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<a href="classEigen_1_1MatrixPower-members.html">List of all members</a> |
<a href="#pub-methods">Public Member Functions</a> </div>
<div class="headertitle">
<div class="title">MatrixPower< MatrixType > Class Template Reference<div class="ingroups"><a class="el" href="group__MatrixFunctions__Module.html">Matrix functions module</a></div></div> </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<typename MatrixType><br/>
class Eigen::MatrixPower< MatrixType ></h3>
<p>Class for computing matrix powers. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">MatrixType</td><td>type of the base, expected to be an instantiation of the Matrix class template.</td></tr>
</table>
</dd>
</dl>
<p>This class is capable of computing real/complex matrices raised to an arbitrary real power. Meanwhile, it saves the result of Schur decomposition if an non-integral power has even been calculated. Therefore, if you want to compute multiple (>= 2) matrix powers for the same matrix, using the class directly is more efficient than calling MatrixBase::pow().</p>
<p>Example: </p>
<div class="fragment"><div class="line"><span class="preprocessor">#include <unsupported/Eigen/MatrixFunctions></span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"></div>
<div class="line"><span class="keyword">using namespace </span>Eigen;</div>
<div class="line"></div>
<div class="line"><span class="keywordtype">int</span> main()</div>
<div class="line">{</div>
<div class="line"> Matrix4cd A = Matrix4cd::Random();</div>
<div class="line"> <a class="code" href="classEigen_1_1MatrixPower.html">MatrixPower<Matrix4cd></a> Apow(A);</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"The matrix A is:\n"</span> << A << <span class="stringliteral">"\n\n"</span></div>
<div class="line"> <span class="stringliteral">"A^3.1 is:\n"</span> << Apow(3.1) << <span class="stringliteral">"\n\n"</span></div>
<div class="line"> <span class="stringliteral">"A^3.3 is:\n"</span> << Apow(3.3) << <span class="stringliteral">"\n\n"</span></div>
<div class="line"> <span class="stringliteral">"A^3.7 is:\n"</span> << Apow(3.7) << <span class="stringliteral">"\n\n"</span></div>
<div class="line"> <span class="stringliteral">"A^3.9 is:\n"</span> << Apow(3.9) << std::endl;</div>
<div class="line"> <span class="keywordflow">return</span> 0;</div>
<div class="line">}</div>
</div><!-- fragment --><p> Output: </p>
<pre class="fragment">The matrix A is:
(-0.211234,0.680375) (0.10794,-0.444451) (0.434594,0.271423) (-0.198111,-0.686642)
(0.59688,0.566198) (0.257742,-0.0452059) (0.213938,-0.716795) (-0.782382,-0.740419)
(-0.604897,0.823295) (0.0268018,-0.270431) (-0.514226,-0.967399) (-0.563486,0.997849)
(0.536459,-0.329554) (0.83239,0.904459) (0.608354,-0.725537) (0.678224,0.0258648)
A^3.1 is:
(2.80575,-0.607662) (-1.16847,-0.00660555) (-0.760385,1.01461) (-0.38073,-0.106512)
(1.4041,-3.61891) (1.00481,0.186263) (-0.163888,0.449419) (-0.388981,-1.22629)
(-2.07957,-1.58136) (0.825866,2.25962) (5.09383,0.155736) (0.394308,-1.63034)
(-0.818997,0.671026) (2.11069,-0.00768024) (-1.37876,0.140165) (2.50512,-0.854429)
A^3.3 is:
(2.83571,-0.238717) (-1.48174,-0.0615217) (-0.0544396,1.68092) (-0.292699,-0.621726)
(2.0521,-3.58316) (0.87894,0.400548) (0.738072,-0.121242) (-1.07957,-1.63492)
(-3.00106,-1.10558) (1.52205,1.92407) (5.29759,-1.83562) (-0.532038,-1.50253)
(-0.491353,-0.4145) (2.5761,0.481286) (-1.21994,0.0367069) (2.67112,-1.06331)
A^3.7 is:
(1.42126,0.33362) (-1.39486,-0.560486) (1.44968,2.47066) (-0.324079,-1.75879)
(2.65301,-1.82427) (0.357333,-0.192429) (2.01017,-1.4791) (-2.71518,-2.35892)
(-3.98544,0.964861) (2.26033,0.554254) (3.18211,-5.94352) (-2.22888,0.128951)
(0.944969,-2.14683) (3.31345,1.66075) (-0.0623743,-0.848324) (2.3897,-1.863)
A^3.9 is:
(0.0720766,0.378685) (-0.931961,-0.978624) (1.9855,2.34105) (-0.530547,-2.17664)
(2.40934,-0.265286) (0.0299975,-1.08827) (1.98974,-2.05886) (-3.45767,-2.50235)
(-3.71666,2.3874) (2.054,-0.303) (0.844348,-7.29588) (-2.59136,1.57689)
(1.87645,-2.38798) (3.52111,2.10508) (0.799055,-1.6122) (1.93452,-2.44408)
</pre> </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:a95d38473ae16ef259e0d334538d050d6"><td class="memTemplParams" colspan="2">template<typename ResultType > </td></tr>
<tr class="memitem:a95d38473ae16ef259e0d334538d050d6"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixPower.html#a95d38473ae16ef259e0d334538d050d6">compute</a> (ResultType &res, RealScalar p)</td></tr>
<tr class="memdesc:a95d38473ae16ef259e0d334538d050d6"><td class="mdescLeft"> </td><td class="mdescRight">Compute the matrix power. <a href="#a95d38473ae16ef259e0d334538d050d6">More...</a><br/></td></tr>
<tr class="separator:a95d38473ae16ef259e0d334538d050d6"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0c03931b4fff167eeaf6bab5161ae9cd"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixPower.html#a0c03931b4fff167eeaf6bab5161ae9cd">MatrixPower</a> (const MatrixType &A)</td></tr>
<tr class="memdesc:a0c03931b4fff167eeaf6bab5161ae9cd"><td class="mdescLeft"> </td><td class="mdescRight">Constructor. <a href="#a0c03931b4fff167eeaf6bab5161ae9cd">More...</a><br/></td></tr>
<tr class="separator:a0c03931b4fff167eeaf6bab5161ae9cd"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a77c0aa664c889e4aac24406385196e8a"><td class="memItemLeft" align="right" valign="top">const MatrixPowerRetval<br class="typebreak"/>
< MatrixType > </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixPower.html#a77c0aa664c889e4aac24406385196e8a">operator()</a> (RealScalar p)</td></tr>
<tr class="memdesc:a77c0aa664c889e4aac24406385196e8a"><td class="mdescLeft"> </td><td class="mdescRight">Returns the matrix power. <a href="#a77c0aa664c889e4aac24406385196e8a">More...</a><br/></td></tr>
<tr class="separator:a77c0aa664c889e4aac24406385196e8a"><td class="memSeparator" colspan="2"> </td></tr>
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<h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<td class="memname"><a class="el" href="classEigen_1_1MatrixPower.html">MatrixPower</a> </td>
<td>(</td>
<td class="paramtype">const MatrixType & </td>
<td class="paramname"><em>A</em></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">explicit</span></span> </td>
</tr>
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<p>Constructor. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>the base of the matrix power.</td></tr>
</table>
</dd>
</dl>
<p>The class stores a reference to A, so it should not be changed (or destroyed) before evaluation. </p>
</div>
</div>
<h2 class="groupheader">Member Function Documentation</h2>
<a class="anchor" id="a95d38473ae16ef259e0d334538d050d6"></a>
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<div class="memproto">
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<td class="memname">void compute </td>
<td>(</td>
<td class="paramtype">ResultType & </td>
<td class="paramname"><em>res</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">RealScalar </td>
<td class="paramname"><em>p</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Compute the matrix power. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">p</td><td>exponent, a real scalar. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">res</td><td><img class="formulaInl" alt="$ A^p $" src="form_74.png"/> where A is specified in the constructor. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
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<td class="memname">const MatrixPowerRetval<MatrixType> operator() </td>
<td>(</td>
<td class="paramtype">RealScalar </td>
<td class="paramname"><em>p</em></td><td>)</td>
<td></td>
</tr>
</table>
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<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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<p>Returns the matrix power. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">p</td><td>exponent, a real scalar. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The expression <img class="formulaInl" alt="$ A^p $" src="form_74.png"/>, where A is specified in the constructor. </dd></dl>
</div>
</div>
<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="MatrixPower_8h_source.html">MatrixPower.h</a></li>
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