forked from pytorch/pytorch.github.io
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathbroadcasting.html
767 lines (628 loc) · 60.9 KB
/
broadcasting.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
<!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 charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Broadcasting semantics — PyTorch master documentation</title>
<link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Lato" type="text/css" />
<link rel="stylesheet" href="../_static/css/pytorch_theme.css" type="text/css" />
<link rel="index" title="Index"
href="../genindex.html"/>
<link rel="search" title="Search" href="../search.html"/>
<link rel="top" title="PyTorch master documentation" href="../index.html"/>
<link rel="next" title="CUDA semantics" href="cuda.html"/>
<link rel="prev" title="Autograd mechanics" href="autograd.html"/>
<script src="../_static/js/modernizr.min.js"></script>
</head>
<body class="wy-body-for-nav" role="document">
<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">
<img src="../_static/pytorch-logo-dark.svg" class="logo" />
</a>
<div class="version">
<a href="https://pytorch.org/docs/versions.html"> 0.2.0_1 ▼</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>
<div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
<p class="caption"><span class="caption-text">Notes</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="autograd.html">Autograd mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="autograd.html#excluding-subgraphs-from-backward">Excluding subgraphs from backward</a><ul>
<li class="toctree-l3"><a class="reference internal" href="autograd.html#requires-grad"><code class="docutils literal"><span class="pre">requires_grad</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="autograd.html#volatile"><code class="docutils literal"><span class="pre">volatile</span></code></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="autograd.html#how-autograd-encodes-the-history">How autograd encodes the history</a></li>
<li class="toctree-l2"><a class="reference internal" href="autograd.html#in-place-operations-on-variables">In-place operations on Variables</a></li>
<li class="toctree-l2"><a class="reference internal" href="autograd.html#in-place-correctness-checks">In-place correctness checks</a></li>
</ul>
</li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">Broadcasting semantics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#general-semantics">General semantics</a></li>
<li class="toctree-l2"><a class="reference internal" href="#in-place-semantics">In-place semantics</a></li>
<li class="toctree-l2"><a class="reference internal" href="#backwards-compatibility">Backwards compatibility</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="cuda.html">CUDA semantics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="cuda.html#best-practices">Best practices</a><ul>
<li class="toctree-l3"><a class="reference internal" href="cuda.html#use-pinned-memory-buffers">Use pinned memory buffers</a></li>
<li class="toctree-l3"><a class="reference internal" href="cuda.html#use-nn-dataparallel-instead-of-multiprocessing">Use nn.DataParallel instead of multiprocessing</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="extending.html">Extending PyTorch</a><ul>
<li class="toctree-l2"><a class="reference internal" href="extending.html#extending-torch-autograd">Extending <code class="docutils literal"><span class="pre">torch.autograd</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="extending.html#extending-torch-nn">Extending <code class="docutils literal"><span class="pre">torch.nn</span></code></a><ul>
<li class="toctree-l3"><a class="reference internal" href="extending.html#adding-a-module">Adding a <code class="docutils literal"><span class="pre">Module</span></code></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="extending.html#writing-custom-c-extensions">Writing custom C extensions</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="multiprocessing.html">Multiprocessing best practices</a><ul>
<li class="toctree-l2"><a class="reference internal" href="multiprocessing.html#sharing-cuda-tensors">Sharing CUDA tensors</a></li>
<li class="toctree-l2"><a class="reference internal" href="multiprocessing.html#best-practices-and-tips">Best practices and tips</a><ul>
<li class="toctree-l3"><a class="reference internal" href="multiprocessing.html#avoiding-and-fighting-deadlocks">Avoiding and fighting deadlocks</a></li>
<li class="toctree-l3"><a class="reference internal" href="multiprocessing.html#reuse-buffers-passed-through-a-queue">Reuse buffers passed through a Queue</a></li>
<li class="toctree-l3"><a class="reference internal" href="multiprocessing.html#asynchronous-multiprocess-training-e-g-hogwild">Asynchronous multiprocess training (e.g. Hogwild)</a><ul>
<li class="toctree-l4"><a class="reference internal" href="multiprocessing.html#hogwild">Hogwild</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="serialization.html">Serialization semantics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="serialization.html#best-practices">Best practices</a><ul>
<li class="toctree-l3"><a class="reference internal" href="serialization.html#recommended-approach-for-saving-a-model">Recommended approach for saving a model</a></li>
</ul>
</li>
</ul>
</li>
</ul>
<p class="caption"><span class="caption-text">Package Reference</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../torch.html">torch</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../torch.html#tensors">Tensors</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../torch.html#creation-ops">Creation Ops</a></li>
<li class="toctree-l3"><a class="reference internal" href="../torch.html#indexing-slicing-joining-mutating-ops">Indexing, Slicing, Joining, Mutating Ops</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../torch.html#random-sampling">Random sampling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torch.html#serialization">Serialization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torch.html#parallelism">Parallelism</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torch.html#math-operations">Math operations</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../torch.html#pointwise-ops">Pointwise Ops</a></li>
<li class="toctree-l3"><a class="reference internal" href="../torch.html#reduction-ops">Reduction Ops</a></li>
<li class="toctree-l3"><a class="reference internal" href="../torch.html#comparison-ops">Comparison Ops</a></li>
<li class="toctree-l3"><a class="reference internal" href="../torch.html#other-operations">Other Operations</a></li>
<li class="toctree-l3"><a class="reference internal" href="../torch.html#blas-and-lapack-operations">BLAS and LAPACK Operations</a></li>
</ul>
</li>
</ul>
</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="../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="../nn.html">torch.nn</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#parameters">Parameters</a></li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#containers">Containers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#module"><span class="hidden-section">Module</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#sequential"><span class="hidden-section">Sequential</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#modulelist"><span class="hidden-section">ModuleList</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#parameterlist"><span class="hidden-section">ParameterList</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#convolution-layers">Convolution Layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#conv1d"><span class="hidden-section">Conv1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#conv2d"><span class="hidden-section">Conv2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#conv3d"><span class="hidden-section">Conv3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#convtranspose1d"><span class="hidden-section">ConvTranspose1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#convtranspose2d"><span class="hidden-section">ConvTranspose2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#convtranspose3d"><span class="hidden-section">ConvTranspose3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#pooling-layers">Pooling Layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#maxpool1d"><span class="hidden-section">MaxPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#maxpool2d"><span class="hidden-section">MaxPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#maxpool3d"><span class="hidden-section">MaxPool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#maxunpool1d"><span class="hidden-section">MaxUnpool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#maxunpool2d"><span class="hidden-section">MaxUnpool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#maxunpool3d"><span class="hidden-section">MaxUnpool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#avgpool1d"><span class="hidden-section">AvgPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#avgpool2d"><span class="hidden-section">AvgPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#avgpool3d"><span class="hidden-section">AvgPool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#fractionalmaxpool2d"><span class="hidden-section">FractionalMaxPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#lppool2d"><span class="hidden-section">LPPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#adaptivemaxpool1d"><span class="hidden-section">AdaptiveMaxPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#adaptivemaxpool2d"><span class="hidden-section">AdaptiveMaxPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#adaptiveavgpool1d"><span class="hidden-section">AdaptiveAvgPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#adaptiveavgpool2d"><span class="hidden-section">AdaptiveAvgPool2d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#padding-layers">Padding Layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#reflectionpad2d"><span class="hidden-section">ReflectionPad2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#replicationpad2d"><span class="hidden-section">ReplicationPad2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#replicationpad3d"><span class="hidden-section">ReplicationPad3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#zeropad2d"><span class="hidden-section">ZeroPad2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#constantpad2d"><span class="hidden-section">ConstantPad2d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#non-linear-activations">Non-linear Activations</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#relu"><span class="hidden-section">ReLU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#relu6"><span class="hidden-section">ReLU6</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#elu"><span class="hidden-section">ELU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#selu"><span class="hidden-section">SELU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#prelu"><span class="hidden-section">PReLU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#leakyrelu"><span class="hidden-section">LeakyReLU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#threshold"><span class="hidden-section">Threshold</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#hardtanh"><span class="hidden-section">Hardtanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#sigmoid"><span class="hidden-section">Sigmoid</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#tanh"><span class="hidden-section">Tanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#logsigmoid"><span class="hidden-section">LogSigmoid</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#softplus"><span class="hidden-section">Softplus</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#softshrink"><span class="hidden-section">Softshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#softsign"><span class="hidden-section">Softsign</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#tanhshrink"><span class="hidden-section">Tanhshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#softmin"><span class="hidden-section">Softmin</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#softmax"><span class="hidden-section">Softmax</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#logsoftmax"><span class="hidden-section">LogSoftmax</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#normalization-layers">Normalization layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#batchnorm1d"><span class="hidden-section">BatchNorm1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#batchnorm2d"><span class="hidden-section">BatchNorm2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#batchnorm3d"><span class="hidden-section">BatchNorm3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#instancenorm1d"><span class="hidden-section">InstanceNorm1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#instancenorm2d"><span class="hidden-section">InstanceNorm2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#instancenorm3d"><span class="hidden-section">InstanceNorm3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#recurrent-layers">Recurrent layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#rnn"><span class="hidden-section">RNN</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#lstm"><span class="hidden-section">LSTM</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#gru"><span class="hidden-section">GRU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#rnncell"><span class="hidden-section">RNNCell</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#lstmcell"><span class="hidden-section">LSTMCell</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#grucell"><span class="hidden-section">GRUCell</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#linear-layers">Linear layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#linear"><span class="hidden-section">Linear</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#dropout-layers">Dropout layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#dropout"><span class="hidden-section">Dropout</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#dropout2d"><span class="hidden-section">Dropout2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#dropout3d"><span class="hidden-section">Dropout3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#alphadropout"><span class="hidden-section">AlphaDropout</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#sparse-layers">Sparse layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#embedding"><span class="hidden-section">Embedding</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#embeddingbag"><span class="hidden-section">EmbeddingBag</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#distance-functions">Distance functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#cosinesimilarity"><span class="hidden-section">CosineSimilarity</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#pairwisedistance"><span class="hidden-section">PairwiseDistance</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#loss-functions">Loss functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#l1loss"><span class="hidden-section">L1Loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#mseloss"><span class="hidden-section">MSELoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#crossentropyloss"><span class="hidden-section">CrossEntropyLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#nllloss"><span class="hidden-section">NLLLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#poissonnllloss"><span class="hidden-section">PoissonNLLLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#nllloss2d"><span class="hidden-section">NLLLoss2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#kldivloss"><span class="hidden-section">KLDivLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#bceloss"><span class="hidden-section">BCELoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#bcewithlogitsloss"><span class="hidden-section">BCEWithLogitsLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#marginrankingloss"><span class="hidden-section">MarginRankingLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#hingeembeddingloss"><span class="hidden-section">HingeEmbeddingLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#multilabelmarginloss"><span class="hidden-section">MultiLabelMarginLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#smoothl1loss"><span class="hidden-section">SmoothL1Loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#softmarginloss"><span class="hidden-section">SoftMarginLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#multilabelsoftmarginloss"><span class="hidden-section">MultiLabelSoftMarginLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#cosineembeddingloss"><span class="hidden-section">CosineEmbeddingLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#multimarginloss"><span class="hidden-section">MultiMarginLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#tripletmarginloss"><span class="hidden-section">TripletMarginLoss</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#vision-layers">Vision layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#pixelshuffle"><span class="hidden-section">PixelShuffle</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#upsample"><span class="hidden-section">Upsample</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#upsamplingnearest2d"><span class="hidden-section">UpsamplingNearest2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#upsamplingbilinear2d"><span class="hidden-section">UpsamplingBilinear2d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#dataparallel-layers-multi-gpu-distributed">DataParallel layers (multi-GPU, distributed)</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#dataparallel"><span class="hidden-section">DataParallel</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#distributeddataparallel"><span class="hidden-section">DistributedDataParallel</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#utilities">Utilities</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#clip-grad-norm"><span class="hidden-section">clip_grad_norm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#weight-norm"><span class="hidden-section">weight_norm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#remove-weight-norm"><span class="hidden-section">remove_weight_norm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#packedsequence"><span class="hidden-section">PackedSequence</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#pack-padded-sequence"><span class="hidden-section">pack_padded_sequence</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#pad-packed-sequence"><span class="hidden-section">pad_packed_sequence</span></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../nn.html#torch-nn-functional">torch.nn.functional</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#convolution-functions">Convolution functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id16"><span class="hidden-section">conv1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id17"><span class="hidden-section">conv2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id18"><span class="hidden-section">conv3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#conv-transpose1d"><span class="hidden-section">conv_transpose1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#conv-transpose2d"><span class="hidden-section">conv_transpose2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#conv-transpose3d"><span class="hidden-section">conv_transpose3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#pooling-functions">Pooling functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#avg-pool1d"><span class="hidden-section">avg_pool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#avg-pool2d"><span class="hidden-section">avg_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#avg-pool3d"><span class="hidden-section">avg_pool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#max-pool1d"><span class="hidden-section">max_pool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#max-pool2d"><span class="hidden-section">max_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#max-pool3d"><span class="hidden-section">max_pool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#max-unpool1d"><span class="hidden-section">max_unpool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#max-unpool2d"><span class="hidden-section">max_unpool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#max-unpool3d"><span class="hidden-section">max_unpool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#lp-pool2d"><span class="hidden-section">lp_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#adaptive-max-pool1d"><span class="hidden-section">adaptive_max_pool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#adaptive-max-pool2d"><span class="hidden-section">adaptive_max_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#adaptive-avg-pool1d"><span class="hidden-section">adaptive_avg_pool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#adaptive-avg-pool2d"><span class="hidden-section">adaptive_avg_pool2d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#non-linear-activation-functions">Non-linear activation functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id19"><span class="hidden-section">threshold</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id20"><span class="hidden-section">relu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id21"><span class="hidden-section">hardtanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id22"><span class="hidden-section">relu6</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id23"><span class="hidden-section">elu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id24"><span class="hidden-section">selu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#leaky-relu"><span class="hidden-section">leaky_relu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id25"><span class="hidden-section">prelu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#rrelu"><span class="hidden-section">rrelu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id26"><span class="hidden-section">logsigmoid</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#hardshrink"><span class="hidden-section">hardshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id27"><span class="hidden-section">tanhshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id28"><span class="hidden-section">softsign</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id29"><span class="hidden-section">softplus</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id30"><span class="hidden-section">softmin</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id31"><span class="hidden-section">softmax</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id32"><span class="hidden-section">softshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#log-softmax"><span class="hidden-section">log_softmax</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id33"><span class="hidden-section">tanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id34"><span class="hidden-section">sigmoid</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#normalization-functions">Normalization functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#batch-norm"><span class="hidden-section">batch_norm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#normalize"><span class="hidden-section">normalize</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#linear-functions">Linear functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id35"><span class="hidden-section">linear</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#dropout-functions">Dropout functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id36"><span class="hidden-section">dropout</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#alpha-dropout"><span class="hidden-section">alpha_dropout</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id37"><span class="hidden-section">dropout2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id38"><span class="hidden-section">dropout3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#id39">Distance functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#pairwise-distance"><span class="hidden-section">pairwise_distance</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#cosine-similarity"><span class="hidden-section">cosine_similarity</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#id40">Loss functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#binary-cross-entropy"><span class="hidden-section">binary_cross_entropy</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#poisson-nll-loss"><span class="hidden-section">poisson_nll_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#cosine-embedding-loss"><span class="hidden-section">cosine_embedding_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#cross-entropy"><span class="hidden-section">cross_entropy</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#hinge-embedding-loss"><span class="hidden-section">hinge_embedding_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#kl-div"><span class="hidden-section">kl_div</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#l1-loss"><span class="hidden-section">l1_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#mse-loss"><span class="hidden-section">mse_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#margin-ranking-loss"><span class="hidden-section">margin_ranking_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#multilabel-margin-loss"><span class="hidden-section">multilabel_margin_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#multilabel-soft-margin-loss"><span class="hidden-section">multilabel_soft_margin_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#multi-margin-loss"><span class="hidden-section">multi_margin_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#nll-loss"><span class="hidden-section">nll_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#binary-cross-entropy-with-logits"><span class="hidden-section">binary_cross_entropy_with_logits</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#smooth-l1-loss"><span class="hidden-section">smooth_l1_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#soft-margin-loss"><span class="hidden-section">soft_margin_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#triplet-margin-loss"><span class="hidden-section">triplet_margin_loss</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../nn.html#vision-functions">Vision functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#pixel-shuffle"><span class="hidden-section">pixel_shuffle</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#pad"><span class="hidden-section">pad</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#id42"><span class="hidden-section">upsample</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#upsample-nearest"><span class="hidden-section">upsample_nearest</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#upsample-bilinear"><span class="hidden-section">upsample_bilinear</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#grid-sample"><span class="hidden-section">grid_sample</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="../nn.html#affine-grid"><span class="hidden-section">affine_grid</span></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../nn.html#torch-nn-init">torch.nn.init</a></li>
<li class="toctree-l1"><a class="reference internal" href="../optim.html">torch.optim</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../optim.html#how-to-use-an-optimizer">How to use an optimizer</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../optim.html#constructing-it">Constructing it</a></li>
<li class="toctree-l3"><a class="reference internal" href="../optim.html#per-parameter-options">Per-parameter options</a></li>
<li class="toctree-l3"><a class="reference internal" href="../optim.html#taking-an-optimization-step">Taking an optimization step</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../optim.html#optimizer-step"><code class="docutils literal"><span class="pre">optimizer.step()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="../optim.html#optimizer-step-closure"><code class="docutils literal"><span class="pre">optimizer.step(closure)</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../optim.html#algorithms">Algorithms</a></li>
<li class="toctree-l2"><a class="reference internal" href="../optim.html#how-to-adjust-learning-rate">How to adjust Learning Rate</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../autograd.html">torch.autograd</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../autograd.html#variable">Variable</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../autograd.html#api-compatibility">API compatibility</a></li>
<li class="toctree-l3"><a class="reference internal" href="../autograd.html#in-place-operations-on-variables">In-place operations on Variables</a></li>
<li class="toctree-l3"><a class="reference internal" href="../autograd.html#in-place-correctness-checks">In-place correctness checks</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../autograd.html#function"><span class="hidden-section">Function</span></a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../multiprocessing.html">torch.multiprocessing</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../multiprocessing.html#strategy-management">Strategy management</a></li>
<li class="toctree-l2"><a class="reference internal" href="../multiprocessing.html#sharing-cuda-tensors">Sharing CUDA tensors</a></li>
<li class="toctree-l2"><a class="reference internal" href="../multiprocessing.html#sharing-strategies">Sharing strategies</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../multiprocessing.html#file-descriptor-file-descriptor">File descriptor - <code class="docutils literal"><span class="pre">file_descriptor</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="../multiprocessing.html#file-system-file-system">File system - <code class="docutils literal"><span class="pre">file_system</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../distributed.html">torch.distributed</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../distributed.html#initialization">Initialization</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../distributed.html#tcp-initialization">TCP initialization</a></li>
<li class="toctree-l3"><a class="reference internal" href="../distributed.html#shared-file-system-initialization">Shared file-system initialization</a></li>
<li class="toctree-l3"><a class="reference internal" href="../distributed.html#environment-variable-initialization">Environment variable initialization</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../distributed.html#groups">Groups</a></li>
<li class="toctree-l2"><a class="reference internal" href="../distributed.html#point-to-point-communication">Point-to-point communication</a></li>
<li class="toctree-l2"><a class="reference internal" href="../distributed.html#collective-functions">Collective functions</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../legacy.html">torch.legacy</a></li>
<li class="toctree-l1"><a class="reference internal" href="../cuda.html">torch.cuda</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../cuda.html#communication-collectives">Communication collectives</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cuda.html#streams-and-events">Streams and events</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cuda.html#nvidia-tools-extension-nvtx">NVIDIA Tools Extension (NVTX)</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../ffi.html">torch.utils.ffi</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="../model_zoo.html">torch.utils.model_zoo</a></li>
</ul>
<p class="caption"><span class="caption-text">torchvision Reference</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../torchvision/torchvision.html">torchvision</a></li>
<li class="toctree-l1"><a class="reference internal" href="../torchvision/datasets.html">torchvision.datasets</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#mnist">MNIST</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#coco">COCO</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../torchvision/datasets.html#captions">Captions</a></li>
<li class="toctree-l3"><a class="reference internal" href="../torchvision/datasets.html#detection">Detection</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#lsun">LSUN</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#imagefolder">ImageFolder</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#imagenet-12">Imagenet-12</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#cifar">CIFAR</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#stl10">STL10</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#svhn">SVHN</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/datasets.html#phototour">PhotoTour</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../torchvision/models.html">torchvision.models</a></li>
<li class="toctree-l1"><a class="reference internal" href="../torchvision/transforms.html">torchvision.transforms</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/transforms.html#transforms-on-pil-image">Transforms on PIL.Image</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/transforms.html#transforms-on-torch-tensor">Transforms on torch.*Tensor</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/transforms.html#conversion-transforms">Conversion Transforms</a></li>
<li class="toctree-l2"><a class="reference internal" href="../torchvision/transforms.html#generic-transforms">Generic Transforms</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../torchvision/utils.html">torchvision.utils</a></li>
</ul>
</div>
</div>
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap">
<nav class="wy-nav-top" role="navigation" aria-label="top navigation">
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="../index.html">PyTorch</a>
</nav>
<div class="wy-nav-content">
<div class="rst-content">
<div role="navigation" aria-label="breadcrumbs navigation">
<ul class="wy-breadcrumbs">
<li><a href="../index.html">Docs</a> »</li>
<li>Broadcasting semantics</li>
<li class="wy-breadcrumbs-aside">
<a href="../_sources/notes/broadcasting.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">
<div class="section" id="broadcasting-semantics">
<span id="id1"></span><h1>Broadcasting semantics<a class="headerlink" href="#broadcasting-semantics" title="Permalink to this headline">¶</a></h1>
<p>Many PyTorch operations support <a class="reference external" href="https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html#module-numpy.doc.broadcasting" title="(in NumPy v1.13)"><code class="xref any docutils literal"><span class="pre">NumPy</span> <span class="pre">Broadcasting</span> <span class="pre">Semantics</span></code></a>.</p>
<p>In short, if a PyTorch operation supports broadcast, then its Tensor arguments can be
automatically expanded to be of equal sizes (without making copies of the data).</p>
<div class="section" id="general-semantics">
<h2>General semantics<a class="headerlink" href="#general-semantics" title="Permalink to this headline">¶</a></h2>
<p>Two tensors are “broadcastable” if the following rules hold:</p>
<ul class="simple">
<li>Each tensor has at least one dimension.</li>
<li>When iterating over the dimension sizes, starting at the trailing dimension,
the dimension sizes must either be equal, one of them is 1, or one of them
does not exist.</li>
</ul>
<p>For Example:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="go"># same shapes are always broadcastable (i.e. the above rules always hold)</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</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="go"># x and y are not broadcastable, because x does not have at least 1 dimension</span>
<span class="go"># can line up trailing dimensions</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span> <span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="go"># x and y are broadcastable.</span>
<span class="go"># 1st trailing dimension: both have size 1</span>
<span class="go"># 2nd trailing dimension: y has size 1</span>
<span class="go"># 3rd trailing dimension: x size == y size</span>
<span class="go"># 4th trailing dimension: y dimension doesn't exist</span>
<span class="go"># but:</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span> <span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="go"># x and y are not broadcastable, because in the 3rd trailing dimension 2 != 3</span>
</pre></div>
</div>
<p>If two tensors <code class="xref py py-attr docutils literal"><span class="pre">x</span></code>, <code class="xref py py-attr docutils literal"><span class="pre">y</span></code> are “broadcastable”, the resulting tensor size
is calculated as follows:</p>
<ul class="simple">
<li>If the number of dimensions of <code class="xref py py-attr docutils literal"><span class="pre">x</span></code> and <code class="xref py py-attr docutils literal"><span class="pre">y</span></code> are not equal, prepend 1
to the dimensions of the tensor with fewer dimensions to make them equal length.</li>
<li>Then, for each dimension size, the resulting dimension size is the max of the sizes of
<code class="xref py py-attr docutils literal"><span class="pre">x</span></code> and <code class="xref py py-attr docutils literal"><span class="pre">y</span></code> along that dimension.</li>
</ul>
<p>For Example:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># can line up trailing dimensions to make reading easier</span>
<span class="o">>>></span> <span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="o">>>></span> <span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span> <span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="o">>>></span> <span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="n">torch</span><span class="o">.</span><span class="n">Size</span><span class="p">([</span><span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="c1"># but not necessary:</span>
<span class="o">>>></span> <span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="o">>>></span> <span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">7</span><span class="p">)</span>
<span class="o">>>></span> <span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="n">torch</span><span class="o">.</span><span class="n">Size</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">7</span><span class="p">])</span>
<span class="o">>>></span> <span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="o">>>></span> <span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="o">>>></span> <span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="ne">RuntimeError</span><span class="p">:</span> <span class="n">The</span> <span class="n">size</span> <span class="n">of</span> <span class="n">tensor</span> <span class="n">a</span> <span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="n">must</span> <span class="n">match</span> <span class="n">the</span> <span class="n">size</span> <span class="n">of</span> <span class="n">tensor</span> <span class="n">b</span> <span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="n">at</span> <span class="n">non</span><span class="o">-</span><span class="n">singleton</span> <span class="n">dimension</span> <span class="mi">1</span>
</pre></div>
</div>
</div>
<div class="section" id="in-place-semantics">
<h2>In-place semantics<a class="headerlink" href="#in-place-semantics" title="Permalink to this headline">¶</a></h2>
<p>One complication is that in-place operations do not allow the in-place tensor to change shape
as a result of the broadcast.</p>
<p>For Example:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">y</span><span class="p">))</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="go">torch.Size([5, 3, 4, 1])</span>
<span class="go"># but:</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">7</span><span class="p">)</span>
<span class="gp">>>> </span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">y</span><span class="p">))</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="go">RuntimeError: The expanded size of the tensor (1) must match the existing size (7) at non-singleton dimension 2.</span>
</pre></div>
</div>
</div>
<div class="section" id="backwards-compatibility">
<h2>Backwards compatibility<a class="headerlink" href="#backwards-compatibility" title="Permalink to this headline">¶</a></h2>
<p>Prior versions of PyTorch allowed certain pointwise functions to execute on tensors with different shapes,
as long as the number of elements in each tensor was equal. The pointwise operation would then be carried
out by viewing each tensor as 1-dimensional. PyTorch now supports broadcasting and the “1-dimensional”
pointwise behavior is considered deprecated and will generate a Python warning in cases where tensors are
not broadcastable, but have the same number of elements.</p>
<p>Note that the introduction of broadcasting can cause backwards incompatible changes in the case where
two tensors do not have the same shape, but are broadcastable and have the same number of elements.
For Example:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">),</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span>
</pre></div>
</div>
<p>would previously produce a Tensor with size: torch.Size([4,1]), but now produces a Tensor with size: torch.Size([4,4]).
In order to help identify cases in your code where backwards incompatibilities introduced by broadcasting may exist,
you may set <cite>torch.utils.backcompat.broadcast_warning.enabled</cite> to <cite>True</cite>, which will generate a python warning
in such cases.</p>
<p>For Example:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">backcompat</span><span class="o">.</span><span class="n">broadcast_warning</span><span class="o">.</span><span class="n">enabled</span><span class="o">=</span><span class="kc">True</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">),</span> <span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span>
<span class="go">__main__:1: UserWarning: self and other do not have the same shape, but are broadcastable, and have the same number of elements.</span>
<span class="go">Changing behavior in a backwards incompatible manner to broadcasting rather than viewing as 1-dimensional.</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="articleComments">
</div>
</div>
<footer>
<div class="rst-footer-buttons" role="navigation" aria-label="footer navigation">
<a href="cuda.html" class="btn btn-neutral float-right" title="CUDA semantics" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right"></span></a>
<a href="autograd.html" class="btn btn-neutral" title="Autograd mechanics" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left"></span> Previous</a>
</div>
<hr/>
<div role="contentinfo">
<p>
© Copyright 2017, Torch Contributors.
</p>
</div>
Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>.
</footer>
</div>
</div>
</section>
</div>
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT:'../',
VERSION:'master',
LANGUAGE:'None',
COLLAPSE_INDEX:false,
FILE_SUFFIX:'.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt'
};
</script>
<script type="text/javascript" src="../_static/jquery.js"></script>
<script type="text/javascript" src="../_static/underscore.js"></script>
<script type="text/javascript" src="../_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="../_static/js/theme.js"></script>
<script type="text/javascript">
jQuery(function () {
SphinxRtdTheme.StickyNav.enable();
});
</script>
</body>
</html>