ceph/src/boost/libs/numeric/ublas/doc/products.html

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  16 <h1><img src="../../../../boost.png" align="middle" />Special Products </h1>
  17 <div class="toc" id="toc"></div>
  18
  19 <h2>Functions</h2>
  20
  21 <table summary="" border=0 cellpadding=0 cellspacing=0>
  22 <tr>
  23 <td class="memItemLeft" nowrap align=right valign=top>template&lt;class V, class E1, class E2&gt; BOOST_UBLAS_INLINE V &amp;&nbsp;</td>
  24 <td class="memItemRight" valign=bottom><a class="el" href="#ga8">axpy_prod</a> (const matrix_expression&lt; E1 &gt; &amp;e1, const vector_expression&lt; E2 &gt; &amp;e2, V &amp;v, bool init=true)</td></tr>
  25
  26 <tr>
  27 <td class="mdescLeft">&nbsp;</td>
  28 <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>
  29 <tr>
  30 <td class="memItemLeft" nowrap align=right valign=top>template&lt;class V, class E1, class E2&gt; BOOST_UBLAS_INLINE V &amp;&nbsp;</td>
  31 <td class="memItemRight" valign=bottom><a class="el" href="#ga9">axpy_prod</a> (const vector_expression&lt; E1 &gt; &amp;e1, const matrix_expression&lt; E2 &gt; &amp;e2, V &amp;v, bool init=true)</td></tr>
  32
  33 <tr>
  34 <td class="mdescLeft">&nbsp;</td>
  35 <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>
  36 <tr>
  37 <td class="memItemLeft" nowrap align=right valign=top>template&lt;class M, class E1, class E2&gt; BOOST_UBLAS_INLINE M &amp;&nbsp;</td>
  38 <td class="memItemRight" valign=bottom><a class="el" href="#ga7">axpy_prod</a> (const matrix_expression&lt; E1 &gt; &amp;e1, const matrix_expression&lt; E2 &gt; &amp;e2, M &amp;m, bool init=true)</td></tr>
  39
  40 <tr>
  41 <td class="mdescLeft">&nbsp;</td>
  42 <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>
  43 <tr>
  44 <td class="memItemLeft" nowrap align=right valign=top>template&lt;class M, class E1, class E2&gt; BOOST_UBLAS_INLINE M &amp;&nbsp;</td>
  45 <td class="memItemRight" valign=bottom><a class="el" href="#ga6">opb_prod</a> (const matrix_expression&lt; E1 &gt; &amp;e1, const matrix_expression&lt; E2 &gt; &amp;e2, M &amp;m, bool init=true)</td></tr>
  46
  47 <tr>
  48 <td class="mdescLeft">&nbsp;</td>
  49 <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>
  50 </table>
  51
  52 <hr />
  53
  54 <a class="anchor" name="ga8" doxytag="boost::numeric::ublas::axpy_prod" ></a>
  55 <table summary="" class="mdTable" width="95%" cellpadding="2" cellspacing="0">
  56   <tr>
  57     <td class="mdRow">
  58       <table summary="" cellpadding="0" cellspacing="0" border="0">
  59         <tr>
  60           <td class="md" nowrap valign="top"> BOOST_UBLAS_INLINE V&amp; axpy_prod           </td>
  61           <td class="md" valign="top">(&nbsp;</td>
  62           <td class="md" nowrap valign="top">const matrix_expression&lt; E1 &gt; &amp;&nbsp;</td>
  63           <td class="mdname" nowrap> <em>e1</em>, </td>
  64         </tr>
  65         <tr>
  66           <td class="md" nowrap align="right"></td>
  67           <td></td>
  68           <td class="md" nowrap>const vector_expression&lt; E2 &gt; &amp;&nbsp;</td>
  69           <td class="mdname" nowrap> <em>e2</em>, </td>
  70         </tr>
  71         <tr>
  72           <td class="md" nowrap align="right"></td>
  73           <td></td>
  74           <td class="md" nowrap>V &amp;&nbsp;</td>
  75           <td class="mdname" nowrap> <em>v</em>, </td>
  76         </tr>
  77         <tr>
  78           <td class="md" nowrap align="right"></td>
  79           <td></td>
  80           <td class="md" nowrap>bool&nbsp;</td>
  81           <td class="mdname" nowrap> <em>init</em> = <code>true</code></td>
  82         </tr>
  83         <tr>
  84           <td></td>
  85           <td class="md">)&nbsp;</td>
  86           <td class="md" colspan="2"></td>
  87         </tr>
  88       </table>
  89     </td>
  90   </tr>
  91 </table>
  92 <table summary="" cellspacing=5 cellpadding=0 border=0>
  93   <tr>
  94     <td>
  95       &nbsp;
  96     </td>
  97     <td>
  98
  99 <p>
 100 computes <code>v += A x</code> or <code>v = A x</code> in an optimized fashion.
 101 </p>
 102 <dl compact><dt><b>Parameters:</b></dt><dd>
 103   <table summary="" border="0" cellspacing="2" cellpadding="0">
 104     <tr><td></td><td valign=top><em>e1</em>&nbsp;</td><td>the matrix expression <code>A</code> </td></tr>
 105     <tr><td></td><td valign=top><em>e2</em>&nbsp;</td><td>the vector expression <code>x</code> </td></tr>
 106     <tr><td></td><td valign=top><em>v</em>&nbsp;</td><td>the result vector <code>v</code> </td></tr>
 107     <tr><td></td><td valign=top><em>init</em>&nbsp;</td><td>a boolean parameter</td></tr>
 108   </table>
 109 </dl>
 110 <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>
 111 Up to now there are some specialisation for compressed matrices that give a large speed up compared to prod.    </td>
 112   </tr>
 113 </table>
 114
 115
 116 <a class="anchor" name="ga9" doxytag="boost::numeric::ublas::axpy_prod" ></a>
 117 <table summary="" class="mdTable" width="95%" cellpadding="2" cellspacing="0">
 118   <tr>
 119     <td class="mdRow">
 120       <table summary="" cellpadding="0" cellspacing="0" border="0">
 121         <tr>
 122           <td class="md" nowrap valign="top"> BOOST_UBLAS_INLINE V&amp; axpy_prod           </td>
 123           <td class="md" valign="top">(&nbsp;</td>
 124           <td class="md" nowrap valign="top">const vector_expression&lt; E1 &gt; &amp;&nbsp;</td>
 125           <td class="mdname" nowrap> <em>e1</em>, </td>
 126         </tr>
 127         <tr>
 128           <td class="md" nowrap align="right"></td>
 129           <td></td>
 130           <td class="md" nowrap>const matrix_expression&lt; E2 &gt; &amp;&nbsp;</td>
 131           <td class="mdname" nowrap> <em>e2</em>, </td>
 132         </tr>
 133         <tr>
 134           <td class="md" nowrap align="right"></td>
 135           <td></td>
 136           <td class="md" nowrap>V &amp;&nbsp;</td>
 137           <td class="mdname" nowrap> <em>v</em>, </td>
 138         </tr>
 139         <tr>
 140           <td class="md" nowrap align="right"></td>
 141           <td></td>
 142           <td class="md" nowrap>bool&nbsp;</td>
 143           <td class="mdname" nowrap> <em>init</em> = <code>true</code></td>
 144         </tr>
 145         <tr>
 146           <td></td>
 147           <td class="md">)&nbsp;</td>
 148           <td class="md" colspan="2"></td>
 149         </tr>
 150       </table>
 151     </td>
 152   </tr>
 153 </table>
 154 <table summary="" cellspacing=5 cellpadding=0 border=0>
 155   <tr>
 156     <td>
 157       &nbsp;
 158     </td>
 159     <td>
 160
 161 <p>
 162 computes <code>v += A<sup>T</sup> x</code> or <code>v = A<sup>T</sup> x</code> in an optimized fashion.
 163 </p>
 164 <dl compact><dt><b>Parameters:</b></dt><dd>
 165   <table summary="" border="0" cellspacing="2" cellpadding="0">
 166     <tr><td></td><td valign=top><em>e1</em>&nbsp;</td><td>the vector expression <code>x</code> </td></tr>
 167     <tr><td></td><td valign=top><em>e2</em>&nbsp;</td><td>the matrix expression <code>A</code> </td></tr>
 168     <tr><td></td><td valign=top><em>v</em>&nbsp;</td><td>the result vector <code>v</code> </td></tr>
 169     <tr><td></td><td valign=top><em>init</em>&nbsp;</td><td>a boolean parameter</td></tr>
 170   </table>
 171 </dl>
 172 <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>
 173 Up to now there are some specialisation for compressed matrices that give a large speed up compared to prod.    </td>
 174   </tr>
 175 </table>
 176
 177 <a class="anchor" name="ga7" doxytag="boost::numeric::ublas::axpy_prod" ></a>
 178 <table summary="" class="mdTable" width="95%" cellpadding="2" cellspacing="0">
 179   <tr>
 180     <td class="mdRow">
 181       <table summary="" cellpadding="0" cellspacing="0" border="0">
 182         <tr>
 183           <td class="md" nowrap valign="top"> BOOST_UBLAS_INLINE M&amp; axpy_prod           </td>
 184           <td class="md" valign="top">(&nbsp;</td>
 185           <td class="md" nowrap valign="top">const matrix_expression&lt; E1 &gt; &amp;&nbsp;</td>
 186           <td class="mdname" nowrap> <em>e1</em>, </td>
 187         </tr>
 188         <tr>
 189           <td class="md" nowrap align="right"></td>
 190           <td></td>
 191           <td class="md" nowrap>const matrix_expression&lt; E2 &gt; &amp;&nbsp;</td>
 192           <td class="mdname" nowrap> <em>e2</em>, </td>
 193         </tr>
 194         <tr>
 195           <td class="md" nowrap align="right"></td>
 196           <td></td>
 197           <td class="md" nowrap>M &amp;&nbsp;</td>
 198           <td class="mdname" nowrap> <em>m</em>, </td>
 199         </tr>
 200         <tr>
 201           <td class="md" nowrap align="right"></td>
 202           <td></td>
 203           <td class="md" nowrap>bool&nbsp;</td>
 204           <td class="mdname" nowrap> <em>init</em> = <code>true</code></td>
 205         </tr>
 206         <tr>
 207           <td></td>
 208           <td class="md">)&nbsp;</td>
 209           <td class="md" colspan="2"></td>
 210         </tr>
 211       </table>
 212     </td>
 213   </tr>
 214 </table>
 215 <table summary="" cellspacing=5 cellpadding=0 border=0>
 216   <tr>
 217     <td>
 218       &nbsp;
 219     </td>
 220     <td>
 221
 222 <p>
 223 computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion.
 224 </p>
 225 <dl compact><dt><b>Parameters:</b></dt><dd>
 226   <table summary="" border="0" cellspacing="2" cellpadding="0">
 227     <tr><td></td><td valign=top><em>e1</em>&nbsp;</td><td>the matrix expression <code>A</code> </td></tr>
 228     <tr><td></td><td valign=top><em>e2</em>&nbsp;</td><td>the matrix expression <code>X</code> </td></tr>
 229     <tr><td></td><td valign=top><em>m</em>&nbsp;</td><td>the result matrix <code>M</code> </td></tr>
 230     <tr><td></td><td valign=top><em>init</em>&nbsp;</td><td>a boolean parameter</td></tr>
 231   </table>
 232 </dl>
 233 <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>
 234 Up to now there are no specialisations.    </td>
 235   </tr>
 236 </table>
 237
 238 <a class="anchor" name="ga6" doxytag="boost::numeric::ublas::opb_prod" ></a>
 239
 240 <table summary="" class="mdTable" width="95%" cellpadding="2" cellspacing="0">
 241   <tr>
 242     <td class="mdRow">
 243       <table summary="" cellpadding="0" cellspacing="0" border="0">
 244         <tr>
 245           <td class="md" nowrap valign="top"> BOOST_UBLAS_INLINE M&amp; opb_prod           </td>
 246           <td class="md" valign="top">(&nbsp;</td>
 247           <td class="md" nowrap valign="top">const matrix_expression&lt; E1 &gt; &amp;&nbsp;</td>
 248           <td class="mdname" nowrap> <em>e1</em>, </td>
 249         </tr>
 250         <tr>
 251           <td class="md" nowrap align="right"></td>
 252           <td></td>
 253           <td class="md" nowrap>const matrix_expression&lt; E2 &gt; &amp;&nbsp;</td>
 254           <td class="mdname" nowrap> <em>e2</em>, </td>
 255         </tr>
 256         <tr>
 257           <td class="md" nowrap align="right"></td>
 258           <td></td>
 259           <td class="md" nowrap>M &amp;&nbsp;</td>
 260           <td class="mdname" nowrap> <em>m</em>, </td>
 261         </tr>
 262         <tr>
 263           <td class="md" nowrap align="right"></td>
 264           <td></td>
 265           <td class="md" nowrap>bool&nbsp;</td>
 266           <td class="mdname" nowrap> <em>init</em> = <code>true</code></td>
 267         </tr>
 268         <tr>
 269           <td></td>
 270           <td class="md">)&nbsp;</td>
 271           <td class="md" colspan="2"></td>
 272         </tr>
 273       </table>
 274     </td>
 275   </tr>
 276 </table>
 277 <table summary="" cellspacing=5 cellpadding=0 border=0>
 278   <tr>
 279     <td>
 280       &nbsp;
 281     </td>
 282     <td>
 283
 284 <p>
 285 computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion.
 286 </p>
 287 <dl compact><dt><b>Parameters:</b></dt><dd>
 288   <table summary="" border="0" cellspacing="2" cellpadding="0">
 289     <tr><td></td><td valign=top><em>e1</em>&nbsp;</td><td>the matrix expression <code>A</code> </td></tr>
 290     <tr><td></td><td valign=top><em>e2</em>&nbsp;</td><td>the matrix expression <code>X</code> </td></tr>
 291     <tr><td></td><td valign=top><em>m</em>&nbsp;</td><td>the result matrix <code>M</code> </td></tr>
 292     <tr><td></td><td valign=top><em>init</em>&nbsp;</td><td>a boolean parameter</td></tr>
 293   </table>
 294 </dl>
 295 <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>
 296 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>
 297   </tr>
 298 </table>
 299
 300
 301
 302 <hr />
 303 <p>Copyright (&copy;) 2000-2004 Michael Stevens, Mathias Koch,
 304 Joerg Walter, Gunter Winkler<br />
 305    Use, modification and distribution are subject to the
 306    Boost Software License, Version 1.0.
 307    (See accompanying file LICENSE_1_0.txt
 308    or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
 309       http://www.boost.org/LICENSE_1_0.txt
 310    </a>).
 311 </p>
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