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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_l_d_l_t.html">LDLT</a> </li>
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<div class="title">Eigen::LDLT Class Reference</div> </div>
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<!-- doxytag: class="Eigen::LDLT" --><hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Robust Cholesky decomposition of a matrix with pivoting. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">MatrixType</td><td>the type of the matrix of which to compute the LDL^T Cholesky decomposition</td></tr>
</table>
</dd>
</dl>
<p>Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite matrix <img class="formulaInl" alt="$ A $" src="form_128.png"/> such that <img class="formulaInl" alt="$ A = P^TLDL^*P $" src="form_129.png"/>, where P is a permutation matrix, L is lower triangular with a unit diagonal and D is a diagonal matrix.</p>
<p>The decomposition uses pivoting to ensure stability, so that L will have zeros in the bottom right rank(A) - n submatrix. Avoiding the square root on D also stabilizes the computation.</p>
<p>Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_matrix_base.html#aa30eab339986a69177addcbdef3e95c1">MatrixBase::ldlt()</a>, class <a class="el" href="class_eigen_1_1_l_l_t.html" title="Standard Cholesky decomposition (LL^T) of a matrix and associated features.">LLT</a> </dd></dl>
</div>
<p><a href="class_eigen_1_1_l_d_l_t-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_l_d_l_t.html#ad6b0835cf2c2bcbbf28b52e80a7915cba6e5b2ef125662466d71d8dd7bbb9776b">RowsAtCompileTime</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_l_d_l_t.html#ad6b0835cf2c2bcbbf28b52e80a7915cbae59d42dfd2fa7c351c0eb28c0c584870">ColsAtCompileTime</a> = MatrixType::ColsAtCompileTime,
<a class="el" href="class_eigen_1_1_l_d_l_t.html#ad6b0835cf2c2bcbbf28b52e80a7915cbaa152c05857ad0f9872d390c14b89b03c">Options</a> = MatrixType::Options & ~RowMajorBit,
<a class="el" href="class_eigen_1_1_l_d_l_t.html#ad6b0835cf2c2bcbbf28b52e80a7915cba99a2a317f0a138f240e7071394822635">MaxRowsAtCompileTime</a> = MatrixType::MaxRowsAtCompileTime,
<br/>
  <a class="el" href="class_eigen_1_1_l_d_l_t.html#ad6b0835cf2c2bcbbf28b52e80a7915cba9e21176d3e1b02d40bcc7a9b12c3d19c">MaxColsAtCompileTime</a> = MatrixType::MaxColsAtCompileTime,
<a class="el" href="class_eigen_1_1_l_d_l_t.html#ad6b0835cf2c2bcbbf28b52e80a7915cba671639edbf1b81e52d6628b12a1f4305">UpLo</a> = _UpLo
<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_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a></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_l_d_l_t.html#a67be78735db4c222af61a9ea65c2225e">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>< typename <br class="typebreak"/>
MatrixType::Scalar >::Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#af34406697a66a0c9591cf1ce854b6724">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_l_d_l_t.html#aee3c386120aa1cd5c8c3ee6c7c396357">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_l_d_l_t.html#a67be78735db4c222af61a9ea65c2225e">Scalar</a>, <br class="typebreak"/>
RowsAtCompileTime, 1, Options, <br class="typebreak"/>
MaxRowsAtCompileTime, 1 > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a440c2522789b6cba6d9a4c5da19af74d">TmpMatrixType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="class_eigen_1_1_transpositions.html">Transpositions</a><br class="typebreak"/>
< RowsAtCompileTime, <br class="typebreak"/>
MaxRowsAtCompileTime > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a63e93afb99f8619cf5e21243977ec79a">TranspositionType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="class_eigen_1_1_permutation_matrix.html">PermutationMatrix</a><br class="typebreak"/>
< RowsAtCompileTime, <br class="typebreak"/>
MaxRowsAtCompileTime > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#abd2722eebb00ef42b6903cf264ffbade">PermutationType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef internal::LDLT_Traits<br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a>, UpLo > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#acf0cf9b78875610a35d10be8e8bdbf00">Traits</a></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_l_d_l_t.html#a0d5011de4b9107ef5766d0452c2b3dd6">LDLT</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor. <a href="#a0d5011de4b9107ef5766d0452c2b3dd6"></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_l_d_l_t.html#abe471b98380c70555996542017b3ccdb">LDLT</a> (<a class="el" href="class_eigen_1_1_l_d_l_t.html#aee3c386120aa1cd5c8c3ee6c7c396357">Index</a> size)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor with memory preallocation. <a href="#abe471b98380c70555996542017b3ccdb"></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_l_d_l_t.html#a97b0a84e22950c421ff759c1bb79b8d2">LDLT</a> (const <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a> &matrix)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">Traits::MatrixU </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a23865098c4666ba5175435ce224b1fb3">matrixU</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">Traits::MatrixL </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a64000b2d5b09f8dfb00579df5da5057e">matrixL</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_l_d_l_t.html#a63e93afb99f8619cf5e21243977ec79a">TranspositionType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a284406d8eacfbf8f929887b4e0c1a5cb">transpositionsP</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a>< const <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a2444e31594d7d806e5c8832e595c5106">vectorD</a> (void) const </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_l_d_l_t.html#ab2b2a3779ce99d2fa1a613f0af016ce8">isPositive</a> (void) const </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_l_d_l_t.html#a713b1d4c0754a9166746d8dc74c7878d">isNegative</a> (void) const </td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename Rhs > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">const internal::solve_retval<br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_l_d_l_t.html">LDLT</a>, Rhs > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a8f5509a12108d17586b2fbc6c377ef04">solve</a> (const <a class="el" href="class_eigen_1_1_matrix_base.html">MatrixBase</a>< Rhs > &b) const </td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename Derived > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a6e68086f7522999cae0822eca792eb5d">solveInPlace</a> (<a class="el" href="class_eigen_1_1_matrix_base.html">MatrixBase</a>< Derived > &bAndX) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_d_l_t.html">LDLT</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#afb61e9d4327e9775e042a5afd9b17c7b">compute</a> (const <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Compute / recompute the <a class="el" href="class_eigen_1_1_l_d_l_t.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> decomposition A = L D L^* = U^* D U of <em>matrix</em>. <a href="#afb61e9d4327e9775e042a5afd9b17c7b"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#adcd4a245c32c44244b241de05daa6463">matrixLDLT</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a3748a9f0bb1e5f2bede17ee40b6132a1">reconstructedMatrix</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_d_l_t.html#aee3c386120aa1cd5c8c3ee6c7c396357">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#afd6c0e654039e35edaa2d91446413206">rows</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_d_l_t.html#aee3c386120aa1cd5c8c3ee6c7c396357">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#aef05299b553f0645df77871972813162">cols</a> () const </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_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a99446d52dbf83fe1cf3dabacb24bceac">m_matrix</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a63e93afb99f8619cf5e21243977ec79a">TranspositionType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a1c2b9c398b9c05a79d7f815930770253">m_transpositions</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a440c2522789b6cba6d9a4c5da19af74d">TmpMatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a548a4aa25509b93ac6008871317d6272">m_temporary</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a8efada10a96cd2563751c7d4e94f8f71">m_sign</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_l_d_l_t.html#a8275176d1fd988af598b9258eb8512ca">m_isInitialized</a></td></tr>
</table>
<hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="aee3c386120aa1cd5c8c3ee6c7c396357"></a><!-- doxytag: member="Eigen::LDLT::Index" ref="aee3c386120aa1cd5c8c3ee6c7c396357" args="" -->
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_l_d_l_t.html#aee3c386120aa1cd5c8c3ee6c7c396357">Eigen::LDLT::Index</a></td>
</tr>
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</div>
<div class="memdoc">
<p>Definition at line <a class="el" href="_cholesky_source.html#l00074">74</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a93a304e076b25bafbeaa03f8e2210774"></a><!-- doxytag: member="Eigen::LDLT::MatrixType" ref="a93a304e076b25bafbeaa03f8e2210774" args="" -->
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">Eigen::LDLT::MatrixType</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00063">63</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="abd2722eebb00ef42b6903cf264ffbade"></a><!-- doxytag: member="Eigen::LDLT::PermutationType" ref="abd2722eebb00ef42b6903cf264ffbade" args="" -->
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_permutation_matrix.html">PermutationMatrix</a><RowsAtCompileTime, MaxRowsAtCompileTime> <a class="el" href="class_eigen_1_1_l_d_l_t.html#abd2722eebb00ef42b6903cf264ffbade">Eigen::LDLT::PermutationType</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00078">78</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="af34406697a66a0c9591cf1ce854b6724"></a><!-- doxytag: member="Eigen::LDLT::RealScalar" ref="af34406697a66a0c9591cf1ce854b6724" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a><typename MatrixType::Scalar>::Real <a class="el" href="class_eigen_1_1_l_d_l_t.html#af34406697a66a0c9591cf1ce854b6724">Eigen::LDLT::RealScalar</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00073">73</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a67be78735db4c222af61a9ea65c2225e"></a><!-- doxytag: member="Eigen::LDLT::Scalar" ref="a67be78735db4c222af61a9ea65c2225e" args="" -->
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_l_d_l_t.html#a67be78735db4c222af61a9ea65c2225e">Eigen::LDLT::Scalar</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00072">72</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a440c2522789b6cba6d9a4c5da19af74d"></a><!-- doxytag: member="Eigen::LDLT::TmpMatrixType" ref="a440c2522789b6cba6d9a4c5da19af74d" 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_l_d_l_t.html#a67be78735db4c222af61a9ea65c2225e">Scalar</a>, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> <a class="el" href="class_eigen_1_1_l_d_l_t.html#a440c2522789b6cba6d9a4c5da19af74d">Eigen::LDLT::TmpMatrixType</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00075">75</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="acf0cf9b78875610a35d10be8e8bdbf00"></a><!-- doxytag: member="Eigen::LDLT::Traits" ref="acf0cf9b78875610a35d10be8e8bdbf00" args="" -->
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<td class="memname">typedef internal::LDLT_Traits<<a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a>,UpLo> <a class="el" href="class_eigen_1_1_l_d_l_t.html#acf0cf9b78875610a35d10be8e8bdbf00">Eigen::LDLT::Traits</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00080">80</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a63e93afb99f8619cf5e21243977ec79a"></a><!-- doxytag: member="Eigen::LDLT::TranspositionType" ref="a63e93afb99f8619cf5e21243977ec79a" args="" -->
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_transpositions.html">Transpositions</a><RowsAtCompileTime, MaxRowsAtCompileTime> <a class="el" href="class_eigen_1_1_l_d_l_t.html#a63e93afb99f8619cf5e21243977ec79a">Eigen::LDLT::TranspositionType</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00077">77</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<hr/><h2>Member Enumeration Documentation</h2>
<a class="anchor" id="ad6b0835cf2c2bcbbf28b52e80a7915cb"></a><!-- doxytag: member="Eigen::LDLT::@58" ref="ad6b0835cf2c2bcbbf28b52e80a7915cb" args="" -->
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<td class="memname">anonymous enum</td>
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<dl><dt><b>Enumerator: </b></dt><dd><table border="0" cellspacing="2" cellpadding="0">
<tr><td valign="top"><em><a class="anchor" id="ad6b0835cf2c2bcbbf28b52e80a7915cba6e5b2ef125662466d71d8dd7bbb9776b"></a><!-- doxytag: member="RowsAtCompileTime" ref="ad6b0835cf2c2bcbbf28b52e80a7915cba6e5b2ef125662466d71d8dd7bbb9776b" args="" -->RowsAtCompileTime</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="ad6b0835cf2c2bcbbf28b52e80a7915cbae59d42dfd2fa7c351c0eb28c0c584870"></a><!-- doxytag: member="ColsAtCompileTime" ref="ad6b0835cf2c2bcbbf28b52e80a7915cbae59d42dfd2fa7c351c0eb28c0c584870" args="" -->ColsAtCompileTime</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="ad6b0835cf2c2bcbbf28b52e80a7915cbaa152c05857ad0f9872d390c14b89b03c"></a><!-- doxytag: member="Options" ref="ad6b0835cf2c2bcbbf28b52e80a7915cbaa152c05857ad0f9872d390c14b89b03c" args="" -->Options</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="ad6b0835cf2c2bcbbf28b52e80a7915cba99a2a317f0a138f240e7071394822635"></a><!-- doxytag: member="MaxRowsAtCompileTime" ref="ad6b0835cf2c2bcbbf28b52e80a7915cba99a2a317f0a138f240e7071394822635" args="" -->MaxRowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="ad6b0835cf2c2bcbbf28b52e80a7915cba9e21176d3e1b02d40bcc7a9b12c3d19c"></a><!-- doxytag: member="MaxColsAtCompileTime" ref="ad6b0835cf2c2bcbbf28b52e80a7915cba9e21176d3e1b02d40bcc7a9b12c3d19c" args="" -->MaxColsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="ad6b0835cf2c2bcbbf28b52e80a7915cba671639edbf1b81e52d6628b12a1f4305"></a><!-- doxytag: member="UpLo" ref="ad6b0835cf2c2bcbbf28b52e80a7915cba671639edbf1b81e52d6628b12a1f4305" args="" -->UpLo</em> </td><td>
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</dd>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00064">64</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="a0d5011de4b9107ef5766d0452c2b3dd6"></a><!-- doxytag: member="Eigen::LDLT::LDLT" ref="a0d5011de4b9107ef5766d0452c2b3dd6" args="()" -->
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<td class="memname">Eigen::LDLT::LDLT </td>
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<p>Default Constructor. </p>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via <a class="el" href="class_eigen_1_1_l_d_l_t.html#afb61e9d4327e9775e042a5afd9b17c7b" title="Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of matrix.">LDLT::compute(const MatrixType&)</a>. </p>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00087">87</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="abe471b98380c70555996542017b3ccdb"></a><!-- doxytag: member="Eigen::LDLT::LDLT" ref="abe471b98380c70555996542017b3ccdb" args="(Index size)" -->
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<td class="memname">Eigen::LDLT::LDLT </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_eigen_1_1_l_d_l_t.html#aee3c386120aa1cd5c8c3ee6c7c396357">Index</a> </td>
<td class="paramname"><em>size</em></td><td>)</td>
<td><code> [inline]</code></td>
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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_l_d_l_t.html#a0d5011de4b9107ef5766d0452c2b3dd6" title="Default Constructor.">LDLT()</a> </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00095">95</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a97b0a84e22950c421ff759c1bb79b8d2"></a><!-- doxytag: member="Eigen::LDLT::LDLT" ref="a97b0a84e22950c421ff759c1bb79b8d2" args="(const MatrixType &matrix)" -->
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<td class="paramname"><em>matrix</em></td><td>)</td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00102">102</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="aef05299b553f0645df77871972813162"></a><!-- doxytag: member="Eigen::LDLT::cols" ref="aef05299b553f0645df77871972813162" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_d_l_t.html#aee3c386120aa1cd5c8c3ee6c7c396357">Index</a> Eigen::LDLT::cols </td>
<td>(</td>
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<td> const<code> [inline]</code></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00204">204</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="afb61e9d4327e9775e042a5afd9b17c7b"></a><!-- doxytag: member="Eigen::LDLT::compute" ref="afb61e9d4327e9775e042a5afd9b17c7b" args="(const MatrixType &matrix)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_d_l_t.html">LDLT</a>< <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a>, _UpLo > & Eigen::LDLT::compute </td>
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<td class="paramname"><em>matrix</em></td><td>)</td>
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<p>Compute / recompute the <a class="el" href="class_eigen_1_1_l_d_l_t.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> decomposition A = L D L^* = U^* D U of <em>matrix</em>. </p>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00345">345</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a713b1d4c0754a9166746d8dc74c7878d"></a><!-- doxytag: member="Eigen::LDLT::isNegative" ref="a713b1d4c0754a9166746d8dc74c7878d" args="(void) const " -->
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<dl class="return"><dt><b>Returns:</b></dt><dd>true if the matrix is negative (semidefinite) </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00155">155</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="ab2b2a3779ce99d2fa1a613f0af016ce8"></a><!-- doxytag: member="Eigen::LDLT::isPositive" ref="ab2b2a3779ce99d2fa1a613f0af016ce8" args="(void) const " -->
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<dl class="return"><dt><b>Returns:</b></dt><dd>true if the matrix is positive (semidefinite) </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00141">141</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a64000b2d5b09f8dfb00579df5da5057e"></a><!-- doxytag: member="Eigen::LDLT::matrixL" ref="a64000b2d5b09f8dfb00579df5da5057e" args="() const " -->
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<td class="memname">Traits::MatrixL Eigen::LDLT::matrixL </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>a view of the lower triangular matrix L </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00119">119</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="adcd4a245c32c44244b241de05daa6463"></a><!-- doxytag: member="Eigen::LDLT::matrixLDLT" ref="adcd4a245c32c44244b241de05daa6463" args="() const " -->
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<td class="memname">const <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a>& Eigen::LDLT::matrixLDLT </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the internal <a class="el" href="class_eigen_1_1_l_d_l_t.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> decomposition matrix</dd></dl>
<p>TODO: document the storage layout </p>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00195">195</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a23865098c4666ba5175435ce224b1fb3"></a><!-- doxytag: member="Eigen::LDLT::matrixU" ref="a23865098c4666ba5175435ce224b1fb3" args="() const " -->
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<td class="memname">Traits::MatrixU Eigen::LDLT::matrixU </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>a view of the upper triangular matrix U </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00112">112</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a3748a9f0bb1e5f2bede17ee40b6132a1"></a><!-- doxytag: member="Eigen::LDLT::reconstructedMatrix" ref="a3748a9f0bb1e5f2bede17ee40b6132a1" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a> Eigen::LDLT::reconstructedMatrix </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the matrix represented by the decomposition, i.e., it returns the product: P^T L D L^* P. This function is provided for debug purpose. </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00421">421</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="afd6c0e654039e35edaa2d91446413206"></a><!-- doxytag: member="Eigen::LDLT::rows" ref="afd6c0e654039e35edaa2d91446413206" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_d_l_t.html#aee3c386120aa1cd5c8c3ee6c7c396357">Index</a> Eigen::LDLT::rows </td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00203">203</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a8f5509a12108d17586b2fbc6c377ef04"></a><!-- doxytag: member="Eigen::LDLT::solve" ref="a8f5509a12108d17586b2fbc6c377ef04" args="(const MatrixBase< Rhs > &b) const " -->
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<td class="memname">const internal::solve_retval<<a class="el" href="class_eigen_1_1_l_d_l_t.html">LDLT</a>, Rhs> Eigen::LDLT::solve </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>a solution x of <img class="formulaInl" alt="$ A x = b $" src="form_130.png"/> using the current decomposition of A.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_l_d_l_t.html#a6e68086f7522999cae0822eca792eb5d">solveInPlace()</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#aa30eab339986a69177addcbdef3e95c1">MatrixBase::ldlt()</a> </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00169">169</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a6e68086f7522999cae0822eca792eb5d"></a><!-- doxytag: member="Eigen::LDLT::solveInPlace" ref="a6e68086f7522999cae0822eca792eb5d" args="(MatrixBase< Derived > &bAndX) const " -->
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<td class="paramname"><em>bAndX</em></td><td>)</td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00406">406</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a284406d8eacfbf8f929887b4e0c1a5cb"></a><!-- doxytag: member="Eigen::LDLT::transpositionsP" ref="a284406d8eacfbf8f929887b4e0c1a5cb" args="() const " -->
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<td class="memname">const <a class="el" href="class_eigen_1_1_l_d_l_t.html#a63e93afb99f8619cf5e21243977ec79a">TranspositionType</a>& Eigen::LDLT::transpositionsP </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const<code> [inline]</code></td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the permutation matrix P as a transposition sequence. </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00127">127</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a2444e31594d7d806e5c8832e595c5106"></a><!-- doxytag: member="Eigen::LDLT::vectorD" ref="a2444e31594d7d806e5c8832e595c5106" args="(void) const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_diagonal.html">Diagonal</a><const <a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a>> Eigen::LDLT::vectorD </td>
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<td class="paramname"></td><td>)</td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the coefficients of the diagonal matrix D </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00134">134</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<hr/><h2>Member Data Documentation</h2>
<a class="anchor" id="a8275176d1fd988af598b9258eb8512ca"></a><!-- doxytag: member="Eigen::LDLT::m_isInitialized" ref="a8275176d1fd988af598b9258eb8512ca" args="" -->
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<td class="memname">bool <a class="el" href="class_eigen_1_1_l_d_l_t.html#a8275176d1fd988af598b9258eb8512ca">Eigen::LDLT::m_isInitialized</a><code> [protected]</code></td>
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<a class="anchor" id="a99446d52dbf83fe1cf3dabacb24bceac"></a><!-- doxytag: member="Eigen::LDLT::m_matrix" ref="a99446d52dbf83fe1cf3dabacb24bceac" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a93a304e076b25bafbeaa03f8e2210774">MatrixType</a> <a class="el" href="class_eigen_1_1_l_d_l_t.html#a99446d52dbf83fe1cf3dabacb24bceac">Eigen::LDLT::m_matrix</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00214">214</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<td class="memname">int <a class="el" href="class_eigen_1_1_l_d_l_t.html#a8efada10a96cd2563751c7d4e94f8f71">Eigen::LDLT::m_sign</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00217">217</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a440c2522789b6cba6d9a4c5da19af74d">TmpMatrixType</a> <a class="el" href="class_eigen_1_1_l_d_l_t.html#a548a4aa25509b93ac6008871317d6272">Eigen::LDLT::m_temporary</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00216">216</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_l_d_l_t.html#a63e93afb99f8619cf5e21243977ec79a">TranspositionType</a> <a class="el" href="class_eigen_1_1_l_d_l_t.html#a1c2b9c398b9c05a79d7f815930770253">Eigen::LDLT::m_transpositions</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00215">215</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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