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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_col_piv_householder_q_r.html">ColPivHouseholderQR</a> </li>
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<a href="#pub-types">Public Types</a> |
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<div class="title">Eigen::ColPivHouseholderQR 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::ColPivHouseholderQR" --><hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Householder rank-revealing QR decomposition of a matrix with column-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 column pivoting in order to be rank-revealing and improve numerical stability. 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 faster than <a class="el" href="class_eigen_1_1_full_piv_householder_q_r.html" title="Householder rank-revealing QR decomposition of a matrix with full pivoting.">FullPivHouseholderQR</a>.</p>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_matrix_base.html#a49b321528c6bc3609d3cbe5b10c153d3">MatrixBase::colPivHouseholderQr()</a> </dd></dl>
</div>
<p><a href="class_eigen_1_1_col_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_col_piv_householder_q_r.html#acd38da60a2a9e37dfdca3525ce065677a8e9b93969d2b271dc8424dd44c6699c0">RowsAtCompileTime</a> = MatrixType::RowsAtCompileTime,
<a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#acd38da60a2a9e37dfdca3525ce065677a00d017c1090e266ade1114e8ada1f66e">ColsAtCompileTime</a> = MatrixType::ColsAtCompileTime,
<a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#acd38da60a2a9e37dfdca3525ce065677a28231f5cdb032b739e697816a4773540">Options</a> = MatrixType::Options,
<a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#acd38da60a2a9e37dfdca3525ce065677acc3a6c1d106c63312d22556752011545">MaxRowsAtCompileTime</a> = MatrixType::MaxRowsAtCompileTime,
<br/>
  <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#acd38da60a2a9e37dfdca3525ce065677a659ee3b9eb7712afe9cfe403a502bba0">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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">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_col_piv_householder_q_r.html#a1d0d053fbb59970f2dbd35de6a0b6056">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_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">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_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">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_col_piv_householder_q_r.html#a1d0d053fbb59970f2dbd35de6a0b6056">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_col_piv_householder_q_r.html#a952de7dbd8b9187301f1a267cec1ff4b">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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a> >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a21fce526d4c7a5d53f2c6491a4133a4f">HCoeffsType</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_col_piv_householder_q_r.html#a1aea95c556cf6fe764ccd1f4cb58773f">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__row__type.html">internal::plain_row_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>, <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a431c70c528729251631d82a918c647bc">IntRowVectorType</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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a> >::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a338dbecd93a8c2b3f9f6b7b27e941f00">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__row__type.html">internal::plain_row_type</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>, <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a> ><br class="typebreak"/>
::type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a9c5615ab3c4f9263b28374b6ed68cbcd">RealRowVectorType</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a><br class="typebreak"/>
< <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>, <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a21fce526d4c7a5d53f2c6491a4133a4f">HCoeffsType</a> ><br class="typebreak"/>
::ConjugateReturnType </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a62ff9d1b56defa7915f2467710373386">HouseholderSequenceType</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_col_piv_householder_q_r.html#a6f61ff5e01880ff0700b661dab2b417f">ColPivHouseholderQR</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor. <a href="#a6f61ff5e01880ff0700b661dab2b417f"></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_col_piv_householder_q_r.html#a90973cc2314999be8488073dabdf4361">ColPivHouseholderQR</a> (<a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> rows, <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> cols)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor with memory preallocation. <a href="#a90973cc2314999be8488073dabdf4361"></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_col_piv_householder_q_r.html#a341c22ad8c21d04e3e2c19bc2ae1506a">ColPivHouseholderQR</a> (const <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">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_col_piv_householder_q_r.html">ColPivHouseholderQR</a>, Rhs > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a1d95c7e917d799abc0982d34dad8c24f">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="#a1d95c7e917d799abc0982d34dad8c24f"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a62ff9d1b56defa7915f2467710373386">HouseholderSequenceType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#aad852e77b4a1facb3d89738cab7fc3c3">householderQ</a> (void) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a58cfcfe1749d22e5ff553e75ed3faebc">matrixQR</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html">ColPivHouseholderQR</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ac058935eedd572f6e517de42c3ac82df">compute</a> (const <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a> &matrix)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a1aea95c556cf6fe764ccd1f4cb58773f">PermutationType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a38ee4efb63d5bf0a5e75a5046d835a03">colsPermutation</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_col_piv_householder_q_r.html#ad12c6fb7885a3778f0179ec9ff63e840">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_col_piv_householder_q_r.html#a4d2134ab23fc16b44797b3964b1dcf08">logAbsDeterminant</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a44ec27529fb69374116c3da688bd3173">rank</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#aa824e8c02f282d6b40d6cabcdbdce536">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_col_piv_householder_q_r.html#a49ff9f380e418cdac930226b8148293b">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_col_piv_householder_q_r.html#abc4adaadf2f208334781b600af2d0a9c">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_col_piv_householder_q_r.html#aee3d8f40aa691d8d5e0b434ca586a490">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_col_piv_householder_q_r.html">ColPivHouseholderQR</a>, <br class="typebreak"/>
typename <br class="typebreak"/>
MatrixType::IdentityReturnType > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a2471bdc11f51e656e2b8a0a5708b5c75">inverse</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a0829af58e2e0f970b80cea4335cfc849">rows</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8db3ed49d1f0dcad8c0b89322ecb5d19">cols</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a21fce526d4c7a5d53f2c6491a4133a4f">HCoeffsType</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#af3e3326da8a794768c9fe02222f8b08a">hCoeffs</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html">ColPivHouseholderQR</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660">setThreshold</a> (const <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">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_col_piv_householder_q_r.html#a44ec27529fb69374116c3da688bd3173">rank()</a>, who need to determine when pivots are to be considered nonzero. <a href="#a439472b02b9326c60f5ca4aaf24d1660"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html">ColPivHouseholderQR</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a5fa0fe9a8788be9a83cf071ae23cefd7">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="#a5fa0fe9a8788be9a83cf071ae23cefd7"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab99de422b60befb683208163fe02a589">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_col_piv_householder_q_r.html#a44ec27529fb69374116c3da688bd3173">rank()</a>. <a href="#ab99de422b60befb683208163fe02a589"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a947551bc476d9dbbb1f13d86ff41b844">nonzeroPivots</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a293de505537b3802e2ca0dc6889d4071">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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a4e5ab7894126264655657e61ea441ca3">m_qr</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a21fce526d4c7a5d53f2c6491a4133a4f">HCoeffsType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a71afc64a563aa4b0f6320877eb8c1a5d">m_hCoeffs</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a1aea95c556cf6fe764ccd1f4cb58773f">PermutationType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a467b43512d63145dc599e82784b1cb4d">m_colsPermutation</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a431c70c528729251631d82a918c647bc">IntRowVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab9ec8cab591723f4deac336114369861">m_colsTranspositions</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a338dbecd93a8c2b3f9f6b7b27e941f00">RowVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#aab0a569c89c72f4ae9916e35aad39161">m_temp</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a9c5615ab3c4f9263b28374b6ed68cbcd">RealRowVectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a53a02d7588bb68005c1fb811545f8069">m_colSqNorms</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_col_piv_householder_q_r.html#a4ed462121a0b42999b778365c02b7fde">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_col_piv_householder_q_r.html#a516aa8f6a36aa9575679f89bc6def324">m_usePrescribedThreshold</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a565cb10dfd41ea6025eb66990e7b168a">m_prescribedThreshold</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a46b3b7a0c8f23a1d5ed69b5ef0518152">m_maxpivot</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a43e2e1baca5c7e66da4e711ee1579772">m_nonzero_pivots</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab419bf570cf1efdf0fbde325bda8bfbf">m_det_pq</a></td></tr>
</table>
<hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="a21fce526d4c7a5d53f2c6491a4133a4f"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::HCoeffsType" ref="a21fce526d4c7a5d53f2c6491a4133a4f" 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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>>::type <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a21fce526d4c7a5d53f2c6491a4133a4f">Eigen::ColPivHouseholderQR::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="a62ff9d1b56defa7915f2467710373386"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::HouseholderSequenceType" ref="a62ff9d1b56defa7915f2467710373386" args="" -->
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<td class="memname">typedef <a class="el" href="class_eigen_1_1_householder_sequence.html">HouseholderSequence</a><<a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>,<a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a21fce526d4c7a5d53f2c6491a4133a4f">HCoeffsType</a>>::ConjugateReturnType <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a62ff9d1b56defa7915f2467710373386">Eigen::ColPivHouseholderQR::HouseholderSequenceType</a></td>
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<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="ab35805502719be8d379f2e2661784b7c"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::Index" ref="ab35805502719be8d379f2e2661784b7c" args="" -->
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<td class="memname">typedef MatrixType::Index <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Eigen::ColPivHouseholderQR::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="a431c70c528729251631d82a918c647bc"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::IntRowVectorType" ref="a431c70c528729251631d82a918c647bc" 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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>, <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a>>::type <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a431c70c528729251631d82a918c647bc">Eigen::ColPivHouseholderQR::IntRowVectorType</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="a952de7dbd8b9187301f1a267cec1ff4b"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::MatrixQType" ref="a952de7dbd8b9187301f1a267cec1ff4b" 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_col_piv_householder_q_r.html#a1d0d053fbb59970f2dbd35de6a0b6056">Scalar</a>, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime> <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a952de7dbd8b9187301f1a267cec1ff4b">Eigen::ColPivHouseholderQR::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="a8d9319e9ad7565d4dd3fc07e540f459c"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::MatrixType" ref="a8d9319e9ad7565d4dd3fc07e540f459c" args="" -->
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<td class="memname">typedef _MatrixType <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">Eigen::ColPivHouseholderQR::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="a1aea95c556cf6fe764ccd1f4cb58773f"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::PermutationType" ref="a1aea95c556cf6fe764ccd1f4cb58773f" 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_col_piv_householder_q_r.html#a1aea95c556cf6fe764ccd1f4cb58773f">Eigen::ColPivHouseholderQR::PermutationType</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="a9c5615ab3c4f9263b28374b6ed68cbcd"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::RealRowVectorType" ref="a9c5615ab3c4f9263b28374b6ed68cbcd" 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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>, <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a>>::type <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a9c5615ab3c4f9263b28374b6ed68cbcd">Eigen::ColPivHouseholderQR::RealRowVectorType</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="a6f5b4b7cabbf2c3b570919108d42225d"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::RealScalar" ref="a6f5b4b7cabbf2c3b570919108d42225d" args="" -->
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<td class="memname">typedef MatrixType::RealScalar <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">Eigen::ColPivHouseholderQR::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="a338dbecd93a8c2b3f9f6b7b27e941f00"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::RowVectorType" ref="a338dbecd93a8c2b3f9f6b7b27e941f00" 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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>>::type <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a338dbecd93a8c2b3f9f6b7b27e941f00">Eigen::ColPivHouseholderQR::RowVectorType</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="a1d0d053fbb59970f2dbd35de6a0b6056"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::Scalar" ref="a1d0d053fbb59970f2dbd35de6a0b6056" args="" -->
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<td class="memname">typedef MatrixType::Scalar <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a1d0d053fbb59970f2dbd35de6a0b6056">Eigen::ColPivHouseholderQR::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="acd38da60a2a9e37dfdca3525ce065677"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::@378" ref="acd38da60a2a9e37dfdca3525ce065677" 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="acd38da60a2a9e37dfdca3525ce065677a8e9b93969d2b271dc8424dd44c6699c0"></a><!-- doxytag: member="RowsAtCompileTime" ref="acd38da60a2a9e37dfdca3525ce065677a8e9b93969d2b271dc8424dd44c6699c0" args="" -->RowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="acd38da60a2a9e37dfdca3525ce065677a00d017c1090e266ade1114e8ada1f66e"></a><!-- doxytag: member="ColsAtCompileTime" ref="acd38da60a2a9e37dfdca3525ce065677a00d017c1090e266ade1114e8ada1f66e" args="" -->ColsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="acd38da60a2a9e37dfdca3525ce065677a28231f5cdb032b739e697816a4773540"></a><!-- doxytag: member="Options" ref="acd38da60a2a9e37dfdca3525ce065677a28231f5cdb032b739e697816a4773540" args="" -->Options</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="acd38da60a2a9e37dfdca3525ce065677acc3a6c1d106c63312d22556752011545"></a><!-- doxytag: member="MaxRowsAtCompileTime" ref="acd38da60a2a9e37dfdca3525ce065677acc3a6c1d106c63312d22556752011545" args="" -->MaxRowsAtCompileTime</em> </td><td>
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<tr><td valign="top"><em><a class="anchor" id="acd38da60a2a9e37dfdca3525ce065677a659ee3b9eb7712afe9cfe403a502bba0"></a><!-- doxytag: member="MaxColsAtCompileTime" ref="acd38da60a2a9e37dfdca3525ce065677a659ee3b9eb7712afe9cfe403a502bba0" 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="a6f61ff5e01880ff0700b661dab2b417f"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::ColPivHouseholderQR" ref="a6f61ff5e01880ff0700b661dab2b417f" args="()" -->
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<td class="memname">Eigen::ColPivHouseholderQR::ColPivHouseholderQR </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_col_piv_householder_q_r.html#ac058935eedd572f6e517de42c3ac82df">ColPivHouseholderQR::compute(const MatrixType&)</a>. </p>
<p>Definition at line <a class="el" href="_q_r_source.html#l00080">80</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a90973cc2314999be8488073dabdf4361"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::ColPivHouseholderQR" ref="a90973cc2314999be8488073dabdf4361" args="(Index rows, Index cols)" -->
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<td class="memname">Eigen::ColPivHouseholderQR::ColPivHouseholderQR </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">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_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> </td>
<td class="paramname"><em>cols</em> </td>
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<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_col_piv_householder_q_r.html#a6f61ff5e01880ff0700b661dab2b417f" title="Default Constructor.">ColPivHouseholderQR()</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="a341c22ad8c21d04e3e2c19bc2ae1506a"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::ColPivHouseholderQR" ref="a341c22ad8c21d04e3e2c19bc2ae1506a" args="(const MatrixType &matrix)" -->
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<td class="memname">Eigen::ColPivHouseholderQR::ColPivHouseholderQR </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="ad12c6fb7885a3778f0179ec9ff63e840"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::absDeterminant" ref="ad12c6fb7885a3778f0179ec9ff63e840" args="() const " -->
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<td class="memname">MatrixType::RealScalar Eigen::ColPivHouseholderQR::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_col_piv_householder_q_r.html#a4d2134ab23fc16b44797b3964b1dcf08">logAbsDeterminant()</a> instead.</dd></dl>
<dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a4d2134ab23fc16b44797b3964b1dcf08">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#l00357">357</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a8db3ed49d1f0dcad8c0b89322ecb5d19"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::cols" ref="a8db3ed49d1f0dcad8c0b89322ecb5d19" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> Eigen::ColPivHouseholderQR::cols </td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00271">271</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_col_piv_householder_q_r.html#a1aea95c556cf6fe764ccd1f4cb58773f">PermutationType</a>& Eigen::ColPivHouseholderQR::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="ac058935eedd572f6e517de42c3ac82df"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::compute" ref="ac058935eedd572f6e517de42c3ac82df" args="(const MatrixType &matrix)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html">ColPivHouseholderQR</a>< <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a> > & Eigen::ColPivHouseholderQR::compute </td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00373">373</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="aa824e8c02f282d6b40d6cabcdbdce536"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::dimensionOfKernel" ref="aa824e8c02f282d6b40d6cabcdbdce536" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> Eigen::ColPivHouseholderQR::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_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660" 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#l00212">212</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="af3e3326da8a794768c9fe02222f8b08a"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::hCoeffs" ref="af3e3326da8a794768c9fe02222f8b08a" args="() const " -->
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<td class="memname">const <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a21fce526d4c7a5d53f2c6491a4133a4f">HCoeffsType</a>& Eigen::ColPivHouseholderQR::hCoeffs </td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00272">272</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_col_piv_householder_q_r.html">ColPivHouseholderQR</a>< <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a> >::<a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a62ff9d1b56defa7915f2467710373386">HouseholderSequenceType</a> Eigen::ColPivHouseholderQR::householderQ </td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the matrix Q as a sequence of householder transformations </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00515">515</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_col_piv_householder_q_r.html">ColPivHouseholderQR</a>, typename MatrixType::IdentityReturnType> Eigen::ColPivHouseholderQR::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_col_piv_householder_q_r.html#aee3d8f40aa691d8d5e0b434ca586a490">isInvertible()</a> to first determine whether this matrix is invertible. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00263">263</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
<p>Referenced by <a class="el" href="eigen__plugins_8h_source.html#l00639">leftDivideSquare()</a>, and <a class="el" href="eigen__plugins_8h_source.html#l00648">rightDivideSquare()</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_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660" 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#l00225">225</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_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660" 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#l00250">250</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
<p>Referenced by <a class="el" href="eigen__plugins_8h_source.html#l00639">leftDivideSquare()</a>, and <a class="el" href="eigen__plugins_8h_source.html#l00648">rightDivideSquare()</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 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_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660" 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#l00238">238</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 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_col_piv_householder_q_r.html#ad12c6fb7885a3778f0179ec9ff63e840">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#l00365">365</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_col_piv_householder_q_r.html#a8d9319e9ad7565d4dd3fc07e540f459c">MatrixType</a>& Eigen::ColPivHouseholderQR::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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<a class="anchor" id="a293de505537b3802e2ca0dc6889d4071"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::maxPivot" ref="a293de505537b3802e2ca0dc6889d4071" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a> Eigen::ColPivHouseholderQR::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 R. </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00341">341</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 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_col_piv_householder_q_r.html#a44ec27529fb69374116c3da688bd3173">rank()</a> </dd></dl>
<p>Definition at line <a class="el" href="_q_r_source.html#l00332">332</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a44ec27529fb69374116c3da688bd3173"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::rank" ref="a44ec27529fb69374116c3da688bd3173" args="() const " -->
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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_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660" 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#l00196">196</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
<p>Referenced by <a class="el" href="eigen__plugins_8h_source.html#l00722">rank()</a>.</p>
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<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#l00270">270</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a439472b02b9326c60f5ca4aaf24d1660"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::setThreshold" ref="a439472b02b9326c60f5ca4aaf24d1660" args="(const RealScalar &threshold)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html">ColPivHouseholderQR</a>& Eigen::ColPivHouseholderQR::setThreshold </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a> & </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_col_piv_householder_q_r.html#a44ec27529fb69374116c3da688bd3173">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_col_piv_householder_q_r.html#ab99de422b60befb683208163fe02a589" 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_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660" 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_col_piv_householder_q_r.html#a5fa0fe9a8788be9a83cf071ae23cefd7" 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#l00291">291</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
<p>Referenced by <a class="el" href="eigen__plugins_8h_source.html#l00722">rank()</a>.</p>
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<a class="anchor" id="a5fa0fe9a8788be9a83cf071ae23cefd7"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::setThreshold" ref="a5fa0fe9a8788be9a83cf071ae23cefd7" args="(Default_t)" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html">ColPivHouseholderQR</a>& Eigen::ColPivHouseholderQR::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_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660" 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#l00306">306</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a1d95c7e917d799abc0982d34dad8c24f"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::solve" ref="a1d95c7e917d799abc0982d34dad8c24f" 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_col_piv_householder_q_r.html">ColPivHouseholderQR</a>, Rhs> Eigen::ColPivHouseholderQR::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="ab99de422b60befb683208163fe02a589"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::threshold" ref="ab99de422b60befb683208163fe02a589" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a6f5b4b7cabbf2c3b570919108d42225d">RealScalar</a> Eigen::ColPivHouseholderQR::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_col_piv_householder_q_r.html#a44ec27529fb69374116c3da688bd3173">rank()</a>. </p>
<p>See the documentation of <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a439472b02b9326c60f5ca4aaf24d1660" 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#l00316">316</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<hr/><h2>Member Data Documentation</h2>
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a1aea95c556cf6fe764ccd1f4cb58773f">PermutationType</a> <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a467b43512d63145dc599e82784b1cb4d">Eigen::ColPivHouseholderQR::m_colsPermutation</a><code> [protected]</code></td>
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<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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<a class="anchor" id="a53a02d7588bb68005c1fb811545f8069"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::m_colSqNorms" ref="a53a02d7588bb68005c1fb811545f8069" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a9c5615ab3c4f9263b28374b6ed68cbcd">RealRowVectorType</a> <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a53a02d7588bb68005c1fb811545f8069">Eigen::ColPivHouseholderQR::m_colSqNorms</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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<a class="anchor" id="ab9ec8cab591723f4deac336114369861"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::m_colsTranspositions" ref="ab9ec8cab591723f4deac336114369861" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#a431c70c528729251631d82a918c647bc">IntRowVectorType</a> <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab9ec8cab591723f4deac336114369861">Eigen::ColPivHouseholderQR::m_colsTranspositions</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_q_r_source.html#l00347">347</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="ab419bf570cf1efdf0fbde325bda8bfbf"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::m_det_pq" ref="ab419bf570cf1efdf0fbde325bda8bfbf" args="" -->
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<td class="memname"><a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab35805502719be8d379f2e2661784b7c">Index</a> <a class="el" href="class_eigen_1_1_col_piv_householder_q_r.html#ab419bf570cf1efdf0fbde325bda8bfbf">Eigen::ColPivHouseholderQR::m_det_pq</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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<a class="anchor" id="a71afc64a563aa4b0f6320877eb8c1a5d"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::m_hCoeffs" ref="a71afc64a563aa4b0f6320877eb8c1a5d" args="" -->
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<p>Definition at line <a class="el" href="_q_r_source.html#l00345">345</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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<a class="anchor" id="a4ed462121a0b42999b778365c02b7fde"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::m_isInitialized" ref="a4ed462121a0b42999b778365c02b7fde" args="" -->
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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="a46b3b7a0c8f23a1d5ed69b5ef0518152"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::m_maxpivot" ref="a46b3b7a0c8f23a1d5ed69b5ef0518152" args="" -->
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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="a43e2e1baca5c7e66da4e711ee1579772"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::m_nonzero_pivots" ref="a43e2e1baca5c7e66da4e711ee1579772" args="" -->
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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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<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="a4e5ab7894126264655657e61ea441ca3"></a><!-- doxytag: member="Eigen::ColPivHouseholderQR::m_qr" ref="a4e5ab7894126264655657e61ea441ca3" args="" -->
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<p>Definition at line <a class="el" href="_q_r_source.html#l00344">344</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#l00348">348</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#l00350">350</a> of file <a class="el" href="_q_r_source.html">QR</a>.</p>
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