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<a href="#func-members">Functions</a> </div>
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<h1>boost::numeric::ublas::blas_2 Namespace Reference</h1> </div>
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</div>
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<div class="contents">
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<p>Interface and implementation of BLAS level 2 This includes functions which perform <b>matrix-vector</b> operations. More information about BLAS can be found at <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a>
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<a href="#_details">More...</a></p>
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<table class="memberdecls">
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<tr><td colspan="2"><h2><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr><td class="memTemplParams" colspan="2">template<class V1 , class T1 , class T2 , class M , class V2 > </td></tr>
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<tr><td class="memTemplItemLeft" align="right" valign="top">V1 & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#aa639b6931b803732bf0530076c35c0d0">gmv</a> (V1 &v1, const T1 &t1, const T2 &t2, const M &m, const V2 &v2)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">compute <img class="formulaInl" alt="$ v_1 = t_1.v_1 + t_2.(m.v_2)$" src="form_26.png"/>, a general matrix-vector product <a href="#aa639b6931b803732bf0530076c35c0d0"></a><br/></td></tr>
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<tr><td class="memTemplParams" colspan="2">template<class M , class T , class V1 , class V2 > </td></tr>
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<tr><td class="memTemplItemLeft" align="right" valign="top">M & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a706e332f8bf98b5788557fd52459b56b">gr</a> (M &m, const T &t, const V1 &v1, const V2 &v2)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">Rank 1 update: <img class="formulaInl" alt="$ m = m + t.(v_1.v_2^T)$" src="form_27.png"/>. <a href="#a706e332f8bf98b5788557fd52459b56b"></a><br/></td></tr>
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<tr><td class="memTemplParams" colspan="2">template<class M , class T , class V > </td></tr>
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<tr><td class="memTemplItemLeft" align="right" valign="top">M & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#ab8b9af963db5df7cf00e9cefef06acf8">hr</a> (M &m, const T &t, const V &v)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">hermitian rank 1 update: <img class="formulaInl" alt="$m = m + t.(v.v^H)$" src="form_29.png"/> <a href="#ab8b9af963db5df7cf00e9cefef06acf8"></a><br/></td></tr>
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<tr><td class="memTemplParams" colspan="2">template<class M , class T , class V1 , class V2 > </td></tr>
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<tr><td class="memTemplItemLeft" align="right" valign="top">M & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a73ce3e5bcfc5b27eae66f3f4e5e07be7">hr2</a> (M &m, const T &t, const V1 &v1, const V2 &v2)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">hermitian rank 2 update: <img class="formulaInl" alt="$m=m+t.(v_1.v_2^H) + v_2.(t.v_1)^H)$" src="form_31.png"/> <a href="#a73ce3e5bcfc5b27eae66f3f4e5e07be7"></a><br/></td></tr>
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<tr><td class="memTemplParams" colspan="2">template<class M , class T , class V > </td></tr>
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<tr><td class="memTemplItemLeft" align="right" valign="top">M & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#addeca755eb0e631b7347acc0c81e4fb1">sr</a> (M &m, const T &t, const V &v)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">symmetric rank 1 update: <img class="formulaInl" alt="$m = m + t.(v.v^T)$" src="form_28.png"/> <a href="#addeca755eb0e631b7347acc0c81e4fb1"></a><br/></td></tr>
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<tr><td class="memTemplParams" colspan="2">template<class M , class T , class V1 , class V2 > </td></tr>
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<tr><td class="memTemplItemLeft" align="right" valign="top">M & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a790a1407ea628d1dbf215462ddab3234">sr2</a> (M &m, const T &t, const V1 &v1, const V2 &v2)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">symmetric rank 2 update: <img class="formulaInl" alt="$ m=m+ t.(v_1.v_2^T + v_2.v_1^T)$" src="form_30.png"/> <a href="#a790a1407ea628d1dbf215462ddab3234"></a><br/></td></tr>
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<tr><td class="memTemplParams" colspan="2">template<class V , class M > </td></tr>
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<tr><td class="memTemplItemLeft" align="right" valign="top">V & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a244fe6f03ca3d14341df2dc24e09e04c">tmv</a> (V &v, const M &m)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">multiply vector <code>v</code> with triangular matrix <code>m</code> <a href="#a244fe6f03ca3d14341df2dc24e09e04c"></a><br/></td></tr>
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<tr><td class="memTemplParams" colspan="2">template<class V , class M , class C > </td></tr>
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<tr><td class="memTemplItemLeft" align="right" valign="top">V & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a7ce367369a2ed805bfc4336d0a7e7ede">tsv</a> (V &v, const M &m, C)</td></tr>
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<tr><td class="mdescLeft"> </td><td class="mdescRight">solve <img class="formulaInl" alt="$m.x = v$" src="form_25.png"/> in place, where <code>m</code> is a triangular matrix <a href="#a7ce367369a2ed805bfc4336d0a7e7ede"></a><br/></td></tr>
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</table>
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<hr/><a name="_details"></a><h2>Detailed Description</h2>
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<div class="textblock"><p>Interface and implementation of BLAS level 2 This includes functions which perform <b>matrix-vector</b> operations. More information about BLAS can be found at <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a> </p>
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</div><hr/><h2>Function Documentation</h2>
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<a class="anchor" id="a244fe6f03ca3d14341df2dc24e09e04c"></a><!-- doxytag: member="boost::numeric::ublas::blas_2::tmv" ref="a244fe6f03ca3d14341df2dc24e09e04c" args="(V &v, const M &m)" -->
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template<class V , class M > </div>
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<tr>
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<td class="memname">V& boost::numeric::ublas::blas_2::tmv </td>
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<td>(</td>
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<td class="paramtype">V & </td>
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<td class="paramname"><em>v</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const M & </td>
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<td class="paramname"><em>m</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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<div class="memdoc">
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<p>multiply vector <code>v</code> with triangular matrix <code>m</code> </p>
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<dl><dt><b>Parameters:</b></dt><dd>
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<table class="params">
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<tr><td class="paramname">v</td><td>a vector </td></tr>
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<tr><td class="paramname">m</td><td>a triangular matrix </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the result of the product</dd></dl>
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<dl><dt><b>Template Parameters:</b></dt><dd>
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<table class="">
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<tr><td class="paramname">V</td><td>type of the vector (not needed by default) </td></tr>
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<tr><td class="paramname">M</td><td>type of the matrix (not needed by default) </td></tr>
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</table>
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</dd>
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</dl>
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<p>Definition at line <a class="el" href="a00598_source.html#l00185">185</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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</div>
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</div>
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<a class="anchor" id="a7ce367369a2ed805bfc4336d0a7e7ede"></a><!-- doxytag: member="boost::numeric::ublas::blas_2::tsv" ref="a7ce367369a2ed805bfc4336d0a7e7ede" args="(V &v, const M &m, C)" -->
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template<class V , class M , class C > </div>
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<td class="memname">V& boost::numeric::ublas::blas_2::tsv </td>
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<td>(</td>
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<td class="paramtype">V & </td>
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<td class="paramname"><em>v</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td class="paramtype">const M & </td>
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<td class="paramname"><em>m</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">C </td>
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<td class="paramname"> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div>
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<div class="memdoc">
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<p>solve <img class="formulaInl" alt="$m.x = v$" src="form_25.png"/> in place, where <code>m</code> is a triangular matrix </p>
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<dl><dt><b>Parameters:</b></dt><dd>
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<table class="params">
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<tr><td class="paramname">v</td><td>a vector </td></tr>
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<tr><td class="paramname">m</td><td>a matrix </td></tr>
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<tr><td class="paramname">C</td><td>(this parameter is not needed) </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="return"><dt><b>Returns:</b></dt><dd>a result vector from the above operation</dd></dl>
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<dl><dt><b>Template Parameters:</b></dt><dd>
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<table class="">
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<tr><td class="paramname">V</td><td>type of the vector (not needed by default) </td></tr>
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<tr><td class="paramname">M</td><td>type of the matrix (not needed by default) </td></tr>
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<tr><td class="paramname">C</td><td>n/a </td></tr>
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</table>
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</dd>
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</dl>
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<p>Definition at line <a class="el" href="a00598_source.html#l00202">202</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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</div>
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</div>
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<a class="anchor" id="aa639b6931b803732bf0530076c35c0d0"></a><!-- doxytag: member="boost::numeric::ublas::blas_2::gmv" ref="aa639b6931b803732bf0530076c35c0d0" args="(V1 &v1, const T1 &t1, const T2 &t2, const M &m, const V2 &v2)" -->
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template<class V1 , class T1 , class T2 , class M , class V2 > </div>
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<td class="memname">V1& boost::numeric::ublas::blas_2::gmv </td>
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<td>(</td>
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<td class="paramtype">V1 & </td>
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<td class="paramname"><em>v1</em>, </td>
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<td class="paramtype">const T1 & </td>
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<td class="paramname"><em>t1</em>, </td>
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</tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const T2 & </td>
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<td class="paramname"><em>t2</em>, </td>
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<td class="paramkey"></td>
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<td class="paramname"><em>v2</em> </td>
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<td></td>
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<td>)</td>
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<div class="memdoc">
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<p>compute <img class="formulaInl" alt="$ v_1 = t_1.v_1 + t_2.(m.v_2)$" src="form_26.png"/>, a general matrix-vector product </p>
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<dl><dt><b>Parameters:</b></dt><dd>
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<table class="params">
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<tr><td class="paramname">v1</td><td>a vector </td></tr>
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<tr><td class="paramname">t1</td><td>a scalar </td></tr>
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<tr><td class="paramname">t2</td><td>another scalar </td></tr>
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<tr><td class="paramname">m</td><td>a matrix </td></tr>
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<tr><td class="paramname">v2</td><td>another vector </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="return"><dt><b>Returns:</b></dt><dd>the vector <code>v1</code> with the result from the above operation</dd></dl>
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<dl><dt><b>Template Parameters:</b></dt><dd>
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<table class="">
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<tr><td class="paramname">V1</td><td>type of first vector (not needed by default) </td></tr>
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<tr><td class="paramname">T1</td><td>type of first scalar (not needed by default) </td></tr>
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<tr><td class="paramname">T2</td><td>type of second scalar (not needed by default) </td></tr>
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<tr><td class="paramname">M</td><td>type of matrix (not needed by default) </td></tr>
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<p>Definition at line <a class="el" href="a00598_source.html#l00223">223</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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<a class="anchor" id="a706e332f8bf98b5788557fd52459b56b"></a><!-- doxytag: member="boost::numeric::ublas::blas_2::gr" ref="a706e332f8bf98b5788557fd52459b56b" args="(M &m, const T &t, const V1 &v1, const V2 &v2)" -->
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<p>Rank 1 update: <img class="formulaInl" alt="$ m = m + t.(v_1.v_2^T)$" src="form_27.png"/>. </p>
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<dl><dt><b>Parameters:</b></dt><dd>
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<tr><td class="paramname">M</td><td>type of matrix (not needed by default) </td></tr>
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<p>Definition at line <a class="el" href="a00598_source.html#l00242">242</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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<a class="anchor" id="addeca755eb0e631b7347acc0c81e4fb1"></a><!-- doxytag: member="boost::numeric::ublas::blas_2::sr" ref="addeca755eb0e631b7347acc0c81e4fb1" args="(M &m, const T &t, const V &v)" -->
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<p>symmetric rank 1 update: <img class="formulaInl" alt="$m = m + t.(v.v^T)$" src="form_28.png"/> </p>
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<dl><dt><b>Parameters:</b></dt><dd>
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<table class="params">
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<tr><td class="paramname">m</td><td>a matrix </td></tr>
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<tr><td class="paramname">M</td><td>type of matrix (not needed by default) </td></tr>
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<p>Definition at line <a class="el" href="a00598_source.html#l00263">263</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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<a class="anchor" id="ab8b9af963db5df7cf00e9cefef06acf8"></a><!-- doxytag: member="boost::numeric::ublas::blas_2::hr" ref="ab8b9af963db5df7cf00e9cefef06acf8" args="(M &m, const T &t, const V &v)" -->
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<td class="paramname"><em>m</em>, </td>
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<p>hermitian rank 1 update: <img class="formulaInl" alt="$m = m + t.(v.v^H)$" src="form_29.png"/> </p>
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<dl><dt><b>Parameters:</b></dt><dd>
|
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<table class="params">
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<dl><dt><b>Template Parameters:</b></dt><dd>
|
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<table class="">
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<tr><td class="paramname">M</td><td>type of matrix (not needed by default) </td></tr>
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<tr><td class="paramname">T</td><td>type of scalar (not needed by default) </td></tr>
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<p>Definition at line <a class="el" href="a00598_source.html#l00284">284</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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<a class="anchor" id="a790a1407ea628d1dbf215462ddab3234"></a><!-- doxytag: member="boost::numeric::ublas::blas_2::sr2" ref="a790a1407ea628d1dbf215462ddab3234" args="(M &m, const T &t, const V1 &v1, const V2 &v2)" -->
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<p>symmetric rank 2 update: <img class="formulaInl" alt="$ m=m+ t.(v_1.v_2^T + v_2.v_1^T)$" src="form_30.png"/> </p>
|
|
<dl><dt><b>Parameters:</b></dt><dd>
|
|
<table class="params">
|
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<tr><td class="paramname">m</td><td>a matrix </td></tr>
|
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|
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<p>Definition at line <a class="el" href="a00598_source.html#l00307">307</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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<a class="anchor" id="a73ce3e5bcfc5b27eae66f3f4e5e07be7"></a><!-- doxytag: member="boost::numeric::ublas::blas_2::hr2" ref="a73ce3e5bcfc5b27eae66f3f4e5e07be7" args="(M &m, const T &t, const V1 &v1, const V2 &v2)" -->
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|
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<td class="paramname"><em>m</em>, </td>
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<p>hermitian rank 2 update: <img class="formulaInl" alt="$m=m+t.(v_1.v_2^H) + v_2.(t.v_1)^H)$" src="form_31.png"/> </p>
|
|
<dl><dt><b>Parameters:</b></dt><dd>
|
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<table class="params">
|
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<tr><td class="paramname">m</td><td>a matrix </td></tr>
|
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<dl class="return"><dt><b>Returns:</b></dt><dd>a matrix with the result from the above operation</dd></dl>
|
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<dl><dt><b>Template Parameters:</b></dt><dd>
|
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<table class="">
|
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<tr><td class="paramname">M</td><td>type of matrix (not needed by default) </td></tr>
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<p>Definition at line <a class="el" href="a00598_source.html#l00330">330</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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