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-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Automatic differentiation · TensorOperations.jl</title><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.svg" alt="TensorOperations.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">TensorOperations.jl</a></span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="../indexnotation/">Index notation with macros</a></li><li><a class="tocitem" href="../functions/">Functions</a></li><li><a class="tocitem" href="../interface/">Interface</a></li><li class="is-active"><a class="tocitem" href>Automatic differentiation</a></li><li><a class="tocitem" href="../implementation/">Implementation</a></li></ul></li><li><a class="tocitem" href="../../index/">Index</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Manual</a></li><li class="is-active"><a href>Automatic differentiation</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Automatic differentiation</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/Jutho/TensorOperations.jl/blob/master/docs/src/man/autodiff.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Automatic-differentiation"><a class="docs-heading-anchor" href="#Automatic-differentiation">Automatic differentiation</a><a id="Automatic-differentiation-1"></a><a class="docs-heading-anchor-permalink" href="#Automatic-differentiation" title="Permalink"></a></h1><p>TensorOperations offers experimental support for reverse-mode automatic diffentiation (AD) through the use of <a href="https://github.com/JuliaDiff/ChainRules.jl">ChainRules.jl</a>. As the basic operations are multi-linear, the vector-Jacobian products thereof can all be expressed in terms of the operations defined in VectorInterface and TensorOperations. Thus, any custom type whose tangent type also support these interfaces will automatically inherit reverse-mode AD support.</p><p>As the <a href="../indexnotation/#TensorOperations.@tensor"><code>@tensor</code></a> macro rewrites everything in terms of the basic tensor operations, the reverse-mode rules for these methods are supplied. However, because most AD-engines do not support in-place mutation, effectively these operations will be replaced with a non-mutating version. This is similar to the behaviour found in <a href="https://github.com/JuliaFolds/BangBang.jl">BangBang.jl</a>, as the operations will be in-place, except for the pieces of code that are being differentiated. In effect, this amounts to replacing all assignments (<code>=</code>) with definitions (<code>:=</code>) within the context of <a href="../indexnotation/#TensorOperations.@tensor"><code>@tensor</code></a>.</p><div class="admonition is-warning"><header class="admonition-header">Experimental</header><div class="admonition-body"><p>While some rudimentary tests are run, the AD support is currently not incredibly well-tested. Because of the way it is implemented, the use of AD will tacitly replace mutating operations with a non-mutating variant. This might lead to unwanted bugs that are hard to track down. Additionally, for mixed scalar types their also might be unexpected or unwanted behaviour.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../interface/">« Interface</a><a class="docs-footer-nextpage" href="../implementation/">Implementation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 19 August 2023 07:16">Saturday 19 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Automatic differentiation · TensorOperations.jl</title><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.svg" alt="TensorOperations.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">TensorOperations.jl</a></span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="../indexnotation/">Index notation with macros</a></li><li><a class="tocitem" href="../functions/">Functions</a></li><li><a class="tocitem" href="../interface/">Interface</a></li><li class="is-active"><a class="tocitem" href>Automatic differentiation</a></li><li><a class="tocitem" href="../implementation/">Implementation</a></li></ul></li><li><a class="tocitem" href="../../index/">Index</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Manual</a></li><li class="is-active"><a href>Automatic differentiation</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Automatic differentiation</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/Jutho/TensorOperations.jl/blob/master/docs/src/man/autodiff.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Automatic-differentiation"><a class="docs-heading-anchor" href="#Automatic-differentiation">Automatic differentiation</a><a id="Automatic-differentiation-1"></a><a class="docs-heading-anchor-permalink" href="#Automatic-differentiation" title="Permalink"></a></h1><p>TensorOperations offers experimental support for reverse-mode automatic diffentiation (AD) through the use of <a href="https://github.com/JuliaDiff/ChainRules.jl">ChainRules.jl</a>. As the basic operations are multi-linear, the vector-Jacobian products thereof can all be expressed in terms of the operations defined in VectorInterface and TensorOperations. Thus, any custom type whose tangent type also support these interfaces will automatically inherit reverse-mode AD support.</p><p>As the <a href="../indexnotation/#TensorOperations.@tensor"><code>@tensor</code></a> macro rewrites everything in terms of the basic tensor operations, the reverse-mode rules for these methods are supplied. However, because most AD-engines do not support in-place mutation, effectively these operations will be replaced with a non-mutating version. This is similar to the behaviour found in <a href="https://github.com/JuliaFolds/BangBang.jl">BangBang.jl</a>, as the operations will be in-place, except for the pieces of code that are being differentiated. In effect, this amounts to replacing all assignments (<code>=</code>) with definitions (<code>:=</code>) within the context of <a href="../indexnotation/#TensorOperations.@tensor"><code>@tensor</code></a>.</p><div class="admonition is-warning"><header class="admonition-header">Experimental</header><div class="admonition-body"><p>While some rudimentary tests are run, the AD support is currently not incredibly well-tested. Because of the way it is implemented, the use of AD will tacitly replace mutating operations with a non-mutating variant. This might lead to unwanted bugs that are hard to track down. Additionally, for mixed scalar types their also might be unexpected or unwanted behaviour.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../interface/">« Interface</a><a class="docs-footer-nextpage" href="../implementation/">Implementation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 19 August 2023 09:11">Saturday 19 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>