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<div class="title">ComplexSchur< _MatrixType > Class Template Reference<div class="ingroups"><a class="el" href="group__Eigenvalues__Module.html">Eigenvalues module</a></div></div> </div>
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<div class="textblock"><h3>template<typename _MatrixType><br/>
class Eigen::ComplexSchur< _MatrixType ></h3>
<p>Performs a complex Schur decomposition of a real or complex square matrix. </p>
<p>This is defined in the Eigenvalues module.</p>
<div class="fragment"><div class="line"><span class="preprocessor">#include <Eigen/Eigenvalues></span> </div>
</div><!-- fragment --><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">_MatrixType</td><td>the type of the matrix of which we are computing the Schur decomposition; this is expected to be an instantiation of the <a class="el" href="classEigen_1_1Matrix.html" title="The matrix class, also used for vectors and row-vectors. ">Matrix</a> class template.</td></tr>
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<p>Given a real or complex square matrix A, this class computes the Schur decomposition: <img class="formulaInl" alt="$ A = U T U^*$" src="form_46.png"/> where U is a unitary complex matrix, and T is a complex upper triangular matrix. The diagonal of the matrix T corresponds to the eigenvalues of the matrix A.</p>
<p>Call the function <a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21" title="Computes Schur decomposition of given matrix. ">compute()</a> to compute the Schur decomposition of a given matrix. Alternatively, you can use the <a class="el" href="classEigen_1_1ComplexSchur.html#a797849e56b60a3cb8f80ac23e3eb73f9" title="Constructor; computes Schur decomposition of given matrix. ">ComplexSchur(const MatrixType&, bool)</a> constructor which computes the Schur decomposition at construction time. Once the decomposition is computed, you can use the <a class="el" href="classEigen_1_1ComplexSchur.html#a6a4f89228ca0a093f34029706fd13aeb" title="Returns the unitary matrix in the Schur decomposition. ">matrixU()</a> and <a class="el" href="classEigen_1_1ComplexSchur.html#a868f6394b0c189a3ee3be039d9108095" title="Returns the triangular matrix in the Schur decomposition. ">matrixT()</a> functions to retrieve the matrices U and V in the decomposition.</p>
<dl class="section note"><dt>Note</dt><dd>This code is inspired from Jampack</dd></dl>
<dl class="section see"><dt>See Also</dt><dd>class <a class="el" href="classEigen_1_1RealSchur.html" title="Performs a real Schur decomposition of a square matrix. ">RealSchur</a>, class <a class="el" href="classEigen_1_1EigenSolver.html" title="Computes eigenvalues and eigenvectors of general matrices. ">EigenSolver</a>, class <a class="el" href="classEigen_1_1ComplexEigenSolver.html" title="Computes eigenvalues and eigenvectors of general complex matrices. ">ComplexEigenSolver</a> </dd></dl>
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Public Types</h2></td></tr>
<tr class="memitem:a1333fc417f8ad137effb6a7f751337e5"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>< <a class="el" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>, <br class="typebreak"/>
RowsAtCompileTime, <br class="typebreak"/>
ColsAtCompileTime, Options, <br class="typebreak"/>
MaxRowsAtCompileTime, <br class="typebreak"/>
MaxColsAtCompileTime > </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5">ComplexMatrixType</a></td></tr>
<tr class="memdesc:a1333fc417f8ad137effb6a7f751337e5"><td class="mdescLeft"> </td><td class="mdescRight">Type for the matrices in the Schur decomposition. <a href="#a1333fc417f8ad137effb6a7f751337e5">More...</a><br/></td></tr>
<tr class="separator:a1333fc417f8ad137effb6a7f751337e5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1b9bc0a45616064df3a6168395e3cfcc"><td class="memItemLeft" align="right" valign="top">typedef std::complex< RealScalar > </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a></td></tr>
<tr class="memdesc:a1b9bc0a45616064df3a6168395e3cfcc"><td class="mdescLeft"> </td><td class="mdescRight">Complex scalar type for <code>_MatrixType</code>. <a href="#a1b9bc0a45616064df3a6168395e3cfcc">More...</a><br/></td></tr>
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typedef MatrixType::Scalar </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a></td></tr>
<tr class="memdesc:a3f6fc00047c205ee590f676934aab28f"><td class="mdescLeft"> </td><td class="mdescRight">Scalar type for matrices of type <code>_MatrixType</code>. <br/></td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a9ba3a59c1e385a4a5a80c08bf40f8fd1"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a9ba3a59c1e385a4a5a80c08bf40f8fd1">ComplexSchur</a> (Index size=RowsAtCompileTime==<a class="el" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a>?1:RowsAtCompileTime)</td></tr>
<tr class="memdesc:a9ba3a59c1e385a4a5a80c08bf40f8fd1"><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <a href="#a9ba3a59c1e385a4a5a80c08bf40f8fd1">More...</a><br/></td></tr>
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<tr class="memitem:a797849e56b60a3cb8f80ac23e3eb73f9"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a797849e56b60a3cb8f80ac23e3eb73f9">ComplexSchur</a> (const MatrixType &matrix, bool computeU=true)</td></tr>
<tr class="memdesc:a797849e56b60a3cb8f80ac23e3eb73f9"><td class="mdescLeft"> </td><td class="mdescRight">Constructor; computes Schur decomposition of given matrix. <a href="#a797849e56b60a3cb8f80ac23e3eb73f9">More...</a><br/></td></tr>
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<tr class="memitem:af6c75391a881ca5e56d9aac55f838e21"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21">compute</a> (const MatrixType &matrix, bool computeU=true)</td></tr>
<tr class="memdesc:af6c75391a881ca5e56d9aac55f838e21"><td class="mdescLeft"> </td><td class="mdescRight">Computes Schur decomposition of given matrix. <a href="#af6c75391a881ca5e56d9aac55f838e21">More...</a><br/></td></tr>
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<tr class="memitem:afd453e43385a3b38cb2ddd32d97c5eb7"><td class="memTemplParams" colspan="2">template<typename HessMatrixType , typename OrthMatrixType > </td></tr>
<tr class="memitem:afd453e43385a3b38cb2ddd32d97c5eb7"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#afd453e43385a3b38cb2ddd32d97c5eb7">computeFromHessenberg</a> (const HessMatrixType &matrixH, const OrthMatrixType &matrixQ, bool computeU=true)</td></tr>
<tr class="memdesc:afd453e43385a3b38cb2ddd32d97c5eb7"><td class="mdescLeft"> </td><td class="mdescRight">Compute Schur decomposition from a given Hessenberg matrix. <a href="#afd453e43385a3b38cb2ddd32d97c5eb7">More...</a><br/></td></tr>
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<tr class="memitem:ab6f0a63ea1d26cef5e748207043eb43e"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab6f0a63ea1d26cef5e748207043eb43e"></a>
Index </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#ab6f0a63ea1d26cef5e748207043eb43e">getMaxIterations</a> ()</td></tr>
<tr class="memdesc:ab6f0a63ea1d26cef5e748207043eb43e"><td class="mdescLeft"> </td><td class="mdescRight">Returns the maximum number of iterations. <br/></td></tr>
<tr class="separator:ab6f0a63ea1d26cef5e748207043eb43e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0c06d5c2034ebb329c54235369643ad2"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a0c06d5c2034ebb329c54235369643ad2">info</a> () const </td></tr>
<tr class="memdesc:a0c06d5c2034ebb329c54235369643ad2"><td class="mdescLeft"> </td><td class="mdescRight">Reports whether previous computation was successful. <a href="#a0c06d5c2034ebb329c54235369643ad2">More...</a><br/></td></tr>
<tr class="separator:a0c06d5c2034ebb329c54235369643ad2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a868f6394b0c189a3ee3be039d9108095"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5">ComplexMatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a868f6394b0c189a3ee3be039d9108095">matrixT</a> () const </td></tr>
<tr class="memdesc:a868f6394b0c189a3ee3be039d9108095"><td class="mdescLeft"> </td><td class="mdescRight">Returns the triangular matrix in the Schur decomposition. <a href="#a868f6394b0c189a3ee3be039d9108095">More...</a><br/></td></tr>
<tr class="separator:a868f6394b0c189a3ee3be039d9108095"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6a4f89228ca0a093f34029706fd13aeb"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5">ComplexMatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a6a4f89228ca0a093f34029706fd13aeb">matrixU</a> () const </td></tr>
<tr class="memdesc:a6a4f89228ca0a093f34029706fd13aeb"><td class="mdescLeft"> </td><td class="mdescRight">Returns the unitary matrix in the Schur decomposition. <a href="#a6a4f89228ca0a093f34029706fd13aeb">More...</a><br/></td></tr>
<tr class="separator:a6a4f89228ca0a093f34029706fd13aeb"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8178c4999e63b2bfbdc424ff84a91b10"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a8178c4999e63b2bfbdc424ff84a91b10">setMaxIterations</a> (Index maxIters)</td></tr>
<tr class="memdesc:a8178c4999e63b2bfbdc424ff84a91b10"><td class="mdescLeft"> </td><td class="mdescRight">Sets the maximum number of iterations allowed. <a href="#a8178c4999e63b2bfbdc424ff84a91b10">More...</a><br/></td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-attribs"></a>
Static Public Attributes</h2></td></tr>
<tr class="memitem:afdafb24d67af7529bb903a4c9bff3ea4"><td class="memItemLeft" align="right" valign="top">static const int </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#afdafb24d67af7529bb903a4c9bff3ea4">m_maxIterationsPerRow</a></td></tr>
<tr class="memdesc:afdafb24d67af7529bb903a4c9bff3ea4"><td class="mdescLeft"> </td><td class="mdescRight">Maximum number of iterations per row. <a href="#afdafb24d67af7529bb903a4c9bff3ea4">More...</a><br/></td></tr>
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<h2 class="groupheader">Member Typedef Documentation</h2>
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<td class="memname">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a><<a class="el" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> <a class="el" href="classEigen_1_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5">ComplexMatrixType</a></td>
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<p>Type for the matrices in the Schur decomposition. </p>
<p>This is a square matrix with entries of type <a class="el" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc" title="Complex scalar type for _MatrixType. ">ComplexScalar</a>. The size is the same as the size of <code>_MatrixType</code>. </p>
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<td class="memname">typedef std::complex<RealScalar> <a class="el" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a></td>
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<p>Complex scalar type for <code>_MatrixType</code>. </p>
<p>This is <code>std::complex<Scalar></code> if <a class="el" href="classEigen_1_1ComplexSchur.html#a3f6fc00047c205ee590f676934aab28f" title="Scalar type for matrices of type _MatrixType. ">Scalar</a> is real (e.g., <code>float</code> or <code>double</code>) and just <code>Scalar</code> if <a class="el" href="classEigen_1_1ComplexSchur.html#a3f6fc00047c205ee590f676934aab28f" title="Scalar type for matrices of type _MatrixType. ">Scalar</a> is complex. </p>
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<h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<td class="memname"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> </td>
<td>(</td>
<td class="paramtype">Index </td>
<td class="paramname"><em>size</em> = <code>RowsAtCompileTime==<a class="el" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? 1 : RowsAtCompileTime</code></td><td>)</td>
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<p>Default constructor. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramdir">[in]</td><td class="paramname">size</td><td>Positive integer, size of the matrix whose Schur decomposition will be computed.</td></tr>
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<p>The default constructor is useful in cases in which the user intends to perform decompositions via <a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21" title="Computes Schur decomposition of given matrix. ">compute()</a>. The <code>size</code> parameter is only used as a hint. It is not an error to give a wrong <code>size</code>, but it may impair performance.</p>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21" title="Computes Schur decomposition of given matrix. ">compute()</a> for an example. </dd></dl>
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<td class="memname"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> </td>
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<p>Constructor; computes Schur decomposition of given matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Square matrix whose Schur decomposition is to be computed. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">computeU</td><td>If true, both T and U are computed; if false, only T is computed.</td></tr>
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<p>This constructor calls <a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21" title="Computes Schur decomposition of given matrix. ">compute()</a> to compute the Schur decomposition.</p>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1ComplexSchur.html#a868f6394b0c189a3ee3be039d9108095" title="Returns the triangular matrix in the Schur decomposition. ">matrixT()</a> and <a class="el" href="classEigen_1_1ComplexSchur.html#a6a4f89228ca0a093f34029706fd13aeb" title="Returns the unitary matrix in the Schur decomposition. ">matrixU()</a> for examples. </dd></dl>
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<h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>< MatrixType > & compute </td>
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<p>Computes Schur decomposition of given matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Square matrix whose Schur decomposition is to be computed. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">computeU</td><td>If true, both T and U are computed; if false, only T is computed.</td></tr>
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<dl class="section return"><dt>Returns</dt><dd>Reference to <code>*this</code> </dd></dl>
<p>The Schur decomposition is computed by first reducing the matrix to Hessenberg form using the class <a class="el" href="classEigen_1_1HessenbergDecomposition.html" title="Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation. ">HessenbergDecomposition</a>. The Hessenberg matrix is then reduced to triangular form by performing QR iterations with a single shift. The cost of computing the Schur decomposition depends on the number of iterations; as a rough guide, it may be taken on the number of iterations; as a rough guide, it may be taken to be <img class="formulaInl" alt="$25n^3$" src="form_47.png"/> complex flops, or <img class="formulaInl" alt="$10n^3$" src="form_48.png"/> complex flops if <em>computeU</em> is false.</p>
<p>Example: </p>
<div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#gaec02f1e32a13e5997899a554105ebfd4">MatrixXcf</a> A = <a class="code" href="classEigen_1_1DenseBase.html#a8e759dafdd9ecc446d397b7f5435f60a">MatrixXcf::Random</a>(4,4);</div>
<div class="line">ComplexSchur<MatrixXcf> schur(4);</div>
<div class="line">schur.compute(A);</div>
<div class="line">cout << <span class="stringliteral">"The matrix T in the decomposition of A is:"</span> << endl << schur.matrixT() << endl;</div>
<div class="line">schur.compute(A.inverse());</div>
<div class="line">cout << <span class="stringliteral">"The matrix T in the decomposition of A^(-1) is:"</span> << endl << schur.matrixT() << endl;</div>
</div><!-- fragment --><p> Output: </p>
<pre class="fragment">The matrix T in the decomposition of A is:
(-0.691,-1.63) (0.763,-0.144) (-0.104,-0.836) (-0.462,-0.378)
(0,0) (-0.758,1.22) (-0.65,-0.772) (-0.244,0.113)
(0,0) (0,0) (0.137,0.505) (0.0687,-0.404)
(0,0) (0,0) (0,0) (1.52,-0.402)
The matrix T in the decomposition of A^(-1) is:
(0.501,-1.84) (-1.01,-0.984) (0.636,1.3) (-0.676,0.352)
(0,0) (-0.369,-0.593) (0.0733,0.18) (-0.0658,-0.0263)
(0,0) (0,0) (-0.222,0.521) (-0.191,0.121)
(0,0) (0,0) (0,0) (0.614,0.162)
</pre><dl class="section see"><dt>See Also</dt><dd>compute(const MatrixType&, bool, Index) </dd></dl>
<p>References <a class="el" href="classEigen_1_1ComplexSchur.html#afd453e43385a3b38cb2ddd32d97c5eb7">ComplexSchur< _MatrixType >::computeFromHessenberg()</a>, and <a class="el" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Eigen::Success</a>.</p>
<p>Referenced by <a class="el" href="classEigen_1_1ComplexSchur.html#a797849e56b60a3cb8f80ac23e3eb73f9">ComplexSchur< MatrixType >::ComplexSchur()</a>.</p>
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<td class="memname"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>& computeFromHessenberg </td>
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<td class="paramtype">const HessMatrixType & </td>
<td class="paramname"><em>matrixH</em>, </td>
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<p>Compute Schur decomposition from a given Hessenberg matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramdir">[in]</td><td class="paramname">matrixH</td><td><a class="el" href="classEigen_1_1Matrix.html" title="The matrix class, also used for vectors and row-vectors. ">Matrix</a> in Hessenberg form H </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">matrixQ</td><td>orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T </td></tr>
<tr><td class="paramdir"></td><td class="paramname">computeU</td><td>Computes the matriX U of the Schur vectors </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>Reference to <code>*this</code> </dd></dl>
<p>This routine assumes that the matrix is already reduced in Hessenberg form matrixH using either the class <a class="el" href="classEigen_1_1HessenbergDecomposition.html" title="Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation. ">HessenbergDecomposition</a> or another mean. It computes the upper quasi-triangular matrix T of the Schur decomposition of H When computeU is true, this routine computes the matrix U such that A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix</p>
<p>NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix is not available, the user should give an identity matrix (Q.setIdentity())</p>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21" title="Computes Schur decomposition of given matrix. ">compute(const MatrixType&, bool)</a> </dd></dl>
<p>Referenced by <a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21">ComplexSchur< _MatrixType >::compute()</a>.</p>
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<td class="memname"><a class="el" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> info </td>
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<p>Reports whether previous computation was successful. </p>
<dl class="section return"><dt>Returns</dt><dd><code>Success</code> if computation was succesful, <code>NoConvergence</code> otherwise. </dd></dl>
<p>Referenced by <a class="el" href="classEigen_1_1ComplexEigenSolver.html#a0c06d5c2034ebb329c54235369643ad2">ComplexEigenSolver< _MatrixType >::info()</a>.</p>
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<td class="memname">const <a class="el" href="classEigen_1_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5">ComplexMatrixType</a>& matrixT </td>
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<p>Returns the triangular matrix in the Schur decomposition. </p>
<dl class="section return"><dt>Returns</dt><dd>A const reference to the matrix T.</dd></dl>
<p>It is assumed that either the constructor <a class="el" href="classEigen_1_1ComplexSchur.html#a797849e56b60a3cb8f80ac23e3eb73f9" title="Constructor; computes Schur decomposition of given matrix. ">ComplexSchur(const MatrixType& matrix, bool computeU)</a> or the member function <a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21" title="Computes Schur decomposition of given matrix. ">compute(const MatrixType& matrix, bool computeU)</a> has been called before to compute the Schur decomposition of a matrix.</p>
<p>Note that this function returns a plain square matrix. If you want to reference only the upper triangular part, use: </p>
<div class="fragment"><div class="line">schur.matrixT().triangularView<<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910bae70afef0d3ff7aca74e17e85ff6c9f2e">Upper</a>>() </div>
</div><!-- fragment --><p>Example: </p>
<div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#gaec02f1e32a13e5997899a554105ebfd4">MatrixXcf</a> A = <a class="code" href="classEigen_1_1DenseBase.html#a8e759dafdd9ecc446d397b7f5435f60a">MatrixXcf::Random</a>(4,4);</div>
<div class="line">cout << <span class="stringliteral">"Here is a random 4x4 matrix, A:"</span> << endl << A << endl << endl;</div>
<div class="line">ComplexSchur<MatrixXcf> schurOfA(A, <span class="keyword">false</span>); <span class="comment">// false means do not compute U</span></div>
<div class="line">cout << <span class="stringliteral">"The triangular matrix T is:"</span> << endl << schurOfA.matrixT() << endl;</div>
</div><!-- fragment --><p> Output: </p>
<pre class="fragment">Here is a random 4x4 matrix, A:
(-0.211,0.68) (0.108,-0.444) (0.435,0.271) (-0.198,-0.687)
(0.597,0.566) (0.258,-0.0452) (0.214,-0.717) (-0.782,-0.74)
(-0.605,0.823) (0.0268,-0.27) (-0.514,-0.967) (-0.563,0.998)
(0.536,-0.33) (0.832,0.904) (0.608,-0.726) (0.678,0.0259)
The triangular matrix T is:
(-0.691,-1.63) (0.763,-0.144) (-0.104,-0.836) (-0.462,-0.378)
(0,0) (-0.758,1.22) (-0.65,-0.772) (-0.244,0.113)
(0,0) (0,0) (0.137,0.505) (0.0687,-0.404)
(0,0) (0,0) (0,0) (1.52,-0.402)
</pre>
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<td class="memname">const <a class="el" href="classEigen_1_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5">ComplexMatrixType</a>& matrixU </td>
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<p>Returns the unitary matrix in the Schur decomposition. </p>
<dl class="section return"><dt>Returns</dt><dd>A const reference to the matrix U.</dd></dl>
<p>It is assumed that either the constructor <a class="el" href="classEigen_1_1ComplexSchur.html#a797849e56b60a3cb8f80ac23e3eb73f9" title="Constructor; computes Schur decomposition of given matrix. ">ComplexSchur(const MatrixType& matrix, bool computeU)</a> or the member function <a class="el" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21" title="Computes Schur decomposition of given matrix. ">compute(const MatrixType& matrix, bool computeU)</a> has been called before to compute the Schur decomposition of a matrix, and that <code>computeU</code> was set to true (the default value).</p>
<p>Example: </p>
<div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#gaec02f1e32a13e5997899a554105ebfd4">MatrixXcf</a> A = <a class="code" href="classEigen_1_1DenseBase.html#a8e759dafdd9ecc446d397b7f5435f60a">MatrixXcf::Random</a>(4,4);</div>
<div class="line">cout << <span class="stringliteral">"Here is a random 4x4 matrix, A:"</span> << endl << A << endl << endl;</div>
<div class="line">ComplexSchur<MatrixXcf> schurOfA(A);</div>
<div class="line">cout << <span class="stringliteral">"The unitary matrix U is:"</span> << endl << schurOfA.matrixU() << endl;</div>
</div><!-- fragment --><p> Output: </p>
<pre class="fragment">Here is a random 4x4 matrix, A:
(-0.211,0.68) (0.108,-0.444) (0.435,0.271) (-0.198,-0.687)
(0.597,0.566) (0.258,-0.0452) (0.214,-0.717) (-0.782,-0.74)
(-0.605,0.823) (0.0268,-0.27) (-0.514,-0.967) (-0.563,0.998)
(0.536,-0.33) (0.832,0.904) (0.608,-0.726) (0.678,0.0259)
The unitary matrix U is:
(-0.122,0.271) (0.354,0.255) (-0.7,0.321) (0.0909,-0.346)
(0.247,0.23) (0.435,-0.395) (0.184,-0.38) (0.492,-0.347)
(0.859,-0.0877) (0.00469,0.21) (-0.256,0.0163) (0.133,0.355)
(-0.116,0.195) (-0.484,-0.432) (-0.183,0.359) (0.559,0.231)
</pre>
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<td class="memname"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>& setMaxIterations </td>
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<td class="paramname"><em>maxIters</em></td><td>)</td>
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<p>Sets the maximum number of iterations allowed. </p>
<p>If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size of the matrix. </p>
<p>Referenced by <a class="el" href="classEigen_1_1ComplexEigenSolver.html#a3b1b6c1fccb22b96c7ecc6d8c0a11a1e">ComplexEigenSolver< _MatrixType >::setMaxIterations()</a>.</p>
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<h2 class="groupheader">Member Data Documentation</h2>
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<td class="memname">const int m_maxIterationsPerRow</td>
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<p>Maximum number of iterations per row. </p>
<p>If not otherwise specified, the maximum number of iterations is this number times the size of the matrix. It is currently set to 30. </p>
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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="ComplexSchur_8h_source.html">ComplexSchur.h</a></li>
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