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<li class="navelem"><a class="el" href="namespace_eigen.html">Eigen</a> </li>
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<div class="title">Eigen::PartialPivLU Class Reference<div class="ingroups"><a class="el" href="group___l_u___module.html">LU module</a></div></div> </div>
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<!-- doxytag: class="Eigen::PartialPivLU" --><hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>LU decomposition of a matrix with partial pivoting, and related 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 LU decomposition</td></tr>
</table>
</dd>
</dl>
<p>This class represents a LU decomposition of a <b>square</b> <b>invertible</b> matrix, with partial pivoting: the matrix A is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P is a permutation matrix.</p>
<p>Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible matrices. Thus LAPACK's dgesv and dgesvx require the matrix to be square and invertible. The present class does the same. It will assert that the matrix is square, but it won't (actually it can't) check that the matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices.</p>
<p>The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided by class <a class="el" href="class_eigen_1_1_full_piv_l_u.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a>.</p>
<p>This is <b>not</b> a rank-revealing LU decomposition. Many features are intentionally absent from this class, such as rank computation. If you need these features, use class <a class="el" href="class_eigen_1_1_full_piv_l_u.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a>.</p>
<p>This LU decomposition is suitable to invert invertible matrices. It is what <a class="el" href="class_eigen_1_1_matrix_base.html#a008dc30f0dfd362c4c8d27008eff6920">MatrixBase::inverse()</a> uses in the general case. On the other hand, it is <b>not</b> suitable to determine whether a given matrix is invertible.</p>
<p>The data of the LU decomposition can be directly accessed through the methods <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a84783f70be9192999a9508b441c96f70">matrixLU()</a>, <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aba4c4eba28c03129135f0470075647e5">permutationP()</a>.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_matrix_base.html#a304945c50984b3fd0175a1fdc9a03f49">MatrixBase::partialPivLu()</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#aeaa1e616a5c11b439fcf23282f582c89">MatrixBase::determinant()</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#a008dc30f0dfd362c4c8d27008eff6920">MatrixBase::inverse()</a>, MatrixBase::computeInverse(), class <a class="el" href="class_eigen_1_1_full_piv_l_u.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a> </dd></dl>
</div>
<p><a href="class_eigen_1_1_partial_piv_l_u-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_partial_piv_l_u.html#a662dde762d76426c57e0b1092eb00c6caf3dbc267d37275cb563f3040031202c4">RowsAtCompileTime</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a662dde762d76426c57e0b1092eb00c6ca4c3e0db17b081ae1dc6f65cb782acaa1">ColsAtCompileTime</a> = MatrixType::ColsAtCompileTime,
<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a662dde762d76426c57e0b1092eb00c6caa2232bdfb08525a307769ea9e76e20bc">Options</a> = MatrixType::Options,
<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a662dde762d76426c57e0b1092eb00c6ca4a0dd4927ba82786d0596c62c6254c4c">MaxRowsAtCompileTime</a> = MatrixType::MaxRowsAtCompileTime,
<br/>
  <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a662dde762d76426c57e0b1092eb00c6cad1ae85bad9c29e5fc3067d475e5d1544">MaxColsAtCompileTime</a> = MatrixType::MaxColsAtCompileTime
<br/>
}</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef _MatrixType </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">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_partial_piv_l_u.html#a79d16b164387e765c0917f348b710406">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_partial_piv_l_u.html#a12e94b8707c39e147c3ed45e8e7376b1">RealScalar</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef internal::traits<br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> >::<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ab87609291b48ede7f1e29fafaeaf4b77">StorageKind</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ab87609291b48ede7f1e29fafaeaf4b77">StorageKind</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_partial_piv_l_u.html#aa9875baae541cc75c1981bec77aa86a5">Index</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_partial_piv_l_u.html#a35042babd31f5c1a462429d377576718">PermutationType</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_partial_piv_l_u.html#ab3b3aca35ae872374f9678b626fcf2cb">TranspositionType</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_partial_piv_l_u.html#a27d5af4e6d13c175794233329c8c05cd">PartialPivLU</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor. <a href="#a27d5af4e6d13c175794233329c8c05cd"></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_partial_piv_l_u.html#a708eda30806d4ad4731c5b7ad4accade">PartialPivLU</a> (<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aa9875baae541cc75c1981bec77aa86a5">Index</a> size)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor with memory preallocation. <a href="#a708eda30806d4ad4731c5b7ad4accade"></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_partial_piv_l_u.html#a5f094883093a41bd07ec3c402918f438">PartialPivLU</a> (const <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> &matrix)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor. <a href="#a5f094883093a41bd07ec3c402918f438"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html">PartialPivLU</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a3fa3b2237624f261b9c6ead8fb201920">compute</a> (const <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> &matrix)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a84783f70be9192999a9508b441c96f70">matrixLU</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a35042babd31f5c1a462429d377576718">PermutationType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aba4c4eba28c03129135f0470075647e5">permutationP</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_partial_piv_l_u.html">PartialPivLU</a>, Rhs > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ac301a4e957b4d643aff3ee7742bd8488">solve</a> (const <a class="el" href="class_eigen_1_1_matrix_base.html">MatrixBase</a>< Rhs > &b) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">This method returns the solution x to the equation Ax=b, where A is the matrix of which *this is the LU decomposition. <a href="#ac301a4e957b4d643aff3ee7742bd8488"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const internal::solve_retval<br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_partial_piv_l_u.html">PartialPivLU</a>, typename <br class="typebreak"/>
MatrixType::IdentityReturnType > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a40cbcf0790d090f766b10c586fd5c9f8">inverse</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">internal::traits< <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> ><br class="typebreak"/>
::<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a79d16b164387e765c0917f348b710406">Scalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ad34b4c5187afe94b84b1cbe6a0174d89">determinant</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ad404f6ad2c85faa0b61e295bd691e00d">reconstructedMatrix</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aa9875baae541cc75c1981bec77aa86a5">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a49d2cb1f94e234e00e1870c9db82627e">rows</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aa9875baae541cc75c1981bec77aa86a5">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aa0c80ad4d403e526adb3c019a0fba9ff">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_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a7995db96fbe492ae2b80b7129f15b02f">m_lu</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a35042babd31f5c1a462429d377576718">PermutationType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af93d7bdcc215aa9597f58ed31807a9e4">m_p</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ab3b3aca35ae872374f9678b626fcf2cb">TranspositionType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ae0722be51a97b2ee2d91adb8ff721ec8">m_rowsTranspositions</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aa9875baae541cc75c1981bec77aa86a5">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af19e11100e105225937cb0f992fbe797">m_det_p</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_partial_piv_l_u.html#accb4e2aef0f63f1c62783e2a283212fd">m_isInitialized</a></td></tr>
</table>
<hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="aa9875baae541cc75c1981bec77aa86a5"></a><!-- doxytag: member="Eigen::PartialPivLU::Index" ref="aa9875baae541cc75c1981bec77aa86a5" args="" -->
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aa9875baae541cc75c1981bec77aa86a5">Eigen::PartialPivLU::Index</a></td>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_l_u_source.html#l00076">76</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="af931d0a34b12985a2b993cfcdf635887"></a><!-- doxytag: member="Eigen::PartialPivLU::MatrixType" ref="af931d0a34b12985a2b993cfcdf635887" args="" -->
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">Eigen::PartialPivLU::MatrixType</a></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00065">65</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a35042babd31f5c1a462429d377576718"></a><!-- doxytag: member="Eigen::PartialPivLU::PermutationType" ref="a35042babd31f5c1a462429d377576718" 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_partial_piv_l_u.html#a35042babd31f5c1a462429d377576718">Eigen::PartialPivLU::PermutationType</a></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00077">77</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a12e94b8707c39e147c3ed45e8e7376b1"></a><!-- doxytag: member="Eigen::PartialPivLU::RealScalar" ref="a12e94b8707c39e147c3ed45e8e7376b1" 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_partial_piv_l_u.html#a12e94b8707c39e147c3ed45e8e7376b1">Eigen::PartialPivLU::RealScalar</a></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00074">74</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a79d16b164387e765c0917f348b710406"></a><!-- doxytag: member="Eigen::PartialPivLU::Scalar" ref="a79d16b164387e765c0917f348b710406" args="" -->
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a79d16b164387e765c0917f348b710406">Eigen::PartialPivLU::Scalar</a></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00073">73</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="ab87609291b48ede7f1e29fafaeaf4b77"></a><!-- doxytag: member="Eigen::PartialPivLU::StorageKind" ref="ab87609291b48ede7f1e29fafaeaf4b77" args="" -->
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<td class="memname">typedef internal::traits<<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a>>::<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ab87609291b48ede7f1e29fafaeaf4b77">StorageKind</a> <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ab87609291b48ede7f1e29fafaeaf4b77">Eigen::PartialPivLU::StorageKind</a></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00075">75</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="ab3b3aca35ae872374f9678b626fcf2cb"></a><!-- doxytag: member="Eigen::PartialPivLU::TranspositionType" ref="ab3b3aca35ae872374f9678b626fcf2cb" 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_partial_piv_l_u.html#ab3b3aca35ae872374f9678b626fcf2cb">Eigen::PartialPivLU::TranspositionType</a></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00078">78</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<hr/><h2>Member Enumeration Documentation</h2>
<a class="anchor" id="a662dde762d76426c57e0b1092eb00c6c"></a><!-- doxytag: member="Eigen::PartialPivLU::@375" ref="a662dde762d76426c57e0b1092eb00c6c" 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="a662dde762d76426c57e0b1092eb00c6caf3dbc267d37275cb563f3040031202c4"></a><!-- doxytag: member="RowsAtCompileTime" ref="a662dde762d76426c57e0b1092eb00c6caf3dbc267d37275cb563f3040031202c4" args="" -->RowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a662dde762d76426c57e0b1092eb00c6ca4c3e0db17b081ae1dc6f65cb782acaa1"></a><!-- doxytag: member="ColsAtCompileTime" ref="a662dde762d76426c57e0b1092eb00c6ca4c3e0db17b081ae1dc6f65cb782acaa1" args="" -->ColsAtCompileTime</em> </td><td>
</td></tr>
<tr><td valign="top"><em><a class="anchor" id="a662dde762d76426c57e0b1092eb00c6caa2232bdfb08525a307769ea9e76e20bc"></a><!-- doxytag: member="Options" ref="a662dde762d76426c57e0b1092eb00c6caa2232bdfb08525a307769ea9e76e20bc" args="" -->Options</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a662dde762d76426c57e0b1092eb00c6ca4a0dd4927ba82786d0596c62c6254c4c"></a><!-- doxytag: member="MaxRowsAtCompileTime" ref="a662dde762d76426c57e0b1092eb00c6ca4a0dd4927ba82786d0596c62c6254c4c" args="" -->MaxRowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a662dde762d76426c57e0b1092eb00c6cad1ae85bad9c29e5fc3067d475e5d1544"></a><!-- doxytag: member="MaxColsAtCompileTime" ref="a662dde762d76426c57e0b1092eb00c6cad1ae85bad9c29e5fc3067d475e5d1544" args="" -->MaxColsAtCompileTime</em> </td><td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00066">66</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="a27d5af4e6d13c175794233329c8c05cd"></a><!-- doxytag: member="Eigen::PartialPivLU::PartialPivLU" ref="a27d5af4e6d13c175794233329c8c05cd" args="()" -->
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<td class="memname">Eigen::PartialPivLU::PartialPivLU </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_partial_piv_l_u.html#a3fa3b2237624f261b9c6ead8fb201920">PartialPivLU::compute(const MatrixType&)</a>. </p>
<p>Definition at line <a class="el" href="_l_u_source.html#l00196">196</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a708eda30806d4ad4731c5b7ad4accade"></a><!-- doxytag: member="Eigen::PartialPivLU::PartialPivLU" ref="a708eda30806d4ad4731c5b7ad4accade" args="(Index size)" -->
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<td class="memname">Eigen::PartialPivLU::PartialPivLU </td>
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<td class="paramtype"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aa9875baae541cc75c1981bec77aa86a5">Index</a> </td>
<td class="paramname"><em>size</em></td><td>)</td>
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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a27d5af4e6d13c175794233329c8c05cd" title="Default Constructor.">PartialPivLU()</a> </dd></dl>
<p>Definition at line <a class="el" href="_l_u_source.html#l00206">206</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a5f094883093a41bd07ec3c402918f438"></a><!-- doxytag: member="Eigen::PartialPivLU::PartialPivLU" ref="a5f094883093a41bd07ec3c402918f438" args="(const MatrixType &matrix)" -->
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<td class="memname">Eigen::PartialPivLU::PartialPivLU </td>
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<p>Constructor. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">matrix</td><td>the matrix of which to compute the LU decomposition.</td></tr>
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</dd>
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<dl class="warning"><dt><b>Warning:</b></dt><dd>The matrix should have full rank (e.g. if it's square, it should be invertible). If you need to deal with non-full rank, use class <a class="el" href="class_eigen_1_1_full_piv_l_u.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a> instead. </dd></dl>
<p>Definition at line <a class="el" href="_l_u_source.html#l00216">216</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="aa0c80ad4d403e526adb3c019a0fba9ff"></a><!-- doxytag: member="Eigen::PartialPivLU::cols" ref="aa0c80ad4d403e526adb3c019a0fba9ff" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#aa9875baae541cc75c1981bec77aa86a5">Index</a> Eigen::PartialPivLU::cols </td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00185">185</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a3fa3b2237624f261b9c6ead8fb201920"></a><!-- doxytag: member="Eigen::PartialPivLU::compute" ref="a3fa3b2237624f261b9c6ead8fb201920" args="(const MatrixType &matrix)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html">PartialPivLU</a>< <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> > & Eigen::PartialPivLU::compute </td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00401">401</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="ad34b4c5187afe94b84b1cbe6a0174d89"></a><!-- doxytag: member="Eigen::PartialPivLU::determinant" ref="ad34b4c5187afe94b84b1cbe6a0174d89" args="() const " -->
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<td class="memname">internal::traits< <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> >::<a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a79d16b164387e765c0917f348b710406">Scalar</a> Eigen::PartialPivLU::determinant </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the determinant of the matrix of which *this is the LU decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the LU decomposition has already been computed.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>For fixed-size matrices of size up to 4, <a class="el" href="class_eigen_1_1_matrix_base.html#aeaa1e616a5c11b439fcf23282f582c89">MatrixBase::determinant()</a> offers optimized paths.</dd></dl>
<dl class="warning"><dt><b>Warning:</b></dt><dd>a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_matrix_base.html#aeaa1e616a5c11b439fcf23282f582c89">MatrixBase::determinant()</a> </dd></dl>
<p>Definition at line <a class="el" href="_l_u_source.html#l00421">421</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a40cbcf0790d090f766b10c586fd5c9f8"></a><!-- doxytag: member="Eigen::PartialPivLU::inverse" ref="a40cbcf0790d090f766b10c586fd5c9f8" args="() const " -->
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<td class="memname">const internal::solve_retval<<a class="el" href="class_eigen_1_1_partial_piv_l_u.html">PartialPivLU</a>,typename MatrixType::IdentityReturnType> Eigen::PartialPivLU::inverse </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the inverse of the matrix of which *this is the LU decomposition.</dd></dl>
<dl class="warning"><dt><b>Warning:</b></dt><dd>The matrix being decomposed here is assumed to be invertible. If you need to check for invertibility, use class <a class="el" href="class_eigen_1_1_full_piv_l_u.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a> instead.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_matrix_base.html#a008dc30f0dfd362c4c8d27008eff6920">MatrixBase::inverse()</a>, LU::inverse() </dd></dl>
<p>Definition at line <a class="el" href="_l_u_source.html#l00160">160</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a84783f70be9192999a9508b441c96f70"></a><!-- doxytag: member="Eigen::PartialPivLU::matrixLU" ref="a84783f70be9192999a9508b441c96f70" args="() const " -->
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<td class="memname">const <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a>& Eigen::PartialPivLU::matrixLU </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the LU decomposition matrix: the upper-triangular part is U, the unit-lower-triangular part is L (at least for square matrices; in the non-square case, special care is needed, see the documentation of class <a class="el" href="class_eigen_1_1_full_piv_l_u.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a>).</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd>matrixL(), matrixU() </dd></dl>
<p>Definition at line <a class="el" href="_l_u_source.html#l00114">114</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="aba4c4eba28c03129135f0470075647e5"></a><!-- doxytag: member="Eigen::PartialPivLU::permutationP" ref="aba4c4eba28c03129135f0470075647e5" args="() const " -->
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<dl class="return"><dt><b>Returns:</b></dt><dd>the permutation matrix P. </dd></dl>
<p>Definition at line <a class="el" href="_l_u_source.html#l00122">122</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> Eigen::PartialPivLU::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^{-1} L U. This function is provided for debug purpose. </dd></dl>
<p>Definition at line <a class="el" href="_l_u_source.html#l00431">431</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="a49d2cb1f94e234e00e1870c9db82627e"></a><!-- doxytag: member="Eigen::PartialPivLU::rows" ref="a49d2cb1f94e234e00e1870c9db82627e" args="() const " -->
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<p>Definition at line <a class="el" href="_l_u_source.html#l00184">184</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="ac301a4e957b4d643aff3ee7742bd8488"></a><!-- doxytag: member="Eigen::PartialPivLU::solve" ref="ac301a4e957b4d643aff3ee7742bd8488" args="(const MatrixBase< Rhs > &b) const " -->
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<p>This method returns the solution x to the equation Ax=b, where A is the matrix of which *this is the LU decomposition. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">b</td><td>the right-hand-side of the equation to solve. Can be a vector or a matrix, the only requirement in order for the equation to make sense is that b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.</td></tr>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the solution.</dd></dl>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><p>Since this <a class="el" href="class_eigen_1_1_partial_piv_l_u.html" title="LU decomposition of a matrix with partial pivoting, and related features.">PartialPivLU</a> class assumes anyway that the matrix A is invertible, the solution theoretically exists and is unique regardless of b.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_triangular_view.html#a1975e4658d4e74b103d1da66ec2816c8">TriangularView::solve()</a>, <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a40cbcf0790d090f766b10c586fd5c9f8">inverse()</a>, computeInverse() </dd></dl>
<p>Definition at line <a class="el" href="_l_u_source.html#l00147">147</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<hr/><h2>Member Data Documentation</h2>
<a class="anchor" id="af19e11100e105225937cb0f992fbe797"></a><!-- doxytag: member="Eigen::PartialPivLU::m_det_p" ref="af19e11100e105225937cb0f992fbe797" args="" -->
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<p>Definition at line <a class="el" href="_l_u_source.html#l00191">191</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00192">192</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af931d0a34b12985a2b993cfcdf635887">MatrixType</a> <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a7995db96fbe492ae2b80b7129f15b02f">Eigen::PartialPivLU::m_lu</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00188">188</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#a35042babd31f5c1a462429d377576718">PermutationType</a> <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#af93d7bdcc215aa9597f58ed31807a9e4">Eigen::PartialPivLU::m_p</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00189">189</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<a class="anchor" id="ae0722be51a97b2ee2d91adb8ff721ec8"></a><!-- doxytag: member="Eigen::PartialPivLU::m_rowsTranspositions" ref="ae0722be51a97b2ee2d91adb8ff721ec8" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ab3b3aca35ae872374f9678b626fcf2cb">TranspositionType</a> <a class="el" href="class_eigen_1_1_partial_piv_l_u.html#ae0722be51a97b2ee2d91adb8ff721ec8">Eigen::PartialPivLU::m_rowsTranspositions</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_l_u_source.html#l00190">190</a> of file <a class="el" href="_l_u_source.html">LU</a>.</p>
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<br><hr><br> <table border="0" width="100%"> <tr> <td> Page generated by <a href="http://www.doxygen.org" target="_blank">Doxygen 1.7.5</a> for MRPT 0.9.5 SVN: at Sun Sep 25 17:20:18 UTC 2011</td><td></td> <td width="100"> </td> <td width="150"> </td></tr> </table> </body></html>
