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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_full_piv_householder_q_r.html">FullPivHouseholderQR</a> </li>
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<a href="#pub-types">Public Types</a> |
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<div class="title">Eigen::FullPivHouseholderQR Class Reference<div class="ingroups"><a class="el" href="group___q_r___module.html">QR module</a></div></div> </div>
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<!-- doxytag: class="Eigen::FullPivHouseholderQR" --><hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Householder rank-revealing QR decomposition of a matrix with full 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 we are computing the QR decomposition</td></tr>
</table>
</dd>
</dl>
<p>This class performs a rank-revealing QR decomposition of a matrix <b>A</b> into matrices <b>P</b>, <b>Q</b> and <b>R</b> such that </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R} \]" src="form_265.png"/>
</p>
<p> by using Householder transformations. Here, <b>P</b> is a permutation matrix, <b>Q</b> a unitary matrix and <b>R</b> an upper triangular matrix.</p>
<p>This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal numerical stability. The trade-off is that it is slower than <a class="el" href="class_eigen_1_1_householder_q_r.html" title="Householder QR decomposition of a matrix.">HouseholderQR</a> and <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html" title="Householder rank-revealing QR decomposition of a matrix with column-pivoting.">ColPivHouseholderQR</a>.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_matrix_base.html#aae85761ed3996df278690b2a825d1235">MatrixBase::fullPivHouseholderQr()</a> </dd></dl>
</div>
<p><a href="class_eigen_1_1_full_piv_householder_q_r-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_full_piv_householder_q_r.html#a8b167c70c49bf065b6b85b7e0774765aa2c720108835407aa7c71cc43a8ac365f">RowsAtCompileTime</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8b167c70c49bf065b6b85b7e0774765aa9251ed0b8e9b2840751a2ac39b10caf3">ColsAtCompileTime</a> = MatrixType::ColsAtCompileTime,
<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8b167c70c49bf065b6b85b7e0774765aa60679e222c5f2e551e2e165bb9e1305e">Options</a> = MatrixType::Options,
<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8b167c70c49bf065b6b85b7e0774765aa3b74ffcf7a853f39cf018772473f6776">MaxRowsAtCompileTime</a> = MatrixType::MaxRowsAtCompileTime,
<br/>
  <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8b167c70c49bf065b6b85b7e0774765aa6de5fa38028124637cb0fe8c8c6a09e4">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_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">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_full_piv_householder_q_r.html#a1df92827b1134d5a8096720b6f021394">Scalar</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef MatrixType::RealScalar </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">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_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">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_full_piv_householder_q_r.html#a1df92827b1134d5a8096720b6f021394">Scalar</a>, <br class="typebreak"/>
RowsAtCompileTime, <br class="typebreak"/>
RowsAtCompileTime, Options, <br class="typebreak"/>
MaxRowsAtCompileTime, <br class="typebreak"/>
MaxRowsAtCompileTime > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#abf33889a5be7456ed8e110b2843cc3e6">MatrixQType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1plain__diag__type.html">internal::plain_diag_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8443db51953fe2b6bd71a8798be5743f">HCoeffsType</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_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a>, <br class="typebreak"/>
1, ColsAtCompileTime, RowMajor, <br class="typebreak"/>
1, MaxColsAtCompileTime > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a7b1536e5301ae2d95f866625d08a2bdc">IntRowVectorType</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"/>
< ColsAtCompileTime, <br class="typebreak"/>
MaxColsAtCompileTime > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0545a38a4f0129df04bb0e070aa6ee62">PermutationType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1plain__col__type.html">internal::plain_col_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a>, <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a35439a1afa2b3835a1aeea5b7fcfa651">IntColVectorType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1plain__row__type.html">internal::plain_row_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ae3b5fdfbec7497a0ebb0edb4f961a01b">RowVectorType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <br class="typebreak"/>
<a class="el" href="struct_eigen_1_1internal_1_1plain__col__type.html">internal::plain_col_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a457c63e985e3b55f600e954a2e23a72e">ColVectorType</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_full_piv_householder_q_r.html#a2e304eeb6878b07674785744c9e1fecb">FullPivHouseholderQR</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor. <a href="#a2e304eeb6878b07674785744c9e1fecb"></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_full_piv_householder_q_r.html#a2ed43c16429d7c10a69a5c76605881ca">FullPivHouseholderQR</a> (<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> rows, <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> cols)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor with memory preallocation. <a href="#a2ed43c16429d7c10a69a5c76605881ca"></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_full_piv_householder_q_r.html#ad084afe3d44a94323a173e8b43bb09bd">FullPivHouseholderQR</a> (const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> &matrix)</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_full_piv_householder_q_r.html">FullPivHouseholderQR</a>, Rhs > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a1abfe1ddabe06d4a7b459626c0e1598e">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 finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists. <a href="#a1abfe1ddabe06d4a7b459626c0e1598e"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#abf33889a5be7456ed8e110b2843cc3e6">MatrixQType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a55c9d76f16e8aa8c70f26a32c42213de">matrixQ</a> (void) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a58216d2a56f142d1b75b388708b67489">matrixQR</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a6f853ac593c8f30eb8ab822b68bb3543">compute</a> (const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> &matrix)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0545a38a4f0129df04bb0e070aa6ee62">PermutationType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a7f4053dd11241b5204dcccc8d3ab74af">colsPermutation</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a35439a1afa2b3835a1aeea5b7fcfa651">IntColVectorType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ad6daa76faa7f03eb1ffa40eca734a1d4">rowsTranspositions</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">MatrixType::RealScalar </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a1bd9c5da19697dd56e5491b11695a55a">absDeterminant</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">MatrixType::RealScalar </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0f9adf0fe847629787291da6aa736da8">logAbsDeterminant</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a751266eefdc67400ff2101033bcd58e6">rank</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#abdef43d878a44a8e6ce8a070307b9d7d">dimensionOfKernel</a> () 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_full_piv_householder_q_r.html#a67c699dc8a168b6fa5f3406e489f8c7b">isInjective</a> () 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_full_piv_householder_q_r.html#a0af7eb8188461c1857d09401255ddfc5">isSurjective</a> () 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_full_piv_householder_q_r.html#a4b83996a53d663e4466a184e059f5a81">isInvertible</a> () const </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_full_piv_householder_q_r.html">FullPivHouseholderQR</a>, <br class="typebreak"/>
typename <br class="typebreak"/>
MatrixType::IdentityReturnType > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#abe90b8dd6c9a2935a916af804f2a2ecd">inverse</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a3e106b71e4401f461f9618a8a114a1d2">rows</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a784804a279a8cb7f01dae6eb28dbf2bd">cols</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8443db51953fe2b6bd71a8798be5743f">HCoeffsType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0617400188ffe94d59644effbc1a2180">hCoeffs</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460">setThreshold</a> (const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> &threshold)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Allows to prescribe a threshold to be used by certain methods, such as <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a751266eefdc67400ff2101033bcd58e6">rank()</a>, who need to determine when pivots are to be considered nonzero. <a href="#a8ede9b86bcf677f215eb7f72c536b460"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ae63a18bacb2d9bde47d2f2a02aad85cd">setThreshold</a> (<a class="el" href="struct_eigen_1_1_default__t.html">Default_t</a>)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Allows to come back to the default behavior, letting <a class="el" href="namespace_eigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> use its default formula for determining the threshold. <a href="#ae63a18bacb2d9bde47d2f2a02aad85cd"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a72107f8bbc97f9f1653a7c173e278908">threshold</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the threshold that will be used by certain methods such as <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a751266eefdc67400ff2101033bcd58e6">rank()</a>. <a href="#a72107f8bbc97f9f1653a7c173e278908"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a92552b2f20c9f6bd0a773b1b7f7d70aa">nonzeroPivots</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a476b62f07235653efcab3285e570de56">maxPivot</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_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a5f59fe79142f8b2b05e1d9d09a2c5d69">m_qr</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8443db51953fe2b6bd71a8798be5743f">HCoeffsType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#acba5d4622a5d477955e019ffa2b6183d">m_hCoeffs</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a35439a1afa2b3835a1aeea5b7fcfa651">IntColVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ae4f33fce233c618a9146d5584dc3c010">m_rows_transpositions</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a7b1536e5301ae2d95f866625d08a2bdc">IntRowVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a85d13ca7fc8a320e1c0769765beabd55">m_cols_transpositions</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0545a38a4f0129df04bb0e070aa6ee62">PermutationType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a055278d5b63913c99e937181de714069">m_cols_permutation</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ae3b5fdfbec7497a0ebb0edb4f961a01b">RowVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a01230cb5561a05fbd1faac8496f17369">m_temp</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_full_piv_householder_q_r.html#a73e6d10f5ad46cf3c4c975854e55b4a5">m_isInitialized</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#aa7e48c75d8108ce9e39b8761102005eb">m_usePrescribedThreshold</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#adb7ee4ef865aca24e0bc318dd6a4493b">m_prescribedThreshold</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a869621eca25a35f763492342e3a783a0">m_maxpivot</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a76cace4c0df9b7f805a1cf3058bc2cc2">m_nonzero_pivots</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a21d26b1c78ab4e5885592bd4e259041c">m_precision</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a718b011b410b7497e11a00a16cee2a8f">m_det_pq</a></td></tr>
</table>
<hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="a457c63e985e3b55f600e954a2e23a72e"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::ColVectorType" ref="a457c63e985e3b55f600e954a2e23a72e" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1plain__col__type.html">internal::plain_col_type</a><<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a>>::type <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a457c63e985e3b55f600e954a2e23a72e">Eigen::FullPivHouseholderQR::ColVectorType</a></td>
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<div class="memdoc">
<p>Definition at line <a class="el" href="_q_r_source.html#l00072">72</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a8443db51953fe2b6bd71a8798be5743f"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::HCoeffsType" ref="a8443db51953fe2b6bd71a8798be5743f" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1plain__diag__type.html">internal::plain_diag_type</a><<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a>>::type <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8443db51953fe2b6bd71a8798be5743f">Eigen::FullPivHouseholderQR::HCoeffsType</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00067">67</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="af194e740432f40ff3099eeafcb7904c6"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::Index" ref="af194e740432f40ff3099eeafcb7904c6" args="" -->
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Eigen::FullPivHouseholderQR::Index</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00065">65</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a35439a1afa2b3835a1aeea5b7fcfa651"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::IntColVectorType" ref="a35439a1afa2b3835a1aeea5b7fcfa651" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1plain__col__type.html">internal::plain_col_type</a><<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a>, <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a>>::type <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a35439a1afa2b3835a1aeea5b7fcfa651">Eigen::FullPivHouseholderQR::IntColVectorType</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00070">70</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a7b1536e5301ae2d95f866625d08a2bdc"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::IntRowVectorType" ref="a7b1536e5301ae2d95f866625d08a2bdc" 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_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a>, 1, ColsAtCompileTime, RowMajor, 1, MaxColsAtCompileTime> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a7b1536e5301ae2d95f866625d08a2bdc">Eigen::FullPivHouseholderQR::IntRowVectorType</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00068">68</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="abf33889a5be7456ed8e110b2843cc3e6"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::MatrixQType" ref="abf33889a5be7456ed8e110b2843cc3e6" 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_full_piv_householder_q_r.html#a1df92827b1134d5a8096720b6f021394">Scalar</a>, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#abf33889a5be7456ed8e110b2843cc3e6">Eigen::FullPivHouseholderQR::MatrixQType</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00066">66</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="ab5cd490f03f54c3b673e779dd798a324"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::MatrixType" ref="ab5cd490f03f54c3b673e779dd798a324" args="" -->
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">Eigen::FullPivHouseholderQR::MatrixType</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00055">55</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a0545a38a4f0129df04bb0e070aa6ee62"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::PermutationType" ref="a0545a38a4f0129df04bb0e070aa6ee62" args="" -->
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_permutation_matrix.html">PermutationMatrix</a><ColsAtCompileTime, MaxColsAtCompileTime> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0545a38a4f0129df04bb0e070aa6ee62">Eigen::FullPivHouseholderQR::PermutationType</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00069">69</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="ac76d1c455f593d68e7930ccb75f82507"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::RealScalar" ref="ac76d1c455f593d68e7930ccb75f82507" args="" -->
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<td class="memname">typedef MatrixType::RealScalar <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">Eigen::FullPivHouseholderQR::RealScalar</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00064">64</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="ae3b5fdfbec7497a0ebb0edb4f961a01b"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::RowVectorType" ref="ae3b5fdfbec7497a0ebb0edb4f961a01b" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1internal_1_1plain__row__type.html">internal::plain_row_type</a><<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a>>::type <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ae3b5fdfbec7497a0ebb0edb4f961a01b">Eigen::FullPivHouseholderQR::RowVectorType</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00071">71</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a1df92827b1134d5a8096720b6f021394"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::Scalar" ref="a1df92827b1134d5a8096720b6f021394" args="" -->
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a1df92827b1134d5a8096720b6f021394">Eigen::FullPivHouseholderQR::Scalar</a></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00063">63</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<hr/><h2>Member Enumeration Documentation</h2>
<a class="anchor" id="a8b167c70c49bf065b6b85b7e0774765a"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::@377" ref="a8b167c70c49bf065b6b85b7e0774765a" 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="a8b167c70c49bf065b6b85b7e0774765aa2c720108835407aa7c71cc43a8ac365f"></a><!-- doxytag: member="RowsAtCompileTime" ref="a8b167c70c49bf065b6b85b7e0774765aa2c720108835407aa7c71cc43a8ac365f" args="" -->RowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a8b167c70c49bf065b6b85b7e0774765aa9251ed0b8e9b2840751a2ac39b10caf3"></a><!-- doxytag: member="ColsAtCompileTime" ref="a8b167c70c49bf065b6b85b7e0774765aa9251ed0b8e9b2840751a2ac39b10caf3" args="" -->ColsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a8b167c70c49bf065b6b85b7e0774765aa60679e222c5f2e551e2e165bb9e1305e"></a><!-- doxytag: member="Options" ref="a8b167c70c49bf065b6b85b7e0774765aa60679e222c5f2e551e2e165bb9e1305e" args="" -->Options</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a8b167c70c49bf065b6b85b7e0774765aa3b74ffcf7a853f39cf018772473f6776"></a><!-- doxytag: member="MaxRowsAtCompileTime" ref="a8b167c70c49bf065b6b85b7e0774765aa3b74ffcf7a853f39cf018772473f6776" args="" -->MaxRowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="a8b167c70c49bf065b6b85b7e0774765aa6de5fa38028124637cb0fe8c8c6a09e4"></a><!-- doxytag: member="MaxColsAtCompileTime" ref="a8b167c70c49bf065b6b85b7e0774765aa6de5fa38028124637cb0fe8c8c6a09e4" args="" -->MaxColsAtCompileTime</em> </td><td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00056">56</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="a2e304eeb6878b07674785744c9e1fecb"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::FullPivHouseholderQR" ref="a2e304eeb6878b07674785744c9e1fecb" args="()" -->
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<td class="memname">Eigen::FullPivHouseholderQR::FullPivHouseholderQR </td>
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<td><code> [inline]</code></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_full_piv_householder_q_r.html#a6f853ac593c8f30eb8ab822b68bb3543">FullPivHouseholderQR::compute(const MatrixType&)</a>. </p>
<p>Definition at line <a class="el" href="_q_r_source.html#l00079">79</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a2ed43c16429d7c10a69a5c76605881ca"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::FullPivHouseholderQR" ref="a2ed43c16429d7c10a69a5c76605881ca" args="(Index rows, Index cols)" -->
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<td class="memname">Eigen::FullPivHouseholderQR::FullPivHouseholderQR </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td>
<td class="paramname"><em>rows</em>, </td>
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<td class="paramtype"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> </td>
<td class="paramname"><em>cols</em> </td>
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<td>)</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_full_piv_householder_q_r.html#a2e304eeb6878b07674785744c9e1fecb" title="Default Constructor.">FullPivHouseholderQR()</a> </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00095">95</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="ad084afe3d44a94323a173e8b43bb09bd"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::FullPivHouseholderQR" ref="ad084afe3d44a94323a173e8b43bb09bd" args="(const MatrixType &matrix)" -->
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<td class="memname">Eigen::FullPivHouseholderQR::FullPivHouseholderQR </td>
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<td class="paramtype">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> & </td>
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<td><code> [inline]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00105">105</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a1bd9c5da19697dd56e5491b11695a55a"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::absDeterminant" ref="a1bd9c5da19697dd56e5491b11695a55a" args="() const " -->
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<td class="memname">MatrixType::RealScalar Eigen::FullPivHouseholderQR::absDeterminant </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>This is only for square matrices.</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. One way to work around that is to use <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0f9adf0fe847629787291da6aa736da8">logAbsDeterminant()</a> instead.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0f9adf0fe847629787291da6aa736da8">logAbsDeterminant()</a>, <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="_q_r_source.html#l00363">363</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a784804a279a8cb7f01dae6eb28dbf2bd"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::cols" ref="a784804a279a8cb7f01dae6eb28dbf2bd" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> Eigen::FullPivHouseholderQR::cols </td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00276">276</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a7f4053dd11241b5204dcccc8d3ab74af"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::colsPermutation" ref="a7f4053dd11241b5204dcccc8d3ab74af" args="() const " -->
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<td class="memname">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0545a38a4f0129df04bb0e070aa6ee62">PermutationType</a>& Eigen::FullPivHouseholderQR::colsPermutation </td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00155">155</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a6f853ac593c8f30eb8ab822b68bb3543"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::compute" ref="a6f853ac593c8f30eb8ab822b68bb3543" args="(const MatrixType &matrix)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a>< <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> > & Eigen::FullPivHouseholderQR::compute </td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00379">379</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="abdef43d878a44a8e6ce8a070307b9d7d"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::dimensionOfKernel" ref="abdef43d878a44a8e6ce8a070307b9d7d" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> Eigen::FullPivHouseholderQR::dimensionOfKernel </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the dimension of the kernel of the matrix of which *this is the QR decomposition.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460" title="Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...">setThreshold(const RealScalar&)</a>. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00218">218</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a0617400188ffe94d59644effbc1a2180"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::hCoeffs" ref="a0617400188ffe94d59644effbc1a2180" args="() const " -->
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<td class="memname">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8443db51953fe2b6bd71a8798be5743f">HCoeffsType</a>& Eigen::FullPivHouseholderQR::hCoeffs </td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00277">277</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname">const internal::solve_retval<<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a>, typename MatrixType::IdentityReturnType> Eigen::FullPivHouseholderQR::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 QR decomposition.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>If this matrix is not invertible, the returned matrix has undefined coefficients. Use <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a4b83996a53d663e4466a184e059f5a81">isInvertible()</a> to first determine whether this matrix is invertible. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00268">268</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<dl class="return"><dt><b>Returns:</b></dt><dd>true if the matrix of which *this is the QR decomposition represents an injective linear map, i.e. has trivial kernel; false otherwise.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460" title="Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...">setThreshold(const RealScalar&)</a>. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00231">231</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<dl class="return"><dt><b>Returns:</b></dt><dd>true if the matrix of which *this is the QR decomposition is invertible.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460" title="Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...">setThreshold(const RealScalar&)</a>. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00256">256</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname">bool Eigen::FullPivHouseholderQR::isSurjective </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>true if the matrix of which *this is the QR decomposition represents a surjective linear map; false otherwise.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460" title="Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...">setThreshold(const RealScalar&)</a>. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00244">244</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a0f9adf0fe847629787291da6aa736da8"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::logAbsDeterminant" ref="a0f9adf0fe847629787291da6aa736da8" args="() const " -->
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<dl class="return"><dt><b>Returns:</b></dt><dd>the natural log of the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>This is only for square matrices.</dd>
<dd>
This method is useful to work around the risk of overflow/underflow that's inherent to determinant computation.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a1bd9c5da19697dd56e5491b11695a55a">absDeterminant()</a>, <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="_q_r_source.html#l00371">371</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a>< <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> >::<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#abf33889a5be7456ed8e110b2843cc3e6">MatrixQType</a> Eigen::FullPivHouseholderQR::matrixQ </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the matrix Q </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00516">516</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a>& Eigen::FullPivHouseholderQR::matrixQR </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>a reference to the matrix where the Householder QR decomposition is stored </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00147">147</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> Eigen::FullPivHouseholderQR::maxPivot </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the absolute value of the biggest pivot, i.e. the biggest diagonal coefficient of U. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00346">346</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> Eigen::FullPivHouseholderQR::nonzeroPivots </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the number of nonzero pivots in the QR decomposition. Here nonzero is meant in the exact sense, not in a fuzzy sense. So that notion isn't really intrinsically interesting, but it is still useful when implementing algorithms.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a751266eefdc67400ff2101033bcd58e6">rank()</a> </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00337">337</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the rank of the matrix of which *this is the QR decomposition.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460" title="Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...">setThreshold(const RealScalar&)</a>. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00202">202</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00275">275</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a35439a1afa2b3835a1aeea5b7fcfa651">IntColVectorType</a>& Eigen::FullPivHouseholderQR::rowsTranspositions </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const<code> [inline]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00161">161</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a8ede9b86bcf677f215eb7f72c536b460"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::setThreshold" ref="a8ede9b86bcf677f215eb7f72c536b460" args="(const RealScalar &threshold)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a>& Eigen::FullPivHouseholderQR::setThreshold </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> & </td>
<td class="paramname"><em>threshold</em></td><td>)</td>
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<p>Allows to prescribe a threshold to be used by certain methods, such as <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a751266eefdc67400ff2101033bcd58e6">rank()</a>, who need to determine when pivots are to be considered nonzero. </p>
<p>This is not used for the QR decomposition itself.</p>
<p>When it needs to get the threshold value, <a class="el" href="namespace_eigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> calls <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a72107f8bbc97f9f1653a7c173e278908" title="Returns the threshold that will be used by certain methods such as rank().">threshold()</a>. By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460" title="Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...">setThreshold(const RealScalar&)</a>, your value is used instead.</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">threshold</td><td>The new value to use as the threshold.</td></tr>
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</dd>
</dl>
<p>A pivot will be considered nonzero if its absolute value is strictly greater than <img class="formulaInl" alt="$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert $" src="form_263.png"/> where maxpivot is the biggest pivot.</p>
<p>If you want to come back to the default behavior, call <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ae63a18bacb2d9bde47d2f2a02aad85cd" title="Allows to come back to the default behavior, letting Eigen use its default formula for determining th...">setThreshold(Default_t)</a> </p>
<p>Definition at line <a class="el" href="_q_r_source.html#l00296">296</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="ae63a18bacb2d9bde47d2f2a02aad85cd"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::setThreshold" ref="ae63a18bacb2d9bde47d2f2a02aad85cd" args="(Default_t)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a>& Eigen::FullPivHouseholderQR::setThreshold </td>
<td>(</td>
<td class="paramtype"><a class="el" href="struct_eigen_1_1_default__t.html">Default_t</a> </td>
<td class="paramname"></td><td>)</td>
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<p>Allows to come back to the default behavior, letting <a class="el" href="namespace_eigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> use its default formula for determining the threshold. </p>
<p>You should pass the special object Eigen::Default as parameter here. </p>
<div class="fragment"><pre class="fragment"> qr.setThreshold(Eigen::Default);
</pre></div><p>See the documentation of <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460" title="Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...">setThreshold(const RealScalar&)</a>. </p>
<p>Definition at line <a class="el" href="_q_r_source.html#l00311">311</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a1abfe1ddabe06d4a7b459626c0e1598e"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::solve" ref="a1abfe1ddabe06d4a7b459626c0e1598e" args="(const MatrixBase< Rhs > &b) const " -->
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template<typename Rhs > </div>
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<td class="memname">const internal::solve_retval<<a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html">FullPivHouseholderQR</a>, Rhs> Eigen::FullPivHouseholderQR::solve </td>
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<td class="paramtype">const <a class="el" href="class_eigen_1_1_matrix_base.html">MatrixBase</a>< Rhs > & </td>
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<p>This method finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists. </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.</td></tr>
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<dl class="return"><dt><b>Returns:</b></dt><dd>a solution.</dd></dl>
<dl class="note"><dt><b>Note:</b></dt><dd>The case where b is a matrix is not yet implemented. Also, this code is space inefficient.</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>Definition at line <a class="el" href="_q_r_source.html#l00137">137</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a72107f8bbc97f9f1653a7c173e278908"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::threshold" ref="a72107f8bbc97f9f1653a7c173e278908" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> Eigen::FullPivHouseholderQR::threshold </td>
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<p>Returns the threshold that will be used by certain methods such as <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a751266eefdc67400ff2101033bcd58e6">rank()</a>. </p>
<p>See the documentation of <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8ede9b86bcf677f215eb7f72c536b460" title="Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine ...">setThreshold(const RealScalar&)</a>. </p>
<p>Definition at line <a class="el" href="_q_r_source.html#l00321">321</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<hr/><h2>Member Data Documentation</h2>
<a class="anchor" id="a055278d5b63913c99e937181de714069"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_cols_permutation" ref="a055278d5b63913c99e937181de714069" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a0545a38a4f0129df04bb0e070aa6ee62">PermutationType</a> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a055278d5b63913c99e937181de714069">Eigen::FullPivHouseholderQR::m_cols_permutation</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00353">353</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a7b1536e5301ae2d95f866625d08a2bdc">IntRowVectorType</a> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a85d13ca7fc8a320e1c0769765beabd55">Eigen::FullPivHouseholderQR::m_cols_transpositions</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00352">352</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a718b011b410b7497e11a00a16cee2a8f"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_det_pq" ref="a718b011b410b7497e11a00a16cee2a8f" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#af194e740432f40ff3099eeafcb7904c6">Index</a> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a718b011b410b7497e11a00a16cee2a8f">Eigen::FullPivHouseholderQR::m_det_pq</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00359">359</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="acba5d4622a5d477955e019ffa2b6183d"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_hCoeffs" ref="acba5d4622a5d477955e019ffa2b6183d" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a8443db51953fe2b6bd71a8798be5743f">HCoeffsType</a> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#acba5d4622a5d477955e019ffa2b6183d">Eigen::FullPivHouseholderQR::m_hCoeffs</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00350">350</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a73e6d10f5ad46cf3c4c975854e55b4a5"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_isInitialized" ref="a73e6d10f5ad46cf3c4c975854e55b4a5" args="" -->
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<td class="memname">bool <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a73e6d10f5ad46cf3c4c975854e55b4a5">Eigen::FullPivHouseholderQR::m_isInitialized</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00355">355</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a869621eca25a35f763492342e3a783a0"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_maxpivot" ref="a869621eca25a35f763492342e3a783a0" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ac76d1c455f593d68e7930ccb75f82507">RealScalar</a> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a869621eca25a35f763492342e3a783a0">Eigen::FullPivHouseholderQR::m_maxpivot</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00356">356</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a76cace4c0df9b7f805a1cf3058bc2cc2"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_nonzero_pivots" ref="a76cace4c0df9b7f805a1cf3058bc2cc2" args="" -->
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<p>Definition at line <a class="el" href="_q_r_source.html#l00357">357</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00358">358</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="adb7ee4ef865aca24e0bc318dd6a4493b"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_prescribedThreshold" ref="adb7ee4ef865aca24e0bc318dd6a4493b" args="" -->
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<p>Definition at line <a class="el" href="_q_r_source.html#l00356">356</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a5f59fe79142f8b2b05e1d9d09a2c5d69"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_qr" ref="a5f59fe79142f8b2b05e1d9d09a2c5d69" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ab5cd490f03f54c3b673e779dd798a324">MatrixType</a> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a5f59fe79142f8b2b05e1d9d09a2c5d69">Eigen::FullPivHouseholderQR::m_qr</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00349">349</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#a35439a1afa2b3835a1aeea5b7fcfa651">IntColVectorType</a> <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html#ae4f33fce233c618a9146d5584dc3c010">Eigen::FullPivHouseholderQR::m_rows_transpositions</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00351">351</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a01230cb5561a05fbd1faac8496f17369"></a><!-- doxytag: member="Eigen::FullPivHouseholderQR::m_temp" ref="a01230cb5561a05fbd1faac8496f17369" args="" -->
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<p>Definition at line <a class="el" href="_q_r_source.html#l00354">354</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00355">355</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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