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{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-29T18:54:48","documenter_version":"1.7.0"}}
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>API · TaylorDiff.jl</title><meta name="title" content="API · TaylorDiff.jl"/><meta property="og:title" content="API · TaylorDiff.jl"/><meta property="twitter:title" content="API · TaylorDiff.jl"/><meta name="description" content="Documentation for TaylorDiff.jl."/><meta property="og:description" content="Documentation for TaylorDiff.jl."/><meta property="twitter:description" content="Documentation for TaylorDiff.jl."/><meta property="og:url" content="https://juliadiff.org/TaylorDiff.jl/api/"/><meta property="twitter:url" content="https://juliadiff.org/TaylorDiff.jl/api/"/><link rel="canonical" href="https://juliadiff.org/TaylorDiff.jl/api/"/><script data-outdated-warner src="../assets/warner.js"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 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data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><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"><div class="docs-package-name"><span class="docs-autofit"><a href="../">TaylorDiff.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../theory/">Theory</a></li><li class="is-active"><a class="tocitem" href>API</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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>API</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>API</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/main/docs/src/api.md#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="API"><a class="docs-heading-anchor" href="#API">API</a><a id="API-1"></a><a class="docs-heading-anchor-permalink" href="#API" title="Permalink"></a></h1><p>API for <a href="https://github.com/tansongchen/TaylorDiff.jl">TaylorDiff</a>.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.TaylorArray" href="#TaylorDiff.TaylorArray"><code>TaylorDiff.TaylorArray</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">TaylorArray{T, N, A, P}</code></pre><p>Representation of Taylor polynomials in array mode.</p><p><strong>Fields</strong></p><ul><li><code>value::A</code>: zeroth order coefficient</li><li><code>partials::NTuple{P, A}</code>: i-th element of this stores the i-th derivative</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/array.jl#L3-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.TaylorScalar" href="#TaylorDiff.TaylorScalar"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{T, P}</code></pre><p>Representation of Taylor polynomials.</p><p><strong>Fields</strong></p><ul><li><code>value::T</code>: zeroth order coefficient</li><li><code>partials::NTuple{P, T}</code>: i-th element of this stores the i-th derivative</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/scalar.jl#L3-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.TaylorScalar-Union{Tuple{P}, Tuple{T}, Tuple{T, T}} where {T, P}" href="#TaylorDiff.TaylorScalar-Union{Tuple{P}, Tuple{T}, Tuple{T, T}} where {T, P}"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{P}(value::T, seed::T)</code></pre><p>Convenience function: construct a Taylor polynomial with zeroth and first order coefficient, acting as a seed.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/scalar.jl#L35-L39">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.TaylorScalar-Union{Tuple{P}, Tuple{T}} where {T, P}" href="#TaylorDiff.TaylorScalar-Union{Tuple{P}, Tuple{T}} where {T, P}"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{P}(value::T) where {T, P}</code></pre><p>Convenience function: construct a Taylor polynomial with zeroth order coefficient.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/scalar.jl#L28-L32">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.can_taylorize-Tuple{Type{&lt;:Real}}" href="#TaylorDiff.can_taylorize-Tuple{Type{&lt;:Real}}"><code>TaylorDiff.can_taylorize</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">TaylorDiff.can_taylorize(V::Type)</code></pre><p>Determines whether the type V is allowed as the scalar type in a Dual. By default, only <code>&lt;:Real</code> types are allowed.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/TaylorDiff.jl#L3-L8">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.derivative" href="#TaylorDiff.derivative"><code>TaylorDiff.derivative</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">derivative(f, x, ::Val{P})
derivative(f, x, l, ::Val{P})
derivative(f!, y, x, l, ::Val{P})</code></pre><p>Computes <code>P</code>-th directional derivative of <code>f</code> w.r.t. vector <code>x</code> in direction <code>l</code>. If <code>x</code> is a Number, the direction <code>l</code> can be omitted.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/derivative.jl#L7-L13">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.derivative!" href="#TaylorDiff.derivative!"><code>TaylorDiff.derivative!</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">derivative!(result, f, x, l, ::Val{P})
derivative!(result, f!, y, x, l, ::Val{P})</code></pre><p>In-place derivative calculation APIs. <code>result</code> is expected to be pre-allocated and have the same shape as <code>y</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/derivative.jl#L20-L25">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.derivatives" href="#TaylorDiff.derivatives"><code>TaylorDiff.derivatives</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">derivatives(f, x, l, ::Val{P})
derivatives(f!, y, x, l, ::Val{P})</code></pre><p>Computes all derivatives of <code>f</code> at <code>x</code> up to order <code>P</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/derivative.jl#L33-L38">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.get_term_raiser-Tuple{Any}" href="#TaylorDiff.get_term_raiser-Tuple{Any}"><code>TaylorDiff.get_term_raiser</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Pick a strategy for raising the derivative of a function. If the derivative is like 1 over something, raise with the division rule; otherwise, raise with the multiplication rule.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/utils.jl#L11-L15">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="TaylorDiff.@immutable-Tuple{Any}" href="#TaylorDiff.@immutable-Tuple{Any}"><code>TaylorDiff.@immutable</code></a> — <span class="docstring-category">Macro</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">immutable(def)</code></pre><p>Transform a function definition to a @generated function.</p><ol><li>Allocations are removed by replacing the output with scalar variables;</li><li>Loops are unrolled;</li><li>Indices are modified to use 1-based indexing;</li></ol></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/aeeceef978b73d65fa1b23b7043545ae9fe4e17f/src/utils.jl#L103-L111">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../theory/">« Theory</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Tuesday 29 October 2024 18:54">Tuesday 29 October 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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