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<li class="navelem"><a class="el" href="namespace_quant_lib.html">QuantLib</a></li><li class="navelem"><a class="el" href="class_quant_lib_1_1_symmetric_schur_decomposition.html">SymmetricSchurDecomposition</a></li> </ul>
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<div class="title">SymmetricSchurDecomposition Class Reference</div> </div>
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<p>symmetric threshold Jacobi algorithm.
<a href="class_quant_lib_1_1_symmetric_schur_decomposition.html#details">More...</a></p>
<p><code>#include <ql/math/matrixutilities/symmetricschurdecomposition.hpp></code></p>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a43ff4c0e9abb6877c224127f7b70e8e6"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_symmetric_schur_decomposition.html#a43ff4c0e9abb6877c224127f7b70e8e6">SymmetricSchurDecomposition</a> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &s)</td></tr>
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const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td><td class="memItemRight" valign="bottom"><b>eigenvalues</b> () const</td></tr>
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const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><b>eigenvectors</b> () const</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>symmetric threshold Jacobi algorithm. </p>
<p>Given a real symmetric matrix S, the Schur decomposition finds the eigenvalues and eigenvectors of S. If D is the diagonal matrix formed by the eigenvalues and U the unitarian matrix of the eigenvectors we can write the Schur decomposition as </p><p class="formulaDsp">
\[ S = U \cdot D \cdot U^T \, ,\]
</p>
<p> where \( \cdot \) is the standard matrix product and \( ^T \) is the transpose operator. This class implements the Schur decomposition using the symmetric threshold Jacobi algorithm. For details on the different Jacobi transfomations see "Matrix computation," second edition, by Golub and Van Loan, The Johns Hopkins University Press</p>
<dl class="test"><dt><b><a class="el" href="test.html#_test000056">Tests:</a></b></dt><dd>the correctness of the returned values is tested by checking their properties. </dd></dl>
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<h2 class="memtitle"><span class="permalink"><a href="#a43ff4c0e9abb6877c224127f7b70e8e6">◆ </a></span>SymmetricSchurDecomposition()</h2>
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<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td>
<td class="paramname"><em>s</em></td><td>)</td>
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<dl class="section pre"><dt>Precondition</dt><dd>s must be symmetric </dd></dl>
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