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<a href="#pub-methods">Public Member Functions</a> |
<a href="#pro-methods">Protected Member Functions</a> </div>
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<div class="title">SVDBase< _MatrixType > Class Template Reference<div class="ingroups"><a class="el" href="group__SVD__Module.html">SVD 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::SVDBase< _MatrixType ></h3>
<p>Mother class of SVD classes algorithms. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">MatrixType</td><td>the type of the matrix of which we are computing the SVD decomposition SVD decomposition consists in decomposing any n-by-p matrix <em>A</em> as a product <p class="formulaDsp">
<img class="formulaDsp" alt="\[ A = U S V^* \]" src="form_93.png"/>
</p>
where <em>U</em> is a n-by-n unitary, <em>V</em> is a p-by-p unitary, and <em>S</em> is a n-by-p real positive matrix which is zero outside of its main diagonal; the diagonal entries of S are known as the <em>singular</em> <em>values</em> of <em>A</em> and the columns of <em>U</em> and <em>V</em> are known as the left and right <em>singular</em> <em>vectors</em> of <em>A</em> respectively.</td></tr>
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</dd>
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<p>Singular values are always sorted in decreasing order.</p>
<p>You can ask for only <em>thin</em> <em>U</em> or <em>V</em> to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting <em>m</em> be the smaller value among <em>n</em> and <em>p</em>, there are only <em>m</em> singular vectors; the remaining columns of <em>U</em> and <em>V</em> do not correspond to actual singular vectors. Asking for <em>thin</em> <em>U</em> or <em>V</em> means asking for only their <em>m</em> first columns to be formed. So <em>U</em> is then a n-by-m matrix, and <em>V</em> is then a p-by-m matrix. Notice that thin <em>U</em> and <em>V</em> are all you need for (least squares) solving.</p>
<p>If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to terminate in finite (and reasonable) time. </p>
<dl class="section see"><dt>See Also</dt><dd>MatrixBase::genericSvd() </dd></dl>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for SVDBase< _MatrixType >:</div>
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<map name="SVDBase_3_01__MatrixType_01_4_inherit__map" id="SVDBase_3_01__MatrixType_01_4_inherit__map">
<area shape="rect" id="node2" href="classEigen_1_1BDCSVD.html" title="class Bidiagonal Divide and Conquer SVD " alt="" coords="5,483,179,810"/><area shape="rect" id="node3" href="classEigen_1_1JacobiSVD.html" title="Two-sided Jacobi SVD decomposition of a rectangular matrix. " alt="" coords="204,557,388,737"/></map>
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<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:a83297cc5d915af5132f5161b62a7a650"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1SVDBase.html">SVDBase</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a83297cc5d915af5132f5161b62a7a650">compute</a> (const MatrixType &matrix, unsigned int computationOptions)</td></tr>
<tr class="memdesc:a83297cc5d915af5132f5161b62a7a650"><td class="mdescLeft"> </td><td class="mdescRight">Method performing the decomposition of given matrix using custom options. <a href="#a83297cc5d915af5132f5161b62a7a650">More...</a><br/></td></tr>
<tr class="separator:a83297cc5d915af5132f5161b62a7a650"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a7af4db91caadd1b5e12cdc1384a18bd7"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1SVDBase.html">SVDBase</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a7af4db91caadd1b5e12cdc1384a18bd7">compute</a> (const MatrixType &matrix)</td></tr>
<tr class="memdesc:a7af4db91caadd1b5e12cdc1384a18bd7"><td class="mdescLeft"> </td><td class="mdescRight">Method performing the decomposition of given matrix using current options. <a href="#a7af4db91caadd1b5e12cdc1384a18bd7">More...</a><br/></td></tr>
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<tr class="memitem:a1ffab6aab715fe0918a841611a95e9aa"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a1ffab6aab715fe0918a841611a95e9aa">computeU</a> () const </td></tr>
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<tr class="memitem:a92e99646eefbeb071ef220841555a703"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a92e99646eefbeb071ef220841555a703">computeV</a> () const </td></tr>
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<tr class="memitem:a49e16a4adf4fe58a2d65a5e5a31e7654"><td class="memItemLeft" align="right" valign="top">const MatrixUType & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a49e16a4adf4fe58a2d65a5e5a31e7654">matrixU</a> () const </td></tr>
<tr class="separator:a49e16a4adf4fe58a2d65a5e5a31e7654"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae5158ab7ca44a705c2a3b56ec926b42a"><td class="memItemLeft" align="right" valign="top">const MatrixVType & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#ae5158ab7ca44a705c2a3b56ec926b42a">matrixV</a> () const </td></tr>
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<tr class="memitem:aa468765ea9b7f0e92380fa206e6498bd"><td class="memItemLeft" align="right" valign="top">Index </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#aa468765ea9b7f0e92380fa206e6498bd">nonzeroSingularValues</a> () const </td></tr>
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<tr class="memitem:a48d4068b97dfbb83d62599e56e26797a"><td class="memItemLeft" align="right" valign="top">const SingularValuesType & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a48d4068b97dfbb83d62599e56e26797a">singularValues</a> () const </td></tr>
<tr class="separator:a48d4068b97dfbb83d62599e56e26797a"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr class="memitem:aa64c67571945053f2fe3ec5163045bbd"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#aa64c67571945053f2fe3ec5163045bbd">SVDBase</a> ()</td></tr>
<tr class="memdesc:aa64c67571945053f2fe3ec5163045bbd"><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor. <a href="#aa64c67571945053f2fe3ec5163045bbd">More...</a><br/></td></tr>
<tr class="separator:aa64c67571945053f2fe3ec5163045bbd"><td class="memSeparator" colspan="2"> </td></tr>
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<h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<p>Default Constructor. </p>
<p>Default constructor of <a class="el" href="classEigen_1_1SVDBase.html" title="Mother class of SVD classes algorithms. ">SVDBase</a> </p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname"><a class="el" href="classEigen_1_1SVDBase.html">SVDBase</a>& compute </td>
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<td class="paramtype">const MatrixType & </td>
<td class="paramname"><em>matrix</em>, </td>
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<p>Method performing the decomposition of given matrix using custom options. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">matrix</td><td>the matrix to decompose </td></tr>
<tr><td class="paramname">computationOptions</td><td>optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU, #ComputeFullV, #ComputeThinV.</td></tr>
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<p>Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not available with the (non-default) FullPivHouseholderQR preconditioner. </p>
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<p>Method performing the decomposition of given matrix using current options. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">matrix</td><td>the matrix to decompose</td></tr>
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<p>This method uses the current <em>computationOptions</em>, as already passed to the constructor or to <a class="el" href="classEigen_1_1SVDBase.html#a83297cc5d915af5132f5161b62a7a650" title="Method performing the decomposition of given matrix using custom options. ">compute(const MatrixType&, unsigned int)</a>. </p>
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<dl class="section return"><dt>Returns</dt><dd>true if <em>U</em> (full or thin) is asked for in this SVD decomposition </dd></dl>
<p>Referenced by <a class="el" href="classEigen_1_1SVDBase.html#a49e16a4adf4fe58a2d65a5e5a31e7654">SVDBase< _MatrixType >::matrixU()</a>.</p>
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<dl class="section return"><dt>Returns</dt><dd>true if <em>V</em> (full or thin) is asked for in this SVD decomposition </dd></dl>
<p>Referenced by <a class="el" href="classEigen_1_1SVDBase.html#ae5158ab7ca44a705c2a3b56ec926b42a">SVDBase< _MatrixType >::matrixV()</a>.</p>
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<dl class="section return"><dt>Returns</dt><dd>the <em>U</em> matrix.</dd></dl>
<p>For the <a class="el" href="classEigen_1_1SVDBase.html" title="Mother class of SVD classes algorithms. ">SVDBase</a> decomposition of a n-by-p matrix, letting <em>m</em> be the minimum of <em>n</em> and <em>p</em>, the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.</p>
<p>The <em>m</em> first columns of <em>U</em> are the left singular vectors of the matrix being decomposed.</p>
<p>This method asserts that you asked for <em>U</em> to be computed. </p>
<p>References <a class="el" href="classEigen_1_1SVDBase.html#a1ffab6aab715fe0918a841611a95e9aa">SVDBase< _MatrixType >::computeU()</a>.</p>
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<dl class="section return"><dt>Returns</dt><dd>the <em>V</em> matrix.</dd></dl>
<p>For the SVD decomposition of a n-by-p matrix, letting <em>m</em> be the minimum of <em>n</em> and <em>p</em>, the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.</p>
<p>The <em>m</em> first columns of <em>V</em> are the right singular vectors of the matrix being decomposed.</p>
<p>This method asserts that you asked for <em>V</em> to be computed. </p>
<p>References <a class="el" href="classEigen_1_1SVDBase.html#a92e99646eefbeb071ef220841555a703">SVDBase< _MatrixType >::computeV()</a>.</p>
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<dl class="section return"><dt>Returns</dt><dd>the number of singular values that are not exactly 0 </dd></dl>
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<dl class="section return"><dt>Returns</dt><dd>the vector of singular values.</dd></dl>
<p>For the SVD decomposition of a n-by-p matrix, letting <em>m</em> be the minimum of <em>n</em> and <em>p</em>, the returned vector has size <em>m</em>. Singular values are always sorted in decreasing order. </p>
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