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<li class="navelem"><a class="el" href="namespace_eigen.html">Eigen</a> </li>
<li class="navelem"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html">ComplexEigenSolver</a> </li>
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<a href="#pub-types">Public Types</a> |
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<div class="title">Eigen::ComplexEigenSolver Class Reference<div class="ingroups"><a class="el" href="group___eigenvalues___module.html">Eigenvalues module</a></div></div> </div>
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<!-- doxytag: class="Eigen::ComplexEigenSolver" --><hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Computes eigenvalues and eigenvectors of general complex matrices</p>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">_MatrixType</td><td>the type of the matrix of which we are computing the eigendecomposition; this is expected to be an instantiation of the <a class="el" href="class_eigen_1_1_matrix.html" title="The matrix class, also used for vectors and row-vectors.">Matrix</a> class template.</td></tr>
</table>
</dd>
</dl>
<p>The eigenvalues and eigenvectors of a matrix <img class="formulaInl" alt="$ A $" src="form_128.png"/> are scalars <img class="formulaInl" alt="$ \lambda $" src="form_168.png"/> and vectors <img class="formulaInl" alt="$ v $" src="form_144.png"/> such that <img class="formulaInl" alt="$ Av = \lambda v $" src="form_169.png"/>. If <img class="formulaInl" alt="$ D $" src="form_170.png"/> is a diagonal matrix with the eigenvalues on the diagonal, and <img class="formulaInl" alt="$ V $" src="form_171.png"/> is a matrix with the eigenvectors as its columns, then <img class="formulaInl" alt="$ A V = V D $" src="form_172.png"/>. The matrix <img class="formulaInl" alt="$ V $" src="form_171.png"/> is almost always invertible, in which case we have <img class="formulaInl" alt="$ A = V D V^{-1} $" src="form_173.png"/>. This is called the eigendecomposition.</p>
<p>The main function in this class is <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a46c55fd0cc9f188569710e6b55363167" title="Computes eigendecomposition of given matrix.">compute()</a>, which computes the eigenvalues and eigenvectors of a given function. The documentation for that function contains an example showing the main features of the class.</p>
<dl class="see"><dt><b>See also:</b></dt><dd>class <a class="el" href="class_eigen_1_1_eigen_solver.html">EigenSolver</a>, class <a class="el" href="class_eigen_1_1_self_adjoint_eigen_solver.html">SelfAdjointEigenSolver</a> </dd></dl>
</div>
<p><a href="class_eigen_1_1_complex_eigen_solver-members.html">List of all members.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">enum  </td><td class="memItemRight" valign="bottom">{ <br/>
  <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1c2a1c1a128d08e43f2c39097f5d2869aa611f4906e81b0ddaafb0ba828ca828c">RowsAtCompileTime</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1c2a1c1a128d08e43f2c39097f5d2869a757e4bf47ca1263eb460ade9460687dd">ColsAtCompileTime</a> = MatrixType::ColsAtCompileTime,
<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1c2a1c1a128d08e43f2c39097f5d2869a550449fd2af3dfd449b4581aa098c39f">Options</a> = MatrixType::Options,
<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1c2a1c1a128d08e43f2c39097f5d2869a8dcf81470f5725bdb422b998eeddaf0d">MaxRowsAtCompileTime</a> = MatrixType::MaxRowsAtCompileTime,
<br/>
  <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1c2a1c1a128d08e43f2c39097f5d2869a487ef8e80e9832628c86a9ba2bd6c6e6">MaxColsAtCompileTime</a> = MatrixType::MaxColsAtCompileTime
<br/>
}</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef _MatrixType </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044">MatrixType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Synonym for the template parameter <code>_MatrixType</code>. <a href="#a666247cd2d09d9f6a4c61833e56af044"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef MatrixType::Scalar </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af353ed560fcab6e61bc8720ed69069ad">Scalar</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Scalar type for matrices of type <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044" title="Synonym for the template parameter _MatrixType.">MatrixType</a>. <a href="#af353ed560fcab6e61bc8720ed69069ad"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a>< <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af353ed560fcab6e61bc8720ed69069ad">Scalar</a> >::Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af8631e913fed82cdae941dd03fe8962a">RealScalar</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef MatrixType::Index </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a2e68a6469c18e9408c119684f11784cc">Index</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classstd_1_1complex.html">std::complex</a>< <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af8631e913fed82cdae941dd03fe8962a">RealScalar</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1be5536a07ec3fb084db0226e5885f2e">ComplexScalar</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Complex scalar type for <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044" title="Synonym for the template parameter _MatrixType.">MatrixType</a>. <a href="#a1be5536a07ec3fb084db0226e5885f2e"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="class_eigen_1_1_matrix.html">Matrix</a>< <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1be5536a07ec3fb084db0226e5885f2e">ComplexScalar</a>, <br class="typebreak"/>
ColsAtCompileTime, 1, Options <br class="typebreak"/>
&(~RowMajor), <br class="typebreak"/>
MaxColsAtCompileTime, 1 > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a6992daec05a0149c178dc86c59610b8c">EigenvalueType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Type for vector of eigenvalues as returned by <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#addd3beba6fe3dc854923e5d84738c02e" title="Returns the eigenvalues of given matrix.">eigenvalues()</a>. <a href="#a6992daec05a0149c178dc86c59610b8c"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="class_eigen_1_1_matrix.html">Matrix</a>< <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1be5536a07ec3fb084db0226e5885f2e">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="class_eigen_1_1_complex_eigen_solver.html#a134eaafcc1e9aa20baedadb31900bcae">EigenvectorType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Type for matrix of eigenvectors as returned by <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#acfa5e9870305d3874bb213e8bc545283" title="Returns the eigenvectors of given matrix.">eigenvectors()</a>. <a href="#a134eaafcc1e9aa20baedadb31900bcae"></a><br/></td></tr>
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a4b64d7a2a851cab240a40adcd3cb3cab">ComplexEigenSolver</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <a href="#a4b64d7a2a851cab240a40adcd3cb3cab"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a91ba2d24da6b061fb0fef6b934f9916d">ComplexEigenSolver</a> (<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a2e68a6469c18e9408c119684f11784cc">Index</a> size)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor with memory preallocation. <a href="#a91ba2d24da6b061fb0fef6b934f9916d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a22fd738bfa540b543f27e220b51a70ec">ComplexEigenSolver</a> (const <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044">MatrixType</a> &matrix, bool computeEigenvectors=true)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor; computes eigendecomposition of given matrix. <a href="#a22fd738bfa540b543f27e220b51a70ec"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a134eaafcc1e9aa20baedadb31900bcae">EigenvectorType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#acfa5e9870305d3874bb213e8bc545283">eigenvectors</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the eigenvectors of given matrix. <a href="#acfa5e9870305d3874bb213e8bc545283"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a6992daec05a0149c178dc86c59610b8c">EigenvalueType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#addd3beba6fe3dc854923e5d84738c02e">eigenvalues</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the eigenvalues of given matrix. <a href="#addd3beba6fe3dc854923e5d84738c02e"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html">ComplexEigenSolver</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a46c55fd0cc9f188569710e6b55363167">compute</a> (const <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044">MatrixType</a> &matrix, bool computeEigenvectors=true)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes eigendecomposition of given matrix. <a href="#a46c55fd0cc9f188569710e6b55363167"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespace_eigen.html#a85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a40a2b6946d19902738e9818d592adf03">info</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Reports whether previous computation was successful. <a href="#a40a2b6946d19902738e9818d592adf03"></a><br/></td></tr>
<tr><td colspan="2"><h2><a name="pro-attribs"></a>
Protected Attributes</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a134eaafcc1e9aa20baedadb31900bcae">EigenvectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a18a4c512bc013720e2951993e43c61d2">m_eivec</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a6992daec05a0149c178dc86c59610b8c">EigenvalueType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a7e0a02c12a7f3d2553e5551ab3f3b101">m_eivalues</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_complex_schur.html">ComplexSchur</a>< <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044">MatrixType</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a6aeea78ce18b2a39ee700bf60391c757">m_schur</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a2801a3c72dc42cde3f13c65d71a5c9ef">m_isInitialized</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#aabd1f4a7801ad90cbdf267fe60a52d7d">m_eigenvectorsOk</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a134eaafcc1e9aa20baedadb31900bcae">EigenvectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#adca8e49feebf609d30d6c1d0cefc67eb">m_matX</a></td></tr>
<tr><td colspan="2"><h2><a name="pri-methods"></a>
Private Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#adf0d23ac2690d464f3d6634e6d8158b9">doComputeEigenvectors</a> (<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af8631e913fed82cdae941dd03fe8962a">RealScalar</a> matrixnorm)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a299c8e57c239444552bcf1b6181a5667">sortEigenvalues</a> (bool computeEigenvectors)</td></tr>
</table>
<hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="a1be5536a07ec3fb084db0226e5885f2e"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::ComplexScalar" ref="a1be5536a07ec3fb084db0226e5885f2e" args="" -->
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<td class="memname">typedef <a class="el" href="classstd_1_1complex.html">std::complex</a><<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af8631e913fed82cdae941dd03fe8962a">RealScalar</a>> <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1be5536a07ec3fb084db0226e5885f2e">Eigen::ComplexEigenSolver::ComplexScalar</a></td>
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<p>Complex scalar type for <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044" title="Synonym for the template parameter _MatrixType.">MatrixType</a>. </p>
<p>This is <code>std::complex<Scalar></code> if <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af353ed560fcab6e61bc8720ed69069ad" 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="class_eigen_1_1_complex_eigen_solver.html#af353ed560fcab6e61bc8720ed69069ad" title="Scalar type for matrices of type MatrixType.">Scalar</a> is complex. </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00085">85</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a6992daec05a0149c178dc86c59610b8c"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::EigenvalueType" ref="a6992daec05a0149c178dc86c59610b8c" args="" -->
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_matrix.html">Matrix</a><<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1be5536a07ec3fb084db0226e5885f2e">ComplexScalar</a>, ColsAtCompileTime, 1, Options&(~RowMajor), MaxColsAtCompileTime, 1> <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a6992daec05a0149c178dc86c59610b8c">Eigen::ComplexEigenSolver::EigenvalueType</a></td>
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<p>Type for vector of eigenvalues as returned by <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#addd3beba6fe3dc854923e5d84738c02e" title="Returns the eigenvalues of given matrix.">eigenvalues()</a>. </p>
<p>This is a column vector with entries of type <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1be5536a07ec3fb084db0226e5885f2e" title="Complex scalar type for MatrixType.">ComplexScalar</a>. The length of the vector is the size of <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044" title="Synonym for the template parameter _MatrixType.">MatrixType</a>. </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00092">92</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a134eaafcc1e9aa20baedadb31900bcae"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::EigenvectorType" ref="a134eaafcc1e9aa20baedadb31900bcae" args="" -->
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_matrix.html">Matrix</a><<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1be5536a07ec3fb084db0226e5885f2e">ComplexScalar</a>, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a134eaafcc1e9aa20baedadb31900bcae">Eigen::ComplexEigenSolver::EigenvectorType</a></td>
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<p>Type for matrix of eigenvectors as returned by <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#acfa5e9870305d3874bb213e8bc545283" title="Returns the eigenvectors of given matrix.">eigenvectors()</a>. </p>
<p>This is a square matrix with entries of type <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a1be5536a07ec3fb084db0226e5885f2e" title="Complex scalar type for MatrixType.">ComplexScalar</a>. The size is the same as the size of <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044" title="Synonym for the template parameter _MatrixType.">MatrixType</a>. </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00099">99</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a2e68a6469c18e9408c119684f11784cc">Eigen::ComplexEigenSolver::Index</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00077">77</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044">Eigen::ComplexEigenSolver::MatrixType</a></td>
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<p>Synonym for the template parameter <code>_MatrixType</code>. </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00064">64</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="af8631e913fed82cdae941dd03fe8962a"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::RealScalar" ref="af8631e913fed82cdae941dd03fe8962a" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a><<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af353ed560fcab6e61bc8720ed69069ad">Scalar</a>>::Real <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af8631e913fed82cdae941dd03fe8962a">Eigen::ComplexEigenSolver::RealScalar</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00076">76</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="af353ed560fcab6e61bc8720ed69069ad"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::Scalar" ref="af353ed560fcab6e61bc8720ed69069ad" args="" -->
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#af353ed560fcab6e61bc8720ed69069ad">Eigen::ComplexEigenSolver::Scalar</a></td>
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<p>Scalar type for matrices of type <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044" title="Synonym for the template parameter _MatrixType.">MatrixType</a>. </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00075">75</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<hr/><h2>Member Enumeration Documentation</h2>
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<dl><dt><b>Enumerator: </b></dt><dd><table border="0" cellspacing="2" cellpadding="0">
<tr><td valign="top"><em><a class="anchor" id="a1c2a1c1a128d08e43f2c39097f5d2869aa611f4906e81b0ddaafb0ba828ca828c"></a><!-- doxytag: member="RowsAtCompileTime" ref="a1c2a1c1a128d08e43f2c39097f5d2869aa611f4906e81b0ddaafb0ba828ca828c" args="" -->RowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a1c2a1c1a128d08e43f2c39097f5d2869a757e4bf47ca1263eb460ade9460687dd"></a><!-- doxytag: member="ColsAtCompileTime" ref="a1c2a1c1a128d08e43f2c39097f5d2869a757e4bf47ca1263eb460ade9460687dd" args="" -->ColsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a1c2a1c1a128d08e43f2c39097f5d2869a487ef8e80e9832628c86a9ba2bd6c6e6"></a><!-- doxytag: member="MaxColsAtCompileTime" ref="a1c2a1c1a128d08e43f2c39097f5d2869a487ef8e80e9832628c86a9ba2bd6c6e6" args="" -->MaxColsAtCompileTime</em> </td><td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00066">66</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="a4b64d7a2a851cab240a40adcd3cb3cab"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::ComplexEigenSolver" ref="a4b64d7a2a851cab240a40adcd3cb3cab" args="()" -->
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<td class="memname">Eigen::ComplexEigenSolver::ComplexEigenSolver </td>
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<p>Default constructor. </p>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a46c55fd0cc9f188569710e6b55363167" title="Computes eigendecomposition of given matrix.">compute()</a>. </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00106">106</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname">Eigen::ComplexEigenSolver::ComplexEigenSolver </td>
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<td class="paramtype"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a2e68a6469c18e9408c119684f11784cc">Index</a> </td>
<td class="paramname"><em>size</em></td><td>)</td>
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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a4b64d7a2a851cab240a40adcd3cb3cab" title="Default constructor.">ComplexEigenSolver()</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00121">121</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="paramtype">const <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044">MatrixType</a> & </td>
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<p>Constructor; computes eigendecomposition of given matrix. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Square matrix whose eigendecomposition is to be computed. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">computeEigenvectors</td><td>If true, both the eigenvectors and the eigenvalues are computed; if false, only the eigenvalues are computed.</td></tr>
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<p>This constructor calls <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a46c55fd0cc9f188569710e6b55363167" title="Computes eigendecomposition of given matrix.">compute()</a> to compute the eigendecomposition. </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00139">139</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<hr/><h2>Member Function Documentation</h2>
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<td class="memname"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html">ComplexEigenSolver</a>< <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044">MatrixType</a> > & Eigen::ComplexEigenSolver::compute </td>
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<p>Computes eigendecomposition of given matrix. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Square matrix whose eigendecomposition is to be computed. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">computeEigenvectors</td><td>If true, both the eigenvectors and the eigenvalues are computed; if false, only the eigenvalues are computed. </td></tr>
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<dl class="return"><dt><b>Returns:</b></dt><dd>Reference to <code>*this</code> </dd></dl>
<p>This function computes the eigenvalues of the complex matrix <code>matrix</code>. The <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#addd3beba6fe3dc854923e5d84738c02e" title="Returns the eigenvalues of given matrix.">eigenvalues()</a> function can be used to retrieve them. If <code>computeEigenvectors</code> is true, then the eigenvectors are also computed and can be retrieved by calling <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#acfa5e9870305d3874bb213e8bc545283" title="Returns the eigenvectors of given matrix.">eigenvectors()</a>.</p>
<p>The matrix is first reduced to Schur form using the <a class="el" href="class_eigen_1_1_complex_schur.html">ComplexSchur</a> class. The Schur decomposition is then used to compute the eigenvalues and eigenvectors.</p>
<p>The cost of the computation is dominated by the cost of the Schur decomposition, which is <img class="formulaInl" alt="$ O(n^3) $" src="form_208.png"/> where <img class="formulaInl" alt="$ n $" src="form_183.png"/> is the size of the matrix.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00252">252</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname">void Eigen::ComplexEigenSolver::doComputeEigenvectors </td>
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<td><code> [private]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00276">276</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname">const <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a6992daec05a0149c178dc86c59610b8c">EigenvalueType</a>& Eigen::ComplexEigenSolver::eigenvalues </td>
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<p>Returns the eigenvalues of given matrix. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>A const reference to the column vector containing the eigenvalues.</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a22fd738bfa540b543f27e220b51a70ec" title="Constructor; computes eigendecomposition of given matrix.">ComplexEigenSolver(const MatrixType& matrix, bool)</a> or the member function <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a46c55fd0cc9f188569710e6b55363167" title="Computes eigendecomposition of given matrix.">compute(const MatrixType& matrix, bool)</a> has been called before to compute the eigendecomposition of a matrix.</dd></dl>
<p>This function returns a column vector containing the eigenvalues. Eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix. The eigenvalues are not sorted in any particular order.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00195">195</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname">const <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a134eaafcc1e9aa20baedadb31900bcae">EigenvectorType</a>& Eigen::ComplexEigenSolver::eigenvectors </td>
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<p>Returns the eigenvectors of given matrix. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>A const reference to the matrix whose columns are the eigenvectors.</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a22fd738bfa540b543f27e220b51a70ec" title="Constructor; computes eigendecomposition of given matrix.">ComplexEigenSolver(const MatrixType& matrix, bool)</a> or the member function <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a46c55fd0cc9f188569710e6b55363167" title="Computes eigendecomposition of given matrix.">compute(const MatrixType& matrix, bool)</a> has been called before to compute the eigendecomposition of a matrix, and <code>computeEigenvectors</code> was set to true (the default).</dd></dl>
<p>This function returns a matrix whose columns are the eigenvectors. Column <img class="formulaInl" alt="$ k $" src="form_195.png"/> is an eigenvector corresponding to eigenvalue number <img class="formulaInl" alt="$ k $" src="form_195.png"/> as returned by <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#addd3beba6fe3dc854923e5d84738c02e" title="Returns the eigenvalues of given matrix.">eigenvalues()</a>. The eigenvectors are normalized to have (Euclidean) norm equal to one. The matrix returned by this function is the matrix <img class="formulaInl" alt="$ V $" src="form_171.png"/> in the eigendecomposition <img class="formulaInl" alt="$ A = V D V^{-1} $" src="form_173.png"/>, if it exists.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00170">170</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname"><a class="el" href="namespace_eigen.html#a85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> Eigen::ComplexEigenSolver::info </td>
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<p>Reports whether previous computation was successful. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd><code>Success</code> if computation was succesful, <code>NoConvergence</code> otherwise. </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00231">231</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname">void Eigen::ComplexEigenSolver::sortEigenvalues </td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00314">314</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<hr/><h2>Member Data Documentation</h2>
<a class="anchor" id="aabd1f4a7801ad90cbdf267fe60a52d7d"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::m_eigenvectorsOk" ref="aabd1f4a7801ad90cbdf267fe60a52d7d" args="" -->
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<td class="memname">bool <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#aabd1f4a7801ad90cbdf267fe60a52d7d">Eigen::ComplexEigenSolver::m_eigenvectorsOk</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00242">242</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a7e0a02c12a7f3d2553e5551ab3f3b101"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::m_eivalues" ref="a7e0a02c12a7f3d2553e5551ab3f3b101" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a6992daec05a0149c178dc86c59610b8c">EigenvalueType</a> <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a7e0a02c12a7f3d2553e5551ab3f3b101">Eigen::ComplexEigenSolver::m_eivalues</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00239">239</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a18a4c512bc013720e2951993e43c61d2"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::m_eivec" ref="a18a4c512bc013720e2951993e43c61d2" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a134eaafcc1e9aa20baedadb31900bcae">EigenvectorType</a> <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a18a4c512bc013720e2951993e43c61d2">Eigen::ComplexEigenSolver::m_eivec</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00238">238</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a2801a3c72dc42cde3f13c65d71a5c9ef"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::m_isInitialized" ref="a2801a3c72dc42cde3f13c65d71a5c9ef" args="" -->
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<td class="memname">bool <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a2801a3c72dc42cde3f13c65d71a5c9ef">Eigen::ComplexEigenSolver::m_isInitialized</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00241">241</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="adca8e49feebf609d30d6c1d0cefc67eb"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::m_matX" ref="adca8e49feebf609d30d6c1d0cefc67eb" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a134eaafcc1e9aa20baedadb31900bcae">EigenvectorType</a> <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#adca8e49feebf609d30d6c1d0cefc67eb">Eigen::ComplexEigenSolver::m_matX</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00243">243</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a6aeea78ce18b2a39ee700bf60391c757"></a><!-- doxytag: member="Eigen::ComplexEigenSolver::m_schur" ref="a6aeea78ce18b2a39ee700bf60391c757" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_complex_schur.html">ComplexSchur</a><<a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a666247cd2d09d9f6a4c61833e56af044">MatrixType</a>> <a class="el" href="class_eigen_1_1_complex_eigen_solver.html#a6aeea78ce18b2a39ee700bf60391c757">Eigen::ComplexEigenSolver::m_schur</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00240">240</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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