utilities.txt

=============
Miscellaneous
=============

.. _how-to-plot:

Plotting Samples and Filters
++++++++++++++++++++++++++++

.. note::
    The code for this section is available for download `here`_.

.. _here: http://deeplearning.net/tutorial/code/utils.py


To plot a sample, what we need to do is to take the visible units, which
are a flattened image (there is no 2D structure to the visible units,
just a 1D string of unit activations) and reshape it into a 2D image. The order in
which the points from the 1D array go into the 2D image is given by the
order in which the inital MNIST images where converted into a 1D array.
Lucky for us this is just a call of the ``numpy.reshape`` function.

Plotting the weights is a bit more tricky. We have ``n_hidden`` hidden
units, each of them corresponding to a column of the weight matrix. A
column has the same shape as the visible, where the weight corresponding
to the connection with visible unit `j` is at position `j`. Therefore,
if we reshape every such column, using ``numpy.reshape``, we get a
filter image that tells us how this hidden unit is influenced by
the input image.

We need a utility function that takes a minibatch, or the weight matrix,
and converts each row ( for the weight matrix we do a transpose ) into a
2D image and then tile these images together.  Once we converted the
minibatch or the weights in this image of tiles, we can use PIL to plot
and save. `PIL <http://www.pythonware.com/products/pil/>`_ is a standard
python libarary to deal with images.

Tiling minibatches together is done for us by the
``tile_raster_image`` function which we provide here.

.. code-block:: python


  def scale_to_unit_interval(ndar, eps=1e-8):
    """ Scales all values in the ndarray ndar to be between 0 and 1 """
    ndar = ndar.copy()
    ndar -= ndar.min()
    ndar *= 1.0 / (ndar.max() + eps)
    return ndar


  def tile_raster_images(X, img_shape, tile_shape, tile_spacing=(0, 0),
                         scale_rows_to_unit_interval=True,
                         output_pixel_vals=True):
    """
    Transform an array with one flattened image per row, into an array in
    which images are reshaped and layed out like tiles on a floor.

    This function is useful for visualizing datasets whose rows are images,
    and also columns of matrices for transforming those rows
    (such as the first layer of a neural net).

    :type X: a 2-D ndarray or a tuple of 4 channels, elements of which can
    be 2-D ndarrays or None;
    :param X: a 2-D array in which every row is a flattened image.

    :type img_shape: tuple; (height, width)
    :param img_shape: the original shape of each image

    :type tile_shape: tuple; (rows, cols)
    :param tile_shape: the number of images to tile (rows, cols)

    :param output_pixel_vals: if output should be pixel values (i.e. int8
    values) or floats

    :param scale_rows_to_unit_interval: if the values need to be scaled before
    being plotted to [0,1] or not


    :returns: array suitable for viewing as an image.
    (See:`Image.fromarray`.)
    :rtype: a 2-d array with same dtype as X.

    """

    assert len(img_shape) == 2
    assert len(tile_shape) == 2
    assert len(tile_spacing) == 2

    # The expression below can be re-written in a more C style as
    # follows :
    #
    # out_shape = [0,0]
    # out_shape[0] = (img_shape[0] + tile_spacing[0]) * tile_shape[0] -
    #                tile_spacing[0]
    # out_shape[1] = (img_shape[1] + tile_spacing[1]) * tile_shape[1] -
    #                tile_spacing[1]
    out_shape = [(ishp + tsp) * tshp - tsp for ishp, tshp, tsp
                        in zip(img_shape, tile_shape, tile_spacing)]

    if isinstance(X, tuple):
        assert len(X) == 4
        # Create an output numpy ndarray to store the image
        if output_pixel_vals:
            out_array = numpy.zeros((out_shape[0], out_shape[1], 4), dtype='uint8')
        else:
            out_array = numpy.zeros((out_shape[0], out_shape[1], 4), dtype=X.dtype)

        #colors default to 0, alpha defaults to 1 (opaque)
        if output_pixel_vals:
            channel_defaults = [0, 0, 0, 255]
        else:
            channel_defaults = [0., 0., 0., 1.]

        for i in range(4):
            if X[i] is None:
                # if channel is None, fill it with zeros of the correct
                # dtype
                out_array[:, :, i] = numpy.zeros(out_shape,
                        dtype='uint8' if output_pixel_vals else out_array.dtype
                        ) + channel_defaults[i]
            else:
                # use a recurrent call to compute the channel and store it
                # in the output
                out_array[:, :, i] = tile_raster_images(X[i], img_shape, tile_shape, tile_spacing, scale_rows_to_unit_interval, output_pixel_vals)
        return out_array

    else:
        # if we are dealing with only one channel
        H, W = img_shape
        Hs, Ws = tile_spacing

        # generate a matrix to store the output
        out_array = numpy.zeros(out_shape, dtype='uint8' if output_pixel_vals else X.dtype)


        for tile_row in range(tile_shape[0]):
            for tile_col in range(tile_shape[1]):
                if tile_row * tile_shape[1] + tile_col < X.shape[0]:
                    if scale_rows_to_unit_interval:
                        # if we should scale values to be between 0 and 1
                        # do this by calling the `scale_to_unit_interval`
                        # function
                        this_img = scale_to_unit_interval(X[tile_row * tile_shape[1] + tile_col].reshape(img_shape))
                    else:
                        this_img = X[tile_row * tile_shape[1] + tile_col].reshape(img_shape)
                    # add the slice to the corresponding position in the
                    # output array
                    out_array[
                        tile_row * (H+Hs): tile_row * (H + Hs) + H,
                        tile_col * (W+Ws): tile_col * (W + Ws) + W
                        ] \
                        = this_img * (255 if output_pixel_vals else 1)
        return out_array