319 lines
14 KiB
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319 lines
14 KiB
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<title>Special Products</title>
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<meta name="AUTHOR" content="Gunter Winkler" />
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<h1><img src="../../../../boost.png" align="middle" />Special Products </h1>
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<div class="toc" id="toc"></div>
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<h2>Functions</h2>
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<table summary="" border=0 cellpadding=0 cellspacing=0>
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<tr>
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<td class="memItemLeft" nowrap align=right valign=top>template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & </td>
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<td class="memItemRight" valign=bottom><a class="el" href="#ga8">axpy_prod</a> (const matrix_expression< E1 > &e1, const vector_expression< E2 > &e2, V &v, bool init=true)</td></tr>
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<tr>
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<td class="mdescLeft"> </td>
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<td class="mdescRight">computes <code>v += A x</code> or <code>v = A x</code> in an optimized fashion. <a href="#ga8"></a><br /><br /></td></tr>
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<tr>
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<td class="memItemLeft" nowrap align=right valign=top>template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & </td>
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<td class="memItemRight" valign=bottom><a class="el" href="#ga9">axpy_prod</a> (const vector_expression< E1 > &e1, const matrix_expression< E2 > &e2, V &v, bool init=true)</td></tr>
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<tr>
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<td class="mdescLeft"> </td>
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<td class="mdescRight">computes <code>v += A<sup>T</sup> x</code> or <code>v = A<sup>T</sup> x</code> in an optimized fashion. <a href="#ga9"></a><br /><br /></td></tr>
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<tr>
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<td class="memItemLeft" nowrap align=right valign=top>template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & </td>
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<td class="memItemRight" valign=bottom><a class="el" href="#ga7">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>
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<td class="mdescLeft"> </td>
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<td class="mdescRight">computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion. <a href="#ga7"></a><br /><br /></td></tr>
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<tr>
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<td class="memItemLeft" nowrap align=right valign=top>template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & </td>
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<td class="memItemRight" valign=bottom><a class="el" href="#ga6">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>
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<td class="mdescLeft"> </td>
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<td class="mdescRight">computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion. <a href="#ga6"></a><br /><br /></td></tr>
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</table>
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<hr />
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<a class="anchor" name="ga8" doxytag="boost::numeric::ublas::axpy_prod" ></a>
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<table summary="" class="mdTable" width="95%" 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"> BOOST_UBLAS_INLINE V& axpy_prod </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">const matrix_expression< E1 > & </td>
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<td class="mdname" nowrap> <em>e1</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 vector_expression< E2 > & </td>
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<td class="mdname" nowrap> <em>e2</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>V & </td>
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<td class="mdname" nowrap> <em>v</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>bool </td>
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<td class="mdname" nowrap> <em>init</em> = <code>true</code></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>
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computes <code>v += A x</code> or <code>v = A x</code> in an optimized fashion.
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</p>
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<dl compact><dt><b>Parameters:</b></dt><dd>
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<table summary="" border="0" cellspacing="2" cellpadding="0">
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<tr><td></td><td valign=top><em>e1</em> </td><td>the matrix expression <code>A</code> </td></tr>
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<tr><td></td><td valign=top><em>e2</em> </td><td>the vector expression <code>x</code> </td></tr>
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<tr><td></td><td valign=top><em>v</em> </td><td>the result vector <code>v</code> </td></tr>
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<tr><td></td><td valign=top><em>init</em> </td><td>a boolean parameter</td></tr>
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</table>
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</dl>
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<code>axpy_prod(A, x, v, init)</code> implements the well known axpy-product. Setting <em>init</em> to <code>true</code> is equivalent to call <code>v.clear()</code> before <code>axpy_prod</code>. Currently <em>init</em> defaults to <code>true</code>, but this may change in the future.<p>
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Up to now there are some specialisation for compressed matrices that give a large speed up compared to prod. </td>
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</tr>
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</table>
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<a class="anchor" name="ga9" doxytag="boost::numeric::ublas::axpy_prod" ></a>
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<table summary="" class="mdTable" width="95%" 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"> BOOST_UBLAS_INLINE V& axpy_prod </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">const vector_expression< E1 > & </td>
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<td class="mdname" nowrap> <em>e1</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 matrix_expression< E2 > & </td>
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<td class="mdname" nowrap> <em>e2</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>V & </td>
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<td class="mdname" nowrap> <em>v</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>bool </td>
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<td class="mdname" nowrap> <em>init</em> = <code>true</code></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>
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computes <code>v += A<sup>T</sup> x</code> or <code>v = A<sup>T</sup> x</code> in an optimized fashion.
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</p>
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<dl compact><dt><b>Parameters:</b></dt><dd>
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<table summary="" border="0" cellspacing="2" cellpadding="0">
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<tr><td></td><td valign=top><em>e1</em> </td><td>the vector expression <code>x</code> </td></tr>
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<tr><td></td><td valign=top><em>e2</em> </td><td>the matrix expression <code>A</code> </td></tr>
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<tr><td></td><td valign=top><em>v</em> </td><td>the result vector <code>v</code> </td></tr>
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<tr><td></td><td valign=top><em>init</em> </td><td>a boolean parameter</td></tr>
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</table>
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</dl>
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<code>axpy_prod(x, A, v, init)</code> implements the well known axpy-product. Setting <em>init</em> to <code>true</code> is equivalent to call <code>v.clear()</code> before <code>axpy_prod</code>. Currently <em>init</em> defaults to <code>true</code>, but this may change in the future.<p>
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Up to now there are some specialisation for compressed matrices that give a large speed up compared to prod. </td>
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</tr>
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</table>
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<a class="anchor" name="ga7" doxytag="boost::numeric::ublas::axpy_prod" ></a>
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<table summary="" class="mdTable" width="95%" 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"> BOOST_UBLAS_INLINE M& axpy_prod </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">const matrix_expression< E1 > & </td>
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<td class="mdname" nowrap> <em>e1</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 matrix_expression< E2 > & </td>
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<td class="mdname" nowrap> <em>e2</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>M & </td>
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<td class="mdname" nowrap> <em>m</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>bool </td>
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<td class="mdname" nowrap> <em>init</em> = <code>true</code></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>
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computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion.
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</p>
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<dl compact><dt><b>Parameters:</b></dt><dd>
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<table summary="" border="0" cellspacing="2" cellpadding="0">
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<tr><td></td><td valign=top><em>e1</em> </td><td>the matrix expression <code>A</code> </td></tr>
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<tr><td></td><td valign=top><em>e2</em> </td><td>the matrix expression <code>X</code> </td></tr>
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<tr><td></td><td valign=top><em>m</em> </td><td>the result matrix <code>M</code> </td></tr>
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<tr><td></td><td valign=top><em>init</em> </td><td>a boolean parameter</td></tr>
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</table>
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</dl>
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<code>axpy_prod(A, X, M, init)</code> implements the well known axpy-product. Setting <em>init</em> to <code>true</code> is equivalent to call <code>M.clear()</code> before <code>axpy_prod</code>. Currently <em>init</em> defaults to <code>true</code>, but this may change in the future.<p>
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Up to now there are no specialisations. </td>
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</tr>
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</table>
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<a class="anchor" name="ga6" doxytag="boost::numeric::ublas::opb_prod" ></a>
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<table summary="" class="mdTable" width="95%" 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"> BOOST_UBLAS_INLINE M& opb_prod </td>
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<td class="md" valign="top">( </td>
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<td class="md" nowrap valign="top">const matrix_expression< E1 > & </td>
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<td class="mdname" nowrap> <em>e1</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 matrix_expression< E2 > & </td>
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<td class="mdname" nowrap> <em>e2</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>M & </td>
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<td class="mdname" nowrap> <em>m</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>bool </td>
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<td class="mdname" nowrap> <em>init</em> = <code>true</code></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>
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computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion.
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</p>
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<dl compact><dt><b>Parameters:</b></dt><dd>
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<table summary="" border="0" cellspacing="2" cellpadding="0">
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<tr><td></td><td valign=top><em>e1</em> </td><td>the matrix expression <code>A</code> </td></tr>
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<tr><td></td><td valign=top><em>e2</em> </td><td>the matrix expression <code>X</code> </td></tr>
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<tr><td></td><td valign=top><em>m</em> </td><td>the result matrix <code>M</code> </td></tr>
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<tr><td></td><td valign=top><em>init</em> </td><td>a boolean parameter</td></tr>
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</table>
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</dl>
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<code>opb_prod(A, X, M, init)</code> implements the well known axpy-product. Setting <em>init</em> to <code>true</code> is equivalent to call <code>M.clear()</code> before <code>opb_prod</code>. Currently <em>init</em> defaults to <code>true</code>, but this may change in the future.<p>
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This function may give a speedup if <code>A</code> has less columns than rows, because the product is computed as a sum of outer products. </td>
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</tr>
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</table>
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<hr />
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<p>Copyright (©) 2000-2004 Michael Stevens, Mathias Koch,
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Joerg Walter, Gunter Winkler<br />
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Use, modification and distribution are subject to the
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Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt
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or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
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http://www.boost.org/LICENSE_1_0.txt
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</a>).
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</p>
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