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<title>Eigen::Tridiagonalization< _MatrixType > Class Template Reference</title>
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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_tridiagonalization.html">Tridiagonalization</a> </li>
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<div class="title">Eigen::Tridiagonalization< _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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<!-- doxytag: class="Eigen::Tridiagonalization" --><hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><h3>template<typename _MatrixType><br/>
class Eigen::Tridiagonalization< _MatrixType ></h3>
<p>Tridiagonal decomposition of a selfadjoint matrix</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 tridiagonal decomposition; 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>This class performs a tridiagonal decomposition of a selfadjoint matrix <img class="formulaInl" alt="$ A $" src="form_128.png"/> such that: <img class="formulaInl" alt="$ A = Q T Q^* $" src="form_158.png"/> where <img class="formulaInl" alt="$ Q $" src="form_159.png"/> is unitary and <img class="formulaInl" alt="$ T $" src="form_160.png"/> a real symmetric tridiagonal matrix.</p>
<p>A tridiagonal matrix is a matrix which has nonzero elements only on the main diagonal and the first diagonal below and above it. The Hessenberg decomposition of a selfadjoint matrix is in fact a tridiagonal decomposition. This class is used in <a class="el" href="class_eigen_1_1_self_adjoint_eigen_solver.html">SelfAdjointEigenSolver</a> to compute the eigenvalues and eigenvectors of a selfadjoint matrix.</p>
<p>Call the function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute()</a> to compute the tridiagonal decomposition of a given matrix. Alternatively, you can use the <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> constructor which computes the tridiagonal Schur decomposition at construction time. Once the decomposition is computed, you can use the <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a> and <a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a> functions to retrieve the matrices Q and T in the decomposition.</p>
<p>The documentation of <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> contains an example of the typical use of this class.</p>
<dl class="see"><dt><b>See also:</b></dt><dd>class <a class="el" href="class_eigen_1_1_hessenberg_decomposition.html">HessenbergDecomposition</a>, class <a class="el" href="class_eigen_1_1_self_adjoint_eigen_solver.html">SelfAdjointEigenSolver</a> </dd></dl>
<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>
</div>
<p><a href="class_eigen_1_1_tridiagonalization-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_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca">Size</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1">SizeMinusOne</a> = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50">Options</a> = MatrixType::Options,
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a">MaxSize</a> = MatrixType::MaxRowsAtCompileTime,
<br/>
  <a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f">MaxSizeMinusOne</a> = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)
<br/>
}</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_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca">Size</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1">SizeMinusOne</a> = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50">Options</a> = MatrixType::Options,
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a">MaxSize</a> = MatrixType::MaxRowsAtCompileTime,
<br/>
  <a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f">MaxSizeMinusOne</a> = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)
<br/>
}</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_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca">Size</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1">SizeMinusOne</a> = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50">Options</a> = MatrixType::Options,
<a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a">MaxSize</a> = MatrixType::MaxRowsAtCompileTime,
<br/>
  <a class="el" href="class_eigen_1_1_tridiagonalization.html#abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f">MaxSizeMinusOne</a> = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)
<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_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Synonym for the template parameter <code>_MatrixType</code>. <a href="#add0f4b2216d0ea8ee0f7d8525deaf0a9"></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> >::Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">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_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>, <br class="typebreak"/>
SizeMinusOne, 1, Options <br class="typebreak"/>
&~RowMajor, MaxSizeMinusOne, 1 > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1plain__col__type.html">internal::plain_col_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a> ><br class="typebreak"/>
::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac5303dbff6921f9a1b9dad0cacfe00c">DiagonalType</a></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_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a>, <br class="typebreak"/>
SizeMinusOne, 1, Options <br class="typebreak"/>
&~RowMajor, MaxSizeMinusOne, 1 > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a68729d89d61edbae954fc7ad0b72a5b8">SubDiagonalType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1remove__all.html">internal::remove_all</a><br class="typebreak"/>
< typename <br class="typebreak"/>
MatrixType::RealReturnType ><br class="typebreak"/>
::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1_tridiagonalization_matrix_t_return_type.html">internal::TridiagonalizationMatrixTReturnType</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><br class="typebreak"/>
< <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a>< <a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> ><br class="typebreak"/>
::IsComplex, const typename <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> ><br class="typebreak"/>
::RealReturnType, const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> ><br class="typebreak"/>
>::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><br class="typebreak"/>
< <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a>< <a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> ><br class="typebreak"/>
::IsComplex, const typename <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a>< const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, SizeMinusOne, <br class="typebreak"/>
SizeMinusOne ><br class="typebreak"/>
>::RealReturnType, const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a>< const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, SizeMinusOne, <br class="typebreak"/>
SizeMinusOne > > >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> ><br class="typebreak"/>
::ConjugateReturnType </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Return type of <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a> <a href="#aac9a2a2556bb1d7bce1a69ea50f6611e"></a><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_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Synonym for the template parameter <code>_MatrixType</code>. <a href="#add0f4b2216d0ea8ee0f7d8525deaf0a9"></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> >::Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">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_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>, <br class="typebreak"/>
SizeMinusOne, 1, Options <br class="typebreak"/>
&~RowMajor, MaxSizeMinusOne, 1 > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1plain__col__type.html">internal::plain_col_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a> ><br class="typebreak"/>
::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac5303dbff6921f9a1b9dad0cacfe00c">DiagonalType</a></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_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a>, <br class="typebreak"/>
SizeMinusOne, 1, Options <br class="typebreak"/>
&~RowMajor, MaxSizeMinusOne, 1 > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a68729d89d61edbae954fc7ad0b72a5b8">SubDiagonalType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1remove__all.html">internal::remove_all</a><br class="typebreak"/>
< typename <br class="typebreak"/>
MatrixType::RealReturnType ><br class="typebreak"/>
::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1_tridiagonalization_matrix_t_return_type.html">internal::TridiagonalizationMatrixTReturnType</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><br class="typebreak"/>
< <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a>< <a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> ><br class="typebreak"/>
::IsComplex, const typename <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> ><br class="typebreak"/>
::RealReturnType, const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> ><br class="typebreak"/>
>::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><br class="typebreak"/>
< <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a>< <a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> ><br class="typebreak"/>
::IsComplex, const typename <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a>< const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, SizeMinusOne, <br class="typebreak"/>
SizeMinusOne ><br class="typebreak"/>
>::RealReturnType, const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a>< const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, SizeMinusOne, <br class="typebreak"/>
SizeMinusOne > > >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> ><br class="typebreak"/>
::ConjugateReturnType </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Return type of <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a> <a href="#aac9a2a2556bb1d7bce1a69ea50f6611e"></a><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_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Synonym for the template parameter <code>_MatrixType</code>. <a href="#add0f4b2216d0ea8ee0f7d8525deaf0a9"></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> >::Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">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_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a></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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>, <br class="typebreak"/>
SizeMinusOne, 1, Options <br class="typebreak"/>
&~RowMajor, MaxSizeMinusOne, 1 > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1plain__col__type.html">internal::plain_col_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a> ><br class="typebreak"/>
::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac5303dbff6921f9a1b9dad0cacfe00c">DiagonalType</a></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_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a>, <br class="typebreak"/>
SizeMinusOne, 1, Options <br class="typebreak"/>
&~RowMajor, MaxSizeMinusOne, 1 > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a68729d89d61edbae954fc7ad0b72a5b8">SubDiagonalType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1remove__all.html">internal::remove_all</a><br class="typebreak"/>
< typename <br class="typebreak"/>
MatrixType::RealReturnType ><br class="typebreak"/>
::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1_tridiagonalization_matrix_t_return_type.html">internal::TridiagonalizationMatrixTReturnType</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><br class="typebreak"/>
< <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a>< <a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> ><br class="typebreak"/>
::IsComplex, const typename <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> ><br class="typebreak"/>
::RealReturnType, const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> ><br class="typebreak"/>
>::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><br class="typebreak"/>
< <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a>< <a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a> ><br class="typebreak"/>
::IsComplex, const typename <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a>< const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, SizeMinusOne, <br class="typebreak"/>
SizeMinusOne ><br class="typebreak"/>
>::RealReturnType, const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a>< const <br class="typebreak"/>
<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, SizeMinusOne, <br class="typebreak"/>
SizeMinusOne > > >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> ><br class="typebreak"/>
::ConjugateReturnType </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Return type of <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a> <a href="#aac9a2a2556bb1d7bce1a69ea50f6611e"></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_tridiagonalization.html#af280466dc3161afe1d1a07d31c92d7f8">Tridiagonalization</a> (<a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a> size=Size==<a class="el" href="namespace_eigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>?2:Size)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <a href="#af280466dc3161afe1d1a07d31c92d7f8"></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_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf">Tridiagonalization</a> (const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor; computes tridiagonal decomposition of given matrix. <a href="#a51c8b61d87a4733394cc43ea2a170fbf"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439">compute</a> (const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes tridiagonal decomposition of given matrix. <a href="#a0e9d8f7c64d09b733293dce291e97439"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d">householderCoefficients</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the Householder coefficients. <a href="#aa39d6361c6f9bf2f433aaf9f43859f9d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2">packedMatrix</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the internal representation of the decomposition. <a href="#a4ed409603902d102639ad62ad803fed2"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb">matrixQ</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the unitary matrix Q in the decomposition. <a href="#a240e784d4ba6caade29c7259c45276bb"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1">matrixT</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns an expression of the tridiagonal matrix T in the decomposition. <a href="#aea1afe412205b5dc9d5902ffde96bbe1"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6">diagonal</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the diagonal of the tridiagonal matrix T in the decomposition. <a href="#a3dd920223b4ef709c483199a9b5f56f6"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da">subDiagonal</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the subdiagonal of the tridiagonal matrix T in the decomposition. <a href="#a575eabe0d43e5a360e887e80d48d06da"></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_tridiagonalization.html#af280466dc3161afe1d1a07d31c92d7f8">Tridiagonalization</a> (<a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a> size=Size==<a class="el" href="namespace_eigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>?2:Size)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <a href="#af280466dc3161afe1d1a07d31c92d7f8"></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_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf">Tridiagonalization</a> (const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor; computes tridiagonal decomposition of given matrix. <a href="#a51c8b61d87a4733394cc43ea2a170fbf"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439">compute</a> (const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes tridiagonal decomposition of given matrix. <a href="#a0e9d8f7c64d09b733293dce291e97439"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d">householderCoefficients</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the Householder coefficients. <a href="#aa39d6361c6f9bf2f433aaf9f43859f9d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2">packedMatrix</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the internal representation of the decomposition. <a href="#a4ed409603902d102639ad62ad803fed2"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb">matrixQ</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the unitary matrix Q in the decomposition. <a href="#a240e784d4ba6caade29c7259c45276bb"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1">matrixT</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns an expression of the tridiagonal matrix T in the decomposition. <a href="#aea1afe412205b5dc9d5902ffde96bbe1"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ac524f3b5f7d839825676d0800715b7f0">diagonal</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the diagonal of the tridiagonal matrix T in the decomposition. <a href="#ac524f3b5f7d839825676d0800715b7f0"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a27f2d820c0c4f55ec3d0329add240723">subDiagonal</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the subdiagonal of the tridiagonal matrix T in the decomposition. <a href="#a27f2d820c0c4f55ec3d0329add240723"></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_tridiagonalization.html#af280466dc3161afe1d1a07d31c92d7f8">Tridiagonalization</a> (<a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a> size=Size==<a class="el" href="namespace_eigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>?2:Size)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <a href="#af280466dc3161afe1d1a07d31c92d7f8"></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_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf">Tridiagonalization</a> (const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor; computes tridiagonal decomposition of given matrix. <a href="#a51c8b61d87a4733394cc43ea2a170fbf"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439">compute</a> (const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes tridiagonal decomposition of given matrix. <a href="#a0e9d8f7c64d09b733293dce291e97439"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d">householderCoefficients</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the Householder coefficients. <a href="#aa39d6361c6f9bf2f433aaf9f43859f9d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2">packedMatrix</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the internal representation of the decomposition. <a href="#a4ed409603902d102639ad62ad803fed2"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb">matrixQ</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the unitary matrix Q in the decomposition. <a href="#a240e784d4ba6caade29c7259c45276bb"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1">matrixT</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns an expression of the tridiagonal matrix T in the decomposition. <a href="#aea1afe412205b5dc9d5902ffde96bbe1"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ac524f3b5f7d839825676d0800715b7f0">diagonal</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the diagonal of the tridiagonal matrix T in the decomposition. <a href="#ac524f3b5f7d839825676d0800715b7f0"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a27f2d820c0c4f55ec3d0329add240723">subDiagonal</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the subdiagonal of the tridiagonal matrix T in the decomposition. <a href="#a27f2d820c0c4f55ec3d0329add240723"></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_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad42459daade3a276a0bb2846e18fabf6">m_matrix</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a78512d647c0ab9ee6271f7afa5d25140">m_hCoeffs</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_tridiagonalization.html#acc6410d0df0ef3deba95d9cdfcd7fd65">m_isInitialized</a></td></tr>
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<hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="ad8891a972b6b5c5588dc4109597d6b58"></a><!-- doxytag: member="Eigen::Tridiagonalization::CoeffVectorType" ref="ad8891a972b6b5c5588dc4109597d6b58" 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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00094">94</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="ad8891a972b6b5c5588dc4109597d6b58"></a><!-- doxytag: member="Eigen::Tridiagonalization::CoeffVectorType" ref="ad8891a972b6b5c5588dc4109597d6b58" 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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00094">94</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="ad8891a972b6b5c5588dc4109597d6b58"></a><!-- doxytag: member="Eigen::Tridiagonalization::CoeffVectorType" ref="ad8891a972b6b5c5588dc4109597d6b58" 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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00094">94</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a9ef2d09cd4c647cdecfa58f07c950b39"></a><!-- doxytag: member="Eigen::Tridiagonalization::DiagonalReturnType" ref="a9ef2d09cd4c647cdecfa58f07c950b39" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><<a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>>::IsComplex, const typename <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>>::RealReturnType, const <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>> >::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00103">103</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a9ef2d09cd4c647cdecfa58f07c950b39"></a><!-- doxytag: member="Eigen::Tridiagonalization::DiagonalReturnType" ref="a9ef2d09cd4c647cdecfa58f07c950b39" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><<a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>>::IsComplex, const typename <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>>::RealReturnType, const <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>> >::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00103">103</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a9ef2d09cd4c647cdecfa58f07c950b39"></a><!-- doxytag: member="Eigen::Tridiagonalization::DiagonalReturnType" ref="a9ef2d09cd4c647cdecfa58f07c950b39" args="" -->
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00103">103</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="aac5303dbff6921f9a1b9dad0cacfe00c"></a><!-- doxytag: member="Eigen::Tridiagonalization::DiagonalType" ref="aac5303dbff6921f9a1b9dad0cacfe00c" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1plain__col__type.html">internal::plain_col_type</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a>>::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#aac5303dbff6921f9a1b9dad0cacfe00c">DiagonalType</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00095">95</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="aac5303dbff6921f9a1b9dad0cacfe00c"></a><!-- doxytag: member="Eigen::Tridiagonalization::DiagonalType" ref="aac5303dbff6921f9a1b9dad0cacfe00c" args="" -->
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00095">95</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="aac5303dbff6921f9a1b9dad0cacfe00c"></a><!-- doxytag: member="Eigen::Tridiagonalization::DiagonalType" ref="aac5303dbff6921f9a1b9dad0cacfe00c" args="" -->
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00095">95</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="aac9a2a2556bb1d7bce1a69ea50f6611e"></a><!-- doxytag: member="Eigen::Tridiagonalization::HouseholderSequenceType" ref="aac9a2a2556bb1d7bce1a69ea50f6611e" args="" -->
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,<a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a>>::ConjugateReturnType <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a></td>
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<p>Return type of <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a> </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00113">113</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,<a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a>>::ConjugateReturnType <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a></td>
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<div class="memdoc">
<p>Return type of <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a> </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00113">113</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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</div>
<a class="anchor" id="aac9a2a2556bb1d7bce1a69ea50f6611e"></a><!-- doxytag: member="Eigen::Tridiagonalization::HouseholderSequenceType" ref="aac9a2a2556bb1d7bce1a69ea50f6611e" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,<a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a>>::ConjugateReturnType <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a></td>
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<p>Return type of <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a> </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00113">113</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="abce4160673963b902a9588f82bb2739f"></a><!-- doxytag: member="Eigen::Tridiagonalization::Index" ref="abce4160673963b902a9588f82bb2739f" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00084">84</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="abce4160673963b902a9588f82bb2739f"></a><!-- doxytag: member="Eigen::Tridiagonalization::Index" ref="abce4160673963b902a9588f82bb2739f" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00084">84</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="abce4160673963b902a9588f82bb2739f"></a><!-- doxytag: member="Eigen::Tridiagonalization::Index" ref="abce4160673963b902a9588f82bb2739f" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00084">84</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="af7d2f1a605207a321f494d9ee216f8f5"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixTReturnType" ref="af7d2f1a605207a321f494d9ee216f8f5" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1_tridiagonalization_matrix_t_return_type.html">internal::TridiagonalizationMatrixTReturnType</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a>> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00098">98</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="af7d2f1a605207a321f494d9ee216f8f5"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixTReturnType" ref="af7d2f1a605207a321f494d9ee216f8f5" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1_tridiagonalization_matrix_t_return_type.html">internal::TridiagonalizationMatrixTReturnType</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a>> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a></td>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00098">98</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="af7d2f1a605207a321f494d9ee216f8f5"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixTReturnType" ref="af7d2f1a605207a321f494d9ee216f8f5" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1_tridiagonalization_matrix_t_return_type.html">internal::TridiagonalizationMatrixTReturnType</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a>> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#af7d2f1a605207a321f494d9ee216f8f5">MatrixTReturnType</a></td>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00098">98</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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</div>
<a class="anchor" id="add0f4b2216d0ea8ee0f7d8525deaf0a9"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixType" ref="add0f4b2216d0ea8ee0f7d8525deaf0a9" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">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#l00080">80</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="add0f4b2216d0ea8ee0f7d8525deaf0a9"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixType" ref="add0f4b2216d0ea8ee0f7d8525deaf0a9" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">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#l00080">80</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="add0f4b2216d0ea8ee0f7d8525deaf0a9"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixType" ref="add0f4b2216d0ea8ee0f7d8525deaf0a9" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a></td>
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<div class="memdoc">
<p>Synonym for the template parameter <code>_MatrixType</code>. </p>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00080">80</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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</div>
<a class="anchor" id="a28b71fa9329f5881fa2fc6732941c2b3"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixTypeRealView" ref="a28b71fa9329f5881fa2fc6732941c2b3" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1remove__all.html">internal::remove_all</a><typename MatrixType::RealReturnType>::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a></td>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00097">97</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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</div>
<a class="anchor" id="a28b71fa9329f5881fa2fc6732941c2b3"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixTypeRealView" ref="a28b71fa9329f5881fa2fc6732941c2b3" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1remove__all.html">internal::remove_all</a><typename MatrixType::RealReturnType>::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a></td>
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</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00097">97</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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</div>
<a class="anchor" id="a28b71fa9329f5881fa2fc6732941c2b3"></a><!-- doxytag: member="Eigen::Tridiagonalization::MatrixTypeRealView" ref="a28b71fa9329f5881fa2fc6732941c2b3" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1remove__all.html">internal::remove_all</a><typename MatrixType::RealReturnType>::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a28b71fa9329f5881fa2fc6732941c2b3">MatrixTypeRealView</a></td>
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</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00097">97</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="a9d33e4c11dad35a8b147cbe048974700"></a><!-- doxytag: member="Eigen::Tridiagonalization::RealScalar" ref="a9d33e4c11dad35a8b147cbe048974700" args="" -->
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template<typename _MatrixType> </div>
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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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>>::Real <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a></td>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00083">83</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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</div>
<a class="anchor" id="a9d33e4c11dad35a8b147cbe048974700"></a><!-- doxytag: member="Eigen::Tridiagonalization::RealScalar" ref="a9d33e4c11dad35a8b147cbe048974700" args="" -->
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template<typename _MatrixType> </div>
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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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>>::Real <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a></td>
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</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00083">83</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="a9d33e4c11dad35a8b147cbe048974700"></a><!-- doxytag: member="Eigen::Tridiagonalization::RealScalar" ref="a9d33e4c11dad35a8b147cbe048974700" args="" -->
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<div class="memproto">
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template<typename _MatrixType> </div>
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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_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>>::Real <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a></td>
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</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00083">83</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="af3f9d8d46f2a1663013e207ff568b5f9"></a><!-- doxytag: member="Eigen::Tridiagonalization::Scalar" ref="af3f9d8d46f2a1663013e207ff568b5f9" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a></td>
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</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00082">82</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="af3f9d8d46f2a1663013e207ff568b5f9"></a><!-- doxytag: member="Eigen::Tridiagonalization::Scalar" ref="af3f9d8d46f2a1663013e207ff568b5f9" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a></td>
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</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00082">82</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="af3f9d8d46f2a1663013e207ff568b5f9"></a><!-- doxytag: member="Eigen::Tridiagonalization::Scalar" ref="af3f9d8d46f2a1663013e207ff568b5f9" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a></td>
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</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00082">82</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="a79285e569631541c048a020cfb23da05"></a><!-- doxytag: member="Eigen::Tridiagonalization::SubDiagonalReturnType" ref="a79285e569631541c048a020cfb23da05" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><<a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>>::IsComplex, const typename <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,SizeMinusOne,SizeMinusOne> >::RealReturnType, const <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,SizeMinusOne,SizeMinusOne> > >::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00110">110</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="a79285e569631541c048a020cfb23da05"></a><!-- doxytag: member="Eigen::Tridiagonalization::SubDiagonalReturnType" ref="a79285e569631541c048a020cfb23da05" args="" -->
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<div class="memtemplate">
template<typename _MatrixType> </div>
<table class="memname">
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><<a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>>::IsComplex, const typename <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,SizeMinusOne,SizeMinusOne> >::RealReturnType, const <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,SizeMinusOne,SizeMinusOne> > >::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00110">110</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="a79285e569631541c048a020cfb23da05"></a><!-- doxytag: member="Eigen::Tridiagonalization::SubDiagonalReturnType" ref="a79285e569631541c048a020cfb23da05" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1conditional.html">internal::conditional</a><<a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a><<a class="el" href="class_eigen_1_1_tridiagonalization.html#af3f9d8d46f2a1663013e207ff568b5f9">Scalar</a>>::IsComplex, const typename <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,SizeMinusOne,SizeMinusOne> >::RealReturnType, const <a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< <a class="el" href="class_eigen_1_1_block.html">Block</a><const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>,SizeMinusOne,SizeMinusOne> > >::type <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a></td>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00110">110</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="a68729d89d61edbae954fc7ad0b72a5b8"></a><!-- doxytag: member="Eigen::Tridiagonalization::SubDiagonalType" ref="a68729d89d61edbae954fc7ad0b72a5b8" args="" -->
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template<typename _MatrixType> </div>
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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_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a>, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a68729d89d61edbae954fc7ad0b72a5b8">SubDiagonalType</a></td>
</tr>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00096">96</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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</div>
<a class="anchor" id="a68729d89d61edbae954fc7ad0b72a5b8"></a><!-- doxytag: member="Eigen::Tridiagonalization::SubDiagonalType" ref="a68729d89d61edbae954fc7ad0b72a5b8" args="" -->
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template<typename _MatrixType> </div>
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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_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a>, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a68729d89d61edbae954fc7ad0b72a5b8">SubDiagonalType</a></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00096">96</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a68729d89d61edbae954fc7ad0b72a5b8"></a><!-- doxytag: member="Eigen::Tridiagonalization::SubDiagonalType" ref="a68729d89d61edbae954fc7ad0b72a5b8" args="" -->
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template<typename _MatrixType> </div>
<table class="memname">
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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_tridiagonalization.html#a9d33e4c11dad35a8b147cbe048974700">RealScalar</a>, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a68729d89d61edbae954fc7ad0b72a5b8">SubDiagonalType</a></td>
</tr>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00096">96</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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</div>
<hr/><h2>Member Enumeration Documentation</h2>
<a class="anchor" id="aec3f28d60cd7f8e079fbc9808a81d4cc"></a><!-- doxytag: member="Eigen::Tridiagonalization::@333" ref="aec3f28d60cd7f8e079fbc9808a81d4cc" args="" -->
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template<typename _MatrixType> </div>
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<td class="memname">anonymous enum</td>
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<div class="memdoc">
<dl><dt><b>Enumerator: </b></dt><dd><table border="0" cellspacing="2" cellpadding="0">
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca"></a><!-- doxytag: member="Size" ref="abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca" args="" -->Size</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1"></a><!-- doxytag: member="SizeMinusOne" ref="abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1" args="" -->SizeMinusOne</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50"></a><!-- doxytag: member="Options" ref="abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50" args="" -->Options</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a"></a><!-- doxytag: member="MaxSize" ref="abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a" args="" -->MaxSize</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f"></a><!-- doxytag: member="MaxSizeMinusOne" ref="abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f" args="" -->MaxSizeMinusOne</em> </td><td>
</td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00086">86</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="a8d1a8b7a7f2b858bcd77f7e4b1723369"></a><!-- doxytag: member="Eigen::Tridiagonalization::@339" ref="a8d1a8b7a7f2b858bcd77f7e4b1723369" args="" -->
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template<typename _MatrixType> </div>
<table class="memname">
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<td class="memname">anonymous enum</td>
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<div class="memdoc">
<dl><dt><b>Enumerator: </b></dt><dd><table border="0" cellspacing="2" cellpadding="0">
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca"></a><!-- doxytag: member="Size" ref="abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca" args="" -->Size</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1"></a><!-- doxytag: member="SizeMinusOne" ref="abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1" args="" -->SizeMinusOne</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50"></a><!-- doxytag: member="Options" ref="abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50" args="" -->Options</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a"></a><!-- doxytag: member="MaxSize" ref="abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a" args="" -->MaxSize</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f"></a><!-- doxytag: member="MaxSizeMinusOne" ref="abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f" args="" -->MaxSizeMinusOne</em> </td><td>
</td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00086">86</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81"></a><!-- doxytag: member="Eigen::Tridiagonalization::@341" ref="abeab7e2ad7f0c6443c048fe234832b81" args="" -->
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template<typename _MatrixType> </div>
<table class="memname">
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<td class="memname">anonymous enum</td>
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<div class="memdoc">
<dl><dt><b>Enumerator: </b></dt><dd><table border="0" cellspacing="2" cellpadding="0">
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca"></a><!-- doxytag: member="Size" ref="abeab7e2ad7f0c6443c048fe234832b81ab46b967281225d339d5d9e071d4bf2ca" args="" -->Size</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1"></a><!-- doxytag: member="SizeMinusOne" ref="abeab7e2ad7f0c6443c048fe234832b81a66edebfb8bcdfc96f5fc48571d8c82c1" args="" -->SizeMinusOne</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50"></a><!-- doxytag: member="Options" ref="abeab7e2ad7f0c6443c048fe234832b81a5bd6309b04d1a23a5cd3999ed2de1c50" args="" -->Options</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a"></a><!-- doxytag: member="MaxSize" ref="abeab7e2ad7f0c6443c048fe234832b81a46e1f6d781d98905eaf497f4aa2e759a" args="" -->MaxSize</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f"></a><!-- doxytag: member="MaxSizeMinusOne" ref="abeab7e2ad7f0c6443c048fe234832b81ad12828db5eddb02e1c9e466ca3508c5f" args="" -->MaxSizeMinusOne</em> </td><td>
</td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00086">86</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="af280466dc3161afe1d1a07d31c92d7f8"></a><!-- doxytag: member="Eigen::Tridiagonalization::Tridiagonalization" ref="af280466dc3161afe1d1a07d31c92d7f8" args="(Index size=Size==Dynamic?2:Size)" -->
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template<typename _MatrixType> </div>
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a> </td>
<td class="paramname"><em>size</em> = <code>Size==<a class="el" href="namespace_eigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? 2 : Size</code></td><td>)</td>
<td><code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Default constructor. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">size</td><td>Positive integer, size of the matrix whose tridiagonal decomposition will be computed.</td></tr>
</table>
</dd>
</dl>
<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_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal 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="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute()</a> for an example. </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00127">127</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="a51c8b61d87a4733394cc43ea2a170fbf"></a><!-- doxytag: member="Eigen::Tridiagonalization::Tridiagonalization" ref="a51c8b61d87a4733394cc43ea2a170fbf" args="(const MatrixType &matrix)" -->
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template<typename _MatrixType> </div>
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td>
<td class="paramname"><em>matrix</em></td><td>)</td>
<td><code> [inline]</code></td>
</tr>
</table>
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<div class="memdoc">
<p>Constructor; computes tridiagonal decomposition 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>Selfadjoint matrix whose tridiagonal decomposition is to be computed.</td></tr>
</table>
</dd>
</dl>
<p>This constructor calls <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute()</a> to compute the tridiagonal decomposition.</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#l00143">143</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
</div>
<a class="anchor" id="af280466dc3161afe1d1a07d31c92d7f8"></a><!-- doxytag: member="Eigen::Tridiagonalization::Tridiagonalization" ref="af280466dc3161afe1d1a07d31c92d7f8" args="(Index size=Size==Dynamic?2:Size)" -->
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template<typename _MatrixType> </div>
<table class="memname">
<tr>
<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a> </td>
<td class="paramname"><em>size</em> = <code>Size==<a class="el" href="namespace_eigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? 2 : Size</code></td><td>)</td>
<td><code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Default constructor. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">size</td><td>Positive integer, size of the matrix whose tridiagonal decomposition will be computed.</td></tr>
</table>
</dd>
</dl>
<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_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal 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="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute()</a> for an example. </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00127">127</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
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<a class="anchor" id="a51c8b61d87a4733394cc43ea2a170fbf"></a><!-- doxytag: member="Eigen::Tridiagonalization::Tridiagonalization" ref="a51c8b61d87a4733394cc43ea2a170fbf" args="(const MatrixType &matrix)" -->
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<td>(</td>
<td class="paramtype">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td>
<td class="paramname"><em>matrix</em></td><td>)</td>
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<p>Constructor; computes tridiagonal decomposition 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>Selfadjoint matrix whose tridiagonal decomposition is to be computed.</td></tr>
</table>
</dd>
</dl>
<p>This constructor calls <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute()</a> to compute the tridiagonal decomposition.</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#l00143">143</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
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<a class="anchor" id="af280466dc3161afe1d1a07d31c92d7f8"></a><!-- doxytag: member="Eigen::Tridiagonalization::Tridiagonalization" ref="af280466dc3161afe1d1a07d31c92d7f8" args="(Index size=Size==Dynamic?2:Size)" -->
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<td>(</td>
<td class="paramtype"><a class="el" href="class_eigen_1_1_tridiagonalization.html#abce4160673963b902a9588f82bb2739f">Index</a> </td>
<td class="paramname"><em>size</em> = <code>Size==<a class="el" href="namespace_eigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? 2 : Size</code></td><td>)</td>
<td><code> [inline]</code></td>
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<p>Default constructor. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">size</td><td>Positive integer, size of the matrix whose tridiagonal decomposition will be computed.</td></tr>
</table>
</dd>
</dl>
<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_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal 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="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute()</a> for an example. </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00127">127</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a51c8b61d87a4733394cc43ea2a170fbf"></a><!-- doxytag: member="Eigen::Tridiagonalization::Tridiagonalization" ref="a51c8b61d87a4733394cc43ea2a170fbf" args="(const MatrixType &matrix)" -->
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<td>(</td>
<td class="paramtype">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td>
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<td><code> [inline]</code></td>
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<p>Constructor; computes tridiagonal decomposition 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>Selfadjoint matrix whose tridiagonal decomposition is to be computed.</td></tr>
</table>
</dd>
</dl>
<p>This constructor calls <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute()</a> to compute the tridiagonal decomposition.</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#l00143">143</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
</div>
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<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a0e9d8f7c64d09b733293dce291e97439"></a><!-- doxytag: member="Eigen::Tridiagonalization::compute" ref="a0e9d8f7c64d09b733293dce291e97439" args="(const MatrixType &matrix)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a>& <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::compute </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td>
<td class="paramname"><em>matrix</em></td><td>)</td>
<td><code> [inline]</code></td>
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<p>Computes tridiagonal decomposition 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>Selfadjoint matrix whose tridiagonal decomposition is to be computed. </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>Reference to <code>*this</code> </dd></dl>
<p>The tridiagonal decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections. The cost is <img class="formulaInl" alt="$ 4n^3/3 $" src="form_182.png"/> flops, where <img class="formulaInl" alt="$ n $" src="form_183.png"/> denotes the size of the given matrix.</p>
<p>This method reuses of the allocated data in the <a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> object, if the size of the matrix does not change.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00169">169</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a0e9d8f7c64d09b733293dce291e97439"></a><!-- doxytag: member="Eigen::Tridiagonalization::compute" ref="a0e9d8f7c64d09b733293dce291e97439" args="(const MatrixType &matrix)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a>& <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::compute </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td>
<td class="paramname"><em>matrix</em></td><td>)</td>
<td><code> [inline]</code></td>
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<div class="memdoc">
<p>Computes tridiagonal decomposition of given matrix. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Selfadjoint matrix whose tridiagonal decomposition is to be computed. </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>Reference to <code>*this</code> </dd></dl>
<p>The tridiagonal decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections. The cost is <img class="formulaInl" alt="$ 4n^3/3 $" src="form_182.png"/> flops, where <img class="formulaInl" alt="$ n $" src="form_183.png"/> denotes the size of the given matrix.</p>
<p>This method reuses of the allocated data in the <a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> object, if the size of the matrix does not change.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00169">169</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td>(</td>
<td class="paramtype">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> & </td>
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<td><code> [inline]</code></td>
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<div class="memdoc">
<p>Computes tridiagonal decomposition of given matrix. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Selfadjoint matrix whose tridiagonal decomposition is to be computed. </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>Reference to <code>*this</code> </dd></dl>
<p>The tridiagonal decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections. The cost is <img class="formulaInl" alt="$ 4n^3/3 $" src="form_182.png"/> flops, where <img class="formulaInl" alt="$ n $" src="form_183.png"/> denotes the size of the given matrix.</p>
<p>This method reuses of the allocated data in the <a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a> object, if the size of the matrix does not change.</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#l00169">169</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="ac524f3b5f7d839825676d0800715b7f0"></a><!-- doxytag: member="Eigen::Tridiagonalization::diagonal" ref="ac524f3b5f7d839825676d0800715b7f0" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::diagonal </td>
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<p>Returns the diagonal of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression representing the diagonal of T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> </dd></dl>
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<a class="anchor" id="ac524f3b5f7d839825676d0800715b7f0"></a><!-- doxytag: member="Eigen::Tridiagonalization::diagonal" ref="ac524f3b5f7d839825676d0800715b7f0" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a9ef2d09cd4c647cdecfa58f07c950b39">DiagonalReturnType</a> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::diagonal </td>
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<p>Returns the diagonal of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression representing the diagonal of T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> </dd></dl>
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<p>Returns the diagonal of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression representing the diagonal of T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00319">319</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="aa39d6361c6f9bf2f433aaf9f43859f9d"></a><!-- doxytag: member="Eigen::Tridiagonalization::householderCoefficients" ref="aa39d6361c6f9bf2f433aaf9f43859f9d" args="() const " -->
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<p>Returns the Householder coefficients. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>a const reference to the vector of Householder coefficients</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>The Householder coefficients allow the reconstruction of the matrix <img class="formulaInl" alt="$ Q $" src="form_159.png"/> in the tridiagonal decomposition from the packed data.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2" title="Returns the internal representation of the decomposition.">packedMatrix()</a>, <a class="el" href="group___householder___module.html">Householder module</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00194">194</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::householderCoefficients </td>
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<p>Returns the Householder coefficients. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>a const reference to the vector of Householder coefficients</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>The Householder coefficients allow the reconstruction of the matrix <img class="formulaInl" alt="$ Q $" src="form_159.png"/> in the tridiagonal decomposition from the packed data.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2" title="Returns the internal representation of the decomposition.">packedMatrix()</a>, <a class="el" href="group___householder___module.html">Householder module</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00194">194</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<p>Returns the Householder coefficients. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>a const reference to the vector of Householder coefficients</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>The Householder coefficients allow the reconstruction of the matrix <img class="formulaInl" alt="$ Q $" src="form_159.png"/> in the tridiagonal decomposition from the packed data.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2" title="Returns the internal representation of the decomposition.">packedMatrix()</a>, <a class="el" href="group___householder___module.html">Householder module</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00194">194</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html#aac9a2a2556bb1d7bce1a69ea50f6611e">HouseholderSequenceType</a> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::matrixQ </td>
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<p>Returns the unitary matrix Q in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>object representing the matrix Q</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>This function returns a light-weight object of template class <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a>. You can either apply it directly to a matrix or you can convert it to a matrix of type <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9" title="Synonym for the template parameter _MatrixType.">MatrixType</a>.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a>, class <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a> </dd></dl>
<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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<p>Returns the unitary matrix Q in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>object representing the matrix Q</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>This function returns a light-weight object of template class <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a>. You can either apply it directly to a matrix or you can convert it to a matrix of type <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9" title="Synonym for the template parameter _MatrixType.">MatrixType</a>.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a>, class <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a> </dd></dl>
<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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<p>Returns the unitary matrix Q in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>object representing the matrix Q</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>This function returns a light-weight object of template class <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a>. You can either apply it directly to a matrix or you can convert it to a matrix of type <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9" title="Synonym for the template parameter _MatrixType.">MatrixType</a>.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a>, class <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a> </dd></dl>
<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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<p>Returns an expression of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression object representing the matrix T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>Currently, this function can be used to extract the matrix T from internal data and copy it to a dense matrix object. In most cases, it may be sufficient to directly use the packed matrix or the vector expressions returned by <a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a> and <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> instead of creating a new dense copy matrix with this function.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2" title="Returns the internal representation of the decomposition.">packedMatrix()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00277">277</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<p>Returns an expression of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression object representing the matrix T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>Currently, this function can be used to extract the matrix T from internal data and copy it to a dense matrix object. In most cases, it may be sufficient to directly use the packed matrix or the vector expressions returned by <a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a> and <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> instead of creating a new dense copy matrix with this function.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2" title="Returns the internal representation of the decomposition.">packedMatrix()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00277">277</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<p>Returns an expression of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression object representing the matrix T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>Currently, this function can be used to extract the matrix T from internal data and copy it to a dense matrix object. In most cases, it may be sufficient to directly use the packed matrix or the vector expressions returned by <a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a> and <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> instead of creating a new dense copy matrix with this function.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a240e784d4ba6caade29c7259c45276bb" title="Returns the unitary matrix Q in the decomposition.">matrixQ()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a4ed409603902d102639ad62ad803fed2" title="Returns the internal representation of the decomposition.">packedMatrix()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a>, <a class="el" href="class_eigen_1_1_tridiagonalization.html#a575eabe0d43e5a360e887e80d48d06da" title="Returns the subdiagonal of the tridiagonal matrix T in the decomposition.">subDiagonal()</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00277">277</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<p>Returns the internal representation of the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>a const reference to a matrix with the internal representation of the decomposition.</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>The returned matrix contains the following information:</p>
<ul>
<li>the strict upper triangular part is equal to the input matrix A.</li>
<li>the diagonal and lower sub-diagonal represent the real tridiagonal symmetric matrix T.</li>
<li>the rest of the lower part contains the Householder vectors that, combined with Householder coefficients returned by <a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d" title="Returns the Householder coefficients.">householderCoefficients()</a>, allows to reconstruct the matrix Q as <img class="formulaInl" alt="$ Q = H_{N-1} \ldots H_1 H_0 $" src="form_184.png"/>. Here, the matrices <img class="formulaInl" alt="$ H_i $" src="form_185.png"/> are the Householder transformations <img class="formulaInl" alt="$ H_i = (I - h_i v_i v_i^T) $" src="form_186.png"/> where <img class="formulaInl" alt="$ h_i $" src="form_187.png"/> is the <img class="formulaInl" alt="$ i $" src="form_188.png"/>th Householder coefficient and <img class="formulaInl" alt="$ v_i $" src="form_189.png"/> is the Householder vector defined by <img class="formulaInl" alt="$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T $" src="form_190.png"/> with M the matrix returned by this function.</li>
</ul>
<p>See LAPACK for further details on this packed storage.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d" title="Returns the Householder coefficients.">householderCoefficients()</a> </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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<a class="anchor" id="a4ed409603902d102639ad62ad803fed2"></a><!-- doxytag: member="Eigen::Tridiagonalization::packedMatrix" ref="a4ed409603902d102639ad62ad803fed2" args="() const " -->
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<td class="memname">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>& <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::packedMatrix </td>
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<p>Returns the internal representation of the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>a const reference to a matrix with the internal representation of the decomposition.</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>The returned matrix contains the following information:</p>
<ul>
<li>the strict upper triangular part is equal to the input matrix A.</li>
<li>the diagonal and lower sub-diagonal represent the real tridiagonal symmetric matrix T.</li>
<li>the rest of the lower part contains the Householder vectors that, combined with Householder coefficients returned by <a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d" title="Returns the Householder coefficients.">householderCoefficients()</a>, allows to reconstruct the matrix Q as <img class="formulaInl" alt="$ Q = H_{N-1} \ldots H_1 H_0 $" src="form_184.png"/>. Here, the matrices <img class="formulaInl" alt="$ H_i $" src="form_185.png"/> are the Householder transformations <img class="formulaInl" alt="$ H_i = (I - h_i v_i v_i^T) $" src="form_186.png"/> where <img class="formulaInl" alt="$ h_i $" src="form_187.png"/> is the <img class="formulaInl" alt="$ i $" src="form_188.png"/>th Householder coefficient and <img class="formulaInl" alt="$ v_i $" src="form_189.png"/> is the Householder vector defined by <img class="formulaInl" alt="$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T $" src="form_190.png"/> with M the matrix returned by this function.</li>
</ul>
<p>See LAPACK for further details on this packed storage.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d" title="Returns the Householder coefficients.">householderCoefficients()</a> </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">const <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a>& <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::packedMatrix </td>
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<p>Returns the internal representation of the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>a const reference to a matrix with the internal representation of the decomposition.</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<p>The returned matrix contains the following information:</p>
<ul>
<li>the strict upper triangular part is equal to the input matrix A.</li>
<li>the diagonal and lower sub-diagonal represent the real tridiagonal symmetric matrix T.</li>
<li>the rest of the lower part contains the Householder vectors that, combined with Householder coefficients returned by <a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d" title="Returns the Householder coefficients.">householderCoefficients()</a>, allows to reconstruct the matrix Q as <img class="formulaInl" alt="$ Q = H_{N-1} \ldots H_1 H_0 $" src="form_184.png"/>. Here, the matrices <img class="formulaInl" alt="$ H_i $" src="form_185.png"/> are the Householder transformations <img class="formulaInl" alt="$ H_i = (I - h_i v_i v_i^T) $" src="form_186.png"/> where <img class="formulaInl" alt="$ h_i $" src="form_187.png"/> is the <img class="formulaInl" alt="$ i $" src="form_188.png"/>th Householder coefficient and <img class="formulaInl" alt="$ v_i $" src="form_189.png"/> is the Householder vector defined by <img class="formulaInl" alt="$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T $" src="form_190.png"/> with M the matrix returned by this function.</li>
</ul>
<p>See LAPACK for further details on this packed storage.</p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#aa39d6361c6f9bf2f433aaf9f43859f9d" title="Returns the Householder coefficients.">householderCoefficients()</a> </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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<a class="anchor" id="a27f2d820c0c4f55ec3d0329add240723"></a><!-- doxytag: member="Eigen::Tridiagonalization::subDiagonal" ref="a27f2d820c0c4f55ec3d0329add240723" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::subDiagonal </td>
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<p>Returns the subdiagonal of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression representing the subdiagonal of T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a> </dd></dl>
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html">Tridiagonalization</a>< <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a79285e569631541c048a020cfb23da05">SubDiagonalReturnType</a> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< <a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> >::subDiagonal </td>
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<p>Returns the subdiagonal of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression representing the subdiagonal of T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a> </dd></dl>
<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00327">327</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="a27f2d820c0c4f55ec3d0329add240723"></a><!-- doxytag: member="Eigen::Tridiagonalization::subDiagonal" ref="a27f2d820c0c4f55ec3d0329add240723" args="() const " -->
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<p>Returns the subdiagonal of the tridiagonal matrix T in the decomposition. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>expression representing the subdiagonal of T</dd></dl>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Either the constructor <a class="el" href="class_eigen_1_1_tridiagonalization.html#a51c8b61d87a4733394cc43ea2a170fbf" title="Constructor; computes tridiagonal decomposition of given matrix.">Tridiagonalization(const MatrixType&)</a> or the member function <a class="el" href="class_eigen_1_1_tridiagonalization.html#a0e9d8f7c64d09b733293dce291e97439" title="Computes tridiagonal decomposition of given matrix.">compute(const MatrixType&)</a> has been called before to compute the tridiagonal decomposition of a matrix.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_tridiagonalization.html#a3dd920223b4ef709c483199a9b5f56f6" title="Returns the diagonal of the tridiagonal matrix T in the decomposition.">diagonal()</a> for an example, <a class="el" href="class_eigen_1_1_tridiagonalization.html#aea1afe412205b5dc9d5902ffde96bbe1" title="Returns an expression of the tridiagonal matrix T in the decomposition.">matrixT()</a> </dd></dl>
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<hr/><h2>Member Data Documentation</h2>
<a class="anchor" id="a78512d647c0ab9ee6271f7afa5d25140"></a><!-- doxytag: member="Eigen::Tridiagonalization::m_hCoeffs" ref="a78512d647c0ab9ee6271f7afa5d25140" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html#ad8891a972b6b5c5588dc4109597d6b58">CoeffVectorType</a> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#a78512d647c0ab9ee6271f7afa5d25140">m_hCoeffs</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00313">313</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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<a class="anchor" id="acc6410d0df0ef3deba95d9cdfcd7fd65"></a><!-- doxytag: member="Eigen::Tridiagonalization::m_isInitialized" ref="acc6410d0df0ef3deba95d9cdfcd7fd65" args="" -->
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<td class="memname">bool <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#acc6410d0df0ef3deba95d9cdfcd7fd65">m_isInitialized</a><code> [protected]</code></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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<a class="anchor" id="ad42459daade3a276a0bb2846e18fabf6"></a><!-- doxytag: member="Eigen::Tridiagonalization::m_matrix" ref="ad42459daade3a276a0bb2846e18fabf6" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_tridiagonalization.html#add0f4b2216d0ea8ee0f7d8525deaf0a9">MatrixType</a> <a class="el" href="class_eigen_1_1_tridiagonalization.html">Eigen::Tridiagonalization</a>< _MatrixType >::<a class="el" href="class_eigen_1_1_tridiagonalization.html#ad42459daade3a276a0bb2846e18fabf6">m_matrix</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_eigenvalues_source.html#l00312">312</a> of file <a class="el" href="_eigenvalues_source.html">Eigenvalues</a>.</p>
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