如何将 numpy 数组分割成重叠的图块？

Question

如何将a数组转换为b数组，正如下面在 Python 中指定的那样并使用 numpy 库？我正在寻找一种非常有效的方法，因为我想使用此方法的实际数组非常大。我应该指出的是，这些数字可以是任何数字，并且数字之间没有任何关系。另外，我尝试在下图中展示我想要如何对数组进行切片。

import numpy as np
a = np.arange(1, 49).reshape(6, 8)


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]]

b =[[1, 2, 9, 10], [2, 3, 10, 11], [3, 4, 11, 12], [4, 5, 12, 13],
    [5, 6, 13, 14], [6, 7, 14, 15], [7, 8, 15, 16], [9, 10, 17, 18],
    [10, 11, 18, 19], [11, 12, 19, 20], [12, 13, 20, 21], [13, 14, 21, 22],
    [14, 15, 22, 23], [15, 16, 23, 24], [17, 18, 25, 26], [18, 19, 26, 27],
    [19, 20, 27, 28], [20, 21, 28, 29], [21, 22, 29, 30], [22, 23, 30, 31],
    [23, 24, 31, 32], [25, 26, 33, 34], [26, 27, 34, 35], [27, 28, 35, 36],
    [28, 29, 36, 37], [29, 30, 37, 38], [30, 31, 38, 39], [31, 32, 39, 40], 
    [33, 34, 41, 42], [34, 35, 42, 43], [35, 36, 43, 44], [36, 37, 44, 45],
    [37, 38, 45, 46], [38, 39, 46, 47], [39, 40, 47, 48]]

我试图找到一种具有重塑和转置功能的方法，但问题是我找不到包含边界的方法。c显示了我对解决方案的想法。

c = a.reshape(3, 2, 4, 2).transpose(0, 2, 3, 1).reshape(3*4, 2*2).

图片： https: //ibb.co/QC7tkPM。

Answer 1

使用 numpy 1.20 或更高版本，您可以使用np.lib.stride_tricks.sliding_window_view：

import numpy as np
a = np.arange(12).reshape(3, 4)
print(a)

给出：

[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]

下图(2,2)是滑动窗口的形状：

windows = np.lib.stride_tricks.sliding_window_view(a, (2,2))
print(windows)

它给：

[[[[ 0  1]
   [ 4  5]]

  [[ 1  2]
   [ 5  6]]

  [[ 2  3]
   [ 6  7]]]


 [[[ 4  5]
   [ 8  9]]

  [[ 5  6]
   [ 9 10]]

  [[ 6  7]
   [10 11]]]]

在 numpy 的早期版本中，可以使用以下命令获得类似的结果np.lib.index_tricks.as_strided：

w = 2  # width and height of the sliding window

r, c = a.shape
size = a.itemsize
ast = np.lib.index_tricks.as_strided
windows_ast = ast(a,
                  shape=(r - w + 1, c - w + 1, w, w),
                  strides=(c * size, size, c * size, size))
print(windows_ast)

它给：

[[[[ 0  1]
   [ 4  5]]

  [[ 1  2]
   [ 5  6]]

  [[ 2  3]
   [ 6  7]]]


 [[[ 4  5]
   [ 8  9]]

  [[ 5  6]
   [ 9 10]]

  [[ 6  7]
   [10 11]]]]

请注意，numpy 文档警告说np.lib.stride_tricks.as_strided应尽可能避免这种情况，因为其结果可能会导致多个问题。如果输入数组没有连续的内存布局，上面的代码也可能会失败。

无论如何，您都可以将结果重塑为所需的形状：

windows.reshape(-1, 4)

它给：

array([[ 0,  1,  4,  5],
       [ 1,  2,  5,  6],
       [ 2,  3,  6,  7],
       [ 4,  5,  8,  9],
       [ 5,  6,  9, 10],
       [ 6,  7, 10, 11]])