NumPy的实用函数整理之sliding_window_view

NumPy函数sliding_window_view()使用给定的窗口形状在数组中创建一个滑动窗口视图，产生一个增加了滑动窗口维度的数据集。

numpy.lib.stride_tricks.sliding_window_view()

sliding_window_view(x, window_shape, axis=None, *, subok=False, writeable=False)
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其中参数：
x: numpy数组，为需要创建滑窗数组的多维numpy数组。
window_shape ： int 或者 tuple of int，参与滑动窗口的每个轴上的窗口大小。如果axis=None，滑窗需要与输入数阵列尺寸具有相同维度。
axis：int 或者 tuple of int，可选参数，默认为None。axis为滑窗进行的维度，如果为None，默认对所有维度进行滑窗，如果不为None，可以指定维度进行滑窗。window_shape[i]将指x的i轴。如果axis是int的元组，那么window_shape[i]将指x的axis[i]轴。单整数i被视为元组(i,)，此时window_shape可以赋值为整数int。
subok：布尔值，可选参数，默认为False。如果传入True，将返回子类数组，否则返回的阵列将被迫为基类数组（默认值）
writable：布尔值，可选参数，默认为False。当传入True时，允许写回视图。默认值是False的，因为应该谨慎使用：返回的视图多次包含相同的内存位置，因此写到一个位置会导致其他位置更改。

函数返回值：
view：numpy数组，为输入数组x的滑窗视图数组，滑窗维度插入到了数组的最后，并且初始的维度根据滑窗进行了裁剪，即view.shape = x_shape_trimmed + window_shape，其中“x_shape_trimmed”为“x.shape”，每个条目比相应的窗口大小减少(window_shape-1)

bottleneck提供了更快的滑窗方法 https://github.com/pydata/bottleneck
scipy.signal.fftconvolve也可以在某些滑窗情景使用
scipy.ndimage也可以生成滑窗视图

应用举例:采用源代码案例

>>>from numpy.lib.stride_tricks import  sliding_window_view

>>> x = np.arange(6)
>>> x.shape
(6,)
>>> v = sliding_window_view(x, 3)
>>> v.shape
(4, 3)
>>> v
array([[0, 1, 2],
       [1, 2, 3],
       [2, 3, 4],
       [3, 4, 5]])

This also works in more dimensions, e.g.

>>> i, j = np.ogrid[:3, :4]
>>> x = 10*i + j
>>> x.shape
(3, 4)
>>> x
array([[ 0,  1,  2,  3],
       [10, 11, 12, 13],
       [20, 21, 22, 23]])
>>> shape = (2,2)
>>> v = sliding_window_view(x, shape)
>>> v.shape
(2, 3, 2, 2)
>>> v
array([[[[ 0,  1],
         [10, 11]],
        [[ 1,  2],
         [11, 12]],
        [[ 2,  3],
         [12, 13]]],
       [[[10, 11],
         [20, 21]],
        [[11, 12],
         [21, 22]],
        [[12, 13],
         [22, 23]]]])

The axis can be specified explicitly:

>>> v = sliding_window_view(x, window_shape=3, axis=0)
>>> v.shape
(1, 4, 3)
>>> v
array([[[ 0, 10, 20],
        [ 1, 11, 21],
        [ 2, 12, 22],
        [ 3, 13, 23]]])

The same axis can be used several times. In that case, every use reduces
the corresponding original dimension:

>>> v = sliding_window_view(x, (2, 3), (1, 1))
>>> v.shape
(3, 1, 2, 3)
>>> v
array([[[[ 0,  1,  2],
         [ 1,  2,  3]]],
       [[[10, 11, 12],
         [11, 12, 13]]],
       [[[20, 21, 22],
         [21, 22, 23]]]])

Combining with stepped slicing (`::step`), this can be used to take sliding
views which skip elements:

>>> x = np.arange(7)
>>> sliding_window_view(x, 5)[:, ::2]
array([[0, 2, 4],
       [1, 3, 5],
       [2, 4, 6]])

or views which move by multiple elements

>>> x = np.arange(7)
>>> sliding_window_view(x, 3)[::2, :]
array([[0, 1, 2],
       [2, 3, 4],
       [4, 5, 6]])

A common application of `sliding_window_view` is the calculation of running
statistics. The simplest example is the
`moving average <https://en.wikipedia.org/wiki/Moving_average>`_:

>>> x = np.arange(6)
>>> x.shape
(6,)
>>> v = sliding_window_view(x, 3)
>>> v.shape
(4, 3)
>>> v
array([[0, 1, 2],
       [1, 2, 3],
       [2, 3, 4],
       [3, 4, 5]])
>>> moving_average = v.mean(axis=-1)
>>> moving_average
array([1., 2., 3., 4.])
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