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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Matrix/vector representation · HYPRE.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://fredrikekre.github.io/HYPRE.jl/stable/hypre-matrix-vector/"/><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"><div class="docs-package-name"><span class="docs-autofit"><a href="../">HYPRE.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 class="is-active"><a class="tocitem" href>Matrix/vector representation</a><ul class="internal"><li><a class="tocitem" href="#PartitionedArrays.jl-(multi-process)"><span>PartitionedArrays.jl (multi-process)</span></a></li><li><a class="tocitem" href="#SparseMatrixCSC-/-SparseMatrixCSR-(single-process)"><span><code>SparseMatrixCSC</code> / <code>SparseMatrixCSR</code> (single-process)</span></a></li><li><a class="tocitem" href="#SparseMatrixCSC-/-SparseMatrixCSR-(multi-process)"><span><code>SparseMatrixCSC</code> / <code>SparseMatrixCSR</code> (multi-process)</span></a></li></ul></li><li><a class="tocitem" href="../libhypre/">LibHYPRE C 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"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Matrix/vector representation</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Matrix/vector representation</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/fredrikekre/HYPRE.jl" title="View the repository on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/fredrikekre/HYPRE.jl/blob/master/docs/src/hypre-matrix-vector.md" title="Edit source on GitHub"><span class="docs-icon fas"></span></a><a class="docs-settings-button docs-navbar-link fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button docs-navbar-link fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Matrix/vector-representation"><a class="docs-heading-anchor" href="#Matrix/vector-representation">Matrix/vector representation</a><a id="Matrix/vector-representation-1"></a><a class="docs-heading-anchor-permalink" href="#Matrix/vector-representation" title="Permalink"></a></h1><p>HYPRE.jl defines the structs <code>HYPREMatrix</code> and <code>HYPREVector</code> representing HYPREs datastructures. Specifically it uses the <a href="https://hypre.readthedocs.io/en/latest/api-int-ij.html">IJ System Interface</a> which can be used for general sparse matrices.</p><p>HYPRE.jl defines conversion methods from standard Julia datastructures to <code>HYPREMatrix</code> and <code>HYPREVector</code>, respectively. See the following sections for details:</p><ul><li><a href="#PartitionedArrays.jl-(multi-process)">PartitionedArrays.jl (multi-process)</a></li><li><a href="#SparseMatrixCSC-/-SparseMatrixCSR-(single-process)"><code>SparseMatrixCSC</code> / <code>SparseMatrixCSR</code> (single-process)</a></li><li><a href="#SparseMatrixCSC-/-SparseMatrixCSR-(multi-process)"><code>SparseMatrixCSC</code> / <code>SparseMatrixCSR</code> (multi-process)</a></li></ul><h2 id="PartitionedArrays.jl-(multi-process)"><a class="docs-heading-anchor" href="#PartitionedArrays.jl-(multi-process)">PartitionedArrays.jl (multi-process)</a><a id="PartitionedArrays.jl-(multi-process)-1"></a><a class="docs-heading-anchor-permalink" href="#PartitionedArrays.jl-(multi-process)" title="Permalink"></a></h2><p>HYPRE.jl integrates seemlessly with <code>PSparseMatrix</code> and <code>PVector</code> from the <a href="https://github.com/fverdugo/PartitionedArrays.jl">PartitionedArrays.jl</a> package. These can be passed directly to <code>solve</code> and <code>solve!</code>. Internally this will construct a <code>HYPREMatrix</code> and <code>HYPREVector</code>s and then convert the solution back to a <code>PVector</code>.</p><p>The <code>HYPREMatrix</code> constructor support both <code>SparseMatrixCSC</code> and <code>SparseMatrixCSR</code> as storage backends for the <code>PSparseMatrix</code>. However, since HYPREs internal storage is also CSR based it can be <em>slightly</em> more resource efficient to use <code>SparseMatrixCSR</code>.</p><p>The constructors also support both PartitionedArrays.jl backends: When using the <code>MPI</code> backend the communicator of the <code>PSparseMatrix</code>/<code>PVector</code> is used also for the <code>HYPREMatrix</code>/<code>HYPREVector</code>, and when using the <code>Sequential</code> backend it is assumed to be a single-process setup, and the <code>MPI.COMM_SELF</code> communicator is used.</p><p><strong>Example pseudocode</strong></p><pre><code class="language-julia hljs"># Assemble linear system (see documentation for PartitionedArrays) |
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A = PSparseMatrix(...) |
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b = PVector(...) |
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# Solve with zero initial guess |
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x = solve(solver, A, b) |
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# Inplace solve with x as initial guess |
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x = PVector(...) |
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solve!(solver, x, A, b)</code></pre><hr/><p>It is also possible to construct the arrays explicitly. This can save some resources when performing multiple consecutive solves (multiple time steps, Newton iterations, etc). To copy data back and forth between <code>PSparseMatrix</code>/<code>PVector</code> and <code>HYPREMatrix</code>/<code>HYPREVector</code> use the <code>copy!</code> function.</p><p><strong>Example pseudocode</strong></p><pre><code class="language-julia hljs">A = PSparseMatrix(...) |
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x = PVector(...) |
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b = PVector(...) |
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# Construct the HYPRE arrays |
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A_h = HYPREMatrix(A) |
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x_h = HYPREVector(x) |
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b_h = HYPREVector(b) |
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# Solve |
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solve!(solver, x_h, A_h, b_h) |
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# Copy solution back to x |
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copy!(x, x_h)</code></pre><h2 id="SparseMatrixCSC-/-SparseMatrixCSR-(single-process)"><a class="docs-heading-anchor" href="#SparseMatrixCSC-/-SparseMatrixCSR-(single-process)"><code>SparseMatrixCSC</code> / <code>SparseMatrixCSR</code> (single-process)</a><a id="SparseMatrixCSC-/-SparseMatrixCSR-(single-process)-1"></a><a class="docs-heading-anchor-permalink" href="#SparseMatrixCSC-/-SparseMatrixCSR-(single-process)" title="Permalink"></a></h2><p>HYPRE.jl also support working directly with <code>SparseMatrixCSC</code> (from the <a href="https://github.com/JuliaSparse/SparseArrays.jl">SparseArrays.jl</a> standard library) and <code>SparseMatrixCSR</code> (from the <a href="https://github.com/gridap/SparseMatricesCSR.jl">SparseMatricesCSR.jl</a> package). This makes it possible to use solvers and preconditioners even for single-process problems. When using these type of spars matrices it is assumed that the right hand side and solution vectors are regular Julia <code>Vector</code>s.</p><p>Just like when using the PartitionedArrays.jl package, it is possible to pass sparse matrices directly to <code>solve</code> and <code>solve!</code>, but it is also possible to create <code>HYPREMatrix</code> and <code>HYPREVector</code> explicitly, possibly saving some resources when doing multiple consecutive linear solves (see previous section).</p><p><strong>Example pseudocode</strong></p><pre><code class="language-julia hljs">A = SparseMatrixCSC(...) |
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x = Vector(...) |
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b = Vector(...) |
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# Solve with zero initial guess |
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x = solve(solver, A, b) |
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# Inplace solve with x as initial guess |
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x = zeros(length(b)) |
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solve!(solver, x, A, b)</code></pre><h2 id="SparseMatrixCSC-/-SparseMatrixCSR-(multi-process)"><a class="docs-heading-anchor" href="#SparseMatrixCSC-/-SparseMatrixCSR-(multi-process)"><code>SparseMatrixCSC</code> / <code>SparseMatrixCSR</code> (multi-process)</a><a id="SparseMatrixCSC-/-SparseMatrixCSR-(multi-process)-1"></a><a class="docs-heading-anchor-permalink" href="#SparseMatrixCSC-/-SparseMatrixCSR-(multi-process)" title="Permalink"></a></h2><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>This interface isn't finalized yet and is therefore not documented since it is subject to change.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../libhypre/">LibHYPRE C API »</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 0.28.0-DEV on <span class="colophon-date" title="Wednesday 27 July 2022 17:53">Wednesday 27 July 2022</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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