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<h1>blas.hpp File Reference</h1> </div>
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<div class="textblock"><code>#include &lt;boost/numeric/ublas/traits.hpp&gt;</code><br/>
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<img id="dynsection-0-trigger" src="closed.png"/> Include dependency graph for blas.hpp:</div>
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Namespaces</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00648.html">boost</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00649.html">boost::numeric</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00595.html">boost::numeric::ublas</a></td></tr>
<p><tr><td class="mdescLeft">&#160;</td><td class="mdescRight"><p>contains all important classes and functions of uBLAS </p>
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<tr><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00651.html">boost::numeric::ublas::blas_1</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00652.html">boost::numeric::ublas::blas_2</a></td></tr>
<p><tr><td class="mdescLeft">&#160;</td><td class="mdescRight"><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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<tr><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="a00599.html">boost::numeric::ublas::blas_3</a></td></tr>
<p><tr><td class="mdescLeft">&#160;</td><td class="mdescRight"><p>Interface and implementation of BLAS level 3 This includes functions which perform <b>matrix-matrix</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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Functions</h2></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">type_traits&lt; typename <br class="typebreak"/>
V::value_type &gt;::real_type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a576c07d6b09c0b951eb5c8830de4b93a">boost::numeric::ublas::blas_1::amax</a> (const V &amp;v)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V &gt; </td></tr>
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<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class T , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">V1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#aabc7566ce5b699e5620e7d39b1de40fd">boost::numeric::ublas::blas_1::axpy</a> (V1 &amp;v1, const T &amp;t, const V2 &amp;v2)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class V2 &gt; </td></tr>
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<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">promote_traits&lt; typename <br class="typebreak"/>
V1::value_type, typename <br class="typebreak"/>
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<tr><td class="memTemplParams" colspan="2">template&lt;class M1 , class T1 , class T2 , class M2 , class M3 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00599.html#ae516fcacfaeb952ef7714fcde005c6d1">boost::numeric::ublas::blas_3::gmm</a> (M1 &amp;m1, const T1 &amp;t1, const T2 &amp;t2, const M2 &amp;m2, const M3 &amp;m3)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">general matrix multiplication <img class="formulaInl" alt="$m_1=t_1.m_1 + t_2.m_2.m_3$" src="form_37.png"/> <a href="#ae516fcacfaeb952ef7714fcde005c6d1"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class T1 , class T2 , class M , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">V1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#aa639b6931b803732bf0530076c35c0d0">boost::numeric::ublas::blas_2::gmv</a> (V1 &amp;v1, const T1 &amp;t1, const T2 &amp;t2, const M &amp;m, const V2 &amp;v2)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">compute <img class="formulaInl" alt="$ v_1 = t_1.v_1 + t_2.(m.v_2)$" src="form_26.png"/>, a general matrix-vector product <a href="#aa639b6931b803732bf0530076c35c0d0"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M , class T , class V1 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a706e332f8bf98b5788557fd52459b56b">boost::numeric::ublas::blas_2::gr</a> (M &amp;m, const T &amp;t, const V1 &amp;v1, const V2 &amp;v2)</td></tr>
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<tr><td class="memTemplParams" colspan="2">template&lt;class M , class T , class V &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#ab8b9af963db5df7cf00e9cefef06acf8">boost::numeric::ublas::blas_2::hr</a> (M &amp;m, const T &amp;t, const V &amp;v)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">hermitian rank 1 update: <img class="formulaInl" alt="$m = m + t.(v.v^H)$" src="form_29.png"/> <a href="#ab8b9af963db5df7cf00e9cefef06acf8"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M , class T , class V1 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a73ce3e5bcfc5b27eae66f3f4e5e07be7">boost::numeric::ublas::blas_2::hr2</a> (M &amp;m, const T &amp;t, const V1 &amp;v1, const V2 &amp;v2)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">hermitian rank 2 update: <img class="formulaInl" alt="$m=m+t.(v_1.v_2^H) + v_2.(t.v_1)^H)$" src="form_31.png"/> <a href="#a73ce3e5bcfc5b27eae66f3f4e5e07be7"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M1 , class T1 , class T2 , class M2 , class M3 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00599.html#ad4c048402e77418e0bd209565223b815">boost::numeric::ublas::blas_3::hr2k</a> (M1 &amp;m1, const T1 &amp;t1, const T2 &amp;t2, const M2 &amp;m2, const M3 &amp;m3)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">generalized hermitian rank <em>k</em> update: * <img class="formulaInl" alt="$m_1=t_1.m_1+t_2.(m_2.m_3^H)+(m_3.(t_2.m_2)^H)$" src="form_41.png"/> <a href="#ad4c048402e77418e0bd209565223b815"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M1 , class T1 , class T2 , class M2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00599.html#a8ce9ff31a8d62bde74fbae9dd391790d">boost::numeric::ublas::blas_3::hrk</a> (M1 &amp;m1, const T1 &amp;t1, const T2 &amp;t2, const M2 &amp;m2)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">hermitian rank <em>k</em> update: <img class="formulaInl" alt="$m_1=t.m_1+t_2.(m_2.m2^H)$" src="form_39.png"/> <a href="#a8ce9ff31a8d62bde74fbae9dd391790d"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">type_traits&lt; typename <br class="typebreak"/>
V::value_type &gt;::real_type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#ae7d8e65daedd8de344f4d169cfe22dc9">boost::numeric::ublas::blas_1::nrm2</a> (const V &amp;v)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class T1 , class V1 , class T2 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a69badeae884488668d2e31c387427da0">boost::numeric::ublas::blas_1::rot</a> (const T1 &amp;t1, V1 &amp;v1, const T2 &amp;t2, V2 &amp;v2)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V , class T &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">V &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a8e5af6ed9ca0d90e6daf640151c2b46a">boost::numeric::ublas::blas_1::scal</a> (V &amp;v, const T &amp;t)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M , class T , class V &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#addeca755eb0e631b7347acc0c81e4fb1">boost::numeric::ublas::blas_2::sr</a> (M &amp;m, const T &amp;t, const V &amp;v)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">symmetric rank 1 update: <img class="formulaInl" alt="$m = m + t.(v.v^T)$" src="form_28.png"/> <a href="#addeca755eb0e631b7347acc0c81e4fb1"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M , class T , class V1 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a790a1407ea628d1dbf215462ddab3234">boost::numeric::ublas::blas_2::sr2</a> (M &amp;m, const T &amp;t, const V1 &amp;v1, const V2 &amp;v2)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">symmetric rank 2 update: <img class="formulaInl" alt="$ m=m+ t.(v_1.v_2^T + v_2.v_1^T)$" src="form_30.png"/> <a href="#a790a1407ea628d1dbf215462ddab3234"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M1 , class T1 , class T2 , class M2 , class M3 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00599.html#a0e0f51634ff9e11be9670c5c88ff64b6">boost::numeric::ublas::blas_3::sr2k</a> (M1 &amp;m1, const T1 &amp;t1, const T2 &amp;t2, const M2 &amp;m2, const M3 &amp;m3)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">generalized symmetric rank <em>k</em> update: <img class="formulaInl" alt="$m_1=t_1.m_1+t_2.(m_2.m3^T)+t_2.(m_3.m2^T)$" src="form_40.png"/> <a href="#a0e0f51634ff9e11be9670c5c88ff64b6"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M1 , class T1 , class T2 , class M2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00599.html#ab29a975ac7bc32c85eb0363e800f439f">boost::numeric::ublas::blas_3::srk</a> (M1 &amp;m1, const T1 &amp;t1, const T2 &amp;t2, const M2 &amp;m2)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">symmetric rank <em>k</em> update: <img class="formulaInl" alt="$m_1=t.m_1+t_2.(m_2.m_2^T)$" src="form_38.png"/> <a href="#ab29a975ac7bc32c85eb0363e800f439f"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a7359c42bdbf22249101e062d45c8fec6">boost::numeric::ublas::blas_1::swap</a> (V1 &amp;v1, V2 &amp;v2)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M1 , class T , class M2 , class M3 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00599.html#ac37ed088f63339d4d384bb66dbc43aa8">boost::numeric::ublas::blas_3::tmm</a> (M1 &amp;m1, const T &amp;t, const M2 &amp;m2, const M3 &amp;m3)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">triangular matrix multiplication <img class="formulaInl" alt="$m_1=t.m_2.m_3$" src="form_32.png"/> where <img class="formulaInl" alt="$m_2$" src="form_33.png"/> and <img class="formulaInl" alt="$m_3$" src="form_34.png"/> are triangular <a href="#ac37ed088f63339d4d384bb66dbc43aa8"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V , class M &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">V &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a244fe6f03ca3d14341df2dc24e09e04c">boost::numeric::ublas::blas_2::tmv</a> (V &amp;v, const M &amp;m)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">multiply vector <code>v</code> with triangular matrix <code>m</code> <a href="#a244fe6f03ca3d14341df2dc24e09e04c"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class M1 , class T , class M2 , class C &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">M1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00599.html#a1b82ba61192fb957f032cabd64867e6a">boost::numeric::ublas::blas_3::tsm</a> (M1 &amp;m1, const T &amp;t, const M2 &amp;m2, C)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">triangular solve <img class="formulaInl" alt="$ m_2.x = t.m_1$" src="form_35.png"/> in place, <img class="formulaInl" alt="$m_2$" src="form_33.png"/> is a triangular matrix <a href="#a1b82ba61192fb957f032cabd64867e6a"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V , class M , class C &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">V &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00652.html#a7ce367369a2ed805bfc4336d0a7e7ede">boost::numeric::ublas::blas_2::tsv</a> (V &amp;v, const M &amp;m, C)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">solve <img class="formulaInl" alt="$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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