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<h1 class="page-title">Class: ComplexCholesky</h1>
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<h2>
<span class="ancestors"><a href="module-LinearAlgebra.html">LinearAlgebra</a>.</span>
ComplexCholesky
</h2>
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<dt>
<h4 class="name" id="ComplexCholesky"><span class="type-signature"></span>new ComplexCholesky()</h4>
</dt>
<dd>
<div class="description">
<p>This class represents a complex Choleksy LL^T factorization of a square and<br>
positive definite <a href="module-LinearAlgebra.ComplexSparseMatrix.html">ComplexSparseMatrix</a>. The factorization is computed on the<br>
first call to solvePositiveDefinite, and is reused in subsequent calls to<br>
solvePositiveDefinite (e.g. when only the right hand side b of the linear system<br>
Ax = b changes) unless the complex sparse matrix itself is altered through<br>
operations such as *=, += and -=. Do not use the constructor to initialize<br>
this class, instead access the complex Choleksy factorization of a complex<br>
sparse 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
// and complex positive definite sparse matrix
let A = ComplexSparseMatrix.identity(5, 5);
let b = ComplexDenseMatrix.ones(5, 1);
let llt = A.chol();
let x = llt.solvePositiveDefinite(b);
b.scaleBy(new Complex(5, 0));
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 and complex positive<br>
definite sparse matrix.</p>
</div>
<h5>Parameters:</h5>
<table class="params table table-striped">
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<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.ComplexDenseMatrix.html">module:LinearAlgebra.ComplexDenseMatrix</a></span>
</td>
<td class="description last"><p>The complex 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.ComplexDenseMatrix.html">module:LinearAlgebra.ComplexDenseMatrix</a></span>
</dd>
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