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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_l_t.html">LLT</a> </li>
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<div class="title">Eigen::LLT Class Reference</div> </div>
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<!-- doxytag: class="Eigen::LLT" --><hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Standard Cholesky decomposition (LL^T) of a matrix and associated features. </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 we are computing the LL^T Cholesky decomposition</td></tr>
</table>
</dd>
</dl>
<p>This class performs a LL^T Cholesky decomposition of a symmetric, positive definite matrix A such that A = LL^* = U^*U, where L is lower triangular.</p>
<p>While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, for that purpose, we recommend the Cholesky decomposition without square root which is more stable and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other situations like generalised eigen problems with hermitian matrices.</p>
<p>Remember that Cholesky decompositions are not rank-revealing. This <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> decomposition is only stable on positive definite matrices, use <a class="el" href="class_eigen_1_1_l_d_l_t.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> instead for the semidefinite case. 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#ad31d26a57bda07126375b706a9d9e4bf">MatrixBase::llt()</a>, class <a class="el" href="class_eigen_1_1_l_d_l_t.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> </dd></dl>
</div>
<p><a href="class_eigen_1_1_l_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">{ <a class="el" href="class_eigen_1_1_l_l_t.html#a33449d358e030bb7ecf16edf49fef6dfa93cc3caaad3e7a4850b2c1a1b0506c31">RowsAtCompileTime</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_l_l_t.html#a33449d358e030bb7ecf16edf49fef6dfaa6f81cc65bd9584e7e8b73ce30723602">ColsAtCompileTime</a> = MatrixType::ColsAtCompileTime,
<a class="el" href="class_eigen_1_1_l_l_t.html#a33449d358e030bb7ecf16edf49fef6dfadf2f19de8ab24d94e1c794fa3ee996f4">Options</a> = MatrixType::Options,
<a class="el" href="class_eigen_1_1_l_l_t.html#a33449d358e030bb7ecf16edf49fef6dfaeaa528b0e1f7b6fb0f0861ecded813c2">MaxColsAtCompileTime</a> = MatrixType::MaxColsAtCompileTime
}</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">enum  </td><td class="memItemRight" valign="bottom">{ <a class="el" href="class_eigen_1_1_l_l_t.html#a2d5fde2768b68d50e563fbe953615bccafc6cd5eedabd03fe47681b147da353bc">PacketSize</a> = internal::packet_traits<Scalar>::size,
<a class="el" href="class_eigen_1_1_l_l_t.html#a2d5fde2768b68d50e563fbe953615bccae695b3e9f0ed5687164f95dee5aa5772">AlignmentMask</a> = int(PacketSize)-1,
<a class="el" href="class_eigen_1_1_l_l_t.html#a2d5fde2768b68d50e563fbe953615bcca1919156012d3f74053a6ae44f053f728">UpLo</a> = _UpLo
}</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_l_t.html#a9702706f16068689984429a8e5126103">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_l_t.html#a40ff541348dbe6f13e7db2a1b08dfa4c">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_l_t.html#a68e88fb2bda7743b13491b3123c5ded2">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_l_t.html#aa3730a2c98347e6f3e8080f917b6c787">Index</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef internal::LLT_Traits<br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a>, UpLo > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#a8d415f022e229f4ef964fec79f9b01f5">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_l_t.html#a4bdd0f5243ea1f632da85061499e954b">LLT</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor. <a href="#a4bdd0f5243ea1f632da85061499e954b"></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_l_t.html#aee46a0413cfeb5089cc33f09aa33b968">LLT</a> (<a class="el" href="class_eigen_1_1_l_l_t.html#aa3730a2c98347e6f3e8080f917b6c787">Index</a> size)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor with memory preallocation. <a href="#aee46a0413cfeb5089cc33f09aa33b968"></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_l_t.html#ae455f2f7a0b3a8d5bcd7a00bfaf95e46">LLT</a> (const <a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">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_l_t.html#a7e89a9e6861b04055ec25470d418eb8f">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_l_t.html#a129084eaf639bc4750fc64100bf5e9c9">matrixL</a> () 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_l_t.html">LLT</a>, Rhs > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#a6195607d3b3b7f4cca2a199de5b117b5">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">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#ad3cb55145e02bb3ec1c5b6b45aea9449">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_l_t.html">LLT</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#a89f56c93902711c45e76e286240621fa">compute</a> (const <a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of <em>matrix</em>. <a href="#a89f56c93902711c45e76e286240621fa"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#a0aa79fc42d3452a75062232d0763d670">matrixLLT</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#a70fe757d507a7f791ea804a8c06d5fd7">reconstructedMatrix</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespace_eigen.html#a85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#a366f42dcf9e0ec0cf4e9b3d1aad3cc82">info</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Reports whether previous computation was successful. <a href="#a366f42dcf9e0ec0cf4e9b3d1aad3cc82"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_l_t.html#aa3730a2c98347e6f3e8080f917b6c787">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#ac0aad05eb3b349f96d5602fc1ac287ed">rows</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_l_l_t.html#aa3730a2c98347e6f3e8080f917b6c787">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#a6621d8f154654f8d7de7edaa04bfca4c">cols</a> () const </td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename VectorType > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#a304eabbc6101d0cc9ec2f362f01b5e76">rankUpdate</a> (const VectorType &vec)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Performs a rank one update of the current decomposition. <a href="#a304eabbc6101d0cc9ec2f362f01b5e76"></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_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#af02cef2041b85ef7ab9553b3b5ce93d9">m_matrix</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_l_t.html#aa74565d80cec43789e38ed9cc611a543">m_isInitialized</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespace_eigen.html#a85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_l_l_t.html#af2c173f55ddac0a6ae924fe1937d95c7">m_info</a></td></tr>
</table>
<hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="aa3730a2c98347e6f3e8080f917b6c787"></a><!-- doxytag: member="Eigen::LLT::Index" ref="aa3730a2c98347e6f3e8080f917b6c787" args="" -->
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_l_l_t.html#aa3730a2c98347e6f3e8080f917b6c787">Eigen::LLT::Index</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00071">71</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a9702706f16068689984429a8e5126103"></a><!-- doxytag: member="Eigen::LLT::MatrixType" ref="a9702706f16068689984429a8e5126103" args="" -->
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">Eigen::LLT::MatrixType</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00062">62</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a68e88fb2bda7743b13491b3123c5ded2"></a><!-- doxytag: member="Eigen::LLT::RealScalar" ref="a68e88fb2bda7743b13491b3123c5ded2" 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_l_t.html#a68e88fb2bda7743b13491b3123c5ded2">Eigen::LLT::RealScalar</a></td>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_cholesky_source.html#l00070">70</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a40ff541348dbe6f13e7db2a1b08dfa4c"></a><!-- doxytag: member="Eigen::LLT::Scalar" ref="a40ff541348dbe6f13e7db2a1b08dfa4c" args="" -->
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_l_l_t.html#a40ff541348dbe6f13e7db2a1b08dfa4c">Eigen::LLT::Scalar</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00069">69</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a8d415f022e229f4ef964fec79f9b01f5"></a><!-- doxytag: member="Eigen::LLT::Traits" ref="a8d415f022e229f4ef964fec79f9b01f5" args="" -->
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<td class="memname">typedef internal::LLT_Traits<<a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a>,UpLo> <a class="el" href="class_eigen_1_1_l_l_t.html#a8d415f022e229f4ef964fec79f9b01f5">Eigen::LLT::Traits</a></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00079">79</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="a33449d358e030bb7ecf16edf49fef6df"></a><!-- doxytag: member="Eigen::LLT::@56" ref="a33449d358e030bb7ecf16edf49fef6df" 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="a33449d358e030bb7ecf16edf49fef6dfa93cc3caaad3e7a4850b2c1a1b0506c31"></a><!-- doxytag: member="RowsAtCompileTime" ref="a33449d358e030bb7ecf16edf49fef6dfa93cc3caaad3e7a4850b2c1a1b0506c31" args="" -->RowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a33449d358e030bb7ecf16edf49fef6dfaa6f81cc65bd9584e7e8b73ce30723602"></a><!-- doxytag: member="ColsAtCompileTime" ref="a33449d358e030bb7ecf16edf49fef6dfaa6f81cc65bd9584e7e8b73ce30723602" args="" -->ColsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a33449d358e030bb7ecf16edf49fef6dfadf2f19de8ab24d94e1c794fa3ee996f4"></a><!-- doxytag: member="Options" ref="a33449d358e030bb7ecf16edf49fef6dfadf2f19de8ab24d94e1c794fa3ee996f4" args="" -->Options</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a33449d358e030bb7ecf16edf49fef6dfaeaa528b0e1f7b6fb0f0861ecded813c2"></a><!-- doxytag: member="MaxColsAtCompileTime" ref="a33449d358e030bb7ecf16edf49fef6dfaeaa528b0e1f7b6fb0f0861ecded813c2" args="" -->MaxColsAtCompileTime</em> </td><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="a2d5fde2768b68d50e563fbe953615bcc"></a><!-- doxytag: member="Eigen::LLT::@57" ref="a2d5fde2768b68d50e563fbe953615bcc" 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="a2d5fde2768b68d50e563fbe953615bccafc6cd5eedabd03fe47681b147da353bc"></a><!-- doxytag: member="PacketSize" ref="a2d5fde2768b68d50e563fbe953615bccafc6cd5eedabd03fe47681b147da353bc" args="" -->PacketSize</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a2d5fde2768b68d50e563fbe953615bccae695b3e9f0ed5687164f95dee5aa5772"></a><!-- doxytag: member="AlignmentMask" ref="a2d5fde2768b68d50e563fbe953615bccae695b3e9f0ed5687164f95dee5aa5772" args="" -->AlignmentMask</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a2d5fde2768b68d50e563fbe953615bcca1919156012d3f74053a6ae44f053f728"></a><!-- doxytag: member="UpLo" ref="a2d5fde2768b68d50e563fbe953615bcca1919156012d3f74053a6ae44f053f728" args="" -->UpLo</em> </td><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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<hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="a4bdd0f5243ea1f632da85061499e954b"></a><!-- doxytag: member="Eigen::LLT::LLT" ref="a4bdd0f5243ea1f632da85061499e954b" args="()" -->
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<td class="memname">Eigen::LLT::LLT </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_l_t.html#a89f56c93902711c45e76e286240621fa" title="Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of matrix.">LLT::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="aee46a0413cfeb5089cc33f09aa33b968"></a><!-- doxytag: member="Eigen::LLT::LLT" ref="aee46a0413cfeb5089cc33f09aa33b968" args="(Index size)" -->
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<td class="memname">Eigen::LLT::LLT </td>
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<td class="paramtype"><a class="el" href="class_eigen_1_1_l_l_t.html#aa3730a2c98347e6f3e8080f917b6c787">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_l_t.html#a4bdd0f5243ea1f632da85061499e954b" title="Default Constructor.">LLT()</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="ae455f2f7a0b3a8d5bcd7a00bfaf95e46"></a><!-- doxytag: member="Eigen::LLT::LLT" ref="ae455f2f7a0b3a8d5bcd7a00bfaf95e46" args="(const MatrixType &matrix)" -->
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<td class="memname">Eigen::LLT::LLT </td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00098">98</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="a6621d8f154654f8d7de7edaa04bfca4c"></a><!-- doxytag: member="Eigen::LLT::cols" ref="a6621d8f154654f8d7de7edaa04bfca4c" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_l_t.html#aa3730a2c98347e6f3e8080f917b6c787">Index</a> Eigen::LLT::cols </td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00180">180</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a89f56c93902711c45e76e286240621fa"></a><!-- doxytag: member="Eigen::LLT::compute" ref="a89f56c93902711c45e76e286240621fa" args="(const MatrixType &matrix)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_l_t.html">LLT</a>< <a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a>, _UpLo > & Eigen::LLT::compute </td>
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<p>Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of <em>matrix</em>. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>a reference to *this </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00342">342</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a366f42dcf9e0ec0cf4e9b3d1aad3cc82"></a><!-- doxytag: member="Eigen::LLT::info" ref="a366f42dcf9e0ec0cf4e9b3d1aad3cc82" args="() const " -->
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<td class="memname"><a class="el" href="namespace_eigen.html#a85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> Eigen::LLT::info </td>
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<p>Reports whether previous computation was successful. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd><code>Success</code> if computation was succesful, <code>NumericalIssue</code> if the matrix.appears to be negative. </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00173">173</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
<p>Referenced by <a class="el" href="eigen__plugins_8h_source.html#l00710">chol()</a>.</p>
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<a class="anchor" id="a129084eaf639bc4750fc64100bf5e9c9"></a><!-- doxytag: member="Eigen::LLT::matrixL" ref="a129084eaf639bc4750fc64100bf5e9c9" args="() const " -->
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<td class="memname">Traits::MatrixL Eigen::LLT::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#l00113">113</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a0aa79fc42d3452a75062232d0763d670"></a><!-- doxytag: member="Eigen::LLT::matrixLLT" ref="a0aa79fc42d3452a75062232d0763d670" args="() const " -->
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<td class="memname">const <a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a>& Eigen::LLT::matrixLLT </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the <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> decomposition matrix</dd></dl>
<p>TODO: document the storage layout </p>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00159">159</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a7e89a9e6861b04055ec25470d418eb8f"></a><!-- doxytag: member="Eigen::LLT::matrixU" ref="a7e89a9e6861b04055ec25470d418eb8f" args="() const " -->
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<td class="memname">Traits::MatrixU Eigen::LLT::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#l00106">106</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
<p>Referenced by <a class="el" href="eigen__plugins_8h_source.html#l00710">chol()</a>.</p>
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<a class="anchor" id="a304eabbc6101d0cc9ec2f362f01b5e76"></a><!-- doxytag: member="Eigen::LLT::rankUpdate" ref="a304eabbc6101d0cc9ec2f362f01b5e76" args="(const VectorType &vec)" -->
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<p>Performs a rank one update of the current decomposition. </p>
<p>If A = LL^* before the rank one update, then after it we have LL^* = A + vv^* where <em>v</em> must be a vector of same dimension. </p>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00364">364</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="a70fe757d507a7f791ea804a8c06d5fd7"></a><!-- doxytag: member="Eigen::LLT::reconstructedMatrix" ref="a70fe757d507a7f791ea804a8c06d5fd7" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a> Eigen::LLT::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: L L^*. This function is provided for debug purpose. </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00413">413</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="ac0aad05eb3b349f96d5602fc1ac287ed"></a><!-- doxytag: member="Eigen::LLT::rows" ref="ac0aad05eb3b349f96d5602fc1ac287ed" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_l_l_t.html#aa3730a2c98347e6f3e8080f917b6c787">Index</a> Eigen::LLT::rows </td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00179">179</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<td class="memname">const internal::solve_retval<<a class="el" href="class_eigen_1_1_l_l_t.html">LLT</a>, Rhs> Eigen::LLT::solve </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the solution x of <img class="formulaInl" alt="$ A x = b $" src="form_130.png"/> using the current decomposition of A.</dd></dl>
<p>Since this <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> class assumes anyway that the matrix A is invertible, the solution theoretically exists and is unique regardless of b.</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_l_l_t.html#ad3cb55145e02bb3ec1c5b6b45aea9449">solveInPlace()</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#ad31d26a57bda07126375b706a9d9e4bf">MatrixBase::llt()</a> </dd></dl>
<p>Definition at line <a class="el" href="_cholesky_source.html#l00131">131</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="ad3cb55145e02bb3ec1c5b6b45aea9449"></a><!-- doxytag: member="Eigen::LLT::solveInPlace" ref="ad3cb55145e02bb3ec1c5b6b45aea9449" args="(MatrixBase< Derived > &bAndX) const " -->
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00401">401</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="af2c173f55ddac0a6ae924fe1937d95c7"></a><!-- doxytag: member="Eigen::LLT::m_info" ref="af2c173f55ddac0a6ae924fe1937d95c7" args="" -->
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<td class="memname"><a class="el" href="namespace_eigen.html#a85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="el" href="class_eigen_1_1_l_l_t.html#af2c173f55ddac0a6ae924fe1937d95c7">Eigen::LLT::m_info</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00192">192</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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<a class="anchor" id="aa74565d80cec43789e38ed9cc611a543"></a><!-- doxytag: member="Eigen::LLT::m_isInitialized" ref="aa74565d80cec43789e38ed9cc611a543" args="" -->
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<td class="memname">bool <a class="el" href="class_eigen_1_1_l_l_t.html#aa74565d80cec43789e38ed9cc611a543">Eigen::LLT::m_isInitialized</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00191">191</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_l_t.html#a9702706f16068689984429a8e5126103">MatrixType</a> <a class="el" href="class_eigen_1_1_l_l_t.html#af02cef2041b85ef7ab9553b3b5ce93d9">Eigen::LLT::m_matrix</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_cholesky_source.html#l00190">190</a> of file <a class="el" href="_cholesky_source.html">Cholesky</a>.</p>
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