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{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-09-27T23:11:31","documenter_version":"1.0.1"}}
{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-11-07T23:53:01","documenter_version":"1.1.2"}}
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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script data-outdated-warner src="../assets/warner.js"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 href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/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="../search_index.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"><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 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.TaylorScalar" href="#TaylorDiff.TaylorScalar"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{T, N}</code></pre><p>Representation of Taylor polynomials.</p><p><strong>Fields</strong></p><ul><li><code>value::NTuple{N, T}</code>: i-th element of this stores the (i-1)-th derivative</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/61326eff60fb6940511b622de97cceeb500d6347/src/scalar.jl#L7-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.TaylorScalar-Union{Tuple{N}, Tuple{T}, Tuple{T, T}} where {T, N}" href="#TaylorDiff.TaylorScalar-Union{Tuple{N}, Tuple{T}, Tuple{T, T}} where {T, N}"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{T, N}(x::T, d::T) where {T, N}</code></pre><p>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/61326eff60fb6940511b622de97cceeb500d6347/src/scalar.jl#L36-L40">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{N}, Tuple{T}} where {T, N}" href="#TaylorDiff.TaylorScalar-Union{Tuple{N}, Tuple{T}} where {T, N}"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{T, N}(x::T) where {T, N}</code></pre><p>Construct a Taylor polynomial with zeroth order coefficient.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/61326eff60fb6940511b622de97cceeb500d6347/src/scalar.jl#L24-L28">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></header><section><div><pre><code class="language-julia hljs">derivative(f, x::T, order::Int64)
<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 href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/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="../search_index.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"><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 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.TaylorScalar" href="#TaylorDiff.TaylorScalar"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{T, N}</code></pre><p>Representation of Taylor polynomials.</p><p><strong>Fields</strong></p><ul><li><code>value::NTuple{N, T}</code>: i-th element of this stores the (i-1)-th derivative</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/6f0fcd5d545219b0de19dff47726d9bbd74e1531/src/scalar.jl#L7-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.TaylorScalar-Union{Tuple{N}, Tuple{T}, Tuple{T, T}} where {T, N}" href="#TaylorDiff.TaylorScalar-Union{Tuple{N}, Tuple{T}, Tuple{T, T}} where {T, N}"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{T, N}(x::T, d::T) where {T, N}</code></pre><p>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/6f0fcd5d545219b0de19dff47726d9bbd74e1531/src/scalar.jl#L36-L40">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{N}, Tuple{T}} where {T, N}" href="#TaylorDiff.TaylorScalar-Union{Tuple{N}, Tuple{T}} where {T, N}"><code>TaylorDiff.TaylorScalar</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">TaylorScalar{T, N}(x::T) where {T, N}</code></pre><p>Construct a Taylor polynomial with zeroth order coefficient.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/6f0fcd5d545219b0de19dff47726d9bbd74e1531/src/scalar.jl#L24-L28">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></header><section><div><pre><code class="language-julia hljs">derivative(f, x::T, order::Int64)
derivative(f, x::T, ::Val{N})</code></pre><p>Computes <code>order</code>-th derivative of <code>f</code> w.r.t. scalar <code>x</code>.</p><pre><code class="nohighlight hljs">derivative(f, x::AbstractVector{T}, l::AbstractVector{T}, order::Int64)
derivative(f, x::AbstractVector{T}, l::AbstractVector{T}, ::Val{N})</code></pre><p>Computes <code>order</code>-th directional derivative of <code>f</code> w.r.t. vector <code>x</code> in direction <code>l</code>.</p><pre><code class="nohighlight hljs">derivative(f, x::AbstractMatrix{T}, order::Int64)
derivative(f, x::AbstractMatrix{T}, ::Val{N})
derivative(f, x::AbstractMatrix{T}, l::AbstractVector{T}, order::Int64)
derivative(f, x::AbstractMatrix{T}, l::AbstractVector{T}, ::Val{N})</code></pre><p>Shorthand notations for multiple calculations. For a M-by-N matrix, calculate the directional derivative for each column. For a 1-by-N matrix (row vector), calculate the derivative for each scalar.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/61326eff60fb6940511b622de97cceeb500d6347/src/derivative.jl#L5-L24">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.0.1 on <span class="colophon-date" title="Wednesday 27 September 2023 23:11">Wednesday 27 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
derivative(f, x::AbstractMatrix{T}, l::AbstractVector{T}, ::Val{N})</code></pre><p>Shorthand notations for multiple calculations. For a M-by-N matrix, calculate the directional derivative for each column. For a 1-by-N matrix (row vector), calculate the derivative for each scalar.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaDiff/TaylorDiff.jl/blob/6f0fcd5d545219b0de19dff47726d9bbd74e1531/src/derivative.jl#L5-L24">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Tuesday 7 November 2023 23:53">Tuesday 7 November 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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