-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathlinalg.html
4580 lines (4185 loc) · 395 KB
/
linalg.html
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 lang="en" data-content_root="" >
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta property="og:title" content="torch.linalg" />
<meta property="og:type" content="website" />
<meta property="og:url" content="http://pytorch.org/linalg.html" />
<meta property="og:site_name" content="PyTorch" />
<meta property="og:description" content="Common linear algebra operations. See Linear algebra (torch.linalg) for some common numerical edge-cases. Matrix Properties: Decompositions: Solvers: Inverses: Matrix Functions: Matrix Products: Te..." />
<meta property="og:image" content="https://pytorch.org/assets/images/social-share.jpg" />
<meta property="og:image:alt" content="PyTorch" />
<meta name="description" content="Common linear algebra operations. See Linear algebra (torch.linalg) for some common numerical edge-cases. Matrix Properties: Decompositions: Solvers: Inverses: Matrix Functions: Matrix Products: Te..." />
<title>torch.linalg — PyTorch main documentation</title>
<script data-cfasync="false">
document.documentElement.dataset.mode = localStorage.getItem("mode") || "";
document.documentElement.dataset.theme = localStorage.getItem("theme") || "";
</script>
<!-- Loaded before other Sphinx assets -->
<link href="_static/styles/theme.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="_static/styles/bootstrap.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="_static/styles/pydata-sphinx-theme.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="_static/vendor/fontawesome/6.5.2/css/all.min.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-solid-900.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
<link rel="stylesheet" type="text/css" href="_static/pygments.css" />
<link rel="stylesheet" type="text/css" href="_static/css/theme.css" />
<link rel="stylesheet" type="text/css" href="_static/copybutton.css" />
<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" />
<link rel="stylesheet" type="text/css" href="_static/katex-math.css" />
<link rel="stylesheet" type="text/css" href="_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css" />
<link rel="stylesheet" type="text/css" href="_static/css/jit.css" />
<link rel="stylesheet" type="text/css" href="_static/css/custom.css" />
<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" />
<!-- Pre-loaded scripts that we'll load fully later -->
<link rel="preload" as="script" href="_static/scripts/bootstrap.js?digest=dfe6caa3a7d634c4db9b" />
<link rel="preload" as="script" href="_static/scripts/pydata-sphinx-theme.js?digest=dfe6caa3a7d634c4db9b" />
<script src="_static/vendor/fontawesome/6.5.2/js/all.min.js?digest=dfe6caa3a7d634c4db9b"></script>
<script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
<script src="_static/jquery.js"></script>
<script src="_static/underscore.js"></script>
<script src="_static/_sphinx_javascript_frameworks_compat.js"></script>
<script src="_static/doctools.js"></script>
<script src="_static/sphinx_highlight.js"></script>
<script src="_static/clipboard.min.js"></script>
<script src="_static/copybutton.js"></script>
<script src="_static/design-tabs.js"></script>
<script>DOCUMENTATION_OPTIONS.pagename = 'linalg';</script>
<script>
DOCUMENTATION_OPTIONS.theme_version = '0.15.4';
DOCUMENTATION_OPTIONS.theme_switcher_json_url = 'https://pytorch.org/docs/pytorch-versions.json';
DOCUMENTATION_OPTIONS.theme_switcher_version_match = 'main';
DOCUMENTATION_OPTIONS.show_version_warning_banner = true;
</script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="torch.linalg.norm" href="generated/torch.linalg.norm.html" />
<link rel="prev" title="TorchScript Unsupported PyTorch Constructs" href="jit_unsupported.html" />
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta name="docsearch:language" content="en"/>
<script src="https://code.jquery.com/jquery-3.7.1.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/list.js/2.3.1/list.min.js"></script>
<link rel="stylesheet" type="text/css" href="_static/css/theme.css">
<script type="text/javascript" src="_static/js/theme.js"></script>
<link rel="stylesheet" href="_static/webfonts/all.min.css">
<meta name="pytorch_project" content="docs">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-T8XT4PS"
height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- End Google Tag Manager (noscript) -->
<!-- Google Tag Manager -->
<script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':
new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],
j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src=
'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);
j.onload = function() {
window.dispatchEvent(new Event('gtm_loaded'));
console.log('GTM loaded successfully');
};
})(window,document,'script','dataLayer','GTM-T8XT4PS');
</script>
<!-- End Google Tag Manager -->
<!-- Facebook Pixel Code -->
<script>
!function(f,b,e,v,n,t,s)
{if(f.fbq)return;n=f.fbq=function(){n.callMethod?
n.callMethod.apply(n,arguments):n.queue.push(arguments)};
if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';
n.queue=[];t=b.createElement(e);t.async=!0;
t.src=v;s=b.getElementsByTagName(e)[0];
s.parentNode.insertBefore(t,s)}(window,document,'script',
'https://connect.facebook.net/en_US/fbevents.js');
fbq('init', '243028289693773');
fbq('track', 'PageView');
</script>
<script>
document.documentElement.setAttribute('data-version', 'main (2.8.0a0+git334aab0 )');
</script>
<noscript>
<img height="1" width="1" src="https://www.facebook.com/tr?id=243028289693773&ev=PageView&noscript=1"/>
</noscript>
<script>
function gtag() {
window.dataLayer.push(arguments);
}
</script>
<!-- End Facebook Pixel Code -->
<script async src="https://cse.google.com/cse.js?cx=e65585f8c3ea1440e"></script>
<!--
Search engines should not index the main version of documentation.
Stable documentation are built without release == 'main'.
-->
<meta name="robots" content="noindex">
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta name="docsearch:language" content="en"/>
</head>
<body data-feedback-url="https://github.com/pytorch/pytorch" class="pytorch-body">
<div class="container-fluid header-holder tutorials-header" id="header-holder">
<div class="header-container-wrapper">
<div class="header-container">
<a class="header-logo" href="https://pytorch.org/" aria-label="PyTorch"></a>
<div class="main-menu">
<ul>
<li class="main-menu-item">
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="with-down-arrow">
Learn
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/get-started">
<span class=dropdown-title>Get Started</span>
<p>Run PyTorch locally or get started quickly with one of the supported cloud platforms</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/tutorials">
<span class="dropdown-title">Tutorials</span>
<p>Whats new in PyTorch tutorials</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/tutorials/beginner/basics/intro.html">
<span class="dropdown-title">Learn the Basics</span>
<p>Familiarize yourself with PyTorch concepts and modules</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/tutorials/recipes/recipes_index.html">
<span class="dropdown-title">PyTorch Recipes</span>
<p>Bite-size, ready-to-deploy PyTorch code examples</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/tutorials/beginner/introyt.html">
<span class="dropdown-title">Intro to PyTorch - YouTube Series</span>
<p>Master PyTorch basics with our engaging YouTube tutorial series</p>
</a>
</div>
</div>
</li>
<li>
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="with-down-arrow">
Ecosystem
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/ecosystem">
<span class="dropdown-title">Tools</span>
<p>Learn about the tools and frameworks in the PyTorch Ecosystem</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/#community-module">
<span class=dropdown-title>Community</span>
<p>Join the PyTorch developer community to contribute, learn, and get your questions answered</p>
</a>
<a class="nav-dropdown-item" href="https://discuss.pytorch.org/" target="_blank">
<span class=dropdown-title>Forums</span>
<p>A place to discuss PyTorch code, issues, install, research</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/resources">
<span class=dropdown-title>Developer Resources</span>
<p>Find resources and get questions answered</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/ecosystem/contributor-awards-2024">
<span class="dropdown-title">Contributor Awards - 2024</span>
<p>Award winners announced at this year's PyTorch Conference</p>
</a>
</div>
</div>
</li>
<li>
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="with-down-arrow">
Edge
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/edge">
<span class="dropdown-title">About PyTorch Edge</span>
<p>Build innovative and privacy-aware AI experiences for edge devices</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/executorch-overview">
<span class="dropdown-title">ExecuTorch</span>
<p>End-to-end solution for enabling on-device inference capabilities across mobile and edge devices</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/executorch/stable/index.html">
<span class="dropdown-title">ExecuTorch Docs</span>
</a>
</div>
</div>
</li>
<li class="main-menu-item">
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="with-down-arrow">
Docs
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/docs/stable/index.html">
<span class="dropdown-title">PyTorch</span>
<p>Explore the documentation for comprehensive guidance on how to use PyTorch</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/pytorch-domains">
<span class="dropdown-title">PyTorch Domains</span>
<p>Read the PyTorch Domains documentation to learn more about domain-specific libraries</p>
</a>
</div>
</div>
</li>
<li>
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="with-down-arrow">
Blogs & News
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/blog/">
<span class="dropdown-title">PyTorch Blog</span>
<p>Catch up on the latest technical news and happenings</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/community-blog">
<span class="dropdown-title">Community Blog</span>
<p>Stories from the PyTorch ecosystem</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/videos">
<span class="dropdown-title">Videos</span>
<p>Learn about the latest PyTorch tutorials, new, and more </p>
<a class="nav-dropdown-item" href="https://pytorch.org/community-stories">
<span class="dropdown-title">Community Stories</span>
<p>Learn how our community solves real, everyday machine learning problems with PyTorch</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/events">
<span class="dropdown-title">Events</span>
<p>Find events, webinars, and podcasts</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/newsletter">
<span class="dropdown-title">Newsletter</span>
<p>Stay up-to-date with the latest updates</p>
</a>
</div>
</li>
<li>
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="with-down-arrow">
About
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/foundation">
<span class="dropdown-title">PyTorch Foundation</span>
<p>Learn more about the PyTorch Foundation</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/governing-board">
<span class="dropdown-title">Governing Board</span>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/credits">
<span class="dropdown-title">Cloud Credit Program</span>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/tac">
<span class="dropdown-title">Technical Advisory Council</span>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/staff">
<span class="dropdown-title">Staff</span>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/contact-us">
<span class="dropdown-title">Contact Us</span>
</a>
</div>
</div>
</li>
<li class="main-menu-item">
<div class="no-dropdown">
<a href="https://pytorch.org/join" data-cta="join">
Become a Member
</a>
</div>
</li>
<li>
<div class="main-menu-item">
<a href="https://github.com/pytorch/pytorch" class="github-icon">
</a>
</div>
</li>
<!--- TODO: This block adds the search icon to the nav bar. We will enable it later.
<li>
<div class="main-menu-item">
<a href="https://github.com/pytorch/pytorch" class="search-icon">
</a>
</div>
</li>
--->
</ul>
</div>
<a class="main-menu-open-button" href="#" data-behavior="open-mobile-menu">
<i class="fa-solid fa-ellipsis"></i>
</a>
</div>
</div>
</div>
<!-- Begin Mobile Menu -->
<div class="mobile-main-menu">
<div class="container-fluid">
<div class="header-container-wrapper">
<div class="mobile-main-menu-header-container">
<a class="header-logo" href="https://pytorch.org/" aria-label="PyTorch"></a>
<a class="main-menu-close-button" href="#" data-behavior="close-mobile-menu">
<i class="fa-solid fa-xmark"></i>
</a>
</div>
</div>
</div>
<div class="mobile-main-menu-links-container">
<div class="main-menu">
<ul>
<li class="resources-mobile-menu-title">
<a>Learn</a>
</li>
<ul class="resources-mobile-menu-items">
<li>
<a href="https://pytorch.org/get-started">Get Started</a>
</li>
<li>
<a href="https://pytorch.org/tutorials">Tutorials</a>
</li>
<li>
<a href="https://pytorch.org/tutorials/beginner/basics/intro.html">Learn the Basics</a>
</li>
<li>
<a href="https://pytorch.org/tutorials/recipes/recipes_index.html">PyTorch Recipes</a>
</li>
<li>
<a href="https://pytorch.org/tutorials/beginner/introyt.html">Introduction to PyTorch - YouTube Series</a>
</li>
</ul>
<li class="resources-mobile-menu-title">
<a>Ecosystem</a>
</li>
<ul class="resources-mobile-menu-items">
<li>
<a href="https://pytorch.org/ecosystem">Tools</a>
</li>
<li>
<a href="https://pytorch.org/#community-module">Community</a>
</li>
<li>
<a href="https://discuss.pytorch.org/">Forums</a>
</li>
<li>
<a href="https://pytorch.org/resources">Developer Resources</a>
</li>
<li>
<a href="https://pytorch.org/ecosystem/contributor-awards-2023">Contributor Awards - 2024</a>
</li>
</ul>
<li class="resources-mobile-menu-title">
<a>Edge</a>
</li>
<ul class="resources-mobile-menu-items">
<li>
<a href="https://pytorch.org/edge">About PyTorch Edge</a>
</li>
<li>
<a href="https://pytorch.org/executorch-overview">ExecuTorch</a>
</li>
<li>
<a href="https://pytorch.org/executorch/stable/index.html">ExecuTorch Documentation</a>
</li>
</ul>
<li class="resources-mobile-menu-title">
<a>Docs</a>
</li>
<ul class="resources-mobile-menu-items">
<li>
<a href="https://pytorch.org/docs/stable/index.html">PyTorch</a>
</li>
<li>
<a href="https://pytorch.org/pytorch-domains">PyTorch Domains</a>
</li>
</ul>
<li class="resources-mobile-menu-title">
<a>Blog & News</a>
</li>
<ul class="resources-mobile-menu-items">
<li>
<a href="https://pytorch.org/blog/">PyTorch Blog</a>
</li>
<li>
<a href="https://pytorch.org/community-blog">Community Blog</a>
</li>
<li>
<a href="https://pytorch.org/videos">Videos</a>
</li>
<li>
<a href="https://pytorch.org/community-stories">Community Stories</a>
</li>
<li>
<a href="https://pytorch.org/events">Events</a>
</li>
<li>
<a href="https://pytorch.org/newsletter">Newsletter</a>
</li>
</ul>
<li class="resources-mobile-menu-title">
<a>About</a>
</li>
<ul class="resources-mobile-menu-items">
<li>
<a href="https://pytorch.org/foundation">PyTorch Foundation</a>
</li>
<li>
<a href="https://pytorch.org/governing-board">Governing Board</a>
</li>
<li>
<a href="https://pytorch.org/credits">Cloud Credit Program</a>
</li>
<li>
<a href="https://pytorch.org/tac">Technical Advisory Council</a>
</li>
<li>
<a href="https://pytorch.org/staff">Staff</a>
</li>
<li>
<a href="https://pytorch.org/contact-us">Contact Us</a>
</li>
</ul>
</ul>
</div>
</div>
</div>
<!-- End Mobile Menu -->
<body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="">
<div id="pst-skip-link" class="skip-link d-print-none"><a href="#main-content">Skip to main content</a></div>
<div id="pst-scroll-pixel-helper"></div>
<button type="button" class="btn rounded-pill" id="pst-back-to-top">
<i class="fa-solid fa-arrow-up"></i>Back to top</button>
<input type="checkbox"
class="sidebar-toggle"
id="pst-primary-sidebar-checkbox"/>
<label class="overlay overlay-primary" for="pst-primary-sidebar-checkbox"></label>
<input type="checkbox"
class="sidebar-toggle"
id="pst-secondary-sidebar-checkbox"/>
<label class="overlay overlay-secondary" for="pst-secondary-sidebar-checkbox"></label>
<div class="search-button__wrapper">
<div class="search-button__overlay"></div>
<div class="search-button__search-container">
<form class="bd-search d-flex align-items-center"
action="search.html"
method="get">
<i class="fa-solid fa-magnifying-glass"></i>
<input type="search"
class="form-control"
name="q"
id="search-input"
placeholder="Search the docs ..."
aria-label="Search the docs ..."
autocomplete="off"
autocorrect="off"
autocapitalize="off"
spellcheck="false"/>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form></div>
</div>
<div class="pst-async-banner-revealer d-none">
<aside id="bd-header-version-warning" class="d-none d-print-none" aria-label="Version warning"></aside>
</div>
<header class="bd-header navbar navbar-expand-lg bd-navbar d-print-none">
<div class="bd-header__inner bd-page-width">
<button class="pst-navbar-icon sidebar-toggle primary-toggle" aria-label="Site navigation">
<span class="fa-solid fa-bars"></span>
</button>
<div class=" navbar-header-items__start">
<div class="navbar-item">
<script>
document.write(`
<div class="version-switcher__container dropdown">
<button id="pst-version-switcher-button-2"
type="button"
class="version-switcher__button btn btn-sm dropdown-toggle"
data-bs-toggle="dropdown"
aria-haspopup="listbox"
aria-controls="pst-version-switcher-list-2"
aria-label="Version switcher list"
>
Choose version <!-- this text may get changed later by javascript -->
<span class="caret"></span>
</button>
<div id="pst-version-switcher-list-2"
class="version-switcher__menu dropdown-menu list-group-flush py-0"
role="listbox" aria-labelledby="pst-version-switcher-button-2">
<!-- dropdown will be populated by javascript on page load -->
</div>
</div>
`);
</script></div>
<div class="navbar-item">
<a class="navbar-brand logo" href="index.html">
<p class="title logo__title">Home</p>
</a></div>
</div>
<div class=" navbar-header-items">
<div class="me-auto navbar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item current active">
<a class="nav-link nav-internal" href="pytorch-api.html">
Python API
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="notes.html">
Developer Notes
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://pytorch.org/tutorials/">
Tutorials
</a>
</li>
</ul>
</nav></div>
</div>
<div class="navbar-header-items__end">
<div class="navbar-item">
<div class="search-container-wrapper">
<div id="sphinx-search" class="search-container">
<form class="bd-search d-flex align-items-center"
action="search.html"
method="get">
<i class="fa-solid fa-magnifying-glass"></i>
<input type="search"
class="form-control"
name="q"
id="search-input"
placeholder="Search the docs ..."
aria-label="Search the docs ..."
autocomplete="off"
autocorrect="off"
autocapitalize="off"
spellcheck="false"/>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form>
</div>
<div id="google-search" class="search-container" style="display:none;">
<div class="gcse-search-wrapper">
<i class="fa-solid fa-magnifying-glass" aria-hidden="true"></i>
<div class="gcse-search"></div>
</div>
</div>
<div class="search-toggle-container" data-bs-title="Google Search Off" data-bs-placement="bottom" data-bs-toggle="tooltip">
<div class="search-toggle-inner">
<label class="switch">
<input type="checkbox" id="search-toggle">
<span class="slider round"></span>
</label>
</div>
</div>
</div>
<script>
document.addEventListener('DOMContentLoaded', function() {
// Define the search callback
const myWebSearchStartingCallback = (gname, query) => {
if (typeof dataLayer !== 'undefined' && query) {
window.dataLayer = [];
dataLayer.push({
'event': 'google_search',
'search_term': query,
'event_category': 'Search',
'event_label': 'Google Search'
});
console.log('GA event sent via callback: google_search - ' + query);
}
return '';
};
// Set up the GCSE search callbacks
window.__gcse || (window.__gcse = {});
window.__gcse.searchCallbacks = {
web: {
starting: myWebSearchStartingCallback,
},
};
if (window.location.pathname.includes('/search.html')) {
document.body.classList.add('search-page');
}
// Function to reinitialize Google CSE
function reinitializeGoogleSearch() {
if (window.__gcse) {
// Force Google CSE to reinitialize
if (window.__gcse.initializationCallback) {
window.__gcse.initializationCallback();
}
}
}
// Function to handle search toggle
function handleSearchToggle(toggle, sphinxSearch, googleSearch) {
if (!toggle || !sphinxSearch || !googleSearch) return;
// Check if the URL contains /stable/ or /tutorials/
const currentUrl = window.location.href;
const shouldDefaultToGoogle = currentUrl.includes('/stable/') || currentUrl.includes('/tutorials/');
// Check if there's a saved preference, otherwise use the URL-based default
const savedPreference = localStorage.getItem('searchPreference');
if (savedPreference === 'google' || (savedPreference === null && shouldDefaultToGoogle)) {
toggle.checked = true;
sphinxSearch.style.display = 'none';
googleSearch.style.display = 'block';
// Save the preference if it wasn't already saved
if (savedPreference === null) {
localStorage.setItem('searchPreference', 'google');
}
// Ensure Google search is properly initialized
reinitializeGoogleSearch();
} else {
toggle.checked = false;
sphinxSearch.style.display = 'block';
googleSearch.style.display = 'none';
}
// Update tooltip based on initial state
const tooltipElement = document.querySelector('.search-toggle-container');
if (tooltipElement) {
tooltipElement.setAttribute('data-bs-title', toggle.checked ? 'Google Search On' : 'Google Search Off');
// Reinitialize tooltip if Bootstrap's tooltip is already initialized
if (bootstrap && bootstrap.Tooltip) {
const tooltipInstance = bootstrap.Tooltip.getInstance(tooltipElement);
if (tooltipInstance) tooltipInstance.dispose();
new bootstrap.Tooltip(tooltipElement);
}
}
// Add a data attribute to track if this toggle has been initialized
if (toggle.hasAttribute('data-initialized')) {
return; // Skip adding another event listener if already initialized
}
toggle.setAttribute('data-initialized', 'true');
toggle.addEventListener('change', function() {
if (this.checked) {
sphinxSearch.style.display = 'none';
googleSearch.style.display = 'block';
localStorage.setItem('searchPreference', 'google');
// Reinitialize Google search when switching to it
reinitializeGoogleSearch();
const tooltipElement = document.querySelector('.search-toggle-container');
if (tooltipElement) {
tooltipElement.setAttribute('data-bs-title', 'Google Search On');
// Refresh tooltip
if (bootstrap && bootstrap.Tooltip) {
const tooltipInstance = bootstrap.Tooltip.getInstance(tooltipElement);
if (tooltipInstance) tooltipInstance.dispose();
new bootstrap.Tooltip(tooltipElement);
}
}
if (typeof dataLayer !== 'undefined') {
window.dataLayer = [];
dataLayer.push({
'event': 'search_engine_switch',
'event_category': 'Search',
'event_label': 'Google'
});
console.log('GA event sent via dataLayer: search_engine_switch - Google');
} else {
console.log('GA not available: Cannot track Google search switch');
}
} else {
sphinxSearch.style.display = 'block';
googleSearch.style.display = 'none';
localStorage.setItem('searchPreference', 'sphinx');
const tooltipElement = document.querySelector('.search-toggle-container');
if (tooltipElement) {
tooltipElement.setAttribute('data-bs-title', 'Google Search Off');
// Refresh tooltip
if (bootstrap && bootstrap.Tooltip) {
const tooltipInstance = bootstrap.Tooltip.getInstance(tooltipElement);
if (tooltipInstance) tooltipInstance.dispose();
new bootstrap.Tooltip(tooltipElement);
}
}
if (typeof dataLayer !== 'undefined') {
window.dataLayer = [];
dataLayer.push({
'event': 'search_engine_switch',
'event_category': 'Search',
'event_label': 'Sphinx'
});
console.log('GA event sent via dataLayer: search_engine_switch - Sphinx');
} else {
console.log('GA not available: Cannot track Sphinx search switch');
}
}
// Also update mobile search if it exists
updateMobileSearch(false); // Pass false to prevent triggering another event
});
}
// Function to update mobile search based on current toggle state
function updateMobileSearch() {
const toggle = document.getElementById('search-toggle');
if (!toggle) return;
// Find mobile search container
const mobileSearchContainer = document.querySelector('.sidebar-header-items__end .navbar-item .search-container-wrapper');
if (mobileSearchContainer) {
const mobileSphinxSearch = mobileSearchContainer.querySelector('#sphinx-search');
const mobileGoogleSearch = mobileSearchContainer.querySelector('#google-search');
if (mobileSphinxSearch && mobileGoogleSearch) {
if (toggle.checked) {
mobileSphinxSearch.style.display = 'none';
mobileGoogleSearch.style.display = 'block';
// Reinitialize Google search in mobile view
reinitializeGoogleSearch();
} else {
mobileSphinxSearch.style.display = 'block';
mobileGoogleSearch.style.display = 'none';
}
}
}
}
// Initialize desktop search toggle
const toggle = document.getElementById('search-toggle');
const sphinxSearch = document.getElementById('sphinx-search');
const googleSearch = document.getElementById('google-search');
handleSearchToggle(toggle, sphinxSearch, googleSearch);
// Set placeholder text for Google search input
const observer = new MutationObserver(function(mutations, obs) {
const searchInputs = document.querySelectorAll('.gsc-input input');
searchInputs.forEach(input => {
if (input) {
input.setAttribute('placeholder', 'Search the docs ...');
if (!input.hasAttribute('data-tracking-added')) {
input.setAttribute('data-tracking-added', 'true');
}
}
});
});
observer.observe(document.body, { childList: true, subtree: true });
// Watch for mobile menu creation
const mobileMenuObserver = new MutationObserver(function(mutations) {
for (const mutation of mutations) {
const mobileSearchInputs = document.querySelectorAll('.sidebar-header-items__end .navbar-item .search-container-wrapper .gsc-input input');
mobileSearchInputs.forEach(input => {
if (input) {
input.setAttribute('placeholder', 'Search the docs ...');
input.style.paddingLeft = '36px';
}
});
if (mutation.addedNodes.length) {
// Check if the mobile search container was added
const mobileSearchContainer = document.querySelector('.sidebar-header-items__end .navbar-item .search-container-wrapper');
if (mobileSearchContainer) {
// Clone the toggle for mobile if needed
const mobileToggle = mobileSearchContainer.querySelector('#search-toggle');
if (mobileToggle) {
// Sync mobile toggle with desktop toggle
mobileToggle.checked = toggle.checked;
// Update mobile search display
updateMobileSearch();
// Add event listener to mobile toggle
mobileToggle.addEventListener('change', function() {
// Sync desktop toggle with mobile toggle
toggle.checked = this.checked;
// Trigger change event on desktop toggle to update both
toggle.dispatchEvent(new Event('change'));
});
}
}
}
}
});
mobileMenuObserver.observe(document.body, { childList: true, subtree: true });
// Ensure Google CSE is properly loaded
if (window.__gcse) {
window.__gcse.callback = function() {
// This will run after Google CSE is fully loaded
if (toggle && toggle.checked) {
// If Google search is active, make sure it's properly initialized
reinitializeGoogleSearch();
}
};
} else {
// If Google CSE hasn't loaded yet, set up a callback
window.__gcse = {
callback: function() {
if (toggle && toggle.checked) {
reinitializeGoogleSearch();
}
}
};
}
});
</script>
</div>
<div class="navbar-item">
<script>
document.write(`
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button" title="light/dark" aria-label="light/dark" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto"></i>
</button>
`);
</script></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://x.com/PyTorch" title="X" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-x-twitter fa-lg" aria-hidden="true"></i>
<span class="sr-only">X</span></a>
</li>
<li class="nav-item">
<a href="https://github.com/pytorch/pytorch" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-github fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitHub</span></a>
</li>
<li class="nav-item">
<a href="https://discuss.pytorch.org/" title="PyTorch Forum" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-discourse fa-lg" aria-hidden="true"></i>
<span class="sr-only">PyTorch Forum</span></a>
</li>
<li class="nav-item">
<a href="https://pypi.org/project/torch/" title="PyPi" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-python fa-lg" aria-hidden="true"></i>
<span class="sr-only">PyPi</span></a>
</li>
</ul></div>
</div>
</div>
<button class="pst-navbar-icon sidebar-toggle secondary-toggle" aria-label="On this page">
<span class="fa-solid fa-outdent"></span>
</button>
</div>
</header>
<div class="bd-container">
<div class="bd-container__inner bd-page-width">
<div class="bd-sidebar-primary bd-sidebar">