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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> |
| <li class="toctree-l2"><a class="reference internal" href="../../tutorials/getting-started/index.html">Getting Started</a><ul> |
| <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> |
| </li> |
| <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> |
| <li class="toctree-l3"><a class="reference internal" href="../../tutorials/packages/gluon/index.html">Gluon</a><ul> |
| <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> |
| </ul> |
| </li> |
| <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> |
| </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> |
| </li> |
| <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> |
| </li> |
| <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> |
| </li> |
| </ul> |
| </li> |
| <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> |
| </li> |
| <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> |
| <li class="toctree-l5"><a class="reference internal" href="../../tutorials/packages/legacy/ndarray/sparse/index.html">Tutorials</a><ul> |
| <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> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| <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> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../tutorials/packages/onnx/index.html">ONNX</a><ul> |
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| <span class="mdl-layout-title toc">Table Of Contents</span> |
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| |
| |
| <nav class="mdl-navigation"> |
| <ul class="current"> |
| <li class="toctree-l1"><a class="reference internal" href="../../tutorials/index.html">Python Tutorials</a><ul> |
| <li class="toctree-l2"><a class="reference internal" href="../../tutorials/getting-started/index.html">Getting Started</a><ul> |
| <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> |
| </li> |
| <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> |
| <li class="toctree-l3"><a class="reference internal" href="../../tutorials/packages/gluon/index.html">Gluon</a><ul> |
| <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> |
| </ul> |
| </li> |
| <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> |
| </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> |
| </li> |
| <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> |
| </li> |
| <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> |
| </li> |
| </ul> |
| </li> |
| <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> |
| </li> |
| <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> |
| <li class="toctree-l5"><a class="reference internal" href="../../tutorials/packages/legacy/ndarray/sparse/index.html">Tutorials</a><ul> |
| <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> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| <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> |
| </ul> |
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| |
| <div class="section" id="indexing"> |
| <span id="arrays-indexing"></span><h1>Indexing<a class="headerlink" href="#indexing" title="Permalink to this headline">¶</a></h1> |
| <p id="index-0"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarrays</span></code> can be indexed using the standard Python |
| <code class="docutils literal notranslate"><span class="pre">x[obj]</span></code> syntax, where <em>x</em> is the array and <em>obj</em> the selection. |
| There are three kinds of indexing available: basic |
| slicing, advanced indexing, and boolean mask indexing. Which one occurs depends on <em>obj</em>.</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>In Python, <code class="docutils literal notranslate"><span class="pre">x[(exp1,</span> <span class="pre">exp2,</span> <span class="pre">...,</span> <span class="pre">expN)]</span></code> is equivalent to |
| <code class="docutils literal notranslate"><span class="pre">x[exp1,</span> <span class="pre">exp2,</span> <span class="pre">...,</span> <span class="pre">expN]</span></code>; the latter is just syntactic sugar |
| for the former.</p> |
| </div> |
| <div class="section" id="basic-slicing-and-indexing"> |
| <h2>Basic Slicing and Indexing<a class="headerlink" href="#basic-slicing-and-indexing" title="Permalink to this headline">¶</a></h2> |
| <p>Basic slicing extends Python’s basic concept of slicing to N |
| dimensions. Basic slicing occurs when <em>obj</em> is a <code class="xref py py-class docutils literal notranslate"><span class="pre">slice</span></code> object |
| (constructed by <code class="docutils literal notranslate"><span class="pre">start:stop:step</span></code> notation inside of brackets), an |
| integer, or a tuple of slice objects and integers. <code class="xref py py-const docutils literal notranslate"><span class="pre">Ellipsis</span></code> |
| and <code class="xref py py-const docutils literal notranslate"><span class="pre">newaxis</span></code> objects can be interspersed with these as |
| well.</p> |
| <p>The simplest case of indexing with <em>N</em> integers returns an array |
| scalar representing the corresponding item. As in |
| Python, all indices are zero-based: for the <em>i</em>-th index <span class="math notranslate nohighlight">\(n_i\)</span>, |
| the valid range is <span class="math notranslate nohighlight">\(0 \le n_i < d_i\)</span> where <span class="math notranslate nohighlight">\(d_i\)</span> is the |
| <em>i</em>-th element of the shape of the array. Negative indices are |
| interpreted as counting from the end of the array (<em>i.e.</em>, if |
| <span class="math notranslate nohighlight">\(n_i < 0\)</span>, it means <span class="math notranslate nohighlight">\(n_i + d_i\)</span>).</p> |
| <p>All arrays generated by basic slicing are always views |
| of the original array if the fetched elements are contiguous in memory.</p> |
| <p>The standard rules of sequence slicing apply to basic slicing on a |
| per-dimension basis (including using a step index). Some useful |
| concepts to remember include:</p> |
| <ul> |
| <li><p>The basic slice syntax is <code class="docutils literal notranslate"><span class="pre">i:j:k</span></code> where <em>i</em> is the starting index, |
| <em>j</em> is the stopping index, and <em>k</em> is the step (<span class="math notranslate nohighlight">\(k\neq0\)</span>). |
| This selects the <em>m</em> elements (in the corresponding dimension) with |
| index values <em>i</em>, <em>i + k</em>, …, <em>i + (m - 1) k</em> where |
| <span class="math notranslate nohighlight">\(m = q + (r\neq0)\)</span> and <em>q</em> and <em>r</em> are the quotient and remainder |
| obtained by dividing <em>j - i</em> by <em>k</em>: <em>j - i = q k + r</em>, so that |
| <em>i + (m - 1) k < j</em>.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">])</span> |
| <span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">7</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span> |
| <span class="go">array([1, 3, 5])</span> |
| </pre></div> |
| </div> |
| </div> |
| </li> |
| <li><p>Negative <em>i</em> and <em>j</em> are interpreted as <em>n + i</em> and <em>n + j</em> where |
| <em>n</em> is the number of elements in the corresponding dimension. |
| Negative <em>k</em> makes stepping go towards smaller indices.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:</span><span class="mi">10</span><span class="p">]</span> |
| <span class="go">array([8, 9])</span> |
| <span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> |
| <span class="go">array([7, 6, 5, 4])</span> |
| </pre></div> |
| </div> |
| </div> |
| </li> |
| <li><p>Assume <em>n</em> is the number of elements in the dimension being |
| sliced. Then, if <em>i</em> is not given it defaults to 0 for <em>k > 0</em> and |
| <em>n - 1</em> for <em>k < 0</em> . If <em>j</em> is not given it defaults to <em>n</em> for <em>k > 0</em> |
| and <em>-n-1</em> for <em>k < 0</em> . If <em>k</em> is not given it defaults to 1. Note that |
| <code class="docutils literal notranslate"><span class="pre">::</span></code> is the same as <code class="docutils literal notranslate"><span class="pre">:</span></code> and means select all indices along this |
| axis.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="mi">5</span><span class="p">:]</span> |
| <span class="go">array([5, 6, 7, 8, 9])</span> |
| </pre></div> |
| </div> |
| </div> |
| </li> |
| <li><p>If the number of objects in the selection tuple is less than |
| <em>N</em> , then <code class="docutils literal notranslate"><span class="pre">:</span></code> is assumed for any subsequent dimensions.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[[</span><span class="mi">1</span><span class="p">],[</span><span class="mi">2</span><span class="p">],[</span><span class="mi">3</span><span class="p">]],</span> <span class="p">[[</span><span class="mi">4</span><span class="p">],[</span><span class="mi">5</span><span class="p">],[</span><span class="mi">6</span><span class="p">]]])</span> |
| <span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">shape</span> |
| <span class="go">(2, 3, 1)</span> |
| <span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span> |
| <span class="go">array([[[4],</span> |
| <span class="go"> [5],</span> |
| <span class="go"> [6]]])</span> |
| </pre></div> |
| </div> |
| </div> |
| </li> |
| <li><p><code class="xref py py-const docutils literal notranslate"><span class="pre">Ellipsis</span></code> expands to the number of <code class="docutils literal notranslate"><span class="pre">:</span></code> objects needed for the |
| selection tuple to index all dimensions. In most cases, this means that |
| length of the expanded selection tuple is <code class="docutils literal notranslate"><span class="pre">x.ndim</span></code>. There may only be a |
| single ellipsis present.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> |
| <span class="go">array([[1, 2, 3],</span> |
| <span class="go"> [4, 5, 6]])</span> |
| </pre></div> |
| </div> |
| </div> |
| </li> |
| <li><p>Each <code class="xref py py-const docutils literal notranslate"><span class="pre">newaxis</span></code> object in the selection tuple serves to expand |
| the dimensions of the resulting selection by one unit-length |
| dimension. The added dimension is the position of the <code class="xref py py-const docutils literal notranslate"><span class="pre">newaxis</span></code> |
| object in the selection tuple.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="p">[:,</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,:,:]</span><span class="o">.</span><span class="n">shape</span> |
| <span class="go">(2, 1, 3, 1)</span> |
| </pre></div> |
| </div> |
| </div> |
| </li> |
| <li><p>An integer, <em>i</em>, returns the same values as <code class="docutils literal notranslate"><span class="pre">i:i+1</span></code> |
| <strong>except</strong> the dimensionality of the returned object is reduced by |
| 1. In particular, a selection tuple with the <em>p</em>-th |
| element an integer (and all other entries <code class="docutils literal notranslate"><span class="pre">:</span></code>) returns the |
| corresponding sub-array with dimension <em>N - 1</em>. If <em>N = 1</em> |
| then the returned object is an scalar <cite>ndarray</cite> whose <cite>ndim=0</cite>.</p></li> |
| <li><p>If the selection tuple has all entries <code class="docutils literal notranslate"><span class="pre">:</span></code> except the |
| <em>p</em>-th entry which is a slice object <code class="docutils literal notranslate"><span class="pre">i:j:k</span></code>, |
| then the returned array has dimension <em>N</em> formed by |
| concatenating the sub-arrays returned by integer indexing of |
| elements <em>i</em>, <em>i+k</em>, …, <em>i + (m - 1) k < j</em>,</p></li> |
| <li><p>Basic slicing with more than one non-<code class="docutils literal notranslate"><span class="pre">:</span></code> entry in the slicing |
| tuple, acts like repeated application of slicing using a single |
| non-<code class="docutils literal notranslate"><span class="pre">:</span></code> entry, where the non-<code class="docutils literal notranslate"><span class="pre">:</span></code> entries are successively taken |
| (with all other non-<code class="docutils literal notranslate"><span class="pre">:</span></code> entries replaced by <code class="docutils literal notranslate"><span class="pre">:</span></code>). Thus, |
| <code class="docutils literal notranslate"><span class="pre">x[ind1,...,ind2,:]</span></code> acts like <code class="docutils literal notranslate"><span class="pre">x[ind1][...,ind2,:]</span></code> under basic |
| slicing.</p> |
| <div class="admonition warning"> |
| <p class="admonition-title">Warning</p> |
| <p>The above is <strong>not</strong> true for advanced indexing.</p> |
| </div> |
| </li> |
| <li><p>You may use slicing to set values in the array, but (unlike lists) you |
| can never grow the array. The size of the value to be set in |
| <code class="docutils literal notranslate"><span class="pre">x[obj]</span> <span class="pre">=</span> <span class="pre">value</span></code> must be (broadcastable) to the same shape as |
| <code class="docutils literal notranslate"><span class="pre">x[obj]</span></code>.</p></li> |
| </ul> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>Remember that a slicing tuple can always be constructed as <em>obj</em> |
| and used in the <code class="docutils literal notranslate"><span class="pre">x[obj]</span></code> notation. Slice objects can be used in |
| the construction in place of the <code class="docutils literal notranslate"><span class="pre">[start:stop:step]</span></code> |
| notation. For example, <code class="docutils literal notranslate"><span class="pre">x[1:10:5,::-1]</span></code> can also be implemented |
| as <code class="docutils literal notranslate"><span class="pre">obj</span> <span class="pre">=</span> <span class="pre">(slice(1,10,5),</span> <span class="pre">slice(None,None,-1));</span> <span class="pre">x[obj]</span></code> . This |
| can be useful for constructing generic code that works on arrays |
| of arbitrary dimension.</p> |
| </div> |
| <dl class="data"> |
| <dt> |
| <code class="sig-name descname">newaxis</code></dt> |
| <dd><p>The <code class="xref py py-const docutils literal notranslate"><span class="pre">newaxis</span></code> object can be used in all slicing operations to |
| create an axis of length one. <code class="xref py py-const docutils literal notranslate"><span class="pre">newaxis</span></code> is an alias for |
| ‘None’, and ‘None’ can be used in place of this with the same result.</p> |
| </dd></dl> |
| |
| </div> |
| <div class="section" id="advanced-indexing"> |
| <h2>Advanced Indexing<a class="headerlink" href="#advanced-indexing" title="Permalink to this headline">¶</a></h2> |
| <p>Advanced indexing is triggered when the selection object, <em>obj</em>, is a |
| non-tuple sequence object, an <code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code> (of data type integer or bool), |
| or a tuple with at least one sequence object or ndarray (of data type |
| integer or bool). There are two types of advanced indexing: integer |
| and Boolean.</p> |
| <p>Advanced indexing always returns a <em>copy</em> of the data (contrast with |
| some cases in basic slicing that returns a view).</p> |
| <div class="admonition warning"> |
| <p class="admonition-title">Warning</p> |
| <p>The definition of advanced indexing means that <code class="docutils literal notranslate"><span class="pre">x[(1,2,3),]</span></code> is |
| fundamentally different than <code class="docutils literal notranslate"><span class="pre">x[(1,2,3)]</span></code>. The latter is |
| equivalent to <code class="docutils literal notranslate"><span class="pre">x[1,2,3]</span></code> which will trigger basic selection while |
| the former will trigger advanced indexing. Be sure to understand |
| why this occurs.</p> |
| <p>Also recognize that <code class="docutils literal notranslate"><span class="pre">x[[1,2,3]]</span></code> will trigger advanced indexing, |
| whereas due to the deprecated Numeric compatibility mentioned above, |
| <code class="docutils literal notranslate"><span class="pre">x[[1,2,slice(None)]]</span></code> will trigger basic slicing in the official NumPy |
| which is not currently supported in MXNet <cite>numpy</cite> module.</p> |
| </div> |
| <div class="section" id="integer-array-indexing"> |
| <h3>Integer array indexing<a class="headerlink" href="#integer-array-indexing" title="Permalink to this headline">¶</a></h3> |
| <p>Integer array indexing allows selection of arbitrary items in the array |
| based on their <em>N</em>-dimensional index. Each integer array represents a number |
| of indexes into that dimension.</p> |
| <div class="section" id="purely-integer-array-indexing"> |
| <h4>Purely integer array indexing<a class="headerlink" href="#purely-integer-array-indexing" title="Permalink to this headline">¶</a></h4> |
| <p>When the index consists of as many integer arrays as the array being indexed |
| has dimensions, the indexing is straight forward, but different from slicing.</p> |
| <p>Advanced indexes always are broadcasting and |
| iterated as <em>one</em>:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">result</span><span class="p">[</span><span class="n">i_1</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="n">i_M</span><span class="p">]</span> <span class="o">==</span> <span class="n">x</span><span class="p">[</span><span class="n">ind_1</span><span class="p">[</span><span class="n">i_1</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="n">i_M</span><span class="p">],</span> <span class="n">ind_2</span><span class="p">[</span><span class="n">i_1</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="n">i_M</span><span class="p">],</span> |
| <span class="o">...</span><span class="p">,</span> <span class="n">ind_N</span><span class="p">[</span><span class="n">i_1</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="n">i_M</span><span class="p">]]</span> |
| </pre></div> |
| </div> |
| <p>Note that the result shape is identical to the (broadcast) indexing array |
| shapes <code class="docutils literal notranslate"><span class="pre">ind_1,</span> <span class="pre">...,</span> <span class="pre">ind_N</span></code>.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <p>From each row, a specific element should be selected. The row index is just |
| <code class="docutils literal notranslate"><span class="pre">[0,</span> <span class="pre">1,</span> <span class="pre">2]</span></code> and the column index specifies the element to choose for the |
| corresponding row, here <code class="docutils literal notranslate"><span class="pre">[0,</span> <span class="pre">1,</span> <span class="pre">0]</span></code>. Using both together the task |
| can be solved using advanced indexing:</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span> |
| <span class="gp">>>> </span><span class="n">x</span><span class="p">[[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]]</span> |
| <span class="go">array([1, 4, 5])</span> |
| </pre></div> |
| </div> |
| </div> |
| </div> |
| <div class="section" id="combining-advanced-and-basic-indexing"> |
| <h4>Combining advanced and basic indexing<a class="headerlink" href="#combining-advanced-and-basic-indexing" title="Permalink to this headline">¶</a></h4> |
| <p>When there is at least one slice (<code class="docutils literal notranslate"><span class="pre">:</span></code>), ellipsis (<code class="docutils literal notranslate"><span class="pre">...</span></code>) or <code class="xref py py-const docutils literal notranslate"><span class="pre">newaxis</span></code> |
| in the index (or the array has more dimensions than there are advanced indexes), |
| then the behaviour can be more complicated. It is like concatenating the |
| indexing result for each advanced index element</p> |
| <p>In the simplest case, there is only a <em>single</em> advanced index. A single |
| advanced index can for example replace a slice and the result array will be |
| the same, however, it is a copy and may have a different memory layout. |
| A slice is preferable when it is possible.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">]</span> |
| <span class="go">array([[4, 5]])</span> |
| <span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]</span> |
| <span class="go">array([[4, 5]])</span> |
| </pre></div> |
| </div> |
| </div> |
| <p>The easiest way to understand the situation may be to think in |
| terms of the result shape. There are two parts to the indexing operation, |
| the subspace defined by the basic indexing (excluding integers) and the |
| subspace from the advanced indexing part. Two cases of index combination |
| need to be distinguished:</p> |
| <ul class="simple"> |
| <li><p>The advanced indexes are separated by a slice, <code class="xref py py-const docutils literal notranslate"><span class="pre">Ellipsis</span></code> or <code class="xref py py-const docutils literal notranslate"><span class="pre">newaxis</span></code>. |
| For example <code class="docutils literal notranslate"><span class="pre">x[arr1,</span> <span class="pre">:,</span> <span class="pre">arr2]</span></code>.</p></li> |
| <li><p>The advanced indexes are all next to each other. |
| For example <code class="docutils literal notranslate"><span class="pre">x[...,</span> <span class="pre">arr1,</span> <span class="pre">arr2,</span> <span class="pre">:]</span></code> but <em>not</em> <code class="docutils literal notranslate"><span class="pre">x[arr1,</span> <span class="pre">:,</span> <span class="pre">1]</span></code> |
| since <code class="docutils literal notranslate"><span class="pre">1</span></code> is an advanced index in this regard.</p></li> |
| </ul> |
| <p>In the first case, the dimensions resulting from the advanced indexing |
| operation come first in the result array, and the subspace dimensions after |
| that. |
| In the second case, the dimensions from the advanced indexing operations |
| are inserted into the result array at the same spot as they were in the |
| initial array (the latter logic is what makes simple advanced indexing |
| behave just like slicing).</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <p>Suppose <code class="docutils literal notranslate"><span class="pre">x.shape</span></code> is (10,20,30) and <code class="docutils literal notranslate"><span class="pre">ind</span></code> is a (2,3,4)-shaped |
| indexing <code class="xref py py-class docutils literal notranslate"><span class="pre">intp</span></code> array, then <code class="docutils literal notranslate"><span class="pre">result</span> <span class="pre">=</span> <span class="pre">x[...,ind,:]</span></code> has |
| shape (10,2,3,4,30) because the (20,)-shaped subspace has been |
| replaced with a (2,3,4)-shaped broadcasted indexing subspace. If |
| we let <em>i, j, k</em> loop over the (2,3,4)-shaped subspace then |
| <code class="docutils literal notranslate"><span class="pre">result[...,i,j,k,:]</span> <span class="pre">=</span> <span class="pre">x[...,ind[i,j,k],:]</span></code>. This example |
| produces the same result as <code class="xref py py-meth docutils literal notranslate"><span class="pre">x.take(ind,</span> <span class="pre">axis=-2)</span></code>.</p> |
| </div> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <p>Let <code class="docutils literal notranslate"><span class="pre">x.shape</span></code> be (10,20,30,40,50) and suppose <code class="docutils literal notranslate"><span class="pre">ind_1</span></code> |
| and <code class="docutils literal notranslate"><span class="pre">ind_2</span></code> can be broadcast to the shape (2,3,4). Then |
| <code class="docutils literal notranslate"><span class="pre">x[:,ind_1,ind_2]</span></code> has shape (10,2,3,4,40,50) because the |
| (20,30)-shaped subspace from X has been replaced with the |
| (2,3,4) subspace from the indices. However, |
| <code class="docutils literal notranslate"><span class="pre">x[:,ind_1,:,ind_2]</span></code> has shape (2,3,4,10,30,50) because there |
| is no unambiguous place to drop in the indexing subspace, thus |
| it is tacked-on to the beginning. It is always possible to use |
| <code class="xref py py-meth docutils literal notranslate"><span class="pre">.transpose()</span></code> to move the subspace |
| anywhere desired. Note that this example cannot be replicated |
| using <code class="xref py py-func docutils literal notranslate"><span class="pre">take()</span></code>.</p> |
| </div> |
| </div> |
| </div> |
| <div class="section" id="boolean-array-indexing"> |
| <h3>Boolean array indexing<a class="headerlink" href="#boolean-array-indexing" title="Permalink to this headline">¶</a></h3> |
| <p>This advanced indexing occurs when obj is an array object of Boolean |
| type, such as may be returned from comparison operators. A single |
| boolean index array is practically identical to <code class="docutils literal notranslate"><span class="pre">x[obj.nonzero()]</span></code> where, |
| as described above, <code class="xref py py-meth docutils literal notranslate"><span class="pre">obj.nonzero()</span></code> returns a |
| tuple (of length <code class="xref py py-attr docutils literal notranslate"><span class="pre">obj.ndim</span></code>) of integer index |
| arrays showing the <code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code> elements of <em>obj</em>. However, it is |
| faster when <code class="docutils literal notranslate"><span class="pre">obj.shape</span> <span class="pre">==</span> <span class="pre">x.shape</span></code>.</p> |
| <p>If <code class="docutils literal notranslate"><span class="pre">obj.ndim</span> <span class="pre">==</span> <span class="pre">x.ndim</span></code>, <code class="docutils literal notranslate"><span class="pre">x[obj]</span></code> returns a 1-dimensional array |
| filled with the elements of <em>x</em> corresponding to the <code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code> |
| values of <em>obj</em>. The search order will be row-major, |
| C-style. If <em>obj</em> has <code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code> values at entries that are outside |
| of the bounds of <em>x</em>, then an index error will be raised. If <em>obj</em> is |
| smaller than <em>x</em> it is identical to filling it with <code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code>.</p> |
| <div class="admonition note"> |
| <p class="admonition-title">Note</p> |
| <p>Boolean indexing currently only supports a single boolean ndarray as a index. |
| An composite index including a boolean array is not supported for now.</p> |
| </div> |
| <p>If there is only one Boolean array and no integer indexing array present, |
| this is straight forward. Care must only be taken to make sure that the |
| boolean index has <em>exactly</em> as many dimensions as it is supposed to work |
| with.</p> |
| <div class="admonition-example admonition"> |
| <p class="admonition-title">Example</p> |
| <p>From an array, select all rows which sum up to less or equal two:</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="n">rowsum</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="n">rowsum</span> <span class="o"><=</span> <span class="mi">2</span><span class="p">]</span> |
| <span class="go">array([[0, 1],</span> |
| <span class="go"> [1, 1]], dtype=int32)</span> |
| </pre></div> |
| </div> |
| <p>But if <code class="docutils literal notranslate"><span class="pre">rowsum</span></code> would have two dimensions as well:</p> |
| <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">rowsum</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| <span class="gp">>>> </span><span class="n">rowsum</span><span class="o">.</span><span class="n">shape</span> |
| <span class="go">(3, 1)</span> |
| <span class="gp">>>> </span><span class="n">x</span><span class="p">[</span><span class="n">rowsum</span> <span class="o"><=</span> <span class="mi">2</span><span class="p">]</span> <span class="c1"># fail</span> |
| <span class="go">IndexError: boolean index did not match indexed array along dimension 1</span> |
| </pre></div> |
| </div> |
| </div> |
| </div> |
| </div> |
| <div class="section" id="detailed-notes"> |
| <h2>Detailed notes<a class="headerlink" href="#detailed-notes" title="Permalink to this headline">¶</a></h2> |
| <p>These are some detailed notes, which are not of importance for day to day |
| indexing (in no particular order):</p> |
| <ul class="simple"> |
| <li><p>For advanced assignments, there is in general no guarantee for the |
| iteration order. This means that if an element is set more than once, |
| it is not possible to predict the final result.</p></li> |
| <li><p>An empty (tuple) index is a full scalar index into a zero dimensional array. |
| <code class="docutils literal notranslate"><span class="pre">x[()]</span></code> returns a <em>scalar</em> <cite>ndarray</cite> if <code class="docutils literal notranslate"><span class="pre">x</span></code> has zero dimensions. |
| On the other hand <code class="docutils literal notranslate"><span class="pre">x[...]</span></code> always returns a view.</p></li> |
| <li><p>If a zero dimensional array is present in the index <em>and</em> it is <em>not considered as</em> a full |
| integer index as in NumPy. Advanced indexing is not triggered.</p></li> |
| <li><p>the <code class="docutils literal notranslate"><span class="pre">nonzero</span></code> equivalence for Boolean arrays does not hold for zero |
| dimensional boolean arrays.</p></li> |
| <li><p>When the result of an advanced indexing operation has no elements but an |
| individual index is out of bounds, currently no <code class="docutils literal notranslate"><span class="pre">IndexError</span></code> is |
| raised as in NumPy.</p></li> |
| </ul> |
| <span class="target" id="index-1"></span></div> |
| </div> |
| |
| |
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| <div class="localtoc"> |
| <p class="caption"> |
| <span class="caption-text">Table Of Contents</span> |
| </p> |
| <ul> |
| <li><a class="reference internal" href="#">Indexing</a><ul> |
| <li><a class="reference internal" href="#basic-slicing-and-indexing">Basic Slicing and Indexing</a></li> |
| <li><a class="reference internal" href="#advanced-indexing">Advanced Indexing</a><ul> |
| <li><a class="reference internal" href="#integer-array-indexing">Integer array indexing</a><ul> |
| <li><a class="reference internal" href="#purely-integer-array-indexing">Purely integer array indexing</a></li> |
| <li><a class="reference internal" href="#combining-advanced-and-basic-indexing">Combining advanced and basic indexing</a></li> |
| </ul> |
| </li> |
| <li><a class="reference internal" href="#boolean-array-indexing">Boolean array indexing</a></li> |
| </ul> |
| </li> |
| <li><a class="reference internal" href="#detailed-notes">Detailed notes</a></li> |
| </ul> |
| </li> |
| </ul> |
| |
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