在数组轴上滚动或滑动 window 的通用方法

Question

如何有效地制作一个滑动数组 windows 跨越给定数组的任意轴？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]]

window 尺寸为 4，我希望能够在第一个维度上滑动 window，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]]]

还要跨越二次元，像这样：

[[[ 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

您可以在恒定时间内高效地构建这样的数组，并且无需使用任何额外内存，如果您需要连续数组，请使用 numpy.lib.stride_tricks.as_strided. The resulting array will be a view with some limitations, but you can always make a copy。

以下函数解决了一般问题：

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)

在数组轴上滚动或滑动 window 的通用方法

Generalized method for rolling or sliding window over array axis

python

numpy

sliding-window