Repository navigation
Expand file tree
/
Copy pathot.utils.html
More file actions
3202 lines (2967 loc) · 300 KB
/
Copy pathot.utils.html
File metadata and controls
3202 lines (2967 loc) · 300 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
<!DOCTYPE html>
<html class="writer-html5" lang="en" data-content_root="../">
<head>
<meta charset="utf-8" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>ot.utils — POT Python Optimal Transport 0.9.8.dev documentation</title>
<link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b86133f3" />
<link rel="stylesheet" type="text/css" href="../_static/css/theme.css?v=9edc463e" />
<link rel="stylesheet" type="text/css" href="../_static/sg_gallery.css?v=c83e6b79" />
<link rel="stylesheet" type="text/css" href="../_static/sg_gallery-binder.css?v=f4aeca0c" />
<link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
<link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
<script src="../_static/jquery.js?v=5d32c60e"></script>
<script src="../_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
<script src="../_static/documentation_options.js?v=dd0b68c4"></script>
<script src="../_static/doctools.js?v=fd6eb6e6"></script>
<script src="../_static/sphinx_highlight.js?v=6ffebe34"></script>
<script src="../_static/sg-tags.js?v=d80f6fa4"></script>
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@4/tex-mml-chtml.js"></script>
<script src="../_static/js/theme.js"></script>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="ot.weak" href="ot.weak.html" />
<link rel="prev" title="ot.unbalanced" href="ot.unbalanced.html" />
</head>
<body class="wy-body-for-nav">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-scroll">
<div class="wy-side-nav-search" >
<a href="../index.html" class="icon icon-home">
POT Python Optimal Transport
<img src="../_static/logo_dark.svg" class="logo" alt="Logo"/>
</a>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="../search.html" method="get">
<input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../index.html">POT: Python Optimal Transport</a></li>
<li class="toctree-l1"><a class="reference internal" href="../auto_examples/plot_quickstart_guide.html">Quickstart Guide</a></li>
<li class="toctree-l1"><a class="reference internal" href="../auto_examples/index.html">Examples gallery</a></li>
<li class="toctree-l1"><a class="reference internal" href="../user_guide.html">User guide</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="../all.html">API and modules</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="ot.backend.html">ot.backend</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.batch.html">ot.batch</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.bregman.html">ot.bregman</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.bsp.html">ot.bsp</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.coot.html">ot.coot</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.da.html">ot.da</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.datasets.html">ot.datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.dr.html">ot.dr</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.factored.html">ot.factored</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.gaussian.html">ot.gaussian</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.gmm.html">ot.gmm</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.gnn.html">ot.gnn</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.gromov.html">ot.gromov</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.lowrank.html">ot.lowrank</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.lp.html">ot.lp</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.mapping.html">ot.mapping</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.optim.html">ot.optim</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.partial.html">ot.partial</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.plot.html">ot.plot</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.regpath.html">ot.regpath</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.sliced.html">ot.sliced</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.sgot.html">ot.sgot</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.smooth.html">ot.smooth</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.stochastic.html">ot.stochastic</a></li>
<li class="toctree-l2"><a class="reference internal" href="ot.unbalanced.html">ot.unbalanced</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">ot.utils</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#functions">Functions</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.apply_scaler"><code class="docutils literal notranslate"><span class="pre">apply_scaler()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.check_marginal"><code class="docutils literal notranslate"><span class="pre">check_marginal()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.check_number_threads"><code class="docutils literal notranslate"><span class="pre">check_number_threads()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.check_params"><code class="docutils literal notranslate"><span class="pre">check_params()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.check_random_state"><code class="docutils literal notranslate"><span class="pre">check_random_state()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.clean_zeros"><code class="docutils literal notranslate"><span class="pre">clean_zeros()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.cost_normalization"><code class="docutils literal notranslate"><span class="pre">cost_normalization()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.dist"><code class="docutils literal notranslate"><span class="pre">dist()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.dist0"><code class="docutils literal notranslate"><span class="pre">dist0()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-utils-dist0">Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.dist0</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-utils-proj-sdp">Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.proj_SDP</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-utils-proj-simplex">Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.proj_simplex</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#classes">Classes</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#ot.utils.BaryResult"><code class="docutils literal notranslate"><span class="pre">BaryResult</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-utils-baryresult">Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.BaryResult</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-utils-baseestimator">Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.BaseEstimator</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-utils-datascaler">Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.DataScaler</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-utils-lazytensor">Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.LazyTensor</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#examples-using-ot-utils-otresult">Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.OTResult</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#exceptions">Exceptions</a></li>
<li class="toctree-l3"><a class="reference internal" href="#id22"><code class="docutils literal notranslate"><span class="pre">BaryResult</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id23"><code class="docutils literal notranslate"><span class="pre">BaryResult.X</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id24"><code class="docutils literal notranslate"><span class="pre">BaryResult.C</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id25"><code class="docutils literal notranslate"><span class="pre">BaryResult.b</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id26"><code class="docutils literal notranslate"><span class="pre">BaryResult.value</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id27"><code class="docutils literal notranslate"><span class="pre">BaryResult.value_linear</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id28"><code class="docutils literal notranslate"><span class="pre">BaryResult.value_quad</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id29"><code class="docutils literal notranslate"><span class="pre">BaryResult.log</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id30"><code class="docutils literal notranslate"><span class="pre">BaryResult.list_res</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id31"><code class="docutils literal notranslate"><span class="pre">BaryResult.status</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id32"><code class="docutils literal notranslate"><span class="pre">BaryResult.backend</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id33"><code class="docutils literal notranslate"><span class="pre">BaryResult.C</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id34"><code class="docutils literal notranslate"><span class="pre">BaryResult.X</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id35"><code class="docutils literal notranslate"><span class="pre">BaryResult.b</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id36"><code class="docutils literal notranslate"><span class="pre">BaryResult.citation</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id37"><code class="docutils literal notranslate"><span class="pre">BaryResult.list_res</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id38"><code class="docutils literal notranslate"><span class="pre">BaryResult.log</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id39"><code class="docutils literal notranslate"><span class="pre">BaryResult.status</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id40"><code class="docutils literal notranslate"><span class="pre">BaryResult.value</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id41"><code class="docutils literal notranslate"><span class="pre">BaryResult.value_linear</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id42"><code class="docutils literal notranslate"><span class="pre">BaryResult.value_quad</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id43"><code class="docutils literal notranslate"><span class="pre">BaseEstimator</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id44"><code class="docutils literal notranslate"><span class="pre">BaseEstimator.get_params()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id45"><code class="docutils literal notranslate"><span class="pre">BaseEstimator.set_params()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id46"><code class="docutils literal notranslate"><span class="pre">DataScaler</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id47"><code class="docutils literal notranslate"><span class="pre">DataScaler.norm</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id48"><code class="docutils literal notranslate"><span class="pre">DataScaler.mean_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id49"><code class="docutils literal notranslate"><span class="pre">DataScaler.std_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id50"><code class="docutils literal notranslate"><span class="pre">DataScaler.min_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id51"><code class="docutils literal notranslate"><span class="pre">DataScaler.max_</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id52"><code class="docutils literal notranslate"><span class="pre">DataScaler.fit()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id53"><code class="docutils literal notranslate"><span class="pre">DataScaler.fit_transform()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id54"><code class="docutils literal notranslate"><span class="pre">DataScaler.transform()</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#id55"><code class="docutils literal notranslate"><span class="pre">LazyTensor</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id56"><code class="docutils literal notranslate"><span class="pre">OTResult</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#id57"><code class="docutils literal notranslate"><span class="pre">OTResult.potentials</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id58"><code class="docutils literal notranslate"><span class="pre">OTResult.potential_a</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id59"><code class="docutils literal notranslate"><span class="pre">OTResult.potential_b</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id60"><code class="docutils literal notranslate"><span class="pre">OTResult.value</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id61"><code class="docutils literal notranslate"><span class="pre">OTResult.value_linear</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id62"><code class="docutils literal notranslate"><span class="pre">OTResult.value_quad</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id63"><code class="docutils literal notranslate"><span class="pre">OTResult.plan</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id64"><code class="docutils literal notranslate"><span class="pre">OTResult.sparse_plan</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id65"><code class="docutils literal notranslate"><span class="pre">OTResult.lazy_plan</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id66"><code class="docutils literal notranslate"><span class="pre">OTResult.marginals</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id67"><code class="docutils literal notranslate"><span class="pre">OTResult.marginal_a</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id68"><code class="docutils literal notranslate"><span class="pre">OTResult.marginal_b</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id69"><code class="docutils literal notranslate"><span class="pre">OTResult.a_to_b</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id70"><code class="docutils literal notranslate"><span class="pre">OTResult.b_to_a</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id71"><code class="docutils literal notranslate"><span class="pre">OTResult.citation</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id72"><code class="docutils literal notranslate"><span class="pre">OTResult.lazy_plan</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id73"><code class="docutils literal notranslate"><span class="pre">OTResult.log</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id74"><code class="docutils literal notranslate"><span class="pre">OTResult.marginal_a</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id75"><code class="docutils literal notranslate"><span class="pre">OTResult.marginal_b</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id76"><code class="docutils literal notranslate"><span class="pre">OTResult.marginals</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id77"><code class="docutils literal notranslate"><span class="pre">OTResult.plan</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id78"><code class="docutils literal notranslate"><span class="pre">OTResult.potential_a</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id79"><code class="docutils literal notranslate"><span class="pre">OTResult.potential_b</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id80"><code class="docutils literal notranslate"><span class="pre">OTResult.potentials</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id81"><code class="docutils literal notranslate"><span class="pre">OTResult.sparse_plan</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id82"><code class="docutils literal notranslate"><span class="pre">OTResult.status</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id83"><code class="docutils literal notranslate"><span class="pre">OTResult.value</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id84"><code class="docutils literal notranslate"><span class="pre">OTResult.value_linear</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#id85"><code class="docutils literal notranslate"><span class="pre">OTResult.value_quad</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#ot.utils.UndefinedParameter"><code class="docutils literal notranslate"><span class="pre">UndefinedParameter</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id86"><code class="docutils literal notranslate"><span class="pre">apply_scaler()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id87"><code class="docutils literal notranslate"><span class="pre">check_marginal()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id88"><code class="docutils literal notranslate"><span class="pre">check_number_threads()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id89"><code class="docutils literal notranslate"><span class="pre">check_params()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id90"><code class="docutils literal notranslate"><span class="pre">check_random_state()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id91"><code class="docutils literal notranslate"><span class="pre">clean_zeros()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id92"><code class="docutils literal notranslate"><span class="pre">cost_normalization()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id93"><code class="docutils literal notranslate"><span class="pre">deprecated</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id94"><code class="docutils literal notranslate"><span class="pre">dist()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id95"><code class="docutils literal notranslate"><span class="pre">dist0()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id96"><code class="docutils literal notranslate"><span class="pre">dots()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id97"><code class="docutils literal notranslate"><span class="pre">euclidean_distances()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id98"><code class="docutils literal notranslate"><span class="pre">exp_bures()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id99"><code class="docutils literal notranslate"><span class="pre">fun_to_numpy()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id100"><code class="docutils literal notranslate"><span class="pre">get_coordinate_circle()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id101"><code class="docutils literal notranslate"><span class="pre">get_lowrank_lazytensor()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id102"><code class="docutils literal notranslate"><span class="pre">get_parameter_pair()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id103"><code class="docutils literal notranslate"><span class="pre">is_all_finite()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id104"><code class="docutils literal notranslate"><span class="pre">kernel()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id105"><code class="docutils literal notranslate"><span class="pre">label_normalization()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id106"><code class="docutils literal notranslate"><span class="pre">labels_to_masks()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id107"><code class="docutils literal notranslate"><span class="pre">laplacian()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id108"><code class="docutils literal notranslate"><span class="pre">list_to_array()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id109"><code class="docutils literal notranslate"><span class="pre">parmap()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id110"><code class="docutils literal notranslate"><span class="pre">proj_SDP()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id111"><code class="docutils literal notranslate"><span class="pre">proj_simplex()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id112"><code class="docutils literal notranslate"><span class="pre">projection_sparse_simplex()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id114"><code class="docutils literal notranslate"><span class="pre">reduce_lazytensor()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id115"><code class="docutils literal notranslate"><span class="pre">sparse_ot_dist()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id116"><code class="docutils literal notranslate"><span class="pre">split_sample_ratio()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id117"><code class="docutils literal notranslate"><span class="pre">tic()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id118"><code class="docutils literal notranslate"><span class="pre">toc()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id119"><code class="docutils literal notranslate"><span class="pre">toq()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#id120"><code class="docutils literal notranslate"><span class="pre">unif()</span></code></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="ot.weak.html">ot.weak</a></li>
<li class="toctree-l2"><a class="reference internal" href="../all.html#module-ot">Main <code class="xref py py-mod docutils literal notranslate"><span class="pre">ot</span></code> functions</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../releases.html">Releases</a></li>
<li class="toctree-l1"><a class="reference internal" href="../contributors.html">Contributors</a></li>
<li class="toctree-l1"><a class="reference internal" href="../contributing.html">Contributing to POT</a></li>
<li class="toctree-l1"><a class="reference internal" href="../code_of_conduct.html">Code of conduct</a></li>
</ul>
</div>
</div>
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="../index.html">POT Python Optimal Transport</a>
</nav>
<div class="wy-nav-content">
<div class="rst-content">
<div role="navigation" aria-label="Page navigation">
<ul class="wy-breadcrumbs">
<li><a href="../index.html" class="icon icon-home" aria-label="Home"></a></li>
<li class="breadcrumb-item"><a href="../all.html">API and modules</a></li>
<li class="breadcrumb-item active">ot.utils</li>
<li class="wy-breadcrumbs-aside">
<a href="../_sources/gen_modules/ot.utils.rst.txt" rel="nofollow"> View page source</a>
</li>
</ul>
<hr/>
</div>
<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<div itemprop="articleBody">
<section id="module-ot.utils">
<span id="ot-utils"></span><h1>ot.utils<a class="headerlink" href="#module-ot.utils" title="Link to this heading"></a></h1>
<p>Various useful functions</p>
<section id="functions">
<h2>Functions<a class="headerlink" href="#functions" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="ot.utils.apply_scaler">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">apply_scaler</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X_s</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">X_t</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scaler</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#apply_scaler"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.apply_scaler" title="Link to this definition"></a></dt>
<dd><p>Apply a scaler to two arrays.</p>
<p>Dispatches based on the type of <code class="docutils literal notranslate"><span class="pre">scaler</span></code>:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">None</span></code> : returns inputs unchanged.</p></li>
<li><p>Object with a <code class="docutils literal notranslate"><span class="pre">.transform()</span></code> method : calls <code class="docutils literal notranslate"><span class="pre">scaler.transform()</span></code> on each.</p></li>
<li><p>Callable : calls <code class="docutils literal notranslate"><span class="pre">scaler()</span></code> on each (covers functions, lambdas,
PyTorch transforms, neural network encoders, etc.).</p></li>
</ul>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>X_s</strong> (<em>array-like</em>) – Source samples.</p></li>
<li><p><strong>X_t</strong> (<em>array-like</em>) – Target samples.</p></li>
<li><p><strong>scaler</strong> (<em>None</em><em>, </em><em>object with .transform</em><em>(</em><em>)</em><em>, or </em><em>callable</em><em>, </em><em>optional</em>) – Preprocessing to apply.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>X_s_out</strong> (<em>array-like</em>) – Possibly transformed source samples.</p></li>
<li><p><strong>X_t_out</strong> (<em>array-like</em>) – Possibly transformed target samples.</p></li>
</ul>
</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.check_marginal">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">check_marginal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">type_as</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#check_marginal"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.check_marginal" title="Link to this definition"></a></dt>
<dd><p>Validate or fill a marginal <span class="math notranslate nohighlight">\(\mathbf{a}\)</span> against an expected shape.</p>
<p>When <code class="docutils literal notranslate"><span class="pre">a</span></code> is <code class="docutils literal notranslate"><span class="pre">None</span></code> it is filled with the uniform marginal of the given
<code class="docutils literal notranslate"><span class="pre">shape</span></code> on the backend, device and dtype of <code class="docutils literal notranslate"><span class="pre">type_as</span></code> (via <a class="reference internal" href="#id120" title="ot.utils.unif"><code class="xref py py-func docutils literal notranslate"><span class="pre">unif()</span></code></a>).
When provided, its shape is checked against <code class="docutils literal notranslate"><span class="pre">shape</span></code> and, if <code class="docutils literal notranslate"><span class="pre">type_as</span></code> is
given, it must share <code class="docutils literal notranslate"><span class="pre">type_as</span></code>’s dtype and device – otherwise an explicit
error is raised instead of a deep error later in the solver.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>a</strong> (array-like, shape <code class="docutils literal notranslate"><span class="pre">shape</span></code>, or None) – The marginal to validate, or None to fill with a uniform marginal.</p></li>
<li><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#tuple" title="(in Python v3.15)"><em>tuple</em></a><em> of </em><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a>) – Expected shape of the marginal (see <a class="reference internal" href="#id120" title="ot.utils.unif"><code class="xref py py-func docutils literal notranslate"><span class="pre">unif()</span></code></a>).</p></li>
<li><p><strong>type_as</strong> (<em>array-like</em><em>, </em><em>optional</em>) – Array fixing the backend, device and dtype of the filled/validated marginal.</p></li>
<li><p><strong>nx</strong> (<em>backend object</em><em>, </em><em>optional</em>) – Numerical backend to use. If None, it is inferred from <code class="docutils literal notranslate"><span class="pre">type_as</span></code>.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>a</strong> – The validated marginal.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape <code class="docutils literal notranslate"><span class="pre">shape</span></code></p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.check_number_threads">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">check_number_threads</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">numThreads</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#check_number_threads"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.check_number_threads" title="Link to this definition"></a></dt>
<dd><p>Checks whether or not the requested number of threads has a valid value.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>numThreads</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#str" title="(in Python v3.15)"><em>str</em></a>) – The requested number of threads, should either be a strictly positive integer or “max” or None</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>numThreads</strong> – Corrected number of threads</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)">int</a></p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.check_params">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">check_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#check_params"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.check_params" title="Link to this definition"></a></dt>
<dd><p>check_params: check whether some parameters are missing</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.check_random_state">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">check_random_state</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">seed</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#check_random_state"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.check_random_state" title="Link to this definition"></a></dt>
<dd><p>Turn <cite>seed</cite> into a np.random.RandomState instance</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>seed</strong> (<em>None</em><em> | </em><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em> | </em><em>instance</em><em> of </em><em>RandomState</em>) – If <cite>seed</cite> is None, return the RandomState singleton used by np.random.
If <cite>seed</cite> is an int, return a new RandomState instance seeded with <cite>seed</cite>.
If <cite>seed</cite> is already a RandomState instance, return it.
Otherwise raise ValueError.</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.clean_zeros">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">clean_zeros</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#clean_zeros"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.clean_zeros" title="Link to this definition"></a></dt>
<dd><p>Remove all components with zeros weights in <span class="math notranslate nohighlight">\(\mathbf{a}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{b}\)</span></p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.cost_normalization">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">cost_normalization</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">C</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">return_value</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">value</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#cost_normalization"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.cost_normalization" title="Link to this definition"></a></dt>
<dd><p>Apply normalization to the loss matrix</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>C</strong> (<em>ndarray</em><em>, </em><em>shape</em><em> (</em><em>n1</em><em>, </em><em>n2</em><em>)</em>) – The cost matrix to normalize.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#str" title="(in Python v3.15)"><em>str</em></a>) – Type of normalization from ‘median’, ‘max’, ‘log’, ‘loglog’. Any
other value do not normalize.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>C</strong> – The input cost matrix normalized according to given norm.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray, shape (<cite>n1</cite>, <cite>n2</cite>)</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.dist">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">dist</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x2</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">metric</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sqeuclidean'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">w</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">backend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'auto'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">use_tensor</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#dist"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.dist" title="Link to this definition"></a></dt>
<dd><p>Compute distance between samples in <span class="math notranslate nohighlight">\(\mathbf{x_1}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{x_2}\)</span></p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This function is backend-compatible and will work on arrays
from all compatible backends for the following metrics:
‘sqeuclidean’, ‘euclidean’, ‘cityblock’, ‘minkowski’, ‘cosine’, ‘correlation’.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x1</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n1</em><em>,</em><em>d</em><em>)</em>) – matrix with <cite>n1</cite> samples of size <cite>d</cite></p></li>
<li><p><strong>x2</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n2</em><em>,</em><em>d</em><em>)</em><em>, </em><em>optional</em>) – matrix with <cite>n2</cite> samples of size <cite>d</cite> (if None then <span class="math notranslate nohighlight">\(\mathbf{x_2} = \mathbf{x_1}\)</span>)</p></li>
<li><p><strong>metric</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#str" title="(in Python v3.15)"><em>str</em></a><em> | </em><em>callable</em><em>, </em><em>optional</em>) – ‘sqeuclidean’ or ‘euclidean’ on all backends. On numpy the function also
accepts from the scipy.spatial.distance.cdist function : ‘braycurtis’,
‘canberra’, ‘chebyshev’, ‘cityblock’, ‘correlation’, ‘cosine’, ‘dice’,
‘euclidean’, ‘hamming’, ‘jaccard’, ‘kulczynski1’, ‘mahalanobis’,
‘matching’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’,
‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘wminkowski’, ‘yule’.</p></li>
<li><p><strong>p</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – p-norm for the Minkowski and the Weighted Minkowski metrics. Default value is 2.</p></li>
<li><p><strong>w</strong> (<em>array-like</em><em>, </em><em>rank 1</em>) – Weights for the weighted metrics.</p></li>
<li><p><strong>backend</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#str" title="(in Python v3.15)"><em>str</em></a><em>, </em><em>optional</em>) – Backend to use for the computation. If ‘auto’, the backend is
automatically selected based on the input data. if ‘scipy’,
the <code class="docutils literal notranslate"><span class="pre">scipy.spatial.distance.cdist</span></code> function is used (and gradients are
detached).</p></li>
<li><p><strong>use_tensor</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – If true use tensorized computation for the distance matrix which can
cause memory issues for large datasets. Default is False and the
parameter is used only for the ‘cityblock’ and ‘minkowski’ metrics.</p></li>
<li><p><strong>nx</strong> (<a class="reference internal" href="ot.backend.html#id0" title="ot.backend.Backend"><em>Backend</em></a><em>, </em><em>optional</em>) – Backend to perform computations on. If omitted, the backend defaults to that of <cite>x1</cite>.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>M</strong> – distance matrix computed with given metric</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (<cite>n1</cite>, <cite>n2</cite>)</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.dist0">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">dist0</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'lin_square'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#dist0"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.dist0" title="Link to this definition"></a></dt>
<dd><p>Compute standard cost matrices of size (<cite>n</cite>, <cite>n</cite>) for OT problems</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a>) – Size of the cost matrix.</p></li>
<li><p><strong>method</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#str" title="(in Python v3.15)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Type of loss matrix chosen from:</p>
<ul>
<li><p>’lin_square’ : linear sampling between 0 and <cite>n-1</cite>, quadratic loss</p></li>
</ul>
</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>M</strong> – Distance matrix computed with given metric.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray, shape (<cite>n1</cite>, <cite>n2</cite>)</p>
</dd>
</dl>
</dd></dl>
<section id="examples-using-ot-utils-dist0">
<h3>Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.dist0</span></code><a class="headerlink" href="#examples-using-ot-utils-dist0" title="Link to this heading"></a></h3>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wasserstein Barycenter as proposed in [3]."><img alt="" src="../_images/sphx_glr_plot_barycenter_1D_thumb.png" />
<p><a class="reference internal" href="../auto_examples/barycenters/plot_barycenter_1D.html"><span class="doc">1D Wasserstein barycenter demo</span></a></p>
<div class="sphx-glr-thumbnail-title">1D Wasserstein barycenter demo</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of the debiased Sinkhorn barycenter as proposed in [37]_."><img alt="" src="../_images/sphx_glr_plot_debiased_barycenter_thumb.png" />
<p><a class="reference internal" href="../auto_examples/barycenters/plot_debiased_barycenter.html"><span class="doc">Debiased Sinkhorn barycenter demo</span></a></p>
<div class="sphx-glr-thumbnail-title">Debiased Sinkhorn barycenter demo</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wasserstein Barycenter as proposed in [3] and exact LP barycenters using standard LP solver."><img alt="" src="../_images/sphx_glr_plot_barycenter_lp_vs_entropic_thumb.png" />
<p><a class="reference internal" href="../auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html"><span class="doc">1D Wasserstein barycenter: exact LP vs entropic regularization</span></a></p>
<div class="sphx-glr-thumbnail-title">1D Wasserstein barycenter: exact LP vs entropic regularization</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wasserstein Barycenter as proposed in [10] for Unbalanced inputs."><img alt="" src="../_images/sphx_glr_plot_UOT_barycenter_1D_thumb.png" />
<p><a class="reference internal" href="../auto_examples/unbalanced-partial/plot_UOT_barycenter_1D.html"><span class="doc">1D Wasserstein barycenter demo for Unbalanced distributions</span></a></p>
<div class="sphx-glr-thumbnail-title">1D Wasserstein barycenter demo for Unbalanced distributions</div>
</div></div><div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.dots">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">dots</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#dots"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.dots" title="Link to this definition"></a></dt>
<dd><p>dots function for multiple matrix multiply</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.euclidean_distances">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">euclidean_distances</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">squared</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#euclidean_distances"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.euclidean_distances" title="Link to this definition"></a></dt>
<dd><p>Considering the rows of <span class="math notranslate nohighlight">\(\mathbf{X}\)</span> (and <span class="math notranslate nohighlight">\(\mathbf{Y} = \mathbf{X}\)</span>) as vectors, compute the
distance matrix between each pair of vectors.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This function is backend-compatible and will work on arrays
from all compatible backends.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>X</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_samples_1</em><em>, </em><em>n_features</em><em>)</em>)</p></li>
<li><p><strong>Y</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_samples_2</em><em>, </em><em>n_features</em><em>)</em>)</p></li>
<li><p><strong>squared</strong> (<em>boolean</em><em>, </em><em>optional</em>) – Return squared Euclidean distances.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>distances</strong></p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (<cite>n_samples_1</cite>, <cite>n_samples_2</cite>)</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.exp_bures">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">exp_bures</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">S</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#exp_bures"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.exp_bures" title="Link to this definition"></a></dt>
<dd><p>Exponential map in Bures-Wasserstein space at Sigma:</p>
<div class="math notranslate nohighlight">
\[\exp_\Sigma(S) = (I_d+S)\Sigma(I_d+S).\]</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Sigma</strong> (<em>array-like</em><em> (</em><em>d</em><em>,</em><em>d</em><em>)</em>) – SPD matrix</p></li>
<li><p><strong>S</strong> (<em>array-like</em><em> (</em><em>d</em><em>,</em><em>d</em><em>)</em>) – Symmetric matrix</p></li>
<li><p><strong>nx</strong> (<em>module</em><em>, </em><em>optional</em>) – The numerical backend module to use. If not provided, the backend will
be fetched from the input matrices <cite>Sigma, S</cite>.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>P</strong> – SPD matrix obtained as the exponential map of S at Sigma</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like (d,d)</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.fun_to_numpy">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">fun_to_numpy</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">fun</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">warn</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#fun_to_numpy"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.fun_to_numpy" title="Link to this definition"></a></dt>
<dd><p>Convert a function to a numpy function.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>fun</strong> (<em>callable</em>) – The function to convert.</p></li>
<li><p><strong>arr</strong> (<em>array-like</em>) – The input to test the function. Can be from any backend.</p></li>
<li><p><strong>nx</strong> (<a class="reference internal" href="ot.backend.html#id0" title="ot.backend.Backend"><em>Backend</em></a>) – The backend to use for the conversion.</p></li>
<li><p><strong>warn</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – Whether to raise a warning if the function is not compatible with numpy.
Default is True.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>fun_numpy</strong> – The converted function.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>callable</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.get_coordinate_circle">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">get_coordinate_circle</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#get_coordinate_circle"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.get_coordinate_circle" title="Link to this definition"></a></dt>
<dd><p>For <span class="math notranslate nohighlight">\(x\in S^1 \subset \mathbb{R}^2\)</span>, returns the coordinates in
turn (in [0,1[).</p>
<div class="math notranslate nohighlight">
\[u = \frac{\pi + \mathrm{atan2}(-x_2,-x_1)}{2\pi}\]</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>x</strong> (<em>ndarray</em><em>, </em><em>shape</em><em> (</em><em>n</em><em>, </em><em>2</em><em>)</em>) – Samples on the circle with ambient coordinates</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>x_t</strong> – Coordinates on [0,1[</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray, shape (n,)</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">0.2</span><span class="p">,</span><span class="mf">0.5</span><span class="p">,</span><span class="mf">0.8</span><span class="p">]])</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">x1</span><span class="p">,</span> <span class="n">y1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">u</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
<span class="gp">>>> </span><span class="n">get_coordinate_circle</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go">array([0.2, 0.5, 0.8])</span>
</pre></div>
</div>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.get_lowrank_lazytensor">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">get_lowrank_lazytensor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Q</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">R</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">d</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#get_lowrank_lazytensor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.get_lowrank_lazytensor" title="Link to this definition"></a></dt>
<dd><p>Get a low rank LazyTensor <a class="reference external" href="mailto:T=Q%40R^T">T=Q<span>@</span>R^T</a> or T=Q@diag(d)@R^T</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>Q</strong> (<em>ndarray</em><em>, </em><em>shape</em><em> (</em><em>n</em><em>, </em><em>r</em><em>)</em>) – First factor of the lowrank tensor</p></li>
<li><p><strong>R</strong> (<em>ndarray</em><em>, </em><em>shape</em><em> (</em><em>m</em><em>, </em><em>r</em><em>)</em>) – Second factor of the lowrank tensor</p></li>
<li><p><strong>d</strong> (<em>ndarray</em><em>, </em><em>shape</em><em> (</em><em>r</em><em>,</em><em>)</em><em>, </em><em>optional</em>) – Diagonal of the lowrank tensor</p></li>
<li><p><strong>nx</strong> (<a class="reference internal" href="ot.backend.html#id0" title="ot.backend.Backend"><em>Backend</em></a><em>, </em><em>optional</em>) – Backend to use for the reduction</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>T</strong> – Lowrank tensor <a class="reference external" href="mailto:T=Q%40R^T">T=Q<span>@</span>R^T</a> or T=Q@diag(d)@R^T</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#id55" title="ot.utils.LazyTensor">LazyTensor</a></p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.get_parameter_pair">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">get_parameter_pair</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">parameter</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#get_parameter_pair"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.get_parameter_pair" title="Link to this definition"></a></dt>
<dd><p>Extract a pair of parameters from a given parameter
Used in unbalanced OT and COOT solvers
to handle marginal regularization and entropic regularization.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>parameter</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em> or </em><em>indexable object</em>)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>param_1</strong> (<em>float</em>)</p></li>
<li><p><strong>param_2</strong> (<em>float</em>)</p></li>
</ul>
</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.is_all_finite">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">is_all_finite</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#is_all_finite"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.is_all_finite" title="Link to this definition"></a></dt>
<dd><p>Tests element-wise for finiteness in all arguments.</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.kernel">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">kernel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'gaussian'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#kernel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.kernel" title="Link to this definition"></a></dt>
<dd><p>Compute kernel matrix</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.label_normalization">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">label_normalization</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#label_normalization"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.label_normalization" title="Link to this definition"></a></dt>
<dd><p>Transform labels to start at a given value</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>y</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n</em><em>, </em><em>)</em>) – The vector of labels to be normalized.</p></li>
<li><p><strong>start</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a>) – Desired value for the smallest label in <span class="math notranslate nohighlight">\(\mathbf{y}\)</span> (default=0)</p></li>
<li><p><strong>nx</strong> (<a class="reference internal" href="ot.backend.html#id0" title="ot.backend.Backend"><em>Backend</em></a><em>, </em><em>optional</em>) – Backend to perform computations on. If omitted, the backend defaults to that of <cite>y</cite>.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>y</strong> – The input vector of labels normalized according to given start value.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (<cite>n1</cite>, )</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.labels_to_masks">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">labels_to_masks</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">type_as</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#labels_to_masks"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.labels_to_masks" title="Link to this definition"></a></dt>
<dd><p>Transforms (n_samples,) vector of labels into a (n_samples, n_labels) matrix of masks.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>y</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_samples</em><em>, </em><em>)</em>) – The vector of labels.</p></li>
<li><p><strong>type_as</strong> (<em>array_like</em>) – Array of the same type of the expected output.</p></li>
<li><p><strong>nx</strong> (<a class="reference internal" href="ot.backend.html#id0" title="ot.backend.Backend"><em>Backend</em></a><em>, </em><em>optional</em>) – Backend to perform computations on. If omitted, the backend defaults to that of <cite>y</cite>.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>masks</strong> – The (n_samples, n_labels) matrix of label masks.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (n_samples, n_labels)</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.laplacian">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">laplacian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#laplacian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.laplacian" title="Link to this definition"></a></dt>
<dd><p>Compute Laplacian matrix</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.list_to_array">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">list_to_array</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">lst</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#list_to_array"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.list_to_array" title="Link to this definition"></a></dt>
<dd><p>Convert a list if in numpy format</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.parmap">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">parmap</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">X</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nprocs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'default'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#parmap"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.parmap" title="Link to this definition"></a></dt>
<dd><p>parallel map for multiprocessing.
The function has been deprecated and only performs a regular map.</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.proj_SDP">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">proj_SDP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">S</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vmin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#proj_SDP"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.proj_SDP" title="Link to this definition"></a></dt>
<dd><p>Project a symmetric matrix onto the space of symmetric matrices with
eigenvalues larger or equal to <cite>vmin</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>S</strong> (<em>array_like</em><em> (</em><em>n</em><em>, </em><em>d</em><em>, </em><em>d</em><em>) or </em><em>(</em><em>d</em><em>, </em><em>d</em><em>)</em>) – The input symmetric matrix or matrices.</p></li>
<li><p><strong>nx</strong> (<em>module</em><em>, </em><em>optional</em>) – The numerical backend module to use. If not provided, the backend will
be fetched from the input matrix <cite>S</cite>.</p></li>
<li><p><strong>vmin</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – The minimum value for the eigenvalues. Eigenvalues below this value will
be clipped to vmin.</p></li>
<li><p><strong>note:</strong> (<em>..</em>) – This function is backend-compatible and will work on arrays: from all compatible backends.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>P</strong> – The projected symmetric positive definite matrix.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray (n, d, d) or (d, d)</p>
</dd>
</dl>
</dd></dl>
</section>
<section id="examples-using-ot-utils-proj-sdp">
<h3>Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.proj_SDP</span></code><a class="headerlink" href="#examples-using-ot-utils-proj-sdp" title="Link to this heading"></a></h3>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="Illustration of the flow of a Gaussian Mixture with respect to its GMM-OT distance with respect to a fixed GMM."><img alt="" src="../_images/sphx_glr_plot_GMM_flow_thumb.png" />
<p><a class="reference internal" href="../auto_examples/gaussian_gmm/plot_GMM_flow.html"><span class="doc">Gradient Flow for GMM-OT distance</span></a></p>
<div class="sphx-glr-thumbnail-title">Gradient Flow for GMM-OT distance</div>
</div></div><div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.proj_simplex">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">proj_simplex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#proj_simplex"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.proj_simplex" title="Link to this definition"></a></dt>
<dd><p>Compute the closest point (orthogonal projection) on the
generalized <cite>(n-1)</cite>-simplex of a vector <span class="math notranslate nohighlight">\(\mathbf{v}\)</span> wrt. to the Euclidean
distance, thus solving:</p>
<div class="math notranslate nohighlight">
\[ \begin{align}\begin{aligned}\mathcal{P}(w) \in \mathop{\arg \min}_\gamma \| \gamma - \mathbf{v} \|_2\\s.t. \ \gamma^T \mathbf{1} = z\\ \gamma \geq 0\end{aligned}\end{align} \]</div>
<p>If <span class="math notranslate nohighlight">\(\mathbf{v}\)</span> is a 2d array, compute all the projections wrt. axis 0</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This function is backend-compatible and will work on arrays
from all compatible backends.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>{array-like}</em><em>, </em><em>shape</em><em> (</em><em>n</em><em>, </em><em>d</em><em>)</em>)</p></li>
<li><p><strong>z</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – ‘size’ of the simplex (each vectors sum to z, 1 by default)</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>h</strong> – Array of projections on the simplex</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray, shape (<cite>n</cite>, <cite>d</cite>)</p>
</dd>
</dl>
</dd></dl>
</section>
<section id="examples-using-ot-utils-proj-simplex">
<h3>Examples using <code class="docutils literal notranslate"><span class="pre">ot.utils.proj_simplex</span></code><a class="headerlink" href="#examples-using-ot-utils-proj-simplex" title="Link to this heading"></a></h3>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="In this example we estimate mixing parameters from distributions that minimize the Wasserstein distance. In other words we suppose that a target distribution \mu^t can be expressed as a weighted sum of source distributions \mu^s_k with the following model:"><img alt="" src="../_images/sphx_glr_plot_unmix_optim_torch_thumb.png" />
<p><a class="reference internal" href="../auto_examples/backends/plot_unmix_optim_torch.html"><span class="doc">Wasserstein unmixing with PyTorch</span></a></p>
<div class="sphx-glr-thumbnail-title">Wasserstein unmixing with PyTorch</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="In this small example, we consider the following minimization problem:"><img alt="" src="../_images/sphx_glr_plot_wass1d_torch_thumb.png" />
<p><a class="reference internal" href="../auto_examples/backends/plot_wass1d_torch.html"><span class="doc">Wasserstein 1D (flow and barycenter) with PyTorch</span></a></p>
<div class="sphx-glr-thumbnail-title">Wasserstein 1D (flow and barycenter) with PyTorch</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="In this example, we use the pytorch backend to optimize the Gromov-Wasserstein (GW) loss between two graphs expressed as empirical distribution."><img alt="" src="../_images/sphx_glr_plot_optim_gromov_pytorch_thumb.png" />
<p><a class="reference internal" href="../auto_examples/backends/plot_optim_gromov_pytorch.html"><span class="doc">Optimizing the Gromov-Wasserstein distance with PyTorch</span></a></p>
<div class="sphx-glr-thumbnail-title">Optimizing the Gromov-Wasserstein distance with PyTorch</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Illustration of the flow of a Gaussian Mixture with respect to its GMM-OT distance with respect to a fixed GMM."><img alt="" src="../_images/sphx_glr_plot_GMM_flow_thumb.png" />
<p><a class="reference internal" href="../auto_examples/gaussian_gmm/plot_GMM_flow.html"><span class="doc">Gradient Flow for GMM-OT distance</span></a></p>
<div class="sphx-glr-thumbnail-title">Gradient Flow for GMM-OT distance</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="In this example, we consider two point clouds living in different Euclidean spaces, where the outliers are artificially injected into the target data. We illustrate two methods which allow to filter out these outliers."><img alt="" src="../_images/sphx_glr_plot_outlier_detection_with_COOT_and_unbalanced_COOT_thumb.png" />
<p><a class="reference internal" href="../auto_examples/others/plot_outlier_detection_with_COOT_and_unbalanced_COOT.html"><span class="doc">Detecting outliers by learning sample marginal distribution with CO-Optimal Transport and by using unbalanced Co-Optimal Transport</span></a></p>
<div class="sphx-glr-thumbnail-title">Detecting outliers by learning sample marginal distribution with CO-Optimal Transport and by using unbalanced Co-Optimal Transport</div>
</div></div><div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.projection_sparse_simplex">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">projection_sparse_simplex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">V</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_nz</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#projection_sparse_simplex"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.projection_sparse_simplex" title="Link to this definition"></a></dt>
<dd><p>Projection of <span class="math notranslate nohighlight">\(\mathbf{V}\)</span> onto the simplex with cardinality constraint (maximum number of non-zero elements) and then scaled by <cite>z</cite>.</p>
<div class="math notranslate nohighlight">
\[\begin{split}P\left(\mathbf{V}, \text{max_nz}, z\right) = \mathop{\arg \min}_{\substack{\mathbf{y} >= 0 \\ \sum_i \mathbf{y}_i = z} \\ ||p||_0 \le \text{max_nz}} \quad \|\mathbf{y} - \mathbf{V}\|^2\end{split}\]</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>V</strong> (<em>1-dim</em><em> or </em><em>2-dim ndarray</em>)</p></li>
<li><p><strong>max_nz</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a>) – Maximum number of non-zero elements in the projection.
If <cite>max_nz</cite> is larger than the number of elements in <cite>V</cite>, then
the projection is equivalent to <cite>proj_simplex(V, z)</cite>.</p></li>
<li><p><strong>z</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em> or </em><em>array</em>) – If array, len(z) must be compatible with <span class="math notranslate nohighlight">\(\mathbf{V}\)</span></p></li>
<li><p><strong>axis</strong> (<em>None</em><em> or </em><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a>) – <ul>
<li><p>axis=None: project <span class="math notranslate nohighlight">\(\mathbf{V}\)</span> by <span class="math notranslate nohighlight">\(P(\mathbf{V}.\mathrm{ravel}(), \text{max_nz}, z)\)</span></p></li>
<li><p>axis=1: project each <span class="math notranslate nohighlight">\(\mathbf{V}_i\)</span> by <span class="math notranslate nohighlight">\(P(\mathbf{V}_i, \text{max_nz}, z_i)\)</span></p></li>
<li><p>axis=0: project each <span class="math notranslate nohighlight">\(\mathbf{V}_{:, j}\)</span> by <span class="math notranslate nohighlight">\(P(\mathbf{V}_{:, j}, \text{max_nz}, z_j)\)</span></p></li>
</ul>
</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>projection</strong></p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray, shape <span class="math notranslate nohighlight">\(\mathbf{V}\)</span>.shape</p>
</dd>
</dl>
<p class="rubric">References</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id1" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Sparse projections onto the simplex
Anastasios Kyrillidis, Stephen Becker, Volkan Cevher and, Christoph Koch
ICML 2013
<a class="reference external" href="https://arxiv.org/abs/1206.1529">https://arxiv.org/abs/1206.1529</a></p>
</aside>
</aside>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.reduce_lazytensor">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">reduce_lazytensor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">func</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">batch_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#reduce_lazytensor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.reduce_lazytensor" title="Link to this definition"></a></dt>
<dd><p>Reduce a LazyTensor along an axis with function fun using batches.</p>
<p>When axis=None, reduce the LazyTensor to a scalar as a sum of fun over
batches taken along dim.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>This function works for tensor of any order but the reduction can be done
only along the first two axis (or global). Also, in order to work, it requires that the slice of size <cite>batch_size</cite> along the axis to reduce (or axis 0 if <cite>axis=None</cite>) is can be computed and fits in memory.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>a</strong> (<a class="reference internal" href="#id55" title="ot.utils.LazyTensor"><em>LazyTensor</em></a>) – LazyTensor to reduce</p></li>
<li><p><strong>func</strong> (<em>callable</em>) – Function to apply to the LazyTensor</p></li>
<li><p><strong>axis</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Axis along which to reduce the LazyTensor. If None, reduce the
LazyTensor to a scalar as a sum of fun over batches taken along axis 0.
If 0 or 1 reduce the LazyTensor to a vector/matrix as a sum of fun over
batches taken along axis.</p></li>
<li><p><strong>nx</strong> (<a class="reference internal" href="ot.backend.html#id0" title="ot.backend.Backend"><em>Backend</em></a><em>, </em><em>optional</em>) – Backend to use for the reduction</p></li>
<li><p><strong>batch_size</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Size of the batches to use for the reduction (default=100)</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>res</strong> – Result of the reduction</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.sparse_ot_dist">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">sparse_ot_dist</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">i</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">j</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">w</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">metric</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sqeuclidean'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">batch_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#sparse_ot_dist"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.sparse_ot_dist" title="Link to this definition"></a></dt>
<dd><p>Compute ot distance between samples in <span class="math notranslate nohighlight">\(\mathbf{x_1}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{x_2}\)</span>
with sparse weights given by <cite>w</cite> for the pairs of samples with indices <cite>i</cite> and <cite>j</cite>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This function is backend-compatible and will work on arrays
from all compatible backends for the following metrics:
‘sqeuclidean’, ‘euclidean’, ‘cityblock’, ‘minkowski’.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x1</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n1</em><em>,</em><em>d</em><em>)</em>) – matrix with <cite>n1</cite> samples of size <cite>d</cite></p></li>
<li><p><strong>x2</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n2</em><em>,</em><em>d</em><em>)</em><em>, </em><em>optional</em>) – matrix with <cite>n2</cite> samples of size <cite>d</cite> (if None then <span class="math notranslate nohighlight">\(\mathbf{x_2} = \mathbf{x_1}\)</span>)</p></li>
<li><p><strong>i</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>k</em><em>,</em><em>)</em>) – indices of samples in <cite>x1</cite> to compute distance from</p></li>
<li><p><strong>j</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>k</em><em>,</em><em>)</em>) – indices of samples in <cite>x2</cite> to compute distance to</p></li>
<li><p><strong>w</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>k</em><em>,</em><em>)</em><em>, </em><em>optional</em>) – weights for each pair of samples to compute distance between.
If None, all pairs are weighted equally (=1/k).</p></li>
<li><p><strong>metric</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#str" title="(in Python v3.15)"><em>str</em></a><em> | </em><em>callable</em><em>, </em><em>optional</em>) – ‘sqeuclidean’, ‘euclidean’, ‘cityblock’ or ‘minkowski’.</p></li>
<li><p><strong>p</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – p-norm for the Minkowski metric. Default value is 2.</p></li>
<li><p><strong>batch_size</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – If specified, compute the distance in batches of size <cite>batch_size</cite> to avoid memory issues for large datasets. Default is None (no batching).</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>dist</strong> – sum of the distance between <span class="math notranslate nohighlight">\(\mathbf{x_1}_i\)</span> and <span class="math notranslate nohighlight">\(\mathbf{x_2}_j\)</span> computed with given metric and weighted by <cite>w</cite></p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)">float</a></p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.split_sample_ratio">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">split_sample_ratio</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X_a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">a</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">random_split</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">random_state</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#split_sample_ratio"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.split_sample_ratio" title="Link to this definition"></a></dt>
<dd><p>Split distribution according to a ratio of weights (using point ordering).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>X_a</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_samples_a</em><em>, </em><em>dim</em><em>)</em>) – samples in the source domain</p></li>
<li><p><strong>a</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>dim_a</em><em>,</em><em>)</em><em>, </em><em>optional</em>) – Samples weights in the source domain (default is uniform)</p></li>
<li><p><strong>nx</strong> (<a class="reference internal" href="#id32" title="ot.utils.BaryResult.backend"><em>backend</em></a><em>, </em><em>optional</em>) – Backend for array operations, by default None (auto-detect)</p></li>
<li><p><strong>ratio</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>optional</em>) – Ratio of the split, by default 0.5</p></li>
<li><p><strong>random_split</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#bool" title="(in Python v3.15)"><em>bool</em></a><em>, </em><em>optional</em>) – Whether to split randomly, by default False</p></li>
<li><p><strong>random_state</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em>, </em><em>optional</em>) – Random state for reproducibility, by default None</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>X_a1</strong> (<em>array-like, shape (n_samples_a1, dim)</em>) – First half of the samples in the source domain</p></li>
<li><p><strong>X_a2</strong> (<em>array-like, shape (n_samples_a2, dim)</em>) – Second half of the samples in the source domain</p></li>
<li><p><strong>a1</strong> (<em>array-like, shape (dim_a1,)</em>) – First half of the weights in the source domain</p></li>
<li><p><strong>a2</strong> (<em>array-like, shape (dim_a2,)</em>) – Second half of the weights in the source domain</p></li>
<li><p><strong>sel_a1</strong> (<em>slice, ndarray-like</em>) – Slice or indexes for the first half of the samples in the source domain</p></li>
<li><p><strong>sel_a2</strong> (<em>slice, ndarray-like</em>) – Slice or indexes for the second half of the samples in the source domain</p></li>
</ul>
</p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.tic">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">tic</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#tic"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.tic" title="Link to this definition"></a></dt>
<dd><p>Python implementation of Matlab tic() function</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.toc">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">toc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">message</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Elapsed</span> <span class="pre">time</span> <span class="pre">:</span> <span class="pre">{}</span> <span class="pre">s'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#toc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.toc" title="Link to this definition"></a></dt>
<dd><p>Python implementation of Matlab toc() function</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.toq">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">toq</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#toq"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.toq" title="Link to this definition"></a></dt>
<dd><p>Python implementation of Julia toc() function</p>
</dd></dl>
<div class="sphx-glr-clear"></div><dl class="py function">
<dt class="sig sig-object py" id="ot.utils.unif">
<span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">unif</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">type_as</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#unif"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.unif" title="Link to this definition"></a></dt>
<dd><p>Return a uniform histogram normalized over its last dimension (simplex).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#tuple" title="(in Python v3.15)"><em>tuple</em></a><em> of </em><a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a>) – Number of bins in the histogram, or the full output shape. An integer
<code class="docutils literal notranslate"><span class="pre">n</span></code> is equivalent to <code class="docutils literal notranslate"><span class="pre">(n,)</span></code>. For a shape <code class="docutils literal notranslate"><span class="pre">(...,</span> <span class="pre">n)</span></code> the output is
normalized over the last dimension, e.g. <code class="docutils literal notranslate"><span class="pre">(B,</span> <span class="pre">n)</span></code> returns <code class="docutils literal notranslate"><span class="pre">B</span></code>
uniform histograms of length <code class="docutils literal notranslate"><span class="pre">n</span></code>.</p></li>
<li><p><strong>type_as</strong> (<em>array-like</em>) – array of the same type of the expected output (numpy/pytorch/jax)</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>h</strong> – uniform histogram(s) such that each slice along the last dimension sums
to one, i.e. every entry equals <span class="math notranslate nohighlight">\(\frac{1}{n}\)</span> with <code class="docutils literal notranslate"><span class="pre">n</span></code> the last
dimension.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape <code class="docutils literal notranslate"><span class="pre">shape</span></code></p>
</dd>
</dl>
</dd></dl>
<div class="sphx-glr-clear"></div></section>
</section>
<section id="classes">
<h2>Classes<a class="headerlink" href="#classes" title="Link to this heading"></a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="ot.utils.BaryResult">
<span class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></span><span class="sig-prename descclassname"><span class="pre">ot.utils.</span></span><span class="sig-name descname"><span class="pre">BaryResult</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">C</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">value</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">value_linear</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">value_quad</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">list_res</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">status</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">backend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ot/utils.html#BaryResult"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ot.utils.BaryResult" title="Link to this definition"></a></dt>
<dd><p>Base class for OT barycenter results.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>X</strong> (array-like, shape (<cite>n</cite>, <cite>d</cite>)) – Barycenter features.</p></li>
<li><p><strong>C</strong> (array-like, shape (<cite>n</cite>, <cite>n</cite>)) – Barycenter structure for Gromov Wasserstein solutions.</p></li>
<li><p><strong>b</strong> (array-like, shape (<cite>n</cite>,)) – Barycenter weights.</p></li>
<li><p><strong>value</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>array-like</em>) – Full transport cost, including possible regularization terms and
quadratic term for Gromov Wasserstein solutions.</p></li>
<li><p><strong>value_linear</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>array-like</em>) – The linear part of the transport cost, i.e. the product between the
transport plan and the cost.</p></li>
<li><p><strong>value_quad</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#float" title="(in Python v3.15)"><em>float</em></a><em>, </em><em>array-like</em>) – The quadratic part of the transport cost for Gromov-Wasserstein
solutions.</p></li>
<li><p><strong>log</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#dict" title="(in Python v3.15)"><em>dict</em></a>) – Dictionary containing potential information about the solver.</p></li>
<li><p><strong>list_res</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#list" title="(in Python v3.15)"><em>list</em></a><em> of </em><a class="reference internal" href="#id56" title="ot.utils.OTResult"><em>OTResult</em></a>) – List of results for the individual OT matching with input distributions considered as
sources and the learned barycenter distribution as target.</p></li>
<li><p><strong>status</strong> (<a class="reference external" href="https://docs.python.org/3/builtins/functions.html#int" title="(in Python v3.15)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/builtins/stdtypes.html#str" title="(in Python v3.15)"><em>str</em></a>) – Status of the solver.</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="ot.utils.BaryResult.X">
<span class="sig-name descname"><span class="pre">X</span></span><a class="headerlink" href="#ot.utils.BaryResult.X" title="Link to this definition"></a></dt>
<dd><p>Barycenter features.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (<cite>n</cite>, <cite>d</cite>)</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="ot.utils.BaryResult.C">
<span class="sig-name descname"><span class="pre">C</span></span><a class="headerlink" href="#ot.utils.BaryResult.C" title="Link to this definition"></a></dt>
<dd><p>Barycenter structure for Gromov Wasserstein solutions.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (<cite>n</cite>, <cite>n</cite>)</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="ot.utils.BaryResult.b">
<span class="sig-name descname"><span class="pre">b</span></span><a class="headerlink" href="#ot.utils.BaryResult.b" title="Link to this definition"></a></dt>
<dd><p>Barycenter weights.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array-like, shape (<cite>n</cite>,)</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">