fnn

import numpy as np

try:

from cs231n.im2col_cython import col2im_cython, im2col_cython

from cs231n.im2col_cython import col2im_6d_cython

except ImportError:

print 'run the following from the cs231n directory and try again:'

print 'python setup.py build_ext --inplace'

print 'You may also need to restart your iPython kernel'

from cs231n.im2col import *

def conv_forward_im2col(x, w, b, conv_param):

"""

A fast implementation of the forward pass for a convolutional layer

based on im2col and col2im.

"""

N, C, H, W = x.shape

num_filters, _, filter_height, filter_width = w.shape

stride, pad = conv_param['stride'], conv_param['pad']

# Check dimensions

assert (W + 2 * pad - filter_width) % stride == 0, 'width does not work'

assert (H + 2 * pad - filter_height) % stride == 0, 'height does not work'

# Create output

out_height = (H + 2 * pad - filter_height) / stride + 1

out_width = (W + 2 * pad - filter_width) / stride + 1

out = np.zeros((N, num_filters, out_height, out_width), dtype=x.dtype)

# x_cols = im2col_indices(x, w.shape[2], w.shape[3], pad, stride)

x_cols = im2col_cython(x, w.shape[2], w.shape[3], pad, stride)

res = w.reshape((w.shape[0], -1)).dot(x_cols) + b.reshape(-1, 1)

out = res.reshape(w.shape[0], out.shape[2], out.shape[3], x.shape[0])

out = out.transpose(3, 0, 1, 2)

cache = (x, w, b, conv_param, x_cols)

return out, cache

def conv_forward_strides(x, w, b, conv_param):

N, C, H, W = x.shape

F, _, HH, WW = w.shape

stride, pad = conv_param['stride'], conv_param['pad']

# Check dimensions

assert (W + 2 * pad - WW) % stride == 0, 'width does not work'

assert (H + 2 * pad - HH) % stride == 0, 'height does not work'

# Pad the input

p = pad

x_padded = np.pad(x, ((0, 0), (0, 0), (p, p), (p, p)), mode='constant')

# Figure out output dimensions

H += 2 * pad

W += 2 * pad

out_h = (H - HH) / stride + 1

out_w = (W - WW) / stride + 1

# Perform an im2col operation by picking clever strides

shape = (C, HH, WW, N, out_h, out_w)

strides = (H * W, W, 1, C * H * W, stride * W, stride)

strides = x.itemsize * np.array(strides)

x_stride = np.lib.stride_tricks.as_strided(x_padded,

shape=shape, strides=strides)

x_cols = np.ascontiguousarray(x_stride)

x_cols.shape = (C * HH * WW, N * out_h * out_w)

# Now all our convolutions are a big matrix multiply

res = w.reshape(F, -1).dot(x_cols) + b.reshape(-1, 1)

# Reshape the output

res.shape = (F, N, out_h, out_w)

out = res.transpose(1, 0, 2, 3)

# Be nice and return a contiguous array

# The old version of conv_forward_fast doesn't do this, so for a fair

# comparison we won't either

out = np.ascontiguousarray(out)

cache = (x, w, b, conv_param, x_cols)

return out, cache

def conv_backward_strides(dout, cache):

x, w, b, conv_param, x_cols = cache

stride, pad = conv_param['stride'], conv_param['pad']

N, C, H, W = x.shape

F, _, HH, WW = w.shape

_, _, out_h, out_w = dout.shape

db = np.sum(dout, axis=(0, 2, 3))

dout_reshaped = dout.transpose(1, 0, 2, 3).reshape(F, -1)

dw = dout_reshaped.dot(x_cols.T).reshape(w.shape)

dx_cols = w.reshape(F, -1).T.dot(dout_reshaped)

dx_cols.shape = (C, HH, WW, N, out_h, out_w)

dx = col2im_6d_cython(dx_cols, N, C, H, W, HH, WW, pad, stride)

return dx, dw, db

def conv_backward_im2col(dout, cache):

"""

A fast implementation of the backward pass for a convolutional layer

based on im2col and col2im.

"""

x, w, b, conv_param, x_cols = cache

stride, pad = conv_param['stride'], conv_param['pad']

db = np.sum(dout, axis=(0, 2, 3))

num_filters, _, filter_height, filter_width = w.shape

dout_reshaped = dout.transpose(1, 2, 3, 0).reshape(num_filters, -1)

dw = dout_reshaped.dot(x_cols.T).reshape(w.shape)

dx_cols = w.reshape(num_filters, -1).T.dot(dout_reshaped)

# dx = col2im_indices(dx_cols, x.shape, filter_height, filter_width, pad, stride)

dx = col2im_cython(dx_cols, x.shape[0], x.shape[1], x.shape[2], x.shape[3],

filter_height, filter_width, pad, stride)

return dx, dw, db

conv_forward_fast = conv_forward_strides

conv_backward_fast = conv_backward_strides

def max_pool_forward_fast(x, pool_param):

"""

A fast implementation of the forward pass for a max pooling layer.

This chooses between the reshape method and the im2col method. If the pooling

regions are square and tile the input image, then we can use the reshape

method which is very fast. Otherwise we fall back on the im2col method, which

is not much faster than the naive method.

"""

N, C, H, W = x.shape

pool_height, pool_width = pool_param['pool_height'], pool_param['pool_width']

stride = pool_param['stride']

same_size = pool_height == pool_width == stride

tiles = H % pool_height == 0 and W % pool_width == 0

if same_size and tiles:

out, reshape_cache = max_pool_forward_reshape(x, pool_param)

cache = ('reshape', reshape_cache)

else:

out, im2col_cache = max_pool_forward_im2col(x, pool_param)

cache = ('im2col', im2col_cache)

return out, cache

def max_pool_backward_fast(dout, cache):

"""

A fast implementation of the backward pass for a max pooling layer.

This switches between the reshape method an the im2col method depending on

which method was used to generate the cache.

"""

method, real_cache = cache

if method == 'reshape':

return max_pool_backward_reshape(dout, real_cache)

elif method == 'im2col':

return max_pool_backward_im2col(dout, real_cache)

else:

raise ValueError('Unrecognized method "%s"' % method)

def max_pool_forward_reshape(x, pool_param):

"""

A fast implementation of the forward pass for the max pooling layer that uses

some clever reshaping.

This can only be used for square pooling regions that tile the input.

"""

N, C, H, W = x.shape

pool_height, pool_width = pool_param['pool_height'], pool_param['pool_width']

stride = pool_param['stride']

assert pool_height == pool_width == stride, 'Invalid pool params'

assert H % pool_height == 0

assert W % pool_height == 0

x_reshaped = x.reshape(N, C, H / pool_height, pool_height,

W / pool_width, pool_width)

out = x_reshaped.max(axis=3).max(axis=4)

cache = (x, x_reshaped, out)

return out, cache

def max_pool_backward_reshape(dout, cache):

"""

A fast implementation of the backward pass for the max pooling layer that

uses some clever broadcasting and reshaping.

This can only be used if the forward pass was computed using

max_pool_forward_reshape.

NOTE: If there are multiple argmaxes, this method will assign gradient to

ALL argmax elements of the input rather than picking one. In this case the

gradient will actually be incorrect. However this is unlikely to occur in

practice, so it shouldn't matter much. One possible solution is to split the

upstream gradient equally among all argmax elements; this should result in a

valid subgradient. You can make this happen by uncommenting the line below;

however this results in a significant performance penalty (about 40% slower)

and is unlikely to matter in practice so we don't do it.

"""

x, x_reshaped, out = cache

dx_reshaped = np.zeros_like(x_reshaped)

out_newaxis = out[:, :, :, np.newaxis, :, np.newaxis]

mask = (x_reshaped == out_newaxis)

dout_newaxis = dout[:, :, :, np.newaxis, :, np.newaxis]

dout_broadcast, _ = np.broadcast_arrays(dout_newaxis, dx_reshaped)

dx_reshaped[mask] = dout_broadcast[mask]

dx_reshaped /= np.sum(mask, axis=(3, 5), keepdims=True)

dx = dx_reshaped.reshape(x.shape)

return dx

def max_pool_forward_im2col(x, pool_param):

"""

An implementation of the forward pass for max pooling based on im2col.

This isn't much faster than the naive version, so it should be avoided if

possible.

"""

N, C, H, W = x.shape

pool_height, pool_width = pool_param['pool_height'], pool_param['pool_width']

stride = pool_param['stride']

assert (H - pool_height) % stride == 0, 'Invalid height'

assert (W - pool_width) % stride == 0, 'Invalid width'

out_height = (H - pool_height) / stride + 1

out_width = (W - pool_width) / stride + 1

x_split = x.reshape(N * C, 1, H, W)

x_cols = im2col(x_split, pool_height, pool_width, padding=0, stride=stride)

x_cols_argmax = np.argmax(x_cols, axis=0)

x_cols_max = x_cols[x_cols_argmax, np.arange(x_cols.shape[1])]

out = x_cols_max.reshape(out_height, out_width, N, C).transpose(2, 3, 0, 1)

cache = (x, x_cols, x_cols_argmax, pool_param)

return out, cache

def max_pool_backward_im2col(dout, cache):

"""

An implementation of the backward pass for max pooling based on im2col.

This isn't much faster than the naive version, so it should be avoided if

possible.

"""

x, x_cols, x_cols_argmax, pool_param = cache

N, C, H, W = x.shape

pool_height, pool_width = pool_param['pool_height'], pool_param['pool_width']

stride = pool_param['stride']

dout_reshaped = dout.transpose(2, 3, 0, 1).flatten()

dx_cols = np.zeros_like(x_cols)

dx_cols[x_cols_argmax, np.arange(dx_cols.shape[1])] = dout_reshaped

dx = col2im_indices(dx_cols, (N * C, 1, H, W), pool_height, pool_width,

padding=0, stride=stride)

dx = dx.reshape(x.shape)

return dx