Module acd.util.conv2dnp
code from https://github.com/renmengye/np-conv2d
Expand source code
'''code from https://github.com/renmengye/np-conv2d
'''
from __future__ import division
import numpy as np
def calc_pad(pad, in_siz, out_siz, stride, ksize):
"""Calculate padding width.
Args:
pad: padding method, "SAME", "VALID", or manually speicified.
ksize: kernel size [I, J].
Returns:
pad_: Actual padding width.
"""
if pad == 'SAME':
return (out_siz - 1) * stride + ksize - in_siz
elif pad == 'VALID':
return 0
else:
return pad
def calc_size(h, kh, pad, sh):
"""Calculate output image size on one dimension.
Args:
h: input image size.
kh: kernel size.
pad: padding strategy.
sh: stride.
Returns:
s: output size.
"""
if pad == 'VALID':
return np.ceil((h - kh + 1) / sh)
elif pad == 'SAME':
return np.ceil(h / sh)
else:
return int(np.ceil((h - kh + pad + 1) / sh))
def extract_sliding_windows_gradw(x,
ksize,
pad,
stride,
orig_size,
floor_first=True):
"""Extracts dilated windows.
Args:
x: [N, H, W, C]
k: [KH, KW]
pad: [PH, PW]
stride: [SH, SW]
Returns:
y: [N, H', W', KH, KW, C]
"""
n = x.shape[0]
h = x.shape[1]
w = x.shape[2]
c = x.shape[3]
kh = ksize[0]
kw = ksize[1]
sh = stride[0]
sw = stride[1]
h2 = orig_size[0]
w2 = orig_size[1]
ph = int(calc_pad(pad, h, h2, 1, ((kh - 1) * sh + 1)))
pw = int(calc_pad(pad, w, w2, 1, ((kw - 1) * sw + 1)))
ph2 = int(np.ceil(ph / 2))
ph3 = int(np.floor(ph / 2))
pw2 = int(np.ceil(pw / 2))
pw3 = int(np.floor(pw / 2))
if floor_first:
pph = (ph3, ph2)
ppw = (pw3, pw2)
else:
pph = (ph2, ph3)
ppw = (pw2, pw3)
x = np.pad(
x, ((0, 0), (ph3, ph2), (pw3, pw2), (0, 0)),
mode='constant',
constant_values=(0.0,))
p2h = (-x.shape[1]) % sh
p2w = (-x.shape[2]) % sw
if p2h > 0 or p2w > 0:
x = np.pad(
x, ((0, 0), (0, p2h), (0, p2w), (0, 0)),
mode='constant',
constant_values=(0.0,))
x = x.reshape([n, int(x.shape[1] / sh), sh, int(x.shape[2] / sw), sw, c])
y = np.zeros([n, h2, w2, kh, kw, c])
for ii in range(h2):
for jj in range(w2):
h0 = int(np.floor(ii / sh))
w0 = int(np.floor(jj / sw))
y[:, ii, jj, :, :, :] = x[:, h0:h0 + kh, ii % sh, w0:w0 + kw, jj %
sw, :]
return y
def extract_sliding_windows_gradx(x,
ksize,
pad,
stride,
orig_size,
floor_first=False):
"""Extracts windows on a dilated image.
Args:
x: [N, H', W', C] (usually dy)
k: [KH, KW]
pad: [PH, PW]
stride: [SH, SW]
orig_size: [H, W]
Returns:
y: [N, H, W, KH, KW, C]
"""
n = x.shape[0]
h = x.shape[1]
w = x.shape[2]
c = x.shape[3]
kh = ksize[0]
kw = ksize[1]
ph = pad[0]
pw = pad[1]
sh = stride[0]
sw = stride[1]
h2 = orig_size[0]
w2 = orig_size[1]
xs = np.zeros([n, x.shape[1], sh, x.shape[2], sw, c])
xs[:, :, 0, :, 0, :] = x
xss = xs.shape
x = xs.reshape([xss[0], xss[1] * xss[2], xss[3] * xss[4], xss[5]])
x = x[:, :h2, :w2, :]
ph2 = int(np.ceil(ph / 2))
ph3 = int(np.floor(ph / 2))
pw2 = int(np.ceil(pw / 2))
pw3 = int(np.floor(pw / 2))
if floor_first:
pph = (ph3, ph2)
ppw = (pw3, pw2)
else:
pph = (ph2, ph3)
ppw = (pw2, pw3)
x = np.pad(
x, ((0, 0), pph, ppw, (0, 0)),
mode='constant',
constant_values=(0.0,))
y = np.zeros([n, h2, w2, kh, kw, c])
for ii in range(h2):
for jj in range(w2):
y[:, ii, jj, :, :, :] = x[:, ii:ii + kh, jj:jj + kw, :]
return y
def extract_sliding_windows(x, ksize, pad, stride, floor_first=True):
"""Converts a tensor to sliding windows.
Args:
x: [N, H, W, C]
k: [KH, KW]
pad: [PH, PW]
stride: [SH, SW]
Returns:
y: [N, (H-KH+PH+1)/SH, (W-KW+PW+1)/SW, KH * KW, C]
"""
n = x.shape[0]
h = x.shape[1]
w = x.shape[2]
c = x.shape[3]
kh = ksize[0]
kw = ksize[1]
sh = stride[0]
sw = stride[1]
h2 = int(calc_size(h, kh, pad, sh))
w2 = int(calc_size(w, kw, pad, sw))
ph = int(calc_pad(pad, h, h2, sh, kh))
pw = int(calc_pad(pad, w, w2, sw, kw))
ph0 = int(np.floor(ph / 2))
ph1 = int(np.ceil(ph / 2))
pw0 = int(np.floor(pw / 2))
pw1 = int(np.ceil(pw / 2))
if floor_first:
pph = (ph0, ph1)
ppw = (pw0, pw1)
else:
pph = (ph1, ph0)
ppw = (pw1, pw0)
x = np.pad(
x, ((0, 0), pph, ppw, (0, 0)),
mode='constant',
constant_values=(0.0,))
y = np.zeros([n, h2, w2, kh, kw, c])
for ii in range(h2):
for jj in range(w2):
xx = ii * sh
yy = jj * sw
y[:, ii, jj, :, :, :] = x[:, xx:xx + kh, yy:yy + kw, :]
return y
def conv2dnp(x, w, pad='SAME', stride=(1, 1)):
"""2D convolution (technically speaking, correlation).
Args:
x: [N, H, W, C]
w: [I, J, C, K]
pad: [PH, PW]
stride: [SH, SW]
Returns:
y: [N, H', W', K]
"""
ksize = w.shape[:2]
x = extract_sliding_windows(x, ksize, pad, stride)
ws = w.shape
w = w.reshape([ws[0] * ws[1] * ws[2], ws[3]])
xs = x.shape
x = x.reshape([xs[0] * xs[1] * xs[2], -1])
y = x.dot(w)
y = y.reshape([xs[0], xs[1], xs[2], -1])
return y
def conv2d_gradw(x, dy, ksize, pad='SAME', stride=(1, 1)):
"""2D convolution gradient wrt. filters.
Args:
dy: [N, H', W', K]
x: [N, H, W, C]
ksize: original w ksize [I, J].
Returns:
dw: [I, J, C, K]
"""
dy = np.transpose(dy, [1, 2, 0, 3])
x = np.transpose(x, [3, 1, 2, 0])
ksize2 = dy.shape[:2]
x = extract_sliding_windows_gradw(x, ksize2, pad, stride, ksize)
dys = dy.shape
dy = dy.reshape([dys[0] * dys[1] * dys[2], dys[3]])
xs = x.shape
x = x.reshape([xs[0] * xs[1] * xs[2], -1])
dw = x.dot(dy)
dw = dw.reshape([xs[0], xs[1], xs[2], -1])
dw = np.transpose(dw, [1, 2, 0, 3])
dw = dw[:ksize[0], :ksize[1], :, :]
return dw
def conv2d_gradx(w, dy, xsize, pad='SAME', stride=(1, 1)):
"""2D convolution gradient wrt. input.
Args:
dy: [N, H', W', K]
w: [I, J, C, K]
xsize: Original image size, [H, W]
Returns:
dx: [N, H, W, C]
"""
ksize = w.shape[:2]
if pad == 'SAME':
dys = dy.shape[1:3]
pad2h = int(
calc_pad('SAME',
max(dys[0], dys[0] * stride[0] - 1), xsize[0], 1, ksize[
0]))
pad2w = int(
calc_pad('SAME',
max(dys[0], dys[0] * stride[1] - 1), xsize[1], 1, ksize[
1]))
pad2 = (pad2h, pad2w)
elif pad == 'VALID':
pad2 = (int(calc_pad('SAME', 0, 0, 1, ksize[0])),
int(calc_pad('SAME', 0, 0, 1, ksize[1])))
pad2 = (pad2[0] * 2, pad2[1] * 2)
else:
pad2 = pad
w = np.transpose(w, [0, 1, 3, 2])
ksize = w.shape[:2]
dx = extract_sliding_windows_gradx(dy, ksize, pad2, stride, xsize)
dxs = dx.shape
dx = dx.reshape([dxs[0] * dxs[1] * dxs[2], -1])
w = w[::-1, ::-1, :, :]
ws = w.shape
w = w.reshape([ws[0] * ws[1] * ws[2], ws[3]])
dx = dx.dot(w)
return dx.reshape([dxs[0], dxs[1], dxs[2], -1])Functions
def calc_pad(pad, in_siz, out_siz, stride, ksize)-
Calculate padding width.
Args
pad- padding method, "SAME", "VALID", or manually speicified.
ksize- kernel size [I, J].
Returns
pad_- Actual padding width.
Expand source code
def calc_pad(pad, in_siz, out_siz, stride, ksize): """Calculate padding width. Args: pad: padding method, "SAME", "VALID", or manually speicified. ksize: kernel size [I, J]. Returns: pad_: Actual padding width. """ if pad == 'SAME': return (out_siz - 1) * stride + ksize - in_siz elif pad == 'VALID': return 0 else: return pad def calc_size(h, kh, pad, sh)-
Calculate output image size on one dimension.
Args
h- input image size.
kh- kernel size.
pad- padding strategy.
sh- stride.
Returns
s- output size.
Expand source code
def calc_size(h, kh, pad, sh): """Calculate output image size on one dimension. Args: h: input image size. kh: kernel size. pad: padding strategy. sh: stride. Returns: s: output size. """ if pad == 'VALID': return np.ceil((h - kh + 1) / sh) elif pad == 'SAME': return np.ceil(h / sh) else: return int(np.ceil((h - kh + pad + 1) / sh)) def conv2d_gradw(x, dy, ksize, pad='SAME', stride=(1, 1))-
2D convolution gradient wrt. filters.
Args
dy- [N, H', W', K]
x- [N, H, W, C]
ksize- original w ksize [I, J].
Returns
dw- [I, J, C, K]
Expand source code
def conv2d_gradw(x, dy, ksize, pad='SAME', stride=(1, 1)): """2D convolution gradient wrt. filters. Args: dy: [N, H', W', K] x: [N, H, W, C] ksize: original w ksize [I, J]. Returns: dw: [I, J, C, K] """ dy = np.transpose(dy, [1, 2, 0, 3]) x = np.transpose(x, [3, 1, 2, 0]) ksize2 = dy.shape[:2] x = extract_sliding_windows_gradw(x, ksize2, pad, stride, ksize) dys = dy.shape dy = dy.reshape([dys[0] * dys[1] * dys[2], dys[3]]) xs = x.shape x = x.reshape([xs[0] * xs[1] * xs[2], -1]) dw = x.dot(dy) dw = dw.reshape([xs[0], xs[1], xs[2], -1]) dw = np.transpose(dw, [1, 2, 0, 3]) dw = dw[:ksize[0], :ksize[1], :, :] return dw def conv2d_gradx(w, dy, xsize, pad='SAME', stride=(1, 1))-
2D convolution gradient wrt. input.
Args
dy- [N, H', W', K]
w- [I, J, C, K]
xsize- Original image size, [H, W]
Returns
dx- [N, H, W, C]
Expand source code
def conv2d_gradx(w, dy, xsize, pad='SAME', stride=(1, 1)): """2D convolution gradient wrt. input. Args: dy: [N, H', W', K] w: [I, J, C, K] xsize: Original image size, [H, W] Returns: dx: [N, H, W, C] """ ksize = w.shape[:2] if pad == 'SAME': dys = dy.shape[1:3] pad2h = int( calc_pad('SAME', max(dys[0], dys[0] * stride[0] - 1), xsize[0], 1, ksize[ 0])) pad2w = int( calc_pad('SAME', max(dys[0], dys[0] * stride[1] - 1), xsize[1], 1, ksize[ 1])) pad2 = (pad2h, pad2w) elif pad == 'VALID': pad2 = (int(calc_pad('SAME', 0, 0, 1, ksize[0])), int(calc_pad('SAME', 0, 0, 1, ksize[1]))) pad2 = (pad2[0] * 2, pad2[1] * 2) else: pad2 = pad w = np.transpose(w, [0, 1, 3, 2]) ksize = w.shape[:2] dx = extract_sliding_windows_gradx(dy, ksize, pad2, stride, xsize) dxs = dx.shape dx = dx.reshape([dxs[0] * dxs[1] * dxs[2], -1]) w = w[::-1, ::-1, :, :] ws = w.shape w = w.reshape([ws[0] * ws[1] * ws[2], ws[3]]) dx = dx.dot(w) return dx.reshape([dxs[0], dxs[1], dxs[2], -1]) def conv2dnp(x, w, pad='SAME', stride=(1, 1))-
2D convolution (technically speaking, correlation).
Args
x- [N, H, W, C]
w- [I, J, C, K]
pad- [PH, PW]
stride- [SH, SW]
Returns
y- [N, H', W', K]
Expand source code
def conv2dnp(x, w, pad='SAME', stride=(1, 1)): """2D convolution (technically speaking, correlation). Args: x: [N, H, W, C] w: [I, J, C, K] pad: [PH, PW] stride: [SH, SW] Returns: y: [N, H', W', K] """ ksize = w.shape[:2] x = extract_sliding_windows(x, ksize, pad, stride) ws = w.shape w = w.reshape([ws[0] * ws[1] * ws[2], ws[3]]) xs = x.shape x = x.reshape([xs[0] * xs[1] * xs[2], -1]) y = x.dot(w) y = y.reshape([xs[0], xs[1], xs[2], -1]) return y def extract_sliding_windows(x, ksize, pad, stride, floor_first=True)-
Converts a tensor to sliding windows.
Args
x- [N, H, W, C]
k- [KH, KW]
pad- [PH, PW]
stride- [SH, SW]
Returns
y- [N, (H-KH+PH+1)/SH, (W-KW+PW+1)/SW, KH * KW, C]
Expand source code
def extract_sliding_windows(x, ksize, pad, stride, floor_first=True): """Converts a tensor to sliding windows. Args: x: [N, H, W, C] k: [KH, KW] pad: [PH, PW] stride: [SH, SW] Returns: y: [N, (H-KH+PH+1)/SH, (W-KW+PW+1)/SW, KH * KW, C] """ n = x.shape[0] h = x.shape[1] w = x.shape[2] c = x.shape[3] kh = ksize[0] kw = ksize[1] sh = stride[0] sw = stride[1] h2 = int(calc_size(h, kh, pad, sh)) w2 = int(calc_size(w, kw, pad, sw)) ph = int(calc_pad(pad, h, h2, sh, kh)) pw = int(calc_pad(pad, w, w2, sw, kw)) ph0 = int(np.floor(ph / 2)) ph1 = int(np.ceil(ph / 2)) pw0 = int(np.floor(pw / 2)) pw1 = int(np.ceil(pw / 2)) if floor_first: pph = (ph0, ph1) ppw = (pw0, pw1) else: pph = (ph1, ph0) ppw = (pw1, pw0) x = np.pad( x, ((0, 0), pph, ppw, (0, 0)), mode='constant', constant_values=(0.0,)) y = np.zeros([n, h2, w2, kh, kw, c]) for ii in range(h2): for jj in range(w2): xx = ii * sh yy = jj * sw y[:, ii, jj, :, :, :] = x[:, xx:xx + kh, yy:yy + kw, :] return y def extract_sliding_windows_gradw(x, ksize, pad, stride, orig_size, floor_first=True)-
Extracts dilated windows.
Args
x- [N, H, W, C]
k- [KH, KW]
pad- [PH, PW]
stride- [SH, SW]
Returns
y- [N, H', W', KH, KW, C]
Expand source code
def extract_sliding_windows_gradw(x, ksize, pad, stride, orig_size, floor_first=True): """Extracts dilated windows. Args: x: [N, H, W, C] k: [KH, KW] pad: [PH, PW] stride: [SH, SW] Returns: y: [N, H', W', KH, KW, C] """ n = x.shape[0] h = x.shape[1] w = x.shape[2] c = x.shape[3] kh = ksize[0] kw = ksize[1] sh = stride[0] sw = stride[1] h2 = orig_size[0] w2 = orig_size[1] ph = int(calc_pad(pad, h, h2, 1, ((kh - 1) * sh + 1))) pw = int(calc_pad(pad, w, w2, 1, ((kw - 1) * sw + 1))) ph2 = int(np.ceil(ph / 2)) ph3 = int(np.floor(ph / 2)) pw2 = int(np.ceil(pw / 2)) pw3 = int(np.floor(pw / 2)) if floor_first: pph = (ph3, ph2) ppw = (pw3, pw2) else: pph = (ph2, ph3) ppw = (pw2, pw3) x = np.pad( x, ((0, 0), (ph3, ph2), (pw3, pw2), (0, 0)), mode='constant', constant_values=(0.0,)) p2h = (-x.shape[1]) % sh p2w = (-x.shape[2]) % sw if p2h > 0 or p2w > 0: x = np.pad( x, ((0, 0), (0, p2h), (0, p2w), (0, 0)), mode='constant', constant_values=(0.0,)) x = x.reshape([n, int(x.shape[1] / sh), sh, int(x.shape[2] / sw), sw, c]) y = np.zeros([n, h2, w2, kh, kw, c]) for ii in range(h2): for jj in range(w2): h0 = int(np.floor(ii / sh)) w0 = int(np.floor(jj / sw)) y[:, ii, jj, :, :, :] = x[:, h0:h0 + kh, ii % sh, w0:w0 + kw, jj % sw, :] return y def extract_sliding_windows_gradx(x, ksize, pad, stride, orig_size, floor_first=False)-
Extracts windows on a dilated image.
Args
x- [N, H', W', C] (usually dy)
k- [KH, KW]
pad- [PH, PW]
stride- [SH, SW]
orig_size- [H, W]
Returns
y- [N, H, W, KH, KW, C]
Expand source code
def extract_sliding_windows_gradx(x, ksize, pad, stride, orig_size, floor_first=False): """Extracts windows on a dilated image. Args: x: [N, H', W', C] (usually dy) k: [KH, KW] pad: [PH, PW] stride: [SH, SW] orig_size: [H, W] Returns: y: [N, H, W, KH, KW, C] """ n = x.shape[0] h = x.shape[1] w = x.shape[2] c = x.shape[3] kh = ksize[0] kw = ksize[1] ph = pad[0] pw = pad[1] sh = stride[0] sw = stride[1] h2 = orig_size[0] w2 = orig_size[1] xs = np.zeros([n, x.shape[1], sh, x.shape[2], sw, c]) xs[:, :, 0, :, 0, :] = x xss = xs.shape x = xs.reshape([xss[0], xss[1] * xss[2], xss[3] * xss[4], xss[5]]) x = x[:, :h2, :w2, :] ph2 = int(np.ceil(ph / 2)) ph3 = int(np.floor(ph / 2)) pw2 = int(np.ceil(pw / 2)) pw3 = int(np.floor(pw / 2)) if floor_first: pph = (ph3, ph2) ppw = (pw3, pw2) else: pph = (ph2, ph3) ppw = (pw2, pw3) x = np.pad( x, ((0, 0), pph, ppw, (0, 0)), mode='constant', constant_values=(0.0,)) y = np.zeros([n, h2, w2, kh, kw, c]) for ii in range(h2): for jj in range(w2): y[:, ii, jj, :, :, :] = x[:, ii:ii + kh, jj:jj + kw, :] return y