在 Python 中实现 MATLAB 的 im2col “滑动”答案

【问题标题】：Implement MATLAB's im2col 'sliding' in Python在 Python 中实现 MATLAB 的 im2col “滑动”
【发布时间】：2015-07-18 11:57:35
【问题描述】：

问：如何加快速度？

下面是我对 Matlab 的 im2col 'sliding' 的实现，它具有返回每第 n 列的附加功能。该函数获取一个图像（或任何 2 个暗淡数组）并从左到右、从上到下滑动，选取给定大小的每个重叠子图像，并返回一个其列是子图像的数组。

import numpy as np

def im2col_sliding(image, block_size, skip=1):

    rows, cols = image.shape
    horz_blocks = cols - block_size[1] + 1
    vert_blocks = rows - block_size[0] + 1

    output_vectors = np.zeros((block_size[0] * block_size[1], horz_blocks * vert_blocks))
    itr = 0
    for v_b in xrange(vert_blocks):
        for h_b in xrange(horz_blocks):
            output_vectors[:, itr] = image[v_b: v_b + block_size[0], h_b: h_b + block_size[1]].ravel()
            itr += 1

    return output_vectors[:, ::skip]

示例：

a = np.arange(16).reshape(4, 4)
print a
print im2col_sliding(a, (2, 2))  # return every overlapping 2x2 patch
print im2col_sliding(a, (2, 2), 4)  # return every 4th vector

返回：

[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]
 [12 13 14 15]]
[[  0.   1.   2.   4.   5.   6.   8.   9.  10.]
 [  1.   2.   3.   5.   6.   7.   9.  10.  11.]
 [  4.   5.   6.   8.   9.  10.  12.  13.  14.]
 [  5.   6.   7.   9.  10.  11.  13.  14.  15.]]
[[  0.   5.  10.]
 [  1.   6.  11.]
 [  4.   9.  14.]
 [  5.  10.  15.]]

性能不是很好，特别是考虑到我是否调用im2col_sliding(big_matrix, (8, 8))（62001 列）或im2col_sliding(big_matrix, (8, 8), 10)（6201 列；仅保留每 10 个向量）将花费相同的时间 [其中 big_matrix 的大小256 x 256]。

我正在寻找任何想法来加快速度。

【问题讨论】：

this 回答对您有帮助吗？或者您是否专门寻找您的代码的加速？
@ljetibo 我已经查看并使用了该帖子中接受的答案，但没有将其扩展为我想要的。我愿意接受任何解决方案。

标签： python performance python-2.7 image-processing numpy

【解决方案1】：

方法#1

我们可以在这里使用一些broadcasting 来一次性获取所有这些滑动窗口的所有索引，从而通过索引实现vectorized solution。这是受到Efficient Implementation of im2col and col2im 的启发。

这是实现 -

def im2col_sliding_broadcasting(A, BSZ, stepsize=1):
    # Parameters
    M,N = A.shape
    col_extent = N - BSZ[1] + 1
    row_extent = M - BSZ[0] + 1
    
    # Get Starting block indices
    start_idx = np.arange(BSZ[0])[:,None]*N + np.arange(BSZ[1])
    
    # Get offsetted indices across the height and width of input array
    offset_idx = np.arange(row_extent)[:,None]*N + np.arange(col_extent)
    
    # Get all actual indices & index into input array for final output
    return np.take (A,start_idx.ravel()[:,None] + offset_idx.ravel()[::stepsize])

方法 #2

使用新获得的NumPy array strides 知识让我们创建这样的滑动窗口，我们将有另一个有效的解决方案 -

def im2col_sliding_strided(A, BSZ, stepsize=1):
    # Parameters
    m,n = A.shape
    s0, s1 = A.strides    
    nrows = m-BSZ[0]+1
    ncols = n-BSZ[1]+1
    shp = BSZ[0],BSZ[1],nrows,ncols
    strd = s0,s1,s0,s1
    
    out_view = np.lib.stride_tricks.as_strided(A, shape=shp, strides=strd)
    return out_view.reshape(BSZ[0]*BSZ[1],-1)[:,::stepsize]

方法#3

上一个方法中列出的跨步方法已被合并到scikit-image module 中，以减少混乱，就像这样 -

from skimage.util import view_as_windows as viewW

def im2col_sliding_strided_v2(A, BSZ, stepsize=1):
    return viewW(A, (BSZ[0],BSZ[1])).reshape(-1,BSZ[0]*BSZ[1]).T[:,::stepsize]

示例运行 -

In [106]: a      # Input array
Out[106]: 
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19]])

In [107]: im2col_sliding_broadcasting(a, (2,3))
Out[107]: 
array([[ 0,  1,  2,  5,  6,  7, 10, 11, 12],
       [ 1,  2,  3,  6,  7,  8, 11, 12, 13],
       [ 2,  3,  4,  7,  8,  9, 12, 13, 14],
       [ 5,  6,  7, 10, 11, 12, 15, 16, 17],
       [ 6,  7,  8, 11, 12, 13, 16, 17, 18],
       [ 7,  8,  9, 12, 13, 14, 17, 18, 19]])

In [108]: im2col_sliding_broadcasting(a, (2,3), stepsize=2)
Out[108]: 
array([[ 0,  2,  6, 10, 12],
       [ 1,  3,  7, 11, 13],
       [ 2,  4,  8, 12, 14],
       [ 5,  7, 11, 15, 17],
       [ 6,  8, 12, 16, 18],
       [ 7,  9, 13, 17, 19]])

运行时测试

In [183]: a = np.random.randint(0,255,(1024,1024))

In [184]: %timeit im2col_sliding(img, (8,8), skip=1)
     ...: %timeit im2col_sliding_broadcasting(img, (8,8), stepsize=1)
     ...: %timeit im2col_sliding_strided(img, (8,8), stepsize=1)
     ...: %timeit im2col_sliding_strided_v2(img, (8,8), stepsize=1)
     ...: 
1 loops, best of 3: 1.29 s per loop
1 loops, best of 3: 226 ms per loop
10 loops, best of 3: 84.5 ms per loop
10 loops, best of 3: 111 ms per loop

In [185]: %timeit im2col_sliding(img, (8,8), skip=4)
     ...: %timeit im2col_sliding_broadcasting(img, (8,8), stepsize=4)
     ...: %timeit im2col_sliding_strided(img, (8,8), stepsize=4)
     ...: %timeit im2col_sliding_strided_v2(img, (8,8), stepsize=4)
     ...: 
1 loops, best of 3: 1.31 s per loop
10 loops, best of 3: 104 ms per loop
10 loops, best of 3: 84.4 ms per loop
10 loops, best of 3: 109 ms per loop

在 16x 附近，使用 strided 方法比原来的 loopy 版本加速！

【讨论】：

我知道我不应该（规则），但这让我大吃一惊。花了一大堆论文来弄清楚为什么会这样，并且其中有很多巧妙使用的 numpy 矩阵运算属性。如果可以的话，我会给你买一杯啤酒\upvote 两次....谢谢，这让我度过了一个愉快的夜晚。
@ljetibo 谢谢！！你的评论也是我的！好吧，我从 MATLAB 跳到 Numpy 并没有正确地使用 for 循环，称之为恩惠或诅咒，但我很喜欢它，特别是因为在 numpy 中循环似乎很昂贵。另外，最近，我偶然发现了这个漂亮的工具np.take，以前我无法在任何 SO 问题上使用它，但在这里很适合。好吧，欣赏好话！:)
@Scott 你不喜欢那些东西吗！ ;) 我知道我知道！好吧，愿原力保持强大！
@Divakar 在 MATLAB 标签上非常流行。他的回答是PFM。
@rayryeng 说真的，你从哪里得到这些文字术语！？ ;)

【解决方案2】：

对于不同图像通道上的滑动窗口，我们可以使用 Divakar@Implement MATLAB's im2col 'sliding' in Python 提供的代码的更新版本，即

import numpy as np
A = np.random.randint(0,9,(2,4,4)) # Sample input array
                    # Sample blocksize (rows x columns)
B = [2,2]
skip=[2,2]
# Parameters 
D,M,N = A.shape
col_extent = N - B[1] + 1
row_extent = M - B[0] + 1

# Get Starting block indices
start_idx = np.arange(B[0])[:,None]*N + np.arange(B[1])

# Generate Depth indeces
didx=M*N*np.arange(D)
start_idx=(didx[:,None]+start_idx.ravel()).reshape((-1,B[0],B[1]))

# Get offsetted indices across the height and width of input array
offset_idx = np.arange(row_extent)[:,None]*N + np.arange(col_extent)

# Get all actual indices & index into input array for final output
out = np.take (A,start_idx.ravel()[:,None] + offset_idx[::skip[0],::skip[1]].ravel())

测试样品运行

A=
[[[6 2 8 5]
[6 4 7 6]
[8 6 5 2]
[3 1 3 7]]

[[6 0 4 3]
[7 6 4 6]
[2 6 7 1]
[7 6 7 7]]]

out=
[6 8 8 5]
[2 5 6 2]
[6 7 3 3]
[4 6 1 7]
[6 4 2 7]
[0 3 6 1]
[7 4 7 7]
[6 6 6 7]

【讨论】：

感谢您将这些放在一起，这可能会派上用场。您可以考虑添加一个%timeit 部分，将其与糟糕的循环进行比较。
感谢您提供更通用的版本！

【解决方案3】：

为了进一步提高性能（例如卷积），我们还可以使用基于扩展代码的批处理实现，由 M Elyia@Implement Matlab's im2col 'sliding' in python 提供，即

import numpy as np

A = np.arange(3*1*4*4).reshape(3,1,4,4)+1 # 3 Sample input array with 1 channel
B = [2,2] # Sample blocksize (rows x columns)
skip = [2,2]

# Parameters 
batch, D,M,N = A.shape
col_extent = N - B[1] + 1
row_extent = M - B[0] + 1

# Get batch block indices
batch_idx = np.arange(batch)[:, None, None] * D * M * N

# Get Starting block indices
start_idx = np.arange(B[0])[None, :,None]*N + np.arange(B[1])

# Generate Depth indeces
didx=M*N*np.arange(D)
start_idx=(didx[None, :, None]+start_idx.ravel()).reshape((-1,B[0],B[1]))

# Get offsetted indices across the height and width of input array
offset_idx = np.arange(row_extent)[None, :, None]*N + np.arange(col_extent)

# Get all actual indices & index into input array for final output
act_idx = (batch_idx + 
    start_idx.ravel()[None, :, None] + 
    offset_idx[:,::skip[0],::skip[1]].ravel())

out = np.take (A, act_idx)

测试示例运行：

A = 
[[[[ 1  2  3  4]
   [ 5  6  7  8]
   [ 9 10 11 12]
   [13 14 15 16]]]


 [[[17 18 19 20]
   [21 22 23 24]
   [25 26 27 28]
   [29 30 31 32]]]


 [[[33 34 35 36]
   [37 38 39 40]
   [41 42 43 44]
   [45 46 47 48]]]] 


out = 
[[[ 1  2  3  9 10 11]
  [ 2  3  4 10 11 12]
  [ 5  6  7 13 14 15]
  [ 6  7  8 14 15 16]]

 [[17 18 19 25 26 27]
  [18 19 20 26 27 28]
  [21 22 23 29 30 31]
  [22 23 24 30 31 32]]

 [[33 34 35 41 42 43]
  [34 35 36 42 43 44]
  [37 38 39 45 46 47]
  [38 39 40 46 47 48]]]

【讨论】：

【解决方案4】：

我已经使用Numba JIT 编译器实现了快速解决方案。根据块大小和跳过大小，它提供了从5.67x 到3597x 的加速。

加速意味着与原始算法相比，numba 算法快多少倍，例如20x 的加速意味着如果原始算法采用 200ms，那么快速 numba 算法采用 10ms。

我的代码需要通过python -m pip install numpy numba timerit matplotlib 安装一次以下 pip 模块。

接下来是定位代码，然后是加速图，然后是时间测量的控制台输出。

Try it online!

import numpy as np

# ----- Original Implementation -----

def im2col_sliding(image, block_size, skip = 1):
    rows, cols = image.shape
    horz_blocks = cols - block_size[1] + 1
    vert_blocks = rows - block_size[0] + 1
    
    if vert_blocks <= 0 or horz_blocks <= 0:
        return np.zeros((block_size[0] * block_size[1], 0), dtype = image.dtype)

    output_vectors = np.zeros((block_size[0] * block_size[1], horz_blocks * vert_blocks), dtype = image.dtype)
    itr = 0
    
    for v_b in range(vert_blocks):
        for h_b in range(horz_blocks):
            output_vectors[:, itr] = image[v_b: v_b + block_size[0], h_b: h_b + block_size[1]].ravel()
            itr += 1

    return output_vectors[:, ::skip]


# ----- Fast Numba Implementation -----
    
import numba

@numba.njit(cache = True)
def im2col_sliding_numba(image, block_size, skip = 1):
    assert skip >= 1
    rows, cols = image.shape
    horz_blocks = cols - block_size[1] + 1
    vert_blocks = rows - block_size[0] + 1
    
    if vert_blocks <= 0 or horz_blocks <= 0:
        return np.zeros((block_size[0] * block_size[1], 0), dtype = image.dtype)
    
    res = np.zeros((block_size[0] * block_size[1], (horz_blocks * vert_blocks + skip - 1) // skip), dtype = image.dtype)
    itr, to_skip, v_b = 0, 0, 0
    
    while True:
        v_b += to_skip // horz_blocks
        if v_b >= vert_blocks:
            break
        h_b_start = to_skip % horz_blocks
        h_cnt = (horz_blocks - h_b_start + skip - 1) // skip
        for i, h_b in zip(range(itr, itr + h_cnt), range(h_b_start, horz_blocks, skip)):
            ii = 0
            for iv in range(v_b, v_b + block_size[0]):
                for ih in range(h_b, h_b + block_size[1]):
                    res[ii, i] = image[iv, ih]
                    ii += 1
        to_skip = skip - (horz_blocks - h_b_start - skip * (h_cnt - 1))
        itr += h_cnt
        v_b += 1
        
    assert itr == res.shape[1]#, (itr, res.shape)

    return res


# ----- Testing -----

from timerit import Timerit
Timerit._default_asciimode = True

side = 256
a = np.random.randint(0, 256, (side, side), dtype = np.uint8)

stats = []

for block_size in [16, 8, 4, 2, 1]:
    for skip_size in [1, 2, 5, 11, 23]:
        print(f'block_size {block_size} skip_size {skip_size}', flush = True)
        for ifn, f in enumerate([im2col_sliding, im2col_sliding_numba]):
            print(f'{f.__name__}: ', end = '', flush = True)
            tim = Timerit(num = 3, verbose = 1)
            for i, t in enumerate(tim):
                if i == 0 and ifn == 1:
                    f(a, (block_size, block_size), skip_size)
                with t:
                    r = f(a, (block_size, block_size), skip_size)
            rt = tim.mean()
            if ifn == 0:
                bt, ba = rt, r
            else:
                assert np.array_equal(ba, r)
                print(f'speedup {round(bt / rt, 2)}x')
                stats.append({
                    'block_size': block_size,
                    'skip_size': skip_size,
                    'speedup': bt / rt,
                })

stats = sorted(stats, key = lambda e: e['speedup'])

import math, matplotlib, matplotlib.pyplot as plt

x = np.arange(len(stats))
y = np.array([e['speedup'] for e in stats])

plt.rcParams['figure.figsize'] = (12.8, 7.2)

for scale in ['linear', 'log']:
    plt.clf()
    plt.xlabel('iteration')
    plt.ylabel(f'speedup_{scale}')
    plt.yscale(scale)
    plt.scatter(x, y, marker = '.')
    for i in range(x.size):
        plt.annotate(
            (f"b{str(stats[i]['block_size']).zfill(2)}s{str(stats[i]['skip_size']).zfill(2)}\n" +
             f"x{round(stats[i]['speedup'], 2 if stats[i]['speedup'] < 100 else 1 if stats[i]['speedup'] < 1000 else None)}"),
            (x[i], y[i]), fontsize = 'small',
        )
    plt.subplots_adjust(left = 0.055, right = 0.99, bottom = 0.08, top = 0.99)
    plt.xlim(left = -0.1)
    if scale == 'linear':
        ymin, ymax = np.amin(y), np.amax(y)
        plt.ylim((ymin - (ymax - ymin) * 0.02, ymax + (ymax - ymin) * 0.05))
        plt.yticks([ymin] + [e for e in plt.yticks()[0] if ymin + 0.01 < e < ymax - 0.01] + [ymax])
        #plt.gca().get_yaxis().set_major_formatter(matplotlib.ticker.FormatStrFormatter('%.1f'))
    plt.savefig(f'im2col_numba_{scale}.png', dpi = 150)
    plt.show()

下一个图的迭代为x 轴，加速为y 轴，第一个图有lineary 轴，第二个图有logarithmicy 轴。此外，每个点都有标签bXXsYYxZZ，其中XX 等于块大小，YY 等于跳过（步长）大小，ZZ 等于加速。

线性图：

对数图：

控制台输出：

block_size 16 skip_size 1
im2col_sliding: Timed best=549.069 ms, mean=549.069 +- 0.0 ms
im2col_sliding_numba: Timed best=96.841 ms, mean=96.841 +- 0.0 ms
speedup 5.67x
block_size 16 skip_size 2
im2col_sliding: Timed best=559.396 ms, mean=559.396 +- 0.0 ms
im2col_sliding_numba: Timed best=71.132 ms, mean=71.132 +- 0.0 ms
speedup 7.86x
block_size 16 skip_size 5
im2col_sliding: Timed best=561.030 ms, mean=561.030 +- 0.0 ms
im2col_sliding_numba: Timed best=15.000 ms, mean=15.000 +- 0.0 ms
speedup 37.4x
block_size 16 skip_size 11
im2col_sliding: Timed best=559.045 ms, mean=559.045 +- 0.0 ms
im2col_sliding_numba: Timed best=6.719 ms, mean=6.719 +- 0.0 ms
speedup 83.21x
block_size 16 skip_size 23
im2col_sliding: Timed best=562.462 ms, mean=562.462 +- 0.0 ms
im2col_sliding_numba: Timed best=2.514 ms, mean=2.514 +- 0.0 ms
speedup 223.72x
block_size 8 skip_size 1
im2col_sliding: Timed best=373.790 ms, mean=373.790 +- 0.0 ms
im2col_sliding_numba: Timed best=17.441 ms, mean=17.441 +- 0.0 ms
speedup 21.43x
block_size 8 skip_size 2
im2col_sliding: Timed best=375.858 ms, mean=375.858 +- 0.0 ms
im2col_sliding_numba: Timed best=8.791 ms, mean=8.791 +- 0.0 ms
speedup 42.75x
block_size 8 skip_size 5
im2col_sliding: Timed best=376.767 ms, mean=376.767 +- 0.0 ms
im2col_sliding_numba: Timed best=3.115 ms, mean=3.115 +- 0.0 ms
speedup 120.94x
block_size 8 skip_size 11
im2col_sliding: Timed best=378.284 ms, mean=378.284 +- 0.0 ms
im2col_sliding_numba: Timed best=1.406 ms, mean=1.406 +- 0.0 ms
speedup 268.97x
block_size 8 skip_size 23
im2col_sliding: Timed best=376.268 ms, mean=376.268 +- 0.0 ms
im2col_sliding_numba: Timed best=661.404 us, mean=661.404 +- 0.0 us
speedup 568.89x
block_size 4 skip_size 1
im2col_sliding: Timed best=378.813 ms, mean=378.813 +- 0.0 ms
im2col_sliding_numba: Timed best=4.950 ms, mean=4.950 +- 0.0 ms
speedup 76.54x
block_size 4 skip_size 2
im2col_sliding: Timed best=377.620 ms, mean=377.620 +- 0.0 ms
im2col_sliding_numba: Timed best=2.119 ms, mean=2.119 +- 0.0 ms
speedup 178.24x
block_size 4 skip_size 5
im2col_sliding: Timed best=374.792 ms, mean=374.792 +- 0.0 ms
im2col_sliding_numba: Timed best=854.986 us, mean=854.986 +- 0.0 us
speedup 438.36x
block_size 4 skip_size 11
im2col_sliding: Timed best=373.296 ms, mean=373.296 +- 0.0 ms
im2col_sliding_numba: Timed best=415.028 us, mean=415.028 +- 0.0 us
speedup 899.45x
block_size 4 skip_size 23
im2col_sliding: Timed best=374.075 ms, mean=374.075 +- 0.0 ms
im2col_sliding_numba: Timed best=219.491 us, mean=219.491 +- 0.0 us
speedup 1704.28x
block_size 2 skip_size 1
im2col_sliding: Timed best=377.698 ms, mean=377.698 +- 0.0 ms
im2col_sliding_numba: Timed best=1.477 ms, mean=1.477 +- 0.0 ms
speedup 255.67x
block_size 2 skip_size 2
im2col_sliding: Timed best=378.155 ms, mean=378.155 +- 0.0 ms
im2col_sliding_numba: Timed best=841.298 us, mean=841.298 +- 0.0 us
speedup 449.49x
block_size 2 skip_size 5
im2col_sliding: Timed best=376.381 ms, mean=376.381 +- 0.0 ms
im2col_sliding_numba: Timed best=392.541 us, mean=392.541 +- 0.0 us
speedup 958.83x
block_size 2 skip_size 11
im2col_sliding: Timed best=374.720 ms, mean=374.720 +- 0.0 ms
im2col_sliding_numba: Timed best=193.093 us, mean=193.093 +- 0.0 us
speedup 1940.62x
block_size 2 skip_size 23
im2col_sliding: Timed best=378.092 ms, mean=378.092 +- 0.0 ms
im2col_sliding_numba: Timed best=105.101 us, mean=105.101 +- 0.0 us
speedup 3597.42x
block_size 1 skip_size 1
im2col_sliding: Timed best=203.410 ms, mean=203.410 +- 0.0 ms
im2col_sliding_numba: Timed best=686.335 us, mean=686.335 +- 0.0 us
speedup 296.37x
block_size 1 skip_size 2
im2col_sliding: Timed best=202.865 ms, mean=202.865 +- 0.0 ms
im2col_sliding_numba: Timed best=361.255 us, mean=361.255 +- 0.0 us
speedup 561.56x
block_size 1 skip_size 5
im2col_sliding: Timed best=200.929 ms, mean=200.929 +- 0.0 ms
im2col_sliding_numba: Timed best=164.740 us, mean=164.740 +- 0.0 us
speedup 1219.68x
block_size 1 skip_size 11
im2col_sliding: Timed best=202.163 ms, mean=202.163 +- 0.0 ms
im2col_sliding_numba: Timed best=96.791 us, mean=96.791 +- 0.0 us
speedup 2088.65x
block_size 1 skip_size 23
im2col_sliding: Timed best=202.492 ms, mean=202.492 +- 0.0 ms
im2col_sliding_numba: Timed best=64.527 us, mean=64.527 +- 0.0 us
speedup 3138.1x

【讨论】：

我不知道 numba。谢谢，非常酷的解决方案。
@Scott Numba 是一个特殊的 python 模块，它允许将任何非常简单的 python 函数转换为 C++ 优化代码并将其编译为机器代码。如果函数有很多循环和与 numpy 数组的交互，所有这些操作都会转换为相应的 C++ 操作。这样 numba 平均可以优化任何 python 代码以更快地运行它50x-300x 倍。不需要特别的知识，你只需将@numba.njit装饰器添加到function并完成！

【解决方案5】：

我不认为你可以做得更好。显然，您必须运行一个大小为

的循环

cols - block_size[1] * rows - block_size[0]

但您在示例中使用的是 3、3 补丁，而不是 2、2。

【讨论】：

在我的示例中，列的长度为 4 (2x2)。我是否有错误或输入错误？
不，这只是令人困惑，因为您在 2, 2 上调用您的函数，它给出了 sub 3, 3 矩阵。就是这样。

【解决方案6】：

您还可以对 M Eliya 的 answer 进行进一步优化（虽然不是那么重要）

不是在最后“应用”跳过，而是可以在生成偏移数组时应用它，所以不是：

# Get offsetted indices across the height and width of input array
offset_idx = np.arange(row_extent)[:,None]*N + np.arange(col_extent)

# Get all actual indices & index into input array for final output
out = np.take (A,start_idx.ravel()[:,None] + offset_idx[::skip[0],::skip[1]].ravel())

您可以使用 numpy 的 arange 函数的 step 参数添加跳过：

# Get offsetted indices across the height and width of input array and add skips
offset_idx = np.arange(row_extent, step=skip[0])[:, None] * N + np.arange(col_extent, step=skip[1])

然后只添加没有 [::] 索引的偏移量数组

# Get all actual indices & index into input array for final output

out = np.take(A, start_idx.ravel()[:, None] + offset_idx.ravel())

对于小的跳过值，它几乎不会节省任何时间：

In[25]:
A = np.random.randint(0,9,(3, 1024, 1024))
B = [2, 2]
skip = [2, 2]

In[26]: %timeit im2col(A, B, skip)
10 loops, best of 3: 19.7 ms per loop

In[27]: %timeit im2col_optimized(A, B, skip)
100 loops, best of 3: 17.5 ms per loop

但是，使用较大的跳过值可以节省更多时间：

In[28]: skip = [10, 10]
In[29]: %timeit im2col(A, B, skip)
100 loops, best of 3: 3.85 ms per loop

In[30]: %timeit im2col_optimized(A, B, skip)
1000 loops, best of 3: 1.02 ms per loop

A = np.random.randint(0,9,(3, 2000, 2000))
B = [10, 10]
skip = [10, 10]

In[43]: %timeit im2col(A, B, skip)
10 loops, best of 3: 87.8 ms per loop

In[44]: %timeit im2col_optimized(A, B, skip)
10 loops, best of 3: 76.3 ms per loop

【讨论】：