Question

如何有效地在给定数组的任意轴上制作一个滑动窗口数组？例如，如果我有以下数组：

[[ 0  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]]

窗口大小为4，我希望能够在第一个维度上创建一个滑动窗口，如下所示：

[[[ 0  1  2  3  4]
  [ 5  6  7  8  9]
  [10 11 12 13 14]
  [15 16 17 18 19]]

 [[ 5  6  7  8  9]
  [10 11 12 13 14]
  [15 16 17 18 19]
  [20 21 22 23 24]]

 [[10 11 12 13 14]
  [15 16 17 18 19]
  [20 21 22 23 24]
  [25 26 27 28 29]]]

而且在第二维上也是这样，

[[[ 0  1  2  3]
  [ 5  6  7  8]
  [10 11 12 13]
  [15 16 17 18]
  [20 21 22 23]
  [25 26 27 28]]

 [[ 1  2  3  4]
  [ 6  7  8  9]
  [11 12 13 14]
  [16 17 18 19]
  [21 22 23 24]
  [26 27 28 29]]]

Answer 1

使用numpy.lib.stride_tricks.as_strided，可以在恒定的时间内高效地构建这样的阵列，而无需使用任何额外的内存。生成的数组将是一个有一些局限性的视图，但是如果需要连续的数组，则始终可以制作一个copy。

以下功能解决了一般问题：

import numpy as np

def as_sliding_window(x, window_size, axis=0, window_axis=None,
                      subok=False, writeable=True):
    """
    Make a sliding window across an axis.

    Uses ``numpy.lib.stride_tricks.as_strided``, similar caveats apply.

    Parameters
    ----------
    x : array_like
        Array from where the sliding window is created.
    window_size: int
        Size of the sliding window.
    axis: int
        Dimension across which the sliding window is created.
    window_axis: int
        New dimension for the sliding window. By default, the new
        dimension is inserted before ``axis``.
    subok: bool
        If True, subclasses are preserved
        (see ``numpy.lib.stride_tricks.as_strided``).
    writeable: bool
        If set to False, the returned array will always be readonly.
        Otherwise it will be writable if the original array was. It
        is advisable to set this to False if possible
        (see ``numpy.lib.stride_tricks.as_strided``).

    Returns
    --------
    sliding_window: ndarray
        View of the given array as a sliding window along ``axis``.
    """
    from numpy.lib.stride_tricks import as_strided
    x = np.asarray(x)
    axis %= x.ndim
    if window_axis is None:
        window_axis = axis
    window_axis %= x.ndim + 1
    # Make shape
    shape = list(x.shape)
    n = shape[axis]
    shape[axis] = window_size
    shape.insert(window_axis, max(n - window_size + 1, 0))
    # Make strides
    strides = list(x.strides)
    strides.insert(window_axis, strides[axis])
    # Make sliding window view
    sliding_window = as_strided(x, shape, strides,
                                subok=subok, writeable=writeable)
    return sliding_window

示例：

x = np.arange(30).reshape((6, 5))
window_size = 4
print(x)
# [[ 0  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]]

print(as_sliding_window(x, window_size))
# [[[ 0  1  2  3  4]
#   [ 5  6  7  8  9]
#   [10 11 12 13 14]
#   [15 16 17 18 19]]
#
#  [[ 5  6  7  8  9]
#   [10 11 12 13 14]
#   [15 16 17 18 19]
#   [20 21 22 23 24]]
#
#  [[10 11 12 13 14]
#   [15 16 17 18 19]
#   [20 21 22 23 24]
#   [25 26 27 28 29]]]

print(as_sliding_window(x, window_size, axis=1, window_axis=0))
# [[[ 0  1  2  3]
#   [ 5  6  7  8]
#   [10 11 12 13]
#   [15 16 17 18]
#   [20 21 22 23]
#   [25 26 27 28]]
#
#  [[ 1  2  3  4]
#   [ 6  7  8  9]
#   [11 12 13 14]
#   [16 17 18 19]
#   [21 22 23 24]
#   [26 27 28 29]]]

# You can make sliding windows of sliding windows
print(as_sliding_window(as_sliding_window(x, window_size), window_size, axis=2).shape)
# (3, 4, 2, 4)

# New dimension can be put at the end with window_axis=-1
print(as_sliding_window(x, window_size, axis=0, window_axis=-1).shape)
# (4, 5, 3)

在阵列轴上滚动或滑动窗口的通用方法

1 个答案: