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| <title>BLAS</title> |
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| <meta name="AUTHOR" content="Gunter Winkler" /> |
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| <h1>Level 3 BLAS</h1> |
| <div class="toc" id="toc"></div> |
| <hr /> |
| <a name="_details"></a> |
| |
| <table summary="" border=0 cellpadding=0 cellspacing=0> |
| <tr><td></td></tr> |
| <tr><td colspan=2><br /><h2>Functions</h2></td></tr> |
| <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> |
| |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">triangular matrix multiplication <a href="#ga0"></a><br /><br /></td></tr> |
| <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> |
| <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> |
| |
| <tr><td class="mdescLeft"> </td><td class="mdescRight">general matrix multiplication <a href="#ga2"></a><br /><br /></td></tr> |
| <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> |
| |
| <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> |
| <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> |
| <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> |
| |
| <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> |
| <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> |
| |
| <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> |
| <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.htm#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.htm#ga7"></a><br /><br /></td></tr> |
| <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.htm#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.htm#ga8"></a><br /><br /></td></tr> |
| </table> |
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| <hr /> |
| |
| <h2>Function Documentation</h2> |
| |
| <a class="anchor" name="ga0" doxytag="boost::numeric::ublas::blas_3::tmm" ></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& tmm </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 T & </td> |
| <td class="mdname" nowrap> <em>t</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>triangular matrix multiplication </p> |
| </td> |
| </tr> |
| </table> |
| <a class="anchor" name="ga1" doxytag="boost::numeric::ublas::blas_3::tsm" ></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& tsm </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 T & </td> |
| <td class="mdname" nowrap> <em>t</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>C </td> |
| <td class="mdname" nowrap></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> |
| triangular solve <em>m2</em> * <em>x</em> = <em>t</em> * <em>m1</em> in place, <em>m2</em> is a triangular matrix |
| </p> |
| </td> |
| </tr> |
| </table> |
| <a class="anchor" name="ga2" doxytag="boost::numeric::ublas::blas_3::gmm" ></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& gmm </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> |
| general matrix multiplication |
| </p> |
| </td> |
| </tr> |
| </table> |
| <a class="anchor" name="ga3" doxytag="boost::numeric::ublas::blas_3::srk" ></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& srk </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></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> |
| 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>) |
| </p> |
| <dl compact><dt><b>Todo:</b></dt><dd>use opb_prod() </dd></dl> |
| </td> |
| </tr> |
| </table> |
| <a class="anchor" name="ga4" doxytag="boost::numeric::ublas::blas_3::hrk" ></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& hrk </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></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> |
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