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1"""
2Utilities that manipulate strides to achieve desirable effects.
4An explanation of strides can be found in the :ref:`arrays.ndarray`.
6"""
7import numpy as np
8from numpy._core.numeric import normalize_axis_tuple
9from numpy._core.overrides import array_function_dispatch, set_module
11__all__ = ['broadcast_to', 'broadcast_arrays', 'broadcast_shapes']
14class DummyArray:
15 """Dummy object that just exists to hang __array_interface__ dictionaries
16 and possibly keep alive a reference to a base array.
17 """
19 def __init__(self, interface, base=None):
20 self.__array_interface__ = interface
21 self.base = base
24def _maybe_view_as_subclass(original_array, new_array):
25 if type(original_array) is not type(new_array):
26 # if input was an ndarray subclass and subclasses were OK,
27 # then view the result as that subclass.
28 new_array = new_array.view(type=type(original_array))
29 # Since we have done something akin to a view from original_array, we
30 # should let the subclass finalize (if it has it implemented, i.e., is
31 # not None).
32 if new_array.__array_finalize__:
33 new_array.__array_finalize__(original_array)
34 return new_array
37@set_module("numpy.lib.stride_tricks")
38def as_strided(x, shape=None, strides=None, subok=False, writeable=True):
39 """
40 Create a view into the array with the given shape and strides.
42 .. warning:: This function has to be used with extreme care, see notes.
44 Parameters
45 ----------
46 x : ndarray
47 Array to create a new.
48 shape : sequence of int, optional
49 The shape of the new array. Defaults to ``x.shape``.
50 strides : sequence of int, optional
51 The strides of the new array. Defaults to ``x.strides``.
52 subok : bool, optional
53 If True, subclasses are preserved.
54 writeable : bool, optional
55 If set to False, the returned array will always be readonly.
56 Otherwise it will be writable if the original array was. It
57 is advisable to set this to False if possible (see Notes).
59 Returns
60 -------
61 view : ndarray
63 See also
64 --------
65 broadcast_to : broadcast an array to a given shape.
66 reshape : reshape an array.
67 lib.stride_tricks.sliding_window_view :
68 userfriendly and safe function for a creation of sliding window views.
70 Notes
71 -----
72 ``as_strided`` creates a view into the array given the exact strides
73 and shape. This means it manipulates the internal data structure of
74 ndarray and, if done incorrectly, the array elements can point to
75 invalid memory and can corrupt results or crash your program.
76 It is advisable to always use the original ``x.strides`` when
77 calculating new strides to avoid reliance on a contiguous memory
78 layout.
80 Furthermore, arrays created with this function often contain self
81 overlapping memory, so that two elements are identical.
82 Vectorized write operations on such arrays will typically be
83 unpredictable. They may even give different results for small, large,
84 or transposed arrays.
86 Since writing to these arrays has to be tested and done with great
87 care, you may want to use ``writeable=False`` to avoid accidental write
88 operations.
90 For these reasons it is advisable to avoid ``as_strided`` when
91 possible.
92 """
93 # first convert input to array, possibly keeping subclass
94 x = np.array(x, copy=None, subok=subok)
95 interface = dict(x.__array_interface__)
96 if shape is not None:
97 interface['shape'] = tuple(shape)
98 if strides is not None:
99 interface['strides'] = tuple(strides)
101 array = np.asarray(DummyArray(interface, base=x))
102 # The route via `__interface__` does not preserve structured
103 # dtypes. Since dtype should remain unchanged, we set it explicitly.
104 array.dtype = x.dtype
106 view = _maybe_view_as_subclass(x, array)
108 if view.flags.writeable and not writeable:
109 view.flags.writeable = False
111 return view
114def _sliding_window_view_dispatcher(x, window_shape, axis=None, *,
115 subok=None, writeable=None):
116 return (x,)
119@array_function_dispatch(
120 _sliding_window_view_dispatcher, module="numpy.lib.stride_tricks"
121)
122def sliding_window_view(x, window_shape, axis=None, *,
123 subok=False, writeable=False):
124 """
125 Create a sliding window view into the array with the given window shape.
127 Also known as rolling or moving window, the window slides across all
128 dimensions of the array and extracts subsets of the array at all window
129 positions.
131 .. versionadded:: 1.20.0
133 Parameters
134 ----------
135 x : array_like
136 Array to create the sliding window view from.
137 window_shape : int or tuple of int
138 Size of window over each axis that takes part in the sliding window.
139 If `axis` is not present, must have same length as the number of input
140 array dimensions. Single integers `i` are treated as if they were the
141 tuple `(i,)`.
142 axis : int or tuple of int, optional
143 Axis or axes along which the sliding window is applied.
144 By default, the sliding window is applied to all axes and
145 `window_shape[i]` will refer to axis `i` of `x`.
146 If `axis` is given as a `tuple of int`, `window_shape[i]` will refer to
147 the axis `axis[i]` of `x`.
148 Single integers `i` are treated as if they were the tuple `(i,)`.
149 subok : bool, optional
150 If True, sub-classes will be passed-through, otherwise the returned
151 array will be forced to be a base-class array (default).
152 writeable : bool, optional
153 When true, allow writing to the returned view. The default is false,
154 as this should be used with caution: the returned view contains the
155 same memory location multiple times, so writing to one location will
156 cause others to change.
158 Returns
159 -------
160 view : ndarray
161 Sliding window view of the array. The sliding window dimensions are
162 inserted at the end, and the original dimensions are trimmed as
163 required by the size of the sliding window.
164 That is, ``view.shape = x_shape_trimmed + window_shape``, where
165 ``x_shape_trimmed`` is ``x.shape`` with every entry reduced by one less
166 than the corresponding window size.
168 See Also
169 --------
170 lib.stride_tricks.as_strided: A lower-level and less safe routine for
171 creating arbitrary views from custom shape and strides.
172 broadcast_to: broadcast an array to a given shape.
174 Notes
175 -----
176 For many applications using a sliding window view can be convenient, but
177 potentially very slow. Often specialized solutions exist, for example:
179 - `scipy.signal.fftconvolve`
181 - filtering functions in `scipy.ndimage`
183 - moving window functions provided by
184 `bottleneck <https://github.com/pydata/bottleneck>`_.
186 As a rough estimate, a sliding window approach with an input size of `N`
187 and a window size of `W` will scale as `O(N*W)` where frequently a special
188 algorithm can achieve `O(N)`. That means that the sliding window variant
189 for a window size of 100 can be a 100 times slower than a more specialized
190 version.
192 Nevertheless, for small window sizes, when no custom algorithm exists, or
193 as a prototyping and developing tool, this function can be a good solution.
195 Examples
196 --------
197 >>> import numpy as np
198 >>> from numpy.lib.stride_tricks import sliding_window_view
199 >>> x = np.arange(6)
200 >>> x.shape
201 (6,)
202 >>> v = sliding_window_view(x, 3)
203 >>> v.shape
204 (4, 3)
205 >>> v
206 array([[0, 1, 2],
207 [1, 2, 3],
208 [2, 3, 4],
209 [3, 4, 5]])
211 This also works in more dimensions, e.g.
213 >>> i, j = np.ogrid[:3, :4]
214 >>> x = 10*i + j
215 >>> x.shape
216 (3, 4)
217 >>> x
218 array([[ 0, 1, 2, 3],
219 [10, 11, 12, 13],
220 [20, 21, 22, 23]])
221 >>> shape = (2,2)
222 >>> v = sliding_window_view(x, shape)
223 >>> v.shape
224 (2, 3, 2, 2)
225 >>> v
226 array([[[[ 0, 1],
227 [10, 11]],
228 [[ 1, 2],
229 [11, 12]],
230 [[ 2, 3],
231 [12, 13]]],
232 [[[10, 11],
233 [20, 21]],
234 [[11, 12],
235 [21, 22]],
236 [[12, 13],
237 [22, 23]]]])
239 The axis can be specified explicitly:
241 >>> v = sliding_window_view(x, 3, 0)
242 >>> v.shape
243 (1, 4, 3)
244 >>> v
245 array([[[ 0, 10, 20],
246 [ 1, 11, 21],
247 [ 2, 12, 22],
248 [ 3, 13, 23]]])
250 The same axis can be used several times. In that case, every use reduces
251 the corresponding original dimension:
253 >>> v = sliding_window_view(x, (2, 3), (1, 1))
254 >>> v.shape
255 (3, 1, 2, 3)
256 >>> v
257 array([[[[ 0, 1, 2],
258 [ 1, 2, 3]]],
259 [[[10, 11, 12],
260 [11, 12, 13]]],
261 [[[20, 21, 22],
262 [21, 22, 23]]]])
264 Combining with stepped slicing (`::step`), this can be used to take sliding
265 views which skip elements:
267 >>> x = np.arange(7)
268 >>> sliding_window_view(x, 5)[:, ::2]
269 array([[0, 2, 4],
270 [1, 3, 5],
271 [2, 4, 6]])
273 or views which move by multiple elements
275 >>> x = np.arange(7)
276 >>> sliding_window_view(x, 3)[::2, :]
277 array([[0, 1, 2],
278 [2, 3, 4],
279 [4, 5, 6]])
281 A common application of `sliding_window_view` is the calculation of running
282 statistics. The simplest example is the
283 `moving average <https://en.wikipedia.org/wiki/Moving_average>`_:
285 >>> x = np.arange(6)
286 >>> x.shape
287 (6,)
288 >>> v = sliding_window_view(x, 3)
289 >>> v.shape
290 (4, 3)
291 >>> v
292 array([[0, 1, 2],
293 [1, 2, 3],
294 [2, 3, 4],
295 [3, 4, 5]])
296 >>> moving_average = v.mean(axis=-1)
297 >>> moving_average
298 array([1., 2., 3., 4.])
300 Note that a sliding window approach is often **not** optimal (see Notes).
301 """
302 window_shape = (tuple(window_shape)
303 if np.iterable(window_shape)
304 else (window_shape,))
305 # first convert input to array, possibly keeping subclass
306 x = np.array(x, copy=None, subok=subok)
308 window_shape_array = np.array(window_shape)
309 if np.any(window_shape_array < 0):
310 raise ValueError('`window_shape` cannot contain negative values')
312 if axis is None:
313 axis = tuple(range(x.ndim))
314 if len(window_shape) != len(axis):
315 raise ValueError(f'Since axis is `None`, must provide '
316 f'window_shape for all dimensions of `x`; '
317 f'got {len(window_shape)} window_shape elements '
318 f'and `x.ndim` is {x.ndim}.')
319 else:
320 axis = normalize_axis_tuple(axis, x.ndim, allow_duplicate=True)
321 if len(window_shape) != len(axis):
322 raise ValueError(f'Must provide matching length window_shape and '
323 f'axis; got {len(window_shape)} window_shape '
324 f'elements and {len(axis)} axes elements.')
326 out_strides = x.strides + tuple(x.strides[ax] for ax in axis)
328 # note: same axis can be windowed repeatedly
329 x_shape_trimmed = list(x.shape)
330 for ax, dim in zip(axis, window_shape):
331 if x_shape_trimmed[ax] < dim:
332 raise ValueError(
333 'window shape cannot be larger than input array shape')
334 x_shape_trimmed[ax] -= dim - 1
335 out_shape = tuple(x_shape_trimmed) + window_shape
336 return as_strided(x, strides=out_strides, shape=out_shape,
337 subok=subok, writeable=writeable)
340def _broadcast_to(array, shape, subok, readonly):
341 shape = tuple(shape) if np.iterable(shape) else (shape,)
342 array = np.array(array, copy=None, subok=subok)
343 if not shape and array.shape:
344 raise ValueError('cannot broadcast a non-scalar to a scalar array')
345 if any(size < 0 for size in shape):
346 raise ValueError('all elements of broadcast shape must be non-'
347 'negative')
348 extras = []
349 it = np.nditer(
350 (array,), flags=['multi_index', 'refs_ok', 'zerosize_ok'] + extras,
351 op_flags=['readonly'], itershape=shape, order='C')
352 with it:
353 # never really has writebackifcopy semantics
354 broadcast = it.itviews[0]
355 result = _maybe_view_as_subclass(array, broadcast)
356 # In a future version this will go away
357 if not readonly and array.flags._writeable_no_warn:
358 result.flags.writeable = True
359 result.flags._warn_on_write = True
360 return result
363def _broadcast_to_dispatcher(array, shape, subok=None):
364 return (array,)
367@array_function_dispatch(_broadcast_to_dispatcher, module='numpy')
368def broadcast_to(array, shape, subok=False):
369 """Broadcast an array to a new shape.
371 Parameters
372 ----------
373 array : array_like
374 The array to broadcast.
375 shape : tuple or int
376 The shape of the desired array. A single integer ``i`` is interpreted
377 as ``(i,)``.
378 subok : bool, optional
379 If True, then sub-classes will be passed-through, otherwise
380 the returned array will be forced to be a base-class array (default).
382 Returns
383 -------
384 broadcast : array
385 A readonly view on the original array with the given shape. It is
386 typically not contiguous. Furthermore, more than one element of a
387 broadcasted array may refer to a single memory location.
389 Raises
390 ------
391 ValueError
392 If the array is not compatible with the new shape according to NumPy's
393 broadcasting rules.
395 See Also
396 --------
397 broadcast
398 broadcast_arrays
399 broadcast_shapes
401 Examples
402 --------
403 >>> import numpy as np
404 >>> x = np.array([1, 2, 3])
405 >>> np.broadcast_to(x, (3, 3))
406 array([[1, 2, 3],
407 [1, 2, 3],
408 [1, 2, 3]])
409 """
410 return _broadcast_to(array, shape, subok=subok, readonly=True)
413def _broadcast_shape(*args):
414 """Returns the shape of the arrays that would result from broadcasting the
415 supplied arrays against each other.
416 """
417 # use the old-iterator because np.nditer does not handle size 0 arrays
418 # consistently
419 b = np.broadcast(*args[:32])
420 # unfortunately, it cannot handle 32 or more arguments directly
421 for pos in range(32, len(args), 31):
422 # ironically, np.broadcast does not properly handle np.broadcast
423 # objects (it treats them as scalars)
424 # use broadcasting to avoid allocating the full array
425 b = broadcast_to(0, b.shape)
426 b = np.broadcast(b, *args[pos:(pos + 31)])
427 return b.shape
430_size0_dtype = np.dtype([])
433@set_module('numpy')
434def broadcast_shapes(*args):
435 """
436 Broadcast the input shapes into a single shape.
438 :ref:`Learn more about broadcasting here <basics.broadcasting>`.
440 .. versionadded:: 1.20.0
442 Parameters
443 ----------
444 *args : tuples of ints, or ints
445 The shapes to be broadcast against each other.
447 Returns
448 -------
449 tuple
450 Broadcasted shape.
452 Raises
453 ------
454 ValueError
455 If the shapes are not compatible and cannot be broadcast according
456 to NumPy's broadcasting rules.
458 See Also
459 --------
460 broadcast
461 broadcast_arrays
462 broadcast_to
464 Examples
465 --------
466 >>> import numpy as np
467 >>> np.broadcast_shapes((1, 2), (3, 1), (3, 2))
468 (3, 2)
470 >>> np.broadcast_shapes((6, 7), (5, 6, 1), (7,), (5, 1, 7))
471 (5, 6, 7)
472 """
473 arrays = [np.empty(x, dtype=_size0_dtype) for x in args]
474 return _broadcast_shape(*arrays)
477def _broadcast_arrays_dispatcher(*args, subok=None):
478 return args
481@array_function_dispatch(_broadcast_arrays_dispatcher, module='numpy')
482def broadcast_arrays(*args, subok=False):
483 """
484 Broadcast any number of arrays against each other.
486 Parameters
487 ----------
488 *args : array_likes
489 The arrays to broadcast.
491 subok : bool, optional
492 If True, then sub-classes will be passed-through, otherwise
493 the returned arrays will be forced to be a base-class array (default).
495 Returns
496 -------
497 broadcasted : tuple of arrays
498 These arrays are views on the original arrays. They are typically
499 not contiguous. Furthermore, more than one element of a
500 broadcasted array may refer to a single memory location. If you need
501 to write to the arrays, make copies first. While you can set the
502 ``writable`` flag True, writing to a single output value may end up
503 changing more than one location in the output array.
505 .. deprecated:: 1.17
506 The output is currently marked so that if written to, a deprecation
507 warning will be emitted. A future version will set the
508 ``writable`` flag False so writing to it will raise an error.
510 See Also
511 --------
512 broadcast
513 broadcast_to
514 broadcast_shapes
516 Examples
517 --------
518 >>> import numpy as np
519 >>> x = np.array([[1,2,3]])
520 >>> y = np.array([[4],[5]])
521 >>> np.broadcast_arrays(x, y)
522 (array([[1, 2, 3],
523 [1, 2, 3]]),
524 array([[4, 4, 4],
525 [5, 5, 5]]))
527 Here is a useful idiom for getting contiguous copies instead of
528 non-contiguous views.
530 >>> [np.array(a) for a in np.broadcast_arrays(x, y)]
531 [array([[1, 2, 3],
532 [1, 2, 3]]),
533 array([[4, 4, 4],
534 [5, 5, 5]])]
536 """
537 # nditer is not used here to avoid the limit of 32 arrays.
538 # Otherwise, something like the following one-liner would suffice:
539 # return np.nditer(args, flags=['multi_index', 'zerosize_ok'],
540 # order='C').itviews
542 args = [np.array(_m, copy=None, subok=subok) for _m in args]
544 shape = _broadcast_shape(*args)
546 result = [array if array.shape == shape
547 else _broadcast_to(array, shape, subok=subok, readonly=False)
548 for array in args]
549 return tuple(result)