Repository navigation
Expand file tree
/
Copy pathfromnumeric.py
More file actions
4271 lines (3484 loc) · 141 KB
/
Copy pathfromnumeric.py
File metadata and controls
4271 lines (3484 loc) · 141 KB
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
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
"""Module containing non-deprecated functions borrowed from Numeric.
"""
import functools
import math
import types
import numpy as np
from numpy._utils import set_module
from . import _methods, multiarray as mu, numerictypes as nt, overrides, umath as um
from ._multiarray_umath import _array_converter
from .multiarray import asanyarray, asarray, concatenate
_dt_ = nt.sctype2char
# functions that are methods
__all__ = [
'all', 'amax', 'amin', 'any', 'argmax',
'argmin', 'argpartition', 'argsort', 'around', 'choose', 'clip',
'compress', 'cumprod', 'cumsum', 'cumulative_prod', 'cumulative_sum',
'diagonal', 'mean', 'max', 'min', 'matrix_transpose',
'ndim', 'nonzero', 'partition', 'prod', 'ptp', 'put',
'ravel', 'repeat', 'reshape', 'resize', 'round',
'searchsorted', 'shape', 'size', 'sort', 'squeeze',
'std', 'sum', 'swapaxes', 'take', 'trace', 'transpose', 'var',
]
_gentype = types.GeneratorType
# save away Python sum
_sum_ = sum
array_function_dispatch = functools.partial(
overrides.array_function_dispatch, module='numpy')
# functions that are now methods
def _wrapit(obj, method, *args, **kwds):
conv = _array_converter(obj)
# As this already tried the method, subok is maybe quite reasonable here
# but this follows what was done before. TODO: revisit this.
arr, = conv.as_arrays(subok=False)
result = getattr(arr, method)(*args, **kwds)
return conv.wrap(result, to_scalar=False)
def _wrapfunc(obj, method, *args, **kwds):
bound = getattr(obj, method, None)
if bound is None:
return _wrapit(obj, method, *args, **kwds)
try:
return bound(*args, **kwds)
except TypeError:
# A TypeError occurs if the object does have such a method in its
# class, but its signature is not identical to that of NumPy's. This
# situation has occurred in the case of a downstream library like
# 'pandas'.
#
# Call _wrapit from within the except clause to ensure a potential
# exception has a traceback chain.
return _wrapit(obj, method, *args, **kwds)
def _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs):
passkwargs = {k: v for k, v in kwargs.items()
if v is not np._NoValue}
if type(obj) is not mu.ndarray:
try:
reduction = getattr(obj, method)
except AttributeError:
pass
else:
# This branch is needed for reductions like any which don't
# support a dtype.
if dtype is not None:
return reduction(axis=axis, dtype=dtype, out=out, **passkwargs)
else:
return reduction(axis=axis, out=out, **passkwargs)
return ufunc.reduce(obj, axis, dtype, out, **passkwargs)
def _wrapreduction_any_all(obj, ufunc, method, axis, out, **kwargs):
# Same as above function, but dtype is always bool (but never passed on)
passkwargs = {k: v for k, v in kwargs.items()
if v is not np._NoValue}
if type(obj) is not mu.ndarray:
try:
reduction = getattr(obj, method)
except AttributeError:
pass
else:
return reduction(axis=axis, out=out, **passkwargs)
return ufunc.reduce(obj, axis, bool, out, **passkwargs)
def _take_dispatcher(a, indices, axis=None, out=None, mode=None):
return (a, out)
@array_function_dispatch(_take_dispatcher)
def take(a, indices, axis=None, out=None, mode='raise'):
"""
Take elements from an array along an axis.
When axis is not None, this function does the same thing as "fancy"
indexing (indexing arrays using arrays); however, it can be easier to use
if you need elements along a given axis. A call such as
``np.take(arr, indices, axis=3)`` is equivalent to
``arr[:,:,:,indices,...]``.
Explained without fancy indexing, this is equivalent to the following use
of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of
indices::
Ni, Nk = a.shape[:axis], a.shape[axis+1:]
Nj = indices.shape
for ii in ndindex(Ni):
for jj in ndindex(Nj):
for kk in ndindex(Nk):
out[ii + jj + kk] = a[ii + (indices[jj],) + kk]
Parameters
----------
a : array_like (Ni..., M, Nk...)
The source array.
indices : array_like (Nj...)
The indices of the values to extract.
Also allow scalars for indices.
axis : int, optional
The axis over which to select values. By default, the flattened
input array is used.
out : ndarray, optional (Ni..., Nj..., Nk...)
If provided, the result will be placed in this array. It should
be of the appropriate shape and dtype. Note that `out` is always
buffered if `mode='raise'`; use other modes for better performance.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices will behave.
* 'raise' -- raise an error (default)
* 'wrap' -- wrap around
* 'clip' -- clip to the range
'clip' mode means that all indices that are too large are replaced
by the index that addresses the last element along that axis. Note
that this disables indexing with negative numbers.
Returns
-------
out : ndarray (Ni..., Nj..., Nk...)
The returned array has the same type as `a`.
See Also
--------
compress : Take elements using a boolean mask
ndarray.take : equivalent method
take_along_axis : Take elements by matching the array and the index arrays
Notes
-----
By eliminating the inner loop in the description above, and using `s_` to
build simple slice objects, `take` can be expressed in terms of applying
fancy indexing to each 1-d slice::
Ni, Nk = a.shape[:axis], a.shape[axis+1:]
for ii in ndindex(Ni):
for kk in ndindex(Nk):
out[ii + s_[...,] + kk] = a[ii + s_[:,] + kk][indices]
For this reason, it is equivalent to (but faster than) the following use
of `apply_along_axis`::
out = np.apply_along_axis(lambda a_1d: a_1d[indices], axis, a)
Examples
--------
>>> import numpy as np
>>> a = [4, 3, 5, 7, 6, 8]
>>> indices = [0, 1, 4]
>>> np.take(a, indices)
array([4, 3, 6])
In this example if `a` is an ndarray, "fancy" indexing can be used.
>>> a = np.array(a)
>>> a[indices]
array([4, 3, 6])
If `indices` is not one dimensional, the output also has these dimensions.
>>> np.take(a, [[0, 1], [2, 3]])
array([[4, 3],
[5, 7]])
"""
return _wrapfunc(a, 'take', indices, axis=axis, out=out, mode=mode)
def _reshape_dispatcher(a, /, shape, order=None, *, copy=None):
return (a,)
@array_function_dispatch(_reshape_dispatcher)
def reshape(a, /, shape, order='C', *, copy=None):
"""
Returns a reshaped ndarray without changing data.
Parameters
----------
a : array_like
Array to be reshaped.
shape : int or tuple of ints
The new shape should be compatible with the original shape. If
an integer, then the result will be a 1-D array of that length.
One shape dimension can be -1. In this case, the value is
inferred from the length of the array and remaining dimensions.
order : {'C', 'F', 'A'}, optional
Read the elements of ``a`` using this index order, and place the
elements into the reshaped array using this index order. 'C'
means to read / write the elements using C-like index order,
with the last axis index changing fastest, back to the first
axis index changing slowest. 'F' means to read / write the
elements using Fortran-like index order, with the first index
changing fastest, and the last index changing slowest. Note that
the 'C' and 'F' options take no account of the memory layout of
the underlying array, and only refer to the order of indexing.
'A' means to read / write the elements in Fortran-like index
order if ``a`` is Fortran *contiguous* in memory, C-like order
otherwise.
copy : bool, optional
If ``True``, then the array data is copied. If ``None``, a copy will
only be made if it's required by ``order``. For ``False`` it raises
a ``ValueError`` if a copy cannot be avoided. Default: ``None``.
Returns
-------
reshaped_array : ndarray
This will be a new view object if possible; otherwise, it will
be a copy. Note there is no guarantee of the *memory layout* (C- or
Fortran- contiguous) of the returned array.
See Also
--------
ndarray.reshape : Equivalent method.
Notes
-----
It is not always possible to change the shape of an array without copying
the data.
The ``order`` keyword gives the index ordering both for *fetching*
the values from ``a``, and then *placing* the values into the output
array. For example, let's say you have an array:
>>> a = np.arange(6).reshape((3, 2))
>>> a
array([[0, 1],
[2, 3],
[4, 5]])
You can think of reshaping as first raveling the array (using the given
index order), then inserting the elements from the raveled array into the
new array using the same kind of index ordering as was used for the
raveling.
>>> np.reshape(a, (2, 3)) # C-like index ordering
array([[0, 1, 2],
[3, 4, 5]])
>>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape
array([[0, 1, 2],
[3, 4, 5]])
>>> np.reshape(a, (2, 3), order='F') # Fortran-like index ordering
array([[0, 4, 3],
[2, 1, 5]])
>>> np.reshape(np.ravel(a, order='F'), (2, 3), order='F')
array([[0, 4, 3],
[2, 1, 5]])
Examples
--------
>>> import numpy as np
>>> a = np.array([[1,2,3], [4,5,6]])
>>> np.reshape(a, 6)
array([1, 2, 3, 4, 5, 6])
>>> np.reshape(a, 6, order='F')
array([1, 4, 2, 5, 3, 6])
>>> np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2
array([[1, 2],
[3, 4],
[5, 6]])
"""
if copy is not None:
return _wrapfunc(a, 'reshape', shape, order=order, copy=copy)
return _wrapfunc(a, 'reshape', shape, order=order)
def _choose_dispatcher(a, choices, out=None, mode=None):
yield a
yield from choices
yield out
@array_function_dispatch(_choose_dispatcher)
def choose(a, choices, out=None, mode='raise'):
"""
Construct an array from an index array and a list of arrays to choose from.
First of all, if confused or uncertain, definitely look at the Examples -
in its full generality, this function is less simple than it might
seem from the following code description::
np.choose(a,c) == np.array([c[a[I]][I] for I in np.ndindex(a.shape)])
But this omits some subtleties. Here is a fully general summary:
Given an "index" array (`a`) of integers and a sequence of ``n`` arrays
(`choices`), `a` and each choice array are first broadcast, as necessary,
to arrays of a common shape; calling these *Ba* and *Bchoices[i], i =
0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape``
for each ``i``. Then, a new array with shape ``Ba.shape`` is created as
follows:
* if ``mode='raise'`` (the default), then, first of all, each element of
``a`` (and thus ``Ba``) must be in the range ``[0, n-1]``; now, suppose
that ``i`` (in that range) is the value at the ``(j0, j1, ..., jm)``
position in ``Ba`` - then the value at the same position in the new array
is the value in ``Bchoices[i]`` at that same position;
* if ``mode='wrap'``, values in `a` (and thus `Ba`) may be any (signed)
integer; modular arithmetic is used to map integers outside the range
`[0, n-1]` back into that range; and then the new array is constructed
as above;
* if ``mode='clip'``, values in `a` (and thus ``Ba``) may be any (signed)
integer; negative integers are mapped to 0; values greater than ``n-1``
are mapped to ``n-1``; and then the new array is constructed as above.
Parameters
----------
a : int array
This array must contain integers in ``[0, n-1]``, where ``n`` is the
number of choices, unless ``mode=wrap`` or ``mode=clip``, in which
cases any integers are permissible.
choices : sequence of arrays
Choice arrays. `a` and all of the choices must be broadcastable to the
same shape. If `choices` is itself an array (not recommended), then
its outermost dimension (i.e., the one corresponding to
``choices.shape[0]``) is taken as defining the "sequence".
out : array, optional
If provided, the result will be inserted into this array. It should
be of the appropriate shape and dtype. Note that `out` is always
buffered if ``mode='raise'``; use other modes for better performance.
mode : {'raise' (default), 'wrap', 'clip'}, optional
Specifies how indices outside ``[0, n-1]`` will be treated:
* 'raise' : an exception is raised
* 'wrap' : value becomes value mod ``n``
* 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1
Returns
-------
merged_array : array
The merged result.
Raises
------
ValueError: shape mismatch
If `a` and each choice array are not all broadcastable to the same
shape.
See Also
--------
ndarray.choose : equivalent method
numpy.take_along_axis : Preferable if `choices` is an array
Notes
-----
To reduce the chance of misinterpretation, even though the following
"abuse" is nominally supported, `choices` should neither be, nor be
thought of as, a single array, i.e., the outermost sequence-like container
should be either a list or a tuple.
Examples
--------
>>> import numpy as np
>>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],
... [20, 21, 22, 23], [30, 31, 32, 33]]
>>> np.choose([2, 3, 1, 0], choices
... # the first element of the result will be the first element of the
... # third (2+1) "array" in choices, namely, 20; the second element
... # will be the second element of the fourth (3+1) choice array, i.e.,
... # 31, etc.
... )
array([20, 31, 12, 3])
>>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)
array([20, 31, 12, 3])
>>> # because there are 4 choice arrays
>>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)
array([20, 1, 12, 3])
>>> # i.e., 0
A couple examples illustrating how choose broadcasts:
>>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]
>>> choices = [-10, 10]
>>> np.choose(a, choices)
array([[ 10, -10, 10],
[-10, 10, -10],
[ 10, -10, 10]])
>>> # With thanks to Anne Archibald
>>> a = np.array([0, 1]).reshape((2,1,1))
>>> c1 = np.array([1, 2, 3]).reshape((1,3,1))
>>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))
>>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2
array([[[ 1, 1, 1, 1, 1],
[ 2, 2, 2, 2, 2],
[ 3, 3, 3, 3, 3]],
[[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5]]])
"""
return _wrapfunc(a, 'choose', choices, out=out, mode=mode)
def _repeat_dispatcher(a, repeats, axis=None):
return (a,)
@array_function_dispatch(_repeat_dispatcher)
def repeat(a, repeats, axis=None):
"""
Repeat each element of an array after themselves
Parameters
----------
a : array_like
Input array.
repeats : int or array of ints
The number of repetitions for each element. `repeats` is broadcasted
to fit the shape of the given axis.
axis : int, optional
The axis along which to repeat values. By default, use the
flattened input array, and return a flat output array.
Returns
-------
repeated_array : ndarray
Output array which has the same shape as `a`, except along
the given axis.
See Also
--------
tile : Tile an array.
unique : Find the unique elements of an array.
Examples
--------
>>> import numpy as np
>>> np.repeat(3, 4)
array([3, 3, 3, 3])
>>> x = np.array([[1,2],[3,4]])
>>> np.repeat(x, 2)
array([1, 1, 2, 2, 3, 3, 4, 4])
>>> np.repeat(x, 3, axis=1)
array([[1, 1, 1, 2, 2, 2],
[3, 3, 3, 4, 4, 4]])
>>> np.repeat(x, [1, 2], axis=0)
array([[1, 2],
[3, 4],
[3, 4]])
"""
return _wrapfunc(a, 'repeat', repeats, axis=axis)
def _put_dispatcher(a, ind, v, mode=None):
return (a, ind, v)
@array_function_dispatch(_put_dispatcher)
def put(a, ind, v, mode='raise'):
"""
Replaces specified elements of an array with given values.
The indexing works on the flattened target array. `put` is roughly
equivalent to:
::
a.flat[ind] = v
Parameters
----------
a : ndarray
Target array.
ind : array_like
Target indices, interpreted as integers.
v : array_like
Values to place in `a` at target indices. If `v` is shorter than
`ind` it will be repeated as necessary.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices will behave.
* 'raise' -- raise an error (default)
* 'wrap' -- wrap around
* 'clip' -- clip to the range
'clip' mode means that all indices that are too large are replaced
by the index that addresses the last element along that axis. Note
that this disables indexing with negative numbers. In 'raise' mode,
if an exception occurs the target array may still be modified.
See Also
--------
putmask, place
put_along_axis : Put elements by matching the array and the index arrays
Examples
--------
>>> import numpy as np
>>> a = np.arange(5)
>>> np.put(a, [0, 2], [-44, -55])
>>> a
array([-44, 1, -55, 3, 4])
>>> a = np.arange(5)
>>> np.put(a, 22, -5, mode='clip')
>>> a
array([ 0, 1, 2, 3, -5])
"""
try:
put = a.put
except AttributeError as e:
raise TypeError(f"argument 1 must be numpy.ndarray, not {type(a)}") from e
return put(ind, v, mode=mode)
def _swapaxes_dispatcher(a, axis1, axis2):
return (a,)
@array_function_dispatch(_swapaxes_dispatcher)
def swapaxes(a, axis1, axis2):
"""
Interchange two axes of an array.
Parameters
----------
a : array_like
Input array.
axis1 : int
First axis.
axis2 : int
Second axis.
Returns
-------
a_swapped : ndarray
For NumPy >= 1.10.0, if `a` is an ndarray, then a view of `a` is
returned; otherwise a new array is created. For earlier NumPy
versions a view of `a` is returned only if the order of the
axes is changed, otherwise the input array is returned.
Examples
--------
>>> import numpy as np
>>> x = np.array([[1,2,3]])
>>> np.swapaxes(x,0,1)
array([[1],
[2],
[3]])
>>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
>>> x
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> np.swapaxes(x,0,2)
array([[[0, 4],
[2, 6]],
[[1, 5],
[3, 7]]])
"""
return _wrapfunc(a, 'swapaxes', axis1, axis2)
def _transpose_dispatcher(a, axes=None):
return (a,)
@array_function_dispatch(_transpose_dispatcher)
def transpose(a, axes=None):
"""
Returns an array with axes transposed.
For a 1-D array, this returns an unchanged view of the original array, as a
transposed vector is simply the same vector.
To convert a 1-D array into a 2-D column vector, an additional dimension
must be added, e.g., ``np.atleast_2d(a).T`` achieves this, as does
``a[:, np.newaxis]``.
For a 2-D array, this is the standard matrix transpose.
For an n-D array, if axes are given, their order indicates how the
axes are permuted (see Examples). If axes are not provided, then
``transpose(a).shape == a.shape[::-1]``.
Parameters
----------
a : array_like
Input array.
axes : tuple or list of ints, optional
If specified, it must be a tuple or list which contains a permutation
of [0, 1, ..., N-1] where N is the number of axes of `a`. Negative
indices can also be used to specify axes. The i-th axis of the returned
array will correspond to the axis numbered ``axes[i]`` of the input.
If not specified, defaults to ``range(a.ndim)[::-1]``, which reverses
the order of the axes.
Returns
-------
p : ndarray
`a` with its axes permuted. A view is returned whenever possible.
See Also
--------
ndarray.transpose : Equivalent method.
moveaxis : Move axes of an array to new positions.
argsort : Return the indices that would sort an array.
Notes
-----
Use ``transpose(a, argsort(axes))`` to invert the transposition of tensors
when using the `axes` keyword argument.
Examples
--------
>>> import numpy as np
>>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
[3, 4]])
>>> np.transpose(a)
array([[1, 3],
[2, 4]])
>>> a = np.array([1, 2, 3, 4])
>>> a
array([1, 2, 3, 4])
>>> np.transpose(a)
array([1, 2, 3, 4])
>>> a = np.ones((1, 2, 3))
>>> np.transpose(a, (1, 0, 2)).shape
(2, 1, 3)
>>> a = np.ones((2, 3, 4, 5))
>>> np.transpose(a).shape
(5, 4, 3, 2)
>>> a = np.arange(3*4*5).reshape((3, 4, 5))
>>> np.transpose(a, (-1, 0, -2)).shape
(5, 3, 4)
"""
return _wrapfunc(a, 'transpose', axes)
def _matrix_transpose_dispatcher(x):
return (x,)
@array_function_dispatch(_matrix_transpose_dispatcher)
def matrix_transpose(x, /):
"""
Transposes a matrix (or a stack of matrices) ``x``.
This function is Array API compatible.
Parameters
----------
x : array_like
Input array having shape (..., M, N) and whose two innermost
dimensions form ``MxN`` matrices.
Returns
-------
out : ndarray
An array containing the transpose for each matrix and having shape
(..., N, M).
See Also
--------
transpose : Generic transpose method.
Examples
--------
>>> import numpy as np
>>> np.matrix_transpose([[1, 2], [3, 4]])
array([[1, 3],
[2, 4]])
>>> np.matrix_transpose([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
array([[[1, 3],
[2, 4]],
[[5, 7],
[6, 8]]])
"""
x = asanyarray(x)
if x.ndim < 2:
raise ValueError(
f"Input array must be at least 2-dimensional, but it is {x.ndim}"
)
return swapaxes(x, -1, -2)
def _partition_dispatcher(a, kth, axis=None, kind=None, order=None):
return (a,)
@array_function_dispatch(_partition_dispatcher)
def partition(a, kth, axis=-1, kind='introselect', order=None):
"""
Return a partitioned copy of an array.
Creates a copy of the array and partially sorts it in such a way that
the value of the element in k-th position is in the position it would be
in a sorted array. In the output array, all elements smaller than the k-th
element are located to the left of this element and all equal or greater
are located to its right. The ordering of the elements in the two
partitions on the either side of the k-th element in the output array is
undefined.
Parameters
----------
a : array_like
Array to be sorted.
kth : int or sequence of ints
Element index to partition by. The k-th value of the element
will be in its final sorted position and all smaller elements
will be moved before it and all equal or greater elements behind
it. The order of all elements in the partitions is undefined. If
provided with a sequence of k-th it will partition all elements
indexed by k-th of them into their sorted position at once.
axis : int or None, optional
Axis along which to sort. If None, the array is flattened before
sorting. The default is -1, which sorts along the last axis.
kind : {'introselect'}, optional
Selection algorithm. Default is 'introselect'.
order : str or list of str, optional
When `a` is an array with fields defined, this argument
specifies which fields to compare first, second, etc. A single
field can be specified as a string. Not all fields need be
specified, but unspecified fields will still be used, in the
order in which they come up in the dtype, to break ties.
Returns
-------
partitioned_array : ndarray
Array of the same type and shape as `a`.
See Also
--------
ndarray.partition : Method to sort an array in-place.
argpartition : Indirect partition.
sort : Full sorting
Notes
-----
The various selection algorithms are characterized by their average
speed, worst case performance, work space size, and whether they are
stable. A stable sort keeps items with the same key in the same
relative order. The available algorithms have the following
properties:
================= ======= ============= ============ =======
kind speed worst case work space stable
================= ======= ============= ============ =======
'introselect' 1 O(n) 0 no
================= ======= ============= ============ =======
All the partition algorithms make temporary copies of the data when
partitioning along any but the last axis. Consequently,
partitioning along the last axis is faster and uses less space than
partitioning along any other axis.
The sort order for complex numbers is lexicographic. If both the
real and imaginary parts are non-nan then the order is determined by
the real parts except when they are equal, in which case the order
is determined by the imaginary parts.
The sort order of ``np.nan`` is bigger than ``np.inf``.
Examples
--------
>>> import numpy as np
>>> a = np.array([7, 1, 7, 7, 1, 5, 7, 2, 3, 2, 6, 2, 3, 0])
>>> p = np.partition(a, 4)
>>> p
array([0, 1, 2, 1, 2, 5, 2, 3, 3, 6, 7, 7, 7, 7]) # may vary
``p[4]`` is 2; all elements in ``p[:4]`` are less than or equal
to ``p[4]``, and all elements in ``p[5:]`` are greater than or
equal to ``p[4]``. The partition is::
[0, 1, 2, 1], [2], [5, 2, 3, 3, 6, 7, 7, 7, 7]
The next example shows the use of multiple values passed to `kth`.
>>> p2 = np.partition(a, (4, 8))
>>> p2
array([0, 1, 2, 1, 2, 3, 3, 2, 5, 6, 7, 7, 7, 7])
``p2[4]`` is 2 and ``p2[8]`` is 5. All elements in ``p2[:4]``
are less than or equal to ``p2[4]``, all elements in ``p2[5:8]``
are greater than or equal to ``p2[4]`` and less than or equal to
``p2[8]``, and all elements in ``p2[9:]`` are greater than or
equal to ``p2[8]``. The partition is::
[0, 1, 2, 1], [2], [3, 3, 2], [5], [6, 7, 7, 7, 7]
"""
if axis is None:
# flatten returns (1, N) for np.matrix, so always use the last axis
a = asanyarray(a).flatten()
axis = -1
else:
a = asanyarray(a).copy(order="K")
a.partition(kth, axis=axis, kind=kind, order=order)
return a
def _argpartition_dispatcher(a, kth, axis=None, kind=None, order=None):
return (a,)
@array_function_dispatch(_argpartition_dispatcher)
def argpartition(a, kth, axis=-1, kind='introselect', order=None):
"""
Perform an indirect partition along the given axis using the
algorithm specified by the `kind` keyword. It returns an array of
indices of the same shape as `a` that index data along the given
axis in partitioned order.
Parameters
----------
a : array_like
Array to sort.
kth : int or sequence of ints
Element index to partition by. The k-th element will be in its
final sorted position and all smaller elements will be moved
before it and all larger elements behind it. The order of all
elements in the partitions is undefined. If provided with a
sequence of k-th it will partition all of them into their sorted
position at once.
axis : int or None, optional
Axis along which to sort. The default is -1 (the last axis). If
None, the flattened array is used.
kind : {'introselect'}, optional
Selection algorithm. Default is 'introselect'
order : str or list of str, optional
When `a` is an array with fields defined, this argument
specifies which fields to compare first, second, etc. A single
field can be specified as a string, and not all fields need be
specified, but unspecified fields will still be used, in the
order in which they come up in the dtype, to break ties.
Returns
-------
index_array : ndarray, int
Array of indices that partition `a` along the specified axis.
If `a` is one-dimensional, ``a[index_array]`` yields a partitioned `a`.
More generally, ``np.take_along_axis(a, index_array, axis=axis)``
always yields the partitioned `a`, irrespective of dimensionality.
See Also
--------
partition : Describes partition algorithms used.
ndarray.partition : Inplace partition.
argsort : Full indirect sort.
take_along_axis : Apply ``index_array`` from argpartition
to an array as if by calling partition.
Notes
-----
The returned indices are not guaranteed to be sorted according to
the values. Furthermore, the default selection algorithm ``introselect``
is unstable, and hence the returned indices are not guaranteed
to be the earliest/latest occurrence of the element.
`argpartition` works for real/complex inputs with nan values,
see `partition` for notes on the enhanced sort order and
different selection algorithms.
Examples
--------
One dimensional array:
>>> import numpy as np
>>> x = np.array([3, 4, 2, 1])
>>> x[np.argpartition(x, 3)]
array([2, 1, 3, 4]) # may vary
>>> x[np.argpartition(x, (1, 3))]
array([1, 2, 3, 4]) # may vary
>>> x = [3, 4, 2, 1]
>>> np.array(x)[np.argpartition(x, 3)]
array([2, 1, 3, 4]) # may vary
Multi-dimensional array:
>>> x = np.array([[3, 4, 2], [1, 3, 1]])
>>> index_array = np.argpartition(x, kth=1, axis=-1)
>>> # below is the same as np.partition(x, kth=1)
>>> np.take_along_axis(x, index_array, axis=-1)
array([[2, 3, 4],
[1, 1, 3]])
"""
return _wrapfunc(a, 'argpartition', kth, axis=axis, kind=kind, order=order)
def _sort_dispatcher(
a, axis=None, kind=None, order=None, *, stable=None, descending=None
):
return (a,)
@array_function_dispatch(_sort_dispatcher)
def sort(a, axis=-1, kind=None, order=None, *, stable=None, descending=np._NoValue):
"""
Return a sorted copy of an array.
Parameters
----------
a : array_like
Array to be sorted.
axis : int or None, optional
Axis along which to sort. If None, the array is flattened before
sorting. The default is -1, which sorts along the last axis.
kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
and 'mergesort' use timsort or radix sort under the covers and,
in general, the actual implementation will vary with data type.
The 'mergesort' option is retained for backwards compatibility.
order : str or list of str, optional
When `a` is an array with fields defined, this argument specifies
which fields to compare first, second, etc. A single field can
be specified as a string, and not all fields need be specified,
but unspecified fields will still be used, in the order in which
they come up in the dtype, to break ties.
stable : bool, optional
Sort stability. If ``True``, the returned array will maintain
the relative order of ``a`` values which compare as equal.
If ``False`` or ``None``, this is not guaranteed. Internally,
this option selects ``kind='stable'``. Default: ``None``.
.. versionadded:: 2.0.0
descending : bool, optional
Sort order. If ``True``, the returned array will be sorted in
descending order. If ``False`` or ``None``, the returned array will
be sorted in ascending order. Values that are NaN are sorted to the
end for both orders. Default: ``None``.
.. versionadded:: 2.5.0
Returns
-------
sorted_array : ndarray
Array of the same type and shape as `a`.
See Also
--------
ndarray.sort : Method to sort an array in-place.
argsort : Indirect sort.
lexsort : Indirect stable sort on multiple keys.
searchsorted : Find elements in a sorted array.
partition : Partial sort.
Notes
-----
The various sorting algorithms are characterized by their average speed,
worst case performance, work space size, and whether they are stable. A
stable sort keeps items with the same key in the same relative
order. The four algorithms implemented in NumPy have the following
properties:
=========== ======= ============= ============ ========