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453 lines
18 KiB
HTML
453 lines
18 KiB
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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml">
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<head>
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<title>BLAS</title>
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<meta name="GENERATOR" content="Quanta Plus" />
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<meta name="AUTHOR" content="Gunter Winkler" />
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
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<link rel="stylesheet" href="../../../../boost.css" type="text/css"/>
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<link rel="stylesheet" href="ublas.css" type="text/css" />
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<script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script>
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<script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script>
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</head>
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<body>
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<h1>Level 3 BLAS</h1>
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<div class="toc" id="toc"></div>
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<hr />
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<a name="_details"></a>
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<table summary="" border=0 cellpadding=0 cellspacing=0>
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<tr><td></td></tr>
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<tr><td colspan=2><br /><h2>Functions</h2></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M1, class T, class M2, class M3> M1 & </td><td class="memItemRight" valign=bottom><a class="el" href="#ga0">boost::numeric::ublas::blas_3::tmm</a> (M1 &m1, const T &t, const M2 &m2, const M3 &m3)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">triangular matrix multiplication <a href="#ga0"></a><br /><br /></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M1, class T, class M2, class C> M1 & </td><td class="memItemRight" valign=bottom><a class="el" href="#ga1">boost::numeric::ublas::blas_3::tsm</a> (M1 &m1, const T &t, const M2 &m2, C)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">triangular solve <em>m2</em> * <em>x</em> = <em>t</em> * <em>m1</em> in place, <em>m2</em> is a triangular matrix <a href="#ga1"></a><br /><br /></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M1, class T1, class T2, class M2, class M3> M1 & </td><td class="memItemRight" valign=bottom><a class="el" href="#ga2">boost::numeric::ublas::blas_3::gmm</a> (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">general matrix multiplication <a href="#ga2"></a><br /><br /></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M1, class T1, class T2, class M2> M1 & </td><td class="memItemRight" valign=bottom><a class="el" href="#ga3">boost::numeric::ublas::blas_3::srk</a> (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">symmetric rank k update: <em>m1</em> = <em>t</em> * <em>m1</em> + <em>t2</em> * (<em>m2</em> * <em>m2<sup>T</sup></em>) <a href="#ga3"></a><br /><br /></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M1, class T1, class T2, class M2> M1 & </td><td class="memItemRight" valign=bottom><a class="el" href="#ga4">boost::numeric::ublas::blas_3::hrk</a> (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">hermitian rank k update: <em>m1</em> = <em>t</em> * <em>m1</em> + <em>t2</em> * (<em>m2</em> * <em>m2<sup>H</sup></em>) <a href="#ga4"></a><br /><br /></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M1, class T1, class T2, class M2, class M3> M1 & </td><td class="memItemRight" valign=bottom><a class="el" href="#ga5">boost::numeric::ublas::blas_3::sr2k</a> (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">generalized symmetric rank k update: <em>m1</em> = <em>t1</em> * <em>m1</em> + <em>t2</em> * (<em>m2</em> * <em>m3<sup>T</sup></em>) + <em>t2</em> * (<em>m3</em> * <em>m2<sup>T</sup></em>) <a href="#ga5"></a><br /><br /></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M1, class T1, class T2, class M2, class M3> M1 & </td><td class="memItemRight" valign=bottom><a class="el" href="#ga6">boost::numeric::ublas::blas_3::hr2k</a> (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">generalized hermitian rank k update: <em>m1</em> = <em>t1</em> * <em>m1</em> + <em>t2</em> * (<em>m2</em> * <em>m3<sup>H</sup></em>) + (<em>m3</em> * (<em>t2</em> * <em>m2</em>)<sup>H</sup>) <a href="#ga6"></a><br /><br /></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & </td><td class="memItemRight" valign=bottom><a class="el" href="products.html#ga7">boost::numeric::ublas::axpy_prod</a> (const matrix_expression< E1 > &e1, const matrix_expression< E2 > &e2, M &m, bool init=true)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion. <a href="products.html#ga7"></a><br /><br /></td></tr>
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<tr><td class="memItemLeft" nowrap align=right valign=top>template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & </td><td class="memItemRight" valign=bottom><a class="el" href="products.html#ga8">boost::numeric::ublas::opb_prod</a> (const matrix_expression< E1 > &e1, const matrix_expression< E2 > &e2, M &m, bool init=true)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion. <a href="products.html#ga8"></a><br /><br /></td></tr>
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</table>
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<hr />
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<h2>Function Documentation</h2>
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<a class="anchor" name="ga0" doxytag="boost::numeric::ublas::blas_3::tmm" ></a>
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<table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
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<tr>
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<td class="mdRow">
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<table summary="" cellpadding="0" cellspacing="0" border="0">
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<tr>
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<td class="md" nowrap valign="top"> M1& tmm </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">M1 & </td>
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<td class="mdname" nowrap> <em>m1</em>, </td>
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</tr>
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<tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const T & </td>
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<td class="mdname" nowrap> <em>t</em>, </td>
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</tr>
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<tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const M2 & </td>
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<td class="mdname" nowrap> <em>m2</em>, </td>
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</tr>
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<tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const M3 & </td>
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<td class="mdname" nowrap> <em>m3</em></td>
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</tr>
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<tr>
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<td></td>
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<td class="md">) </td>
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<td class="md" colspan="2"></td>
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</tr>
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</table>
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</td>
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</tr>
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</table>
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<table summary="" cellspacing=5 cellpadding=0 border=0>
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<tr>
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<td>
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</td>
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<td>
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<p>triangular matrix multiplication </p>
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</td>
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</tr>
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</table>
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<a class="anchor" name="ga1" doxytag="boost::numeric::ublas::blas_3::tsm" ></a>
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<table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
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<tr>
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<td class="mdRow">
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<table summary="" cellpadding="0" cellspacing="0" border="0">
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<tr>
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<td class="md" nowrap valign="top"> M1& tsm </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">M1 & </td>
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<td class="mdname" nowrap> <em>m1</em>, </td>
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</tr>
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<tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const T & </td>
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<td class="mdname" nowrap> <em>t</em>, </td>
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</tr>
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<tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const M2 & </td>
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<td class="mdname" nowrap> <em>m2</em>, </td>
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</tr>
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<tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>C </td>
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<td class="mdname" nowrap></td>
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</tr>
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<tr>
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<td></td>
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<td class="md">) </td>
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<td class="md" colspan="2"></td>
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</tr>
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</table>
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</td>
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</tr>
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</table>
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<table summary="" cellspacing=5 cellpadding=0 border=0>
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</td>
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<td>
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<p>
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triangular solve <em>m2</em> * <em>x</em> = <em>t</em> * <em>m1</em> in place, <em>m2</em> is a triangular matrix
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</p>
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</td>
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</tr>
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</table>
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<a class="anchor" name="ga2" doxytag="boost::numeric::ublas::blas_3::gmm" ></a>
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<table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
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<tr>
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<td class="mdRow">
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<table summary="" cellpadding="0" cellspacing="0" border="0">
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<tr>
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<td class="md" nowrap valign="top"> M1& gmm </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">M1 & </td>
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<td class="mdname" nowrap> <em>m1</em>, </td>
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</tr>
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<tr>
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<td></td>
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<td class="md" nowrap>const T1 & </td>
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<td class="mdname" nowrap> <em>t1</em>, </td>
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</tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const T2 & </td>
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<td class="mdname" nowrap> <em>t2</em>, </td>
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<td></td>
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<td class="md" nowrap>const M2 & </td>
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<td class="mdname" nowrap> <em>m2</em>, </td>
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</tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const M3 & </td>
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<td class="mdname" nowrap> <em>m3</em></td>
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</tr>
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<td></td>
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<td class="md">) </td>
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<td class="md" colspan="2"></td>
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</tr>
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</table>
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</td>
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</td>
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<p>
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general matrix multiplication
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</p>
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</td>
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</tr>
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</table>
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<a class="anchor" name="ga3" doxytag="boost::numeric::ublas::blas_3::srk" ></a>
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<table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
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<tr>
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<td class="mdRow">
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<tr>
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<td class="md" nowrap valign="top"> M1& srk </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">M1 & </td>
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<td class="mdname" nowrap> <em>m1</em>, </td>
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</tr>
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<tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const T1 & </td>
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<td class="mdname" nowrap> <em>t1</em>, </td>
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</tr>
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<tr>
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<td class="md" nowrap align="right"></td>
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<td></td>
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<td class="md" nowrap>const T2 & </td>
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<td class="mdname" nowrap> <em>t2</em>, </td>
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<td></td>
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<td class="md" nowrap>const M2 & </td>
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<td class="mdname" nowrap> <em>m2</em></td>
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</tr>
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<tr>
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<td></td>
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<td class="md">) </td>
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</td>
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<td>
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<p>
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symmetric rank k update: <em>m1</em> = <em>t</em> * <em>m1</em> + <em>t2</em> * (<em>m2</em> * <em>m2<sup>T</sup></em>)
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</p>
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<dl compact><dt><b>Todo:</b></dt><dd>use opb_prod() </dd></dl>
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</td>
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</tr>
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</table>
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<a class="anchor" name="ga4" doxytag="boost::numeric::ublas::blas_3::hrk" ></a>
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<table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
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<tr>
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<td class="mdRow">
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<tr>
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<td class="md" nowrap valign="top"> M1& hrk </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">M1 & </td>
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<td class="mdname" nowrap> <em>m1</em>, </td>
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</tr>
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<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const T1 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>t1</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const T2 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>t2</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const M2 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>m2</em></td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td></td>
|
||
|
|
<td class="md">) </td>
|
||
|
|
<td class="md" colspan="2"></td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
<table summary="" cellspacing=5 cellpadding=0 border=0>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
hermitian rank k update: <em>m1</em> = <em>t</em> * <em>m1</em> + <em>t2</em> * (<em>m2</em> * <em>m2<sup>H</sup></em>)
|
||
|
|
</p>
|
||
|
|
<dl compact><dt><b>Todo:</b></dt><dd>use opb_prod()</dd></dl>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
<a class="anchor" name="ga5" doxytag="boost::numeric::ublas::blas_3::sr2k" ></a>
|
||
|
|
<table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
|
||
|
|
<tr>
|
||
|
|
<td class="mdRow">
|
||
|
|
<table summary="" cellpadding="0" cellspacing="0" border="0">
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap valign="top"> M1& sr2k </td>
|
||
|
|
<td class="md" valign="top">( </td>
|
||
|
|
<td class="md" nowrap valign="top">M1 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>m1</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const T1 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>t1</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const T2 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>t2</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const M2 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>m2</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const M3 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>m3</em></td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td></td>
|
||
|
|
<td class="md">) </td>
|
||
|
|
<td class="md" colspan="2"></td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
<table summary="" cellspacing=5 cellpadding=0 border=0>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
generalized symmetric rank k update: <em>m1</em> = <em>t1</em> * <em>m1</em> + <em>t2</em> * (<em>m2</em> * <em>m3<sup>T</sup></em>) + <em>t2</em> * (<em>m3</em> * <em>m2<sup>T</sup></em>)
|
||
|
|
</p>
|
||
|
|
<dl compact><dt><b>Todo:</b></dt><dd>use opb_prod()</dd></dl>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
<a class="anchor" name="ga6" doxytag="boost::numeric::ublas::blas_3::hr2k" ></a>
|
||
|
|
<table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
|
||
|
|
<tr>
|
||
|
|
<td class="mdRow">
|
||
|
|
<table summary="" cellpadding="0" cellspacing="0" border="0">
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap valign="top"> M1& hr2k </td>
|
||
|
|
<td class="md" valign="top">( </td>
|
||
|
|
<td class="md" nowrap valign="top">M1 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>m1</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const T1 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>t1</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const T2 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>t2</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const M2 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>m2</em>, </td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="md" nowrap align="right"></td>
|
||
|
|
<td></td>
|
||
|
|
<td class="md" nowrap>const M3 & </td>
|
||
|
|
<td class="mdname" nowrap> <em>m3</em></td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td></td>
|
||
|
|
<td class="md">) </td>
|
||
|
|
<td class="md" colspan="2"></td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
<table summary="" cellspacing=5 cellpadding=0 border=0>
|
||
|
|
<tr>
|
||
|
|
<td>
|
||
|
|
|
||
|
|
</td>
|
||
|
|
<td>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
generalized hermitian rank k update: <em>m1</em> = <em>t1</em> * <em>m1</em> + <em>t2</em> * (<em>m2</em> * <em>m3<sup>H</sup></em>) + (<em>m3</em> * (<em>t2</em> * <em>m2</em>)<sup>H</sup>)
|
||
|
|
</p>
|
||
|
|
<dl compact><dt><b>Todo:</b></dt><dd>use opb_prod()</dd></dl>
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</table>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<hr />
|
||
|
|
<p>Copyright (©) 2000-2004 Michael Stevens, Mathias Koch,
|
||
|
|
Joerg Walter, Gunter Winkler<br />
|
||
|
|
Use, modification and distribution are subject to the
|
||
|
|
Boost Software License, Version 1.0.
|
||
|
|
(See accompanying file LICENSE_1_0.txt
|
||
|
|
or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
|
||
|
|
http://www.boost.org/LICENSE_1_0.txt</a>).
|
||
|
|
</p>
|
||
|
|
<script type="text/javascript">
|
||
|
|
(function($) {
|
||
|
|
$('#toc').toc();
|
||
|
|
})(jQuery);
|
||
|
|
</script>
|
||
|
|
</body>
|
||
|
|
</html>
|