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
