-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathtorch.cholesky.html
709 lines (513 loc) · 37.8 KB
/
torch.cholesky.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
<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
<meta name="robots" content="noindex">
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>torch.cholesky — PyTorch 1.7.0 documentation</title>
<link rel="canonical" href="https://pytorch.org/docs/stable/generated/torch.cholesky.html"/>
<link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
<!-- <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" type="text/css" />
<link rel="stylesheet" href="../_static/css/jit.css" type="text/css" />
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" type="text/css" />
<link rel="stylesheet" href="../_static/katex-math.css" type="text/css" />
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="torch.cholesky_inverse" href="torch.cholesky_inverse.html" />
<link rel="prev" title="torch.chain_matmul" href="torch.chain_matmul.html" />
<script src="../_static/js/modernizr.min.js"></script>
<!-- Preload the theme fonts -->
<link rel="preload" href="../_static/fonts/FreightSans/freight-sans-book.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="../_static/fonts/FreightSans/freight-sans-medium.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="../_static/fonts/IBMPlexMono/IBMPlexMono-Medium.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="../_static/fonts/FreightSans/freight-sans-bold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="../_static/fonts/FreightSans/freight-sans-medium-italic.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="../_static/fonts/IBMPlexMono/IBMPlexMono-SemiBold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<!-- Preload the katex fonts -->
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Math-Italic.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Main-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Main-Bold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size1-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size4-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size2-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size3-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Caligraphic-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
</head>
<div class="container-fluid header-holder tutorials-header" id="header-holder">
<div class="container">
<div class="header-container">
<a class="header-logo" href="https://pytorch.org/" aria-label="PyTorch"></a>
<div class="main-menu">
<ul>
<li>
<a href="https://pytorch.org/get-started">Get Started</a>
</li>
<li>
<div class="ecosystem-dropdown">
<a id="dropdownMenuButton" data-toggle="ecosystem-dropdown">
Ecosystem
</a>
<div class="ecosystem-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/hub"">
<span class=dropdown-title>Models (Beta)</span>
<p>Discover, publish, and reuse pre-trained models</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/ecosystem">
<span class=dropdown-title>Tools & Libraries</span>
<p>Explore the ecosystem of tools and libraries</p>
</a>
</div>
</div>
</li>
<li>
<a href="https://pytorch.org/mobile">Mobile</a>
</li>
<li>
<a href="https://pytorch.org/blog/">Blog</a>
</li>
<li>
<a href="https://pytorch.org/tutorials">Tutorials</a>
</li>
<li class="active">
<a href="https://pytorch.org/docs/stable/index.html">Docs</a>
</li>
<li>
<div class="resources-dropdown">
<a id="resourcesDropdownButton" data-toggle="resources-dropdown">
Resources
</a>
<div class="resources-dropdown-menu">
<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/features">
<span class=dropdown-title>About</span>
<p>Learn about PyTorch’s features and capabilities</p>
</a>
</div>
</div>
</li>
<li>
<a href="https://github.com/pytorch/pytorch">Github</a>
</li>
</ul>
</div>
<a class="main-menu-open-button" href="#" data-behavior="open-mobile-menu"></a>
</div>
</div>
</div>
<body class="pytorch-body">
<div class="table-of-contents-link-wrapper">
<span>Table of Contents</span>
<a href="#" class="toggle-table-of-contents" data-behavior="toggle-table-of-contents"></a>
</div>
<nav data-toggle="wy-nav-shift" class="pytorch-left-menu" id="pytorch-left-menu">
<div class="pytorch-side-scroll">
<div class="pytorch-menu pytorch-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
<div class="pytorch-left-menu-search">
<div class="version">
<a href='http://pytorch.org/docs/versions.html'>1.7.0 ▼</a>
</div>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="../search.html" method="get">
<input type="text" name="q" placeholder="Search Docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<p class="caption"><span class="caption-text">Notes</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../notes/amp_examples.html">Automatic Mixed Precision examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/autograd.html">Autograd mechanics</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/broadcasting.html">Broadcasting semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/cpu_threading_torchscript_inference.html">CPU threading and TorchScript inference</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/cuda.html">CUDA semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/ddp.html">Distributed Data Parallel</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/extending.html">Extending PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/faq.html">Frequently Asked Questions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/large_scale_deployments.html">Features for large-scale deployments</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/multiprocessing.html">Multiprocessing best practices</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/randomness.html">Reproducibility</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/serialization.html">Serialization semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notes/windows.html">Windows FAQ</a></li>
</ul>
<p class="caption"><span class="caption-text">Language Bindings</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../cpp_index.html">C++</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/javadoc/">Javadoc</a></li>
</ul>
<p class="caption"><span class="caption-text">Python API</span></p>
<ul class="current">
<li class="toctree-l1 current"><a class="reference internal" href="../torch.html">torch</a></li>
<li class="toctree-l1"><a class="reference internal" href="../nn.html">torch.nn</a></li>
<li class="toctree-l1"><a class="reference internal" href="../nn.functional.html">torch.nn.functional</a></li>
<li class="toctree-l1"><a class="reference internal" href="../tensors.html">torch.Tensor</a></li>
<li class="toctree-l1"><a class="reference internal" href="../tensor_attributes.html">Tensor Attributes</a></li>
<li class="toctree-l1"><a class="reference internal" href="../tensor_view.html">Tensor Views</a></li>
<li class="toctree-l1"><a class="reference internal" href="../autograd.html">torch.autograd</a></li>
<li class="toctree-l1"><a class="reference internal" href="../cuda.html">torch.cuda</a></li>
<li class="toctree-l1"><a class="reference internal" href="../amp.html">torch.cuda.amp</a></li>
<li class="toctree-l1"><a class="reference internal" href="../backends.html">torch.backends</a></li>
<li class="toctree-l1"><a class="reference internal" href="../distributed.html">torch.distributed</a></li>
<li class="toctree-l1"><a class="reference internal" href="../distributions.html">torch.distributions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../fft.html">torch.fft</a></li>
<li class="toctree-l1"><a class="reference internal" href="../futures.html">torch.futures</a></li>
<li class="toctree-l1"><a class="reference internal" href="../hub.html">torch.hub</a></li>
<li class="toctree-l1"><a class="reference internal" href="../jit.html">torch.jit</a></li>
<li class="toctree-l1"><a class="reference internal" href="../linalg.html">torch.linalg</a></li>
<li class="toctree-l1"><a class="reference internal" href="../nn.init.html">torch.nn.init</a></li>
<li class="toctree-l1"><a class="reference internal" href="../onnx.html">torch.onnx</a></li>
<li class="toctree-l1"><a class="reference internal" href="../optim.html">torch.optim</a></li>
<li class="toctree-l1"><a class="reference internal" href="../complex_numbers.html">Complex Numbers</a></li>
<li class="toctree-l1"><a class="reference internal" href="../quantization.html">Quantization</a></li>
<li class="toctree-l1"><a class="reference internal" href="../rpc.html">Distributed RPC Framework</a></li>
<li class="toctree-l1"><a class="reference internal" href="../random.html">torch.random</a></li>
<li class="toctree-l1"><a class="reference internal" href="../sparse.html">torch.sparse</a></li>
<li class="toctree-l1"><a class="reference internal" href="../storage.html">torch.Storage</a></li>
<li class="toctree-l1"><a class="reference internal" href="../bottleneck.html">torch.utils.bottleneck</a></li>
<li class="toctree-l1"><a class="reference internal" href="../checkpoint.html">torch.utils.checkpoint</a></li>
<li class="toctree-l1"><a class="reference internal" href="../cpp_extension.html">torch.utils.cpp_extension</a></li>
<li class="toctree-l1"><a class="reference internal" href="../data.html">torch.utils.data</a></li>
<li class="toctree-l1"><a class="reference internal" href="../dlpack.html">torch.utils.dlpack</a></li>
<li class="toctree-l1"><a class="reference internal" href="../mobile_optimizer.html">torch.utils.mobile_optimizer</a></li>
<li class="toctree-l1"><a class="reference internal" href="../model_zoo.html">torch.utils.model_zoo</a></li>
<li class="toctree-l1"><a class="reference internal" href="../tensorboard.html">torch.utils.tensorboard</a></li>
<li class="toctree-l1"><a class="reference internal" href="../type_info.html">Type Info</a></li>
<li class="toctree-l1"><a class="reference internal" href="../named_tensor.html">Named Tensors</a></li>
<li class="toctree-l1"><a class="reference internal" href="../name_inference.html">Named Tensors operator coverage</a></li>
<li class="toctree-l1"><a class="reference internal" href="../__config__.html">torch.__config__</a></li>
</ul>
<p class="caption"><span class="caption-text">Libraries</span></p>
<ul>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/audio">torchaudio</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/text">torchtext</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/vision">torchvision</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/elastic/">TorchElastic</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/serve">TorchServe</a></li>
<li class="toctree-l1"><a class="reference external" href="http://pytorch.org/xla/">PyTorch on XLA Devices</a></li>
</ul>
<p class="caption"><span class="caption-text">Community</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../community/contribution_guide.html">PyTorch Contribution Guide</a></li>
<li class="toctree-l1"><a class="reference internal" href="../community/governance.html">PyTorch Governance</a></li>
<li class="toctree-l1"><a class="reference internal" href="../community/persons_of_interest.html">PyTorch Governance | Persons of Interest</a></li>
</ul>
</div>
</div>
</nav>
<div class="pytorch-container">
<div class="pytorch-page-level-bar" id="pytorch-page-level-bar">
<div class="pytorch-breadcrumbs-wrapper">
<div role="navigation" aria-label="breadcrumbs navigation">
<ul class="pytorch-breadcrumbs">
<li>
<a href="../index.html">
Docs
</a> >
</li>
<li><a href="../torch.html">torch</a> ></li>
<li>torch.cholesky</li>
<li class="pytorch-breadcrumbs-aside">
<a href="../_sources/generated/torch.cholesky.rst.txt" rel="nofollow"><img src="../_static/images/view-page-source-icon.svg"></a>
</li>
</ul>
</div>
</div>
<div class="pytorch-shortcuts-wrapper" id="pytorch-shortcuts-wrapper">
Shortcuts
</div>
</div>
<section data-toggle="wy-nav-shift" id="pytorch-content-wrap" class="pytorch-content-wrap">
<div class="pytorch-content-left">
<div class="rst-content">
<div role="main" class="main-content" itemscope="itemscope" itemtype="http://schema.org/Article">
<article itemprop="articleBody" id="pytorch-article" class="pytorch-article">
<div class="section" id="torch-cholesky">
<h1>torch.cholesky<a class="headerlink" href="#torch-cholesky" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.cholesky">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">cholesky</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">upper=False</em>, <em class="sig-param">*</em>, <em class="sig-param">out=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.cholesky" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the Cholesky decomposition of a symmetric positive-definite
matrix <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span></span></span></span>
</span> or for batches of symmetric positive-definite matrices.</p>
<p>If <code class="xref py py-attr docutils literal notranslate"><span class="pre">upper</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code>, the returned matrix <code class="docutils literal notranslate"><span class="pre">U</span></code> is upper-triangular, and
the decomposition has the form:</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>A</mi><mo>=</mo><msup><mi>U</mi><mi>T</mi></msup><mi>U</mi></mrow><annotation encoding="application/x-tex">A = U^TU</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8913309999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span></span></span></span></span>
</div><p>If <code class="xref py py-attr docutils literal notranslate"><span class="pre">upper</span></code> is <code class="docutils literal notranslate"><span class="pre">False</span></code>, the returned matrix <code class="docutils literal notranslate"><span class="pre">L</span></code> is lower-triangular, and
the decomposition has the form:</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>A</mi><mo>=</mo><mi>L</mi><msup><mi>L</mi><mi>T</mi></msup></mrow><annotation encoding="application/x-tex">A = LL^T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8913309999999999em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span></span></span></span></span>
</div><p>If <code class="xref py py-attr docutils literal notranslate"><span class="pre">upper</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code>, and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span></span></span></span>
</span> is a batch of symmetric positive-definite
matrices, then the returned tensor will be composed of upper-triangular Cholesky factors
of each of the individual matrices. Similarly, when <code class="xref py py-attr docutils literal notranslate"><span class="pre">upper</span></code> is <code class="docutils literal notranslate"><span class="pre">False</span></code>, the returned
tensor will be composed of lower-triangular Cholesky factors of each of the individual
matrices.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span></span></span></span>
</span> of size <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>∗</mo><mo separator="true">,</mo><mi>n</mi><mo separator="true">,</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(*, n, n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">∗</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>
</span> where <cite>*</cite> is zero or more
batch dimensions consisting of symmetric positive-definite matrices.</p></li>
<li><p><strong>upper</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a><em>, </em><em>optional</em>) – flag that indicates whether to return a
upper or lower triangular matrix. Default: <code class="docutils literal notranslate"><span class="pre">False</span></code></p></li>
</ul>
</dd>
<dt class="field-even">Keyword Arguments</dt>
<dd class="field-even"><p><strong>out</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a><em>, </em><em>optional</em>) – the output matrix</p>
</dd>
</dl>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">t</span><span class="p">())</span> <span class="c1"># make symmetric positive-definite</span>
<span class="gp">>>> </span><span class="n">l</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cholesky</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span>
<span class="go">tensor([[ 2.4112, -0.7486, 1.4551],</span>
<span class="go"> [-0.7486, 1.3544, 0.1294],</span>
<span class="go"> [ 1.4551, 0.1294, 1.6724]])</span>
<span class="gp">>>> </span><span class="n">l</span>
<span class="go">tensor([[ 1.5528, 0.0000, 0.0000],</span>
<span class="go"> [-0.4821, 1.0592, 0.0000],</span>
<span class="go"> [ 0.9371, 0.5487, 0.7023]])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="o">.</span><span class="n">t</span><span class="p">())</span>
<span class="go">tensor([[ 2.4112, -0.7486, 1.4551],</span>
<span class="go"> [-0.7486, 1.3544, 0.1294],</span>
<span class="go"> [ 1.4551, 0.1294, 1.6724]])</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">))</span> <span class="o">+</span> <span class="mf">1e-03</span> <span class="c1"># make symmetric positive-definite</span>
<span class="gp">>>> </span><span class="n">l</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cholesky</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">z</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">z</span> <span class="o">-</span> <span class="n">a</span><span class="p">))</span> <span class="c1"># Max non-zero</span>
<span class="go">tensor(2.3842e-07)</span>
</pre></div>
</div>
</dd></dl>
</div>
</article>
</div>
<footer>
<div class="rst-footer-buttons" role="navigation" aria-label="footer navigation">
<a href="torch.cholesky_inverse.html" class="btn btn-neutral float-right" title="torch.cholesky_inverse" accesskey="n" rel="next">Next <img src="../_static/images/chevron-right-orange.svg" class="next-page"></a>
<a href="torch.chain_matmul.html" class="btn btn-neutral" title="torch.chain_matmul" accesskey="p" rel="prev"><img src="../_static/images/chevron-right-orange.svg" class="previous-page"> Previous</a>
</div>
<hr>
<div role="contentinfo">
<p>
© Copyright 2019, Torch Contributors.
</p>
</div>
<div>
Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/rtfd/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>.
</div>
</footer>
</div>
</div>
<div class="pytorch-content-right" id="pytorch-content-right">
<div class="pytorch-right-menu" id="pytorch-right-menu">
<div class="pytorch-side-scroll" id="pytorch-side-scroll-right">
<ul>
<li><a class="reference internal" href="#">torch.cholesky</a></li>
</ul>
</div>
</div>
</div>
</section>
</div>
<script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
<script src="../_static/jquery.js"></script>
<script src="../_static/underscore.js"></script>
<script src="../_static/doctools.js"></script>
<script src="../_static/language_data.js"></script>
<script type="text/javascript" src="../_static/js/vendor/popper.min.js"></script>
<script type="text/javascript" src="../_static/js/vendor/bootstrap.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/list.js/1.5.0/list.min.js"></script>
<script type="text/javascript" src="../_static/js/theme.js"></script>
<script type="text/javascript">
jQuery(function () {
SphinxRtdTheme.Navigation.enable(true);
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-90545585-1', 'auto');
ga('send', 'pageview');
</script>
<script async src="https://www.googletagmanager.com/gtag/js?id=UA-117752657-2"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());
gtag('config', 'UA-117752657-2');
</script>
<img height="1" width="1" style="border-style:none;" alt="" src="https://www.googleadservices.com/pagead/conversion/795629140/?label=txkmCPmdtosBENSssfsC&guid=ON&script=0"/>
<!-- Begin Footer -->
<div class="container-fluid docs-tutorials-resources" id="docs-tutorials-resources">
<div class="container">
<div class="row">
<div class="col-md-4 text-center">
<h2>Docs</h2>
<p>Access comprehensive developer documentation for PyTorch</p>
<a class="with-right-arrow" href="https://pytorch.org/docs/stable/index.html">View Docs</a>
</div>
<div class="col-md-4 text-center">
<h2>Tutorials</h2>
<p>Get in-depth tutorials for beginners and advanced developers</p>
<a class="with-right-arrow" href="https://pytorch.org/tutorials">View Tutorials</a>
</div>
<div class="col-md-4 text-center">
<h2>Resources</h2>
<p>Find development resources and get your questions answered</p>
<a class="with-right-arrow" href="https://pytorch.org/resources">View Resources</a>
</div>
</div>
</div>
</div>
<footer class="site-footer">
<div class="container footer-container">
<div class="footer-logo-wrapper">
<a href="https://pytorch.org/" class="footer-logo"></a>
</div>
<div class="footer-links-wrapper">
<div class="footer-links-col">
<ul>
<li class="list-title"><a href="https://pytorch.org/">PyTorch</a></li>
<li><a href="https://pytorch.org/get-started">Get Started</a></li>
<li><a href="https://pytorch.org/features">Features</a></li>
<li><a href="https://pytorch.org/ecosystem">Ecosystem</a></li>
<li><a href="https://pytorch.org/blog/">Blog</a></li>
<li><a href="https://github.com/pytorch/pytorch/blob/master/CONTRIBUTING.md">Contributing</a></li>
</ul>
</div>
<div class="footer-links-col">
<ul>
<li class="list-title"><a href="https://pytorch.org/resources">Resources</a></li>
<li><a href="https://pytorch.org/tutorials">Tutorials</a></li>
<li><a href="https://pytorch.org/docs/stable/index.html">Docs</a></li>
<li><a href="https://discuss.pytorch.org" target="_blank">Discuss</a></li>
<li><a href="https://github.com/pytorch/pytorch/issues" target="_blank">Github Issues</a></li>
<li><a href="https://pytorch.org/assets/brand-guidelines/PyTorch-Brand-Guidelines.pdf" target="_blank">Brand Guidelines</a></li>
</ul>
</div>
<div class="footer-links-col follow-us-col">
<ul>
<li class="list-title">Stay Connected</li>
<li>
<div id="mc_embed_signup">
<form
action="https://twitter.us14.list-manage.com/subscribe/post?u=75419c71fe0a935e53dfa4a3f&id=91d0dccd39"
method="post"
id="mc-embedded-subscribe-form"
name="mc-embedded-subscribe-form"
class="email-subscribe-form validate"
target="_blank"
novalidate>
<div id="mc_embed_signup_scroll" class="email-subscribe-form-fields-wrapper">
<div class="mc-field-group">
<label for="mce-EMAIL" style="display:none;">Email Address</label>
<input type="email" value="" name="EMAIL" class="required email" id="mce-EMAIL" placeholder="Email Address">
</div>
<div id="mce-responses" class="clear">
<div class="response" id="mce-error-response" style="display:none"></div>
<div class="response" id="mce-success-response" style="display:none"></div>
</div> <!-- real people should not fill this in and expect good things - do not remove this or risk form bot signups-->
<div style="position: absolute; left: -5000px;" aria-hidden="true"><input type="text" name="b_75419c71fe0a935e53dfa4a3f_91d0dccd39" tabindex="-1" value=""></div>
<div class="clear">
<input type="submit" value="" name="subscribe" id="mc-embedded-subscribe" class="button email-subscribe-button">
</div>
</div>
</form>
</div>
</li>
</ul>
<div class="footer-social-icons">
<a href="https://www.facebook.com/pytorch" target="_blank" class="facebook"></a>
<a href="https://twitter.com/pytorch" target="_blank" class="twitter"></a>
<a href="https://www.youtube.com/pytorch" target="_blank" class="youtube"></a>
</div>
</div>
</div>
</div>
</footer>
<div class="cookie-banner-wrapper">
<div class="container">
<p class="gdpr-notice">To analyze traffic and optimize your experience, we serve cookies on this site. By clicking or navigating, you agree to allow our usage of cookies. As the current maintainers of this site, Facebook’s Cookies Policy applies. Learn more, including about available controls: <a href="https://www.facebook.com/policies/cookies/">Cookies Policy</a>.</p>
<img class="close-button" src="../_static/images/pytorch-x.svg">
</div>
</div>
<!-- End Footer -->
<!-- Begin Mobile Menu -->
<div class="mobile-main-menu">
<div class="container-fluid">
<div class="container">
<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"></a>
</div>
</div>
</div>
<div class="mobile-main-menu-links-container">
<div class="main-menu">
<ul>
<li>
<a href="https://pytorch.org/get-started">Get Started</a>
</li>
<li>
<a href="https://pytorch.org/features">Features</a>
</li>
<li>
<a href="https://pytorch.org/ecosystem">Ecosystem</a>
</li>
<li>
<a href="https://pytorch.org/mobile">Mobile</a>
</li>
<li>
<a href="https://pytorch.org/hub">PyTorch Hub</a>
</li>
<li>
<a href="https://pytorch.org/blog/">Blog</a>
</li>
<li>
<a href="https://pytorch.org/tutorials">Tutorials</a>
</li>
<li class="active">
<a href="https://pytorch.org/docs/stable/index.html">Docs</a>
</li>
<li>
<a href="https://pytorch.org/resources">Resources</a>
</li>
<li>
<a href="https://github.com/pytorch/pytorch">Github</a>
</li>
</ul>
</div>
</div>
</div>
<!-- End Mobile Menu -->
<script type="text/javascript" src="../_static/js/vendor/anchor.min.js"></script>
<script type="text/javascript">
$(document).ready(function() {
mobileMenu.bind();
mobileTOC.bind();
pytorchAnchors.bind();
sideMenus.bind();
scrollToAnchor.bind();
highlightNavigation.bind();
mainMenuDropdown.bind();
filterTags.bind();
// Add class to links that have code blocks, since we cannot create links in code blocks
$("article.pytorch-article a span.pre").each(function(e) {
$(this).closest("a").addClass("has-code");
});
})
</script>
</body>
</html>