numpy.lib.stride_tricks

Parameters

x : ndarray

Array to create a new.

shape : sequence of int, optional

The shape of the new array. Defaults to x.shape.

strides : sequence of int, optional

The strides of the new array. Defaults to x.strides.

subok : bool, optional

New in version 1.10.

If True, subclasses are preserved.

writeable : bool, optional

New in version 1.12.

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 Notes).

Returns

view : ndarray

See also

broadcast_to : broadcast an array to a given shape. reshape : reshape an array. lib.stride_tricks.sliding_window_view :

userfriendly and safe function for the creation of sliding window views.

Notes

as_strided creates a view into the array given the exact strides and shape. This means it manipulates the internal data structure of ndarray and, if done incorrectly, the array elements can point to invalid memory and can corrupt results or crash your program. It is advisable to always use the original x.strides when calculating new strides to avoid reliance on a contiguous memory layout.

Furthermore, arrays created with this function often contain self overlapping memory, so that two elements are identical. Vectorized write operations on such arrays will typically be unpredictable. They may even give different results for small, large, or transposed arrays. Since writing to these arrays has to be tested and done with great care, you may want to use writeable=False to avoid accidental write operations.

For these reasons it is advisable to avoid as_strided when possible.

Parameters

x : array_like

Array to create the sliding window view from.

window_shape : int or tuple of int

Size of window over each axis that takes part in the sliding window. If axis is not present, must have same length as the number of input array dimensions. Single integers i are treated as if they were the tuple (i,).

axis : int or tuple of int, optional

Axis or axes along which the sliding window is applied. By default, the sliding window is applied to all axes and window_shape[i] will refer to axis i of x. If axis is given as a tuple of int, window_shape[i] will refer to the axis axis[i] of x. Single integers i are treated as if they were the tuple (i,).

subok : bool, optional

If True, sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array (default).

writeable : bool, optional

When true, allow writing to the returned view. The default is false, as this should be used with caution: the returned view contains the same memory location multiple times, so writing to one location will cause others to change.

Returns

view : ndarray

Sliding window view of the array. The sliding window dimensions are inserted at the end, and the original dimensions are trimmed as required by the size of the sliding window. That is, view.shape = x_shape_trimmed + window_shape, where x_shape_trimmed is x.shape with every entry reduced by one less than the corresponding window size.

See Also

lib.stride_tricks.as_strided: A lower-level and less safe routine for

creating arbitrary views from custom shape and strides.

broadcast_to: broadcast an array to a given shape.

Notes

For many applications using a sliding window view can be convenient, but potentially very slow. Often specialized solutions exist, for example:

• scipy.signal.fftconvolve
• filtering functions in scipy.ndimage
• moving window functions provided by bottleneck.

As a rough estimate, a sliding window approach with an input size of N and a window size of W will scale as O(N*W) where frequently a special algorithm can achieve O(N). That means that the sliding window variant for a window size of 100 can be a 100 times slower than a more specialized version.

Nevertheless, for small window sizes, when no custom algorithm exists, or as a prototyping and developing tool, this function can be a good solution.

Examples

>>> 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, 3, 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:

>>> 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.])

Note that a sliding window approach is often not optimal (see Notes).