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{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-02-09T17:14:38","documenter_version":"1.2.1"}}
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>KLU.jl · KLU</title><meta name="title" content="KLU.jl · KLU"/><meta property="og:title" content="KLU.jl · KLU"/><meta property="twitter:title" content="KLU.jl · KLU"/><meta name="description" content="Documentation for KLU."/><meta property="og:description" content="Documentation for KLU."/><meta property="twitter:description" content="Documentation for KLU."/><script data-outdated-warner src="assets/warner.js"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>KLU</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 class="is-active"><a class="tocitem" href>KLU.jl</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>KLU.jl</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>KLU.jl</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaSparse/KLU.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaSparse/KLU.jl/blob/main/docs/src/index.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="KLU.jl"><a class="docs-heading-anchor" href="#KLU.jl">KLU.jl</a><a id="KLU.jl-1"></a><a class="docs-heading-anchor-permalink" href="#KLU.jl" title="Permalink"></a></h1><p>Documentation for KLU.jl</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="KLU.klu" href="#KLU.klu"><code>KLU.klu</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">klu(A::SparseMatrixCSC) -&gt; K::KLUFactorization
klu(n, colptr::Vector{Ti}, rowval::Vector{Ti}, nzval::Vector{Tv}) -&gt; K::KLUFactorization</code></pre><p>Compute the LU factorization of a sparse matrix <code>A</code> using KLU<sup class="footnote-reference"><a id="citeref-ACM907" href="#footnote-ACM907">[ACM907]</a></sup>.</p><p>For sparse <code>A</code> with real or complex element type, the return type of <code>K</code> is <code>KLUFactorization{Tv, Ti}</code>, with <code>Tv</code> = <code>Float64</code> or <code>ComplexF64</code> respectively and <code>Ti</code> is an integer type (<code>Int32</code> or <code>Int64</code>).</p><p>The individual components of the factorization <code>K</code> can be accessed by indexing:</p><table><tr><th style="text-align: left">Component</th><th style="text-align: left">Description</th></tr><tr><td style="text-align: left"><code>L</code></td><td style="text-align: left"><code>L</code> (lower triangular) part of <code>LU</code> of the diagonal blocks</td></tr><tr><td style="text-align: left"><code>U</code></td><td style="text-align: left"><code>U</code> (upper triangular) part of <code>LU</code> of the diagonal blocks</td></tr><tr><td style="text-align: left"><code>F</code></td><td style="text-align: left"><code>F</code> (upper triangular) part of <code>LU + F</code>, the off-diagonal blocks</td></tr><tr><td style="text-align: left"><code>p</code></td><td style="text-align: left">right permutation <code>Vector</code></td></tr><tr><td style="text-align: left"><code>q</code></td><td style="text-align: left">left permutation <code>Vector</code></td></tr><tr><td style="text-align: left"><code>Rs</code></td><td style="text-align: left"><code>Vector</code> of scaling factors</td></tr></table><p>The relation between <code>K</code> and <code>A</code> is</p><p><code>K.L * K.U + K.F == K.Rs</code>` A[K.p, K.q]`</p><p><code>K</code> further supports the following functions:</p><ul><li><code>LinearAlgebra.\</code></li></ul><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p><code>klu(A::SparseMatrixCSC)</code> uses the KLU<sup class="footnote-reference"><a id="citeref-ACM907" href="#footnote-ACM907">[ACM907]</a></sup> library that is part of SuiteSparse. As this library only supports sparse matrices with <a href="@ref"><code>Float64</code></a> or <code>ComplexF64</code> elements, <code>lu</code> converts <code>A</code> into a copy that is of type <code>SparseMatrixCSC{Float64}</code> or <code>SparseMatrixCSC{ComplexF64}</code> as appropriate.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSparse/KLU.jl/blob/fd8c0f224d81da78d9674d5877a750d113a8cfe6/src/KLU.jl#L491-L528">source</a></section></article><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-ACM907"><a class="tag is-link" href="#citeref-ACM907">ACM907</a>Davis, Timothy A., &amp; Palamadai Natarajan, E. (2010). Algorithm 907: KLU, A Direct Sparse Solver for Circuit Simulation Problems. ACM Trans. Math. Softw., 37(3). doi:10.1145/1824801.1824814</li></ul></section></article><nav class="docs-footer"><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 1.2.1 on <span class="colophon-date" title="Friday 9 February 2024 17:14">Friday 9 February 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
klu(n, colptr::Vector{Ti}, rowval::Vector{Ti}, nzval::Vector{Tv}) -&gt; K::KLUFactorization</code></pre><p>Compute the LU factorization of a sparse matrix <code>A</code> using KLU<sup class="footnote-reference"><a id="citeref-ACM907" href="#footnote-ACM907">[ACM907]</a></sup>.</p><p>For sparse <code>A</code> with real or complex element type, the return type of <code>K</code> is <code>KLUFactorization{Tv, Ti}</code>, with <code>Tv</code> = <code>Float64</code> or <code>ComplexF64</code> respectively and <code>Ti</code> is an integer type (<code>Int32</code> or <code>Int64</code>).</p><p>The individual components of the factorization <code>K</code> can be accessed by indexing:</p><table><tr><th style="text-align: left">Component</th><th style="text-align: left">Description</th></tr><tr><td style="text-align: left"><code>L</code></td><td style="text-align: left"><code>L</code> (lower triangular) part of <code>LU</code> of the diagonal blocks</td></tr><tr><td style="text-align: left"><code>U</code></td><td style="text-align: left"><code>U</code> (upper triangular) part of <code>LU</code> of the diagonal blocks</td></tr><tr><td style="text-align: left"><code>F</code></td><td style="text-align: left"><code>F</code> (upper triangular) part of <code>LU + F</code>, the off-diagonal blocks</td></tr><tr><td style="text-align: left"><code>p</code></td><td style="text-align: left">right permutation <code>Vector</code></td></tr><tr><td style="text-align: left"><code>q</code></td><td style="text-align: left">left permutation <code>Vector</code></td></tr><tr><td style="text-align: left"><code>Rs</code></td><td style="text-align: left"><code>Vector</code> of scaling factors</td></tr></table><p>The relation between <code>K</code> and <code>A</code> is</p><p><code>K.L * K.U + K.F == K.Rs</code>` A[K.p, K.q]`</p><p><code>K</code> further supports the following functions:</p><ul><li><code>LinearAlgebra.\</code></li></ul><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p><code>klu(A::SparseMatrixCSC)</code> uses the KLU<sup class="footnote-reference"><a id="citeref-ACM907" href="#footnote-ACM907">[ACM907]</a></sup> library that is part of SuiteSparse. As this library only supports sparse matrices with <a href="@ref"><code>Float64</code></a> or <code>ComplexF64</code> elements, <code>lu</code> converts <code>A</code> into a copy that is of type <code>SparseMatrixCSC{Float64}</code> or <code>SparseMatrixCSC{ComplexF64}</code> as appropriate.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSparse/KLU.jl/blob/7c8757de09c53b7e04962414d6bb5b1c5c17b0dc/src/KLU.jl#L491-L528">source</a></section></article><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-ACM907"><a class="tag is-link" href="#citeref-ACM907">ACM907</a>Davis, Timothy A., &amp; Palamadai Natarajan, E. (2010). Algorithm 907: KLU, A Direct Sparse Solver for Circuit Simulation Problems. ACM Trans. Math. Softw., 37(3). doi:10.1145/1824801.1824814</li></ul></section></article><nav class="docs-footer"><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 1.2.1 on <span class="colophon-date" title="Friday 9 February 2024 17:17">Friday 9 February 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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