im2col

import numpy as np

def get_im2col_indices(x_shape, field_height, field_width, padding=1, stride=1):

# First figure out what the size of the output should be

N, C, H, W = x_shape

assert (H + 2 * padding - field_height) % stride == 0

assert (W + 2 * padding - field_height) % stride == 0

out_height = (H + 2 * padding - field_height) / stride + 1

out_width = (W + 2 * padding - field_width) / stride + 1

i0 = np.repeat(np.arange(field_height), field_width)

i0 = np.tile(i0, C)

i1 = stride * np.repeat(np.arange(out_height), out_width)

j0 = np.tile(np.arange(field_width), field_height * C)

j1 = stride * np.tile(np.arange(out_width), out_height)

i = i0.reshape(-1, 1) + i1.reshape(1, -1)

j = j0.reshape(-1, 1) + j1.reshape(1, -1)

k = np.repeat(np.arange(C), field_height * field_width).reshape(-1, 1)

return (k, i, j)

def im2col_indices(x, field_height, field_width, padding=1, stride=1):

""" An implementation of im2col based on some fancy indexing """

# Zero-pad the input

p = padding

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

k, i, j = get_im2col_indices(x.shape, field_height, field_width, padding,

stride)

cols = x_padded[:, k, i, j]

C = x.shape[1]

cols = cols.transpose(1, 2, 0).reshape(field_height * field_width * C, -1)

return cols

def col2im_indices(cols, x_shape, field_height=3, field_width=3, padding=1,

stride=1):

""" An implementation of col2im based on fancy indexing and np.add.at """

N, C, H, W = x_shape

H_padded, W_padded = H + 2 * padding, W + 2 * padding

x_padded = np.zeros((N, C, H_padded, W_padded), dtype=cols.dtype)

k, i, j = get_im2col_indices(x_shape, field_height, field_width, padding,

stride)

cols_reshaped = cols.reshape(C * field_height * field_width, -1, N)

cols_reshaped = cols_reshaped.transpose(2, 0, 1)

np.add.at(x_padded, (slice(None), k, i, j), cols_reshaped)

if padding == 0:

return x_padded

return x_padded[:, :, padding:-padding, padding:-padding]

pass