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<!DOCTYPE html>
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<p class="caption"><span class="caption-text">Notes</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../../notes/autograd.html">Autograd mechanics</a><ul>
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<p class="caption"><span class="caption-text">Package Reference</span></p>
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<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>
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<h1>Source code for torch.functional</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">._utils</span> <span class="k">import</span> <span class="n">_range</span>
<span class="kn">from</span> <span class="nn">operator</span> <span class="k">import</span> <span class="n">mul</span>
<span class="kn">from</span> <span class="nn">functools</span> <span class="k">import</span> <span class="n">reduce</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
<span class="s1">'split'</span><span class="p">,</span> <span class="s1">'chunk'</span><span class="p">,</span> <span class="s1">'stack'</span><span class="p">,</span> <span class="s1">'unbind'</span><span class="p">,</span> <span class="s1">'btriunpack'</span><span class="p">,</span> <span class="s1">'matmul'</span><span class="p">,</span>
<span class="p">]</span>
<div class="viewcode-block" id="split"><a class="viewcode-back" href="../../torch.html#torch.split">[docs]</a><span class="k">def</span> <span class="nf">split</span><span class="p">(</span><span class="n">tensor</span><span class="p">,</span> <span class="n">split_size</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="sd">"""Splits the tensor into equally sized chunks (if possible).</span>
<span class="sd"> Last chunk will be smaller if the tensor size along a given dimension</span>
<span class="sd"> is not divisible by ``split_size``.</span>
<span class="sd"> Arguments:</span>
<span class="sd"> tensor (Tensor): tensor to split.</span>
<span class="sd"> split_size (int): size of a single chunk.</span>
<span class="sd"> dim (int): dimension along which to split the tensor.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">dim</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">dim</span> <span class="o">+=</span> <span class="n">tensor</span><span class="o">.</span><span class="n">dim</span><span class="p">()</span>
<span class="n">dim_size</span> <span class="o">=</span> <span class="n">tensor</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span>
<span class="n">num_splits</span> <span class="o">=</span> <span class="p">(</span><span class="n">dim_size</span> <span class="o">+</span> <span class="n">split_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="n">split_size</span>
<span class="n">last_split_size</span> <span class="o">=</span> <span class="n">split_size</span> <span class="o">-</span> <span class="p">(</span><span class="n">split_size</span> <span class="o">*</span> <span class="n">num_splits</span> <span class="o">-</span> <span class="n">dim_size</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">get_split_size</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">return</span> <span class="n">split_size</span> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="n">num_splits</span> <span class="o">-</span> <span class="mi">1</span> <span class="k">else</span> <span class="n">last_split_size</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">tensor</span><span class="o">.</span><span class="n">narrow</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">dim</span><span class="p">),</span> <span class="nb">int</span><span class="p">(</span><span class="n">i</span> <span class="o">*</span> <span class="n">split_size</span><span class="p">),</span> <span class="nb">int</span><span class="p">(</span><span class="n">get_split_size</span><span class="p">(</span><span class="n">i</span><span class="p">)))</span> <span class="k">for</span> <span class="n">i</span>
<span class="ow">in</span> <span class="n">_range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">num_splits</span><span class="p">))</span></div>
<div class="viewcode-block" id="chunk"><a class="viewcode-back" href="../../torch.html#torch.chunk">[docs]</a><span class="k">def</span> <span class="nf">chunk</span><span class="p">(</span><span class="n">tensor</span><span class="p">,</span> <span class="n">chunks</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="sd">"""Splits a tensor into a number of chunks along a given dimension.</span>
<span class="sd"> Arguments:</span>
<span class="sd"> tensor (Tensor): tensor to split.</span>
<span class="sd"> chunks (int): number of chunks to return.</span>
<span class="sd"> dim (int): dimension along which to split the tensor.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">dim</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">dim</span> <span class="o">+=</span> <span class="n">tensor</span><span class="o">.</span><span class="n">dim</span><span class="p">()</span>
<span class="n">split_size</span> <span class="o">=</span> <span class="p">(</span><span class="n">tensor</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span> <span class="o">+</span> <span class="n">chunks</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="n">chunks</span>
<span class="k">return</span> <span class="n">split</span><span class="p">(</span><span class="n">tensor</span><span class="p">,</span> <span class="n">split_size</span><span class="p">,</span> <span class="n">dim</span><span class="p">)</span></div>
<div class="viewcode-block" id="stack"><a class="viewcode-back" href="../../torch.html#torch.stack">[docs]</a><span class="k">def</span> <span class="nf">stack</span><span class="p">(</span><span class="n">sequence</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""Concatenates sequence of tensors along a new dimension.</span>
<span class="sd"> All tensors need to be of the same size.</span>
<span class="sd"> Arguments:</span>
<span class="sd"> sequence (Sequence): sequence of tensors to concatenate.</span>
<span class="sd"> dim (int): dimension to insert. Has to be between 0 and the number</span>
<span class="sd"> of dimensions of concatenated tensors (inclusive).</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">sequence</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"stack expects a non-empty sequence of tensors"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">dim</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">dim</span> <span class="o">+=</span> <span class="n">sequence</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">dim</span><span class="p">()</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">inputs</span> <span class="o">=</span> <span class="p">[</span><span class="n">t</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">sequence</span><span class="p">]</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">dim</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">dim</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">out</span><span class="p">)</span></div>
<div class="viewcode-block" id="unbind"><a class="viewcode-back" href="../../torch.html#torch.unbind">[docs]</a><span class="k">def</span> <span class="nf">unbind</span><span class="p">(</span><span class="n">tensor</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="sd">"""Removes a tensor dimension.</span>
<span class="sd"> Returns a tuple of all slices along a given dimension, already without it.</span>
<span class="sd"> Arguments:</span>
<span class="sd"> tensor (Tensor): tensor to unbind.</span>
<span class="sd"> dim (int): dimension to remove.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">tensor</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="n">dim</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">_range</span><span class="p">(</span><span class="n">tensor</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">dim</span><span class="p">)))</span></div>
<span class="k">def</span> <span class="nf">btriunpack</span><span class="p">(</span><span class="n">LU_data</span><span class="p">,</span> <span class="n">LU_pivots</span><span class="p">,</span> <span class="n">unpack_data</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">unpack_pivots</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""Unpacks the data and pivots from a batched LU factorization (btrifact) of a tensor.</span>
<span class="sd"> Returns a tuple indexed by:</span>
<span class="sd"> 0: The pivots.</span>
<span class="sd"> 1: The L tensor.</span>
<span class="sd"> 2: The U tensor.</span>
<span class="sd"> Arguments:</span>
<span class="sd"> LU_data (Tensor): The packed LU factorization data.</span>
<span class="sd"> LU_pivots (Tensor): The packed LU factorization pivots.</span>
<span class="sd"> unpack_data (bool): Flag indicating if the data should be unpacked.</span>
<span class="sd"> unpack_pivots (bool): Flag indicating if the pivots should be unpacked.</span>
<span class="sd"> """</span>
<span class="n">nBatch</span><span class="p">,</span> <span class="n">sz</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">LU_data</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="k">if</span> <span class="n">unpack_data</span><span class="p">:</span>
<span class="n">I_U</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">triu</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="n">sz</span><span class="p">,</span> <span class="n">sz</span><span class="p">))</span><span class="o">.</span><span class="n">type_as</span><span class="p">(</span><span class="n">LU_data</span><span class="p">)</span><span class="o">.</span><span class="n">byte</span><span class="p">()</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">nBatch</span><span class="p">,</span> <span class="n">sz</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span>
<span class="n">I_L</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">I_U</span>
<span class="n">L</span> <span class="o">=</span> <span class="n">LU_data</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">LU_data</span><span class="o">.</span><span class="n">size</span><span class="p">())</span><span class="o">.</span><span class="n">zero_</span><span class="p">()</span>
<span class="n">U</span> <span class="o">=</span> <span class="n">LU_data</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">LU_data</span><span class="o">.</span><span class="n">size</span><span class="p">())</span><span class="o">.</span><span class="n">zero_</span><span class="p">()</span>
<span class="n">I_diag</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">sz</span><span class="p">)</span><span class="o">.</span><span class="n">type_as</span><span class="p">(</span><span class="n">LU_data</span><span class="p">)</span><span class="o">.</span><span class="n">byte</span><span class="p">()</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">nBatch</span><span class="p">,</span> <span class="n">sz</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span>
<span class="n">L</span><span class="p">[</span><span class="n">I_diag</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span>
<span class="n">L</span><span class="p">[</span><span class="n">I_L</span><span class="p">]</span> <span class="o">=</span> <span class="n">LU_data</span><span class="p">[</span><span class="n">I_L</span><span class="p">]</span>
<span class="n">U</span><span class="p">[</span><span class="n">I_U</span><span class="p">]</span> <span class="o">=</span> <span class="n">LU_data</span><span class="p">[</span><span class="n">I_U</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">L</span> <span class="o">=</span> <span class="n">U</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">if</span> <span class="n">unpack_pivots</span><span class="p">:</span>
<span class="n">P</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">sz</span><span class="p">)</span><span class="o">.</span><span class="n">type_as</span><span class="p">(</span><span class="n">LU_data</span><span class="p">)</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">nBatch</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="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">nBatch</span><span class="p">):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">sz</span><span class="p">):</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">LU_pivots</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">P</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">clone</span><span class="p">()</span>
<span class="n">P</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">P</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:,</span> <span class="n">k</span><span class="p">]</span>
<span class="n">P</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:,</span> <span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">P</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">return</span> <span class="n">P</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">U</span>
<div class="viewcode-block" id="matmul"><a class="viewcode-back" href="../../torch.html#torch.matmul">[docs]</a><span class="k">def</span> <span class="nf">matmul</span><span class="p">(</span><span class="n">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""Matrix product of two tensors.</span>
<span class="sd"> The behavior depends on the dimensionality of the tensors as follows:</span>
<span class="sd"> - If both tensors are 1-dimensional, the dot product (scalar) is returned.</span>
<span class="sd"> - If both arguments are 2-dimensional, the matrix-matrix product is returned.</span>
<span class="sd"> - If the first argument is 1-dimensional and the second argument is 2-dimensional,</span>
<span class="sd"> a 1 is prepended to its dimension for the purpose of the matrix multiply.</span>
<span class="sd"> After the matrix multiply, the prepended dimension is removed.</span>
<span class="sd"> - If the first argument is 2-dimensional and the second argument is 1-dimensional,</span>
<span class="sd"> the matrix-vector product is returned.</span>
<span class="sd"> - If both arguments are at least 1-dimensional and at least one argument is</span>
<span class="sd"> N-dimensional (where N > 2), then a batched matrix multiply is returned. If the first</span>
<span class="sd"> argument is 1-dimensional, a 1 is prepended to its dimension for the purpose of the</span>
<span class="sd"> batched matrix multiply and removed after. If the second argument is 1-dimensional, a</span>
<span class="sd"> 1 is appended to its dimension for the purpose of the batched matrix multiple and removed after.</span>
<span class="sd"> The non-matrix (i.e. batch) dimensions are :ref:`broadcasted <broadcasting-semantics>` (and thus</span>
<span class="sd"> must be broadcastable). For example, if :attr:`tensor1` is a `j x 1 x n x m` Tensor</span>
<span class="sd"> and :attr:`tensor2` is a `k x m x p` Tensor, :attr:`out` will be an `j x k x n x p` Tensor.</span>
<span class="sd"> .. note::</span>
<span class="sd"> The 1-dimensional dot product version of this function does not support an :attr:`out` parameter.</span>
<span class="sd"> Arguments:</span>
<span class="sd"> tensor1 (Tensor): First tensor to be multiplied</span>
<span class="sd"> tensor2 (Tensor): Second tensor to be multiplied</span>
<span class="sd"> out (Tensor, optional): Output tensor</span>
<span class="sd"> """</span>
<span class="n">dim_tensor1</span> <span class="o">=</span> <span class="n">tensor1</span><span class="o">.</span><span class="n">dim</span><span class="p">()</span>
<span class="n">dim_tensor2</span> <span class="o">=</span> <span class="n">tensor2</span><span class="o">.</span><span class="n">dim</span><span class="p">()</span>
<span class="k">if</span> <span class="n">dim_tensor1</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">and</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"out must be None for 1-d tensor matmul, returns a scalar"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">dim_tensor1</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">mv</span><span class="p">(</span><span class="n">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">mv</span><span class="p">(</span><span class="n">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">out</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">dim_tensor1</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">and</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">tensor1</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">tensor2</span><span class="p">)</span><span class="o">.</span><span class="n">squeeze_</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">tensor1</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">tensor2</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">out</span><span class="p">)</span><span class="o">.</span><span class="n">squeeze_</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">dim_tensor1</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">out</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">dim_tensor1</span> <span class="o">>=</span> <span class="mi">3</span> <span class="ow">and</span> <span class="p">(</span><span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
<span class="c1"># optimization: use mm instead of bmm by folding tensor1's batch into</span>
<span class="c1"># its leading matrix dimension.</span>
<span class="k">if</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">tensor2</span> <span class="o">=</span> <span class="n">tensor2</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">size1</span> <span class="o">=</span> <span class="n">tensor1</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="n">size2</span> <span class="o">=</span> <span class="n">tensor2</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="n">output_size</span> <span class="o">=</span> <span class="n">size1</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">size2</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">:]</span>
<span class="c1"># fold the batch into the first dimension</span>
<span class="n">tensor1</span> <span class="o">=</span> <span class="n">tensor1</span><span class="o">.</span><span class="n">contiguous</span><span class="p">()</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">size1</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="ow">not</span> <span class="n">out</span><span class="o">.</span><span class="n">is_contiguous</span><span class="p">():</span>
<span class="n">output</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">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">output</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">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">out</span><span class="p">)</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">output</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">output_size</span><span class="p">)</span>
<span class="k">if</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">output</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">out</span><span class="o">.</span><span class="n">set_</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
<span class="k">return</span> <span class="n">out</span>
<span class="k">return</span> <span class="n">output</span>
<span class="k">elif</span> <span class="p">(</span><span class="n">dim_tensor1</span> <span class="o">>=</span> <span class="mi">1</span> <span class="ow">and</span> <span class="n">dim_tensor2</span> <span class="o">>=</span> <span class="mi">1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">dim_tensor1</span> <span class="o">>=</span> <span class="mi">3</span> <span class="ow">or</span> <span class="n">dim_tensor2</span> <span class="o">>=</span> <span class="mi">3</span><span class="p">):</span>
<span class="c1"># ensure each tensor size is at least 3-dimensional</span>
<span class="n">tensor1_exp_size</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Size</span><span class="p">((</span><span class="mi">1</span><span class="p">,)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="mi">3</span> <span class="o">-</span> <span class="n">tensor1</span><span class="o">.</span><span class="n">dim</span><span class="p">(),</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">tensor1</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
<span class="c1"># rhs needs to be a separate case since we can't freely expand 1s on the rhs, but can on lhs</span>
<span class="k">if</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">tensor2</span> <span class="o">=</span> <span class="n">tensor2</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="n">tensor2_exp_size</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Size</span><span class="p">((</span><span class="mi">1</span><span class="p">,)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="mi">3</span> <span class="o">-</span> <span class="n">tensor2</span><span class="o">.</span><span class="n">dim</span><span class="p">(),</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">tensor2</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
<span class="c1"># expand the batch portion (i.e. cut off matrix dimensions and expand rest)</span>
<span class="n">expand_batch_portion</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">_C</span><span class="o">.</span><span class="n">_infer_size</span><span class="p">(</span><span class="n">tensor1_exp_size</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="n">tensor2_exp_size</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span>
<span class="c1"># flatten expanded batches</span>
<span class="n">tensor1_expanded</span> <span class="o">=</span> <span class="n">tensor1</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">expand_batch_portion</span> <span class="o">+</span> <span class="n">tensor1_exp_size</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:]))</span> \
<span class="o">.</span><span class="n">contiguous</span><span class="p">()</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">reduce</span><span class="p">(</span><span class="n">mul</span><span class="p">,</span> <span class="n">expand_batch_portion</span><span class="p">),</span> <span class="o">*</span><span class="n">tensor1_exp_size</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:])</span>
<span class="n">tensor2_expanded</span> <span class="o">=</span> <span class="n">tensor2</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">expand_batch_portion</span> <span class="o">+</span> <span class="n">tensor2_exp_size</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:]))</span> \
<span class="o">.</span><span class="n">contiguous</span><span class="p">()</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">reduce</span><span class="p">(</span><span class="n">mul</span><span class="p">,</span> <span class="n">expand_batch_portion</span><span class="p">),</span> <span class="o">*</span><span class="n">tensor2_exp_size</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:])</span>
<span class="c1"># reshape batches back into result</span>
<span class="n">total_expansion</span> <span class="o">=</span> <span class="n">expand_batch_portion</span> <span class="o">+</span> <span class="p">(</span><span class="n">tensor1_exp_size</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="n">tensor2_exp_size</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="k">def</span> <span class="nf">maybeSqueeze</span><span class="p">(</span><span class="n">tensor</span><span class="p">):</span>
<span class="k">if</span> <span class="n">dim_tensor1</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">tensor</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">dim_tensor2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">tensor</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">tensor</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="ow">not</span> <span class="n">out</span><span class="o">.</span><span class="n">is_contiguous</span><span class="p">():</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">bmm</span><span class="p">(</span><span class="n">tensor1_expanded</span><span class="p">,</span> <span class="n">tensor2_expanded</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">bmm</span><span class="p">(</span><span class="n">tensor1_expanded</span><span class="p">,</span> <span class="n">tensor2_expanded</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">out</span><span class="p">)</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">maybeSqueeze</span><span class="p">(</span><span class="n">output</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">total_expansion</span><span class="p">))</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">out</span><span class="o">.</span><span class="n">set_</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
<span class="k">return</span> <span class="n">out</span>
<span class="k">return</span> <span class="n">output</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"both arguments to __matmul__ need to be at least 1D, "</span>
<span class="s2">"but they are </span><span class="si">{}</span><span class="s2">D and </span><span class="si">{}</span><span class="s2">D"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">dim_tensor1</span><span class="p">,</span> <span class="n">dim_tensor2</span><span class="p">))</span></div>
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