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<div class="title">Eigen::JacobiRotation Class Reference<div class="ingroups"><a class="el" href="group___jacobi___module.html">Jacobi module</a></div></div> </div>
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<!-- doxytag: class="Eigen::JacobiRotation" --><hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Rotation given by a cosine-sine pair.</p>
<p>This class represents a Jacobi or Givens rotation. This is a 2D rotation in the plane <code>J</code> of angle <img class="formulaInl" alt="$ \theta $" src="form_251.png"/> defined by its cosine <code>c</code> and sine <code>s</code> as follow: <img class="formulaInl" alt="$ J = \left ( \begin{array}{cc} c & \overline s \\ -s & \overline c \end{array} \right ) $" src="form_252.png"/></p>
<p>You can apply the respective counter-clockwise rotation to a column vector <code>v</code> by applying its adjoint on the left: <img class="formulaInl" alt="$ v = J^* v $" src="form_253.png"/> that translates to the following <a class="el" href="namespace_eigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> code: </p>
<div class="fragment"><pre class="fragment"> v.applyOnTheLeft(J.adjoint());
</pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_matrix_base.html#a9885400152e84d4ec66c75db81ea1efd" title="replaces *this by *this * other.">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#ac55d95621af611ba203816897935d108" title="replaces *this by *this * other.">MatrixBase::applyOnTheRight()</a> </dd></dl>
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<p><a href="class_eigen_1_1_jacobi_rotation-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">typedef <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a>< Scalar >::Real </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#a32dae27026e885ddb04532200a28b3b7">RealScalar</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_jacobi_rotation.html#a2d8cd006c58ec7f89ffadf182a2f5926">JacobiRotation</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor without any initialization. <a href="#a2d8cd006c58ec7f89ffadf182a2f5926"></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_jacobi_rotation.html#a0a86ccb0947e7e37dfd91c656483f207">JacobiRotation</a> (const Scalar &c, const Scalar &s)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Construct a planar rotation from a cosine-sine pair (<em>c</em>, <code>s</code>). <a href="#a0a86ccb0947e7e37dfd91c656483f207"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">Scalar & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#abc5f4e69c76a83346d679f18369eac2f">c</a> ()</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">Scalar </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#a7484f4f31952c17a2904763bae8bbbc0">c</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">Scalar & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#aa4cffb43f9acd3e2be4719f60c226c9f">s</a> ()</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">Scalar </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#aad3f01e2a6c69a956049e46c93b21323">s</a> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_jacobi_rotation.html">JacobiRotation</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#af97d161cc650d4675ac87efb970e599d">operator*</a> (const <a class="el" href="class_eigen_1_1_jacobi_rotation.html">JacobiRotation</a> &other)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Concatenates two planar rotation. <a href="#af97d161cc650d4675ac87efb970e599d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_jacobi_rotation.html">JacobiRotation</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#ac2064d659d2d1f21d1b48759eeed6564">transpose</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the transposed transformation. <a href="#ac2064d659d2d1f21d1b48759eeed6564"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_eigen_1_1_jacobi_rotation.html">JacobiRotation</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#acc31d4b9771cda0ba87bacd3dabe1cb7">adjoint</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the adjoint transformation. <a href="#acc31d4b9771cda0ba87bacd3dabe1cb7"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename Derived > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#af8b31f8fcfb00f2abff8d41d260060c0">makeJacobi</a> (const <a class="el" href="class_eigen_1_1_matrix_base.html">MatrixBase</a>< Derived > &, typename Derived::Index p, typename Derived::Index q)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">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 )$" src="form_256.png"/> yields a diagonal matrix <img class="formulaInl" alt="$ A = J^* B J $" src="form_255.png"/>. <a href="#af8b31f8fcfb00f2abff8d41d260060c0"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#a2caf22a0377708c1b25c09cffdaae69a">makeJacobi</a> (<a class="el" href="class_eigen_1_1_jacobi_rotation.html#a32dae27026e885ddb04532200a28b3b7">RealScalar</a> x, Scalar y, <a class="el" href="class_eigen_1_1_jacobi_rotation.html#a32dae27026e885ddb04532200a28b3b7">RealScalar</a> z)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Makes <code>*this</code> as a Jacobi rotation <em>J</em> such that applying <em>J</em> on both the right and left sides of the selfadjoint 2x2 matrix <img class="formulaInl" alt="$ B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )$" src="form_254.png"/> yields a diagonal matrix <img class="formulaInl" alt="$ A = J^* B J $" src="form_255.png"/>. <a href="#a2caf22a0377708c1b25c09cffdaae69a"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#ae8feec85feb7a1a359751e3716c496c1">makeGivens</a> (const Scalar &p, const Scalar &q, Scalar *z=0)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Makes <code>*this</code> as a Givens rotation <code>G</code> such that applying <img class="formulaInl" alt="$ G^* $" src="form_257.png"/> to the left of the vector <img class="formulaInl" alt="$ V = \left ( \begin{array}{c} p \\ q \end{array} \right )$" src="form_258.png"/> yields: <img class="formulaInl" alt="$ G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )$" src="form_259.png"/>. <a href="#ae8feec85feb7a1a359751e3716c496c1"></a><br/></td></tr>
<tr><td colspan="2"><h2><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#a70d6e4fbb497155382f5d6df5d4e5060">makeGivens</a> (const Scalar &p, const Scalar &q, Scalar *z, <a class="el" href="struct_eigen_1_1internal_1_1true__type.html">internal::true_type</a>)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#abcba4ccc77d811dced4e61cc0a404b3d">makeGivens</a> (const Scalar &p, const Scalar &q, Scalar *z, <a class="el" href="struct_eigen_1_1internal_1_1false__type.html">internal::false_type</a>)</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">Scalar </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#a8e26aba4ce54bc39dbbc94de7a986bec">m_c</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">Scalar </td><td class="memItemRight" valign="bottom"><a class="el" href="class_eigen_1_1_jacobi_rotation.html#a8b1dfe814f6fe2c18bd2d3f20fe8b58e">m_s</a></td></tr>
</table>
<hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="a32dae27026e885ddb04532200a28b3b7"></a><!-- doxytag: member="Eigen::JacobiRotation::RealScalar" ref="a32dae27026e885ddb04532200a28b3b7" args="" -->
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<td class="memname">typedef <a class="el" href="struct_eigen_1_1_num_traits.html">NumTraits</a><Scalar>::Real <a class="el" href="class_eigen_1_1_jacobi_rotation.html#a32dae27026e885ddb04532200a28b3b7">Eigen::JacobiRotation::RealScalar</a></td>
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00051">51</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="a2d8cd006c58ec7f89ffadf182a2f5926"></a><!-- doxytag: member="Eigen::JacobiRotation::JacobiRotation" ref="a2d8cd006c58ec7f89ffadf182a2f5926" args="()" -->
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<td class="memname">Eigen::JacobiRotation::JacobiRotation </td>
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<p>Default constructor without any initialization. </p>
<p>Definition at line <a class="el" href="_jacobi_source.html#l00054">54</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<a class="anchor" id="a0a86ccb0947e7e37dfd91c656483f207"></a><!-- doxytag: member="Eigen::JacobiRotation::JacobiRotation" ref="a0a86ccb0947e7e37dfd91c656483f207" args="(const Scalar &c, const Scalar &s)" -->
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<p>Construct a planar rotation from a cosine-sine pair (<em>c</em>, <code>s</code>). </p>
<p>Definition at line <a class="el" href="_jacobi_source.html#l00057">57</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="acc31d4b9771cda0ba87bacd3dabe1cb7"></a><!-- doxytag: member="Eigen::JacobiRotation::adjoint" ref="acc31d4b9771cda0ba87bacd3dabe1cb7" args="() const " -->
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<td class="memname"><a class="el" href="class_eigen_1_1_jacobi_rotation.html">JacobiRotation</a> Eigen::JacobiRotation::adjoint </td>
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<p>Returns the adjoint transformation. </p>
<p>Definition at line <a class="el" href="_jacobi_source.html#l00075">75</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<a class="anchor" id="abc5f4e69c76a83346d679f18369eac2f"></a><!-- doxytag: member="Eigen::JacobiRotation::c" ref="abc5f4e69c76a83346d679f18369eac2f" args="()" -->
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<td class="memname">Scalar& Eigen::JacobiRotation::c </td>
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00059">59</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00060">60</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<td class="memname">void Eigen::JacobiRotation::makeGivens </td>
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<p>Makes <code>*this</code> as a Givens rotation <code>G</code> such that applying <img class="formulaInl" alt="$ G^* $" src="form_257.png"/> to the left of the vector <img class="formulaInl" alt="$ V = \left ( \begin{array}{c} p \\ q \end{array} \right )$" src="form_258.png"/> yields: <img class="formulaInl" alt="$ G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )$" src="form_259.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"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><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="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_matrix_base.html#a9885400152e84d4ec66c75db81ea1efd" title="replaces *this by *this * other.">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#ac55d95621af611ba203816897935d108" title="replaces *this by *this * other.">MatrixBase::applyOnTheRight()</a> </dd></dl>
<p>Definition at line <a class="el" href="_jacobi_source.html#l00159">159</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<td class="memname">void Eigen::JacobiRotation::makeGivens </td>
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00167">167</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<a class="anchor" id="abcba4ccc77d811dced4e61cc0a404b3d"></a><!-- doxytag: member="Eigen::JacobiRotation::makeGivens" ref="abcba4ccc77d811dced4e61cc0a404b3d" args="(const Scalar &p, const Scalar &q, Scalar *z, internal::false_type)" -->
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00222">222</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<a class="anchor" id="af8b31f8fcfb00f2abff8d41d260060c0"></a><!-- doxytag: member="Eigen::JacobiRotation::makeJacobi" ref="af8b31f8fcfb00f2abff8d41d260060c0" args="(const MatrixBase< Derived > &, typename Derived::Index p, typename Derived::Index q)" -->
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<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 )$" src="form_256.png"/> yields a diagonal matrix <img class="formulaInl" alt="$ A = J^* B J $" src="form_255.png"/>. </p>
<p>Example: </p>
<div class="fragment"><pre class="fragment"></pre></div><p> Output: </p>
<div class="fragment"><pre class="fragment"></pre></div><dl class="see"><dt><b>See also:</b></dt><dd><a class="el" href="class_eigen_1_1_jacobi_rotation.html#a2caf22a0377708c1b25c09cffdaae69a" title="Makes *this as a Jacobi rotation J such that applying J on both the right and left sides of the selfa...">JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar)</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#a9885400152e84d4ec66c75db81ea1efd" title="replaces *this by *this * other.">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#ac55d95621af611ba203816897935d108" title="replaces *this by *this * other.">MatrixBase::applyOnTheRight()</a> </dd></dl>
<p>Definition at line <a class="el" href="_jacobi_source.html#l00137">137</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<p>Makes <code>*this</code> as a Jacobi rotation <em>J</em> such that applying <em>J</em> on both the right and left sides of the selfadjoint 2x2 matrix <img class="formulaInl" alt="$ B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )$" src="form_254.png"/> yields a diagonal matrix <img class="formulaInl" alt="$ A = J^* B J $" src="form_255.png"/>. </p>
<dl class="see"><dt><b>See also:</b></dt><dd>MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), <a class="el" href="class_eigen_1_1_matrix_base.html#a9885400152e84d4ec66c75db81ea1efd" title="replaces *this by *this * other.">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="class_eigen_1_1_matrix_base.html#ac55d95621af611ba203816897935d108" title="replaces *this by *this * other.">MatrixBase::applyOnTheRight()</a> </dd></dl>
<p>Definition at line <a class="el" href="_jacobi_source.html#l00096">96</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<td class="memname"><a class="el" href="class_eigen_1_1_jacobi_rotation.html">JacobiRotation</a> Eigen::JacobiRotation::operator* </td>
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<p>Concatenates two planar rotation. </p>
<p>Definition at line <a class="el" href="_jacobi_source.html#l00065">65</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00061">61</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00062">62</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<p>Returns the transposed transformation. </p>
<p>Definition at line <a class="el" href="_jacobi_source.html#l00072">72</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<hr/><h2>Member Data Documentation</h2>
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<td class="memname">Scalar <a class="el" href="class_eigen_1_1_jacobi_rotation.html#a8e26aba4ce54bc39dbbc94de7a986bec">Eigen::JacobiRotation::m_c</a><code> [protected]</code></td>
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00087">87</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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<p>Definition at line <a class="el" href="_jacobi_source.html#l00087">87</a> of file <a class="el" href="_jacobi_source.html">Jacobi</a>.</p>
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