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<!DOCTYPE html>
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<li class="toctree-l1"><a class="reference internal" href="notes/autograd.html">Autograd mechanics</a><ul>
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<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#softmax2d"><span class="hidden-section">Softmax2d</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>
<li class="toctree-l3"><a class="reference internal" href="nn.html#bilinear"><span class="hidden-section">Bilinear</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#id14"><span class="hidden-section">conv1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id15"><span class="hidden-section">conv2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id16"><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-max-pool3d"><span class="hidden-section">adaptive_max_pool3d</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>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptive-avg-pool3d"><span class="hidden-section">adaptive_avg_pool3d</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#id17"><span class="hidden-section">threshold</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id18"><span class="hidden-section">relu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id19"><span class="hidden-section">hardtanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id20"><span class="hidden-section">relu6</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id21"><span class="hidden-section">elu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id22"><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#id23"><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#glu"><span class="hidden-section">glu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id24"><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#id25"><span class="hidden-section">tanhshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id26"><span class="hidden-section">softsign</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id27"><span class="hidden-section">softplus</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id28"><span class="hidden-section">softmin</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id29"><span class="hidden-section">softmax</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id30"><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#id31"><span class="hidden-section">tanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id32"><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#id33"><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#id34"><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#id35"><span class="hidden-section">dropout2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id36"><span class="hidden-section">dropout3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#id37">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#id38">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#id40"><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>
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<div class="section" id="torch-sparse">
<h1>torch.sparse<a class="headerlink" href="#torch-sparse" title="Permalink to this headline">¶</a></h1>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">This API is currently experimental and may change in the near future.</p>
</div>
<p>Torch supports sparse tensors in COO(rdinate) format, which can
efficiently store and process tensors for which the majority of elements
are zeros.</p>
<p>A sparse tensor is represented as a pair of dense tensors: a tensor
of values and a 2D tensor of indices. A sparse tensor can be constructed
by providing these two tensors, as well as the size of the sparse tensor
(which cannot be inferred from these tensors!) Suppose we want to define
a sparse tensor with the entry 3 at location (0, 2), entry 4 at
location (1, 0), and entry 5 at location (1, 2). We would then write:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">i</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">LongTensor</span><span class="p">([[</span><span class="mi">0</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"> [2, 0, 2]])</span>
<span class="gp">>>> </span><span class="n">v</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">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">sparse</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">v</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]))</span><span class="o">.</span><span class="n">to_dense</span><span class="p">()</span>
<span class="go"> 0 0 3</span>
<span class="go"> 4 0 5</span>
<span class="go">[torch.FloatTensor of size 2x3]</span>
</pre></div>
</div>
<p>Note that the input to LongTensor is NOT a list of index tuples. If you want
to write your indices this way, you should transpose before passing them to
the sparse constructor:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">i</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">LongTensor</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">v</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">4</span><span class="p">,</span> <span class="mi">5</span> <span class="p">])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">sparse</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">t</span><span class="p">(),</span> <span class="n">v</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]))</span><span class="o">.</span><span class="n">to_dense</span><span class="p">()</span>
<span class="go"> 0 0 3</span>
<span class="go"> 4 0 5</span>
<span class="go">[torch.FloatTensor of size 2x3]</span>
</pre></div>
</div>
<p>You can also construct hybrid sparse tensors, where only the first n
dimensions are sparse, and the rest of the dimensions are dense.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">i</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">LongTensor</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="gp">>>> </span><span class="n">v</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="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">sparse</span><span class="o">.</span><span class="n">FloatTensor</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span><span class="o">.</span><span class="n">to_dense</span><span class="p">()</span>
<span class="go"> 0 0</span>
<span class="go"> 0 0</span>
<span class="go"> 1 3</span>
<span class="go"> 0 0</span>
<span class="go"> 5 7</span>
<span class="go">[torch.FloatTensor of size 5x2]</span>
</pre></div>
</div>
<p>An empty sparse tensor can be constructed by specifying its size:</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">sparse</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">3</span><span class="p">)</span>
<span class="go">SparseFloatTensor of size 2x3 with indices:</span>
<span class="go">[torch.LongTensor with no dimension]</span>
<span class="go">and values:</span>
<span class="go">[torch.FloatTensor with no dimension]</span>
</pre></div>
</div>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p>Our sparse tensor format permits <em>uncoalesced</em> sparse tensors, where
there may be duplicate coordinates in the indices; in this case,
the interpretation is that the value at that index is the sum of all
duplicate value entries. Uncoalesced tensors permit us to implement
certain operators more efficiently.</p>
<p>For the most part, you shouldn’t have to care whether or not a
sparse tensor is coalesced or not, as most operations will work
identically given a coalesced or uncoalesced sparse tensor.
However, there are two cases in which you may need to care.</p>
<p>First, if you repeatedly perform an operation that can produce
duplicate entries (e.g., <a class="reference internal" href="#torch.sparse.FloatTensor.add" title="torch.sparse.FloatTensor.add"><code class="xref py py-func docutils literal"><span class="pre">torch.sparse.FloatTensor.add()</span></code></a>), you
should occasionally coalesce your sparse tensors to prevent
them from growing too large.</p>
<p>Second, some operators will produce different values depending on
whether or not they are coalesced or not (e.g.,
<a class="reference internal" href="#torch.sparse.FloatTensor._values" title="torch.sparse.FloatTensor._values"><code class="xref py py-func docutils literal"><span class="pre">torch.sparse.FloatTensor._values()</span></code></a> and
<a class="reference internal" href="#torch.sparse.FloatTensor._indices" title="torch.sparse.FloatTensor._indices"><code class="xref py py-func docutils literal"><span class="pre">torch.sparse.FloatTensor._indices()</span></code></a>, as well as
<code class="xref py py-func docutils literal"><span class="pre">torch.Tensor._sparse_mask()</span></code>). These operators are
prefixed by an underscore to indicate that they reveal internal
implementation details and should be used with care, since code
that works with coalesced sparse tensors may not work with
uncoalesced sparse tensors; generally speaking, it is safest
to explicitly coalesce before working with these operators.</p>
<p class="last">For example, suppose that we wanted to implement an operator
by operating directly on <a class="reference internal" href="#torch.sparse.FloatTensor._values" title="torch.sparse.FloatTensor._values"><code class="xref py py-func docutils literal"><span class="pre">torch.sparse.FloatTensor._values()</span></code></a>.
Multiplication by a scalar can be implemented in the obvious way,
as multiplication distributes over addition; however, square root
cannot be implemented directly, since <code class="docutils literal"><span class="pre">sqrt(a</span> <span class="pre">+</span> <span class="pre">b)</span> <span class="pre">!=</span> <span class="pre">sqrt(a)</span> <span class="pre">+</span>
<span class="pre">sqrt(b)</span></code> (which is what would be computed if you were given an
uncoalesced tensor.)</p>
</div>
<dl class="class">
<dt id="torch.sparse.FloatTensor">
<em class="property">class </em><code class="descclassname">torch.sparse.</code><code class="descname">FloatTensor</code><a class="reference internal" href="_modules/torch/sparse.html#FloatTensor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.sparse.FloatTensor" title="Permalink to this definition">¶</a></dt>
<dd><dl class="method">
<dt id="torch.sparse.FloatTensor.add">
<code class="descname">add</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.add" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.add_">
<code class="descname">add_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.add_" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.clone">
<code class="descname">clone</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.clone" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.dim">
<code class="descname">dim</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.dim" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.div">
<code class="descname">div</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.div" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.div_">
<code class="descname">div_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.div_" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.get_device">
<code class="descname">get_device</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.get_device" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.hspmm">
<code class="descname">hspmm</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.hspmm" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.mm">
<code class="descname">mm</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.mm" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.mul">
<code class="descname">mul</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.mul" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.mul_">
<code class="descname">mul_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.mul_" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.resizeAs_">
<code class="descname">resizeAs_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.resizeAs_" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.size">
<code class="descname">size</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.size" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.spadd">
<code class="descname">spadd</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.spadd" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.spmm">
<code class="descname">spmm</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.spmm" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.sspaddmm">
<code class="descname">sspaddmm</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.sspaddmm" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.sspmm">
<code class="descname">sspmm</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.sspmm" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.sub">
<code class="descname">sub</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.sub" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.sub_">
<code class="descname">sub_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.sub_" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.t_">
<code class="descname">t_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.t_" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.toDense">
<code class="descname">toDense</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.toDense" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.transpose">
<code class="descname">transpose</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.transpose" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.transpose_">
<code class="descname">transpose_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.transpose_" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.zero_">
<code class="descname">zero_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.zero_" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.coalesce">
<code class="descname">coalesce</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.coalesce" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor.is_coalesced">
<code class="descname">is_coalesced</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor.is_coalesced" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor._indices">
<code class="descname">_indices</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor._indices" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor._values">
<code class="descname">_values</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor._values" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="torch.sparse.FloatTensor._nnz">
<code class="descname">_nnz</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.sparse.FloatTensor._nnz" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
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