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| <span class="mdl-layout-title toc">Table Of Contents</span> |
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| <li class="toctree-l1"><a class="reference internal" href="../../../../tutorials/index.html">Python Tutorials</a><ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/index.html">Crash Course</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/0-introduction.html">Introduction</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/1-nparray.html">Step 1: Manipulate data with NP on MXNet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/2-create-nn.html">Step 2: Create a neural network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/3-autograd.html">Step 3: Automatic differentiation with autograd</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/4-components.html">Step 4: Necessary components that are not in the network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/5-datasets.html">Step 5: <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/5-datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/5-datasets.html#Using-your-own-data-with-custom-Datasets">Using your own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/5-datasets.html#New-in-MXNet-2.0:-faster-C++-backend-dataloaders">New in MXNet 2.0: faster C++ backend dataloaders</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/6-train-nn.html">Step 6: Train a Neural Network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/7-use-gpus.html">Step 7: Load and Run a NN using GPU</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/gluon_migration_guide.html">Gluon2.0: Migration Guide</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/logistic_regression_explained.html">Logistic regression explained</a></li> |
| <li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li> |
| </ul> |
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| <li class="toctree-l2"><a class="reference internal" href="../../../../tutorials/packages/index.html">Packages</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/packages/autograd/index.html">Automatic Differentiation</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/index.html">Blocks</a><ul> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/image/index.html">Image Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/loss/index.html">Losses</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/loss/custom-loss.html">Custom Loss Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/loss/loss.html">Loss functions</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/text/index.html">Text Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/index.html">Training</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/trainer.html">Trainer</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul> |
| <li class="toctree-l6"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/normalization/index.html">Normalization Blocks</a></li> |
| </ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/packages/kvstore/index.html">KVStore</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li> |
| </ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/packages/legacy/index.html">Legacy</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/index.html">NDArray</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li> |
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| <li class="toctree-l6"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/packages/np/index.html">What is NP on MXNet</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/np/cheat-sheet.html">The NP on MXNet cheat sheet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/np/np-vs-numpy.html">Differences between NP on MXNet and NumPy</a></li> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/packages/onnx/index.html">ONNX</a><ul> |
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| <li class="toctree-l1"><a class="reference internal" href="../../../../tutorials/index.html">Python Tutorials</a><ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/index.html">Crash Course</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/0-introduction.html">Introduction</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/1-nparray.html">Step 1: Manipulate data with NP on MXNet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/2-create-nn.html">Step 2: Create a neural network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/3-autograd.html">Step 3: Automatic differentiation with autograd</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/4-components.html">Step 4: Necessary components that are not in the network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/5-datasets.html">Step 5: <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/5-datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/5-datasets.html#Using-your-own-data-with-custom-Datasets">Using your own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/5-datasets.html#New-in-MXNet-2.0:-faster-C++-backend-dataloaders">New in MXNet 2.0: faster C++ backend dataloaders</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/6-train-nn.html">Step 6: Train a Neural Network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/crash-course/7-use-gpus.html">Step 7: Load and Run a NN using GPU</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/getting-started/to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/gluon_migration_guide.html">Gluon2.0: Migration Guide</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/getting-started/logistic_regression_explained.html">Logistic regression explained</a></li> |
| <li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li> |
| </ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/packages/autograd/index.html">Automatic Differentiation</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/index.html">Blocks</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/custom-layer.html">Custom Layers</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/hybridize.html">Hybridize</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/init.html">Initialization</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/nn.html">Layers and Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/parameters.html">Parameter Management</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/index.html">Data Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/data_augmentation.html">Image Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/image/index.html">Image Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/loss/index.html">Losses</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/loss/custom-loss.html">Custom Loss Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/loss/loss.html">Loss functions</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/text/index.html">Text Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/index.html">Training</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/trainer.html">Trainer</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul> |
| <li class="toctree-l6"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/gluon/training/normalization/index.html">Normalization Blocks</a></li> |
| </ul> |
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| </ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/packages/kvstore/index.html">KVStore</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li> |
| </ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../tutorials/packages/legacy/index.html">Legacy</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/index.html">NDArray</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../tutorials/packages/legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li> |
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| <div class="section" id="module-mxnet.ndarray.linalg"> |
| <span id="ndarray-linalg"></span><h1>ndarray.linalg<a class="headerlink" href="#module-mxnet.ndarray.linalg" title="Permalink to this headline">¶</a></h1> |
| <p>Linear Algebra NDArray API of MXNet.</p> |
| <p><strong>Functions</strong></p> |
| <table class="longtable docutils align-default"> |
| <colgroup> |
| <col style="width: 10%" /> |
| <col style="width: 90%" /> |
| </colgroup> |
| <tbody> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.det" title="mxnet.ndarray.linalg.det"><code class="xref py py-obj docutils literal notranslate"><span class="pre">det</span></code></a>([A, out, name])</p></td> |
| <td><p>Compute the determinant of a matrix.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.extractdiag" title="mxnet.ndarray.linalg.extractdiag"><code class="xref py py-obj docutils literal notranslate"><span class="pre">extractdiag</span></code></a>([A, offset, out, name])</p></td> |
| <td><p>Extracts the diagonal entries of a square matrix.</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.extracttrian" title="mxnet.ndarray.linalg.extracttrian"><code class="xref py py-obj docutils literal notranslate"><span class="pre">extracttrian</span></code></a>([A, offset, lower, out, name])</p></td> |
| <td><p>Extracts a triangular sub-matrix from a square matrix.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.gelqf" title="mxnet.ndarray.linalg.gelqf"><code class="xref py py-obj docutils literal notranslate"><span class="pre">gelqf</span></code></a>([A, out, name])</p></td> |
| <td><p>LQ factorization for general matrix.</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.gemm" title="mxnet.ndarray.linalg.gemm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">gemm</span></code></a>([A, B, C, transpose_a, transpose_b, …])</p></td> |
| <td><p>Performs general matrix multiplication and accumulation.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.gemm2" title="mxnet.ndarray.linalg.gemm2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">gemm2</span></code></a>([A, B, transpose_a, transpose_b, …])</p></td> |
| <td><p>Performs general matrix multiplication.</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.inverse" title="mxnet.ndarray.linalg.inverse"><code class="xref py py-obj docutils literal notranslate"><span class="pre">inverse</span></code></a>([A, out, name])</p></td> |
| <td><p>Compute the inverse of a matrix.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.makediag" title="mxnet.ndarray.linalg.makediag"><code class="xref py py-obj docutils literal notranslate"><span class="pre">makediag</span></code></a>([A, offset, out, name])</p></td> |
| <td><p>Constructs a square matrix with the input as diagonal.</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.maketrian" title="mxnet.ndarray.linalg.maketrian"><code class="xref py py-obj docutils literal notranslate"><span class="pre">maketrian</span></code></a>([A, offset, lower, out, name])</p></td> |
| <td><p>Constructs a square matrix with the input representing a specific triangular sub-matrix.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.potrf" title="mxnet.ndarray.linalg.potrf"><code class="xref py py-obj docutils literal notranslate"><span class="pre">potrf</span></code></a>([A, out, name])</p></td> |
| <td><p>Performs Cholesky factorization of a symmetric positive-definite matrix.</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.potri" title="mxnet.ndarray.linalg.potri"><code class="xref py py-obj docutils literal notranslate"><span class="pre">potri</span></code></a>([A, out, name])</p></td> |
| <td><p>Performs matrix inversion from a Cholesky factorization.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.slogdet" title="mxnet.ndarray.linalg.slogdet"><code class="xref py py-obj docutils literal notranslate"><span class="pre">slogdet</span></code></a>([A, out, name])</p></td> |
| <td><p>Compute the sign and log of the determinant of a matrix.</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.sumlogdiag" title="mxnet.ndarray.linalg.sumlogdiag"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sumlogdiag</span></code></a>([A, out, name])</p></td> |
| <td><p>Computes the sum of the logarithms of the diagonal elements of a square matrix.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.syevd" title="mxnet.ndarray.linalg.syevd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">syevd</span></code></a>([A, out, name])</p></td> |
| <td><p>Eigendecomposition for symmetric matrix.</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.syrk" title="mxnet.ndarray.linalg.syrk"><code class="xref py py-obj docutils literal notranslate"><span class="pre">syrk</span></code></a>([A, transpose, alpha, out, name])</p></td> |
| <td><p>Multiplication of matrix with its transpose.</p></td> |
| </tr> |
| <tr class="row-even"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.trmm" title="mxnet.ndarray.linalg.trmm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">trmm</span></code></a>([A, B, transpose, rightside, lower, …])</p></td> |
| <td><p>Performs multiplication with a lower triangular matrix.</p></td> |
| </tr> |
| <tr class="row-odd"><td><p><a class="reference internal" href="#mxnet.ndarray.linalg.trsm" title="mxnet.ndarray.linalg.trsm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">trsm</span></code></a>([A, B, transpose, rightside, lower, …])</p></td> |
| <td><p>Solves matrix equation involving a lower triangular matrix.</p></td> |
| </tr> |
| </tbody> |
| </table> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.det"> |
| <code class="sig-name descname">det</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.det" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Compute the determinant of a matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> is a square matrix. We compute:</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>det(A)</em></p> |
| </div></blockquote> |
| <p>If <em>n>2</em>, <em>det</em> is performed separately on the trailing two dimensions |
| for all inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>There is no gradient backwarded when A is non-invertible (which is |
| equivalent to det(A) = 0) because zero is rarely hit upon in float |
| point computation and the Jacobi’s formula on determinant gradient |
| is not computationally efficient when A is non-invertible.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">determinant</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]]</span> |
| <span class="n">det</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.</span><span class="p">]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">determinant</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]]]</span> |
| <span class="n">det</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L1074</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of square matrix</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.extractdiag"> |
| <code class="sig-name descname">extractdiag</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">offset=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.extractdiag" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Extracts the diagonal entries of a square matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, then <em>A</em> represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor.</p> |
| <p>If <em>n>2</em>, then <em>A</em> represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an <em>n-1</em>-dimensional tensor.</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">diagonal</span> <span class="n">extraction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| |
| <span class="n">extractdiag</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]</span> |
| |
| <span class="n">extractdiag</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">2.0</span><span class="p">]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">diagonal</span> <span class="n">extraction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">5.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">7.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">]]]</span> |
| |
| <span class="n">extractdiag</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">5.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L543</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of square matrices</p></li> |
| <li><p><strong>offset</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default='0'</em>) – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.extracttrian"> |
| <code class="sig-name descname">extracttrian</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">offset=_Null</em>, <em class="sig-param">lower=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.extracttrian" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Extracts a triangular sub-matrix from a square matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, then <em>A</em> represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor.</p> |
| <p>If <em>n>2</em>, then <em>A</em> represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an <em>n-1</em>-dimensional tensor.</p> |
| <p>The <em>offset</em> and <em>lower</em> parameters determine the triangle to be extracted:</p> |
| <ul class="simple"> |
| <li><p>When <em>offset = 0</em> either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter <em>lower</em>.</p></li> |
| <li><p>When <em>offset = k > 0</em> the upper triangle with respect to the k-th diagonal above the main diagonal is extracted.</p></li> |
| <li><p>When <em>offset = k < 0</em> the lower triangle with respect to the k-th diagonal below the main diagonal is extracted.</p></li> |
| </ul> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">triagonal</span> <span class="n">extraction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| |
| <span class="n">extracttrian</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]</span> |
| <span class="n">extracttrian</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">lower</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]</span> |
| <span class="n">extracttrian</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">2.0</span><span class="p">]</span> |
| <span class="n">extracttrian</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">3.0</span><span class="p">]</span> |
| |
| <span class="n">Batch</span> <span class="n">triagonal</span> <span class="n">extraction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">5.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">7.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">]]]</span> |
| |
| <span class="n">extracttrian</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">5.0</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L661</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of square matrices</p></li> |
| <li><p><strong>offset</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default='0'</em>) – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.</p></li> |
| <li><p><strong>lower</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.gelqf"> |
| <code class="sig-name descname">gelqf</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.gelqf" title="Permalink to this definition">¶</a></dt> |
| <dd><p>LQ factorization for general matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, we compute the LQ factorization (LAPACK <em>gelqf</em>, followed by <em>orglq</em>). <em>A</em> |
| must have shape <em>(x, y)</em> with <em>x <= y</em>, and must have full rank <em>=x</em>. The LQ |
| factorization consists of <em>L</em> with shape <em>(x, x)</em> and <em>Q</em> with shape <em>(x, y)</em>, so |
| that:</p> |
| <blockquote> |
| <div><p><em>A</em> = <em>L</em> * <em>Q</em></p> |
| </div></blockquote> |
| <p>Here, <em>L</em> is lower triangular (upper triangle equal to zero) with nonzero diagonal, |
| and <em>Q</em> is row-orthonormal, meaning that</p> |
| <blockquote> |
| <div><p><em>Q</em> * <em>Q</em><sup>T</sup></p> |
| </div></blockquote> |
| <p>is equal to the identity matrix of shape <em>(x, x)</em>.</p> |
| <p>If <em>n>2</em>, <em>gelqf</em> is performed separately on the trailing two dimensions for all |
| inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">LQ</span> <span class="n">factorization</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]]</span> |
| <span class="n">Q</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="n">gelqf</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">Q</span> <span class="o">=</span> <span class="p">[[</span><span class="o">-</span><span class="mf">0.26726124</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.53452248</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.80178373</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.87287156</span><span class="p">,</span> <span class="mf">0.21821789</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.43643578</span><span class="p">]]</span> |
| <span class="n">L</span> <span class="o">=</span> <span class="p">[[</span><span class="o">-</span><span class="mf">3.74165739</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">8.55235974</span><span class="p">,</span> <span class="mf">1.96396101</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">LQ</span> <span class="n">factorization</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">7.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">],</span> <span class="p">[</span><span class="mf">10.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">]]]</span> |
| <span class="n">Q</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="n">gelqf</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">Q</span> <span class="o">=</span> <span class="p">[[[</span><span class="o">-</span><span class="mf">0.26726124</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.53452248</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.80178373</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.87287156</span><span class="p">,</span> <span class="mf">0.21821789</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.43643578</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="o">-</span><span class="mf">0.50257071</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.57436653</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.64616234</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.7620735</span><span class="p">,</span> <span class="mf">0.05862104</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.64483142</span><span class="p">]]]</span> |
| <span class="n">L</span> <span class="o">=</span> <span class="p">[[[</span><span class="o">-</span><span class="mf">3.74165739</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">8.55235974</span><span class="p">,</span> <span class="mf">1.96396101</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="o">-</span><span class="mf">13.92838828</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">19.09768702</span><span class="p">,</span> <span class="mf">0.52758934</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L867</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices to be factorized</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.gemm"> |
| <code class="sig-name descname">gemm</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">B=None</em>, <em class="sig-param">C=None</em>, <em class="sig-param">transpose_a=_Null</em>, <em class="sig-param">transpose_b=_Null</em>, <em class="sig-param">alpha=_Null</em>, <em class="sig-param">beta=_Null</em>, <em class="sig-param">axis=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.gemm" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs general matrix multiplication and accumulation. |
| Input are tensors <em>A</em>, <em>B</em>, <em>C</em>, each of dimension <em>n >= 2</em> and having the same shape |
| on the leading <em>n-2</em> dimensions.</p> |
| <p>If <em>n=2</em>, the BLAS3 function <em>gemm</em> is performed:</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>alpha</em> * <em>op</em>(<em>A</em>) * <em>op</em>(<em>B</em>) + <em>beta</em> * <em>C</em></p> |
| </div></blockquote> |
| <p>Here, <em>alpha</em> and <em>beta</em> are scalar parameters, and <em>op()</em> is either the identity or |
| matrix transposition (depending on <em>transpose_a</em>, <em>transpose_b</em>).</p> |
| <p>If <em>n>2</em>, <em>gemm</em> is performed separately for a batch of matrices. The column indices of the matrices |
| are given by the last dimensions of the tensors, the row indices by the axis specified with the <em>axis</em> |
| parameter. By default, the trailing two dimensions will be used for matrix encoding.</p> |
| <p>For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes |
| calls. For example let <em>A</em>, <em>B</em>, <em>C</em> be 5 dimensional tensors. Then gemm(<em>A</em>, <em>B</em>, <em>C</em>, axis=1) is equivalent |
| to the following without the overhead of the additional swapaxis operations:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A1</span> <span class="o">=</span> <span class="n">swapaxes</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">dim1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span> |
| <span class="n">B1</span> <span class="o">=</span> <span class="n">swapaxes</span><span class="p">(</span><span class="n">B</span><span class="p">,</span> <span class="n">dim1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="n">swapaxes</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="n">dim1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="n">gemm</span><span class="p">(</span><span class="n">A1</span><span class="p">,</span> <span class="n">B1</span><span class="p">,</span> <span class="n">C</span><span class="p">)</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="n">swapaxis</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="n">dim1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE |
| and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use |
| pseudo-float16 precision (float32 math with float16 I/O) precision in order to use |
| Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">multiply</span><span class="o">-</span><span class="n">add</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">gemm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">transpose_b</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">,</span> <span class="n">beta</span><span class="o">=</span><span class="mf">10.0</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[</span><span class="mf">14.0</span><span class="p">,</span> <span class="mf">14.0</span><span class="p">,</span> <span class="mf">14.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">14.0</span><span class="p">,</span> <span class="mf">14.0</span><span class="p">,</span> <span class="mf">14.0</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">multiply</span><span class="o">-</span><span class="n">add</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">10.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.01</span><span class="p">]]]</span> |
| <span class="n">gemm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">transpose_b</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span> <span class="p">,</span> <span class="n">beta</span><span class="o">=</span><span class="mf">10.0</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[[</span><span class="mf">104.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.14</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L88</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</p></li> |
| <li><p><strong>B</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</p></li> |
| <li><p><strong>C</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</p></li> |
| <li><p><strong>transpose_a</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply with transposed of first input (A).</p></li> |
| <li><p><strong>transpose_b</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply with transposed of second input (B).</p></li> |
| <li><p><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor multiplied with A*B.</p></li> |
| <li><p><strong>beta</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor multiplied with C.</p></li> |
| <li><p><strong>axis</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default='-2'</em>) – Axis corresponding to the matrix rows.</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.gemm2"> |
| <code class="sig-name descname">gemm2</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">B=None</em>, <em class="sig-param">transpose_a=_Null</em>, <em class="sig-param">transpose_b=_Null</em>, <em class="sig-param">alpha=_Null</em>, <em class="sig-param">axis=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.gemm2" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs general matrix multiplication. |
| Input are tensors <em>A</em>, <em>B</em>, each of dimension <em>n >= 2</em> and having the same shape |
| on the leading <em>n-2</em> dimensions.</p> |
| <p>If <em>n=2</em>, the BLAS3 function <em>gemm</em> is performed:</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>alpha</em> * <em>op</em>(<em>A</em>) * <em>op</em>(<em>B</em>)</p> |
| </div></blockquote> |
| <p>Here <em>alpha</em> is a scalar parameter and <em>op()</em> is either the identity or the matrix |
| transposition (depending on <em>transpose_a</em>, <em>transpose_b</em>).</p> |
| <p>If <em>n>2</em>, <em>gemm</em> is performed separately for a batch of matrices. The column indices of the matrices |
| are given by the last dimensions of the tensors, the row indices by the axis specified with the <em>axis</em> |
| parameter. By default, the trailing two dimensions will be used for matrix encoding.</p> |
| <p>For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes |
| calls. For example let <em>A</em>, <em>B</em> be 5 dimensional tensors. Then gemm(<em>A</em>, <em>B</em>, axis=1) is equivalent to |
| the following without the overhead of the additional swapaxis operations:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A1</span> <span class="o">=</span> <span class="n">swapaxes</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">dim1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span> |
| <span class="n">B1</span> <span class="o">=</span> <span class="n">swapaxes</span><span class="p">(</span><span class="n">B</span><span class="p">,</span> <span class="n">dim1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="n">gemm2</span><span class="p">(</span><span class="n">A1</span><span class="p">,</span> <span class="n">B1</span><span class="p">)</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="n">swapaxis</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="n">dim1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE |
| and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use |
| pseudo-float16 precision (float32 math with float16 I/O) precision in order to use |
| Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">gemm2</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">transpose_b</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">gemm2</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">transpose_b</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[[</span><span class="mf">4.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.04</span> <span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L170</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</p></li> |
| <li><p><strong>B</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</p></li> |
| <li><p><strong>transpose_a</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply with transposed of first input (A).</p></li> |
| <li><p><strong>transpose_b</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply with transposed of second input (B).</p></li> |
| <li><p><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor multiplied with A*B.</p></li> |
| <li><p><strong>axis</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default='-2'</em>) – Axis corresponding to the matrix row indices.</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.inverse"> |
| <code class="sig-name descname">inverse</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.inverse" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Compute the inverse of a matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> is a square matrix. We compute:</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>A</em><sup>-1</sup></p> |
| </div></blockquote> |
| <p>If <em>n>2</em>, <em>inverse</em> is performed separately on the trailing two dimensions |
| for all inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">inverse</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]]</span> |
| <span class="n">inverse</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="o">-</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.4</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.2</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">inverse</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]]]</span> |
| <span class="n">inverse</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="o">-</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.4</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.2</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="o">-</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L1009</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of square matrix</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.makediag"> |
| <code class="sig-name descname">makediag</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">offset=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.makediag" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Constructs a square matrix with the input as diagonal. |
| Input is a tensor <em>A</em> of dimension <em>n >= 1</em>.</p> |
| <p>If <em>n=1</em>, then <em>A</em> represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor. |
| If <em>n>1</em>, then <em>A</em> represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an <em>n+1</em>-dimensional tensor.</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">diagonal</span> <span class="n">matrix</span> <span class="n">construction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]</span> |
| |
| <span class="n">makediag</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]</span> |
| |
| <span class="n">makediag</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">diagonal</span> <span class="n">matrix</span> <span class="n">construction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| |
| <span class="n">makediag</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L599</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of diagonal entries</p></li> |
| <li><p><strong>offset</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default='0'</em>) – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.maketrian"> |
| <code class="sig-name descname">maketrian</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">offset=_Null</em>, <em class="sig-param">lower=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.maketrian" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Constructs a square matrix with the input representing a specific triangular sub-matrix. |
| This is basically the inverse of <em>linalg.extracttrian</em>. Input is a tensor <em>A</em> of dimension <em>n >= 1</em>.</p> |
| <p>If <em>n=1</em>, then <em>A</em> represents the entries of a triangular matrix which is lower triangular if <em>offset<0</em> or <em>offset=0</em>, <em>lower=true</em>. The resulting matrix is derived by first constructing the square |
| matrix with the entries outside the triangle set to zero and then adding <em>offset</em>-times an additional |
| diagonal with zero entries to the square matrix.</p> |
| <p>If <em>n>1</em>, then <em>A</em> represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an <em>n+1</em>-dimensional tensor.</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">construction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]</span> |
| |
| <span class="n">maketrian</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]]</span> |
| |
| <span class="n">maketrian</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">lower</span><span class="o">=</span><span class="n">false</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]]</span> |
| |
| <span class="n">maketrian</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]]</span> |
| <span class="n">maketrian</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">offset</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">construction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">]]</span> |
| |
| <span class="n">maketrian</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">5.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">]]]</span> |
| |
| <span class="n">maketrian</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L734</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of triangular matrices stored as vectors</p></li> |
| <li><p><strong>offset</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default='0'</em>) – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.</p></li> |
| <li><p><strong>lower</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.potrf"> |
| <code class="sig-name descname">potrf</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.potrf" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs Cholesky factorization of a symmetric positive-definite matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, the Cholesky factor <em>B</em> of the symmetric, positive definite matrix <em>A</em> is |
| computed. <em>B</em> is triangular (entries of upper or lower triangle are all zero), has |
| positive diagonal entries, and:</p> |
| <blockquote> |
| <div><p><em>A</em> = <em>B</em> * <em>B</em><sup>T</sup> if <em>lower</em> = <em>true</em> |
| <em>A</em> = <em>B</em><sup>T</sup> * <em>B</em> if <em>lower</em> = <em>false</em></p> |
| </div></blockquote> |
| <p>If <em>n>2</em>, <em>potrf</em> is performed separately on the trailing two dimensions for all inputs |
| (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">factorization</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.25</span><span class="p">]]</span> |
| <span class="n">potrf</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">factorization</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.25</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">16.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">17.0</span><span class="p">]]]</span> |
| <span class="n">potrf</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L227</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices to be decomposed</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.potri"> |
| <code class="sig-name descname">potri</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.potri" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs matrix inversion from a Cholesky factorization. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> is a triangular matrix (entries of upper or lower triangle are all zero) |
| with positive diagonal. We compute:</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>A</em><sup>-T</sup> * <em>A</em><sup>-1</sup> if <em>lower</em> = <em>true</em> |
| <em>out</em> = <em>A</em><sup>-1</sup> * <em>A</em><sup>-T</sup> if <em>lower</em> = <em>false</em></p> |
| </div></blockquote> |
| <p>In other words, if <em>A</em> is the Cholesky factor of a symmetric positive definite matrix |
| <em>B</em> (obtained by <em>potrf</em>), then</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>B</em><sup>-1</sup></p> |
| </div></blockquote> |
| <p>If <em>n>2</em>, <em>potri</em> is performed separately on the trailing two dimensions for all inputs |
| (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>Use this operator only if you are certain you need the inverse of <em>B</em>, and |
| cannot use the Cholesky factor <em>A</em> (<em>potrf</em>), together with backsubstitution |
| (<em>trsm</em>). The latter is numerically much safer, and also cheaper.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">inverse</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]</span> |
| <span class="n">potri</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.26563</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.0625</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.0625</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">inverse</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]]</span> |
| <span class="n">potri</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">0.26563</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.0625</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.0625</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">0.06641</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.01562</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.01562</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span><span class="mi">0625</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L295</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of lower triangular matrices</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.slogdet"> |
| <code class="sig-name descname">slogdet</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.slogdet" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Compute the sign and log of the determinant of a matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> is a square matrix. We compute:</p> |
| <blockquote> |
| <div><p><em>sign</em> = <em>sign(det(A))</em> |
| <em>logabsdet</em> = <em>log(abs(det(A)))</em></p> |
| </div></blockquote> |
| <p>If <em>n>2</em>, <em>slogdet</em> is performed separately on the trailing two dimensions |
| for all inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The gradient is not properly defined on sign, so the gradient of |
| it is not backwarded.</p> |
| </div> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>No gradient is backwarded when A is non-invertible. Please see |
| the docs of operator det for detail.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">signed</span> <span class="n">log</span> <span class="n">determinant</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]]</span> |
| <span class="n">sign</span><span class="p">,</span> <span class="n">logabsdet</span> <span class="o">=</span> <span class="n">slogdet</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">sign</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.</span><span class="p">]</span> |
| <span class="n">logabsdet</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.609438</span><span class="p">]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">signed</span> <span class="n">log</span> <span class="n">determinant</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]]]</span> |
| <span class="n">sign</span><span class="p">,</span> <span class="n">logabsdet</span> <span class="o">=</span> <span class="n">slogdet</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">sign</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">]</span> |
| <span class="n">logabsdet</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.609438</span><span class="p">,</span> <span class="o">-</span><span class="n">inf</span><span class="p">,</span> <span class="mf">1.609438</span><span class="p">]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L1139</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of square matrix</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.sumlogdiag"> |
| <code class="sig-name descname">sumlogdiag</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.sumlogdiag" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Computes the sum of the logarithms of the diagonal elements of a square matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> must be square with positive diagonal entries. We sum the natural |
| logarithms of the diagonal elements, the result has shape (1,).</p> |
| <p>If <em>n>2</em>, <em>sumlogdiag</em> is performed separately on the trailing two dimensions for all |
| inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">reduction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">]]</span> |
| <span class="n">sumlogdiag</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.9459</span><span class="p">]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">reduction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">17.0</span><span class="p">]]]</span> |
| <span class="n">sumlogdiag</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.9459</span><span class="p">,</span> <span class="mf">3.9318</span><span class="p">]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L487</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of square matrices</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.syevd"> |
| <code class="sig-name descname">syevd</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.syevd" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Eigendecomposition for symmetric matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> must be symmetric, of shape <em>(x, x)</em>. We compute the eigendecomposition, |
| resulting in the orthonormal matrix <em>U</em> of eigenvectors, shape <em>(x, x)</em>, and the |
| vector <em>L</em> of eigenvalues, shape <em>(x,)</em>, so that:</p> |
| <blockquote> |
| <div><p><em>U</em> * <em>A</em> = <em>diag(L)</em> * <em>U</em></p> |
| </div></blockquote> |
| <p>Here:</p> |
| <blockquote> |
| <div><p><em>U</em> * <em>U</em><sup>T</sup> = <em>U</em><sup>T</sup> * <em>U</em> = <em>I</em></p> |
| </div></blockquote> |
| <p>where <em>I</em> is the identity matrix. Also, <em>L(0) <= L(1) <= L(2) <= …</em> (ascending order).</p> |
| <p>If <em>n>2</em>, <em>syevd</em> is performed separately on the trailing two dimensions of <em>A</em> (batch |
| mode). In this case, <em>U</em> has <em>n</em> dimensions like <em>A</em>, and <em>L</em> has <em>n-1</em> dimensions.</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>Derivatives for this operator are defined only if <em>A</em> is such that all its |
| eigenvalues are distinct, and the eigengaps are not too small. If you need |
| gradients, do not apply this operator to matrices with multiple eigenvalues.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">symmetric</span> <span class="n">eigendecomposition</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]]</span> |
| <span class="n">U</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="n">syevd</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">U</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.89442719</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.4472136</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.4472136</span><span class="p">,</span> <span class="mf">0.89442719</span><span class="p">]]</span> |
| <span class="n">L</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">]</span> |
| |
| <span class="n">Batch</span> <span class="n">symmetric</span> <span class="n">eigendecomposition</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">]]]</span> |
| <span class="n">U</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="n">syevd</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">U</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">0.89442719</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.4472136</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.4472136</span><span class="p">,</span> <span class="mf">0.89442719</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">0.92387953</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.38268343</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.38268343</span><span class="p">,</span> <span class="mf">0.92387953</span><span class="p">]]]</span> |
| <span class="n">L</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.17157288</span><span class="p">,</span> <span class="mf">5.82842712</span><span class="p">]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L947</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices to be factorized</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.syrk"> |
| <code class="sig-name descname">syrk</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">transpose=_Null</em>, <em class="sig-param">alpha=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.syrk" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Multiplication of matrix with its transpose. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, the operator performs the BLAS3 function <em>syrk</em>:</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>alpha</em> * <em>A</em> * <em>A</em><sup>T</sup></p> |
| </div></blockquote> |
| <p>if <em>transpose=False</em>, or</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>alpha</em> * <em>A</em><sup>T</sup> * <em>A</em></p> |
| </div></blockquote> |
| <p>if <em>transpose=True</em>.</p> |
| <p>If <em>n>2</em>, <em>syrk</em> is performed separately on the trailing two dimensions for all |
| inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]]</span> |
| <span class="n">syrk</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">transpose</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[</span><span class="mf">14.</span><span class="p">,</span> <span class="mf">32.</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">32.</span><span class="p">,</span> <span class="mf">77.</span><span class="p">]]</span> |
| <span class="n">syrk</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">transpose</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[</span><span class="mf">17.</span><span class="p">,</span> <span class="mf">22.</span><span class="p">,</span> <span class="mf">27.</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">22.</span><span class="p">,</span> <span class="mf">29.</span><span class="p">,</span> <span class="mf">36.</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">27.</span><span class="p">,</span> <span class="mf">36.</span><span class="p">,</span> <span class="mf">45.</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">syrk</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.</span><span class="p">,</span> <span class="n">transpose</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">4.</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.04</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L795</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</p></li> |
| <li><p><strong>transpose</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Use transpose of input matrix.</p></li> |
| <li><p><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor to be applied to the result.</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.trmm"> |
| <code class="sig-name descname">trmm</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">B=None</em>, <em class="sig-param">transpose=_Null</em>, <em class="sig-param">rightside=_Null</em>, <em class="sig-param">lower=_Null</em>, <em class="sig-param">alpha=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.trmm" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs multiplication with a lower triangular matrix. |
| Input are tensors <em>A</em>, <em>B</em>, each of dimension <em>n >= 2</em> and having the same shape |
| on the leading <em>n-2</em> dimensions.</p> |
| <p>If <em>n=2</em>, <em>A</em> must be triangular. The operator performs the BLAS3 function |
| <em>trmm</em>:</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>alpha</em> * <em>op</em>(<em>A</em>) * <em>B</em></p> |
| </div></blockquote> |
| <p>if <em>rightside=False</em>, or</p> |
| <blockquote> |
| <div><p><em>out</em> = <em>alpha</em> * <em>B</em> * <em>op</em>(<em>A</em>)</p> |
| </div></blockquote> |
| <p>if <em>rightside=True</em>. Here, <em>alpha</em> is a scalar parameter, and <em>op()</em> is either the |
| identity or the matrix transposition (depending on <em>transpose</em>).</p> |
| <p>If <em>n>2</em>, <em>trmm</em> is performed separately on the trailing two dimensions for all inputs |
| (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">triangular</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">trmm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">triangular</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">]]]</span> |
| <span class="n">trmm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L359</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of lower triangular matrices</p></li> |
| <li><p><strong>B</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of matrices</p></li> |
| <li><p><strong>transpose</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Use transposed of the triangular matrix</p></li> |
| <li><p><strong>rightside</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply triangular matrix from the right to non-triangular one.</p></li> |
| <li><p><strong>lower</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – True if the triangular matrix is lower triangular, false if it is upper triangular.</p></li> |
| <li><p><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor to be applied to the result.</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.trsm"> |
| <code class="sig-name descname">trsm</code><span class="sig-paren">(</span><em class="sig-param">A=None</em>, <em class="sig-param">B=None</em>, <em class="sig-param">transpose=_Null</em>, <em class="sig-param">rightside=_Null</em>, <em class="sig-param">lower=_Null</em>, <em class="sig-param">alpha=_Null</em>, <em class="sig-param">out=None</em>, <em class="sig-param">name=None</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.trsm" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Solves matrix equation involving a lower triangular matrix. |
| Input are tensors <em>A</em>, <em>B</em>, each of dimension <em>n >= 2</em> and having the same shape |
| on the leading <em>n-2</em> dimensions.</p> |
| <p>If <em>n=2</em>, <em>A</em> must be triangular. The operator performs the BLAS3 function |
| <em>trsm</em>, solving for <em>out</em> in:</p> |
| <blockquote> |
| <div><p><em>op</em>(<em>A</em>) * <em>out</em> = <em>alpha</em> * <em>B</em></p> |
| </div></blockquote> |
| <p>if <em>rightside=False</em>, or</p> |
| <blockquote> |
| <div><p><em>out</em> * <em>op</em>(<em>A</em>) = <em>alpha</em> * <em>B</em></p> |
| </div></blockquote> |
| <p>if <em>rightside=True</em>. Here, <em>alpha</em> is a scalar parameter, and <em>op()</em> is either the |
| identity or the matrix transposition (depending on <em>transpose</em>).</p> |
| <p>If <em>n>2</em>, <em>trsm</em> is performed separately on the trailing two dimensions for all inputs |
| (batch mode).</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Single</span> <span class="n">matrix</span> <span class="n">solve</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| <span class="n">trsm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| |
| <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">solve</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">8.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">]]]</span> |
| <span class="n">trsm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in /work/mxnet/src/operator/tensor/la_op.cc:L430</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>A</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of lower triangular matrices</p></li> |
| <li><p><strong>B</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of matrices</p></li> |
| <li><p><strong>transpose</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Use transposed of the triangular matrix</p></li> |
| <li><p><strong>rightside</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply triangular matrix from the right to non-triangular one.</p></li> |
| <li><p><strong>lower</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – True if the triangular matrix is lower triangular, false if it is upper triangular.</p></li> |
| <li><p><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor to be applied to the result.</p></li> |
| <li><p><strong>out</strong> (<a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><strong>out</strong> – The output of this function.</p> |
| </dd> |
| <dt class="field-odd">Return type</dt> |
| <dd class="field-odd"><p><a class="reference internal" href="../ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| </div> |
| |
| |
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