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<h1 class="page-title">Class: Cholesky</h1>
<section>
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<h2>
<span class="ancestors"><a href="module-LinearAlgebra.html">LinearAlgebra</a>.</span>
Cholesky
</h2>
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<dt>
<h4 class="name" id="Cholesky"><span class="type-signature"></span>new Cholesky()</h4>
</dt>
<dd>
<div class="description">
<p>This class represents a Choleksy LL^T factorization of a square positive definite<br>
<a href="module-LinearAlgebra.SparseMatrix.html">SparseMatrix</a>. The factorization is computed on the first call to solvePositiveDefinite,<br>
and is reused in subsequent calls to solvePositiveDefinite (e.g. when only the<br>
right hand side b of the linear system Ax = b changes) unless the sparse matrix<br>
itself is altered through operations such as *=, += and -=. Do not use the constructor<br>
to initialize this class, instead access the Choleksy factorization of a sparse<br>
matrix directly from the matrix itself.</p>
</div>
<dl class="details">
</dl>
<h5>Example</h5>
<pre class="sunlight-highlight-javascript">// solve the linear system Ax = b, where A is a square positive definite sparse matrix
let A = SparseMatrix.identity(5, 5);
let b = DenseMatrix.ones(5, 1);
let llt = A.chol();
let x = llt.solvePositiveDefinite(b);
b.scaleBy(5);
x = llt.solvePositiveDefinite(b); // factorization is reused</pre>
</dd>
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<h3 class="subsection-title">Methods</h3>
<dl>
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<dt>
<h4 class="name" id="solvePositiveDefinite"><span class="type-signature"></span>solvePositiveDefinite(b)</h4>
</dt>
<dd>
<div class="description">
<p>Solves the linear system Ax = b, where A is a square positive definite sparse matrix.</p>
</div>
<h5>Parameters:</h5>
<table class="params table table-striped">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
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<td class="name"><code>b</code></td>
<td class="type">
<span class="param-type"><a href="module-LinearAlgebra.DenseMatrix.html">module:LinearAlgebra.DenseMatrix</a></span>
</td>
<td class="description last"><p>The dense right hand side of the linear system Ax = b.</p></td>
</tr>
</tbody>
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<dl class="details">
</dl>
<h5>Returns:</h5>
<dl>
<dt>
Type
</dt>
<dd>
<span class="param-type"><a href="module-LinearAlgebra.DenseMatrix.html">module:LinearAlgebra.DenseMatrix</a></span>
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