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<div class="title">Transpositions< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > Class Template Reference<div class="ingroups"><a class="el" href="group__Core__Module.html">Core 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<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType><br/>
class Eigen::Transpositions< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType ></h3>
<p>Represents a sequence of transpositions (row/column interchange) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">SizeAtCompileTime</td><td>the number of transpositions, or Dynamic </td></tr>
<tr><td class="paramname">MaxSizeAtCompileTime</td><td>the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.</td></tr>
</table>
</dd>
</dl>
<p>This class represents a permutation transformation as a sequence of <em>n</em> transpositions <img class="formulaInl" alt="$[T_{n-1} \ldots T_{i} \ldots T_{0}]$" src="form_31.png"/>. It is internally stored as a vector of integers <code>indices</code>. Each transposition <img class="formulaInl" alt="$ T_{i} $" src="form_32.png"/> applied on the left of a matrix ( <img class="formulaInl" alt="$ T_{i} M$" src="form_33.png"/>) interchanges the rows <code>i</code> and <code>indices</code>[i] of the matrix <code>M</code>. A transposition applied on the right (e.g., <img class="formulaInl" alt="$ M T_{i}$" src="form_34.png"/>) yields a column interchange.</p>
<p>Compared to the class <a class="el" href="classEigen_1_1PermutationMatrix.html" title="Permutation matrix. ">PermutationMatrix</a>, such a sequence of transpositions is what is computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.</p>
<p>To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example: </p>
<div class="fragment"><div class="line">* Transpositions tr;</div>
<div class="line">* <a class="code" href="group__matrixtypedefs.html#gabab09c32e96cfa9829a88400627af162">MatrixXf</a> mat;</div>
<div class="line">* mat = tr * mat;</div>
<div class="line">* </div>
</div><!-- fragment --><p> In this example, we detect that the matrix appears on both side, and so the transpositions are applied in-place without any temporary or extra copy.</p>
<dl class="section see"><dt>See Also</dt><dd>class <a class="el" href="classEigen_1_1PermutationMatrix.html" title="Permutation matrix. ">PermutationMatrix</a> </dd></dl>
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<p>Inherits TranspositionsBase< Derived >.</p>
<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:a47cd9d9f732693e925c964971272931a"><td class="memItemLeft" align="right" valign="top">const Index & </td><td class="memItemRight" valign="bottom"><b>coeff</b> (Index i) const </td></tr>
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<tr class="memitem:a211863b210e48a78bb0f133aeb6ef27b"><td class="memItemLeft" align="right" valign="top">Index & </td><td class="memItemRight" valign="bottom"><b>coeffRef</b> (Index i)</td></tr>
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<tr class="memitem:a8876d615d17aad77b054a8f58b699e7d"><td class="memItemLeft" align="right" valign="top">const IndicesType & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transpositions.html#a8876d615d17aad77b054a8f58b699e7d">indices</a> () const </td></tr>
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<tr class="memitem:a53f29dec699d5e93db152c51545bc20a"><td class="memItemLeft" align="right" valign="top">IndicesType & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transpositions.html#a53f29dec699d5e93db152c51545bc20a">indices</a> ()</td></tr>
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<tr class="memitem:ab7061cd876ca7cf9b3247aceb71ce546"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transpose.html">Transpose</a>< TranspositionsBase > </td><td class="memItemRight" valign="bottom"><b>inverse</b> () const </td></tr>
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<tr class="memitem:a1e67206dcb38999b1521c2f170727162"><td class="memItemLeft" align="right" valign="top">const Index & </td><td class="memItemRight" valign="bottom"><b>operator()</b> (Index i) const </td></tr>
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<tr class="memitem:ac47e1eeff8cc989d49e677fe34269906"><td class="memItemLeft" align="right" valign="top">Index & </td><td class="memItemRight" valign="bottom"><b>operator()</b> (Index i)</td></tr>
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<tr class="memitem:aa7fa08a35030d776f2588b5ea55a6be5"><td class="memTemplParams" colspan="2">template<typename OtherDerived > </td></tr>
<tr class="memitem:aa7fa08a35030d776f2588b5ea55a6be5"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transpositions.html">Transpositions</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transpositions.html#aa7fa08a35030d776f2588b5ea55a6be5">operator=</a> (const TranspositionsBase< OtherDerived > &other)</td></tr>
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<tr class="memitem:ae3d76eb2876f1784a913c22166cf9470"><td class="memItemLeft" align="right" valign="top">const Index & </td><td class="memItemRight" valign="bottom"><b>operator[]</b> (Index i) const </td></tr>
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<tr class="memitem:ab81f2ddae2cd2adea24fa20675d131a5"><td class="memItemLeft" align="right" valign="top">Index & </td><td class="memItemRight" valign="bottom"><b>operator[]</b> (Index i)</td></tr>
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<tr class="memitem:ab8b22b9d0f25d76dda44f79aeabd826f"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><b>resize</b> (int newSize)</td></tr>
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<tr class="memitem:a382e6ad7e6721b121e510959e1011be3"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><b>setIdentity</b> ()</td></tr>
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<tr class="memitem:a76f5bc8a03ec105ab4be1f2b91b7b5d5"><td class="memItemLeft" align="right" valign="top">Index </td><td class="memItemRight" valign="bottom"><b>size</b> () const </td></tr>
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<tr class="memitem:ae153935f0ffecbcf48bd3c982122a372"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transpose.html">Transpose</a>< TranspositionsBase > </td><td class="memItemRight" valign="bottom"><b>transpose</b> () const </td></tr>
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<tr class="memitem:a1aa3f20aefdb81543ce83baa35c4c412"><td class="memTemplParams" colspan="2">template<typename OtherDerived > </td></tr>
<tr class="memitem:a1aa3f20aefdb81543ce83baa35c4c412"><td class="memTemplItemLeft" align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transpositions.html#a1aa3f20aefdb81543ce83baa35c4c412">Transpositions</a> (const TranspositionsBase< OtherDerived > &other)</td></tr>
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<tr class="memitem:a65fdb58351000ca12164022742d61080"><td class="memTemplParams" colspan="2">template<typename Other > </td></tr>
<tr class="memitem:a65fdb58351000ca12164022742d61080"><td class="memTemplItemLeft" align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transpositions.html#a65fdb58351000ca12164022742d61080">Transpositions</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>< Other > &a_indices)</td></tr>
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<tr class="memitem:a9b6182d7f0e8067f117afab16f94d98f"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transpositions.html#a9b6182d7f0e8067f117afab16f94d98f">Transpositions</a> (Index size)</td></tr>
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<h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<p>Copy constructor. </p>
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<p>Generic constructor from expression of the transposition indices. </p>
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<td class="paramname"><em>size</em></td><td>)</td>
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<p>Constructs an uninitialized permutation matrix of given size. </p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname">const Index& coeff </td>
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<p>Direct access to the underlying index vector </p>
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<p>Direct access to the underlying index vector </p>
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<p>const version of <a class="el" href="classEigen_1_1Transpositions.html#a53f29dec699d5e93db152c51545bc20a">indices()</a>. </p>
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<dl class="section return"><dt>Returns</dt><dd>a reference to the stored array representing the transpositions. </dd></dl>
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<td class="memname"><a class="el" href="classEigen_1_1Transpose.html">Transpose</a><TranspositionsBase> inverse </td>
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<dl class="section return"><dt>Returns</dt><dd>the inverse transformation </dd></dl>
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<p>Direct access to the underlying index vector </p>
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<p>Direct access to the underlying index vector </p>
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<td class="memname"><a class="el" href="classEigen_1_1Transpositions.html">Transpositions</a>& operator= </td>
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<p>Copies the <em>other</em> transpositions into <code>*this</code> </p>
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<td class="memname">const Index& operator[] </td>
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<p>Direct access to the underlying index vector </p>
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<td class="memname">Index& operator[] </td>
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<p>Direct access to the underlying index vector </p>
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<td class="memname">void resize </td>
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<p>Resizes to given size. </p>
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<td class="memname">void setIdentity </td>
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<p>Sets <code>*this</code> to represents an identity transformation </p>
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<td class="memname">Index size </td>
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<dl class="section return"><dt>Returns</dt><dd>the number of transpositions </dd></dl>
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<td class="memname"><a class="el" href="classEigen_1_1Transpose.html">Transpose</a><TranspositionsBase> transpose </td>
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<dl class="section return"><dt>Returns</dt><dd>the tranpose transformation </dd></dl>
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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="Transpositions_8h_source.html">Transpositions.h</a></li>
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