<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/> <meta http-equiv="X-UA-Compatible" content="IE=9"/> <meta name="generator" content="Doxygen 1.8.5"/> <title>Eigen: JacobiRotation< Scalar > Class Template Reference</title> <link href="tabs.css" rel="stylesheet" type="text/css"/> <script type="text/javascript" src="jquery.js"></script> <script type="text/javascript" src="dynsections.js"></script> <link href="navtree.css" rel="stylesheet" type="text/css"/> <script type="text/javascript" src="resize.js"></script> <script type="text/javascript" src="navtree.js"></script> <script type="text/javascript"> $(document).ready(initResizable); $(window).load(resizeHeight); </script> <link href="search/search.css" rel="stylesheet" type="text/css"/> <script type="text/javascript" src="search/search.js"></script> <script type="text/javascript"> $(document).ready(function() { searchBox.OnSelectItem(0); }); </script> <link href="doxygen.css" rel="stylesheet" type="text/css" /> <link href="eigendoxy.css" rel="stylesheet" type="text/css"> <!-- --> <script type="text/javascript" src="eigen_navtree_hacks.js"></script> <!-- <script type="text/javascript"> --> <!-- </script> --> </head> <body> <div id="top"><!-- do not remove this div, it is closed by doxygen! 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This is a 2D rotation in the plane <code>J</code> of angle <img class="formulaInl" alt="$ \theta $" src="form_144.png"/> defined by its cosine <code>c</code> and sine <code>s</code> as follow: <img class="formulaInl" alt="$ J = \left ( \begin{array}{cc} c & \overline s \\ -s & \overline c \end{array} \right ) $" src="form_145.png"/></p> <p>You can apply the respective counter-clockwise rotation to a column vector <code>v</code> by applying its adjoint on the left: <img class="formulaInl" alt="$ v = J^* v $" src="form_146.png"/> that translates to the following <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library. ">Eigen</a> code: </p> <div class="fragment"><div class="line">* v.applyOnTheLeft(J.adjoint());</div> <div class="line">* </div> </div><!-- fragment --><dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a9aaee4fba54baa7d0ca508e094f2d6f9">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a6e5b1e71a1916ddd01e7c324831c40dc">MatrixBase::applyOnTheRight()</a> </dd></dl> </div><table class="memberdecls"> <tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a> Public Member Functions</h2></td></tr> <tr class="memitem:acf21a38021bf2100bb50268a166317f1"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#acf21a38021bf2100bb50268a166317f1">adjoint</a> () const </td></tr> <tr class="separator:acf21a38021bf2100bb50268a166317f1"><td class="memSeparator" colspan="2"> </td></tr> <tr class="memitem:a5700212c7e79eccd3cde8b07d6816e9d"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">JacobiRotation</a> ()</td></tr> <tr class="separator:a5700212c7e79eccd3cde8b07d6816e9d"><td class="memSeparator" colspan="2"> </td></tr> <tr class="memitem:a7999227436ed5e6bbe679fd40564abf1"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a7999227436ed5e6bbe679fd40564abf1">JacobiRotation</a> (const Scalar &c, const Scalar &s)</td></tr> <tr class="separator:a7999227436ed5e6bbe679fd40564abf1"><td class="memSeparator" colspan="2"> </td></tr> <tr class="memitem:a459c7bb56a9862bc2b66d03070b4a3e0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0">makeGivens</a> (const Scalar &p, const Scalar &q, Scalar *z=0)</td></tr> <tr class="separator:a459c7bb56a9862bc2b66d03070b4a3e0"><td class="memSeparator" colspan="2"> </td></tr> <tr class="memitem:a7349f180eaab3d2b4c654b32a41f8932"><td class="memTemplParams" colspan="2">template<typename Derived > </td></tr> <tr class="memitem:a7349f180eaab3d2b4c654b32a41f8932"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a7349f180eaab3d2b4c654b32a41f8932">makeJacobi</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>< Derived > &, typename Derived::Index p, typename Derived::Index q)</td></tr> <tr class="separator:a7349f180eaab3d2b4c654b32a41f8932"><td class="memSeparator" colspan="2"> </td></tr> <tr class="memitem:aa44fbe850470b9f08adceff2655decdf"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#aa44fbe850470b9f08adceff2655decdf">makeJacobi</a> (const RealScalar &x, const Scalar &y, const RealScalar &z)</td></tr> <tr class="separator:aa44fbe850470b9f08adceff2655decdf"><td class="memSeparator" colspan="2"> </td></tr> <tr class="memitem:a693f65729440b5c31feb6d86d1b075d1"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a693f65729440b5c31feb6d86d1b075d1">operator*</a> (const <a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> &other)</td></tr> <tr class="separator:a693f65729440b5c31feb6d86d1b075d1"><td class="memSeparator" colspan="2"> </td></tr> <tr class="memitem:a535dd93be32736dbe23a201c33c279d7"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a535dd93be32736dbe23a201c33c279d7">transpose</a> () const </td></tr> <tr class="separator:a535dd93be32736dbe23a201c33c279d7"><td class="memSeparator" colspan="2"> </td></tr> </table> <h2 class="groupheader">Constructor & Destructor Documentation</h2> <a class="anchor" id="a5700212c7e79eccd3cde8b07d6816e9d"></a> <div class="memitem"> <div class="memproto"> <table class="mlabels"> <tr> <td class="mlabels-left"> <table class="memname"> <tr> <td class="memname"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> </td> <td>(</td> <td class="paramname"></td><td>)</td> <td></td> </tr> </table> </td> <td class="mlabels-right"> <span class="mlabels"><span class="mlabel">inline</span></span> </td> </tr> </table> </div><div class="memdoc"> <p>Default constructor without any initialization. </p> <p>Referenced by <a class="el" href="classEigen_1_1JacobiRotation.html#acf21a38021bf2100bb50268a166317f1">JacobiRotation< Scalar >::adjoint()</a>, <a class="el" href="classEigen_1_1JacobiRotation.html#a693f65729440b5c31feb6d86d1b075d1">JacobiRotation< Scalar >::operator*()</a>, and <a class="el" href="classEigen_1_1JacobiRotation.html#a535dd93be32736dbe23a201c33c279d7">JacobiRotation< Scalar >::transpose()</a>.</p> </div> </div> <a class="anchor" id="a7999227436ed5e6bbe679fd40564abf1"></a> <div class="memitem"> <div class="memproto"> <table class="mlabels"> <tr> <td class="mlabels-left"> <table class="memname"> <tr> <td class="memname"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> </td> <td>(</td> <td class="paramtype">const Scalar & </td> <td class="paramname"><em>c</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">const Scalar & </td> <td class="paramname"><em>s</em> </td> </tr> <tr> <td></td> <td>)</td> <td></td><td></td> </tr> </table> </td> <td class="mlabels-right"> <span class="mlabels"><span class="mlabel">inline</span></span> </td> </tr> </table> </div><div class="memdoc"> <p>Construct a planar rotation from a cosine-sine pair (<em>c</em>, <code>s</code>). </p> </div> </div> <h2 class="groupheader">Member Function Documentation</h2> <a class="anchor" id="acf21a38021bf2100bb50268a166317f1"></a> <div class="memitem"> <div class="memproto"> <table class="mlabels"> <tr> <td class="mlabels-left"> <table class="memname"> <tr> <td class="memname"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> adjoint </td> <td>(</td> <td class="paramname"></td><td>)</td> <td> const</td> </tr> </table> </td> <td class="mlabels-right"> <span class="mlabels"><span class="mlabel">inline</span></span> </td> </tr> </table> </div><div class="memdoc"> <p>Returns the adjoint transformation </p> <p>References <a class="el" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">JacobiRotation< Scalar >::JacobiRotation()</a>.</p> </div> </div> <a class="anchor" id="a459c7bb56a9862bc2b66d03070b4a3e0"></a> <div class="memitem"> <div class="memproto"> <table class="memname"> <tr> <td class="memname">void makeGivens </td> <td>(</td> <td class="paramtype">const Scalar & </td> <td class="paramname"><em>p</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">const Scalar & </td> <td class="paramname"><em>q</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">Scalar * </td> <td class="paramname"><em>z</em> = <code>0</code> </td> </tr> <tr> <td></td> <td>)</td> <td></td><td></td> </tr> </table> </div><div class="memdoc"> <p>Makes <code>*this</code> as a Givens rotation <code>G</code> such that applying <img class="formulaInl" alt="$ G^* $" src="form_150.png"/> to the left of the vector <img class="formulaInl" alt="$ V = \left ( \begin{array}{c} p \\ q \end{array} \right )$" src="form_151.png"/> yields: <img class="formulaInl" alt="$ G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )$" src="form_152.png"/>.</p> <p>The value of <em>z</em> is returned if <em>z</em> is not null (the default is null). Also note that G is built such that the cosine is always real.</p> <p>Example: </p> <div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga7f1b1fd6061c265796ef9f5742854bee">Vector2f</a> v = <a class="code" href="classEigen_1_1DenseBase.html#a8e759dafdd9ecc446d397b7f5435f60a">Vector2f::Random</a>();</div> <div class="line">JacobiRotation<float> G;</div> <div class="line">G.makeGivens(v.x(), v.y());</div> <div class="line">cout << <span class="stringliteral">"Here is the vector v:"</span> << endl << v << endl;</div> <div class="line">v.applyOnTheLeft(0, 1, G.adjoint());</div> <div class="line">cout << <span class="stringliteral">"Here is the vector J' * v:"</span> << endl << v << endl;</div> </div><!-- fragment --><p> Output: </p> <pre class="fragment">Here is the vector v: 0.68 -0.211 Here is the vector J' * v: 0.712 0 </pre><p>This function implements the continuous Givens rotation generation algorithm found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem. LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.</p> <dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a9aaee4fba54baa7d0ca508e094f2d6f9">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a6e5b1e71a1916ddd01e7c324831c40dc">MatrixBase::applyOnTheRight()</a> </dd></dl> </div> </div> <a class="anchor" id="a7349f180eaab3d2b4c654b32a41f8932"></a> <div class="memitem"> <div class="memproto"> <table class="mlabels"> <tr> <td class="mlabels-left"> <table class="memname"> <tr> <td class="memname">bool makeJacobi </td> <td>(</td> <td class="paramtype">const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>< Derived > & </td> <td class="paramname"><em>m</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">typename Derived::Index </td> <td class="paramname"><em>p</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">typename Derived::Index </td> <td class="paramname"><em>q</em> </td> </tr> <tr> <td></td> <td>)</td> <td></td><td></td> </tr> </table> </td> <td class="mlabels-right"> <span class="mlabels"><span class="mlabel">inline</span></span> </td> </tr> </table> </div><div class="memdoc"> <p>Makes <code>*this</code> as a Jacobi rotation <code>J</code> such that applying <em>J</em> on both the right and left sides of the 2x2 selfadjoint matrix <img class="formulaInl" alt="$ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\text{this}_{pq})^* & \text{this}_{qq} \end{array} \right )$" src="form_149.png"/> yields a diagonal matrix <img class="formulaInl" alt="$ A = J^* B J $" src="form_148.png"/></p> <p>Example: </p> <div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga535a919504bb3bc463b8995c196c1eed">Matrix2f</a> m = <a class="code" href="classEigen_1_1DenseBase.html#a8e759dafdd9ecc446d397b7f5435f60a">Matrix2f::Random</a>();</div> <div class="line">m = (m + m.adjoint()).eval();</div> <div class="line">JacobiRotation<float> J;</div> <div class="line">J.makeJacobi(m, 0, 1);</div> <div class="line">cout << <span class="stringliteral">"Here is the matrix m:"</span> << endl << m << endl;</div> <div class="line">m.applyOnTheLeft(0, 1, J.adjoint());</div> <div class="line">m.applyOnTheRight(0, 1, J);</div> <div class="line">cout << <span class="stringliteral">"Here is the matrix J' * m * J:"</span> << endl << m << endl;</div> </div><!-- fragment --><p> Output: </p> <pre class="fragment">Here is the matrix m: 1.36 0.355 0.355 1.19 Here is the matrix J' * m * J: 1.64 0 0 0.913 </pre><dl class="section see"><dt>See Also</dt><dd>JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), <a class="el" href="classEigen_1_1MatrixBase.html#a9aaee4fba54baa7d0ca508e094f2d6f9">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a6e5b1e71a1916ddd01e7c324831c40dc">MatrixBase::applyOnTheRight()</a> </dd></dl> </div> </div> <a class="anchor" id="aa44fbe850470b9f08adceff2655decdf"></a> <div class="memitem"> <div class="memproto"> <table class="memname"> <tr> <td class="memname">bool makeJacobi </td> <td>(</td> <td class="paramtype">const RealScalar & </td> <td class="paramname"><em>x</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">const Scalar & </td> <td class="paramname"><em>y</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">const RealScalar & </td> <td class="paramname"><em>z</em> </td> </tr> <tr> <td></td> <td>)</td> <td></td><td></td> </tr> </table> </div><div class="memdoc"> <p>Makes <code>*this</code> as a Jacobi rotation <em>J</em> such that applying <em>J</em> on both the right and left sides of the selfadjoint 2x2 matrix <img class="formulaInl" alt="$ B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )$" src="form_147.png"/> yields a diagonal matrix <img class="formulaInl" alt="$ A = J^* B J $" src="form_148.png"/></p> <dl class="section see"><dt>See Also</dt><dd>MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), <a class="el" href="classEigen_1_1MatrixBase.html#a9aaee4fba54baa7d0ca508e094f2d6f9">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a6e5b1e71a1916ddd01e7c324831c40dc">MatrixBase::applyOnTheRight()</a> </dd></dl> </div> </div> <a class="anchor" id="a693f65729440b5c31feb6d86d1b075d1"></a> <div class="memitem"> <div class="memproto"> <table class="mlabels"> <tr> <td class="mlabels-left"> <table class="memname"> <tr> <td class="memname"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> operator* </td> <td>(</td> <td class="paramtype">const <a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a>< Scalar > & </td> <td class="paramname"><em>other</em></td><td>)</td> <td></td> </tr> </table> </td> <td class="mlabels-right"> <span class="mlabels"><span class="mlabel">inline</span></span> </td> </tr> </table> </div><div class="memdoc"> <p>Concatenates two planar rotation </p> <p>References <a class="el" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">JacobiRotation< Scalar >::JacobiRotation()</a>.</p> </div> </div> <a class="anchor" id="a535dd93be32736dbe23a201c33c279d7"></a> <div class="memitem"> <div class="memproto"> <table class="mlabels"> <tr> <td class="mlabels-left"> <table class="memname"> <tr> <td class="memname"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> transpose </td> <td>(</td> <td class="paramname"></td><td>)</td> <td> const</td> </tr> </table> </td> <td class="mlabels-right"> <span class="mlabels"><span class="mlabel">inline</span></span> </td> </tr> </table> </div><div class="memdoc"> <p>Returns the transposed transformation </p> <p>References <a class="el" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">JacobiRotation< Scalar >::JacobiRotation()</a>.</p> <p>Referenced by <a class="el" href="classEigen_1_1JacobiSVD.html#a2c4a669a1daef0b1ab3ee4e13ae85ca3">JacobiSVD< MatrixType, QRPreconditioner >::compute()</a>.</p> </div> </div> <hr/>The documentation for this class was generated from the following files:<ul> <li><a class="el" href="ForwardDeclarations_8h_source.html">ForwardDeclarations.h</a></li> <li><a class="el" href="Jacobi_8h_source.html">Jacobi.h</a></li> </ul> </div><!-- contents --> </div><!-- doc-content --> <!-- start footer part --> <div id="nav-path" class="navpath"><!-- id is needed for treeview function! --> <ul> <li class="navelem"><a class="el" href="namespaceEigen.html">Eigen</a></li><li class="navelem"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a></li> <li class="footer">Generated on Mon Oct 28 2013 11:04:29 for Eigen by <a href="http://www.doxygen.org/index.html"> 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