one of these for the computer's play.\n", + " * Announce who won.\n", + " * Keep playing until a player says that they no longer want to play.\n", + " * When all games are done, print out how many games were won by the player and by the computer " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 2: Pascal's triangle\n", + "\n", + "Pascal's triangle is created such that each layer has 1 more element than the previous, with `1`s on the side and in the interior, the numbers are the sum of the two above it, e.g.,:\n", + "```\n", + " 1\n", + " 1 1\n", + " 1 2 1\n", + " 1 3 3 1\n", + " 1 4 6 4 1\n", + " 1 5 10 10 5 1\n", + "```\n", + "\n", + "Write a function to return the first `n` rows of Pascal's triangle. The return should be a list of length `n`, with each element itself a list containing the numbers for that row.\n", + "\n", + " If you want to add complexity, write a function to print out Pascal's triangle with proper formatting, so the numbers in each row are centered between the ones in the row above" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 3: Panagrams\n", + "\n", + "A _panagram_ is a sentence that includes all 26 letters of the alphabet, e.g., \"_The quick brown fox jumps over the lazy dog_.\"\n", + "\n", + "Write a function that takes as an argument a sentence and returns `True` or `False`, indicating whether the sentence is a panagram." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 4: Math practice\n", + "\n", + "We want to make a simple table of trigonometric functions for different angles. Write a code that outputs in columns, the following data:\n", + "```\n", + "angle (degrees) angle (radians) sin(angle) cos(angle) sin(angle)**2 + cos(angle)**2\n", + "```\n", + "\n", + "For all angles spaced 30 degrees apart in the range 0 to 360 degrees.\n", + "\n", + "Keep in mind that the trig functions expect the input in radians." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 5: Calendar events\n", + "\n", + "We want to keep a schedule of events. We will do this by creating a class called `Day`. It is sketched out below. A `Day` holds a list of events and has methods that allow you to add an delete events. Our events will be instances of a class `Event`, which holds the time, location, and description of the event.\n", + "\n", + "Finally, we can keep track of a list of all the `Day`s for which we have events to make our schedule.\n", + "\n", + "Fill in these classes and write some code to demonstrate their use:\n", + "\n", + " * Create a full week of days in your calendar\n", + " * Add an event every day at noon called \"lunch\"\n", + " * Randomly add some other events to fill out your calendar\n", + " * Write some code that tells you the start time of your first meeting and the end time of your last meeting (this is the length of your work day)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "class Day:\n", + " \"\"\"a single day keeping track of the events scheduled\"\"\"\n", + " def __init__(month, day, year):\n", + " # store the month, day, and year as data in the class\n", + " \n", + " # keep track of the events\n", + " self.events = []\n", + " \n", + " def add_event(name, time=None, location=None):\n", + " pass\n", + " \n", + " def delete_event(name):\n", + " pass\n", + " \n", + " \n", + "class Event:\n", + " \"\"\"a single event in our calendar\"\"\"\n", + " def __init__(name, time=9, location=None, duration=1):\n", + " self.name = name\n", + " self.time = time\n", + " self.location = location\n", + " self.duration = duration" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.9.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/02-numpy/numpy-advanced.ipynb b/content/02-numpy/numpy-advanced.ipynb new file mode 100644 index 00000000..bf09cdb1 --- /dev/null +++ b/content/02-numpy/numpy-advanced.ipynb @@ -0,0 +1,941 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# NumPy Advanced Operations" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Copying Arrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{important}\n", + "Simply using `=` does not make a copy, but much like with lists, you will just have multiple names pointing to the same ndarray object\n", + "\n", + "Therefore, we need to understand if two arrays, `A` and `B` point to:\n", + "* the same array, including shape and data/memory space\n", + "* the same data/memory space, but perhaps different shapes (a _view_)\n", + "* a separate copy of the data (i.e. stored completely separately in memory)\n", + "\n", + "All of these are possible.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All of these are possible:\n", + "\n", + "* `B = A`\n", + " \n", + " this is _assignment_. No copy is made. `A` and `B` point to the same data in memory and share the same shape, etc. They are just two different labels for the same object in memory\n", + " \n", + "\n", + "* `B = A[:]`\n", + "\n", + " this is a _view_ or _shallow copy_. The shape info for A and B are stored independently, but both point to the same memory location for data\n", + " \n", + " \n", + "* `B = A.copy()`\n", + "\n", + " this is a _deep_ copy. A completely separate object will be created in memory, with a completely separate location in memory.\n", + " \n", + "Let's look at examples" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(10)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is assignment—we can just use the `is` operator to test for equality" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b = a\n", + "b is a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since `b` and `a` are the same, changes to the shape of one are reflected in the other—no copy is made." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 1 2 3 4]\n", + " [5 6 7 8 9]]\n" + ] + }, + { + "data": { + "text/plain": [ + "(2, 5)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b.shape = (2, 5)\n", + "print(b)\n", + "a.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b is a" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 1, 2, 3, 4],\n", + " [5, 6, 7, 8, 9]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "a shallow copy creates a new *view* into the array—the _data_ is the same, but the array properties can be different" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3]\n", + " [ 4 5 6 7]\n", + " [ 8 9 10 11]]\n", + "[ 0 1 2 3 4 5 6 7 8 9 10 11]\n" + ] + } + ], + "source": [ + "a = np.arange(12)\n", + "c = a[:]\n", + "a.shape = (3,4)\n", + "\n", + "print(a)\n", + "print(c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "since the underlying data is the same memory, changing an element of one is reflected in the other" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, -1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c[1] = -1\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even slices into an array are just views, still pointing to the same memory" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([3, 4, 5, 6, 7])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d = c[3:8]\n", + "d" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "d[:] = 0 " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 -1 2 0]\n", + " [ 0 0 0 0]\n", + " [ 8 9 10 11]]\n", + "[ 0 -1 2 0 0 0 0 0 8 9 10 11]\n", + "[0 0 0 0 0]\n" + ] + } + ], + "source": [ + "print(a)\n", + "print(c)\n", + "print(d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are lots of ways to inquire if two arrays are the same, views, own their own data, etc" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "False\n", + "True\n", + "False\n", + "True\n" + ] + } + ], + "source": [ + "print(c is a)\n", + "print(c.base is a)\n", + "print(c.flags.owndata)\n", + "print(a.flags.owndata)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "to make a copy of the data of the array that you can deal with independently of the original, you need a _deep copy_" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 -1 2 0]\n", + " [ 0 0 0 0]\n", + " [ 8 9 10 11]]\n", + "[[0 0 0 0]\n", + " [0 0 0 0]\n", + " [0 0 0 0]]\n" + ] + } + ], + "source": [ + "d = a.copy()\n", + "d[:,:] = 0.0\n", + "\n", + "print(a)\n", + "print(d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Boolean Indexing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are lots of fun ways to index arrays to access only those elements that meet a certain condition" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we set all the elements in the array that are > 4 to zero" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 1, 2, 3],\n", + " [4, 0, 0, 0],\n", + " [0, 0, 0, 0]])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a > 4] = 0\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and now, all the zeros to -1" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-1, 1, 2, 3],\n", + " [ 4, -1, -1, -1],\n", + " [-1, -1, -1, -1]])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a == 0] = -1\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ True, False, False, False],\n", + " [False, True, True, True],\n", + " [ True, True, True, True]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a == -1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "if we have 2 tests, we need to use `logical_and()` or `logical_or()`" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[100, 1, 2, 3],\n", + " [100, 100, 100, 100],\n", + " [100, 100, 10, 11]])" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[np.logical_or(a == 0, np.logical_and(a > 3, a <= 9))] = 100.0\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our test that we index the array with returns a boolean array of the same shape:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ True, False, False, False],\n", + " [ True, True, True, True],\n", + " [ True, True, True, True]])" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a > 4" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Avoiding Loops" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In general, you want to avoid loops over elements on an array.\n", + "\n", + "Here, let's create 1-d x and y coordinates and then try to fill some larger array" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(128,)\n", + "(256,)\n" + ] + } + ], + "source": [ + "M = 128\n", + "N = 256\n", + "xmin = ymin = 0.0\n", + "xmax = ymax = 1.0\n", + "\n", + "x = np.linspace(xmin, xmax, M, endpoint=False)\n", + "y = np.linspace(ymin, ymax, N, endpoint=False)\n", + "\n", + "print(x.shape)\n", + "print(y.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we'll time out code" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "import time" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "time elapsed: 0.05113625526428223 s\n" + ] + } + ], + "source": [ + "t0 = time.time()\n", + "\n", + "g = np.zeros((M, N))\n", + "\n", + "for j in range(N):\n", + " for i in range(M):\n", + "\n", + " g[i,j] = np.sin(2.0*np.pi*x[i]*y[j])\n", + " \n", + "t1 = time.time()\n", + "print(f\"time elapsed: {t1-t0} s\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's instead do this using all array syntax. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{tip}\n", + "First will extend our 1-d coordinate arrays to be 2-d. \n", + "NumPy has a function for this (`meshgrid()`)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at how `meshgrid()` works first" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 0, 0],\n", + " [1, 1, 1],\n", + " [2, 2, 2],\n", + " [3, 3, 3]])" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x2d, y2d = np.meshgrid([0, 1, 2, 3], [10, 20, 30], indexing=\"ij\")\n", + "x2d" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[10, 20, 30],\n", + " [10, 20, 30],\n", + " [10, 20, 30],\n", + " [10, 20, 30]])" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y2d" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that this creates 2 two-dimensional arrays, one with the x-values changing across rows and one with y-values changing across columns. This means we can index all points\n", + "(`x[i]`, `y[j]`) through the pair `x2d`, `y2d`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's do our same example this method." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "time elapsed: 0.0024487972259521484 s\n" + ] + } + ], + "source": [ + "t0 = time.time()\n", + "x2d, y2d = np.meshgrid(x, y, indexing=\"ij\")\n", + "g2 = np.sin(2.0*np.pi*x2d*y2d)\n", + "t1 = time.time()\n", + "print(f\"time elapsed: {t1-t0} s\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A final check to make sure they give the same answer" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0\n" + ] + } + ], + "source": [ + "print(np.max(np.abs(g2-g)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Numerical differencing on NumPy arrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we want to construct a derivative, \n", + "\n", + "$$\n", + "\\frac{d f}{dx}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [], + "source": [ + "x = np.linspace(0, 2*np.pi, 25)\n", + "f = np.sin(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We want to do this without loops—we'll use views into arrays offset from one another. Recall from calculus that a derivative is approximately:\n", + "\n", + "$$\n", + "\\frac{df}{dx} = \\frac{f(x+h) - f(x)}{h}\n", + "$$\n", + "\n", + "Here, we'll take $h$ to be a single adjacent element" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [], + "source": [ + "dx = x[1] - x[0]\n", + "dfdx = (f[1:] - f[:-1])/dx" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.98861593, 0.92124339, 0.79108963, 0.60702442, 0.38159151,\n", + " 0.13015376, -0.13015376, -0.38159151, -0.60702442, -0.79108963,\n", + " -0.92124339, -0.98861593, -0.98861593, -0.92124339, -0.79108963,\n", + " -0.60702442, -0.38159151, -0.13015376, 0.13015376, 0.38159151,\n", + " 0.60702442, 0.79108963, 0.92124339, 0.98861593])" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dfdx" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9886159294653692\n", + "0.9212433876373748\n", + "0.7910896313685742\n", + "0.6070244240594342\n", + "0.38159150540593506\n", + "0.13015375626880096\n", + "-0.13015375626880055\n", + "-0.38159150540593506\n", + "-0.6070244240594342\n", + "-0.7910896313685731\n", + "-0.9212433876373752\n", + "-0.9886159294653699\n", + "-0.9886159294653681\n", + "-0.9212433876373755\n", + "-0.7910896313685738\n", + "-0.6070244240594346\n", + "-0.38159150540593545\n", + "-0.1301537562688014\n", + "0.13015375626880013\n", + "0.3815915054059342\n", + "0.607024424059435\n", + "0.7910896313685731\n", + "0.9212433876373736\n", + "0.9886159294653716\n" + ] + } + ], + "source": [ + "for i in range(len(x)-1):\n", + " print((f[i+1] - f[i]) / dx)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/02-numpy/numpy-basics.ipynb b/content/02-numpy/numpy-basics.ipynb new file mode 100644 index 00000000..0658305f --- /dev/null +++ b/content/02-numpy/numpy-basics.ipynb @@ -0,0 +1,788 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# NumPy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook is based on the SciPy NumPy tutorial" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{note}\n", + " \n", + "Note that the traditional way to import numpy is to rename it `np`. This saves on typing and makes your code a little more compact.\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "NumPy provides a multidimensional array class as well as a _large_ number of functions that operate on arrays.\n", + "\n", + "NumPy arrays allow you to write fast (optimized) code that works on arrays of data. To do this, there are some restrictions on arrays:\n", + "\n", + "* all elements are of the same data type (e.g. float)\n", + "* the size of the array is fixed in memory, and specified when you create the array (e.g., you cannot grow the array like you do with lists)\n", + "\n", + "The nice part is that arithmetic operations work on entire arrays—this means that you can avoid writing loops in python (which tend to be slow). Instead the \"looping\" is done in the underlying compiled code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array Creation and Properties" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a lot of ways to create arrays. Let's look at a few\n", + "\n", + "Here we create an array using `arange` and then change its shape to be 3 rows and 5 columns. Note the _row-major ordering_—you'll see that the rows are together in the inner `[]` (more on this in a bit)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.arange(15)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.arange(15).reshape(3,5)\n", + "\n", + "print(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "an array is an object of the `ndarray` class, and it has methods that know how to work on the array data. Here, `.reshape()` is one of the many methods." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A NumPy array has a lot of meta-data associated with it describing its shape, datatype, etc." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(a.ndim)\n", + "print(a.shape)\n", + "print(a.size)\n", + "print(a.dtype)\n", + "print(a.itemsize)\n", + "print(type(a))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#help(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can also create an array from a list" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b = np.array( [1.0, 2.0, 3.0, 4.0] )\n", + "print(b)\n", + "print(b.dtype)\n", + "print(type(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can create a multi-dimensional array of a specified size initialized all to 0 easily, using the `zeros()` function." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b = np.zeros((10,8))\n", + "b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is also an analogous `ones()` and `empty()` array routine. Note that here we can explicitly set the datatype for the array in this function if we wish. \n", + "\n", + "Unlike lists in python, all of the elements of a numpy array are of the same datatype" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "c = np.eye(10, dtype=np.float64)\n", + "c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`linspace` creates an array with evenly space numbers. The `endpoint` optional argument specifies whether the upper range is in the array or not" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "d = np.linspace(0, 1, 10, endpoint=False)\n", + "print(d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + "\n", + "Analogous to `linspace()`, there is a `logspace()` function that creates an array with elements equally spaced in log. Use `help(np.logspace)` to see the arguments, and create an array with 10 elements from $10^{-6}$ to $10^3$.\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array Operations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "most operations (`+`, `-`, `*`, `/`) will work on an entire array at once, element-by-element.\n", + "\n", + "Note that that the multiplication operator is not a matrix multiply, but `@` will do matrix multiplication." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's create a simply array to start with" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "print(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Multiplication by a scalar multiplies every element" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a*2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "adding two arrays adds element-by-element" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a + a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "multiplying two arrays multiplies element-by-element" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "a*a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + "\n", + "What do you think `1./a` will do? Try it and see\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can think of our 2-d array as a 3 x 4 matrix (3 rows, 4 columns). We can take the transpose to geta 4 x 3 matrix, and then we can do a matrix multiplication" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can do some basic linear algebra operations on arrays. The operator `@` is a matrix multiplication / dot-product operator" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b = a.transpose()\n", + "b" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a @ b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can sum the elements of an array:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a.sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + "\n", + "`sum()` takes an optional argument, `axis=N`, where `N` is the axis to sum over. Sum the elements of `a` across rows to create an array with just the sum along each column of `a`.\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also easily get the extrema" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(a.min(), a.max())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## universal functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "universal functions work element-by-element. Let's create a new array scaled by `pi / 12`" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b = a*np.pi/12.0\n", + "print(b)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "c = np.cos(b)\n", + "print(c)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "d = b + c " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + "\n", + "We will often want to write our own function that operates on an array and returns a new array. We can do this just like we did with functions previously—the key is to use the methods from the `np` module to do any operations, since they work on, and return, arrays.\n", + "\n", + "Write a simple function that returns $\\sin(2\\pi x)$ for an input array `x`. Then test it \n", + "by passing in an array `x` that you create via `linspace()`\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Slicing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "slicing works very similarly to how we saw with strings. Remember, python uses 0-based indexing\n", + "\n", + "Consider the following array:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.arange(9)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now look at accessing a single element vs. a range (using slicing)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Giving a single (0-based) index just references a single value" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a[2]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we do a range, like `a[2:5]`, then we get the elements starting at index 2 and up to, *but not including* index 5.\n", + "\n", + "That is, slicing uses the interval: [begin, end)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a[2:5]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a[2:4]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `:` can be used to specify all of the elements in that dimension" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a[:]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multidimensional Arrays\n", + "\n", + "Multidimensional arrays are stored in a contiguous space in memory -- this means that the columns / rows need to be unraveled (flattened) so that it can be thought of as a single one-dimensional array. Different programming languages do this via different conventions:\n", + "\n", + "![](row_column_major.png)\n", + "\n", + "Storage order:\n", + "\n", + "* Python/C use *row-major* storage: rows are stored one after the other\n", + "* Fortran/matlab use *column-major* storage: columns are stored one after another\n", + "\n", + "The ordering matters when \n", + "\n", + "* passing arrays between languages (we'll talk about this later this semester)\n", + "* looping over arrays -- you want to access elements that are next to one-another in memory\n", + " * e.g, in Fortran:\n", + " \n", + " ```\n", + " double precision :: A(M,N)\n", + " do j = 1, N\n", + " do i = 1, M\n", + " A(i,j) = …\n", + " enddo\n", + " enddo\n", + " ```\n", + " \n", + " * in C\n", + " \n", + " ```\n", + " double A[M][N];\n", + " for (i = 0; i < M; i++) {\n", + " for (j = 0; j < N; j++) {\n", + " A[i][j] = …\n", + " }\n", + " } \n", + " ```\n", + " \n", + "\n", + "In python, using NumPy, we'll try to avoid explicit loops over elements as much as possible\n", + "\n", + "Let's look at multidimensional arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.arange(15).reshape(3,5)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the output of `a` shows the row-major storage. The rows are grouped together in the inner `[...]`\n", + "\n", + "Giving a single index (0-based) for each dimension just references a single value in the array" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a[1,1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Doing slices will access a range of elements. Think of the start and stop in the slice as referencing the left-edge of the slots in the array." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a[0:2,0:2]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Access a specific column" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a[:,1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes we want a one-dimensional view into the array -- here we see the memory layout (row-major) more explicitly" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a.flatten()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can also iterate -- this is done over the first axis (rows)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "for row in a:\n", + " print(row)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or element by element" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "for e in a.flat:\n", + " print(e)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generally speaking, we want to avoid looping over the elements of an array in python—this is slow. Instead we want to write and use functions that operate on the entire array at once." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{admonition} Quick Exercise\n", + "\n", + "Consider the array defined as:\n", + "\n", + "```\n", + "\n", + " q = np.array([[1, 2, 3, 2, 1],\n", + " [2, 4, 4, 4, 2],\n", + " [3, 4, 4, 4, 3],\n", + " [2, 4, 4, 4, 2],\n", + " [1, 2, 3, 2, 1]])\n", + " \n", + "```\n", + "\n", + " * using slice notation, create an array that consists of only the `4`'s in `q` (this will be called a _view_, as we'll see shortly)\n", + " * zero out all of the elements in your view\n", + " * how does `q` change?\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.13.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/02-numpy/numpy-exercises.ipynb b/content/02-numpy/numpy-exercises.ipynb new file mode 100644 index 00000000..1a352e89 --- /dev/null +++ b/content/02-numpy/numpy-exercises.ipynb @@ -0,0 +1,233 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# NumPy exercises" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some of these come from / are inspired from https://github.com/rougier/numpy-100 and http://www.scipy-lectures.org/intro/numpy/exercises.html\n", + "\n", + "You might want to look over these lists as well." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q1\n", + "\n", + "We can use `np.random.random_sample()` to create an array with random values. By default, these will be in the range `[0.0, 1.0)`. You can\n", + "multiple the output and add a scalar to it to get it to be in a different range.\n", + "\n", + "Create a 10 x 10 array initialized with random numbers that lie between 0 and 10.\n", + "\n", + "Then compute the average of the array (there is a numpy function for this, `np.mean()`)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q2\n", + "\n", + "Create the array: \n", + "```\n", + "[[1, 6, 11],\n", + " [2, 7, 12],\n", + " [3, 8, 13],\n", + " [4, 9, 14],\n", + " [5, 10, 15]]\n", + "```\n", + "with out explicitly typing it in.\n", + "\n", + "Now create a new array containing only its 2nd and 4th rows." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q3\n", + "\n", + "Create a 2d array with `1` on the border and `0` on the inside, e.g., like:\n", + "```\n", + "1 1 1 1 1\n", + "1 0 0 0 1\n", + "1 0 0 0 1\n", + "1 1 1 1 1\n", + "```\n", + "\n", + "Do this using array slice notation to let it work for an arbitrary-sized array" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q4\n", + "\n", + " * Create an array with angles in degrees 0, 15, 30, ... 90 (i.e., every 15 degrees up to 90).\n", + "\n", + " * Now create 3 new arrays with the sine, cosine, and tangent of the elements of the first array\n", + " \n", + " * Finally, calculate the inverse sine, inverse cosine, and inverse tangent the arrays above and compare to the original angles" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q5\n", + "\n", + "Given the array:\n", + "```\n", + "x = np.array([1, -1, 2, 5, 8, 4, 10, 12, 3])\n", + "```\n", + "calculate the difference of each element with its neighbor." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q6\n", + "\n", + "Here we will read in columns of numbers from a file and create a histogram, using NumPy routines. Make sure you have the data file\n", + "\"`sample.txt`\" in the same directory as this notebook (you can download it from https://raw.githubusercontent.com/sbu-python-summer/python-tutorial/master/day-3/sample.txt\n", + "\n", + " * Use `np.loadtxt()` to read this file in. \n", + "\n", + " * Next, use `np.histogram()` to create a histogram array. The output returns both the count and an array of edges.\n", + " \n", + " * Finally, loop over the bins and print out the bin center (averaging the left and right edges of the bin) and the count for that bin." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q7\n", + "\n", + "NumPy has a standard deviation function, `np.std()`, but here we'll write our own that works on a 1-d array (vector). The standard\n", + "deviation is a measure of the \"width\" of the distribution of numbers\n", + "in the vector.\n", + "\n", + "Given an array, $a$, and an average $\\bar{a}$, the standard deviation\n", + "is:\n", + "\n", + "$$\n", + "\\sigma = \\left [ \\frac{1}{N} \\sum_{i=1}^N (a_i - \\bar{a})^2 \\right ]^{1/2}\n", + "$$\n", + "\n", + "Write a function to calculate the standard deviation for an input array, `a`:\n", + "\n", + " * First compute the average of the elements in `a` to define $\\bar{a}$\n", + " * Next compute the sum over the squares of $a - \\bar{a}$\n", + " * Then divide the sum by the number of elements in the array\n", + " * Finally take the square root (you can use `np.sqrt()`)\n", + " \n", + "Test your function on a random array, and compare to the built-in `np.std()`" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.12.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/02-numpy/numpy.md b/content/02-numpy/numpy.md new file mode 100644 index 00000000..19ab63c9 --- /dev/null +++ b/content/02-numpy/numpy.md @@ -0,0 +1,3 @@ +# NumPy + +The NumPy library provides a class for n-dimensional arrays of data. diff --git a/lectures/02-numpy/row_column_major.png b/content/02-numpy/row_column_major.png similarity index 100% rename from lectures/02-numpy/row_column_major.png rename to content/02-numpy/row_column_major.png diff --git a/content/02-numpy/sample.txt b/content/02-numpy/sample.txt new file mode 100644 index 00000000..2c311fcd --- /dev/null +++ b/content/02-numpy/sample.txt @@ -0,0 +1,100 @@ +0 -4.756772745910339 +1 6.889533541096673 +2 8.996896092374172 +3 -1.7461017125141964 +4 1.0304402925205614 +5 4.635768431188638 +6 5.177225916739488 +7 15.964690203916664 +8 -12.021098174294892 +9 -18.10087879725122 +10 -25.178886598285644 +11 4.518925348029733 +12 9.043916771177502 +13 -0.5221535906039717 +14 -3.1338886609447583 +15 -6.914714941474996 +16 -6.314263548047582 +17 6.706901891085466 +18 -25.971636440421232 +19 -4.435372425747847 +20 0.4889050161324564 +21 -0.036004810755168606 +22 -4.372545660650671 +23 0.4047031759550273 +24 3.090597990424291 +25 19.306526596830842 +26 6.48611581937894 +27 -10.781128554191731 +28 -12.85791882558559 +29 -1.0278401126239605 +30 -30.58842788782183 +31 -6.517109634143572 +32 -7.489210194855196 +33 -11.105721713012358 +34 4.120721916704712 +35 -3.153239578756935 +36 1.4135041696471733 +37 22.583374665055885 +38 -12.27556599640208 +39 -4.793102896606837 +40 -7.128537547009972 +41 -17.279019221677267 +42 19.655635821341445 +43 -1.2745066768475497 +44 3.738058165511088 +45 10.481959096601695 +46 -12.814187304346124 +47 -22.424530149878166 +48 4.137834007998959 +49 -0.04131996932026964 +50 7.375298054261892 +51 -4.098385522108854 +52 -5.599571617055626 +53 -13.253443154026934 +54 16.290743431455287 +55 10.424184766192798 +56 -4.27251751782754 +57 19.01684691299122 +58 3.15448738602801 +59 -9.704807918052413 +60 -0.0008101176931862717 +61 6.104424953162043 +62 24.47811290783359 +63 14.846618329919092 +64 -2.186378655814549 +65 9.86177633783792 +66 12.724976950604734 +67 4.037245731028271 +68 -0.656843975486256 +69 15.37262575716834 +70 -7.880872346846276 +71 2.54070374695715 +72 -1.022544832116583 +73 20.91034858050119 +74 9.222541985448974 +75 -11.056628565277206 +76 27.93950830400997 +77 -6.032857683782997 +78 18.098345716611153 +79 38.59487842850004 +80 -0.8720942826849941 +81 1.7229720788142675 +82 -4.174088180887814 +83 -8.318962830280652 +84 14.512558782294388 +85 5.630837289759344 +86 13.097667005419458 +87 9.517210836578036 +88 -3.2730322970019206 +89 14.22975371499751 +90 -12.903078745763068 +91 10.69546941555894 +92 -6.12535752853502 +93 -0.0538615350527278 +94 8.344238543768178 +95 12.569544805707704 +96 -1.5730683048208713 +97 9.588349649640545 +98 -17.791062662128468 +99 -4.613995471504272 diff --git a/lectures/02-numpy/slicing.png b/content/02-numpy/slicing.png similarity index 100% rename from lectures/02-numpy/slicing.png rename to content/02-numpy/slicing.png diff --git a/content/03-practices/git-single.md b/content/03-practices/git-single.md new file mode 100644 index 00000000..a82a2436 --- /dev/null +++ b/content/03-practices/git-single.md @@ -0,0 +1,162 @@ +A single-user interaction with git: + +* Make your project + + We'll start by making our project directory and moving into it: + + ``` + $ mkdir myproject + $ cd myproject/ + ``` + +* Now have git track this + + Now we do `git init .` -- this tells git to initialize this + directory under version control + + ``` + $ git init . + ``` + + If we do `ls` at this point, we see nothing. However, there is a + "hidden" directory called `.git/` which we can see by passing `-a` + to `ls`: + + ``` + $ ls -al + $ ls -l .git + ``` + + In that directory are the files that git uses to keep track of + changes and the history. + +* Create a file + + We'll create a file called `README` (use whatever editor you like, + I'll use emacs): + + ``` + $ emacs -nw README + ``` + + Add some descriptive text to the file and save it. At the moment, + git doesn't know about this file -- you can see this via `git + status`: + + ``` + $ git status + ``` + +* Tell git about the file + + Now we need to tell git to start tracking the file. We use + `git add` for this. Then we need to tell git to store the current + state of the file -- we use `git commit` for this: + + ``` + $ git add README + $ git commit README + ``` + + Notice that an editor window pops up -- take the time to give a + descriptive message about the changes. + + If you make more changes to the file, git won't store them until + you commit them. So you'll commit the same file over and over as + it changes, but only add it once. + +* Create another file + + Let's create a python program, `awesome.py` with the line: + + ``` + print("hello") + ``` + + Now add that file and commit it too + + ``` + $ git add awesome.py + $ git commit . + ``` + +* Look at your log + + `git log` will show you all the commits, the message you entered + when you made the commit (that helps you understand what was done). + It will also have a "hash" next to the commit (like + `dbc2916bb609759d54ca7668558bc639bab9b60b`) + + ``` + $ git log + ``` + +* Add to you code + + Edit `awesome.py` and make it a function and have your program call + the function. Now we need to commit this again: + + ``` + $ git commit awesome.py + ``` + + And `git log` will show this commit as separate from the one we made + when we created the file. + +* Go back in time + + Suppose our code is not working anymore, and we know it was in the + past. We can go back to any previous version of the code by using + `checkout` and the hash next to that commit (note: your hashes will + be different than mine). + + ``` + $ git log + $ git checkout dbc2916bb609759d54ca7668558bc639bab9b60b + ``` + + Look at the file, and you'll see it is different. + + If you want to go back to the latest version, you can checkout `master` + -- that's the name of the main "branch" git recognizes. + + ``` + git checkout master + ``` + +* Working with branches + + Suppose we want to do some development that might be invasive and we + don't want to break the working code on "master". We can use a + branch for this -- thing of this as a parallel development that can + track the master branch and merge back and forth with it. We can + work on this new branch until we are happy, and then incorporate our + changes back to `master`. + + Here we'll create a new branch called `development`: + + ``` + $ git checkout -b development + ``` + + Now make some changes to `awesome.py` and commit them. + + ``` + $ emacs -nw awesome.py + $ git commit awesome.py + ``` + + If you go back to `master`, you won't see these changes: + + ``` + $ git checkout master + $ more awesome.py + ``` + + If you are happy with the changes, you can do a merge. While on + `master`, merge `development` into `master` with: + + ``` + $ git merge development + ``` + diff --git a/lectures/03-practices/git.png b/content/03-practices/git.png similarity index 100% rename from lectures/03-practices/git.png rename to content/03-practices/git.png diff --git a/lectures/03-practices/git.txt b/content/03-practices/git.txt similarity index 100% rename from lectures/03-practices/git.txt rename to content/03-practices/git.txt diff --git a/lectures/03-practices/python-style.ipynb b/content/03-practices/python-style.ipynb similarity index 85% rename from lectures/03-practices/python-style.ipynb rename to content/03-practices/python-style.ipynb index ff82e6a8..3eca3af9 100644 --- a/lectures/03-practices/python-style.ipynb +++ b/content/03-practices/python-style.ipynb @@ -18,21 +18,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### code lay-out" + "## code lay-out" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "#### indentation" + "### indentation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Intentation should use 4 spaces per indentation level (and NOT tabs). Python 3 does not allow for a mixture of tabs and spaces. Note that a lot of editors will map the tab key into a sequence of spaces\n", + "Indentation should use 4 spaces per indentation level (and NOT tabs). Python 3 does not allow for a mixture of tabs and spaces. Note that a lot of editors will map the tab key into a sequence of spaces\n", "\n", "Continuation lines should align wrapped elements either vertically inside parentheses, brackets, or braces, or using a hanging indent (with no arguments on the first line)\n", "\n", @@ -65,7 +65,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## line length" + "### line length" ] }, { @@ -78,14 +78,17 @@ "\n", "Comments and docstrings should be limited to 72-characters\n", "\n", - "Implied line continuation is automatic inside paranthesis, brackets" + "Implied line continuation is automatic inside parenthesis, brackets" ] }, { "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": false + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } }, "outputs": [], "source": [] @@ -93,23 +96,23 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3 (ipykernel)", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.10" + "pygments_lexer": "ipython3", + "version": "3.10.2" } }, "nbformat": 4, - "nbformat_minor": 0 + "nbformat_minor": 4 } diff --git a/lectures/04-matplotlib/NOTES b/content/04-matplotlib/NOTES similarity index 100% rename from lectures/04-matplotlib/NOTES rename to content/04-matplotlib/NOTES diff --git a/lectures/04-matplotlib/anatomy1.png b/content/04-matplotlib/anatomy1.png similarity index 100% rename from lectures/04-matplotlib/anatomy1.png rename to content/04-matplotlib/anatomy1.png diff --git a/content/04-matplotlib/ipyvolume-example.ipynb b/content/04-matplotlib/ipyvolume-example.ipynb new file mode 100644 index 00000000..fd588bc9 --- /dev/null +++ b/content/04-matplotlib/ipyvolume-example.ipynb @@ -0,0 +1,310 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import ipyvolume" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "N = 64\n", + "x = np.linspace(0.0, 1.0, N)\n", + "y = np.linspace(0.0, 1.0, N)\n", + "z = np.linspace(0.0, 1.0, N)\n", + "\n", + "x3d, y3d, z3d = np.meshgrid(x, y, z, indexing=\"ij\")\n", + "\n", + "r = np.sqrt((x3d - 0.5)**2 + (y3d - 0.5)**2 + (z3d - 0.5)**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "f = 1.0 + np.sin(x3d*np.pi*5)*np.sin(y3d*np.pi*7)*np.cos(z3d*np.pi*2) * np.exp(-r**2/0.25**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zingale/.local/lib/python3.6/site-packages/ipyvolume/serialize.py:66: RuntimeWarning: invalid value encountered in true_divide\n", + " gradient = gradient / np.sqrt(gradient[0]**2 + gradient[1]**2 + gradient[2]**2)\n" + ] + } + ], + "source": [ + "a = ipyvolume.volshow(f)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "71282540aea047f289ece9c4179a7715", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

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There are others to explore as well (which we'll chat about on slack)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "There are different interfaces for interacting with matplotlib, an interactive, function-driven (state machine) command-set and an object-oriented version. We'll focus on the OO interface.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{tip}\n", + "To enable interactivity in the plots, install the [ipympl package](https://matplotlib.org/ipympl/) and then\n", + "in a cell, run:\n", + "\n", + "```\n", + "%matplotlib widget\n", + "```\n", + "\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Matplotlib concepts\n", + "\n", + "Matplotlib was designed with the following goals (from mpl docs):\n", + "\n", + "* Plots should look great---publication quality (e.g. antialiased)\n", + "* Postscript/PDF output for inclusion with TeX documents\n", + "* Embeddable in a graphical user interface for application development\n", + "* Code should be easy to understand it and extend\n", + "* Making plots should be easy\n", + "\n", + "Matplotlib is mostly for 2-d data, but there are some basic 3-d (surface) interfaces.\n", + "\n", + "Volumetric data requires a different approach" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Gallery\n", + "\n", + "Matplotlib has a great gallery on their webpage -- find something there close to what you are trying to do and use it as a starting point:\n", + "\n", + "https://matplotlib.org/stable/gallery/index.html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Importing\n", + "\n", + "There are several different interfaces for matplotlib (see https://matplotlib.org/3.1.1/faq/index.html)\n", + "\n", + "Basic ideas:\n", + "\n", + "* `matplotlib` is the entire package\n", + "* `matplotlib.pyplot` is a module within matplotlib that provides easy access to the core plotting routines\n", + "* `pylab` combines pyplot and numpy into a single namespace to give a MatLab like interface. You should avoid this—it might be removed in the future.\n", + "\n", + "There are a number of modules that extend its behavior, e.g. `basemap` for plotting on a sphere, `mplot3d` for 3-d surfaces\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Anatomy of a figure\n", + "\n", + "Figures are the highest level object and can include multiple axes\n", + "![](anatomy1.png)\n", + "\n", + "(figure from: http://matplotlib.org/faq/usage_faq.html#parts-of-a-figure )\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Backends\n", + "\n", + "Interactive backends: pygtk, wxpython, tkinter, ...\n", + "\n", + "Hardcopy backends: PNG, PDF, PS, SVG, ...\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Basic plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "x = np.linspace(0.0, 2.0*np.pi, 50)\n", + "y = np.cos(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`plot()` is the most basic command.\n", + "\n", + "We'll use `plt.subplots()` to create a `Figure` and `Axis` object" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.0, 6.283185307179586)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "8286ca027462470cabce2c4cb4998daa", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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", 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\n", + " " + ], + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(x, y)\n", + "ax.set_xlabel(r\"$x$\")\n", + "ax.set_ylabel(r\"$\\cos(x)$\")\n", + "ax.set_xlim(0, 2*np.pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we also see that we can use LaTeX notation for the axes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} Quick Exercise\n", + "We can plot 2 lines on a plot simply by calling plot twice. Make a plot with both `sin(x)` and `cos(x)` drawn\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can use symbols instead of lines pretty easily too—and label them" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "f3f7f95a7f434092af09d81f07d17747", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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eakVaI5x1mnJlXcq6vHevvalsPmNQgAc/Te7DgLcjKargcq+x+Hcze80+bg7ys6lFMEIIO3V6F3xzN1w6D43aQZswqNNAyruoTBJAW1HVcvhhc6DfVOUNdjZOSQJH/wCtBpofV0lPRGuz68R5xi3dUZL8WXt9v9p28vzFCpM/E6kXKIRQRUU9eY9Gwbf/B4W5UM8PxkdA3SrOSzLyV2tkDqC9qOsND/4GXi2UeRVf3wn7fiu933QJWatTM8or2nH8PGO/iCUnv4gbWzXkw1HBFXbPcORLnI46P1IIYeVMBZ5N8/j2/Qrf3KMkfwDdxlSd/IlaJSOA9sS1PkyJhcX94dxB+H4sjPgQclLKzx+0Apd3+DAajUz4aicXC/T0bePN52N7UcdFx21dAmy6vl9Nc+T5kUIIK1Z2Ht/Zf+FQBBgNxfe9AINeVDU8YU4SQHvj5AqPxcCSwcpKqzVPKvutLPmrqMOHSf+2jVgytiduzspopa3X96tp1akXeHn/YyGEqBUDpsGZXXDwz9J9A2fAwOlqRiUqIJeA7ZFWB5OiQFPmv9c/WM2IzJg6fFRW5++eHk1Lkj9RXnXqBT7Ut6VDj5IKIVRy6G84vLb0e52LJH9WShJAe7XxbWXo3ZQEfjcaknarHdUVO3xogLl/HZCCxldQWb1AF52S9H226Sgn0y+qFJ0QwiEl7YYfxpde9pUCz1ZNEkB7VLZm4MwU8GquvAmX3gKZZ1QN7UodPsquYBVVC+/kz+YXBvPtxBv5cFQw3068kW0vhtHBrz5p2fmM/XI753Ly1Q5TCOEIMs/AyntLF3wMmC4Fnq2cJID25vKC0U4u8MhGcPeGgmz4bCDkZ6sWnqxgrVmm+ZF3BDchtLU3Deu6sPyh3jRtUIfj6RcZv3QHOflFaocphLBn+dmw8j7ILu5C1G9qabmxAdMkCbRSkgDam4oKRtfxgomR4OwOuanw40OgVycpkBWslufr4cZXD/WmYV0X9pzJ5NGvd3GpQC89g4UQNU9fpFz2TdmjfMbc+DiEzTI/xpQESoFnq6IxGo3ySXCNsrKy8PT0JDMzEw8PD7XDubLTu2DZrVB0CXpNgFveAU3tLhQo0hvo9Orf5BUaKrzf1OFj8wuDZRHDdfrvVAb3L9nGxQI9bs5as9+5v6cbs0YEOWwtRSFEDTAa4Y9nYecX4FQHxv9hM12obO7z2wJkBNCRNO0Bdy1R0qwdn0PMwloP4YvNx6pM/nDgDh81rWugFw/3awlQ7ndu6hkckZCkUnRCCJsX87GS/KFRPltsJPkTCkkAHU3HETD0dWV77Uuwf02t/dORB1J5K+IAAKN6BeIvHT4sSm8w8uOu0xXeZxr2n71mn1wOFkJcvX2/wdqXle2hbyifLcKmSCFoRxQ6Bc4fU/5y+2EcPLRWGR0sq4b7Bh9JzebJb//FaIT/C2nGnJGdMBiRDh8WdDUrrqXQthCiQhX19z29C36epJxFArpB6ONqRiiukYwAOiKNBobPh4atwVAEy2+DCydK76/hvsEZFwuYsHwn2flF9G7ZkFdH3IBGoym3glWSv5olK66FENft8v6+F07At/cpc8kB2obX+lxyUTNkBNBR6ZzgkWhY0F1ZGbxkMDyxC2I/u+6+wWV7/HrXdWFRVCLH0y/StEEdFo3ujouT/N1RG2TFtRDiupXt71t4CQ78Ablpyr7+z8Eg6fJhqyQBdGSu9ZWWcQt7w8VzML+FsqrrOpK/ynr8ujhpWTK2J971XGsoeHEl0jNYCFEjBkxTPhui3izd1+cJGPKymlGJ6yRDMY7OswmM+0PZNhpBo7uu5K+yHr8FRQZOpOdeb7TiKlSnZ/DtXQPk0rsQ4srcPEu3tc7Kwg9h0yQBFOaNu416pa7TVapOj19ZcVr7KusZXNdVmd+5Mvak9AwWQlQtaTf8/aKyrdGBoVC6etgBuQTs6EwLPga+CGfj4FCEUiOwTgMY/FK1n0ZWnFqv8E7+3BzkZ7biulszL/5vyTbiTmbw+Mo4fpwciqtTzSz6EULYkYJc+HqkMjjg3Ram7ICNbyufG3DNV4yE+mQE0JGV7Rs88AW44xOo56fct/Htq/oLT1acWrfLV1y7Oev4+P+64+XuzJ4zmbz5x361QxRCWKOlt8DFdHCpBw/9raz4lf6+dsGmEsCFCxfSokUL3NzcCAkJITY2ttJjBw4ciEajKXe79dZbS44ZN25cufvDw8Nr6aexApf3Da7rDXd+WjpjLGVvtZ9KVpzangCvOrx/bzAAy2NO8Mdu6QoihChj72pIile2R61UPiNMpL+vzbOZS8DfffcdU6dOZfHixYSEhPDBBx8wbNgwDh48iI+PT7njf/75ZwoKCkq+T09Pp2vXrtxzzz1mx4WHh7N06dKS711dHWiVakVFnlsNhH7PwOb34GgkZJwEr2ZXfKreLRvSqJ4L53IKKrzf1ONXVpxal0EdfHh0QGsWRyfywk+76eBXn9TsfCnOLYSjyzgJvz2lbPd/FloNKH+MXP61aTaTAL733ntMnDiR8ePHA7B48WL++OMPvvzyS6ZPL1+HqGFD80Rj1apVuLu7l0sAXV1d8fPzs3D0NmbQi3BsI5zZCT9NVFYJ66p+qegNRuq4VDyHTHr8WrfnhrZj14nz7Dh+gWEfbKSozEIdf083Zo0IkvZ8QjgSfRH8NAHyM6FJTxhYMx2hhHWxiUvABQUF7Nq1i7CwsJJ9Wq2WsLAwYmJiqvUcX3zxBaNGjaJu3bpm+6OiovDx8aF9+/ZMnjyZ9PT0Sp8jPz+frKwss5td0jnDXZ+DS304tQ02XnmOx4frD3Hq/CXcXXT41DcfRZUev9bNSaflzu5NAcySP4DkzDwmr4gjIkEuDwvhMKLnwant4OoBd3+hfCYIu2MTI4Dnzp1Dr9fj6+trtt/X15cDBw5c8fGxsbEkJCTwxRdfmO0PDw/nzjvvpGXLliQmJvLiiy8yfPhwYmJi0OnKj2bNnTuX2bNn18BPZAMatoQRH8BPDysLQloOgBZ9Kzx05/HzLIpKBODde7oy9AY/6fFrQ/QGIwvWH67wPmOZEj43B/nJ/6MQ9u74Ztj0jrJ92/vQoIXaEQkLsYkE8Hp98cUXdO7cmd69e5vtHzVqVMl2586d6dKlC61btyYqKoohQ4aUe54ZM2YwderUku+zsrIIDAy0cPQq6nw3HFkP/62EnyfCo5vB3fzSenZeIc98H4/BCHd1b8rwzsoon5R6sR1SwkcIAcDF8/DzJDAaIHi08hkg7JZNXAJu1KgROp2OlJQUs/0pKSlXnL+Xm5vLqlWrePjhh6/477Rq1YpGjRpx5MiRCu93dXXFw8PD7Gb3bpkPbg0g6wz89oTSLaSMrV+8wF1ZX9O0QR1evT1ItTDFtZMSPkI4oMi55iVcjEblHJ91RqkDW8+3qkcLO2ATCaCLiws9evRg/fr1JfsMBgPr168nNDS0ysf+8MMP5OfnM2bMmCv+O6dPnyY9PR1/f5mrVsK1PnT6n7J94HfYVbpi+vD3LzMs7QsMaHnv3mDqu8k8EVskJXyEcEBanXkdv51fKud4jRYuXQDnOmpHKCzMZi4BT506lQcffJCePXvSu3dvPvjgA3Jzc0tWBY8dO5YmTZowd+5cs8d98cUXjBw5Em9v80tXOTk5zJ49m7vuugs/Pz8SExOZNm0abdq0YdiwYbX6s1m9296HCycgcT38+Tw0CyUnfjVt9y3g3cK7Ker/vJR3sWG9WzbE39ON5My8Slv5+UsJHyHsi6mES+QcyEmFf79WvjcazOvDCrtlMwngfffdR1paGq+88grJyckEBwcTERFRsjDk5MmTaLXmA5oHDx5k8+bNrF27ttzz6XQ6du/ezfLly8nIyCAgIIChQ4fy+uuvO1YtwOoa/SPGj3qguXAU4yeh1MPIu4V3s8F3HKvD2qkdnbgOOq2GWSOCmLwiDk3xnL/LvXKblPARwu4MmKYUco5+q3TfwBcl+XMQGqPRWNkf/eIKsrKy8PT0JDMz0+7nA0YkJPHRb1v4Pf9hNBooMmppk7+CV24L4qF+LdUOT9SAiIQkZq/ZV+GCkPfu7VpSKkYIYUc2fwD/zFK2dc7w8jm1I6oVjvT5XRmbGQEU6olISGLyijim6P5CUzzNz0lj4CWnr3n99wcI8HKTGn92ILyTPzcHmZfw2XniPO+uPcTsNfvo17aRzAMUwp6cPwobXle2tU6gL1TmBMoIoEOwiUUgQj16g5HZa/YxRfczzzr/yLuFd7NVr6z2neD0F0/ofmb2mn3oDTKQbA90Wg2hrb25I7gJoa29eXRAa24I8CDzUiGzfq1+b2ghhJUzGuHr/4GhCLyaKyN/g2aaLwwRdk0SQFGl2GPnuTtnZUny95H+Tl4seph8ozIUONX5R+7OWUnssfNqhyoswFmnZf7dXXDSavgrIZk/90hHECHswncPwIXjysjfA6tBo1FG/iQJdBiSAIoqpWbnodMYSpI/gONGfz4sUkrDXDS6UFdzSWrE2bEbAjyZPLA1AK/8msCF3AK1QxJCXI/cc3BknbI96EXwbl16nykJNOhVC0/UDkkARZV86rvxQVFp8mfymf429hsCcdcU0FiTKXPD7NyUwW1o61OPczkFvPb7PrXDEUJcj79fhKI88O0EfZ4sf/+AaTBohhqRiVokCaCoUu+WDfFyL1/guQgnZhROxGDUcJduM70N/6kSn6gdrk465t/dBa0GVv97hg0HUqrxKCGE1TmyHnZ/p3T5HrFAWfkrHJIkgKJKlwr1FReGA/4ztuEr/VAAdH8+AwUXazc4Uau6NWvAw8Ulf2b8tIf1+1P4Nf4MMYnpsghICFtQkAu/P6NshzwCTXuoHZFQkZSBEVV6f90hMi4V0qieC05aDclZ+SX3+Xm60SR8DkTuVSYTR82Foa+rGq+wrKk3t+eXf8+Qkp3Pw8t3luz393Rj1oggKQckhDWLmgsZJ8CjKQx+Se1ohMokARSVSjiTydItxwB4556u9G/b2KxGXO+WDZXuEO7vwLejIGYhdL4b/LuqHbqwkOhDqaTllF8EkpyZx+QVcSwa012SQCGs0dl45RwNcNt7Sp934dDkErCokN5gZOYvCRiMcGsXfwa29ylXI66kNVj74RA0Eox6+O1J0BepHb6wAFNNyIqYLgBLTUghrJC+CNY8qfT5veF/0E763QtJAEUlvo09yX+nMqjn6sQrtwVd+QHD54OrJyTFQ+yntRGiqGWxx85X2CbOxAgkZeZJTUghrM32xZD0H7h5Qvg8taMRVkISQFFOWnY+8yIOAPDc0Hb4elSjxEt9X2geqmxveAMunDC/P3o+RM61RLiillS31qPUhBRCRZFzzYs4XziuFHYGaN4Xdn6pWmjCukgCKMqZ88c+svOK6NzEkwdCW1T/gQHdla+FF+GPqUqrIUzJ3xzQ6iwTsKgV1a31KDUhhVCRVlfaycNohD+eVc7Jns3g4J9yHhYlZBGIMLPlyDl+iT+LRgNz/tepdJ5fdQx8AS6dVy43HPkHEn5Smo1HzlEqy0uDcZvWu2VD/D3dSM7Mq6wyEP6eyuIgIYRKTOfZyDmQnKCcizU6yDwp52FhRhJAgd5gJPbYec5kXOSdvw8BMPbG5nRp6nX1TzZ8HqTug2Mb4aeHlX1y0rELOq2GWSOCmLwiDg0Vl4d88ZaOV/dHgxCi5g2YpnT62PSu8r1RL+dhUY4kgA4uIiGJ2Wv2mU3u12qga+A1JH8mo3+CNxor2xqdnHTsSHgnfxaN6V7ha8ZghLMZl1SNTwhRzFCmGoPORc7DohxJAB1YREISk1fElRvJMRjh2e//w91Fd2013bZ8ULpt1EPEdAh/67rjFdYhvJM/Nwf5mdWEPHXhItN+3M2C9Yf5X7cm+FRn4ZAQwjLOH4WtHyvbWifQFyhzAiUJFGXIIhAHZarpVlXFtmuq6WZa8DHwRWg9WNm3bZH5qjRh8y6vCXl396YEB3qRW6DnreIV5EIIlay8T/nju0ErePmccvnXtDBEiGKSADooi9R0MyV/g2YqC0KGvalcAgY5+dg5rVbD7NtvQKOBn+POsOvEBbVDEsIx/TIZzh0CNHD/t6DRKCN/kgSKy0gC6KAsUtPNcNlEY5+O0PMhZbuuD+gLryVUYSO6Bnpxb49AAF79ba90BBGithn0cGidst17Ivh0KL3PlAQa9KqFJ6yLJIAOyiI13QbNKD/HZNCLSvX53FTwCLjKKIWteT68PfVdndhzJpMfdp5SOxwhHEvccriYBm5eMHBG+fsHTFPO00JIAui4erdsiE9910rv19RUTTf3hqUnog1vQF7m9T2fsGqN6rny9M3tAJj/90EyL8morxC14lKGco4F5ZzrLvU4RdUkAXRQOq2GDv71K7zPVMVt1oigmqnp1msCNGoHF8/Bxrev//mEVRsb2pw2PvU4n1vAB/8cUjscIRzDxrfhYjo0ag+9HlY7GmEDJAF0UIdTstlyJB2AhnVdzO7z83Rj0Zju11YCpiI6Z2VBCMC2xZCeWDPPK6ySs07LqyNuAGD51uP8sPMUv8afISYxXeYFCmEJ6Ymw/VNle9ibyjlXiCuQOoAO6s0/96M3GBka5MuiMT3Marr1btmw5rs5tL0Z2twMR9bB2peU1WnCbvVr24jgQC/iT2Xw/I+7S/b7e7oxa0RQzf1xIYSAv2eCoRDaDoW2YWpHI2yEjAA6oE2H04g8mIaTVsP04R3K1XSzWCuvYXOUsjAH/4TESMv8G8IqRCQkEX8qo9z+5Mw8Jq+IIyIhSZW4hLA7iRvg0F9Kweehc9SORtgQSQAdjN5gZM4f+wF4ILQ5rRrXq71/vHF7pTQBwN8vgr7oSo8QNshUZLwipgvA11RkXAhhTl8EES8q270mQuN2akckbIgkgA7mh52nOJCcjYebE08NaVv7AQx4Aeo0gNR9ELes9v99YXEWKTIuhChv11JI2w91GirF94W4CpIAOpCc/CLeXaesynxySFu83F2u+Jga594QmvRUtjfMgUuXdYyIng+Rc2s/LlFjLFJkXAhHFznXvIvHpQsQWby4rmkvZYGdEFdBEkAH8ml0ImnZ+bTwdmdsaAv1AjElgJfOQ3SZsjCmVnJanWqhietnkSLjQjg6rc68lVv0fOUc6t4IDv8t501x1WQVsIM4m3GJJZuOAjB9eAdcnFTM/QdNhwvHYPcq2L4Ieo6HvatL+whf3k1E2JTeLRvi7+lGcmYelc3yq5Ei40I4EtN5MXIO5J6DnV8o3188J+dNcU1sagRw4cKFtGjRAjc3N0JCQoiNja302GXLlqHRaMxubm7mIw5Go5FXXnkFf39/6tSpQ1hYGIcPH66Fn6T2vfP3QfIKDfRu0ZBhN/ipHQ7c+Sl4twGjARb2kuTPjui0GmaNCIIyRcUvV2NFxoVwJKZ+vrGfgqF4EZ2cN8U1spkE8LvvvmPq1KnMmjWLuLg4unbtyrBhw0hNTa30MR4eHiQlJZXcTpw4YXb//PnzWbBgAYsXL2b79u3UrVuXYcOGkZdn+3OT9AYjMYnp/Bp/hm+2neDnf88A8NJtHdForOSD9/7vlK9Go1LCQE5idiO8kz+LxnTHz7Piy7xNG7jXekxC2IVmN5Zua53lvCmumcZoNNpELYaQkBB69erFxx9/DIDBYCAwMJAnnniC6dOnlzt+2bJlPP3002RklK9FRvHoX0BAAM8++yzPPfccAJmZmfj6+rJs2TJGjRp1xZiysrLw9PQkMzMTDw+P6/4Za0pEQhKz1+wrtxKzd8uGfP9IqGpxlWOa82cy8EVZyWZn9AajWZHxb2NP8Nt/SfRv24ivHw5ROzwhbIvRCO8FQfZZ0GiVKygyAnhNrPXzuzbZxAhgQUEBu3btIiystMK5VqslLCyMmJiYSh+Xk5ND8+bNCQwM5I477mDv3r0l9x07dozk5GSz5/T09CQkJKTS58zPzycrK8vsZm0iEpKYvCKuwjIcscfOW08BXlPy1+dJcC4eDYp603yVm7B5lxcZf25oB5x1GjYdPsfmw+fUDk8I2/LTBCX50zrD1ANK8ld2YYgQV8EmEsBz586h1+vx9fU12+/r60tycnKFj2nfvj1ffvklv/76KytWrMBgMNCnTx9Onz4NUPK4q3nOuXPn4unpWXILDAysoZ+wZpgK8FY2pKuxlgK8puRv0EwY+jrcOFnZ795ITmZ2rpm3O6NDmgMwL+IABrVfi0LYiqi3IOFHZbvvU1Dft3ROoJw3xTWwiQTwWoSGhjJ27FiCg4MZMGAAP//8M40bN+bTTz+95uecMWMGmZmZJbdTp07VaMzXy2YK8Br05pct+jwJbl7KarYOI5T7hd16YnAb6rk6sedMJn/ssZIRaSGsXVJxT203L+jzROl+UxIo501xlWwiAWzUqBE6nY6UlBSz/SkpKfj5VW9Fq7OzM926dePIkSMAJY+7mud0dXXFw8PD7GZNbKYA76AZ5nNW6nhBv2eU7aT/oP9U1UITluddz5VJN7UC4J21BykoMqgdkhDWrSgfkosTwP5TlXNmWQOmKedVIa6CTSSALi4u9OjRg/Xr15fsMxgMrF+/ntDQ6i1q0Ov17NmzB39/fwBatmyJn5+f2XNmZWWxffv2aj+ntbHpAry9J0F9f8g8CbukRZy9m9C/JY3quXIi/SLfxp5UOxwhrNvOpZB5SjlH9p6kdjTCTthEAggwdepUlixZwvLly9m/fz+TJ08mNzeX8ePHAzB27FhmzCj9C+i1115j7dq1HD16lLi4OMaMGcOJEyeYMGECABqNhqeffpo33niD3377jT179jB27FgCAgIYOXKkaj/n9TAV4K2syIvGmgvwuriXjgpGz4f8bLUjEhbk7uLE02FKL+oF6w+Tk1+kdkhCWKf8bNhY3DFpwAvgXEftiISdsJkE8L777uOdd97hlVdeITg4mPj4eCIiIkoWcZw8eZKkpNL5RBcuXGDixIl07NiRW265haysLLZu3UpQUFDJMdOmTeOJJ55g0qRJ9OrVi5ycHCIiIsoVjLYVpgK8FU2rNyWFVl2At9sD0LCVMhdw2yK1oxEWdl+vQFo2qkt6bgFLNh5VOxwhrFPMJ8o5sWFr6DZG7WiEHbGZOoDWyBrrCKVm59HvrUgK9Obzqvw93Zg1IojwTv6qxVYtCT/Bjw+BS3146j+o6612RMKC/tyTxGPfxOHuoiP6+UE0ru+qdkhCWI/cdPiwKxRkw91LodOdakdkN6zx87u2SS9gO/NJZCIFegNdmnoyY3gHUrPz8amvXPa12pG/soL+B34fKBOeN78Hw+ZU40HCVg3v5EfXQC/+O5XBh+sPcWvngJKi0TbzmhXCUja/pyR//l0hyDanJgnrJSOA18Ha/oI4k3GJQW9HUaA38M2EEPq2aaR2SNfm8D/wzV2gc4Un48CzqdoRCQuKSUzn/iXbyu23mVFrISwh4xR81AP0+TDmJ2gTVo0Hieqyts9vNdjMHEBxZQv+OUyB3kBoK2/bTf4A2gyB5v2UE1/UW2pHIyws81JBhfuTM/OYvCLOerrXCFGbot9SzoEt+kPrIWpHI+yQJIB2IjEthx/jlC4nzw1rr3Y410ejgbBZynb8N5B2SO2IhIWYutdUxHRpwiq61whRm9IOQfxKZXvILOWcKEQNkwTQTry/7hB6g5EhHXzo0byB2uFcv8De0P5Wpdl55BtqRyMsxGa61whRmza8rpz7OtwGgb3UjkbYKUkA7cC+s1n8vlu5TPbsUBsf/SurfnFHln2/wpld5vdFz4fIuaqEJWqOzXSvEcJSIuea9/E9swv2/6YU7/IIkPOcsBhJAO3Au2sPAnBbF3+CAuxoMmv9Mi351r9Wuh09X2l+rtWpEpaoOTbdvUaImqDVKeczUxL4z2zlq18niP1MznPCYqQMjI3bdeIC6w+kotNqmHpzO7XDqVkDpsGlDNi2EI5GKbdTscrJctBM837CwiaZutckZ+ZVWsDcz1q71whRE0znscg5cP4oHIsGjQ6S98h5TliUjADaMKPRyNt/HwDg7u5NadW4ntoh1bzwN6Fp8RyYr0ZK8mdnTN1rKNOt5nJW3b1GiJowYBoMfBH++1b53qiX85ywOEkAbYzeYCQmMZ1f48+wZNMxth09j4tOy5PFfVXt0qjikyJG0DrJSdHOhHfyZ9GY7vh5lr/M+9SQtlIHUDgGv06l2zpnOc8Ji5NLwDYkIiGJ2Wv2lVs12beNN0287LhB+K6lpduGIoiaBwNfUDMiUcPCO/lzc5AfscfOk5qdx597kvh7bwqbj5zjqbC2aKQMhrBnRiP8/rSyrdGBvlCZEyhJoLAgGQG0EREJSUxeEVdhyYzIg2n2WyzXtOCj7zPgUnyJO+pN81Vzwi7otBpCW3tzR3ATXrujE65OWnaeuMCmw+fUDk0Iy/ppAuSkgs4Fnj+iXP4tuzBECAuQBNAGmIrlVlYKV2OvxXJNyd+gmXDzq9B7krK/nq+cHO2cr4cbo0OaA/D+P4eQjpXCbkXNg4Qfle0+T4B7Q2XkT5JAYWGSANoAhy2Wa7hsInToFGUUMCcFOt2t3C/s1qMDW+HmrOXfkxlEHUpTOxwhLCNNWciHSz3lHGdiSgLlPCcsRBJAG+CwxXIHzTCfA1PXu3QU8NxBGDhdtdCE5fnUd2NsaAso7nQjo4DC7hiNkH5Y2Q55RBn9K2vANOU8KIQFSAJoA6RYbhl9nlD+Uk7eAwf/VDsaYWGP3NQKdxcdu09nsn5/qtrhCFGzDvyhnMtc6puP/glRCyQBtAGmYrmVrYPUAP6OUizXvaHylzJA1FzlL2hht7zrufJgn+JRQJkLKOyJ0QjRbynbFY3+CWFhkgDaAFOx3Mo6JeBoxXJNcwGT9yh/QQu7Nql/K+q66Nh7Nou1+1LUDkeImnHg9zKjf4+rHY1wQJIA2oihQX74e5S/xOvn6caiMd0dq1hu2VHA6LdkFNDONajrwvi+LaF4LqDB3la7C8djMCirf5HRP6EeKQRtI/5MSCIpK496rjo+GNWN3PwifOorl30dZuSvrNApsP2z0lHAjrepHZGwoAn9W7J863EOJGfz554kvOu5kpqd59jvAWG7Dv4BKTL6J9QlCaANMBiMfLT+CAAP92tFWEdftUNSn2kUcNM7yihgh1tBukXYLS93Fx7q15IP1x/m6e/iKSozCujv6casEUGONQoubFfZ0b8bH5XRP6EauQRsA/7em8zBlGzquzrxUPGlMIHyl7NL/eJRwN/VjkZYWDNvdwCz5A8gOTOPySvi7LcbjrAvB34vHf278TG1oxEOTBJAK2cwGPlwvVInanzfFni6O6sdkvUwWxE8T/nLWtglvcHIO38frPA+Uzpol91whH0xGCBaRv+EdZAE0Mqt3ZfCgeRs6rk68VA/Gf0rxzQKmLJHmVcj7JLDdsMR9uXA75CSAK4eMvonVCcJoBUzGo0sKB79e7BPc7zcXdQOyfq4N1T+kkZGAe2Zw3bDEfaj7OhfiIz+CfVJAmjF/tmfyr6kLOq66JjQr5Xa4VivGx8rHQWUuYB2SbrhCJt3YE2Z0b/JakcjhCSA1spoNPLh+kMAjO3TggZ1ZfSvUts/Bf8uynb0ZaOA0fMhcq5qoYmaId1whM2JnKucf7i87t+jsONzOS8J1UkCaKU2HEgl4UwW7i46JvaX0b8qaXVwYgvoXJW/sE2jgNHzIXKOcr+waaZuOJTpfnM5h+qGI6yfVqecf6LnK6N/qXuV0T9DkZyXhFWQOoBWSBn9U+b+PRDanIYy+le1AdOUr5FzlK/R8yB1P0S9CYNmlt4vbFp4J38WjenO7DX7zBaEOOs0LBjVTeoACutS9rxUt7Gy7d8FNr8n5yVhFSQBtEJRh9LYfTqTOs46JsnoX/UMmAaFF2Hz+8ooYEqCnGTtUHgnf24O8iP22HmOncvh1d/2UaA34OYioynCCg2YBqkHYO9PyvfHN8t5SVgNuQRsJfQGIzGJ6fz67xne+H0fFI/+eddzVTs02xH2KmhMiYAGbnpe5YCEJei0GkJbe/N/Ic15sE9zAD5afxij9IQW1sZohPTDpd/rXCT5E1bDphLAhQsX0qJFC9zc3AgJCSE2NrbSY5csWUL//v1p0KABDRo0ICwsrNzx48aNQ6PRmN3Cw8Nr4ScxF5GQRL95G7h/yTae+i6exLRcAFo3rlfrsdi06Plg1Bd/Y4TVj6ockLC0iTe1wsVJS9zJDGKOpqsdjhDmjvwDybuVbZ0L6AtKF4YIoTKbSQC/++47pk6dyqxZs4iLi6Nr164MGzaM1NTUCo+Piori/vvvJzIykpiYGAIDAxk6dChnzpwxOy48PJykpKSS27fffltLP5EiIiGJySviKixyO/2n3dLeqrpMCz4GzYTQKcq+3atKV94Ju+RT3437ewUClPTLFsIqGI2w5mllOzAEXk5Tzk+mhSFCqMxmEsD33nuPiRMnMn78eIKCgli8eDHu7u58+eWXFR7/zTff8NhjjxEcHEyHDh34/PPPMRgMrF+/3uw4V1dX/Pz8Sm4NGjSopZ9Iuew7e80+qrpwJe2tqqFs8jdgmpIA6ooXzkS9KSdbO/fIgNY46zTEHE1n53HpBCKsxK+PQ9ZpZVrKvV8p+wZMkyRQWA2bSAALCgrYtWsXYWFhJfu0Wi1hYWHExMRU6zkuXrxIYWEhDRua1wmLiorCx8eH9u3bM3nyZNLTK7+MlJ+fT1ZWltntekh7qxpi0JtPrPbwh24PKNsNWir3C7sV4FWHu3s0BeCjDTIKKKzE8c3K157job5f6X5TEijnJaEym0gAz507h16vx9fX12y/r68vycnJ1XqOF154gYCAALMkMjw8nK+++or169czb948oqOjGT58OHp9xW/MuXPn4unpWXILDAy8rp9L2lvVkEEzyk+s7vuU8pf3hWPQdqhakYlaMnlAG3RaDdGH0th9OkPtcISjO70TMk6A1kk5F11uwDTlvCWEimwiAbxeb731FqtWrWL16tW4uZW2iho1ahS33347nTt3ZuTIkfz+++/s2LGDqKioCp9nxowZZGZmltxOnTp1XXFJeysLatAcuo5Stje9o3Y0wsKaebtzR3AAAB/LKKBQ28bic06XUeDVTO1ohKiQTSSAjRo1QqfTkZKSYrY/JSUFPz+/Sh8H8M477/DWW2+xdu1aunTpUuWxrVq1olGjRhw5UvEHiKurKx4eHma362Fqb1UZaW91nfo9o/wWD/4JyQlqRyMs7LGBbdBoYO2+FPYnXd/0DCGuWfIeOPQXaLTF5yAhrJNNJIAuLi706NHDbAGHaUFHaGhopY+bP38+r7/+OhEREfTs2fOK/87p06dJT0/H3792OgqUbW91OVNDK2lvdR0atYUbRirbm95VOxphYW186nFrZ+W9uzBSRgGFSkznmqCR0KiN2tEIUSmbSAABpk6dypIlS1i+fDn79+9n8uTJ5ObmMn78eADGjh3LjBmlcyrmzZvHyy+/zJdffkmLFi1ITk4mOTmZnJwcAHJycnj++efZtm0bx48fZ/369dxxxx20adOGYcOG1drPVVmtPz9PNxaN6S7tra5X/+eUr3tXw7nDVzpa2Lgpg5UP3D/2JHEkNUftcISjOXcY9v6ibPd/Vu1ohKiSzbSCu++++0hLS+OVV14hOTmZ4OBgIiIiShaGnDx5Eq22NJ9dtGgRBQUF3H333WbPM2vWLF599VV0Oh27d+9m+fLlZGRkEBAQwNChQ3n99ddxda297huLohIBGBbky7i+LUnNzsOnvnLZV0b+aoBfJ2g3XLkks/l9GPmJ2hEJC+rg58HQIF/W7kthYeRh7u3ZTN5TovZsek+p39D+FuXcI4QV0xilf9I1y8rKwtPTk8zMzGuaD3gy/SKD3o1CbzCyZko/Ojf1tEicDu/0Tvh8iLIi74k4ZYGIsFu7T2dw+8dbyu3393Rj1oggGVUXlnHhBCzopnQjmrABmvZQOyJRhev9/LYHNnMJ2B4t3piI3mDkpnaNJfmzpKY9odVAMBTBlg/VjkZY2NmMSxXuT87MY/KKOOmuIyxjywdK8tdqkCR/wiZIAqiSlKw8ftx5GoApg2SisMXd9Lzy9d8VkF292pHC9pi661TEdKlDuuuIGpeVpJxbKHOuEcLKSQKokiUbj1KgN9CrRQMp81IbmveFwBtBnw9bP1I7GmEh0l1HqCLmY9AXQLNQaNFX7WiEqBZJAFVwPreAb7afBOBxGf2rHRpN6V/mO7+E3Mpb/gnbJd11RK3LTVfOKQA3Pad2NEJUmySAKli25RiXCvV0auLBgHaN1Q7HcbQZAv7BUHgRti9SOxphAdJdR9S6bZ8o5xT/YGg9RO1ohKg2SQBrWXZeIcu2Hgfg8YFt0GikLEWtiXoLGrZWtrd/BnmZpfdFz4fIuaqFJmqGqbtOZe8q6a4jrlvkXOV8AXApA2I/U7Zveg42vi3nEWEzJAGsZSu2nSQrr4jWjesy7Iaq29iJGqbVwd6fwL0R5GdC7BJlf/R8iJyj3C9sWtnuOpUlgdJdR1wXrU45X0TPhx1LID8LGneElH1yHhE2xWYKQduDvEI9X2w+CsV9S7XyIVS7BkxTvkbOUb5u+wSK8pS/2gfNLL1f2LTwTv4sGtOd2Wv2mS0I0Wrg/fuCpQ6guD5lzyNOdZTtRu0g6k05jwibIglgLVoVe5JzOQU0bVCH24MD1A7HMQ2YBgYDRM+Fi+mS/Nmp8E7+3BzkR+yx8yRnXuLNv/aTll1AxsVCtUMT9mDANDi1HY78o3y//1c5jwibI5eALUxvMBKTmM7Pu07z0QalF+0jA1rjrJNfvWoGTTe/TNP3aTWjERai02oIbe3N/7o35ckh7QD4bONRCvUGtUMTtq4oX7nka6JzkeRP2BzJQiwoIiGJfvM2cP+SbUz94T/ScwvRasDTTQZeVRU9Hwz60u9/GKdmNKIW3NOjKY3quXIm4xK/xp9VOxxh63Z/B9nFryOdi1ID0LQwRAgbIQmghUQkJDF5RVy5orQGIzy1Kl7aUanFtOBj0EwY+oay7+AfygphYbfcnHVM6N8SgMXRiRikE4i4VgY9rHtF2W49BF5OU84npoUhQtgISQAtwNSOqqqPGGlHpYKyyd+AadBjHLh5KfdFzZWTt50bHdIMDzcnjqTmsHZfitrhCFv108Nw6QI4ucG9Xyn7BkyTJFDYHEkALUDaUVkpg958orZrfQh5RNmu5weGIlXDE5ZV382ZsaEtAPgk6ghGo/wBJq6S0QjHtyjbfZ8G13ql95mSwLLTS4SwYpIAWoC0o7JSg2aUn6jd+xFwdoecZAgMUSsyUUvG922Bm7OW3acz2XJE2gGKq5S4HnJTlXOG6Y/HsgZMU84zQtgASQAtQNpR2ZC63tD9QWV78/tqRyMszLueK6N6NYPiUUAhrsqm4nNEj3HgLt1khG2TBNACTO2oKiPtqKxMnymgdYbjm+DUDrWjERY28aZWOGk1bE1M59+TF9QOR9iKU7FwYrNyrgidonY0Qlw3SQAtoGw7qsuZen9IOyor4tkUutynbMsooN1r4lWH/3VrAsAnUYlqhyNshenc0PU+8GyidjRCXDdJAC2kuXfdCvf7ebqxaEx3aUdlbfo9raTnB/+A1P1qRyMs7NGBrdFoYN2+FA6lZKsdjrB2Kfvg4J/KOUIKxws7IRWJLWRxtDKycEtnPx64sQWp2Xn41Fcu+8rInxVq1BY6joD9v8HmD+DOT9WOSFhQ68b1CL/Bj78SklkUlcj79wWrHZKwZls+UL4G3a6cK4SwAzICaAEn0y+y5j+lSvxjA9sQ2tqbO4KbENraW5I/a9Z/qvJ1zw9w4YTa0QgLe2xgGwB+jT/Db/Fn+DX+DDGJ6VKfU5i7cBz2/Khs95uqdjRC1BgZAbSAzzYlYjDCTe0a06mJp9rhiOoK6AatBsHRSNj6Edz6jtoRCQvq3NSTjv712Z+UzZOr4kv2+3u6MWtEkEzTEIqtH4FRD60HQ4CMFAv7ISOANSw1O4/vd54G4LGBrdUOR1wt0yjgv19DTqra0QgLikhIYn9S+fl/yZl5TF4RJ+0ahXIO+HeFsi2jf8LOSAJYw5ZuOU5BkYFuzbwIkTIvtqdFf2jSE4ryYNsitaMRFmJq11gR0wVgadco2PaJci5o2gta9FM7GiFqlCSANSgrr5AVMcrcsccGtkGjkfl+NkejKR0F3PE55GWqHZGwAGnXKK4oLxN2fKFs95uqnBuEsCOSANagr2NOkJ1fRFufegzp4KN2OOJatRsOjTtAflbpB4CwK9KuUVzRjs+Vc0DjjtAuXO1ohKhxkgDWkLxCPUu3HANg8sDWaGW1r+2KngfexaUetn0ChZfK3DcfIueqFpqoGdKuUZQTOVd5f4PynjdNAen3NGx6R973wu5IAlhDfth5inM5BTTxqsOIrgFqhyOuh1YHB9aAqyfkpkH8N8r+6PkQOUe5X9g0U7vGyv5Mk3aNDkirU97f0fOVhR+5aeDZDM4fk/e9sEtSBqYGFOkNfLrxKACTbmqFs07yaps2YJryNXKO8nXLAsg5B9FzYdDM0vuFzTK1a5y8Ig5NmYUfZUm7RgdT9n3vVly+y6cjRL8l73thlyRTqQERCcmcvnAJ77ou3NszUO1wRE0YMA1uel7ZzjghyZ8dCu/kz6Ix3fHzLH+Zd1zfFlIH0BENmAYdby9d/HX4b3nfC7slI4A14KMNhwEt4/u2oI6LXCawG4Nfgk3vKUVg0UD/59SOSNSw8E7+3BzkR+yx86Rm57E1MZ3vdpxi65F0jEajrOR3NAYDnDtc+r3ORZI/O6Q3GIk9Kiv8bWoEcOHChbRo0QI3NzdCQkKIjY2t8vgffviBDh064ObmRufOnfnzzz/N7jcajbzyyiv4+/tTp04dwsLCOHz4cKXPV5kzGXnKnCGvOlf9WGHFoucXJ38oFwlXP6JyQMISdFpNSbvGF2/pSD1XJw6mZLPhgBQCdziH/4a0/cq2zgX0BaULQ4RdiEhIot+8DTy0fIfaoajOZhLA7777jqlTpzJr1izi4uLo2rUrw4YNIzW14pP01q1buf/++3n44Yf5999/GTlyJCNHjiQhIaHkmPnz57NgwQIWL17M9u3bqVu3LsOGDSMv7+pLPxiB577/T7oH2AvTgo9BM6HvU8q+Pd/Lh4Gd86zjzOiQZgAsikpUOxxRm4xG+ONZZbtZKLycprz/TQtDhM2LSEhi8oq4KmuAOhKN0Wi0iVL3ISEh9OrVi48//hgAg8FAYGAgTzzxBNOnTy93/H333Udubi6///57yb4bb7yR4OBgFi9ejNFoJCAggGeffZbnnlMu7WVmZuLr68uyZcsYNWrUFWPKysrC09OTwKe/R+vqjgbw83Rj8wuDZfK4LSub/A2YBtnJ8EEX0Ocr98ucILuWmpVHv3mRFOgN/PBoKL1ayEpgh/Dr48rqX40Opu6H+r7K/svPB8Im6Q1G+s3bUJL8GfIvcuqDe8nMzMTDw0Pt8FRhEyOABQUF7Nq1i7CwsJJ9Wq2WsLAwYmJiKnxMTEyM2fEAw4YNKzn+2LFjJCcnmx3j6elJSEhIpc+Zn59PVlaW2a0s6R5gJwx685N9fT8I/j9lu2Fr5X5ht3w83LirR1MAPok8onY4orYc36p87fFgafJH8cKQQTPlfW/jrtT9xxHZRAJ47tw59Ho9vr6+Zvt9fX1JTk6u8DHJyclVHm/6ejXPOXfuXDw9PUtugYEVr/iV7gE2btCM8n/p930SNFo4nwgdb1MrMlFLHrmpFVoNRB5MY39SVjUeIWxa0m64cFR5j/d5ovz9A6Yp5wVhs+RzuTybSACtxYwZM8jMzCy5nTp1qsLjpHuAHWrYCm74n7K9+QO1oxEW1qJRXW7prJSBWRwtcwHt3pbi9/QNdyrvdWF35HO5PJtIABs1aoROpyMlJcVsf0pKCn5+fhU+xs/Pr8rjTV+v5jldXV3x8PAwu5Ul3QPsXN+nla97f4bzR9WORljYowNaA7Dmv7OcTL+odjjCUtITYe9qZbvf02pHIyzE1P1HlLKJBNDFxYUePXqwfv36kn0Gg4H169cTGhpa4WNCQ0PNjgdYt25dyfEtW7bEz8/P7JisrCy2b99e6XNWxbTkQ7oH2DH/LtAmDIwG2PqR2tEIC+vUxJMB7RpjMMJnm2QU0G5t/Uh5T7e5Gfw6qx2NsBBT9x9RyiYSQICpU6eyZMkSli9fzv79+5k8eTK5ubmMHz8egLFjxzJjRukcjaeeeoqIiAjeffddDhw4wKuvvsrOnTuZMmUKABqNhqeffpo33niD3377jT179jB27FgCAgIYOXLkVcfn5+nGojHdpXuAves3Vfn67zeQnXKlo4WNmzxQGQX8fudpmUNkj7KTS3t995+qdjTCwro3a4CTDNCUsJlOIPfddx9paWm88sorJCcnExwcTERERMkijpMnT6LVluazffr0YeXKlbz00ku8+OKLtG3bll9++YVOnTqVHDNt2jRyc3OZNGkSGRkZ9OvXj4iICNzcrm6Y+MsHezGoS3MZ+XMEzftA095wOha2fQI3z1Y7ImFBIS0b0q2ZF/+ezGDpluO8EN5B7ZBETdr2iVLsOTBEqf0n7NoXW45RZDDSvZkXj/UJ4mYHn85tM3UArZGpDqAj1xFySAf+hFX3g6sHPJNQ2jhe2KV1+1KY+NVO6rno+PD+buTkF+FTX5nrK3/02bBLGfB+JyjIhvtXQfvhakckLCjzUiF939pATn4RXzzYk15N6jj857fNjAAKYTXahUPjjkrLqB2fQ/9n1Y5IWNCQDj74e7iRlJXHw8t3luz393Rj1oggmfZhq3Z8riR/PkHQdpja0QgL+zrmODn5RbT3rc+g9j7k5GSrHZLqbGYOoBBWQ6stXS24bREUXlI7ImFBa/clk5RVfv5fcmYek1fESftHW1R4SXnvUry6XysfhfbsUoGepVuOQ/G8Xq2M3IMkgEJco053gWczyE1T2kcJu6Q3GJm9Zl+F95nmzsxesw+9QWbS2JR/V8DFc+DVTHkvC7v2/c5TpOcW0LRBHW7rIiP2JpIACnEtdM6lHQO2LgB9kdoRCQu4Uvsoaf9og/SFsGWBst3nSdDJTCh7Vqg38NlGpW7rIze1wkknaY+J/CaEuFbdxoB7I8g4qRSHFnanuqVfpESMDUn4GTJPKu/d4NFqRyMsbM1/ZzmTcYlG9Vy4p2fF7VsdlSSAQlwrF3e48VFle/P7IAvq7U5120dJmykbYTAo71WAGycr72FhtwwGY0krx/F9W+LmrFM7JKsiCaAQ1yM/G3QukLoPDv1tfl/0fIicq1ZkogaY2kdVNmVc2j9auci5yvvQ5PDfyup9l/pQkCvvTzu3/kAqh1JyqO/qxAOhzdUOx+pIAijE9XCppxSShdKRBUzJ3xzQyl+ctqxs+6jKkkBp/2jFtDrlfRg9Xxmh3/Sest/vBtj8nrw/7ZjRaOSTqCMAjL6xOR5uzmqHZHVk9qsQ12PANGUUcOsCOLUNTmyF45uVD51BM5X7hU0L7+TPojHdmb1mX7kFIc/c3E7qAFoz0/svcg5knFA6+Gh0cHKbvD/t3PZj5/n3ZAYuTloe6tdC7XCskiSAQlyvoa/DsY2QFA9Lb1HWhsqHi10J7+TPzUF+xB47T2p2Hmv+O8s/+1PZeeKC2qGJKymbBAIY9fL+dACfRClz/+7p0VTm6FZCLgELURPu/rJ4wwhaZ/lwsUM6rYbQ1t7cEdyEWSNuQKfVsPFQGntOZ6odmriSdmU6fcj7027pDUZiEtNZGHmEjYfS0ACP3NRa7bCsliSAQtSEhJ9Ktw2F5hPPhd0JbOjO7V0DAFgUfUTtcMSV/DxJ+arRyvvTTkUkJNFv3gbuX7KNt/8+CICrs5Z9SfIHWmUkARTiepkWfPSaULrPNPFc2K3JA5WRhb8SkklMy1E7HFGZv16AtAPK9qOblcu/8v60KxEJSUxeEVdujm5eoUHaNVZBEkAhrocp+Rs0E259F9qFK/v9u8iHjJ1r51ufsI6+GI2wuHi+kbAy0fNh+2Jlu91w8L1BufwrSaDdMLVrrKoKq7RrrJgkgEJcD8NlE8r7P6t8TdkHoVOU+4XdemyQMgq4+t8znM24pHY44nIXzyuXfSnz3oTSJFDenzZP2jVeO0kAhbgeg2aYTygP7A0t+oOhSLkNmqFmdMLCujdrQGgrb4oMRpZsOqp2OOJyRoNya9EfAnuZ3zdgmrw/7YC0a7x2kgAKUdP6T1W+7loOuefUjkZYmGkU8NvYk6Tn5KsdjjDJSYO4r5TtsqN/wq5Iu8ZrJwmgEDWt1SAI6AZFl2DbIrWjERbWr00jujT1JK/QwLKtx9UOR5hsX6S8BwO6Q6uBakcjLMTUrrEy0q6xcpIAClHTNJrSEYfYJZAnZQjsmUaj4bHiFcHLtx4nO69Q7ZBEXqby3qN49E8jrfrslU6rYdqw9hXeZ/pfl3aNFZMEUAhLaH8rNGoP+Zmw4wu1oxEWNjTIj9aN65KVV8TK7SfVDkfs+Bzys6BxB2h/i9rRCAtLylLm912e5Pl5urFoTHdp11gJaQUnhCVotcpcwNWPQMxCCHkUXNzVjkpYiFarYfLANjz3w398vvkYD/ZpgZuzTu2wHFPBRYj5RNnuN1V5Lwq7dalAzxebjgHw1p2dadrAndTsPHzqK5d9ZeSvcvLOEMJSOt0FXs3g4jn4d4Xa0QgLuyM4gCZedUjLzmd+xAF+jT9DTGK61B+rbf9+rbznvJop70Fh177bcZL03AKaNqjDyG5NSto1hrb2luTvCiQBFMJSdM7Q9ylle8uHUFSgdkTCgpx1Wvq1aQTAl1uO89SqeO5fso1+8zZIJ4LaUlQAWxYo232fBp1c5LJnBUUGPtuolF96ZEBrnHWS0lwN+W0JYUnBY6CuD2Sdhj0/qB2NsKCIhCS+33mq3P7kzDxpR1Vb9nyvvNfq+ULwaLWjERb2y79nOJuZh099V+7p0VTtcGyOJIBCWJKzG/SZomxvfl86D9ipqtpRmfZJOyoLM+iV9xgoXXicpe6bPdMbjCyKVlowTuzfSubcXgNJAIWwtJ4PgZsnpB+GA7+rHY2wAGlHZQX2r4H0I+DmBT3Hqx2NsLA/9yRx7FwuXu7O/F9IM7XDsUmSAAphaa71lVXAAJveBaOMAtkbaUelMqNReW+B8l5zra92RMKCjEYjCyOPADC+T0vquspcz2shCaAQtaEwD7TOkPQfJK43vy96PkTOVSsyUQOkHVUti5yrvG9MjqyH5N3gXBf0+fJ+snMbDqRyIDmbui46xvVpoXY4NksSQCFqg2s9MBR3iNj0Xun+6PkQOQe0Mn/FlpnaUVVWdELaUdUwrU5535iSQNPon18nZR6gvJ/sltFo5OPi0b8xoc3xdHdWOySbJeOmQtSGAdOUzgRbP4ITW+BEDBzfpHyIDZqp3C9slk6rYdaIICaviENTZuGHiVHaUdUs0/slcg5knISTW0Gjg1Pb5f1k52KOpvPvyQxcnbRM6NdK7XBsmowAClFbhr4B/sHK9tLhkvzZmfBO/iwa0x2/ChrTd/CrJ+2oatqAacr759+vle+Nenk/OQDT3L9RvQJpXN9V7XBsmtUngOfPn2f06NF4eHjg5eXFww8/TE5OTpXHP/HEE7Rv3546derQrFkznnzySTIzM82O02g05W6rVq2qhZ9IOLR7lhZvGJU5gfJhZVfCO/mz+YXBfDvxRj4cFcxH93fDSQsHknPYdeKC2uHZnzZDSrfl/WS39AYjMYnpLFh/iC1H0tFpYNKA1mqHZfOs/hLw6NGjSUpKYt26dRQWFjJ+/HgmTZrEypUrKzz+7NmznD17lnfeeYegoCBOnDjBo48+ytmzZ/nxxx/Njl26dCnh4eEl33t5eVn85xEObk+Z16ChUJnDJB9adkWn1RDa2rvk+y1HzrFqxyk+3nCYpeN7qxqb3fn5EeWrRivvJzsVkZDE7DX7zMosuTjp2HM6gyZedVSNzdZpjEbrrUmxf/9+goKC2LFjBz179gQgIiKCW265hdOnTxMQEFCt5/nhhx8YM2YMubm5ODkpOa9Go2H16tWMHDnymuPLysrC09OTzMxMPDw8rvl5hIMwLfgIeRS2f1o6U0wuW9m1E+m5DH43Gr3ByJop/ejc1FPtkOzD71Nh5xfKEpspO2DvaplWYWciEpKYvCKuwgLrGmDRmO7XPLVCPr+t/BJwTEwMXl5eJckfQFhYGFqtlu3bt1f7eUz/wabkz+Txxx+nUaNG9O7dmy+//JIr5cL5+flkZWWZ3YSoFlPyN2gmDJ8Hne5U9jdqb76aUdid5t51uaOr8sfqx5GH1Q7HPkTPL07+gE53QaO2pXMC5f1kF6rqrmMi3XWuj1UngMnJyfj4+Jjtc3JyomHDhiQnJ1frOc6dO8frr7/OpEmTzPa/9tprfP/996xbt4677rqLxx57jI8++qjK55o7dy6enp4lt8DAwGv4qYRDMlw2Qf2m55Wv5w5Cr4nSIs7OPTaoDRoN/L03hQPJ8ofjdcs2nf81cNNzpftNSaC8n2yedNexPFUSwOnTp1e4CKPs7cCBA9f972RlZXHrrbcSFBTEq6++anbfyy+/TN++fenWrRsvvPAC06ZN4+23367y+WbMmEFmZmbJ7dSp8o3fhajQoBnml6V8OkLH25XtS+eV+4XdauNTj1s6K5eqFkYmqh2O7btUvKAm6HblvVTWgGnyfrID0l3H8lRJAJ999ln2799f5a1Vq1b4+fmRmppq9tiioiLOnz+Pn59flf9GdnY24eHh1K9fn9WrV+PsXHWxyJCQEE6fPk1+fn6lx7i6uuLh4WF2E+KamUYBE36GtENqRyMsbMqgNgD8vvssiWmVVzIQV5B2SJnvR5n3kLA70l3H8lRZBdy4cWMaN258xeNCQ0PJyMhg165d9OjRA4ANGzZgMBgICQmp9HFZWVkMGzYMV1dXfvvtN9zcrvwCiY+Pp0GDBri6Sl0hUUv8u0D7W+Dgn0ongzs/VTsiYUEd/T0I6+jLP/tT+CQykXfv7ap2SLZp0zvKBcD2t4JfZ7WjERZi6q5T2WVgDeAn3XWui1XPAezYsSPh4eFMnDiR2NhYtmzZwpQpUxg1alTJCuAzZ87QoUMHYmNjoTj5Gzp0KLm5uXzxxRdkZWWRnJxMcnIyer0yL2TNmjV8/vnnJCQkcOTIERYtWsSbb77JE088oerPKxyQaQRjzw+QLpcG7d0Tg5VRwF/iz3Dq/EW1w7E96YnKewVggIz+2TOdVsPjxaPmlzP105HuOtfHqhNAgG+++YYOHTowZMgQbrnlFvr168dnn31Wcn9hYSEHDx7k4kXlZBoXF8f27dvZs2cPbdq0wd/fv+RmmrPn7OzMwoULCQ0NJTg4mE8//ZT33nuPWbNmqfZzCgfVpDu0Hap0Mdj8XjUeIGxZ10AvbmrXGL3ByCdRkvBftU3vgdEAbYdBQDe1oxEWlnBGaeDg4mSeqvh5ul1XCRihsOo6gNZO6giJGnFqB3wRBloneCIOGjRXOyJhQTuPn+fuxTE4aeHDUd0oMhjxqa9cypLRjCpcOA4Luit/LE1YD017VuNBwladOn+RQe9EUWQw8v0jN6I3KAs+auq9Ip/fNtAJRAi7F9gLWg2Co5Gw+X0Y8YHaEQkL6tmiIe1863EoJYfHV/5bst/f041ZI4JkVKMym99Xkr/WgyX5cwCLohMpMhjp16YRvVt6V+MR4mpZ/SVgIRyCqUTMvysg87Ta0QgLikhI4lBK+VXAyZl5TF4RR0RCkipxWbWMU/DvN8r2TdLlw96dybjEDzuVKVtPhbVVOxy7JQmgENageR9o0V/pZ7rlQ7WjERZi6m5QEdNcHOluUIEtHyrvjRb9oXmo2tEIC1sUdYRCvZHQVt70aiGrfC1FEkAhrIVpRfCu5WU6HQh7It0NrkFWEsR9pWxLj1+7l5R5ie93KFdBZPTPsiQBFMJatLwJAm8EfT5sWaB2NMICpLvBNdi6QHlPNAtVRgCFXVsUlUiB3kBIy4bc2Erm/lmSJIBCWAuNBryaKds7v4ScNPP7o+dD5FxVQhM1Q7obXEHkXOV1bpKTqrwXALyaQ9RbqoUmLC85M49VsTL3r7ZIAiiENfEuLnxadAliPirdHz0fIueAVqdaaOL6mbobVFbAQlO8Gthhuxtodcrr3JQEbv0IivKgfgDsXiWvfzu3OFoZ/evVogGhMvpncZIACmFNBr4Ane9VtmM+gdz00uRv0EyZA2XjdFoNs0YEQZluBmUZHb27wYBpyus8cg6sexV2fKHszz4rr387l5qVx8rYkwA8NaQdGo2DvgdqkdQBFMLa3PkZHIuGnBR4p61S+0w+/OxGeCd/Fo3pzuw1+8otCBnSwUfqAJpe55FzSvcNfFFe/3ZucfRRCooM9GjegL5tZPSvNsgIoBDWRqOBW99Vto160LnIh5+dCe/kz+YXBvPtxBv5cFQwM4Z3AGDzkXOkZskCEHo+XLqtdVJGxoXdSs3O45vtJwB4akhbGf2rJZIACmGNUsrUitMXmE+MF3ZBp9UQ2tqbO4KbMOmmVvRs3oD8IoP0CAZY9X/FGxowFMnr307pDUZiEtN54cfd5BcZCA70pH/bRmqH5TAkARTC2kTPh6g3S+cCap3MJ8YLu6PRaHjm5nYArIw9SVLmJbVDUs/aV+DUNmX7/74rnRMor3+7EpGQRL95G7h/yTYiDyoVD06kX+TvvVIDtbZIAiiENSm74OPOz6BJT2UEpGkv+RC0c31ae9O7ZUMKigx8Eumgo4DR82FrcSecJj2h7VDzhSHy+rcLEQlJTF4RV24ObMbFQmmHWIskARTCmhjKLPjQaGDwTGV/0m4IfUK5X9gljUbD1OJRwFU7TnImwwFHAS9dAE1xqZfBLynvAcqsDpbXv80ztUOsqNmhtEOsXZIACmFNBs0wX/DRahA076t0QijMVe4XduvGVt70ae1Nod7IxxuOqB1O7Su8pCx8at4PWg00v2/ANHn92wFph2g9JAEUwpppNMrIB0Dc13DhuNoRCQszzQX8YecpTp2/qHY4tefCcfj3a2V78MzS0T9hV6QdovWQBFAIa9eirzISaCiE6LfVjkZYWK8WDenfthFFBgcbBYyer8x3bT0YmvdROxphIdIO0XpIAiiELRj8kvL1v5VwzoGSAgf1dJgyCvhj3GlOpOeqHY7lnTsM/32rbA96Se1ohAX1btmQxvVcK73f4dsh1iJJAIWwBU17QrtwMBog+i21oxEW1qN5Awa2b4zeYGTBegdI+KPeUl7b7YZD0x5qRyMsSKfV0Kpx3QrvM130d+h2iLVIEkAhbMWgF5Wve340LxQt7NIzxaOAP8ed5ue40/waf4aYxHT7Wx2Zsg8SflK2Ta9xYbcOpWQTe1xZ4OFdz8XsPj9PNxaN6S7tEGuJ9AIWwlb4d4WOt8P+3yBqLtz3tdoRCQvqGuhFlyYe7D6TxdTv/yvZ7+/pxqwRQfbzIRn1prL2M+gO8O+idjTCwt5bewijEYbd4Msno3sQe+w8qdl5+NRXLvvKyF/tkRFAIWzJoBeVCyX7f4Oz8WpHIywoIiGJ3Weyyu1Pzsyzn2K5Z/+F/WuU1/RAGf2zd7tPZxCxNxmNBp4d2t6sHWJoa29J/mqZJIBC2BKfjtD5bmU78k21oxEWYiqWWxG7KpZreg13vgd8OqgdjbCwd9YeAmBkcBPa+dZXOxyHJwmgELZmwHSlW8Lhv+HUDrWjERbgEMVyT8XC4bXKa3ngdLWjERa2/Wg6Gw+l4aTV8HRYW7XDEZIACmGDGrWBrvcr25FvqB2NsACHKJa7ofi1G3w/eLdWOxphQUajkXfWHgTg3l6BNPeueBWwqF2SAAphi1zrgUYLR6Pg+Gbz+6LnQ+RctSITNcDuiuVGzlVelybHNsGxaNA6g6unvF7tXPShNHYcv4CLk5YnB8von7WQBFAIW+TurdRNA9gwB4zFc8Gi50PkHNDqVA1PXJ/eLRvi7+lGZVPiba5YrlanvC6j5yuv1cg5yn6/zrBtobxe7VjZ0b8HQ5vj52kjf7Q4ACkDI4QtGjAN8rIg5iM4uRWORsLpncoH66CZyv3CZum0GmaNCGLyijg0ZRZ+mBhtrViu6fUYOQfSE+FkjDL372ycvF7tXERCMglnsqjromPywDZqhyPKkBFAIWzVsDegaW9l++s7JfmzM+Gd/Fk0pnuFIyZ+Hm6EdfRVJa5rNmCaUupl9yrle6NeXq92Tm8oHf17uH8rGtZ1ueJjRO2REUAhbNmob+CdtsqYkNZJPkztTHgnf24O8ispllvP1Ymp38eTnJXHT3Gnua9XM7VDvDqN25Vu65zl9Wqn9AYjscfO8/vusySm5eLh5sSE/i3VDktcRkYAhbBlu5aVbhuKZDK9HSpbLHdIR1+eKJ5E//66w1wq0KsdXvUVFcCap5VtjQ70heYLQ4RdiEhIot+8Ddy/ZBvfbD8JxVMWth45p3Zo4jJWnwCeP3+e0aNH4+HhgZeXFw8//DA5OTlVPmbgwIFoNBqz26OPPmp2zMmTJ7n11ltxd3fHx8eH559/nqKiIgv/NELUINOCj/7PQV2f4n1vyYeqnXsgtDlNvOqQnJXHsq3H1Q6n+lb9H+RlgEtdmH5SufxrWhgi7EJEQhKTV8SVq2GZk1dkP91r7IjVJ4CjR49m7969rFu3jt9//52NGzcyadKkKz5u4sSJJCUlldzmzy89yej1em699VYKCgrYunUry5cvZ9myZbzyyisW/mmEqCGm5G/QTBjyMgyaoex3qiMfqnbO1UnHs0OVS6mfRB0h42KB2iFd2T+z4cg6ZXvoHKWM0YBpkgTaEVP3mop609hV9xo7YtUJ4P79+4mIiODzzz8nJCSEfv368dFHH7Fq1SrOnj1b5WPd3d3x8/MruXl4eJTct3btWvbt28eKFSsIDg5m+PDhvP766yxcuJCCAhs4mQphuGwCfbex0KgdFF2CZqHK/cJu3RHchA5+9cnOK+KTqES1w7myE1uUr43aQ7cHSvebkkB5vdo8h+heY2esOgGMiYnBy8uLnj17luwLCwtDq9Wyffv2Kh/7zTff0KhRIzp16sSMGTO4ePGi2fN27twZX9/SVXTDhg0jKyuLvXv3Vvqc+fn5ZGVlmd2EUMWgGeYT6HVOEDZb2T77L3R/oNKHCtun02p4YbjSO3fZ1uOcybikdkiVyzgFZ+OV7ZtnK6/VsgZMKx3BFjbLIbrX2BmrTgCTk5Px8fEx2+fk5ETDhg1JTk6u9HH/93//x4oVK4iMjGTGjBl8/fXXjBkzxux5yyZ/QMn3VT3v3Llz8fT0LLkFBgZex08nRA1rPxya94WivNI2W8JuDWzXmNBW3hQUGXh/3SG1w6nchjdAnw/N+0G7cLWjERZid91rHIAqCeD06dPLLdK4/HbgwIFrfv5JkyYxbNgwOnfuzOjRo/nqq69YvXo1iYnXd6lkxowZZGZmltxOnTp1Xc8nRI3SaGDo68r2f6sgabfaEQkL0mg0TC8eBfwp7jQHkq3wikTSf7D7O2V76OvKa1TYpd4tG9KoXuV1/myue40DUCUBfPbZZ9m/f3+Vt1atWuHn50dqaqrZY4uKijh//jx+fn7V/vdCQkIAOHLkCAB+fn6kpKSYHWP6vqrndXV1xcPDw+wmhFVp0gM63aXMuFkni5rsXddAL27t7I/RCPMjDqodjjmj6TVohE53Q5PuakckLEin1VTa5s2U9ttU9xoHoEoh6MaNG9O4ceMrHhcaGkpGRga7du2iR48eAGzYsAGDwVCS1FVHfLwy/8Tf37/keefMmUNqamrJJeZ169bh4eFBUFDQNf5UQliJIa/Avt+U9nBH/oE2YWpHJCzouWHtidibzIYDqWw9cg6NRkNqdh4+9ZXRFtU+cI+sh6NRoHNRVqoLu7b58DkSzmSh1YB3XRfSckoXVPp5ujFrRBDhnfxVjVGY0xiNRqtekz18+HBSUlJYvHgxhYWFjB8/np49e7Jy5UoAzpw5w5AhQ/jqq6/o3bs3iYmJrFy5kltuuQVvb292797NM888Q9OmTYmOjobiMjDBwcEEBAQwf/58kpOTeeCBB5gwYQJvvvlmtWPLysrC09OTzMxMGQ0U1iXiRdi2EHxugEc3gVandkTCgl76ZQ8rtp3EWaehUF96SvdX64PXoIfF/SB1H4ROgWFzavffF7VKbzBy64JNHEjOZlyfFrx8W1BJ9xrV/xCphHx+W/kiEIpX83bo0IEhQ4Zwyy230K9fPz777LOS+wsLCzl48GDJKl8XFxf++ecfhg4dSocOHXj22We56667WLNmTcljdDodv//+OzqdjtDQUMaMGcPYsWN57bXXVPkZhahxNz0Hbp6QuleZDyjsWucmngBmyR9AcmaeOgV4//tWSf7cPKH/s7X7b4ta9+OuUxxIzsbDzYmnhrQ1614T2trb6pI/obD6EUBrJn9BCKu2ZQGsexnqB8ATu8DFXe2IhAXoDUb6zdtQaQ02TfEluM0vDK6dD+KCi/BRd8hOgqFvQJ8nLP9vCtXk5hcx8J0o0rLzeenWjkzo30rtkKpFPr9tYARQCHGNek8Cz2aQfRa2faJ2NMJCrK4A77aFSvLn1Ux5DQq79ml0ImnZ+TT3dmdsaAu1wxFXQRJAIeyVs1vp5PvNH0BOmtoRCQuwqgK8OWmw+UNle/Ar4ORq+X9TqOZsxiU+23QUgBnDO+DiJCmFLZH/LSHs2bkjUM8PCrJh42X9VqPnQ+RctSITNUTVAryRc837+EbPU15r/sFw/qi8vuzcO38fJK/QQO8WDRl2Q/VLswnrIAmgEPZM5wQ5xd1tdn6pJISYkr85sjrYDvRu2RB/Tzcqm91n0QK8Wp3yOoqer7y2di1V9vveAFFvyuvLju0+ncHP/54BYOatHdFIkW+bo0odQCFELTH1C46cA4YiWP8q+HVRvh8007yfsLBJOq2GWSOCmLwiDk3xnL/LWawAb9nX154flNeYdxuI/0ZeX3bMaDTyxh/7AfhftyZ0DfRSOyRxDSQBFMLeDZgGuWkQ+xnsX6Pc5MPZroR38mfRmO7MXrOv3IKQCf1bWrYO4IBpcOG4kvQBpB+R15cd0huMJbX9TqRfJPbYeVydtDw/rL3aoYlrJAmgEI7glrdhx+dgNCgXBfs9o3ZEooaFd/Ln5iC/kg/pjYfS+CnuDH/uSWbqze2p42Khy7H6Qji9s/R7nYskf3YmIiGpwj8uBnfwIcCrjmpxiesjcwCFcATR84uTP5SLhCvvUzkgYQllC/C+MbIzTbzqcCbjEoujEy33j25bBOeK+xDrXEBfYL4wRNi0iIQkJq+Iq7DUUERCcu0XGRc1RhJAIeydacHHoJlw+8fKvsT1sFb6s9qzOi46Zt7aEYDF0YmcOn+x5v+RrLOwvriDUofb4OU05XVmWhgibJreYGT2mn0Vzis1mb1mH3qD9JOwRZIACmHPyiZ/A6ZB8Gho2ku5b+sC+ZC2c8M7+RHaypv8IgNv/rm/5v+BFXeBoRA8msC9Xyv7BkyTJNBOWF2RcVGjJAEUwp4Z9OYT8rVauOUd0BS/9c8fVTU8YVkajYZXb78BnVbDXwnJbDlyruae/Gi00u8XDdz/rfLaMjElgQZ9zf17otZZVZFxUeMkARTCng2aUX5CfkAw9HxY2T4Tp0ziF3arvV99HrixOQCv/raXQr3hio+5oqIC+PN5Zbv3RPDvWv6YAdOU15+wWaoWGRcWJwmgEI5o8Exwb6RM3t+2SO1ohIU9E9aOhnVdOJyaw9cxJ67/CbcXL/xwb6SM9Am7ZCoyXhmLFhkXFicJoBCOqE4DuLl48n7UW5B5Ru2IhAV5ujuX1Gt7/59DpGTlEZOYzq/xZ4hJTL+6SfyZZyBqnrI99HWoI0WA7ZVOq+HpsLYV3mcqK26xIuPC4qQOoBCOquv9ELccTm2HtS/BPUvVjkhY0L09A/lm+wkSzmQx8O0oLhWWzs/z93Rj1oig6hWMXjsTCnMh8EboMsqyQQvVbTmSDoCzTkOhvvQPBb+rec0IqyQJoBCOyrQg5LMBsPdn6PEgtBqodlTCQnRaDcM7+ZFwJsss+QNIzsxj8oo4Fo3pXvUHemIk7F2tLCK69R3zhR/C7mw6nMZv/51Fq4EfHunDpUI9qdl5+NRXLvvKyJ9tk3evEI7Mvwv0mqBs//m8Mrlf2CW9wciKbScrvM80rlNlTbeyCz96TQS/zhaKVFiDvEI9L/+SAMDY0BYEN/MqKTIe2tpbkj87IAmgEI5ukGlByCHY9ona0QgLue6abtsWQvphqNsYBr1ouUCFVVgUlcjx9Iv41Hfl2aHt1A5HWIAkgEI4ujpeEBiibEfPL78gJHo+RM5VJTRRc66qplvkXPMizpmnS78PvFFWjtu5o2k5LIpS2gfOGnED9d2c1Q5JWIAkgEKI0jpuhbnKJH8TUycRrU610ETNuKqablqdeSePv2dC4UXwDIQDa+T1YMeMRiMv/5pAgd7AgHaNuaWzn9ohCQuRRSBCCBj4AuSmwo7PlUn+3R+E0zvM28gJm2aq6ZacmVdhb1dN8crO3i0bQuvi/+/IOUq3mH2/KEdknpLXg5377b+zbDmSjquTltfuuAGNRub62StJAIUQilvfhaT/lMTv6/8ps8Lkw95u6LQaZo0IYvKKODRlFn6UZVbTbcA0MBRBdHHNP3k92CW9wUjssfOkZudR18WJ19bsBeCJwW1o7l1X7fCEBUkCKIQoNfpHmNdc+bDX6OTD3s6Ed/Jn0ZjuzF6zr9yCkBtbeZcvAWMoKt3Wucjrwc5EJCRV+Frw9XBl4k2tVItL1A6ZAyiEKBX7Wem2UQ9rnlYzGmEB4Z382fzCYL6deCMfjgrm1RFBAMQcTSf6UFrpgad3wab3lG2tE+gLzBeGCJsWkZDE5BVxFa4MT8nKJ/JAqipxidojCaAQQmFa8DFoJnS6S9m3aylseFPtyEQN02k1JTXdxvVtybg+LQB48ec95OQXQeElWHmPMhLsEwSvpCuvi7ILQ4TN0huMzF6zr8JpABTPB62yJqSwC5IACiHMk78B05QOIfV8lfs2zpMPfTs3Lbw9gQ3rcCbjEvP+OgBf3QEX08GlLoz7QzlowDRJAu3EddeEFHZBEkAhBBj05hP83RvCiA9L779wQrXQhOW5uzjx1p1dANi//W+Mp7Yrd9z1pfJaMDElgQZ9Jc8kbMFV1YQUdksWgQghYNCM8vvaD4eu/wf/rYSTW6EgVxkREnapb5tGjO3ZiId2f4oGKOpyP07tw8sfKAtBbN5V1YQUdktGAIUQlQufC/UDlFpw/8xWOxphYS+5fE8LbQpnjQ350OlhtcMRFmKqCVkZDeBvqgkp7JYkgEKIytXxgjs+UrZjP4VjG9WOSFjK0Whc4j4H4IXCSSyMSWXXiQvEJKbza/wZYhLTZVGAndBpNYy5sVmF95nKPpvVhBR2SS4BCyGq1iYMeoyDXcvg18dh8lZwra92VKIm5WXBr1OU7R7j8c4NxxB/lvs+jaGoTNLn7+nGrBFB5esFCpuSk1/EdztOA1DHWculQkPJfX7yf+wwrH4E8Pz584wePRoPDw+8vLx4+OGHycnJqfT448ePo9FoKrz98MMPJcdVdP+qVatq6acSwsYMfQO8mkHGSVj7ktrRiJq29iXIPKn8Hw99nX5tGgGYJX8AyZl5TF4RR0RCkkqBiprw2pq9nDx/kSZeddg6Y0hJTchvJ97I5hcGS/LnIKw+ARw9ejR79+5l3bp1/P7772zcuJFJkyZVenxgYCBJSUlmt9mzZ1OvXj2GDx9uduzSpUvNjhs5cmQt/ERC2CDX+nDHQmV71zI48o/aEYmacvgfiFuubN/xCXrnery77lCFh5rSQakRZ7v+3pvM9ztPo9HAe/d2pYG7S0lNyNDW3nLZ14FY9SXg/fv3ExERwY4dO+jZsycAH330EbfccgvvvPMOAQEB5R6j0+nw8/Mz27d69Wruvfde6tWrZ7bfy8ur3LFCiEq0vAkCesDZXfDrE/BYjDJH0CR6fnE5mQpWFAvrEDkXtGVa/F3KgN+eULab9oLjm4k1BFW7Rlxoa+9aClzUhNTsPGb8vAeASTe1IqSV/P85MqseAYyJicHLy6sk+QMICwtDq9Wyffv2aj3Hrl27iI+P5+GHy69oe/zxx2nUqBG9e/fmyy+/xGis+i/a/Px8srKyzG5COJQ2g5Wv2WchokyiZyokrdWpFpqoBq3OvJBzxHTl/7JOAzi9A7Q6qRFnp4xGI9N+3M353AI6+nsw9eZ2aockVGbVI4DJycn4+PiY7XNycqJhw4YkJydX6zm++OILOnbsSJ8+fcz2v/baawwePBh3d3fWrl3LY489Rk5ODk8++WSlzzV37lxmz5ZSGMKBDX4JclIg7iulPmDHEZCSYN5FRFgv0/9P5BxIOwQJPyjrPi9dKPn/80lMr9ZTSY0427Ji+0miDqbh4qTlw1HBuDrJH2uOTpUEcPr06cybN6/KY/bv33/d/86lS5dYuXIlL7/8crn7yu7r1q0bubm5vP3221UmgDNmzGDq1Kkl32dlZREYGHjdcQphU27/CNIOwqntsOp+ZZ8kf7ZjwDQouAhb3i/eYTT7/zPViEvOzKu0V6zUiLN+eoOR2GPnSc3Oo8hg5I3f9wLwQngH2vnKKn6hUgL47LPPMm7cuCqPadWqFX5+fqSmpprtLyoq4vz589Wau/fjjz9y8eJFxo4de8VjQ0JCeP3118nPz8fV1bXCY1xdXSu9TwiHMvY3mONXPCNMA/2fVTsiUV0GPSTFl36vczFL3nVaDbNGBDF5RRyaMgs/ypo+vIMsFrBiEQlJzF6zr9xczg5+9Rjfp4VqcQnrosocwMaNG9OhQ4cqby4uLoSGhpKRkcGuXbtKHrthwwYMBgMhISFX/He++OILbr/9dho3bnzFY+Pj42nQoIEkeEJUx9YFZVIDIywfoXJAotoi58DRSGVb6wz6gtI5gcXCO/mzaEx3/C7rFmHK+bYcOVdr4YqrE5GQxOQVcRUu5DmQnMPafdWbPiXsn1XPAezYsSPh4eFMnDiRxYsXU1hYyJQpUxg1alTJCuAzZ84wZMgQvvrqK3r37l3y2CNHjrBx40b+/PPPcs+7Zs0aUlJSuPHGG3Fzc2PdunW8+eabPPfcc7X68wlhk0wLPgbNhAYt4ecJcGIL/Pgw3P2F2tGJquz/HTa9q2wHjYR7l5f+f2Le5ze8kz83B/mVXEb0qe+GXm/ggaWxfL/zNCEtvbmrR1OVfhBREb3ByOw1+yq9dK8pLuFzc5CfjOAK604AAb755humTJnCkCFD0Gq13HXXXSxYsKDk/sLCQg4ePMjFixfNHvfll1/StGlThg4dWu45nZ2dWbhwIc888wxGo5E2bdrw3nvvMXHiRIv8DHq9nsLCQos8tzDn4uKCVmvVi9ttW9nkz5QsnNkF2xdBwo9QtxEMr3p+r1DJucPw43hlu2lvJfnjsoUhUO5y8OWlXp4e0o73/znES78k0KWpJ21lPpnViD12Xkr4iGrTGK9U+0RUKisrC09PTzIzM/Hw8Ch3v9FoJDk5mYyMDFXic0RarZaWLVvi4uKidij26fI6cgD6Qlh+O5zcCu7e8NRucK1X1bOI2pafA58PgbQD4NkMnowDnbP5MdWs46g3GHnwy1g2HzlHW596/DqlL+4uVj+W4BB+jT/DU6vir3jch6OCuSO4Sa3EZK2u9PntCORda0Gm5M/Hxwd3d3c0GhlytySDwcDZs2dJSkqiWbNm8vu2hIqSA50z3LMMPr0JcpLhtylw91KQ3791MBqVHs5pB6C+P0z4p3zyB9Vexa3TavhgVDC3fLiJw6k5vPRLAvPv6sKO4xdKLhX3btlQLjGqoLqleaSEj0ASQMvR6/UlyZ+3twy115bGjRtz9uxZioqKcHau4ENOWEZ9X7j3K1h2C+xdDU16Qp8pakclAGI+hn2/KAs+7lmu/F9dp0b1XFlwfzf+b8k2fo47w/r9qWReKp3m4u/pxqwRQdJTtpb1btkQDzcnsvKKKrxfA/hJCR9RTCZLWYhpzp+7u7vaoTgU06VfvV6vdiiOp1kIDJurbK97BY5tUjsicWyj8n8BED5X+T+qITe28mZEV2UxXtnkDyA5M4/JK+KISEiqsX9PXFnssfPk5Fee/AHMGhEko7MCJAG0PLkMWbvk962y3hOhy31g1MMP4yDzjNoROa7M0/DDeDAaoMso6DWhRp9ebzCy/ej5Cu8zTSyfvWYfeoNMM68NJ9Mv8tg3uzAYoVeLBuVK+Ph5urFoTHcZlRUl5BKwEKLmaDRw2weQGAm5qfD9WBj/JziVqa9ZzcUG4ipcvjinKF/53V88B/V8wKNJjc/JjD12nuQsWXFqDXLyi5j41U4uXCykS1NPvn44BGed1qyEj8zLFJeTEUBRbePGjWPkyJFqhyGsnYs7dL5b2T6zEyKml95nKiOjlT6kNUqrU36vpoLOf72glOdxcoOcVHCu+Un/qdmVJ3/Xcpy4NgaDkWe+i+dgSjY+9V357IGeuDnrSkr43BHchNDW3pL8iXJkBNDKle3nqPZfcR9++CFSNUhUS/hcuJgOu7+DnV9Ckx6QdbZ8DUFRM8rW8jsbDwf/UL4vyrPY71tWnKrj8s+ETYfTWLcvBRcnLZ8+0KPcpV8hKiMJoBWrqJ+jmqvrPD09a/3fFDbszs8gKwmOb1TKkIAkf5Y0YBpknYFdy0r3WfD33btlQ/w93UjOzKu084S/rDitUZX1+AV4687OdGvWQJW4hG2SS8BWqrJ+jrWxuu7HH3+kc+fO1KlTB29vb8LCwsjNzS13CXjgwIE8+eSTTJs2jYYNG+Ln58err75q9lwZGRlMmDCBxo0b4+HhweDBg/nvv/8sFruwMmN/NZ971v4WNaOxb8kJsPeX0u91LhZNtnVaDbNGBEGZFaaXu7tHU7n0WEOq6vEL4O4i0yrE1ZEEsBYZjUYuFhRd8ZadV8is3/ZW+Fe1ad+rv+0jO6+wWs93NZdtk5KSuP/++3nooYfYv38/UVFR3HnnnZU+x/Lly6lbty7bt29n/vz5vPbaa6xbt67k/nvuuYfU1FT++usvdu3aRffu3RkyZAjnz1e8elDYmU3vKIWITSnCFzdD2iG1o7I/aYfgqzsgr7jrkM4F9AWlcwItJLyTP4vGdC932dHNWflo+WLzMeJPSSek61XdHr+y4lpcDbkEXIsuFeoJeuXv634eI5CclUfnV9dW6/h9rw2rdqumpKQkioqKuPPOO2nevDkAnTt3rvT4Ll26MGvWLADatm3Lxx9/zPr167n55pvZvHkzsbGxpKam4uqqrAJ95513+OWXX/jxxx+ZNGlStWISNqps3+Dek2BhL2VBwpJB8OhmaNhS7Qjtw/mj8NXtyopfgH5TIWxW6e+f6nf5uBbhnfy5OcjPbF5acKAXk77eyabD53ho2Q5+eDSU1o2lPeC1kh6/whJkBFCY6dq1K0OGDKFz587cc889LFmyhAsXLlR6fJcuXcy+9/f3JzU1FYD//vuPnJwcvL29qVevXsnt2LFjJCYmWvxnESoqm/wNmAZ1vGByDLg3goIc+GyAUqdOXJ/M07D8DsgunhLS9xkl+aM46Rs003x1sIVcvuK0jouOxWN60LWpJ+dzCxj7RSwpWXnoDUZiEtP5Nf4MMYnpMmJVTbLiWliCjADWojrOOva9NuyKx8UeO8+4pTuueNyy8b2qNcG6jnP154bodDrWrVvH1q1bWbt2LR999BEzZ85k+/btFR5/ebs1jUaDwWAAICcnB39/f6Kioso9zsvLq9oxCRtk0JdfgFC3EUzeAp/cCJcuKJcsx/+l1KkTVy87BZbfDpknwc0Luo+Fm83n4Jb8/g213xmnrqsTX47rxd2LYzh2Lpf/LdyC3mgkJSu/5BhpGVc9suJaWIIkgLVIo9FU61Js/7aNq1xdZ+rn2L9tY4tMsNZoNPTt25e+ffvyyiuv0Lx5c1avXn3Vz9O9e3eSk5NxcnKiRYsWNR6nsGKVFXmu7wePbIKlwyH9iJIEjvsD3GWl6FW5eB6+HgnnE8EzUEmkvQIrPlbFVdfe9Vz56qHe3LpgE2cruIRpWtQmHSqq1s63Hs5aDYWVjJhKj19xLeQSsBWqanWdpfs5bt++nTfffJOdO3dy8uRJfv75Z9LS0ujYseNVP1dYWBihoaGMHDmStWvXcvz4cbZu3crMmTPZuXNnjccubIRXoLI6uJ4fpO6Dr/8HeZlqR2U7LmUoyV/qPuV3+OBvlSd/ViDAqw4uThV/1EjLuCu7kFvA2C9jq0z+kB6/4hpIAmilKltdZ+l+jh4eHmzcuJFbbrmFdu3a8dJLL/Huu+8yfPjwq34ujUbDn3/+yU033cT48eNp164do0aN4sSJE/j6+lokfmEjvFsrSaC7NyTFwyd9ID+n/HHR85U2Z44ocm75uXv5OfDNPZD0HzjVUZK/hq3UirBaYo+d51xOQaX3l13AIMyl5+Rz/5Jt7D2bRaN6Lrx8WxD+0uNX1BCNUVo7XLOsrCw8PT3JzMzEw8PD7L68vDyOHTtGy5YtcXO79nkZ1tQJxBbU1O9d1JKk3fBFmNK71qs5PL4dnOso912+kMTRXP7zF15Skr/jm5T7e02AW99VO8or+jX+DE+tir/icR+OCuaO4Ca1EpM1uvxc37JRXcZ+uZ1DKTk0ru/KtxNDaONTXz4TakhVn9+OQuYAWjnT6joh7JJ/Fxj3pzInMOMELOoLj22DLR84dvLHZe3dDHo4G1ea/PUYZxPJH7KAoVoq6vCh02rQG4z4eriycuKNJWV05DNB1BRJAIUQ6mraEx5YrSwIOZ8Ib/goFwYdOfkzGTANCi5C9Ful+7qNgREfqhnVValOy7jG9VwddgGDqcPH5b8b05zIxwe2kRqKwiJkDqAQQn0t+sH/fV/8TfFHYbsrl0yye2fjIeGn0u+1TnDHQjUjumrVaRmXnVdITGJ6rcZlDa7U4QNgUXSiLJARFiEJoBDCOpzZZf79ksGw+we1olHf7u/hy2FKnT8ArTMYiixe1NkSKlvU5uvhSuvGdckrMjBuaSzf7zgFxYmRIxSMvlKHD2SBjLAguQQshFCfWdu4ibBkiHI5+OcJcPZfuPk10DnI6UpfBOtehm2flO6r5fZullBRy7jeLRtSZDAw7cfd/Bp/lmk/7Wb9gRT+O5VJclZpYmSvBaOlw4dQk4OcUYUQVqui1b5TdsDyEXBiC2xbCMm74Z5lSjcRe5Z7Dn4YV7rYA2DgDBg4XdkuuzAE20sCK1rAoNPq+OC+YJo3dGfBhiP8vTel3OPstWC0ezW7NDnyAhlhOXIJWAihroraxml1MP5PuOEu5dLn8U2woBv8/kzFz2FL9QIrqu9H8Xy/Bd2Un9WlHgT9T/m9mJI/E1OPXxXau1mKRqPhqbB2eNZxrvB+eywYvf1oOi/9klDlMZri0U9HXSAjLEtGAIUQ6qqsbRzAPV9C6n5YNVq5JLzzS2WU7L6vS48pO4JoC7S68iN4/62CXx9X5vjVaQDjI8CnQ+XPYWMjf9URe+w8mZcKK72/bMFoWyqDcnndvh7NG7AoKpEP1x/CYATf+q6kZOejKZPoIh0+RC2QBFAIYd18OsLEDfDzJDj8N+z/DT6/WRkh3Py+7dULvLy+X14mbF+k7PNuAxPWQx0vVUNUgz3Oh6uovp+LTkOBXkn17urelNfuuIFNh9PKHednp/MehfWQBFDUmldffZVffvmF+PgrdwUQwkwdL7h/FUTNhY3z4XQsvN5YGTMZ+KLtJH8mNz0P6UfM6/u16Adj14DWMWfmVHeem3ddl5Jta+6KUVl9P1PyN65Pc169vRNUsUDGWn4WYZ+kFdx1qI1WcPYkJyeH/Px8vL0td/lGfu8OYP/v8N3o0u9b9IebZ0OTHmpGVX2nd8E/s8wXemid4BXHq4NXlt5gpN+8DVUWjAZo51OP10d24sLFgnKjZtayWtj0s1RV4sXf043NLwyWJE8l0gpOFoFYr8omimNjE97LqFevnkWTP+EgUvcpXzXFp6/jm5Sagd8/COmJ6r13rvTv/vE8fD8WPh+sxKwpXgGqc7HZ+n41qaqC0abv67roOJSaw32fbePRFXHlEizTauGIhCSLx1tVrUKp7ydsgSSA1so0UfzyDwXThHdt9coHXAuDwcD8+fNp06YNrq6uNGvWjDlzlEnre/bsYfDgwdSpUwdvb28mTZpETk5OyWOjoqLo3bs3devWxcvLi759+3LixAkovgQcHBxccuy4ceMYOXIk77zzDv7+/nh7e/P4449TWFg6ETw/P5/nnnuOJk2aULduXUJCQoiKirLYzy6sXNkFH7MuQOjjpfft+wU+7gWH16rz3qnsPbv2ZWX/jiWw71clnfHrAsbi1c8vpylfK3qsg6msYLSfpxuLx3Rn8wuDGdU7sNLH19Zq4YiEJPrN28D9S7bx1Kp47l+yjX7zNhCRkMTJ9It8tOFwtZ7HluYzCvsjcwBrk9EIhRerd2zo46AvUD4U9AXQ7xllwvvGt5X5Q6GPQ0Fu9Z7L2R001b/MMGPGDJYsWcL7779Pv379SEpK4sCBA+Tm5jJs2DBCQ0PZsWMHqampTJgwgSlTprBs2TKKiooYOXIkEydO5Ntvv6WgoIDY2Fg0VfzbkZGR+Pv7ExkZyZEjR7jvvvsIDg5m4sSJAEyZMoV9+/axatUqAgICWL16NeHh4ezZs4e2bdtW+2cSdqCieoHD3gQ3L2V/wzZw/gicjVNKx0TOgaI8GPJKxY+taZfX6At5FL69H05sLj7ACO3CwTNQSQbLxmLj9f1q0pXmw93RtQmrYk9V+viKVgtfzVzBKx1b2dy+pMw8Hl0RV241b1Wkvp9Qk9XPAZwzZw5//PEH8fHxuLi4kJGRccXHGI1GZs2axZIlS8jIyKBv374sWrTILGE4f/48TzzxBGvWrEGr1XLXXXfx4YcfUq9e9ZtuX/UcwIJceDPgan78mvHiWXCpW61Ds7Ozady4MR9//DETJkwwu2/JkiW88MILnDp1irp1lef7888/GTFiBGfPnsXZ2Rlvb2+ioqIYMGBAuee+fBHIuHHjiIqKIjExEZ1OGZW599570Wq1rFq1ipMnT9KqVStOnjxJQEDp7y0sLIzevXvz5ptvlvs3ZA6gHYucq4yyVZQcRc9XVtS27A/rZsGZnaX3aXTKaNuA6eYlZ6rzfINmVP84AH2hUqvw36/Nj2vSU5mn2KLf1T2fKOfX+DM8terKC8ne/F8n/i+keYUrcSubK3ilY6sztw+gfxtv9iZlcyG3oMJkUFM8qilzANUjcwBtYASwoKCAe+65h9DQUL744otqPWb+/PksWLCA5cuX07JlS15++WWGDRvGvn37SpKC0aNHk5SUxLp16ygsLGT8+PFMmjSJlStXWvgnsm779+8nPz+fIUOGVHhf165dS5I/gL59+2IwGDh48CA33XQT48aNY9iwYdx8882EhYVx77334u9f+YTsG264oST5A/D392fPnj1QfLlZr9fTrl07s8dYeiGJsFJVJUVlk6kJ/yilYta/pqy0NRYXTI4p7ijSahC0HqzMIaxoxO3yuoIV1e0re1zIo7D9M0jcAMc3Q0G2eWz3fg0dR5SOwlf35xAVqu6o2Uu/JLBi20n2JWWVu6+iziKVjeyVPdazjssVkz+Axwa1JfNSAZMrGBGU+n7CWlh9Ajh79mwAli1bVq3jjUYjH3zwAS+99BJ33HEHAF999RW+vr788ssvjBo1iv379xMREcGOHTvo2bMnAB999BG33HIL77zzjtloU41ydldG466G6bKvzkW5FHzT88rl4Kv9d6upTp06V/fcl1m6dClPPvkkERERfPfdd7z00kusW7eOG2+8seLQnM0r/2s0GgwGAxSvGtbpdOzatcssSaR4QYkQFdJoIOgOSNmnlFnRaMFoUBKzg38qN1AuxfoHK0lc4UUIe7XiS8WXX57tNQF+nwr7VoOrB2xfbP7vO9WBokvKyl5DEaQdgKDba/M3YNd6t2yIv6dblauFnbQaigzGCpM/yiRkr/62l7COvmg0Gmav2Vfh85n2Pb0qHlfn6k2bT83O447gJiwa013q+wmrZfUJ4NU6duwYycnJhIWFlezz9PQkJCSEmJgYRo0aRUxMDF5eXiXJH8WXFbVaLdu3b+d///tfhc+dn59Pfn5+yfdZWRWfXCql0VT7UiwUjzBsfLv0w8j04aRzsdhIQdu2balTpw7r168vdwm4Y8eOLFu2jNzc3JJRwC1btqDVamnfvn3Jcd26daNbt27MmDGD0NBQVq5cWWkCWJVu3bqh1+tJTU2lf//+NfDTCYcRPV9J/kzvnah5EPUmtBqoXGI9tR0yTyk3iv/Q2vy+su1SF3Z8rtzKcqmrvP9MiSBAfpbyfmx2ozKymHlK6VZy+XsWGd2rKabVwlWNrn38f924VKDnme//q/K5krPyaffSX7i76MjJr7q1Xl6RgbwiQ7ViNI1SSn0/Yc3sLgFMTk4GwNfX12y/r69vyX3Jycn4+PiY3e/k5ETDhg1LjqnI3LlzS0YkLa46IxEW+EBxc3PjhRdeYNq0abi4uNC3b1/S0tLYu3cvo0ePZtasWTz44IO8+uqrpKWl8cQTT/DAAw/g6+vLsWPH+Oyzz7j99tsJCAjg4MGDHD58mLFjx15TLO3atWP06NGMHTuWd999l27dupGWlsb69evp0qULt956a43//MIOVPTeGfiC8geYaf//fQcntkJipHLpNm1/6eMLcquxwEoDNz4GrQdB8z5Kchg93zz5QxZ3WIpptXBVo2u/xp+p1nMZjFwx+TOZMqg1P+w6TWpWfpVz+8r27tVpNTbVuk44DlUSwOnTpzNv3rwqj9m/fz8dOlTRC1MFM2bMYOrUqSXfZ2VlERhYeUmC62LQV7xi0fS9BRvBv/zyyzg5OfHKK69w9uxZ/P39efTRR3F3d+fvv//mqaeeolevXri7u3PXXXfx3nvvAeDu7s6BAwdYvnw56enp+Pv78/jjj/PII49ccyxLly7ljTfe4Nlnn+XMmTM0atSIG2+8kdtuu60Gf2JhV6rz3nGpC21vVm4l5WGcwVCoXOLtMa788+5apowK6pyVxR51vJTHX82/K2rMlUbXqjtX8JPR3cnNL+L5H3df8di+bRrTqYmnzO0TdkGVVcBpaWmkp1dd9b5Vq1a4uJS2/Fm2bBlPP/30FVcBHz16lNatW/Pvv/+a1ZwbMGAAwcHBfPjhh3z55Zc8++yzXLhwoeT+oqIi3Nzc+OGHHyq9BHw56QRifeT3Lq7K5aOFlZWLqe5xwmpcqbNI2ZW4QLWP1Wk1V7WyWFgnWQWs0ghg48aNady4sUWeu2XLlvj5+bF+/fqSBDArK4vt27czefJkAEJDQ8nIyGDXrl306KG0j9qwYQMGg4GQkBCLxCWEsDLVnWah0nQMcX2qM1ew7Gjd1Rwrc/uEPbD6TiAnT54kPj6ekydPotfriY+PJz4+3qz7RIcOHVi9ejUUryJ9+umneeONN/jtt9/Ys2cPY8eOJSAggJEjR0LxYobw8HAmTpxIbGwsW7ZsYcqUKYwaNcpyK4CFENalqku2g2aWXrKt7nHC6lTVWaRsCZirPZYyc/vuCG5CaGtvSf6EzbH6QtDjxo1j+fLl5fZHRkYycOBAKE76li5dyrhxyrwdUyHozz77jIyMDPr168cnn3xiVk/u/PnzTJkyxawQ9IIFCyxbCFpYnPzehRCXq8lOIMI+yCVgG0gArZkkgNZHfu9CCCGuRBJAG7gEbOskv65d8vsWQgghrkwSQAsxdbi4ePGi2qE4lIKCAoBynUOEEEIIUcruCkFbC51Oh5eXF6mpqVBcI0+jkXkklmQwGEhLS8Pd3R0nJ3lpCyGEEJWRT0kL8vPzAyhJAoXlabVamjVrJsm2EEIIUQVJAC1Io9Hg7++Pj48PhYWFaofjEFxcXNBqZWaDEEIIURVJAGuBTqeTOWlCCCGEsBoyVCKEEEII4WAkARRCCCGEcDCSAAohhBBCOBiZA3gdTEWHs7Ky1A5FCCGEENVk+tx25OYBkgBeh/T0dAACAwPVDkUIIYQQVyk7OxtPT0+1w1CFJIDXoWHDhgCcPHnSYV9A1yorK4vAwEBOnTrlsH0Yr5X87q6d/O6unfzurp387q6dpX53RqOR7OxsAgICauw5bY0kgNfBVG/O09NT3tTXyMPDQ35310h+d9dOfnfXTn53105+d9fOEr87Rx+4kUUgQgghhBAORhJAIYQQQggHIwngdXB1dWXWrFm4urqqHYrNkd/dtZPf3bWT3921k9/dtZPf3bWT353laIyOvAZaCCGEEMIByQigEEIIIYSDkQRQCCGEEMLBSAIohBBCCOFgJAEUQgghhHAwkgBeo4ULF9KiRQvc3NwICQkhNjZW7ZBswsaNGxkxYgQBAQFoNBp++eUXtUOyGXPnzqVXr17Ur18fHx8fRo4cycGDB9UOyyYsWrSILl26lBSTDQ0N5a+//lI7LJvz1ltvodFoePrpp9UOxeq9+uqraDQas1uHDh3UDstmnDlzhjFjxuDt7U2dOnXo3LkzO3fuVDssuyIJ4DX47rvvmDp1KrNmzSIuLo6uXbsybNgwUlNT1Q7N6uXm5tK1a1cWLlyodig2Jzo6mscff5xt27axbt06CgsLGTp0KLm5uWqHZvWaNm3KW2+9xa5du9i5cyeDBw/mjjvuYO/evWqHZjN27NjBp59+SpcuXdQOxWbccMMNJCUlldw2b96sdkg24cKFC/Tt2xdnZ2f++usv9u3bx7vvvkuDBg3UDs2uSBmYaxASEkKvXr34+OOPATAYDAQGBvLEE08wffp0tcOzGRqNhtWrVzNy5Ei1Q7FJaWlp+Pj4EB0dzU033aR2ODanYcOGvP322zz88MNqh2L1cnJy6N69O5988glvvPEGwcHBfPDBB2qHZdVeffVVfvnlF+Lj49UOxeZMnz6dLVu2sGnTJrVDsWsyAniVCgoK2LVrF2FhYSX7tFotYWFhxMTEqBqbcCyZmZlQnMiI6tPr9axatYrc3FxCQ0PVDscmPP7449x6661m5z1xZYcPHyYgIIBWrVoxevRoTp48qXZINuG3336jZ8+e3HPPPfj4+NCtWzeWLFmidlh2RxLAq3Tu3Dn0ej2+vr5m+319fUlOTlYtLuFYDAYDTz/9NH379qVTp05qh2MT9uzZQ7169XB1deXRRx9l9erVBAUFqR2W1Vu1ahVxcXHMnTtX7VBsSkhICMuWLSMiIoJFixZx7Ngx+vfvT3Z2ttqhWb2jR4+yaNEi2rZty99//83kyZN58sknWb58udqh2RUntQMQQly9xx9/nISEBJlTdBXat29PfHw8mZmZ/Pjjjzz44INER0dLEliFU6dO8dRTT7Fu3Trc3NzUDsemDB8+vGS7S5cuhISE0Lx5c77//nuZdnAFBoOBnj178uabbwLQrVs3EhISWLx4MQ8++KDa4dkNGQG8So0aNUKn05GSkmK2PyUlBT8/P9XiEo5jypQp/P7770RGRtK0aVO1w7EZLi4utGnThh49ejB37ly6du3Khx9+qHZYVm3Xrl2kpqbSvXt3nJyccHJyIjo6mgULFuDk5IRer1c7RJvh5eVFu3btOHLkiNqhWD1/f/9yf5h17NhRLqHXMEkAr5KLiws9evRg/fr1JfsMBgPr16+X+UTCooxGI1OmTGH16tVs2LCBli1bqh2STTMYDOTn56sdhlUbMmQIe/bsIT4+vuTWs2dPRo8eTXx8PDqdTu0QbUZOTg6JiYn4+/urHYrV69u3b7kSV4cOHaJ58+aqxWSP5BLwNZg6dSoPPvggPXv2pHfv3nzwwQfk5uYyfvx4tUOzejk5OWZ/AR87doz4+HgaNmxIs2bNVI3N2j3++OOsXLmSX3/9lfr165fMOfX09KROnTpqh2fVZsyYwfDhw2nWrBnZ2dmsXLmSqKgo/v77b7VDs2r169cvN8e0bt26eHt7y9zTK3juuecYMWIEzZs35+zZs8yaNQudTsf999+vdmhW75lnnqFPnz68+eab3HvvvcTGxvLZZ5/x2WefqR2afTGKa/LRRx8ZmzVrZnRxcTH27t3buG3bNrVDsgmRkZFGoNztwQcfVDs0q1fR7w0wLl26VO3QrN5DDz1kbN68udHFxcXYuHFj45AhQ4xr165VOyybNGDA/7dzB0USAkEUBW+DBgIDHPCwMloGfrCBHbz0ymB2X6aCf3yHivqZ53m+PePrjTHmuq7z8/nMbdvmGGM+z/P2rD/jvu95HMdclmXu+z6v63p70r/jDyAAQIwbQACAGAEIABAjAAEAYgQgAECMAAQAiBGAAAAxAhAAIEYAAgDECEAAgBgBCAAQIwABAGIEIABAjAAEAIgRgAAAMQIQACBGAAIAxAhAAIAYAQgAECMAAQBiBCAAQIwABACIEYAAADECEAAgRgACAMQIQACAGAEIABAjAAEAYgQgAECMAAQAiBGAAAAxAhAAIOYXkz7CNItkjQoAAAAASUVORK5CYII=", + "text/html": [ + "\n", + "
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\n", + " " + ], + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(x, np.sin(x), marker=\"o\", label=\"sine\")\n", + "ax.plot(x, np.cos(x), marker=\"x\", label=\"cosine\")\n", + "ax.set_xlim(0.0, 2.0*np.pi)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{tip}\n", + "We can also specify basic style using a \"format string\" (see https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.plot.html)\n", + "\n", + "This has the form `'[marker][line][color]'`\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we can change the linestyle and thickness" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "ad63aee9437e40dfbf9256dcff07dfe0", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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Generally you need to start from the figure creation for these to take effect" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['Solarize_Light2',\n", + " '_classic_test_patch',\n", + " '_mpl-gallery',\n", + " '_mpl-gallery-nogrid',\n", + " 'bmh',\n", + " 'classic',\n", + " 'dark_background',\n", + " 'fast',\n", + " 'fivethirtyeight',\n", + " 'ggplot',\n", + " 'grayscale',\n", + " 'petroff10',\n", + " 'seaborn-v0_8',\n", + " 'seaborn-v0_8-bright',\n", + " 'seaborn-v0_8-colorblind',\n", + " 'seaborn-v0_8-dark',\n", + " 'seaborn-v0_8-dark-palette',\n", + " 'seaborn-v0_8-darkgrid',\n", + " 'seaborn-v0_8-deep',\n", + " 'seaborn-v0_8-muted',\n", + " 'seaborn-v0_8-notebook',\n", + " 'seaborn-v0_8-paper',\n", + " 'seaborn-v0_8-pastel',\n", + " 'seaborn-v0_8-poster',\n", + " 'seaborn-v0_8-talk',\n", + " 'seaborn-v0_8-ticks',\n", + " 'seaborn-v0_8-white',\n", + " 'seaborn-v0_8-whitegrid',\n", + " 'tableau-colorblind10']" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plt.style.available" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.0, 6.283185307179586)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "e144370f89a6484b8f885b0651dc4b65", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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\n", + " Figure\n", + "
\n", + " \n", + "
\n", + " " + ], + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.style.use(\"fivethirtyeight\")\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111)\n", + "ax.plot(x, np.sin(x), linestyle=\"--\", linewidth=3.0)\n", + "ax.plot(x, np.cos(x), linestyle=\"-\")\n", + "ax.set_xlim(0.0, 2.0*np.pi)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "plt.style.use(\"default\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Multiple axes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a wide range of methods for putting multiple axes on a grid. We'll look at the simplest method.\n", + "\n", + "The `add_subplot()` method we've been using can take 3 numbers: the number of rows, number of columns, and current index" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "c7195c39fb524d3b876a020ad0442837", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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", + "text/html": [ + "\n", + "
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Here we create a 2-d Gaussian, using the `meshgrid()` function to define a rectangular set of points." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def g(x, y):\n", + " return np.exp(-((x-0.5)**2)/0.1**2 - ((y-0.5)**2)/0.2**2)\n", + "\n", + "N = 100\n", + "\n", + "x = np.linspace(0.0, 1.0, N)\n", + "y = x.copy()\n", + "\n", + "xv, yv = np.meshgrid(x, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A \"heatmap\" style plot assigns colors to the data values. A lot of work has gone into the latest matplotlib to define a colormap that works good for colorblindness and black-white printing." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "e3b68b5884bd4efa9bf1b5c83467a933", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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The `contour()` function does this for us." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(np.float64(0.0), np.float64(99.0), np.float64(0.0), np.float64(99.0))" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "a2eaad70173f4c69857d24aab2b89e81", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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+ "text/html": [ + "\n", + "
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\n", + " \n", + "
\n", + " " + ], + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "contours = ax.contour(g(xv, yv))\n", + "ax.axis(\"equal\") # this adjusts the size of image to make x and y lengths equal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} Quick Exercise\n", + "Contour plots can label the contours, using the `ax.clabel()` function.\n", + "Try adding labels to this contour plot.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Error bars" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For experiments, we often have errors associated with the $y$ values. Here we create some data and add some noise to it, then plot it with errors." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "def y_experiment(a1, a2, sigma, x):\n", + " \"\"\" return the experimental data in a linear + random fashion a1\n", + " is the intercept, a2 is the slope, and sigma is the error \"\"\"\n", + "\n", + " N = len(x)\n", + "\n", + " # standard_normal gives samples from the \"standard normal\" distribution\n", + " rng = np.random.default_rng()\n", + " r = rng.standard_normal(N)\n", + " y = a1 + a2*x + sigma*r\n", + " return y\n", + "\n", + "N = 40\n", + "x = np.linspace(0.0, 100.0, N)\n", + "sigma = 25.0*np.ones(N)\n", + "y = y_experiment(10.0, 3.0, sigma, x)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + 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"model_id": "31ec1b1113bb49359a1197a1b1f96bf0", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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", 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\n", + " \n", + "
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", + "text/plain": [ + "
" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.spines['right'].set_visible(False)\n", + "ax.spines['top'].set_visible(False)\n", + "ax.xaxis.set_ticks_position('bottom') \n", + "ax.yaxis.set_ticks_position('left') \n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Annotations with an arrow are also possible" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.05, 0.05, 'a polar annotation')" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "6b992ce606244997a6dae7cfde77bd52", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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", + "text/html": [ + "\n", + "
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\n", + " " + ], + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#example from http://matplotlib.org/examples/pylab_examples/annotation_demo.html\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111, projection='polar')\n", + "r = np.arange(0, 1, 0.001)\n", + "theta = 2*2*np.pi*r\n", + "line, = ax.plot(theta, r, color='#ee8d18', lw=3)\n", + "\n", + "ind = 800\n", + "thisr, thistheta = r[ind], theta[ind]\n", + "ax.plot([thistheta], [thisr], 'o')\n", + "ax.annotate('a polar annotation',\n", + " xy=(thistheta, thisr), # theta, radius\n", + " xytext=(0.05, 0.05), # fraction, fraction\n", + " textcoords='figure fraction',\n", + " arrowprops=dict(facecolor='black', shrink=0.05),\n", + " horizontalalignment='left',\n", + " verticalalignment='bottom',\n", + " )\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Surface plots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "matplotlib can't deal with true 3-d data (i.e., x,y,z + a value), but it can plot 2-d surfaces and lines in 3-d." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "d13bb5530e0f448f92f662c4ac3a4163", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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", 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\n", + " \n", + "
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\n", + " Figure\n", + "
\n", + " \n", + "
\n", + " " + ], + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = plt.axes(projection=\"3d\")\n", + "\n", + "X = np.arange(-5,5, 0.25)\n", + "Y = np.arange(-5,5, 0.25)\n", + "X, Y = np.meshgrid(X, Y)\n", + "R = np.sqrt(X**2 + Y**2)\n", + "Z = np.sin(R)\n", + "\n", + "surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=\"coolwarm\")\n", + "\n", + "# and the view (note: most interactive backends will allow you to rotate this freely)\n", + "ax.azim = 90\n", + "ax.elev = 40" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Histograms" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "here we generate a bunch of gaussian-normalized random numbers and make a histogram. The probability distribution should match\n", + "$$y(x) = \\frac{1}{\\sigma \\sqrt{2\\pi}} e^{-x^2/(2\\sigma^2)}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0, 'x')" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N = 10000\n", + "rng = np.random.default_rng()\n", + "r = rng.standard_normal(N)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.hist(r, density=True, bins=20)\n", + "\n", + "x = np.linspace(-5,5,200)\n", + "sigma = 1.0\n", + "ax.plot(x, np.exp(-x**2/(2*sigma**2)) / (sigma*np.sqrt(2.0*np.pi)),\n", + " c=\"r\", lw=2)\n", + "ax.set_xlabel(\"x\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Plotting data from a file" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`numpy.loadtxt()` provides an easy way to read columns of data from an ASCII file" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(128, 8)\n" + ] + } + ], + "source": [ + "data = np.loadtxt(\"test1.exact.128.out\")\n", + "print(data.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "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", + "ax.plot(data[:,1], data[:,2]/np.max(data[:,2]), label=r\"$\\rho$\")\n", + "ax.plot(data[:,1], data[:,3]/np.max(data[:,3]), label=r\"$u$\")\n", + "ax.plot(data[:,1], data[:,4]/np.max(data[:,4]), label=r\"$p$\")\n", + "ax.plot(data[:,1], data[:,5]/np.max(data[:,5]), label=r\"$T$\")\n", + "ax.set_ylim(0,1.1)\n", + "ax.legend(frameon=False, fontsize=12)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Final fun" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "if you want to make things look hand-drawn in the style of xkcd, rerun these examples after doing\n", + "plt.xkcd()" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plt.xkcd()" + ] + } + ], + "metadata": { + "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": "3.13.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/04-matplotlib/matplotlib-exercises.ipynb b/content/04-matplotlib/matplotlib-exercises.ipynb new file mode 100644 index 00000000..126e4c0a --- /dev/null +++ b/content/04-matplotlib/matplotlib-exercises.ipynb @@ -0,0 +1,321 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# matplotlib exercises" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q1: planetary positions\n", + "\n", + "The distances of the planets from the Sun (technically, their semi-major axes) are:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.array([0.39, 0.72, 1.00, 1.52, 5.20, 9.54, 19.22, 30.06, 39.48])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are in units where the Earth-Sun distance is 1 (astronomical units).\n", + "\n", + "The corresponding periods of their orbits (how long they take to go once around the Sun) are, in years" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "P = np.array([0.24, 0.62, 1.00, 1.88, 11.86, 29.46, 84.01, 164.8, 248.09])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, the names of the planets corresponding to these are:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "names = [\"Mercury\", \"Venus\", \"Earth\", \"Mars\", \"Jupiter\", \"Saturn\", \n", + " \"Uranus\", \"Neptune\", \"Pluto\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(technically, pluto isn't a planet anymore, but we still love it :)\n", + "\n", + " * Plot as points, the periods vs. distances for each planet on a log-log plot.\n", + "\n", + " * Write the name of the planet next to the point for that planet on the plot" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q2: drawing a circle\n", + "\n", + "For an angle $\\theta$ in the range $\\theta \\in [0, 2\\pi]$, the polar equations of a circle of radius $R$ are:\n", + "\n", + "$$x = R\\cos(\\theta)$$\n", + "\n", + "$$y = R\\sin(\\theta)$$\n", + "\n", + "We want to draw a circle. \n", + "\n", + " * Create an array to hold the theta values—the more we use, the smoother the circle will be\n", + " * Create `x` and `y` arrays from `theta` for your choice of $R$\n", + " * Plot `y` vs. `x`\n", + " \n", + "Now, look up the matplotlib `fill()` function, and draw a circle filled in with a solid color." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q3: Circles, circles, circles...\n", + "\n", + "Generalize your circle drawing commands to produce a function, \n", + "```\n", + "draw_circle(x0, y0, R, color)\n", + "```\n", + "that draws the circle. Here, `(x0, y0)` is the center of the circle, `R` is the radius, and `color` is the color of the circle. \n", + "\n", + "Now randomly draw 10 circles at different locations, with random radii, and random colors on the same plot." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q4: Climate\n", + "\n", + "Download the data file of global surface air temperature averages from here:\n", + "https://raw.githubusercontent.com/sbu-python-summer/python-tutorial/master/day-4/nasa-giss.txt\n", + "\n", + "(this data comes from: https://data.giss.nasa.gov/gistemp/graphs/)\n", + "\n", + "There are 3 columns here: the year, the temperature change, and a smoothed representation of the temperature change. \n", + "\n", + " * Read in this data using `np.loadtxt()`. \n", + " * Plot as a line the smoothed representation of the temperature changes. \n", + " * Plot as points the temperature change (no smoothing). Color the points blue if they are < 0 and color them red if they are >= 0\n", + " \n", + "You might find the NumPy `where()` function useful." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q5: subplots\n", + "\n", + "matplotlib has a number of ways to create multiple axes in a figure -- look at `plt.subplots()` (http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.subplot)\n", + "\n", + "Create an `x` array using NumPy with a number of points, spanning from $[0, 2\\pi]$. \n", + "\n", + "Create 3 axes vertically, and do the following:\n", + "\n", + "* Define a new numpy array `f` initialized to a function of your choice.\n", + "* Plot f in the top axes\n", + "* Compute a numerical derivative of `f`,\n", + " $$ f' = \\frac{f_{i+1} - f_i}{\\Delta x}$$\n", + " and plot this in the middle axes\n", + "* Do this again, this time on $f'$ to compute the second derivative and plot that in the bottom axes\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q6: Mandelbrot set\n", + "\n", + "The [Mandelbrot set](https://en.wikipedia.org/wiki/Mandelbrot_set) is defined such that $z_{k+1} = z_k^2 + c$\n", + "remains bounded, which is usually taken as $|z_{k+1}| \\le 2$\n", + "where $c$ is a complex number and we start with $z_0 = 0$\n", + "\n", + "We want to consider a range of $c$, as complex numbers $c = x + iy$,\n", + "where $-2 < x < 2$ and $-2 < y < 2$.\n", + "\n", + "For each $c$, identify its position on a Cartesian grid as $(x,y)$ and \n", + "assign a value $N$ that is the number of iterations, $k$, required for $|z_{k+1}|$ to become greater than $2$.\n", + "\n", + "The plot of this function is called the Mandelbrot set.\n", + "\n", + "Here's a simple implementation that just does a fixed number of iterations and then colors points in Z depending on whether they satisfy $|z| \\le 2$. \n", + "\n", + "Your task is to extend this to record the number of iterations it takes for each point in the Z-plane to violate that constraint,\n", + "and then plot that data -- it will show more structure\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "N = 256\n", + "x = np.linspace(-2, 2, N)\n", + "y = np.linspace(-2, 2, N)\n", + "\n", + "xv, yv = np.meshgrid(x, y, indexing=\"ij\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "c = xv + 1j*y\n", + "\n", + "z = np.zeros((N, N), dtype=np.complex128)\n", + "\n", + "for i in range(10):\n", + " z = z**2 + c\n", + " \n", + "m = np.ones((N, N))\n", + "m[np.abs(z) <= 2] = 0.0" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.imshow(m)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/04-matplotlib/matplotlib.md b/content/04-matplotlib/matplotlib.md new file mode 100644 index 00000000..c089ad68 --- /dev/null +++ b/content/04-matplotlib/matplotlib.md @@ -0,0 +1,3 @@ +# matplotlib + +matplotlib is the core plotting library for python. diff --git 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"outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fitting\n", + "\n", + "Fitting is used to match a model to experimental data. E.g. we have N points of $(x_i, y_i)$ with associated errors, $\\sigma_i$, and we want to find a simply function that best represents the data.\n", + "\n", + "Usually this means that we will need to define a metric, often called the residual, for how well our function matches the data, and then minimize this residual. [Least-squares fitting](https://en.wikipedia.org/wiki/Least_squares) is a popular formulation.\n", + "\n", + "We want to fit our data to a function $Y(x, \\{a_j\\})$, where $a_j$ are model parameters we can adjust. We want to find the optimal $a_j$ to minimize the distance of $Y$ from our data, *measured parallel to the $y$-axis*:\n", + "\n", + "$$\\Delta_i = Y(x_i, \\{a_j\\}) - y_i$$\n", + "\n", + "[Least-squares](https://en.wikipedia.org/wiki/Ordinary_least_squares) minimizes the distance between the\n", + "data points and the model line parallel to the $y$-axis. We write this as $\\chi^2$:\n", + "\n", + "$$\\chi^2(\\{a_j\\}) = \\sum_{i=1}^N \\left ( \\frac{\\Delta_i}{\\sigma_i} \\right )^2$$" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import optimize" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### general linear least squares" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we'll make some experimental data (a quadratic with random fashion). We use the [standard_normal](https://numpy.org/doc/stable/reference/random/generated/numpy.random.Generator.standard_normal.html) function to provide Gaussian normalized errors." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def y_experiment2(a1, a2, a3, sigma, x):\n", + " \"\"\" return the experimental data in a quadratic + random fashion, \n", + " with a1, a2, a3 the coefficients of the quadratic and sigma is \n", + " the error. This will be poorly matched to a linear fit for \n", + " a3 != 0 \"\"\"\n", + "\n", + " N = len(x)\n", + "\n", + " # standard_normal gives samples from the \"standard normal\" distribution\n", + " rng = np.random.default_rng()\n", + " r = rng.standard_normal(N)\n", + "\n", + " y = a1 + a2*x + a3*x*x + sigma*r\n", + "\n", + " return y" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "N = 40\n", + "sigma = 5.0*np.ones(N)\n", + "\n", + "x = np.linspace(0, 100.0, N)\n", + "y = y_experiment2(2.0, 1.50, -0.02, sigma, x)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "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", + "ax.scatter(x,y)\n", + "ax.errorbar(x, y, yerr=sigma, fmt=\"o\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "\"linear\" in general linear least squares means that the fit parameters enter into the fitting function linearly,\n", + "the function itself can be nonlinear in $x$.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use the [leastsq()](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html) function to minimize the square of the residual. \n", + "\n", + "First our function to compute the residual." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def resid(avec, x, y, sigma):\n", + " \"\"\" the residual function -- this is what will be minimized by the\n", + " scipy.optimize.leastsq() routine. avec is the parameters we\n", + " are optimizing -- they are packed in here, so we unpack to\n", + " begin. (x, y) are the data points \n", + "\n", + " scipy.optimize.leastsq() minimizes:\n", + "\n", + " x = arg min(sum(func(y)**2,axis=0))\n", + " y\n", + "\n", + " so this should just be the distance from a point to the curve,\n", + " and it will square it and sum over the points\n", + " \"\"\"\n", + "\n", + " a0, a1, a2 = avec\n", + " \n", + " return (y - (a0 + a1*x + a2*x**2))/sigma" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-1.15667857 1.51771559 -0.01948624]\n" + ] + } + ], + "source": [ + "# initial guesses\n", + "a0, a1, a2 = 1, 1, 1\n", + "\n", + "afit, flag = optimize.leastsq(resid, [a0, a1, a2], args=(x, y, sigma))\n", + "\n", + "print(afit)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.plot(x, afit[0] + afit[1]*x + afit[2]*x*x )\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that we represent the data quite well." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compute the [reduced $\\chi^2$](https://en.wikipedia.org/wiki/Ordinary_least_squares#Reduced_chi-squared)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.2945742468418153\n" + ] + } + ], + "source": [ + "chisq = sum(np.power(resid(afit, x, y, sigma),2))\n", + "normalization = len(x)-len(afit)\n", + "print(chisq/normalization)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In general a (reduced) $\\chi^2 < 1$ indicates a good fit." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### a nonlinear example" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The same interface works with nonlinear data.\n", + "\n", + "We'll create a new set of experimental data---an exponential" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "a0 = 2.5\n", + "a1 = 2./3.\n", + "sigma = 5.0\n", + "\n", + "a0_orig, a1_orig = a0, a1\n", + "\n", + "rng = np.random.default_rng()\n", + "\n", + "x = np.linspace(0.0, 4.0, 25)\n", + "y = a0*np.exp(a1*x) + sigma * rng.standard_normal(len(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "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", + "ax.scatter(x,y)\n", + "ax.errorbar(x, y, yerr=sigma, fmt=\"o\", label=\"_nolegend_\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "our function to minimize" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "def resid(avec, x, y):\n", + " \"\"\" the residual function -- this is what will be minimized by the \n", + " scipy.optimize.leastsq() routine. avec is the parameters we \n", + " are optimizing -- they are packed in here, so we unpack to \n", + " begin. (x, y) are the data points \n", + " \n", + " scipy.optimize.leastsq() minimizes: \n", + " \n", + " x = arg min(sum(func(y)**2,axis=0)) \n", + " y \n", + " \n", + " so this should just be the distance from a point to the curve, \n", + " and it will square it and sum over the points \n", + " \"\"\"\n", + "\n", + " a0, a1 = avec\n", + "\n", + " # note: if we wanted to deal with error bars, we would weight each \n", + " # residual accordingly \n", + " return y - a0*np.exp(a1*x)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "[3.22621618 0.58391382]\n" + ] + } + ], + "source": [ + "a0, a1 = 1, 1\n", + "afit, flag = optimize.leastsq(resid, [a0, a1], args=(x, y))\n", + "\n", + "print(flag)\n", + "print(afit)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.plot(x, afit[0]*np.exp(afit[1]*x),\n", + " label=r\"$a_0 = $ %f; $a_1 = $ %f\" % (afit[0], afit[1]))\n", + "ax.plot(x, a0_orig*np.exp(a1_orig*x), \":\", label=\"original function\")\n", + "ax.legend(numpoints=1, frameon=False)\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "What about uncertainties in both $x$ and $y$? SciPy has an\n", + "[orthogonal distance regression](https://docs.scipy.org/doc/scipy/reference/odr.html) implementation based on ODRPACK for this.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## FFTs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Fourier transforms](https://en.wikipedia.org/wiki/Fourier_transform) convert a physical-space (or time series) representation of a function into frequency space. This provides an equivalent representation of the data with a new view.\n", + "\n", + "The FFT and its inverse in NumPy use:\n", + "\n", + "$$F_k = \\sum_{n=0}^{N-1} f_n e^{-2\\pi i nk/N}$$\n", + "\n", + "$$f_n = \\frac{1}{N} \\sum_{k=0}^{N-1} F_k \n", + " e^{2\\pi i n k/N}$$\n", + " \n", + "\n", + "Both NumPy and SciPy have FFT routines that are similar. However, the NumPy version returns the data in a more convenient form." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{tip}\n", + "It's always best to start with something you understand---let's do a simple sine wave. Since our function is real, we can use the rfft routines in NumPy---the understand that we are working with real data and they don't return the negative frequency components.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{important}\n", + "FFTs assume that you are periodic. If you include both endpoints of the domain in the points that comprise your sample then you will not match this assumption. Here we use `endpoint=False` with `linspace()`\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "For real-valued data, we'll use `np.fft.rfft()`, which will return N/2 complex values given N real samples.\n", + "\n", + "To get the frequencies, we can use `np.fft.rfftfreq()`, which will return dimensionless frequencies of the form\n", + "$0, 1/N, 2/N, 3/N, ...$. We know that the shortest lowest frequency corresponds to a single wavelength in the domain, so physically, $1/N$ corresponds to a frequency $1/L$, where $L$ is the domain size. This means that\n", + "we can convert the frequencies by dividing by $\\Delta x = L/N$.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To make our life easier, we'll define a function that plots all the stages of the FFT process" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_FFT(xx, f):\n", + "\n", + " npts = len(xx)\n", + " dx = xx[1] - xx[0]\n", + "\n", + " # Forward transform: f(x) -> F(k)\n", + " fk = np.fft.rfft(f)\n", + "\n", + " # Normalization -- the '2' here comes from the fact that we are\n", + " # neglecting the negative portion of the frequency space, since\n", + " # the FFT of a real function contains redundant information, so\n", + " # we are only dealing with 1/2 of the frequency space.\n", + " #\n", + " # technically, we should only scale the 0 bin by N, since k=0 is\n", + " # not duplicated -- we won't worry about that for these plots\n", + " norm = 2.0 / npts\n", + "\n", + " fk = fk * norm\n", + "\n", + " fk_r = fk.real\n", + " fk_i = fk.imag\n", + "\n", + " # rfftfreq returns the frequencies as 0, 1/N, 2/N, 3/N, ...\n", + " k = np.fft.rfftfreq(npts)\n", + "\n", + " # to make these dimensional, we need to divide by dx.\n", + " kfreq = k / dx\n", + "\n", + " # Inverse transform: F(k) -> f(x) -- without the normalization\n", + " fkinv = np.fft.irfft(fk/norm)\n", + "\n", + " # plots\n", + " fig, ax = plt.subplots(nrows=4, ncols=1)\n", + " \n", + " ax[0].plot(xx, f)\n", + " ax[0].set_xlabel(\"x\")\n", + " ax[0].set_ylabel(\"f(x)\")\n", + "\n", + " ax[1].plot(kfreq, fk_r, label=r\"Re($\\mathcal{F}$)\")\n", + " ax[1].plot(kfreq, fk_i, ls=\":\", label=r\"Im($\\mathcal{F}$)\")\n", + " ax[1].set_xlabel(r\"$\\nu_k$\")\n", + " ax[1].set_ylabel(\"F(k)\")\n", + "\n", + " ax[1].legend(fontsize=\"small\", frameon=False)\n", + "\n", + " ax[2].plot(kfreq, np.abs(fk))\n", + " ax[2].set_xlabel(r\"$\\nu_k$\")\n", + " ax[2].set_ylabel(r\"|F(k)|\")\n", + "\n", + " ax[3].plot(xx, fkinv.real)\n", + " ax[3].set_xlabel(r\"$\\nu_k$\")\n", + " ax[3].set_ylabel(r\"inverse F(k)\")\n", + "\n", + " f = plt.gcf()\n", + " \n", + " f.set_size_inches(10,8)\n", + " plt.tight_layout()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll test it on $f(x) = \\sin(2\\pi \\nu_0 x)$, where $\\nu_0$ is a frequency we set." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "def single_freq_sine(npts):\n", + "\n", + " # a pure sine with no phase shift will result in pure imaginary\n", + " # signal\n", + " f_0 = 0.2\n", + "\n", + " xmax = 10.0/f_0\n", + " \n", + " xx = np.linspace(0.0, xmax, npts, endpoint=False)\n", + "\n", + " f = np.sin(2.0*np.pi*f_0*xx)\n", + "\n", + " return xx, f" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "npts = 128\n", + "xx, f = single_freq_sine(npts)\n", + "plot_FFT(xx, f)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that all of the power is at our single frequency, *and* it is all in the imaginary components, which is expected since $e^{ix} = \\cos(x) + i\\sin(x)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we can try $f(x) = \\cos(2\\pi\\nu_0 x)$, and we know that a cosine is just a sine shifted in phase by $\\pi/2$." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "def single_freq_cosine(npts):\n", + "\n", + " # a pure cosine with no phase shift will result in pure real\n", + " # signal\n", + " f_0 = 0.2\n", + "\n", + " xmax = 10.0/f_0\n", + "\n", + " xx = np.linspace(0.0, xmax, npts, endpoint=False)\n", + "\n", + " f = np.cos(2.0*np.pi*f_0*xx)\n", + "\n", + " return xx, f" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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7DR2+IO/xxzja3oPNR9yQJOCCicVqDycuGHTr0NIpJUA0rZJ6vbOjHl3+ECpy0zC7sn/dnieXuXDLWZFjw+5+bRs6vJzkCM2dPmWXpj8THACYUu7C4glFCMvA77nb3UeXL4jHP470G7j93DGw9uPoKofVjKujDVeeXsU6ulir9jXjhfU1kCTg11dOOW1mi3D5jMhixwe7GuHu5uddiHQqbgcALJ1c0u/vK3DaMWd4LgAuBB9LZF5dOr2s3x3Jbzt3NEYWZKCxw4dfvbUzwSPUl9eqauHxBjEsNx1nj+1fR/KvfW4U0m1mbD3qxns7udsd64NdjdhyxI00qxn/3c/jUz83pgDD89LR4Q3i1SouXMb61Vu70ODxYWR+Bu44b0y/vsfEheCTejt6P5lTmduvBSE9YNCtQ0smFkGSIqm/de7jz1FMVWKCc/n0sgGdy3nn4jGozEtHnduLP0WbsBHwwroa+ENhTKvIxrSK7H5/352LIzebf2+uxb5GdokWnll9GC1dflTmpeOKfmRiCNfOq4RJAlYfaMHeBr6ewk9fjzSquW5+JWZV5vb7+yaWZmF8sRP+UBivb61N4Aj15Z0dkQnOzGHZSvfi/lo6ObIL8fZ2Bt1Ca5df6fJ8xWlSy2M5rGb86orIsYv/WFuDXfWehI1RT2L7i1y/oLLfixi5GTbcuDCyaMxO5r1kWcZD70V2uW9YOBz5/chkQzRIvC66CP/s6sN8PaP2NHTg72t6T3kZyBFg4vrw8Z4mtHSyv5AgFnEvnGyMXW4w6NanwiwHZkXP7X2bOwtAtFvkir2RDqWXzzx92m4sh9WspEVz0hgRDIXxt2jt3PWnaFZzIpPLXFgyqQiyDDz8Hne7AaDTF8SfPonUct8Rc3xdf5Rmp+H8iZEGTM+waywQbaa0q74DFpOE75w/bsDfL8pPuLPQ662tg5/gLIl+z/rDbWjsYOdtAHh9Sy2CYRmTSrMwtujUvQaONXdELhZPiNTOvrOdKacAsO5QG3bVd8BhNZ2yAeWJ3HLWSGTaLdhR58HbfD0BAO/uaMC2ox5k2Pq/yy18YVY50qxm7KrvwNqD7LoNAO9E547nji/E/JGnLyWJNbrQiSllLgTDMv6zmQvBANDU4cO6w5H31hIG3aQ2MTFaziARAPDvqlqE5UgzrxGnaa5yIovGFcAkAXsaOlmXCOC9nY2oc3uRm2HDxVP7n2oqiHO739haxzORATy96hDaugMYmZ+hpJINhEjvf3njEZZAAEpTpDnDc0/aXftULp1eBkmKBInVLfy8t3b5seZgCwDgwkkD/7yXuNIwvSIbsswgUVAyrwaQ1RLrvAmRhTY2AIt4JnpM2GXTywb8mc/JsCldpB9+b0/Kn4kcDst4KLogfuMZw5GbYRvQ97vSrLgs+r7mQnDEh7sjmz7nTTjxsaqnoywEb+JCMKKZV7IMTCt3nbKhp94w6NapJZMiQffag61MR4m5UA0kjS9WdroNs6J14OLimcrEBOfqORUDSpMSJpRk4aIpxdHd7j0JGKF+dHgDStnCHecNbJdbWDAqD6MLM9HlDymT+VT2wa5IIHLuSc6NP51ilwNnjMoHOMkBALy3owFhGZhYknXcmbL9dSFTzBUHmjpRVdMOkwT8v0EssiF6nBCiJ0ik+j2+weNVUk2vWzCwzCvh5jNHwmm3YFd9R8r3w3lnRz121nmQabcoPW0GSjRUe3t7PerdqZ3d0tblx6bqNiDmcztQ/296KcwmCZuPuNmENia13Ei73GDQrV8VuemYUuZCWI6kCaWyPQ0d2F7rgcUkKWceDsY50Qn8h7tSe2dhb0MHVu1vgUkCrh1ganmsb50X2e1evr0+pSeNb22th7sngJEFGbhk2uDen5IkKZOcp1cfSuk6ui5fEGsORNLOzhlk0I2YnYVXq46m9OsJAG9FT31YOoQJzoXRheDV+1vQ3m2MM1UH69XoQs5ZYwpQ6BxYfbxQ7HJgYkkWZDlS65nK/r6mGsGwjNmVOZhU6hrUc7jSrbjpzBGR51ub2ruzz0Vrj29cOBzZ6QPb5RYmlGRh7vBcBMMy/r42tY8P+3hPE8IyML7YidJB7srmZ9rxuTGRheBXU3wh2N0dwOr9IvOKQTdpBFPMI8TO36JxhQNOk4olVihX7W9O6fMSRbrY4glFQ0rrGVfsxPhiJ2QZ+DR6AU1Fn0R7DXx+amQle7CumFmOTLsFB5q68Om+1H09P93XDH8ojIrcNIwqGHgpiXDh5GKkWc042NyFqpr2uI5RTzzegPJ+GkrDmuH5GRhf7EQwLKd0l2hZlvFK1dAyr4Rzxkc6dH+QwgvB/mBYCequX9i/UzRO5v9FFz3XHWpL2Xu8NxBS6rAHU+oUSxzH9vc11fAHw3EZnx6Jz+dQFoER04/olU1HU7oE4r2dDQiGZYwrcmJkQabaw4krBt06JiZIn+5rTtnzPMNhGa/FaYIzvtiJEpcD3kAYqw+kZlDT4Q3g5Y1HgGhH06E6K7pyu3Jvau7UhMMyVkUXHMRrMViZdguunCnq6A7FZXx6JMo/zh1XOKBTCo6VYbdgyaRI3Wwqp5h/uKsR/lAYowoyMGaADb+OJY4aWx7dOU9F6w+3oaa1Bxk285DPlhXlE5/saUIwlJpBzdvb69HU4UOB0z7kXa9RBRkocTngD4ZTtgHY+kNt8AXDKMqyY3Th0AKaJZOKUei0o7nTl7KbP6GwrGSiDLbcSbhgYhEy7RYcaevB+sNtcRqh/oj3kpG6lgsMunVsVEEmxhRmIhCSUzYl+rMDLahze+F0WIZ8wZMkKeVTzF/eeBRd/hBGFWRg4aiBdeA8kTPHRHZqVu5tTskU3h11HrR2+ZFpt2D6AI5dOxlxVMt7OxtSsuGfLMvKMUxD3VVAzM7CfzbXpuxOTTyPZRHP8cneZnT6gkN+Pj0SmVcXTi5Bmm3g/TBiTa/IQU66FR5vUDlDPdWIBcYvzR0Gm2VoU1ZJknDm6OhC8L7muIxPb1bsiwSIZ44uGNKiJQBYzSZcOy+y2/3MqtRcCN5U3QZ3TwCuNCtmDPEe77CalRKfVzYdidMI9aXLF8Qn0UUMBt2kOeID+laK7iy8HN2h+vzUkkE1/DrWudEU8w92NaZkkPhSdJf7+gXDh3xDBoC5w3NhM5tQ6/biQHNXHEaoLyv2RiZ280fmwjqIBmrHGl2YiTNG5yEsp2bd1866DtS5vXBYTQM+luVEzhiVhwKnHW3dgZSsm+3xh/BRNHNA7FIPxdiiTIzMz4A/GE7JhUtvIIQ3tkSO/Blq5hUAmE0Szh6buinm1S3dWHeoDWaThC/NGxaX5zwzmnEkrs2pZmX07z3UzCvhmnkVsJgkrD/chkMpeI8Xn8uzxxYMqknqsS6PXjde31KXkiUQH+1ugi8YRmVeOsYXDy3zSosYdOuc6Oz38Z4mdPtTa2ehxx/CW1sjiw2XzxjY2dwns3B0HmwWE4609aRcB0l3TwDbjrqBOK4wptnMmD080hV+ZQpOclYquwrxmeAgtmFVCpZAiOOTzhiVH5dFNovZhEujdZ6puLPw8Z4m9ARCKMtOw6TSrCE/nyRJyj0pFdNNP9zVCI83iOIsR1wWhRCT0fFRCh4dtvpA5J4xc1g2irIG15DuWGdEr8U76zxo6kitBp8tnT5sr/UAMa/DUBU6HZgZPfklNe9JkXu86L8wVPNH5KHU5UCHN5iSC21iA/HCycVx2fjRGgbdOjexJAsVuWnwBsJKSkaqeGdHPbr8IZTnpGF29KI/VOk2izJZSrUL3rqDrQjLwMj8jLhNcJDCOwveQAjrDkXqskSafTwsiKb9R2rzUmsl/MM4NayJJXYW3tvZmHK9Md6OqZ2L1wRHLAp9uKsx5XZqRObVpTOG1jQx1tljC2CSgF31HTja3hOX59QL0cF4QZwWMBDtEj2xJLLAtGp/at2TREPT8cVOFDjtcXte8e+zOsUapta5e7CzzgNJAs4eG597kskk4dLoyRqpdjyoNxBS7vFG61ouMOjWOUmSlLTAVDt7UjQ/unxGGUxxmuAAwLnjUjOdT6xSz4vjBAcAzhodeT0/O9CCQAo1A1p7sBX+YBglLseQumwfa1RBJvIz7fAFw6hKoTrPti4/NoqzUOMYdE8sycK4Iif8wTDe3Jo6ZTr+YBjv7YwcNzmUo8KONbXchVKXA93+UEottLV1+ZXd6CvilHkFANnpNswcFllUTqWUfVmWlXtSvLIGhLNSdCFYNDSNV2q5IP59Vh9oSamyvA93RV7PGRXZQzo551hXRIPuj3Y3orUrdY5fXLm3GV3+EEpcDkwrH3oPHC1i0G0AS6IrQh/sbEyZna/mTp9ywxTn7caLmNCvP9QGjzd1dr4+i05wFsShgVqsiaVZyE63otMXxOYUOppJNOo5Y3R+XNOkJEnC/JG5AIDPDqROB95P9kbOQh1X5BzSUXbHkiRJ2e1+JYV2Flbtb0aHN4gCp10J6uKhT4p5Ci0Ev761DoGQHFnEiXMtYio2+DzU0o0Gjw82s0lJX44XkVqdSg0+ZVlWSrzilVouzBiWDZvFhKYOX0r1blGOChsXv0VgABhT5MTksiwEwzJej/aISAWiJGnJpOK4bqRpCYNuA5hRkY2iLDs6fEGsSpHzez/d14xQODLBifc5fpV5GRhZkIFgWE6ZOuT2bj921EVqveaPyI3rc5tNEs4YlXo7Cyvi3LAmVu/OQuq8nolILRcuidZ1rz/cmjJdt0VAvGRSUdwnOCL76r2dDSmT3SLKuz4/begN6Y4lJvWf7m9OmZR9kao8fVh2XPo3xJo7Ihc2iwn1Hm/K9G450NyFWrcXNrMJ80bEd2HdYTVj5rDIzmSqpJj7giF8Gl1YT8g9aWrknpQqZaOBUBjv7ohkXhmxa7nAoNsATCZJ2e1OlZ2FdYciO3zx3pUVYruYp4K1B1shy5FzTAvjWM8tiLruVDmmpanDh5118W1YE0u87zdWt6fEJDyeZ6GeSFl2Gipy0xCWgY0pcD5qKCzjHTHBmRT/IHFWZQ7yM21w9wSUDBojC4dlrBf3pDinQgPAhBInSlwOeAPhlHg9EZt5lYDX02E1Y060wWeqLASLDYRZlTlDPsruRBaMjNznUuX9ueZAK3oCIRRl2ePShPJYYmF93aE2hMPGz8ZYc6AV7p4A8jJsmDM8vhs/WsKg2yDEytA7O+oRTIGdhbUHIxOcRH04z43pGJsKF7xE1c4Jont3VU07OlIgZV806JlQkoX8zPg1rBFG5megwGmHPxjGphSo666qaUNbdwBZDouyoxJv4loiri1GtvZgK1q7/MhOt2LeyPhfQ80mCRdMEsdZGn8heF9TJ9q6A0izmjG5zBX355ckCYvGpU6KeSLruYUzo71GPk2RhWCx4H1mAjKvED0WE9GSp1RI2Y9NLU9El+1JpVlIt5nh7glgT2NH3J9fa0TX8gsmFcWtCaUWMeg2iLnDc5GTbkVbdwBrDxl70tjW5ceehkhKmFitjrfZw3ORabegudOPrdFjtIxM1AYnKnOgIjcdw/PSEQrLKVGHHO+zUI8lSZKyA5QKOwtigvO5OJ2FeiJzRdBt8OsnYrqWL55QFJfz409EdJ99Z3sDQgZfuBQLNTOGZSfs9TxHNPjc3Wj4oOZAcxeaOnywWUyYkaBFNnFt/uxAq+FLIIKhMD6Lpn0n6p40fVg27BYTmjt9hk/Zl2VZOb5yUZzruQWL2aT02lhn8IXgUFjG29sjmVdLDNq1XGDQbRAWswkXTIy8Wd82+M7C+mj656iCDOQlYBcRAGwWk7I7+6HBz0dt6/IrqdCJ2lVAbIr5XmPXKMmy3LurkIDUciG2Y6zRiS6xiUgtF+ZEexlU1bQbuiGlLMtK0B3PruXHWjAqD1kOC5o7fUrXeaMS5U6JTIs8Y3Q+bGYTalp7sL/J2M2qRF3wrGE5ca/nFiaWZCE3w4ZOXxBVBm/wuflIOzp8QWSnWzGpNP6ZGABgt5gxS5zXbfC67oPNXTjc0g2rWUpY5gBis68OGfv6uam6Dc2dPjgdFiwclbjXUwsYdBvIuRMiE9JVBr/grT0Y+fvNjXMzkGOdmyIdY9dEX88xhZkJSYUWRDrfCoOn8+1v6kKd2wubxYS5cW5KF0tkJVQZvK673u3FDuUs1Pidd36skfkZyM+0wR8MY+sR42a3HGzufX8mot+AYDWbcHZ0F8jIDT5lWVZ2uucl8POeYbcopQBGvyclOrUc0V44C6PXUKPXdYu/3xmj8hOaursgRRaCRebVvBF5yLRbEvZzxPxh3UFjp+yLmOVzYwtgsxg7LDX23y7FzI6uMu5t7ER7t3HP9hOrfnNHJCa1XFgUTefbfMSNpg5fQn+WmhKdWi4sGJUHkwQcaOpCbXtPQn+WmsRO/pzhidulAYDheekoyrLDHwobuvmXyDSZVp6dsMwWRFP2xc7CGgOn84lMoallroS+PxFT/rP+sHFfzyNtPahze2ExSZgRx6PXTuScFGjwKcsy1iTo+MpjnZUi2Vei3CmRu7IAMH+UKHkydpDYm1qeuEVgKOUqEuo9XtS0GnfOJO5Jc+J8NKAWMeg2kLxMO0bmZwCAYdP5uv1BbI/WWCe6w2FhlgOTyyJdKT8ycIq5SAVL5K4CALjSrJhWEanPM/JRbL2p5Ym9IcfWdRt5Z0EEGIlMLRfENWWdgeu6xQLNrAT1w4gl0k03Vbcbtq5bvFcml7kS0hU6lvgMrDvUCo9BG1Lua+xEc6cfdosJ0yoSkwotnDmmd2HdqK9nhzeATdH0+USWOyG6MOqwmtAa03fHaDp9QSWzJdH3JIfVjCnRxoxG7TUSDsvYFL0nzTZw13KBQbfBiEnOBoPufG2qbkcwLKMsOw3lOekJ/3ni6LCPdhtzJbyl04fdDZHOmIlMjRTOit70jZpiHgiFlcyBRDWsiTXf4M3UYs9CTUbQLdL5NhxqM2yQKHYVZlcm/vM+vjgLmXYLOn1B7GkwZgdeEXQn4/o5PD8DI/MzEAzL+NSgC5fiWjZ7eA7slsQuYpRlp2FkfgZCYdmwdcifHWhFKCxjeF46KnITO2eyWUzKdcWo96SVe5sRCEVez5EFmQn/eXNiUsyNaE9jBzp8QaTbzBhf7FR7OAnHoNtgZot0PoM2XlijHBWWnDSURdGJ/id7mgzZ4VS8nuOKnAlN3RXEzsKn+5oNeRRbVU07On1B5GbYMLEk/md3Hkup665pR4/feHXdaw+2otsfQoHTnpTXc0JJJEjs8AWxq96T8J+XbO3dfuxrjOxAzUpCKp/ZJCndp9cbdCF4TYKPrzzWIoOnmCv13Anu2SL0Nvg05iKGSJ1PdGq5IO5JRl3EEP0UEtW1/FhiMc+o2VciVpkxLDthJ5NoifH/hilmVnSVcfORdkMGiWK1b04SdhUQTZfKSbeiwxc05NFhnyWpdk6YMSwbGTYzWrv82FFnvKBGNKxZOCoPpiScNTksNx0lLgcCIdmQ2S2fRhtwnT22ICmvp9kkKcGoEc/rFu+RkQUZyM2wJeVnKtlXBpw0Nnf6cCDaSXx2khaCzxkfWbg0YsNUWZaT1mNEECnXKw2afbUiSeVOgjive83BFkMurH+6P/J6JrqeW5hVmQtJihyj19jhTcrPTCZxT5qVhMwrLWDQbTCjCjKQnW6FNxDG9lpjBTX+YBibaqJN1JK0q2A2ScpZiUZsVpWsem7BajYpP8uIkxyxq5CM1HIcV9dtvNdT9KZIVmYLYjvGGjBI7E0tT97rKdJNjbjTvf5Qb6ZQdnpyFjFmDMuBSQKOtvegwWOsSfiehk60dvmRZjVjanlizuc+1vxReTCbJBxs7sKRtu6k/MxkqW3vwYGmLpik5C1iTC3PRrrNjLbugFK6ZhSNHV4caeuBJCUnUwjRXjjjiiJp10bMYBVNNpN5T1ITg26DkSQJs4aJFHNjTRq3HnXDGwgjN8OG0YWJr6URZsY0AzKSpg4f9jZ2QpKSU48oGDWdz+MNYHP0qCmRRp8M8w2azhcIhbHlSOQzNzPBXaFjKWejHmwzXAfe3l2F5L2e04dlwyRFunwbLUgUqeWJPBrwWJl2C8ZGJ+FGWwheHd1FnD08J2lHB2U5rJhu0Aaf4u8zrSIbrjRrUn6m1WxSGmIZ7Z608XDkfjS20AmnIzmvJ2KuL0bLvmqMdmWXpMh9IhUw6DYg0ZXWaOmmYudpdmUOJCnxqaaCqEk0Wkd4cT73+OIs5CQp1RQxu8BrD7Ua6nzp1ftbEArLGJmfgbLstKT9XLHTveWIG12+YNJ+bqLtquuANxBGlsOCUUloWCNMLXfBZjahudOHQy3G2fnyB8PYHO1inMxUvky7BeOLI/X4RtupEfekZJU7CWIh2Gj3JJFanqzMK+FMgzb4FH+fsxLctfxYIsXcaM3UNkU/bzOTvCtr1FM1RIwyrsiJrCQuYqiJQbcBxabzGWmnZp0KuwqI1nWbTRLq3F7UuY1zVmJvanlyX89RBZkoznLAHwwb6iaSrLNQj1WRm46y7DQEw7KhUnhFQDFjWE5S6rkFh9Ws7HytPWicSeP2Wjd8wTBy0q0YVZCR1J8924ALwR3eAHZES7iSVe4kiGy2jQbKvgqHZXx2MLnlToJYCF5loAaf4bCsnPyQzMwrxCwErznYapjXEzH3pJlJ3pUVc94ddR5DHW2nlDslsXxMbQy6DWhquQtWs4SmDh+OtBkjSAyH5d5dhSRPcDLsFuUoA5FeZARKE7UkT3AkSepNMTfQzoJosJLos1BPxIhHh/VOcJJ/Q54zQjRTM06QGJtansxMIfQ5ytI4i2wbq9sRloGK3DQUuxxJ/dlip23rUTf8QWM0TN3d0IH27gDSbWZMLU/s+dzHmlaRjUy7BW3dAcM0+NxV34HWLj8ybGYlWy9ZJpe5kGEzw90TwE6DnALhD4axJVo+luyd7qIsByrz0iHLxlq4TObxlVrBoNuAHFYzJpdFblrrDTLJ2d3QAY83cpbfpNLEHx10LKWZmkHS+Ro9Xuxv6orWcyc36EZMkLjJIIsYbV1+pYuxGq+nEY9pUYLuyuTXehkxnU+kdqvRJVbUeG6v9RjmaDuRBTF3ePI/78Pz0pGbYYM/GMb2WmOcqiGuXbOH58Ka5KODInXIxrrHb4hJhVbj9RQlF0a5J+2s88AXDCM73YqR+cnNFELsPckgdd09/hC2R08ESmaPEbUx6Dao3mZqxriBiMnvrMocVc7yExN/o9yQP4teuCeWZMGVnvxaGrHyvuWoMY62q4rWyo4qyFDl9RQlAluPutFpgLrupg5fb4OViuQH3bMqIx2iq1u7Ue/Wf/MvWZaVSbgaE5xSlwPFWQ4Ew7LyWdG7ddEsiLkjkv96SpKEGRXinmSM11OtzCthRoWxGqZuUjFTCH2yr4wRJCrlThXZSc8UQkwJi1EWgrccaUcwLKPQaUd5TvJ64KiNQbdBGa2GTnRtTHZquSBuXNuPegzR/EusPqs1wRmRlwFXWuRou931+j9WZFNM/bEaynPSUZGbhlBMGYaeiQlOsrvECk6HFROjGTVrDfB61rT2oKnDB6tZSnrqLsSpGsONk2LuC4ZQFe2sr9o9yUDN1MJhWekEn6yjrY4lFoI3GeD1BICq6OJBslPLhd667kiDUb0Ti1tqLWKIuu7NNW5DzEFj67nVWMRQC4NugxIphJG0bH03XpDl3kAi2U3UhGG56cjLsMEfMkY635oD6jSsEUwmSdnBNMIkZ1ONuhMcAJg/wjh13eIoJDVSywUjpfOJMqPJZS44rGZVxjC70jgLwVuORGqp8zPtGKFCqiliT9UwwOu5s94Dd08AmXYLJqtQPoZoXTcAHGrpRmuXX5UxxEtblx8HmiPlTmpkCgHApNIsZNot6PAGsdMAdfK99yR1gu7KvHQUOO3wh3pPodCz3h4jqVPPDQbdxlXgtCuNF/SeLlXd2o0GT2SXRq0biCRJyi6m3pupNXi8ONDcBZOU/KNuYvXuLOj79QyH5d5dhQr1apPEDtFnBqih26hy5gAMls7X27BGvddTNMvZcLhN9x2N1yonaai3SzOtPHL+uRFO1RCZV3OGq1M+BgCuNCtGF0aOJqyq0fdChsjCGFmQgez05B0HGstiNimbJHqv627weHG0vQcmqXdxJtkkSTLMPSkclpWgW817khoYdBuY0jFW5x9QMcGZWp6t2i4NDFTXLXZCJ5W64EpT72xEEVBt0vmq7f6mTnT4Ik3+xhYl7zzpY4msBb3XdffpEqti0C2af0W6Kut752uDik3UhAklTqTbzPB4g9jX1KnaOOJB7XInKKdqRHaF9b4QLFLL1cq8EmZUGGMheJMGFoER02tkjc6PXhS73GOLnMi0W1Qbx5xoic5anfdq2t/UCXdPAGlWs1LGlSoYdBtY7HndeqbWUWHHiu1grufzz8UNWe2OkdPLIxOcg81daNNxOp94PaeUuVTbpQGA0uw0lLocCMuRJiV6JbrEutLU6RIrFDjtGFmQAVnWd0NKd08AexojfRPU/MxbzCYlU0nPr2coZpdG9XuSARaCZVlWrqFqn9c73SDZV6Jka7qK5U6IWeTbVN2u6znTxmp1U8uFudESsg2HWhHUcQNacf2cVuFKemd9taXW3zbFiAlWVU27rj+gYldhnoqp0Iief242SWjw+FCr447GWqg/BgBXuhUjCyJBlZ47Gm+qUT8VWlCyB3Q8aexNLc+GyaRugxUjpPNtqm6DLPfWBKpJ3JP0fJTlzjoPOn1BOO0WTChRd5fGCEdZHmnrQXOnDxaThEmlyW/yF0vsDFfVtOu2+Vc45oSAGSqlQguTSrNgNUto6fKjplW/JRBqN1ETxhU74XRY0OUPYWedfhvQrlfqudWfMyUbg24DG1OYiSyHBd06/oA2dnhxqKUbkqT+KmO6zYIJJU5Ax81rfMEQdtZGmpqonXqGPse06PP1RGwqn8qLGIhpmqPnRQwxwZmlgUUMsZOp5w7mGzQ0wZllgGZqYhF41vAcmFVeFIo9VcMX1GdHY3GtmliapWr5GACMLcpEus2MTl8Q+3VaAnGguRMd3iAcVhPGFztVHYvDasbE6MLUJp3WyfuDYWzVyHnSZpOk1EAb4Z40O8WaqIFBt7GZTJISqOr1mBZxFur44ixV648Fve8s7Kj1wB8KIzfDhopc9c9GVJqp6TRI7PQFsbshsqCl9q4CYtIJq2r0m86ndpfYWKIR0NYjbvT49RnUiFRuLUxwZlbmQJKAwy3daOrwqT2cQdFKuROiHY1zo6dqbDuqzw7RIuhWq0lqLIvZpBypp9eFYLFoObU8W9VyJ0HvC8HbayMnFeRm2DA8L13t4SjNb/V6qkZzpw8Ho5311c4cUIP6n0hKqNlKOp8+byDKUWEq13oJvUG3Pm8gvQ1WsjVxNqIIuquq23XZ0XhLTTtkGSjLTkNhlkPt4WByqQsWk4SmDh+Otusvna9RA11iY5XnpKHE5UAwLOtypyYYCiuTXbXrZQEgy2HFuKLI7psed7u1cHxlLEmSMFPn50tviikn0QK9l+hoKfMKBng9N2psziTKLNcdatXlwnpvU7pMuNLV30hLNgbdBjcr5pgWPVJ2FTQwwUFMetGOWje8Af3tfGlpVwEAxhU5kWY1o0On6XxaqY8X0mxmjI+WQOhxZ0FkkKjdJVaQJCnmvG79XUN31nWgJxBClsOC0QXqddaPNUvH2VeHWrrR3OmHzdK7I6o2kRGix+wrfzCMbdFyp+kaKHeCATqYK4sYGnk9xVxjR60+SyC00kRNmFKWDbvFhJaYs9j1JFXP5xYYdBvctIpI8686t1d3O1/d/iB21avfdTdWeU4a8jPtCIRkbIvW+eiJlpp+4bh0Pv1NcjZp4DzpY/XWyevv9VQa1mjk8w5A2UnU49m9omHZzMoc1ZvSCbN0nH0lPu9TylywW9StPxaU7CsdHhu2s84DfzCM7HSrJlJ3EVOis6exAx3egNrDGZBOXxB7RLmTRhaCK/PSkZNuhT8Uxo5a/ZVAbDqsrUwMm8WEKWWROVOVDu/xqdxEDQy6jS/dZsGk6Dl463XWeGHrETdCYRnFWQ6UuNSvP8Yx6Xx621lo7vShprUHkgRMrdDGLg36nNetr9cz9qgbrdyQofMaOqWeW0uLGMN6OxrrLZ1vvdKwRjuvp6gt33ZUf9lCseU5WiFO1aj3eFGrs4X12MwrLaTuAkCh04HynDTIMrDliL4W1rccaUc4Wu5UpIFyJ0TnTHq9J9W7vah1eyPlTuXa+cz39sLR15zJGwhha/QzpaV7UjIx6E4Beu0Yq7VUaEFJ59PZzoJYFR1VkIksh3ZqaWbo9GzUmtYetHT5YTOblIUtLRCv59ajkQYweuEPhrElmj0yU0OLGBNKsmCzmNDWHcDhlm61h9NvsixjwyHtpfJV5KahwBnJFtJbUKPckzT0/uxzqobOFoKV86Q1do/vrUPW2+upvfcndFzXLT5P44uzkKGBcidheszRdnqy7agb/lAY+Zk2VGoksyXZBh1079y5E/feey/OPfdcjBo1CiUlJZg6dSpuuOEG/P3vf4fPp8/OpEY0W6d13Vq9gcR2MNfTzpdWzu48lhjP7oYOdPqCag+n38Qq88TSLM2kmgLAiPwMuNKs8AfD2FWvn3S+HdFU05x0K0bkZ6g9HIXN0ruooqedhVq3F/UeLywmSVNBjST1Hnujp3uSNxDCzjpRf6yd1xM6TjFX7kkaymyBjuu6tZiJAR1nX/WepKGx1zM6J95Z16GrUzVij6/USmZLsg046N64cSMWL16MGTNmYOXKlZg3bx7uvPNO/OxnP8OXv/xlyLKMH/3oRygtLcWvf/1rBt8aILrW7qzz6Cqo0WqQOLU80iG6UWcdorW4SwMAhVkOlGVH0/l0dFPWYmo5dJzOt/Fwb3281m7Iok5eTzV0opxoUmkW0mzaWRSCTpupbTvqRjAso8BpR1m2NsqdBD0eZdnW5cehaObIdA2l7uKYoyz1srAuy7LSd0JrixjiJIrq1m60dOonJlCaqGns9Sx1OVDotCMUlrGtVj/ZQutT+HxuYcBB95VXXokrrrgC9fX1eP/993Hffffh9ttvx80334zvf//7eOaZZ3Dw4EG8/vrr2LRpEx588MHEjJz6rSgrUqMUlvUzaaxz96De44XZJGGKRrrECg6rGROjO1962akJh2VsVhYxtHUDgU7P69ZiEzVhug53ajYoExxtTcARs1Clp/enls47P9bs4b3ZV3oJarRYfyyIoGC7jk7VEK/nyIIMzR0dNLE0CzazCa1dflS36qOk5EhbD5o7/bCaJU2VOwGAK82KUQWR7CW9LAT7giFsOxrJbNFa0B27sK6XEghZljV9T0qWAQfde/bswTe/+U1kZ596YrRgwQI8//zz+N73vjeU8VGczFSaAenjAyoWB8YVOZFu004tjTBTZzVK+5s60eELIs1qxtgibRwdFEtvNXTeQAjbo51YtZaJgdjzz3UywUFMl1itTXAQ82+8s86jm6BGLBBosUvsRB3WyWs1swXROvn8TJuuTtXYpNGeLQBgt5gxqSxaUqKTe7zYlZ1Y6oLDqq3MFhzTkFIPth31wB8KIzdDm/XHens9Y3vgTC7T1qJQMg046LZa+7ci2d3dPaDHD9QjjzyC4cOHw+FwYN68eVi7dm1Cfo5R6K1ZlVZToYUZOutgLv7dp5a7YDFrr39i7PtTDztf22sjqab5mXaU52gr1RQxE9mDzV1o6/KrPZzT6tMlVoOT8MhRgZGgZrsOjr3xBkLK8TxazMSIPfZGL3XyWm3siejO1wydpZhrOVMIfY5e1Mvrqc1yPEFv2VebYlLLtZbZgtg6eb28ntHr/KQybfXASbYhzb7PO+88HD169Livr127FtOnTx/KU5/SCy+8gGXLluHee+/Fxo0bMW3aNCxZsgSNjY0J+5l613sskz6CGq3fQMRu3I5afex8bdL4IsakaDpfS5cfNa3ar5OP3fXS4g05O92GkdFmZFVHtH9T1mqXWCGSzqefSbioPy502lHq0sbRQcfSU7OqRo8XR9t7YJKAqRqrPxb01Eytb7mTNl9PvZU8barRbiYGYsa1uaYd4bD256BKPbfGmqgJU8tdMEmRhpkNHq/awzmt3jm9NhfZkmVIQbfD4cDUqVPxwgsvAADC4TB+/OMf48wzz8RFF10UrzEe57e//S1uueUW3HTTTZg4cSIee+wxpKen48knn0zYz9Q7kc6nhxqlYCiMLUe1fQMpz4kcexMM6+PYG2VXQaMTHLult05eDztfWk41FfS0s6DVLrGx9JSyr/VFIejsGCER0IwtciJTg4tCiOmFoIdTNQ40d8HjDcJuMWFcsVPt4ZyQ+LzrYWE9ktkijlvUZlAzrsiJNKsZHb4g9jd1qj2c0xKLV1p9PTPsFowtinx2dHENVTJbtHuPT4YhBd1vvPEGfvrTn+IrX/kKvvSlL+HMM8/EE088gddffx0PP/xw/EYZw+/3Y8OGDVi8eLHyNZPJhMWLF2P16tUJ+ZlGYLOYMLlUHzVKu+o74A2E4XRYMDJfe/XHiO58zdRJinmXL4g9DR2AhlP5oLMSiN5FDO2+ntN1FCRqtUtsLD0tYmzSaBfjWDOUY288mj/2Rjm+UqOLlkBkB14vp2qIa9LUchesGix3AoCy7N6Fda3XyW+v9SAQkpGfadNkuRMAWMyxJSXavobWtvc28p2qsUa+sXqzMbQ9B+3TA4dB99DceuutuOOOO/D8889j/fr1ePHFF3HBBRfEZ3Qn0NzcjFAohKKioj5fLyoqQn19/Qm/x+fzwePx9PmVivTSrCq2ds5k0uYuDfqk82n79dx61I2wDJS4HCjK0maqKXT0/oytP9b0DTm6IKD1dD4td4mNNbXcBUkCjrb3oLFD2+l8Wi/PAcT1KBrUaPzYm96jmLT7eqbZzJhQEllY36jxhSHxemp5EUOSJN2UQIh75vQKbdYfC3rJFhKLwBNKtNnIV9DLUZaiB44Wj1tMtiEF3W1tbbjyyivx6KOP4vHHH8cXv/hFXHDBBfjjH/8YvxHGwX333QeXy6X8qqioUHtIqtBLjZKWG9bEEl2BN2q8+ZceUqEREyBs13g6n5gwjtNo/bEwvsQJu8UEd08AB1u61B7OSW2v1XaXWMHpsGJMYSTzRsuTnDp3D+rc2jxuMVYkqNH+QlsopoRouoYzWxB7T9L4QnDvPUnbr2dvLxyNv54ar+cW9JItpPXUckFks2054kYwFFZ7OCcVuwis5UWhZBhS0D158mQ0NDRg06ZNuOWWW/C3v/0Nf/nLX3D33Xfj4osvjt8oY+Tn58NsNqOhoaHP1xsaGlBcXHzC77nrrrvgdruVXzU1NQkZm9bN0EnzL73Ufkwuc8FqltDc6cORNu2m8+lhVwFKh+jIztd2De986WURwxqTzqflIFGp59Zw/bGg7CxoeOFS/FuPL9b2Lg10UlKyp6ED3f4QMu0WjC7UZrmT0Pt6ajdI7PGHsKs+Uu6k9XuSHt6fiPnMa/2eJOagu+s96PYH1R7OSemh3AkARhdkwmm3oCcQwp4G7dbJ62WRLRmGFHR//etfxyeffIIRI0YoX7vqqquwefNm+P2JOabGZrNh1qxZeP/995WvhcNhvP/++1iwYMEJv8dutyMrK6vPr1RU6nKgUOM1Su6eAPY3RXblpmm0S6zgsJoxsTQS1Gi1rluWZd1c8CLH3mh/kqOH1F1B2VnQ8E6NXt6fiNlZ0PT7Uye7XtBJM7XY+mOzhsudEBMkaDlbaOtRN0JhGUVZdpRotLO+IDpE17m9qHNrc2G9QQed9YVilwPFWQ6EZWi2AW2k/ljbTekEk0nC1ArtH72ol420ZBhS0H333XfDZDr+KcrLy/Huu+8O5alPadmyZXjiiSfw9NNPY+fOnfjGN76Brq4u3HTTTQn7mUagh6BGHCNSmZeOvEy72sM5LaWZmkbT+ercXjR2+GA2SZhcqt1UU0Hr789An8762r4hI2aMWt6Z1cuuAmLen1uOtCOk0Tp5PTT5E6aURQLZeo92gxo9TRhjT9XYqtGF9djMK61ntqTbLBhfHNmk0Wq2kLhXarmzfiyt13Vvr3UrTekqcrVff6z1um699MBJlgEH3dXV1QN6/InO8R6qq666Cr/5zW9wzz33YPr06aiqqsLy5cuPa65Gx1POmtXoqphe6rkFpZmaRi94m2JSTdNsZrWHc1q9NV/afH/u7tNZP0Pt4ZzWdKVDdIcmO0TH1h9Pq9D+DXlMoRMZNjO6/CHsbexQezjHCYTCyg6SHoLENJsZ44u1fexN7z1J+4sYfU7V0OhCcG8neO2/nojNbtFokLhJB03+Ymn9Hi/quWcM03ZTOqE3m02b70+xyDa+OEvz5U7JMOCge86cOfja176GdevWnfQxbrcbTzzxBCZPnoyXXnppqGM8odtuuw2HDx+Gz+fDmjVrMG/evIT8HKPR+k6i1s+TPtbMaOOaHXXarFHSQ9fdWFPLs2GSgFq3F/Vu7XWI7u0Sq+3O+oIoKQlptEO0mODoof4YQPQImehOjQavobvqOuALhuFKs2KEDhaFoPE65A5vAHsbI7WS+lsI1t7riZhFDL3ck8RcROuLGHrIbMExJSVabECrp8wrxCwK7WvshLsnoPZwjqOXHjjJMuCge+fOncjIyMD555+P4uJiXHzxxbjllltw++2348tf/jJmzpyJwsJCPPnkk7j//vtxxx13JGbkNCharlGSZbl3V0EnF7zS6LE3sR1utURvuwqZdgvGRdP5NmhwkrP+sL5uyJIkaXpnQfwbi67LeqDluu7YXS897NIgJljQ4uu55Ygbstybtq0HYiF4w2HtBTX1bi/qoqmmosmj1onXc8tRN3xBbWUL+YNhpSRvZqU+ghpRUtLY4UOdxhbWZVnW3T0pP9OupMFvOaK9a6ieerYkw4CD7iNHjuCBBx5AXV0dHnnkEYwZMwbNzc3Yu3cvAODaa6/Fhg0bsHr1alx00UWJGDMNgZZrlKpbu9HWHYDNbMKEEqfaw+mXSDqfNncWAqGwUtenp1XG2cqkUVuvJwCsPxQZ0+zh+rmBaLmuW2+7CojZ8dTi66m3XS/EXJu2HnXDH9TWsTd6K3dCNKixmLR5qoZejluMNTI/A7kZNviDYWyv9ag9nD6217rhC4aRnW7FyHxtd9YXYktKtHYNPdreg8YOHywmSVf1x9M1WtfdtweOfq6hiTTgoHvGjBlobW1FWloavve97+Huu+/GK6+8guXLl+Nvf/sbvvOd72Dy5MmJGS3FhVbP6xYTxkllWbBbtF9/LChB92FtvZ676yOpplkOC0bk6SPVFDEB7YbDrWoPpY96d2+XWD1NwpUgUWM3ZD11iY0l0k33NHagw6utdD49Nf0SRuRnwJVmhS8Yxq56bQU1va+nft6fDqsZk0ojC+taWwjepMNFjNiF9Q2HtPV6Kruyw3J0Ue4kaHXhUvTmmViaBYdVP3PQGRqt6xY9cFxpVl3NQRNpwEF3dnY2Dhw4AAA4dOgQwmFtrUzT6fXW1GjrBqLHXQXEpHVtqm7TVDqfUn+ssxty7LE3Wmr+JSY444qz4HRY1R5Ov4mSklq3Fw0e7aTz6a1LrFCY5UBZdhpkGdiqoZKS1i4/DrV0AwCm6egaqtVTNfqUO+no9UTMPV5rdch6re8UqcbrNbYQLO5JM3WSCi1oteRpo87Kx4TpMR3hNTkH1UkPnGQYcNB95ZVX4uyzz8aIESMgSRJmz56NkSNHnvAXaVPvsTduBELaWTTR464CAEwqdcFqltDS5Ud1a7faw1HocVcB0WNvirIix95oaSVcTLhm62yCk2G3YGyR9jpE661LbCwtdjQWqbujCzPhStPPohD61HVrZxJ+pK0HzZ1+WM2SsnOsFyII09KpGsFQWFmk0kujVKE3+0o7C+uyLCs9RvR2TxJzvK1HtToH1df7c1JpFmxmE1q7/Khp1U5JiV4X2RJpwEU1f/rTn3DFFVdg3759uOOOO3DLLbfA6dRH/S1FjMiLpPO5ewLYVdeBKRqoXfEGQthRF0kt1NsNOZLO50JVTTs2VrehUiNpNFVKfae+Xk9JkjC7MhdvbK3DhsOtWDAqT+0hATG7Cnqq5xZmDMvGrvoObKpuw4WTi9UeDqDTem5hRkU23thSp6lFjE06/bxDoyVPYiwTS/SVagpAOTZsZ10kW0gLx0XubuhATyAEp92CUQX6qD8WppS5YDOb0Nzpx+GWbgzXwMkANa09aOrwwWqWdJXZgmidvNNhQYc3qKk5qKjZ19s9yW4xY0JpFjbXtGNTTRuG5aWrPSQg5hqqt420RBpUJ4sLL7wQALBhwwZ861vfYtCtMyZTpKPxx3uasKmmTRMXvO21HiXVtDxHP6mmwsxhOZGg+3A7Lp9RrvZw0Nzpw4HmLkCHO92IpvNFgm5t7Hx1+4PKDVkvXU1jzRiWg3+srVF2RtQmy3JM0K2/9+eMY9L5tLBTr+cusSJoONzSjZZOH/Iy1e8UrtfMKwAoy05DodOOxg4fthxpx7yR6i9ciiaU04fpL9XUYTVjclkWNla3Y8PhNk0E3SLzalKpS3eLQiaThBnDcvDJniasP9yqiTno1qNuBMMyCpx2Xc5BZ1RkR4Lu6nZcOr1M7eGgrcuPg2IOWq6/e3yiDDi9PNZf//pXBtw6pbUautjaOS1MYAdK1HVrpXHN+kORG/K4IidyMmxqD2fAYtP5wmH10/k217gRCssojtbz6s28EblA9EgRb0D9OvlIfbnoEqu/G/KkUm11iA7FlGLoMZXPlWbF6MLI7qdWSkr0Ws+N407V0MbruTZ6T5o7PFftoQzK7Oi4tbJwuUGnqeWCuCetO6SNOvneem59zkG1li0krp+jCjLgStdXuVMiDSnoJv3SWjM1PU9wELP7uau+A93+oNrDwdqDkX/XOSP0eUOeUJKFNKsZHm8Q+5o61R6O0kl91nD91R8DwLDcdBQ67QiEtFEnLyY4E0qyNJH6OlAOqxkTSqJHL2rg9dzf1IlOXxDpNrNSv683SgdeDQSJvmBvqqne70laWAiWZRnrDkauoXNG6DPonlWprVM19FzuBABzoosYaw9qo05ez+VOiLlO7az1aOI8eT1nCiUSg+4UJdI9DrV0o7XLr/ZwdP8BLXGlocTlQCgsY3ON+h2NxerxHJ3uKljNJkyriKScrdfAMS3rY45m0SNJkpTJrpj8qknPqeWClrKFxPVzWnk2zDpL3RWUheAa9T/vO+s64A+GkZNuRaVG6iMHSkunalS3dqMxWn+s10UMEYztaeiEu1vdowLdPQHsbuiIjEunO91Ty0WdvE85dUEtkXKnyHVcr6/nsNz0yHnyIW2cJ79Jx5lXicSgO0W50q0YVRCpS6pSeZLT1BFJ0ZSkyIVYr3rT+dR9PTu8AeX847k63VUAgNmVkbGrXdcdDsvKzqxedxUQk9a5VgPpfHqf4KDPWbPqB4lG6BIrxi5KOdRUFXPUjR4zWxBzqkZzp/odjddEF/qmlmfrrv5YKHDaMTy6ALNR5c98ZCFFZDA5VB3LYDmsZmVhfe3BFlXHcqSttyndlDJ9zkElqXdBq0rlheBwWI5p5Kvfe3wiMOhOYb0p5up+QEV65pjCTF2df3ys3p0vdW/IG6vbEZaBitw0lLj0V38szBqujXS+vY2d8HiDSItJKdYjsQCz8XAbgioe0+INhLAjuiik11Q+xFw/t2kgnU/PTdSEsUVOpNvM6PQFsa9R3ZISI3TdFadqQAMLwSK7Rs+LwAAwSywEq5x9pfd6bkG8H0Q5nFrE52OiDpvSxRIlOmp/3vc3daJDKXfS10kFicagO4VpJT1SrHLqsSt0rNizUdVM51Nq53SaWi7MHJYDSYqUQDR1+FQbh+gSO70iG1azfi+Z44qcyHJY0OXvPZ5PDduOuhEI6bdLrDA8Lx15GTb4g2FsOaJeSUmHN4A9jZFUU72m7gKA2SRhWrn6C5eyLGNt9Bqq+3uSRrKv1um8iZogMp3Wq7wQLEquZuk48woxcxS1m6mJObCey50Qc71ad6hV1TmoeD2nlrtg0fGcKRH4aqQwkfZRVdOuajrf6gORoHu+Bo41GYpJpVmwmU1o7fKrWqOk9y6xgivNirGFkaZQaqaY671hjWAySUoH3rUq1nVv0HmXWEGSJOWatXq/eumRW464IUczWwqc6h+1NRRaWAg+3NKNOrcXNrNJ15kYiKnrVvP62djhxaGWbkiSvstJELOzXFXTjoBK2ULBUFjJDhQlWHo1qzIHJilS89/g8ao2jt57kr7fnzMrc2Azm9Dg8SnHdalB9OXQc6ZQojDoTmFjizKVdL79KnWIdncHlKYPC3QedNstkbM8EdOdOdl8wZByQ9Zrl9hYWkgxFzdkve96QSM7C3rvEhtr/sjI6/nZAfWCbqUJpQFq57TQTE0sAk+vyNZlZ/1Y4jOm5qka66Kpw+OLs+BK02/5GACMKsiEK80KbyCMHSo1q9pZ14GeQAhOhwVjCvWduut0WJWSLbUWgnv8IeyMZn7pfVHIYTVjenTh8rMD6t3jlXInHWdeJQqD7hRmMZuUxmVqpfOtPdQKWQZGFmSgMEufDUFiqZ3Ot+WIG/5gGPmZNozMz1BlDPEkuoWrtVPT1OHD4egujRFWbecqZ6Oq09HYCF1iYy0YFVko3HC4TbW6biM0URNEenykj4I6HaLFAsr8UfpeBAaA0uw0FGepe6qGKB+bZ4BFYJNJUlKQ1bonidT2mcNyYNLpSQWxeuu61QkStxxpRzAsoyjLjlKX/uegYvNqtUoLwZ2+oNJZf7oB7knxxqA7xandTE2kZeo9tVyIretWw9qYem49p+4KIqV721EPvIHkBzVih31soVP3uzQAMKXMBYc1UgKhRnaL6BJrMem3S2ysUQWZyM+0wxcMq3INlWVZafql53puocBpR0VuGmQZ2KJCkCjLcsw9Sf9BImJSzNVaCF4brT/We48RQZToqBd0G6OJmjBX5ewrZRF4WI4h5kyxJU9qLKxvqWmHLANl2Wm67ayfSAy6U5yYqK1X6QYidhX0nlouiJ3u3fUedPqSn86n9/O5jzUsNx35mXb4Q2FsPZr8SbhRGtYINotJ+cyr0TFWTPwnlWbpukusEKnrVi/F/FBLN1q7/LCZTZhYqt/O+rGmV6jXrOpgcxcaO3ywWfRfzy3MVBbWk/95d/cEsKs+kro7Z4QxXk9RZrT+cPKbVcmyrHRON8o9SSxi7G7oUOX8cyOVOyGa8WSzRM4/39+U/LpusRhlhMyrRGDQneLmDs+FJAH7GjuT3siivduPndEb8jyD7CoUuxwodTkQliMrfskUCvfekPV+NIsgSZKyor9ehWNaNlQba1cBKu8sGOFoq2OJFHM1mqmt3NcMRCc4dov+FzEQk4a8al/yX0+RkjmjQr/nSR9rxrDe7KtkB4kbD0fOkx6ep9/zpI81rTwbFpOEBo8PR9qSe/55rduLeo8XZpNkiMwWRLNbRuZnQJaTv9Amy7KyGCUyQvTOYTUrZXlqpJiLe9I8g2ykxRuD7hSXk2HD5OhZniv3Nif1Z685GKnnHl2YaZgbMgDMqFSnrntnnQcdviAy7RZdnyd9rNkqNVPzBkLYFt1d13uX2FhzR0RuhmrU0Cm7CgZaxBDpfJtq2pNeArFybxMA4Kwx+Un9uYkk/i4bq9uSni0kmg8tMEA9tzC5rPdUjcNJPlVjjUHO546VZjNjUrQ0Jtkp5uujC6WTSrOQbrMk9Wcnklp13TWtPWju9MNqlpQz7Y1A3JOSnX3V5Qsq9/izRhvnnhRPDLoJZ0YnOWKFKlmMVjsnzBymTl232LmcVZkDswEarAginW/D4eQ2/9pypPc86Ypc/Z4nfawZw7JhNkk42t6Do+3J26nxBkJKx1+9n4caa2R+BgqddviD4aQutAVDYayKXkPPHFOQtJ+baJV5GajITUMwLGNNEieNfeu5jRN02y1mTBKnaiR5Idho5U7C7Ep1Gnwa6SSNWOL9sTbJ2Ve95U4uw2S2IGbRcM2B5NZ1rz3YikBIRnlOGirz0pP2c/WEQTcpK1Ir9zUn9QPaW89trBUxcUPcVJ3cIFFMcIy0q4DoDdFuMaGtO4ADSTx7UqS6zTJIgxUhw27B5Gj977ok7ixsOeJWusSWZRtnESP2vO5kHtOy5agbHd4gXGlWQzSli3Xm6MgiwookZl/tb+pEc6cP9pi+B0YxS4VTNbyBELYciSw8G+2e1FvXneydbmMG3eL9sfWIGz3+5GULic+D0V7PaRWROVNzpx/7GpPXMFVcr88ak2+oOVM8MegmzBqeA4fVhKYOn9LqP9Fau/zYVR/5WUap5xYmlmQpQeLBJAWJsiwrjbGMtqtgs5gwrTx6TEsS67rFz5ptkIY1sdTYWYhtWGO0G7LYWfgsiXXdohxo4ag8Q2W2ICbFPJnZV6sP9B7FZKRdL8SeqnE4edlXVTXtCIRkFDrtGJZrrF0vsdO9u96DjiQdbdfpCypN6YxU7gQA5TmRo+2CYRmbapJ3jzdaEzXBbjEr85Zk1nWv3BcpdxKLpnQ8Bt0Eu8Ws1Hkmq65bpA2OLYocuWMksUHiqiRNwg82d6G50wdbzNnrRiI6tSar0Uo4LCtN1Iy2Cg4Ac1SooROfBSO+nmKnu6qmPWk7NeJafaaB6rmFhaPylAafde7klECIBRMj1XML4jO3s96D1i5/Un6mcnzlCGMcXxmrMMuBitw0hOXkHbe6qboN4ehRTMUGOE86liRJSb8ntXf7lXInQ96TRiS3rrvB48Wehk5IUuT6TSfGoJuAY1LMk0FcCIxUOxfr7HGRlb4PdzUm5eeJ1PLpBuq6GyvZNXQHmrvQ3h2A3WIyVIMVQex072vsTMokvNsfVD7zi8YZbxV8eF46irMc8IeSU9fd2adhjfFez+x0G6ZGU+Y/TUIXc1mWDX1PKspyYHyxE7IMfLwnufekeQZLLRfEbnOy7kni5xgx8woxKebJOlXj4z1NCMvA+GKn4RYxEJt9daAV4XDiyxzFIvCUMhdyMmwJ/3l6xaCbgJjdkjUHWuELJn6nZrXBzuc+1jnjCgEAn+5vTkpHYyW13CBnoR5LrETvb+pCWxKCRNEpfVpF5MxLo8nNsGFMYSaQpEnOqn0t8AfDqMhNw6iCzIT/vGSTJClmkpP4IHHNgRYEwzIqctMwzKANa5QGn9EO7Ym0t7ETLV1+OKwmTKsw3iIbAJw7PnJP+nBX4l/PYCiMjYeNWe4kzEryQrASdBtwVxYxR1luPNyOQCic8J8nNkTOiX4ujGZqeTbSrGa0dvmxNwl13WLD7gx2LT8l480maVDGFzuRn2lHTyCU8Lqv5k4f9jRELgJGPctvQokTxVkOeAPhpEzCjdolVshOt2F0NEhMxiRHNKwx6gQHMSnmyWim9sHuyATn3HGFhks1FcQpDMk4r1s0rDFy7Zz4u63cl/gOvOIaPbsy1zDnnR9LBN0f72lCMMFBzY46D7r8IWQ5LBhX5Ezoz1KL2HHeVN2W8NczFJaVNPZZBqvnFsYUZsKVZkVPIITt0bTvRAmFZXy8J7L4dK5Bg26bxdRb170/sRmssiwrQTePCjs1Bt0ERHdqzhwdrevel9iV8DXRhjXji53INWgaiiRJOGd8clLM691eVLd2wyQZszZJEB14k9Ex1qhHs8Sam6RmarIsK5+BRQad4CDmFIbNR9rR7U/s+dLKBMeA9dzCzMrITk1zp09pupkoRj2+Mtb0imy40qxw9wSwqSaxC+uiLnf28FyYDNbkTxhT6ITTbkGXP5Tw9+eueg86fUFk2i0YV2zMRQyTScKcaJC49mBiFy6ratrQ1h2AK82KGQY7qSBWsk7V2N3QgaYOHxxWk9J/h06MQTcpxFmviW6mtvpA5PmNWDsXS6SYf7C7MaE7NSJomliaBafDmrCfo7ZkdeOsd3uVo8mM1tU0lqih217rQZcvcUHirvoO1Lm9cFhNhi0nAYCK3DSUuhwIhOSEZmPUu73Y12j8hjV2i1k52SKR96RwuLee24hN1ASL2YSzx0bu8R8keCFYBN1GOyosltkkKV3hE53NJhaFZgzLNtxJBbHmKs3UEruwLt7/nxtbAIvZuGGQEnQfbEloXbe4Ps8dkWfYTKF4Me67jQbszGhayJajbrR3J65uVqy6GT3oPmN0PmxmE2pae7C/KXFHh4n0YKOmlgtnjyuAJAGba9oT2tH47e31QHSX28gNQUqz01CWnYZQWE5o868Po6nlZ4zKN2STP0GSJMxPQl232OWeWuZCdrpx35+IuSetSGCDzz2NHWjrDiDNasaUMuPueqFPXXfigm5ZlpVsJKPfk8TruXxbfUJ/jrgnGTUVWhDvl/WHE9v8S/Q1OHe8cctzAGBquQvpNjPauwMJPQ6YqeX9x6CbFMUuB8YUZkKWE3fUVWNH7y6NkVP5ACDDblF2ahI5yRH13HMNPsEpdDqUGuu3EzjJEROoCycVJ+xnaMXcJNR1G71hTSyxkJjIum7RWMyIR4Ud66xo9tXagy0Ja0gp/q1mD88xZNPEWGePjSxc7qrvQG17YhYu9zdFTkRwWE2YUmbMpnTCBZOKAAAbqtvQ6PEm5Gc0dniVRYwlBr8nTS5zIc0aCRL3NSWm+Ve924sddR5IEnD2WGPfk6xmE2YPT2yvEV8wpJSMpsI9aaiMfYehARMfmhUJSufrrefOMvwuDWJTzBMUdLd3+5UVzNkGD7oRM+l4K0FBd0unD2ui9WQXTjb2BAcxOwuJqutu7/YrqdapEHSL9PktR9wJSdmPNKyJvD+N3ERNGFuUiUKnHd5AbzfseDPyUWHHysmwKTWsIgMl3kRq8HSDnvwQq8SVhukV2ZBl4O0dDQn5Ge9sb4AsA9PKXSjNTkvIz9AKq9mEGcMi789Endct3vfTK7IN21Mo1oKRic2+2ni4HT2BEPIz7Rhv0H4D8WTsKyINmGjMk6hmakY/KuxYIh1s3aFWeLyBuD//+kNtkGVgZEEGCpz2uD+/1ohAeN2hVjR3+uL+/O/tbEBYBiaVZqEi15hHMcUSO92bqtsTclSgOAt1XJETZQafMAJARW46yrLTEAzLCWn4t6u+A82dPqRZzZhZaexUaCgNPhOXYh4Oy1gTndwbuZ47VqJTzEUTrLkjUuP1XBq9JyUq+0qkll84uSQhz681vXXdiQm6xQbIueOMvwiMmOaQaw4mJmVfxApnjs4z7Mkk8cSgm/qYNyIPVrOEmtYeHG6Jfx1y766C8XdlAWB4fgZG5mcgGJYT0gxIHHsxz8ANa2KV56RjSpkLYRl4NwE7C2+lUGo5AIwqyEB+pg2+YFjJQomnVEotF0Twloh0PnENmTfSuEdbHav3vO74Xz931XegvTuAdJvZ8KnQgvgsfrov/in7wVBYqe9MlXuSWAhefaAFbV3x7YXT3u1XriOpkHmFmKD7033NcT+v2xcM4dPo+zNV7klTylzItFvg7glgR138j2IT12XRiJlOjUE39ZFht2BGtGPzyjjvLDR4vDjQ1AVJigT3qWLRuMTsLPiDYfxnSy0AYGmKrIIjZvIR7+Y1Hm9AuSEvnZIaExxJkpTX89VNR+P63LFnoZ4zLnVuyIlM5xO7vWemUMMa8XfdVuuOe1AjMq/mDM+F1cBdjGNNLMlCUZYdPYGQsssfLyv2NaO504+8DJuhO5fHqszLwISSLITCMt7bGd+F4Pd2NiIYljG+2IkR+RlxfW6tmjs8F/mZNrR0+bFib3wzLtcebEW3P4RCpx2TSrPi+txaZTGblKPY4n1Pau/2Y8tRN5Bi96ShSI27DA2I+PDEe2dBfOAnlmTBlW7co62OpaTz7W6Ka3rPR7sb0d4dQKHTjjNS6IIngsRV+5vh7olfyv4HOxsRCMkYVZCB0YWpU5t0+YxyAMDy7fVxPV+6qqYdbd0BZDkshj7v/Fiig/nWo250xrGu2xsIKam7Z6XQrkJhlgNjixLT4LP3fO7UWQSWJEnpNRLvheBXNkYW7i6ZVpoyixiIyYyK90Lw8m11QAo0UItlMZtwybRSAMDLG+O7ECxSy88ZV5hSqdDzE7QQvGp/C2QZGFOYiWKXI67PbVSpc1WkfhPpfKv2tyAUxyDxsxSr5xbmjshFhs2M5k4fttW64/a8r0R3Ji+dXmroszuPNaogE2OLMhEIyfhgV/x2FsSEKZWyBgBg5rBsDM9LR7c/pNQPxsOHKXIW6rHKstMwLDcdobCsnCwQDxsPt8EbCKPQacfYosy4Pa8eiKZx8ew1EgrLyiJGqtRzCyK19oNdjZDl+NzjO31BvLMjcv24fEZZXJ5TL0Rm1Iq9zXFbaOv0BfHJ3tTKvBKuiC4Ev7ujIa69cFKx3Akx17c1B1vjOqdfoaSWp86mz1ClzkyI+m1qmQtOR6QGZOvR+ASJsizj032pt6sAADaLSbkoxauLubs7gPd3Rp5L7FSmknjvLPT4Q/hoT+T1TJXaOUGSJFwWnSTHc2dBaViTYhMcxPSsWBXHEp3Y1PJU2qVBTIPPFXub4xYkbq91w+MNItNuweQUSTUVzhydD6tZQnVrN/Y3xad3y1tb6+ANhDGyIANTy1OjPl4YU5iJkfkZ8IfCccse+Gh3I/zBMIbnpWNcUepkXgHA5LIsjC7MhC8YxvKt8bnHH2jqxKGWbljNUsoFiRNLsuC0W9DhDWJbnOb0iFkEPSvFXs+hYNBNx7GYTVgYXRlbGaeamjUHW1Hd2o00q1k5uzqVKOl8u+Pzer6xtQ7+UBjji52YmGITRsR0cv14T1NcUqI/3tMIbyCM8py0lKn1iiV2pj7d1xyX82b7noWaOqnQglhoeGXT0bh1hV+ZwrsK80bmwmqWcKStB4dbuuPynP9cXwNEJ4yplImBaO8W0VflozgdHSYyr66YUZZyi0KxvTHitRCsNPWcXJKSr6e4J7286UhcnlPMveaOyEWm3RKX59QLi9mEz0X7qojr3lAdbulCTWsPrGYppXo0DVVq3Wmo30Qnwnid1/3s6sMAgMtmlMHpSJ16bkGkM2050h6Xo65eid6IUi2NT5hQ4sSw3HR4A2F8HIeFjOUxXctTbYKDaDOgWZU5CMvAa1W1Q34+MZGfVp6NvEzjH2V3rPMmFKEoy47mTn9cJuFtXX6lNCUVG9ak2yyYGW3wGY+jwzzegJLVcd38yiE/nx7FppgPVZ27R2lKd+n01LwniaD7w92NQ+4K7w2ElB3zVMu8EkT21WcHWnG0vWfIz/dhTD13KvryvMh17pVNR+OSsi9igxnDcpCRYosYQ8Ggm07orOjEbmN1G7qGWKNU7/ZiebRW9PoFqTnBKcpyYFJpFmQZ+GiIQWJNazfWHWqDJKXuBEeSJOV81LeGGNT4giElVT/VaudiKSnmcehinsqp5QBgNZtwbXSS80x0wXEoPt3fDFkGxhZlojArNRvWnKUcHTb0RbaXNxxBtz+E0YWZKVfPLYjP5tqDregY4iT81U21kOXILmJFbnqcRqgvU8pcKMtOQ7c/hE/2DO09umJvM7r9IZS4HJiWYqn6Qll2mnLs3FBP1uj0BbEm2r8hVe9J80fmYmxRJrr9Iby0YejZA0rmVQouAg8Fg246ocq8dJTnpCEQkofc8fDvaw4jFJYxd0QuJpSkXuquoHQxH+LOgkjjO2NUfkp3jFwSDbo/2NU4pBTeVftb0OELosBpx4yK1OmyfazPTymB1SxhZ50Hu+oHf56nLxhSjhtM1QkOAFw9twJWs4QNh9uGXEe3Yo+Y4KReqr4gsq9W7W+BPzj483tlWcYzn0UWQm5YUJmSmS0AMCI/AyPyMxAMy0M6qUSWZSXz6ooUzbxCdCFYdBlfPsSGlCI7ZkmKZl4JV8yMvJ9e2XR0SL0cVu5tRiAkY3heOkYWpFYTSkGSJFy/YDgQzTwdykk6gVAYq/anbrnTUDDophOSJAmLJxQBAJ789OCgn8cfDOPvayM1JKm6yy2I87o/2duEQGhwk0ZZlpVV31RNLReml2ejKMuOTl9QOV97MESjliWTimBKoS7wx8rJsCmpd68MYWdh3cE2dPtDKHDaMTGFF9kKnQ6lE/4zqw8N+nkaO7x4bXPk32PxhNRdxJhS5kKh044ObxAvbRz8Ts2n+1pwoKkLmXYLLp+Zek0oYy2K1nl+OIS67h11Huxp6ITNYsLSKal18sOxRCr4ezsaBr0wFAiFlfO+UzW1XFg6pQR2iwn7GjuxvXbwC8Gi3GlRiqaWC5fPKIPTbsGB5i5lYXwwXtpwBB5vEPmZdkwtS81MjMFi0E0ndfNZI2A1S/h0XwvWDHK3+61tdWju9KHQaU+psyZPZHpFNnIzbOjwBrHhcNugnmPzETcONHchzWpO+RuyySQNuYt5MBTGu9EJTqodFXYiYmfhtU21gz5apPcs1IKUXsQAgBsWRhYaX6uqRXu3f1DP8fjHB+ANhDG9IjtlU6EBwGyS8PWzRwEA/vDBvkEHNU9HF0CunFmWcg2VjqVkX+1uGvTOlzib+/wJRXClpV6/llizKnOQn2mHxxscdIbgZwda4O4JIC/DhjnDU6/pbKwshxWLJ0Y2fwZ7soYsy8qiUipnXiHaQPHKWZGFxsGWPfmDYfzfB/sAAF8/e2TKNaEcKr5adFLlOen44uwKAMBD7+0Z1HOID/a18yphTfEPp9kkKZ2cB5ti/kp0h2fJpCI2r4hJMX93RwOCg8geWHuoFa1dfmSnWzF3RGpPcBBtruRKs6Le4x30pJETnF4zh+VgUmkWfMHwoLrGNnq8+Fs0Ffrb549N6VRTAPjSvGEodNpxtL1nUK/nkbZuvB9dZLsummqZyuaOyEW6zYymDt+gdhKDoTBe2xxpvJjqmVeI3uMvmBQJEgfba0R83wWTimBO8UVLxJQs/Htz7aDu8dtrPWjw+JBuS82Tc451XTTj9P1dDahpHfhJEC9uqMHR9h4UOO34coo2oRyK1I6C6LRuPWc0bGYTPjvQqtRw9Ne2o25sONwGi0nCNXMrEjZGPREdY1/fUjfgDqeBUBj/2VIHACmfFinMHZ6L3Awb2roDWHuwdcDf/3Z0gnP+hKKUXxQCALvFjIunRnb8B7OzsLG6DQebu2A1SziDDVaidXSRicmznx0ecPbAHz/aD18wjFmVOfgca+fgsJpx6zmjAQCPfLhvwL0cnltTjbAMnDE6D6MLU7O2M5bdYlYaIQ0mZf/T/S1o6vAhN8OGs8elbr+BWEuVheD6AX/eQ2EZ72wXqeXMvAKAz40tQF6GDc2dvkGdXCDuY2eMzofdYk7ACPVlVEEmzhqTD1kG/rZmYLvdvmAIj0R3ub+5aBQcVr6eA8VZJp1SaXYaro4GzA+/u3dAzSzEMWFLp5SkbMfdY503vhBFWZGdmt+9v3dA3/vx7ia0dvlR4LTjjBROM41lMZtw/oTB7SyEw7LS8CbVU/VjiZ2F5dvq0OPvf1DjD4bxw5e3AgAumVqakkcDnsj/m1YGV5oVNa09AzoTud7txd/XVgMAvr2Yu9zCVXMqUJzlQJ3bixfW9X+32xsI4fno63k9d7kVX5o3DIj2HdhypH1A3ysyry6ZWsJFy6j5I/PgSrOiudOP9YcGthC84XAbmjt9cDosWDCS93hET4K4ZFopEFPK0F/bjrqVchJu/PQS178X1tUMaPPnn+tqUOv2oijLjmvmDkvgCI2LV0k6rW8uGg2bxYS1h1rx6b7+pZy2d/vxalXkAnlDijdQi5Vht+Cnl04GAPzpkwPYXtv/rsaiudWl00pZRxPjwugxX29vrx9QXWLVkXY0eHzItFu4KxtjVmUOhuWmo8sfwjs7+r+Q8adP9mNXfQdy0q340cUTEjpGPUmzmXHVnMiEbyB1dH/8KFK3PHd4Ls4YzQm44LCaceu5vbvd/Z00vr6lDm3dAZRlp+E8lj4oFo0rxCXTShGWgR+8tLXfTT67fEG8Hd2VZeZVL6vZpDShHWgX8+UxmVc2C+/xgihdeGdHPTr7eYRtIBTG9/+1BaGwjIunluDc8UUJHqV+nDu+EGXZaWjvDuA/0fKQ0/EGQnjkw/1ANAOWu9yDw081nVaxy4EvRVe1HnpvT792u19cfwS+YBgTS7IwqzJ1j2E6kSWTinHRlGKEwjL+56Wt/apTcvcElIZfl89k7VyshaPy4LRb0Njh6/ckR5ZlPLMqsgJ+zvhC3kBiSJLUe2Z3P3cW9jV24vfvR9LO7r1kEvIy7Qkdo958eV4lJAn4eE8TDjZ3nfbxte09eD566sOd54/hLvcxvji7HKUuBxo8Pvwjunt9Os9Gd7yunT+Mi5bHuPeSichOt2JnnQdPrDjQr+9Zvq0ePYEQRuZnpOxZ0icjMqf+sznSSLY/Wjp9+M+WSAC0hJlXfUwtd2FkQQa8gTDe2lrXr+/5y8qD2FHngSvNih9fMinhY9QTs0lSarufXn2oX3P659dWo97jRYnLoSwi08DxzkP98s1Fo2C3mLDhcBs+Oc2ZnqGwjGejzX+uT+FzUE/lx/9vErIcFmw96u7XkWxvba2DPxjGuCJnSh/DdCJ2S+9O4rJ/VmFT9ek7w//hg314taoWkgRlQYl6iZ2FFXub0NjhPeVjw2EZd728Bf5QGIvGFeDS6aVJGqV+DMtLV45je7Yfu92PfLgP/lAY80fmYuEoZmEcy24x47ZzxwDRuvfT7XZX1bRj8xE3bGYTrprNCeOx8jPtuPviiQCAh9/biwNNnaf9nldijq7kPb6vs8bkY1huOpo7ffjqU+vQ7T/17my3P4ivPL0eTR0+VOSmKQ1XKUKSJKXsqT/HWR5s7sJD70aa//7vxRNQ4OQi8LG+OLsCNosJ2456sKnm1GUl3kAIf/yod5ebtfGDx6Cb+qUwy6F0Knzo3VPvdn+8pxHVrd3Iclhw6XTuyp5IodOB/41Ocn777h4cbjn57pcsy8qO4+UzOcE5kR8sHY+zxxbAGwjjq0+vP+Vu4j/X1+DB6A35x5dMSuljmE5mRH4GZgzLRliOHB92Kn9fW411h9qQbjPj55dN5vvzJERDtRc31JxyEn6krVvpzP3txWOTNj69+cKscpRlp6Gpw6d0eD8ZkdXy+WklzMI4iStmluGsMfnwB8O46+WtpyzVqW3vwafRxqqXsWv5cRxWM/560xzkpFux+Ygbtz638aQZbcFQGLf9fRM217QjO92Kv944l5lXJyDmkqsPtOBoe89JHyfLkUVgXzCMM0fn4wuzWPpwIrkZNvy/aK386RaCn1tTjcYOH8qy05QTjWhwGHRTv3397FFwWE2oqmnHR7ubTvo4Ubd41ZwKpNl48ziZ/5pdjoWj8uANRCY5J1rIaPR48dWn12PtoVZIEriLeBJWswl/vHYmppS50Nrlxw1PrkVTx/FpfR/ubsRd0WZf31g0CjcsZEOlkxE7C79evgu/e2/vCWs969w9+NVbuwAA31syDuU56Ukfp158bkwBhuelo8MbxKunWMh45MN9CIRknDE6D/PYTOmkbBYT7jgvUtv92Mf7T7qQ0dLpw+vRUx9uYAO1k5IkCb+8fArSrGasOdiK50/SpO7Tfc34r8dWQ5Yjp0dU5PIzfyKjCjLxlxvnwGE14cPdTfjfV7cdd4+XZRl3v7YNH+xqhN1iwl9umM2u+idRkZuOuSNyIcvAfz26CitPknH5wroafHagFQ6rCb+8fAoXgU9BXA/f2FJ3wvkSAPT4Q3g0ust927mj2WtgiHT36v3iF7/AwoULkZ6ejuzsbLWHk1IKnHblQ3qi2m5/MIyVe5vx0e4mSBJ4ht9piEmO3WLCqv0teHFD75EtsizjtaqjOP+hT/DBrkbYzCb87NLJKHGlqTpmLcuwW/DkjXMwLDcd1a3d+OrT69AV03Rly5F23PrcRoTCMq6YUYbvLxmn6ni17otzKnDRlGIEwzIeem8PrvjjKuxp6FD+XJZl3P3qNnT6gphekc2O0KdhMknKNfGpVQdxqLnruGtoTWs3XlwfuQ5wl/v0rphZHk3j9Z9wt8bdHcAfP9oPfyiMaeUuTKvgnOFUKnLT8Z0LIu+7+97ciQZPb2lJtz+Ie17bhmv/vAZH23swLDcdP72MtbKnMnNYDv7vmpkwScDz62qOO7Hk9+/vwz/W1sAkAb+/ZgZmVfIc6VP52aWTUZmXjlq3F1/+yxrc/eq2Pvf4Ro8Xv3hzJwDgO+ePw7A8LgidypRyF6ZXZMMfCuOPH+1De7f/uMf87bPDaO6MlD0wa2DoJHkgZ0BpwL333ovs7GwcOXIEf/nLX9DePrAjLgDA4/HA5XLB7XYjK4v1sQPR0unDWfd/iG5/CA/+1zRkpVmx4XAbNh5uw+Yj7fAFI7th54wrwF9vmqv2cHXh8Y/34763dsGVZsW7yz4HsyTh7te24c2tkaZgU8pcePCL0zC2yKn2UHXhYHMXrnx0FVq7/Fg0rgBPXD8bte09uPLRVWju9OPM0fl48sY5XLHtB1mW8e/Ntbjnte1w9wRgM5vwnQvG4uazRmL5tnrc+veNsJolvHHHWXx/9oO7O4D5972PnmgNcl6GDTMrczAr+usfa6vx8sajOGtMPp796jy1h6sLL66vwff+tQW5GTY8+9W52F7rwcbDbdhwuA17G3trkx/8r2m4kpPG0wqFZVzxx0+x+YgbSyYV4fHrZmP9oVZ858XNONzSDQC4bn4l/mfpeGTYLWoPVxeeW3MYP3plGwDgV1dMwdVzh+GFddX4wUuRrKufXTYZ13GTol+6/UH86q1dSkblsNx0/Oa/pmHuiFx8428b8Na2ekwtd+Hlbyxkw8R+eGXTEXz7hc3K70cXZmLWsMj9aFJZFq7/y1q0dPlx/5VT8UU2UDup/saVugu6haeeegp33nkng24V/Hr5LiXd5Fg56VbMqszF/ywdh9GFnIT3RzAUxqWPfIrttR7MrszBweYutHT5YTFJuP3cMfjmOaN4BuoAbapuwzVPfAZvIIxLp5dic007DrV0Y2JJFl742nyeIT1ADR4v/uelLfgwWlYyqzIHh1u60Nzpxx3njcGy87kr21//3lyLp1cdwtYjbvhPUuf58jcXYuYwnvrQH8FQGIt/+zEORQPCY43Mz8DnxhbgRxdP4HW0n3bWeXDJ/61EMCzj/IlFeG9nA2QZKHE5cP8XpuKsMWz0NVAPvrMb//fBPphNEm45aySeWHEAobCMW88Zhe8tGa/28HRn5d5mfP9fm1Hr9kKSgMUTivDujgaYTRL+c9uZmFjKuX1/BEJh/PLNnfh4TxMONJ24F05lXjreW3Y2r5+nwKA7hs/ng8/XW6/g8XhQUVHBoHuQ2rr8OP+hT9Dc6cOYwkzMqszBzMoczK7MwYj8DNbQDMK2o25c+sinCEWb14wrcuLBL07D5DIexTJY7+9swC3PrIfoB1SWnYZXvrkQhVkOtYemS7Is48X1R/DT13coZ6WOLszEG3ecyW6mg+ALhrDtaO+u7PrDbWju9OGiKcX447Wz1B6erry1tQ7feG4j7BYTplVkRzIHhkXuS7kZNrWHp0u/eXs3/vDhPuX3/zWrHHdfMhFZXLAcFFmW8b1/bcG/YsrIrphZhgf/axrnTIPk8Qbw89d34J/re1/Tby4ahe9fyEWMwWjt8mNTdeRetOFwGzbXRLJXH/nSTFw8tUTt4Wkag+4YP/7xj/GTn/zkuK8z6B68Ll8QwbAMVxpvwPHy6Ef78fv39+LGM4bjzsVjGMjEwT/WVuOul7ciO92Kf319IZvUxMGRtm788JVt2HKkHU/eOIc7snEiyzKaO/3ISbcyLXIQmjt9yHJYWTYSJ95ACF964jM0eHz4yf+bhMUTi9Qeku4FQmHc/PR6fLynCZ8bW4C/3DCbu4dx8MGuBtz96nYUZtnxj1vms/t7nPiDYXi8AeTzxIfT0lXQ/T//8z/49a9/fcrH7Ny5E+PH965ecaebjCgclmEycdU7nrYddaPQaecOd5zxvUpkbOGwDEkCd2LjyB8MY8PhNsyqzOECURzJsgxZBu9JpIr+Bt2a6ILxne98BzfeeOMpHzNy5MhBP7/dbofdzpUa0j7eMOKPKfqJwfcqkbHxMx5/NosJC0bxKMB4kyQJXBsirdNE0F1QUICCAjbmICIiIiIiImPRRNA9ENXV1WhtbUV1dTVCoRCqqqoAAKNHj0ZmJus1iYiIiIiISDt0F3Tfc889ePrpp5Xfz5gxAwDw4YcfYtGiRSqOjIiIiIiIiKgvTTRSSza3243s7GzU1NSwkRoRERERERENmGjQ3d7eDpfr5H2EdLfTHQ8dHR0AgIqKCrWHQkRERERERDrW0dFxyqA7JXe6w+Ewamtr4XQ6NX0Uhlg54Y48aRHfn6RlfH+SlvH9SVrH9yhpmZben7Iso6OjA6WlpTCZTn4UYErudJtMJpSXl6s9jH7LyspS/Q1FdDJ8f5KW8f1JWsb3J2kd36OkZVp5f55qh1s4eThOREREREREREPCoJuIiIiIiIgoQRh0a5jdbse9994Lu92u9lCIjsP3J2kZ35+kZXx/ktbxPUpapsf3Z0o2UiMiIiIiIiJKBu50ExERERERESUIg24iIiIiIiKiBGHQTURERERERJQgDLo16pFHHsHw4cPhcDgwb948rF27Vu0hUYr65JNPcMkll6C0tBSSJOHVV1/t8+eyLOOee+5BSUkJ0tLSsHjxYuzdu1e18VLquO+++zBnzhw4nU4UFhbisssuw+7du/s8xuv14tZbb0VeXh4yMzNx5ZVXoqGhQbUxU2p59NFHMXXqVOUs2QULFuCtt95S/pzvT9KSX/3qV5AkCXfeeafyNb5HSS0//vGPIUlSn1/jx49X/lxv700G3Rr0wgsvYNmyZbj33nuxceNGTJs2DUuWLEFjY6PaQ6MU1NXVhWnTpuGRRx454Z/ff//9+P3vf4/HHnsMa9asQUZGBpYsWQKv15v0sVJq+fjjj3Hrrbfis88+w7vvvotAIIALLrgAXV1dymO+/e1v4z//+Q9efPFFfPzxx6itrcUVV1yh6rgpdZSXl+NXv/oVNmzYgPXr1+Pcc8/FpZdeiu3btwN8f5KGrFu3Do8//jimTp3a5+t8j5KaJk2ahLq6OuXXypUrlT/T3XtTJs2ZO3eufOuttyq/D4VCcmlpqXzfffepOi4iAPIrr7yi/D4cDsvFxcXyAw88oHytvb1dttvt8j/+8Q+VRkmpqrGxUQYgf/zxx7IcfS9arVb5xRdfVB6zc+dOGYC8evVqFUdKqSwnJ0f+85//zPcnaUZHR4c8ZswY+d1335XPPvts+Vvf+pYs8xpKKrv33nvladOmnfDP9Pje5E63xvj9fmzYsAGLFy9WvmYymbB48WKsXr1a1bERHevgwYOor6/v8351uVyYN28e36+UdG63GwCQm5sLANiwYQMCgUCf9+f48eMxbNgwvj8p6UKhEJ5//nl0dXVhwYIFfH+SZtx66624+OKL+7wXwWsoacDevXtRWlqKkSNH4tprr0V1dTWg0/emRe0BUF/Nzc0IhUIoKirq8/WioiLs2rVLtXERnUh9fT0QfX/GKioqUv6MKBnC4TDuvPNOnHHGGZg8eTIQfX/abDZkZ2f3eSzfn5RMW7duxYIFC+D1epGZmYlXXnkFEydORFVVFd+fpLrnn38eGzduxLp16477M15DSU3z5s3DU089hXHjxqGurg4/+clPcNZZZ2Hbtm26fG8y6CYiIt279dZbsW3btj71XkRaMG7cOFRVVcHtduNf//oXbrjhBnz88cdqD4sINTU1+Na3voV3330XDodD7eEQ9bF06VLl/6dOnYp58+ahsrIS//znP5GWlqbq2AaD6eUak5+fD7PZfFz3vYaGBhQXF6s2LqITEe9Jvl9JTbfddhtef/11fPjhhygvL1e+XlxcDL/fj/b29j6P5/uTkslms2H06NGYNWsW7rvvPkybNg2/+93v+P4k1W3YsAGNjY2YOXMmLBYLLBYLPv74Y/z+97+HxWJBUVER36OkGdnZ2Rg7diz27duny+sng26NsdlsmDVrFt5//33la+FwGO+//z4WLFig6tiIjjVixAgUFxf3eb96PB6sWbOG71dKOFmWcdttt+GVV17BBx98gBEjRvT581mzZsFqtfZ5f+7evRvV1dV8f5JqwuEwfD4f35+kuvPOOw9bt25FVVWV8mv27Nm49tprlf/ne5S0orOzE/v370dJSYkur59ML9egZcuW4YYbbsDs2bMxd+5cPPzww+jq6sJNN92k9tAoBXV2dmLfvn3K7w8ePIiqqirk5uZi2LBhuPPOO/Hzn/8cY8aMwYgRI3D33XejtLQUl112marjJuO79dZb8fe//x2vvfYanE6nUsflcrmQlpYGl8uFr371q1i2bBlyc3ORlZWF22+/HQsWLMD8+fPVHj6lgLvuugtLly7FsGHD0NHRgb///e/46KOP8Pbbb/P9SapzOp1KDwwhIyMDeXl5ytf5HiW1fPe738Ull1yCyspK1NbW4t5774XZbMY111yjy+sng24Nuuqqq9DU1IR77rkH9fX1mD59OpYvX35csyqiZFi/fj3OOecc5ffLli0DANxwww146qmn8P3vfx9dXV347//+b7S3t+PMM8/E8uXLWR9GCffoo48CABYtWtTn63/9619x4403AgAeeughmEwmXHnllfD5fFiyZAn++Mc/qjJeSj2NjY24/vrrUVdXB5fLhalTp+Ltt9/G+eefD/D9STrA9yip5ciRI7jmmmvQ0tKCgoICnHnmmfjss89QUFAA6PC9KcmRs3eJiIiIiIiIKM5Y001ERERERESUIAy6iYiIiIiIiBKEQTcRERERERFRgjDoJiIiIiIiIkoQBt1ERERERERECcKgm4iIiIiIiChBGHQTERERERERJQiDbiIiIiIiIqIEYdBNRERERERElCAMuomIiIiIiIgShEE3ERERERERUYIw6CYiIiIAQFNTE4qLi/HLX/5S+dqqVatgs9nw/vvvqzo2IiIivZJkWZbVHgQRERFpw5tvvonLLrsMq1atwrhx4zB9+nRceuml+O1vf6v20IiIiHSJQTcRERH1ceutt+K9997D7NmzsXXrVqxbtw52u13tYREREekSg24iIiLqo6enB5MnT0ZNTQ02bNiAKVOmqD0kIiIi3WJNNxEREfWxf/9+1NbWIhwO49ChQ2oPh4iISNe4001EREQKv9+PuXPnYvr06Rg3bhwefvhhbN26FYWFhWoPjYiISJcYdBMREZHie9/7Hv71r39h8+bNyMzMxNlnnw2Xy4XXX39d7aERERHpEtPLiYiICADw0Ucf4eGHH8azzz6LrKwsmEwmPPvss1ixYgUeffRRtYdHRESkS9zpJiIiIiIiIkoQ7nQTERERERERJQiDbiIiIiIiIqIEYdBNRERERERElCAMuomIiIiIiIgShEE3ERERERERUYIw6CYiIiIiIiJKEAbdRERERERERAnCoJuIiIiIiIgoQRh0ExERERERESUIg24iIiIiIiKiBGHQTURERERERJQgDLqJiIiIiIiIEoRBNxEREREREVGCMOgmIiIiIiIiShAG3UREREREREQJwqCbiIiIiIiIKEEsag9ADeFwGLW1tXA6nZAkSe3hEBERERERkc7IsoyOjg6UlpbCZDr5fnZKBt21tbWoqKhQexhERERERESkczU1NSgvLz/pn6dk0O10OoHoi5OVlaX2cIiIiIiIiEhnPB4PKioqlPjyZFQPuj/55BM88MAD2LBhA+rq6vDKK6/gsssuO+X3fPTRR1i2bBm2b9+OiooK/O///i9uvPHGfv9MkVKelZXFoJuIiIiIiIgG7XQly6o3Uuvq6sK0adPwyCOP9OvxBw8exMUXX4xzzjkHVVVVuPPOO3HzzTfj7bffTvhYiYiIiIiIiAZC9Z3upUuXYunSpf1+/GOPPYYRI0bgwQcfBABMmDABK1euxEMPPYQlS5YkcKREREREREREA6P6TvdArV69GosXL+7ztSVLlmD16tWqjYkokd7YUodP9jSpPQwiIiIiIhoE1Xe6B6q+vh5FRUV9vlZUVASPx4Oenh6kpaUd9z0+nw8+n0/5vcfjScpYiYaqudOH2/+xEQ6rGVt/vARmE4+4IyIiIiLSE93tdA/GfffdB5fLpfzicWGkF0fbehCWgW5/CC1dvn58BxERERERaYnugu7i4mI0NDT0+VpDQwOysrJOuMsNAHfddRfcbrfyq6amJkmjJRqaeo9X+f8GN4NuIiIiIiK90V16+YIFC/Dmm2/2+dq7776LBQsWnPR77HY77HZ7EkZHFF8NMUF3vceLKXCpOh4iIiIiIhoY1Xe6Ozs7UVVVhaqqKiB6JFhVVRWqq6uB6C719ddfrzz+61//Og4cOIDvf//72LVrF/74xz/in//8J7797W+r9ncgSpTYoDv2/4mIiIiISB9UD7rXr1+PGTNmYMaMGQCAZcuWYcaMGbjnnnsAAHV1dUoADgAjRozAG2+8gXfffRfTpk3Dgw8+iD//+c88LowMqT4mpZxBNxERERGR/qieXr5o0SLIsnzSP3/qqadO+D2bNm1K8MiI1NcnvdzNoJuIiIiISG9U3+kmopOrP6amm4iIiIiI+uf222/Hc889d9rHBYNBTJky5biG3fHCoJtIw2J3uhs97F5ORERERKlj+PDhSE9PR2ZmJkpLS3HHHXcgFAr163vr6urw5ptv4uqrrz7tYy0WC7761a/i/vvvj8Ooj8egm0ijuv1BdHiDyu+5001EREREqeadd95BZ2cnVqxYgZdeegl/+ctf+vV9zz77LC699FKYzeY+v8/IyEBJSQmuvfZa3HTTTfjhD3+IYDCIq6++Gs8++ywCgUDc/w4Muok0StRwW0wSAMDdE4A30L+VPSIiIiIiIxk1ahTOOOMM5dQrAKiursbFF1+MvLw8TJgwAcuXL1f+bPny5TjrrLMAADt27MD8+fPx2muvIScnBz/96U/x3HPP4YEHHsAzzzyDHTt2oLi4GDk5OVi/fn3cx86gm0ijGqLp5MNy05FmNUe/xt1uIiIiIoo/WZbR7Q8m5depGmmfzJ49e7BixQqMGjUKABAOh3HJJZdgyZIlaGhowJNPPonrrrtOqcveunUrxowZAwCYOHEixowZgz179qCurg6XXXYZACAnJwePPvoopkyZAgAYP348tmzZEsdXNUL17uVEdGIiwC7KciAsyzjU0o16txeVeRlqD42IiIiIDKYnEMLEe95Oys/a8dMlSLf1LxRdunQpZFlGV1cXrrjiCtx6660AgLVr16Knpwd33HEHAGDBggU4++yz8dZbb+HGG29Ee3s7MjMz+zzXG2+8gbS0NNx+++0AgB/96Ee45JJLlD93Op1wu91x/JtGMOgm0ihRw13sigm6udNNRERERCnkrbfewhlnnIF///vfuOOOO9DZ2QmHw4Hq6mocPHgQ2dnZymODwSBmzZoFAHC5XOjs7OzzXK+//jq++c1vnrRhWkdHB1wuV9z/Dgy6iTRK1HSLnW6wgzkRERERJUia1YwdP12StJ81EJIk4dJLL8W///1v/PznP8fDDz+MsrIyTJgw4aTp4FOmTMHevXsxefJkAIDH48GKFStw9913n/Tn7N69Gz/4wQ8G+Lc5PdZ0E2lUY4cIuu0oynIA7GBORERERAkiSRLSbZak/JIkaVBj/O53v4s///nPaG5uxrx58xAOh/Hoo4/C7/fD7/djxYoVqK6uBgBceOGFWLlypfK9b775JvLz85XmasdqaGhAS0sLZs+ePchX8OQYdBNplNjpLs5yMOgmIiIiopQ3YcIEnH322fjd734Hi8WCN954A2+//TbKyspQWlqKX/ziFwiHwwCA6667Dq+++ipCoRD27t2L+++/H08++aRyhNixnn/+eVx33XWw2WxxHzfTy4k0SnQvL3I5EI42eGxwM+gmIiIiotRw6NCh4772xhtvKP9fWVmJV1999YTfW1paiqVLl+KFF17Al770JWzcuPGkPycYDOLPf/4z3n333TiNvC8G3UQaFA7LSnp5cZZDOVahoYNBNxERERFRf/zhD3/o1+MsFgu2bt2asHEw6CbSoNZuPwIhGZIEFDjtCEW3uhs8PsiyPOg6GCIiIiIiSi7WdBNpkKjnzsuww2o2KTXd/mAYbd0BlUdHRERERET9xaCbSIOU1HKXHQBgs5iQlxFp6tDAZmpERERERLrBoJtIg+rd0SZqTofytUJ2MCciIiIi0h0G3UQaJALrIldv0F2cFdn1ZgdzIiIiIiL9YNBNpEENMWd0C8XRAFwcJUZERERERNrHoJtIg8TRYEXR3W0AKHQyvZyIiIiISG8YdBNpkOheXnTCnW4G3UREREREesGgm0iDRGBd3Kemm0E3EREREVF/3H777XjuuedO+7hgMIgpU6agoaEhYWNh0E2kMb5gSDmLO7amu4hBNxERERGlkOHDh2PlypUD/r66ujq8+eabuPrqq0/7WIvFgq9+9au4//77BznK02PQTaQxjdFGaTaLCa40q/J1Ud/d3OmHPxhWbXxERERERFr27LPP4tJLL4XZbO7z+4yMDJSUlODaa6/FTTfdhB/+8IcIBoO4+uqr8eyzzyIQCCRkPAy6iTRGNEorznJAkiTl67kZNtjMkY9sYwd3u4mIiIgodUiShEceeQTDhw9HdnY2Hn/8caxatQoTJ05ETk4OfvaznymPXb58Oc466ywAwI4dOzB//ny89tpryMnJwU9/+lM899xzeOCBB/DMM89gx44dKC4uRk5ODtavX5+QsVsS8qxENGj1JzguDNELTWGWHUfaetDg8aE8J12lERIRERGRYfm7Iv+1pgNiAyjoB8IBwGQBLPbjH2tJA0zR/dxQAAj5AckMWB3HP9aWMeihrVixAjt27MCaNWtw0UUX4aKLLsLKlSvR2NiIGTNm4Nprr8XIkSOxdetWjBkzBgAwceJEAMCePXtQV1eHyy67DACQk5ODRx99FFOmTAEAjB8/Hlu2bMGCBQsGPb6T4U43kcaImu3CmOPCBNZ1ExEREVFC/bI08qu7pfdrq34X+dqb3+372AdGR77urun92tonIl/79219H/vwlMjXh+D73/8+0tPTcc455yArKwvXXnstcnNzMX78eEydOhVbtmwBALS3tyMzM7PP977xxhtIS0vD7bffjquvvho7duzAJZdcomSWOp1OuN3uIY3vZLjTTaQxDZ4T73THfk3shhMRERERpYrCwkLl/9PS0o77fWdnJwDA5XIp/y+8/vrr+OY3v3nShmkdHR1wuVwJGTeDbiKNqY82Uos9LkxQdrpZ001EREREifDD2sh/rTGljAu/Bcz/ZiS9PNb39kX+a0nr/drcW4BZN0TSy2PduTVhQz7WlClTsHfvXkyePBkA4PF4sGLFCtx9990n/Z7du3fjBz/4QULGw/RyIo3pTS8/UdAdSTlv4E43ERERESWCLSPyK6ahLyy2yNcs9hM/1hQTVpqtka9ZHSd+bBJceOGFfY4ae/PNN5Gfn680VztWQ0MDWlpaMHv27ISMh0E3kcacMr08uvtdz5puIiIiIqITuu666/Dqq68iFAph7969uP/++/Hkk08qR4gd6/nnn8d1110Hm82WkPEwvZxIQ2RZPmn3csSkl4uzvImIiIiIjOrQoUPK/8uyfNI/A4CPPvpI+f/S0lIsXboUL7zwAr70pS9h48aNJ/0ZwWAQf/7zn/Huu+/GdeyxGHQTaYinJwhfMAycpHu50kjN44Usy33O8SYiIiIioog//OEP/XqcxWLB1q2JrTdnejmRhoi08ex0KxzW49NfxE53tz+EDl8w6eMjIiIiIqKBYdBNpCH1p6jnBoA0mxlZjkiCCpupERERERFpH4NuIg0RgXTRSYJuxDRTa2BdNxERERGR5jHoJtIQ0bm86AT13EJRFjuYExERERHpBYNuIg05XXo5YoLuBgbdRERERESax6CbSEOUnW7XKdLLGXQTEREREekGg24iDRF12kXOU+10R1LP69lIjYiIiIhI8xh0E2mIkl5+ip1uppcTEREREekHg24ijQiEwmjujO50s3s5EREREZEhMOgm0oimDh9kGbCYJORl2E76OFHT3dTpQygsJ3GEREREREQ0UAy6iTRCpIsXOu0wmaSTPi4v0w6zSUIoLCs740REREREpE0Muok0oj+dywHAbJJQkMlmakREREREesCgm0gjRAB9qjO6hSIXm6kREREREekBg24ijWjoOH0TNaHIGdnpZtBNRERERKRtDLqJNKIhutPdn6BbdDCvZ9BNRERERKRplsF8U3t7O1555RWsWLEChw8fRnd3NwoKCjBjxgwsWbIECxcujP9IiQyu94xu+2kf23tWNxupERERERFp2YB2umtra3HzzTejpKQEP//5z9HT04Pp06fjvPPOQ3l5OT788EOcf/75mDhxIl544YXEjZrIgJRGas5+pJdnsaabiIiIiEgPBrTTPWPGDNxwww3YsGEDJk6ceMLH9PT04NVXX8XDDz+MmpoafPe7343XWIkMTexan657OWKarbF7ORERERGRtg0o6N6xYwfy8vJO+Zi0tDRcc801uOaaa9DS0jLU8RGlhE5fEJ2+INDP7uUiBZ073URERERE2jag9PLYgNvj8Zz0cfv27Tvu8UR0cmLH2mm3IMN++rUwkV7u8QbR4w8lfHxERERERDQ4g+5efvHFF8PnO76J0+7du7Fo0aIBPdcjjzyC4cOHw+FwYN68eVi7du1JH/vUU09BkqQ+vxyO0+8MEmlZY3THujDr9E3UACDTbkG6zQywgzkRERERkaYNOujOzMzE5ZdfjmAwqHxt586dWLRoEa688sp+P88LL7yAZcuW4d5778XGjRsxbdo0LFmyBI2NjSf9nqysLNTV1Sm/Dh8+PNi/BpEm9HYu798CkiRJSho6U8yJiIiIiLRr0EH3yy+/DLfbjWuvvRayLGPbtm1YtGgRrrnmGvzud7/r9/P89re/xS233IKbbroJEydOxGOPPYb09HQ8+eSTJ/0eSZJQXFys/CoqKhrsX4NIE0TQ3Z8zugV2MCciIiIi0r5BB91paWl44403sHv3bnzxi1/Eeeedh+uvvx6//e1v+/0cfr8fGzZswOLFi3sHZDJh8eLFWL169Um/r7OzE5WVlaioqMCll16K7du3n/Ln+Hw+eDyePr+ItKRRdC4fUNAdSUVnB3MiIiIiIu0aUNB9bOBqMpnwwgsvYM2aNbjyyitx9913DyiobW5uRigUOm6nuqioCPX19Sf8nnHjxuHJJ5/Ea6+9hr/97W8Ih8NYuHAhjhw5ctKfc99998Hlcim/KioqBvLXJko4ETj3p3O5II4WY003EREREZF2DejIsOzsbEiSdNzXZVnGY489hscffxyyLEOSJIRCiemovGDBAixYsED5/cKFCzFhwgQ8/vjj+NnPfnbC77nrrruwbNky5fcej4eBN2nKYNLLRYAudsmJiIiIiEh7BhR0f/jhh3H94fn5+TCbzWhoaOjz9YaGBhQXF/frOaxWK2bMmKEcU3Yidrsddnv/ukITqaFBCbr7/z4VATp3uomIiIiItGtAQffZZ58d1x9us9kwa9YsvP/++7jssssAAOFwGO+//z5uu+22fj1HKBTC1q1bcdFFF8V1bETJEg7LaOyI7Fb3t3s5YoNu1nQTEREREWnWgGq6q6urB/TkR48ePe1jli1bhieeeAJPP/00du7ciW984xvo6urCTTfdBAC4/vrrcddddymP/+lPf4p33nkHBw4cwMaNG/HlL38Zhw8fxs033zygsRFpRXOXD6GwDJMEFGT2f6dbBOiNHV7IspzAERIRERER0WANKOieM2cOvva1r2HdunUnfYzb7cYTTzyByZMn46WXXjrtc1511VX4zW9+g3vuuQfTp09HVVUVli9frjRXq66uRl1dnfL4trY23HLLLZgwYQIuuugieDwerFq1ChMnThzIX4VIMxrckV3u/Ew7LOb+fyQLnZEAPRCS0drlT9j4iIiIiIho8CR5AFtkLS0t+MUvfoEnn3wSDocDs2bNQmlpKRwOB9ra2rBjxw5s374dM2fOxN13363ZlG+PxwOXywW3242srCy1h0Mp7r0dDbj5mfWYUubCf24/c0DfO/vn76K504837jgTk0pdCRsjERERERH11d+4ckA73Xl5efjtb3+Luro6/OEPf8CYMWPQ3NyMvXv3AgCuvfZabNiwAatXr9ZswE2kNYPpXC4UsYM5EREREZGmDaiRGgAcOHAAI0aMwBe+8AV84QtfSMyoiFKI6Fxe7Bp4h/3iLAe213rYwZyIiIiISKMGtNMNAGPGjEFTU5Py+6uuuuq4I7+IqP+U48KcA9/pLmQHcyIiIiIiTRtw0H1sCfibb76Jrq6ueI6JKKXUR1PDiwZwXJhQHA26G7jTTURERESkSQMOuokovhqiu9TFg6jpFinpDLqJiIiIiLRpwEG3JEmQJOm4rxHR4AylkZqSXs5GakREREREmjTgRmqyLOPGG2+E3R7ZYfN6vfj617+OjIyMPo97+eWX4zdKIoPyBkJw9wSAwe50M72ciIiIiEjTBhx033DDDX1+/+Uvfzme4yFKKSJYdlhNyEob8MdRCbpbu/zwBUOwW8xxHyMREREREQ3egGf5f/3rXxMzEqIUVB9Tzz2YMo3sdCtsFhP8wTAaPT5U5KYnYJRERERERDRYbKRGpKKGjkgtduEgUssR7adQlMVmakREREREWsWgm0hFQ+lcLvTWdbOZGhERERGR1jDoJlKR6FxePIgzuoUipYM5d7qJiIiIiLSGQTeRikSgXOi0D/o5itjBnIiIiIhIsxh0E6moMQ473SK9XDRlIyIiIiIi7WDQTaQiJb18CDXdRS7udBMRERERaRWDbiKVyLKsND8rGkrQ7WT3ciIiIiIirWLQTaSS9u4A/MEwAKAwa/A13SI1vd7jhSzLcRsfERERERENHYNuIpWI1PLcDBvsFvOgn0fsknsDYXi8wbiNj4iIiIiIho5BN5FKRNA9lNRyAHBYzchOtwJMMSciIiIi0hwG3UQqaVSC7sGnlgtFTnYwJyIiIiLSIgbdRCqpd0eaqA2lc7nADuZERERERNrEoJtIJfFKLweA4ix2MCciIiIi0iIG3UQqaYhj0C2eo55BNxERERGRpjDoJlKJCLqLXXGo6RZBdzRlnYiIiIiItIFBN5FK4rnTLerCGzu4001EREREpCUMuolU4A+G0dzpB+KdXs7u5UREREREmsKgm0gFTZ2RNHCrWUJuum3Iz1cUTVFv7vQhGAoP+fmIiIiIiCg+GHQTqUDsSBc6HTCZpCE/X36GHRaThLAMZQediIiIiIjUx6CbSAW9TdSGnloOACaThEJnZLebHcyJiIiIiLSDQTeRCnqbqA29c7lQyLpuIiIiIiLNYdBNpIL6OHYuF9jBnIiIiIhIexh0E6mgIbobXRzPoNvFnW4iIiIiIq1h0E2kgkTsdBdmsaabiIiIiEhrGHQTqaDREzkyLCHp5dHnJiIiIiIi9THoJkoyWZaV3eh4dS9HTNDNnW4iIiIiIu1g0E2UZB2+ILr9ISBB3csbWNNNRERERKQZDLqJkqwxuhPtdFiQbrPE7XnFrnmHL4guXzBuz0tERERERIPHoJsoyerdkZrreHYuB4BMuwWZ9kgQ38AUcyIiIiIiTWDQTZRkiajnForYwZyIiIiISFMYdBMlmdiFLnQmIuh29PkZRERERESkLgbdREnWoOx0x6+JmlCsBN08NoyIiIiISAsYdBMlWX20u3i8a7oBoCiasl7PDuZERERERJrAoJsoyZT08kQE3U57n59BRERERETqYtBNlGQi9TsRO92iORuDbiIiIiIibWDQTZREobCMps5o0J2Q7uWs6SYiIiIi0hIG3URJ1NzpQygswyQBeRm2uD9/bPfycFiO+/MTEREREdHAMOgmSiKR9l3gtMNijv/Hr8BphyQBwbCMli5/3J+fiIiIiIgGhkE3URIlsnM5AFjNJuRnspkaEREREZFWMOgmSiIRCBclKOhGn7O6GXQTEREREamNQTdREtUnIeguyrL3+VlERERERKQeBt1ESaQcF5aAzuUCO5gTEREREWmHJoLuRx55BMOHD4fD4cC8efOwdu3aUz7+xRdfxPjx4+FwODBlyhS8+eabSRsr0VAkNb3czZ1uIiIiIiK1qR50v/DCC1i2bBnuvfdebNy4EdOmTcOSJUvQ2Nh4wsevWrUK11xzDb761a9i06ZNuOyyy3DZZZdh27ZtSR870UCJRmoiBTwRREDP9HIiIiIiIvWpHnT/9re/xS233IKbbroJEydOxGOPPYb09HQ8+eSTJ3z87373O1x44YX43ve+hwkTJuBnP/sZZs6ciT/84Q9JHzvRQImd7kR1LweAIhcbqRERERERaYVFzR/u9/uxYcMG3HXXXcrXTCYTFi9ejNWrV5/we1avXo1ly5b1+dqSJUvw6quvJny8ybR6fws2VrfBEuoBAARNDkCSAACmcAAmOYiwZEbYZFO+p/exdkAy9XmsLJkQMtmH9NiQyQZZMgMAJDkIczgAGRJCZsegHmsOeSFBRshkhSxZoo8NwRz2D+ixABA0p/U+NuyDJIcRliwIm6wDfizkMCxh33GPNYX9MMmhQT9WDocR8HYi7did7qAfCAcAkxWwRP89ZRkIdEf+35qu/Nv3PtYCWGKew98V/QdIUwL6+lYPHn9va1zeJ7H/nvF4n/T+ew7tfXLcv+cQ3ycn+/cc+vtEhiXsHfhjB/S55zVC79eI0//bx+N9cvy/J68RvEYM5d+e1wheIwb6b89rBK8R/f23lyULLppSghH5GdA7VYPu5uZmhEIhFBUV9fl6UVERdu3adcLvqa+vP+Hj6+vrT/pzfD4ffL7eplIej2fIY0+0T/Y24dGP9uOQ40sAgJnex9CKLADAreZX8T3rP/GP4Dm4K3iL8j077DchXfLhTN/vcEQuAAB8xfwW7rE+i1dDC3Fn4DblsRvsX0Oe1IHzffdjr1wOALja/AF+Zf0z3gnNwn8HvqM8dqX9DpRLzfh/vp9hizwKAHCpaSV+Z/sjVoQm47rAD5XHvmP7HsaajuJq///is/BEAMAFpnX4k+0hrA+PxRf8P1Ye+5rtfzHNdAA3+b+HD8MzAABnmrbib7b7sCNciYv89ymPfd72M8w37cQ3/XfgzfB8AMAsaTdesv8EB8NFOMf/kPLYJ63341xzFb4b+Br+FTobADBROoQ37T9EvZyD+b5HlMc+Yn0YF5vX4u7AjXg2dAEAYLhUh4/s34FHTsdU35+Vx/7G+hi+YP4Evwxcgz+FLgEAFKEVaxy3ISCbMcb3rPLYn1r+iust7+Lh4BV4OPgFAEAWurDTEfn3kq1Nvf/YH/wUWPV/wMLbgQt+HvlaOAj8sjTy/z84DKRlR/5/xYPAx78C5twMXPxg73P8aljke5btRLGrACYJ+GLodXxt5T/wr9Dn8N3A15WHbrHfjCypG4t8D+KQXAIAuM78Dn5mfQpvhObi1sCdymM/s9+KYqkNF/l+iR3ycADAF8wf4zfWx/FBaDq+Evi+8tgPbd/GCFMDrvTdiw3yOADARabP8Efb7/FZeAKu9t+tPPZN212YaDqML/vvwsrwFADAOaZN+KvtAWwOj8Sl/p8rj/2X7ceYbdqD//Z/G++E5wAA5pt24Hnbz7EnXIYL/A8oj33W+kucZd6Gb/m/idfCZwIApkr78W/73Tgi5+NM3++Vx/7J+iAuMG/A/wRuxvOhcwEAY6QjeNf+fbTITszyPa489mHrH3CZeRV+GrgOT4aWAgDKpSastH8L3bIdE31/VR57n+UJXGP5EA8EvohHQpcBAHLhwUZH5N9guPfvymPvsTyDr1iW4w/BS/Gb4FUAgDR4sdPxFQDABO+T6EFk4vBdywv4huU1PBm8ED8NXq88B68REUa5RmyJXiNGe59BMHqLvsvyHL5meQOPBy/Gr4PXAgAsCGKfI/I+mOp9Ah5EJiR3Wv6FOy0v45ng+bgneJPy8/bar4NVCmGe9w9oQC4A4L/N/8EPrbxG8BrBawSvEbxGCLxGaOsa8Vr4TIwtcjLo1ov77rsPP/nJT9QexoBMLXPhqtkVQLRU/bLppeiy5AAApjS6gEZgVEEGriqrUL7Hsl0CZODzU0rQZotcBGc0ZwP1QGVuBq6q6H2sfacJCAFLJxVjpiPy9TmtOUAtUJadhqsqex+bvtsCBIDzJxRhQnrk69Pb84AjkTTpq0b0Pta11wr4gHPGFqIyM/L1iZ6DQDWQn2nDVSN7H5u73wb0AJ8bk49CZ+TrYzrrgUNAdroVV03tfWzBATvQDSwclQ+nK/L1yq424CDgdPR9bMkhB9AJzB2ei//P3n3HSVXe+wP/TJ8ts43ty9J7WxYQBAtKQDREJXoj18o1MSbR/G6Um6IpEkuiSYwxN5fEqImaolhiixqiIoI0Edil94UtbO+zber5/THznJ1F2szOmXPOzOf9evF6yTo7++xwZs7zfZ7v9/uYMgNfL+jtA44BSRYTlk3tf2xxVTLQCcwclgn3kMDXh7gAHAEsJmPg3yBoRE0y0A6UDM3AspzA19M8duAQYDRgwGPH1KYCrcDkgnQsywt83e5zAgcC/98gdq4VkJ5kwS//owRJ2z4BGoARQ5KxbGj/2Cz7jYAf+OKUArTYAl+f2ZIJ1AHFmclYNqz/sUkHTYAXuGJSPqYmBR/blgWcBArS7Vg2ov+xjsMWwA18YUIuxqQEvj614yhQDeSk2gb822cctQB9wGXjclAUvE4mOKuBSiArxTrg3zO7wgr0ABeNyUZmWuDro7qagROB3zX0sfnH7UA3cOGoIbBnBL4+tKcLqACSreYB//ZFlUmAE7hgeCakrMDX8/q8wFHAZjYOeOzw6hSgAygtzsCy7MDXM91m4DBgNhoG/NuPPpkCtAFTi9KxLDfw9RRvGxBcRwx97Lg6B9ACTCpIk68Ti78X2B/4/9fPGAqPMbCiPakhDWgCxuU5sKyg/zn4GREQb58RX5lZDH9wl2VCvQNoBibkO7AsP/BYo+QF9gUe++XSIvSZHACAyQ3pQBMwJjcVywr7f54xeJ1cU1KITktgolTSlMHPCH5G8DOCnxGBx/MzAuBnhOY+I+wZxSjMUK4kM5YMkiRJav1wt9uN5ORkvPbaa1i6dKn89eXLl6O9vR1vvfXW575n2LBhWLFiBe65p38VbeXKlXjzzTexa9eu0/6c0+10FxcXo6OjA2lpaVH/vaJKpA2HmWIMY7Bc3+cBfG7AYAIs9ggf2wNAAsx2wGgKPtYL+FyBdBFLUmSP9fQCkh8w2QBTcP3H7wO8feE9FgbAmhzy2D5A8gEmK2CyRPBYP+ANpLnAGrKy5nUFdpND08DDeew5U8ajk14u/3tG5To53b9nFK4T8e852Ovkc/+eg71OzvDvOdjrJPTfc9DXyRn+PfkZwc+IcP/t+RkRvX97fkac47H8jDjjvyc/Iwb3b8/PiPj+jDBpf3+4s7MT6enp54wrVQ26AWDOnDmYPXs2fve73wEA/H4/hg0bhm9/+9u47777Pvf4ZcuWoaenB//85z/lr82bNw/Tpk3DU089dV4/83xfHCIiIiIiIqLTOd+4UvXlgxUrVmD58uWYNWsWZs+ejSeffBLd3d24/fZAncltt92GoqIiPPpooC7nO9/5DubPn49f//rXWLJkCVavXo3t27fj6aefVvk3ISIiIiIiIhpI9aB72bJlaGpqwgMPPID6+npMnz4da9askZulVVVVwWjsP9ls3rx5ePHFF/HjH/8YP/zhDzF27Fi8+eabmDJlioq/BREREREREdHnqZ5eroaOjg5kZGSgurqa6eVEREREREQUNtErrL29Henp6Wd8nOo73WpwOp0AgOKQDntERERERERE4XI6nWcNuhNyp9vv96O2thYOh0PRo5sGS6yccEc+sfE6IPA6oBC8Fgi8DigErwUCrwPVSJIEp9OJwsLCASXRp0rInW6j0YihQ4eqPYzzlpaWxjcP8ToggNcBheC1QOB1QCF4LRB4HajibDvcwpnDcSIiIiIiIiIaFAbdRERERERERAph0K1hNpsNK1euhM1mU3sopCJeBwReBxSC1wKB1wGF4LVA4HWgeQnZSI2IiIiIiIgoFrjTTURERERERKQQBt1ERERERERECmHQTURERERERKQQBt1ERERERERECmHQraJVq1ZhxIgRsNvtmDNnDrZt23bWx7/66quYMGEC7HY7pk6divfeey9mYyVlhXMtPPPMM7jkkkuQmZmJzMxMLFy48JzXDulDuJ8JwurVq2EwGLB06VLFx0ixEe610N7ejrvvvhsFBQWw2WwYN24c7xFxINzr4Mknn8T48eORlJSE4uJi3Hvvvejr64vZeCn6NmzYgKuvvhqFhYUwGAx48803z/k9H3/8MWbMmAGbzYYxY8bg+eefj8lYSVnhXguvv/46Fi1ahJycHKSlpWHu3Ln497//HbPx0kAMulXy8ssvY8WKFVi5ciV27tyJkpISLF68GI2Njad9/ObNm3HjjTfia1/7GsrKyrB06VIsXboUe/fujfnYKbrCvRY+/vhj3HjjjVi3bh22bNmC4uJiXHHFFTh58mTMx07RE+51IJw4cQLf/e53cckll8RsrKSscK8Ft9uNRYsW4cSJE3jttddw6NAhPPPMMygqKor52Cl6wr0OXnzxRdx3331YuXIlDhw4gD/96U94+eWX8cMf/jDmY6fo6e7uRklJCVatWnVejz9+/DiWLFmCyy+/HOXl5bjnnntwxx13MNiKA+FeCxs2bMCiRYvw3nvvYceOHbj88stx9dVXo6ysTPGx0mlIpIrZs2dLd999t/x3n88nFRYWSo8++uhpH3/DDTdIS5YsGfC1OXPmSN/4xjcUHyspK9xr4VRer1dyOBzSCy+8oOAoSWmRXAder1eaN2+e9Oyzz0rLly+Xrr322hiNlpQU7rXwhz/8QRo1apTkdrtjOEpSWrjXwd133y0tWLBgwNdWrFghXXTRRYqPlWIDgPTGG2+c9THf//73pcmTJw/42rJly6TFixcrPDqKpfO5Fk5n0qRJ0oMPPqjImOjsuNOtArfbjR07dmDhwoXy14xGIxYuXIgtW7ac9nu2bNky4PEAsHjx4jM+nvQhkmvhVD09PfB4PMjKylJwpKSkSK+Dhx56CLm5ufja174Wo5GS0iK5Ft5++23MnTsXd999N/Ly8jBlyhT8/Oc/h8/ni+HIKZoiuQ7mzZuHHTt2yCnoFRUVeO+99/DFL34xZuMm9XG+SGfi9/vhdDo5X1SJWe0BJKLm5mb4fD7k5eUN+HpeXh4OHjx42u+pr68/7ePr6+sVHSspK5Jr4VQ/+MEPUFhY+LmbLOlHJNfBxo0b8ac//Qnl5eUxGiXFQiTXQkVFBT766CPcfPPNeO+993D06FHcdddd8Hg8WLlyZYxGTtEUyXVw0003obm5GRdffDEkSYLX68U3v/lNppcnmDPNFzs7O9Hb24ukpCTVxkbqevzxx9HV1YUbbrhB7aEkJO50E+nYY489htWrV+ONN96A3W5XezgUI06nE7feeiueeeYZZGdnqz0cUpnf70dubi6efvppzJw5E8uWLcOPfvQjPPXUU2oPjWLo448/xs9//nP8/ve/x86dO/H666/j3XffxcMPP6z20IhIZS+++CIefPBBvPLKK8jNzVV7OAmJO90qyM7OhslkQkNDw4CvNzQ0ID8//7Tfk5+fH9bjSR8iuRaExx9/HI899hg+/PBDTJs2TeGRkpLCvQ6OHTuGEydO4Oqrr5a/5vf7AQBmsxmHDh3C6NGjYzByirZIPhMKCgpgsVhgMpnkr02cOBH19fVwu92wWq2Kj5uiK5Lr4Cc/+QluvfVW3HHHHQCAqVOnoru7G3feeSd+9KMfwWjkPksiONN8MS0tjbvcCWr16tW444478OqrrzIrUkX8BFaB1WrFzJkzsXbtWvlrfr8fa9euxdy5c0/7PXPnzh3weAD44IMPzvh40odIrgUA+OUvf4mHH34Ya9aswaxZs2I0WlJKuNfBhAkTsGfPHpSXl8t/rrnmGrlbbXFxcYx/A4qWSD4TLrroIhw9elReeAGAw4cPo6CggAG3TkVyHfT09HwusBYLMYG+S5QIOF+kUC+99BJuv/12vPTSS1iyZInaw0lsandyS1SrV6+WbDab9Pzzz0v79++X7rzzTikjI0Oqr6+XJEmSbr31Vum+++6TH79p0ybJbDZLjz/+uHTgwAFp5cqVksVikfbs2aPib0HREO618Nhjj0lWq1V67bXXpLq6OvmP0+lU8begwQr3OjgVu5fHj3CvhaqqKsnhcEjf/va3pUOHDknvvPOOlJubKz3yyCMq/hY0WOFeBytXrpQcDof00ksvSRUVFdL7778vjR49WrrhhhtU/C1osJxOp1RWViaVlZVJAKQnnnhCKisrkyorKyVJkqT77rtPuvXWW+XHV1RUSMnJydL3vvc96cCBA9KqVaskk8kkrVmzRsXfgqIh3Gvh73//u2Q2m6VVq1YNmC+2t7er+FskLgbdKvrd734nDRs2TLJardLs2bOlrVu3yv9v/vz50vLlywc8/pVXXpHGjRsnWa1WafLkydK7776rwqhJCeFcC8OHD5cAfO7PypUrVRo9RUu4nwmhGHTHl3Cvhc2bN0tz5syRbDabNGrUKOlnP/uZ5PV6VRg5RVM414HH45F++tOfSqNHj5bsdrtUXFws3XXXXVJbW5tKo6doWLdu3Wnv+eLffvny5dL8+fM/9z3Tp0+XrFarNGrUKOm5555TafQUTeFeC/Pnzz/r4ym2DBJzjoiIiIiIiIgUwZpuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIkpwX/ziF7F8+XL57+vWrUN2djZ8Pp+q4yIiIooHDLqJiIgSXFFREU6ePCn/ff78+ejt7cXWrVtVHRcREVE8YNBNRESU4IqKilBTUyP/3Wg0IikpCY2NjXjrrbdwzz33qDo+IiIiPWPQTURElOBO3ekuLy9He3s75s6di927d6OkpETV8REREekZg24iIqIEV1RUhK6uLnR2dsLv9+Pee+/FzTffjPz8fDno7uzsxLXXXounn35a7eESERHpilntARAREZG6ioqKAAA1NTV47rnnUF9fj7feegsAcODAASQlJeGqq67CT3/6UyxatEjl0RIREemLQZIkSe1BEBERkXqam5uRk5ODK6+8EocPH8aGDRtQVFSE3t5eFBYWYsSIEfjb3/6GyZMnqz1UIiIi3WF6ORERUYLLzs6GzWZDZWUl1q9fL+987927F3PnzoXf74fZzOQ4IiKiSPAOSkREROjr6/vc13bv3o1LLrkEixcvxk033YT169cjNTVVlfERERHpFXe6iYiI6LR2796NKVOmYMaMGbjrrrvw1a9+Ve0hERER6Q5ruomIiIiIiIgUwp1uIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSCINuIiIiIiIiIoUw6CYiIiIiIiJSiFntAajB7/ejtrYWDocDBoNB7eEQERERERGRzkiSBKfTicLCQhiNZ97PTsigu7a2FsXFxWoPg4iIiIiIiHSuuroaQ4cOPeP/Vz3o3rBhA371q19hx44dqKurwxtvvIGlS5ee9Xs+/vhjrFixAvv27UNxcTF+/OMf47/+67/O+2c6HA4g+OKkpaUN+ncgIiIiIiKixNLZ2Yni4mI5vjwT1YPu7u5ulJSU4Ktf/Squu+66cz7++PHjWLJkCb75zW/i73//O9auXYs77rgDBQUFWLx48Xn9TJFSnpaWxqCbiIiIiIiIInaukmXVg+6rrroKV1111Xk//qmnnsLIkSPx61//GgAwceJEbNy4Eb/5zW/OO+gmIiIiIiIiigXddS/fsmULFi5cOOBrixcvxpYtW1QbE5GSqlt70OjsU3sYREREREQUAdV3usNVX1+PvLy8AV/Ly8tDZ2cnent7kZSU9LnvcblccLlc8t87OztjMlaiwepyeXHlkxuQkWzFxh9czm77REREREQ6o7ud7kg8+uijSE9Pl/+wcznpRVVLD7rdPpxs70VHr0ft4RARERERUZh0F3Tn5+ejoaFhwNcaGhqQlpZ22l1uALj//vvR0dEh/6muro7RaIkGpyEkrbyh03XWxxIRERERkfboLr187ty5eO+99wZ87YMPPsDcuXPP+D02mw02my0GoyOKroaO/qC7vrMP4/PPfhwBERERERFpi+o73V1dXSgvL0d5eTkQPBKsvLwcVVVVQHCX+rbbbpMf/81vfhMVFRX4/ve/j4MHD+L3v/89XnnlFdx7772q/Q5ESqnvDNnp7mAzNSIiIiIivVE96N6+fTtKS0tRWloKAFixYgVKS0vxwAMPAADq6urkABwARo4ciXfffRcffPABSkpK8Otf/xrPPvssjwujuNQQGnR3MugmIiIiItIb1dPLL7vsMkiSdMb///zzz5/2e8rKyhQeGZH6Quu46xl0ExERERHpjuo73UR0ZvUd3OkmIiIiItIzBt1EGhYaaHOnm4iIiIhIfxh0E2mU2+tHS7db/juPDCMiIiIi0h8G3UQa1egcuLPd3OWCx+dXbTxERERERBQ+Bt1EGiVSy4sykmAxGSBJQJOTu91ERERERHrCoJtIo0Q6eUG6HbkOe/BrrOsmIiIiItITBt1EGiU6l+el2ZGbZgMYdBMRERER6Y7q53QT0emJADsvzQ5/8Cz70CPEiIiIiIhI+xh0E2mUOCIsP90mB90NrOkmIiIiItIVBt1EGhW60y2aljdwp5uIiIiISFcYdBNplGikNiC9nDXdRERERES6wqCbSIMkSZLrt/MZdBMRERER6RaDbiINcrq86PX4gFN2uhs7WdNNRERERKQnPDKMSINE7Xaa3Ywkqwl5aYFzurtcXnS5vCqPjoiIiIiIzheDbiIN6u9cHgi2U2xmOGyBxBQeG0ZEREREpB8Muok0SATWYocbAPKCAXgj67qJiIiIiHSDQTeRBjU6+zuXC3lpNoDN1IiIiIiIdIVBN5EGhXYuF0QAzqCbiIiIiEg/GHQTaZAIrEVKOUICcHYwJyIiIiLSDwbdRBok6rbzHDb5a/JONxupERERERHpBoNuIg06tXs5mF5ORERERKRLDLqJNMbr86Mp2EgttKZbBOANDLqJiIiIiHSDQTeRxrR0u+GXAJPRgCGp/enlck230wW/X1JxhEREREREdL4YdBNpjKjZzkm1wWQ0yF/PTrXCaAB8fgnN3WymRkRERESkBwy6iTTmdJ3LAcBsMiI7uPPd0MGgm4iIiIhIDxh0E2mMqNnOT7N97v+xrpuIiIiISF8YdBNpjAio89Lsn/t/uQ52MCciIiIi0hMG3UQaUx9MHT9d0J2fHkwvZ9BNRERERKQLDLqJNKY/vfw0QXca08uJiIiIiPSEQTeRxpw1vTxNpJezkRoRERERkR4w6CbSGFGvLVLJQ8k73R3c6SYiIiIi0gMG3UQa0uP2wtnnBc5Y0x0Mup0MuomIiIiI9IBBN5GGNATTxlOsJjjsls/9fxGIt/d40OfxxXx8REREREQUHgbdRBpS33Hmem4ASLObYbcE3rZspkZEREREpH0Muok05GxN1ADAYDDIdd31rOsmIiIiItI8Bt1EGtLfRO30QTdCAvIGJzuYExERERFpHYNuIg0RO925aZ/vXC7ksYM5EREREZFuMOgm0hARdOefIb0cIbvg9azpJiIiIiLSPAbdRBoi6rTPFnTLO90MuomIiIiINI9BN5GGiCPDcs8adNuCj2XQTURERESkdQy6iTTC75fQ6Dx3IzW5ezmDbiIiIiIizWPQTaQRrT1ueHwSDAYg13EejdQ6XZAkKYYjJCIiIiKicJnDefBDDz0U0Q+57LLLcOmll0b0vUSJQtRzD0mxwWI683qY6Gzu9vrR3uNBZoo1ZmMkIiIiIqLwhBV0Hz9+PKIfMn369Ii+jyiRiNTyvLMcFwYANrMJWSlWtHa7Ud/Zx6CbiIiIiEjDwgq6n3vuOeVGQpTg6jsCTdTO1rlcyEuzy0H3xIK0GIyOiIiIiIgiwZpuIo0QjdHyztJETcgP7oY3spkaEREREZGmhbXTHcrlcuHTTz9FZWUlenp6kJOTg9LSUowcOTK6IyRKECKAznOc3043QnbHiYiIiIhIm8IOujdt2oTf/va3+Oc//wmPx4P09HQkJSWhtbUVLpcLo0aNwp133olvfvObcDgcyoyaKA6Jne789LPXdCM06OZONxERERGRpoWVXn7NNddg2bJlGDFiBN5//304nU60tLSgpqYGPT09OHLkCH784x9j7dq1GDduHD744APlRk4UZ0T38rzzqOkW53gzvZyIiIiISNvC2ulesmQJ/vGPf8BisZz2/48aNQqjRo3C8uXLsX//ftTV1UVrnERxr9EZSBU/n6BbdDjnTjcRERERkbaFFXR/4xvfOK/HSZKESZMmYdKkSZGOiyihuLw+tHa7gTC6lwNAA4NuIiIiIiJNi7h7+a9+9avTft3n8+Gmm24azJiIEk5jZ2CX22o2IiP59JkkoURg3tzlhsfnV3x8REREREQUmUEF3X/6058GfM3n8+E///M/UV5eHtZzrVq1CiNGjIDdbsecOXOwbdu2Mz72+eefh8FgGPDHbj/3ziCRlslN1NLsMBgM53x8VooVFlPgcSItnYiIiIiItCfioPvdd9/Fd7/7Xbz22msAAK/Xi6985SvYt28f1q1bd97P8/LLL2PFihVYuXIldu7ciZKSEixevBiNjY1n/J60tDTU1dXJfyorKyP9NYg0QaSJi1rtczEYDMh1iGPDmGJORERERKRVEQfdF1xwAf7xj3/gq1/9Kt5++21cf/31OHToENatW4f8/Pzzfp4nnngCX//613H77bdj0qRJeOqpp5CcnIw///nPZ/weg8GA/Px8+U9eXl6kvwaRJoTTuVwQHcxZ101EREREpF0RB90AsGDBAvzlL3/B9ddfj+PHj2P9+vVhBcButxs7duzAwoUL+wdkNGLhwoXYsmXLGb+vq6sLw4cPR3FxMa699lrs27fvrD/H5XKhs7NzwB8iLWkISS8/X/lspkZEREREpHlhdS+/7rrrTvv1nJwcZGRk4M4775S/9vrrr5/z+Zqbm+Hz+T4XqOfl5eHgwYOn/Z7x48fjz3/+M6ZNm4aOjg48/vjjmDdvHvbt24ehQ4ee9nseffRRPPjgg+ccD5FaGjrP/7gwIZfHhhERERERaV5YQXd6evppv7548eJojeec5s6di7lz58p/nzdvHiZOnIg//vGPePjhh0/7Pffffz9WrFgh/72zsxPFxcUxGS/R+RCBc156BDvdrOkmIiIiItKssILu5557Lqo/PDs7GyaTCQ0NDQO+3tDQcN514RaLBaWlpTh69OgZH2Oz2WCznV+DKiI1RJReLtd0s3s5EREREZFWDaqme7CsVitmzpyJtWvXyl/z+/1Yu3btgN3ss/H5fNizZw8KCgoUHCmRciRJCmmkdv6LQ6J7OWu6iYiIiIi0K6yg+8orr8TWrVvP+Tin04lf/OIXWLVq1Tkfu2LFCjzzzDN44YUXcODAAXzrW99Cd3c3br/9dgDAbbfdhvvvv19+/EMPPYT3338fFRUV2LlzJ2655RZUVlbijjvuCOdXIdKMzl4vXF4/EGH38vrOPkiSpNj4iIiIiIgocmGll3/lK1/B9ddfj/T0dFx99dWYNWsWCgsLYbfb0dbWhv3792Pjxo147733sGTJEvzqV78653MuW7YMTU1NeOCBB1BfX4/p06djzZo1cnO1qqoqGI39awNtbW34+te/jvr6emRmZmLmzJnYvHkzJk2aFMnvT6Q6Uc+dkWyB3WI67+8Tqeg9bh+6XF447BbFxkhERERERJExSGFukblcLrz66qt4+eWXsXHjRnR0dASeyGDApEmTsHjxYnzta1/DxIkTlRrzoHV2diI9PR0dHR1IS0tTeziU4NYfbsLyP2/DhHwH1txzaVjfO+2n/0ZnnxcfrrgUY3Idio2RiIiIiIgGOt+4MqydbgSbkt1yyy245ZZbAAAdHR3o7e3FkCFDYLFwp40oXKImOzeM1HIhL82Ozr4u1He4GHQTEREREWnQoBuppaenIz8/nwE3UYTEkV/5YTRRE/o7mLOZGhERERGRFoUddF966aVob2+X//7222+jt7c32uMiShj1ERwXJojGa/UMuomIiIiINCnsoHvjxo1wu93y32+55RbU1dVFe1xECUOcsx1Zerkt+BwMuomIiIiItGjQ6eU8qohocBoGsdMtvkec801ERERERNoy6KCbiAZHTi9Pjzy9vMHpivq4iIiIiIho8MLuXg4A//73v5Geng4A8Pv9WLt2Lfbu3TvgMddcc010RkgUxzw+P5q7RHp5+I3U5KCbO91ERERERJoUUdC9fPnyAX//xje+MeDvBoMBPp9vcCMjSgDNXS5IEmA2GpCdEnn38qYuF3x+CSajQYFREhERERFRpMIOuv1+vzIjIUpAohY712GDMYKAOTvVBpPRAJ9fQkuXK6JmbEREREREpBzWdBOpSDRRy4ugnhsATEYDclIDO+Q8NoyIiIiISHvC2ukeOXIkDIbwd+Puuece/Pd//3fY30cU78RxYXmOyHeo89JsqO/sQ31HH6YNjeLgiIiIiIho0MIKup9//vmIfsiIESMi+j6ieDeYzuVCoJlaBzuYExERERFpUFhB9/z585UbCVECEl3H8wZRiy0CdnYwJyIiIiLSHtZ0E6lI7HTnRXBcmCACdtZ0ExERERFpD4NuIhWJRmr5g9jpls/qZtBNRERERKQ5DLqJVCQ3UhtETXc+g24iIiIiIs1i0E2kki6XF10uLzDImm6Rml7Pmm4iIiIiIs1h0E2kErEznWozI9UWVk/DAcQueWefF71uX9TGR0REREREg8egm0gl/Z3LI2+iBgAOmxnJVlPgOZliTkRERESkKQy6iVQSjTO6AcBgMMh13exgTkRERESkLQy6iVQiN1FzDC7oBoDc4G45d7qJiIiIiLSFQTeRSkSAPJjO5QI7mBMRERERaRODbiKViG7jgzmjWxCBe32Ha9DPRURERERE0cOgm0glov56sI3UEJKizp1uIiIiIiJtYdBNpJJGOeiOQnp5OhupERERERFpEYNuIhX4/RIanYFU8MF2L0dI4M6dbiIiIiIibWHQTaSC5m4XvH4JBgOQnRqF9PJginpjpwuSJEVhhEREREREFA0MuolU0Bg8Liw71QaLafBvw9xgTbfb50drt3vQz0dERERERNHBoJtIBdHsXA4AVrMR2alWIOT8byIiIiIiUh+DbiIV1EexiZrAum4iIiIiIu1h0E2kgoYoHhcmiKCbHcyJiIiIiLSDQTeRCkTQHa30cnCnm4iIiIhIkxh0E6mgPlh3nReF48KEfAbdRERERESaw6CbSAUNHUrUdAdS1UWTNiIiIiIiUh+DbiIVNDgVSC9PFzXd7F5ORERERKQVDLqJYqzP40N7jweIctAtnquR6eVERERERJrBoJsoxkTNtc1sRFqSOWrPK1LVW7rdcHl9UXteIiIiIiKKHINuohhrCKZ/56fbYTAYova8mckWWM2Bt3QjU8yJiIiIiDSBQTdRjNV3Rr+JGgAYDAa5mVqjkynmRERERERawKCbKMZE5/Jo1nML4jnrO7jTTURERESkBQy6iWKsf6fbFvXnzhVBN5upERERERFpAoNuohhrUCi9HOxgTkRERESkOQy6iWJMBN356QqmlzPoJiIiIiLSBAbdRDGmVCM1AMgNpqzXdzDoJiIiIiLSAgbdRDEkSVL/kWFKppc72UiNiIiIiEgLGHQTxVB7jwdurx8I2ZWOJpGyXt/RB0mSov78REREREQUHgbdRDEkUsszky2wmU1Rf36Rst7r8aGzzxv15yciIiIiovAw6CaKISXruQHAbjEhPckChDRsIyIiIiIi9TDoJoqhRgU7lwuirptBNxERERGR+hh0E8VQfYdyTdSEvJC6biIiIiIiUheDbqIYEunluUoG3Y5AgzbudBMRERERqU8TQfeqVaswYsQI2O12zJkzB9u2bTvr41999VVMmDABdrsdU6dOxXvvvRezsRINhpxermDQLVLXxdFkRERERESkHtWD7pdffhkrVqzAypUrsXPnTpSUlGDx4sVobGw87eM3b96MG2+8EV/72tdQVlaGpUuXYunSpdi7d2/Mx04Urnq5pjv6x4UJoklbPXe6iYiIiIhUp3rQ/cQTT+DrX/86br/9dkyaNAlPPfUUkpOT8ec///m0j//tb3+LK6+8Et/73vcwceJEPPzww5gxYwb+7//+L+ZjJwqXSPnOdSiYXs5GakREREREmmFW84e73W7s2LED999/v/w1o9GIhQsXYsuWLaf9ni1btmDFihUDvrZ48WK8+eabio83lmraepgeHGckSUJzlxuIUffyk2292FHZptjPISIiIiJS0uicFGQkW9UexqCpGnQ3NzfD5/MhLy9vwNfz8vJw8ODB035PfX39aR9fX19/xp/jcrngcvUHsJ2dnYMeu9L+/mkV/vDxMbWHQQqwmAzIUvDDIy+Yut7S7cb1f9is2M8hIiIiIlLSM7fNwqJJeefxSG1TNeiOlUcffRQPPvig2sMIS0aSBcOHJKs9DFLA1dMKYTQaFHv+nFQbls0qxtbjLYr9DCIiIiIipSVZTGoPISpUDbqzs7NhMpnQ0NAw4OsNDQ3Iz88/7ffk5+eH9XgAuP/++wekpHd2dqK4uHjQ41fSN+aPxjfmj1Z7GKRDBoMBv/iPaWoPg4iIiIiI1G6kZrVaMXPmTKxdu1b+mt/vx9q1azF37tzTfs/cuXMHPB4APvjggzM+HgBsNhvS0tIG/CEiIiIiIiJSmurp5StWrMDy5csxa9YszJ49G08++SS6u7tx++23AwBuu+02FBUV4dFHHwUAfOc738H8+fPx61//GkuWLMHq1auxfft2PP300yr/JkREREREREQDqR50L1u2DE1NTXjggQdQX1+P6dOnY82aNXKztKqqKhiN/Rvy8+bNw4svvogf//jH+OEPf4ixY8fizTffxJQpU1T8LYiIiIiIiIg+zyBJkqT2IGKto6MDGRkZqK6uZqo5ERERERERhU30Cmtvb0d6evoZH6f6TrcanE4nAGi+mRoRERERERFpm9PpPGvQnZA73X6/H7W1tXA4HDAYlDu6abDEygl35BMbrwMCrwMKwWuBwOuAQvBaIPA6UI0kSXA6nSgsLBxQEn2qhNzpNhqNGDp0qNrDOG/suE7gdUBBvA5I4LVA4HVAIXgtEHgdqOJsO9yCqkeGEREREREREcUzBt1ERERERERECmHQrWE2mw0rV66EzWZTeyikIl4HBF4HFILXAoHXAYXgtUDgdaB5CdlIjYiIiIiIiCgWuNNNREREREREpBAG3UREREREREQKYdBNREREREREpBAG3UREREREREQKYdCtolWrVmHEiBGw2+2YM2cOtm3bdtbHv/rqq5gwYQLsdjumTp2K9957L2ZjJWWFcy0888wzuOSSS5CZmYnMzEwsXLjwnNcO6UO4nwnC6tWrYTAYsHTpUsXHSLER7rXQ3t6Ou+++GwUFBbDZbBg3bhzvEXEg3OvgySefxPjx45GUlITi4mLce++96Ovri9l4Kfo2bNiAq6++GoWFhTAYDHjzzTfP+T0ff/wxZsyYAZvNhjFjxuD555+PyVhJWeFeC6+//joWLVqEnJwcpKWlYe7cufj3v/8ds/HSQAy6VfLyyy9jxYoVWLlyJXbu3ImSkhIsXrwYjY2Np3385s2bceONN+JrX/saysrKsHTpUixduhR79+6N+dgpusK9Fj7++GPceOONWLduHbZs2YLi4mJcccUVOHnyZMzHTtET7nUgnDhxAt/97ndxySWXxGyspKxwrwW3241FixbhxIkTeO2113Do0CE888wzKCoqivnYKXrCvQ5efPFF3HfffVi5ciUOHDiAP/3pT3j55Zfxwx/+MOZjp+jp7u5GSUkJVq1adV6PP378OJYsWYLLL78c5eXluOeee3DHHXcw2IoD4V4LGzZswKJFi/Dee+9hx44duPzyy3H11VejrKxM8bHSaUikitmzZ0t33323/HefzycVFhZKjz766Gkff8MNN0hLliwZ8LU5c+ZI3/jGNxQfKykr3GvhVF6vV3I4HNILL7yg4ChJaZFcB16vV5o3b5707LPPSsuXL5euvfbaGI2WlBTutfCHP/xBGjVqlOR2u2M4SlJauNfB3XffLS1YsGDA11asWCFddNFFio+VYgOA9MYbb5z1Md///velyZMnD/jasmXLpMWLFys8Ooql87kWTmfSpEnSgw8+qMiY6Oy4060Ct9uNHTt2YOHChfLXjEYjFi5ciC1btpz2e7Zs2TLg8QCwePHiMz6e9CGSa+FUPT098Hg8yMrKUnCkpKRIr4OHHnoIubm5+NrXvhajkZLSIrkW3n77bcydOxd333038vLyMGXKFPz85z+Hz+eL4cgpmiK5DubNm4cdO3bIKegVFRV477338MUvfjFm4yb1cb5IZ+L3++F0OjlfVIlZ7QEkoubmZvh8PuTl5Q34el5eHg4ePHja76mvrz/t4+vr6xUdKykrkmvhVD/4wQ9QWFj4uZss6Uck18HGjRvxpz/9CeXl5TEaJcVCJNdCRUUFPvroI9x888147733cPToUdx1113weDxYuXJljEZO0RTJdXDTTTehubkZF198MSRJgtfrxTe/+U2mlyeYM80XOzs70dvbi6SkJNXGRup6/PHH0dXVhRtuuEHtoSQk7nQT6dhjjz2G1atX44033oDdbld7OBQjTqcTt956K5555hlkZ2erPRxSmd/vR25uLp5++mnMnDkTy5Ytw49+9CM89dRTag+NYujjjz/Gz3/+c/z+97/Hzp078frrr+Pdd9/Fww8/rPbQiEhlL774Ih588EG88soryM3NVXs4CYk73SrIzs6GyWRCQ0PDgK83NDQgPz//tN+Tn58f1uNJHyK5FoTHH38cjz32GD788ENMmzZN4ZGSksK9Do4dO4YTJ07g6quvlr/m9/sBAGazGYcOHcLo0aNjMHKKtkg+EwoKCmCxWGAymeSvTZw4EfX19XC73bBarYqPm6IrkuvgJz/5CW699VbccccdAICpU6eiu7sbd955J370ox/BaOQ+SyI403wxLS2Nu9wJavXq1bjjjjvw6quvMitSRfwEVoHVasXMmTOxdu1a+Wt+vx9r167F3LlzT/s9c+fOHfB4APjggw/O+HjSh0iuBQD45S9/iYcffhhr1qzBrFmzYjRaUkq418GECROwZ88elJeXy3+uueYauVttcXFxjH8DipZIPhMuuugiHD16VF54AYDDhw+joKCAAbdORXId9PT0fC6wFgsxgb5LlAg4X6RQL730Em6//Xa89NJLWLJkidrDSWxqd3JLVKtXr5ZsNpv0/PPPS/v375fuvPNOKSMjQ6qvr5ckSZJuvfVW6b777pMfv2nTJslsNkuPP/64dODAAWnlypWSxWKR9uzZo+JvQdEQ7rXw2GOPSVarVXrttdekuro6+Y/T6VTxt6DBCvc6OBW7l8ePcK+FqqoqyeFwSN/+9relQ4cOSe+8846Um5srPfLIIyr+FjRY4V4HK1eulBwOh/TSSy9JFRUV0vvvvy+NHj1auuGGG1T8LWiwnE6nVFZWJpWVlUkApCeeeEIqKyuTKisrJUmSpPvuu0+69dZb5cdXVFRIycnJ0ve+9z3pwIED0qpVqySTySStWbNGxd+CoiHca+Hvf/+7ZDabpVWrVg2YL7a3t6v4WyQuBt0q+t3vficNGzZMslqt0uzZs6WtW7fK/2/+/PnS8uXLBzz+lVdekcaNGydZrVZp8uTJ0rvvvqvCqEkJ4VwLw4cPlwB87s/KlStVGj1FS7ifCaEYdMeXcK+FzZs3S3PmzJFsNps0atQo6Wc/+5nk9XpVGDlFUzjXgcfjkX76059Ko0ePlux2u1RcXCzdddddUltbm0qjp2hYt27dae/54t9++fLl0vz58z/3PdOnT5esVqs0atQo6bnnnlNp9BRN4V4L8+fPP+vjKbYMEnOOiIiIiIiIiBTBmm4iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiSnBf/OIXsXz5cvnv69atQ3Z2Nnw+n6rjIiIiigcMuomIiBJcUVERTp48Kf99/vz56O3txdatW1UdFxERUTxg0E1ERJTgioqKUFNTI//daDQiKSkJjY2NeOutt3DPPfeoOj4iIiI9Y9BNRESU4E7d6S4vL0d7ezvmzp2L3bt3o6SkRNXxERER6RmDbiIiogRXVFSErq4udHZ2wu/3495778XNN9+M/Px8Oeju7OzEtddei6efflrt4RIREemKWe0BEBERkbqKiooAADU1NXjuuedQX1+Pt956CwBw4MABJCUl4aqrrsJPf/pTLFq0SOXREhER6YtBkiRJ7UEQERGRepqbm5GTk4Mrr7wShw8fxoYNG1BUVITe3l4UFhZixIgR+Nvf/obJkyerPVQiIiLdYXo5ERFRgsvOzobNZkNlZSXWr18v73zv3bsXc+fOhd/vh9nM5DgiIqJI8A5KRERE6Ovr+9zXdu/ejUsuuQSLFy/GTTfdhPXr1yM1NVWV8REREekVd7qJiIjotHbv3o0pU6ZgxowZuOuuu/DVr35V7SERERHpDmu6iYiIiIiIiBTCnW4iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlIIg24iIiIiIiIihTDoJiIiIiIiIlKIWe0BqMHv96O2thYOhwMGg0Ht4RAREREREZHOSJIEp9OJwsJCGI1n3s9OyKC7trYWxcXFag+DiIiIiIiIdK66uhpDhw494/9PyKDb4XAAwRcnLS1N7eEQERERERGRznR2dqK4uFiOL89El0H3hg0b8Ktf/Qo7duxAXV0d3njjDSxduvS8v1+klKelpTHoJiIiIiIiooidq2RZl43Uuru7UVJSglWrVqk9FCIiIiIiIqIz0uVO91VXXYWrrrpK7WEobkdlG2YMy2CzNyIiUp0kSbwfERERRUCXO93hcrlc6OzsHPBH6/537RFc/4fN+OOGCrWHEjfae9x45J39+P3HRyFJktrDISIFtPe4cf/ru/HXrZXw+/k+jwaX14c7/7IdF/9iHQ7Uaf/+qRdlVW24Z3UZth1vVXsoRKSQ7Sdacc/qMuysalN7KKQyXe50h+vRRx/Fgw8+qPYwwpJsNQEAHvvXQeSl2fDl0jN3w6NzW3ewET/4x240Ol0AgJFDUnDV1AK1h6VbHp8f+2s7saOyDTuq2tDQ0YdHr5uKsXlnbyJBA738WRVe/qwaEwvSMHN4JmYOz8SwrGTuJg7Cg//cjzfKTgKoxru7a/Gr/yhBcVay2sPSLb9fwv+8sgvv728AAPzXc9vw+l0XoSgjSe2h6ZbL68P/rj2CP3x8DH4J+ORIMz5cMR+ZKVa1h6ZbHT0e7Kxuw87KNuysakNOqg2/+koJLKaE2FuKCq/Pj++/thsNzj7MGJaJGcMzMaM4E+nJFrWHplvtPW5882870Nzlxtu7avHN+aPxnYVjYTOb1B4aqcAg6XzLz2AwnLORmsvlgsvlkv8uusx1dHRoupHaI+/sx7Mbj8NsNOC52y/AJWNz1B6S7jj7PHjknQN4eXs1ACDVZkaXy4schw0f3jufN5MwfFrRgo8PN2FHZRt217Sjz+Mf8P8vGZuNv35tjmrj05vmLhcu+cU69Hp8A76enWrFjGGBAPyLUwsYMIbh40ON+K/nPoPRANjMJvR6fEixmvCjJZNw4+xiLmZEQNyHLCYDCtKTUNXagzG5qXjtm3ORkcwgMVz7azux4pVyHKx3AiH3pOtnDMWvbyhRe3i60efx4d3dddhe2YrtJ9pwpLHrc4/55fXTcMMFPB72fL2yvRrff233574+NjcVM4dnYtaILHxpWgHsFgaM5+t7r+7Cqztq5Pc5AEzId+Dxr5RgSlG62sOjKOns7ER6evo548qEWAK02Wxyp3I9dSz/4Rcn4kvTCuD1S/jmX3dg78kOtYekK5uPNuPKJz/By9urYTAAX7t4JDbdtwCjc1LQ5HTh5+8dUHuIurGruh3Lnt6KP3x8DNuOt6LP40d6kgWXj8/Bfy8YA7PRgE+ONGP7CaZJnq+nN1Sg1+PDhHwH7rh4JEqHZcBiMqC5y4339zfg0X8dxH8+vRVen/88no26XV786I29AIDbLxqJNfdcgtkjstDt9uGHb+zB8uc+Q31Hn9rD1JVnP6nAsxuPAwB+9R8lWH3nhchPs+NoYxe+/pft6DtlwYjOzOvz4/8+OoJrV23EwXonslKs+MPNM/CXr82GwQD8Y2cNNhxuUnuYuvHEB4fxP6/uwkvbquWAe8SQZFw3owhfLi0CAPzvR0fg4efnefH4/PjdR0cAAEunF+L6GUMxMjsFAHCksQurP6vGd1/dhcf/fUjlkerHxiPNeHVHDQwG4IWvzsZTt8zAkBQrDtY7sXTVJvzvWl6fiSYh0sv1ymg04Nc3lKC5y4WtFa24/fnP8Pq35nHn6xx63T78Ys1BPL/5BACgOCsJj/9HCeaMGgIAeOz6afjKU1vw8vZqXDu9EPPGZKs8Yu0Tr+X04gzcOLsYM4dnYlR2KozGwM5hU5cLL22rxm8+PIy/33GhyqPVvkZnH/6yJfCa/uDKCbh8Qi4Q3L3Ze7IDOyrb8If1x3CyvRcf7G9gKcR5ePz9QzjZ3ouhmUn4nyvGIdlqxkt3XojnNh3HL/99CBsON+GK36zHg9dOZrnOeXh7Vy0eeTewMHn/VROwNBjIPP/VC/CVp7bgsxNtuPflcvzfTTNgMjKD4GyONnbhf14px66awML5FZPy8PPrpiI71QYAWD53BJ7ffAI/fGMP3r/3UiRbOTU7mx63Fy9tqwIA3Dh7GC4fn4MZwzPl17PX7cMnR5pR09aL13bU4MbZw1Qesfb9Y0cNqlt7kZ1qxc+vmypfg81dLpRVtePjQ434+6eBcqh7F41Dio3X6Nn0un24/41A1sBtFw7HzOGZAIBZI7Lw4zf2Ys2+ejzxwWF8eKABT9xQgjG5LM1LBLrc6e7q6kJ5eTnKy8sBAMePH0d5eTmqqqrUHlrU2cwm/PHWWZiQ70CT04Xlz21DW7db7WFp2sPv7peDxJvnDMOa71wqB9wAcMGILNx64XAAwP1v7OFuzTk0d7nw7u46AMCD10zGsguGYUyuQw64AeDuy8fAYjJg09EWfFrRouJo9eGP6yvQ5/FjenEGLhvfXzZit5gwa0QWvjF/NG6eE5go/mVLpYoj1Yeyqjb5Pf/zL/dPGE1GA+64ZBTe+++LUTI0HZ19Xtz78i6sO9So8oi1bfOxZnz3lV0AgP+aNwJ3XjpK/n8T8tPw9K2zYDUZ8a+99Xjon/vYmPIs+jw+3PjMVuyq6YDDbsZvlpXgj7fOlANEAPje4vEoykhCTVsvnnj/sKrj1YO3ymvh7PNiWFYyfrZ0Cq6YnD/g9UyymnDXZaMBAP/30VG4vdxNPBu314/ffXQUAPDN+aMHLPpkp9qwaFIeHr52CkYMSYbT5cWb5SdVHK0+/ObDw6hu7UVhuh3fu3KC/PXsVBv+cMsMPLlsOtLsZuyu6cB/Pr2V89AEocuge/v27SgtLUVpaSkAYMWKFSgtLcUDDzyg9tAUkZ5kwfO3z0Zhuh0VTd24g2l9Z9Tj9uLNssAN4Xc3luJnX5562hXZ7185HgXpdlS29OA3H3KSczYvf1YNt8+PkuIMlBRnnPYxQzOTccOsQO0cX8+za+zsw9+2BgLpexeNO2Od8c1zhsNoALZUtOBwgzPGo9QPt9eP+/6xB5IEXDejCJeO+3zvizG5DvzjW/NwXXC3dvW2+FugjZaD9Z34xl92wO3z44tT8/GTL0363DU6d/QQPLEsUH/8wpZKnrJxFmsPNKLJ6UJemg3v33spvlw69HOvZ4rNjJ99eQoA4M+bjmNXdbtKo9U+SZLwQnCB7ba5wwcs/oa6ac4w5DpsONnei1eCPV3o9F7dUY2T7b3IcdhwS3BD4lRGowG3zh0BAPjL5koutJ3F7pp2PPtJ4DPxZ1+eitRT5qAGgwFLS4vw/r3zUZBuR3OXGx8EG1VSfNNl0H3ZZZdBkqTP/Xn++efVHppi8tPteP6rs5FmN2NHZRu+s7qMH3qn8f6+BvS4fRiWlYwvTTtzSq7DbsEjSwOTnGc/Oc56+TPw+vxygHjbGW7Gwt2Xj4HVZMTWilZsPtYcoxHqz+8/PgaX14+ZwzNx6dgzlzYUZiRh0aQ8AJBT0enznlp/DIcanBiSYsVPlkw64+PMJiO+HtyxXXewCe09zBg6VUNnH/7rz5/B6fJi9ogsPHHD9DOmjn9pWiF+8qXA6/3Yvw7i7V21MR6tPrxRVgMAuG7GUBSkn7nj+2Xjc/Hl0iL4JeAH/9jNWs8z+OxEGw7WO2G3GPGVmWdukma3mHD35WMAAKvWHYXLy42K03F5fVgV3OW+67LRZ22S9h8zhyLJYsKhBic+5TF3p+Xx+fGDf+yBXwKunV4ol46dTn66HdfNCCwEi80iGui3Hx7BipfL42YhUpdBd6Ial+fAs8svgNVkxL/3NaAsTi7CaHo9+MG1tLTonJ2KvzAxD1+aVgCfX8IP/rGbDatO48MDDajr6ENWihVLzrKIgWCQeOPswCToyQ+OcFHoNOo7+vBicJd1xVl2uYXlwZ2F13eeRGefJyZj1JOjjU78X3DCuPKayec8cmliQRom5Dvg9vnx7p66GI1SP57bdAL1nX0Ym5uKZ26bdc4uxV+7eCTuuHgkAOAX/zrI9/wpWrpc+PhQoDmayLI4m598aRKygo2Wnmb2wGm9EFyAXDq96Jynjyy7oBgF6XbUdfTh5c+42306r3xWjdqOPuSl2c5Z+56eZJF7O/yVZU+n9cwnFThQ14nMZAse+NKZF4EF0V9k/eEmtHS5zvn4RCJJEl7dUY3Xy06irqNX7eFEBYNunZk9MgtXTskHAPx7b73aw9GUxs4+bDwSmOB8+TwmOACw8urJSE+yYF9tJ/4U7NJL/UQ98X9eUHxex4TcdfkYWM1GbDvRik1HWdt9qt9/HKgvnD0iC/NGDznn4+eOHoIxuanocfvw+o6amIxRL/x+Cff9Yw/cPj8WTMjF1edYFBLEzsIbO7mzEEqSJKzZG1iI+M7Csed9nOJ3F49HksWEk+292HuyU+FR6ss7u+vg9UuYUpSGsXnnbpSUlWKVJ+q/XXsEx5o+fwxWImvo7JPnPbfOPXvmFYK73XeF7HazLG+gPo8Pq9YdA4KZaudzj78t+Lqv2VfP0yBOcby5G09+GOgA/5MvTcKQkD4DZzImNxXThqbD65fwT2YLDbCvthM1bb2wW4ynLRvTIwbdOiSC7jX76rmzEOLtXbXwS0DpsAz5qItzyXHY5BTJJz44jBPN3QqPUj+ONDix+VgLjAbg5nOklgt5aXa5AdhvPjzM6zNEbXsvVm8L7LacrZY7lMFgwPLgJOcvW1lHF+rvn1Zie2UbUqwmPLJ0ynmfwX3t9CIYDcD2yjZUtfQoPk69ONTgxImWHljNRlw2/swpkaeyW0y4fEJgQrRmH7MHQr0RzLwKp1v+tdMLcdn4HLi9ftz/jz3w+/meF178tApev4QLRmRicuH5nXF8w6yhKMpIQkOnS+54TgGrt1WhvrMPBel2LDvP88wnFqRh9sgs+PwSXvyUu91CYBF4N9xePy4dl3PeGz8I2SR6gynmA6wJLrBdNi43bk50YNCtQ/PH5cBmNqKypQcH6thgSRAfWOeTxhfq+hlFuHhMNlxeP55af0yh0emP2OVeODEPRRlnrkU81bfmj4bNbMSOyjZsOMLabmHVuqNw+/y4cFQW5p7HLrfw5RlDkWozo6Kpm9kDQX6/hN+uDaSVf//KCSgM4/rMS7PjouAxgZzk9PvXnsAE59Kx2Z9r/HMuiycHFoL/tZcLwUJFUxfKq9thMhpwTUnheX+fwWDAI0unINlqwrYTrdh8jO95BBsmitIc0dDrfNjM/bXdv//4GHe7g/o8Pvz+4/5dbpv53LvcgtjtfnFbNTvDB2093oJPj7ciyWLCz8JYBAaAq0sKYTIasKumg9ktIdbsC9yTxEZjPGDQrUMpNjPmjxM7C0wxB4DDDU7sq+2ExWTAl6ad/wQHwUmOOBLno4ONnDQCcPZ58PrOQDrz8nnnP8EBgNw0u3wk228+4G43ANS09cgddO9dOC6s7021mXF9MCX6BTZUAwDsPtmB5i4XHDYzbpoT/hm8/TsLNbw+g/4tT3DCPxN+wYRcWE1GVDR142gjJ40IaYx0ydhs5DjOnWYaamhmfyPQjw7yeDsE5zpNThdyHDZcOTm8Sfh/zByKoZlJaHK65Magie7vn1ah0elCUUaSfPLI+Vo8OR+5Dhuau1z4115mtwDARwcC79Ml0wpQnJUc1vdmp9rkOT3LngKONjpxtLELFpMBCyaef+aV1jHo1ik5xZwfeECw0RSCHWDP1UzpdOaMykKy1YRGpwv7almX+PrOk+h2+zA6J+W8ao9P9Y35o2G3GFFe3S43Ekpkq9Ydhccn4aIxQwacGX++xM7O2gMNqGljSrQIRC4Zlw2LKfzb2OLJ+UiymHCipYcNKYO1iAfrnTAbDVgYwQTHYbfg4mAn/n+x1wgkScIb5SK1PLzMK2FBsOsxz5QP+GtwwfGm2cNgNYf3nreajfh/CwK73U+tP4Yet1eRMepFr9uHPwR3ub+9YEzYr6fFZMTNc4JlT2yoBgD4KPg+XXCWbuVnE5pizpKS/tTyi8ZkI81+fv1F9IBBt059YWIezEYDDjd0JXw6it8v4a3yyFLLBZvZJKecrkvwnQVJkuQd1eXzRoSVJiXkOGxy5+1Er+2ubu3Bq9sDWQPh7nILY3JTcfGYbPilwA5FohPv0cvDqD0OlWIzywuX3Fnon+DMHT0EGcnhL1piwEIwg+7tlW2obu1Fqs2MKyZFlhp50ZhsWEwGHG/uxvEE7zWyr7YDn51og9loiCizBcEj24ZlJaO5y53wu91//7QSzV0uFGcl4T9mnn+/gVA3zimGxWTAjsq2hD9ytbKlGxVN3TAbDfLiY7gWTcqDw2bGyfZefHaCx7GJxdur4ii1HAy69Ss9yYJ5wSDx3wmeYr61ogV1HX1Is5sHlYYiJvCJvrOw6WgLKpq6kWI1RbxLAwB3XjoKFpMBu2s6cCKBG1a9tyfQwfjCUVmYNSIr4ucR3XpXb6tK6LrERmcf9gQnefPHR97RVFzb/9xdm/B1iaJMaXGYabuhFk3Mg8lowP66zoRvUCcyr66cko8k6/nXyoZy2C24IPh5kegLweJ4qsVT8pGXZo/oOSwmI7512WgAwFvlid0lWvz+37h0dESZQgCQ67DLpSiJfnyYeH/OGpEZ8a6s3WLCVVODC8EJ3mukurUH+2o7YTQEegrFEwbdOnYVdxaAkLO5l0wrDKsZyKlEB96y6na0drujNj69Ebvc188cCscg0nqGpNowY1gmAGDj0cRtqCZ+90UR7ngJX5iQi6KMJLT1ePDO7sQtKxHlCtOGpiPXEdkEHMGdxByHDe09HnycwAttte292FXdDoMBuGJy5BOczBQrLhwVCBITuYt5n8eHd3cHgppIM68EppgDHT0evBnMZFseRgO10/lCcFF+X21nwt7j27rd2FsbWLRcNGlwAY04WePN8pNo70nM1xMAPgrekyJNLRfEKQfv7qlL6IV1EdPMGTnkvI5d0xMG3Tq2aFIejAZgd00HTrbHx8Hx4ep1+/CvPYEJ3mB2ZQGgID0JEwvSIEnA+sOJOcmpaevB2gMNQEiH0sG4JJhqJc5PTzR9Hh+2HQ+kil0SYdqZYDYZcfOFgdTKvyZwQ7XBppYLJqMB1wa7SotJfSISmVKzhmcOahEDgNzgKpEXgtcdbERnnxf5afaI+jeEujw4if+0ohXdrsSsQ351RzX6PH5MyHfgghGZg3quXIcdE/ID56VvStCF4M3HWiBJwLi81IizBoSZwzMxqSANLq9fLqFKND1uL7ZWBE4YGGzQPWdkFgrT7XD2eRO6gWI8di0XGHTrWHaqTU4/S9RJzvv769Ht9mFoZhJmDR/cDRkAFgR3uz86mJhB4t8/rYJfAi4aMwRjch2Dfr6LxwZez83HWuD1JV4K747KNri8fuSl2TA2N3XQz7dsVjGsZiN21XSgrKotKmPUE7fXj0+Cx9ANdoIDAF8OdoX/8EAjOno9g34+PRK1c5F0LT/V4sn5MBiAnVXtqO/oi8Lo9EdkXl1bGjgGaDBGZadg+JBkuH3+hMwW8vsl/DVYfx1pf5FTXTxGLAQn3usJABuPBuY2F4+JvDRHMBgMWD4v2FBt6wn4ErAB2KajLXB7/SjOSsLonMHd441GA64Nbh69nqC9Rho6+7CjMjC3GUy5k1Yx6NY5sRL07wQNukXty5dLi2Ac5AQHIbtnGw43JWSQ+F4wa0B0Jh2sqUXpSE+ywNnnxe4EbLYiAsSLxmRHZcI4JNWGJVMDwZH4t0ok2ytb0eXyIjvViqlF6YN+vkkFaRif54Db60/I17PJ6ZKb9iweRGq5kJtml0tK3t+fePektm63XKpwXWlkDapCGQwG+Z6UiCUQ+2o7UdnSg1SbGddOD+8o0DMRja42Hm1OuAafkiTJ96TBZl4J15QUwWEzo7q1NyEbqonSj8vH50blHi9KUj4+1JiQJRDvB3e5S4dlID99cJkYWsSgW+fEStBnla1odCbWzkKT0yXfQAabWi6UDstERrIFHb2ehDtKqLa9F5UtPTAZDVG7IZuMBvnIsUTcWRC7CtF6PQHgsmDzsC3BlLZEIlLL54/Ljcoim8FgkHe7E7GL+Qf7GyBJgfr4oZnhnS17JqLXyL/2JF7Q/c7uWnh8UmAxJ3/wmUIISTFfd7Ap4YLELRWBe8ackVlItpqj8pxzRg6B1WTEyfbehOsKX9nSg5q2XlhMBswZFXlTz1BJVpNcRpFo9yRJkvrLnaKQeQUAY/McmFKUBq9fwju7E6/hn0gtj7eu5QKDbp0rzEhCSXEGJCkwgUokb++qhc8voaQ4A6MGmdYjmIwGzB8nUswTa2dB1CVNKUofVAO1U8k7CwkWdLd2u+Uz38VxdNFwYXCCs6+2M+FSosV7Mhqp5cK10wthMADbTrSiujWxum5Ho2v5qcRzfXq8JeF2akRq+XUzorMIjGDAmWQxob6zD/vrOqP2vHqwtSKQhTF39OBq40MlWU2YOTwxG3x+Evx9ZwzLjNoiBkL+fbYmWNB9sN6Juo4+2C1GzB1k/4ZQoqFaoqWYt3W75fd8PKaWg0F3fEjULuZvlAUadwy2Q+yp5KPDEizo3nIscMO8MEor4MIlwdqxnVVt6EqgZkCbjjZDkoAJ+Y5BN6gKlZdmx6jsFEgS5CZtiaCqpQfHmrphGsRZqKdTkJ4kZ2O8mUBHtXT0eLA5OAmP5q5CcVYyphSlwS8BHyRQivnx5m6UVbXDaACuKYlOKjSCRwldNCZwfSbSPcnr88ufbxdGMaBByELwJwm2ECwamkYz8wohc4bPjrfCk0BleWIReN7obNgtkZ+cc6prSgL9IMqr21HR1BW159W6Dw40wOeXMLEgDcOHpKg9HEUw6I4DYkVoy7GWhDm2oaKpC3tPdsJsNODqKE5wAGD+uBwYDYFVzNoE6gq/9Xgg6I7mii0ADBuSjGFZyfD6JXyaQCvhYmf/4ijucgsXJuDOgqidmzU8E+lJ0cvEQMjOwlu7Eiedb+3BBnj9EsblpUYtU0hIxC7m/wxeOxePzUHuILtCn0pOMT+UOA0+99V2osvlRZrdjIkFaVF9bhF0bk2gBp9enx+bgwvrosFptEzMT0N6kgXdbl9C1XWLPgvRSi0Xchw2+Rp9O4HuSeJ+Ea+p5WDQHR9GZqdgQr4DXr+EtQcSYyVc3Dxmj8xCVoo1qs+dmWJFabAZUKKcj1rT1oPq1l6YjAbMGhHdnW4k4M6CJEly6mI0d2UFsfMjshMSgRKp5cIVk/NgMABHG7vQ2JkYvTHEBOdKBdL4RIPPTUdb0NmXGCUQm48F3u9KvJ4i+6qsqg1tCZKyL+qDZ48cMugu8KeaXJiOjGQLnC4vdtUkRu+W3Sc74OzzIj3JEpUmlKGMRgPmjAzMGxKlrru9xy132b58fHQXMRASeG5OkHu8s88jb1TE41FhQkRB94EDB7By5UosWLAAo0ePRkFBAaZNm4bly5fjxRdfhMvliv5I6azERfqvBNlZEGlns0dGP0BEyIdooqTziTqaaUPTkWqLXq2XcMmY/o6xieB4czdOtvfCajJizsjoZg4gJJ3vQH1nQmS39Li98mQu2rsKAJBmt2BifmA3bduJ+E/Z73Z5sf5wYNc0GkeFnWpMrgNjclPh9vkT4jPU5fWhrCoQvClxTyrMSMKEfAf8EuR/t3gnsniiWc8tmIwGXDQ6sRaCRUAzb3T0FzEwoK47/j8/gcD70B887zxaTShDieOAy6vb4fL6ov78WvPRwUa4fX6MykmJyvGqWhVW0L1z504sXLgQpaWl2LhxI+bMmYN77rkHDz/8MG655RZIkoQf/ehHKCwsxC9+8QsG3zEkgu4NR5rQHed1s5IkycfczFZgVxYhE/tNR1vQ54n/DzyxYxrt1HJh3uhseSexriP+U/bF4sLM4ZlIskav1kvIddgxOidQ1/1pAtR1bw6ehVqUkaTYDVkES58lwOu5/nATXF4/hmUlY2JBdLpsnyqRUsz3nuyAy+vHkBQrRucoU4so7kmJ0ODT4/PL70Ol7kmJ1uBTLndSIPMKIdlX208kRl13tLuWn2pkdgqyU61we/3YXRP/Kfv/3tefeRWNo9e0Kqyg+/rrr8d1112H+vp6rF27Fo8++ij+3//7f7jjjjvw/e9/H3/5y19w/PhxvPPOOygrK8Ovf/1r5UZOA4zPc2BkdgrcXn/cp0TXtPWirqMPZqNBTgOPtkkFachPs6PX44v7oEaSJHlXIdoNa4T0ZAumBVPaEmGS84nCExyE7CwkQoq5+ExbMCE6Z6GejthZ2HaiTZHn15J/hdTOKfV6ioXgjw81odcd3wuX244HrpkLRmQp9nqKsor1h5vg88f30WF7Tnag2+1DRrIFE6J09NqpRK+Nsup2OOO8BKLL5cXOqsA1qkSPEQTnoJnJFvS4fdgd5yn7Pr8kZ5wsGK9M0G0wGPrvSXE+B+11+7DuYOD1vEqBzCstCSvoPnz4MO666y5kZGSc9XFz587F6tWr8b3vfW+w46PzZDAY5IZq7++L76PDxAfQ1KHpiuwiIvh6Xj4hMVLMa9p6cbK9F2ajAbNGKLOIgdCdhThPMff6/NgqGtYoNMFByAJJvDdTCz0LVYl6buGCkYFr/2B9fB/F5glJ+V6sYO3c5MI0DM1MQq/Hh0+OxHdK9LZgE8oLFCp3AoDS4gykJ1nQ0etBWVV8LwyJz7Q5I7NgVCAVGsEu+8OHJMPnl+I+JfrTihZ4/RKKs5IU6wodqOtOjBTz8up2tPV44LCb5ePnlCBnX8V5ydPGo83o9fhQlJGEKUXRbZqoNWEF3RZLf8fYmpqaMz5u69atn3s8KU+cL73teCskKX5XwpVOLRcuG9+fzhfPr6fYKS0pzojq2Z2nujh4dFjgKK34fT131XTA6Qo0rJkS5YY1oUTQfbDeGdfnIR9qcKK2ow82s1GxTAwEU/ZHBo9i21EZv5Oc/SFdoacPPfsC+mAYDIYB96R45fNL2B5sqKTkPclsMuLS4OsZ7ynm/cdXKvd+R8ii6KY4XwiWm3qOiX7Dr1CJkn0lFi0vHZcDs0m5ftRip3vHiba4zm4Ri5aXjsuJ69RyDKZ7+RVXXIHW1s/fSDdt2oQrr7xysOOiCEwvzoDZaEB9Zx9qO+K3A69odHSBwkH3xWOyYTUZUdXag4rmbkV/lprkhjUKT3BmDM9AksWE5i43DtY7Ff1ZahLp8xeNUaZhjZCdapPrm8VNKx6JtLN5o4coltkiXBDM9BDpwvFIdNydOTxTsV1EQWTO7IjjndlD9U44+7xIsZoUq48XFojsqzg+Oszj82N7sMRDiSZqoS6RT9WI39cTIfekaJ/PfSq5rruyFW5v/NZ1y+VOCqWWCxML0uCwmeF0eXGgrlPRn6UmcU+apWDWgFZEHHRfeOGFuOKKK+B09k+eN2zYgC9+8YtYuXJltMZHYUiymjC5MJCasT1O01Gau1yoaOqGwaB80J1iM2NOsEt0vKaYS5Ikd4VWelfBZjbJr2c813VvPBqYwCm9q4AE2VmIRWq5ID5T4jmdT57gKPz5CQCzhgd+xt6THXHbkFJcKzNHZCm66wUA88flwmAADtR1xm1Dyt017ej1+JCZbMG4XGUXMeaOzobRABxr6o7b17O+ow9HGrtgMAQWLpU0Li8VQ1Ks6PP44/YotobOPuyr7YTBAMxX4KiwUCajATOCgWi83pP6PD7sPRlYUFCyvFErIr5DPPvssxg2bBiuvvpquFwurFu3DkuWLMFDDz2Ee++9N7qjpPM2MzjJEROreCM6mo7PcyA9WfnyhdAU83hU1dqDuo4+WEwGRWuTBJHO90mcpvN1ubzy0UFK7yogJDshXmvoOno88i7pZQrvKgCQaxJ317THZZAoSRK2B1PnY/F+H5qZhFyHDR6fFLcdeOXjK2MwYcxKsWJ6caAkQGSAxBvxWXbhqCGKZ2KkJ1kwLVhiEa9Hh4nU8mlF6chItir6swwGQ3+vkThdCBaLwNOGZiA71ab4z4v3uu49Jzvg9vmRnWrDsKzoH72mNREH3UajEatXr4bFYsGCBQtwzTXX4NFHH8V3vvOd6I6QwiJWirbHaQfeWKWWC2J3bdvx1rjscCp2SEuLlTna6lSXjBU1nvF5FNvWY4GGNcOHJKM4BjeQOcEJzqEGJ1q64u+Ixg1HAp2ax+amxuT1LM5KQl5aIEgUiyfxpKatFw2dLpiNBpQoWM8tGAz9zRm3x2GdvCRJsb8nxflCsHx8pcK7ssIlcX502MZg6rySJ2mEujCYzbYlTht8xiq1XBBBd7z2ahKxyqzhmXFfz41wg+7du3cP+HPw4EH89Kc/RXV1NW655RZceuml8v8jdYjdi4P1gWY58Uas9inZJTbUyOwUFGclweuPz0l4f2p5bF7PcXmpyHXY0OfxY2ccZmP0N6yJzQQnK8UqH6kTj7vdn4Y0WImF0GNa4nFnQWRATS5Mi8kiGwDMCB7ruCMOF4IrW3rQ5HTBajKipFj5RQyEvBc+O9EKf5w1V3J5ffLijNLlTkJoM7V4ez0lScLGo+Ikjdh8horFkh2VbXB542thXZIkObPl0nGxucdPG5oOq9mI5i43jsdhb6EdMcy80oKwgu7p06ejtLQU06dPl/9ceumlqKmpwR//+Ef5/5WWlio3YjqrvDQ7hmYmwS8h7o4VcfZ5sL82UPuhdOfyUDODk8adcfZ6DjifO0a7CgaDIa5TzEVDnliklgvxfHTYzsrAQlcsb8jxnM7X30Qtdp+fonZ8R1Vb3AU1YgJeUpwOuyU2ixiTCtNgtxjR0euJuwafu2s60OfxY0iKVW4SqbTSYZlItprQ0u3Ggfr4alZ1sN6J5i4XkiwmzBgem0Wh0TmpyE61weX1ozzONiqON3ejrccDm9mIyYXKnUwSymY2yadMxNs9SZKk/ntSAtRzI9yg+/jx46ioqMDx48flP6F/F/9dUVGh3IjpnEQHwHir695R2Qa/BAzLSkZ+uj1mP1c0stgZhzeQhs7ALo3YjYqFi+M0na+uoxfHmrphNAQa9MSKCLrjLZ2v2+XFweAkOJbXpwi6d1S2weuLrw682+UmarF7PScHg8T2nvgLEmOdWg4AFpMR04oCk/B4WwgOPSosVqmm1pCjCOPtniR+nzmjsmAzx2ZRKFDXHZ8p5mIOOLUosPscK/0p5vH1fq8IWcSYEqNFDLWFddUMHz78vP+QemaOiM9map+pMMFByIS/LM52akQ6cumwjJjt0iAknW9vbQfa4uh8adGIZ9rQDKQnKd/kT5gzMgsGA3C0sQtNzvip695V0w6/BBSm22O6yDYu14H0JAt63D7sq42fnS9nnweHgosYsTyaxWIyyvXj8Xb+eazLnYTS4K5lvGWzxTrzShD3pI1xln31SYzLnYR4zb4Si1wzYpwKLT5ftp2Ir9dTlByVDM2I6SKGmsL6Lbdu3Xrej+3p6cG+ffsiGRMNkphQlVW1wxdHQeJnwVW+OTGe4EzIdyDJYoKzz4tjTV0x/dlKitVRYafKTbNjfJ4DkgRsOhY/k5xYnYV6qswUKybkB44KjKdJjuihUBrjCY7RaJA/Q+Mpna+sKrCIUZyVhNy02C1iIE4bfDZ09qGypQdGQ+zrEcVCsCi/iAcur0/eKJgbox4jgvjM3na8NW4afPZ5fNgW7IkhGpjGiqjr3lkVX6dAiD40M4bFJlVfmDEsA0YDUN3ai/qOvpj+bCXJJ2kkSGo5wg26b731VixevBivvvoqurtPnya2f/9+/PCHP8To0aOxY8eOaI2TwjAuzwGHzYyukPRMvevz+FBeHZhgxHpXwWwyYtrQQOpLvKTzhdZzx6pLbCiRYr45To4VkSRJ/l0uivGuAkIa4cVT0N0/wYn9DfmCkI6x8UI+nzuG9dzCrDg8ylJcGxML0pBmj11mC0LeE4cbneiMk1M1yqva4fL6keOwYXRObOq5hTG5qchLC9Qhx8s9vry6HX2ewOs5Li+2r+eo7BTkOGxwe/1x04DW2efB4QYnoMI9yWG3YFJhYGF9WxwtBPffkxh0n9b+/fuxZMkS/PjHP0ZGRgYmT56MRYsW4eqrr8bFF1+M7OxszJgxA8ePH8f777+P2267TbmR0xmZjAZMHybS+eLjBrK7pv8svxFDYn+W34w4q5M/1tSNJqcLNrNRPvc1lkSJQLzckGvaetHc5YLFZFDl9ZwbZ3XdkiT1p/LFeFcBIdfnZyfi55gW8dkV69RIBEtYEKzhi5ej7dQqdwKAHIcNxVlJkCTETbOq0MyrWB8dFHpqQbzck8TvMXtEliqvZ7zdk3ZVd8AvAUUZsc8UQug9KU4Wgtu63TjWFNi8VWNhXS1hBd0WiwX//d//jUOHDmHLli34+te/jilTpqCoqAiXXXYZ/vjHP6K2thYvvfQSpk6dqtyo6ZzEzkK8pPOJCc7skeqc5Sen88XJDVnsiM4YlhnTem5BTMIP1XeiOw6OtisLZmFMKoxdF+NQc0YOgcEAVDR1o7FT/+lnokusNYZdYkNNLUqH3WJEW48HRxv1X1Li9fnl+l81dhUykvu7UcfLwqXY6Z4d48wrYUacnaqxNcbHV56qdFh/WV48EO/3UhUWLRGHdd1q1XMLc+Is+0rcB0bnpCAzxar2cGLGHOk3zpo1C7NmzYruaChqRA1dvExwPhUTHBV2FRBy4zra2IWOHg/Sk2ObThhtW1RMLUfwaLuijCScbO/F7poO1cYRLfIER4VdbgBIT7ZgUkEa9tV2YktFC66dXqTKOKJFrS6xgtVsRGlxJrZUtGDbiVaMzXPEfAzRdLDeiW63Dw6bGeNU+l1mjcjEkcYu7KhqwxWT81UZQ7R09HhwKJhqqsZON4JB91vltXGxENzn8cm/x9wY9xgRxD2+vLoNkiSpsrgfLZIkyQvBagXd4p5eHqzrVmMxOprUzLxCyNGLhxqcaO9xIyNZ34HqdhXLndQU9mzmo48+gter/52peDe9OAMmowEn2/XfeMHnl+T6zljXcwvZqTYMD6a1l1XreyFDkiR8qlITtVCiBELvrydCm36pdENGnO0sqD3BQchnTTyk84nF19LhmTAZ1QkmxNngO+Ig+2p7ZSskqb92VQ3xdKrGzqo2uL1+5DpsGJmdosoYJhemwWoyornLjZq2XlXGEC0n23vR5AyUO6mRKQQAI4YkIy/NBrfPr/vNH79fku/xaqVCZ6faMCon8N6IhwzWHQnYRA2RBN2LFi1Ca2v/JOTCCy/EyZMnoz0uGqQUmxkTCwI7Gtt1fkzLgbpOdLm8cNjMcpdmNcRLivnRxi40d7lhtxhRUqze2YhiV1jv6Xwurw/7a2N/nvSp5spBt77f71C5iZowW67rjocJjvoNa8TP3n2yAy6vvjsaq3E+96kmFDhgtxjj4lQN8Zk1d3Ts67kFm9kkN6vSe8q+uKdOKkhTbYc5tK5b7wvBFc3d6OgNnCc9sUC9OejskF4jeub2+rGrpgNIsCZqiCToPrWpzL59++ByxUdjlHgzc1h8HNMialhmjlBvlwYhu256PxtVTBhnDMuEzaxeyldoDZ2em1Xtq+0MNvmzYmhmkmrjuCB4Xvfx5m40OvWb3dLl8vZ3iVXxhjxjeAbMwWyhmrYe1cYRDSLojvXRVqGGD0nGkBQr3F4/9p7sUG0c0SCyH9TKvELw/PNpwfPP9R4kitdzzkh1y4xKh8XHQnB/5pW6AY3IvvpU59lC4v2l9nnSon+E3l/PvbUdcHv9yEqxqpbZopbEOI08Qc0cER/HtKjdsEYQN7DyqnZdp/OJG7KaE3AE0/ksJgOau1y6TucTr+f04gxV6wDTkyxysyo9dzTeVd0ud4nNU6FLrJBsNWNyUSATRM87C3UdvTjZ3hs41UKlngMI7nyJzxw9LwT3un3YHdylmaPyPSkezuv2+SXsrtHGPUm8P0Q9tF6Jki013+8IWTTdU9MBr8+v6lgGQ+7ZMlzd11Nk1uw92YEet37LfEWJ0Yxh6jRGVlPYQbfBYBjwIp36d9IOkbaxv65Tt29QSZL6O5ermMoHABPyHUi2muB0eXFExx2NxXnnat+Q7RYTJgVTtfQ8yenvEqt+mpT4Ny3X8eu5U8WjrU41O1hvtu24foNEEeBOLHAgxRZx79SoiIcGn2XVbfD6JeSn2VXNbEFI9pWed7qPNAaa/KVYTRiTG9vzpE8lFjH213agz6PPEgiX14d9JwPlTmr2GAGA0TmpSLWZ0evx4XCDfudMYlFL7aOthmYmoSDdDq9f0vXCuih5nZVg9dyINL38C1/4AmbMmIEZM2agp6cHV199tfx38YfUV5iRhMJ0O3x+SbeT8IrmbrR0u2E1GzF1qHr1xwBgNhlRovN0vo7e/iOQ1A66MSDFXJ+vJ0JT+TT1eurz/Q6NNFETLoiDGrodGuoSKzdTq2zTbUnJZ8f7m3qqveEgFqaONHaho9ej6lgiJT6rSoLNX9U0NDMJ2alWeHwS9gX7dOjN/mC5U1aKFcOyklUdi8lokPvG6LVhamefB4cbg+VOKgfdoefJb9PpPUmSJE30GFFL2MveK1euHPD3a6+9NprjoSibOSILtbtqseNEG+aNzlZ7OGETtV6lxRmq1h8LM4ZnYEtFC3ZWtuHG2cPUHk7YRBrfsKxkDElVp+tuqNJhGXh+s36DxMbOPpxs74XBAEzTQNAtFlJ217TD55dUn8SGK/SoG7UnOAgJuo82dqGly6WJ90y4tFDPLUwpSoPVbERLtxsnWnp0Wc8nZ16pnFqOkFM1Klt6UF7djvnjctQeUtjKq7SReYVgUDO9OBMfHmhAWVWbJt4z4QpdBFZ7UQjBf9dNR1tQXtWOm+cMV3s4YdtV3Q5JAoqzklQ7qSDU7JFZeHtXrW7P665q7UFzlxtWkxFTitTdSFPDoINu0rZZwzPxz1218pl4eqOVem6hv4O5Pl9PLRxtFaq0WKTzdcLl9WliYSUcIkAcn+dAqsqpuwAwLi9QAtHt9uFIo1PVbv+RqGjuRnuP+l1ihcwUK8blpeJwQxc+O9GGK6fo63zpbpcX++sCO3ZaSOWzmU0oGZqOz060YfuJVt0F3Z6Q44/ULncSZgzLRGVLD3ZWtuky6BY7oFooz0Hw3vjhgQbdljypfT73qcQ9Xq+vp1ZSywUxFy6raofH54fFpK/WXKLcaerQdN2f3R4Jff1rUdjESu1OnZ7lKRYLZmlkgiMmBseautHe41Z7OGHTSj23UJyVFOho7PPrbYJAmwAATfhJREFUMp1Pa4sYJqMB04JlGHqs+RL13NOGpqvaJTbUBXJDSv3tLOyqDmQ8FKbbUZCubv2xIFKi9VjXfaCuE70e34CmhWrTc123s88j90fRyj1JfJbr8fMTGusxAgDTg6/nUZ2WQPSXO2nj9RyTk4qMZAt6Pf1HlerJdg1lXqlBG7MaUozc/KvPK9el6EVLlwtVrYGjerRyQw494kBvK7eSJMk3ZK28ngaDQdfHtMgTnGLt3ED0XNe9s0pbuwoIPbVAZ+93hE5wNLJoiZDacj1mX4UuWho1Urqh51M1dtd0QAqeVKCF1F0AmDY0A0YDcLK9Fw2d+jp6sdHZh5q2YLmTyj1whOxUG4qzAgt+orxNL/z+/jmTVu5JxpBTKPR4TxKL1wy6KS6ZTUY5qNHbzoL4QBmdk4L0JIvaw5GJ13Onzl7PqtYetPV4YDUZMalQ/dRdQa/N1Lw+v3x0kFZ2uqHzDubiPaWVXRoMqJPvgEdnx95s12DDGjHZOtrYpbtsoTIN1R8Lej5Vo1xjqdAAkGozY1yeA9DhwqXYnR+X64DDrp050/Ti/oUhPTnW1IXOPi/sFiMmFDjUHo5MPtpOZ3Omjh6P3MWeQTfFLbljrM7ORu2/IWvrzanXum7xek4qTNNU7XRpsT53ug81ONHr8cFhM2N0jjZSTRHyeh5udKLLpZ+jAgd0iVX5PNRQo7JTkGY3w+X141C9frKF/H4JZRpM5ctKsWJUTiBbSK+foVoKEs0mo7yrqbfXU4uLGAhdCNZZx22t1XMLpTpdCBbvp2lDMzRVO63X7KudwffTyOwUZOuwKWk0ROUq6uvTVwpOohG7HHpL59Na/bEwIySdz6ejdD6t1R8L04ozYAim8zXqKJ1PnjAO006qKQDkptlRlJEESQJ26+imLLrEDs1MQq7DrvZwZEajASU63Fk43OiE0+VFitWECfna2aVB6D1JRwvBbd1uHG/uBjR8T9JT9pUkSSjXWBM1Qa8lT/313Nq6PkVdd1l1u66OCtRaEzVhevDo2hMtPWjt1k+2kNj409IicKxFHHT7/X48/PDDKCoqQmpqKioqKgAAP/nJT/CnP/0pmmOkQZo+LBDUVLX2oNGpj6DG75fkVCSt3UDG5zuQEuwQfbhBPztfZRpdxEi1mTFepPPpKEjU0vncpwqd5OiFmOBo8Ybcv/Oln9dTBLTTh2XArKFdGoT8G+tpIbg8WI86KjsFGclWtYczgB6zr2raetHc5YbFZMBkDZU7IaQ53e6adnh1UlIysNxJW5+hkwvTYDUZ0drtRnVrr9rDOW/i/aS1e1J6skXOFtqlp3tSgtdzYzBB9yOPPILnn38ev/zlL2G19t+ApkyZgmeffTZa46MoSLNb5KBGLyvhFc1dcLq8SLKY5LFrhSlk50svk5w+jw/7awM3ZK2t2kKnOwtaO+omlB5T9rXWJTaUHtMj+yeM2mmiJogx7apu102dvJbOkz6V+PzU06kaYgFrUkGa5o4OGpWdCofdjD6PHwd1UlJyuKELPe5AudMYDZU7IXhU4MTgwopeUvY7evs762tt4wehdd06uSd5fX7sqg7MQbXUYyTWIg66//KXv+Dpp5/GzTffDJOp/wOzpKQEBw8ejNb4KErEMS16eYOKLsZTh6ZrbpcGA9L59PF67q/rhMcnYUiKFUMztXF0UCj5LE+dLGK097hR0aTNVFOc0kxND+l8WuwSG0q8nhVN3ejo0cexN+VyJ3jtXZ+jsgPNMfVUJ6/VelkAGJJqw4ghyYCO7vFaXsQI7RCtl9dTBLMlGuqsH0pvC8FigXX4kGRN1h/rrQGt3APHrq0eOLEWcTRz8uRJjBkz5nNf9/v98HiUn5SsWrUKI0aMgN1ux5w5c7Bt2zbFf6ae6fUDT4upuwhp9KSXD7zQhjUGgwZvyHI6X4cu0vnE9TkyOwWZKdpKNQWAKUXpMBsNaO5yoaZN++l8Fc3a7BIrZKZY5aCmXAfH3rR1u1Gh0fpjnBrU6OAz1O+X5DTO6Ro6HjCUWKwq00k2mwgSp2twEQM6DGq02rNFKNVZyZPICtXiIjBC5sa7qvVxVGDoHFSLi0KxEnHQPWnSJHzyySef+/prr72G0tLSwY7rrF5++WWsWLECK1euxM6dO1FSUoLFixejsbFR0Z+rZ+IGopcaJa12NRXEzmxFczfadNDIQotdd0ONzkmFw2ZGr8eHQzqok9dyPTcA2C0mTCwIpPPpISVaZIxorUtsKD0FiXL9cY726o8FPZWUHG/pRkevBzazNheFAKB0uKjr1v7r6fb6sa+2Ewi5l2qNuD71csyVVpuoCeLz80BtJ1xen9rDOaf+cidtvp7j8x2wmY3o7PPKC6xa1r8opM33e6xEPLt54IEH8O1vfxu/+MUv4Pf78frrr+PrX/86fvazn+GBBx6I7ihP8cQTT+DrX/86br/9dkyaNAlPPfUUkpOT8ec//1nRn6tn4tgbPdQo9bi9OFQfvCFr9A2aGXLsjR5qlESXWK3u0hiNhv7mXzqY5Gg51VSQJ416CLo1nFou6OmYlv5FIe2/nnrY+RKB19SidM0uCs0MuT61fqrGgbpOuL1+ZCZbMDyYQaI1okO0HhbWO3o8OCaXO2nzPT8sKxlZKVa4fX7sDy64aJXfL2n2yFrBEnJUoC7uSdXaXhSKlYjvHtdeey3++c9/4sMPP0RKSgoeeOABHDhwAP/85z+xaNGi6I4yhNvtxo4dO7Bw4UL5a0ajEQsXLsSWLVsU+7l6Fwhq9DHJ2VPTAb8E5KfZkZ+unaODTqWXuu7mLheqW3thMADTitPVHs4Z6aUEItBZX7tN1AQ97cxqfVcBOquT1/quF0KCmuM6CGq0enxlKHGqRpfLiyON2l5YF9enVsudIBbWswML61ovKRHjGzEkENhqkcEQWlKi7dfzaFMXnH1eJGvwuMVQernHD+iBM1S7n6GxMKgl20suuQQffPABGhsb0dPTg40bN+KKK66I3uhOo7m5GT6fD3l5eQO+npeXh/r6+tN+j8vlQmdn54A/iahUJ29QPewiQkfHtIhdmjE5qUizW9Qezhn173xp+/WsaO6W64/Ha/iGLF7PvbWBXSWt6uzr7xI7Q8NdTScWpMFqNqK9x4MTLT1qD+eMBu7SaPczND3ZgtHBbCGt79Ro+aQCYcCpGhpfCC7XeH28oJfsqzIdLAJDR6dAiHruaRpt5CvoJftKjG+URnvgxFLEV1N1dTVqamrkv2/btg333HMPnn766WiNLWoeffRRpKeny3+Ki4vVHpIq9FKjpOWupqFEM7VdGk/n00taT2iHaC0feyMmONOKtFt/jOCuR0ayBW6vHwfqtLvQWF7VDkkKpB9qsUusYDUbMUUce6PhhbaK5sAujRaPWzyVHppV9bp9OFgX2DnWatMvQS8LwXpZWNfD9QkdNFET5EUMjS+s66HcCSFzpoP1TvS6tVsnL/do0vj1GQsRzxhvuukmrFu3DgBQX1+PhQsXYtu2bfjRj36Ehx56KJpjHCA7OxsmkwkNDQ0Dvt7Q0ID8/PzTfs/999+Pjo4O+U91dbVi49MyOajReDqfHnYVAGBsrgOpNjO63T5NH3ujl12FzBQrRmZrf+dLLxPG0HQ+Lb+eekgtF/SwsyAaaWl9lwY66Wi8t7YDXr+EXIcNhRoud0LIQrCWg+7Wbjcqg5kiJRpfWA/dmdVqh+gBmS0av8eXFGfAYACqW3vR3OVSezhntFM+blHbr2dBuh15aTb4/BL2nOxQezhnVKbx+vhYiviOvHfvXsyePRsA8Morr2Dq1KnYvHkz/v73v+P555+P5hgHsFqtmDlzJtauXSt/ze/3Y+3atZg7d+5pv8dmsyEtLW3An0SUkdzf/EurNUp1Hb1o6HTBZDRgapF2648RTOcTQc0OjU5yfH4Ju6oDH8ZazxyATuq69bKrAJ3UfO0QR7NoOLVc0ENNop66xIogobxKu0FNucaPWwwln6rRpN2FddHUc1RO4Kx2LZuQ74DdYoSzz4uK5i61h3NaeuisL6TZLfIZzVrNuGzvceNosNxJ6/f4gXXy2rzHD+iBo4M5qNIiDro9Hg9stkAq4IcffohrrrkGADBhwgTU1dVFb4SnsWLFCjzzzDN44YUXcODAAXzrW99Cd3c3br/9dkV/bjwQN2WtThrFuCbkO5BkNak9nHMSu3NaPRv1WFMXulyBhiDj8lLVHs45Tdf4zle3q7+zvtYzB6CDndnQXRqt7yogZBJ2oK4TfR5tpvPpoYmaMC4vFclWE5wuL441aTOo0UvmFU5p/qXVFN5yHXTWF8wmI6YViewBbX6Glumgs34ordd1i7nHyOwUDNFwuZOg9Xt8aA8cLTeli5WI36GTJ0/GU089hU8++QQffPABrrzySgBAbW0thgwZEs0xfs6yZcvw+OOP44EHHsD06dNRXl6ONWvWfK65Gn1ef2MQjd6QddAlNlT/2ajafD3Fv/PUIu2nmmLAzlebJne+dgc76xeka7uzviA6hZ5o6UGrBne+9NIlVijKSEJ2qg1ev4S9Gkzn63J5cTh4zr0edhXMJqOc0aTVhWC99BgRSjV+qoYIavRS36n18+T1tMgGHdR1iw0U3byeGs++knvgDM3QxRxUaRG/Ar/4xS/wxz/+EZdddhluvPFGlJSUAADefvttOe1cSd/+9rdRWVkJl8uFTz/9FHPmzFH8Z8YDrdco6W2CMyMYJJ5o6UGLBmuUtH7W5KkmFATS+To1ms63U2cTnPRki7zztUuDK+F66RIraL1OfndNO/xSYHEgN037i0LQ+KkFDZ19qO3og9EA+UxcrdNyXffA+mN9fIaWanyjYqeOykkQMrfbXd2hyTmoXuq5halF6TAagPrOPtR39Kk9nM/RSw+cWIloliNJEkaNGoWqqio0Nzfjz3/+s/z/7rzzTjz11FPRHCNFkZZrlDw+P3af1NcNJPTYGy2uNJbpbBHDYjJiWnB3docGU/ZFkKiXGzI0nrKvly6xobTc/EtP/QYELe8kijGNy3MgxWZWezjnRbyXtHiqRkVzN5w6SzUVvSYONTjR2edRezgDOPs8crnTTB30xACA8XkOJFm0WVLi01m5EwCk2MwYnx/oU1WuwYXLMh2Vk8RCxEH3mDFjUF9fj8zMgS/kiBEjkJubG63xUZSZQ4IardUoHap3os/jh8Nulnfn9ECrx7R0h6aa6mgSPis4edh+Qluvp98vyQ3zZo3IUns4561Uw41W9LargNBsIY19fkJnTdQE8XoeanCiy+VVezgD6OG881ONy9PuqRqhxy3qIbMFAHIddgzLSoYkaW9hqLw6kNkyNDMJeTrJbDGbjJg6VJslJUcaA59BKVYTxutkUQgaTjEP7YGjp89QJUX0qWc0GjF27Fi0tLREf0SkOK3uLJSF1HMbjdruEhtqhkbrukX9cWG6XTc3ZISs2Gttp7uiuQvtPYEusZMK9HMCQmnIzpeW0vk6ejy66RIbalrw2JuT7b1o7NROOp8kSfJOh55ez9w0O4oykiBJwG6NZQ/I9bI62qUxGQ0oKQ4ENVq7J5XrrJ5bkO9JJ1rVHsoAYmFaL7vcglazhUQfhJLiDJh0NAfV6usp5qBFGfpZFFJaxEuNjz32GL73ve9h79690R0RKa6/g7nGbshV+qr1EvrT+Trg9fnVHo5M1EjqdYJT0dytqTp5McEpKc6A1ayPXRoAGJ/vgM0s6uS71R6OTFyfI4Yk66JLrJBqM2NcbmAXREuTnJq2XjR3uWE1GTG5UD+LQtDopNHr88tn3+rtM1Sr2Vd6K3cSxD1pu8YWgsXC9Cy9Bd0azb7SY7kTQl7PPTWcg2pdxDPH2267Ddu2bUNJSQmSkpKQlZU14A9pl5jgHNZYOp+ejmYJNTY3FQ6bGb0eHw5qKJ1PT0ezhMpItmJMbuB4My2VQGzX6QQnUCcf2PnSUvMvPaaWC+IzVFuvZ+D6nFSYBptZ+8cthpKbqWloEn64oQs9bh8cNjPG5Gj/uMVQIvtKS9lsPW4vDumw3AkAZo3oP5ZJK0GN1+eX3y8zh+trzi3e74cbnOjW0BxUDrqH6+v6HJ3TPwcV7zEtKNPpRpqSIu4M8uSTT0Z3JBQzecF0vpPtvdhd0455o7PVHhI6ejyoaArswpXo7A1qNBowfVgGPjnSjLKqNkwpUr/LrSRJujuaJdSs4Zk42tiF7ZWtWDRJG0cBiiZqYgKmJ9OLM/DZiTbsrGrDf8wcqvZwgNDUXZ0tYiD4eq7+rFpTQaIem6gJoSVPkiTBYFA/tVMsqEwrTtdVuRNCTtU43tyN1m43slKsag8Je2o64PNLyEuzoSA9Se3hhGVcrgMOuxnOPi8O1js1cY8/1OBEd3BRSE/1xwjOQQvS7ajr6MMujcxB23vc8hxUbxsVRqMBJcUZ2Hi0GWVV7ZhcqP71KUmSLnuMKC3ioHv58uXRHQnF1PRhGTjZ3ouyKm184O2qCbw5hw9J1sQEIVwzhmXikyPN2FnVjlvnqj0aoLKlB01OF6wh5+DqyczhmVj9WTV2aKSZWkuXS07N1uPO7MzhWXjmk+PYrpGaRL9fkjMxZugwSBQLWbuDgYQW6v/KdHY8YKjJhWmwmoxo6XajurUXw4Ykqz0kuT5eb6nQCDlV41hTN8qq2vCFieovXH4W/OyZpbNdWQSDmhnDMrH+cBO2n2jVRNAtUsunD9NX/bEwc3gm3tldh+0n2jQxBxUB4qjsFGTqcA46PRh0l1e345YLh6s9nGC5kwsWk0F35U5KGlRh4rFjx/DjH/8YN954IxobGwEA//rXv7Bv375ojY8UUqqxbod6T0PRWjO1bcEJzrSh6bBb9JVqipAaut0nO+Dy+tQejjzBGZObioxk/d2QLxgh0vm60NbtVns4ONLYBafoEpunr10aABib60CK1YQet08+IUBNfR4f9tcG6o/1+BlqM5swKTgx08p53Xo/6kZrdd3bgguoF+gwUwgarOvWaxM1YfbIwOLLZxpZCO5PLdfn66m18+TFIvCkQn3OQZUScdC9fv16TJ06FZ9++ilef/11dHUFutDu2rULK1eujOYYSQFiN6S8ug2SpH5HYz3vKiBk3JUtPWjWQPOvz44HbmQXjNTfrgIAjMxOwZAUK9xeP/YGmxmpSa8Na4QhqTb5PHktTBrFBKekWD9HB4UyGQ3y0YtaqOveV9sJj09CdqoNQzP1lboraOlUjc4+D44GzxDWY3kOQheCK9V/Pb0+v1yeo9d70iyNnarRf0/S5+t5QfDYzR2VbZqok9drEzVBzEGPNXWjo1f98+T7T37Q5+enUiKe7dx333145JFH8MEHH8Bq7d/5WbBgAbZu3Rqt8ZFCJhemwWIyoLnLjZq2XlXHEjjqRr+pkQCQnmTB2GDzLy1MGsVO92wdnScdymAwyJNGLUxyRKCq110FhOwsbDuu/lGPYgKu1wkONLazIE9whmVooh46Elpqpra7ugOSBBRnJSFbR531Q8mnatSo3/zrQF2gaavDZsaEfH2mmoo07rqOPtS2qztnquvoxcn2XhgN+l0UGp/nQJrdjB63D/tqO1Udiy+03ElnTdSEIak2DMsKlOXs0sBCsJ57jCgp4qB7z549+PKXv/y5r+fm5qK5uXmw4yKF2S0mTCrUxlmelS09aOvxwGo2YqKOzj8+lZjkqB0kNnb2obKlBwYDMFOnqXwI2VnYrnJdd5/Hhz01gd32WTpdxEBo0K2BOvkdOu0SG0rsLGhhp7u/nlu/r6fYEdlX24k+j7olJf2ZV/r9/BSnavS41T9VQywCzxqRqcv6YwBItpoxKTg/UTtbSNwTJxakIdUWcWsmVRmNBnm3W+0U80P1gaZ0qTYzxubqr9xJ0Mo9yeX1YX9wIUXPC+tKiDjozsjIQF1d3ee+XlZWhqKiosGOi2JAK3XdIuifXJimq/OPTyUCCLUXMcQEZ2J+GtLsFlXHMhiiS/iOSnVLIPbVdsDt82NIihUjNNDgKVJigrPvZAd63Ood06LnLrGhxA7TkcYu1dP59Ho8YKihmYFdZa9fwr5adUtKdur0POlQ4lQNaCB7QO/lToLIdNqhcpCo93In4QI5+0rd11PM2aYX67MpnSAWXdXe+NlX2wm3z4/sVKtuy52UEnGE85//+Z/4wQ9+gPr6ehgMBvj9fmzatAnf/e53cdttt0V3lKQIOT1S5VWxrRWBdFe9pkILYkVvd007PCqm84kJzmydT3CmFKXLHY1PtPSoNo7QhjV6Td0FgKGZyShMt8Prl1RdaNN7l1gh12HHiCHJkKT+95waGjr75FRTcR67HhkMBk3UdXt9/v7PUJ3fk0rlZmrqvZ6SJMk7mXp/PcVCsNo73SKomqnz1zN0p1vNhfX+em79LrJBQ3XyZfKipb7nTEqIOOj++c9/jgkTJqC4uBhdXV2YNGkSLr30UsybNw8//vGPoztKUoQIEvfXdqiazre1InBDvnD0ENXGEA2jc1KRZjejz+PHwTr10vk+FbsKOr8h28wmTA0GEWoedRUP9dyC2Fn4VMUgcadcf6z/13Nu8DNLLByqQUxwxuenIUWnqaaCFoLu/XWdcLq8cNjNckd1vRJBhJrZV8eautHS7YbVbJQ/z/VK3AMO1HWiy6VOtlC3y4v9dZ0DxqNXU4vSYbcY0dbjwdHGLtXGIdcf6/z1nFiQhjS7GV0uL/aqWCcf2mOEBoo46LZarXjmmWdw7NgxvPPOO/jb3/6GgwcP4q9//StMJraH14NAOp8VHp+kWiOLk+29qGrtgSmkvkevAul86h7T0tHrwaHgEUYXjNT3DQQh6XNqvZ6SJMlNv2bpuD5ekI9p0UDQred6buHCUYGge4uaQXd1/ExwRHq8munQW44F/i3njMzSdaopQl5PNU/VELvcpcUZsJn1PTcsSE9CUUYS/JJ6zap2VbfD55dQkG5HUYa+U3etZqN8jW5TaWG9tduN482BcqcZOi7PQfBUjdkjg/ekY+ovBMfDPSnaIg66N27cCAAYNmwYvvjFL+KGG27A2LFjozk2UpjBYJAbxag1ydka/GCYWpSu24YgodTeWdhR2QpJChy5leuwqzKGaJqpcjO14839uzRTivS9S4OQ9M6y6ja4vbFPPxvQJTYedrqDQff+uk509KhT191/nrT+JzjThqbDaABqO/pQ39GnyhhE1oJYUNGz9GQLxqh8qka8lDsJat+T4inzCiHZV2otBIu57+icFKQn67cHjqB29lXjgHIn/d+Toi3ioHvBggUYOXIkfvjDH2L//v3RHRXFjNp13VviaIKDkEBCraB72/HgWahxsCuLkInFkcYutPe4Y/7zRe3ctKJ03e/SAMCY3FRkJlvQ5/FjrwrNqg439HeJHZen3y6xQm6aHaNyUiBJwKcqHMXm9fmxuyZ+dhVSbGaMDx4pJTqIx5LX58dnwWAqfu5J6i4Eix1MvWeyCf113eoEifHSRE2YLdd1q3N96v187lOJheDPTrSq0ltIxBLj8hxxsZEWbREH3bW1tfif//kfrF+/HlOmTMH06dPxq1/9CjU1NdEdISlKTNS2q9TIQqzGzdV5PbcwfVgGDAagurUXTc7Yp/N9FmcTnCGpNozKTgFUmjT2N6yJjxuywWCQjz1TY2dB/BuWFKfrPnVXEMGZ6E0RS4HjtfxIs5sxKjs15j9fCeKeJBYQY2lvbaBWNz3JIh8PpXdi4XKnCs2/att7UdMW2PWaESdBong9y6oCad6x5PdL8meono+vDFUaPP/8ZHsvatpi3zB1Z6U4nzs+rs8J+Q5kJFvQ4/Zhz8nYL6yL/jvxsAishIiD7uzsbHz729/Gpk2bcOzYMXzlK1/BCy+8gBEjRmDBggXRHSUpZsawTFjNRjR0umLeyKK6tQc1bb0wGw1xs2qbZrdgXPCcx1gHiX0en7zrNWdkfCxiIPSYFhUmjdvlXYX4mOAgWKsKlY5pEROcmXGyq4CQnQU16ro3Hm0GgoG/MU4WMcTruSn4u8WSqIOcPTIrbl7P/lM1OmLe0VgsAk+Jk/IxAJiQn4YUqwldLi8ON8S2YerhRiecfV4kW02YkK//TCEEs1tE6Vasz+v2+vzYFZwzxUu6vtFokO/xatR1f3Ik8Lk9d3R2zH+2HkTlUOSRI0fivvvuw2OPPYapU6di/fr10XhaigG7xSSn94g3S6yISeq0oem677obSq3zusuq2uHxSchLs6E4S98NVkKpVUPX3uOWF6L0fpRIKJEFsb2yDf4Y79TIXU3jZIIDAHNGBV7Pg/WdMS+B+ORIEwDgkrHxM8G5aEw2DAbgUIMTjZ2xresW96S5cZJajpBTNXo9Physj22QuC1OTtIIZTIa5JMXYn10mLgHTi/OgNkUlem7JswOZpLFOrvlUIMTPW4fHHYzxuTER6YQBmRfxTbobnK65M+Yi+IkezXaBv2u3bRpE+666y4UFBTgpptuwpQpU/Duu+9GZ3QUExcHJ2wbY7yzEG+p5YK4IZdVxrZOPjS1PJ7ORhQ1dLtifP652FkflZ2CIam2mP1cpU0uTEOy1YSOXg8ON8ZuEt7W7UZFnHSJDZXrsGNMbiokKbYp5j1ur3yNXjw2J2Y/V2lZKVZMDh7VFct7ksfnl1Mj4+mepOapGvFW7iTI2Vcx3pmNt3puIfS87ljaKZ8nnRE3mS0I+fzafiK2DVNFdtLkwrS4mjNFU8RB9/3334+RI0diwYIFqKqqwm9/+1vU19fjr3/9K6688srojpIUdfGYQNC9taIlZm9QSZLkzuXx0rBGkNP5TsY2SBQ3rHjpEiuMyk5FRrD5VyyPtou3LrGC2WSUr9FY1nWLo63ipUtsqAuDu92x3Fn49HgrPD4JRRlJGDEkOWY/NxYuHhNYRNgYw+yr3TUd6HH7kJlswfg4aPIXSm6mFsOd2bZuNw43BDKF4qWxp9DfTC3GO93B5m0z42wRQwTdRxu70BLDo+3KKuOriZowLteBzGQLej0+7DkZu80fkS17cRxlXkVbxEH3hg0b8L3vfQ8nT57EO++8gxtvvBHJyfF1408UkwrSMCTFih63L2ZHh1W39qK2ow8WkyHugppR2SlITwoEiftjFCR6fX55FTzegm6j0SDXAG+P4Ur4jjg6n/tU4hr5NIZB9444neAAwNxR/QuXsSIC0kvGZsdVZgtC0uU3Hm2OWYNP8W83Z2T81McL4j23I4Y73WIReExuatztepUOy4TRANS09aIhRiUQjZ19qG7thcEQf02qMlOsGJcXSO+OZRdz8X6IlyZqgtFokDezYlXXLUkSNh4NljuNiZ/Mq2iLOOgWaeXZ2VzR0Duj0YB5Y2KbYr6lIvBzSoZmINkaP/XcCL6eF8h18k0x+Zn7ajvR4/YhPam/kVs8Ed3DY5Ue6fb6sataNFiJr0UMnJLOF6ugRqyCXxBni0IYUNftRGt3bOq6N8bxrsLM4ZmwmY1odLrk3VKl9Z/PHX/XZ+mwDJiNBlS39uJEsMRDafGaWg4AqTYzJgSPtotVg0/xc8bnOZBmj69MIaiQYl7V0oPKlh6YjYa4W8TAgPO6Y/N6Hm3sQkOnCzazMS43KqJlUDXdR44cwdNPP41HHnkEDz300IA/pC+XBIPuWDVTEx8E8VQ7F+ryCYGVvnWHYhN0ixvVrOGZcbdLg5Du4dtPtMUkSNxX2wGX14+MZAtG56Qo/vNirXRYBiwmAxo6Xahu7VX85zU5XdhdEzi+5LLx8bcKnp1qk3dqPo3BbndjZx8ONThhMAAXxWGXWLvFJGdjxGLh0u31y02q4rHrrsNukYOadYcaY/Izt50QmVfxOQGXU8xjtDO7PY4zrxCSfRWroFu8D2aNyIzLRQyx0729shUur0/xnydih9kjs2C3mBT/eXoVcdD9zDPPYOLEiXjggQfw2muv4Y033pD/vPnmm9EdJSlO7JbsrmlHR49H0Z8lSZKc8hJv9dzC5eNzgWC35rYY7HzJXWLjcBcRwQ73FpMBjU4XatqUDxLl87mHZcZd6i6CQc3U4DEt22Iwyfk4OMGZNjQduQ674j9PDXNj2DFWZCRNKUxHZopV8Z+nhkti2OBzd007ej0+ZKVYMTY3froYh1owIXBP+uig8kF3t8uLfcEzguNxpxsDjrKMTZAYrz1GBHGd7KvtRJfLq/jPE+8D8b6IN2NzUzEkxYo+j19e8FaS+JwWPaLo9CIOuh955BH87Gc/Q319PcrLy1FWVib/2blzZ3RHSYorzEjCqJwU+CXlz5s90dKD+s4+WEMaOsWbwowkTMh3wC8B6w8ru1Pj90tx20RNsFtMmFwYCBK3x2CSI3YvZsbprgIAzA6e5b7tuPJBothVuGx8fE5wELKAGIvzuuM5tVwQzdQ+rWhVvMFn/yJw/JzPfSqRffVpRSu6FQ5qyqra4fUHmvwNzYzPXj8i+N1X24let7I7ib1un7yIMSsOy50QnDMNzUyCzy8p3vCvx+2VP6cvj9N7ksEQu7put9cvLzbH8z0pGiIOutva2vCVr3wluqMhVV0i13UrGySKN+f04gwkWeM3DeXyGO0sHGvqQluPB3aLEVOCgWk8mhWj87olSZIbrMTrBAchaZ9KN67x+Pz45HAgSIzXXQUAmBOc4Bxu6EKzgh14Aw1rgk3U4nhXYUK+A9mpVvR6fIr3cth6PL4zrxA8r7s4Kwlun18+2kcp2+R67vhdtCzKSEJ+mh1ev4TyamU7RO+uCSxi5DpsGJqZpOjPUtPsGNV1bz4aOKlnaGYSxsRpZgsAXDg6NkF3WVUbetw+DEmxYmKw1wGdXsRB91e+8hW8//770R0NqUqc9ar0MS3yrkKc1nMLIsBYf7gJPr9ydchiglNanAmreVBtGjTtArnGU9mOxgfrnWhyumA1GzFtaPwuYswcngWDATje3I1Gp3IdeLefaIPT5cWQFCumFcXv65mVYsWE/EATw08VbF5zuKELjc5Aw5p467obymg04CKxEKzgPcnl9fXXc8dx0G0wGLAguKundK+Rz+K83AnB1/OCGPUd2BB8/gtGZsVluZMgXs9tCp+qITKvFkzIjevXc26wKeTOqjb0eZTLxhCLwPPGZMdtplC0RDxDHzNmDH7yk5/gv/7rv/DrX/8a//u//zvgD+nPhaOyYDIacKKlB9WtPYr8DEmS4rpLbKjS4gykJ1nQ0etR9Ci2RJjgIFjjabcYUdXagwN1TsV+zpq99QCAS8fmxHVDkPSk/vOIlcweEBOc+eNz4v6G3J9irlyQKCb4idCwRtQHfqLgzuyu6kDTxOxUa1zvegHAZcGF4I8PNSq2cOn2+lFWHWyiFqf13MKiSXlA8J6h5EKwuCddEfx58UrUdZdXtyvW/EuSJKwLZh/Ga2q5MDonFdmpNri8fkWzMUQTtXjOvIqWiIPup59+GqmpqVi/fj3+7//+D7/5zW/kP08++WR0R0kx4bBbUFocODpBqeY1Fc3daAzuIsZrPbdgNhlx6bhA9oCSKeZiVXhOnAfdyVYz5gdfzzV76xT7OWKCc9WUfMV+hlbMicHOQrw3rAl14Sjlj2mRU8sToHbukmD21R4FG3yKzKs5o4bE9a4Xgjv5dosRdR19ii1c7jnZgT6PH1kp8b+IsWBCLqwmIyqau3GkUZmj7Y40OHGsqRtWkzHuP0NH56RgSIoVLq8fexRq/nWowYnajj7YLca4PT1HCNR1B+7xSjX47OjxYHdNIKBnPfe5RRx0Hz9+/Ix/KioqojtKihnxplEqnU+88UuLM+J+lwYAFkxQNuiuaetBbUdf3J41eaorg4Hwmn31ijx/RVMXDjU4YTYasHBifO8qIAbpfNWtPTja2AWT0SAHUPHswlGBlP2jjV2KpOy7vD45dV00Gotn+el2jMlNhV8CNh9T9p4Uz/Xcgt1iko+YU+rosNDjK+N9ESPVZpYXv8RibbSJ571ozBA44vBoq1AGg0He7VbqVA0xF5s3Ojsh5qBzFa7r3lLRDL8EjMpJQWFG/PYbiJb4LQCliIgbyKZjzYrUIYs3fryvMArzx+XCYAjUCdd1RP+oKzHBmVyUjmSrOerPrzULJuTBYjLgcEMXjjVFf2dBBPNzRw9BenJ8T3AQkv55oL4TnX3R30mUz0Idnon0pPh/PTOS+xvJKFHXXVYVONoqO7W/fjzeKZli3ufxyU0T47meO5Ro8LlOoYVgUe4UrydpnEosBP9LoaD7X3LmVYEiz681YiH4M4UWgj8+GCjPuTzOswYE8blWVt2uSF13IjT1jKawZukrVqzAww8/jJSUFKxYseKsj33iiScGOzZSQcnQDDhsZrT3eLCvtgPThkZv9zRQzx34IE2EXQUEmytNL85AWVU71h1swk1zhkX1+d/f1wAk0IQxPcmCeaOzsf5wE9bsrcfdl4+J6vP/OzjBuTIBUssBIDfNjlE5Kaho6sbaAw34cunQqD6/2FVIlAkOgp9t++s6saWiBVeXFEb1uUUG0kUJ1LDmkrHZeH7zCUWyr8qq2uH2+pHjsGF0TkrUn1+LxHtxZ1Ub2rrdUT3nvcvlxaZgRkKi3OMXTsyDyWjAgbpOVLZ0Y/iQ6F1HVS092F/XCaMBWBjn9dyCmMtsPtaCzj4P0qK4u9/R45EX2S4fH/+ZQgAwMjsFuQ4bGp0u7Kxqw7zR0Q2O+4+vTIzXc7DC2ukuKyuDx+OR//tMf8rLy5UaLynMbDLKXcU/ifIk51hT4Cgdm9mI6cXxnwotiI6x0U4x7+jxYO2BwHNeE+XJvZbJKeZR3lk42d6LXTUdMBj6G+QkAnHtvL7zZFSft9ftkzNb4r0WMZTI4lGihk7s9l6cQLsKc0YNgdloQFVrD6paotvgMzS1PN5ToYWijCSMz3PAL/V3xY6Wf+2pQ5/Hj1E5KZhcmBhHB2WmWOW62Wjfk9bsC/QumTNyCLKiuDiiZRMLHBiTmwqX1481e6L7eq4/EjhJZlxeatyeH38qg8EQck+KbvZAdWsPTrT0wGQ0xH1j5GgJK+het24dMjIy5P8+05+PPvpIqfFSDFyiUF23mIDPGJaZELU0gthZ2HS0OarpPe/uqYPb58eEfAcmJcgEB8GOsUZDoGFPTVv0JuFil/uC4VnIddij9rxa9+XSIiB4fTZ2Rq8OefOxZri8fhRlJGFsnDdUCjV7RKCuu6KpGw1RfD07ejzYE2xYkwj18UKqzSw33fzkaHSDxC0JcpLGqcQ9KdoLwW+UBRburistSphFDAC4Mpj6He1eI3JTz6mJkXmFYJAo7kmvl9VE9bnXJWDmFUIbfEa5rluklpcWZ8R9v4FoYU03fY7YRdlR2YZed/SCRLHKlij13MLkwjTkOmzo9fii2rDqjeANSdygEkV2qk1uthLNnQXxXIsTJLVcGD4kBTOHZ8IvAW+V10bteRPlLNRTpSdb5F2+aO52bz4WaFgzJjcV+emJsyiEkAafm6JY193n8aG8KrCIkSjlOYLIPFl/uClqvVvqOnrlRYxrpyfWPWnxpDwYDIFyhWj1bqnv6MPO4PV5xaTEuictDc5ptla04mR7dF5Pn1/C+sOBRbsFcX5U2KnE51t5dXtU5/T9qeWJk3k1WAy66XNGZqegKCMJbp8/ah0k3V6/3H02UWq9BIPBIJ8HGa2dherWHnx2og0GQ+JNcBBynNe/o7Sz0OR04bPKwLWeKPXcofp3FqKTYh44C1U0rEmcXVnhwpGBz7j1h6K3M5uIqeVCf9DdErUgcUtFC9w+P3IdNozMTox6bmHGsAyk2QO9W8qDZ2oP1ptltZCkQAO14qzESN0VctPsmBnMxhB9Vgbr/f2Be9uMYRkJt8hWlJEkZ5+8GaV70q6adrR2u+GwmzFjeHwfV3uq4UOSkZ9mh9vnx5aK6Cxc+vyS3L8hEY6vjBYG3fQ5BoNBnthtjFLN17/21qGtx4Nchy0hjrY6ldwx9lAjJGnwk0aRxnfR6OyEuyEjZDd6e2VbVI5men9/PSQJmDY0HUUJeOzFl6YVwGoy4kBdJw7Wdw76+Q43dOFkey9sZiPmjkq8G7JIB313Tx3aut1ReU6xq5CIE5xpRelw2M3o6PVg78nonN/7961VQHABL5EyMRDs3XLpuOgdZylJkpx5dV2CZV4J/V3M66LyfP/ak1hNPU91XbCp5xtlJ6MyZxKp5ZeOy4HFlFihj8FgkK+jFz+tispz7qvtQHuPBw6bGSVRbLgc7xLryqPzJnYWotVM7S9bKgEAN88ZnnAfeAi+nhaTAZUtPaho7h7UcwUmOIGgO9FSy4WC9CRML86AJEVnZ2FNgnUtP1VGslXekX4jCg3V+s9CHYIka+L0bxBmDMvE5MI0uLx+vLqjetDPV9XSg6rWHpiNBsxJsEwhBIPEecGypI1RSDGvbu3BRwcDnxu3zh0x6OfTowVyXffgF9b31XbicEMXrGYjrpqaGEdbnWrx5MC9Y9vxVrR0uQb1XK3dbnx6PJCqf+XkxHw9r5qaD5vZiKONXdh7cvALweKelGip5cKtc4cDANYebER16+B74YjY4MLRQ2BOwDl9pPhK0WldNCZbPl+6yTm4G8jekx3YUdkGi8mAG+cUR22MepJqM2NOMOV0sOejlle343hzN5IspoQNEhESIA82xbyjxyM3+btycuK+nuK4sDfLTw46hTe0njsRGQwGLA8Gc3/dWjno11M0EJsxLBOptrBO+owb4kiaT6KQffX3T6vglwKp+mMSqMlfqPnjcmAwAAfqOlHfMbhsIbEIvGhiHtKTErOhUnFWMqYUpcEvAR8eGNxC8If7G+CXgEkFaRg2JLFS9QWH3SKfIjLYhmoNnX3YV9sJgwGYnyBHhZ1qdE4qLhmbDUkC/vZp5aCfL5EzrwaDQTedVlaKVW4GJHYEIvWXLScAAFdNKUiortCnuiz4YS8CkkiJCc7iyXlISdAJOEIC5C3HWtDeE3kK74cHGuD1Sxif58ConMScgCNYe52eZEFDp0tehIhER48HOyoDdaKXJeiuAgBcM70QGckWVLf24uNBvuc/Ch4NmMgNay4JafA5mJT9Po8PL38WSLG8Lbj7k4iGpNrktNDB3JO8Pr/cgDFRM6+Eq4JdzP81yAafIkX9qgReVAeA62YErqd/7qqF1+eP+HnE5++0oRnITrVFbXx6IxaCX/6selAn6bT3uOV7fCL2GBkMBt10RkumBs7v/eP6iog/8Np73PINOZEnOAjZ9dt2vBVdLm9Ez+H2+vHPXcEJzoyhUR2f3ozITsGEfAe8fgkfHoh80iiOeUm0ruWnsplN+NK0wKRxMDsLG4JnoY7NTU24hkqh7BYTbpgVyOx5YUvkOwv7azux9mAjDIbEnoQPH5KMyYVp8PgkPLuxIuLneWd3oL9IUUYSvjAxL6pj1JsFUTg6bOPRZjR3uZCVYk3YXURBpJhvOtqMzj5PRM/R2efBpqPBzKsEfr8jeDTikBQrmrvcgyp1TPTUcuHyCbkoykhCe48Hb++K/KSSZz85DrfPj4kFaQnXhHKwGHTTGd06dzgyky2oaO6O+CihV7ZXw+X1Y1JBGmYmWMfIU43KScWIIcnw+KSIG9StP9yEth4Pchw2XJRgR6+djpiUrImweU23y4sNwWNEEjm1XBA7VWv21qPHHdnCkCifSNTU8lC3zBkOgwHYcLgJxyPs5fDkh4cBAEumFmBsniPKI9QPg8GA73xhLADg+U0n0BrBbrckSXhhcyDz6uYLh8FkTKwGaqcS79FNR5vh8ka28yUyr66eVpCQ/VpCjclNxZjcVHh8kpydEq51Bxvh9vkxKiclYUsfBIvJiKtLAps/kZ6s4fL65FToRL8nmYwGubb7L1tORNSgrrXbjec2HQcAfOcLYxOuCeVgJfYnJJ1Vqs2Mb8wfDQD434+OhL3b7fNL+OvWwA7P8nnD+eYMSbddF2HzGtEh9tqSQjavCEnn23CkOaLsgY8PNcHl9WP4kGRMLEjcgEaYOTwTw7KS0eP2RdSgzu+X8HFwESORU8uFYUOS5d2Vv0aw2733ZAfe398AgwG4Z+FYBUaoL4sm5WFKURq63T48vSH83e7y6nbsOdkBq9mIZbMSs79IqEkFachx2NDj9mHb8fCPB+1yeeWeGomeeSVcJS8ER5ZiLr4vEbvqn45YCH5/Xz2cEWQPbD/Rhm63D9mpNrlkMpEtm1UMm9mIvSc7UVbdHvb3P/NJBbrdPkwuTMPiyYmdKRQJztrprG6bOxxDUqyobOkJe6Vx/eFGVLf2Ij3JgmtKErvWS/jCxMAE/N09dWE3r+no9chp1F+ewdcTAMblpWJkdgrcXn9EDepE7dyVkznBQXA3cekgzux+a9dJ+SzUWSMSO7NFEDsLr+6oDjt7QOxyX1NSiDG5XBQyGAy4d+E4AMALm0+gOcwu0WLh40vTCjAkgWs7BaPRIC8K/Xnj8bB3vtbsrUefx49R2SkoGZqu0Cj1RaSYf3y4Mez3e6/bh48PicyrxOxafqppQ9MxKicFLq8/7Fp5SZLw542BXdnLx+fAmOCZLQCQmWKVswf+Esz6OV8tXS45U+ieheM4Z4oAg246q2SrGd8M7nb/7qMj8ISx2/3C5sAE54ZZQxPy2KDTmTc6GyXFGehyefGTt/aGNcn51546uL1+jM9zYFIBV2xxyvmTa8LsYt7n8cmBeqLXzoUSOwsbjzSFdQZ6S5cLD/1zPwDgG5eOSvhUU+HSsTkYMSQZzj4v3iw7/zKd3TXt+PBAI4wG4L+/wF1uYcGEXJQMTUevx4c/rj923t/X3OXCO7sDi2zLE/SYsNP5+qUjYTUZse5QU9h1nm+GHF3JCXjA5MI0FGcloc/jl0uXztf6w03o9fhQlJGEKUW8xyN4jxdnv78Z5kLwO7vrsPZgIywmA75+6SiFRqg/4vPvvT31YZ1O9PSGCvS4fZhalI6FE5nJFgnOiuicbrlwOLJTbahu7cU/dpxfg6Xjzd1Yf7gJBkPg+ynAZDTgF9dPhdlowAf7G8JauRU7j1+ewQlOKFGLve5gY1gdOTceaUa324f8NLvcxZeAkdkpKB2WAb8EvB1GL4eH39mPth4PJuQ7cOeloxUdo54YjQb5LOhw6uh+80Fgl3vp9CKMTuCu+qcyGAy4Z1Fgt/uvWyvPe2Ho5c+q4fb5UVKcgZJivt+FMbkO3H35GADAg//cf9618vUdfdh0LFAruzTBu5aHMhgM8j0p3J1Z0ZvkSqaWD3Dt9MD1taWiBXUdvef1PW3dbvz07X0AgLsuG4NxCdwP41RTh6ajdFgG3D6/fJLDuTQ5XXgheBLRvYtYyx0pBt10TklWE751mdjtPgq399y73X8L1nJfPj4Xw4ewu2GoCflpuCv4ej7w1r7zOu6qurUH2463wmAArp1eGINR6se0oekoTLfj/7d372FR1mkfwL8zDAwjh+EoyBlP0IqggBAeVi0MrXU13V0zKzzs214btiK5bW1vor2VVluWZVabqe8mmbYRW/umecBxMxEBR9EQxIiDnAQchtNwmHneP8BJ5CBqwzMj3891cV3O8zx43X/cPPPcz+/+/X7NbXq8m144oN9padPj7a5rZ4d4su3sOldHFlIHOLKQnl+NL9TlkEqAjQtDYSPjV8u1fhPhA4W1Fc5XNgxo7uypkitIz78MK6kET3KUu4cZY90x0c8JunYD3jty47ndHXoDdl1dX2SI76LRmz/OGIWxHvaoa2rDi199P6DfSVNfgiAAUQEuQ3qXgt7M7lprZN/ZSpwe4LzZ06UaY7fWUN6loDe+LsMQFegCQcCAu4Ve/HceapvaMGa4PZ6YyZfA17s62v1xRsmA1mt6X3URuvbOl5YzuV7LLeOTEQ3Ikmg/DHeQ45KmBXuzS/u9trmtA3uyOq95lA84vUq4ZzRGuduhprEVL/9f3g2vT1N3Fj+TR7lihFIxCBFaDolEgtVdI1+bDxfik8z+39x26A148pMcnC7VQKmwxrIpbDW93q9CvWBtJcG5ci0Kqhr6vbaxtQPPfZ4LAFg2JRATOIrYg1JhbRwN/N8BLKi26eAFoKttl1uy9HTt3O5dJ4pRpe1/tPtgXjXK63VwsbPB/eM5V/Z6NjIpNi4MhUTS2VGlGkBbdOo1nVfUXbifE2YEuaO1w4DlO07ixxvsXFBc24TlO05C127AtDFuCPfjehjX++lFcNkNu4X+c+Ey/plTBknXS2C5jNMbrzdnvCdc7WxQqdXhwPf9L5pardUZF0VeHctR7tvBopsGxNbayjg6+87hwn63F0lTl6NB1wF/12GYPmZo79vZF7nMCq8sDAUA7Mkqw7HCvvegrG9ux2ddbf0PTuQKsb35baQv/nRPZ4vkc6m5OJTX+5eIIAh4Pu0cDuZVQy6TYlt8JDsxeuFsZ2NcfXz7sSIYDH0/5Pxtfz7K63XwcVbgqfvGDmKUluWxrheQ+89V9ruIYnZxHY4WdI5y/+kejnL3ZdoYN0T6O6O1w4CtR/qf2/2PjM62yIcm+cLWmg/gvQn3c8bSyZ0vIP/6eS6a+tkN4rvCGpyvbICNTMqXGL2QSCR45+FwhHg7orapDfHbM/tc9K+2sRXxH2WitqkN47wcsfWRCHZe9WLO+BGwkUlRUNVo3Me8N81tHfhraudL4PiYgCG/VW1f5DIrLI7yAwbwInir6iJaOwwI93PC9LF8pr8dLLppwB6K8oOnoy0q6nXYc7L30e5r90F99G5/fnn0IzLABY92zXd/9vNctLT1fJGhKriMuDeP4sfaZjjYyrjgVz9WzxqL30b4wCAACSk5OFVypcc173SNhEskwFsPTURkgIsosVqCq1sqfZJZike2nUDZleYe12QXXzHO83r5wfEYZiMb9DgtxV0jHBEV6IIOg4CUfroxNh3oHOX+TbgP/FzZttuXaztcUjJL+pzrWVjdgGOFtZBKgCVcX6Rfa+4LgreTApc0LXj9m4Ie59s6DHjjm3w8+lEm0NUGrVRYixCp+bOXy/DR0knwdVGguLYZK3ac7LGaeXNbB5bvzMKPtc3wcVZg+7JJsJfzHtobpcIa93c9/8Rvz8Tr3+T3OtXxjW8KUFrXAi+lLdbEBYkQqeV4ONoPVlIJjv9Q22dHW2W9DrtOdH5frZ7FFctvl8UV3S+99BImT56MYcOGwcmJbYyDydbaCgldc2PeSS/stmiVrl2Pkz/W4fVvCnC+sgG21lL8NoL7oN7I07ODMEJpi5K6ZuP2QOhq2X3281zEf5SJSq0OgW52+MeKaH4h90MikeDlBeMxfaw7dO0GrNiZhaJr2vr2ZJXi9a7Fqdb/ehxfYNzAvXcNxwvzxsHWWorvLtZi9pv/wacnS4ytfW0dBjzzzzMQBGBBuDd+yTfgN3R1tHtXRjF2Z5bgQlVDty6CzKI6fFtYA5lUgpVdnRvUt8mjXBEV6IK2DgPeTe8+2l3T2IpvzlVifdeK+rF3ecDbiVNz+mMnl+GlB0MAANu/K+r24vJ8pRbztxzD5sOF0BsE/Cp0BF74dYiI0Zq/4Q622LksCs7DrHG6rB4Ju3KM82c79AasTDmF06UaOA2zxs7lURjuYCt2yGZt/bwQzA3zgt4g4O3DhZi35RjyKrTG86dLNfjoWOcWYS89OJ7PSzfg5aTArLs699p+4cvvsf9cz9XMtx7pXMdpUoAzpo52EynSO4dEuNmNGUWWnJwMJycnlJWVYdu2bdBobn5zd61WC6VSifr6ejg6cluGm9HaocfM146gvF6HJdF+sLW2QnbxFZwrr0e7/qdUWhzlhw0Lxosaq6U4lFeFFTuzIJUA/1o5FQ26Dvz5s9Mou9I5crNsSgCejgvmtmsD1NTagYc+yEDupXr4uQzDP/84GWfL6/H7nVnQGwT8ccYo/GV2sNhhWoyimias2Xsa2cWdD+Azg9yxcWEodmeWYtPBArja2eBg0nQ429mIHarZa9cb8MtX01FxTXu5o60M4f7OiPBzRnp+NXJKNLx/3oTjF2ux+O8ZsLGS4i9zgnGuvB45xVfwY233zoyU30djMh8aB2T1p2qknrqEYE8HfJEwBdu+LcKbBwvQrhfgPMwa/zM/BL8K5YKeA5VTcgUP/z0DunYDFkX6YuPC8Xj281zsPlkKuUyKlP+KRoQ/u64G6t9nKvDfX+TiSnM7rK0kSIwdixVTAzF/yzGcr2zAvAleeOuhiWKHaREyfqjFQx9kdDvm7zoMEX7OGOetxCtfn0eb3sD75w0MtK60uKL7qh07diAxMZFFtwh2nSjGc6lnexx3d5Aj0t8ZEf7OWDTJFw62bDsbqJUpOfjqTAXc7G1Q09i5mrmPswKv/SYMMaNcxQ7P4lxuaMXCrd+hpK4ZQR4OKKlrRku7HgsmeuP134WxReom6Q0Ctn37A/62vwBtegOUCms0t3WgXS9g8+KJ+HUYH8AH6kJVA9LU5cgqrsPp0nq0XLfNnbWVBEf+PJOjsjdh8QcZOP5D93meEgkwdrgDwv2dMX2sm3FFabqxuqY2xL6hQl1TG9wd5MbRr9i7PPDyghCOyN6CA99X4Q//yIJBACb6OeFUiQZSCbD1kQjEjWPX1c263NCKv6bmGhcBu5qnzsOscTBpOlzt5WKHaDH2n6uEquAycoqvIL+qAddXhdGBLtj9+N18buoHi+5rtLa2orX1p5YJrVYLX19fFt23qK3DgCd2ZaOiXodwv84iO8LfGT7OCv5R3qKaxlbEvqGCprkd6OoUeO6Bu9gedRuKapqwcOt3xn1np41xw7b4SdzO6jYUVDXgqT2nkXupHgBwb/BwfBgfyb/7W9SuN+B8RQOyi+uQXaLB9+X1+F2kL/4wnVvc3Ixz5fVI3K2Gh6NtZ9eAvzMm+DpxvvFtSFNfwqrdagCAg60M6+aOw4Jwb/6t34brByxenB+CR7jOwC0TBAGppy4h+V/n0KDrnC+/aVEYF5y9DVpdO06VaJBdfAU5xVdQpdVh06IJCPFWih2aWWPRfY1169Zh/fr1PY6z6CZzcrTgMj46VoSlkwOMK0fT7VGXarBseyZGuttj5/IovsT4GbTrDfj7f37A6VINXpgXAg9HjnoR3WkEQcCr+/NRpdVhzX1B8GLnxc/i7UMX8PbhQjwxcxQSY7nbw8+hor4Ff9tfADcHGzwzO5gvhmjQWVTR/cwzz+CVV17p95q8vDwEB/80D5Mj3UQ0EK0dethYSflFTEREomvt0HPvaKI7yECLbrMY9nnqqaewdOnSfq8ZOXLkLf//crkccjnndxANRXy4ISIic8HvJKKhySyKbnd3d7i7c7sZIiIiIiIiurOYRdF9M0pKSlBXV4eSkhLo9Xqo1Z0LfYwePRr29vZih0dERERERERkZHFF99q1a7Fz507j54kTO/fiS09Px4wZMwb0f1ydxq7Vak0UJREREREREd3JrtaTN1omzSwWUhtsZWVl8PX1FTsMIiIiIiIisnClpaXw8el7y7ohWXQbDAaUl5fDwcHBrFc0vrrKemlpKVdZJ7PD/CRzxvwkc8b8JHPHHCVzZk75KQgCGhoa4OXlBalU2ud1Ftde/nOQSqX9vokwN46OjqInFFFfmJ9kzpifZM6Yn2TumKNkzswlP5VK5Q2v6bscJyIiIiIiIqLbwqKbiIiIiIiIyERYdJsxuVyO5ORkyOVysUMh6oH5SeaM+UnmjPlJ5o45SubMEvNzSC6kRkRERERERDQYONJNREREREREZCIsuomIiIiIiIhMhEU3ERERERERkYmw6CYiIiIiIiIyERbdZmrLli0ICAiAra0toqOjkZmZKXZINEQdPXoUc+fOhZeXFyQSCb744otu5wVBwNq1azFixAgoFArExsbiwoULosVLQ8eGDRswadIkODg4YPjw4Zg/fz7y8/O7XaPT6ZCQkABXV1fY29tj4cKFqKqqEi1mGlq2bt2K0NBQODo6wtHRETExMfj666+N55mfZE42btwIiUSCxMRE4zHmKIll3bp1kEgk3X6Cg4ON5y0tN1l0m6FPP/0USUlJSE5ORk5ODsLCwhAXF4fq6mqxQ6MhqKmpCWFhYdiyZUuv51999VVs3rwZ7733Hk6cOAE7OzvExcVBp9MNeqw0tKhUKiQkJCAjIwMHDhxAe3s77rvvPjQ1NRmvWb16Nb788kvs3bsXKpUK5eXlWLBggahx09Dh4+ODjRs3Ijs7G1lZWbjnnnswb948nDt3DmB+khk5efIk3n//fYSGhnY7zhwlMY0bNw4VFRXGn2+//dZ4zuJyUyCzExUVJSQkJBg/6/V6wcvLS9iwYYOocREBEFJTU42fDQaD4OnpKbz22mvGYxqNRpDL5cInn3wiUpQ0VFVXVwsABJVKJQhduWhtbS3s3bvXeE1eXp4AQDh+/LiIkdJQ5uzsLHz44YfMTzIbDQ0NwpgxY4QDBw4I06dPF1atWiUIvIeSyJKTk4WwsLBez1libnKk28y0tbUhOzsbsbGxxmNSqRSxsbE4fvy4qLERXa+oqAiVlZXd8lWpVCI6Opr5SoOuvr4eAODi4gIAyM7ORnt7e7f8DA4Ohp+fH/OTBp1er8fu3bvR1NSEmJgY5ieZjYSEBDzwwAPdchG8h5IZuHDhAry8vDBy5EgsWbIEJSUlgIXmpkzsAKi7mpoa6PV6eHh4dDvu4eGB8+fPixYXUW8qKyuBrvy8loeHh/Ec0WAwGAxITEzElClTEBISAnTlp42NDZycnLpdy/ykwZSbm4uYmBjodDrY29sjNTUVv/jFL6BWq5mfJLrdu3cjJycHJ0+e7HGO91ASU3R0NHbs2IGgoCBUVFRg/fr1mDZtGs6ePWuRucmim4iILF5CQgLOnj3bbb4XkTkICgqCWq1GfX09PvvsM8THx0OlUokdFhFKS0uxatUqHDhwALa2tmKHQ9TNnDlzjP8ODQ1FdHQ0/P39sWfPHigUClFjuxVsLzczbm5usLKy6rH6XlVVFTw9PUWLi6g3V3OS+UpiWrlyJb766iukp6fDx8fHeNzT0xNtbW3QaDTdrmd+0mCysbHB6NGjERERgQ0bNiAsLAxvvfUW85NEl52djerqaoSHh0Mmk0Emk0GlUmHz5s2QyWTw8PBgjpLZcHJywtixY1FYWGiR908W3WbGxsYGEREROHTokPGYwWDAoUOHEBMTI2psRNcLDAyEp6dnt3zVarU4ceIE85VMThAErFy5EqmpqTh8+DACAwO7nY+IiIC1tXW3/MzPz0dJSQnzk0RjMBjQ2trK/CTR3XvvvcjNzYVarTb+REZGYsmSJcZ/M0fJXDQ2NuLixYsYMWKERd4/2V5uhpKSkhAfH4/IyEhERUXhzTffRFNTE5YtWyZ2aDQENTY2orCw0Pi5qKgIarUaLi4u8PPzQ2JiIl588UWMGTMGgYGBeP755+Hl5YX58+eLGjfd+RISEpCSkoK0tDQ4ODgY53EplUooFAoolUqsWLECSUlJcHFxgaOjI5588knExMTg7rvvFjt8GgKeffZZzJkzB35+fmhoaEBKSgqOHDmC/fv3Mz9JdA4ODsY1MK6ys7ODq6ur8ThzlMSyZs0azJ07F/7+/igvL0dycjKsrKywePFii7x/sug2Q4sWLcLly5exdu1aVFZWYsKECdi3b1+PxaqIBkNWVhZmzpxp/JyUlAQAiI+Px44dO/D000+jqakJjz/+ODQaDaZOnYp9+/ZxfhiZ3NatWwEAM2bM6HZ8+/btWLp0KQBg06ZNkEqlWLhwIVpbWxEXF4d3331XlHhp6KmursZjjz2GiooKKJVKhIaGYv/+/Zg1axbA/CQLwBwlsZSVlWHx4sWora2Fu7s7pk6dioyMDLi7uwMWmJsSoXPvXSIiIiIiIiL6mXFONxEREREREZGJsOgmIiIiIiIiMhEW3UREREREREQmwqKbiIiIiIiIyERYdBMRERERERGZCItuIiIiIiIiIhNh0U1ERERERERkIiy6iYiIiIiIiEyERTcRERERERGRibDoJiIiGuLuv/9+xMfHGz+np6fDzc0Ner1e1LiIiIjuBCy6iYiIhjhvb29cunTJ+Hn69OloaWlBRkaGqHERERHdCVh0ExERDXHe3t4oKyszfpZKpVAoFKiurkZaWhoSExNFjY+IiMiSsegmIiIa4q4f6Var1dBoNIiJicGZM2cQFhYmanxERESWjEU3ERHREOft7Y3GxkZotVoYDAasXr0aS5Ysgaenp7Ho1mq1mDdvHj744AOxwyUiIrIoMrEDICIiInF5e3sDAMrKyrB9+3ZUVlYiLS0NAJCXlweFQoE5c+Zg3bp1mDVrlsjREhERWRaJIAiC2EEQERGReGpqauDu7o7Zs2ejoKAAR48ehbe3N1paWuDl5YWAgAB8/PHHGDdunNihEhERWRy2lxMREQ1xbm5ukMvlKC4uhkqlMo58nz17FjExMTAYDJDJ2BxHRER0K/gNSkRERNDpdD2OnTlzBtOmTUNcXBwefvhhqFQq2NvbixIfERGRpeJINxEREfXqzJkzCAkJQXh4OJ544gksX75c7JCIiIgsDud0ExEREREREZkIR7qJiIiIiIiITIRFNxEREREREZGJsOgmIiIiIiIiMhEW3UREREREREQmwqKbiIiIiIiIyERYdBMRERERERGZCItuIiIiIiIiIhNh0U1ERERERERkIiy6iYiIiIiIiEyERTcRERERERGRibDoJiIiIiIiIjIRFt1EREREREREJvL/ASOeGkXCMDQAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xx, f = single_freq_cosine(npts)\n", + "plot_FFT(xx, f)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, as expected, all of the power is in the real component." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's look at a sine with a $\\pi/4$ phase shift" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "def single_freq_sine_plus_shift(npts):\n", + "\n", + " # a pure sine with no phase shift will result in pure imaginary\n", + " # signal\n", + " f_0 = 0.2\n", + "\n", + " xmax = 10.0/f_0\n", + "\n", + " xx = np.linspace(0.0, xmax, npts, endpoint=False)\n", + "\n", + " f = np.sin(2.0*np.pi*f_0*xx + np.pi/4)\n", + "\n", + " return xx, f" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xx, f = single_freq_sine_plus_shift(npts)\n", + "plot_FFT(xx, f)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "No surprise---the power is now equally in the real and imaginary parts." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### A frequency filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we'll setup a simple two-frequency sine wave and filter a component" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "def two_freq_sine(npts):\n", + "\n", + " # a pure sine with no phase shift will result in pure imaginary \n", + " # signal \n", + " f_0 = 0.2\n", + " f_1 = 0.5\n", + "\n", + " xmax = 10.0/f_0\n", + "\n", + " # we call with endpoint=False -- if we include the endpoint, then for \n", + " # a periodic function, the first and last point are identical -- this \n", + " # shows up as a signal in the FFT. \n", + " xx = np.linspace(0.0, xmax, npts, endpoint=False)\n", + "\n", + " f = 0.5*(np.sin(2.0*np.pi*f_0*xx) + np.sin(2.0*np.pi*f_1*xx))\n", + "\n", + " return xx, f" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "npts = 256\n", + "\n", + "xx, f = two_freq_sine(npts)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(xx, f)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we'll take the transform: $f(x) \\rightarrow F(k)$" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "# normalization factor: the 2 here comes from the fact that we neglect \n", + "# the negative portion of frequency space because our input function \n", + "# is real \n", + "norm = 2.0/npts\n", + "fk = norm*np.fft.rfft(f)\n", + "\n", + "ofk_r = fk.real.copy()\n", + "ofk_i = fk.imag.copy()\n", + "\n", + "# get the frequencies\n", + "k = np.fft.rfftfreq(len(xx))\n", + "\n", + "# since we don't include the endpoint in xx, to normalize things, we need \n", + "# max(xx) + dx to get the true length of the domain\n", + "#\n", + "# This makes the frequencies essentially multiples of 1/dx\n", + "kfreq = k*npts/(max(xx) + xx[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 25, + "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", + "ax.plot(kfreq, fk.real, label=\"real\")\n", + "ax.plot(kfreq, fk.imag, \":\", label=\"imaginary\")\n", + "ax.legend(frameon=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can filter out the higher frequencies---this is done in Fourier space." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "fk[kfreq > 0.4] = 0.0\n", + "\n", + "# element 0 of fk is the DC component \n", + "fk_r = fk.real\n", + "fk_i = fk.imag" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, transform back." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "# Inverse transform: F(k) -> f(x) \n", + "fkinv = np.fft.irfft(fk/norm)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(xx, fkinv.real)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Linear Algebra" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### general manipulations of matrices" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can use regular NumPy arrays or you can use a special matrix class that offers some short cuts." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{tip}\n", + "Since the introduction of the matrix multiplication operator, `@`, using the numpy matrix class is no longer recommended.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's create a simply 2x2 matrix, ${\\bf A}$" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.array([[1.0, 2.0],\n", + " [3.0, 4.0]])" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 2.]\n", + " [3. 4.]]\n", + "[[1. 3.]\n", + " [2. 4.]]\n", + "[[1. 3.]\n", + " [2. 4.]]\n" + ] + } + ], + "source": [ + "print(a)\n", + "print(a.transpose())\n", + "print(a.T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can solve for the inverse" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-2. 1. ]\n", + " [ 1.5 -0.5]]\n" + ] + } + ], + "source": [ + "ainv = np.linalg.inv(a)\n", + "print(ainv)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And multiply ${\\bf A}$ by its inverse, ${\\bf A}^{-1}$" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.0000000e+00, 0.0000000e+00],\n", + " [8.8817842e-16, 1.0000000e+00]])" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a @ ainv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "the eye() function will generate an identity matrix (as will the identity())" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 0.]\n", + " [0. 1.]]\n", + "[[1. 0.]\n", + " [0. 1.]]\n" + ] + } + ], + "source": [ + "print(np.eye(2))\n", + "print(np.identity(2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Linear systems\n", + "we can solve ${\\bf A}{\\bf x} = {\\bf b}$ easily.\n", + "\n", + "```{note}\n", + "Linear system solvers don't usually compute the inverse first and then multiply\n", + "by it. It is much cheaper to solve the system directly (e.g., via Gaussian elimination)\n", + "than to first compute the inverse.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-3. 4.]\n" + ] + } + ], + "source": [ + "b = np.array([5, 7])\n", + "x = np.linalg.solve(a, b)\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### tridiagonal matrix solve" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we'll solve the Poisson problem:\n", + "\n", + "$$f^{\\prime\\prime} = g(x)$$\n", + "\n", + "with $g(x) = \\sin(x)$, and the domain $x \\in [0, 2\\pi]$, with boundary conditions $f(0) = f(2\\pi) = 0$.\n", + "\n", + "The solution is simply $f(x) = -\\sin(x)$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use a grid of $N$ points with $x_0$ on the left boundary and $x_{N-1}$ on the right boundary.\n", + "\n", + "We difference our equation as:\n", + "\n", + "$$f_{i+1} - 2 f_i + f_{i-1} = \\Delta x^2 g_i$$\n", + "\n", + "We keep the boundary points fixed, so we only need to solve for the $N-2$ interior points. Near the boundaries, our difference is:\n", + "\n", + "$$f_2 - 2 f_1 = \\Delta x^2 g_1$$\n", + "\n", + "and\n", + "\n", + "$$-2f_{N-1} + f_{N-2} = \\Delta x^2 g_{N-1}$$\n", + "\n", + "We can write the system of equations for solving for the $N-2$ interior points as:\n", + "\n", + "$${\\bf A} = \\left (\n", + "\\begin{array}{ccccccc}\n", + "-2 & 1 & & & & & \\newline\n", + "1 & -2 & 1 & & & & \\newline\n", + " & 1 & -2 & 1 & & & \\newline\n", + " & & \\ddots & \\ddots & \\ddots & & \\newline\n", + " & & & \\ddots & \\ddots & \\ddots & \\newline\n", + " & & & & 1 & -2 & 1 \\newline\n", + " & & & & & 1 & -2 \\newline\n", + "\\end{array}\n", + "\\right )\n", + "$$\n", + "\n", + "$$\n", + "{\\bf x} = \\left (\n", + "\\begin{array}{c}\n", + "f_\\mathrm{1} \\\\\\\n", + "f_\\mathrm{2} \\\\\\\n", + "f_\\mathrm{3} \\\\\\\n", + "\\vdots \\\\\\\n", + "\\vdots \\\\\\\n", + "f_\\mathrm{N-2} \\\\\\\n", + "f_\\mathrm{N-1} \\\\\\\n", + "\\end{array}\n", + "\\right )\n", + "$$\n", + "\n", + "$$\n", + "{\\bf b} = \\Delta x^2 \\left (\n", + "\\begin{array}{c}\n", + "g_\\mathrm{1} \\\\\\\n", + "g_\\mathrm{2} \\\\\\\n", + "g_\\mathrm{3} \\\\\\\n", + "\\vdots \\\\\\\n", + "\\vdots \\\\\\\n", + "g_\\mathrm{N-2} \\\\\\\n", + "g_\\mathrm{N-1}\\\\\\\n", + "\\end{array}\n", + "\\right )\n", + "$$\n", + "\n", + "Then we just solve ${\\bf A}{\\bf x} = {\\bf b}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "SciPy has banded solvers that work with banded matrices like we have above. They\n", + "will be much more efficient than using a solver based on a dense matrix\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "import scipy.linalg as linalg\n", + "\n", + "# our grid -- including endpoints\n", + "N = 100\n", + "x = np.linspace(0.0, 2.0*np.pi, N, endpoint=True)\n", + "dx = x[1] - x[0]\n", + "\n", + "# our source\n", + "g = np.sin(x)\n", + "\n", + "# our matrix will be tridiagonal, with [1, -2, 1] on the diagonals\n", + "# we only solve for the N-2 interior points\n", + "\n", + "# diagonal\n", + "d = -2 * np.ones(N-2)\n", + "\n", + "# upper -- note that the upper diagonal has 1 less element than the\n", + "# main diagonal. The SciPy banded solver wants the matrix in the \n", + "# form:\n", + "#\n", + "# * a01 a12 a23 a34 a45 <- upper diagonal\n", + "# a00 a11 a22 a33 a44 a55 <- diagonal\n", + "# a10 a21 a32 a43 a54 * <- lower diagonal\n", + "#\n", + "\n", + "u = np.ones(N-2)\n", + "u[0] = 0.0\n", + "\n", + "# lower\n", + "l = np.ones(N-2)\n", + "l[N-3] = 0.0\n", + "\n", + "# put the upper, diagonal, and lower parts together as a banded matrix\n", + "A = np.matrix([u, d, l])\n", + "\n", + "# solve A sol = dx**2 g for the inner N-2 points\n", + "sol = linalg.solve_banded((1,1), A, dx**2*g[1:N-1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot the solution" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 36, + "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", + "ax.plot(x[1:N-1], sol)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks like $-\\sin(x)$, as expected." + ] + } + ], + "metadata": { + "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": "3.13.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/05-scipy/scipy-basics.ipynb b/content/05-scipy/scipy-basics.ipynb new file mode 100644 index 00000000..0bd91e9f --- /dev/null +++ b/content/05-scipy/scipy-basics.ipynb @@ -0,0 +1,1381 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SciPy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[SciPy](https://scipy.org/) is a collection of numerical algorithms with python interfaces. In many cases, these interfaces are wrappers around standard numerical libraries that have been developed in the community and are used with other languages. Usually detailed references are available to explain the implementation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{note}\n", + "There are many subpackages generally, you load the subpackages separately, e.g.\n", + "\n", + "```\n", + "from scipy import linalg, optimize\n", + "```\n", + "then you have access to the methods in those namespaces\n", + "````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{important}\n", + "One thing to keep in mind---all numerical methods have strengths and weaknesses, and make assumptions. You should always do some research into the method to understand what it is doing.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{tip}\n", + "It is also always a good idea to run a new method on some test where you know the answer, to make sure it is behaving as expected.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Integration" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we'll do some integrals of the form\n", + "\n", + "$$I = \\int_a^b f(x) dx$$\n", + "\n", + "We can imagine two situations:\n", + "* our function $f(x)$ is given by an analytic expression. This gives us the freedom to pick our integration points, and in general can allow us to optimize our result and get high accuracy\n", + "* our function $f(x)$ is defined on at a set of (possibly regular spaced) points. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "In numerical analysis, the term [quadrature](https://en.wikipedia.org/wiki/Numerical_integration) is used to describe any integration method that represents the integral as the weighted sum of a discrete number of points.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import integrate\n", + "#help(integrate)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's consider integrating\n", + "\n", + "$$I = \\int_0^{2\\pi} \\sin^2(x) dx$$\n", + "\n", + "[quad()](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html) is the basic integrator for a general (not sampled) function. It uses a general-interface from the Fortran package QUADPACK (QAGS or QAGI). It will return the integral in an interval and an estimate of the error in the approximation" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def f(x):\n", + " return np.sin(x)**2" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "#help(integrate.quad)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`quad` will return the integral and an estimate of the error. We can seek more accuracy by setting `epsabs` and `epsrel`,\n", + "but remember that we can't do better than roundoff error." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.141592653589793\n", + "3.4878684980086318e-15\n" + ] + } + ], + "source": [ + "I, err = integrate.quad(f, 0.0, 2.0*np.pi, epsabs=1.e-14, epsrel=1.e-14)\n", + "print(I)\n", + "print(err)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "#help(integrate.quad)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Additional arguments\n", + "\n", + "Sometimes our integrand function takes optional arguments. Let's consider integrating\n", + "\n", + "$$g(x) = A e^{-(x/\\sigma)^2}$$\n", + "\n", + "now we want to be able to define the amplitude, $A$, and width, $\\sigma$ as part of the function." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def g(x, A, sigma):\n", + " return A*np.exp(-x**2/sigma**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.8451240256511698 2.0484991765669867e-14\n" + ] + } + ], + "source": [ + "I, err = integrate.quad(g, -1.0, 1.0, args=(1.0, 2.0))\n", + "print(I, err)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Integrating to infinity\n", + "\n", + "numpy defines the `inf` quantity which can be used in the integration limits. We can integrate a Gaussian over $[-\\infty, \\infty]$ (we know the answer\n", + "is $\\sqrt{\\pi}$)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "Behind the scenes, what the integration function does is do a variable transform like: $t = x/(c +x)$. This works when one limit is $\\infty$, giving, e.g.,\n", + "\n", + "$$\\int_a^\\infty f(x) dx = c \\int_{a/(c + a)}^1 f\\left (c\\frac{t}{1-t}\\right) (1 - t)^{-2} dt$$\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.7724538509055159 1.4202636780944923e-08\n" + ] + } + ], + "source": [ + "I, err = integrate.quad(g, -np.inf, np.inf, args=(1.0, 1.0))\n", + "print(I, err)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multidimensional integrals" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Multidimensional integration can be done with successive calls to quad(), but there are wrappers that help" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's compute \n", + "\n", + "$$I = \\int_{y=0}^{1/2} \\int_{x=0}^{1-2y} xy dxdy = \\frac{1}{96}$$\n", + "\n", + "(this example comes from the SciPy tutorial)\n", + "\n", + "Notice that the limits of integration in $x$ depend on $y$. This means that we need to do the $x$\n", + "integration first, which gives:\n", + "\n", + "$$I = \\int_{y=0}^{1/2} \\int_{x=0}^{1-2y} xy \\,dxdy = \\frac{1}{2} \\int_{y=0}^{1/2} y \\left [ x^2 \\right |_0^{1-2y} dy = \\frac{1}{2} \\int_0^{1/2} (1-2y)^2 y \\, dy = \\frac{1}{96}$$\n", + "\n", + "Note the form of the function:\n", + "\n", + "```\n", + "dblquad(f, a, b, xlo, xhi)\n", + "```\n", + "where `f` = `f(y, x)` -- the y argument is first to indicate that the $y$ integration is done first and\n", + "then the $x$ and $[a, b]$ are the limits of the $x$ integration. We want the opposite in this example,\n", + "so we'll switch the meaning of $x$ and $y$ in our example below.\n", + "\n", + "The integral will be from: $y = [0, 1/2]$, and $x$ = `xlo(y)`, $x$ = `xhi(y)`" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.010416666666666668 95.99999999999999\n" + ] + } + ], + "source": [ + "def integrand(x, y):\n", + " return x*y\n", + "\n", + "def x_lower_lim(y):\n", + " return 0\n", + " \n", + "def x_upper_lim(y):\n", + " return 1-2*y\n", + "\n", + "# we change the definitions of x and y in this call\n", + "I, err = integrate.dblquad(integrand, 0.0, 0.5, x_lower_lim, x_upper_lim)\n", + "print(I, 1.0/I)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you remember the python lambda functions (one expression functions), you can do this more compactly:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.010416666666666668\n" + ] + } + ], + "source": [ + "I, err = integrate.dblquad(lambda x, y: x*y, 0.0, 0.5, lambda y: 0, lambda y: 1-2*y)\n", + "print(I)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Integration of a sampled function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we integrate a function that is defined only at a sequence of points. A popular method\n", + "is [Simpson's rule](https://en.wikipedia.org/wiki/Simpson%27s_rule) which fits a parabola to 3 consecutive points\n", + "and integrates under the parabola." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's compute\n", + "\n", + "$$I = \\int_0^{2\\pi} f(x_i) dx$$\n", + "\n", + "with $x_i = 0, \\ldots, 2\\pi$ defined at $N$ points" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.141592653589793\n" + ] + } + ], + "source": [ + "N = 17\n", + "x = np.linspace(0.0, 2.0*np.pi, N, endpoint=True)\n", + "y = np.sin(x)**2\n", + "\n", + "I = integrate.simpson(y, x=x)\n", + "print(I)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Romberg integration](https://en.wikipedia.org/wiki/Romberg%27s_method) is specific to equally-spaced samples, where $N = 2^k + 1$ and can be more converge faster (it uses extrapolation of coarser integration results to achieve higher accuracy)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.1430658353300385\n" + ] + } + ], + "source": [ + "N = 17\n", + "x = np.linspace(0.0, 2.0*np.pi, N, endpoint=True)\n", + "y = np.sin(x)**2\n", + "\n", + "I = integrate.romb(y, dx=x[1]-x[0])\n", + "print(I)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Interpolation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Interpolation fills in the gaps between a discrete number of points by making an assumption about the behavior of the functional form of the data.\n", + "\n", + "Many different types of interpolation exist\n", + "* some ensure no new extrema are introduced\n", + "* some conserve the quantity being interpolated\n", + "* some match derivative at end points" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{caution}\n", + "Pathologies exist---it is not always best to use a high-order polynomial to pass through all of the points in your dataset.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [interp1d()](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html) function allows for a variety of 1-d interpolation methods. It returns an object that acts as a function, which can be evaluated at any point." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "import scipy.interpolate as interpolate" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "#help(interpolate.interp1d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's sample \n", + "\n", + "$$f(x) = x \\sin(x)$$\n", + "\n", + "and try to interpolate it." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "def f_exact(x):\n", + " return np.sin(x)*x" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "N = 10\n", + "x = np.linspace(0, 20, N)\n", + "\n", + "y = f_exact(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 18, + "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", + "\n", + "x_fine = np.linspace(0, 20, 10*N)\n", + "\n", + "ax.scatter(x, y)\n", + "ax.plot(x_fine, f_exact(x_fine), ls=\":\", label=\"original function\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we create an interpolant via `interp1d`, it creates a function object" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "f_interp = interpolate.interp1d(x, y, kind=\"cubic\")" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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8md69e7Ns2TI6dOiAk5MTAN9//z0vvvgiH330Ed26dWPHjh3cf//9uLu7c9ddd1U89jPPPMO7775Lt27dcHFxYcmSJeTn5/Paa6/x7bff4uTkxEMPPcTNN99c0ZL/jz/+4LHHHuODDz5g+PDhLFq0iLvvvpuQkBCGDh1a42vw9PRk7ty5BAcHs2fPHu6//348PT15+umnK46Jj49nwYIFLFq0iHPnznHjjTfyxhtv8NprrzFr1iwOHz5Mx44defnllwHw8/O76H9TIYQQtSgsm/ZxdAcHJ4uG0rwSFRt2xRVX8NBDD0HZyMT777/PypUradu2bcWbta+vL4GBgRXnTJ8+nXfffZdrr70WykZe9u/fz2effVYtUZk8eXLFMeVKSkr46KOP6NOnDwDffPMN7du3r0iK3nnnHSZMmFAR05QpU9i4cSPvvPNOrYnK888/X3E9IiKCJ598kvnz51dLVAwGA3PnzsXT0xOAO+64g+XLl/Paa6+h0+lwcnLCzc2t2usUQghx6faezsLd2YEwHze0VlJIS7NLVBzd1JENSz33JejcuXPFdUVRCAwMJDU1tdbj8/LyiI+P59577+X++++vuL20tBSdTlft2J49e15wvoODA7169ar4vl27dnh7e3PgwAF69+7NgQMH+N///lftnAEDBjBr1qxaY/rpp5/48MMPiY+PJzc3l9LSUry8vKodExERUZGkAAQFBdX5OoUQQjSOZ//Yw+5TWXxyW3eucJVExTIU5ZKmXyzp/AJXRVEwGAy1Hp+bmwvAF198UTEqUk6r1Vb73t3d/P8mcXFx3HbbbcyYMYNRo0ah0+mYP38+7777brXjGvo6hRBCNA4XRy0ujhraBnpCsnWs+KHZJSp2qrwmRa/XV9wWEBBAcHAwx44d47bbbmvwY5aWlrJ161Z69+4NwKFDh8jMzKR9+/YAtG/fnvXr11ebQlq/fj2xsbE1Pt6GDRsIDw/nueeeq7jtxIkTDY7Lycmp2usUQgjROH5+oB96gxGNAiSUj6hYPlEx66qfNWvWMHbsWIKDg2ts/jVhwoSK1RvlX6NHjzZnSHbJ398fV1dXFi9eTEpKCllZ6pKyGTNmMHPmTD788EMOHz7Mnj17mDNnDu+99169j+no6MgjjzzCpk2b2LZtGxMmTKBv374VictTTz3F3LlzmT17NkeOHOG9997j999/58knn6zx8Vq3bk1iYiLz588nPj6eDz/8kD/++KPBrzUiIoJNmzZx/Phx0tLSZLRFCCEakVajvhdX9lCx/NSPWROVvLw8unTpwscff1zrMaNHjyYpKani68cffzRnSHbJwcGBDz/8kM8++4zg4GDGjRsHwH333ceXX37JnDlz6NSpE4MHD2bu3LkVy5nr4ubmxtSpU7n11lsZMGAAHh4e/PTTTxX3jx8/nlmzZvHOO+/QoUMHPvvsM+bMmVNtaXRVV199NY8//jgPP/wwXbt2ZcOGDbzwwgsNfq1PPvkkWq2W2NhY/Pz8SExMbPBjCCGEqEf5qh8LL00GUIzGBjb4uNgnUhT++OMPxo8fX3HbhAkTyMzMvKQ269nZ2eh0OrKysi4ozBQXZ+7cuUyePJnMzExLhyKEEKIJvPTXPhLS8nhwcDT9on1hwUOw83sYNh0GTTHLc5r6/m3xhm+rVq3C39+ftm3bMnHiRNLT0+s8vqioiOzs7GpfQgghhLh464+msfrwWYpKy2oAZXmyavTo0Vx77bVERkYSHx/Ps88+y5gxY4iLi7tgZUq5mTNnMmPGjCaPVQghhLBXb17fmQNJ2XQOKZvqsZJ9frD01M/5jh07RnR0NMuWLWPYsGE1HlNUVERRUVHF99nZ2YSGhsrUjxBCCNFYPu4LZw/AnX9CVM21h5fKZqZ+qoqKiqJly5YcPXq01mOcnZ3x8vKq9iWEEEKIRiRTPzU7deoU6enpBAUFWToUIYQQolnYdCyd/BI9nVvp8PVwVm+0olU/Zh1Ryc3NZefOnezcuROAhIQEdu7cSWJiIrm5uTz11FNs3LiR48ePs3z5csaNG0dMTAyjRo0yZ1hCCCGEKPP5mmPcPWcLf+9JUm8oKYDSQvW6vY+obN26tdoGdVOmqEuc7rrrLmbPns3u3bv55ptvyMzMJDg4mJEjR/LKK6/g7OxszrCEEEIIUSbM1402AR60DyorpSif9lG04OxZ57lNwayJypAhQ6irVnfJkiXmfHohhBBC1GP62A7Vb6i64kdRLBJTVVZVoyKEEMKyNh5LZ8GO07QJ8OT2vuE4OVjVmgvRFKyokBZJVIQQQlRVUKLn9+2ncXHUcPeACEuHI8zMaDSqe/tUZWWJiqTKQgghKgxt688LY2O5q39ExRtYdmEJT/y8i9WHz1o6PNHIXll0gCFvr+TnLScrb7SiFT/IiIoQQojVh8/SuZWOFu5OANzRN7za/V+sOcZv20+xIT6NVU8Nwdmh5s7hwvYcTM7meHo+VB1UsbIRFUlUhBCiGVuyL5mHvt9O2wBP5j/QFy8XxwuOeWhIDHtPZzFpaIwkKXbmw1u6cSg5h9b+HpU3SqIihBDCWkT7edDCzZF2gZ64O9X8luDqpGXO3b2bOjTRBFp6ONMy5ryWIFa0zw+SqAghRPMW4+/Bnw8PJNDLBa3GtKWo6blFFOsNBOlczR6fsAArG1GRYlohhGjmWnm7mpykbE7IYNQHa3ls/k70hibZ01aYyYajacxdn8CBpOzqd0iiIoQQwtL+b/kR/tp1psHJRqCXCwXFpSRnFXIoOcds8Qnz+2vXGV5auJ9/ylvnl5NVP0IIISzpdGYBs5YfodRgJNzHjS6hpr8hhfm68d+UwQR5uaAxcRRGWKeOrXSMzCumR/h5IydWNqIiiYoQQjQzHs4OPDqsNYeScxqUpJRr5S21Kfbg9r7h3H7eUnSQREUIIYSF6VwdeXRY60t+HKPRSFJWIcGSuNgPgx4Ky2pWrGTVj9SoCCGEaLBT5/IZ8f4arvhwLUWlekuHIxqouNRAqd5w4R2FWUBZ3ZKV1KhIoiKEEM1EdmEJU37eyb4zWZf8WEE6V3ILSyks0bP/TLYJZwhr8veeM7R/cTFTftpZ/Y7yaR8nD3Bwskhs55OpHyGEaCa+izvB79tPs/d0FksmX3bhZnQNoNUofHZHDyL93GvsZiusW0JaPiV6I86O53UatrIVP0iiIoQQzUeP8Bbc3CuUy9r4XVKSUu5iCnGFdZg8rDU39Qq98A4rK6RFEhUhhGg++kb50jfK1yyPXaI34KiVagJbodEoNa/esrL2+UiNihBCiEtxOrOA+7/dyphZazEapVOtzasYUZFERQghRBMxGo38vOUkSVkFjf7Y3q6OrD+axtHUXPZJUa1NSM8t4uWF+/lhU+KFd1aMqMjUjxBCiCZyOCWXp3/bjbODhp0vjsTVSWvCWaZxd3bgres70zbAk9YBno32uMJ8jqTm8vX6BMJ93bi1T1j1O6VGRQghRFPLKy6lV0QLdK5OjZqklLuqc3CjP6Ywn5YeTtw3MBJ35xpSAFn1I4QQoql1D2vBLw/2r7nBl2h2Yvw9ef6q2JrvlBEVIYQQluJgxlU5+89k88eOU4S0cOOu/hFmex5hZlaYqEgxrRBC2LHTmQWUNMFIyqGUbL5Ym8Av206a/bnEpUnOKkRvqGWFlhUuT5YRFSGEsGOTvt/OsbO5zL69BwNiWprteQbEtOTGniEMau1ntucQl05vMDLorRUoisKap4YSqHOpfoAVjqhIoiKEEHYqr6iU05kF5BSV0trfw6zP5e/pwlvXdzHrc4hLl5JdWHHd39P5wgMkURFCCNFU3J0d2DhtGAeSsvH3cjHhDGHvgr1dOfjKGFJzCtFozttGoaQA9EXqdSta9SM1KkIIYce0GoWOrXQ131lSAHt+hQOLKj9JX6KU7EIW7T7TKI8lzEOrUQjS1dQ+v+x3QNGCs/X0xJERFSGEsENGo7H2jQf1JbDze1j1JuSUJxUKBHWGiEEQMxyihkADNy4sKNYz8M0VlOiNdGqlI9zX/dJfiGg6VdvnN8KmlY1FEhUhhLBDv20/zbdxx7mrXwTX9QhRbzQYYN/vsPI1yDim3ubVCpzcIe0wJO1Sv+I+gl73w5i3QGP6wLurk5ae4T7kFZdyLr+EcPPsfyguwXtLD1NQXMrNvcOI9juvbik/Xb10M1/R9cWQREUIIezQhvg0dp/KIv5srnqDwQA/3wEHF6nfu7WEy56CHhPA0QVykiFhLRxbCTt/gC1fqPUKV81qULLy3b29zdqvRVya37ad4nRmASM7BBJ9/gKtvDT10s26MkxJVIQQwg49MbIt/aJ86RRSVp+y8WM1SdE6w+CnoM9EcK7yidozEDrfoH5FXgYLJsL2b9VponEfg8a01vuSpFi3iUOiiT+bS8z5oylUHVHxafK46iKJihBC2KFW3q7c0DNU/eb0dlg2Q70+eib0urfuk7vcDFpH+O1+2PUj6Ivhms/U20xkMBgp1htwcWz8vYXExbu9b3jtd+ZnqJfu1jX1I6mvEELYs8Js+PUeMJRA+6uh5z2mndfxOrjxG9A4wt7f4I8HwVhLN9PzfLn2GL1eW8ZX6xIuLXbRtPKtc+pHEhUhhLAzP289yaLdZ8jKL4a/n4BzCaALhas/bNhqjvZj4ebvy5KVX+HAXyad5uSgIT2vmM0JGRf/IkSjO51ZQFJWAYba2udXTP1YV6IiUz9CCGFHjEYj7/53iJTsIpYOPYVuz89qX4zrvry4bqNtRsHAybDmbfj3GYi+vN4eG6M7BtIu0IuuodbTNEzAh8uO8NPWk0wZ0YZHh7W+8AArXfUjIypCCGFHikoNXNEpiOGB+cRsLatLGTINwvpe/IMOegJaRKg9V1bOrPdwf08Xekf64OQgbzHWpLBUj4NGIdzXreYD8qxzRMWsv0Vr1qxh7NixBAcHoygKCxYsqHa/0WjkxRdfJCgoCFdXV4YPH86RI0fMGZIQQtg1F0ct08d24MuYDSgleRDWHwZNubQHdXSFK95Vr2+arfZaETZn1s3dOPDKaEZ3DKz5gPIRFfdmlKjk5eXRpUsXPv744xrvf+utt/jwww/59NNP2bRpE+7u7owaNYrCwsIajxdCCGGC/AzY+aN6/fLnTF5aXKfWw6HDNWA0wKLHwaCv8/DkrEL+b/kR3vj34KU/t2g0jloNzg41/D4YjVZbo2LWRGXMmDG8+uqrXHPNNRfcZzQa+eCDD3j++ecZN24cnTt35ttvv+XMmTMXjLwIIYSon9FoJCEtD+O2uVBaAIGdIHxA4z3BqJng5Amnt8G2uXUemltUwrtLD/PNhuOU6g2NF4Mwj+Lcyg0Jm1OiUpeEhASSk5MZPnx4xW06nY4+ffoQFxdX63lFRUVkZ2dX+xJCCAHxZ3MZ8c4y0lZ8pN7Q96HG3bPFKwguf169vnwG5KbWemhUSw+u6x7Ck6PaUlrbKhPRZNYcPsuD323ju40naj6gfDTFwVXdUsGKWCxRSU5OBiAgIKDa7QEBARX31WTmzJnodLqKr9DQULPHKoQQtuBoai5jHbbgZ0wHd3+1F0pj63UfBHWBwixY806th2k0Cu/e2IV7B0ZK0zcrsOd0Fov3JbMzMbPmA6y0kBZbXPUzbdo0srKyKr5Onjxp6ZCEEMIqjO4QyLuh69Vvet0HDs6N/yRaBxj+knp9x7zKbqbCqg1t68/0sbFc3TW45gOstH0+lkxUAgPVquOUlJRqt6ekpFTcVxNnZ2e8vLyqfQkhRHOmNxiJi09nzcp/0CRtx6h1Nr0D7cWIGgoBHaEkD7bNqfPQ7MIStp04Z75YhElig724e0Akg9ucvxNhmYoVP9bVQwVLJiqRkZEEBgayfPnyituys7PZtGkT/fr1s1RYQghhUxbvTWLgmyu45YuNZK+cBcAi40AWHy8135MqCvR/RL2+6TMoLarxsLTcIjq/9B83fLqB/GIzxiMunZW2z8fciUpubi47d+5k586dUFZAu3PnThITE1EUhcmTJ/Pqq6/y119/sWfPHu68806Cg4MZP368OcMSQgi7sHhvEhPnbScpq5BWnGWMZjMAnxSMYOK87Szem2S+J+9wLXgGQ24K7PmlxkNaejgT6OVCqxaunMmUthOWUqI3sDkhg+SsQoy17ddkpV1pMXcL/a1btzJ06NCK76dMUZsO3XXXXcydO5enn36avLw8/ve//5GZmcnAgQNZvHgxLi4u5gxLCCFsnt5gZMbC/ZS/7dzhsBStYmS9vgMHjGEowIyF+xkRG4hW04grf8o5OEHfB2Hpi7DhI+h6W40rjJY/MRh3Z9mtxZJOnSvgxs/icHXUsv/lUTUfZKU9VDD3iMqQIUMwGo0XfM2dq66/VxSFl19+meTkZAoLC1m2bBlt2rQxZ0hCCGEXNidkkJSljlJo0XOTdhUAX+tHA2AEkrIKzbsxYI8Jal+Vswfg6PIaD5EkxfKyC0oI9XElsqU7Sm3L1fOkmFYIIUQjSs2pnErprTlICyWXdKMnqwxdaz2u0bnooMdd6vUNH5rvecQl6RLqzdqnL2fRIwNrP0iKaYUQQjQmf8/KKfKRmq0ALNd3R4+21uPMos+D6u7MCatr3APIYDDy9K+7GPHeas7m1Fx0K5qGpq4pwOY69SOEEMI8ekf6EKRzQcHICO02AP4z9Ky4XwGCdOouxmblHaruAQRqrcp5NBqFHYmZHEnNZfepWpqNCctrrqt+hBBCmIdWozB9bCztlROEKGnkG51Za+gEZUkKwPSxseYppD1f/4fVy72/1dhW/4mRbfjqrp70jLC++ofm4JEfd/DQ99uIP5tb8wH6UigoSyKtcNWPJCpCCGGjRncMYlbX0wCsMXSmCCcAAnUuzL69O6M7BjVNIMHdoFUPMOphz681xjmsfQA6V8emiUdUMBqNrDiQwj97at+ahoJzZeXXgGuLJovNVFKOLYQQNqx1xhoAYgbdyCz/rvh7qtM9TTKSUlWXW9RdlXfPh34PNe1zi1oZjTDr5m4kZuQT0sK15oPK61NcW6hbJFgZ64tICCGEac4dh5Q9oGiIGXg9MZZcWtrhWlg8TS2oTdkPAbHV7j6QlM2OxEyGtfcnwEt6ZTUVjUZheGxA3QdZcSEtMvUjhBA27OA/6mX4AMv3v3D3hdYj1eu7519w97N/7OHZP/aw8Vh608cm6mbFhbRIoiKEEDbskJqofJzUlqOptRRKNqUuN6uXu38Bg77aXQNjWjIwpiUe0gCuSR1Mzmbr8Qwy84trP8iK2+cjUz9CCGGj8jMwnliPAvyY3Ym7dFYwndJmFLh4Q84ZSFgD0ZVbqDwxsq1FQ2uuvlqbwC/bTjFlRBseHda65oPyrbcrLTKiIoQQNurwYhSjgVL/jrx171XWMVLh4Awdr1Wv77pw+kc0PS9XR0JaqO3za5UnNSpCCAs5f6fUP3ee5ruNJziZkW+xmEQjOfg3AA6xY+kfY0VD9l1uUS8PLISiC6ejDAYjxaWGpo+rmXrhqljWTb2csV2Caz/IitvnI4mKEPYpv7iUl/7ax7N/7Kl2+6erj/HCgr38teuMxWITjaA4v3ITwHZXWjqa6kJ6gU8UlOTBwUXV7nphwV46TF8iv3/WRlb9CCGa2oGkbL6JO86Pm09yKDmn4vbL2rTk2m6teHBwtEXjE5fo2EooLeCcYyDfH/ekqFRvwklNRFGgc1lR7a4fq92l1SgUlOg5lJxtmdhEzSpW/VjniIoVTGoKIRpbj3AfnhjRho6tdLQN9Ky4fdqY9tWOMxqNPP3rbq7uGsyg1n4WiFRclLLRlD8LOvPOv4e4uXe4pSOqrvONsOp1OLYass+AlzrtcO/ASG7vG06Er5ulI2wWNhxNY+a/BxkQ05JnxrSr/cD8DPVSRlSEEOZiNBr5Nu44uUWlFbc9fHlrhrT1r/O8X7ed4pdtp7jz683VRl6ElTu+DgDvDsO5rU9Y03ehrY9PJIT1V9uy7/654uZQHzdi/D1w0MpbT1M4kprLntNZJKTVs3Q9r3xExTpX/ciIihB2YO6G48xYuJ8fNiWy8JGBOJr4RnBV52B2n8picBu/aiMvworlpEDaIUBh/LgbGG+lby50vgESN8CBv2DgZEtH0yyN6hBIsLcrXi51vNUX50NpgXrdSotpJVERwg50DvEmwMuZ63uEmJykALg6aXllfEezxiYa2Ql1NIXAjlb7CRiAtlfCoinq/j9Vpn9WHExhc8I5ruocRMdWOktHadcCdS4E1tdfp7yQVusETh5NEldDyfibEHagR3gL/ps8mHsHRl7S4+QWlbLhaFqjxSXMIGEtAOl+fSjVW/EyX88ACO2tXi9bSk3ZdOOnq+PZEC+/Z1ahavt8xcqmEMtIoiKEjSouNZCaU1jxvc7NEeUS/qNJyS7kyg/XcvfcLRxJkXoVq1VWnzJ1m44xs9ZaOpq6lS+drpKoDGsXwO19w+gYLKMp5mQ0Glmw4zTbTmTUndBaeft8JFERwna9/s8Brpi1js0JGY3yeH4ezoT5uNHSw7laUa6wItlJkH4EIwr7HDtaf11Ru6vUy+NroeAcANf1COHV8Z2sq0mdHUrLLWbyTzu5/tM49Oc1fqymYsWP9U4jSo2KEDYot6iUFQdTScstIrugpFEeU6NReP+mrjhqNehcHRvlMUUjO7EeACWoM+vvv4a8YitPKH2jwa89nD0AR5aqy5ZFkygo1tMvypdivQFnB23tB5av+LHSQlokURHCNnk4O7B0ymVsOJrO0HZ1L0EGwGBQixoPL1Y/3bq1hFbdoVUPCO4Grt4AtPRwNn/w4uIlrFEvIwah0Sh4uthAQtnuSjVRObioIlExGo2k5hTh5qS1jddgg8J83fjxf33rP9DKu9IiiYoQtsvZQVt/knJyM2ybC0f+g7yz1e87VFk3QGAnuGoWhPSAsjeSlYdSOZ1ZyB19rayZWHNWVp9CxCBLR2K6dlfC2nfgyDIoKQRHF+6eu4VVh87ywU1dGd+tlaUjbN5sIFGRGhUhbEhxqYF1R9Iu2GzwAvpSWPk6fDUSdn6vJinOXtDhGhj3MYx8DTpcC95lSUjyHpgzGrZ9A8DGYxncM3crr/99gHN5xU3wykS9ss9ARjxGRcOEFQ58ujre0hGZJrgbeLVS9/45tgqAkBauaBRIzi6s93RhZlVX/VgpGVERwobM23iClxft55purXj/pq41H5R1Gn6/v6KegU43QLc7IKwfODhdeHxuKiycrI6wLHwUTm+j75i36BPpQ9dQb2tdsdj8lI2mnPVox6oTRbjrsiwdkWkURR1V2fy5Ov3TdjRPjGjL81fG4uJYR+2EuCT3fbOV1JxCpo+NpUd4HYWyVt4+H0lUhLAteUWlOGk19I6s5T+eQ4thwUQoyFCbN42dBZ2ur/tBPfzhpnmw7j1Y8Sps/wYleQ/zb/oWxTvULK9DXISy+hSX1kN4a3Bngupr5GVNyhOVQ/+CQU8L9xoSZtGo9p7OIjm7EE19nzTyZERFCNGIHhnWmvHdWtX8JrX5C/jnSfV6UBe4fo666sIUGg1c9iQEd4Vf74Uz21G+vRoeWAvO1tmtstkpG1HxajeUG9vYWAIZPgBcvNVphpObIbyfpSOye3Pu7sXJjHxaB9SzhL28RsWKV/1IjYoQNibUx+3CTd32/g7/PKVe73U/3LvU9CSlqpjh8MBqtaYg4xj89zwJaXm89Nc+Ckv0jfMCRMNlnYJzCaBoIcyElRzWRusIbUar1w8uAuC7uONMnLeNHYnnLBubnWof5MXIDoF4ONcxHmEwqKOvWPeIiiQqQtiAv3ad4UxmQc13HlsFv/9P3am2131wxdvgcAnLjFtEwPjZ6vVtc5j9xSfM3XCcn7acvPjHFJembDSlyL8zi4/m1f67YM0qutQuAqORtUfS+HdvMjsSMy0dWfNVmAnGsq61rtbb8E0SFSGsXEp2IU/8vJPL3lrJifS86ncm7YL5t4OhBGLHwZi3Gme/jqjB0HcSADOMsxnX2omuod6X/rji4pTt73PAuQsPztvOK4v2WzqihosZBg4ucO44pB7g2u4hPH9lewa2tt4pB1u193QWf+48Xf9WGOXTPs66mgvtrYQkKkJYuZzCEnpFqCtwwn3dK+/IOAbzrofiHLWvxjWfg6YRV1EMexH82uFanM4s97l0CZG9WSzmuJqoZAb0oUOwl20mjU7uEDFQvR6/nNEdA7lvUBRt6quhEA32954kHpu/k3kbT9R9YEUPFesdTUESFSGsX4y/Jz/c35dv7+1deWNRjpqk5KVCQCe4+XtwbORVII4ucO3noHFUh+t3/tC4jy9Mk30GMk+AomHI8LH8/eggHhh8EfVH1iBmuHp5dJmlI7Frrbxd6RvlQ4f6Nn60gfb5SKIihO1wc6pSFPfvVMiIB68QuP1XcDHTaEdQFxj6LADGf5/m9xXrScqywfoIW3Zys3oZ0AGcbXz0IXqYenkiDorzycovYdOxdGkq2Mhu7xvO/P/148Ze9awOs4GutEiiIoT10huM/Lbt1IWrbfb+rnabVTRw3RfgGWjeQAY8BqF9UYpzKVzxNr9vP23e5xPVndoCgDGkd72HWr2WrUEXBvoiOLGeu+Zs5qbPN7I+Ps3SkTVPkqgIIS7Fkn3JPPHLLsb+37rKlvmZJ2HRZPX6wCkQ3t/8gWi0MPwlAG5wWEukSz0FeqJxlSUqa/Ij6Pv6cj5eedTSEV08RYGYy9XrR5fRPsiTVt6uFJcaLB1Z8ySJimleeuklFEWp9tWuXTtLhyWExekNRoJ1LozpFISiKGDQwx8PQmGWuuvxkGeaLpjwfhhD+uBIKVfkLmi6523uSovhzE4A1hVFkZxdiN5Qzz5P1q58+ufocl4d34n1z1zOtd1DLB2V3TiamkOPV5Zy+5eb6j/YRhIVq+hM26FDB5YtqyyucnCwirCEsKixXYIZ3TGQEn3Zp831s+DEOrU1/rVfqE20mpAycDLMvwW2fg2DngAXryZ9/mYpebc6TeLqw2M3jGLEwBwCvWyodX5NogarjevSj6DNSoQWsjt3YzqZUUB6XjHpptT92ED7fKwlUXFwcCAw0Mzz7ELYIEetBketBk5vh5WvqTeOeevius5eqjajoWVbSDvE8SUfEXTlVJwdZFM5syqb9iGkFx4ujrXv8WRLXHQQ2hsS4yB+OfS8x9IR2ZW+Ub78/ehAikyZTstLVS89/M0e16Ww+NQPwJEjRwgODiYqKorbbruNxMTEWo8tKioiOzu72pcQ9iQ5q5Dtiecq61L0pfDXo2Aohdjx0PVWywSm0cCARwFw3f4ZX6w4yJ87TxMXn2770xHWqnzFT2gvS0fSuGIqp39eWLCXKz9cy6FkqX1qDK5OWjoE6+ge1qL+g3MlUTFJnz59mDt3LosXL2b27NkkJCQwaNAgcnJq/qWdOXMmOp2u4is01MY25xKiHt9tPM61n2zguQV71Rs2fw4pe9RN3a58t3E6z16sTjdwTutLgJLJidVzeWz+Tm75YiMD31zB4r1JlovLXpWNqOyiLZ+tjmffmSxLR9Q4yutUjq3m8JkM9p3J5lB9XVRF4zIYIO+set0jwNLR1MniicqYMWO44YYb6Ny5M6NGjeKff/4hMzOTn3/+ucbjp02bRlZWVsXXyZOy/4iwL6V6I84OGgbGtFSbfZVP+YyYYfHGTIsPZvBJ4SgAHtQuREEdXk7OKmTivO2SrDSm7CTIOgmKhp9O+zHz34P8ty/F0lE1jqCual1EcQ5TO2XzxZ096R9t3XUStuKnLYn8ufM0mfn11KgUnFNHaQHc/Zoktotl8UTlfN7e3rRp04ajR2tegufs7IyXl1e1LyHsybQr2rP52eGMiA2Axc9AcS6E9IZud1o0Lr3ByIyF+/lRfznZRjeiNUmM0GwDdTtEAGYs3C/TQI2lvD7FP5ZurUO4slMQfeyhRoWyacRodZly9+LtjIgNoKXHJWykKSq8/s9BHpu/k+TswroPzC1Let18m7wwv6GsLlHJzc0lPj6eoKAgS4cihMXo3BxxPLYC9v+prpC46j31P3cL2pyQQVJWIbm4MU+vtkJ/wGFRxf1GICmrkM0JGRaM0o6cKqtPCenJDT1D+fi27vSPse5W5w0i7fQbXanewPD2AfSJ9CGkhVvdB5cnKu7WXZ+CNSQqTz75JKtXr+b48eNs2LCBa665Bq1Wyy233GLp0IRoUufyiknNKfsUVFIA/zyhXu/zIAR2smhsQGVswJzS0ZQaNfTQHCFSSar1OHEJTm1VL+2hI21NykZUSNrFnkNH+GXrycql+OKiOGg1vHtjF356oB8ezvUs6rWRQlqsIVE5deoUt9xyC23btuXGG2/E19eXjRs34udn3XNmQjS2ORuO03/mCmYtOwJr34Nzx8EzGIZOs3RoAPh7VvbvOIs36wxq8jRWE1frceIilRbDmR0AZLbsRkGxvt5TbI6HPwR2BmDe93N56tfdnEjPt3RUzUf5iIqVF9JiDYnK/PnzOXPmDEVFRZw6dYr58+cTHW2jO4MKcQmOpuZQajDSwTUd1n+g3jh6ptVsRNc70ocgnQvla44W6vsBcLV2A2BEAYJ0LvbR68PSUvZAaSG4ePPu1hI6TF/Mp6vjLR1V4ytbpjzO8yD9o32llf4lMjSkPqwiUZERFSGEiT65rQdLJl/G0FMfg74YooZC7DhLh1VBq1GYPjYWAAX4z9CTIqMjMZoztFfU1XfTx8ai1Vhw+bS9qJj26cWpzCIMRjUJtDtl0z/9lb38cF8fYoNlccSleOXv/fR4ZSlz1ifUf7CNLE3GWjrTCiFUbYv3wYG/1J2RR71m2Z4pNRjdMYjZt3dnxsL9JGXBSkNXRmu3cLPbZgKuGc/ojlIE3ygqGr31Zs7g3qTmFOLmZIf/XYf0Bq0z5CZD+lF1d2Vx0U6dU9vnO2hNGIOwoakfO/zNF8K25BeXqq3yFWDJs+qN3e6AgA6WDq1GozsGMSI2kM0JGeRuvw72bWGsNg6fDrINRqOpsuIHe677cXRR2+kfXwsJazD6xqgbcIqL8s4NXTh1Lh8/TxOWeksxrRDCVF+tTaDfzOVs+OtzOL1N3XRw6HOWDqtOWo1Cv2hfAnqOJ8/ojE9xEkUntlg6LPuQkwKZieoEW6selo7G/CIvA2D9st/p9dpy6cNzCXSujnQI1pmW2NpQjYqMqFjC2cNweLHadTTnjNqBMjcZPALVP9rIy9RPGY6ulo5UNIEVh1LJyc2ly6FZ6g0DJoOn9Q/HAnQMD+RAyyF0SF+C44HfIcJOl9I2pfJGb37t+G5nJvvPJDK+azB9ouy0c2vkZbDyNdoV7ia9qIDT5woI862nB4i4NPoSyE9Xr8vUj6gmPR5Wvwm7f67Sy7OKzER1yHftO+q8bVhfGDQFooZYIlrRRH5+oB/HF7yG+54z6nLkfpMsHZLJNBqFDiPvhh+XoNn3h1pXo5EdlS9JeaIS2ov/9iWz9kganVrp7DdRCe4Ojm74lmSz8s4Agr3tdJrLzE5m5PPXrjO09vdgZH3TsOWFtIoWXK1/lZ4kKk3h3AlY8xbs/BGMZf0QYoaDfyx4BYNnkJrVph+tmKslJwkSVqtfba+Aka+CryzbtkeOBem0Pvy5+s3w6eBkY58moy8HF506KpgYBxEDLR2RbTutbktAq57c3SaCTq109r3k28EJwvpB/HIisreDVkblLsae01m8veQQ3cK8609Uqk77WLjjtSkkUTG3/X/Bb/eBvkj9vvVIGPosBHe78NjwftD9DjAa1aRly5ew+Qs49A8cWQp9H4TLnlLfFITNMxqNauHg6jehKFvdqK3TjZYOq+EcnMmJHIPngflkbp6PtyQqF89ggKRd6vVW3bk8MIDL21n/0PwlixwE8cvVD2l9H7R0NDbJ39OZa7u3IsLXvf6Dc8uXJlt/fQpSTGtme36FXyaoSUr4QLh3Kdz2S81JSlWKoi7TG/MmPBSnjr4YSmDD/8En/SBpd1O9AmFGC3cnMfHDXzBsnaPeMPJVm/h0U5O52WrRp9Phher8t7g4GfFq0urgAn7tLR1N0ykrqC0+tpZ5cccsHY1N6hnhw3s3duXRYSYs8bahpclIomJGO75XR1KMeuhyK9z1l1og21B+beH23+C2X8EnCrJPw9ej4eA/5ohaNKHft59i9Nmv0RhL1WQ0cpClQ7poUb1Gk6Xxxq00U52uFBfn9Hb1MrAzh9MKOJySQ2lz2P8msAt6J0+cSrL5a/ESjEZZ+WNWNrQhIZKomMmWr+DPh9SC2R53w7iPL73AsPUIuH+lWlhbkgfzb1VHWOQP2ma9N0hhnHaD+s2w6ZYO55Jc2TUMXY/r1W8OLLR0OLbrTFmi0qo7s5YdYeT7a/hqnQldRm2d1gElfAAAE4ITKZJW+g1WVNqA/aBsqIcKkqiYweYv4O8p6vU+E+Gq9xtvON/VWx1Z6XG3mgT99zwsfEyG2m2I3mAkLj6dP3eeRlnxinpjpxsgqLOlQ7t0bUarl0eWSQJ9scpHVIK746BVcHfSNpu28poodfrnCvcjuDjKyrGGMBqNdJ2xlJ6vLiUpq6D+E2xs6keKaRvTmR3w71T1+sDH1U/Jjd1lUeuoJj9+bdUuptu/gYIMuH4uaOXHac0W700qaz1fSF/NfsY5raYULetb3c9gSwfXGCIGYnRwQck+BWcPgn8zqrFoDPpSSC6rP2vVnVldWmMwGGtqZGCfyupUSIxTP3xpHS0dkc1Iyy2moERPYakeX3f76kqLjKg0opJC+ONBtSalwzXmSVLKKQr0nQg3/whaJ3WofeFj6ooBYZUW701i4rztJGUVAkaecfgRgB9KL2fCgjQW702ydIiX7EwerCluB0DJwcWWDsf2nD2g7pjs7AU+aisCjUZpPps8+nfA6OoDxbksX7GEuPh06VJrIj9PZ3a9OJJ/Hh2Ek4N97fODJCqNaMUr6qdId3+48r2m2Uyu7Wi4/mt1A7ud89SpIBlytzp6g5EZC/dXfDIepdlKV008+UZn/q/0GgBmLNxv8/8pB+lc2Oqkrv4pPvifpcOxPeXTPkFdbHb116VYvD+F5QXqipVtq/7kli82MvDNFXaRxDcFnZsj7YNMnCa0oZ2TkUSlkZzYAHEfq9ev/j9wa8LmTO3HqsW6ABs/hjVvN91zC5NsTsgoG0kBLXqedPgZgC/1YziLN0YgKauQzQkZFo700iiKwoQ77gfAPXkLFOVYOiTbUqWQ9vV/DnDrFxtZeSjV0lE1ifIRx9Ul6nRhP81+AJKzCpk4b7skK42pOF9dAo9M/TQfRbmwYKJa3NrtdnWUo6l1vRVGv6leX/kabPy06WMQtUrNKay4fq12La01pzln9OCL0qtqPc5W+Ya3V5fRG0rgmCxTbpAzO9TL4O7ExaezIT6dwuIGrOSwUVVHHDcY1B3De2kO4URJxSikPYw4mtMfO07x8cqjHEzOrv/gvLLk18EFnD3NHltjkETlUv33PJw7DrpQGDXTcnH0fRCGPKteX/wMHF5iuVhENeU7mTpTzGSH3wD4uHQcObjVeJzNaz0SAOORpZaOxHaUFELKPvV6cDfeuK4Tb13XmR4RLSwdmdlVHXGMNwaTavTGRSmhq3IUynZFs4cRR3P6fftp3l5yiD2nsuo/uGohbVOUKDQCSVQuRcIa2FbWVXT8J+Bi4WWEg5+Gnveqf9q/3QdpR6sth5XiNMvoHelDkM6F27TLaaWkk2T04Tv9iIr7lbL6DnvZz2VZibrUumD/YqmZMlXKXjCUgpsveIfRIVjHjb1C7Sd5rUP1kUSFzQa1ILu35mAdx4mqhrcP4NrurUyrUbGxQlpkefIlMBpheVkfjJ73Vi6tsyRFgdFvQOp+SIwj95sbGVc0g/jsynw0SOfC9LGxjO4YZNFQmxOtRuHl0WF0X7AAgFml11KEE5QlKQDTx8bazeqOvQ4dGWh0xK0wGVIPQECspUOyflX6p9jKp9zGcn4ytsnQjqu0G9VERV/7caLSXf0jTD/YBhMVGVG5WMdWwqnN6jzf4KmWjqaSgxPc8A2FrgF45MTzdMEHKFQuW5biNMsYkfU7vkoOCcZAftFXdk0J1Lkw+/budpU4XtUziqzAvuo3R2X6xyTl9SmturP68Fn+25dMem6RpaNqEuUjjuXp2ZayEZXumiNo0dvdiKPF2VgPFSRRuUhGI6wqK17tcTd4WldmmqltwUMlkykyOjBKu5WHtQsq7pPiNAvIS1e3OwDCr3+d7+7rz6ybu/Lj/X1ZN/Vyu0pSAGL8PQnoPlb9RupUTFO+4ie4G5+uiud/321j+cHmseJHq1GYPlYddVOAQ8YQsoxueCiFdFBOgJ2NODa2whI9hSUNaZ8vIyrNw7FVcHKjOpoycLLFwkjKKmDivG2M+2hdtY3L3vz3ICtyw3m+9B4AHnf4jaGaHRX3S3FaE1v3HhTnQGAnNB2uoX9MS8Z1bUW/aF/7/c83Zrh6mbgRCk1YidCcFeXA2UPq9eDutA30pH2QFx2DdZaOrMmM7hjE7Nu7E6hzwYiGLYa2AAxzi7e7EcfGtnhvMu1eWMwD32017YTcsh4q7n5mjasxSY1KQxmNsLp8NGUCeAY22VMfTc0lt6iUrqHeAPi4O7Hm8FnyivWk5BTRytsVgJSyorNf9EPopCRwp8NS3nOczeiiN0ihcvhUitOaQNZpjJu/QAGKBz+PUzNp5JXtHobiHo5n3gl1N+X2Yy0dkvVK2qV+fPBqBZ4BvHS17XzSbUyjOwYxIjaQzQkZeG2/HPbt4NGYVBRJUup0pmxvHy8XE7cckBGVZiBhjboXhdYZBjTdaMoPmxIZ/t5q3lpcWQnv7KDl3Ru78OWdPfF2rfwlvX9QdMX1V0rvYI8hghZKLu87foKmSr2KFKc1gdVvouiL2GRox6DftdVGvuxZem4xv2aptQalh6RLbZ0q+qd0s3QkFqfVKPSL9qVD3zEAGBPjZOVYPSYOjmbniyN4anRb006oqFGRRMU+GY2w6g31eo8J4GW+TL9EbyCroHJX5MFt/XDSavBwdsBQpbZkdMcghscG4O5cOThWtTitBAceLXmEPKMz/bX7eVC7sKI4rVdEC176ax+7T2Wa7XU0a2lHYMc8AL52voO+0S1x0DaPP7kIXzcyW6lFw5p42U25TqcrO9KWNJNEtj7Tt2gpMDqhKcionBYTNVIUBW83J9M+eBqNVUZUpJjWPh1fC4kb1I0AzVibsv5oGiPfX8PbSypHT1p5u7Lx2WF8fmdPNPXUNZxfnJZgDOKl0rsAmOLwC12Vo0wfG8vC3WeYu+E4N3++kaz8kjofU1yEFa+qm1S2GcPsaZN4eVxHS0fUZBRF4fH77gEHFzQ5ZyDtsKVDsl5VCmknfb+dAW+sYOn+FEtHZVEtdZ5sN6j7/pC4wdLh2I/CLNCXrSaTRMVOrX5Lvex+F3gFm/WpEtLyWHXobLWpAh93J5PPr1qcBvCLfjAL9X1xUAx87/M5o2PcGRjjx7iuwUwaGoPOTbZUb1Snt8P+BWqqOOwFNBoFnWsz+zd2dIXQPur1hDWWjsY65Weona1RE5V9Z7I5nVmAp0vzLh+8s38EPS+7Qv3mhCQqtdEbjDy/YA+zV8WbtvKnfNrHWaf+fdqI5v3X0BCpB9QRFY0DDHy8UR/62NlcUnOK6BvlC8CAmJa8c0MXRncMvKSpgqrFaak5hQQ4f4px8Vjcsk7C30/gd90XzLq5G8Yqw/JpuUUkZxXSsVXzWXFgFstnAJDX7jrcAzpYOhqLMUQMQpOwmpKjq3Hsfb+lw7E+STvVyxaR4NqCfx4bxMGkbDqFNO+/P52rI0QPhPVvq4mK0djsGuGZIiW7kHkbE3HQKPzvsqj6T7DBaR9kRKUBymoNaDMadK0a7WHXHUlj1AdrePynnRRU2YDs+h4heDhfeh5ZXpw2rmsrerePRLnuK1C0sOdn2PMrlA3TAxQU67n3m63c8Gkcaw6fveTnbrbiV8KxVRg1jly15zJGf7CGzPxiS0dlES/vbQmA4fhaMEj9xQXOK6TVuTrSJ8oXNyf5DElIL/WDYfZpyEy0dDRWyVGr4dHLY7irf4RprQ7ybK/ZG5KomKi0GHbNV693u6NRH7pnRAv8PV1oF+hJTmET1ImE9YHLnlKv//Mk5CRX3KU3GvFyccDZUUNIC9sZFrQqRmPFaMqZmFs5jfofQrOb9injGtGTPKMLzsWZkLrP0uFYnzNlIyrBXS0didX5YUc6J5zbqN8kxlk6HKvk5+nMlJFteeEqE7epsMGutEiiYqLDiyE/DTwCKxtZXaSNx9J57e/9Fd+7OGr56+EBzLm7N/5eTbRc+LInIbAzFJyDhY9VrMjwcHbg6wm9+PXB/kT5eTRNLPZm/5/qp2QnD1pd/QJbnhvOezd2rRi1am4mDmuHa+uB6jdSp3KhikSlG99vOsHna+I5kZ5n6aiswuJ9yfybUzadIXUqjcMGe6ggiYqJyqd9ut4C2osfkk3NLuSOrzbxxdqEalMrvh7OjRGl6bSOcM1n6uqlw4th5/cVdzlqNcT4VyYpx9PyWNbMVyCYTF8KK8o2quz3MHj4oXNzJDbYwrtqW5CXiyOayLK9jSRRqS4vHbLKpjSCuvBd3Ale/+cgR1JyLR2ZVbimWzCtOl+ufiOJSo3O5hQ1sH2+jKjYp+wzlRurdb29wadX/SXy93Lh7gGR3N43zPJvXgGxMPQ59fq/z9Q4B3wyI5/rZm/goe+3s+lYetPHaGt2fAfpR8HNl5I+Ey0djfUo31n8xAY1mROqpLL6FJ9ocNExrmsrrugUKIXsZa7pFsLYsdeqK+fSj1S2fhcVHv1xB+1eWMzfu03cZFZGVOzUrh/BaICw/tAyxuTTSvQGXvt7P31eX05SWYtjgGlj2vHq+E60bOpRlJr0fwRCeqv70Pw56YJix2BvV3pF+NA6wINIP3eLhWkTinJh5esAGAY9xYiPdzBx3jZSs2Wbgo35weQpHlCUXdYuXsCF9SkTh0TzyW09KloKCMC1BfiX1V9IP5ULZOSpRfoBXia+n0iiYl/0BiNxR9PI3TgXAEPX2xp0vqNWw+5TWWQVlLBgx5mK262qVkGjhWs+BQdXdVh+61fV7tZqFD64uSvz/9dX2u3XJ+4jtaK+RSQ7A67heHo+64+m4dVMi2irMqBhXanaTt+YsNrS4ViP8qXJQVJIW5u8olLSW/ZQvzkhBbXnWzx5EDteGEHnEG/TTiif+rGhDQmxlkTl448/JiIiAhcXF/r06cPmzZstGs/ivUkMfHMF7381F4+8RHKNLgxf7M3ivTUPrxkMRhbvTWbivG3kF1cObT97RXvm3t2LBwebsL7dUnyjYcTL6vWl0yEjodrdLo5aPKtsdrXvTBZ5RTJ8X01OCqz/UL0+fDrdowL559FBvHFdZ1wctZaOzuK6h7egRceyInSpU6lUpZD2TGZBw2oNmgGj0Uif15czfWfZVNiJ9ZYOyeooikILdyecHEx4KzfoIS9NvS4jKg3z008/MWXKFKZPn8727dvp0qULo0aNIjU11SLxLN6bxMR520nKKuQmh1UALNT3IyFbYeK87RXJStU9ORQFZv57gH/3JvPPnsrlvl1CvRnS1t+6RlFq0us+CB8IJXnw1yO19rv4Y8cprvl4A9N+31OtSVyzt2qm+m/XqifEjgcgNtiLKzrJrq+UJbu9h4wDQEncqC73b+7y0iDrpHo9qDOPzd9B7IuLWbIvub4zmw1FUYhs6c5Rl7KtJ1L2QlGOpcOyXfkZ6pYeKODe0tLRNIjFE5X33nuP+++/n7vvvpvY2Fg+/fRT3Nzc+Prrr5s8Fr3ByIyF+zECHuRzhWYTlLWfL39bfvHPfVzz8XoGvbmy4s1aURTuGxTFA4Oj6B3h0+RxXzKNBsb9nzoFdHwtbJtT42GhLdzQG43kF+spKpXmXYC6Ydr2b9XrI1+R7pm18W8Pbi2htABOb7V0NJZXPpriG4PR2YvUnCIMRojwlVqwqn55sB+LX7wZdGFqreAp+d0pt/bIWZ77Y0/DC2ndfNWVnzbEoolKcXEx27ZtY/jwyt4kGo2G4cOHExdX83xkUVER2dnZ1b4ay+aEDJKy1OLHsdo4XJVijhhasd2obo5lBFJzith7Jovk7EKOpVX2O7ijbzjTxrQnzNet0eJpUj5RMHy6en3pizWuAuoZ4cPvE/vzxZ09ZEqj3LKX1E8pba+E8P48+uMO3lx8kNQcKaKtqsRgJMW3NwCGY1KnUrHiJ0jtsbPqySFsenZYtdYAgsr/Z8LK9ow6ucmi8ViTLcfP8f2mRNYdTTPthNyy0TobW5qMpROVtLQ09Ho9AQHV58sCAgJITq55CHTmzJnodLqKr9DQ0EaLp+qbSztFfaP+WT+4bA/iSvcOjGTt00OJtremaL0fgNC+UJwLfz1a0Qiuqi6h3tWmsvSGZjwFdHw9HPpH3ZJg+Eskpufz164zfLo6vnn/u9TAaIRPTqgbeRYeXmnpcCyvSn0KZaOyAV4uprVBb47KN7dM3GjpSKzGgGhfHrk8hmHtTEw8sstGXsy8oa45WHzqp6GmTZtGVlZWxdfJkycb7bGrrmyZXno3Q4re5Wf9kAuOG9zGn1AfGx05qYtGA+M+BgcXOLZS7QtSC73ByDtLDvG/b7diaI5vygYD/Pe8er3HXeDXhiBvF2bf1p2HhkQTpJMtCKpyctDg2V5t3uWasgOK8y0dkmVJ63yTZOQVM/XX3Ty/w1O94dQW6cVTpk+UL0+MbMvwWBMLY7NPq5eSqDRMy5Yt0Wq1pKRU73yakpJCYGBgjec4Ozvj5eVV7aux9I70IUjnUjF+ctwYRBaVoyYKEKRzoXekDdahmKplTGUjuCXPQdbpGg87np7HF2uPsfxgKisPWabw2aJ2/wRntoOTBwx+BsqWpI/pFMRTo9pZOjqr9OTNV4BXKxRDcfMews89C9mn1P9RAjvz+j8HeO6PPRxOkULR87k6avlp60l+SHDH4OSpjvbKnlEXpyJRCbF0JA1m0UTFycmJHj16sHz58orbDAYDy5cvp1+/fk0ej1ajMH2s2lzo/AHY8u+nj421/+HZfpPUFSxF2bBoco1TQNF+Hsy8thMf3dqNYe1ta6nbJSvKVWtTKNs3ybOZvf6LpSiVXWqb8zLlpMpCWly8+HPnab7flNg0m5LaGFcnLc9d0Z73b+6OoVUv9cbEZpzklinVG4g/m9uwJe1ZMqJy0aZMmcIXX3zBN998w4EDB5g4cSJ5eXncfffdFolndMcgZt/e/YLukIE6F2bf3p3RHZvBklONVp0C0jrBkf8qd44+z7XdQ7iqs+390l+yde+phWktIqHvQ4C6PP2XrScpKJZeGHWKUDcoLDm21tKRWE6VaR+j0cjzV8by4OBo2gU23z2h6nL/ZVGM69oKh4iyD68npU7ldGYBw95dTbeXl5reKiK7rPGorpVZYzOHi99hr5HcdNNNnD17lhdffJHk5GS6du3K4sWLLyiwbUqjOwYxIjaQzQkZpOYU4u+pTvfY/UhKVf7tYMgzsPxlWDwVooaAV+1JWmGJng3xaVzezs5HF84dhw0fqddHvgoOzpzOLODzNccwGtWVUZEtZYlpbd480JKpgCaprE7FyQ5rvepzpmzFT3A3FEVhbJdgxnZphgl/Q1UU1MqISlpuMe5OWoK8XU3v01Ux9SOJykV5+OGHefjhhy0dRjVajUK/aF9Lh2FZ/R+D/X+pQ9V/T4Gbf6ixT0h2YQnXfLyehLQ8fnmwHz3C7biG578XQF8EkYOh3ZUAuDtpeWpUWxLO5kmSUg+fVq1JOuRDEBlqYWTUYEuH1PSkdX6DFJXqSUjLI18fTXdFq9b3ZJ4E78Zb8WlreoS3YO+MUeSbOoJbmK1O5SNTP8LeaB1g/GzQOKrLcPf8WuNhXi6OdAnxpqWHM0UldtwILmEtHPgLFA2MnlmRtHm7OfHQkBjevqGLpSO0ejf1CaNlh6HqN82xJXpuatknWwWCOrPpWDpHU3NkOXsdtiScY/QHa3nyr6MQ1Fm9sTkXY5dRFAV3ZxPHGnLKliY768DZ06xxmYMkKqJuAbEw+Gn1+r9PVW5qdZ6XxnVgyeTL6B9jW62ZTWbQw2J1dQ8974GADpaOyCZ5uTjiGKXWqXCiGe6GW16f0rI1OHvy5K+7GP7eGjYeS7d0ZFYrys8dLxcHfN2dMEo/lYuTdUq9tMH6FCRRESYZ+DgEdoKCc7Do8RpXAXm5ONLC3cki4TWJbXPUvUZcdDDk2Yqbv1x7jK3HM2Tvo4YIL0tUTm2B0iJLR9O0kiobvRWXGgjwdMHNSUvHYJ2lI7NaQToXdk0fyS8P9kcJ66ve2MwLal/7ez/PL9hD/Nlc004oL6S1wWkfJFERJtE6wrhPQOMABxfBnl/qPDwuPp3bv9xkP7ss56TAsrIdpoc+D+5q7dKZzAJe/+cA138aR2JGM29g1gB7i/zJ1raA0kI4vd3S4TStM5Wt850cNPw6sT97XhqFzs229l5pSoqiVBaMhpYlKin7mvUGhX/tOsO8jYnkFpr4f6wNN3tDEhVhsqDOMHiqev2fJysz9POU6A089esu1h1NY/aq+KaN0VyWTIOiLLXdea97K242GI1c3yOEYe38CZfN5EymN8LaYnX/LMPxZlanUmXFT7lmtZrwUnkFgXd42QaFWywdjcU8MbItDw+NMX0TSxtu9oYkKqJBBk6B4O5QmAV/PlzjFJCjVsPMaztxS+8wHhgcZZEwG9XR5bD3N7WA9qoP1B4zZUJauPHW9V348q6eFg3R1nQI9sKrrbraR2lOBbXZSWpRo6KpLAoVJlm6P4WbP4/jrcUHoXz6pxkvU76xZyhPjmpr+kicDTd7QxIV0SBaB7jmM3UvoPjlat1GDQa19mPmtZ3wdLHx4eySAvj7CfV67wdq3ZfF5D4GAgAHrYZBw8cDoJzc1Hz2bikfTfFrB07uXPPJem7/chMJVXZhFzXLLSph47EMtp04V6WfSpylw7IdNtzsDUlURIP5tYFh09XrS56HjGP1npKYbqP1G2vfhXMJ4BkMlz9XcbPRaOSrdQmkZhfWebqog38suHhDSR4k7bJ0NE2jyrRPTmEJOxIzWXc0DZ2rjSf0TaBPpC/v3diFF66KrRxRObW1+SS5VZzJLODY2VyKShvQBbuimFYSFdFc9HlQXblRkgcLHlKX7tagVG/gmd92M/TdVew6mdnkYV6Ss4dg3Qfq9TFvVus9EHcsnVcW7Wf4e6sbtteGqKBH4ZyfOmXWbOpUqiQqro5aFj48kPdu7IKPPa+WayTB3q5c2z2Ejq104Nde7QdSkqeuxGtm5m44zuXvrubNfw+ZdkJRjlpjh0z9iOZEo4HxH6s7ByfGwfpZNR7moNWQX6xHbzCyKcGG+kQYDLBoChhKoM1oaD+22t3ODhp6hrdgXNdWuDhqa30YUTuD0cgXJ9Qd0vMOr7Z0OOZnNKq7bQMEd8dBq6FTiI5ru9tmcaNFaTQQWrZBYTNs/FaqN+LmpCXMx9W0E8pHU2y02RuSqIiL1iICRr+hXl/xKpysuQL/pas78PMD/fjfZdFNG9+l2Pw5nFgHjm4w5q0Ltg3oEe7DrxP7q8PQ4qI4ajU4RA0CwC15c62jcnYj6yTkp6tL/KVZ4EU5mZHPkn3JHE7JqVym3AwTlRfHxrJvxihu7xtu2gk23uwNSVTEJel2O3S4Fox6+O0eKLhwesfH3YnekTa098/Zw7CsrAZn5CvQovb/DJwc5M/nUky543pw8kRbnA2p+y0djnmVT/v4x4KjC3PXJ7Bsf4rstt0An6w6ygPfbWPR7iQIKyuoPbnZ0mFZhKIoOGhN/P/Hxpu9IYmKuCSKAmM/UPsaZCbCosk1Llkul5lfzPtLD1Oqt9L9gPQl8Mf/1EZk0cOg573V7k7PLeK3bacoLrXS+G2N1qHyDcfe61TKG9u16k5+cSkzFu3nvm+3klNYYunIbEZskBedWunwcXOEVj1A0aojVeVLb0XNbLzZG5KoiEvmooPrv1aHtPf9Adu/rfEwvcHI9Z/GMWv5Eb5cl9DkYZpk7bvqJ18Xbxj30QVTPt9tPMETv+xi4rxtFgvR7oT3B6AkYZ2lIzGvKoW0uUWlXNOtFX2jfPD3crF0ZDbjjn4RLHxkIBMGRIKTu7qtB81r+udQcg4T5mzm3f9MLKTF9pu9IYmKaBQhPeHy59Xr/06F1IMXHKLVKPzvsihi/D3oFWGFU0Gnt8Pqt9TrV75b46cPXw9n/D2dGdfNdud6rc1XJ9V/59Jj6+ocjbNpRmPlZoTB3fD3dOG9G7sy/3/9LB2ZbSvvp9KMEpWjqbmsOnSW9UfTTD/JDqZ+TNwjWoh69H8Mjq2GYyvh17vhvmXqp54qbugRwriuwTg7WNlKmZIC+OMBtdamw7XQ6foaD7ujbzg39QxFOp43nuKArhQccsK15Jy6JNy/naVDanwZx9TloVpntUZFNI7Q3rD5s2aVqHQO0fHGtZ3wcGnAW3f51JgU04pmT6NRu9a6+6uFkQsmXvAJWVGUaklKgxoWmdPiaZB2GDwC1dGUOjg5aEwvYhP1uqFPFJrypaaJGywdjnmUT/sEdgKto9SlXIKpv+5mwBsr2HA0rbLxW9JuKG4e3X1Dfdy4uXcYV3VuwOiIjTd7QxIV0ag8A+Cm70DjCPv/hLXv1HroP3uSuOytlRxKtvAOqNu/LdsKQFF7w7hdOC31164zbDuRYZHw7F1LD2ecYy5Tv7HXgtoq9SmFJXq6vbyUgW+uICtfEpaGSs8r4nRmAfFpeaALUd98jfrmtwu3qeyg2RuSqIhGF9YXrixLUFa8Cgf/ueAQo9HIb9tOkZJdxGerLbjD8qltlXv5DH0OYoZfcEhWfgnP/7GH62bHNWxeWJiurKCWExvss06lyoqf+LO5lBqMFBTr8XKVmfeGeuTy1vz6YD/GdS17062oU9lo0biayuaEDBLS8kxfOWkHzd6QREWYRY8J0Ot+9frv/7uguFZRFGZe14nHh7fhjesstItsbir8dDvoi6HdVTDoiRoPKzUYGNMxiNggL/pG+TZ5mM3BEcd2lCoOkHNG3VvJnhj0lXsZBXejQ7COXdNH8t29fWQzy4vQJdSbnhE+eJVveBrafPqp6A1GbvtyI0PfWUVKTpFpJ9nB0mQkURFmM3qmuh9QcQ7MvwUKzlW729/ThceGt7ZM0zR9CfwyQX1jbNkGxs9Wa2xq4OvhzJvXd2bBpAFopYrWLLL1juzQR4E97vuTdkTdk8bRXf1dA3SujsQGe1k6MvtQtfGbwb77G2UXlBDZ0h1PFwcCTV3WbgeFtEiiIsxG6wg3fgO6MHXVww83QVFujYcajUb+3HmavKIm2gn1vxfgxHpw8oSbvgeX+t80pAut+XQO0VHcqmyp7gk7K6gt398nqAtorGy1mw0yGIwsP5DCF2uOqcX4AR3VrS4KM9WCeDvWwt2J/x4fzO7pI03/0GQHS5ORREWYlXtLuHW+2hTu5CZ1ZKWk4ILDXvxzH4/N38mMhfvMH9Pa92DTbPX6NZ+CX5saD4s/m8tLf+0jLdfEIVZx0Ry1GgZcfjUAmhN2NqJSpZC2oFjPY/N38PW6BOvtzmzlFAUmz9/Ja/8c4ER6vvqBqFUP9c5msky5QVOG2WX7/NhwszckURFmF9ABbv9d3Wk5YQ38fCeUFlc7ZEynQJwcNLQN9MJozmLKuE9g+Qz1+vCXoP1VtR763tLDzN1wnOl/NUHyJNQhfEUDmScqN1GzB1USlT2ns/hz5xk+WxMv04gXSVEUhscGcGXnICr+BZth4zeT2cmIipSdC/ML6Qm3/gzzroMj/8Fv98L1c9S9XoD+0S1Z+/RQAszZTnzLl7Bkmnp98DMw8PE6D79/UBSHknN49PLW5otJVDA6eVDk1wmX1F0Yjm9A0+VGS4d06fQlkLxHvd6qO0GKC0+MaINGo0gh7SV4/6au1W9oJonKm4sPcjApm3sGRjKotZ9pJ0mNihANEDEAbv4etE5w4C+1IVyVkZWqSUqp3tC4TbG2f1e5DHnAZBjyTL2ndA31Zsnky2gbaLtL+myJ3mBkfoo6PJ15YKWlw2kcqQfUDS6dddAiklAfNx4Z1ppJQ2MsHZl9KW8YmH4U8uy3hcDmhAxWHjpLVkED/m+0g2ZvSKIimlTMMLjhG3UDwz0/w3fjIfdstUNScwq59ctNPPLjDgyGRpgG2joH/npEvd5nojrlU8unWaPRWK0JlwzPNx0HrYa8ILXTqFuSnXwyPr1VvQzuWuuqMnHxKup8XFuAX9nWC3a8TPmZMe2YeW0nuoW1MO0EO2n2hiQqosm1uwJu/hGcvdSVN18MVVtgl0nLKWbXyUy2Hj/H0bM1rxIySXE+LJgEiyYDRuh5j7pkuo4h9wU7TzPknZUs3pt08c8rLtpDd94OgEtWvNrnxtadKktUQnuTXVjC9sRz1rNthA1LTM/nsrdW0nfm8sobm8H0T68IH27pHUYrb1fTTrCTZm9IoiIsos1IddNCn2jIOglfjYS9vwMQG+zFh7d048+HB9Am4CL/uNLj4asRsHOeWqB5+Qtwxbt1JilGo5GftpzkXH4JR1IuIUESF01x8wH/Duo39rBM+dQW9bJVTzbGp3PtJxu45mM7eF0W1tLTicSMfNJyizmXVzZ93AwSlQazk2ZvSDGtsBi/tnD/cvj1Xohfru64HL8Chj7LqA7V/7CKSw1oNQqbEzJIzSnE39OF3pE+F07NGI1q/cufD0NRNri1hOu/gqgh9YajKArf3tOH+VsSubV3WGO/WmGqiAGQuo/ShPU4dBhv6WguXkGVvh4hPck+WIiPuxMdW0mjt0vl5uTAbxP7EerjhrdbWYfa8g0KT2+H0iJwcLZojI3tdGYBx87mEuXnYfqIip0U0iKJirAo1xZw2y+wbDps+D/Y8R3s+QX6PAgDJ4NrC46dzeXGz+LQG4ycq1I/EqRzYfrYWEZ3DFI7Uh5eDOveq/wUG9oXbpjToE8TTg4a7uwXYY5XKky0KCuSq4CsgyvxrX31uPU7vU29bBEJ7i25vgdc170VhSXSP6Ux9Ag/b/NQnyj1g0l+mrplQWhvS4VmFsv2pzD9r32M6hDAZ3f0NO0kO1majCQqwuI0Whj5KrQbC0tfVDcXW/8BbJsLfR/ihwN+5OS2oAinaqclZxXyxLwNBA86S+fjc+HsAfUOrTP0fVCd7tE61vv0n6+Jp0RvlJUYVuJcyx5wCFrkHoX8jBp3s7YJ5fUpIb0qblIUBVcn6U5rFoqijqocXASJG+0uUXF20NDa34PW/g2YDreTZm9IoiKsRlgfuGexOjKy7CU4exBWvc7zwFRnLQeMYewxROGiFBOupBCupOCnZEHZAApOntDrXug7ETwDTXrKHYnneP0fdcPEXhE+9I600TdFOzKqTxeK9kbjnBWv1hu0HWPpkC5O+cheiImffkWDnDqXz9L9KTg5aLitT7h6Y2gfNVGxwzqVm3uHcXNDp6RlREUIM1AU9Y2p9UjY/TMZW39Ff3ILfkoWnZUEOmsu3Fk3yehDSbe7CRv1KLh6N+jpuoW14KlRbSnRGyRJsRL+Xi4QPRC2x8PxdbaZqBiNlUuTQ3qyYMdp5mw4zjVdg5kwINLS0dmFhLQ8ZizcT7Sfe2WiUl6nkrhR/Rk096Z6WVJMK4T5aLTQ9RbWchmPHd1BK9Loqomng+Y4uUYXThgDOWH0J9EYQDbuzIroSpiJSYrBYCSroIQW7upUkkz5WKHwAbD9GzVRsUUZx9TdwrXOENCJzZsPsetkJn0kGW40bQI8GdUhgLaBVYqTg7qo/+b5aerKv5bN+G/baFS3owBoYft1d5KoCKvl7+kCKJzGj9MGP/429K3juPrtP5PNU7/uwtPFgR/v7yttzK3UmRY9CQYMSbvRFGQ2eKTM4sqnfYK7goMTDw2Jpk+kD9F+HpaOzG4EeLlcWFTq4AytukNinFrrZieJyrm8Ym78LI5wXzc+v6MnGlMaUeamQEm+2p5BF9oUYZqVRfuoREREoChKta833njDkiEJK9I70ocgnQu1/VkqZat/PF0c+HD5EY6n5dX5eDo3R46k5rL3dDanzl24i7OwDpkOfhwzBKLBQEmCDY6qVNSnqIW0IS3cGNe1FR1b6SwbV3NQ3k8lcaOlI2k0iRn5HEnNZc/pLNOSFIBzx9VLXQg4ONV3tNWzeMO3l19+maSkpIqvRx55xNIhCSuh1ShMHxsLZUlJVeXfTx8by+/bT/Pe0sO8v+xwxf2HknMY9u4qxv5f5RtdK29XPr61O2ueHkqoj1uTvAbRcO0CPTnrp77hKMfXWjqchqto9NbD0pHYvRK9ofreN+V1KnZUUBvl58539/bm5XEdTT8po6yer4V91ERZPFHx9PQkMDCw4svd3d3SIQkrMrpjELNv706grvr0TqDOhdm3d2d0xyB6R7ZgUOuWjO9a2djIyUFD/Nk8jp3Xhn9EbAA+7rb/CcOeaTQKfYaOA8DhhI2NqBTnQ/Je9XpILzbEp7Fgx2mSsmQEr7HNXZ9A+xcW89rf+ytvLB9RSTusLm+3A54ujgxq7ceoDqatZgTgXHmiYvv1KVhDjcobb7zBK6+8QlhYGLfeeiuPP/44Dg61h1VUVERRUVHF99nZ2U0UqbCU0R2DGBEbWGtn2tEdg9TGb1UEe7vww/198HW3rw6VzUbEIPUyZS/kpYO7r6UjMk3SLjDqwSMQdCF8//cO/t6TxNOj2/LQEPuombAWvh7OlBqMnMyokgS6+UDLtpB2yLaXt1+q8hEVH/sYUbFoovLoo4/SvXt3fHx82LBhA9OmTSMpKYn33nuv1nNmzpzJjBkzmjROYXlajUK/aNPfrJwdtPSPbmnWmIQZefhT6tsOh/SDFBxZjWvXay0dkWmq9k9RFNoFenI6s4Dupu54K0w2tJ0/cdMuJ9DrvGL6sD5qopIYZxeJytL9Kbg5aekS6o2Hs4lv2eU1KjL1U7NnnnnmggLZ878OHlSbbE2ZMoUhQ4bQuXNnHnzwQd59913+7//+r9qIyfmmTZtGVlZWxdfJkycb+yUIIazAwuxoAM7uWWrpUEx3XiHtI8Nas2DSAPpG2ciIkA3xcHYgSOd64eq90PJ+KvZRp/LCgr3c9uUmjqTkmH6STP3U7YknnmDChAl1HhMVFVXj7X369KG0tJTjx4/Ttm3bGo9xdnbG2VmG84Wwd4UhAyDhb3xSbegN51RlozdhIeUFtWd22PwGhXqDkQ7BXrg5a4nwNbF+sygH8s6q12Xqp2Z+fn74+fld1Lk7d+5Eo9Hg7+/f2GEJIWzMjdffAm8/h0dOPOSkgGeApUOqW9ZpyDmj9q4I7kZGXjEt3BylX48ZrTiYwprDaQxp68eQtmXvG1U3KDyzU50KslFajcJXE3qZcGQV58oavbn6gIt9LIm32KqfuLg4PvjgA3bt2sWxY8f4/vvvefzxx7n99ttp0ULmc4Vo7rTuPhBYtiTTFpYpl7fND+gATu7c8dUmer66jC3H7WP1iTVacziNuRuOsyE+vfLG8g0KQW381tzY2bQPlkxUnJ2dmT9/PoMHD6ZDhw689tprPP7443z++eeWCkkIYW0iBwNQEr/a0pHUr0p9SkGxnoS0PNLzigmXnj1mM7itH/+7LIqBMecVzlc0frOhacPGYmcrfrDkqp/u3buzcWMzzHaFECbbpnSgB3Bu33L8x1s6mnqcrExUXJ207HhxBAeTctSNFoVZDG3rz9C2NZQKVB1RseENCmcs3Mf6o2lMGhrDuCp9oupkZyt+sIaGb0IIURtjWD/0RgX/ktMYM614hV9JAZzZrl4v+zTv7KAuKRUWENQFHFwgPx3Sj1o6mot2KDmHwym5lOqNpp8kUz9CCNF0OseEk9+yMwCKNe+mfGor6IvVRm8+Na9qFOahNxhJTM8np7BKK30HZwjurl634X1/3ryuM9/c05uBrRvQE8oOp34kURFCWC0nBw2e7Yaq31hzQe2J9eplxADyivXc9fVmPl55lFK9wdKR2b0bP4vjsrdXsv5oWvU7wmx/g8JQHzcGt/EjwNTpQ30pZJWNPMrUjxBCNJHIsnb6CWvUegNrVD7aEz6AbSfOsfrwWX7YlIiDVv6LNbcwHzecHDRk5JVUvyN8gHpZnkQ2B9mnwFAKWmfwDDLhBNtg8b1+hBCiLsXBfXBQHNBknaQo7RjOftGWDqm60qLKFT8RA2nj5MlLY2Olf0oTeXlcB965oUvF3l8VQnur+6yfS4CcZPBswKZ+VuBwSg7bTpyjY7COTiEm9kOp2DU5HDT2kyTbzysRQtglR1cPdtEagFNb/rZ0OBc6vR1KC9UmYy3bEKhzYcKASO7qbz/FjNbM08XxwiQF1GZn5X14Tmxo8rgu1ZrDZ5n2+x4+XRNv+kl2uOIHSVSEENZOURRKI9U6lZB0K3zDOVE+7dPfZpfB2q2K6R8r/L2pR5DOlSFt/Rq2oaUdrvhBEhUhhC3oNfxGAJxProXSYkuHU135m2DEQBLS8lh5KLX6ChRhVkajkZn/HOCeuVs4m3PehrZh/dTLxDiLxHYpruwcxNy7e3PvwAaMjtjhih8kURFC2ITALuDuB8W5cNKKuo3qSyq7n4YPYMGO09w9ZwvPL9hr6ciaDUVRWLwvmRUHUzmamlv9zvD+6mXKPijItEh8TUqmfoQQwkI0GvRRlwNwastflo6mUtIuKMkD1xbgH4u7s5YwHzd6R/pYOrJm5YHLonl1fEciWp63XYGHP/jGAEbrSnDrYTQaMTZ0hZvRWCVRsa+pH1n1I4SwCeuVblzGT5QeXmrpUCqVL0sO6w8aDf+7LJr/XRaNwWCly6jt1K19wmq/M6yf2p32xHpoM6opw7poCWl5XPnhOtoHefL7QwNMOyk/A4qy1estws0aX1OTERUhhE2I7nMVBhQiShMwZp22dDiqKo3eqtLUtApFWEZFQa3t1KkcT8+joERPQUkDGgaWj6Z4BoOjq9liswRJVIQQNqFVq1CUVmpbdCV+haXDAYO+sutpeH+KSvWWjqjZMhiMnM4sYOOx9AvvDC8rqD2zA4rzmzy2izGotR8rnxzC29d3Nv0kO13xgyQqQghbosSMUK8ctYLpn+Q96lC7sxcEdua+b7Zy+bur2BCfZsLJojGdyy9mwBsruOWLjeQXl1a/0ztcHWUwlMDprZYKsUEctRoiW7rTsZWJjd6w3xU/SKIihLApMcMBMBxdSUmJhZcpl0/7hPWlyADbT5zj2Nk8/D2dLRtXM+Tr4UyAlzMxfh6k5573e6Eolat/bGj6p8HsdMUPUkwrhLAprbqTo/HEszib/VtX0LHfaMvFcrwsUQkfgLODlrhnh7ExPp1oPw/LxdSMbXhmWM0daimb/tn7KyTaRuO3z1bH08LNiVEdA9G5Opp2kkz9CCGEFdBoOerRG4DSQxac/jEYKt/0IgYC4OXiyMgOgbLHj4XUmqRQtioL4ORmtfeNFSvRG3hrySGe/m03BcUNqHuSqR8hhLAO4X2vBqBr0RbLBZG6HwrOgaM7BHWxXBzCNH7t1F43JfmQtNvS0dSpsETPbX3CuLydv+nTiCWFkHNGvW6HUz+SqAghbIpP5yvUK0m7IDfVMkEcW6VehvVhT1I+D3y3lb92nbFMLAKAkxn5/O/brdz25cYL79RoqrTTt+7pH08XR14e15GvJ/QyfZl75gn10tkL3Oyv2aAkKkII2+LhXzmKcXS5ZWI4vFi9bD2S//Yns2RfCov3JlkmFgGAm5OW//ansCE+veYpk/JExQY3KKxX+bRPi3C73BhTimmFEDbnXPBltEjaxealP9G76y1N++QFmZVvdm1GMbbED42i0DXUu2njENX4ejjzyviORPq611yvUt74LTFOrTHSWOfn9PziUlwdtQ2rdUo/ql76RJktLkuyzp+UEELUoTRa7afSLncTSelNvNlc/HIw6qFlW/CJok2AJ4+PaMPQdv5NG4e4wB19wxnYuiVODjW8tQV1VmuKCs6pNUZWatL32+k4fQl/727ACF3qAfXSr73Z4rIkSVSEEDbHr91A8pxa4qXkE3i2iYfyD5VN+7S14NJo0XBax8outcfXWjqaWp3IyCevWE8LNxOXJQOcLUtU/CVREUII66DR4t7tegCU/Qua7nn1pZVdcduM5tdtp9iReE42IbQSuUWlbIhPY/mBlJoPiBikXiasadK4GuLfxwaxbMpguoaZOJVoMEDqQfW6f6xZY7MUSVSEELapw7Xq5cF/1OWZTeHUZnXqwLUF+QHdefaPPVzzyQaOns1tmucXddpzKotbv9jESwv31XxA5GXq5fH16l5NVsjZQUuMvwduTiaWkGadhJI80DpJjYoQQliVkF7oPYKhOIelf81rmucsX+0TM4KsIiMj2gfQPsiL1v7SjdYatAnwINzXjbYBXuhrGuUK6gLOOijKUpe324Py+pSWbUBrn+tjJFERQtgmjYaTwaMAMOz9veY3psZWXp/SZhRBOlc+vq07/zw6ULrRWglfD2dWPzWUL+/qWfPKH40WIspW/1hhncqSfcm8veQgW45nmH5SeWGwndanIImKEMKWtRpwGwDDNNsxFOeZ98kyjkHaIVC0FZsjApKk2BorrlNZuj+Fj1fGExefbvpJZ8vqU/zamS0uS5NERQhhsxzDeoJ3GA76Ahzjzbz3z+H/1Mvw/mQY3MjKt+49Y5o7o7GWEbbIskTlRJzV7fszpK0ft/QOo3dkA7rLVoyo2GchLZKoCCFsmqJAh2vU6/v+MO9zHf5XvWwzmlnLDtP91aXMWnbEvM8pGmzN4bOMen8Nk37YXvMB/h3A1UctQD2zo6nDq9NVnYOZeW0n+kb5mnaCQQ9nD6vXZepHCCGsVNnqn9JDS9h8KNE8z1GYra4UAYxtRnEiIx+9wUj3cOlGa20ctRoOpeSw93R2zQdoNBU7XpOwuklja3QZCaAvAkc38A63dDRmI4mKEMK2BXXhnEsoDvpCti/9wTzPEb8CDCXgG4PSsjVz7+7NksmXMSC6pXmeT1y0TiE65kzoxff39an9oPJlygnWU1CblV9CWm5R7VNWNSmf9vFra7VbAjQG+31lQojmocr0zwjDhob9R2+qw0vUyzaV3WjbBnqavrutaDIezg4MbedPqI9b7QeVJyonN0FpUZPFVpc/dpyi56vLmPzTTtNPKl+abMf1KUiiIoSwBy163QRAdFYcSlFO4z54SWFFfUpu2DCKSw2N+/ii6bVsAx4BUFoIp7ZYOhoA0nKLURQI9nY1/aTy1vl2vOIHSVSEEHYhoIP65qMvhsZuqb/vD7UbrVcIbx1sQf83lvPXrjON+xyiUR1Py+PHzYm1t9JXFKtbpvzkqLYceHk0Dw6ONv0kGVERQggboSjQ7XYACtZ8yPL9Ddh5tj5bvgTA0ONu1h3LIi23GF93p8Z7fNHo1hw5y7Tf9/Dj5jqKq8uXKVtRnYqLoxadq4mbEZYWQ/pR9bodr/hBEhUhhN3oMYESBw9cM4/w9+/fUlTaCHu5nNkBp7eCxhFNjztZMvkyvrqrJ/1MXT4qLKJjKx2DWreke3iL2g8qH1E5tQWK85sstkaTfhQMpeDsBV7Blo7GrMyWqLz22mv0798fNzc3vL1rXsKXmJjIlVdeiZubG/7+/jz11FOUlpaaKyQhhD1z0aH0uhuAh53+pqC4ERKVLV+pl7HjwMMfR62GYe0DpIjWynUPa8F39/bhoSExtR/kEwVeIepqrpMbmzK8C+w7k8XDP2xn7voE00+q2jrfzrsjmy1RKS4u5oYbbmDixIk13q/X67nyyispLi5mw4YNfPPNN8ydO5cXX3zRXCEJIeycQ7+HMGocicrfhXfG7kt7sIJzsOdXAEp63Ns4AQrroShVpn8sW6ey51QWi3YnsfxgquknVdSn2Pe0D+ZMVGbMmMHjjz9Op06darz/v//+Y//+/cybN4+uXbsyZswYXnnlFT7++GOKi4vNFZYQwp55BaN0VlcAsX7WpT3Wzh+htAACOjJ9hwfjP17fsD1YhMUZDEYKS+oYWYsaol7Gr2iymGrSPbwF08a04/oeIaafVLHHjyQqZhMXF0enTp0ICAiouG3UqFFkZ2ezb9++Ws8rKioiOzu72pcQQlTo/wgAxgML+f6fFRe3q7LBUFFEW9L9HlYeOsvOk5mNHakwo9mr4un40hLeX3q49oOiL1cvk3ZBTi0rhJpAmwBPHhgczbiurUw/qRnsmlzOYolKcnJytSQFqPg+OTm51vNmzpyJTqer+AoNDTV7rEIIG+LfDkPrUSgYMW74iCX7av//pFYJqyAjHpw8cex6E4seGci0Me3oG9WAzeKERXm7OZJfrOdwSh19dTz8IaiLet3CoyoNUpyvts/H/pcm09BE5ZlnnkFRlDq/Dh48aL5ogWnTppGVlVXxdfLkSbM+nxDC9mgGPAbAjQ5rCNBkNfwByotou94Czh74ejjzwOBoFDsvWrQnozoEsmzKZXx5V6+6D4wZrl4eXdYkcZ2vqFTPthMZDduNO+0wYAQ3X/DwM2d4VsGhIQc/8cQTTJgwoc5joqKiTHqswMBANm/eXO22lJSUivtq4+zsjLOzs0nPIYRopsL7Y2jVE6fTW+mR8it0eN70c7NOwaF/ANgfciP2/3nVPvm4O+FjSr+bmBGw9t2y/Zz0oNE2RXgVjqTkct3sOFq4ObLjxZGmndRMGr2Va1Ci4ufnh59f42Rv/fr147XXXiM1NRV/f38Ali5dipeXF7GxzeMfXwhhJoqijqr8fAdsnA0dryPLIwadWz3NtIxGWPwMGA0ccunKlT+mMj0ngQkDIpsqctHUQnqBsw4KMuDMTgjp0aRPn11QQpDOhdAWdexNdL6zzWfFD+asUUlMTGTnzp0kJiai1+vZuXMnO3fuJDc3F4CRI0cSGxvLHXfcwa5du1iyZAnPP/88kyZNkhETIcSla3el2tSrOJe8uddz5ZsL2JyQUe0QvcFIXHw6f+48TVx8Ooa178GBhRg1jvwb+ABaRaGPNHezWdtOnGPmvwfq3vJA6wBRg9XrFpj+6R/Tkrhpw/j+/jp2ez5favPY46dcg0ZUGuLFF1/km2++qfi+W7duAKxcuZIhQ4ag1WpZtGgREydOpF+/fri7u3PXXXfx8ssvmyskIURzotHCjd9i/GIo7ueO867xHX7bHEnvSLUgdvHeJGYs3E9SViEAl2l20cfpLQCUK95mcs9buTY9nzDfBnzSFVZl24kMPlt9jCs6BXJ1lzq6t8YMhwN/qYnKkKlNGWIFR20Dxg2a2dSPYjTLnuhNJzs7G51OR1ZWFl5eXpYORwhhbVIPYPxyOEpxLsZud6Jc/SGL9yUzcd52yv/zC1VSWOj0PN5KHj+WDqXFzbMZ3THIwoGLS7X7VCY/bz1Jv6iWXNm5jp9n1il4vwMoGngqHtyseHVXbiq80xpQ4JkT4KKzdEQXzdT3b9nrRwhh3/zbo1w/BxQNyo5vMcR9wgt/7q1IUlwp5HPH9/FW8thhiGF66QRmLNx/cf1XhFXpHOLNq+M71Z2kAOhC1MZpRgMcW9lU4VGiN3DNJ+uZ8tNO8opM3D7mZNkiFP/2Np2kNITZpn6EEMJqtBkJI16B/55DWfo8P+oDKXRyogAndOTRRnOas0YvJhY/RjGOJGUVsjkhg37RUp/SbMQMU4tUjy6Hjtc1yVOeSM9nR2Imh5JzeOeGLqaddHKTehna26yxWRNJVIQQzUO/SZB+BGXbXGI01YsrS4xaJhU/RjKViUlqTqEFghSNzWg0kpJdRKnBQEhdK2tihkPcR2qditHYJBv9BXg58+ntPcjMLzZ9o8tTW9TLEElUhBDCvigKjJ3FzqCbeOP39bhQjDPFuFLMUWMwe43Ve0D5e7pYLFTReD5ZFc/bSw5xQ48Q3q5r1CK8Pzi6QW4KpOyFwJr3qWtMni6OjO5Ye9+wC5QWw+nt6vXQBqwSsnGSqAghmpVO3ftxYmkByVmF1FSFogCBOpeK1UHCtkX7eaDVKOQV11MD4uAMkZfB4cXqqEoTJCoNlrwH9EXg6gO+0ZaOpslIMa0QolnRahSmj1WXdZ4/2F7+/fSxsWhNHYoXVm1oOz/2zRjFJ7eZ0MitvJ3+kabpp/L37iT2ns6iVG8w7YSq9SnNaDsHSVSEEM3O6I5BzL69O4G66tM7gToXZt/eXZYm2xFnBy0ujia2xY8Zpl6e3AiF2WaNK7+4lId/3M5V/7eOc6bu83OqbMVPSD37F9kZmfoRQjRLozsGMSI2kM0JGaTmFOLvqU73yEhKM+YTBb4xkH4UjvwHna4321Odyy+hX5QvablF+Hma2I29fGlyM6pPQRIVIURzptUosgS5GVhz+Cw/bEqkU4iOSUNj6j64/VhY977aqdaMiUorb1d+uL+v6SdknYLs06BooVV3s8VljWTqRwghhF1LyS5k8b5k1h45W//BsePUyyNLoTjf7LGZrHw0JbAjOLlbOpomJYmKEEIIu9Y3ypfnr2zPEyPb1n9wUFfwDoOSfLNuUtjg3WuaYf+UcpKoCCGEsGuhPm7cNyiKXhEmLDlXFGh/tXr9wF9miaeoVE+3V5Zyw6cbyC40sZC2YsVP86pPQRIVIYQQ4jzlicrhJVBa1OgPfyQll8z8Eo6k5uLpbEKpaEkBJO1Wr4c2rxU/SDGtEEKI5iCnsIR9Z7JxctDQPaxF3QeH9ALPIMhJgmOroM2oRo2lXaAn/z1+GSnZhSim9EM5sxMMJeARAN7hjRqLLZARFSGEEHbv122nuPnzjXyyMr7+gzUadfUPwP7Gn/5x0GpoE+DJoNZ+pp1QtX9KM2r0Vk4SFSGEEHavQ7COVt6u+HuZ2LOkfPrn0N+gN7GOxFyaaf+UcjL1I4QQwu71jvRh/TOXm35CeH9wawn5aXB8HUQPbZQ4SvUG3l92mNggHSM7BOCorWe8wGiskqg0vxU/yIiKEEIIUQONFtpdqV5vxNU/x9Ly+HhlPE//ugutKdM4545DXipoHNWl082QJCpCCCGaFZM3AYwtX6a8CAz6RnluR62GW3qHcXXXYDSmbNdQ3j8lqAs4utR3tF2SqR8hhBDNwo7Ec0z7fQ+eLg788mD/+k+IHAwu3uqIxslN6nTQJYps6c7MazuZfkL8CvUyrAHt9u2MjKgIIYRoFlq4OXEwOYddJ7MoKjVhhETrCG2vUK/v/9Ps8V1AXwKH/lGvl09DNUOSqAghhGgWwn3d+PT2HqybOhRnB61pJ3W4Rr3c/fMlN38zGIyk5hSafsLxdVCYpRb1NtMVP0iiIoQQorlQFIXRHQPx92pArUfMMPBqBQUZcGDhJT1/YkY+vV9bzsA3V2AwmLDXT/nztbtSLe5tpiRREUIIIWqj0UL3O9Xr2+Ze0kMlpOehUcDX3an+QlqDAQ7+rV4vbz7XTEmiIoQQotkoLNHz89aTTP9zr+k7GHe7HRQNHF8LaUcv+rmHtvVn34zRfHRr9/oPPr0NcpPB2QsiL7vo57QHkqgIIYRoNjSKwvML9vJN3AmOpeWZdpIuBFqPVK9vv7RRFVcnLaE+bvUfWN67pfVIcDCxm66dkkRFCCFEs+HkoOGWXqE8ODgaF8cG1H30mKBe7vzBLDsqV2M0wsFF6vVmPu2D9FERQgjR3MwY17HhJ8WMAM9gyDmjJhEdr2vQ6clZhby8aB9dQrx5YHB03Qen7oeMY6B1hpjhDY/VzsiIihBCCFEfrUNlUe3WOQ0+Pe5YGv/sSWbR7qT6Dz5QNpoSfTk4ezT4ueyNJCpCCCGaHYPByMHkbPKKSk0/6RKKaruHtWDamHbc0S+8/oPLlyXLtA9IoiKEEKI5unb2BkZ/sJa4+HTTT/IOVaeAALZ/06DnC/d154HB0dzYM7TuAzMSIGUPKFpoO6ZBz2GvJFERQgjR7LQN8MTNSUtqTgMLYyuKar83T1FteRFtxABw82n8x7dBkqgIIYRodp69oj27p4/k1j5hDTux9Ui1qDY/HXbMM+mUPaey2BCfRmGJCfsLldentJNpn3KSqAghhGh2dG6OOGgv4i1Q6wADH1evr5oJRTn1nvLlumPc+sUmPlkVX/eBqQfVXZpp3psQnk8SFSGEEKIhekwAnyjIOwsbPqr3cF93Z/w9nekf7Vv3gatmAkZodxXoWjVevDZOEhUhhBDN0p87T3PrFxv5Lu54w050cILhL6nXN3wIOcl1Hv7i2Fg2PTuM3hF11Jwk7Yb9CwAFhj7bsHjsnNkSlddee43+/fvj5uaGt7d3jccoinLB1/z5880VkhBCCFEhNbuIDfHp/Lc/peEnt78aQnpBSX7ZSEjdFEWpeyPCla+rlx2vg4AODY/HjpmtM21xcTE33HAD/fr146uvvqr1uDlz5jB69OiK72tLaoQQQojGNLpjIA5ahRGxAQ0/WVFgxCswZzRs/xb6PgR+bS84rKBYj6tTPa36T22Fw/+qPVqGTGt4LHbObInKjBkzAJg7t+4NnLy9vQkMDDRXGEIIIUSNQn3cuHtA5MU/QHg/tZ7k4CJY9hLc8mO1uw0GI/3fWE6QzpUv7+pJsLdrzY+z4lX1ssut0DLm4uOxUxavUZk0aRItW7akd+/efP311/Vuu11UVER2dna1LyGEEMIihr+kNmc79A8cX1/trqNnczmXX0JiRj7+nrXsgHx8HRxbCRpHGPx008RsYyyaqLz88sv8/PPPLF26lOuuu46HHnqI//u//6vznJkzZ6LT6Sq+QkPr6fInhBBC1MJgMLLqUCov/rmXolIT+pycr2XryiZwCx+F3LMVd7UJ8GTLc8P58q6eNS+FNhphxWvq9e53QgsT2us3Qw1KVJ555pkaC2Crfh08eNDkx3vhhRcYMGAA3bp1Y+rUqTz99NO8/fbbdZ4zbdo0srKyKr5OnjzZkJcghBBCVDP1t918G3eCDUcb0E6/qiHTwKsVpB+F765Bn5dBXHw6f+48zdHUXHrVttrn8BJI3KDuknzZk5f0GuxZg2pUnnjiCSZMmFDnMVFRURcdTJ8+fXjllVcoKirC2bnmYTJnZ+da7xNCCCEaQqNRuKlXGOm5RQR5u1zcg3j4wV0LYc4YSNnDoXdGcH/BM+TiBkCQzoXpY2MZ3TGo8py9v8OCier1XveBV3BjvBy71KBExc/PDz8/P7MFs3PnTlq0aCGJiBBCiCYzZUSbS38Q32jW9fuS2P9uIZajfO30NncVT6UAF5KzCpk4bzuzb+/O6A6BsOZtWFk25dN6FFz+3KU/vx0z26qfxMREMjIySExMRK/Xs3PnTgBiYmLw8PBg4cKFpKSk0LdvX1xcXFi6dCmvv/46Tz4pw19CCCFsi95g5Kk1JfgUT+NHp9forTnE147v8J1+OMeMwRw3BjLzr52MPPgbmr2/qCf1exhGvAyaepYvN3OKsb5lNhdpwoQJfPPNhdtgr1y5kiFDhrB48WKmTZvG0aNHMRqNxMTEMHHiRO6//340GtNLZ7Kzs9HpdGRlZeHl5dXIr0IIIURzcTIjn6SsQnpHNnzX4rj4dG75YiMA3ZQjfOc0Ew+lsOJ+g1EhF1e8lHzQOMCV71YW4TZTpr5/my1RaSqSqAghhLhUKw+lcvecLUS2dGfFE4NRlDq6yNbgz52neWz+zorvOyrHmODwH9HKGaKUM+iUfACKHb1wumUeRA1u9Ndga0x9/zbb1I8QQghhK3pF+ODqqMXf05ncolI8XRwbdL6/Z/VC3L3GKJ4sebDsOyM+5BCupDDtxqvpfQmLTpojSVSEEEI0ex7ODmx9fjjuzhf3ttg70ocgnQtJWYU13KtwDi+cvfzp0e4SOuE2UxbvTCuEEEJYg4tNUgC0GoXpY2NrvK98Emn62Fi0dW1MKGokiYoQQghRRUZeMSnZNY2M1G10xyCeHNkGZ4fqb62BOhd1aXLVPirCZFJMK4QQQpRZtPsMz/y2hyFt/fjo1u4X9Rh6g5HNCRmk5hTi7+lC70gfGUmpgRTTCiGEEA0U7edBXnEpx9PzKCzR4+LY8B4nWo1Cv2hfs8TXHEmiIoQQQpRpH+TFrw/2p1uoN5oGjILkFJbw164zjOvaCo9LqHURF5IaFSGEEKKKHuEtGpSkAPy58wzP/bGXW8uavonGI4mKEEIIUQO9wcjS/SmYUsrp5epIlJ8747q2apLYmhMZnxJCCCHOYzAYuf7TDexIzOSzO3owqkNgncdf3SWYsZ2DKDXY9PoUqyQjKkIIIcR5NBqFAdEt8XJxIKewtNbj0nKLKq4rioKjVt5WG5v8iwohhBA1eHBINGufvpzre4TUeP/fu5MY9OZKlh9IafLYmhNJVIQQQogaeDg7oHOr3PPn45VH+XR1PNmFJQAs3pdMQYmeZQdSLRil/ZMaFSGEEKIeWfklfLzyKPnFetoFejKkrT/v3diFPpE+3NI7zNLh2TVJVIQQQoh6uDppeXlcR1YeSmVwGz8AHLUabu8bbunQ7J4kKkIIIUQ9nBw0XN8jpNZ6FWE+UqMihBBCCKsliYoQQgghrJYkKkIIIYSwWpKoCCGEEMJqSaIihBBCCKsliYoQQgghrJYkKkIIIYSwWpKoCCGEEMJqSaIihBBCCKsliYoQQgghrJYkKkIIIYSwWpKoCCGEEMJqSaIihBBCCKsliYoQQgghrJaDpQO4VEajEYDs7GxLhyKEEEIIE5W/b5e/j9fG5hOVnJwcAEJDQy0dihBCCCEaKCcnB51OV+v9irG+VMbKGQwGzpw5g6enJ4qiNOpjZ2dnExoaysmTJ/Hy8mrUx7YG8vpsn72/Rnl9ts/eX6O8votnNBrJyckhODgYjab2ShSbH1HRaDSEhISY9Tm8vLzs8hewnLw+22fvr1Fen+2z99cor+/i1DWSUk6KaYUQQghhtSRREUIIIYTVkkSlDs7OzkyfPh1nZ2dLh2IW8vpsn72/Rnl9ts/eX6O8PvOz+WJaIYQQQtgvGVERQgghhNWSREUIIYQQVksSFSGEEEJYLUlUhBBCCGG1mnWi8vHHHxMREYGLiwt9+vRh8+bNdR7/yy+/0K5dO1xcXOjUqRP//PNPk8XaUDNnzqRXr154enri7+/P+PHjOXToUJ3nzJ07F0VRqn25uLg0WcwN8dJLL10Qa7t27eo8x5Z+fgAREREXvEZFUZg0aVKNx1v7z2/NmjWMHTuW4OBgFEVhwYIF1e43Go28+OKLBAUF4erqyvDhwzly5Ei9j9vQv2Nzqus1lpSUMHXqVDp16oS7uzvBwcHceeednDlzps7HvJjfdXOp72c4YcKEC2IdPXp0vY9rLT/D+l5fTX+PiqLw9ttv1/qY1vTzM+V9obCwkEmTJuHr64uHhwfXXXcdKSkpdT7uxf7tmqrZJio//fQTU6ZMYfr06Wzfvp0uXbowatQoUlNTazx+w4YN3HLLLdx7773s2LGD8ePHM378ePbu3dvksZti9erVTJo0iY0bN7J06VJKSkoYOXIkeXl5dZ7n5eVFUlJSxdeJEyeaLOaG6tChQ7VY161bV+uxtvbzA9iyZUu117d06VIAbrjhhlrPseafX15eHl26dOHjjz+u8f633nqLDz/8kE8//ZRNmzbh7u7OqFGjKCwsrPUxG/p3bG51vcb8/Hy2b9/OCy+8wPbt2/n99985dOgQV199db2P25DfdXOq72cIMHr06Gqx/vjjj3U+pjX9DOt7fVVfV1JSEl9//TWKonDdddfV+bjW8vMz5X3h8ccfZ+HChfzyyy+sXr2aM2fOcO2119b5uBfzt9sgxmaqd+/exkmTJlV8r9frjcHBwcaZM2fWePyNN95ovPLKK6vd1qdPH+MDDzxg9lgbQ2pqqhEwrl69utZj5syZY9TpdE0a18WaPn26sUuXLiYfb+s/P6PRaHzssceM0dHRRoPBUOP9tvTzA4x//PFHxfcGg8EYGBhofPvttytuy8zMNDo7Oxt//PHHWh+noX/HTen811iTzZs3GwHjiRMnaj2mob/rTaWm13fXXXcZx40b16DHsdafoSk/v3Hjxhkvv/zyOo+x1p+fsYb3hczMTKOjo6Pxl19+qTjmwIEDRsAYFxdX42Nc7N9uQzTLEZXi4mK2bdvG8OHDK27TaDQMHz6cuLi4Gs+Ji4urdjzAqFGjaj3e2mRlZQHg4+NT53G5ubmEh4cTGhrKuHHj2LdvXxNF2HBHjhwhODiYqKgobrvtNhITE2s91tZ/fsXFxcybN4977rmnzs03bennV1VCQgLJycnVfkY6nY4+ffrU+jO6mL9ja5OVlYWiKHh7e9d5XEN+1y1t1apV+Pv707ZtWyZOnEh6enqtx9ryzzAlJYW///6be++9t95jrfXnd/77wrZt2ygpKan282jXrh1hYWG1/jwu5m+3oZplopKWloZerycgIKDa7QEBASQnJ9d4TnJycoOOtyYGg4HJkyczYMAAOnbsWOtxbdu25euvv+bPP/9k3rx5GAwG+vfvz6lTp5o0XlP06dOHuXPnsnjxYmbPnk1CQgKDBg0iJyenxuNt+ecHsGDBAjIzM5kwYUKtx9jSz+985T+HhvyMLubv2JoUFhYydepUbrnlljo3e2vo77oljR49mm+//Zbly5fz5ptvsnr1asaMGYNer6/xeFv+GX7zzTd4enrWOy1irT+/mt4XkpOTcXJyuiBxru+9kQb+7TaUze+eLOo3adIk9u7dW++8aL9+/ejXr1/F9/3796d9+/Z89tlnvPLKK00QqenGjBlTcb1z58706dOH8PBwfv75Z5M+4diar776ijFjxhAcHFzrMbb082vuSkpKuPHGGzEajcyePbvOY23pd/3mm2+uuN6pUyc6d+5MdHQ0q1atYtiwYRaNrbF9/fXX3HbbbfUWrFvrz8/U9wVr0CxHVFq2bIlWq72gkjklJYXAwMAazwkMDGzQ8dbi4YcfZtGiRaxcuZKQkJAGnevo6Ei3bt04evSo2eJrLN7e3rRp06bWWG315wdw4sQJli1bxn333deg82zp51f+c2jIz+hi/o6tQXmScuLECZYuXVrnaEpN6vtdtyZRUVG0bNmy1lht9We4du1aDh061OC/Sazk51fb+0JgYCDFxcVkZmZWO76+90Ya+LfbUM0yUXFycqJHjx4sX7684jaDwcDy5curfSKtql+/ftWOB1i6dGmtx1ua0Wjk4Ycf5o8//mDFihVERkY2+DH0ej179uwhKCjILDE2ptz/b9/+QZL7wjiAnx/ktVwy+mNRXHGohoYgIXAKKhoKiiZboqmopqCglpC2hmhxiCYboyFoaBAkXaSC6kZRISVCBEYQVL5oBfX9LW+X1+ym9cLP46/vB+5wPfcez+NzHu6D6K9fIhqNGq610PL3J5/PJ6qqqkRPT8+X7iuk/DkcDlFdXZ2Wo4eHB7G7u2uYo+/Ucb69NSnn5+ciEAiI8vLyL8+Rba/L5OrqStze3hqutRBzKH5/w+l0OkVzc/OX781n/rI9F5xOpzCZTGn5iEQi4vLy0jAf36nd7yz8R1pdXYXZbMbKygpOT08xMjICq9WK6+trAMDg4CBmZmb068PhMIqKirCwsICzszN4PB6YTCYcHx/nMQpjY2NjKC0tRSgUQjwe149kMqlf8z7Gubk5+P1+RKNR7O/vY2BgAMXFxTg5OclTFMYmJycRCoUQi8UQDofR2dmJiooK3NzcAP+D/L15eXmBqqqYnp7OGCu0/CUSCWiaBk3TIITA4uIiNE3T//EyPz8Pq9WKjY0NHB0doa+vDw6HA6lUSp+jvb0dXq9XP89WxzLF+Pz8jN7eXtTV1eHw8DCtLp+engxjzLbXZYkvkUhgamoK29vbiMViCAQCaGlpQX19PR4fHw3jkymH2fYoANzf38NisWBpaenDOWTOXy7PhdHRUaiqiq2tLezt7cHlcsHlcqXN09jYiPX1df08l9r9Gz+2UQEAr9cLVVWhKApaW1uxs7Ojj7W1tWFoaCjt+rW1NTQ0NEBRFDQ1NWFzczMPq86NEOLDw+fz6de8j3FiYkL/PGw2G7q7u3FwcJCnCD7ndrtRU1MDRVFQW1sLt9uNi4sLfbzQ8/fG7/dDCIFIJJIxVmj5CwaDH+7JtxheX18xOzsLm80Gs9mMjo6OjLjtdjs8Hk/aa5/V8X/tsxhjsZhhXQaDQX2O9zFm2+uyxJdMJtHV1YXKykqYTCbY7XYMDw9nNBwy5zDbHgWA5eVllJSU4O7u7sM5ZM5fLs+FVCqF8fFxlJWVwWKxoL+/H/F4PGOeP+/JpXb/xj+/35SIiIhIOj/yNypERERUGNioEBERkbTYqBAREZG02KgQERGRtNioEBERkbTYqBAREZG02KgQERGRtNioEBERkbTYqBAREZG02KgQERGRtNioEBERkbTYqBAREZG0/gVnRl3kKUhDxAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ax.plot(x_fine, f_interp(x_fine), label=\"interpolant\")\n", + "\n", + "ax.legend(frameon=False, loc=\"best\")\n", + "fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multi-d interpolation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's an example of mult-d interpolation from the official tutorial.\n", + "\n", + "First we define the \"answer\"---this is the true function that we will sample at a number of points and then try to use interpolation to recover" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "def func(x, y):\n", + " return x*(1-x)*np.cos(4*np.pi*x) * np.sin(4*np.pi*y**2)**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use `np.meshgrid()` to create the two-dimensional rectangular grid of points were we define our data." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "nx = 100\n", + "ny = 200\n", + "\n", + "x = np.linspace(0, 1, nx)\n", + "y = np.linspace(0, 1, ny)\n", + "\n", + "x, y = np.meshgrid(x, y, indexing=\"ij\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "here's what the exact function looks like---note that our function is defined in x,y, but imshow is meant for plotting an array, so the first index is the row. We take the transpose when plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "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", + "data = func(x, y)\n", + "im = ax.imshow(data.T, extent=(0, 1, 0, 1), origin=\"lower\")\n", + "fig.colorbar(im, ax=ax)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll coarsen it by taking only every 4th point" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "coarse = data[::4, ::4]" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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S/Idib04eyNkO5YL6DTh79ix8Ph8SExMD1icmJuKTTz7pMObee+/F2bNnMXHiROi6jra2Nvz0pz/tssugqKgIK1euDObUiIiISEGPt4tUVFRg9erVePHFF7Fv3z784Q9/wI4dO7Bq1apOYxYvXoz6+nr/UlNT09OnSUREBuD7avpj1cWMgnrVgwcPhs1mQ21tbcD62tpaJCUldRizbNkyzJ49Gz/+8Y9x3XXX4Qc/+AFWr16NoqIiaFrHzWwOhwMulytgISIiupSLXQaqS7CCqb776KOPcPfddyMtLQ0WiwXFxcXttlmxYgUsFkvAMmrUqKDPKxhBJQR2ux0ZGRkoLy/3r9M0DeXl5cjKyuowprm5GVZr4GFstn8+b1PXw9B5RkREFELBVt81NzdjxIgRWLNmTad/TAPAtddei1OnTvmXd999twdfheDBRAUFBZg7dy7Gjx+PCRMmoLi4GE1NTcjNzQUAzJkzB8OGDUNRUREAYOrUqVi/fj3GjRuHzMxMHDp0CMuWLcPUqVP9iQEREVEoaLBCU2zyDzb+X6vvAKC0tBQ7duzApk2bsGjRonbb33DDDbjhhhsAoMOfXxQREdFlwhBqQScE06dPx5kzZ7B8+XK43W6kp6ejrKzMP9Dw+PHjAS0CS5cuhcViwdKlS3HixAkMGTIEU6dOxVNPPRXaV0JERKbn0y3wKVYJXIz/ZoWbw+GAw+EIWCepvuuuzz77DCkpKXA6ncjKykJRUREuu+wypX12RVRnk5+fj/z8/A5/VlFREXiAiAgUFhaisLBQdoYhYG2V3xy6QjWRVJusMg0A4B0yQBzraFW40YSz8bUMlZ+vFikOxYUmuzj2L/XyfjwfZLMdNmmObmzVsffrFN5Xj/wvLZ98Ej+0JseL4iIi5K2OepT8nvAkyN8fzS7/fLIIu10trfL31domOF9JTB+Qmpoa8O/CwkKsWLEiYJ2k+q47MjMzsXnzZlx99dU4deoUVq5ciVtuuQUffvghYmNjxfvtCucyICIiwwjlcwhqamoCBrV/s3WgJ333u9/1//+YMWOQmZmJyy+/HL/73e8wb968HjkmEwIiIjIMPQSzHepfxXenyk1SfScRHx+Pq666CocOHQrZPr/JnMWWRERkSD5YQrJ0l6T6TqKxsRGHDx9GcnJyyPb5TWwhICIiUhBs9Z3X68XHH3/s//8TJ06guroaMTExGDlyJADgkUcewdSpU3H55Zfj5MmTKCwshM1mw8yZM3vsdTAhICIiw9B09bkIgh0jHWz13cmTJzFu3Dj/v9etW4d169Zh0qRJ/oH5n3/+OWbOnIkvvvgCQ4YMwcSJE/Hee+9hyJAhSq+tK0wIiIjIMLQQjCGQxAdTfZeWlnbJB/Nt27Yt6HNQxTEEREREZI4WAqtXoflIGqrQZNWqUGLacLm8ljpy8CBxrHQ2VW+M/Dr5FCqA9C8VnkNw+Cpx7Psxqd3Yqj1Nk+fuDQ3yB1vYGuV1/V6X/L2tHxktiosYJn/4gRYhP19vrDxW5bkjFuHs4bYLCs8+EDybRXqeEhos0BTnrVeN769MkRAQEZE5hPJJhWbDLgMiIiJiCwERERlHuAYVGgETAiIiMgwNIXh0sUnHEJgzDSIiIqIAbCEgIiLD0ENQZaCbtIXAFAmBUtmhkLQMD4plSD6VqVS13r9OKl11KtMfRzbID6w1y0riAKDeJotVuZ9sClN4W73yWJX7uHGY7F60aPIySZXvAJX7WFc4ZatPep3kx5TQFaagD1YoZzs0G1MkBEREZA4cVChnzldNREREAdhCQEREhsEuAzkmBEREZBh8dLEcuwyIiIiILQRERGQc7DKQY0JARESGwYRAzhQJQW/X3KpSqUtWiTUTa5v8F97ai1O5hp3C8w94H/cC4fuj8lwL0fH62WewWZkiISAiInNgC4EcEwIiIjIMJgRyrDIgIiIithAQEZFx6CF4jkAvD7HoM5gQEBGRYbDLQI4JARERGQYTAjlTJARaRO83AEmnJYXilLNKsa3yWCmVKYx9TnlsW4z8nvA55bGaXVZ/ZVH4gLJ45LERFxRim+SxthZZnEpJaLim4vbZFY4rjNWt8ntYUrKo28zaCN+/mCIhICIic2ALgRwTAiIiMgwmBHIsOyQiIiK2EBARkXHougW64l/4qvH9FRMCIiIyDA0W5ecQqMb3V+wyICIiInO0EKiUBEkTRYuwbAoAIprlsVFn5dOKOeoVpiQTVhV54uU5aeMweWyryyeOdaWcF8cmxcpi2xRq4k5+GSeO9dYMEMc6T8v/yhrglt2L9kb5+6pFys+3JV4+PeOFIfLj+qJkv3jSckUAsAgusS5/W4LGQYVypkgIiIjIHDiGQI5dBkRERIpKSkqQlpYGp9OJzMxM7N27t9NtP/roI9x9991IS0uDxWJBcXGx8j5DgQkBEREZxsUuA9UlGNu3b0dBQQEKCwuxb98+jB07Fjk5OTh9+nSH2zc3N2PEiBFYs2YNkpKSQrLPUGBCQEREhnGxy0B1AYCGhoaAxePxdHjM9evXIy8vD7m5ubjmmmtQWlqK6OhobNq0qcPtb7jhBjzzzDOYMWMGHA5HSPYZCkwIiIjIMPQQtA5cTAhSU1MRFxfnX4qKitodz+v1oqqqCtnZ2f51VqsV2dnZqKysFL2Gnthnd3BQIRERUQdqamrgcrn8/+7or/mzZ8/C5/MhMTExYH1iYiI++eQT0XF7Yp/dwYSAiIgMQwegK06ueDHc5XIFJARGZ4qEQLMr3B3CThVbx11N3RLZJI+NOSGf/9j+eZ38wMLfwMjUgeJDXhgin//YFief6/m21M/Esbe7PhbFNWsd9zN2x+tR48Sxe74YKY6NVJj+OPYfsodxRLjl97AeLb+frGkKz3qIlT8oRU+Qxfkc8s9Eqzf491XrxW8aDRZYevFJhYMHD4bNZkNtbW3A+tra2k4HDIZjn93BMQRERERCdrsdGRkZKC8v96/TNA3l5eXIysrqM/vsDlO0EBARkTmE48FEBQUFmDt3LsaPH48JEyaguLgYTU1NyM3NBQDMmTMHw4YN8w9K9Hq9+Pjjj/3/f+LECVRXVyMmJgYjR47s1j57AhMCIiIyDE23wNLLjy6ePn06zpw5g+XLl8PtdiM9PR1lZWX+QYHHjx+H1fp1g/zJkycxbtzXXXnr1q3DunXrMGnSJFRUVHRrnz2BCQEREZGi/Px85Ofnd/izi1/yF6WlpUHvxrirrvbZE5gQEBGRYeh6CKoMFOP7KyYERERkGJzcSM4UCYEeoZDuiWc1ld9QSiWL5y6IY/Wak/JYadnhAHmpl6VNHuuMkpdn3hBzVBybE10vimvW5GWSh2LlfY577CPEsTaPfErgiNMNori24yfEx7S5YsSx9oHR4lhrq/xjWPq9pUfKpzrXfcEXp+k2k/7J3c+YIiEgIiJzYAuBHBMCIiIyjHBUGRgFEwIiIjIMDiqU45MKiYiIiC0ERERkHP9sIVAdQxCy0+lXmBAQEZFhcFChHLsMiIiIiC0EhqPQ1iV9lgAAQDNPG5sN8hpuqzAHt1rkf7FY0Q/fG+m9qMvfGyVmbWPug/SvFtV9mBETAiIiMgx2Gcixy4CIiIjYQkBERAbCPgMxUQtBSUkJ0tLS4HQ6kZmZib1793a5fV1dHRYsWIDk5GQ4HA5cddVV2Llzp/SciYiIOvZVl4HKIp4kop8LuoVg+/btKCgoQGlpKTIzM1FcXIycnBwcPHgQQ4cObbe91+vFv/3bv2Ho0KH4/e9/j2HDhuEf//gH4uPjQ/UaiIiIAD6pUEnQCcH69euRl5eH3NxcAEBpaSl27NiBTZs2YdGiRe2237RpE86dO4fdu3cjMjISAJCWlhaKcyciIqIQCSoh8Hq9qKqqwuLFi/3rrFYrsrOzUVlZ2WHMG2+8gaysLCxYsAD/8z//gyFDhuDee+/FY489Bput4+lRPR4PPJ6v5wBuaJBNhXqRxSdv/glHpuiLlMe2xUWJY+3J8mlypRfK65JPYazLZ9eFp0V+kf+vOVUcmxQhm/64SR8gPuZnze1b7rqtVf6747PLD+sbFCuKi2hNER9Tj3KIY1td8herR8ivsUXY2W1pUzimoLJTEiPFKgO5oMYQnD17Fj6fD4mJgV8ciYmJcLvdHcYcOXIEv//97+Hz+bBz504sW7YMzz77LJ588slOj1NUVIS4uDj/kpoq/wAmIiITuTgGQHUxoR4vO9Q0DUOHDsWGDRuQkZGB6dOn4/HHH0dpaWmnMYsXL0Z9fb1/qamp6enTJCIiMrWgugwGDx4Mm82G2tragPW1tbVISkrqMCY5ORmRkZEB3QOjR4+G2+2G1+uF3d6+qc3hcMDhkDffERGROXFQoVxQLQR2ux0ZGRkoLy/3r9M0DeXl5cjKyuow5uabb8ahQ4egaV93In366adITk7uMBkgIiIS00O0mFDQXQYFBQXYuHEjfvvb3+LAgQP42c9+hqamJn/VwZw5cwIGHf7sZz/DuXPn8OCDD+LTTz/Fjh07sHr1aixYsCC0r4SIiIjEgi47nD59Os6cOYPly5fD7XYjPT0dZWVl/oGGx48fh9X6dZ6RmpqKt956CwsXLsSYMWMwbNgwPPjgg3jsscdC+0qIiMj0WGUgJ3p0cX5+PvLz8zv8WUVFRbt1WVlZeO+99ySHCgmrV6HsUDrsUuGGaosWh6I5Sd4No9mHyA8sbGJrGSR/eram0OPUdl5edvhO7Uhx7ClPnCjO45Nfp0++kJcdWlrktZ2+KPnvQPMw2S+BPUbl/pePsb4wSOE6KQyXsvhkcSqfiVZJyaJCmaOISZv8VXFyIyIiIuLkRkREZBzsMpBjQkBERMbB2Q7FmBAQEZGBWL5aVPdhPhxDQERERGwhICIiA2GXgRhbCIiIyDjC9KTCkpISpKWlwel0IjMzE3v37u1y+1dffRWjRo2C0+nEddddh507dwb8/L777oPFYglYJk+eHPyJBcEULQTWNnmsdLCpRSHD9MlnMEbzEHk9tDdWIT8Uvt42hVp1TeHutTXKr9OJEwniWPc5lyxQYdSzr1F+oSIuhOd5Gk1JsvfnQoL8fRU/cwRAW3R4pokOx3MIRNMfK3wG9wfbt29HQUEBSktLkZmZieLiYuTk5ODgwYMYOrT9c0B2796NmTNnoqioCP/+7/+OrVu3Ytq0adi3bx++/e1v+7ebPHkyfvOb3/j/3dNz/LCFgIiIjCMM0x+vX78eeXl5yM3NxTXXXIPS0lJER0dj06ZNHW7/q1/9CpMnT8YvfvELjB49GqtWrcL111+PF154IWA7h8OBpKQk/zJw4EClS3MpTAiIiMgwLs52qLoAQENDQ8Di8XjaHc/r9aKqqgrZ2dn+dVarFdnZ2aisrOzwHCsrKwO2B4CcnJx221dUVGDo0KG4+uqr8bOf/QxffPFFaC5SJ5gQEBERdSA1NRVxcXH+paioqN02Z8+ehc/n88/nc1FiYiLcbneH+3W73ZfcfvLkyXjllVdQXl6Op59+Gn/961/x3e9+Fz6fsJ+oG0wxhoCIiEwihFUGNTU1cLm+HvfT0334/2rGjBn+/7/uuuswZswYXHHFFaioqMAdd9zRI8dkCwERERlHCMcQuFyugKWjhGDw4MGw2Wyora0NWF9bW4ukpKQOTzEpKSmo7QFgxIgRGDx4MA4dOiS8MJfGhICIiEjIbrcjIyMD5eXl/nWapqG8vBxZWVkdxmRlZQVsDwC7du3qdHsA+Pzzz/HFF18gOTk5hGcfyBRdBhaFqTfD8QBLlTIkTTa7LgCgNbb3X61KqZdS2aFCOZ2lVT51MqwKsUKRCl2O1lZ5rMp93JIge38kJXFfB8tDVe5jXV4pCYsmO2mV91XE13ufLRZdrewbgrLxgoICzJ07F+PHj8eECRNQXFyMpqYm5ObmAgDmzJmDYcOG+ccgPPjgg5g0aRKeffZZ3HXXXdi2bRvef/99bNiwAQDQ2NiIlStX4u6770ZSUhIOHz6MRx99FCNHjkROTo7ai+uCKRICIiIyiTA8qXD69Ok4c+YMli9fDrfbjfT0dJSVlfkHDh4/fhxW69dZ40033YStW7di6dKlWLJkCa688kq8/vrr/mcQ2Gw2/N///R9++9vfoq6uDikpKbjzzjuxatWqHh3HwISAiIiMQ/AcgQ73EaT8/Hzk5+d3+LOKiop26+655x7cc889HW4fFRWFt956K+hzUMUxBERERMQWAiIiMhBObiTGhICIiIyDCYEYuwyIiIiILQRERGQgbCEQM0VCoFSbHAYqdckqsWZibZWPQu71Gu5+ivdxLxB+canW6Qd9vN78DA5TlYERsMuAiIiIzNFCQERE5hCOJxUaBRMCIiIyDo4hEGOXARERETEhICIiInYZEBGRgVhCMAbAnDUGZkkIwvHuqtyQCrEq5T3hKM9UmjZWJTZCfpGVyunCcC8q3RMK09ZaFKZdlsaqfBEovTdhmjq537Tx9uZ9z7JDsf5yOxEREVEPMkcLARERmQOrDMSYEBARkXEwIRBjlwERERGxhYCIiIyDTyqUY0JARETGwS4DMVMkBJpNpY5PFmZtU5hNzysORUSLPFbluFKaXR7bOkAe26ZwXF+MvI5PjxTGKpRBWTzynsGIJnEoIlvk5xzRLIuztokPqVQa53PIY9uc8lhNWAKrK3wmSspYdatJv2H7GVMkBEREZBJsIRBjQkBERIbBMQRyrDIgIiIithAQEZGB8NHFYkwIiIjIODiGQIwJARERGQbHEMhxDAERERGZo4VAV3iV0q4klalfbR55rL1OntraG+X19dKM2hMrz0nbnPJ+Pt8A+WuNHHJBHBsXI4v1afLXWt8gf2CD1iovsLd55OfsPCe7oSKb5e+rFiE/X69LHqvbFO5jp+w6aQqfiaLnEPTmNw27DMRMkRAQEZFJhKDLwKwJAbsMiIiIiC0ERERkIOwyEGNCQERExsGEQIxdBkRERIpKSkqQlpYGp9OJzMxM7N27t8vtX331VYwaNQpOpxPXXXcddu7cGfBzXdexfPlyJCcnIyoqCtnZ2fjss8969DUwISAiIsO4+BwC1SUY27dvR0FBAQoLC7Fv3z6MHTsWOTk5OH36dIfb7969GzNnzsS8efOwf/9+TJs2DdOmTcOHH37o32bt2rV47rnnUFpaij179mDAgAHIyclBS4vClLaXYNF1vc83jjQ0NCAuLg5XLFoNmzP4uUJbYxReonDazohGea4VVSsORexJ+fyvzjMK8x8Lb6OWofKyti9Hynu8GkfLX+vVw0+JY6+LPymK8yjUiVWdTRXHnvpsiDg27oBwbl4A8UdaRXH2OnnNruaQn29zovw+bhwm/6y4MERYduhQmP64NfgySa2lBccKH0d9fT1cLpf42F3xf08skX1P/CtfSwsOr17S7fPNzMzEDTfcgBdeeAEAoGkaUlNT8cADD2DRokXttp8+fTqamprw5ptv+tfdeOONSE9PR2lpKXRdR0pKCh5++GE88sgjAID6+nokJiZi8+bNmDFjhtLr6wxbCIiIiDrQ0NAQsHg87RNOr9eLqqoqZGdn+9dZrVZkZ2ejsrKyw/1WVlYGbA8AOTk5/u2PHj0Kt9sdsE1cXBwyMzM73WcoMCEgIiLj0EO0AEhNTUVcXJx/KSoqane4s2fPwufzITExMWB9YmIi3G53h6fodru73P7if4PZZyiwyoCIiAwjlHMZ1NTUBHQZOBzyrqH+gC0ERERkLCFoHQAAl8sVsHSUEAwePBg2mw21tYGDv2pra5GUlNTh6SUlJXW5/cX/BrPPUGBCQEREJGS325GRkYHy8nL/Ok3TUF5ejqysrA5jsrKyArYHgF27dvm3Hz58OJKSkgK2aWhowJ49ezrdZyiwy4CIiIwjDA8mKigowNy5czF+/HhMmDABxcXFaGpqQm5uLgBgzpw5GDZsmH8MwoMPPohJkybh2WefxV133YVt27bh/fffx4YNGwAAFosFDz30EJ588klceeWVGD58OJYtW4aUlBRMmzZN8cV1jgkBEREZRijHEHTX9OnTcebMGSxfvhxutxvp6ekoKyvzDwo8fvw4rNavG+RvuukmbN26FUuXLsWSJUtw5ZVX4vXXX8e3v/1t/zaPPvoompqaMH/+fNTV1WHixIkoKyuDU7GksiumSAh0m/zu0KWlyQp3pE3hcQCOL2X12wAQeapOfmBNNu2sHjlIfEirT3772qLkz2uQPksAAP7N9WE3tmqvWZcPZjrnlU9/fDJysDjW5pH/Dji+kD18xeb+UnxMPVr+QRsZLb8Xra0KPbfCmZO1SPl7YxVMxS3+HO1H8vPzkZ+f3+HPKioq2q275557cM8993S6P4vFgieeeAJPPPFESM+zK6ZICIiIyCQ4l4EYEwIiIjKMcHQZGAWrDIiIiEiWEAQ7q9NF27Ztg8Vi6dFRkkREZGIhfFKh2QSdEAQ7q9NFx44dwyOPPIJbbrlF5XyJiIg6x4RALOiEYP369cjLy0Nubi6uueYalJaWIjo6Gps2beo0xufzYdasWVi5ciVGjBhxyWN4PJ52k0oQERFRzwlqUOHFWZ0WL17sX3epWZ0A4IknnsDQoUMxb948/O///u8lj1NUVISVK1cGc2pdUip5EZcsCuuBAFjllYOwNcprFvVzCiVbPlnZoW1QrPiYFl+UONZul5cdXqkwP/X1Dllp53lN/ifL3qhz4ti/RcjeVwCwtsl/8az1zaI47cxZ8TEtsfJ7MTJJ5T6Wj+3WpR8zKp+JkinhhdPIS3BQoVxQLQSSWZ3effddvPzyy9i4cWO3j7N48WLU19f7l5qammBOk4iIzIpdBmI9WnZ4/vx5zJ49Gxs3bsTgwd1/wInD4TD8rFJERNQD+BwCsaASgmBndTp8+DCOHTuGqVOn+tdpXz3RLiIiAgcPHsQVV1whP3siIiIKiaC6DIKd1WnUqFH44IMPUF1d7V++973v4bbbbkN1dTVSU1ND8yqIiIj+ZQyB6mJGQXcZBDOrk9PpDJisAQDi4+MBoN16IiIiZewyEAs6IQh2ViciIiLq+0SDCoOd1elfbd68WXJINSrtP/LqQfkh5ZVesHh84lit6YI4VvfJjmtVOF+VLN5mk1/kQbZGcexgm2zmwWiLvJw0LkL+vqo83FzpPvbKam99LbJZEgHAGhkpjrV4FV5sGP4a1RXKAHWLYLbDXvwcZdmhHCc3IiIi42CXgRjb9omIiIgtBEREZCBsIRBjQkBERIZhCcHQrzAMHesT2GVAREREbCEgIiIDYZeBGBMCIiIyDJYdyjEhMJowdQJZrMJet37YaeULQw+jBoU6d+oWi6C+/uvgUJ4JKWELgVg//DgmIiKiUGMLARERGYtJ/8JXxYSAiIgMg2MI5NhlQERERGwhICIiA+GgQjEmBEREZBjsMpAzR0KgMvem3vt3hq7QkaPb5W+pdUCU/Lg+WVmcyvmqlHq1tdnEsefaYsSxp30nRXHnNfl9WN8mf19Vqh2V7mOHXRRnjY6WHzTKKQ7VI1XmiZaHig+pyQ8q+bI06xdsf2OOhICIiMyBXQZiTAiIiMgw2GUgxyoDIiIiYkJAREQGoodo6SHnzp3DrFmz4HK5EB8fj3nz5qGxsbHLmJaWFixYsACDBg1CTEwM7r77btTW1gZsY7FY2i3btm0L6tyYEBARkXH08YRg1qxZ+Oijj7Br1y68+eabeOeddzB//vwuYxYuXIg//vGPePXVV/HXv/4VJ0+exH/8x3+02+43v/kNTp065V+mTZsW1LlxDAERERlGKMcQNDQ0BKx3OBxwOBzi/R44cABlZWX4+9//jvHjxwMAnn/+eUyZMgXr1q1DSkpKu5j6+nq8/PLL2Lp1K26//Xbgqy/+0aNH47333sONN97o3zY+Ph5JSUni82MLARERUQdSU1MRFxfnX4qKipT2V1lZifj4eH8yAADZ2dmwWq3Ys2dPhzFVVVVobW1Fdna2f92oUaNw2WWXobKyMmDbBQsWYPDgwZgwYQI2bdoEPciyeVO0EFhUaqnDUCOsKbwrPqc82BbnEsdahM8h8EZFio+pUufe1ip/DsHn3gRx7CetA0RxzZr8r5Jaj/x9hU/+C6ByH2sxstercg/rCs/haHPK7yfdpvBMAGnbtsps2pJD9uao/RCWHdbU1MDl+vqeUmkdAAC3242hQ4cGrIuIiEBCQgLcbnenMXa7HfHx8QHrExMTA2KeeOIJ3H777YiOjsaf/vQn3H///WhsbMTPf/7zbp+fKRICIiIyB4uuw6L4QLmL8S6XKyAh6MyiRYvw9NNPd7nNgQMHlM7pUpYtW+b//3HjxqGpqQnPPPMMEwIiIqLe8vDDD+O+++7rcpsRI0YgKSkJp0+fDljf1taGc+fOddr3n5SUBK/Xi7q6uoBWgtra2i7HC2RmZmLVqlXweDzdbtlgQkBERMYRhicVDhkyBEOGDLnkdllZWairq0NVVRUyMjIAAG+//TY0TUNmZmaHMRkZGYiMjER5eTnuvvtuAMDBgwdx/PhxZGVldXqs6upqDBw4MKhuDiYERERkGH35SYWjR4/G5MmTkZeXh9LSUrS2tiI/Px8zZszwVxicOHECd9xxB1555RVMmDABcXFxmDdvHgoKCpCQkACXy4UHHngAWVlZ/gqDP/7xj6itrcWNN94Ip9OJXbt2YfXq1XjkkUeCOj8mBERERL1ky5YtyM/Pxx133AGr1Yq7774bzz33nP/nra2tOHjwIJqbm/3rfvnLX/q39Xg8yMnJwYsvvuj/eWRkJEpKSrBw4ULouo6RI0di/fr1yMvLC+rcmBAQEZFx9PHJjRISErB169ZOf56WltauXNDpdKKkpAQlJSUdxkyePBmTJ09WPjdTJAQWn1K0LEyhXlGPkN+NbTHyMr6IePm0vtJpotsGyG9BXV7pBV+rvGbxWPMgcez/F3m5KK5Fl1+nUxfCU3aocMpoi5WVd1kT4sTH1BRKYH1R8vtJU7iPpeWDFoX3VTJ1ssp0y0Efqw93GfR1fDARERERmaOFgIiITKKPdxn0ZUwIiIjIMNhlIMeEgIiIjIMtBGIcQ0BERERsISAiImMxa5O/KlMkBGolL71/Z2mR8vNtHSBv9LElyGd7s2iy69QaIz9fldkOdY/CbIeN8d3YqmNRtm+J4jwKtWlnmuTlpBaF8kyl+zhG9tFk8UWLj+lzyF9rq0LZoUr5rPSLz9ImP6ao1FFldsVg6bq4DDpgHybELgMiIiIyRwsBERGZA6sM5JgQEBGRcbDKQIxdBkRERMQWAiIiMg6L9s9FdR9mxISAiIiMg10GYuwyICIiInO0ECg1/yhMYyylyWdhRWu0PMez+hRuB2FGHbb6bYX6+rONA+THFQ5f9mny861vdIpjrQr16prC7eSNFb5ei8IUxnb573pblMI00SrTH0ufQ6Ay/bHgmL05ap9VBnKmSAiIiMgk+GAiMSYERERkGGwhkOMYAiIiImILARERGQirDMSYEBARkWGwy0COXQZERERkkhYChbJDi7A6RyXDVCnXapPPYAyLynzCQirnq1IRavHKg5sbHeLY08L7QlMoO2xttotjI9rk10nlPm6Nlh1Xt6qUsSqUHTr7WdmhymeiILZXn/zHKgMxcyQERERkCuwykGOXAREREbGFgIiIDIRVBmJMCIiIyDDYZSDHLgMiIiJiCwERERmIpv9zUd2HCTEhICIi4+AYAjFTJARKNbC9P/uxUl2yT6EeWum1Cn+BVM5X5bEJ1laFmvNm+a/NBU1YXy+MAwC0yC+Uyu+OrvDpIr0vVH53VO4nTf6oB7XnaUi/uFQ+EyWxvfgcAksIxgCE4WO/T+AYAiIiol5y7tw5zJo1Cy6XC/Hx8Zg3bx4aGxu7jNmwYQNuvfVWuFwuWCwW1NXVhWS/38SEgIiIjOPikwpVlx4ya9YsfPTRR9i1axfefPNNvPPOO5g/f36XMc3NzZg8eTKWLFkS0v1+kym6DIiIyBz6ctnhgQMHUFZWhr///e8YP348AOD555/HlClTsG7dOqSkpHQY99BDDwEAKioqQrrfbxK1EJSUlCAtLQ1OpxOZmZnYu3dvp9tu3LgRt9xyCwYOHIiBAwciOzu7y+2JiIj6goaGhoDF4/Eo7a+yshLx8fH+L20AyM7OhtVqxZ49e8K+36ATgu3bt6OgoACFhYXYt28fxo4di5ycHJw+fbrD7SsqKjBz5kz85S9/QWVlJVJTU3HnnXfixIkTwR6aiIioa3qIFgCpqamIi4vzL0VFRUqn5na7MXTo0IB1ERERSEhIgNvtDvt+g04I1q9fj7y8POTm5uKaa65BaWkpoqOjsWnTpg6337JlC+6//36kp6dj1KhReOmll6BpGsrLyzs9hsfjaZeZERERXYpF10OyAEBNTQ3q6+v9y+LFizs85qJFi2CxWLpcPvnkk16+EsELagyB1+tFVVVVwEWxWq3Izs5GZWVlt/bR3NyM1tZWJCQkdLpNUVERVq5cGcypdU2lPygM9agq5U8+pfKn3i+20SIVglXKtXzyWKtCGZ8mLL+yKNSmWTwKsSplhyr3sXCGaZUpjJXKDhXuY6VZx6X3hcKDd0T96/20rt/lcsHlcl1yu4cffhj33Xdfl9uMGDECSUlJ7VrT29racO7cOSQlJYnPM1T7DSohOHv2LHw+HxITEwPWJyYmdjv7eeyxx5CSkoLs7OxOt1m8eDEKCgr8/25oaEBqamowp0pERGakheC5B0HGDxkyBEOGDLnkdllZWairq0NVVRUyMjIAAG+//TY0TUNmZqb0bEO2314tO1yzZg22bduG1157DU6ns9PtHA6HPzPrboZGREQUyi6DUBs9ejQmT56MvLw87N27F3/729+Qn5+PGTNm+CsBTpw4gVGjRgUMvne73aiursahQ4cAAB988AGqq6tx7ty5bu+3O4JKCAYPHgybzYba2tqA9bW1tZdslli3bh3WrFmDP/3pTxgzZkwwhyUiIjKELVu2YNSoUbjjjjswZcoUTJw4ERs2bPD/vLW1FQcPHkRzc7N/XWlpKcaNG4e8vDwAwHe+8x2MGzcOb7zxRrf32x1BdRnY7XZkZGSgvLwc06ZNAwD/AMH8/PxO49auXYunnnoKb731VkBZBBERUUj18bkMEhISsHXr1k5/npaWBv0bLRQrVqzAihUrlPbbHUE/mKigoABz587F+PHjMWHCBBQXF6OpqQm5ubkAgDlz5mDYsGH+8oynn34ay5cvx9atW5GWluYvgYiJiUFMTIzSyRMREQUIxZMGe/BJhX1Z0AnB9OnTcebMGSxfvhxutxvp6ekoKyvzDzQ8fvw4rNaveyJ+/etfw+v14oc//GHAfgoLCy+Z8RAREQWjLz+psK8TPbo4Pz+/0y6Cbz5a8dixY7IzCyGLykxxYbgzVMqQVGaYU7lMUiqz0ymVHSqMQrZ6Fcr4fL0/fYhFYWZHldHa4SjjC9f9pKkcV+E6iT+elEqxBRdKZUpH6jWcy4CIiIyDXQZiTAiIiMgwLJpaCyAUWxD7M05/TERERGwhICIiA2GXgRgTAiIiMo4+/hyCvoxdBkRERMQWAiIiMo5QzEXQU3MZ9HVMCC4lHPWzYaqHDsPsx2rPXAjT9Mcq10npmRjSY6q8VqVneMhDpc8TUJpKWEG47uNwHFTy7INefZwLxxCIscuAiIiI2EJAREQGoqs9YdO/DxNiQkBERIbBMQRyTAiIiMg49BCMATBnPsAxBERERMQWAiIiMhJWGYiZIiEIy9zWCsdUKqfrb+VPKsdUiVUpu/IpvLnhmDRF4XRVfneU7qf+1nYZrvtYekgjf99pIbimnNyIiIiIzMoULQRERGQOrDKQY0JARETGwTEEYuwyICIiIrYQEBGRgbCFQIwJARERGQcTAjF2GRARERFbCPoklWljw3Tc/kapDltpSuAw/OURlgdMKN7H/FOFpPgcAjEmBEREZBgsO5RjQkBERMbBMQRibJgjIiIithAQEZGBaLr6WB3NnC0ETAiIiMg42GUgxi4DIiIiMklCoCss/Y3FREu4LrGusGiW3l8Uzjd8F9lEi4pwfK71+c9S/etWAunSgyd87tw5zJo1Cy6XC/Hx8Zg3bx4aGxu7jNmwYQNuvfVWuFwuWCwW1NXVtdsmLS0NFoslYFmzZk1Q52aOhICIiMxBNRkIRZdDF2bNmoWPPvoIu3btwptvvol33nkH8+fP7zKmubkZkydPxpIlS7rc7oknnsCpU6f8ywMPPBDUuXEMARERUS84cOAAysrK8Pe//x3jx48HADz//POYMmUK1q1bh5SUlA7jHnroIQBARUVFl/uPjY1FUlKS+PzYQkBERMah6aFZADQ0NAQsHo9H6dQqKysRHx/vTwYAIDs7G1arFXv27FF+6WvWrMGgQYMwbtw4PPPMM2hrawsqni0ERERkHLr2z0V1HwBSU1MDVhcWFmLFihXi3brdbgwdOjRgXUREBBISEuB2u8X7BYCf//znuP7665GQkIDdu3dj8eLFOHXqFNavX9/tfTAhICIi6kBNTQ1cLpf/3w6Ho8PtFi1ahKeffrrLfR04cCDk5/evCgoK/P8/ZswY2O12/OQnP0FRUVGn5/1NTAiIiMg4QvgcApfLFZAQdObhhx/Gfffd1+U2I0aMQFJSEk6fPh2wvq2tDefOnVPq++9IZmYm2tracOzYMVx99dXdimFCcCn9sfSQLk3lfTXRrJC8/w3KyO+rFoKywSCfVDhkyBAMGTLkkttlZWWhrq4OVVVVyMjIAAC8/fbb0DQNmZmZ4tPtSHV1NaxWa7suiq4wISAiIuPow08qHD16NCZPnoy8vDyUlpaitbUV+fn5mDFjhr/C4MSJE7jjjjvwyiuvYMKECcBXYw/cbjcOHToEAPjggw8QGxuLyy67DAkJCaisrMSePXtw2223ITY2FpWVlVi4cCH+8z//EwMHDuz2+bHKgIiIqJds2bIFo0aNwh133IEpU6Zg4sSJ2LBhg//nra2tOHjwIJqbm/3rSktLMW7cOOTl5QEAvvOd72DcuHF44403gK/GNmzbtg2TJk3Ctddei6eeegoLFy4M2G93WHS97z+0uaGhAXFxcbhi0WrYnM5wnw6ZHbsMiILia2nB4TVLUF9f360+eYmL3xPZyT9BhNWutK82zYs/n/p/PXq+fRG7DIiIyDj6cJdBX8cuAyIiImILARERGYimAVB8MJGmGN9PMSEgIiLjYJeBGBMComCZ87OCiAyOCQERERkHWwjEmBAQEZFxhOFJhUbBKgMiIiJiCwERERmHrmvQFac/Vo3vr5gQEBGRcei6epM/xxAQERH1c3oIxhCYNCHgGAIiIiJiCwERERmIpgEWxTEAHENARETUz7HLQIxdBkRERMQWAiIiMg5d06Ardhmw7JCIiKi/Y5eBGLsMiIiIiC0ERERkIJoOWNhCIMGEgIiIjEPXAaiWHZozIWCXAREREbGFgIiIjEPXdOiKXQa6SVsImBAQEZFx6FoIugzMWXYo6jIoKSlBWloanE4nMjMzsXfv3i63f/XVVzFq1Cg4nU5cd9112Llzp/R8iYiIOqVrekgWMwo6Idi+fTsKCgpQWFiIffv2YezYscjJycHp06c73H737t2YOXMm5s2bh/3792PatGmYNm0aPvzww1CcPxEREYWARQ+ysyQzMxM33HADXnjhBQCApmlITU3FAw88gEWLFrXbfvr06WhqasKbb77pX3fjjTciPT0dpaWlHR7D4/HA4/H4/11fX4/LLrsMwxcuh9XhDOZ0iYgozDRPC47+8gnU1dUhLi6uR47R0NCAuLg4TMQURCBSaV9taMW72In6+nq4XK6QnWOfpwfB4/HoNptNf+211wLWz5kzR//e977XYUxqaqr+y1/+MmDd8uXL9TFjxnR6nMLCwouPmuLChQsXLgZZDh8+HMxXTlAuXLigJyUlhexck5KS9AsXLvTY+fZFQQ0qPHv2LHw+HxITEwPWJyYm4pNPPukwxu12d7i92+3u9DiLFy9GQUGB/991dXW4/PLLcfz48R7LLo2goaEBqampqKmpMVdWGyRep0vjNeoeXqfuudjKm5CQ0GPHcDqdOHr0KLxeb0j2Z7fb4XSaq0W6T1YZOBwOOByOduvj4uL4S9cNLpeL16kbeJ0ujdeoe3idusdq7dlH3zidTtN9iYdSUO/O4MGDYbPZUFtbG7C+trYWSUlJHcYkJSUFtT0RERH1vqASArvdjoyMDJSXl/vXaZqG8vJyZGVldRiTlZUVsD0A7Nq1q9PtiYiIqPcF3WVQUFCAuXPnYvz48ZgwYQKKi4vR1NSE3NxcAMCcOXMwbNgwFBUVAQAefPBBTJo0Cc8++yzuuusubNu2De+//z42bNjQ7WM6HA4UFhZ22I1AX+N16h5ep0vjNeoeXqfu4XXqH4IuOwSAF154Ac888wzcbjfS09Px3HPPITMzEwBw6623Ii0tDZs3b/Zv/+qrr2Lp0qU4duwYrrzySqxduxZTpkwJ7SshIiIiMVFCQERERMbC2Q6JiIiICQERERExISAiIiImBERERIS+lBBwSuXuCeY6bdy4EbfccgsGDhyIgQMHIjs7+5LX1QiCvZcu2rZtGywWC6ZNm9bj59gXBHud6urqsGDBAiQnJ8PhcOCqq64yxe9dsNepuLgYV199NaKiopCamoqFCxeipaWl1843HN555x1MnToVKSkpsFgseP311y8ZU1FRgeuvvx4OhwMjR44MqEyjMAn3ZAq6ruvbtm3T7Xa7vmnTJv2jjz7S8/Ly9Pj4eL22trbD7f/2t7/pNptNX7t2rf7xxx/rS5cu1SMjI/UPPvig18+9NwV7ne699169pKRE379/v37gwAH9vvvu0+Pi4vTPP/+818+9twR7jS46evSoPmzYMP2WW27Rv//97/fa+YZLsNfJ4/Ho48eP16dMmaK/++67+tGjR/WKigq9urq618+9NwV7nbZs2aI7HA59y5Yt+tGjR/W33npLT05O1hcuXNjr596bdu7cqT/++OP6H/7wBx1AuwnwvunIkSN6dHS0XlBQoH/88cf6888/r9tsNr2srKzXzpna6xMJwYQJE/QFCxb4/+3z+fSUlBS9qKiow+1/9KMf6XfddVfAuszMTP0nP/lJj59rOAV7nb6pra1Nj42N1X/729/24FmGl+QatbW16TfddJP+0ksv6XPnzjVFQhDsdfr1r3+tjxgxQvd6vb14luEX7HVasGCBfvvttwesKygo0G+++eYeP9e+ojsJwaOPPqpfe+21AeumT5+u5+Tk9PDZUVfC3mXg9XpRVVWF7Oxs/zqr1Yrs7GxUVlZ2GFNZWRmwPQDk5OR0ur0RSK7TNzU3N6O1tbVHZxwLJ+k1euKJJzB06FDMmzevl840vCTX6Y033kBWVhYWLFiAxMREfPvb38bq1avh8/l68cx7l+Q63XTTTaiqqvJ3Kxw5cgQ7d+7kg9i+wYyf4f1B2Gc77K0plfs7yXX6psceewwpKSntfhGNQnKN3n33Xbz88suorq7upbMMP8l1OnLkCN5++23MmjULO3fuxKFDh3D//fejtbUVhYWFvXTmvUtyne69916cPXsWEydOhK7raGtrw09/+lMsWbKkl866f+jsM7yhoQEXLlxAVFRU2M7NzMLeQkC9Y82aNdi2bRtee+01Tg/6lfPnz2P27NnYuHEjBg8eHO7T6dM0TcPQoUOxYcMGZGRkYPr06Xj88cdRWloa7lPrUyoqKrB69Wq8+OKL2LdvH/7whz9gx44dWLVqVbhPjeiSwt5CwCmVu0dynS5at24d1qxZgz//+c8YM2ZMD59p+AR7jQ4fPoxjx45h6tSp/nWapgEAIiIicPDgQVxxxRW9cOa9S3IvJScnIzIyEjabzb9u9OjRcLvd8Hq9sNvtPX7evU1ynZYtW4bZs2fjxz/+MQDguuuuQ1NTE+bPn4/HH38cViv/BkMXn+Eul4utA2EU9ruTUyp3j+Q6AcDatWuxatUqlJWVYfz48b10tuER7DUaNWoUPvjgA1RXV/uX733ve7jttttQXV2N1NTUXn4FvUNyL9188804dOiQP2ECgE8//RTJycmGTAYgvE7Nzc3tvvQvJlGcNuZrZvwM7xfCPapR/6q0x+Fw6Js3b9Y//vhjff78+Xp8fLzudrt1Xdf12bNn64sWLfJv/7e//U2PiIjQ161bpx84cEAvLCw0TdlhMNdpzZo1ut1u13//+9/rp06d8i/nz58P46voWcFeo28yS5VBsNfp+PHjemxsrJ6fn68fPHhQf/PNN/WhQ4fqTz75ZBhfRc8L9joVFhbqsbGx+n//93/rR44c0f/0pz/pV1xxhf6jH/0ojK+i550/f17fv3+/vn//fh2Avn79en3//v36P/7xD13XdX3RokX67Nmz/dtfLDv8xS9+oR84cEAvKSlh2WEf0CcSAl3X9eeff16/7LLLdLvdrk+YMEF/7733/D+bNGmSPnfu3IDtf/e73+lXXXWVbrfb9WuvvVbfsWNHGM669wVznS6//HIdQLulsLAwTGffO4K9l/6VWRICXXCddu/erWdmZuoOh0MfMWKE/tRTT+ltbW1hOPPeFcx1am1t1VesWKFfccUVutPp1FNTU/X7779f//LLL8N09r3jL3/5S4efNRevzdy5c/VJkya1i0lPT9ftdrs+YsQI/Te/+U2Yzp4u4vTHREREFP4xBERERBR+TAiIiIiICQERERExISAiIiImBERERAQmBERERAQmBERERAQmBERERAQmBERERAQmBERERAQmBERERAQA/z+kH3yLx1tYewAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "im = ax.imshow(coarse.T, extent=(0, 1, 0, 1), origin=\"lower\")\n", + "fig.colorbar(im, ax=ax)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's now use interpolation to try to recover the look of the original data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "This is considered structured grid interpolation, and SciPy has the [RegularGridInterpolator()](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.RegularGridInterpolator.html) class for this type of data.\n", + "\n", + "If the data were unstructured, then you should explore [griddata()](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.griddata.html) instead.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import interpolate" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "x_coarse = np.linspace(0, 1, nx//4)\n", + "y_coarse = np.linspace(0, 1, ny//4)\n", + "\n", + "interp = interpolate.RegularGridInterpolator((x_coarse, y_coarse), coarse, method=\"cubic\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now `interp()` is a function that we can use to sample the coarsened data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now interpolate it onto the original grid" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(100, 200)" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "new_data = interp((x, y))\n", + "new_data.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 29, + "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", + "im = ax.imshow(new_data.T, extent=(0, 1, 0, 1), origin=\"lower\")\n", + "fig.colorbar(im, ax=ax)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and let's plot the difference" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "diff = new_data - data\n", + "fig, ax = plt.subplots()\n", + "im = ax.imshow(diff.T, origin=\"lower\", extent=(0, 1, 0, 1))\n", + "fig.colorbar(im, ax=ax)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Root Finding" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Often we need to find a value of a variable that zeros a function -- this is _root finding_. Sometimes, this is a multidimensional problem." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [brentq()](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brentq.html) method offers a very robust method for find roots from a scalar function. You do need to provide an interval that bounds the root." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{tip}\n", + "It's a good idea to plot the function, if you can, so you can learn how the function behaves\n", + "in the vicinity of a root (and how many roots there might be)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's consider:\n", + "\n", + "$f(x) = \\frac{x e^x}{e^x - 1} - 5$" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "import scipy.optimize as optimize" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "def f(x):\n", + " return (x*np.exp(x)/(np.exp(x) - 1.0) - 5.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4.965114231744287\n", + "True\n" + ] + } + ], + "source": [ + "root, r = optimize.brentq(f, 0.1, 10.0, full_output=True)\n", + "\n", + "print(root)\n", + "print(r.converged)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0.1, 10.0, 1000)\n", + "fig, ax = plt.subplots()\n", + "ax.plot(x, f(x))\n", + "ax.scatter(np.array([root]), np.array([f(root)]))\n", + "ax.grid()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ODEs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Many methods exist for integrating ordinary differential equations. Most will want you to write your ODEs as a system of first order equations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [Lorenz system](https://en.wikipedia.org/wiki/Lorenz_system) is a very simple\n", + "model of convection in our atmosphere, but demonstrates the idea of chaos well.\n", + "\n", + "This system of ODEs for the Lorenz system is:\n", + "\n", + "$$\\frac{dx}{dt} = \\sigma (y - x)$$\n", + "$$\\frac{dy}{dt} = rx - y - xz$$\n", + "$$\\frac{dz}{dt} = xy - bz$$\n", + "\n", + "the steady states of this system correspond to:\n", + "\n", + "$${\\bf f}({\\bf x}) = \n", + "\\left (\n", + "\\begin{array}{c}\n", + "\\sigma (y -x) \\\\\n", + "rx - y -xz \\\\\n", + "xy - bz\n", + "\\end{array}\n", + "\\right )\n", + "= 0$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "# system parameters\n", + "sigma = 10.0\n", + "b = 8./3.\n", + "r = 28.0\n", + "\n", + "def rhs(t, x):\n", + " xdot = sigma*(x[1] - x[0])\n", + " ydot = r*x[0] - x[1] - x[0]*x[2]\n", + " zdot = x[0]*x[1] - b*x[2]\n", + "\n", + " return np.array([xdot, ydot, zdot])\n", + "\n", + "def jac(t, x):\n", + "\n", + " return np.array(\n", + " [ [-sigma, sigma, 0.0], \n", + " [r - x[2], -1.0, -x[0]],\n", + " [x[1], x[0], -b] ])\n", + "\n", + "def f(x):\n", + " return rhs(0.,x), jac(0.,x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SciPy has a uniform interface to the different ODE solvers, [solve_ivp()](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html)---we use that here.\n", + "\n", + "These integrators will do error estimation along the way and adapt the stepsize to ensure that the accuracy\n", + "you request is met." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [], + "source": [ + "def ode_integrate(X0, dt, tmax):\n", + " \"\"\" integrate using the VODE method, storing the solution each dt \"\"\"\n", + "\n", + " r = integrate.solve_ivp(rhs, (0.0, tmax), X0,\n", + " method=\"RK45\", dense_output=True)\n", + "\n", + " # get the solution at intermediate times\n", + " ts = np.arange(0.0, tmax, dt)\n", + " \n", + " Xs = r.sol(ts)\n", + " return ts, Xs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{tip}\n", + "Execute\n", + "```\n", + "%matplotlib widget\n", + "```\n", + "in a cell before making this 3D plot and you will be able to interactively\n", + "rotate it in the notebook.\n", + "\n", + "You may need to install the [ipympl](https://matplotlib.org/ipympl/) package first.\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "t, X = ode_integrate([1.0, 1.0, 20.0], 0.02, 30)\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = plt.axes(projection='3d')\n", + "ax.plot(X[0,:], X[1,:], X[2,:])\n", + "fig.set_size_inches(8.0,6.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} try it\n", + "Rerun the integration, but change the initial conditions by 1 part in $10^6$ for one of the components.\n", + "The make a plot of $x$ vs. $t$ comparing the solutions. You'll see that the 2 solutions track well\n", + "for some time but then greatly diverged. This is the sensitivity to initial conditions that is the\n", + "hallmark of chaos.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multi-variate root find" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can find the steady points in this system by doing a multi-variate root find on the RHS vector" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0. 0. 0.]\n", + "[ 8.48528137 8.48528137 27. ]\n", + "[-8.48528137 -8.48528137 27. ]\n" + ] + } + ], + "source": [ + "sol1 = optimize.root(f, [1., 1., 1.], jac=True)\n", + "print(sol1.x)\n", + "\n", + "sol2 = optimize.root(f, [10., 10., 10.], jac=True)\n", + "print(sol2.x)\n", + "\n", + "sol3 = optimize.root(f, [-10., -10., -10.], jac=True)\n", + "print(sol3.x)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0, 'z')" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "fig.set_size_inches(8, 8)\n", + "ax = plt.axes(projection='3d')\n", + "\n", + "ax.plot(X[0,:], X[1,:], X[2,:])\n", + "\n", + "ax.scatter(sol1.x[0], sol1.x[1], sol1.x[2], marker=\"x\", color=\"r\")\n", + "ax.scatter(sol2.x[0], sol2.x[1], sol2.x[2], marker=\"x\", color=\"r\")\n", + "ax.scatter(sol3.x[0], sol3.x[1], sol3.x[2], marker=\"x\", color=\"r\")\n", + "\n", + "ax.set_xlabel(\"x\")\n", + "ax.set_ylabel(\"y\")\n", + "ax.set_zlabel(\"z\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Stiff system of ODEs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A stiff system of ODEs is one where there are multiple disparate timescales for change and we need to respect all of them to get an accurate solution\n", + "\n", + "Here is an example from Chemical Kinetics (see, ex. Byrne & Hindmarsh 1986, or the VODE source code)\n", + "\n", + "$$\n", + "\\frac{d}{dt} \\left (\n", + " \\begin{array}{c} y_1 \\newline y_2 \\newline y_3 \\end{array}\n", + " \\right ) =\n", + "%\n", + "\\left (\n", + " \\begin{array}{rrr}\n", + " -0.04 y_1 & + 10^4 y_2 y_3 & \\newline\n", + " 0.04 y_1 & - 10^4 y_2 y_3 & -3\\times 10^7 y_2^2 \\newline\n", + " & & 3\\times 10^7 y_2^2 \n", + "\\end{array}\n", + "\\right )\n", + "$$\n", + "\n", + "$$\n", + "{\\bf J} = \\left (\n", + "\\begin{array}{ccc}\n", + " -0.04 & 10^4 y_3 & 10^4 y_2 \\newline\n", + " 0.04 & -10^4 y_3 - 6\\times 10^7 y_2 & -10^4 y_2 \\newline\n", + " 0 & 6\\times 10^7 y_2 & 0 \n", + "\\end{array}\n", + "\\right )\n", + "$$\n", + "\n", + "start with $y_1(0) = 1, y_2(0) = y_3(0) = 0$. Long term behavior is $y_1, y_2 \\rightarrow 0; y_3 \\rightarrow 1$" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [], + "source": [ + "def rhs(t, Y):\n", + " \"\"\" RHS of the system -- using 0-based indexing \"\"\"\n", + " y1 = Y[0]\n", + " y2 = Y[1]\n", + " y3 = Y[2]\n", + "\n", + " dy1dt = -0.04*y1 + 1.e4*y2*y3\n", + " dy2dt = 0.04*y1 - 1.e4*y2*y3 - 3.e7*y2**2\n", + " dy3dt = 3.e7*y2**2\n", + "\n", + " return np.array([dy1dt, dy2dt, dy3dt])\n", + "\n", + "def jac(t, Y):\n", + " \"\"\" J_{i,j} = df_i/dy_j \"\"\"\n", + "\n", + " y1 = Y[0]\n", + " y2 = Y[1]\n", + " y3 = Y[2]\n", + "\n", + " df1dy1 = -0.04\n", + " df1dy2 = 1.e4*y3\n", + " df1dy3 = 1.e4*y2\n", + "\n", + " df2dy1 = 0.04\n", + " df2dy2 = -1.e4*y3 - 6.e7*y2\n", + " df2dy3 = -1.e4*y2\n", + "\n", + " df3dy1 = 0.0\n", + " df3dy2 = 6.e7*y2\n", + " df3dy3 = 0.0\n", + "\n", + " return np.array([ [ df1dy1, df1dy2, df1dy3 ],\n", + " [ df2dy1, df2dy2, df2dy3 ],\n", + " [ df3dy1, df3dy2, df3dy3 ] ])" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [], + "source": [ + "def vode_integrate(Y0, tmax):\n", + " \"\"\" integrate using the NDF method \"\"\"\n", + "\n", + " r = integrate.solve_ivp(rhs, (0.0, tmax), Y0,\n", + " method=\"BDF\", jac=jac, rtol=1.e-7, atol=1.e-10)\n", + "\n", + " # Note: this solver does not have a dens_output method, instead we \n", + " # access the solution data where it was evaluated internally via\n", + " # the return object\n", + " \n", + " return r.t, r.y" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0, 'time')" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Y0 = np.array([1.0, 0.0, 0.0])\n", + "tmax = 4.e7\n", + "\n", + "ts, Ys = vode_integrate(Y0, tmax)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.loglog(ts, Ys[0,:], label=r\"$y_1$\")\n", + "ax.loglog(ts, Ys[1,:], label=r\"$y_2$\")\n", + "ax.loglog(ts, Ys[2,:], label=r\"$y_3$\")\n", + "\n", + "ax.legend(loc=\"best\", frameon=False)\n", + "ax.set_xlabel(\"time\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} try it\n", + "Redo this integration, but now use the `RK45` solver instead of `BDF`. Does it work?\n", + "\n", + "You may need to use the `kernel` menu in Jupyter to interrupt the kernel if you get impatient.\n", + "```" + ] + } + ], + "metadata": { + "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": "3.13.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/05-scipy/scipy-exercises-2.ipynb b/content/05-scipy/scipy-exercises-2.ipynb new file mode 100644 index 00000000..75750590 --- /dev/null +++ b/content/05-scipy/scipy-exercises-2.ipynb @@ -0,0 +1,375 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# More SciPy Exercises" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Linear Algebra" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q1: Condition number\n", + "\n", + "For a linear system, ${\\bf A x} = {\\bf b}$, we can only solve for $x$ if the determinant of the matrix ${\\bf A}$ is non-zero. If the determinant is zero, then we call the matrix _singular_. The _condition number_ of a matrix is a measure of how close we are to being singular. The formal definition is:\n", + "\n", + "\\begin{equation}\n", + "\\mathrm{cond}({\\bf A}) = \\| {\\bf A}\\| \\| {\\bf A}^{-1} \\|\n", + "\\end{equation}\n", + "\n", + "But we can think of it as a measure of how much ${\\bf x}$ would change due to a small change in ${\\bf b}$. A large condition number means that our solution for ${\\bf x}$ could be inaccurate.\n", + "\n", + "A _Hilbert matrix_ has $H_{ij} = (i + j + 1)^{-1}$, and is known to have a large condition number. Here's a routine to generate a Hilbert matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def hilbert(n):\n", + " \"\"\" return a Hilbert matrix, H_ij = (i + j - 1)^{-1} \"\"\"\n", + "\n", + " H = np.zeros((n,n), dtype=np.float64)\n", + "\n", + " for i in range(1, n+1):\n", + " for j in range(1, n+1):\n", + " H[i-1,j-1] = 1.0/(i + j - 1.0)\n", + " return H" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's solve ${\\bf Hx} ={\\bf b}$. Create a linear system by picking an ${\\bf x}$ and generating a ${\\bf b}$ by multiplying by the matrix ${\\bf H}$. Then use the `scipy.linalg.solve()` function to recover ${\\bf x}$. Compute the error in ${\\bf x}$ as a function of the size of the matrix.\n", + "\n", + "You won't need a large matrix, $n \\sim 13$ or so, will start showing big errors.\n", + "\n", + "You can compute the condition number with `numpy.linalg.cond()`\n", + "\n", + "There are methods that can do a better job with nearly-singular matrices. Take a look at `scipy.linalg.lstsq()` for example." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# FFTs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q2: Noisy signal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A convolution is defined as: \n", + "\n", + " \\begin{equation} \n", + " (f \\star g)(t) \\equiv \\int_{-\\infty}^{\\infty} f(\\tau) g(t - \\tau) d\\tau \n", + " \\end{equation} \n", + "\n", + " It is easy to compute this with FFTs, via the [convolution theorem](https://en.wikipedia.org/wiki/Convolution_theorem),\n", + " \n", + " \\begin{equation} \n", + " \\mathcal{F}\\{f \\star g\\} = \\mathcal{F}\\{f\\} \\, \\mathcal{F}\\{g\\} \n", + " \\end{equation} \n", + " That is the Fourier transform of the convolution of $f$ and $g$ is simply\n", + " the product of the individual transforms of $f$ and $g$. This allows us\n", + " to compute the convolution via multiplication in Fourier space and then take\n", + " the inverse transform, $\\mathcal{F}^{-1}\\{\\}$, to recover the convolution in real space:\n", + " \n", + " \\begin{equation}\n", + " f \\star g = \\mathcal{F}^{-1}\\{ \\mathcal{F}\\{f\\} \\, \\mathcal{F}\\{g\\}\\}\n", + " \\end{equation}\n", + " \n", + "A common use of a convolution is to smooth noisy data, for example by convolving noisy data with a Gaussian. We'll do that here." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's some noisy data we'll work with" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def fdata(x, L):\n", + " A = L/10.0\n", + " return 2*np.sin(2*np.pi*x/L) + x*(L-x)**2/L**3 * np.cos(x) + \\\n", + " 5*x*(L-x)/L**2 + A/2 + 0.1*A*np.sin(13*np.pi*x/L)\n", + "\n", + "N = 2048\n", + "L = 50.0\n", + "x = np.linspace(0, L, N, endpoint=False)\n", + "orig = fdata(x, L)\n", + "\n", + "rng = np.random.default_rng()\n", + "noisy = orig + 0.5 * rng.standard_normal(N)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, noisy)\n", + "plt.plot(x, orig)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SciPy provides a convolution function `scipy.signal.convolve()` that can do the convolution for us directly. To smooth the data, we want to use a Gaussian, which can be produced by `scipy.signal.gaussian()`.\n", + "\n", + "Convolve the noisy data with a Gaussian and plot the result together with the original data `orig`. You'll need to play with the width of the Gaussian to get a nice smoothing. You also will need to normalize the Gaussian so that it sums to 1, otherwise, your convolved data will be shifted verfically from the original function." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q3: FFT of chaotic pendulum\n", + "\n", + "Last time we looked at ODEs and the chaotic pendulum, and were interested in writing a method to integrate the pendulum in time.\n", + "\n", + "Here we want to examine its behavior in frequency space. The code below will integrate the chaotic pendulum, while requesting that the solution be stored at points spaced with a fixed dt, which makes it suitable for taking the FFT." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "from functools import partial\n", + "from scipy.integrate import solve_ivp\n", + "\n", + "def rhs(t, Y, q, omega_d, b):\n", + " \"\"\" damped driven pendulum system derivatives. Here, Y = (theta, omega) are\n", + " the solution variables. \"\"\"\n", + " f = np.zeros_like(Y)\n", + " \n", + " f[0] = Y[1]\n", + " f[1] = -q*Y[1] - np.sin(Y[0]) + b*np.cos(omega_d*t)\n", + "\n", + " return f\n", + "\n", + "def restrict_theta(theta):\n", + " \"\"\" convert theta to be restricted to lie between -pi and pi\"\"\"\n", + " tnew = theta + np.pi\n", + " tnew += -2.0*np.pi*np.floor(tnew/(2.0*np.pi))\n", + " tnew -= np.pi\n", + " return tnew\n", + "\n", + "def int_pendulum(theta0, q, omega_d, b, tend, dt):\n", + " \"\"\" integrate the pendulum and return solution with dt\"\"\"\n", + "\n", + " # points in time where we'll request the solution\n", + " tpoints = np.arange(0.0, tend, dt)\n", + " \n", + " r = solve_ivp(partial(rhs, q=q, omega_d=omega_d, b=b),\n", + " [0.0, tend], [theta0, 0.0],\n", + " method='RK45', t_eval=tpoints)\n", + "\n", + " return r.t, r.y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The call below will give an undamped pendulum. For a small amplitude, since we have $L = g$ in our pendulum, the period is simply $T = 2\\pi$, and the frequency is $\\nu_k = 1/(2\\pi)$. We plot things in terms of angular frequency, $\\omega_k = 2\\pi \\nu_k$, so all the power will be at $\\omega_k = 1$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "t, y = int_pendulum(np.radians(10), 0.0, 0.6666, 0.0, 200.0, 0.1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Your task is to complete the power spectrum routine below to calculate the FFT of theta and plot it. Experiment with the damping and driving parameters to see the complexity of the pendulum in frequency space when it becomes chaotic. For reference, here's a plot of the solution theta" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\theta$')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t, restrict_theta(y[0,:]))\n", + "plt.xlabel(\"t\")\n", + "plt.ylabel(r\"$\\theta$\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def power_spectrum(t, theta0):\n", + " \"\"\" return the power spectrum of theta. For the frequency\n", + " component, return it in terms of omega \"\"\"\n", + "\n", + " theta = restrict_theta(theta0)\n", + " \n", + " # fill in the rest -- take the FFT of theta and return omega_k and \n", + " # the transform of theta\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fitting" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q4: Let's find the errors on our fit\n", + "\n", + "We looked at fits, but not what the errors are on the fit. Look at `scipy.optimize.curve_fit()`. This is a simplified wrapper on the least squares fitting. It can return the convariance matrix, the diagonals of which can give the error of the fit for the parameters. \n", + "\n", + "Make up some data that models a non-linear function (by introducing some random noise) and perform a fit and find the errors on the parameters." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.13.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/05-scipy/scipy-exercises.ipynb b/content/05-scipy/scipy-exercises.ipynb new file mode 100644 index 00000000..0741ef0e --- /dev/null +++ b/content/05-scipy/scipy-exercises.ipynb @@ -0,0 +1,398 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SciPy exercises" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Integration" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import integrate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Q1: integrating an analytic function\n", + "\n", + "Numerical integration methods work differently depending on whether you have the analytic function available (in which case you can evaluate it freely at any point you please) or if it is sampled for you.\n", + "\n", + "Consider the function $f(x) = e^{-x^2}$. We want to integrate this from $[-5, 5]$. The\n", + "analytic integral is not easily obtained. Use `integrate.quad` to do the integration." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Q2: integrating a sampled function\n", + "\n", + "Consider now that you have data that represents a function sampled a `N` points, but you don't know the analytic form of the function. Here, we create the sampling here for a Gaussian and we will do the same integral as in Q1." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1.38879439e-11, 3.15061953e-10, 5.80457065e-09, 8.68481106e-08,\n", + " 1.05527775e-06, 1.04133225e-05, 8.34503173e-05, 5.43103745e-04,\n", + " 2.87047478e-03, 1.23208538e-02, 4.29481052e-02, 1.21580337e-01,\n", + " 2.79510942e-01, 5.21855680e-01, 7.91258065e-01, 9.74320895e-01,\n", + " 9.74320895e-01, 7.91258065e-01, 5.21855680e-01, 2.79510942e-01,\n", + " 1.21580337e-01, 4.29481052e-02, 1.23208538e-02, 2.87047478e-03,\n", + " 5.43103745e-04, 8.34503173e-05, 1.04133225e-05, 1.05527775e-06,\n", + " 8.68481106e-08, 5.80457065e-09, 3.15061953e-10, 1.38879439e-11])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "N = 32\n", + "x = np.linspace(-5, 5, N)\n", + "f = np.exp(-x**2)\n", + "f" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compute the integral of this sampled function using Simpson's method (`integrate.simps`). Now, vary the number of sample points (try 64, 128, ...) and see how the answer changes. Simpson's method is 4-th order accurate, which means that the error should decrease by $2^4$ when we double the number of sample points" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Optional: Make a plot of the error (compared to the analytic integral from Q1) vs. N" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Interpolation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import interpolate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Q3: interpolation error\n", + "\n", + "There are a large number of different interpolation schemes available through scipy. Let's test them out.\n", + "\n", + "Create a python function, $f(x)$, that is your true function. Now create $N$ samples of it (either regularly spaced or irregularly spaced).\n", + "\n", + "Try some of the different interolation routines. `interpolate.interp1d` takes a `kind` argument that let's you choose the order of the interpolation. Measure the error in the method, by comparing the interpolated result with the actual function value. Also, try using cubic splines (look at `CubicSpline`)\n", + "\n", + "Try plotting the resulting interpolant." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Root Finding" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Q4: scalar function roots\n", + "\n", + "Consider the function\n", + "\n", + "$$q(x) = x^3 - 2x^2 - 11x + 12$$\n", + "\n", + "This has 3 roots, but is known to cause problems for some root-finding methods (it exhibits basis of attraction: https://en.wikipedia.org/wiki/Newton%27s_method#Basins_of_attraction -- very closely spaced initial guesses leave to very different roots)\n", + "\n", + "Use the SciPy `optimize.brentq` method to find the roots. You might need to play around with the intervals to find all 3 roots (try plotting the function to help)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import optimize" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ODEs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Q5: orbits\n", + "\n", + "We want to consider planetary orbits. To do this, we need to solve Newton's second law together with Newton's law of gravity. If we restrict ourselves to the x-y plane, then there are 4 quantities we need to solve for: $x$, $y$, $v_x$, and $v_y$. These evolve according to:\n", + "\n", + "\\begin{align*}\n", + "\\frac{dx}{dt} &= v_x \\\\\n", + "\\frac{dy}{dt} &= v_y \\\\\n", + "\\frac{dv_x}{dt} &= a_x = -\\frac{GM_\\star x}{r^3} \\\\\n", + "\\frac{dv_y}{dt} &= a_y = -\\frac{GM_\\star y}{r^3}\n", + "\\end{align*}\n", + "\n", + "To integrate these forward in time, we need an initial condition for each quantity. We'll setup our system such that the Sun is at the origin (that will be one focus), and the planet begins at perihelion and orbits counterclockwise. \n", + "\n", + "![geometry](orbit_setup.png)\n", + "\n", + "The distance of perihelion from the focus is:\n", + "\n", + "$$r_p = a (1 - e)$$\n", + "\n", + "where $a$ is the semi-major axis and $e$ is the eccentricity. The perihelion velocity is all in the $y$ direction and is:\n", + "\n", + "$$v_y = v_p = \\sqrt{\\frac{GM_\\star}{a} \\frac{1+e}{1-e}}$$\n", + "\n", + "We'll work in units of AU, years, and solar masses, in which case, $GM_\\star = 4\\pi^2$ (for the Sun). \n", + "\n", + "Your initial conditions should be:\n", + "\n", + " * $x(t=0) = r_p$\n", + " * $y(t=0) = 0$\n", + " * $v_x(t=0) = 0$\n", + " * $v_y(t=0) = v_p$\n", + "\n", + "Here's a righthand side function for the ODEs:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def rhs(t, Y, GM=4*np.pi**2):\n", + " \"\"\"RHS for orbits, Y is the solution vector, containing\n", + " x, y, v_x, and v_y\"\"\"\n", + "\n", + " x, y, vx, vy = Y\n", + " f = np.zeros_like(Y)\n", + "\n", + " # dx/dt = vx\n", + " f[0] = vx\n", + "\n", + " # dy/dt = vy\n", + " f[1] = vy\n", + "\n", + " # d(vx)/dt = -GMx/r**3\n", + " r = np.sqrt(x**2 + y**2)\n", + " f[2] = -GM*x/r**3\n", + "\n", + " # d(vy)/dt = -GMy/r**3\n", + " f[3] = -GM*y/r**3\n", + "\n", + " return f" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Use the SciPy ODE integration methods to integrate an orbit and plot it" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Q6: damped driven pendulum and chaos" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a large class of ODE integration methods available through the `scipy.integrate.ode()` function. Not all of them provide _dense output_ -- most will just give you the value at the end of the integration. \n", + "\n", + "The explicit Runge-Kutta integrator will give you access to the solution at intermediate points and provides methods to interpolate to any value. You enable this via `dense_output=True` (see the example in our out-of-class notebook).\n", + "\n", + "The damped driven pendulum obeys the following equations:\n", + "\n", + "$$\\dot{\\theta} = \\omega$$\n", + "\n", + "$$\\dot{\\omega} = -q \\omega - \\sin \\theta + b \\cos \\omega_d t$$\n", + "\n", + "here, $\\theta$ is the angle of the pendulum from vertical and $\\omega$ is the angular velocity. $q$ is a damping coefficient, $b$ is a forcing amplitude, and $\\omega_d$ is a driving frequency.\n", + "\n", + "Choose $q = 0.5$ and $\\omega_d = 2/3$.\n", + "\n", + "Integrate the system for different values of $b$ (start with $b = 0.9$ and increase by $0.05$, and plot the results ($\\theta$ vs. $t$). Here's a RHS function to get you started:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def rhs(t, Y, q, omega_d, b):\n", + " \"\"\" damped driven pendulum system derivatives. Here, Y = (theta, omega) are\n", + " the solution variables. \"\"\"\n", + " f = np.zeros_like(Y)\n", + " \n", + " f[0] = Y[1]\n", + " f[1] = -q*Y[1] - np.sin(Y[0]) + b*np.cos(omega_d*t)\n", + "\n", + " return f" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the pendulum can flip over, giving values of $\\theta$ outside of $[-\\pi, \\pi]$. The following function can be used to restrict it back to $[-\\pi, \\pi]$ for plotting." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def restrict_theta(theta):\n", + " \"\"\" convert theta to be restricted to lie between -pi and pi\"\"\"\n", + " tnew = theta + np.pi\n", + " tnew += -2.0*np.pi*np.floor(tnew/(2.0*np.pi))\n", + " tnew -= np.pi\n", + " return tnew" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Write a function that takes an initial angle, $\\theta_0$, and integrates the system and returns the solution.\n", + "\n", + "Note, the righthand side function, `rhs`, takes additional arguments that you need to pass through the integrator. The preferred method to do this with the `solve_ivp()` interface appears to be to use `functools.partial()`, as:\n", + "```\n", + "from functools import partial\n", + "\n", + "r = solve_ivp(partial(rhs, q=q, omega_d=omega_d, b=b), ...)\n", + "```\n", + "\n", + "Some values of $b$ will show very non-periodic behavior. To see chaos, integrate two different pendula that are the same except for $\\theta_0$, with only a small difference between then (like 60 degrees and 60.0001 degrees. You'll see the solutions track for a while, but then diverge." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.12.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/05-scipy/scipy.md b/content/05-scipy/scipy.md new file mode 100644 index 00000000..e0c7b9e5 --- /dev/null +++ b/content/05-scipy/scipy.md @@ -0,0 +1,3 @@ +# SciPy + +SciPy provides implementations of many common numerical methods. diff --git a/lectures/05-scipy/scipy.png b/content/05-scipy/scipy.png similarity index 100% rename from lectures/05-scipy/scipy.png rename to content/05-scipy/scipy.png diff --git a/lectures/05-scipy/simpsons.png b/content/05-scipy/simpsons.png similarity index 100% rename from lectures/05-scipy/simpsons.png rename to content/05-scipy/simpsons.png diff --git a/lectures/05-scipy/trapezoid.png b/content/05-scipy/trapezoid.png similarity index 100% rename from lectures/05-scipy/trapezoid.png rename to content/05-scipy/trapezoid.png diff --git a/content/06-sympy/sympy-examples.ipynb b/content/06-sympy/sympy-examples.ipynb new file mode 100644 index 00000000..002f7b3c --- /dev/null +++ b/content/06-sympy/sympy-examples.ipynb @@ -0,0 +1,2420 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SymPy examples" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "sources:\n", + "http://docs.sympy.org/latest/tutorial/\n", + "http://nbviewer.ipython.org/github/ipython/ipython/blob/master/examples/notebooks/SymPy%20Examples.ipynb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SymPy provides support for symbolic math to python, similar to what you would do with Mathematica or Maple. The major difference is that it acts just like any other python module, so you can use the symbolic math together in your own python projects with the rest of python functionality.\n", + "\n", + "The following import and function (`init_session()`) sets up a nice environment for us when working in Jupyter" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "IPython console for SymPy 1.13.3 (Python 3.13.2-64-bit) (ground types: gmpy)\n", + "\n", + "These commands were executed:\n", + ">>> from sympy import *\n", + ">>> x, y, z, t = symbols('x y z t')\n", + ">>> k, m, n = symbols('k m n', integer=True)\n", + ">>> f, g, h = symbols('f g h', cls=Function)\n", + ">>> init_printing()\n", + "\n", + "Documentation can be found at https://docs.sympy.org/1.13.3/\n", + "\n" + ] + } + ], + "source": [ + "from sympy import init_session\n", + "init_session(use_latex=\"mathjax\")" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import math" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## SymPy types and basic symbolic manipulation\n", + "\n", + "Sympy defines its own types, you can convert them to python types, but you don't always want to (and will probably lose accuracy when you do). " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.4142135623730951\n" + ] + } + ], + "source": [ + "print(math.sqrt(2))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sqrt(2)\n" + ] + } + ], + "source": [ + "print(sqrt(2))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2*sqrt(2)\n" + ] + } + ], + "source": [ + "print(sqrt(8))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "#help(sqrt(8))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can do symbolic math not just on numbers, but we can tell SymPy what to treat as a symbol, using `symbols()`" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "from sympy import symbols\n", + "x, y, z = symbols(\"x y z\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x + 2 y$" + ], + "text/plain": [ + "x + 2⋅y" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = x + 2*y\n", + "expr" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x + 2 y - 1$" + ], + "text/plain": [ + "x + 2⋅y - 1" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr - 1" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x + y$" + ], + "text/plain": [ + "x + y" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr - y" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x \\left(x + 2 y\\right)$" + ], + "text/plain": [ + "x⋅(x + 2⋅y)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f = x*expr\n", + "f" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x^{2} + 2 x y$" + ], + "text/plain": [ + " 2 \n", + "x + 2⋅x⋅y" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g = expand(f)\n", + "g" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x \\left(x + 2 y\\right)$" + ], + "text/plain": [ + "x⋅(x + 2⋅y)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "factor(g)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## substitution\n", + "\n", + "SymPy provides methods to substitute values for symbols in symbolic expressions. Note, the follow likely does not do what you expect:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\sin{\\left(2 \\pi z \\right)}$" + ], + "text/plain": [ + "sin(2⋅π⋅z)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = sin(z*2*pi)\n", + "z = 0\n", + "expr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We've now redefined `z` to be a python type" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "int" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(z)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "to do substitution, we use the `subs()` method" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\sin{\\left(2 \\pi x \\right)}$" + ], + "text/plain": [ + "sin(2⋅π⋅x)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = sin(x*2*pi)\n", + "expr" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{\\sqrt{2}}{2}$" + ], + "text/plain": [ + "√2\n", + "──\n", + "2 " + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = expr.subs(x, 0.125)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that this is not a floating point number -- it is still a SymPy object. To make it floating point, we can use evalf()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.707106781186548 \n" + ] + } + ], + "source": [ + "b = a.evalf()\n", + "print(b, type(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is still a SymPy object, because SymPy can do arbitrary precision " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 0.70710678118654752440084436210484903928483593768847$" + ], + "text/plain": [ + "0.70710678118654752440084436210484903928483593768847" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.evalf(50)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "want regular python types?" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.7071067811865476 \n" + ] + } + ], + "source": [ + "c = float(b)\n", + "print(c, type(c))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Python and SymPy" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "x, y, z, t = symbols('x y z t')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SymPy symbols are just objects and when you do operations on two sympy objects the result is a sympy object. \n", + "\n", + "When you combine a sympy and python object, the result is also a sympy object. \n", + "\n", + "But we need to be careful when doing fractions. For instance doing `x + 1/3` will first compute `1/3` in python (giving `0.333...`) and then add it to the sympy `x` symbol. The `Rational()` function makes this all happen in sympy" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\sin{\\left(2 \\pi x \\right)} + \\frac{1}{3}$" + ], + "text/plain": [ + "sin(2⋅π⋅x) + 1/3" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f = expr + Rational(1,3)\n", + "f" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\sin{\\left(2 \\pi x \\right)} + 0.333333333333333$" + ], + "text/plain": [ + "sin(2⋅π⋅x) + 0.333333333333333" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr + 1/3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## equality" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`=` is still the assignment operator of python (it does not mean symbolic equality), and `==` is still the logical test (exact structural equality). There is a separate object, `Eq()` to specify symbolic equality.\n", + "\n", + "And testing for _algebraic_ equality is not always accomplished using `==`, since that tests for _structural equality_." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x + 1 == 4" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x + 1 = 4$" + ], + "text/plain": [ + "x + 1 = 4" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Eq(x + 1, 4)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "a = (x + 1)**2\n", + "b = x**2 + 2*x + 1 # these are algebraically equal" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a == b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use `simplify()` to test for algebraic equality" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 0$" + ], + "text/plain": [ + "0" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplify(a - b)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle i \\sin{\\left(x \\right)} + \\cos{\\left(x \\right)}$" + ], + "text/plain": [ + "ⅈ⋅sin(x) + cos(x)" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = cos(x) + I*sin(x)\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle e^{i x}$" + ], + "text/plain": [ + " ⅈ⋅x\n", + "ℯ " + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplify(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More substitution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "note that substitution returns a new expression: SymPy expressions are immutable" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 1$" + ], + "text/plain": [ + "1" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = cos(x)\n", + "expr.subs(x, 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\cos{\\left(x \\right)}$" + ], + "text/plain": [ + "cos(x)" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x$" + ], + "text/plain": [ + "x" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "multiple substitutions, pass a list of tuples" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x^{3} + 4 x y - z$" + ], + "text/plain": [ + " 3 \n", + "x + 4⋅x⋅y - z" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = x**3 + 4*x*y - z\n", + "expr" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 40$" + ], + "text/plain": [ + "40" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr.subs([(x, 2), (y, 4), (z, 0)])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## simplifying" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is not unique definition of what the simplest form of an expression is.\n", + "\n", + "`simplify()` tries lots of methods for simplification" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 1$" + ], + "text/plain": [ + "1" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplify(sin(x)**2 + cos(x)**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x - 1$" + ], + "text/plain": [ + "x - 1" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplify( (x**3 + x**2 - x - 1)/(x**2 + 2*x + 1) )" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left(x - 2\\right) \\left(x - 1\\right)$" + ], + "text/plain": [ + "(x - 2)⋅(x - 1)" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplify(gamma(x)/gamma(x - 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "but sometimes it doesn't have your idea of what the simplest form is" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x^{2} + 2 x + 1$" + ], + "text/plain": [ + " 2 \n", + "x + 2⋅x + 1" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplify(x**2 + 2*x + 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "instead factor may be what you want" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left(x + 1\\right)^{2}$" + ], + "text/plain": [ + " 2\n", + "(x + 1) " + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "factor(x**2 + 2*x + 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### polynomial simplification" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x^{2} + 2 x + 1$" + ], + "text/plain": [ + " 2 \n", + "x + 2⋅x + 1" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expand((x + 1)**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x^{2} - x - 6$" + ], + "text/plain": [ + " 2 \n", + "x - x - 6" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expand((x + 2)*(x - 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle -2$" + ], + "text/plain": [ + "-2" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expand( (x + 1)*(x - 2) - (x - 1)*x)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle z \\left(x + 2 y\\right)^{2}$" + ], + "text/plain": [ + " 2\n", + "z⋅(x + 2⋅y) " + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "factor(x**2*z + 4*x*y*z + 4*y**2*z)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left( 1, \\ \\left[ \\left( z, \\ 1\\right), \\ \\left( x + 2 y, \\ 2\\right)\\right]\\right)$" + ], + "text/plain": [ + "(1, [(z, 1), (x + 2⋅y, 2)])" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "factor_list(x**2*z + 4*x*y*z + 4*y**2*z)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "collect collects common powers" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x^{3} - x^{2} z + 2 x^{2} + x y + x - 3$" + ], + "text/plain": [ + " 3 2 2 \n", + "x - x ⋅z + 2⋅x + x⋅y + x - 3" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = x*y + x - 3 + 2*x**2 - z*x**2 + x**3\n", + "expr" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle x^{3} + x^{2} \\left(2 - z\\right) + x \\left(y + 1\\right) - 3$" + ], + "text/plain": [ + " 3 2 \n", + "x + x ⋅(2 - z) + x⋅(y + 1) - 3" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "collected_expr = collect(expr, x)\n", + "collected_expr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "cancel cancels" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{x^{2} + 2 x + 1}{x^{2} + x}$" + ], + "text/plain": [ + " 2 \n", + "x + 2⋅x + 1\n", + "────────────\n", + " 2 \n", + " x + x " + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = (x**2 + 2*x + 1)/(x**2 + x)\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{x + 1}{x}$" + ], + "text/plain": [ + "x + 1\n", + "─────\n", + " x " + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cancel(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "trigsimp simplifies trigonometric identities" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{\\cos{\\left(4 x \\right)}}{2} + \\frac{1}{2}$" + ], + "text/plain": [ + "cos(4⋅x) 1\n", + "──────── + ─\n", + " 2 2" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trigsimp(sin(x)**4 - 2*cos(x)**2*sin(x)**2 + cos(x)**4)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\sin^{2}{\\left(x \\right)}$" + ], + "text/plain": [ + " 2 \n", + "sin (x)" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trigsimp(sin(x)*tan(x)/sec(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "the tutorial discusses some of the nuances of simplification of powers and special functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculus" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calculus operations are simple in SymPy\n", + "\n", + "### derivatives" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle - \\sin{\\left(x \\right)}$" + ], + "text/plain": [ + "-sin(x)" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(cos(x), x)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 2 x e^{x^{2}}$" + ], + "text/plain": [ + " ⎛ 2⎞\n", + " ⎝x ⎠\n", + "2⋅x⋅ℯ " + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(exp(x**2), x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "third derivative" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 24 x$" + ], + "text/plain": [ + "24⋅x" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(x**4, x, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "differentiate different variables" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left(x^{2} y^{2} z^{2} + 3 x y z + 1\\right) e^{x y z}$" + ], + "text/plain": [ + "⎛ 2 2 2 ⎞ x⋅y⋅z\n", + "⎝x ⋅y ⋅z + 3⋅x⋅y⋅z + 1⎠⋅ℯ " + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = exp(x*y*z)\n", + "diff(expr, x, y, z)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "unevaluated derivatives can be useful for building up ODEs and PDEs" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{\\partial^{3}}{\\partial z\\partial y\\partial x} e^{x y z}$" + ], + "text/plain": [ + " 3 \n", + " ∂ ⎛ x⋅y⋅z⎞\n", + "────────⎝ℯ ⎠\n", + "∂z ∂y ∂x " + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "deriv = Derivative(expr, x, y, z)\n", + "deriv" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left(x^{2} y^{2} z^{2} + 3 x y z + 1\\right) e^{x y z}$" + ], + "text/plain": [ + "⎛ 2 2 2 ⎞ x⋅y⋅z\n", + "⎝x ⋅y ⋅z + 3⋅x⋅y⋅z + 1⎠⋅ℯ " + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "deriv.doit()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### integrals\n", + "\n", + "definite and indefinite integrals are supported" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\sin{\\left(x \\right)}$" + ], + "text/plain": [ + "sin(x)" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "integrate(cos(x), x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "definite integral -- note the construction of the infinity" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 1$" + ], + "text/plain": [ + "1" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "integrate(exp(-x), (x, 0, oo))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "double integral" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\pi$" + ], + "text/plain": [ + "π" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "integrate(exp(-x**2 - y**2), (x, -oo, oo), (y, -oo, oo))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "if it is unable to do the integral, it returns an Integral object" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Integral(x**x, x)\n" + ] + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\int x^{x}\\, dx$" + ], + "text/plain": [ + "⌠ \n", + "⎮ x \n", + "⎮ x dx\n", + "⌡ " + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = integrate(x**x, x)\n", + "print(expr)\n", + "expr" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{x}{\\sqrt{x^{4} + 10 x^{2} - 96 x - 71}}$" + ], + "text/plain": [ + " x \n", + "───────────────────────────\n", + " ________________________\n", + " ╱ 4 2 \n", + "╲╱ x + 10⋅x - 96⋅x - 71 " + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = x / sqrt(x**4 + 10*x**2 - 96*x - 71) # example from Wikipedia Risch algorithm page)\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\int \\frac{x}{\\sqrt{x^{4} + 10 x^{2} - 96 x - 71}}\\, dx$" + ], + "text/plain": [ + "⌠ \n", + "⎮ x \n", + "⎮ ─────────────────────────── dx\n", + "⎮ ________________________ \n", + "⎮ ╱ 4 2 \n", + "⎮ ╲╱ x + 10⋅x - 96⋅x - 71 \n", + "⌡ " + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "integrate(a, x) # this has a known solution, but SymPy fails to find it" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### limits" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 1$" + ], + "text/plain": [ + "1" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "limit(sin(x)/x, x, 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### series expansions" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 1 + x + \\frac{x^{2}}{2} - \\frac{x^{4}}{8} - \\frac{x^{5}}{15} - \\frac{x^{6}}{240} + \\frac{x^{7}}{90} + \\frac{31 x^{8}}{5760} + \\frac{x^{9}}{5670} + O\\left(x^{10}\\right)$" + ], + "text/plain": [ + " 2 4 5 6 7 8 9 \n", + " x x x x x 31⋅x x ⎛ 10⎞\n", + "1 + x + ── - ── - ── - ─── + ── + ───── + ──── + O⎝x ⎠\n", + " 2 8 15 240 90 5760 5670 " + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expr = exp(sin(x))\n", + "a = expr.series(x, 0, 10)\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle -1 - \\frac{\\left(x - 1\\right)^{2}}{2} + \\frac{\\left(x - 1\\right)^{3}}{3} - \\frac{\\left(x - 1\\right)^{4}}{4} + \\frac{\\left(x - 1\\right)^{5}}{5} + x + O\\left(\\left(x - 1\\right)^{6}; x\\rightarrow 1\\right)$" + ], + "text/plain": [ + " 2 3 4 5 \n", + " (x - 1) (x - 1) (x - 1) (x - 1) ⎛ 6 ⎞\n", + "-1 - ──────── + ──────── - ──────── + ──────── + x + O⎝(x - 1) ; x → 1⎠\n", + " 2 3 4 5 " + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = log(x).series(x, x0=1, n=6)\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{x^{5}}{5} - \\frac{5 x^{4}}{4} + \\frac{10 x^{3}}{3} - 5 x^{2} + 5 x - \\frac{137}{60}$" + ], + "text/plain": [ + " 5 4 3 \n", + "x 5⋅x 10⋅x 2 137\n", + "── - ──── + ───── - 5⋅x + 5⋅x - ───\n", + "5 4 3 60 " + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplify(c.removeO())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## solvers\n", + "\n", + "`solveset()` is the main interface to solvers in SymPy. Note that it used to be `solve()`, but this has been replaced (see http://docs.sympy.org/latest/modules/solvers/solveset.html)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If no Eq() is done, then it is assumed to be equal to 0" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left\\{0, 1\\right\\}$" + ], + "text/plain": [ + "{0, 1}" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "solveset(x**2 - x, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "you can restrict the domain of the solution (e.g. to reals). Recall that Z is the set of integers" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left\\{2 n \\pi + \\frac{\\pi}{2}\\; \\middle|\\; n \\in \\mathbb{Z}\\right\\}$" + ], + "text/plain": [ + "⎧ π │ ⎫\n", + "⎨2⋅n⋅π + ─ │ n ∊ ℤ⎬\n", + "⎩ 2 │ ⎭" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "solveset(sin(x) - 1, x, domain=S.Reals)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### linear systems\n", + "\n", + "`linsolve()` is the interface to linear systems" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left\\{\\left( \\frac{1}{2}, \\ \\frac{5}{2}\\right)\\right\\}$" + ], + "text/plain": [ + "{(1/2, 5/2)}" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "linsolve([x - y + 2, x + y - 3], [x, y])" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left\\{\\left( - y - 1, \\ y, \\ 2\\right)\\right\\}$" + ], + "text/plain": [ + "{(-y - 1, y, 2)}" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "linsolve([x + y + z - 1, x + y + 2*z - 3 ], (x, y, z))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "roots will report if a solution is multiple by listing it multiple times" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left\\{ 0 : 1, \\ 3 : 2\\right\\}$" + ], + "text/plain": [ + "{0: 1, 3: 2}" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "roots(x**3 - 6*x**2 + 9*x, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "0 is 1 root, and 3 is 2 more roots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Differential equations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "you need an undefined function (f and g already are by our init_session() above, but we've probably reset these" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [], + "source": [ + "f, g = symbols('f g', cls=Function)" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle f{\\left(x \\right)}$" + ], + "text/plain": [ + "f(x)" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{d}{d x} f{\\left(x \\right)}$" + ], + "text/plain": [ + "d \n", + "──(f(x))\n", + "dx " + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f(x).diff(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [], + "source": [ + "diffeq = Eq(f(x).diff(x, 2) - 2*f(x).diff(x) + f(x), sin(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle f{\\left(x \\right)} - 2 \\frac{d}{d x} f{\\left(x \\right)} + \\frac{d^{2}}{d x^{2}} f{\\left(x \\right)} = \\sin{\\left(x \\right)}$" + ], + "text/plain": [ + " 2 \n", + " d d \n", + "f(x) - 2⋅──(f(x)) + ───(f(x)) = sin(x)\n", + " dx 2 \n", + " dx " + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diffeq" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle f{\\left(x \\right)} = \\left(C_{1} + C_{2} x\\right) e^{x} + \\frac{\\cos{\\left(x \\right)}}{2}$" + ], + "text/plain": [ + " x cos(x)\n", + "f(x) = (C₁ + C₂⋅x)⋅ℯ + ──────\n", + " 2 " + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dsolve(diffeq, f(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Matrices" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "consider the Euler equations:\n", + "\n", + "$$q_t + A(q) q_x = 0$$\n", + "\n", + "where\n", + "\n", + "$$q = \\left ( \\begin{array}{c} \\rho \\\\ u \\\\ p \\end{array} \\right )\n", + "\\qquad\n", + "A(q) = \\left ( \\begin{array}{ccc} u & \\rho & 0 \\\\ \n", + " 0 & u & 1/\\rho \\\\ \n", + " 0 & c^2 \\rho & u \\end{array} \\right ) $$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}u & \\rho & 0\\\\0 & u & \\frac{1}{\\rho}\\\\0 & c^{2} \\rho & u\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡u ρ 0⎤\n", + "⎢ ⎥\n", + "⎢ 1⎥\n", + "⎢0 u ─⎥\n", + "⎢ ρ⎥\n", + "⎢ ⎥\n", + "⎢ 2 ⎥\n", + "⎣0 c ⋅ρ u⎦" + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sympy.abc import rho\n", + "rho, u, c = symbols('rho u c')\n", + "A = Matrix([[u, rho, 0], [0, u, rho**-1], [0, c**2 * rho, u]])\n", + "A" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}u & \\rho & 0\\end{matrix}\\right]$" + ], + "text/plain": [ + "[u ρ 0]" + ] + }, + "execution_count": 80, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.row(0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The eigenvalues of the system are the speeds at which information propagates" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left\\{ u : 1, \\ - c + u : 1, \\ c + u : 1\\right\\}$" + ], + "text/plain": [ + "{u: 1, -c + u: 1, c + u: 1}" + ] + }, + "execution_count": 81, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.eigenvals()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can diagonalize it, such that\n", + "$$ A = PDP^{-1}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": {}, + "outputs": [], + "source": [ + "P, D = A.diagonalize()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$D$ will be a matrix of the eigenvalues" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}u & 0 & 0\\\\0 & - c + u & 0\\\\0 & 0 & c + u\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡u 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢0 -c + u 0 ⎥\n", + "⎢ ⎥\n", + "⎣0 0 c + u⎦" + ] + }, + "execution_count": 83, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$P$ will be the matrix of right eigenvectors" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}1 & \\frac{1}{c^{2}} & \\frac{1}{c^{2}}\\\\0 & - \\frac{1}{c \\rho} & \\frac{1}{c \\rho}\\\\0 & 1 & 1\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡ 1 1 ⎤\n", + "⎢1 ── ── ⎥\n", + "⎢ 2 2 ⎥\n", + "⎢ c c ⎥\n", + "⎢ ⎥\n", + "⎢ -1 1 ⎥\n", + "⎢0 ─── ───⎥\n", + "⎢ c⋅ρ c⋅ρ⎥\n", + "⎢ ⎥\n", + "⎣0 1 1 ⎦" + ] + }, + "execution_count": 84, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Inverse" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{u} & - \\frac{\\rho}{- c^{2} + u^{2}} & \\frac{1}{- c^{2} u + u^{3}}\\\\0 & \\frac{u}{- c^{2} + u^{2}} & - \\frac{1}{- c^{2} \\rho + \\rho u^{2}}\\\\0 & - \\frac{c^{2} \\rho}{- c^{2} + u^{2}} & \\frac{u}{- c^{2} + u^{2}}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡1 -ρ 1 ⎤\n", + "⎢─ ───────── ─────────── ⎥\n", + "⎢u 2 2 2 3 ⎥\n", + "⎢ - c + u - c ⋅u + u ⎥\n", + "⎢ ⎥\n", + "⎢ u -1 ⎥\n", + "⎢0 ───────── ─────────────⎥\n", + "⎢ 2 2 2 2⎥\n", + "⎢ - c + u - c ⋅ρ + ρ⋅u ⎥\n", + "⎢ ⎥\n", + "⎢ 2 ⎥\n", + "⎢ -c ⋅ρ u ⎥\n", + "⎢0 ───────── ───────── ⎥\n", + "⎢ 2 2 2 2 ⎥\n", + "⎣ - c + u - c + u ⎦" + ] + }, + "execution_count": 85, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A**-1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Units\n", + "\n", + "Sympy can attach units to numbers and propagate them through" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": {}, + "outputs": [], + "source": [ + "from sympy.physics.units import newton, kilogram, meter, second, convert_to" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 9.81 \\text{N}$" + ], + "text/plain": [ + "9.81⋅newton" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "F = 1 * kilogram * 9.81 * meter / second**2\n", + "convert_to(F, newton)" + ] + } + ], + "metadata": { + "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": "3.13.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/06-sympy/sympy-exercises.ipynb b/content/06-sympy/sympy-exercises.ipynb new file mode 100644 index 00000000..72b50736 --- /dev/null +++ b/content/06-sympy/sympy-exercises.ipynb @@ -0,0 +1,261 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SymPy Exercises" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "IPython console for SymPy 1.9 (Python 3.10.2-64-bit) (ground types: gmpy)\n", + "\n", + "These commands were executed:\n", + ">>> from __future__ import division\n", + ">>> from sympy import *\n", + ">>> x, y, z, t = symbols('x y z t')\n", + ">>> k, m, n = symbols('k m n', integer=True)\n", + ">>> f, g, h = symbols('f g h', cls=Function)\n", + ">>> init_printing()\n", + "\n", + "Documentation can be found at https://docs.sympy.org/1.9/\n", + "\n" + ] + } + ], + "source": [ + "import sympy as sym\n", + "from sympy import init_session\n", + "init_session()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q1: Creating an expression\n", + "\n", + "Create the expression:\n", + "\n", + "$$f = x e^{-x} + x (1-x)$$\n", + "\n", + "Then evaluate it for \n", + "\n", + "$$x = 0, 0.1, 0.2, 0.4, 0.8$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q2: Factoring a polynomial, and finding its roots\n", + "\n", + "Factor\n", + "\n", + "$$x^{4} - 6 x^{3} + x^{2} + 24 x + 16$$\n", + "\n", + "Then find its zeros." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q3: Integratation and differentiation\n", + "\n", + "Integrate the function:\n", + "\n", + "$$f = \\sin(x) e^{-x}$$\n", + "\n", + "Then differentiate the result to see if you get back the original function" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q4: Parsing an expression\n", + "\n", + "Write a program that reads in a mathematical expression as a string (e.g., `\"sin(2*pi*x)\"`), converts it to a SymPy expression, and then evaluates it as needed. \n", + "\n", + "Have your program either make a plot of the entered function, or use the input function as the function to fit a dataset to using curvefit.\n", + "\n", + "The following will be helpful:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`parse_expr()` will convert a string into a SymPy expression" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from sympy.parsing.sympy_parser import parse_expr" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/latex": [ + "$\\displaystyle \\sin{\\left(2 \\pi x \\right)}$" + ], + "text/plain": [ + "sin(2⋅π⋅x)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "s = \"sin(2*pi*x)\"\n", + "a = parse_expr(s)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`sympy.lambdify()` will convert a SymPy expression into a function that is callable by python. You can make it a numpy-compatible function too (this means, e.g., that any `sin()` in your SymPy expression will be evaluate using `np.sin()`)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "f = sym.lambdify(x, a, \"numpy\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/latex": [ + "$\\displaystyle -2.44929359829471 \\cdot 10^{-16}$" + ], + "text/plain": [ + "-2.4492935982947064e-16" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f(1.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "#help(lambdify)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q5: Units\n", + "\n", + "SymPy can deal with physical units. See:\n", + "\n", + "http://docs.sympy.org/latest/modules/physics/units/quantities.html\n", + "\n", + "Let's try this out. Newton's 2nd law is\n", + "\n", + "$$F = ma$$\n", + "\n", + "Create a mass of 1 kg and an acceleration of 10 m/s$^2$, and compute the force, $F$, and express the result in Newtons.\n", + "\n", + "Note: the `convert_to` function was added in SymPy 1.1, so if you are using an earlier version, you will need to divide by the target unit to do the conversion." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/06-sympy/sympy.md b/content/06-sympy/sympy.md new file mode 100644 index 00000000..0a3160ad --- /dev/null +++ b/content/06-sympy/sympy.md @@ -0,0 +1,5 @@ +# SymPy + +SymPy is the symbolic math library for python. A key design feature +of it is that it can interoperate with all of the libraries we've +already seen. diff --git a/lectures/07-pandas/exercises.txt b/content/07-pandas/exercises.txt similarity index 100% rename from lectures/07-pandas/exercises.txt rename to content/07-pandas/exercises.txt diff --git a/content/07-pandas/ideas.txt b/content/07-pandas/ideas.txt new file mode 100644 index 00000000..7236428d --- /dev/null +++ b/content/07-pandas/ideas.txt @@ -0,0 +1 @@ +https://gist.github.com/jakevdp/9ffd72a81c1af80a10314cba0569af84 diff --git a/content/07-pandas/pandas-babynames.ipynb b/content/07-pandas/pandas-babynames.ipynb new file mode 100644 index 00000000..1f1176ee --- /dev/null +++ b/content/07-pandas/pandas-babynames.ipynb @@ -0,0 +1,6652 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# pandas exercises" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use the sample dataset from the Social Secury Administration on baby names:\n", + "https://www.ssa.gov/oact/babynames/limits.html\n", + "\n", + "Download the \"National\" version and unzip it. There will be one file for each year.\n", + "\n", + "This example follows the _Python for Data Analysis_ book closely" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start by reading in just a single dataset, for the first year available (1880). We give the names of the columns here. The index will just be the line / record number in the file (not really important for us)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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namesexbirths
0MaryF7065
1AnnaF2604
2EmmaF2003
3ElizabethF1939
4MinnieF1746
5MargaretF1578
6IdaF1472
7AliceF1414
8BerthaF1320
9SarahF1288
10AnnieF1258
11ClaraF1226
12EllaF1156
13FlorenceF1063
14CoraF1045
15MarthaF1040
16LauraF1012
17NellieF995
18GraceF982
19CarrieF949
20MaudeF858
21MabelF808
22BessieF796
23JennieF793
24GertrudeF787
25JuliaF783
26HattieF769
27EdithF768
28MattieF704
29RoseF700
............
1970PhiloM5
1971PhineasM5
1972PresleyM5
1973RansomM5
1974ReeceM5
1975ReneM5
1976RoswellM5
1977RowlandM5
1978SampsonM5
1979SamualM5
1980SantosM5
1981SchuylerM5
1982SheppardM5
1983SpurgeonM5
1984StarlingM5
1985SylvanusM5
1986TheadoreM5
1987TheophileM5
1988TilmonM5
1989TommyM5
1990UnknownM5
1991VannM5
1992WesM5
1993WinstonM5
1994WoodM5
1995WoodieM5
1996WorthyM5
1997WrightM5
1998YorkM5
1999ZachariahM5
\n", + "

2000 rows × 3 columns

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" + ], + "text/plain": [ + " name sex births\n", + "0 Mary F 7065\n", + "1 Anna F 2604\n", + "2 Emma F 2003\n", + "3 Elizabeth F 1939\n", + "4 Minnie F 1746\n", + "5 Margaret F 1578\n", + "6 Ida F 1472\n", + "7 Alice F 1414\n", + "8 Bertha F 1320\n", + "9 Sarah F 1288\n", + "10 Annie F 1258\n", + "11 Clara F 1226\n", + "12 Ella F 1156\n", + "13 Florence F 1063\n", + "14 Cora F 1045\n", + "15 Martha F 1040\n", + "16 Laura F 1012\n", + "17 Nellie F 995\n", + "18 Grace F 982\n", + "19 Carrie F 949\n", + "20 Maude F 858\n", + "21 Mabel F 808\n", + "22 Bessie F 796\n", + "23 Jennie F 793\n", + "24 Gertrude F 787\n", + "25 Julia F 783\n", + "26 Hattie F 769\n", + "27 Edith F 768\n", + "28 Mattie F 704\n", + "29 Rose F 700\n", + "... ... .. ...\n", + "1970 Philo M 5\n", + "1971 Phineas M 5\n", + "1972 Presley M 5\n", + "1973 Ransom M 5\n", + "1974 Reece M 5\n", + "1975 Rene M 5\n", + "1976 Roswell M 5\n", + "1977 Rowland M 5\n", + "1978 Sampson M 5\n", + "1979 Samual M 5\n", + "1980 Santos M 5\n", + "1981 Schuyler M 5\n", + "1982 Sheppard M 5\n", + "1983 Spurgeon M 5\n", + "1984 Starling M 5\n", + "1985 Sylvanus M 5\n", + "1986 Theadore M 5\n", + "1987 Theophile M 5\n", + "1988 Tilmon M 5\n", + "1989 Tommy M 5\n", + "1990 Unknown M 5\n", + "1991 Vann M 5\n", + "1992 Wes M 5\n", + "1993 Winston M 5\n", + "1994 Wood M 5\n", + "1995 Woodie M 5\n", + "1996 Worthy M 5\n", + "1997 Wright M 5\n", + "1998 York M 5\n", + "1999 Zachariah M 5\n", + "\n", + "[2000 rows x 3 columns]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "names_1880 = pd.read_csv('babynames/yob1880.txt', names=[\"name\", \"sex\", \"births\"])\n", + "names_1880" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## number of births\n", + "\n", + "Now we want to start doing some analysis. `.groupby()` creates a new type of container that groups items. Here, we'll group by sex.\n", + "\n", + "See this:\n", + "http://pandas.pydata.org/pandas-docs/stable/groupby.html\n", + "https://community.modeanalytics.com/python/tutorial/pandas-groupby-and-python-lambda-functions/\n", + "\n", + "for a nice explanation of this method." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "sex\n", + "F 90992\n", + "M 110490\n", + "Name: births, dtype: int64" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "names_1880.groupby(\"sex\")[\"births\"].sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that we can use a column name as a parameter of the object, so we can equivalently do this as:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "sex\n", + "F 90992\n", + "M 110490\n", + "Name: births, dtype: int64" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "names_1880.groupby(\"sex\").births.sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On its own, you can't print a `GroupBy` object. You need to do a transformation or filter on it to get back a `Series` or `DataFrame`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "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", + "
namebirths
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" + ], + "text/plain": [ + " name births\n", + "sex \n", + "F 942 942\n", + "M 1058 1058" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "gb = names_1880.groupby(\"sex\")\n", + "gb.count()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we saw in the intro, we can propagate a scalar to all indices in the `DataFrame`. We'll use this to add a new column that represents the year:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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namesexbirthsyear
0MaryF70651880
1AnnaF26041880
2EmmaF20031880
3ElizabethF19391880
4MinnieF17461880
5MargaretF15781880
6IdaF14721880
7AliceF14141880
8BerthaF13201880
9SarahF12881880
10AnnieF12581880
11ClaraF12261880
12EllaF11561880
13FlorenceF10631880
14CoraF10451880
15MarthaF10401880
16LauraF10121880
17NellieF9951880
18GraceF9821880
19CarrieF9491880
20MaudeF8581880
21MabelF8081880
22BessieF7961880
23JennieF7931880
24GertrudeF7871880
25JuliaF7831880
26HattieF7691880
27EdithF7681880
28MattieF7041880
29RoseF7001880
...............
1970PhiloM51880
1971PhineasM51880
1972PresleyM51880
1973RansomM51880
1974ReeceM51880
1975ReneM51880
1976RoswellM51880
1977RowlandM51880
1978SampsonM51880
1979SamualM51880
1980SantosM51880
1981SchuylerM51880
1982SheppardM51880
1983SpurgeonM51880
1984StarlingM51880
1985SylvanusM51880
1986TheadoreM51880
1987TheophileM51880
1988TilmonM51880
1989TommyM51880
1990UnknownM51880
1991VannM51880
1992WesM51880
1993WinstonM51880
1994WoodM51880
1995WoodieM51880
1996WorthyM51880
1997WrightM51880
1998YorkM51880
1999ZachariahM51880
\n", + "

2000 rows × 4 columns

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" + ], + "text/plain": [ + " name sex births year\n", + "0 Mary F 7065 1880\n", + "1 Anna F 2604 1880\n", + "2 Emma F 2003 1880\n", + "3 Elizabeth F 1939 1880\n", + "4 Minnie F 1746 1880\n", + "5 Margaret F 1578 1880\n", + "6 Ida F 1472 1880\n", + "7 Alice F 1414 1880\n", + "8 Bertha F 1320 1880\n", + "9 Sarah F 1288 1880\n", + "10 Annie F 1258 1880\n", + "11 Clara F 1226 1880\n", + "12 Ella F 1156 1880\n", + "13 Florence F 1063 1880\n", + "14 Cora F 1045 1880\n", + "15 Martha F 1040 1880\n", + "16 Laura F 1012 1880\n", + "17 Nellie F 995 1880\n", + "18 Grace F 982 1880\n", + "19 Carrie F 949 1880\n", + "20 Maude F 858 1880\n", + "21 Mabel F 808 1880\n", + "22 Bessie F 796 1880\n", + "23 Jennie F 793 1880\n", + "24 Gertrude F 787 1880\n", + "25 Julia F 783 1880\n", + "26 Hattie F 769 1880\n", + "27 Edith F 768 1880\n", + "28 Mattie F 704 1880\n", + "29 Rose F 700 1880\n", + "... ... .. ... ...\n", + "1970 Philo M 5 1880\n", + "1971 Phineas M 5 1880\n", + "1972 Presley M 5 1880\n", + "1973 Ransom M 5 1880\n", + "1974 Reece M 5 1880\n", + "1975 Rene M 5 1880\n", + "1976 Roswell M 5 1880\n", + "1977 Rowland M 5 1880\n", + "1978 Sampson M 5 1880\n", + "1979 Samual M 5 1880\n", + "1980 Santos M 5 1880\n", + "1981 Schuyler M 5 1880\n", + "1982 Sheppard M 5 1880\n", + "1983 Spurgeon M 5 1880\n", + "1984 Starling M 5 1880\n", + "1985 Sylvanus M 5 1880\n", + "1986 Theadore M 5 1880\n", + "1987 Theophile M 5 1880\n", + "1988 Tilmon M 5 1880\n", + "1989 Tommy M 5 1880\n", + "1990 Unknown M 5 1880\n", + "1991 Vann M 5 1880\n", + "1992 Wes M 5 1880\n", + "1993 Winston M 5 1880\n", + "1994 Wood M 5 1880\n", + "1995 Woodie M 5 1880\n", + "1996 Worthy M 5 1880\n", + "1997 Wright M 5 1880\n", + "1998 York M 5 1880\n", + "1999 Zachariah M 5 1880\n", + "\n", + "[2000 rows x 4 columns]" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "names_1880[\"year\"] = 1880\n", + "names_1880" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## all data sets\n", + "\n", + "Now we can read in all of the datasets. We will read them in one-by-one and add the \"year\" column to them. We'll keep a list of all the `DataFrame`s and then we'll use a pandas method to transform this list of `DataFrame`s into a single `DataFrame`" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "years = range(1880, 2016)\n", + "\n", + "pieces = []\n", + "columns = [\"name\", \"sex\", \"births\"]\n", + "\n", + "for yr in years:\n", + " frame = pd.read_csv(\"babynames/yob{}.txt\".format(yr), names=columns)\n", + " \n", + " # this creates a new column and gives all rows the same value -- the year\n", + " frame[\"year\"] = yr\n", + " pieces.append(frame)\n", + "\n", + "# create a single dataframe through concatenation -- ignore_index means that\n", + "# we don't care about the original line numbers\n", + "names = pd.concat(pieces, ignore_index=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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namesexbirthsyear
0MaryF70651880
1AnnaF26041880
2EmmaF20031880
3ElizabethF19391880
4MinnieF17461880
5MargaretF15781880
6IdaF14721880
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9SarahF12881880
10AnnieF12581880
11ClaraF12261880
12EllaF11561880
13FlorenceF10631880
14CoraF10451880
15MarthaF10401880
16LauraF10121880
17NellieF9951880
18GraceF9821880
19CarrieF9491880
20MaudeF8581880
21MabelF8081880
22BessieF7961880
23JennieF7931880
24GertrudeF7871880
25JuliaF7831880
26HattieF7691880
27EdithF7681880
28MattieF7041880
29RoseF7001880
...............
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1858684ZykellM52015
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1858687ZyrusM52015
1858688ZyusM52015
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1858689 rows × 4 columns

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" + ], + "text/plain": [ + " name sex births year\n", + "0 Mary F 7065 1880\n", + "1 Anna F 2604 1880\n", + "2 Emma F 2003 1880\n", + "3 Elizabeth F 1939 1880\n", + "4 Minnie F 1746 1880\n", + "5 Margaret F 1578 1880\n", + "6 Ida F 1472 1880\n", + "7 Alice F 1414 1880\n", + "8 Bertha F 1320 1880\n", + "9 Sarah F 1288 1880\n", + "10 Annie F 1258 1880\n", + "11 Clara F 1226 1880\n", + "12 Ella F 1156 1880\n", + "13 Florence F 1063 1880\n", + "14 Cora F 1045 1880\n", + "15 Martha F 1040 1880\n", + "16 Laura F 1012 1880\n", + "17 Nellie F 995 1880\n", + "18 Grace F 982 1880\n", + "19 Carrie F 949 1880\n", + "20 Maude F 858 1880\n", + "21 Mabel F 808 1880\n", + "22 Bessie F 796 1880\n", + "23 Jennie F 793 1880\n", + "24 Gertrude F 787 1880\n", + "25 Julia F 783 1880\n", + "26 Hattie F 769 1880\n", + "27 Edith F 768 1880\n", + "28 Mattie F 704 1880\n", + "29 Rose F 700 1880\n", + "... ... .. ... ...\n", + "1858659 Zavon M 5 2015\n", + "1858660 Zay M 5 2015\n", + "1858661 Zaylor M 5 2015\n", + "1858662 Zayquan M 5 2015\n", + "1858663 Zecharia M 5 2015\n", + "1858664 Zecharya M 5 2015\n", + "1858665 Zee M 5 2015\n", + "1858666 Zeev M 5 2015\n", + "1858667 Zeik M 5 2015\n", + "1858668 Zekariah M 5 2015\n", + "1858669 Zepplin M 5 2015\n", + "1858670 Zerek M 5 2015\n", + "1858671 Zeyd M 5 2015\n", + "1858672 Zhi M 5 2015\n", + "1858673 Ziel M 5 2015\n", + "1858674 Zihan M 5 2015\n", + "1858675 Zihao M 5 2015\n", + "1858676 Ziheng M 5 2015\n", + "1858677 Zimere M 5 2015\n", + "1858678 Ziyi M 5 2015\n", + "1858679 Ziyu M 5 2015\n", + "1858680 Zoel M 5 2015\n", + "1858681 Zohar M 5 2015\n", + "1858682 Zolton M 5 2015\n", + "1858683 Zyah M 5 2015\n", + "1858684 Zykell M 5 2015\n", + "1858685 Zyking M 5 2015\n", + "1858686 Zykir M 5 2015\n", + "1858687 Zyrus M 5 2015\n", + "1858688 Zyus M 5 2015\n", + "\n", + "[1858689 rows x 4 columns]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "names" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pivot tables" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "a _pivot table_ creates a new dataframe from our original one, usually summarizing the data in a new way. In particular, with a pivot table, we can create a new index and columns, with the data in the `DataFrame` reduced via some operation across another column.\n", + "\n", + "Here, the column that we are going to aggregate is \"births\", and the function will will use for the aggregating is `sum` (to sum over the names)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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namesexbirthsyear
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" + ], + "text/plain": [ + " name sex births year\n", + "0 Mary F 7065 1880\n", + "1 Anna F 2604 1880\n", + "2 Emma F 2003 1880\n", + "3 Elizabeth F 1939 1880\n", + "4 Minnie F 1746 1880" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "names.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "total_births = names.pivot_table(\"births\", index=\"year\", columns=\"sex\", aggfunc=sum)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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sexFM
year
188090992110490
188191953100743
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1883112318104627
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1886144534110785
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1908334315154343
1909347232163999
.........
198617147841840347
198717379811865804
198817799751912764
198918431752000082
199018978072052662
199118744892019523
199218433831996492
199318085081960486
199417851841931313
199517580101902971
199617523641893548
199717399631884324
199817660751910424
199917727881918984
200018147381962556
200117991991941401
200217953671939950
200318255091973612
200418343791983010
200518456401995115
200618987762052652
200719197752072505
200818876602036750
200918334611979895
201017734401914629
201117544241894262
201217552541890889
201317475441883945
201417772421910876
201517693251898858
\n", + "

136 rows × 2 columns

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1874489 2019523\n", + "1992 1843383 1996492\n", + "1993 1808508 1960486\n", + "1994 1785184 1931313\n", + "1995 1758010 1902971\n", + "1996 1752364 1893548\n", + "1997 1739963 1884324\n", + "1998 1766075 1910424\n", + "1999 1772788 1918984\n", + "2000 1814738 1962556\n", + "2001 1799199 1941401\n", + "2002 1795367 1939950\n", + "2003 1825509 1973612\n", + "2004 1834379 1983010\n", + "2005 1845640 1995115\n", + "2006 1898776 2052652\n", + "2007 1919775 2072505\n", + "2008 1887660 2036750\n", + "2009 1833461 1979895\n", + "2010 1773440 1914629\n", + "2011 1754424 1894262\n", + "2012 1755254 1890889\n", + "2013 1747544 1883945\n", + "2014 1777242 1910876\n", + "2015 1769325 1898858\n", + "\n", + "[136 rows x 2 columns]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "total_births" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "total_births.plot()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## `.apply()` and new columns" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll use `.groupby()` again to allow use to derive a new column -- the fraction of the births with the name specified by the index. \n", + "\n", + "`apply()` uses what Pandas calls the _split-apply-combine_ rules, e.g., it splits the data into groups, applies your function, and then intelligently concatenates it back together. Here, the result will be a `DataFrame` with the original information and this new column." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "def add_prop(group):\n", + " group[\"prop\"] = group[\"births\"]/group[\"births\"].sum()\n", + " return group\n", + "\n", + "names = names.groupby([\"year\", \"sex\"]).apply(add_prop)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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namesexbirthsyearprop
0MaryF706518800.077644
1AnnaF260418800.028618
2EmmaF200318800.022013
3ElizabethF193918800.021310
4MinnieF174618800.019189
5MargaretF157818800.017342
6IdaF147218800.016177
7AliceF141418800.015540
8BerthaF132018800.014507
9SarahF128818800.014155
10AnnieF125818800.013825
11ClaraF122618800.013474
12EllaF115618800.012704
13FlorenceF106318800.011682
14CoraF104518800.011485
15MarthaF104018800.011430
16LauraF101218800.011122
17NellieF99518800.010935
18GraceF98218800.010792
19CarrieF94918800.010429
20MaudeF85818800.009429
21MabelF80818800.008880
22BessieF79618800.008748
23JennieF79318800.008715
24GertrudeF78718800.008649
25JuliaF78318800.008605
26HattieF76918800.008451
27EdithF76818800.008440
28MattieF70418800.007737
29RoseF70018800.007693
..................
1858659ZavonM520150.000003
1858660ZayM520150.000003
1858661ZaylorM520150.000003
1858662ZayquanM520150.000003
1858663ZechariaM520150.000003
1858664ZecharyaM520150.000003
1858665ZeeM520150.000003
1858666ZeevM520150.000003
1858667ZeikM520150.000003
1858668ZekariahM520150.000003
1858669ZepplinM520150.000003
1858670ZerekM520150.000003
1858671ZeydM520150.000003
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1858673ZielM520150.000003
1858674ZihanM520150.000003
1858675ZihaoM520150.000003
1858676ZihengM520150.000003
1858677ZimereM520150.000003
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1858680ZoelM520150.000003
1858681ZoharM520150.000003
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1858684ZykellM520150.000003
1858685ZykingM520150.000003
1858686ZykirM520150.000003
1858687ZyrusM520150.000003
1858688ZyusM520150.000003
\n", + "

1858689 rows × 5 columns

\n", + "
" + ], + "text/plain": [ + " name sex births year prop\n", + "0 Mary F 7065 1880 0.077644\n", + "1 Anna F 2604 1880 0.028618\n", + "2 Emma F 2003 1880 0.022013\n", + "3 Elizabeth F 1939 1880 0.021310\n", + "4 Minnie F 1746 1880 0.019189\n", + "5 Margaret F 1578 1880 0.017342\n", + "6 Ida F 1472 1880 0.016177\n", + "7 Alice F 1414 1880 0.015540\n", + "8 Bertha F 1320 1880 0.014507\n", + "9 Sarah F 1288 1880 0.014155\n", + "10 Annie F 1258 1880 0.013825\n", + "11 Clara F 1226 1880 0.013474\n", + "12 Ella F 1156 1880 0.012704\n", + "13 Florence F 1063 1880 0.011682\n", + "14 Cora F 1045 1880 0.011485\n", + "15 Martha F 1040 1880 0.011430\n", + "16 Laura F 1012 1880 0.011122\n", + "17 Nellie F 995 1880 0.010935\n", + "18 Grace F 982 1880 0.010792\n", + "19 Carrie F 949 1880 0.010429\n", + "20 Maude F 858 1880 0.009429\n", + "21 Mabel F 808 1880 0.008880\n", + "22 Bessie F 796 1880 0.008748\n", + "23 Jennie F 793 1880 0.008715\n", + "24 Gertrude F 787 1880 0.008649\n", + "25 Julia F 783 1880 0.008605\n", + "26 Hattie F 769 1880 0.008451\n", + "27 Edith F 768 1880 0.008440\n", + "28 Mattie F 704 1880 0.007737\n", + "29 Rose F 700 1880 0.007693\n", + "... ... .. ... ... ...\n", + "1858659 Zavon M 5 2015 0.000003\n", + "1858660 Zay M 5 2015 0.000003\n", + "1858661 Zaylor M 5 2015 0.000003\n", + "1858662 Zayquan M 5 2015 0.000003\n", + "1858663 Zecharia M 5 2015 0.000003\n", + "1858664 Zecharya M 5 2015 0.000003\n", + "1858665 Zee M 5 2015 0.000003\n", + "1858666 Zeev M 5 2015 0.000003\n", + "1858667 Zeik M 5 2015 0.000003\n", + "1858668 Zekariah M 5 2015 0.000003\n", + "1858669 Zepplin M 5 2015 0.000003\n", + "1858670 Zerek M 5 2015 0.000003\n", + "1858671 Zeyd M 5 2015 0.000003\n", + "1858672 Zhi M 5 2015 0.000003\n", + "1858673 Ziel M 5 2015 0.000003\n", + "1858674 Zihan M 5 2015 0.000003\n", + "1858675 Zihao M 5 2015 0.000003\n", + "1858676 Ziheng M 5 2015 0.000003\n", + "1858677 Zimere M 5 2015 0.000003\n", + "1858678 Ziyi M 5 2015 0.000003\n", + "1858679 Ziyu M 5 2015 0.000003\n", + "1858680 Zoel M 5 2015 0.000003\n", + "1858681 Zohar M 5 2015 0.000003\n", + "1858682 Zolton M 5 2015 0.000003\n", + "1858683 Zyah M 5 2015 0.000003\n", + "1858684 Zykell M 5 2015 0.000003\n", + "1858685 Zyking M 5 2015 0.000003\n", + "1858686 Zykir M 5 2015 0.000003\n", + "1858687 Zyrus M 5 2015 0.000003\n", + "1858688 Zyus M 5 2015 0.000003\n", + "\n", + "[1858689 rows x 5 columns]" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "names" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q1: Sanity check\n", + "\n", + "Verify that within each of the groups we just used above that the \"prop\" column sums to 1 (it should be close, to roundoff). The `np.allclose()` function might be useful here." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we will group by \"year\" and \"sex\" and then sort by births to get just the top N most popular names.\n", + "\n", + "Notice that we simply append any additional arguments to our apply function after the function name (this is an example of the `**kwargs` behavior in python" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "def get_top(group, N=1000):\n", + " return group.sort_values(by=\"births\", ascending=False)[:N]\n", + "\n", + "grouped = names.groupby([\"year\", \"sex\"])\n", + "top = grouped.apply(get_top, 1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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namesexbirthsyearprop
yearsex
1880F0MaryF706518800.077644
1AnnaF260418800.028618
2EmmaF200318800.022013
3ElizabethF193918800.021310
4MinnieF174618800.019189
5MargaretF157818800.017342
6IdaF147218800.016177
7AliceF141418800.015540
8BerthaF132018800.014507
9SarahF128818800.014155
10AnnieF125818800.013825
11ClaraF122618800.013474
12EllaF115618800.012704
13FlorenceF106318800.011682
14CoraF104518800.011485
15MarthaF104018800.011430
16LauraF101218800.011122
17NellieF99518800.010935
18GraceF98218800.010792
19CarrieF94918800.010429
20MaudeF85818800.009429
21MabelF80818800.008880
22BessieF79618800.008748
23JennieF79318800.008715
24GertrudeF78718800.008649
25JuliaF78318800.008605
26HattieF76918800.008451
27EdithF76818800.008440
28MattieF70418800.007737
29RoseF70018800.007693
........................
2015M1845703YadielM21120150.000111
1845704YahyaM21120150.000111
1845700AarushM21120150.000111
1845702RobinM21120150.000111
1845701DeangeloM21120150.000111
1845705BodenM20920150.000110
1845707KyeM20920150.000110
1845708KylenM20920150.000110
1845709ToddM20920150.000110
1845710TrumanM20920150.000110
1845706EanM20920150.000110
1845712GilbertM20820150.000110
1845713HaidenM20820150.000110
1845711ChevyM20820150.000110
1845715DangeloM20720150.000109
1845716JuelzM20720150.000109
1845717OsvaldoM20720150.000109
1845714BrixtonM20720150.000109
1845718BishopM20620150.000108
1845719FreddyM20620150.000108
1845720ReaganM20620150.000108
1845721FrankieM20520150.000108
1845722MalakiM20520150.000108
1845725JayvionM20420150.000107
1845726LeroyM20420150.000107
1845724DeshawnM20420150.000107
1845723CamrenM20420150.000107
1845728JaydonM20320150.000107
1845727BriarM20320150.000107
1845730AyanM20220150.000106
\n", + "

271877 rows × 5 columns

\n", + "
" + ], + "text/plain": [ + " name sex births year prop\n", + "year sex \n", + "1880 F 0 Mary F 7065 1880 0.077644\n", + " 1 Anna F 2604 1880 0.028618\n", + " 2 Emma F 2003 1880 0.022013\n", + " 3 Elizabeth F 1939 1880 0.021310\n", + " 4 Minnie F 1746 1880 0.019189\n", + " 5 Margaret F 1578 1880 0.017342\n", + " 6 Ida F 1472 1880 0.016177\n", + " 7 Alice F 1414 1880 0.015540\n", + " 8 Bertha F 1320 1880 0.014507\n", + " 9 Sarah F 1288 1880 0.014155\n", + " 10 Annie F 1258 1880 0.013825\n", + " 11 Clara F 1226 1880 0.013474\n", + " 12 Ella F 1156 1880 0.012704\n", + " 13 Florence F 1063 1880 0.011682\n", + " 14 Cora F 1045 1880 0.011485\n", + " 15 Martha F 1040 1880 0.011430\n", + " 16 Laura F 1012 1880 0.011122\n", + " 17 Nellie F 995 1880 0.010935\n", + " 18 Grace F 982 1880 0.010792\n", + " 19 Carrie F 949 1880 0.010429\n", + " 20 Maude F 858 1880 0.009429\n", + " 21 Mabel F 808 1880 0.008880\n", + " 22 Bessie F 796 1880 0.008748\n", + " 23 Jennie F 793 1880 0.008715\n", + " 24 Gertrude F 787 1880 0.008649\n", + " 25 Julia F 783 1880 0.008605\n", + " 26 Hattie F 769 1880 0.008451\n", + " 27 Edith F 768 1880 0.008440\n", + " 28 Mattie F 704 1880 0.007737\n", + " 29 Rose F 700 1880 0.007693\n", + "... ... .. ... ... ...\n", + "2015 M 1845703 Yadiel M 211 2015 0.000111\n", + " 1845704 Yahya M 211 2015 0.000111\n", + " 1845700 Aarush M 211 2015 0.000111\n", + " 1845702 Robin M 211 2015 0.000111\n", + " 1845701 Deangelo M 211 2015 0.000111\n", + " 1845705 Boden M 209 2015 0.000110\n", + " 1845707 Kye M 209 2015 0.000110\n", + " 1845708 Kylen M 209 2015 0.000110\n", + " 1845709 Todd M 209 2015 0.000110\n", + " 1845710 Truman M 209 2015 0.000110\n", + " 1845706 Ean M 209 2015 0.000110\n", + " 1845712 Gilbert M 208 2015 0.000110\n", + " 1845713 Haiden M 208 2015 0.000110\n", + " 1845711 Chevy M 208 2015 0.000110\n", + " 1845715 Dangelo M 207 2015 0.000109\n", + " 1845716 Juelz M 207 2015 0.000109\n", + " 1845717 Osvaldo M 207 2015 0.000109\n", + " 1845714 Brixton M 207 2015 0.000109\n", + " 1845718 Bishop M 206 2015 0.000108\n", + " 1845719 Freddy M 206 2015 0.000108\n", + " 1845720 Reagan M 206 2015 0.000108\n", + " 1845721 Frankie M 205 2015 0.000108\n", + " 1845722 Malaki M 205 2015 0.000108\n", + " 1845725 Jayvion M 204 2015 0.000107\n", + " 1845726 Leroy M 204 2015 0.000107\n", + " 1845724 Deshawn M 204 2015 0.000107\n", + " 1845723 Camren M 204 2015 0.000107\n", + " 1845728 Jaydon M 203 2015 0.000107\n", + " 1845727 Briar M 203 2015 0.000107\n", + " 1845730 Ayan M 202 2015 0.000106\n", + "\n", + "[271877 rows x 5 columns]" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "top" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q2: split by sex\n", + "\n", + "create two new dataframes, one `boys` with just those in `top` that are \"M\" and one `girls` with those in `top` who are \"F\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'boys' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\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[0mboys\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mNameError\u001b[0m: name 'boys' is not defined" + ] + } + ], + "source": [ + "boys" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How many times does each name appear, by year? This dataframe is the total number of births by year and name" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/lib64/python3.6/site-packages/pandas/core/reshape/pivot.py:135: FutureWarning: 'year' is both a column name and an index level.\n", + "Defaulting to column but this will raise an ambiguity error in a future version\n", + " grouped = data.groupby(keys)\n" + ] + } + ], + "source": [ + "total_births = top.pivot_table(\"births\", index=\"year\", columns=\"name\", aggfunc=sum)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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1906NaNNaNNaNNaN96.0NaNNaNNaNNaNNaN...NaN19.0NaNNaN59.0NaN37.064.058.0NaN
1907NaNNaNNaNNaN130.0NaNNaNNaNNaNNaN...NaN19.0NaNNaN53.011.039.092.072.0NaN
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1909NaNNaNNaNNaN142.0NaNNaNNaNNaNNaN...NaN22.0NaNNaN59.0NaN39.057.076.0NaN
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1880F228JohnF4618800.000506
M942JohnM965518800.087383
1881F2312JohnF2618810.000283
M2938JohnM876918810.087043
1882F4212JohnF4018820.000371
M4963JohnM955718820.084065
1883F6340JohnF4018830.000356
M7116JohnM889418830.085007
1884F8454JohnF4018840.000310
M9318JohnM938818840.082032
1885F10739JohnF4518850.000338
M11640JohnM875618850.081225
1886F13036JohnF4818860.000332
M14019JohnM902618860.081473
1887F15414JohnF5618870.000384
M16435JohnM811018870.079968
1888F17834JohnF5218880.000291
M18976JohnM924718880.076516
1889F20498JohnF5218890.000292
M21632JohnM854818890.077300
1890F23086JohnF5618900.000294
M24277JohnM850218900.076577
1891F25816JohnF4418910.000237
M26971JohnM768018910.075895
1892F28460JohnF5418920.000254
M29759JohnM903918920.074068
1893F31361JohnF6118930.000287
M32671JohnM804918930.071663
1894F34211JohnF6018940.000269
M35552JohnM823818940.071158
........................
1987M1015237JohnM2953519870.015830
1988F1024361JohnF16719880.000094
M1037259JohnM2939419880.015367
1989M1060288JohnM2983819890.014918
1990M1084747JohnM2906619900.014160
1991M1109686JohnM2779819910.013765
1992M1134943JohnM2624119920.013144
1993M1160554JohnM2498919930.012746
1994M1186469JohnM2417519940.012517
1995M1212466JohnM2323219950.012208
1996M1238683JohnM2216919960.011708
1997M1265371JohnM2137219970.011342
1998M1292776JohnM2061519980.010791
1999M1321012JohnM2034119990.010600
2000M1350272JohnM2008420000.010234
2001M1380350JohnM1887920010.009724
2002M1410730JohnM1744220020.008991
2003M1441635JohnM1722220030.008726
2004M1473212JohnM1643920040.008290
2005M1505607JohnM1576020050.007899
2006M1539014JohnM1515320060.007382
2007M1573596JohnM1442420070.006960
2008M1608427JohnM1331020080.006535
2009M1643211JohnM1210320090.006113
2010M1677534JohnM1154320100.006029
2011M1711330JohnM1102720110.005821
2012M1745139JohnM1060720120.005610
2013M1778561JohnM1068720130.005673
2014M1811736JohnM1065920140.005578
2015M1844755JohnM1030320150.005426
\n", + "

245 rows × 5 columns

\n", + "
" + ], + "text/plain": [ + " name sex births year prop\n", + "year sex \n", + "1880 F 228 John F 46 1880 0.000506\n", + " M 942 John M 9655 1880 0.087383\n", + "1881 F 2312 John F 26 1881 0.000283\n", + " M 2938 John M 8769 1881 0.087043\n", + "1882 F 4212 John F 40 1882 0.000371\n", + " M 4963 John M 9557 1882 0.084065\n", + "1883 F 6340 John F 40 1883 0.000356\n", + " M 7116 John M 8894 1883 0.085007\n", + "1884 F 8454 John F 40 1884 0.000310\n", + " M 9318 John M 9388 1884 0.082032\n", + "1885 F 10739 John F 45 1885 0.000338\n", + " M 11640 John M 8756 1885 0.081225\n", + "1886 F 13036 John F 48 1886 0.000332\n", + " M 14019 John M 9026 1886 0.081473\n", + "1887 F 15414 John F 56 1887 0.000384\n", + " M 16435 John M 8110 1887 0.079968\n", + "1888 F 17834 John F 52 1888 0.000291\n", + " M 18976 John M 9247 1888 0.076516\n", + "1889 F 20498 John F 52 1889 0.000292\n", + " M 21632 John M 8548 1889 0.077300\n", + "1890 F 23086 John F 56 1890 0.000294\n", + " M 24277 John M 8502 1890 0.076577\n", + "1891 F 25816 John F 44 1891 0.000237\n", + " M 26971 John M 7680 1891 0.075895\n", + "1892 F 28460 John F 54 1892 0.000254\n", + " M 29759 John M 9039 1892 0.074068\n", + "1893 F 31361 John F 61 1893 0.000287\n", + " M 32671 John M 8049 1893 0.071663\n", + "1894 F 34211 John F 60 1894 0.000269\n", + " M 35552 John M 8238 1894 0.071158\n", + "... ... .. ... ... ...\n", + "1987 M 1015237 John M 29535 1987 0.015830\n", + "1988 F 1024361 John F 167 1988 0.000094\n", + " M 1037259 John M 29394 1988 0.015367\n", + "1989 M 1060288 John M 29838 1989 0.014918\n", + "1990 M 1084747 John M 29066 1990 0.014160\n", + "1991 M 1109686 John M 27798 1991 0.013765\n", + "1992 M 1134943 John M 26241 1992 0.013144\n", + "1993 M 1160554 John M 24989 1993 0.012746\n", + "1994 M 1186469 John M 24175 1994 0.012517\n", + "1995 M 1212466 John M 23232 1995 0.012208\n", + "1996 M 1238683 John M 22169 1996 0.011708\n", + "1997 M 1265371 John M 21372 1997 0.011342\n", + "1998 M 1292776 John M 20615 1998 0.010791\n", + "1999 M 1321012 John M 20341 1999 0.010600\n", + "2000 M 1350272 John M 20084 2000 0.010234\n", + "2001 M 1380350 John M 18879 2001 0.009724\n", + "2002 M 1410730 John M 17442 2002 0.008991\n", + "2003 M 1441635 John M 17222 2003 0.008726\n", + "2004 M 1473212 John M 16439 2004 0.008290\n", + "2005 M 1505607 John M 15760 2005 0.007899\n", + "2006 M 1539014 John M 15153 2006 0.007382\n", + "2007 M 1573596 John M 14424 2007 0.006960\n", + "2008 M 1608427 John M 13310 2008 0.006535\n", + "2009 M 1643211 John M 12103 2009 0.006113\n", + "2010 M 1677534 John M 11543 2010 0.006029\n", + "2011 M 1711330 John M 11027 2011 0.005821\n", + "2012 M 1745139 John M 10607 2012 0.005610\n", + "2013 M 1778561 John M 10687 2013 0.005673\n", + "2014 M 1811736 John M 10659 2014 0.005578\n", + "2015 M 1844755 John M 10303 2015 0.005426\n", + "\n", + "[245 rows x 5 columns]" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "top[top.name==\"John\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Which names are the most popular of all time?" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "name\n", + "James 5142912.0\n", + "John 5116313.0\n", + "Robert 4822265.0\n", + "Michael 4343106.0\n", + "Mary 4131873.0\n", + "William 4086383.0\n", + "David 3600738.0\n", + "Joseph 2589732.0\n", + "Richard 2565300.0\n", + "Charles 2381863.0\n", + "Thomas 2295502.0\n", + "Christopher 2011702.0\n", + "Daniel 1886299.0\n", + "Elizabeth 1613326.0\n", + "Patricia 1574798.0\n", + "Matthew 1569338.0\n", + "Jennifer 1467548.0\n", + "George 1465334.0\n", + "Linda 1454380.0\n", + "Barbara 1436646.0\n", + "Anthony 1417510.0\n", + "Donald 1412138.0\n", + "Paul 1385235.0\n", + "Mark 1347586.0\n", + "Edward 1286089.0\n", + "Steven 1276499.0\n", + "Kenneth 1269967.0\n", + "Andrew 1267471.0\n", + "Margaret 1244662.0\n", + "Joshua 1187636.0\n", + " ... \n", + "Amado 5.0\n", + "Pryor 5.0\n", + "Laban 5.0\n", + "Sheppard 5.0\n", + "Vinia 5.0\n", + "Tella 5.0\n", + "Tilford 5.0\n", + "Estie 5.0\n", + "Jep 5.0\n", + "Ollis 5.0\n", + "Clide 5.0\n", + "Tilmon 5.0\n", + "Affie 5.0\n", + "Lovisa 5.0\n", + "Alys 5.0\n", + "Etter 5.0\n", + "Lenzy 5.0\n", + "Maryland 5.0\n", + "Orlie 5.0\n", + "Orr 5.0\n", + "Lovey 5.0\n", + "Mathis 5.0\n", + "Orva 5.0\n", + "Matthews 5.0\n", + "Mattye 5.0\n", + "Voyle 5.0\n", + "Fronnie 5.0\n", + "Cordella 5.0\n", + "Bertina 5.0\n", + "Manervia 5.0\n", + "Length: 7062, dtype: float64" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = total_births.sum()\n", + "a.sort_values(ascending=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot naming trends, for a few of the most popular names" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "subset = total_births[[\"Michael\", \"Jennifer\"]]\n", + "subset.plot()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercises" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q3: unique names\n", + "\n", + "how many unique names appear in our top 1000 list? Use the `.unique()` method on the \"name\" `Series` to get a an array (it will actually be a NumPy `ndarray` of objects)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q4: gender neutral names\n", + "\n", + "What are all the names that appear for both boys and girls?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Q5: name diversity\n", + "\n", + "We want to make a plot of how many names it takes to reach 50% of the births in a given year. Let's start with the boys names:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "boys = top[top.sex == \"M\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, to understand the process, let's work just on a particular year, 2015" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "b15 = boys[boys.year == 2015]" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b15.info" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll use the `cumsum()` property to do a cumulative sum over the `prop` column we added previously" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "prop_cumsum = b15.sort_values(by=\"prop\", ascending=False)[\"prop\"].cumsum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and now we can use `searchsorted` to return the position where \"if the corresponding elements in v were inserted before the indices, the order of self would be preserved.\" (see http://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.searchsorted.html)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([134])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "prop_cumsum.searchsorted(0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since we start counting at 0, we add 1 to this to get the number of names needed in this year to reach 50% of births." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now generalize this to a function that you can use `apply()` on and make a plot of the number of names to reach 50% by year" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/content/07-pandas/pandas-experiments.ipynb b/content/07-pandas/pandas-experiments.ipynb new file mode 100644 index 00000000..21660d13 --- /dev/null +++ b/content/07-pandas/pandas-experiments.ipynb @@ -0,0 +1,719 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sort by Two Columns" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "df = pd.DataFrame(np.random.randint(1, 5, (10,2)), columns=['a','b'])\n", + "df.sort_values([\"a\", \"b\"], inplace=True) " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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You can kind of think about this functionality as operating how a spreadsheet might work.\n", "\n", - "In this manner, its main competition is R -- the data frame provides the functionality for data analysis that R natively presents.\n", + "In this manner, it provides much of the same functionality of R -- the data frame provides the basis for data analysis.\n", "\n", "Nice documentation is here:\n", "\n", @@ -28,12 +22,8 @@ }, { "cell_type": "code", - "execution_count": 44, - "metadata": { - "collapsed": true, - "deletable": true, - "editable": true - }, + "execution_count": 1, + "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", @@ -43,10 +33,7 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "## series\n", "\n", @@ -57,25 +44,21 @@ }, { "cell_type": "code", - "execution_count": 45, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 2, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "a 0.950095\n", - "b -0.134197\n", - "c -0.290576\n", - "d -1.697814\n", - "e -0.474797\n", + "a -0.272166\n", + "b -0.594024\n", + "c -0.533180\n", + "d -0.666801\n", + "e -0.749968\n", "dtype: float64" ] }, - "execution_count": 45, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -87,12 +70,8 @@ }, { "cell_type": "code", - "execution_count": 46, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 3, + "metadata": {}, "outputs": [ { "data": { @@ -100,7 +79,7 @@ "Index(['a', 'b', 'c', 'd', 'e'], dtype='object')" ] }, - "execution_count": 46, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -111,35 +90,28 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "If you don't specify an index, one will be made up for you" ] }, { "cell_type": "code", - "execution_count": 47, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 4, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0 0.577677\n", - "1 -3.042981\n", - "2 0.334862\n", - "3 -0.530684\n", - "4 1.018501\n", + "0 -0.098297\n", + "1 -0.840109\n", + "2 1.282849\n", + "3 0.475101\n", + "4 -0.283392\n", "dtype: float64" ] }, - "execution_count": 47, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -150,22 +122,15 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "you can initialize from a dictionary. By default it will use the dictionary keys (sorted) as the index" ] }, { "cell_type": "code", - "execution_count": 48, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 5, + "metadata": {}, "outputs": [ { "data": { @@ -176,7 +141,7 @@ "dtype: float64" ] }, - "execution_count": 48, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -188,12 +153,8 @@ }, { "cell_type": "code", - "execution_count": 49, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 6, + "metadata": {}, "outputs": [ { "data": { @@ -205,7 +166,7 @@ "dtype: float64" ] }, - "execution_count": 49, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -216,45 +177,35 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "Note that NaN indicates a missing value" ] }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "you can operate on a series as you would any ndarray" ] }, { "cell_type": "code", - "execution_count": 50, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 7, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "a 0.950095\n", - "b -0.134197\n", - "c -0.290576\n", - "d -1.697814\n", - "e -0.474797\n", + "a -0.272166\n", + "b -0.594024\n", + "c -0.533180\n", + "d -0.666801\n", + "e -0.749968\n", "dtype: float64" ] }, - "execution_count": 50, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -265,20 +216,16 @@ }, { "cell_type": "code", - "execution_count": 51, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 8, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.95009491421204317" + "-0.27216618170818768" ] }, - "execution_count": 51, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -289,23 +236,19 @@ }, { "cell_type": "code", - "execution_count": 52, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 9, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "a 0.950095\n", - "b -0.134197\n", - "c -0.290576\n", + "a -0.272166\n", + "b -0.594024\n", + "c -0.533180\n", "dtype: float64" ] }, - "execution_count": 52, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -316,22 +259,18 @@ }, { "cell_type": "code", - "execution_count": 53, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 10, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "a 0.950095\n", - "b -0.134197\n", + "a -0.272166\n", + "c -0.533180\n", "dtype: float64" ] }, - "execution_count": 53, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -342,25 +281,21 @@ }, { "cell_type": "code", - "execution_count": 54, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 11, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "a 2.585955\n", - "b 0.874418\n", - "c 0.747833\n", - "d 0.183083\n", - "e 0.622011\n", + "a 0.761728\n", + "b 0.552101\n", + "c 0.586736\n", + "d 0.513348\n", + "e 0.472382\n", "dtype: float64" ] }, - "execution_count": 54, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -371,30 +306,23 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "you can also index by label -- this mimics the behavior of a dictionary" ] }, { "cell_type": "code", - "execution_count": 55, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 12, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.95009491421204317" + "-0.27216618170818768" ] }, - "execution_count": 55, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -405,20 +333,16 @@ }, { "cell_type": "code", - "execution_count": 56, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 13, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "-0.47479706644484226" + "-0.74996754801095999" ] }, - "execution_count": 56, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -429,12 +353,8 @@ }, { "cell_type": "code", - "execution_count": 57, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 14, + "metadata": {}, "outputs": [ { "data": { @@ -442,7 +362,7 @@ "True" ] }, - "execution_count": 57, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -453,22 +373,15 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ - "The `get()` method can be used to safely access an element if it is possible it does not exist -- you can specify a default to return in that case" + "The `get()` method can be used to safely access an element if it is possible it does not exist -- you can specify a default to return in that case. The alternative is to use a `try` / `except` block." ] }, { "cell_type": "code", - "execution_count": 58, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 15, + "metadata": {}, "outputs": [ { "data": { @@ -476,7 +389,7 @@ "nan" ] }, - "execution_count": 58, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } @@ -487,35 +400,28 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "Operations, like those you use with an ndarray work fine on a Series" ] }, { "cell_type": "code", - "execution_count": 59, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 16, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "a 1.900190\n", - "b -0.268393\n", - "c -0.581152\n", - "d -3.395627\n", - "e -0.949594\n", + "a -0.544332\n", + "b -1.188048\n", + "c -1.066360\n", + "d -1.333602\n", + "e -1.499935\n", "dtype: float64" ] }, - "execution_count": 59, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } @@ -526,25 +432,21 @@ }, { "cell_type": "code", - "execution_count": 60, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 17, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "a 1.900190\n", - "b -0.268393\n", - "c -0.581152\n", - "d -3.395627\n", - "e -0.949594\n", + "a -0.544332\n", + "b -1.188048\n", + "c -1.066360\n", + "d -1.333602\n", + "e -1.499935\n", "dtype: float64" ] }, - "execution_count": 60, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } @@ -555,35 +457,28 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "note that operations are always done on like labels, so the following is not exactly the same as numpy arrays. In this sense, pandas results respect the union of indices " ] }, { "cell_type": "code", - "execution_count": 61, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 18, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ "a NaN\n", - "b -0.268393\n", - "c -0.581152\n", - "d -3.395627\n", + "b -1.188048\n", + "c -1.066360\n", + "d -1.333602\n", "e NaN\n", "dtype: float64" ] }, - "execution_count": 61, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -592,93 +487,30 @@ "s[1:] + s[:-1]" ] }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "b -0.134197\n", - "c -0.290576\n", - "d -1.697814\n", - "e -0.474797\n", - "dtype: float64" - ] - }, - "execution_count": 62, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "s[1:]" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "a 0.950095\n", - "b -0.134197\n", - "c -0.290576\n", - "d -1.697814\n", - "dtype: float64" - ] - }, - "execution_count": 63, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "s[:-1]" - ] - }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "a series can have a name" ] }, { "cell_type": "code", - "execution_count": 64, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 19, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0 -0.099532\n", - "1 0.326121\n", - "2 1.500657\n", - "3 -0.937690\n", - "4 -0.315212\n", + "0 1.026684\n", + "1 0.306580\n", + "2 0.135363\n", + "3 -0.352485\n", + "4 -0.188115\n", "Name: something, dtype: float64" ] }, - "execution_count": 64, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -690,10 +522,7 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "## DataFrame\n", "\n", @@ -709,12 +538,8 @@ }, { "cell_type": "code", - "execution_count": 66, - "metadata": { - "collapsed": true, - "deletable": true, - "editable": true - }, + "execution_count": 20, + "metadata": {}, "outputs": [], "source": [ "d = {'one' : pd.Series([1., 2., 3.], index=['b', 'a', 'c']),\n", @@ -723,17 +548,26 @@ }, { "cell_type": "code", - "execution_count": 67, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 21, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "\n", " \n", " \n", @@ -775,7 +609,7 @@ "d NaN 4.0" ] }, - "execution_count": 67, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -787,12 +621,8 @@ }, { "cell_type": "code", - "execution_count": 68, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 22, + "metadata": {}, "outputs": [ { "data": { @@ -802,7 +632,7 @@ "dtype: float64" ] }, - "execution_count": 68, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -813,27 +643,33 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "You can exclude some labels" ] }, { "cell_type": "code", - "execution_count": 69, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 23, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -869,7 +705,7 @@ "a 2.0 1.0" ] }, - "execution_count": 69, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -880,22 +716,15 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "Here's initialization from lists / ndarrays" ] }, { "cell_type": "code", - "execution_count": 70, - "metadata": { - "collapsed": true, - "deletable": true, - "editable": true - }, + "execution_count": 24, + "metadata": {}, "outputs": [], "source": [ "d = {'one' : [1., 2., 3., 4.],\n", @@ -904,17 +733,26 @@ }, { "cell_type": "code", - "execution_count": 71, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 25, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -956,7 +794,7 @@ "3 4.0 1.0" ] }, - "execution_count": 71, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -967,17 +805,26 @@ }, { "cell_type": "code", - "execution_count": 72, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 26, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -1019,7 +866,7 @@ "d 4.0 1.0" ] }, - "execution_count": 72, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -1031,9 +878,7 @@ { "cell_type": "markdown", "metadata": { - "collapsed": true, - "deletable": true, - "editable": true + "collapsed": true }, "source": [ "there are lots of other initialization methods, e.g, list of dicts" @@ -1041,17 +886,26 @@ }, { "cell_type": "code", - "execution_count": 73, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 27, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -1084,7 +938,7 @@ "second 5 10 20.0" ] }, - "execution_count": 73, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -1096,10 +950,7 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "### working with the dataframe\n", "\n", @@ -1114,12 +965,8 @@ }, { "cell_type": "code", - "execution_count": 74, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 28, + "metadata": {}, "outputs": [ { "data": { @@ -1131,7 +978,7 @@ "Name: one, dtype: float64" ] }, - "execution_count": 74, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -1142,17 +989,26 @@ }, { "cell_type": "code", - "execution_count": 75, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 29, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -1194,7 +1050,7 @@ "d NaN 4.0" ] }, - "execution_count": 75, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -1205,12 +1061,8 @@ }, { "cell_type": "code", - "execution_count": 76, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 30, + "metadata": {}, "outputs": [ { "data": { @@ -1218,7 +1070,7 @@ "pandas.core.series.Series" ] }, - "execution_count": 76, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -1229,17 +1081,26 @@ }, { "cell_type": "code", - "execution_count": 77, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 31, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -1291,7 +1152,7 @@ "d NaN 4.0 NaN False" ] }, - "execution_count": 77, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -1304,22 +1165,46 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ - "you can delete or pop columns" + "you can also treat any index name as if it were a property" ] }, { "cell_type": "code", - "execution_count": 78, - "metadata": { - "collapsed": true, - "deletable": true, - "editable": true - }, + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "a 2.0\n", + "b 2.0\n", + "c 9.0\n", + "d NaN\n", + "Name: three, dtype: float64" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.three" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "you can delete or pop columns---popping returns a `Series`" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, "outputs": [], "source": [ "del df['two']" @@ -1327,12 +1212,8 @@ }, { "cell_type": "code", - "execution_count": 79, - "metadata": { - "collapsed": true, - "deletable": true, - "editable": true - }, + "execution_count": 34, + "metadata": {}, "outputs": [], "source": [ "three = df.pop('three')" @@ -1340,17 +1221,26 @@ }, { "cell_type": "code", - "execution_count": 80, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 35, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -1392,7 +1282,7 @@ "d NaN False" ] }, - "execution_count": 80, + "execution_count": 35, "metadata": {}, "output_type": "execute_result" } @@ -1403,12 +1293,8 @@ }, { "cell_type": "code", - "execution_count": 81, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 36, + "metadata": {}, "outputs": [ { "data": { @@ -1420,7 +1306,7 @@ "Name: three, dtype: float64" ] }, - "execution_count": 81, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } @@ -1429,24 +1315,37 @@ "three" ] }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "pandas.core.series.Series" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(three)" + ] + }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ - "initialize with a scalar" + "initializing with a scalar propagates that scalar to all the rows" ] }, { "cell_type": "code", - "execution_count": 82, - "metadata": { - "collapsed": true, - "deletable": true, - "editable": true - }, + "execution_count": 38, + "metadata": {}, "outputs": [], "source": [ "df['foo'] = 'bar'" @@ -1454,17 +1353,26 @@ }, { "cell_type": "code", - "execution_count": 83, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 39, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -1511,7 +1419,7 @@ "d NaN False bar" ] }, - "execution_count": 83, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" } @@ -1522,10 +1430,7 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "## CSV\n", "\n", @@ -1538,12 +1443,8 @@ }, { "cell_type": "code", - "execution_count": 58, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 40, + "metadata": {}, "outputs": [], "source": [ "grades = pd.read_csv('sample.csv', index_col=\"student\", skipinitialspace=True)" @@ -1551,17 +1452,26 @@ }, { "cell_type": "code", - "execution_count": 59, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 41, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "
\n", " \n", " \n", @@ -1584,16 +1494,16 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -1601,15 +1511,15 @@ " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -1617,22 +1527,22 @@ " \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", @@ -1640,80 +1550,80 @@ " \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", " \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", @@ -1725,26 +1635,26 @@ "text/plain": [ " hw 1 hw 2 hw 3 hw 4 exam\n", "student \n", - "A 10 9 10 7 97\n", - "B 8 7 9 9 82\n", - "C NaN 9 6 5 75\n", - "D 8 9 9 9 90\n", - "E NaN 10 10 10 95\n", - "F 8 2 6 7 66\n", - "G 6 NaN 4 5 60\n", - "H 8 8 9 8 84\n", - "I 10 7 10 10 92\n", - "J 10 6 9 9 91\n", - "K 8 7 6 8 87\n", - "L 3 8 5 7 71\n", - "M 9 9 8 9 94\n", - "N 8 10 9 9 90\n", - "O 10 10 10 9 99\n", - "P 8 9 8 10 94\n", - "Q 5 7 6 5 78" + "A 10.0 9.0 10 7 97\n", + "B 8.0 7.0 9 9 82\n", + "C NaN 9.0 6 5 75\n", + "D 8.0 9.0 9 9 90\n", + "E NaN 10.0 10 10 95\n", + "F 8.0 2.0 6 7 66\n", + "G 6.0 NaN 4 5 60\n", + "H 8.0 8.0 9 8 84\n", + "I 10.0 7.0 10 10 92\n", + "J 10.0 6.0 9 9 91\n", + "K 8.0 7.0 6 8 87\n", + "L 3.0 8.0 5 7 71\n", + "M 9.0 9.0 8 9 94\n", + "N 8.0 10.0 9 9 90\n", + "O 10.0 10.0 10 9 99\n", + "P 8.0 9.0 8 10 94\n", + "Q 5.0 7.0 6 5 78" ] }, - "execution_count": 59, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" } @@ -1755,12 +1665,8 @@ }, { "cell_type": "code", - "execution_count": 60, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 42, + "metadata": {}, "outputs": [ { "data": { @@ -1770,7 +1676,7 @@ " dtype='object', name='student')" ] }, - "execution_count": 60, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } @@ -1781,12 +1687,8 @@ }, { "cell_type": "code", - "execution_count": 61, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 43, + "metadata": {}, "outputs": [ { "data": { @@ -1794,7 +1696,7 @@ "Index(['hw 1', 'hw 2', 'hw 3', 'hw 4', 'exam'], dtype='object')" ] }, - "execution_count": 61, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" } @@ -1803,69 +1705,75 @@ "grades.columns" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A single student's grades" + ] + }, { "cell_type": "code", - "execution_count": 62, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 47, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "hw 1 10\n", - "hw 2 9\n", - "hw 3 10\n", - "hw 4 7\n", - "exam 97\n", + "hw 1 10.0\n", + "hw 2 9.0\n", + "hw 3 10.0\n", + "hw 4 7.0\n", + "exam 97.0\n", "Name: A, dtype: float64" ] }, - "execution_count": 62, + "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "grades.ix[\"A\"]" + "grades.loc[\"A\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All the grades for the first homework" ] }, { "cell_type": "code", - "execution_count": 63, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 48, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ "student\n", - "A 10\n", - "B 8\n", - "C NaN\n", - "D 8\n", - "E NaN\n", - "F 8\n", - "G 6\n", - "H 8\n", - "I 10\n", - "J 10\n", - "K 8\n", - "L 3\n", - "M 9\n", - "N 8\n", - "O 10\n", - "P 8\n", - "Q 5\n", + "A 10.0\n", + "B 8.0\n", + "C NaN\n", + "D 8.0\n", + "E NaN\n", + "F 8.0\n", + "G 6.0\n", + "H 8.0\n", + "I 10.0\n", + "J 10.0\n", + "K 8.0\n", + "L 3.0\n", + "M 9.0\n", + "N 8.0\n", + "O 10.0\n", + "P 8.0\n", + "Q 5.0\n", "Name: hw 1, dtype: float64" ] }, - "execution_count": 63, + "execution_count": 48, "metadata": {}, "output_type": "execute_result" } @@ -1874,14 +1782,17 @@ "grades['hw 1']" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Creating a new column based on the existing ones" + ] + }, { "cell_type": "code", - "execution_count": 64, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 49, + "metadata": {}, "outputs": [], "source": [ "grades['hw average'] = (grades['hw 1'] + grades['hw 2'] + grades['hw 3'] + grades['hw 4'])/4.0" @@ -1889,17 +1800,26 @@ }, { "cell_type": "code", - "execution_count": 65, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 50, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n", " \n", " \n", @@ -2183,8 +2101,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2192,8 +2110,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2201,8 +2119,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2210,8 +2128,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2219,8 +2137,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2228,8 +2146,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2237,8 +2155,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2246,8 +2164,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2255,8 +2173,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2264,8 +2182,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2273,8 +2191,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2282,8 +2200,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2291,8 +2209,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2300,8 +2218,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2309,8 +2227,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2318,8 +2236,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2327,8 +2245,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2341,26 +2259,26 @@ "text/plain": [ " hw 1 hw 2 hw 3 hw 4 exam hw average\n", "student \n", - "A 10 9 10 7 97 9.00\n", - "B 8 7 9 9 82 8.25\n", - "C 0 9 6 5 75 5.00\n", - "D 8 9 9 9 90 8.75\n", - "E 0 10 10 10 95 7.50\n", - "F 8 2 6 7 66 5.75\n", - "G 6 0 4 5 60 3.75\n", - "H 8 8 9 8 84 8.25\n", - "I 10 7 10 10 92 9.25\n", - "J 10 6 9 9 91 8.50\n", - "K 8 7 6 8 87 7.25\n", - "L 3 8 5 7 71 5.75\n", - "M 9 9 8 9 94 8.75\n", - "N 8 10 9 9 90 9.00\n", - "O 10 10 10 9 99 9.75\n", - "P 8 9 8 10 94 8.75\n", - "Q 5 7 6 5 78 5.75" + "A 10.0 9.0 10 7 97 9.00\n", + "B 8.0 7.0 9 9 82 8.25\n", + "C 0.0 9.0 6 5 75 5.00\n", + "D 8.0 9.0 9 9 90 8.75\n", + "E 0.0 10.0 10 10 95 7.50\n", + "F 8.0 2.0 6 7 66 5.75\n", + "G 6.0 0.0 4 5 60 3.75\n", + "H 8.0 8.0 9 8 84 8.25\n", + "I 10.0 7.0 10 10 92 9.25\n", + "J 10.0 6.0 9 9 91 8.50\n", + "K 8.0 7.0 6 8 87 7.25\n", + "L 3.0 8.0 5 7 71 5.75\n", + "M 9.0 9.0 8 9 94 8.75\n", + "N 8.0 10.0 9 9 90 9.00\n", + "O 10.0 10.0 10 9 99 9.75\n", + "P 8.0 9.0 8 10 94 8.75\n", + "Q 5.0 7.0 6 5 78 5.75" ] }, - "execution_count": 68, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" } @@ -2371,27 +2289,33 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "For big dataframes, we can view just pieces" ] }, { "cell_type": "code", - "execution_count": 69, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 54, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n", " \n", " \n", @@ -2416,8 +2340,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2425,8 +2349,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2434,8 +2358,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2443,8 +2367,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2452,8 +2376,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2466,14 +2390,14 @@ "text/plain": [ " hw 1 hw 2 hw 3 hw 4 exam hw average\n", "student \n", - "A 10 9 10 7 97 9.00\n", - "B 8 7 9 9 82 8.25\n", - "C 0 9 6 5 75 5.00\n", - "D 8 9 9 9 90 8.75\n", - "E 0 10 10 10 95 7.50" + "A 10.0 9.0 10 7 97 9.00\n", + "B 8.0 7.0 9 9 82 8.25\n", + "C 0.0 9.0 6 5 75 5.00\n", + "D 8.0 9.0 9 9 90 8.75\n", + "E 0.0 10.0 10 10 95 7.50" ] }, - "execution_count": 69, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } @@ -2484,17 +2408,26 @@ }, { "cell_type": "code", - "execution_count": 70, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 55, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n", " \n", " \n", @@ -2519,8 +2452,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2528,8 +2461,8 @@ " \n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", @@ -2542,11 +2475,11 @@ "text/plain": [ " hw 1 hw 2 hw 3 hw 4 exam hw average\n", "student \n", - "P 8 9 8 10 94 8.75\n", - "Q 5 7 6 5 78 5.75" + "P 8.0 9.0 8 10 94 8.75\n", + "Q 5.0 7.0 6 5 78 5.75" ] }, - "execution_count": 70, + "execution_count": 55, "metadata": {}, "output_type": "execute_result" } @@ -2557,37 +2490,40 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "### statistics" ] }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ - "we get lots of statistics" + "we can get lots of statistics" ] }, { "cell_type": "code", - "execution_count": 71, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 56, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n", " \n", " \n", @@ -2689,7 +2625,7 @@ "max 10.000000 10.000000 10.000000 10.000000 99.000000 9.750000" ] }, - "execution_count": 71, + "execution_count": 56, "metadata": {}, "output_type": "execute_result" } @@ -2700,27 +2636,33 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "want to sort by values?" ] }, { "cell_type": "code", - "execution_count": 72, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 57, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n", @@ -4426,26 +4385,26 @@ "text/plain": [ " hw 1 hw 2 hw 3 hw 4 exam hw average new\n", "student \n", - "A 10 9 10 7 97 9.00 0.672079\n", - "B 8 7 9 9 82 8.25 0.435800\n", - "C 0 9 6 5 80 5.00 0.031942\n", - "D 8 9 9 9 90 8.75 0.638359\n", - "E 0 10 10 10 95 7.50 0.450061\n", - "F 8 2 6 7 80 5.75 0.498565\n", - "G 6 0 4 5 80 3.75 0.721334\n", - "H 8 8 9 8 84 8.25 0.546910\n", - "I 10 7 10 10 92 9.25 0.472119\n", - "J 10 6 9 9 91 8.50 0.493867\n", - "K 8 7 6 8 87 7.25 0.228334\n", - "L 3 8 5 7 80 5.75 0.937931\n", - "M 9 9 8 9 94 8.75 0.955794\n", - "N 8 10 9 9 90 9.00 0.597320\n", - "O 10 10 10 9 99 9.75 0.290944\n", - "P 8 9 8 10 94 8.75 0.864325\n", - "Q 5 7 6 5 80 5.75 0.544261" + "A 10.0 9.0 10 7 97 9.00 0.848599\n", + "B 8.0 7.0 9 9 82 8.25 0.394722\n", + "C 0.0 9.0 6 5 80 5.00 0.957668\n", + "D 8.0 9.0 9 9 90 8.75 0.953680\n", + "E 0.0 10.0 10 10 95 7.50 0.000388\n", + "F 8.0 2.0 6 7 80 5.75 0.898409\n", + "G 6.0 0.0 4 5 80 3.75 0.346747\n", + "H 8.0 8.0 9 8 84 8.25 0.716042\n", + "I 10.0 7.0 10 10 92 9.25 0.965628\n", + "J 10.0 6.0 9 9 91 8.50 0.124690\n", + "K 8.0 7.0 6 8 87 7.25 0.694847\n", + "L 3.0 8.0 5 7 80 5.75 0.930668\n", + "M 9.0 9.0 8 9 94 8.75 0.606070\n", + "N 8.0 10.0 9 9 90 9.00 0.212891\n", + "O 10.0 10.0 10 9 99 9.75 0.905785\n", + "P 8.0 9.0 8 10 94 8.75 0.415708\n", + "Q 5.0 7.0 6 5 80 5.75 0.145941" ] }, - "execution_count": 91, + "execution_count": 75, "metadata": {}, "output_type": "execute_result" } @@ -4456,22 +4415,15 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "## histogramming" ] }, { "cell_type": "code", - "execution_count": 92, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 76, + "metadata": {}, "outputs": [ { "data": { @@ -4490,7 +4442,7 @@ "Name: exam, dtype: int64" ] }, - "execution_count": 92, + "execution_count": 76, "metadata": {}, "output_type": "execute_result" } @@ -4501,22 +4453,15 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "## plotting" ] }, { "cell_type": "code", - "execution_count": 93, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 77, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" @@ -4524,28 +4469,24 @@ }, { "cell_type": "code", - "execution_count": 94, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 78, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 94, + "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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PMnHiRDZu3Eh0dHTHNbybk566EKJLtMdydrGxsU2X6OhoNE0jLi4OvV7f4e3v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\nmM/Ly2tk8gUFBeTl5bU75efnNys7cOAA/fp59xM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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -4558,28 +4499,24 @@ }, { "cell_type": "code", - "execution_count": 95, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 79, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 95, + "execution_count": 79, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -4592,27 +4529,33 @@ }, { "cell_type": "markdown", - "metadata": { - "deletable": true, - "editable": true - }, + "metadata": {}, "source": [ "A lot more examples at: http://pandas.pydata.org/pandas-docs/stable/visualization.html" ] }, { "cell_type": "code", - "execution_count": 96, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 80, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "\n", " \n", " \n", @@ -4639,173 +4582,173 @@ " \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", " \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", " \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", - " \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", "
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\n", @@ -4814,26 +4757,26 @@ "text/plain": [ " hw 1 hw 2 hw 3 hw 4 exam hw average new\n", "student \n", - "A 10 9 10 7 97 9.00 0.672079\n", - "B 8 7 9 9 82 8.25 0.435800\n", - "C 0 9 6 5 80 5.00 0.031942\n", - "D 8 9 9 9 90 8.75 0.638359\n", - "E 0 10 10 10 95 7.50 0.450061\n", - "F 8 2 6 7 80 5.75 0.498565\n", - "G 6 0 4 5 80 3.75 0.721334\n", - "H 8 8 9 8 84 8.25 0.546910\n", - "I 10 7 10 10 92 9.25 0.472119\n", - "J 10 6 9 9 91 8.50 0.493867\n", - "K 8 7 6 8 87 7.25 0.228334\n", - "L 3 8 5 7 80 5.75 0.937931\n", - "M 9 9 8 9 94 8.75 0.955794\n", - "N 8 10 9 9 90 9.00 0.597320\n", - "O 10 10 10 9 99 9.75 0.290944\n", - "P 8 9 8 10 94 8.75 0.864325\n", - "Q 5 7 6 5 80 5.75 0.544261" + "A 10.0 9.0 10 7 97 9.00 0.848599\n", + "B 8.0 7.0 9 9 82 8.25 0.394722\n", + "C 0.0 9.0 6 5 80 5.00 0.957668\n", + "D 8.0 9.0 9 9 90 8.75 0.953680\n", + "E 0.0 10.0 10 10 95 7.50 0.000388\n", + "F 8.0 2.0 6 7 80 5.75 0.898409\n", + "G 6.0 0.0 4 5 80 3.75 0.346747\n", + "H 8.0 8.0 9 8 84 8.25 0.716042\n", + "I 10.0 7.0 10 10 92 9.25 0.965628\n", + "J 10.0 6.0 9 9 91 8.50 0.124690\n", + "K 8.0 7.0 6 8 87 7.25 0.694847\n", + "L 3.0 8.0 5 7 80 5.75 0.930668\n", + "M 9.0 9.0 8 9 94 8.75 0.606070\n", + "N 8.0 10.0 9 9 90 9.00 0.212891\n", + "O 10.0 10.0 10 9 99 9.75 0.905785\n", + "P 8.0 9.0 8 10 94 8.75 0.415708\n", + "Q 5.0 7.0 6 5 80 5.75 0.145941" ] }, - "execution_count": 96, + "execution_count": 80, "metadata": {}, "output_type": "execute_result" } @@ -4844,12 +4787,8 @@ }, { "cell_type": "code", - "execution_count": 97, - "metadata": { - "collapsed": true, - "deletable": true, - "editable": true - }, + "execution_count": 81, + "metadata": {}, "outputs": [], "source": [ "g2.loc[\"R\", :] = 1" @@ -4857,17 +4796,26 @@ }, { "cell_type": "code", - "execution_count": 98, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 82, + "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "\n", " \n", " \n", @@ -4894,181 +4842,181 @@ " \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", - " \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", + " \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", + " \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", + " \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", @@ -5079,27 +5027,27 @@ "text/plain": [ " hw 1 hw 2 hw 3 hw 4 exam hw average new\n", "student \n", - "A 10 9 10 7 97 9.00 0.672079\n", - "B 8 7 9 9 82 8.25 0.435800\n", - "C 0 9 6 5 80 5.00 0.031942\n", - "D 8 9 9 9 90 8.75 0.638359\n", - "E 0 10 10 10 95 7.50 0.450061\n", - "F 8 2 6 7 80 5.75 0.498565\n", - "G 6 0 4 5 80 3.75 0.721334\n", - "H 8 8 9 8 84 8.25 0.546910\n", - "I 10 7 10 10 92 9.25 0.472119\n", - "J 10 6 9 9 91 8.50 0.493867\n", - "K 8 7 6 8 87 7.25 0.228334\n", - "L 3 8 5 7 80 5.75 0.937931\n", - "M 9 9 8 9 94 8.75 0.955794\n", - "N 8 10 9 9 90 9.00 0.597320\n", - "O 10 10 10 9 99 9.75 0.290944\n", - "P 8 9 8 10 94 8.75 0.864325\n", - "Q 5 7 6 5 80 5.75 0.544261\n", - "R 1 1 1 1 1 1.00 1.000000" + "A 10.0 9.0 10.0 7.0 97.0 9.00 0.848599\n", + "B 8.0 7.0 9.0 9.0 82.0 8.25 0.394722\n", + "C 0.0 9.0 6.0 5.0 80.0 5.00 0.957668\n", + "D 8.0 9.0 9.0 9.0 90.0 8.75 0.953680\n", + "E 0.0 10.0 10.0 10.0 95.0 7.50 0.000388\n", + "F 8.0 2.0 6.0 7.0 80.0 5.75 0.898409\n", + "G 6.0 0.0 4.0 5.0 80.0 3.75 0.346747\n", + "H 8.0 8.0 9.0 8.0 84.0 8.25 0.716042\n", + "I 10.0 7.0 10.0 10.0 92.0 9.25 0.965628\n", + "J 10.0 6.0 9.0 9.0 91.0 8.50 0.124690\n", + "K 8.0 7.0 6.0 8.0 87.0 7.25 0.694847\n", + "L 3.0 8.0 5.0 7.0 80.0 5.75 0.930668\n", + "M 9.0 9.0 8.0 9.0 94.0 8.75 0.606070\n", + "N 8.0 10.0 9.0 9.0 90.0 9.00 0.212891\n", + "O 10.0 10.0 10.0 9.0 99.0 9.75 0.905785\n", + "P 8.0 9.0 8.0 10.0 94.0 8.75 0.415708\n", + "Q 5.0 7.0 6.0 5.0 80.0 5.75 0.145941\n", + "R 1.0 1.0 1.0 1.0 1.0 1.00 1.000000" ] }, - "execution_count": 98, + "execution_count": 82, "metadata": {}, "output_type": "execute_result" } @@ -5110,20 +5058,16 @@ }, { "cell_type": "code", - "execution_count": 99, - "metadata": { - "collapsed": false, - "deletable": true, - "editable": true - }, + "execution_count": 83, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "'\\\\begin{tabular}{lrrrrrrr}\\n\\\\toprule\\n{} & hw 1 & hw 2 & hw 3 & hw 4 & exam & hw average & new \\\\\\\\\\nstudent & & & & & & & \\\\\\\\\\n\\\\midrule\\nA & 10 & 9 & 10 & 7 & 97 & 9.00 & 0.672079 \\\\\\\\\\nB & 8 & 7 & 9 & 9 & 82 & 8.25 & 0.435800 \\\\\\\\\\nC & 0 & 9 & 6 & 5 & 80 & 5.00 & 0.031942 \\\\\\\\\\nD & 8 & 9 & 9 & 9 & 90 & 8.75 & 0.638359 \\\\\\\\\\nE & 0 & 10 & 10 & 10 & 95 & 7.50 & 0.450061 \\\\\\\\\\nF & 8 & 2 & 6 & 7 & 80 & 5.75 & 0.498565 \\\\\\\\\\nG & 6 & 0 & 4 & 5 & 80 & 3.75 & 0.721334 \\\\\\\\\\nH & 8 & 8 & 9 & 8 & 84 & 8.25 & 0.546910 \\\\\\\\\\nI & 10 & 7 & 10 & 10 & 92 & 9.25 & 0.472119 \\\\\\\\\\nJ & 10 & 6 & 9 & 9 & 91 & 8.50 & 0.493867 \\\\\\\\\\nK & 8 & 7 & 6 & 8 & 87 & 7.25 & 0.228334 \\\\\\\\\\nL & 3 & 8 & 5 & 7 & 80 & 5.75 & 0.937931 \\\\\\\\\\nM & 9 & 9 & 8 & 9 & 94 & 8.75 & 0.955794 \\\\\\\\\\nN & 8 & 10 & 9 & 9 & 90 & 9.00 & 0.597320 \\\\\\\\\\nO & 10 & 10 & 10 & 9 & 99 & 9.75 & 0.290944 \\\\\\\\\\nP & 8 & 9 & 8 & 10 & 94 & 8.75 & 0.864325 \\\\\\\\\\nQ & 5 & 7 & 6 & 5 & 80 & 5.75 & 0.544261 \\\\\\\\\\nR & 1 & 1 & 1 & 1 & 1 & 1.00 & 1.000000 \\\\\\\\\\n\\\\bottomrule\\n\\\\end{tabular}\\n'" + "'\\\\begin{tabular}{lrrrrrrr}\\n\\\\toprule\\n{} & hw 1 & hw 2 & hw 3 & hw 4 & exam & hw average & new \\\\\\\\\\nstudent & & & & & & & \\\\\\\\\\n\\\\midrule\\nA & 10.0 & 9.0 & 10.0 & 7.0 & 97.0 & 9.00 & 0.848599 \\\\\\\\\\nB & 8.0 & 7.0 & 9.0 & 9.0 & 82.0 & 8.25 & 0.394722 \\\\\\\\\\nC & 0.0 & 9.0 & 6.0 & 5.0 & 80.0 & 5.00 & 0.957668 \\\\\\\\\\nD & 8.0 & 9.0 & 9.0 & 9.0 & 90.0 & 8.75 & 0.953680 \\\\\\\\\\nE & 0.0 & 10.0 & 10.0 & 10.0 & 95.0 & 7.50 & 0.000388 \\\\\\\\\\nF & 8.0 & 2.0 & 6.0 & 7.0 & 80.0 & 5.75 & 0.898409 \\\\\\\\\\nG & 6.0 & 0.0 & 4.0 & 5.0 & 80.0 & 3.75 & 0.346747 \\\\\\\\\\nH & 8.0 & 8.0 & 9.0 & 8.0 & 84.0 & 8.25 & 0.716042 \\\\\\\\\\nI & 10.0 & 7.0 & 10.0 & 10.0 & 92.0 & 9.25 & 0.965628 \\\\\\\\\\nJ & 10.0 & 6.0 & 9.0 & 9.0 & 91.0 & 8.50 & 0.124690 \\\\\\\\\\nK & 8.0 & 7.0 & 6.0 & 8.0 & 87.0 & 7.25 & 0.694847 \\\\\\\\\\nL & 3.0 & 8.0 & 5.0 & 7.0 & 80.0 & 5.75 & 0.930668 \\\\\\\\\\nM & 9.0 & 9.0 & 8.0 & 9.0 & 94.0 & 8.75 & 0.606070 \\\\\\\\\\nN & 8.0 & 10.0 & 9.0 & 9.0 & 90.0 & 9.00 & 0.212891 \\\\\\\\\\nO & 10.0 & 10.0 & 10.0 & 9.0 & 99.0 & 9.75 & 0.905785 \\\\\\\\\\nP & 8.0 & 9.0 & 8.0 & 10.0 & 94.0 & 8.75 & 0.415708 \\\\\\\\\\nQ & 5.0 & 7.0 & 6.0 & 5.0 & 80.0 & 5.75 & 0.145941 \\\\\\\\\\nR & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.00 & 1.000000 \\\\\\\\\\n\\\\bottomrule\\n\\\\end{tabular}\\n'" ] }, - "execution_count": 99, + "execution_count": 83, "metadata": {}, "output_type": "execute_result" } @@ -5135,11 +5079,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true, - "deletable": true, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [] } @@ -5160,9 +5100,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.3" + "version": "3.6.5" } }, "nbformat": 4, - "nbformat_minor": 0 + "nbformat_minor": 1 } diff --git a/lectures/07-pandas/pandas-worldbank.ipynb b/content/07-pandas/pandas-worldbank.ipynb similarity index 100% rename from lectures/07-pandas/pandas-worldbank.ipynb rename to content/07-pandas/pandas-worldbank.ipynb diff --git a/content/07-pandas/pandas_solutions.txt b/content/07-pandas/pandas_solutions.txt new file mode 100644 index 00000000..1db8c26b --- /dev/null +++ b/content/07-pandas/pandas_solutions.txt @@ -0,0 +1,37 @@ +Q1: + +np.allclose(names.groupby(["year", "sex"]).prop.sum(), 1.0) + + +Q2: + +boys = top[top.sex == "M"] +girls = top[top.sex == "F"] + +Q3: + +all_names = top["name"].unique() +all_names.dtype + +len(all_names) + + +Q4: + +what are all the names that appear for both boys and girls? + +boy_names = top[top["sex"] == "M"]["name"].unique() +girl_names = top[top["sex"] == "F"]["name"].unique() +joint = np.intersect1d(boy_names, girl_names) + + +Q5: + +def get_count(group, q=0.5): + group = group.sort_values(by="prop", ascending=False) + return group["prop"].cumsum().searchsorted(0.5)[0] + 1 + +diversity = top.groupby(["year", "sex"]).apply(get_count) +diversity = diversity.unstack("sex") +diversity.plot() + diff --git a/lectures/07-pandas/sample.csv b/content/07-pandas/sample.csv similarity index 100% rename from lectures/07-pandas/sample.csv rename to content/07-pandas/sample.csv diff --git a/lectures/09-packages/NOTES b/content/09-packages/NOTES similarity index 100% rename from lectures/09-packages/NOTES rename to content/09-packages/NOTES diff --git a/content/09-packages/argparse_example.py b/content/09-packages/argparse_example.py new file mode 100644 index 00000000..003893a2 --- /dev/null +++ b/content/09-packages/argparse_example.py @@ -0,0 +1,43 @@ +#!/usr/bin/env python3 + +# to get usage: use -h +import argparse + + +def setup_args(): + + # simple example of argparse + + parser = argparse.ArgumentParser() + parser.add_argument("-a", help="the -a option", action="store_true") + parser.add_argument("-b", help="-b takes a number", type=int, default=0) + parser.add_argument("-c", help="-c takes a string", type=str, default=None) + parser.add_argument("--darg", help="the --darg option", action="store_true") + parser.add_argument("--earg", help="--earg takes a string", type=str, metavar="test", + default="example string") + + # extra arguments (positional) + parser.add_argument("extras", metavar="extra", type=str, nargs="*", + help="optional positional arguments") + + return parser.parse_args() + + +if __name__ == "__main__": + + args = setup_args() + + + if args.a: + print("-a set") + print(f"-b = {args.b}") + print(f"-c = {args.c}") + if args.darg: + print("--dargs set") + print(f"--earg value = {args.earg}") + + print(" ") + print("extra positional arguments: ") + if len(args.extras) > 0: + for e in args.extras: + print(e) diff --git a/content/09-packages/packaging.pdf b/content/09-packages/packaging.pdf new file mode 100644 index 00000000..9b324497 Binary files /dev/null and b/content/09-packages/packaging.pdf differ diff --git a/content/09-packages/python-arguments.md b/content/09-packages/python-arguments.md new file mode 100644 index 00000000..0cbb2683 --- /dev/null +++ b/content/09-packages/python-arguments.md @@ -0,0 +1,21 @@ +# Command line arguments + +For standalone programs, we often want to have our program take +command line arguments that affect the runtime behavior of our +program. There are a variety of mechanisms to do this in python, but +the best option is the [argparse +module](https://docs.python.org/3/library/argparse.html). + +Here's an example of using `argparse` to take a variety of options: + +```{literalinclude} argparse_example.py +--- +language: python +``` + +A nice feature of `argparse` is that it automatically generates help for us. If +we place the above code in `argparse_example.py` then we can do: + +```python +python argparse_example.py --help +``` diff --git a/content/09-packages/python-modules.md b/content/09-packages/python-modules.md new file mode 100644 index 00000000..9aa264c0 --- /dev/null +++ b/content/09-packages/python-modules.md @@ -0,0 +1,91 @@ +# Python Modules + +So far, we've been writing our code all in Jupyter. But when it comes +time to write code that we want to reuse, we want to put it into a +standalone `*.py` file. + +Then we can load it on in python (or Jupyter) and use the capabilities +it provides or make it a standalone program that can be run from the +command line. + +```{tip} +Jupyter is great for interactive explorations and sharing your workflow with others +in a self-contained way. But if there is an operation that you do over and over, +you should put it into a separate module that you import. That way you only need to +maintain and debug a single instance of the function, and all your workflows can reuse it. +``` + + +## Editors + +There are a number of popular editors for writing python source. Some +popular ones include: + +* spyder: https://www.spyder-ide.org/ + +* VS Code: https://code.visualstudio.com/ + +* emacs / vi + + +## Standalone module + +Here's a very simply module (lets call it `hello.py`): + +```python +def hello(): + print("hello") + +if __name__ == "__main__": + hello() +``` + +There are two ways we can use this. + +* Inside of python (or IPython), we can do: + + ```python + import hello + hello.hello() + ``` + +* From the command line, we can do: + + ```python + python hello.py + ``` + +Additionally, on a Unix system, we can add: + +```python +#!/usr/bin/env python3 +``` + +to the top and then mark the file as executable, via: + +```bash +chmod a+x hello.py +``` + +allowing us to execute it simply as: + +```bash +./hello.py +``` + +```{hint} +Here we see how the `__name__` variable is treated by python: + +* If we import our module into python, then `__name__` is set to the module name + +* If we run the module from the command line, then `__name__` is set to `__main__` +``` + +## Changing module contents + +If we make changes to our module file, then we need to re-import it. This can be done as: + +```python +import importlib +example = importlib.reload(example) +``` diff --git a/content/09-packages/python-more-modules.md b/content/09-packages/python-more-modules.md new file mode 100644 index 00000000..bf8936c2 --- /dev/null +++ b/content/09-packages/python-more-modules.md @@ -0,0 +1,57 @@ +# Module Paths + +How does python find modules? It has a [search order](https://docs.python.org/3/tutorial/modules.html#the-module-search-path): + +* current directory + +* `PYTHONPATH` environment variable (this follows the same format as + the shell `PATH` environment variable) + +* System-wide python installation default path (usually has a + `site-packages` directory) + +We can look at the path via ``sys.path``. On my machine I get: + +``` +['/home/zingale/.local/bin', + '/home/zingale/classes/python-science/content/09-packages', + '/home/zingale/classes/numerical_exercises', + '/home/zingale/classes/astro_animations', + '/usr/lib64/python312.zip', + '/usr/lib64/python3.12', + '/usr/lib64/python3.12/lib-dynload', + '', + '/home/zingale/.local/lib/python3.12/site-packages', + '/usr/lib64/python3.12/site-packages', + '/usr/lib/python3.12/site-packages'] + +``` + +```{note} +You can explicitly add paths to the ``sys.path`` by setting the `PYTHONPATH` +environment variable. +``` + + +Notice that the general places that it looks are in `~/.local` and in +`/usr`. The first is the user-specific path—you can install things +here without admin privileges. The second is a system-wide path. + +You can find your user-specific path via: + +```bash +python3 -m site --user-site +``` + +on my machine, this gives: + +``` +/home/zingale/.local/lib/python3.12/site-packages +``` + +```{tip} +Using `PYTHONPATH` to quickly add a module to your search path is an easy hack, +but if you are developing a library that will be used by others, it is better +to make the modules installable to the system search paths. This is where +_packaging_ comes into play. +``` diff --git a/content/09-packages/python-packages.md b/content/09-packages/python-packages.md new file mode 100644 index 00000000..e37c3905 --- /dev/null +++ b/content/09-packages/python-packages.md @@ -0,0 +1,205 @@ +# Packaging + + + +Let's look at the structure of creating an installable python package. + +```{note} +The python packaging system is constantly evolving, and the current recommendations +of tools is list here: https://packaging.python.org/en/latest/guides/tool-recommendations/ +``` + +![xkcd](python_environment.png) + +(from https://xkcd.com) + + +## Our example + +We'll work on an example that builds on the Mandelbrot set exercise +from our matplotlib discussion. Our example is hosted here: + +https://github.com/sbu-python-class/mymodule + +On your local computer, if you have `git` installed, you can clone this via: + +``` +git clone https://github.com/sbu-python-class/mymodule.git +``` + +The directory structure appears as: + +``` +mymodule/ +├── mymodule +│   ├── __init__.py +│   └── mandel.py +├── pyproject.toml +└── README.md +``` + +This is a rather common way of structuring a project: + +* The top-level `mymodule` directory is not part of the python + package, but instead is where the source control (e.g. git) begins, + and also hosts setup files that are used for installation + +* `mymodule/mymodule` is the actual python module that we will load. + + ```{important} + To make python recognize this as a module, we need an `__init__.py` + file there—it can be completely empty. + ``` + +* The actual `*.py` files that make up our module are in `mymodule/mymodule` + +Right now, this package does not appear in our python search path, so +the only way to load it is to work in the top-level `mymodule/` +directory, and then we can do: + +```python +import mymodule.mandel +``` + +we could also do: + +```python +from mymodule.mandel import mandelbrot +``` + + +## setuptools + +A popular set of packages are: + +* Installation: + + * `pip` to install packages from PyPI + * `conda` for disctribution cross-platform software stacks + +* Packaging tools: + + * `setuptools` to create source distributions + * `build` for binary distributions + * `twine` to upload to PyPI + +We'll look at how to use [`setuptools`](https://setuptools.pypa.io/en/latest/build_meta.html) to package our library. + +```{note} +A lot of setuptools documentation is out-of-date and +inconsistent with the packaging guidelines. + +Packages used to create a `setup.py` file that had all of the project information, +but this is deprecated. Instead we should create a +[pyproject.toml](https://packaging.python.org/en/latest/guides/writing-pyproject-toml/) file---this +is consistent with [PEP 517](https://peps.python.org/pep-0517/). +``` + +Here's a first `pyproject.toml`: + +```toml +[build-system] +requires = ["setuptools"] +build-backend = "setuptools.build_meta" + +[project] +name = "mymodule" +description = "test module for PHY 546" +readme = "README.md" +license.text = "BSD" +version="0.1.0" +authors = [ + {name="Michael Zingale"}, + {email="michael.zingale@stonybrook.edu"}, +] + +dependencies = [ + "numpy", + "matplotlib", +] + +``` + +Some notes: + +* We have a `[build-system]` table that specifies the build tool. + Here we choose `setuptools`. + +* We have a lot of metadata for our project defined in the `[project]` + table. + +* We also list the dependencies of our project in the `[project]` table. + This will allow the installer to install any missing packages that are + required. + +There are many additional options to specify how to find files that +are part of the project as well as data files, etc. + + +```{tip} +`pyproject.toml` also allows you to specify defaults for tools, like +`pylint`, `flake8`, and others with a `[tool.X]` subtable. +``` + +```{note} +Some projects also contain a `setup.cfg` +file when using `setuptools`. This is +usually not needed, since we can put everything +in the `[project]` table. +``` + + +## Installing + +We can now install simply as: + +```bash +pip install . +``` + +```{tip} +Look in your `.local/lib/python3.12/site-packages` directory, and you'll +see the module there. +``` + +If instead, we want to install in a way that still allows us to edit the source, +we can install as "editable" via: + +```bash +pip install -e . +``` + +To uninstall, we can do: + +```bash +pip uninstall mymodule +``` + +in a directory outside of our project (otherwise, `pip` may get confused). + +## Using our module + +Once the module is installed, we can use it from any directory. For example, if we do: + +```python +import mymodule +print(mymodule.__file__) +``` + +it shows us where the module is installed on our system. In my case, it is: + +``` +/home/zingale/.local/lib/python3.12/site-packages/mymodule-0.1.0-py3.12.egg/mymodule/__init__.py +``` + +Let's generate a plot: + +```python +from mymodule.mandel import mandelbrot +fig = mandelbrot(128) +fig.savefig("test.png") +``` + +This produces the plot shown below: + +![sample Mandelbrot set image using 128x128 points](test.png) diff --git a/content/09-packages/python-tools.md b/content/09-packages/python-tools.md new file mode 100644 index 00000000..9add0512 --- /dev/null +++ b/content/09-packages/python-tools.md @@ -0,0 +1,63 @@ +# Tools to Make Your Life Easier + +## Version control + +Generally, you should put your project into version control. The most widely used +package today is [git](https://git-scm.com/book/en/v2/Getting-Started-About-Version-Control). +git will track the changes you make to your code, allow you to revert changes, collaboratively +develop with others, work on several different features independently from one another while +keeping the main codebase clean and more. + +git is often used together with [github](https://github.com), which provides a web-based view +of your source code and provides additional mechanisms for collaboration. + +A nice introduction to git/github is provided by the [Software +Carpentry _Version Control with Git_ +lesson](https://swcarpentry.github.io/git-novice/). + + +## Code checkers + +There are a number of tools that help check code for formatting and +syntax errors that are quite useful for developers. Many projects +automatically enforce these tools on changes submitted to github. + +```{tip} +Many editors have plugins that can automatically run these tools +as your write your code. +``` + +* [flake8](https://flake8.pycqa.org/en/latest/) + + `flake8` is a checker for [PEP 8](https://peps.python.org/pep-0008/) + style conformance. You can turn off checks that you don't like + via a [`.flake8` + file](https://flake8.pycqa.org/en/latest/user/configuration.html#configuration-locations). + +* [pylint](https://pypi.org/project/pylint/) + + `pylint` is a static code analyzer. It can find errors and also suggest improvements + to your code. You can [generate a configuration file](https://pylint.readthedocs.io/en/latest/user_guide/configuration/index.html) + to customize its behavior (or add a section to `pyproject.toml`). + +* [black](https://pypi.org/project/black/) + + `black` is an _uncompromising code formatted_. It will automatically rewrite your code + based on PEP-8 style. + +* [pyupgrade](https://github.com/asottile/pyupgrade) + + `pyupgrade` will upgrade source to a later python standard, making + use of new features where available. For instance, you can run as: + + ``` + pyupgrade --py39-plus file.py + ``` + + to update to python 3.9 support. + +* [isort](https://pycqa.github.io/isort/) + + `isort` simply sorts the module imports at the top of your modules, + grouping the standard python ones together followed by + package-specific ones. diff --git a/content/09-packages/python_environment.png b/content/09-packages/python_environment.png new file mode 100644 index 00000000..a8e8fd61 Binary files /dev/null and b/content/09-packages/python_environment.png differ diff --git a/content/09-packages/test.png b/content/09-packages/test.png new file mode 100644 index 00000000..062a8207 Binary files /dev/null and b/content/09-packages/test.png differ diff --git a/content/10-testing/more-pytest.md b/content/10-testing/more-pytest.md new file mode 100644 index 00000000..d84611a3 --- /dev/null +++ b/content/10-testing/more-pytest.md @@ -0,0 +1,130 @@ +# More pytest + +Unit tests sometimes require some setup to be done before the test is run. +Fixtures provide this capability, allowing tests to run with a consistent +environment and data. + +Standard pytest fixtures are written as functions with the `@pytest.fixture` +decorator: +```python +@pytest.fixture +def message(): + return "Hello world!" +``` + +A fixture may return an object, which will be passed to any function +that requests it, or it may just do some setup tasks (like creating a file or +connecting to a database). + +Test functions can request a fixture by specifying a parameter with the same +name as the fixture: +```python +def test_split(message): + assert len(message.split()) == 2 +``` + +An alternate method for initializing test state is with explicit setup/teardown +functions, which we'll look at a bit later. This is a style that's available in +many other languages as well: see https://en.wikipedia.org/wiki/XUnit. + +## Fixtures examples + +Fixtures are reusable across different tests. This lets us avoid repeating the +same setup code in multiple places, especially as we add more tests or need +more complicated inputs. + +Here are some tests for the `Item` class that use fixtures, adapted from the +[shopping cart exercise](w4-exercise-1). The full code is available +[here](https://github.com/sbu-python-class/python-science/blob/main/examples/testing/pytest/fixtures/test_item.py) +on the github repository for this site. You can download this file and run +the tests with `pytest -v test_item.py`. + +```{literalinclude} ../../examples/testing/pytest/fixtures/test_item.py +:lines: 58-68 +``` + +All the fixtures that a test depends on will run once for each test. +This gives each test a fresh copy of the data, so any changes made to the +fixture results inside a test won't impact other tests. +```{literalinclude} ../../examples/testing/pytest/fixtures/test_item.py +:lines: 70-83 +``` + +We can also test that a function raises specific exceptions with `pytest.raises`: +```{literalinclude} ../../examples/testing/pytest/fixtures/test_item.py +:lines: 85-91 +``` + +### Fixtures can request other fixtures + +This is useful to split up complex initialization into smaller parts. +A fixture can also modify the results of the fixtures it requests, which *will* +be visible to anything that includes the fixture. + +Here is a set of tests that show how this can be used ([test_list.py](https://github.com/sbu-python-class/python-science/blob/main/examples/testing/pytest/fixtures/test_list.py)): +```{literalinclude} ../../examples/testing/pytest/fixtures/test_list.py +:lines: 1-13 +``` + +Note that `append_1()` and `append_2()` only modify `numbers`, and don't return +anything. `append_2()` requires `append_1`, to make sure they are run in the +right order. + +This test only requires `numbers`, so it will receive an empty list: +```{literalinclude} ../../examples/testing/pytest/fixtures/test_list.py +:lines: 15-16 +``` + +This test requires `append_1`, but not `append_2`: +```{literalinclude} ../../examples/testing/pytest/fixtures/test_list.py +:lines: 18-19 +``` + +This test requires `append_2`, which itself pulls in `append_1`: +```{literalinclude} ../../examples/testing/pytest/fixtures/test_list.py +:lines: 21-22 +``` + + +## Example class + +It is common to use a class to organize a set of related unit tests. This is +not a full-fledged class -- it simply helps to organize tests and data. In particular, +there is no constructor, `__init__()`. See https://stackoverflow.com/questions/21430900/py-test-skips-test-class-if-constructor-is-defined + +We'll look at an example with a NumPy array + +* We'll use xunit-style setup/teardown methods to store the array as a class + member + + * This way we don't have to ask for it in each of the tests + +* We'll use NumPy's own assertion functions: https://numpy.org/doc/stable/reference/routines.testing.html + + +Here's an example: + +```{include} ../../examples/testing/pytest/class/test_class.py +:code: python +``` + +```{note} +Here we see the [`@classmethod` decorator](https://docs.python.org/3/library/functions.html#classmethod). +This means that the function receives the class itself as the first argument rather than an instance, +e.g., `self`. +``` + +Put this into a file called `test_class.py` and then we can run as: + +```bash +pytest -v +``` + +```{admonition} Quick Exercise +Try adding a new test that modifies `self.a`, above `test_max()`. +Does this behave as you expect? What happens if you move the array creation +into `setup_class()` instead? +``` + +% By default, pytest will capture stdout and only show it on failures. To make it +% always show stdout, we add the `-s` flag. diff --git a/content/10-testing/notes.txt b/content/10-testing/notes.txt new file mode 100644 index 00000000..610ab83c --- /dev/null +++ b/content/10-testing/notes.txt @@ -0,0 +1,24 @@ +-- define testing: unit, integration, regression testing + + (also verification and validation) + +-- nose and unit tests + + very nice: + http://ivory.idyll.org/articles/nose-intro.html + + + http://pythontesting.net/framework/nose/nose-introduction/ + +-- regression tests + + * write a comparison tool + * self-documenting file helps + +-- reproducibility + +-- coverage + + http://blog.jameskyle.org/2010/10/nose-unit-testing-quick-start/ + + nosetests-3 -sv --with-coverage --cover-erase --cover-inclusive --cover-package=. diff --git a/content/10-testing/pytest b/content/10-testing/pytest new file mode 100644 index 00000000..fb7db8c3 --- /dev/null +++ b/content/10-testing/pytest @@ -0,0 +1,11 @@ +pip3 install -U pytest --user + +note: it might install it in ~/.local/bin/ but you might have a +different version of pytest elsewhere in your path. + +the older version was `py.test` now, it is `pytest` + +to make sure that you get the version consistent with your install, you can do: + +python3 -m pytest + diff --git a/content/10-testing/pytest.md b/content/10-testing/pytest.md new file mode 100644 index 00000000..89b97892 --- /dev/null +++ b/content/10-testing/pytest.md @@ -0,0 +1,110 @@ +# pytest + +`pytest` is a unit testing framework for python code. + +Basic elements: + +* Discoverability: it will find the tests + +* Automation + +* Fixtures (setup and teardown) + +## Installing + +You can install `pytest` for a single user as: + +``` +pip install pytest +``` + +This should put `pytest` in your search path, likely in `~/.local/bin`. + +If you want to generate coverage reports, you should also install `pytest-cov`: + +``` +pip install pytest-cov +``` + +## Test discovery + +Adhering to these naming conventions will ensure that your tests are automatically found: + +* File names should start or end with "test": + + * `test_example.py` + * `example_test.py` + +* For tests in a class, the class name should begin with `Test` + + * e.g., `TestExample` + * There should be no `__init__()` + +* Test method / function names should start with `test_` + + * e.g., `test_example()` + +## Assertions + +Tests use assertions (via python’s `assert` statement) to check behavior at runtime + +* https://docs.python.org/3/reference/simple_stmts.html#assert + +* Basic usage: `assert expression` + + * Raises `AssertionError` if expression is not true + + * e.g., `assert 1 == 0` will fail with an exception + +* pytest does some magic under the hood to add more details about what + exactly went wrong, which we will see below + +## Simple pytest example + +Create a file named `test_simple.py` with the following content: + +```python +def multiply(a, b): + return a*b + +def test_multiply(): + assert multiply(4, 6) == 24 + +def test_multiply2(): + assert multiply(5, 6) == 2 +``` + +then we can run the tests as: + +``` +pytest -v +``` + +and we get the output: + +``` +============================= test session starts ============================== +platform linux -- Python 3.11.3, pytest-7.2.2, pluggy-1.0.0 -- /usr/bin/python3 +cachedir: .pytest_cache +rootdir: /home/zingale/temp/pytest +plugins: anyio-3.6.2 +collected 2 items + +test_simple.py::test_multiply PASSED [ 50%] +test_simple.py::test_multiply2 FAILED [100%] + +=================================== FAILURES =================================== +________________________________ test_multiply2 ________________________________ + + def test_multiply2(): +> assert multiply(5, 6) == 2 +E assert 30 == 2 +E + where 30 = multiply(5, 6) + +test_simple.py:8: AssertionError +=========================== short test summary info ============================ +FAILED test_simple.py::test_multiply2 - assert 30 == 2 +========================= 1 failed, 1 passed in 0.04s ========================== +``` + +this is telling us that one of our tests has failed. diff --git a/content/10-testing/real-world-example.md b/content/10-testing/real-world-example.md new file mode 100644 index 00000000..aaae6179 --- /dev/null +++ b/content/10-testing/real-world-example.md @@ -0,0 +1,92 @@ +# Real World Example + +Let's look at the testing in a larger python package. We'll use our +group's python hydrodynamics code, pyro, as a test: + +https://github.com/python-hydro/pyro2 + +## Installing + +We need to install the package first, via the `setup.py`: + +```bash +python setup.py install --user +``` + +or alternately as + +```bash +pip install . +``` + +## Running the tests + +We can run the tests via: + +```bash +pytest -v pyro +``` + +## Using notebooks as tests + +Sometimes we want to use Jupyter notebooks as tests themselves—this +is enabled via the [nbval plugin](https://nbval.readthedocs.io/en/latest/). In +this way, pytest will execute the cells in the notebook and compare +the result to the result stored in the notebook. If they agree, then +the test passes. + +Sometimes there's a particular cell that we don't want to be part of the +testing—we can disable these on a cell-by-cell basis by [adding +tags to a cell](https://nbval.readthedocs.io/en/latest/#Using-tags-instead-of-comments). + +We can test notebooks as: + +```bash +pytest -v --nbval pyro +``` + +## Coverage report + +The [pytest-cov](https://pytest-cov.readthedocs.io/en/latest/) plugin enables the generation +of a coverage report. This will tell you what fraction of each python file was tested. +We run this as: + +```bash +pytest -v --cov=pyro --nbval pyro +``` + +We can also generate a more detailed interactive report with + +```bash +coverage html +``` + +## Other types of tests + +Unit tests are only one form of testing—they test a function in +isolation of others. Sometimes we need to test everything working together. +For scientific codes, regression testing is often used. The basic workflow +is: + +* Start with the project working in a way you are happy with + +* Store the output of one (or more) runs as a _benchmark_. + +* Each time you make changes, run the code and compare the new output + to the stored benchmark. + + * If there are no differences, then your changes are likely good + (but there is always the case of some feature not being tested). + + * If there are differences, then either you introduced a bug, in which + case you should fix it, or you fixed a bug, in which case you should + update the benchmarks. + +For our example code, pyro, the regression test runs simulations using +all the different solvers and compares against the stored output, zone-by-zone +for any differences. The comparison itself is built into the main driver +of the code and can be invoked as: + +```bash +./pyro/test.py +``` diff --git a/content/10-testing/testing.fodp b/content/10-testing/testing.fodp new file mode 100644 index 00000000..1e9af130 --- /dev/null +++ b/content/10-testing/testing.fodp @@ -0,0 +1,177709 @@ + + + + Michael Zingale2013-01-02T12:36:142019-07-23T20:09:25.108117001P1DT13H52M28S192LibreOffice/6.2.5.2$Linux_X86_64 LibreOffice_project/20$Build-2 + + + -301 + -4555 + 37578 + 21870 + + + view1 + true + false + true + true + true + true + false + false + true + 1500 + false + Hw== + Hw== + + false + true + true + 0 + 19 + false + true + true + 4 + 0 + -331 + -9360 + 47262 + 21862 + 2540 + 2540 + 254 + 254 + 254 + 1 + 254 + 1 + false + 1500 + true + false + + + + + true + $(brandbaseurl)/share/palette%3B$(user)/config/standard.sob + 0 + $(brandbaseurl)/share/palette%3B$(user)/config/standard.soc + $(brandbaseurl)/share/palette%3B$(user)/config/standard.sod + 1270 + true + true + false + true + false + + + en + US + + + + + + $(brandbaseurl)/share/palette%3B$(user)/config/standard.sog + true + $(brandbaseurl)/share/palette%3B$(user)/config/standard.soh + false + false + true + true + false + true + false + false + true + false + false + false + false + false + $(brandbaseurl)/share/palette%3B$(user)/config/standard.soe + false + 4 + false + 0 + low-resolution + LaserJet-P2055dn + false + 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 + true + false + 6 + 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<number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number> + + + + + + + + + + + + + + + + + + + + + + + + + <number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number><number> + + + + + + + + + + + + Testing + + + + + + + + + + + + + + What Kinds of Testing Exist? + + + + + + + This is a big topic: + + + https://en.wikipedia.org/wiki/Software_testing + + + + + We most commonly hear about: + + + Unit testing + + + Tests that a single function does what it was designed to do + + + + + Integration testing + + + Tests whether the individual pieces work together as intended + + + Sometimes done one piece at a time (iteratively) + + + + + Regression testing + + + Checks whether changes have changed answers + + + + + Verification & Validation (from the science perspective) + + + Verification: are we solving the equations correctly? + + + Validation: are we using the right equations in the first place? + + + + + + + + + + + + + + + + + + + + Automation + + + + + + + The best testing is automated—you don’t need to remember to run it + + + Developers can forget to manually run tests + + + + + Github / bitbucket have continuous integration service that can be run on pull requests + + + This is commonly used on large development projects + + + + + + + + + + + + + + + + + + Unit Testing + + + + + + + We want to test the smallest piece of functionality alone + + + E.g., a simple test that ensures that a function does what it is designed to do + + + + + Unit testing alone is not enough + + + Although it gives you confidence that each piece works alone as designed, it doesn’t test what happens when you put it all together + + + 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development (TDD): https://en.wikipedia.org/wiki/Test-driven_development + + + This helps you understand the interface, return values, side-effects, etc. of what you intend to write + + + + + Often we already have code, so we can start by writing tests to cover some core functionality + + + Add new tests when you encounter a bug, precisely to ensure that this bug doesn’t arise again + + + + + + + Tests should be short + + + You want to be able to run them frequently + + + + + + + + + + + + + + + + + + Unit Testing + + + + + + + There are several frameworks for unit testing in python—we’ll focus on pytest + + + Note: like packaging, unit testing frameworks in python appear in a state of flux + + + For a long time, nose was one of the most popular frameworks, but its development has ceased + + + nose2 is a successor to nose that may become standard soon + + + + + unittest is built into python, and may interact with nose2 in the future + + + pytest (sometimes py.test) seems to be the most popular now—we’ll explore that + + + + + Basic elements: + + + Discoverability: it will find the tests + + + Automation + + + Fixtures (setup and teardown) + + + + + + + + + + + + + + + + + + pytest Unit Testing + + + + + + + Install (single-user) via: pip3 install -U pytest –user + + + pytest should now be in your path + + + Note: older name was py.test + + + + + For user-install, it may be that ~/.local/bin/ comes later in your PATH than a system-wide directory with an older pytest + + + You may need to explicitly alias it + + + + + + + For coverage reports: pip3 install -U pytest-cov --user + + + + + + + + + + + + + + + + pytest Unit Testing + + + + + + + Test discovery makes unit testing easy—adhere to these conventions and your tests will be found: + + + File names should start or end with “test”: + + + test_example.py + + + example_test.py + + + + + For tests in a class, the class name should begin with “Test” + + + e.g., TestExample + + + There should be no __init__() + + + + + Test method / function names should start with “test_” + + + e.g., test_example() + + + + + + + + + + + + https://pytest.readthedocs.io/en/reorganize-docs/new-docs/user/naming_conventions.html + + + + + + + + + + + + + + pytest Unit Testing + + + + + + + Tests use assertions (via python’s assert statement) to check behavior at runtime + + + https://docs.python.org/3/reference/simple_stmts.html#assert + + + Basic usage: assert expression + + + Raises AssertionError if expression is not true + + + e.g., assert 1 == 0 will fail with an exception + + + + + + + + + + + + + + + + + + + + + Simple pytest Example + + + + + + + Here’s a simple example (examples/testing/pytest/simple/ in our git repo): + + + + + + + + There are 2 tests here + + + First will pass, second will fail + + + + + Run the tests as: pytest -v . + + + + + + + + + def multiply(a, b): + return a*b + + def test_multiply(): + assert multiply(4, 6) == 24 + + def test_multiply2(): + assert multiply(5, 6) == 24 + + + + + + + + + + + + + + pytest Fixtures + + + + + + + Unit tests sometimes require some setup to be done before the test + + + Fixtures provide this capability + + + We’ll look at setup and teardown functions/methods for tests + + + These are sometimes referred to the standard xUnit fixtures + + + pytest supports a more flexible system for fixtures in addition to these, but we won’t look at it here + + + http://pytest.org/dev/fixture.html + + + + + + + By default, pytest will capture stdout, and only show it on failures + + + See, e.g., https://docs.pytest.org/en/latest/capture.html + + + This can be changed with the -s flag + + + + + Example of function-level setup/teardown in examples/testing/pytest/function_setup/ + + + + + + + + + + + + + + + + + pytest Unit Testing + + + + + + + Class example + + + Note, a class used for testing is not a full-fledged class—it simply helps to organize data used for a bunch of tests with common needs + + + In particular, it does not have a constructor (__init__()) + + + See, e.g., https://stackoverflow.com/questions/21430900/py-test-skips-test-class-if-constructor-is-defined + + + + + + + We’ll look at an example with a NumPy array + + + examples/testing/pytest/class/ in our class git + + + We always want the array to exist for our tests, so we’ll use fixtures (in particular setup_method()) to create the array + + + Using a class means that we can access the array created in setup from our class + + + + + NumPy has its own assertion functions + + + https://docs.scipy.org/doc/numpy/reference/routines.testing.html + + + Note in particular, the approximately equal tests + + + + + + + + + + + + + + + + + + + pytest Coverage + + + + + + + We can determine the coverage of our testing + + + Note just because a line / function is covered in our suite, doesn’t mean we’ll capture every error—there can always be corner-cases, things you don’t anticipate + + + Adding unit tests is an ongoing process + + + + + Basic running: + + + pytest --cov . + + + Here, ‘.’ is the path we are testing + + + + + Detailed report (lines missed): + + + pytest --cov-report term-missing --cov . + + + + + + + + + + + + + + + + + + pytest Coverage + + + + + + + Let’s look at a larger example: + + + pyro is my tutorial hydrodynamics code: https://github.com/zingale/pyro2 + + + + + pyro has both unit tests (via pytest) and regression testing (more on that later) + + + Tests are stored in the various tests/ subdirectories + + + + + + + . + ├── advection + │   ├── problems + │   └── tests + ├── advection_rk + │   ├── problems -> ../advection/problems + │   └── tests + ├── analysis + ├── compressible + │   ├── problems + │   └── tests + ├── compressible_react + ├── compressible_rk + │   ├── problems -> ../compressible/problems + │   └── tests + ├── diffusion + │   ├── problems + │   └── tests + ├── incompressible + │   ├── problems + │   └── tests + ├── lm_atm + │   ├── problems + │   └── tests + ├── lm_combustion + ├── mesh + │   ├── experiments + │   └── tests + ├── multigrid + │   └── tests + ├── radhydro + ├── util + │   └── tests + └── www + + + + + + + + + + + + + + Regression Testing + + + + + + + Basic idea: + + + Pick some problems / workflows that exercise your codebase + + + Might need many tests to get good coverage / explore all options + + + + + Store a benchmark containing the “right” answer + + + Each time you change your code, run the regression tests + + + Compare the new answer to the stored benchmark + + + + + If a regression test fails, then either: + + + You’ve introduced a bug—look at what changed and fix it + + + You fixed a bug—update the benchmarks + + + + + + + + + + + + + + + + + + Regression Testing + + + + + + + Automating the testing + + + You need a tool to do the comparisons + + + Store benchmarks in a separate directory (so they are not overwritten when you run) + + + Run your code, at the end of the run, compare the new output to the stored benchmark and report + + + + + Our 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+ + + + + + + + + + + Next Semester: Numerical Methods + + + + + + + I’m offering PHY 604: Computational Methods in Physics and Astronomy II next semester + + + All the “II” means is that you know how to program + + + + + Topics: + + + basic of computing + + + software engineering (git, testing, …) + + + differentiation and integration + + + interpolation + + + root finding + + + ODEs (explicit/implicit methods, two point boundary problems, eigenvalue problems) + + + linear algebra + + + fast Fourier transforms + + + fitting + + + Monte Carlo (integration, Markov chain Monte Carlo, simulated annealing) + + + PDEs (hyperbolic, elliptic/multigrid, & parabolic) + + + genetic algorithms + + + machine learning / neural nets + + + intro to parallel computing + + + computational fluid dynamics + + + + + + + + + http://bender.astro.sunysb.edu/classes/numerical_methods/ + + + + + + + + + + + + + \ No newline at end of file diff --git a/content/10-testing/testing.md b/content/10-testing/testing.md new file mode 100644 index 00000000..c7f3be34 --- /dev/null +++ b/content/10-testing/testing.md @@ -0,0 +1,55 @@ +# Testing + +Testing is an integral part of the software development process. We want to catch +mistakes early, before they go on to affect our results. + +## Types of testing + +There are a lot of different types of software testing that exist. +Most commonly, for scientific codes, we hear about: + +* Unit testing : Tests that a single function does what it was designed to do + +* Integration testing : Tests whether the individual pieces work together as intended. + Sometimes done one piece at a time (iteratively) + +* Regression testing : Checks whether code changes have changed answers + +* Verification & Validation (from the science perspective) + + * Verification: are we solving the equations correctly? + + * Validation: are we solving the correct equations? + +## Automating testing + +The best testing is automated. Github provides a *continuous integration* service that can +be run on pull requests. You write a short definition (a Github workflow) that tells Github +how to run your tests and then any time there is a change, the tests are run. + +## Unit testing + +* When to write tests? + + * Some people advocate writing a unit test for a specification + before you write the functions they will test + + * This is called Test-driven development (TDD): + https://en.wikipedia.org/wiki/Test-driven_development + + * This helps you understand the interface, return values, + side-effects, etc. of what you intend to write + +* Often we already have code, so we can start by writing tests to + cover some core functionality + + * Add new tests when you encounter a bug, precisely to ensure that + this bug doesn’t arise again + +* Tests should be short and simple + + * You want to be able to run them frequently + + * The more granular your tests are, the easier it will be to track down bugs + + diff --git a/content/10-testing/unit_integration.gif b/content/10-testing/unit_integration.gif new file mode 100644 index 00000000..07c463bf Binary files /dev/null and b/content/10-testing/unit_integration.gif differ diff --git a/content/11-machine-learning/README b/content/11-machine-learning/README new file mode 100644 index 00000000..56cc6456 --- /dev/null +++ b/content/11-machine-learning/README @@ -0,0 +1,15 @@ +Note: on older machines, tensorflow generates an illegal instruction +and crashes python on import. The issue is the CPU instructions it +was compiled with. The solution seems to be to drop down to +tensorflow 1.5: + +https://github.com/tensorflow/tensorflow/issues/17411 + +On my system, I need to make sure I got numpy from pip (instead of the +Fedora package manager). + + + +clustering examples: + +https://laxmikants.github.io/blog/neural-network-using-make-moons-dataset/ diff --git a/content/11-machine-learning/gradient-descent.ipynb b/content/11-machine-learning/gradient-descent.ipynb new file mode 100644 index 00000000..489d03cb --- /dev/null +++ b/content/11-machine-learning/gradient-descent.ipynb @@ -0,0 +1,355 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "50dc4c55-a121-4353-8271-aec309b81a74", + "metadata": {}, + "source": [ + "# Gradient Descent" + ] + }, + { + "cell_type": "markdown", + "id": "d1eea374-2243-44dd-ba94-98ab1bda1fbb", + "metadata": {}, + "source": [ + "[Gradient descent](https://en.wikipedia.org/wiki/Gradient_descent) is a simple algorithm for finding the minimum of a function of multiple variables. It works on the principle of looking at the local gradient of a function then then moving in the direction where it decreases the fastest." + ] + }, + { + "cell_type": "markdown", + "id": "13513127-4294-4910-bcdb-6ae9803b7e58", + "metadata": {}, + "source": [ + "```{warning}\n", + "There is no guarantee that you arrive at the global minimum instead of a local minimum.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "1b29e298-853d-4941-9411-72ddd1f0edf2", + "metadata": {}, + "source": [ + "Given a function $f({\\bf x})$, where ${\\bf x} = (x_0, x_1, \\ldots, x_{N-1})$,\n", + "the idea is to first compute the derivative:\n", + "\n", + "$$\\partial f / \\partial {\\bf x} = (\\partial f/\\partial x_0, \\partial f/\\partial x_1, \\ldots, \\partial f/\\partial x_{N-1})$$\n", + "\n", + "and then move in the opposite direction by some fraction, $\\eta$:\n", + "\n", + "$${\\bf x} \\leftarrow {\\bf x} - \\eta \\frac{\\partial f}{\\partial {\\bf x}}$$\n", + "\n", + "There are different ways to define what $\\eta$ should be, but we'll use a fixed value. We'll call $\\eta$ the _learning rate_." + ] + }, + { + "cell_type": "markdown", + "id": "3bdcd77d-f54b-4cf3-9e13-7754d4d66906", + "metadata": {}, + "source": [ + "Let's demonstrate this." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "62e0fa3e-74c3-474e-82f7-a7b8276a18b7", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "22754331-6821-4de0-b85f-8468a174be4d", + "metadata": {}, + "source": [ + "## Test function\n", + "\n", + "The [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function)\n", + "or the _banana function_ is a very difficult problem for minimization. It\n", + "has the form:\n", + "\n", + "$$f(x, y) = (a - x)^2 + b (y - x^2)^2$$\n", + "\n", + "and for $a = 1$ and $b = 100$, the minimimum is at a point $(a, a^2)$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1a017bb2-fa5c-40af-9bf9-c27e0f905179", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def rosenbrock(x0, x1, a, b):\n", + " return (a - x0)**2 + b*(x1 - x0**2)**2\n", + "\n", + "def drosdx(x, a, b):\n", + " x0 = x[0]\n", + " x1 = x[1]\n", + " return np.array([-2.0*(a - x0) - 4.0*b*(x1 - x0**2)*x0,\n", + " 2.0*b*(x1 - x0**2)])" + ] + }, + { + "cell_type": "markdown", + "id": "6ffe26a7-8bcf-4e87-b293-0d6ef27519ca", + "metadata": {}, + "source": [ + "Let's plot the function" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "189e89c6-3328-4bc2-b8e3-4f218fb0ed85", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "xmin = -2.0\n", + "xmax = 2.0\n", + "ymin = -1.0\n", + "ymax = 3.0" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "bb125ea6-baab-446a-adef-1095f5006021", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "a = 1.0\n", + "b = 100.0" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "997582fc-e0d6-4368-9c58-2575ac567fb5", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "N = 256\n", + "x = np.linspace(xmin, xmax, N)\n", + "y = np.linspace(ymin, ymax, N)\n", + "\n", + "x2d, y2d = np.meshgrid(x, y, indexing=\"ij\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "f3f72877-be76-4a9c-b052-e793cbeb09b3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "im = ax.imshow(np.log10(np.transpose(rosenbrock(x2d, y2d, a, b))),\n", + " origin=\"lower\", extent=[xmin, xmax, ymin, ymax])\n", + "\n", + "fig.colorbar(im, ax=ax)" + ] + }, + { + "cell_type": "markdown", + "id": "516c5508-6ebc-4b66-ba57-1a164ac78a6b", + "metadata": { + "tags": [] + }, + "source": [ + "## Implementing gradient descent" + ] + }, + { + "cell_type": "markdown", + "id": "f7bf4946-7f78-4744-8ba9-d17345a8fff4", + "metadata": {}, + "source": [ + "Let's start with an initial guess. We'll keep guessing until the change in the solution is small.\n", + "\n", + "Note: our success is very sensitive to our choice of $\\eta$." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c41e0313-4a3f-4d8d-ac23-f63292cf0552", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "x0 = np.array([-1.0, 1.5])" + ] + }, + { + "cell_type": "markdown", + "id": "44e78938-96d9-46ad-9841-07d5b02cbec4", + "metadata": {}, + "source": [ + "We'll set a tolerance and keep iterating until the change in the solution, `dx` is small" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ff9fbe69-a68c-4a52-a1ec-a8d96b9116ac", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def do_descent(dfdx, x0, eps=1.e-5, eta=2.e-3, args=None, ax=None):\n", + "\n", + " # dx will be the change in the solution -- we'll iterate until this\n", + " # is small\n", + " dx = 1.e30\n", + " xp_old = x0.copy()\n", + "\n", + " if args:\n", + " grad = dfdx(xp_old, *args)\n", + " else:\n", + " grad = dfdx(xp_old)\n", + "\n", + " while dx > eps:\n", + "\n", + " xp = xp_old - eta * grad\n", + " \n", + " if ax:\n", + " ax.plot([xp_old[0], xp[0]], [xp_old[1], xp[1]], color=\"C1\")\n", + " \n", + " dx = np.linalg.norm(xp - xp_old)\n", + " \n", + " if args:\n", + " grad_new = dfdx(xp, *args)\n", + " else:\n", + " grad_new = dfdx(xp)\n", + " \n", + " #eta_new = np.abs(np.transpose(xp) @ (grad_new - grad)) / np.linalg.norm(grad_new - grad)**2\n", + " #eta = min(10*eta, eta_new)\n", + " \n", + " grad = grad_new\n", + " \n", + " xp_old[:] = xp" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "dc9db9da-a87b-480a-9c45-fab0ddd8368d", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "do_descent(drosdx, x0, args=(a, b), ax=ax)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "989577fb-6a21-4bd1-a5de-fc2da3eff011", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fig" + ] + }, + { + "cell_type": "markdown", + "id": "ab5fb353-278d-422d-b190-a4f08d38f6b5", + "metadata": { + "tags": [] + }, + "source": [ + "## momentum" + ] + }, + { + "cell_type": "markdown", + "id": "1d785f3a-cf4c-4485-a2fd-cfce97872809", + "metadata": {}, + "source": [ + "A variation on gradient descent is to add \"momentum\"\n", + "to the update. This means that the correct depends\n", + "on the past gradients as well as the current one,\n", + "via some combination. This has the effect of reducing\n", + "the zig-zag effect that we see in our attempt above." + ] + } + ], + "metadata": { + "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": "3.13.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/content/11-machine-learning/ideas.txt b/content/11-machine-learning/ideas.txt new file mode 100644 index 00000000..09e3df03 --- /dev/null +++ b/content/11-machine-learning/ideas.txt @@ -0,0 +1,18 @@ +Packages to try: + + -- keras + -- tensorflow + -- scikit-learn + +Some nice tutorials: + + -- https://github.com/zotroneneis/machine_learning_basics + + +https://elitedatascience.com/keras-tutorial-deep-learning-in-python + + +types of machine learning: + +https://towardsdatascience.com/the-mostly-complete-chart-of-neural-networks-explained-3fb6f2367464 + diff --git a/content/11-machine-learning/keras-clustering.ipynb b/content/11-machine-learning/keras-clustering.ipynb new file mode 100644 index 00000000..86900705 --- /dev/null +++ b/content/11-machine-learning/keras-clustering.ipynb @@ -0,0 +1,807 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "d8726fab-28bc-4600-82b1-83eb9f7abb37", + "metadata": {}, + "source": [ + "# Clustering" + ] + }, + { + "cell_type": "markdown", + "id": "935a9130-4606-44d1-a670-b96e997118b1", + "metadata": {}, + "source": [ + "[Clustering](https://en.wikipedia.org/wiki/Cluster_analysis) seeks to group data into clusters based on their properties and then allow us to predict which cluster a new member belongs." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5aef60e6-70d3-4bd5-b0e6-7ee4d58b4028", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "1f841dc4-8484-44af-9ac9-c5bac1caf163", + "metadata": {}, + "source": [ + "We'll use a dataset generator that is part of [scikit-learn](https://scikit-learn.org/stable/index.html) called [`make_moons`](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_moons.html). This generates data that falls into 2 different sets with a shape that looks like half-moons." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "360de666-828d-4fe3-a8cb-ce7243373a64", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from sklearn import datasets" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "dcea3bcf-3f35-4133-8a52-064985382b4a", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def generate_data():\n", + " xvec, val = datasets.make_moons(200, noise=0.2)\n", + "\n", + " # encode the output to be 2 elements\n", + " x = []\n", + " v = []\n", + " for xv, vv in zip(xvec, val):\n", + " x.append(np.array(xv))\n", + " v.append(vv)\n", + "\n", + " return np.array(x), np.array(v)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0f675629-596c-4e5c-9975-4e57a60bd4d2", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "x, v = generate_data()" + ] + }, + { + "cell_type": "markdown", + "id": "980e1976-2da3-46a9-89cd-7b61042bc758", + "metadata": {}, + "source": [ + "Let's look at a point and it's value" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "68b11f44-9f9e-40b8-a6f2-e0cf93d35717", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [0.69873964 0.40237326], value = 0\n" + ] + } + ], + "source": [ + "print(f\"x = {x[0]}, value = {v[0]}\")" + ] + }, + { + "cell_type": "markdown", + "id": "e0a3a621-f8c8-44ae-84ed-a50425b9766f", + "metadata": {}, + "source": [ + "Now let's plot the data" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "56cee5e7-415d-4f5f-9aa0-16dee740d754", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def plot_data(x, v):\n", + " xpt = [q[0] for q in x]\n", + " ypt = [q[1] for q in x]\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.scatter(xpt, ypt, s=40, c=v, cmap=\"viridis\")\n", + " ax.set_aspect(\"equal\")\n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "e5789e05-4b8b-45c3-bb38-5f29f0ae6f36", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(x, v)" + ] + }, + { + "cell_type": "markdown", + "id": "26822875-799a-4ceb-8cb2-3e1e0abcaa0c", + "metadata": { + "tags": [] + }, + "source": [ + "We want to partition this domain into 2 regions, such that when we come in with a new point, we know which group it belongs to." + ] + }, + { + "cell_type": "markdown", + "id": "2b2779ae-6435-4112-a95b-ddd72e75f731", + "metadata": {}, + "source": [ + "First we setup and train our network" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "83d69d84-10a3-47e4-a91c-b9963f60ea86", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from keras.models import Sequential\n", + "from keras.layers import Dense, Dropout, Activation, Input\n", + "from keras.optimizers import RMSprop" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "ecb97643-ec86-48cd-a510-f782a2adacd5", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "model = Sequential()\n", + "model.add(Input(shape=(2,)))\n", + "model.add(Dense(50, activation=\"relu\"))\n", + "model.add(Dense(20, activation=\"relu\"))\n", + "model.add(Dense(1, activation=\"sigmoid\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "097b8c96-7342-4ab6-8e5a-54da12af7aec", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "rms = RMSprop()\n", + "model.compile(loss='binary_crossentropy',\n", + " optimizer=rms, metrics=['accuracy'])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "fb0c9a41-844f-4352-ad83-cff6de8a1afd", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
Model: \"sequential\"\n",
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\n" + ], + "text/plain": [ + "\u001b[1mModel: \"sequential\"\u001b[0m\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
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+       "┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃\n",
+       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
+       "│ dense (Dense)                   │ (None, 50)             │           150 │\n",
+       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
+       "│ dense_1 (Dense)                 │ (None, 20)             │         1,020 │\n",
+       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
+       "│ dense_2 (Dense)                 │ (None, 1)              │            21 │\n",
+       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n",
+       "
\n" + ], + "text/plain": [ + "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n", + "┃\u001b[1m \u001b[0m\u001b[1mLayer (type) \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mOutput Shape \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1m Param #\u001b[0m\u001b[1m \u001b[0m┃\n", + "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n", + "│ dense (\u001b[38;5;33mDense\u001b[0m) │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m50\u001b[0m) │ \u001b[38;5;34m150\u001b[0m │\n", + "├─────────────────────────────────┼────────────────────────┼───────────────┤\n", + "│ dense_1 (\u001b[38;5;33mDense\u001b[0m) │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m20\u001b[0m) │ \u001b[38;5;34m1,020\u001b[0m │\n", + "├─────────────────────────────────┼────────────────────────┼───────────────┤\n", + "│ dense_2 (\u001b[38;5;33mDense\u001b[0m) │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m1\u001b[0m) │ \u001b[38;5;34m21\u001b[0m │\n", + "└─────────────────────────────────┴────────────────────────┴───────────────┘\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
 Total params: 1,191 (4.65 KB)\n",
+       "
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 Trainable params: 1,191 (4.65 KB)\n",
+       "
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 Non-trainable params: 0 (0.00 B)\n",
+       "
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loss: 0.5496\n", + "Epoch 6/100\n", + "4/4 - 0s - 4ms/step - accuracy: 0.7950 - loss: 0.5323\n", + "Epoch 7/100\n", + "4/4 - 0s - 5ms/step - accuracy: 0.8000 - loss: 0.5164\n", + "Epoch 8/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8050 - loss: 0.5016\n", + "Epoch 9/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8050 - loss: 0.4872\n", + "Epoch 10/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8100 - loss: 0.4733\n", + "Epoch 11/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8200 - loss: 0.4604\n", + "Epoch 12/100\n", + "4/4 - 0s - 4ms/step - accuracy: 0.8200 - loss: 0.4478\n", + "Epoch 13/100\n", + "4/4 - 0s - 4ms/step - accuracy: 0.8300 - loss: 0.4367\n", + "Epoch 14/100\n", + "4/4 - 0s - 4ms/step - accuracy: 0.8300 - loss: 0.4263\n", + "Epoch 15/100\n", + "4/4 - 0s - 4ms/step - accuracy: 0.8300 - loss: 0.4153\n", + "Epoch 16/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8350 - loss: 0.4062\n", + "Epoch 17/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8300 - loss: 0.3967\n", + "Epoch 18/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8350 - loss: 0.3888\n", + "Epoch 19/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8400 - loss: 0.3811\n", + "Epoch 20/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8400 - loss: 0.3741\n", + "Epoch 21/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8400 - loss: 0.3670\n", + "Epoch 22/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8450 - loss: 0.3602\n", + "Epoch 23/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8400 - loss: 0.3547\n", + "Epoch 24/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8500 - loss: 0.3496\n", + "Epoch 25/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8500 - loss: 0.3456\n", + "Epoch 26/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8550 - loss: 0.3396\n", + "Epoch 27/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8550 - loss: 0.3355\n", + "Epoch 28/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8600 - loss: 0.3315\n", + "Epoch 29/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8650 - loss: 0.3297\n", + "Epoch 30/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8600 - loss: 0.3257\n", + "Epoch 31/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8650 - loss: 0.3215\n", + "Epoch 32/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8650 - loss: 0.3209\n", + "Epoch 33/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8650 - loss: 0.3167\n", + "Epoch 34/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8650 - loss: 0.3140\n", + "Epoch 35/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8700 - loss: 0.3129\n", + "Epoch 36/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8700 - loss: 0.3095\n", + "Epoch 37/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8750 - loss: 0.3078\n", + "Epoch 38/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8700 - loss: 0.3058\n", + "Epoch 39/100\n", + "4/4 - 0s - 2ms/step - accuracy: 0.8700 - loss: 0.3042\n", + "Epoch 40/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8700 - loss: 0.3027\n", + "Epoch 41/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.3009\n", + "Epoch 42/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2991\n", + "Epoch 43/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2978\n", + "Epoch 44/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2954\n", + "Epoch 45/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2946\n", + "Epoch 46/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2936\n", + "Epoch 47/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2917\n", + "Epoch 48/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8850 - loss: 0.2914\n", + "Epoch 49/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2895\n", + "Epoch 50/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8750 - loss: 0.2887\n", + "Epoch 51/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8850 - loss: 0.2871\n", + "Epoch 52/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8850 - loss: 0.2864\n", + "Epoch 53/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8900 - loss: 0.2861\n", + "Epoch 54/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2871\n", + "Epoch 55/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2835\n", + "Epoch 56/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2820\n", + "Epoch 57/100\n", + "4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2822\n", + "Epoch 58/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2801\n", + "Epoch 59/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8800 - loss: 0.2803\n", + "Epoch 60/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8900 - loss: 0.2785\n", + "Epoch 61/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8850 - loss: 0.2786\n", + "Epoch 62/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8850 - loss: 0.2766\n", + "Epoch 63/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8850 - loss: 0.2765\n", + "Epoch 64/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8900 - loss: 0.2750\n", + "Epoch 65/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8900 - loss: 0.2739\n", + "Epoch 66/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8900 - loss: 0.2729\n", + "Epoch 67/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8850 - loss: 0.2730\n", + "Epoch 68/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8900 - loss: 0.2716\n", + "Epoch 69/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2711\n", + "Epoch 70/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8850 - loss: 0.2700\n", + "Epoch 71/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2697\n", + "Epoch 72/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2679\n", + "Epoch 73/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2679\n", + "Epoch 74/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2666\n", + "Epoch 75/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2657\n", + "Epoch 76/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2651\n", + "Epoch 77/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2633\n", + "Epoch 78/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2623\n", + "Epoch 79/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2614\n", + "Epoch 80/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2623\n", + "Epoch 81/100\n", + "4/4 - 0s - 2ms/step - accuracy: 0.8950 - loss: 0.2604\n", + "Epoch 82/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2585\n", + "Epoch 83/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2589\n", + "Epoch 84/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2577\n", + "Epoch 85/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2556\n", + "Epoch 86/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2560\n", + "Epoch 87/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2549\n", + "Epoch 88/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2528\n", + "Epoch 89/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2524\n", + "Epoch 90/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2512\n", + "Epoch 91/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2498\n", + "Epoch 92/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2506\n", + "Epoch 93/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2489\n", + "Epoch 94/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2471\n", + "Epoch 95/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2475\n", + "Epoch 96/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2467\n", + "Epoch 97/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2433\n", + "Epoch 98/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2435\n", + "Epoch 99/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.9000 - loss: 0.2413\n", + "Epoch 100/100\n", + "4/4 - 0s - 3ms/step - accuracy: 0.8950 - loss: 0.2408\n" + ] + } + ], + "source": [ + "epochs = 100\n", + "results = model.fit(x, v, batch_size=50, epochs=epochs, verbose=2)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "ade4dc3f-8e67-4d03-8d35-8d6e6922390a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "score = 0.2388213872909546\n", + "accuracy = 0.8999999761581421\n" + ] + } + ], + "source": [ + "score = model.evaluate(x, v, verbose=0)\n", + "print(f\"score = {score[0]}\")\n", + "print(f\"accuracy = {score[1]}\")" + ] + }, + { + "cell_type": "markdown", + "id": "a4f23a95-64b2-4839-8ff8-fbae663328b7", + "metadata": {}, + "source": [ + "Let's look at a prediction. We need to feed in a single point as an array of shape `(N, 2)`, where `N` is the number of points" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "8f45aba4-4253-4c0c-8f35-21a3c55e8427", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[1m1/1\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 3ms/step\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[1.043571e-07]], dtype=float32)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res = model.predict(np.array([[-2, 2]]))\n", + "res" + ] + }, + { + "cell_type": "markdown", + "id": "814a2748-ff76-4dd0-9587-40384001463a", + "metadata": {}, + "source": [ + "We see that we get a floating point number. We will need to convert this to 0 or 1 by rounding." + ] + }, + { + "cell_type": "markdown", + "id": "75417e5d-3dd3-4710-be34-caa03a5e1e5b", + "metadata": {}, + "source": [ + "Let's plot the partitioning" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "a7518506-ba8b-4dac-a680-8bb229e8877f", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "M = 128\n", + "N = 128\n", + "\n", + "xmin = -1.75\n", + "xmax = 2.5\n", + "ymin = -1.25\n", + "ymax = 1.75\n", + "\n", + "xpt = np.linspace(xmin, xmax, M)\n", + "ypt = np.linspace(ymin, ymax, N)" + ] + }, + { + "cell_type": "markdown", + "id": "27a9a3c8-806d-441f-9246-dd7af6757b8e", + "metadata": { + "tags": [] + }, + "source": [ + "To make the prediction go faster, we want to feed in a vector of these points, of the form:\n", + "```\n", + "[[xpt[0], ypt[0]],\n", + " [xpt[1], ypt[1]],\n", + " ...\n", + "]\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "2de12ce3-8d36-4868-a37f-c3e311f5f1f9", + "metadata": {}, + "source": [ + "We can see that this packs them into the vector" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "64d168f1-e962-45a1-884a-f6942bf4eafb", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-1.75, -1.25])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pairs = np.array(np.meshgrid(xpt, ypt)).T.reshape(-1, 2)\n", + "pairs[0]" + ] + }, + { + "cell_type": "markdown", + "id": "928f9bef-f23c-4f48-a063-57a137ad59bf", + "metadata": { + "tags": [] + }, + "source": [ + "Now we do the prediction. We will get a vector out, which we reshape to match the original domain." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "729b336f-b3ef-49ef-9c87-25a1615a5b9c", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "res = model.predict(pairs, verbose=0)\n", + "res.shape = (M, N)" + ] + }, + { + "cell_type": "markdown", + "id": "04fc2d82-ec13-491b-a903-4aabe372d2a1", + "metadata": {}, + "source": [ + "Finally, round to 0 or 1" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "cf8c78ed-02db-480b-b8c6-09aa27ceeae8", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "domain = np.where(res > 0.5, 1, 0)" + ] + }, + { + "cell_type": "markdown", + "id": "1915a8cc-60ac-417d-92c9-f36d9d4025ac", + "metadata": {}, + "source": [ + "and we can plot the data" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "bbc4e2c1-4682-46ea-9e2a-6a1bfb4bcb53", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.imshow(domain.T, origin=\"lower\",\n", + " extent=[xmin, xmax, ymin, ymax], alpha=0.25)\n", + "xpt = [q[0] for q in x]\n", + "ypt = [q[1] for q in x]\n", + "\n", + "ax.scatter(xpt, ypt, s=40, c=v, cmap=\"viridis\")" + ] + } + ], + "metadata": { + "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": "3.13.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/content/11-machine-learning/keras-mnist.ipynb b/content/11-machine-learning/keras-mnist.ipynb new file mode 100644 index 00000000..049d965c --- /dev/null +++ b/content/11-machine-learning/keras-mnist.ipynb @@ -0,0 +1,1129 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# KERAS and MNIST" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We’ll apply the ideas we just learned to a neural network that does character recognition using the [MNIST database](https://en.wikipedia.org/wiki/MNIST_database). This is a set of handwritten digits (0–9) represented as a 28×28 pixel grayscale image.\n", + "\n", + "There are 2 datasets, the training set with 60,000 images and the test set with 10,000 images." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import keras" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{important}\n", + "Keras requires a backend, which can be [tensorflow](https://www.tensorflow.org/), [pytorch](https://pytorch.org/), or [jax](https://docs.jax.dev/en/latest/index.html).\n", + "\n", + "By default, it will assume tensorflow.\n", + "\n", + "This notebook has been tested with both pytorch and tensorflow.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{tip}\n", + "To have keras use pytorch, set the environment variable `KERAS_BACKEND` as:\n", + "```\n", + "export KERAS_BACKEND=\"torch\"\n", + "```\n", + "````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We follow the example for setting up the network:\n", + "https://github.com/Vict0rSch/deep_learning/tree/master/keras/feedforward" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{note}\n", + "For visualization of the network, you need to have `pydot` installed.\n", + "````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The MNIST data\n", + "\n", + "The keras library can download the MNIST data directly and provides a function to give us both the training and test images and the corresponding digits. This is already in a format that Keras wants, so we don't use the classes that we defined earlier." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from keras.datasets import mnist" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "(X_train, y_train), (X_test, y_test) = mnist.load_data()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As before, the training set consists of 60000 digits represented as a 28x28 array (there are no color channels, so this is grayscale data). They are also integer data." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(60000, 28, 28)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X_train.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "dtype('uint8')" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X_train.dtype" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at the first digit and the \"y\" value (target) associated with it—that's the correct answer." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(X_train[0], cmap=\"gray_r\")\n", + "print(y_train[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Preparing the Data\n", + "\n", + "The neural network takes a 1-d vector of input and will return a 1-d vector of output. We need to convert our data to this form." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll scale the image data to fall in [0, 1) and the numerical output to be categorized as an array. Finally, we need the input data to be one-dimensional, so we fill flatten the 28x28 images into a single 784 vector." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "X_train = X_train.astype('float32')/255\n", + "X_test = X_test.astype('float32')/255\n", + "\n", + "X_train = np.reshape(X_train, (60000, 784))\n", + "X_test = np.reshape(X_test, (10000, 784))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 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"output_type": "execute_result" + } + ], + "source": [ + "X_train[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will use categorical data. Keras includes routines to categorize data. In our case, since there are 10 possible digits, we want to put the output into 10 categories (represented by 10 neurons)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from keras.utils import to_categorical\n", + "\n", + "y_train = to_categorical(y_train, 10)\n", + "y_test = to_categorical(y_test, 10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's look at the target for the first training digit. We know from above that it was '5'. Here we see that there is a `1` in the index corresponding to `5` (remember we start counting at `0` in python)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0., 0., 0., 0., 0., 1., 0., 0., 0., 0.])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y_train[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Build the Neural Network" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we'll build the neural network. We will have 2 hidden layers, and the number of neurons will look like:\n", + "\n", + "784 → 500 → 300 → 10" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Layers\n", + "\n", + "Let's start by setting up the layers. For each layer, we tell keras the number of output neurons. It infers the number of inputs from the previous layer (with the exception of the input layer, where we need to tell it what to expect as input).\n", + "\n", + "Properties on the layers:\n", + "\n", + " * Dense layers: We will use a _dense_ network. This means that all neurons in one\n", + " layer are connected to all neurons in the next layer (sometimes the\n", + " term \"fully-connected\" is used here).\n", + "\n", + " * Activation function: We previously used the _sigmoid_ function. Now we'll\n", + " use [_rectified linear unit_](https://en.wikipedia.org/wiki/Rectifier_(neural_networks)) (see also http://ml-cheatsheet.readthedocs.io/en/latest/activation_functions.html#relu) for all but the last layer. \n", + "\n", + " For the very last layer (the output layer), we use a [softmax activation](https://en.wikipedia.org/wiki/Softmax_function). This is commonly used with categorical data (like we have) and has the nice property that all of entries add to 1 (so we can interpret them as probabilities).\n", + "\n", + " See https://keras.io/api/layers/activations/ for a list of activation functions supported.\n", + "\n", + " * Dropout: for some of the layers, we will specify a _dropout_. This means that\n", + " we will ignore some of the neurons in a layer during training (randomly selected\n", + " at the specified probability). This can help present overfitting of the network.\n", + " \n", + " Here's a nice discussion: https://medium.com/@amarbudhiraja/https-medium-com-amarbudhiraja-learning-less-to-learn-better-dropout-in-deep-machine-learning-74334da4bfc5" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from keras.models import Sequential\n", + "from keras.layers import Dense, Dropout, Activation, Input\n", + "\n", + "model = Sequential()\n", + "model.add(Input(shape=(784,)))\n", + "model.add(Dense(500, activation=\"relu\"))\n", + "model.add(Dropout(0.4))\n", + "model.add(Dense(300, activation=\"relu\"))\n", + "model.add(Dropout(0.4))\n", + "model.add(Dense(10, activation=\"softmax\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Loss function\n", + "\n", + "We need to specify what we want to optimize and how we are going to do it. \n", + "\n", + "Recall: the loss (or cost) function measures how well our predictions match the expected target.\n", + "Previously we were using the sum of the squares of the error.\n", + "\n", + "For categorical data, like we have, the \"cross-entropy\" metric is often used. See here for an explanation: https://jamesmccaffrey.wordpress.com/2013/11/05/why-you-should-use-cross-entropy-error-instead-of-classification-error-or-mean-squared-error-for-neural-network-classifier-training/" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Optimizer\n", + "\n", + "We also need to specify an optimizer. This could be gradient descent, as we used before. Here's a list of the optimizers supoprted by keras: https://keras.io/api/optimizers/ We'll use `RMPprop`, which builds off of gradient descent and includes some momentum.\n", + "\n", + "Finally, we need to specify a metric that is evaluated during training and testing. We'll use `\"accuracy\"` here. This means that we'll see the accuracy of our model reported as we are training and testing.\n", + "\n", + "More details on these options is here: https://keras.io/api/models/model/" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from keras.optimizers import RMSprop\n", + "\n", + "rms = RMSprop()\n", + "model.compile(loss='categorical_crossentropy',\n", + " optimizer=rms, metrics=['accuracy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Network summary\n", + "\n", + "Let's take a look at the network:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
Model: \"sequential\"\n",
+       "
\n" + ], + "text/plain": [ + "\u001b[1mModel: \"sequential\"\u001b[0m\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
+       "┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃\n",
+       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
+       "│ dense (Dense)                   │ (None, 500)            │       392,500 │\n",
+       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
+       "│ dropout (Dropout)               │ (None, 500)            │             0 │\n",
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+       "│ dense_1 (Dense)                 │ (None, 300)            │       150,300 │\n",
+       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
+       "│ dropout_1 (Dropout)             │ (None, 300)            │             0 │\n",
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 Total params: 545,810 (2.08 MB)\n",
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 Trainable params: 545,810 (2.08 MB)\n",
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\n" + ], + "text/plain": [ + "\u001b[1m Non-trainable params: \u001b[0m\u001b[38;5;34m0\u001b[0m (0.00 B)\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "model.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that there are > 500k parameters that we will be training" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Train\n", + "\n", + "For training, we pass in the inputs and target and the number of epochs to run and it will optimize the network by adjusting the weights between the nodes in the layers.\n", + "\n", + "The number of epochs is the number of times the entire data set is passed forward and backward through the network. The batch size is the number of training pairs you pass through the network at a given time. You update the parameter in your model (the weights) once for each batch. This makes things more efficient and less noisy." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.8868 - loss: 0.3697 - val_accuracy: 0.9540 - val_loss: 0.1459\n", + "Epoch 2/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9529 - loss: 0.1573 - val_accuracy: 0.9682 - val_loss: 0.1009\n", + "Epoch 3/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9642 - loss: 0.1172 - val_accuracy: 0.9735 - val_loss: 0.0821\n", + "Epoch 4/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9702 - loss: 0.0959 - val_accuracy: 0.9793 - val_loss: 0.0693\n", + "Epoch 5/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9748 - loss: 0.0826 - val_accuracy: 0.9788 - val_loss: 0.0682\n", + "Epoch 6/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9772 - loss: 0.0732 - val_accuracy: 0.9815 - val_loss: 0.0638\n", + "Epoch 7/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9801 - loss: 0.0646 - val_accuracy: 0.9813 - val_loss: 0.0620\n", + "Epoch 8/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9814 - loss: 0.0592 - val_accuracy: 0.9808 - val_loss: 0.0636\n", + "Epoch 9/20\n", + "235/235 - 2s - 7ms/step - accuracy: 0.9832 - loss: 0.0540 - val_accuracy: 0.9803 - val_loss: 0.0641\n", + "Epoch 10/20\n", + "235/235 - 2s - 7ms/step - accuracy: 0.9847 - loss: 0.0486 - val_accuracy: 0.9837 - val_loss: 0.0622\n", + "Epoch 11/20\n", + "235/235 - 2s - 7ms/step - accuracy: 0.9858 - loss: 0.0449 - val_accuracy: 0.9828 - val_loss: 0.0608\n", + "Epoch 12/20\n", + "235/235 - 2s - 7ms/step - accuracy: 0.9872 - loss: 0.0412 - val_accuracy: 0.9840 - val_loss: 0.0599\n", + "Epoch 13/20\n", + "235/235 - 2s - 7ms/step - accuracy: 0.9875 - loss: 0.0391 - val_accuracy: 0.9836 - val_loss: 0.0604\n", + "Epoch 14/20\n", + "235/235 - 2s - 7ms/step - accuracy: 0.9876 - loss: 0.0374 - val_accuracy: 0.9845 - val_loss: 0.0595\n", + "Epoch 15/20\n", + "235/235 - 2s - 7ms/step - accuracy: 0.9887 - loss: 0.0351 - val_accuracy: 0.9847 - val_loss: 0.0579\n", + "Epoch 16/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9895 - loss: 0.0331 - val_accuracy: 0.9849 - val_loss: 0.0611\n", + "Epoch 17/20\n", + "235/235 - 2s - 6ms/step - accuracy: 0.9898 - loss: 0.0321 - val_accuracy: 0.9834 - val_loss: 0.0638\n", + "Epoch 18/20\n", + "235/235 - 2s - 6ms/step - accuracy: 0.9901 - loss: 0.0303 - val_accuracy: 0.9856 - val_loss: 0.0590\n", + "Epoch 19/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9904 - loss: 0.0275 - val_accuracy: 0.9846 - val_loss: 0.0702\n", + "Epoch 20/20\n", + "235/235 - 1s - 6ms/step - accuracy: 0.9906 - loss: 0.0291 - val_accuracy: 0.9842 - val_loss: 0.0664\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "epochs = 20\n", + "batch_size = 256\n", + "model.fit(X_train, y_train, epochs=epochs, batch_size=batch_size,\n", + " validation_data=(X_test, y_test), verbose=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test\n", + "\n", + "keras has a routine, `evaluate()` that can take the inputs and targets of a test data set and return the loss value and accuracy (or other defined metrics) on this data.\n", + "\n", + "Here we see we are > 98% accurate on the test data—this is the data that the model has never seen before (and was not trained with)." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[1m625/625\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 2ms/step - accuracy: 0.9806 - loss: 0.0810\n", + "0.9842000007629395\n" + ] + } + ], + "source": [ + "loss_value, accuracy = model.evaluate(X_test, y_test, batch_size=16)\n", + "print(accuracy)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Predicting\n", + "\n", + "Suppose we simply want to ask our neural network to predict the target for an input. We can use the `predict()` method to return the category array with the predictions. We can then use `np.argmax()` to select the most probable." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[1m1/1\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 7ms/step\n" + ] + }, + { + "data": { + "text/plain": [ + "np.int64(7)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.argmax(model.predict(np.array([X_test[0]])))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0., 0., 0., 0., 0., 0., 0., 1., 0., 0.])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y_test[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's loop over the test set and print out what we predict vs. the true answer for those we get wrong. We can also plot the image of the digit." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 8: prediction = 6, truth is 5\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 247: prediction = 2, truth is 4\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 321: prediction = 7, truth is 2\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 340: prediction = 3, truth is 5\n" + ] + }, + { + "data": { + "image/png": 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unMLhsF599VWtXbtW3/3udyVJq1ev1je/+U1t375d3/nOdxI7PQCg07qi94DC4bAkKS0tTZK0a9cunTlzRoWFhdF9hg8froEDB6qqqqrN79HS0qJIJBKzAQC6vrgD1NraqiVLlui2227TyJEjJUkNDQ3q1auX+vbtG7NvZmamGhoa2vw+ZWVlCgQC0S07OzvekQAAnUjcASopKdG+ffv05ptvXtEApaWlCofD0a2uru6Kvh8AoHOI6x+iLl68WJs2bdK2bds0YMCA6OPBYFCnT5/W8ePHY66CGhsbFQwG2/xefr9ffr8/njEAAJ2Ypysg55wWL16s9evXa+vWrcrJyYl5fvTo0erZs6fKy8ujj1VXV+vQoUMqKChI3NQAgE7P0xVQSUmJ1q5dq40bNyolJSX6vk4gEFDv3r0VCAR0//33a+nSpUpLS1NqaqoefPBBFRQU8Ak4AEAMTwF6+eWXJUl33XVXzOOrV6/W3LlzJUnPP/+8unXrphkzZqilpUVFRUV66aWXEjkzAKAL8Ll47oqYRJFIRIFAQOFwOO4bKcKb+vr6uNaNGDHC85ovP7rvRTw34ezovvre6eX69re/7XnNQw895HmNJI0fPz6udYA8/BznXnAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwEddvREXXEgqF4lq3YcMGz2t2794d17G8euGFF+Jad/6vGrkcubm5ntcsWbLE8xqgq+EKCABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAw4XPOOeshvioSiSgQCCgcDis1NdV6HACAR5f7c5wrIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMCEpwCVlZVpzJgxSklJUUZGhqZOnarq6uqYfe666y75fL6YbeHChYmeGwDQyXkKUGVlpUpKSrR9+3Zt2bJFZ86c0cSJE9Xc3Byz37x583T48OHotnz58kTPDQDo5Hp42Xnz5s0xX69Zs0YZGRnatWuXxo0bF328T58+CgaDiZsSANDlXNF7QOFwWJKUlpYW8/jrr7+u9PR0jRw5UqWlpTp58uRFv0dLS4sikUjMBgDo+jxdAX1Va2urlixZottuu00jR46MPj579mwNGjRIoVBIe/fu1WOPPabq6mq98847bX6fsrIyPf300/GOAQDopHzOORfPwkWLFukvf/mLPvjgAw0YMOCi+23dulUTJkxQTU2NhgwZcsHzLS0tamlpiX4diUSUnZ2tcDis1NTUeEYDABiKRCIKBAKX/Dke1xXQ4sWLtWnTJm3btu1r4yNJ+fn5knTRAPn9fvn9/njGAAB0Yp4C5JzTgw8+qPXr16uiokI5OTmXXLNnzx5JUlZWVvxTAgC6HE8BKikp0dq1a7Vx40alpKSooaFBkhQIBNS7d28dOHBAa9eu1fe+9z3169dPe/fu1cMPP6xx48YpNzc3Wf8NAIBOyNN7QD6fr83HV69erblz56qurk4//OEPtW/fPjU3Nys7O1vTpk3T448/ftnv51zu3x0CADqmpLwHdKlWZWdnq7Ky0su3BABcpbgXHADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADARA/rAc7nnJMkRSIR61EAAHH48uf3lz/PL6bDBaipqUmSlJ2dbT0KAOAKNDU1KRAIXPR5n7tUotpZa2ur6uvrlZKSIp/PF/NcJBJRdna26urqlJqaajajNc7DOZyHczgP53AezukI58E5p6amJoVCIXXrdvF3ejrcFVC3bt00YMCAr90nNTX1qn6BfYnzcA7n4RzOwzmch3Osz8PXXfl8iQ8hAABMECAAgIlOFSC/369ly5bJ7/dbj2KK83AO5+EczsM5nIdzOtN56HAfQgAAXB061RUQAKDrIEAAABMECABgggABAEx0mgCtXLlSN9xwg6655hrl5+fr73//u/VI7e6pp56Sz+eL2YYPH249VtJt27ZNkydPVigUks/n04YNG2Ked87pySefVFZWlnr37q3CwkLt37/fbN5kudR5mDt37gWvj0mTJpnNmwxlZWUaM2aMUlJSlJGRoalTp6q6ujpmn1OnTqmkpET9+vXTddddpxkzZqixsdFs5mS4nPNw1113XfB6WLhwodnMbekUAXrrrbe0dOlSLVu2TB9++KHy8vJUVFSkI0eOWI/W7kaMGKHDhw9Htw8++MB6pKRrbm5WXl6eVq5c2ebzy5cv1wsvvKBVq1Zpx44duvbaa1VUVKRTp061+6zJdKnzIEmTJk2KeX288cYb7TpjslVWVqqkpETbt2/Xli1bdObMGU2cOFHNzc3RfR5++GG9++67WrdunSorK1VfX6/p06ebzp1ol3MeJGnevHkxr4fly5ebzdwm1wmMHTvWlZSURL8+e/asC4VCrqyszHSu9rZs2TKXl5dnPYYpSW79+vXRr1tbW10wGHTPPvts9LHjx487v9/v3njjDaMpk+/88+Ccc3PmzHFTpkwxm8nCkSNHnCRXWVnp3Bf/t+/Zs6dbt25ddJ9//vOfTpKrqqoynDS5zj8Pzjl35513uoceesh0rkvp8FdAp0+f1q5du1RYWBh9rFu3biosLFRVVZXpbBb279+vUCikwYMH695779WhQ4esRzJVW1urhoaGmNdHIBBQfn7+Vfn6qKioUEZGhoYNG6ZFixbp2LFj1iMlVTgcliSlpaVJknbt2qUzZ87EvB6GDx+ugQMHdunXw/nn4Uuvv/660tPTNXLkSJWWlurkyZNGE7atw92M9HxHjx7V2bNnlZmZGfN4Zmam/vWvf5nNZSE/P19r1qzRsGHDdPjwYT399NO64447tG/fPqWkpFiPZ6KhoUH64vXwVZmZmdHnrhaTJk3S9OnTlZOTowMHDuhnP/uZiouLVVVVpe7du1uPl3Ctra1asmSJbrvtNo0cOVL64vXQq1cv9e3bN2bfrvx6aOs8SNLs2bM1aNAghUIh7d27V4899piqq6v1zjvvmM77VR0+QPif4uLi6J9zc3OVn5+vQYMG6e2339b9999vOhvszZo1K/rnUaNGKTc3V0OGDFFFRYUmTJhgOlsylJSUaN++fVfF+6Bf52LnYf78+dE/jxo1SllZWZowYYIOHDigIUOGGEx6oQ7/V3Dp6enq3r37BZ9iaWxsVDAYNJurI+jbt6+GDh2qmpoa61HMfPka4PVxocGDBys9Pb1Lvj4WL16sTZs26f3334/59S3BYFCnT5/W8ePHY/bvqq+Hi52HtuTn50tSh3o9dPgA9erVS6NHj1Z5eXn0sdbWVpWXl6ugoMB0NmsnTpzQgQMHlJWVZT2KmZycHAWDwZjXRyQS0Y4dO67618enn36qY8eOdanXh3NOixcv1vr167V161bl5OTEPD969Gj17Nkz5vVQXV2tQ4cOdanXw6XOQ1v27NkjSR3r9WD9KYjL8eabbzq/3+/WrFnjPvroIzd//nzXt29f19DQYD1au/rJT37iKioqXG1trfvrX//qCgsLXXp6ujty5Ij1aEnV1NTkdu/e7Xbv3u0kueeee87t3r3bHTx40Dnn3P/93/+5vn37uo0bN7q9e/e6KVOmuJycHPfZZ59Zj55QX3cempqa3COPPOKqqqpcbW2te++999wtt9zibrrpJnfq1Cnr0RNm0aJFLhAIuIqKCnf48OHodvLkyeg+CxcudAMHDnRbt251O3fudAUFBa6goMB07kS71HmoqalxP//5z93OnTtdbW2t27hxoxs8eLAbN26c9egxOkWAnHPuxRdfdAMHDnS9evVyY8eOddu3b7ceqd3NnDnTZWVluV69ernrr7/ezZw509XU1FiPlXTvv/++k3TBNmfOHOe++Cj2E0884TIzM53f73cTJkxw1dXV1mMn3Nedh5MnT7qJEye6/v37u549e7pBgwa5efPmdbn/J62t/35JbvXq1dF9PvvsM/fAAw+4b3zjG65Pnz5u2rRp7vDhw6ZzJ9qlzsOhQ4fcuHHjXFpamvP7/e7GG290P/3pT104HLYePQa/jgEAYKLDvwcEAOiaCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAAT/w8EYeB3dji4VwAAAABJRU5ErkJggg==", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 445: prediction = 0, truth is 6\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 449: prediction = 5, truth is 3\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 495: prediction = 0, truth is 8\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 582: prediction = 2, truth is 8\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 619: prediction = 8, truth is 1\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "test 659: prediction = 7, truth is 2\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "wrong = 0\n", + "max_wrong = 10\n", + "\n", + "for n, (x, y) in enumerate(zip(X_test, y_test)):\n", + " try:\n", + " res = model.predict(np.array([x]), verbose=0)\n", + " if np.argmax(res) != np.argmax(y):\n", + " print(f\"test {n}: prediction = {np.argmax(res)}, truth is {np.argmax(y)}\")\n", + " plt.imshow(x.reshape(28, 28), cmap=\"gray_r\")\n", + " plt.show()\n", + " wrong += 1\n", + " if (wrong > max_wrong-1):\n", + " break\n", + " except KeyboardInterrupt:\n", + " print(\"stopping\")\n", + " break\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Experimenting" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are a number of things we can play with to see how the network performance\n", + "changes:\n", + "\n", + "* batch size\n", + "\n", + "* adding or removing hidden layers\n", + "\n", + "* changing the dropout\n", + "\n", + "* changing the activation function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Callbacks\n", + "\n", + "Keras allows for callbacks each epoch to store some information. These can allow you to,\n", + "for example, plot of the accuracy vs. epoch by adding a callback. Take a look here for some inspiration:\n", + "\n", + "https://www.tensorflow.org/api_docs/python/tf/keras/callbacks/History\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Going Further\n", + "\n", + "Convolutional neural networks are often used for image recognition, especially with larger images. They use filter to try to recognize patterns in portions of images (A tile). See this for a keras example: \n", + "\n", + "https://www.tensorflow.org/tutorials/images/cnn\n" + ] + } + ], + "metadata": { + "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": "3.13.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/content/11-machine-learning/machine-learning-basics.ipynb b/content/11-machine-learning/machine-learning-basics.ipynb new file mode 100644 index 00000000..dcc7a97e --- /dev/null +++ b/content/11-machine-learning/machine-learning-basics.ipynb @@ -0,0 +1,246 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f324283b-1ab5-4c9c-8b41-0d96e76ff84d", + "metadata": {}, + "source": [ + "# Machine Learning Introduction" + ] + }, + { + "cell_type": "markdown", + "id": "c1346fda-937c-4521-80fd-879674bf8d58", + "metadata": {}, + "source": [ + "## Neural networks\n", + "\n", + "When we talk about machine learning, we usually mean an [_artifical neural network_](https://en.wikipedia.org/wiki/Artificial_neural_network).\n", + "A neural network mimics the action of neurons in your brain. \n", + "\n", + "Basic idea:\n", + "\n", + "* Create a nonlinear fitting routine with free parameters\n", + "* Train the network on data with known inputs and outputs to set the parameters\n", + "* Use the trained network on new data to predict the outcome\n", + "\n", + "We can think of a neural network as a map that takes a set of n parameters and returns a set of m parameters, $\\mathbb{R}^n \\rightarrow \\mathbb{R}^m$ and we can express this as:\n", + "\n", + "$${\\bf z} = {\\bf A} {\\bf x}$$\n", + "\n", + "where ${\\bf x} \\in \\mathbb{R}^n$ are the inputs, ${\\bf z} \\in \\mathbb{R}^m$ are the outputs, and ${\\bf A}$ is an $m \\times n$ matrix.\n", + "\n", + "Our goal is to determine the matrix elements of ${\\bf A}$." + ] + }, + { + "cell_type": "markdown", + "id": "b0eddb35-abe2-4026-a064-ee05f232fbe8", + "metadata": {}, + "source": [ + "### Some nomeclature\n", + "\n", + "We can visualize a neural network as:\n", + "\n", + "![NN diagram](nn_fig2.png)\n", + "\n", + "* Neural networks are divided into _layers_\n", + "\n", + " * There is always an _input layer_—it doesn't do any processing\n", + " \n", + " * There is always an _output layer_\n", + " \n", + "* Within a layer there are neurons or _nodes_.\n", + "\n", + " * For input, there will be one node for each input variable.\n", + " \n", + "* Every node in the first layer connects to every node in the next layer\n", + "\n", + " * The _weight_ associated with the _connection_ can vary—these are the matrix elements.\n", + " \n", + "* In this example, the processing is done in layer 2 (the output)\n", + "\n", + "* When you train the neural network, you are adjusting the weights connecting to the nodes\n", + "\n", + " * Some connections might have zero weight\n", + " \n", + " * This mimics nature—a single neuron can connect to several (or lots) of other neurons." + ] + }, + { + "cell_type": "markdown", + "id": "c678e3c3-4b2f-4d4a-abf0-3716c59d2f0d", + "metadata": {}, + "source": [ + "## Universal approximation theorem and non-linearity\n", + "\n", + "A neural network can be designed to approximate any function, $f(x)$. For this to work, there must be a source of non-linearity in the network. This is applied on a layer. This is a result of the [universal approximation theorem](https://en.wikipedia.org/wiki/Universal_approximation_theorem).\n", + "\n", + "We call this an [_activation function_](https://en.wikipedia.org/wiki/Activation_function) and it has the form:\n", + "\n", + "\n", + "$$g({\\bf x}) = \\left ( \\begin{array}{c} g(x_0) \\\\ g(x_1) \\\\ \\vdots \\\\ g(x_{n-1}) \\end{array} \\right )$$\n", + "\n", + "Then our neural network has the form: ${\\bf z} = g({\\bf A x})$\n", + "\n", + "We want to choose a $g(x)$ that is differentiable. A common choice is the _sigmoid function_:\n", + "\n", + "$$g(p) = \\frac{1}{1 + e^{-p}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "2a029ea0-33bd-4058-bc58-26dde63ddd14", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d9d672b0-594f-4a03-9065-496e24abe89b", + "metadata": {}, + "outputs": [], + "source": [ + "def sigmoid(p):\n", + " return 1 / (1 + np.exp(-p))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "69eebe24-d010-4c40-905a-eb014bee84ee", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = np.linspace(-10, 10, 200)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(p, sigmoid(p))\n" + ] + }, + { + "cell_type": "markdown", + "id": "9eaf8794-cfa8-475b-a255-711560c5f0c2", + "metadata": {}, + "source": [ + "Notice that the sigmoid scales all output to be in $z_i \\in (0, 1)$\n", + "\n", + "This means that we need to ensure that our training set set is likewise mapped to $(0, 1)$, and if not, we need to transform it." + ] + }, + { + "cell_type": "markdown", + "id": "c193973c-d51c-4dfd-a30e-8667fd330158", + "metadata": {}, + "source": [ + "## Basic algorithm\n", + "\n", + "* Training\n", + "\n", + " * We have $T$ pairs $(x^k, y^k)$ for $k = 1, \\ldots, T$\n", + " \n", + " * We require that $g({\\bf A x}^k) = {\\bf y}^k$ for all $k$\n", + " \n", + " Recall that $g(p)$ is a scalar function that works element-by-element:\n", + " \n", + " $$z_i = g([{\\bf A x}]_i) = g \\left ( \\sum_j A_{ij} x_j \\right )$$\n", + " \n", + " * Find the elements of ${\\bf A}$\n", + " \n", + " This is a minimization problem, where we are minimizing:\n", + " \n", + " $$f(A_{ij}) = \\| g({\\bf A x}^k) - {\\bf y}^k \\|^2$$\n", + " \n", + " We call this function the _cost function_.\n", + " \n", + " A common minimization technique is [_gradient descent_](https://en.wikipedia.org/wiki/Gradient_descent).\n", + " \n", + " Some caveats:\n", + " \n", + " * When you minimize with one set of training data, there is no guarantee that your are still minimimzed with respect to the others. We do multiple _epochs_ or passes through the training data to fix this.\n", + " \n", + " * We often don't apply the full correction from gradient descent, but instead scale it by some $\\eta < 1$ called the _learning rate_.\n", + " \n", + "* Using the network\n", + "\n", + " With the trained ${\\bf A}$, we can now use the network on data we haven't seen before" + ] + }, + { + "cell_type": "markdown", + "id": "f9801589-7251-48b2-9099-e8b22f9c9250", + "metadata": {}, + "source": [ + "## Hidden layers\n", + "\n", + "We can get better performance from a neural network by adding a hidden layer:\n", + "\n", + "![hidden layers](nn_fig_hidden.png)\n", + "\n", + "The side of the hidden layer is independent of the size of the input and output layers. Now we have an additional matrix ${\\bf B}$ to train. This can all be done together using the same algorithm described above. Where we now minimize:\n", + "\n", + "$$f(A_{ls}, B_{ij}) = \\sum_{l=1}^m (z_l - y_l)^2$$\n", + "\n", + "$$\\tilde{z}_i = g \\left ( \\sum_{j=1}^n B_{ij} x_j \\right )$$\n", + "\n", + "$$z_l = g \\left ( \\sum_{s=1}^k A_{ls} \\tilde{z}_s \\right )$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7409a682-1905-4bde-a8a9-1d0c4d4d8347", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/content/11-machine-learning/machine-learning-libraries.md b/content/11-machine-learning/machine-learning-libraries.md new file mode 100644 index 00000000..756e5c3b --- /dev/null +++ b/content/11-machine-learning/machine-learning-libraries.md @@ -0,0 +1,106 @@ +# Diving Deeper into Machine Learning + +We've focused on neural networks, using labeled data that we +can use to learn the trends in our data. This is an example +of _supervised learning_. + +Broadly speaking there are +3 main [approaches to machine learning](https://en.wikipedia.org/wiki/Machine_learning#Approaches) + +* [Supervised learning](https://en.wikipedia.org/wiki/Supervised_learning) + + This uses labeled pairs (input and output) to train the model + to learn how to predict the outputs from the inputs. + +* [Unsupervised learning](https://en.wikipedia.org/wiki/Unsupervised_learning) + + No labeled data is provided. Instead the machine learning + algorithm seeks to find the structure on its own. The goal + is to learn patterns and features to be able to produce + new data. + +* [Reinforcement learning](https://en.wikipedia.org/wiki/Reinforcement_learning) + + As with unsupervised learning, no labeled data is used, + but the model is "rewarded" when it does something right, + and the model tries to maximize rewards (think: self-driving + cars). + +## Libraries + +There are a number of popular libraries that implement machine learning algorithms. +Their features and performance vary quite a bit. An comparison of their +features is provided by Wikipedia: [Comparison of deep learning software](https://en.wikipedia.org/wiki/Comparison_of_deep_learning_software). + +Some additional comparisons are provided here: https://ritza.co/articles/scikit-learn-vs-tensorflow-vs-pytorch-vs-keras/ + +* [TensorFlow](https://www.tensorflow.org/) + + This is an open source machine learning library released by Google. It has support + for CPUs, GPUs, and [TPUs](https://en.wikipedia.org/wiki/Tensor_Processing_Unit), + and provides all the features you need to build deep learning workflows: + [TensorFlow feactures](https://en.wikipedia.org/wiki/TensorFlow#Features). + + You can install tensorflow via: + + ``` + pip install tensorflow + ``` + + ```{note} + At the moment, tensorflow only supports python <= 3.12. So I'll be using + pytorch instead (since I am running python 3.13). + ``` + +* [PyTorch](https://pytorch.org/) + + This is a machine learning library build off of the Torch library, originally + developed by Facebook. + + You can install pytorch via: + + ``` + pip install torch + ``` + +* [scikit-learn](https://scikit-learn.org/stable/) + + This is a python library developed for machine learning. It has a lot of + sample datasets that provide a nice means to learn how different methods work. + It is designed to work with NumPy and SciPy. + + General recommendations on the web seem to be to use Scikit-learn to get + started with machine learning and to explore ideas, but to switch to + one of the other packages for computationally-intensive work. + + You can install scikit-learn via: + + ``` + pip install scikit-learn + ``` + + Scikit-learn provides some nice sample datasets: + + https://scikit-learn.org/stable/datasets/toy_dataset.html + + as well as generators for + datasets: + + https://scikit-learn.org/stable/datasets/sample_generators.html + +There are also tools that provide higher-level interfaces to these + +* [Keras](https://keras.io/) + + Keras provides a common python interface to several different machine learning + libraries, including tensorflow and torch. This hides a lot of the implementation + details and makes it easy to get started using these libraries. + +## Keras + +We'll focus on Keras. + +There are a large number of examples provided by Keras: + +https://keras.io/examples/ + diff --git a/content/11-machine-learning/machine-learning.md b/content/11-machine-learning/machine-learning.md new file mode 100644 index 00000000..21e8d859 --- /dev/null +++ b/content/11-machine-learning/machine-learning.md @@ -0,0 +1,3 @@ +# Machine Learning + +We'll look at a popular library for machine learning. diff --git a/content/11-machine-learning/model.png b/content/11-machine-learning/model.png new file mode 100644 index 00000000..a95a93b2 Binary files /dev/null and b/content/11-machine-learning/model.png differ diff --git a/content/11-machine-learning/neural-net-basics.md b/content/11-machine-learning/neural-net-basics.md new file mode 100644 index 00000000..38f938bb --- /dev/null +++ b/content/11-machine-learning/neural-net-basics.md @@ -0,0 +1,151 @@ +# Artificial Neural Network Basics + +## Neural networks + +An [_artifical +neural +network_](https://en.wikipedia.org/wiki/Artificial_neural_network) +mimics the action of neurons in your brain to form connections +between nodes (neurons) that link the input to the output. + +```{note} +We'll loosely +follow the notation from _Computational Methods for Physics_ by +Franklin. +``` + +Basic idea: + +* Create a nonlinear fitting routine with free parameters +* Train the network on data with known inputs and outputs to set the parameters +* Use the trained network on new data to predict the outcome + +We can think of a neural network as a map that takes a set of +$N_\mathrm{in}$ parameters and returns a set of $N_\mathrm{out}$ +parameters, which we can express this as: + +$${\bf z} = {\bf A} {\bf x}$$ + +where + +$${\bf x} = (x_1, x_2, \ldots, x_{N_\mathrm{in}})$$ + +are the inputs, + +$${\bf z} = (z_1, z_2, \ldots, z_{N_\mathrm{out}})$$ + +are the outputs, and +${\bf A}$ is an $N_\mathrm{out} \times N_\mathrm{in}$ matrix. + +Our goal is to determine the matrix elements of ${\bf A}$. + +## Nomenclature + +We can visualize a neural network as: + +![NN diagram](nn_fig.png) + +* Neural networks are divided into _layers_ + + * There is always an _input layer_—it doesn't do any processing. + + * There is always an _output layer_. + +* Within a layer there are neurons or _nodes_. + + * For input, there will be one node for each input variable. In this figure, + there are 3 nodes on the input layer. + + * The output layer will have as many nodes are needed to convey the answer + we are seeking from the network. In this case, there are 2 nodes on the + output layer. + +* Every node in the first layer connects to every node in the next layer + + * The _weight_ associated with the _connection_ can vary—these are the matrix elements. + + ```{note} + This is called a _dense layer_. There are alternate types of layers + we can explore where the nodes are connected differently. + ``` + +* In this example, the processing is done in layer 2 (the output) + +* When you train the neural network, you are adjusting the weights connecting to the nodes + + * Some connections might have zero weight + + * This mimics nature—a single neuron can connect to several (or lots) of other neurons. + +## Universal approximation theorem + +A neural network can be designed to approximate any function, $f(x)$. For this to work, there must be a source of non-linearity in the network—this is a result of the [universal approximation theorem](https://en.wikipedia.org/wiki/Universal_approximation_theorem). + +We use a nonlinear [_activation function_](https://en.wikipedia.org/wiki/Activation_function) that is applied in a layer. It has +the form: + +$$g({\bf v}) = \left ( \begin{array}{c} g(v_0) \\ g(v_1) \\ \vdots \\ g(v_{n-1}) \end{array} \right )$$ + +```{note} +The activation function, $g({\bf v})$ works element-by-element on the vector ${\bf v}$. +``` + +Then our neural network has the form: ${\bf z} = g({\bf A x})$ + +We want to choose a function $g(\xi)$ that is differentiable. A common choice is the _sigmoid function_: + +$$g(\xi) = \frac{1}{1 + e^{-\xi}}$$ + +```{figure} sigmoid.png +--- +align: center +--- +The sigmoid function +``` + +```{note} +There are [many choices for the activation function](https://en.wikipedia.org/wiki/Activation_function) which have +different properties. Often the choice of activation function will be empirical, by experimenting with the +performance of the network. +``` + +## Basic algorithm + +We'll consider the case where we have training data---a set of inputs, ${\bf x}^k$, +together with the expected output (answer), ${\bf y}^k$. These training pairs +allow us to constrain the output of the network and train the weights. + +* Training + + * Loop over the $T$ pairs $({\bf x}^k, {\bf y}^k)$ for $k = 1, \ldots, T$ + + * Predict the output for ${\bf x}^k$ as: + + $$z_i = g([{\bf A x}^k]_i) = g \left ( \sum_{j=1}^{N_\mathrm{in}} A_{ij} x^k_j \right )$$ + + * Constrain that ${\bf z} = {\bf y}^k$. + + This is a minimization problem, where we are minimizing: + + \begin{align*} + \mathcal{L}(A_{ij}) &= \| g({\bf A x}^k) - {\bf y}^k \|^2 \\ + &= \sum_{i=1}^{N_\mathrm{out}} \left [ g\left (\sum_{j=1}^{N_\mathrm{in}} A_{ij} x^k_j \right ) - y^k_i \right ]^2 + \end{align*} + + We call this function, $\mathcal{L}$, the _cost function_ or [loss function](https://en.wikipedia.org/wiki/Loss_function). + + ```{note} + This is called the _mean square error_ loss function, and is one possible choice for $\mathcal{L}(A_{ij})$, but [many others exist](https://en.wikipedia.org/wiki/Loss_function). + ``` + + * Update the matrix ${\bf A}$ based on the training pair $({\bf x}^k, {\bf y^{k}})$. + +* Using the network + + With the trained ${\bf A}$, we can now use the network on data we haven't seen before, $\boldsymbol \chi$: + + $$z_i = g([{\bf A {\boldsymbol \chi}}^k]_i) = g \left ( \sum_{j=1}^{N_\mathrm{in}} A_{ij} \chi^k_j \right )$$ + +There are a lot of details that we still need to figure out involving the training and minimization. +We'll start with minimization: a common minimization technique used with +neural networks is [_gradient descent_](https://en.wikipedia.org/wiki/Gradient_descent). diff --git a/content/11-machine-learning/neural-net-derivation.md b/content/11-machine-learning/neural-net-derivation.md new file mode 100644 index 00000000..c13f6a41 --- /dev/null +++ b/content/11-machine-learning/neural-net-derivation.md @@ -0,0 +1,93 @@ +# Deriving the Learning Correction + +For gradient descent, we need to derive the update to the matrix +${\bf A}$ based on training on a set of our data, $({\bf x}^k, {\bf y}^k)$. + +```{important} +The derivation we do here is specific to our choice of loss function, $\mathcal{L}(A_{ij})$ +and activation function, $g(\xi)$. +``` + +Let's start with our cost function: + +$$\mathcal{L}(A_{ij}) = \sum_{i=1}^{N_\mathrm{out}} (z_i - y_i^k)^2 = \sum_{i=1}^{N_\mathrm{out}} + \Biggl [ g\biggl (\underbrace{\sum_{j=1}^{N_\mathrm{in}} A_{ij} x^k_j}_{\equiv \alpha_i} \biggr ) - y^k_i \Biggr ]^2$$ + +where we'll refer to the product ${\boldsymbol \alpha} \equiv {\bf +Ax}$ to help simplify notation. This means that ${\bf z} = g({\boldsymbol \alpha})$. + +We can compute the derivative with respect to a single matrix +element, $A_{pq}$ by applying the chain rule: + +$$\frac{\partial \mathcal{L}}{\partial A_{pq}} = + 2 \sum_{i=1}^{N_\mathrm{out}} (z_i - y^k_i) \left . \frac{\partial g}{\partial \xi} \right |_{\xi=\alpha_i} \frac{\partial \alpha_i}{\partial A_{pq}}$$ + + +with + +$$\frac{\partial \alpha_i}{\partial A_{pq}} = \sum_{j=1}^{N_\mathrm{in}} \frac{\partial A_{ij}}{\partial A_{pq}} x^k_j = \sum_{j=1}^{N_\mathrm{in}} \delta_{ip} \delta_{jq} x^k_j = \delta_{ip} x^k_q$$ + +and for $g(\xi)$, we will assume the sigmoid function,so + +$$\frac{\partial g}{\partial \xi} + = \frac{\partial}{\partial \xi} \frac{1}{1 + e^{-\xi}} + =- (1 + e^{-\xi})^{-2} (- e^{-\xi}) + = g(\xi) \frac{e^{-\xi}}{1+ e^{-\xi}} = g(\xi) (1 - g(\xi))$$ + +which gives us: + +\begin{align*} +\frac{\partial \mathcal{L}}{\partial A_{pq}} &= 2 \sum_{i=1}^{N_\mathrm{out}} + (z_i - y^k_i) z_i (1 - z_i) \delta_{ip} x^k_q \\ + &= 2 (z_p - y^k_p) z_p (1- z_p) x^k_q +\end{align*} + +where we used the fact that the $\delta_{ip}$ means that only a single term contributes to the sum. + +```{note} +Observe that: + +* $e_p^k \equiv (z_p - y_p^k)$ is the error on the output layer, + and the correction is proportional to the error (as we would + expect). + +* The $k$ superscripts here remind us that this is the result of + only a single pair of data from the training set. +``` + +Now ${\bf z}$ and ${\bf y}^k$ are all vectors of size $N_\mathrm{out} \times 1$ and ${\bf x}^k$ is a vector of size $N_\mathrm{in} \times 1$, so we can write this expression for the matrix as a whole as: + +$$\frac{\partial \mathcal{L}}{\partial {\bf A}} = 2 ({\bf z} - {\bf y}^k) \circ {\bf z} \circ (1 - {\bf z}) \cdot ({\bf x}^k)^\intercal$$ + +where the operator $\circ$ represents _element-by-element_ multiplication (the [Hadamard product](https://en.wikipedia.org/wiki/Hadamard_product_(matrices))). + +## Performing the update + +We could do the update like we just saw with our gradient descent +example: take a single data point, $({\bf x}^k, {\bf y}^k)$ and +do the full minimization, continually estimating the correction, +$\partial \mathcal{L}/\partial {\bf A}$ and updating ${\bf A}$ until we +reach a minimum. The problem with this is that $({\bf x}^k, {\bf y}^k)$ is only one point in our training data, and there is no +guarantee that if we minimize completely with point $k$ that we will +also be a minimum with point $k+1$. + +Instead we take multiple passes through the training data (called _epochs_) and apply only a single push in the direction that gradient +descent suggests, scaled by a _learning rate_ $\eta$. + +The overall minimization appears as: + +```{card} Minimization +* Loop over epochs + + * Loop over the training data, $\{ ({\bf x}^0, {\bf y}^0), ({\bf x}^1, {\bf y}^1), \ldots \}$. We'll refer to the current training + pair as $({\bf x}^k, {\bf y}^k)$ + + * Propagate ${\bf x}^k$ through the network, getting the output + ${\bf z} = g({\bf A x}^k)$ + + * Compute the error on the output layer, ${\bf e}^k = {\bf z} - {\bf y}^k$ + + * Update the matrix ${\bf A}$ according to: + + $${\bf A} \leftarrow {\bf A} - 2 \,\eta\, {\bf e}^k \circ {\bf z} \circ (1 - {\bf z}) \cdot ({\bf x}^k)^\intercal$$ +``` diff --git a/content/11-machine-learning/neural-net-hidden.md b/content/11-machine-learning/neural-net-hidden.md new file mode 100644 index 00000000..1e27c737 --- /dev/null +++ b/content/11-machine-learning/neural-net-hidden.md @@ -0,0 +1,111 @@ +# Hidden Layers + + + We can get better performance from a neural network by adding a hidden layer: + +![hidden layers](nn_fig_hidden.png) + +The size of the hidden layer is independent of the size of the input and output +layers. In this case, we have a hidden layer that is larger +than either the input or output layers. + +Now we have an additional matrix ${\bf B}$ to train. The matrix sizes are: + +* ${\bf A}$ : $N_\mathrm{out} \times N_\mathrm{hidden}$ +* ${\bf B}$ : $N_\mathrm{hidden} \times N_\mathrm{in}$ + + +```{note} +Neglecting the activation functions, the action of the network +is to do ${\bf z} = {\bf A B x}$ which has size $N_\mathrm{out}$. +``` + +The derivation of the corrections to matrices ${\bf A}$ and ${\bf B}$ can be done +via the chain rule. + +```{note} +We'll consider the case of a single hidden layer, but the derivation we +do here generalizes to multiple hidden layers. +``` + +\begin{equation} +\mathcal{L}(A_{lm}, B_{ij}) = \sum_{l=1}^{N_\mathrm{out}} (z_l - y^k_l)^2 +\end{equation} + +$$\tilde{z}_i = g \biggl ( \underbrace{\sum_{j=1}^{N_\mathrm{in}} B_{ij} x^k_j}_{\equiv \beta_i} \biggr )$$ + +$$z_l = g \biggl ( \underbrace{\sum_{m=1}^{N_\mathrm{hidden}} A_{lm} \tilde{z}_m}_{\equiv \alpha_l} \biggr )$$ + +Note that we are assuming here that the same activation function, $g(\xi)$ +is used on each layer. + +## Updates to ${\bf A}$ + +Matrix ${\bf A}$ is trained based on the output layer, we know the error there +directly, ${\bf e}^k = {\bf z} - {\bf y}^k$. As a result, we can just use +the result that we got for a single layer, but now the input is $\tilde{\bf z}$ +instead of ${\bf x}$: + +$$\frac{\partial \mathcal{L}}{\partial {\bf A}} = 2 {\bf e}^k \circ {\bf z} \circ (1 - {\bf z}) \cdot \tilde{\bf z}^\intercal$$ + +## Updates to ${\bf B}$ + +To find the corrections to matrix ${\bf B}$, we essentially need to know what the +error is on the hidden layer. But we only know the error on the output layer, so +by applying the chainrule on our cost function, we will work out this correction, +and in the process see how the error on the output layer informs the error on the +hidden layer—a process called _backpropagation_. + +Let's start with our cost function: + +\begin{align*} +\mathcal{L}(A_{lm}, B_{ij}) &= \sum_{l=1}^{N_\mathrm{out}} (z_l - y^k_l)^2 \\ + &= \sum_{l=1}^{N_\mathrm{out}} \Biggl [ g \biggl ( \sum_{m=1}^{N_\mathrm{hidden}} A_{lm} \tilde{z}_m \biggr ) - y_l^k \Biggr ]^2 \\ + &= \sum_{l=1}^{N_\mathrm{out}} \Biggl [ g \biggl ( \sum_{m=1}^{N_\mathrm{hidden}} A_{lm} \,g \biggl ( \sum_{j=1}^{N_\mathrm{in}} B_{mj} x_j^k \biggr ) \biggr ) - y_l^k \Biggr ]^2 +\end{align*} + +Differentiating with respect to an element in matrix ${\bf B}$, we apply the chain rule over and over, +giving: + +$$\frac{\partial \mathcal{L}}{\partial B_{pq}} = 2 \sum_{l=1}^{N_\mathrm{out}} (z_l - y_l^k) + \left .\frac{\partial g}{\partial \xi} \right |_{\xi = \alpha_l} + \sum_{m=1}^{N_\mathrm{hidden}} A_{lm}\, \left . \frac{\partial g}{\partial \xi} \right |_{\xi = \beta_m} + \sum_{j=1}^{N_\mathrm{in}} \frac{\partial B_{mj}}{\partial B_{pq}} x_j^k $$ + + +Now we have 3 derivatives left, which are straightforward: + +$$\left .\frac{\partial g}{\partial \xi} \right |_{\xi = \alpha_l} = g(\alpha_l)\left [ 1 - g(\alpha_l)\right ] + = z_l (1 - z_l)$$ + +$$\left .\frac{\partial g}{\partial \xi} \right |_{\xi = \beta_m} = g(\beta_m)\left [ 1 - g(\beta_m)\right ] + = \tilde{z}_m (1 - \tilde{z}_m)$$ + +$$\frac{\partial B_{mj}}{\partial B_{pq}} = \delta_{mp} \delta_{jq}$$ + +Inserting these dervatives and using the $\delta$'s, we are left with: + +$$\frac{\partial \mathcal{L}}{\partial B_{pq}} = 2 \sum_{l=1}^{N_\mathrm{out}} + \underbrace{(z_l - y_l^k)}_{ = e_l^k} z_l (1 - z_l) A_{lp} \tilde{z}_p (1 - \tilde{z}_p) x^k_q$$ + +Now, that remaining sum is contracting on the first of the indices of +the matrix ${\bf A}$, indicating a matrix vector product involving +${\bf A}^\intercal$. This allows us to define the error _backpropagated_ to the hidden layer: + +$$\tilde{e}_p^k = \sum_{l=1}^{N_\mathrm{out}} e_l^k z_l (1 - z_l) A_{lp} + = \left [ {\bf A}^\intercal \cdot ({\bf e}^k \circ {\bf z} \circ (1 - {\bf z})) \right ]_p$$ + +and we can write + +$$\frac{\partial \mathcal{L}}{\partial {\bf B}} = 2 \tilde{\bf e}^k \circ \tilde{\bf z} \circ (1 - \tilde{\bf z}) \cdot ({\bf x}^k)^\intercal$$ + + +Notice the symmetry in the update of each matrix: + +\begin{align*} +\frac{\partial \mathcal{L}}{\partial {\bf A}} &= 2 {\bf e}^k \circ {\bf z} \circ (1 - {\bf z}) \cdot \tilde{\bf z}^\intercal \\ +\frac{\partial \mathcal{L}}{\partial {\bf B}} &= 2 \tilde{\bf e}^k \circ \tilde{\bf z} \circ (1 - \tilde{\bf z}) \cdot ({\bf x}^k)^\intercal +\end{align*} + +Adding additional hidden layers would continue the trend, with each hidden layer's matrix update depending +on the error backpropagated to that layer. diff --git a/content/11-machine-learning/neural-net-improvements.md b/content/11-machine-learning/neural-net-improvements.md new file mode 100644 index 00000000..d894d4c3 --- /dev/null +++ b/content/11-machine-learning/neural-net-improvements.md @@ -0,0 +1,103 @@ +# Improvements + +There are many ways we could improve the performance of our network, but these will add +a lot of complexity to the simple class that we wrote. Fortunately there are a lot of +machine learning libraries that provide these features, and work efficiently, so for +real applications we would want to use one of those libraries (we'll explore these next). + +## Batching + +Right now, we did our training as: + +* Loop over the $T$ pairs $({\bf x}^k, {\bf y}^k)$ for $k = 1, \ldots, T$ + + * Propagate $({\bf x}^k, {\bf y}^k)$ through the network + * Compute the corrections $\partial \mathcal{L}/\partial {\bf A}$, $\partial \mathcal{L}/\partial {\bf B}$ + * Update the matrices: + + $${\bf A} \leftarrow {\bf A} - \eta \frac{\partial \mathcal{L}}{\partial {\bf A}}$$ + + $${\bf B} \leftarrow {\bf B} - \eta \frac{\partial \mathcal{L}}{\partial {\bf B}}$$ + +In this manner, each training pair sees slightly different +matrices ${\bf A}$ and ${\bf B}$, as each previous pair +updates it immediately. + +We could instead divide our training set into $N$ batches, +each with $\tau = T/N$ training pairs and do our update as: + +* Loop over $N$ batches + + * Loop over the $\tau$ pairs $({\bf x}^k, {\bf y}^k)$ for $k = 1, \ldots, \tau$ in the current batch + + * Propagate $({\bf x}^k, {\bf y}^k)$ through the network + * Compute the gradients $\partial \mathcal{L}/\partial {\bf A}^k$, $\partial \mathcal{L}/\partial {\bf B}^k$ from the current pair + + * Accumulate the gradients: + + $$\frac{\partial \mathcal{L}}{\partial {\bf A}} = \frac{\partial \mathcal{L}}{\partial {\bf A}} + \frac{\partial \mathcal{L}}{\partial {\bf A}^k}$$ + + $$\frac{\partial \mathcal{L}}{\partial {\bf B}} = \frac{\partial \mathcal{L}}{\partial {\bf B}} + \frac{\partial \mathcal{L}}{\partial {\bf B}^k}$$ + + * Apply a single update to the matrices for this batch: + + $${\bf A} \leftarrow {\bf A} - \frac{\eta}{\tau} \frac{\partial \mathcal{L}}{\partial {\bf A}}$$ + + $${\bf B} \leftarrow {\bf B} - \frac{\eta}{\tau} \frac{\partial \mathcal{L}}{\partial {\bf B}}$$ + +```{note} +We normalize the accumulated gradients by the batch size, $\tau$, which means that +we are applying the average gradient over the batch. +``` + +The advantage of this is that the $\tau$ trainings in a batch +can all be done in parallel now, spread across many CPU cores +or GPU cores. This greatly accelerates the training time. + + +## Different activation or cost functions + +We used a simple cost function: the sum of the square of the errors. This is analogous to the $L_2$ norm we discussed previously. But there are a lot of other cost functions +we could explore. Changing the cost function will require +us to recompute our derivatives. + +Likewise, there are a wide number of activation functions, +some of which are not differentiable. The choice of activation +function can depend on what type of data you are using. You +might also want to use a different activation function +on each layer. Again, this would require us to redo +our derivatives. + + +## Use a different minimization technique + +We only explored gradient descent. But there are improvements +to this (like momentum that we mentioned previously) as well +as alternate minimization techniques we could use (some of +which don't need the gradient at all). + + +## Different types of layers / connections + +We only considered a dense network: every node on one +layer was connected to every node on the adjacent layer. +But there are alternatives. + +For example, a [convolutional neural network](https://en.wikipedia.org/wiki/Convolutional_neural_network) performs a convolution on a layer with some kernel. This +helps identifying features. + +## More hidden layers + +There is no restriction on the number of hidden layers we +can use. Each additional hidden layer means an additional +matrix is added to our network. For our code, we'd simply need to backpropagate +the error to each hidden layer and compute the update to +the new matrix. + +## Auto-differentiation libraries + +At some point, with all of these options, doing all of the +differentiation / chain-rule by hand becomes burdensome and +prone to errors. For this reason, libraries often use +automatic differentiation libraries, like [JAX](https://jax.readthedocs.io/en/latest/) which can take +the derivatives of our python functions themselves. \ No newline at end of file diff --git a/content/11-machine-learning/nn_fig.png b/content/11-machine-learning/nn_fig.png new file mode 100644 index 00000000..6c9dea83 Binary files /dev/null and b/content/11-machine-learning/nn_fig.png differ diff --git a/content/11-machine-learning/nn_fig.py b/content/11-machine-learning/nn_fig.py new file mode 100644 index 00000000..97e5cb4a --- /dev/null +++ b/content/11-machine-learning/nn_fig.py @@ -0,0 +1,180 @@ +import random + +import matplotlib.pyplot as plt +import numpy as np + + +class Neuron(object): + def __init__(self, x, y, R=0.35): + self.x = x + self.y = y + self.R = R + + def draw(self, color="C0", label=None): + theta = np.linspace(0, 2*np.pi, 180) + xc = self.x + self.R*np.cos(theta) + yc = self.y + self.R*np.sin(theta) + + plt.fill(xc, yc, color=color, alpha=0.75) + + if label is not None: + plt.text(self.x, self.y, label, color="k", + horizontalalignment="center", verticalalignment="center") + + +class Layer(object): + def __init__(self, x, num_neurons=3, dy=1.0): + self.x = x + self.dy = dy + self.num_neurons = num_neurons + self.neurons = [] + + for i in range(self.num_neurons): + y = -i*self.dy + self.neurons.append(Neuron(self.x, y)) + + def draw(self, color="C1", label=None, top_label=None): + # compute the bounding box + ys = [q.y for q in self.neurons] + + ymin = min(ys) - self.neurons[0].R + ymax = max(ys) + self.neurons[0].R + + xmin = self.neurons[0].x - self.neurons[0].R + xmax = self.neurons[0].x + self.neurons[0].R + + dx = xmax - xmin + xmin -= 0.25*dx + xmax += 0.25*dx + ymin -= 0.25*dx + ymax += 0.25*dx + + plt.fill([xmin, xmin, xmax, xmax, xmin], + [ymin, ymax, ymax, ymin, ymin], + color=color, zorder=-100, alpha=0.5, edgecolor="none") + + for i, n in enumerate(self.neurons): + n.draw(label="{}".format(i)) + + if label is not None: + plt.text(self.x, ymin-0.5*dx, label, + horizontalalignment="center", color="k") + + if top_label is not None: + plt.text(self.x, ymax+0.25*dx, top_label, + horizontalalignment="center", color="k") + +class NeuralNet(object): + + def __init__(self, dx=2.0, nlayers=2, neurons_in=3, neurons_out=2): + self.nlayers = nlayers + + self.layers = [] + for i in range(self.nlayers): + if i == 0: + neurons = neurons_in + elif i == nlayers-1: + neurons = neurons_out + else: + neurons = int(1.5*neurons_in) + + self.layers.append(Layer(i*dx, num_neurons=neurons, dy=1.5)) + + def draw(self): + for i, l in enumerate(self.layers): + if i == 0: + label = "input\nlayer {}".format(i+1) + top_label = r"${\bf x}$" + elif i == len(self.layers)-1: + label = "output\nlayer {}".format(i+1) + if len(self.layers) == 3: + top_label = r"${\bf z} = g({\bf A}\tilde{\bf z})$" + else: + top_label = r"${\bf z} = g({\bf A}{\bf x})$" + else: + label = "hidden\nlayer {}".format(i+1) + top_label = r"$\tilde{\bf z} = g({\bf B x})$" + + l.draw(label=label, top_label=top_label) + + colors = ["0.5", "C1", "C2", "C3", "C4", "C5", "C6"] + + # now connect + for i in range(0, len(self.layers)-1): + for j, n in enumerate(self.layers[i].neurons): + x0 = n.x + y0 = n.y + R0 = n.R + + c = random.choice(colors) + + for q in self.layers[i+1].neurons: + xt = q.x + yt = q.y + Rt = q.R + + # figure out the angle + theta = np.arctan2(yt-y0, xt-x0) + L = np.sqrt((xt - x0)**2 + (yt - y0)**2) - Rt - R0 + + plt.arrow(x0+R0*np.cos(theta), y0+R0*np.sin(theta), + L*np.cos(theta), L*np.sin(theta), + head_width=0.075, zorder=-50, + color=c, + length_includes_head=True) + + xc = 0.5*(self.layers[i].x + self.layers[i+1].x) + yc = self.layers[i].neurons[0].y + 0.25*(self.layers[i].neurons[0].y - self.layers[i].neurons[1].y) + if i == 0 and self.nlayers > 2: + label = r"${\bf B}$" + else: + label = r"${\bf A}$" + + plt.text(xc, yc, label, color="r") + + # draw inputs and outputs + ls = self.layers[0] + xf = ls.neurons[0].x - 1.5*ls.neurons[0].R + L = 2.0*ls.neurons[0].R + + for n in ls.neurons: + plt.arrow(xf - L, n.y, L, 0, head_width=0.075, color="k") + + ls = self.layers[-1] + xf = ls.neurons[0].x + 1.25*ls.neurons[0].R + L = 2.0*ls.neurons[0].R + + for n in ls.neurons: + plt.arrow(xf, n.y, L, 0, head_width=0.075, color="k") + + +# simple version +nn = NeuralNet() +nn.draw() + +plt.axis("off") +ax = plt.gca() +ax.set_aspect("equal", "datalim") + +f = plt.gcf() +f.set_size_inches(5, 5) + +plt.tight_layout() +plt.savefig("nn_fig.png", dpi=150, bbox_inches="tight") + +# hidden layer +plt.clf() + +nn = NeuralNet(nlayers=3) +nn.draw() + +plt.axis("off") +ax = plt.gca() +ax.set_aspect("equal", "datalim") + +f = plt.gcf() +f.set_size_inches(7, 5.5) +plt.tight_layout() +plt.savefig("nn_fig_hidden.png", dpi=150) + +# add some labels diff --git a/content/11-machine-learning/nn_fig2.png b/content/11-machine-learning/nn_fig2.png new file mode 100644 index 00000000..a010b5d6 Binary files /dev/null and b/content/11-machine-learning/nn_fig2.png differ diff --git a/content/11-machine-learning/nn_fig_hidden.png b/content/11-machine-learning/nn_fig_hidden.png new file mode 100644 index 00000000..9b329fec Binary files /dev/null and b/content/11-machine-learning/nn_fig_hidden.png differ diff --git a/content/11-machine-learning/sigmoid.png b/content/11-machine-learning/sigmoid.png new file mode 100644 index 00000000..1f11dd14 Binary files /dev/null and b/content/11-machine-learning/sigmoid.png differ diff --git a/content/11-machine-learning/sigmoid.py b/content/11-machine-learning/sigmoid.py new file mode 100644 index 00000000..58eb1f96 --- /dev/null +++ b/content/11-machine-learning/sigmoid.py @@ -0,0 +1,14 @@ +import matplotlib.pyplot as plt +import numpy as np + + +def sigmoid(p): + return 1 / (1 + np.exp(-p)) + +p = np.linspace(-10, 10, 200) + +fig, ax = plt.subplots() + +ax.plot(p, sigmoid(p)) + +fig.savefig("sigmoid.png") diff --git a/content/12-extensions/extensions-example.md b/content/12-extensions/extensions-example.md new file mode 100644 index 00000000..f4e89cf2 --- /dev/null +++ b/content/12-extensions/extensions-example.md @@ -0,0 +1,305 @@ +# Example Extension + +Let's rewrite our Mandelbrot generator using different languages +to see how the performance differs. + +Recall the Mandelbrot set is defined as the set such that $z_{k+1} = z_k^2 + c$ +remains bounded, defined as $|z_{k+1}| \le 2$, where $c$ is a complex number, +$c = x + iy$, in the complex plane, and $z_0 = 0$ is the starting condition. + +We'll do a fixed number of iterations, and store the iteration for which $|z_{k+1}|$ +first becomes larger than 2. + + + +## NumPy array syntax + +Here's an example of a python implementation using NumPy array operations: + + +```{literalinclude} ../../examples/extensions/python/mandel.py +:language: python +``` + +We can test this as: + +```{literalinclude} ../../examples/extensions/python/test_mandel.py +:language: python +``` + +Here's the resulting image + +```{image} test.png +:align: center +``` + +## Python with explicit loops + +Here's a version where the loops are explicitly written out in python: + +```{literalinclude} ../../examples/extensions/python-slow/mandel.py +:language: python +``` + +This can be run using the same driver as the numpy vectorized version. + + +## Numba version + +We can install Numba simply by doing: + +```bash +pip install numba +``` + +To get a Numba optimized version of the python with explicit loops we just add: + +```python +from numba import njit +``` + +and then right before the function definition: + +```python +@njit() +``` + +Here's the full code: + +```{literalinclude} ../../examples/extensions/numba/mandel.py +:language: python +``` + +Again, this uses the same driver. + + +```{note} +We didn't need to do anything special to *compile* the numba code. +This is done for us when we first encounter it. +``` + +```{tip} +We run it twice in our driver, since the first call will have the overhead +of the JIT compilation. +``` + +```{literalinclude} ../../examples/extensions/numba/test_mandel.py +:language: python +``` + +````{tip} +We can get even better performance if we let numba do things in parallel, with + +``` +@njit(parallel=True) +``` +```` + +## Cython version + +We can install Cython by doing + +```bash +pip install Cython +``` + +For Cython, we mainly need to specify the datatypes of the different +variables. We use the extension `.pyx` for a cython file. + +Here's the full code: + +```{literalinclude} ../../examples/extensions/cython/mandel.pyx +:language: python +``` + +To build it, we can use a `setup.py` file: + +```{literalinclude} ../../examples/extensions/cython/setup.py +:language: python +``` + +and make the extension as: + +```bash +python setup.py build_ext --inplace +``` + +```{note} +This build process will likely change in the near future, as +the community is transitioning away from `setup.py`, but the +docs don't seem to be fully up to date on the new way to build. +``` + +````{tip} +To help understand where the slow parts of your Cython code are, you +can do +``` +cythonize -a mandel.pyx +``` +This will produce an HTML file with the parts of the code that interact +with python highlighted. (Make sure there are no `.c` files hanging around). +These highlighted lines are places you should try to optimize. + +For our example, if we do +``` +np.abs(z[i,j]) +``` +instead of +``` +abs(z[i,j]) +``` +we get a dramatic slowdown! + +Thanks to Eric Johnson for pointing this out. + +```` + + +## Fortran implementation + +If we want to write the code in Fortran, we need to [compile it into a shared +object library](https://numpy.org/doc/stable/f2py/usage.html) that python can import. +This is where `f2py` comes in---it is part of the numpy project, so you probably +already have it installed. + +```{note} +Support for this is in transition at the moment. The old official way to do this +was to use `distutils`, but this is removed in python 3.12. + +Instead, we will use the [meson build system](https://mesonbuild.com/). +``` + +We need to install `meson` and `ninja`: + +```bash +pip install meson ninja +``` + +Here's our Fortran implementation for the Mandelbrot generator: + +```{literalinclude} ../../examples/extensions/f2py/mandel.f90 +:language: fortran +``` + +To build the extension, we can do: + +```bash +f2py -c mandel.f90 -m mandel_f2py +``` + +````{note} +If the `f2py` command-line tool is not available, you can try running it as a module instead: +```bash +python -m numpy.f2py -c mandel.f90 -m mandel_f2py +``` +```` + +````{tip} +The build doesn't show you the compilation commands used to make the library. But if you look +at the output, it will say something like: +``` +The Meson build system +Version: 1.4.0 +Source dir: /tmp/tmp0sbl86zt +Build dir: /tmp/tmp0sbl86zt/bbdir +Build type: native build +Project name: mandel_f2py +``` +If you then look in the build directory, there will be a file `compile_commands.json` that +lists the commands that meson + f2py use to compile the extension. In our case, +it is using the optimization flag `-O3`. +```` + +This will create a library (on my machine, it is called `mandel_f2py.cpython-312-x86_64-linux-gnu.so`) +which we can import as `import mandel_f2py`. + +Here's a driver: + +```{literalinclude} ../../examples/extensions/f2py/test_mandel.py +:language: python +``` + +```{note} + Even though our Fortran subroutine takes the array `m` as an + argument, since it is marked as `intent(out)`, the python module + will use this as the return value. +``` + +```{note} +The numpy array returned to python will have Fortran ordering (column-major) instead +of the usual row-major ordering (take a look at the ``.flags`` attributes). +``` + +## C++ / pybind11 implementation + +pybind11 allows you to construct a numpy-compatible array in C++ +and return it. There are different constructors for this---here +we use on that allows us to specify the shape and stride. + +We can install pybind11 via pip: + +```bash +pip install pybind11 +``` + +Inside of the `mandelbrot()` function, we need temporary +two-dimensional arrays to store $z$ and $c$. With C++23 +we could use `std::mdspan` to give us nice multidimensional +indexing. For now, we need to do something different. +Our first attempt will use `std::vector>>`. + +Here's the implementation of our Mandelbrot generator: + + +```{literalinclude} ../../examples/extensions/pybind11/mandel.cpp +:language: c++ +``` + +We build the shared library as: + +```bash +g++ -DNDEBUG -O3 -Wall -Wextra -shared -std=c++17 -fPIC $(python3 -m pybind11 --includes) mandel.cpp -o mandel$(python3-config --extension-suffix) +``` + +Our driver is essentially the same as the Fortran one. + + +```{literalinclude} ../../examples/extensions/pybind11/test_mandel.py +:language: python +``` + +A slightly more complicated version that creates a contiguous `Array` class +that can be indexed with `()` runs faster. That code is here: + +```{literalinclude} ../../examples/extensions/pybind11/contiguous/mandel.cpp +:language: C++ +``` + +It uses the same driver. + + +## Timings + +On my machine, (python 3.13, numpy 2.2.5, Cython 3.0.12, GCC 15, numba +0.61.2, pybind11 2.13.6) here are some timings (average of 3 runs): + + +| technique | timings (s) | +| -------------------------------------------- | -------------- | +| python / numpy | 0.218 | +| python w/ explicit loops | 17.4 | +| Numba(*) | 0.0922 | +| Cython | 0.0866 | +| Fortran + f2py | 0.0860 | +| C++ + pybind11 (vector of vector) | 0.120 | +| C++ + pybind11 (contiguous `Array`) | 0.108 | + + +(*) timing for the second invocation, which excludes JIT overhead. + + +We see that Numba, Cython, and Fortran are all quite close in +performance, with C++ contiguous only slightly slower, and all of +these much faster than the other implementations. It may be possible +to further optimize the numpy version, but it is so much easier to +just use Numba in this situation. diff --git a/content/12-extensions/extensions-overview.md b/content/12-extensions/extensions-overview.md new file mode 100644 index 00000000..376b510e --- /dev/null +++ b/content/12-extensions/extensions-overview.md @@ -0,0 +1,77 @@ +# Extensions + +Python code can be slow, so we sometimes turn to _extension modules_ to +get performance in critical parts of our algorithms There are a number +of ways to write extension modules in python -- these can be in +another language like C or Fortran or use a library that converts +python into compiled code (with some restrictions) like Cython or +Numba. + +We'll look at some examples of these and talk about their strengths +and weaknesses. + + +## Methods + +* C++ + + * [pybind11](https://github.com/pybind/pybind11) : this is a + header-only library that allows you to call C++ functions directly + from python. + + A related library is [nanobind](https://github.com/wjakob/nanobind), + which has similar syntax but may be more efficient. + +* C + + * [C-API](https://docs.python.org/3/c-api/index.html) : the + standard python interpreter (cpython) is written in C, so it is + natural that we can write C code to interact with our python code. + This is the python C-API. Since NumPy is also written in C, we + can work with NumPy arrays in C code as well. + + This will give us the performance of C compiled code, but the + downside is that we lose a lot of what makes python great. We + need to pass data into C as pointers and cast them into types that + represent the arrays we use. This means writing a lot of + boilerplate code just to deal with some simple operations. + + This underlies many of the techniques that we'll see here. + + ```{note} + These days, there are better methods for most applications, + and you should probably not use the C-API directly. + ``` + + * [ctypes](https://docs.python.org/3/library/ctypes.html) : this + is a module that allows you to call functions in shared libraries. + This is part of standard python. + + With ctypes, you don't need to modify your C code -- you just need to + define an interface to the C function in python. However, the calling + mechanism can be slow. + + There is support for NumPy through numpy.ctypeslib. + +* Fortran + + * [f2py](https://numpy.org/doc/stable/f2py/) : this is part of + NumPy. It allows for easy calling of Fortran from python. + + You essentially just need to add some comments to your Fortran + code to allow f2py to build an interface. f2py understands the + different orderings of indices between C and Fortran arrays. + +* python + + * [Cython](https://cython.org/) : this is a superset of python that can convert python into + compiled C code. + + The advantage here is that the code looks like python, with some + declarations of the variable types with `cdef`. Performance can be + really great when you need to explicitly write out loops over + NumPy array indices. + + * [Numba](https://numba.pydata.org/) : this is a just-in-time + compiler. It just requires a simple decorator and then it will + compile a python function the first time it is encountered. diff --git a/content/12-extensions/test.png b/content/12-extensions/test.png new file mode 100644 index 00000000..fcf011ff Binary files /dev/null and b/content/12-extensions/test.png differ diff --git a/content/CHANGES b/content/CHANGES new file mode 100644 index 00000000..66dc0cf4 --- /dev/null +++ b/content/CHANGES @@ -0,0 +1,8 @@ +-- make this S/U grading + +-- perhaps have BB "grade" participation on the forum? + + +debugging: + +memray: https://github.com/bloomberg/memray diff --git a/content/Introduction.md b/content/Introduction.md new file mode 100644 index 00000000..b6b5091c --- /dev/null +++ b/content/Introduction.md @@ -0,0 +1,55 @@ +# PHY 546: Python for Scientific Computing + +![xkcd](01-python/python.png) + +(from https://xkcd.com) + +## Why python? + +* Python is a very high-level language + + * it provides many complex data-structures (lists, dictionaries, ...) + + * your code is shorter than a comparable algorithm in a compiled language + +* Many powerful libraries to perform complex tasks + + * Parse structured inputs files + + * send e-mail + + * interact with the operating system + + * make plots + + * make GUIs + + * do scientific computations + + * ... + +* Python makes it easy to prototype new tools + +* Python is cross-platform and Free + +## Language Features + +Some of the language features are: + +* Dynamical typing + +* Object-oriented foundation + +* Extensible (easy to call Fortran, C/C++, ...) + +* Automatic memory management (garbage collection) + +* Ease of readability (whitespace matters) + + +## Scientific python + +Perhaps most importantly, and why we are here: + +> Python has been widely adopted in the scientific community. + diff --git a/lectures/NOTES b/content/NOTES similarity index 100% rename from lectures/NOTES rename to content/NOTES diff --git a/content/_config.yml b/content/_config.yml new file mode 100644 index 00000000..2c0567e0 --- /dev/null +++ b/content/_config.yml @@ -0,0 +1,57 @@ +# Book settings +# Learn more at https://jupyterbook.org/customize/config.html + +title: "PHY 546: Python for Scientific Computing" +author: Michael Zingale +#logo: logo.png +copyright: "2022" + +# Force re-execution of notebooks on each build. +# See https://jupyterbook.org/content/execute.html +execute: + execute_notebooks: force + allow_errors: true + +# Define the name of the latex output file for PDF builds +latex: + latex_documents: + targetname: book.tex + +# Information about where the book exists on the web +repository: + url: https://github.com/sbu-python-class/python-science + path_to_book: content # Optional path to your book, relative to the repository root + branch: main # Which branch of the repository should be used when creating links (optional) + +# Add GitHub buttons to your book +# See https://jupyterbook.org/customize/config.html#add-a-link-to-your-repository +html: + use_issues_button: true + use_repository_button: true + extra_footer: | +

+ © 2023-2025; CC-BY-NC-SA 4.0 +

+ +sphinx: + config: + html_show_copyright: false + nbsphinx_timeout: 300 + nb_execution_timeout: 300 + +launch_buttons: + binderhub_url: "https://mybinder.org" + colab_url: "https://colab.research.google.com" + +parse: + extensions: + - myst_parser + - sphinx_design + + myst_enable_extensions: + # don't forget to list any other extensions you want enabled, + # including those that are enabled by default! + - amsmath + - dollarmath + - linkify + - colon_fence diff --git a/content/_static/myfile.css b/content/_static/myfile.css new file mode 100644 index 00000000..aeeec947 --- /dev/null +++ b/content/_static/myfile.css @@ -0,0 +1,10 @@ +@import url('https://fonts.googleapis.com/css2?family=Lato:ital,wght@0,100;0,300;0,400;0,700;0,900;1,100;1,300;1,400;1,700;1,900&display=swap'); +@import url('https://fonts.googleapis.com/css2?family=Open+Sans:ital,wght@0,300;0,400;0,500;0,600;0,700;1,300;1,400;1,500;1,600;1,700&display=swap'); + +body { + font-family: "Open Sans", sans-serif; +} + +.heading-style, h1, h2, h3, h4, h5, h6 { + font-family: "Open Sans", sans-serif; +} diff --git a/content/_toc.yml b/content/_toc.yml new file mode 100644 index 00000000..6a8039a8 --- /dev/null +++ b/content/_toc.yml @@ -0,0 +1,97 @@ +format: jb-book +root: Introduction +parts: + - caption: Getting Started + chapters: + - file: 01-python/installing + - file: 01-python/using + - file: 01-python/w1-jupyter.ipynb + + - caption: Python Basics + chapters: + - file: 01-python/basics + sections: + - file: 01-python/w1-python-datatypes.ipynb + - file: 01-python/w2-python-advanced-datatypes.ipynb + - file: 01-python/w2-python-control-flow.ipynb + - file: 01-python/w2-python-exercises.ipynb + - file: 01-python/functions-classes + sections: + - file: 01-python/w3-python-functions.ipynb + - file: 01-python/w3-python-exercises.ipynb + - file: 01-python/w4-python-classes.ipynb + - file: 01-python/w4-python-modules.ipynb + - file: 01-python/w4-python-exercises.ipynb + - file: 01-python/misc + sections: + - file: 01-python/w3-python-exceptions.ipynb + - file: 01-python/python-io.ipynb + - file: 01-python/w5-python-more-examples.ipynb + + - caption: Arrays + chapters: + - file: 02-numpy/numpy + sections: + - file: 02-numpy/numpy-basics.ipynb + - file: 02-numpy/numpy-advanced.ipynb + - file: 02-numpy/numpy-exercises.ipynb + + - caption: Scientific Python + chapters: + - file: 04-matplotlib/matplotlib + sections: + - file: 04-matplotlib/matplotlib-basics.ipynb + - file: 04-matplotlib/matplotlib-exercises.ipynb + - file: 05-scipy/scipy + sections: + - file: 05-scipy/scipy-basics.ipynb + - file: 05-scipy/scipy-exercises.ipynb + - file: 05-scipy/scipy-basics-2.ipynb + - file: 05-scipy/scipy-exercises-2.ipynb + - file: 06-sympy/sympy + sections: + - file: 06-sympy/sympy-examples.ipynb + - file: 06-sympy/sympy-exercises.ipynb + + - caption: Machine Learning + chapters: + - file: 11-machine-learning/neural-net-basics + sections: + - file: 11-machine-learning/gradient-descent + - file: 11-machine-learning/neural-net-derivation + - file: 11-machine-learning/neural-net-hidden + sections: + - file: 11-machine-learning/neural-net-improvements + - file: 11-machine-learning/machine-learning-libraries + sections: + - file: 11-machine-learning/keras-mnist + - file: 11-machine-learning/keras-clustering + + - caption: Python packaging and applications + chapters: + - file: 09-packages/python-modules + - file: 09-packages/python-arguments + - file: 09-packages/python-more-modules + - file: 09-packages/python-packages + - file: 09-packages/python-tools + + - caption: Git and Github + chapters: + - file: git/version-control + - file: git/git + - file: git/github + - file: git/pull-requests + + - caption: Unit tests + chapters: + - file: 10-testing/testing + - file: 10-testing/pytest + sections: + - file: 10-testing/more-pytest + - file: 10-testing/real-world-example + + - caption: Extensions + chapters: + - file: 12-extensions/extensions-overview + - file: 12-extensions/extensions-example + diff --git a/content/git/distributed_version_control.png b/content/git/distributed_version_control.png new file mode 100644 index 00000000..347c19ad Binary files /dev/null and b/content/git/distributed_version_control.png differ diff --git a/content/git/git-branches.md b/content/git/git-branches.md new file mode 100644 index 00000000..c404318a --- /dev/null +++ b/content/git/git-branches.md @@ -0,0 +1,374 @@ +# Git Branches + +When we develop as a team, we often use *branches* to organize our +changes. Here we walk through an example of branches. + +To get more practice, we'll start a new project and initialize it. + +```{figure} https://imgs.xkcd.com/comics/git.png + :width: 75% + :align: center + :alt: xkcd comic on git + + from XKCD +``` + +1. Let's repeat the setup we did before... + + ```bash + mkdir project2 + cd project2 + echo "a second git project" > README + git init + ``` + +2. Now let's add our `README` to git and commit: + + ```bash + git add README + git commit + ``` + + (Remember to enter a log and save...) + +3. Let's create and add another file. + + We write a simple shell script. Open a new file, called `myscript`, e.g., with nano: + + ```bash + nano myscript + ``` + + and copy-paste the following content into it: + + ```bash + ls -l > script.out + ``` + + be sure to end with a new line. + + Now, this script is not that fancy and it needs to be run as: + + ```bash + bash ./myscript + ``` + + when you do this, you should see the output `script.out` created. + + Now let's tell git that we want it to track this: + + ```bash + git add myscript + git commit + ``` + + Be sure to add a useful message. + +4. Ignoring things. + + Let's look at the status of our project: + + ```bash + git status + ``` + + You'll see something like: + + ``` + On branch main + Untracked files: + (use "git add ..." to include in what will be committed) + + script.out + + nothing added to commit but untracked files present (use "git add" to track) + ``` + + It is telling us that it is not keeping track of `script.out`. + But we don't want it to—that is the output from running out + script, and generally we don't keep the output of our codes in + version control. + + So we'd like to tell git to ignore that file. The way to do this is to + create a `.gitignore` file: + + ```bash + nano .gitignore + ``` + + and add the following: + + ``` + *.out + ``` + + now if you do `git status`, that file will not appear, but `.gitignore` does! + + Be sure to add `.gitignore` to git by doing `git add` followed + by `git commit`. + + + +## A Feature Branch + +Now let's imagine that our project is mature and we don't want to break it as +we test out some new ideas. This is where *branches* come into play. + +Let's create a new branch called `feature` that we can work on without +disturbing our code in ``main``. + +```bash +git checkout -b feature +``` + +This creates a new branch called `feature` that is initially identical to `main`. + +You can tell what branch you are on by doing: + +```bash +git branch +``` + +and we see: + +``` +* feature + main +``` + +The `*` indicates which branch we are currently on. + +What about the log? + +```bash +git log +``` + +we see: + +``` +commit 69eb3bf482bd78c3bf63e890f52b9aac33d5ee2a (HEAD -> feature, main) +Author: Michael Zingale +Date: Tue Feb 1 10:21:19 2022 -0500 + + add an ignore file + +commit 9b0ae624393bd28f26f37d633d9692be3c2929f0 +Author: Michael Zingale +Date: Tue Feb 1 10:18:53 2022 -0500 + + add my first script + +commit 9625926dd4bc26e04d37988ffceaa7eba64a76da +Author: Michael Zingale +Date: Tue Feb 1 10:18:02 2022 -0500 + + start of our new project +``` + +Notice that the most recent commit line shows that both `feature` and `main` +are at the same hash, and it also calls that commit `HEAD`. +`HEAD` is the most recent change on the branch. + + +Now let's make a change. + +Let's put a "Hello, World" code in our repo! Create a file called +`hello.cpp` and add the following: + +```c++ +#include + +int main() { + + std::cout << "Hello, World!" << std::endl; + +} +``` + +Let's add it to git control: + +```bash +git add hello.cpp +git commit +``` + +Now look at the log: + +``` +Author: Michael Zingale +Date: Tue Feb 1 10:23:51 2022 -0500 + + add hello world + +commit 69eb3bf482bd78c3bf63e890f52b9aac33d5ee2a (main) +Author: Michael Zingale +Date: Tue Feb 1 10:21:19 2022 -0500 + + add an ignore file + +commit 9b0ae624393bd28f26f37d633d9692be3c2929f0 +Author: Michael Zingale +Date: Tue Feb 1 10:18:53 2022 -0500 + + add my first script + +commit 9625926dd4bc26e04d37988ffceaa7eba64a76da +Author: Michael Zingale +Date: Tue Feb 1 10:18:02 2022 -0500 + + start of our new project +``` + +Now it is clear that `main` is still on the last commit but +`feature` is on the latest (`HEAD`) commit. + + +Recall that we can compile our `hello.cpp` via: + +```bash +g++ -o hello hello.cpp +``` + +```{tip} +We don't want the executable `hello` to be under git control, so +add it to your `.gitignore` and commit that change. +``` + + +## Switching Branches + +Let's go back to `main`. The `checkout` command does this for us: + +```bash +git checkout main +``` + +Now notice that if you do `ls`, you don't see `hello.cpp`! That +file is in your `feature` branch, and under git control, and git +knows it is not on `main` so when you switch to main, it does not +appear. + +Let's add an `authors.txt` file to our project, just containing your name. + +```{admonition} Try it... +create an `authors.txt` and add it to git control. +``` + +Note that this is on `main`. If you switch to `feature` you won't see it: + +```bash +git checkout feature +``` + +````{tip} +Just like we can use ``cd -`` to switch to the previous directory we were on, +we can use + +```bash +git checkout - +``` +to switch back to the previous branch we were on -- in this case, `main` +```` + +Switch back to ``main``. + + +## Diff + +Let's look at the differences between our branches. Since we're on +`main`, we can ask git what the difference between our current code +and the code in `feature` is via: + +```bash +git diff feature +``` + +As you use git more and more, you'll see that `diff` is very handy. + + +## Merging + +Now we're happy with the changes we made on `feature` and we want to +incorporate them into `main`—this is called *merging*, we +accomplish this by doing + +```bash +git merge feature +``` + +This is a special type of commit, and your editor will pop up with a +merge commit already entered. Just save this, and it will be logged. + + +## Going back in time... + +If we look at our project history so far: + +```bash +git log +``` + +We see something like this (again, your hashes will be different) + +``` +commit 42596acdd432e1dbdc4f8abd668dffa30c707473 (HEAD -> main) +Merge: c8904ec bb38a3d +Author: Michael Zingale +Date: Tue Feb 1 10:54:51 2022 -0500 + + Merge branch 'feature' into main + +commit c8904ec0bd8ac1bc3449ec79ade971ee9902c14e +Author: Michael Zingale +Date: Tue Feb 1 10:31:03 2022 -0500 + + add authors + +commit bb38a3d1f3f4f2971ced93a1f203c52c276f37a5 (feature) +Author: Michael Zingale +Date: Tue Feb 1 10:27:09 2022 -0500 + + don't track executable + +commit 22e1d58cee38021da961516b24dde689d3b8a66e +Author: Michael Zingale +Date: Tue Feb 1 10:23:51 2022 -0500 + + add hello world + +commit 69eb3bf482bd78c3bf63e890f52b9aac33d5ee2a +Author: Michael Zingale +Date: Tue Feb 1 10:21:19 2022 -0500 + + add an ignore file + +commit 9b0ae624393bd28f26f37d633d9692be3c2929f0 +Author: Michael Zingale +Date: Tue Feb 1 10:18:53 2022 -0500 + + add my first script + +commit 9625926dd4bc26e04d37988ffceaa7eba64a76da +Author: Michael Zingale +Date: Tue Feb 1 10:18:02 2022 -0500 + + start of our new project +``` + +Imagine that our current code is not working, but we remember that it +was before we did our branching and added the `hello.cpp`. Looking +at the log or the graph shows that that change came in with the commit +`22e1d58cee38021da961516b24dde689d3b8a66e`. We can checkout the +state of the code before that commit by using the hash from the +previous commit: + +```bash +git checkout 69eb3bf482bd78c3bf63e890f52b9aac33d5ee2a +``` + +Note that you don't need to type out the entire hash—you only need the starting bits, +as long as it is unique. + +This command puts you in a detached branch, but you could make it a named branch by using +`git checkout -b name`. diff --git a/content/git/git-remotes.md b/content/git/git-remotes.md new file mode 100644 index 00000000..6b7971a2 --- /dev/null +++ b/content/git/git-remotes.md @@ -0,0 +1,110 @@ +# Git Remotes + +## Bare Repository + +So far, we've just been using our git repo for ourselves. + +Let's look back at the figure illustrating ways we can share with distributed version control: + +```{image} distributed_version_control.png +:align: center +``` + +When multiple developers are working on the same code together, it is +convenient to have a central repository that everyone can communicate +with. + +We use a special `bare` repository for this purpose. A bare repo +has all of the metadata for the project, but we don't work directly in +it. This way we avoid the risk of having unsaved changed in the repo +that other people are using to synchronize with. + +Let's create a bare repo from our `project2` project. From your home directory +(assuming that project2 is `~/project2/`, we do: + +```bash +git clone --bare project2 +``` + +Now we see a new directory `project2.git`. + + + +## A First Example of Collaboration + +Let's pretend we are a different user. Let's make a directory for our +pretend user and clone our project: + +```bash +cd ~ +mkdir newuser +cd newuser +git clone ~/project2.git +``` + +The `clone` command make a new git repo for our user called `project2/` + +If we do a `git log` in it, we'll see the whole history we had from +our earlier work. + +Now, this repo knows where it was cloned from, through a concept +called *remotes*. A remote is a repo (usually a bare repo) that we +communicate with the share our changes (a *push*) of get changes from +other users (a *pull*). We can see our remote by doing: + +```bash +git remote -v +``` + +We'll see something like: + +``` +origin /home/campus.stonybrook.edu/mzingale/project2.git (fetch) +origin /home/campus.stonybrook.edu/mzingale/project2.git (push) +``` + +Now's let's make a change + +```{admonition} try it... +add the new user's name to `authors.txt` and commit the change. +``` + +Now we can share our changes with our remote—the bare repo by doing a *push*. + +```bash +git push +``` + +This pushes our changes back to the bare repo. Now go back to our original repo: + +```bash +cd +cd project2 +``` + +We need to add a remote to this original repo (if you do `git +remote` it will show nothing). We'll add a remote called `origin`. + +```bash +git remote add origin ~/project2.git +``` + +Now, we can communicate with the bare repo and get the changes that +the other user made by doing a *pull*: + +```bash +git pull origin main +``` + +To make our life easier, we can tell git what remote branch to track: + +```bash +git branch --set-upstream-to=origin/main main +``` + +then we can do just + +```bash +git pull +``` + diff --git a/content/git/git.md b/content/git/git.md new file mode 100644 index 00000000..f47bed76 --- /dev/null +++ b/content/git/git.md @@ -0,0 +1,222 @@ +# A Git Walkthrough + +We'll do a walkthrough on git. + +```{note} +An alternate walkthrough is provided by the [Software +Carpentry](https://software-carpentry.org/) lesson [_Version Control +with Git_](https://swcarpentry.github.io/git-novice/index.html) and it +is highly suggested that you work through that on your own. +``` + +There are a few ways in which we can use git. We'll start by assuming +that we are the only developer on a project and learn the basics and +then we'll see how to share what we've done locally and remotely using +GitHub. + +```{important} +You should create a [GitHub account](https://github.com). Pick a +username that is professional and meaningful. +``` + +Let's start by setting up our git environment: + +```bash +git config --global user.name "name" +git config --global user.email "email" +git config --global core.editor "nano -w" +``` + +Replace `name` with your name and `email` with your email. This sets `nano` +as our default editor, but you can choose something else that you are comfortable +with (see https://swcarpentry.github.io/git-novice/02-setup.html). + +This information will be stored in a file called ``.gitconfig`` in your home directory. + + +Our goal here is to create a project (we'll call the directory +`project/`) and have git keep track of the files and changes to our +project. + +1. First create a project directory with some basic content: + + ```bash + mkdir project + cd project + echo "this is the start of my awesome new project" > README + ``` + +2. Now let's tell git that we want to track this directory. + + ```bash + git init + ``` + + If you do `ls` it will look like nothing has changed, but this + command created a `.git/` sub-directory in our project, which you + can see by doing: + + ```bash + ls -a + ``` + +3. At this point, we haven't told git about any of our files. To tell git + to track the file `README` we do: + + ```bash + git add README + git commit README + ``` + + ```{note} + When you `commit`, and editor window will pop up asking you to + make a commit message. This is where you describe the change so + "future you" or someone else can understand why the change was + made. + ``` + + The editor will be whatever your default is. + We can now ask git the state of our project with + + ```bash + git status + ``` + + You should see something like: + + ``` + On branch main + nothing to commit, working tree clean + ``` + + We can also see our log message: + + ```bash + git log + ``` + + The output will look like: + + ``` + commit 2001a0e996110926a576dcb5fc13fc8022864d0b (HEAD -> main) + Author: Michael Zingale + Date: Sun Jan 30 13:11:24 2022 -0500 + + my first change + ``` + + But should show your name, and the long string of numbers of + letters after `commit` on the first line will be different. We'll call + the string the `hash`. More on that later... + +4. Now let's modify the file + + Open the file with nano and add a second line of text: + + ```bash + nano README + ``` + + Here's my file: + + ```bash + cat README + ``` + + ``` + this is the start of my awesome new project + this is now under version control! + ``` + + What does git think about our changes? + + ```bash + git status + ``` + + you should see something like: + + ``` + On branch main + Changes not staged for commit: + (use "git add ..." to update what will be committed) + (use "git checkout -- ..." to discard changes in working directory) + + modified: README + + no changes added to commit (use "git add" and/or "git commit -a") + ``` + + This is telling you that you have local changes but you haven't yet told git to care about them. + + Let's `add` the changes: + + ```bash + git add README + ``` + + and now `git status` will show something like: + + ``` + On branch main + Changes to be committed: + (use "git reset HEAD ..." to unstage) + + modified: README + ``` + + ```{admonition} What is `add` really doing? + + Git has a concept call the *staging area*. When we ``add`` a + file, git puts the changes into the staging area. We can add + multiple changes via separate ``git add`` invocations, and git + will accumulate these in the staging area. + + Once we do `git commit`, git will record the all of the + changes that are staged into a "commit". + ``` + + To have git track these changes, we can now just do: + + ```bash + git commit + ``` + + Notice that we didn't specify the file here -- all the changes that + were staged were part of that commit. + + If we now do `git log`, we'll see that there is a second commit + in our project, and it has a different unique hash: + + ``` + commit 78b6925752e8388dddb3d65b6355bfeeb87b87a7 (HEAD -> main) + Author: Michael Zingale + Date: Sun Jan 30 14:23:09 2022 -0500 + + make some modifications + + commit 2001a0e996110926a576dcb5fc13fc8022864d0b + Author: Michael Zingale + Date: Sun Jan 30 13:11:24 2022 -0500 + + my first change + ``` + +This repo now captures the state of our project. Next we'll see how to use branches to +help our development process. + + +Summary +======= + +We learned: + +* `git init` + +* `git add` + +* `git commit` + +* `git status` + +* `git log` diff --git a/content/git/github-clone.png b/content/git/github-clone.png new file mode 100644 index 00000000..b67b29a2 Binary files /dev/null and b/content/git/github-clone.png differ diff --git a/content/git/github-copy-ssh.png b/content/git/github-copy-ssh.png new file mode 100644 index 00000000..7ef27d8e Binary files /dev/null and b/content/git/github-copy-ssh.png differ diff --git a/content/git/github-create.png b/content/git/github-create.png new file mode 100644 index 00000000..9be0a783 Binary files /dev/null and b/content/git/github-create.png differ diff --git a/content/git/github-fork.png b/content/git/github-fork.png new file mode 100644 index 00000000..119be9ff Binary files /dev/null and b/content/git/github-fork.png differ diff --git a/content/git/github-new.png b/content/git/github-new.png new file mode 100644 index 00000000..9f0712c3 Binary files /dev/null and b/content/git/github-new.png differ diff --git a/content/git/github-pr.png b/content/git/github-pr.png new file mode 100644 index 00000000..1541900e Binary files /dev/null and b/content/git/github-pr.png differ diff --git a/content/git/github-pr2.png b/content/git/github-pr2.png new file mode 100644 index 00000000..ce62d3d5 Binary files /dev/null and b/content/git/github-pr2.png differ diff --git a/content/git/github-workflow.odg b/content/git/github-workflow.odg new file mode 100644 index 00000000..120f9608 Binary files /dev/null and b/content/git/github-workflow.odg differ diff --git a/content/git/github-workflow.pdf b/content/git/github-workflow.pdf new file mode 100644 index 00000000..fdae4f22 Binary files /dev/null and b/content/git/github-workflow.pdf differ diff --git a/content/git/github-workflow.png b/content/git/github-workflow.png new file mode 100644 index 00000000..e2c7001d Binary files /dev/null and b/content/git/github-workflow.png differ diff --git a/content/git/github.md b/content/git/github.md new file mode 100644 index 00000000..527d157e --- /dev/null +++ b/content/git/github.md @@ -0,0 +1,194 @@ +# github + +Github provides a web-based way to interact with git repositories. At +its heart it hosts a bare repo that we can push-pull to/from, but it +also provides features to make it easier for users to request their +changes be incorporated. + + +## Creating a repository on github + +Let's start by creating a new git repository using github's web interface. Start +on your github home page and click on the "+" icon and select "New repository": + +```{image} github-new.png +:align: center +``` + +Now we give the repository a name. Let's use our initials, followed +by `_class_repo`, so for me, it will be `mz_class_repo`. + +Make sure that it defaults the repo to be public, which means anyone on the internet +can see the contents—that's what we want. + +Finally, check the box to add a `README` file—this means that our repository will +not be empty initially. + +```{image} github-create.png +:align: center +``` + +Our project is now found at: ``https://github.com/ [username]/ [reponame]``, +where *username* is your Github username and *reponame* is the name of +the repository you just created. + + +## SSH interlude + +Github works best is we communicate via [secure +shell](https://en.wikipedia.org/wiki/Secure_Shell) or *SSH*. + +There is some nice documentation describing key pairs in the Software +Carpentry [Create an SSH key pair](https://swcarpentry.github.io/git-novice/07-github.html#ssh-background-and-setup) +section. + +Here's how we will set things up: + +1. A the bash prompt generate a new key pair: + + ```bash + ssh-keygen -t ed25519 + ``` + + The `-t` option picks a secure encryption method. + + It will ask you for a passpharse—just hit "Enter" to keep it + empty (if other people had access to your account, the you would + want to pick a passphrase). + + If you do + + ```bash + ls -l ~/.ssh + ``` + + you'll see 2 files: `id_ed25519` and `id_ed25519.pub` this is + the private and public key for encryption. + + ```{caution} + Never share your private key (`id_ed25519`) with anyone. + + Our public key (`id_ed25519.pub`) is meant to be public, and + we can give it to places we want to communicate with, like github + ``` + +2. Go to you Github profile SSH keys settings: https://github.com/settings/keys + + Click on the *New SSH key* button and: + + * give a *title* which is descriptive of the machine you are using, like + ``MathLab`` + + * copy and paste the contents of `id_ed25519.pub` into the *key* + text box. You can see the contents by doing: + + ```bash + cat ~/.ssh/id_ed25519.pub + ``` + + * Click on ``Add SSH key`` + +3. Test things out: + + ```bash + ssh -T git@github.com + ``` + + It will ask you if we want to save the *fingerprint*—say "yes", and then + it should report: + + ``` + Hi zingale! You've successfully authenticated, but GitHub does + not provide shell access. + ``` + +That means everything is working. + + +## Working remotely + +Now we can git clone this repo. From the github project page, click on the +*code* button. + +```{image} github-clone.png +:align: center +``` + +Copy the string in the text box there and then on your command line clone +the repo as: + +```bash +git clone git@github.com:zingale/mz_class_repo.git +``` + +(replacing my repo and username with your own). + +Now we can go into our repo and look around. + +```bash +cd mz_class_repo +ls -al +``` + +Notice that there is a +`.git/` directory. Also look at the remotes: + +```bash +git remote -v +``` + +``` +origin git@github.com:zingale/mz_class_repo.git (fetch) +origin git@github.com:zingale/mz_class_repo.git (push) +``` + +This is just like the example or remotes we did previously, except now +github is acting as our remote. + +This means that we call push to github and pull from there. + +Let's add a `hello.py`: + +```python +#!/usr/bin/env python + +def main(): + print("hello, world") + +if __name__ == "__main__": + main() +``` + +```bash +git add hello.py +git commit +git push +``` + +Notice that the `git push` pushes to our remote: github. If you refresh +your browser page, you'll see that our file now appears on github. + +As a single user, this will allow you to develop from any computer +and keep the code base in sync across all of them. + +If the project has multiple developers, this can be where all of the +developers sync up their projects. + + +### `README.md` is special + +The web interface that github provides to our repo has a number of features. + +First, the `README.md` file is always displayed on the main project +page. This is where you can put descriptions of what your project is, +how people can contribute, even share the status of testing and +documentation builds (we'll talk about those later in class). + +This file is in github-flavored [Markdown +format](https://docs.github.com/en/get-started/writing-on-github/getting-started-with-writing-and-formatting-on-github/basic-writing-and-formatting-syntax) +(that's what the `.md` extension signifies). Markdown allows you to +do basic formatting. + +Here's an example of what you can do in a `README.md` from one of my +projects: https://github.com/pynucastro/pynucastro + diff --git a/content/git/pull-requests.md b/content/git/pull-requests.md new file mode 100644 index 00000000..21ddcbe1 --- /dev/null +++ b/content/git/pull-requests.md @@ -0,0 +1,130 @@ +# Pull requests + +Github allows you to give permissions to users to contribute to a +repository (read, write, or admin access). But the best type of workflow +is one where users don't push directly to the git repo. Instead it is based +around pulls. + +How do we contribute to a project that we don't own? + +Here's a github *organization* for our class: https://github.com/sbu-python-class + +and here's a simple repo in this organization: https://github.com/sbu-python-class/test_repo + +```{note} +An organization is meant to be used by a collection of developers who +can all have different access permissions. It provides tools for +managing who can do different things to the repos under its control. +``` + +Let's clone this repo: + +```bash +git clone git@github.com:sbu-python-class/test_repo.git +cd test_repo +``` + +Now, let's each try to add a file of the form *username.txt* containing +your full name. Ex: + +```bash +echo Michael Zingale > zingale.txt +git add zingale.txt +git commit +``` + +Now try to push it to the repo we clone: + +```bash +git push +``` + +what happened? + +The issue is that you don't have *write* permission to that repo, +since I own it. So you are denied access. + +This is okay. The workflow that github emphasizes is one based around +*pulls* not *pushes*, so let's see how we do that. + +First, we need to *fork* the repo -- this creates a clone under our +control that we can do with as we please. Click on the "fork" button. + +```{image} github-fork.png +:align: center +``` + +It may ask you where you want the fork to live—you want it to live +under your profile / username. + +This will bring you to a new github page, displaying the fork, with a +URL that should look something like: ``https://github.com/zingale/test_repo`` + +Now click on the *code* button and copy the SSH location. + +```{image} github-copy-ssh.png +:align: center +``` + +We want to add this fork as a new remote: + +```bash +git remote add myfork git@github.com:zingale/test_repo.git +``` + +(again, make sure you replace that with the link to your repo). + +Now you can do: + +```bash +git push myfork +``` + +If you reload your github page, you should see your change there. + +Now we can do all *pull-request*. Select "pull requests" + +```{image} github-pr.png +:align: center +``` + +Then click on the "New pull request" button, and you'll see something like: + +```{image} github-pr2.png +:align: center +``` + +This is showing that you are asking to merge the changes in your fork into the +class ``test_repo`` repository. + +Click on *create pull request*, type in a comment about what this does, and then click +on the *create pull request* button again. + +Now it is out of your hands. + +The owner of the class repo (me) will get a notification that you want +to incorporate your changes into the class repo, and I can merge them +via the github web tools. + + +The overall workflow that we did: fork, push to our fork, issue a PR, looks like: + +```{image} github-workflow.png +:align: center +:width: 80% +``` + + + +## Our class notes github + +Let's take a tour of our class notes on github: https://github.com/sbu-python-class/python-science + +There are a lot of other features that github provides that we can use to make our life easier, including: + +* github actions : automating some workflows (like testing) on our code + +* github pages : building and hosting web pages for our project + + + diff --git a/content/git/version-control.md b/content/git/version-control.md new file mode 100644 index 00000000..ecc99778 --- /dev/null +++ b/content/git/version-control.md @@ -0,0 +1,153 @@ +# Version Control + +````{note} +To follow along, you will need to install `git` on your computer. +You can follow the instructions from the [Software Carpentry lessons](https://carpentries.github.io/workshop-template/install_instructions/#git). In particular, for: + +* Windows: use [git for Windows](https://gitforwindows.org/) + +* Mac: in a teminal, do: + + ``` + git --version + ``` + + If it is not already installed, it will prompt you for installation. + +* Linux: it is probably already installed, but otherwise, use your + package manager. +```` + +## Why use version control? + +When we develop code, we are going to be making lots of changes over +time. And you will find yourself in the following situations: + +* *You swear that the code worked perfectly 6 months ago* but today it doesn't and + you can't figure out what changed. + +* *The code looks different than you remembered and you don't know why it changed*. + +* *Your research group is all working on the same code* and you need to sync up with + everyone's changes and make sure that no one breaks the code. + +This is what [version control](https://en.wikipedia.org/wiki/Version_control) does for us. + + +```{note} +Version control systems keep track of the history of changes to +source code and allow multiple developers to all work on the same code +base. +``` + +In particular: + +* Logs tell you what changes have been made to each file over time. + +* You can request the source as it was at any time in the past. + +* Multiple developers can all work on the same source code and share and synchronize changes. + + * Changes by different developers to the same file are merged. + + * If two developers changed the same part of a file, version control + provides mechanisms to resolve conflicts. + +* You can make a branch and work on new features without breaking the + current working code, and when you are ready, merge those changes + into the main version. + + +```{note} +Even for a single developer, version control is a great asset. + +Common task: you notice your code is giving different answers than you've +seen in the past. + +With version control, you can checkout an old copy when you know it +was working, and ask for the difference with the current code. +``` + +```{tip} +Version control is not just for source code. You can use it for +writing papers in LaTeX, course notes, etc. + +These course notes are in git, hosted on github here: +https://github.com/zingale/computational_astrophysics +``` + +## Centralized vs. distributed version control + +Broadly speaking, there are two different types of version control: +centralized and distributed. We'll call the collection of code under +version control the *repository*. + +### Centralized version control + +Examples: [CVS](https://en.wikipedia.org/wiki/Concurrent_Versions_System) , [subversion](https://en.wikipedia.org/wiki/Apache_Subversion) + +* A server holds the master copy of the source, stores the history, changes + +* Each user communicates with the server: + + * "checkout" source + * "commit" changes back to the source + * request the log (history) of a file from the server + * "diff" your local version with the version on the server + +This is the older style of version control, and not widely used for new projects. + + +### Distributed version control + +Examples: [git](https://en.wikipedia.org/wiki/Git), [mercurial](https://en.wikipedia.org/wiki/Mercurial) + +* Everyone has a full-fledged repository + +* Commits, history, diff, logs, etc. are all local operations + +* You can clone another person's repo and they can pull your changes + back to their version + +* Each copy is a backup of the whole history of the project + +* Easy to "fork" -- just clone and go. + +```{tip} +Any version control system is better than no version control. + +Git is the most popular right now, so we'll focus on that. +``` + +Consider the figure below: + +```{image} distributed_version_control.png +:align: center +``` + +We see: + +* You in the upper left box interacting with your local computer. + You can add changes to your repo and query the log, etc. all just + using your own machine. + +* Your colleague in the upper right. They can also interact with + their own computer, using their own version of the repo. + + Now, imagine that they make a change that you want. You can *pull* + their version of the code into your repo, getting all of their + changes. + +* Suppose you both want to efficiently share work as a group. So you + setup a group server and you can both synchronize your repo with + that server by doing *pull* and *push*. + + This server provides a mechanism for everyone in the group to stay + in sync. + +* Imagine now that you have an external collaborator who doesn't have + access to your server. 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91.6666666667%; + clear: none; + margin-left: 0; + } + + .\31 0u\28large\29, .\31 0u\24\28large\29 { + width: 83.3333333333%; + clear: none; + margin-left: 0; + } + + .\39 u\28large\29, .\39 u\24\28large\29 { + width: 75%; + clear: none; + margin-left: 0; + } + + .\38 u\28large\29, .\38 u\24\28large\29 { + width: 66.6666666667%; + clear: none; + margin-left: 0; + } + + .\37 u\28large\29, .\37 u\24\28large\29 { + width: 58.3333333333%; + clear: none; + margin-left: 0; + } + + .\36 u\28large\29, .\36 u\24\28large\29 { + width: 50%; + clear: none; + margin-left: 0; + } + + .\35 u\28large\29, .\35 u\24\28large\29 { + width: 41.6666666667%; + clear: none; + margin-left: 0; + } + + .\34 u\28large\29, .\34 u\24\28large\29 { + width: 33.3333333333%; + clear: none; + margin-left: 0; + } + + .\33 u\28large\29, .\33 u\24\28large\29 { + width: 25%; + clear: none; + margin-left: 0; + } + + .\32 u\28large\29, .\32 u\24\28large\29 { + width: 16.6666666667%; + clear: none; + margin-left: 0; + } + + 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padding: 0 0 0 0.375em; + } + + .row.\32 5\25 { + margin: 0 0 -1px -0.375em; + } + + .row.uniform.\32 5\25 > * { + padding: 0.375em 0 0 0.375em; + } + + .row.uniform.\32 5\25 { + margin: -0.375em 0 -1px -0.375em; + } + + .\31 2u\28medium\29, .\31 2u\24\28medium\29 { + width: 100%; + clear: none; + margin-left: 0; + } + + .\31 1u\28medium\29, .\31 1u\24\28medium\29 { + width: 91.6666666667%; + clear: none; + margin-left: 0; + } + + .\31 0u\28medium\29, .\31 0u\24\28medium\29 { + width: 83.3333333333%; + clear: none; + margin-left: 0; + } + + .\39 u\28medium\29, .\39 u\24\28medium\29 { + width: 75%; + clear: none; + margin-left: 0; + } + + .\38 u\28medium\29, .\38 u\24\28medium\29 { + width: 66.6666666667%; + clear: none; + margin-left: 0; + } + + .\37 u\28medium\29, .\37 u\24\28medium\29 { + width: 58.3333333333%; + clear: none; + margin-left: 0; + } + + .\36 u\28medium\29, .\36 u\24\28medium\29 { + width: 50%; + clear: none; + margin-left: 0; + } + + .\35 u\28medium\29, .\35 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+ } + + .\39 u\28small\29, .\39 u\24\28small\29 { + width: 75%; + clear: none; + margin-left: 0; + } + + .\38 u\28small\29, .\38 u\24\28small\29 { + width: 66.6666666667%; + clear: none; + margin-left: 0; + } + + .\37 u\28small\29, .\37 u\24\28small\29 { + width: 58.3333333333%; + clear: none; + margin-left: 0; + } + + .\36 u\28small\29, .\36 u\24\28small\29 { + width: 50%; + clear: none; + margin-left: 0; + } + + .\35 u\28small\29, .\35 u\24\28small\29 { + width: 41.6666666667%; + clear: none; + margin-left: 0; + } + + .\34 u\28small\29, .\34 u\24\28small\29 { + width: 33.3333333333%; + clear: none; + margin-left: 0; + } + + .\33 u\28small\29, .\33 u\24\28small\29 { + width: 25%; + clear: none; + margin-left: 0; + } + + .\32 u\28small\29, .\32 u\24\28small\29 { + width: 16.6666666667%; + clear: none; + margin-left: 0; + } + + .\31 u\28small\29, .\31 u\24\28small\29 { + width: 8.3333333333%; + clear: none; + margin-left: 0; + } + + .\31 2u\24\28small\29 + *, + .\31 1u\24\28small\29 + *, + .\31 0u\24\28small\29 + *, + .\39 u\24\28small\29 + *, + .\38 u\24\28small\29 + *, + .\37 u\24\28small\29 + *, + .\36 u\24\28small\29 + *, + .\35 u\24\28small\29 + *, + .\34 u\24\28small\29 + *, + .\33 u\24\28small\29 + *, + .\32 u\24\28small\29 + *, + .\31 u\24\28small\29 + * { + clear: left; + } + + .\-11u\28small\29 { + margin-left: 91.66667%; + } + + .\-10u\28small\29 { + margin-left: 83.33333%; + } + + .\-9u\28small\29 { + margin-left: 75%; + } + + .\-8u\28small\29 { + margin-left: 66.66667%; + } + + .\-7u\28small\29 { + margin-left: 58.33333%; + } + + .\-6u\28small\29 { + margin-left: 50%; + } + + .\-5u\28small\29 { + margin-left: 41.66667%; + } + + .\-4u\28small\29 { + margin-left: 33.33333%; + } + + .\-3u\28small\29 { + margin-left: 25%; + } + + .\-2u\28small\29 { + margin-left: 16.66667%; + } + + .\-1u\28small\29 { + margin-left: 8.33333%; + } + +} + +@media screen and (max-width: 480px) { + + .row > * { + padding: 0 0 0 1.25em; + } + + .row { + margin: 0 0 -1px -1.25em; 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width: 33.3333333333%; + clear: none; + margin-left: 0; + } + + .\33 u\28xsmall\29, .\33 u\24\28xsmall\29 { + width: 25%; + clear: none; + margin-left: 0; + } + + .\32 u\28xsmall\29, .\32 u\24\28xsmall\29 { + width: 16.6666666667%; + clear: none; + margin-left: 0; + } + + .\31 u\28xsmall\29, .\31 u\24\28xsmall\29 { + width: 8.3333333333%; + clear: none; + margin-left: 0; + } + + .\31 2u\24\28xsmall\29 + *, + .\31 1u\24\28xsmall\29 + *, + .\31 0u\24\28xsmall\29 + *, + .\39 u\24\28xsmall\29 + *, + .\38 u\24\28xsmall\29 + *, + .\37 u\24\28xsmall\29 + *, + .\36 u\24\28xsmall\29 + *, + .\35 u\24\28xsmall\29 + *, + .\34 u\24\28xsmall\29 + *, + .\33 u\24\28xsmall\29 + *, + .\32 u\24\28xsmall\29 + *, + .\31 u\24\28xsmall\29 + * { + clear: left; + } + + .\-11u\28xsmall\29 { + margin-left: 91.66667%; + } + + .\-10u\28xsmall\29 { + margin-left: 83.33333%; + } + + .\-9u\28xsmall\29 { + margin-left: 75%; + } + + .\-8u\28xsmall\29 { + margin-left: 66.66667%; + } + + .\-7u\28xsmall\29 { + margin-left: 58.33333%; + } + + .\-6u\28xsmall\29 { + margin-left: 50%; + } + + .\-5u\28xsmall\29 { + margin-left: 41.66667%; + } + + .\-4u\28xsmall\29 { + margin-left: 33.33333%; + } + + .\-3u\28xsmall\29 { + margin-left: 25%; + } + + .\-2u\28xsmall\29 { + margin-left: 16.66667%; + } + + .\-1u\28xsmall\29 { + margin-left: 8.33333%; + } + +} + +/* Basic */ + +@-ms-viewport { + width: device-width; +} + +body { + -ms-overflow-style: scrollbar; +} + +@media screen and (max-width: 480px) { + + html, body { + min-width: 320px; + } + +} + +body { + background: #fff; +} + +body.is-loading *, body.is-loading *:before, body.is-loading *:after { + -moz-animation: none !important; + -webkit-animation: none !important; + -ms-animation: none !important; + animation: none !important; + -moz-transition: none !important; + -webkit-transition: none !important; + -ms-transition: none !important; + transition: none !important; +} + +/* Type */ + +body { + background-color: #fff; + color: #777; +} + +body, input, select, textarea { + font-family: Arial, Helvetica, sans-serif; + font-size: 13pt; + font-weight: normal; + line-height: 2; +} + +@media screen and (max-width: 1680px) { + + body, input, select, textarea { + font-size: 13.5pt; + } + +} + +@media screen and (max-width: 1366px) { + + body, input, select, textarea { + font-size: 12.5pt; + } + +} + +@media screen and (max-width: 980px) { + + body, input, select, textarea { + font-size: 12pt; + } + +} + +@media screen and (max-width: 736px) { + + body, input, select, textarea { + font-size: 11.5pt; + } + +} + +@media screen and (max-width: 480px) { + + body, input, select, textarea { + font-size: 11.5pt; + } + +} + +a { + -moz-transition: color 0.2s ease; + -webkit-transition: color 0.2s ease; + -ms-transition: color 0.2s ease; + transition: color 0.2s ease; + text-decoration: underline; +} + +a:hover { + color: #00BC8A !important; + text-decoration: none; +} + +strong, b { + font-weight: bold; +} + +em, i { + font-style: italic; +} + +p { + margin: 0 0 2em 0; +} + +h1, h2, h3, h4, h5, h6 { + font-weight: bold; + line-height: 1.5; + margin: 0 0 1em 0; +} + +h1 a, h2 a, h3 a, h4 a, h5 a, h6 a { + color: inherit; + text-decoration: none; +} + +h2 { + font-size: 1.75em; +} + + +h3 { + font-size: 1.35em; +} + +h4 { + font-size: 1.1em; +} + +h5 { + font-size: 0.9em; +} + +h6 { + font-size: 0.7em; +} + +sub { + font-size: 0.8em; + position: relative; + top: 0.5em; +} + +sup { + font-size: 0.8em; + position: relative; + top: -0.5em; +} + +blockquote { + border-left: solid 4px; + font-style: italic; + margin: 0 0 2em 0; + padding: 0.5em 0 0.5em 2em; +} + +code { + border-radius: 0; + border: solid 1px; + font-family: "Courier New", monospace; + font-size: 0.9em; + margin: 0 0.25em; + padding: 0.25em 0.65em; +} + +pre { + -webkit-overflow-scrolling: touch; + font-family: "Courier New", monospace; + font-size: 0.9em; + margin: 0 0 2em 0; +} + +pre code { + display: block; + line-height: 1.75; + padding: 1em 1.5em; + overflow-x: auto; +} + +hr { + border: 0; + border-bottom: solid 1px; + margin: 2em 0; +} + +hr.major { + margin: 3em 0; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-right { + text-align: right; +} + +input, select, textarea { + color: #666; +} + +a { + color: #0089FF; +} + +strong, b { + color: #666; +} + +h1, h2, h3, h4, h5, h6 { + color: #666; +} + +blockquote { + border-left-color: rgba(144, 144, 144, 0.25); +} + +code { + background: rgba(144, 144, 144, 0.075); + border-color: rgba(144, 144, 144, 0.25); +} + +hr { + border-bottom-color: rgba(144, 144, 144, 0.25); +} + +/* Box */ + +.box { + border-radius: 0; + border: solid 1px; + margin-bottom: 2em; + padding: 1.5em; +} + +.box > :last-child, +.box > :last-child > :last-child, +.box > :last-child > :last-child > :last-child { + margin-bottom: 0; +} + +.box.alt { + border: 0; + border-radius: 0; + padding: 0; +} + +.box { + border-color: rgba(144, 144, 144, 0.25); +} + +/* Button */ + +input[type="submit"], +input[type="reset"], +input[type="button"], +button, +.button { + -moz-appearance: none; + -webkit-appearance: none; + -ms-appearance: none; + appearance: none; + -moz-transition: background-color 0.2s ease-in-out, color 0.2s ease-in-out; + -webkit-transition: background-color 0.2s ease-in-out, color 0.2s ease-in-out; + -ms-transition: background-color 0.2s ease-in-out, color 0.2s ease-in-out; + transition: background-color 0.2s ease-in-out, color 0.2s ease-in-out; + border-radius: 2em; + border: 0; + cursor: pointer; + display: inline-block; + font-size: 0.8em; + font-weight: bold; + height: 3.5em; + letter-spacing: 0.1em; + line-height: 3.65em; + padding: 0 3em; + text-align: center; + text-decoration: none; + text-transform: uppercase; + white-space: nowrap; +} + +input[type="submit"].icon, +input[type="reset"].icon, +input[type="button"].icon, +button.icon, +.button.icon { + padding-left: 1.35em; +} + +input[type="submit"].icon:before, +input[type="reset"].icon:before, +input[type="button"].icon:before, +button.icon:before, +.button.icon:before { + margin-right: 0.5em; +} + +input[type="submit"].fit, +input[type="reset"].fit, +input[type="button"].fit, +button.fit, +.button.fit { + display: block; + margin: 0 0 1em 0; + width: 100%; +} + +input[type="submit"].small, +input[type="reset"].small, +input[type="button"].small, +button.small, +.button.small { + font-size: 0.8em; +} + +input[type="submit"].big, +input[type="reset"].big, +input[type="button"].big, +button.big, +.button.big { + font-size: 1.35em; +} + +input[type="submit"].disabled, input[type="submit"]:disabled, +input[type="reset"].disabled, +input[type="reset"]:disabled, +input[type="button"].disabled, +input[type="button"]:disabled, +button.disabled, +button:disabled, +.button.disabled, +.button:disabled { + -moz-pointer-events: none; + -webkit-pointer-events: none; + -ms-pointer-events: none; + pointer-events: none; + opacity: 0.25; +} + +@media screen and (max-width: 480px) { + + input[type="submit"], + input[type="reset"], + input[type="button"], + button, + .button { + padding: 0; + } + +} + +input[type="submit"], +input[type="reset"], +input[type="button"], +button, +.button { + background-color: #fafafa; + color: #666 !important; +} + +input[type="submit"]:hover, +input[type="reset"]:hover, +input[type="button"]:hover, +button:hover, +.button:hover { + background-color: white; +} + +input[type="submit"]:active, +input[type="reset"]:active, +input[type="button"]:active, +button:active, +.button:active { + background-color: #ededed; +} + +input[type="submit"].alt, +input[type="reset"].alt, +input[type="button"].alt, +button.alt, +.button.alt { + background-color: transparent; + box-shadow: inset 0 0 0 2px rgba(144, 144, 144, 0.25); + color: #666 !important; +} + +input[type="submit"].alt:hover, +input[type="reset"].alt:hover, +input[type="button"].alt:hover, +button.alt:hover, +.button.alt:hover { + background-color: rgba(144, 144, 144, 0.075); +} + +input[type="submit"].alt:active, +input[type="reset"].alt:active, +input[type="button"].alt:active, +button.alt:active, +.button.alt:active { + background-color: rgba(144, 144, 144, 0.2); +} + +input[type="submit"].alt.icon:before, +input[type="reset"].alt.icon:before, +input[type="button"].alt.icon:before, +button.alt.icon:before, +.button.alt.icon:before { + color: #bbb; +} + +input[type="submit"].special, +input[type="reset"].special, +input[type="button"].special, +button.special, +.button.special { + background-color: #00BC8A; + color: #ffffff !important; +} + +input[type="submit"].special:hover, +input[type="reset"].special:hover, +input[type="button"].special:hover, +button.special:hover, +.button.special:hover { + background-color: #00d69d; +} + +input[type="submit"].special:active, +input[type="reset"].special:active, +input[type="button"].special:active, +button.special:active, +.button.special:active { + background-color: #00a377; +} + +/* Form */ + +form { + margin: 0 0 2em 0; +} + +label { + display: block; + font-size: 0.9em; + font-weight: bold; + margin: 0 0 1em 0; +} + +input[type="text"], +input[type="password"], +input[type="email"], +select, +textarea { + -moz-appearance: none; + -webkit-appearance: none; + -ms-appearance: none; + appearance: none; + border-radius: 0; + border: none; + border: solid 1px; + color: inherit; + display: block; + outline: 0; + padding: 0 1em; + text-decoration: none; + width: 100%; +} + +input[type="text"]:invalid, +input[type="password"]:invalid, +input[type="email"]:invalid, +select:invalid, +textarea:invalid { + box-shadow: none; +} + +.select-wrapper { + text-decoration: none; + display: block; + position: relative; +} + +.select-wrapper:before { + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + font-family: FontAwesome; + font-style: normal; + font-weight: normal; + text-transform: none !important; +} + +.select-wrapper:before { + content: '\f078'; + display: block; + height: 2.75em; + line-height: 2.75em; + pointer-events: none; + position: absolute; + right: 0; + text-align: center; + top: 0; + width: 2.75em; +} + +.select-wrapper select::-ms-expand { + display: none; +} + +input[type="text"], +input[type="password"], +input[type="email"], +select { + height: 2.75em; +} + +textarea { + padding: 0.75em 1em; +} + +input[type="checkbox"], +input[type="radio"] { + -moz-appearance: none; + -webkit-appearance: none; + -ms-appearance: none; + appearance: none; + display: block; + float: left; + margin-right: -2em; + opacity: 0; + width: 1em; + z-index: -1; +} + +input[type="checkbox"] + label, +input[type="radio"] + label { + text-decoration: none; + cursor: pointer; + display: inline-block; + font-size: 1em; + font-weight: normal; + padding-left: 2.4em; + padding-right: 0.75em; + position: relative; +} + +input[type="checkbox"] + label:before, +input[type="radio"] + label:before { + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + font-family: FontAwesome; + font-style: normal; + font-weight: normal; + text-transform: none !important; +} + +input[type="checkbox"] + label:before, +input[type="radio"] + label:before { + border-radius: 0; + border: solid 1px; + content: ''; + display: inline-block; + height: 1.65em; + left: 0; + line-height: 1.58125em; + position: absolute; + text-align: center; + top: 0; + width: 1.65em; +} + +input[type="checkbox"]:checked + label:before, +input[type="radio"]:checked + label:before { + content: '\f00c'; +} + +input[type="checkbox"] + label:before { + border-radius: 0; +} + +input[type="radio"] + label:before { + border-radius: 100%; +} + +::-webkit-input-placeholder { + opacity: 1.0; +} + +:-moz-placeholder { + opacity: 1.0; +} + +::-moz-placeholder { + opacity: 1.0; +} + +:-ms-input-placeholder { + opacity: 1.0; +} + +.formerize-placeholder { + opacity: 1.0; +} + +label { + color: #666; +} + +input[type="text"], +input[type="password"], +input[type="email"], +select, +textarea { + background: rgba(144, 144, 144, 0.075); + border-color: rgba(144, 144, 144, 0.25); +} + +input[type="text"]:focus, +input[type="password"]:focus, +input[type="email"]:focus, +select:focus, +textarea:focus { + border-color: #00BC8A; + box-shadow: 0 0 0 1px #00BC8A; +} + +.select-wrapper:before { + color: rgba(144, 144, 144, 0.25); +} + +input[type="checkbox"] + label, +input[type="radio"] + label { + color: #777; +} + +input[type="checkbox"] + label:before, +input[type="radio"] + label:before { + background: rgba(144, 144, 144, 0.075); + border-color: rgba(144, 144, 144, 0.25); +} + +input[type="checkbox"]:checked + label:before, +input[type="radio"]:checked + label:before { + background-color: #00BC8A; + border-color: #00BC8A; + color: #ffffff; +} + +input[type="checkbox"]:focus + label:before, +input[type="radio"]:focus + label:before { + border-color: #00BC8A; + box-shadow: 0 0 0 1px #00BC8A; +} + +::-webkit-input-placeholder { + color: #bbb !important; +} + +:-moz-placeholder { + color: #bbb !important; +} + +::-moz-placeholder { + color: #bbb !important; +} + +:-ms-input-placeholder { + color: #bbb !important; +} + +.formerize-placeholder { + color: #bbb !important; +} + +form.alt input[type="text"], +form.alt input[type="password"], +form.alt input[type="email"], +form.alt select, +form.alt textarea { + background-color: transparent; +} + +/* Icon */ + +.icon { + text-decoration: none; + border-bottom: none; + position: relative; +} + +.icon:before { + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + font-family: FontAwesome; + font-style: normal; + font-weight: normal; + text-transform: none !important; +} + +.icon > .label { + display: none; +} + +/* Image */ + +.image { + border-radius: 0; + border: 0; + display: inline-block; + position: relative; +} + +.image img { + border-radius: 0; + display: block; +} + +.image.left, .image.right { + max-width: 40%; +} + +.image.left img, .image.right img { + width: 100%; +} + +.image.left { + float: left; + margin: 0 1.5em 1em 0; + top: 0.25em; +} + +.image.right { + float: right; + margin: 0 0 1em 1.5em; + top: 0.25em; +} + +.image.fit { + display: block; + margin: 0 0 2em 0; + width: 100%; +} + +.image.fit img { + width: 100%; +} + +.image.main { + display: block; + margin: 0 0 3em 0; + width: 100%; +} + +.image.main img { + width: 100%; +} + +/* List */ + +ol { + list-style: decimal; + margin: 0 0 2em 0; + padding-left: 1.25em; +} + +ol li { + padding-left: 0.25em; +} + +ul { + list-style: disc; + margin: 0 0 2em 0; + padding-left: 1em; +} + +ul li { + padding-left: 0.5em; + padding-top: 0.5em; + line-height: 1.6; +} + +ul li ul li { + list-style: square; + padding-top: 0.0em; +} + +ul li ul { + margin-top: 0em; + margin-bottom: 0em; +} + +ul.special { + text-align: center; +} + +ul.alt { + list-style: none; + padding-left: 0; +} + +ul.alt li { + border-top: solid 1px; + padding: 0.5em 0; +} + +ul.alt li:first-child { + border-top: 0; + padding-top: 0; +} + +ul.checklist { + list-style: none; + padding-left: 0; +} + +ul.checklist li { + text-decoration: none; + margin-bottom: 1.5em; + padding-left: 0; +} + +ul.checklist li:before { + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + font-family: FontAwesome; + font-style: normal; + font-weight: normal; + text-transform: none !important; +} + +ul.checklist li:before { + content: '\f00c'; + margin-right: 0.75em; +} + +ul.icons { + cursor: default; + list-style: none; + padding-left: 0; +} + +ul.icons li { + display: inline-block; + padding: 0 1em 0 0; +} + +ul.icons li:last-child { + padding-right: 0; +} + +ul.icons li .icon:before { + font-size: 2em; +} + +ul.contact { + list-style: none; + padding: 0; +} + +ul.contact li { + text-decoration: none; + padding: 0.65em 0 0 2em; +} + +ul.contact li:before { + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + font-family: FontAwesome; + font-style: normal; + font-weight: normal; + text-transform: none !important; +} + +ul.contact li:before { + float: left; + margin-left: -2em; +} + +ul.contact li:first-child { + padding-top: 0; +} + +ul.contact li a { + color: inherit; + text-decoration: none; +} + +ul.actions { + cursor: default; + list-style: none; + padding-left: 0; +} + +form ul.actions { + margin-top: 2em; +} + +ul.actions li { + display: inline-block; + padding: 0 1em 0 0; + vertical-align: middle; +} + +ul.actions li:last-child { + padding-right: 0; +} + + +ul.actions.small li { + padding: 0 0.5em 0 0; +} + +ul.actions.vertical li { + display: block; + padding: 1em 0 0 0; +} + +ul.actions.vertical li:first-child { + padding-top: 0; +} + +ul.actions.vertical li > * { + margin-bottom: 0; +} + +ul.actions.vertical.small li { + padding: 0.5em 0 0 0; +} + +ul.actions.vertical.small li:first-child { + padding-top: 0; +} + +ul.actions.fit { + display: table; + margin-left: -1em; + padding: 0; + table-layout: fixed; + width: calc(100% + 1em); +} + +ul.actions.fit li { + display: table-cell; + padding: 0 0 0 1em; +} + +ul.actions.fit li > * { + margin-bottom: 0; +} + +ul.actions.fit.small { + margin-left: -0.5em; + width: calc(100% + 0.5em); +} + +ul.actions.fit.small li { + padding: 0 0 0 0.5em; +} + + + +ul.instructors { + cursor: default; + margin: 0; + margin-top: -1em; + padding: 0; + padding-left: 2em; +} + +ul.instructors li { + margin: 0; + padding: 0; +} + +ul.instructors li:last-child { + padding-right: 0; +} + + +@media screen and (max-width: 480px) { + + ul.actions { + margin: 0 0 2em 0; + } + + ul.actions li { + padding: 1em 0 0 0; + display: block; + text-align: center; + width: 100%; + } + + ul.actions li:first-child { + padding-top: 0; + } + + ul.actions li > * { + width: 100%; + margin: 0 !important; + } + + ul.actions li > *.icon:before { + margin-left: -2em; + } + + ul.actions.small li { + padding: 0.5em 0 0 0; + } + + ul.actions.small li:first-child { + padding-top: 0; + } + +} + +dl { + margin: 0 0 2em 0; +} + +dl dt { + display: block; + font-weight: bold; + margin: 0 0 1em 0; +} + +dl dd { + margin-left: 2em; +} + +ul.alt li { + border-top-color: rgba(144, 144, 144, 0.25); +} + +ul.checklist li:before { + color: #00BC8A; +} + +ul.contact li:before { + color: #00BC8A; +} + +/* Section/Article */ + +section.special, article.special { + text-align: center; +} + +header p { + position: relative; + margin: 0 0 1.5em 0; +} + +header h2 + p { + font-size: 1.25em; + margin-top: -1em; +} + +header h3 + p { + font-size: 1.1em; + margin-top: -0.8em; +} + +header h4 + p, +header h5 + p, +header h6 + p { + font-size: 0.9em; + margin-top: -0.6em; +} + +header p { + color: #bbb; +} + +/* Table */ + +.table-wrapper { + -webkit-overflow-scrolling: touch; + overflow-x: auto; +} + +table { + margin: 0 0 2em 0; + width: 100%; +} + +table tbody tr { + border: solid 1px; + border-left: 0; + border-right: 0; +} + +table td { + padding: 0.75em 0.75em; +} + +table th { + font-size: 0.9em; + font-weight: bold; + padding: 0 0.75em 0.75em 0.75em; + text-align: left; +} + +table thead { + border-bottom: solid 2px; +} + +table tfoot { + border-top: solid 2px; +} + +table.alt { + border-collapse: separate; +} + +table.alt tbody tr td { + border: solid 1px; + border-left-width: 0; + border-top-width: 0; +} + +table.alt tbody tr td:first-child { + border-left-width: 1px; +} + +table.alt tbody tr:first-child td { + border-top-width: 1px; +} + +table.alt thead { + border-bottom: 0; +} + +table.alt tfoot { + border-top: 0; +} + +table tbody tr { + border-color: rgba(144, 144, 144, 0.25); +} + +table tbody tr:nth-child(2n + 1) { + background-color: rgba(144, 144, 144, 0.075); +} + +table th { + color: #666; +} + +table thead { + border-bottom-color: rgba(144, 144, 144, 0.25); +} + +table tfoot { + border-top-color: rgba(144, 144, 144, 0.25); +} + +table.alt tbody tr td { + border-color: rgba(144, 144, 144, 0.25); +} + +/* Split */ + +.split { + display: -moz-flex; + display: -webkit-flex; + display: -ms-flex; + display: flex; + -moz-flex-wrap: wrap; + -webkit-flex-wrap: wrap; + -ms-flex-wrap: wrap; + flex-wrap: wrap; + padding-bottom: 2em; +} + +.split > * { + width: 50%; +} + +.split > *:nth-child(odd) { + padding-right: 3em; +} + +.split > *:nth-child(even) { + padding-left: 3em; + border-left: solid 2px; +} + +.split > * > :last-child, +.split > * > :last-child > :last-child, +.split > * > :last-child > :last-child > :last-child { + margin-bottom: 0; +} + +@media screen and (max-width: 980px) { + + .split > :nth-child(odd) { + padding-right: 2em; + } + + .split > :nth-child(even) { + padding-left: 2em; + } + +} + +@media screen and (max-width: 736px) { + + .split { + padding-bottom: 0; + } + + .split > * { + width: 100%; + margin-bottom: 2em; + } + + .split > *:nth-child(odd) { + padding-right: 0; + } + + .split > *:nth-child(even) { + border-left: none; + padding-left: 0; + } + +} + +.split > :nth-child(even) { + border-left-color: rgba(144, 144, 144, 0.25); +} + +/* Spotlight */ + +.spotlight { + display: -moz-flex; + display: -webkit-flex; + display: -ms-flex; + display: flex; + flex-wrap: wrap; + border-bottom: solid 2px; + margin-bottom: 3em; +} + + +.spotlight .content { + padding: 0.5em 3em 0.1em 3em; + padding-top: 0em; + margin: 0; + width: 100%; +} + +.spotlight .contentw { + padding: 2em 3em 0.1em 3em; + width: 100%; +} + +.spotlight .contentw h2 { + margin-bottom: 0.0em; +} + + + +@media screen and (max-width: 980px) { + + .spotlight .content { + padding: 0.5em 2em 0.1em 2em; + width: 95%; + } + + .spotlight .contentw { + padding: 1.5em 2em 0.1em 2em; + width: 100%; + } + +} + +@media screen and (max-width: 736px) { + + .spotlight { + display: block; + margin-bottom: 2em; + } + + + .spotlight .content { + padding: 0.5em 2em 0.1em 2em; + width: 100%; + } + + .spotlight .contentw { + padding: 1em 2em 0.1em 2em; + width: 100%; + } + +} + +@media screen and (max-width: 980px) { + + .spotlight .content { + padding: 0.5em 1.5em 0.1em 1.5em; + } + + .spotlight .contentw { + padding: 1em 1.5em 0.1em 1.5em; + } + +} + +.spotlight { + background-color: white; + border-bottom-color: rgba(144, 144, 144, 0.25); +} + +.spotlight .contentw { + background-color: #ebebeb; + margin-bottom: 1em; +} + +/* Wrapper */ + +.wrapper { + padding: 5em 0 3em 0; + position: relative; +} + +.wrapper > .inner { + margin-left: auto; + margin-right: auto; + width: 70em; + max-width: 100%; +} + +.wrapper.alt { + border-top: solid 2px; + border-top-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style1 { + background-color: #00BC8A; + color: #bfeee1; +} + +.wrapper.style1 input, .wrapper.style1 select, .wrapper.style1 textarea { + color: #ffffff; +} + +.wrapper.style1 a { + color: #ffffff; +} + +.wrapper.style1 strong, .wrapper.style1 b { + color: #ffffff; +} + +.wrapper.style1 h1, .wrapper.style1 h2, .wrapper.style1 h3, .wrapper.style1 h4, .wrapper.style1 h5, .wrapper.style1 h6 { + color: #ffffff; +} + +.wrapper.style1 blockquote { + border-left-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 code { + background: rgba(255, 255, 255, 0.075); + border-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 hr { + border-bottom-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 .box { + border-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 input[type="submit"], +.wrapper.style1 input[type="reset"], +.wrapper.style1 input[type="button"], +.wrapper.style1 button, +.wrapper.style1 .button { + background-color: #fafafa; + color: #666 !important; +} + +.wrapper.style1 input[type="submit"]:hover, +.wrapper.style1 input[type="reset"]:hover, +.wrapper.style1 input[type="button"]:hover, +.wrapper.style1 button:hover, +.wrapper.style1 .button:hover { + background-color: white; +} + +.wrapper.style1 input[type="submit"]:active, +.wrapper.style1 input[type="reset"]:active, +.wrapper.style1 input[type="button"]:active, +.wrapper.style1 button:active, +.wrapper.style1 .button:active { + background-color: #ededed; +} + +.wrapper.style1 input[type="submit"].alt, +.wrapper.style1 input[type="reset"].alt, +.wrapper.style1 input[type="button"].alt, +.wrapper.style1 button.alt, +.wrapper.style1 .button.alt { + background-color: transparent; + box-shadow: inset 0 0 0 2px rgba(255, 255, 255, 0.25); + color: #ffffff !important; +} + +.wrapper.style1 input[type="submit"].alt:hover, +.wrapper.style1 input[type="reset"].alt:hover, +.wrapper.style1 input[type="button"].alt:hover, +.wrapper.style1 button.alt:hover, +.wrapper.style1 .button.alt:hover { + background-color: rgba(255, 255, 255, 0.075); +} + +.wrapper.style1 input[type="submit"].alt:active, +.wrapper.style1 input[type="reset"].alt:active, +.wrapper.style1 input[type="button"].alt:active, +.wrapper.style1 button.alt:active, +.wrapper.style1 .button.alt:active { + background-color: rgba(255, 255, 255, 0.2); +} + +.wrapper.style1 input[type="submit"].alt.icon:before, +.wrapper.style1 input[type="reset"].alt.icon:before, +.wrapper.style1 input[type="button"].alt.icon:before, +.wrapper.style1 button.alt.icon:before, +.wrapper.style1 .button.alt.icon:before { + color: #99e4d0; +} + +.wrapper.style1 input[type="submit"].special, +.wrapper.style1 input[type="reset"].special, +.wrapper.style1 input[type="button"].special, +.wrapper.style1 button.special, +.wrapper.style1 .button.special { + background-color: #ffffff; + color: #00BC8A !important; +} + +.wrapper.style1 label { + color: #ffffff; +} + +.wrapper.style1 input[type="text"], +.wrapper.style1 input[type="password"], +.wrapper.style1 input[type="email"], +.wrapper.style1 select, +.wrapper.style1 textarea { + background: rgba(255, 255, 255, 0.075); + border-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 input[type="text"]:focus, +.wrapper.style1 input[type="password"]:focus, +.wrapper.style1 input[type="email"]:focus, +.wrapper.style1 select:focus, +.wrapper.style1 textarea:focus { + border-color: #ffffff; + box-shadow: 0 0 0 1px #ffffff; +} + +.wrapper.style1 .select-wrapper:before { + color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 input[type="checkbox"] + label, +.wrapper.style1 input[type="radio"] + label { + color: #bfeee1; +} + +.wrapper.style1 input[type="checkbox"] + label:before, +.wrapper.style1 input[type="radio"] + label:before { + background: rgba(255, 255, 255, 0.075); + border-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 input[type="checkbox"]:checked + label:before, +.wrapper.style1 input[type="radio"]:checked + label:before { + background-color: #ffffff; + border-color: #ffffff; + color: #00BC8A; +} + +.wrapper.style1 input[type="checkbox"]:focus + label:before, +.wrapper.style1 input[type="radio"]:focus + label:before { + border-color: #ffffff; + box-shadow: 0 0 0 1px #ffffff; +} + +.wrapper.style1 ::-webkit-input-placeholder { + color: #99e4d0 !important; +} + +.wrapper.style1 :-moz-placeholder { + color: #99e4d0 !important; +} + +.wrapper.style1 ::-moz-placeholder { + color: #99e4d0 !important; +} + +.wrapper.style1 :-ms-input-placeholder { + color: #99e4d0 !important; +} + +.wrapper.style1 .formerize-placeholder { + color: #99e4d0 !important; +} + +.wrapper.style1 form.alt input[type="text"], +.wrapper.style1 form.alt input[type="password"], +.wrapper.style1 form.alt input[type="email"], +.wrapper.style1 form.alt select, +.wrapper.style1 form.alt textarea { + background-color: transparent; +} + +.wrapper.style1 ul.alt li { + border-top-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 ul.checklist li:before { + color: #00BC8A; +} + +.wrapper.style1 ul.contact li:before { + color: #00BC8A; +} + +.wrapper.style1 header p { + color: #99e4d0; +} + +.wrapper.style1 table tbody tr { + border-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 table tbody tr:nth-child(2n + 1) { + background-color: rgba(255, 255, 255, 0.075); +} + +.wrapper.style1 table th { + color: #ffffff; +} + +.wrapper.style1 table thead { + border-bottom-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 table tfoot { + border-top-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 table.alt tbody tr td { + border-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 .split > :nth-child(even) { + border-left-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1 .spotlight { + background-color: #0affbe; + border-bottom-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style1.alt { + border-top-color: rgba(255, 255, 255, 0.25); +} + +.wrapper.style2 { + background-color: #fafafa; + color: #777; +} + +.wrapper.style2 input, .wrapper.style2 select, .wrapper.style2 textarea { + color: #666; +} + +.wrapper.style2 a { + color: #00BC8A; +} + +.wrapper.style2 strong, .wrapper.style2 b { + color: #666; +} + +.wrapper.style2 h1, .wrapper.style2 h2, .wrapper.style2 h3, .wrapper.style2 h4, .wrapper.style2 h5, .wrapper.style2 h6 { + color: #666; +} + +.wrapper.style2 blockquote { + border-left-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 code { + background: rgba(144, 144, 144, 0.075); + border-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 hr { + border-bottom-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 .box { + border-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 input[type="submit"], +.wrapper.style2 input[type="reset"], +.wrapper.style2 input[type="button"], +.wrapper.style2 button, +.wrapper.style2 .button { + background-color: #666; + color: #fafafa !important; +} + +.wrapper.style2 input[type="submit"].alt, +.wrapper.style2 input[type="reset"].alt, +.wrapper.style2 input[type="button"].alt, +.wrapper.style2 button.alt, +.wrapper.style2 .button.alt { + background-color: transparent; + box-shadow: inset 0 0 0 2px rgba(144, 144, 144, 0.25); + color: #666 !important; +} + +.wrapper.style2 input[type="submit"].alt:hover, +.wrapper.style2 input[type="reset"].alt:hover, +.wrapper.style2 input[type="button"].alt:hover, +.wrapper.style2 button.alt:hover, +.wrapper.style2 .button.alt:hover { + background-color: rgba(144, 144, 144, 0.075); +} + +.wrapper.style2 input[type="submit"].alt:active, +.wrapper.style2 input[type="reset"].alt:active, +.wrapper.style2 input[type="button"].alt:active, +.wrapper.style2 button.alt:active, +.wrapper.style2 .button.alt:active { + background-color: rgba(144, 144, 144, 0.2); +} + +.wrapper.style2 input[type="submit"].alt.icon:before, +.wrapper.style2 input[type="reset"].alt.icon:before, +.wrapper.style2 input[type="button"].alt.icon:before, +.wrapper.style2 button.alt.icon:before, +.wrapper.style2 .button.alt.icon:before { + color: #bbb; +} + +.wrapper.style2 input[type="submit"].special, +.wrapper.style2 input[type="reset"].special, +.wrapper.style2 input[type="button"].special, +.wrapper.style2 button.special, +.wrapper.style2 .button.special { + background-color: #00BC8A; + color: #ffffff !important; +} + +.wrapper.style2 input[type="submit"].special:hover, +.wrapper.style2 input[type="reset"].special:hover, +.wrapper.style2 input[type="button"].special:hover, +.wrapper.style2 button.special:hover, +.wrapper.style2 .button.special:hover { + background-color: #00d69d; +} + +.wrapper.style2 input[type="submit"].special:active, +.wrapper.style2 input[type="reset"].special:active, +.wrapper.style2 input[type="button"].special:active, +.wrapper.style2 button.special:active, +.wrapper.style2 .button.special:active { + background-color: #00a377; +} + +.wrapper.style2 label { + color: #666; +} + +.wrapper.style2 input[type="text"], +.wrapper.style2 input[type="password"], +.wrapper.style2 input[type="email"], +.wrapper.style2 select, +.wrapper.style2 textarea { + background: rgba(144, 144, 144, 0.075); + border-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 input[type="text"]:focus, +.wrapper.style2 input[type="password"]:focus, +.wrapper.style2 input[type="email"]:focus, +.wrapper.style2 select:focus, +.wrapper.style2 textarea:focus { + border-color: #00BC8A; + box-shadow: 0 0 0 1px #00BC8A; +} + +.wrapper.style2 .select-wrapper:before { + color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 input[type="checkbox"] + label, +.wrapper.style2 input[type="radio"] + label { + color: #777; +} + +.wrapper.style2 input[type="checkbox"] + label:before, +.wrapper.style2 input[type="radio"] + label:before { + background: rgba(144, 144, 144, 0.075); + border-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 input[type="checkbox"]:checked + label:before, +.wrapper.style2 input[type="radio"]:checked + label:before { + background-color: #00BC8A; + border-color: #00BC8A; + color: #ffffff; +} + +.wrapper.style2 input[type="checkbox"]:focus + label:before, +.wrapper.style2 input[type="radio"]:focus + label:before { + border-color: #00BC8A; + box-shadow: 0 0 0 1px #00BC8A; +} + +.wrapper.style2 ::-webkit-input-placeholder { + color: #bbb !important; +} + +.wrapper.style2 :-moz-placeholder { + color: #bbb !important; +} + +.wrapper.style2 ::-moz-placeholder { + color: #bbb !important; +} + +.wrapper.style2 :-ms-input-placeholder { + color: #bbb !important; +} + +.wrapper.style2 .formerize-placeholder { + color: #bbb !important; +} + +.wrapper.style2 form.alt input[type="text"], +.wrapper.style2 form.alt input[type="password"], +.wrapper.style2 form.alt input[type="email"], +.wrapper.style2 form.alt select, +.wrapper.style2 form.alt textarea { + background-color: transparent; +} + +.wrapper.style2 ul.alt li { + border-top-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 ul.checklist li:before { + color: #00BC8A; +} + +.wrapper.style2 ul.contact li:before { + color: #00BC8A; +} + +.wrapper.style2 header p { + color: #bbb; +} + +.wrapper.style2 table tbody tr { + border-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 table tbody tr:nth-child(2n + 1) { + background-color: rgba(144, 144, 144, 0.075); +} + +.wrapper.style2 table th { + color: #666; +} + +.wrapper.style2 table thead { + border-bottom-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 table tfoot { + border-top-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 table.alt tbody tr td { + border-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 .split > :nth-child(even) { + border-left-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2 .spotlight { + background-color: white; + border-bottom-color: rgba(144, 144, 144, 0.25); +} + +.wrapper.style2.alt { + border-top-color: rgba(144, 144, 144, 0.25); +} + +@media screen and (max-width: 1366px) { + + .wrapper { + padding: 4em 2.5em 2em 2.5em; + } + +} + +@media screen and (max-width: 980px) { + + .wrapper { + padding: 4em 2em 2em 2em; + } + +} + +@media screen and (max-width: 736px) { + + .wrapper { + padding: 3em 2em 1em 2em; + } + +} + +@media screen and (max-width: 480px) { + + .wrapper { + padding: 3em 2em 1em 2em; + } + +} + +/* Banner */ + +#banner { + background-image: url("images/0101_banner.png"), -moz-linear-gradient(45deg, #4A4771 0%, #7C3875 100%); + background-image: url("images/0101_banner.png"), -webkit-linear-gradient(45deg, #4A4771 0%, #7C3875 100%); + background-image: url("images/0101_banner.png"), -ms-linear-gradient(45deg, #4A4771 0%, #7C3875 100%); + background-image: url("images/0101_banner.png"), linear-gradient(45deg, #4A4771 0%, #7C3875 100%); + background-size: cover; + background-position: center; + color: rgba(255, 255, 255, 0.7); + padding: 14em 0 4em; +} + +#banner h2 { + font-size: 2.5em; + line-height: 1.3; + margin-bottom: 0; + color: #fff; +} + +#banner h3 { + font-size: 1.5em; + line-height: 1.2; + margin-bottom: 0; + color: #eee; +} + +#banner p { + font-size: 1.15em; + font-weight: bold; + line-height: 1.5em; + margin-bottom: 1.5em; +} + +#banner > .inner { + margin-left: auto; + margin-right: auto; + max-width: 70em; + width: 100%; +} + + +#banner a { + color: #ffffff; +} + +@media screen and (max-width: 1366px) { + + #banner { + padding: 10em 2.5em 3em; + } + + #banner h2 { + font-size: 2em; + } + +} + +@media screen and (max-width: 980px) { + + #banner { + padding: 10em 2em 2em; + } + +} + +@media screen and (max-width: 736px) { + + #banner { + padding: 8em 2em 2em; + } + + #banner h2 { + font-size: 1.75em; + } + + #banner p { + font-size: 1.1em; + } + +} + +@media screen and (max-width: 480px) { + + #banner { + padding: 8em 2em 2em; + } + +} + +/* Main */ + +#main { + padding: 4em 0 2em 0; +} + +@media screen and (max-width: 736px) { + + #main { + padding: 3em 0 1em 0; + } + +} + +/* Footer */ + +#footer { + background-color: #fafafa; + border-top: solid 2px rgba(144, 144, 144, 0.25); + color: #777; +} + +#footer .copyright { + color: #bbb; + font-size: 0.9em; + padding: 4em 2em; + text-align: right; +} + +#footer .image { + color: #bbb; + font-size: 0.9em; + padding: 1em 1em; + text-align: left; +} + +#footer .image.left { + float: left; + margin: 0 1.5em 1em 0; + top: 0.25em; +} + +#footer .copyright li { + border-left: solid 1px rgba(144, 144, 144, 0.25); + display: inline-block; + list-style: none; + margin-left: 1.5em; + padding-left: 1.5em; +} + +#footer .copyright li:first-child { + border-left: 0; + margin-left: 0; + padding-left: 0; +} + +#footer a { + color: inherit; + text-decoration: none; +} + +@media screen and (max-width: 980px) { + + #footer .copyright { + padding: 3em 2em; + } + +} + +@media screen and (max-width: 736px) { + + #footer .copyright li { + display: block; + border-left: 0; + margin-left: 0; + padding-left: 0; + } + +} + +@media screen and (max-width: 480px) { + + #footer .copyright { + padding: 2em 1em; + } + +} + + + +label { + text-align: right; + float: right; +} + +label:hover { text-decoration:underline } +input { + position: absolute; + left: -999em +} +.hide { + width: 100%; + min-height: 0em; + max-height: 120em; + opacity: 1; + height: auto; + overflow: hidden; + transition: opacity 0.25s linear, max-height 0.25s linear; +} + +input[type=checkbox]:checked + div { + opacity:0; + max-height:0; + border:none; +} + +.follow{border-top: 1px solid blue; margin: 0} + 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