`_.
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).
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Broadcast the input shapes into a single shape.
:ref:`Learn more about broadcasting here `.
.. versionadded:: 1.20.0
Parameters
----------
`*args` : tuples of ints, or ints
The shapes to be broadcast against each other.
Returns
-------
tuple
Broadcasted shape.
Raises
------
ValueError
If the shapes are not compatible and cannot be broadcast according
to NumPy's broadcasting rules.
See Also
--------
broadcast
broadcast_arrays
broadcast_to
Examples
--------
>>> np.broadcast_shapes((1, 2), (3, 1), (3, 2))
(3, 2)
>>> np.broadcast_shapes((6, 7), (5, 6, 1), (7,), (5, 1, 7))
(5, 6, 7)
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Broadcast any number of arrays against each other.
Parameters
----------
`*args` : array_likes
The arrays to broadcast.
subok : bool, optional
If True, then sub-classes will be passed-through, otherwise
the returned arrays will be forced to be a base-class array (default).
Returns
-------
broadcasted : list of arrays
These arrays are views on the original arrays. They are typically
not contiguous. Furthermore, more than one element of a
broadcasted array may refer to a single memory location. If you need
to write to the arrays, make copies first. While you can set the
``writable`` flag True, writing to a single output value may end up
changing more than one location in the output array.
.. deprecated:: 1.17
The output is currently marked so that if written to, a deprecation
warning will be emitted. A future version will set the
``writable`` flag False so writing to it will raise an error.
See Also
--------
broadcast
broadcast_to
broadcast_shapes
Examples
--------
>>> x = np.array([[1,2,3]])
>>> y = np.array([[4],[5]])
>>> np.broadcast_arrays(x, y)
[array([[1, 2, 3],
[1, 2, 3]]), array([[4, 4, 4],
[5, 5, 5]])]
Here is a useful idiom for getting contiguous copies instead of
non-contiguous views.
>>> [np.array(a) for a in np.broadcast_arrays(x, y)]
[array([[1, 2, 3],
[1, 2, 3]]), array([[4, 4, 4],
[5, 5, 5]])]
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