问题
How can I efficiently make an array of sliding windows across an arbitrary axis of a given array? For example, if I have the following array:
[[ 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]]
And a window size of 4, I would like to be able to make a sliding window across the first dimension, like this:
[[[ 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]]]
But also across the second dimension, like this:
[[[ 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]]]
回答1:
You can build such an array efficiently, in constant time and and without using any additional memory, using numpy.lib.stride_tricks.as_strided. The resulting array will be a view with some limitations, but you can always make a copy if you need a contiguous array.
The following function solves the general problem:
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
Examples:
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)
来源：https://stackoverflow.com/questions/53263678/generalized-method-for-rolling-or-sliding-window-over-array-axis