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1"""

2Utilities that manipulate strides to achieve desirable effects.

4An explanation of strides can be found in the "ndarray.rst" file in the

5NumPy reference guide.

7"""

8import numpy as np

9from numpy.core.numeric import normalize_axis_tuple

10from numpy.core.overrides import array_function_dispatch, set_module

12__all__ = ['broadcast_to', 'broadcast_arrays', 'broadcast_shapes']

15class DummyArray:

16 """Dummy object that just exists to hang __array_interface__ dictionaries

17 and possibly keep alive a reference to a base array.

18 """

20 def __init__(self, interface, base=None):

21 self.__array_interface__ = interface

22 self.base = base

25def _maybe_view_as_subclass(original_array, new_array):

26 if type(original_array) is not type(new_array):

27 # if input was an ndarray subclass and subclasses were OK,

28 # then view the result as that subclass.

29 new_array = new_array.view(type=type(original_array))

30 # Since we have done something akin to a view from original_array, we

31 # should let the subclass finalize (if it has it implemented, i.e., is

32 # not None).

33 if new_array.__array_finalize__:

34 new_array.__array_finalize__(original_array)

35 return new_array

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 .. versionadded:: 1.10

55 If True, subclasses are preserved.

56 writeable : bool, optional

57 .. versionadded:: 1.12

59 If set to False, the returned array will always be readonly.

60 Otherwise it will be writable if the original array was. It

61 is advisable to set this to False if possible (see Notes).

63 Returns

64 -------

65 view : ndarray

67 See also

68 --------

69 broadcast_to : broadcast an array to a given shape.

70 reshape : reshape an array.

71 lib.stride_tricks.sliding_window_view :

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

74 Notes

75 -----

76 ``as_strided`` creates a view into the array given the exact strides

77 and shape. This means it manipulates the internal data structure of

78 ndarray and, if done incorrectly, the array elements can point to

79 invalid memory and can corrupt results or crash your program.

80 It is advisable to always use the original ``x.strides`` when

81 calculating new strides to avoid reliance on a contiguous memory

82 layout.

84 Furthermore, arrays created with this function often contain self

85 overlapping memory, so that two elements are identical.

86 Vectorized write operations on such arrays will typically be

87 unpredictable. They may even give different results for small, large,

88 or transposed arrays.

90 Since writing to these arrays has to be tested and done with great

91 care, you may want to use ``writeable=False`` to avoid accidental write

92 operations.

94 For these reasons it is advisable to avoid ``as_strided`` when

95 possible.

96 """

97 # first convert input to array, possibly keeping subclass

98 x = np.array(x, copy=False, subok=subok)

99 interface = dict(x.__array_interface__)

100 if shape is not None:

101 interface['shape'] = tuple(shape)

102 if strides is not None:

103 interface['strides'] = tuple(strides)

104

105 array = np.asarray(DummyArray(interface, base=x))

106 # The route via `__interface__` does not preserve structured

107 # dtypes. Since dtype should remain unchanged, we set it explicitly.

108 array.dtype = x.dtype

109

110 view = _maybe_view_as_subclass(x, array)

111

112 if view.flags.writeable and not writeable:

113 view.flags.writeable = False

114

115 return view

116

117

118def _sliding_window_view_dispatcher(x, window_shape, axis=None, *,

119 subok=None, writeable=None):

120 return (x,)

121

122

123@array_function_dispatch(_sliding_window_view_dispatcher)

124def sliding_window_view(x, window_shape, axis=None, *,

125 subok=False, writeable=False):

126 """

127 Create a sliding window view into the array with the given window shape.

128

129 Also known as rolling or moving window, the window slides across all

130 dimensions of the array and extracts subsets of the array at all window

131 positions.

132

133 .. versionadded:: 1.20.0

134

135 Parameters

136 ----------

137 x : array_like

138 Array to create the sliding window view from.

139 window_shape : int or tuple of int

140 Size of window over each axis that takes part in the sliding window.

141 If `axis` is not present, must have same length as the number of input

142 array dimensions. Single integers `i` are treated as if they were the

143 tuple `(i,)`.

144 axis : int or tuple of int, optional

145 Axis or axes along which the sliding window is applied.

146 By default, the sliding window is applied to all axes and

147 `window_shape[i]` will refer to axis `i` of `x`.

148 If `axis` is given as a `tuple of int`, `window_shape[i]` will refer to

149 the axis `axis[i]` of `x`.

150 Single integers `i` are treated as if they were the tuple `(i,)`.

151 subok : bool, optional

152 If True, sub-classes will be passed-through, otherwise the returned

153 array will be forced to be a base-class array (default).

154 writeable : bool, optional

155 When true, allow writing to the returned view. The default is false,

156 as this should be used with caution: the returned view contains the

157 same memory location multiple times, so writing to one location will

158 cause others to change.

159

160 Returns

161 -------

162 view : ndarray

163 Sliding window view of the array. The sliding window dimensions are

164 inserted at the end, and the original dimensions are trimmed as

165 required by the size of the sliding window.

166 That is, ``view.shape = x_shape_trimmed + window_shape``, where

167 ``x_shape_trimmed`` is ``x.shape`` with every entry reduced by one less

168 than the corresponding window size.

169

170 See Also

171 --------

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

173 creating arbitrary views from custom shape and strides.

174 broadcast_to: broadcast an array to a given shape.

175

176 Notes

177 -----

178 For many applications using a sliding window view can be convenient, but

179 potentially very slow. Often specialized solutions exist, for example:

180

181 - `scipy.signal.fftconvolve`

182

183 - filtering functions in `scipy.ndimage`

184

185 - moving window functions provided by

186 `bottleneck <https://github.com/pydata/bottleneck>`_.

187

188 As a rough estimate, a sliding window approach with an input size of `N`

189 and a window size of `W` will scale as `O(N*W)` where frequently a special

190 algorithm can achieve `O(N)`. That means that the sliding window variant

191 for a window size of 100 can be a 100 times slower than a more specialized

192 version.

193

194 Nevertheless, for small window sizes, when no custom algorithm exists, or

195 as a prototyping and developing tool, this function can be a good solution.

196

197 Examples

198 --------

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]])

210

211 This also works in more dimensions, e.g.

212

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]]]])

238

239 The axis can be specified explicitly:

240

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]]])

249

250 The same axis can be used several times. In that case, every use reduces

251 the corresponding original dimension:

252

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]]]])

263

264 Combining with stepped slicing (`::step`), this can be used to take sliding

265 views which skip elements:

266

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]])

272

273 or views which move by multiple elements

274

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]])

280

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>`_:

284

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.])

299

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=False, subok=subok)

307

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')

311

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.')

325

326 out_strides = x.strides + tuple(x.strides[ax] for ax in axis)

327

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)

338

339

340def _broadcast_to(array, shape, subok, readonly):

341 shape = tuple(shape) if np.iterable(shape) else (shape,)

342 array = np.array(array, copy=False, 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

361

362

363def _broadcast_to_dispatcher(array, shape, subok=None):

364 return (array,)

365

366

367@array_function_dispatch(_broadcast_to_dispatcher, module='numpy')

368def broadcast_to(array, shape, subok=False):

369 """Broadcast an array to a new shape.

370

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).

381

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.

388

389 Raises

390 ------

391 ValueError

392 If the array is not compatible with the new shape according to NumPy's

393 broadcasting rules.

394

395 See Also

396 --------

397 broadcast

398 broadcast_arrays

399 broadcast_shapes

400

401 Notes

402 -----

403 .. versionadded:: 1.10.0

404

405 Examples

406 --------

407 >>> x = np.array([1, 2, 3])

408 >>> np.broadcast_to(x, (3, 3))

409 array([[1, 2, 3],

410 [1, 2, 3],

411 [1, 2, 3]])

412 """

413 return _broadcast_to(array, shape, subok=subok, readonly=True)

414

415

416def _broadcast_shape(*args):

417 """Returns the shape of the arrays that would result from broadcasting the

418 supplied arrays against each other.

419 """

420 # use the old-iterator because np.nditer does not handle size 0 arrays

421 # consistently

422 b = np.broadcast(*args[:32])

423 # unfortunately, it cannot handle 32 or more arguments directly

424 for pos in range(32, len(args), 31):

425 # ironically, np.broadcast does not properly handle np.broadcast

426 # objects (it treats them as scalars)

427 # use broadcasting to avoid allocating the full array

428 b = broadcast_to(0, b.shape)

429 b = np.broadcast(b, *args[pos:(pos + 31)])

430 return b.shape

431

432

433@set_module('numpy')

434def broadcast_shapes(*args):

435 """

436 Broadcast the input shapes into a single shape.

437

438 :ref:`Learn more about broadcasting here <basics.broadcasting>`.

439

440 .. versionadded:: 1.20.0

441

442 Parameters

443 ----------

444 `*args` : tuples of ints, or ints

445 The shapes to be broadcast against each other.

446

447 Returns

448 -------

449 tuple

450 Broadcasted shape.

451

452 Raises

453 ------

454 ValueError

455 If the shapes are not compatible and cannot be broadcast according

456 to NumPy's broadcasting rules.

457

458 See Also

459 --------

460 broadcast

461 broadcast_arrays

462 broadcast_to

463

464 Examples

465 --------

466 >>> np.broadcast_shapes((1, 2), (3, 1), (3, 2))

467 (3, 2)

468

469 >>> np.broadcast_shapes((6, 7), (5, 6, 1), (7,), (5, 1, 7))

470 (5, 6, 7)

471 """

472 arrays = [np.empty(x, dtype=[]) for x in args]

473 return _broadcast_shape(*arrays)

474

475

476def _broadcast_arrays_dispatcher(*args, subok=None):

477 return args

478

479

480@array_function_dispatch(_broadcast_arrays_dispatcher, module='numpy')

481def broadcast_arrays(*args, subok=False):

482 """

483 Broadcast any number of arrays against each other.

484

485 Parameters

486 ----------

487 `*args` : array_likes

488 The arrays to broadcast.

489

490 subok : bool, optional

491 If True, then sub-classes will be passed-through, otherwise

492 the returned arrays will be forced to be a base-class array (default).

493

494 Returns

495 -------

496 broadcasted : list of arrays

497 These arrays are views on the original arrays. They are typically

498 not contiguous. Furthermore, more than one element of a

499 broadcasted array may refer to a single memory location. If you need

500 to write to the arrays, make copies first. While you can set the

501 ``writable`` flag True, writing to a single output value may end up

502 changing more than one location in the output array.

503

504 .. deprecated:: 1.17

505 The output is currently marked so that if written to, a deprecation

506 warning will be emitted. A future version will set the

507 ``writable`` flag False so writing to it will raise an error.

508

509 See Also

510 --------

511 broadcast

512 broadcast_to

513 broadcast_shapes

514

515 Examples

516 --------

517 >>> x = np.array([[1,2,3]])

518 >>> y = np.array([[4],[5]])

519 >>> np.broadcast_arrays(x, y)

520 [array([[1, 2, 3],

521 [1, 2, 3]]), array([[4, 4, 4],

522 [5, 5, 5]])]

523

524 Here is a useful idiom for getting contiguous copies instead of

525 non-contiguous views.

526

527 >>> [np.array(a) for a in np.broadcast_arrays(x, y)]

528 [array([[1, 2, 3],

529 [1, 2, 3]]), array([[4, 4, 4],

530 [5, 5, 5]])]

531

532 """

533 # nditer is not used here to avoid the limit of 32 arrays.

534 # Otherwise, something like the following one-liner would suffice:

535 # return np.nditer(args, flags=['multi_index', 'zerosize_ok'],

536 # order='C').itviews

537

538 args = [np.array(_m, copy=False, subok=subok) for _m in args]

539

540 shape = _broadcast_shape(*args)

541

542 if all(array.shape == shape for array in args):

543 # Common case where nothing needs to be broadcasted.

544 return args

545

546 return [_broadcast_to(array, shape, subok=subok, readonly=False)

547 for array in args]

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