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  1. <?xml version="1.0" encoding="UTF-8"?>
    2. 

  2. <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
    3. 

  3. <html xmlns="http://www.w3.org/1999/xhtml">
    4. 

  4. <head>
    5. 

  5.   <title>BLAS</title>
    6. 

  6.   <meta name="GENERATOR" content="Quanta Plus" />
    7. 

  7.   <meta name="AUTHOR" content="Gunter Winkler" />
    8. 

  8.   <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
    9. 

  9.   <link rel="stylesheet" href="../../../../boost.css" type="text/css"/>
    10. 

  10.   <link rel="stylesheet" href="ublas.css" type="text/css" />
    11. 

  11.   <script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script>
    12. 

  12.   <script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script>
    13. 

  13. </head>
    14. 

  14. <body>
    15. 

  15. 

  16. 

  17. <h1>Level 3 BLAS</h1>
    18. 

  18. <div class="toc" id="toc"></div>
    19. 

  19. <hr />
    20. 

  20. <a name="_details"></a>
    21. 

  21. 

  22. <table summary="" border=0 cellpadding=0 cellspacing=0>
    23. 

  23. <tr><td></td></tr>
    24. 

  24. <tr><td colspan=2><br /><h2>Functions</h2></td></tr>
    25. 

  25. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M1, class T, class M2, class M3&gt; M1 &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="#ga0">boost::numeric::ublas::blas_3::tmm</a> (M1 &amp;m1, const T &amp;t, const M2 &amp;m2, const M3 &amp;m3)</td></tr>
    26. 

  26. 

  27. <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">triangular matrix multiplication  <a href="#ga0"></a><br /><br /></td></tr>
    28. 

  28. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M1, class T, class M2, class C&gt; M1 &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="#ga1">boost::numeric::ublas::blas_3::tsm</a> (M1 &amp;m1, const T &amp;t, const M2 &amp;m2, C)</td></tr>
    29. 

  29. 

  30. <tr><td class="mdescLeft">&nbsp;</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>
    31. 

  31. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M1, class T1, class T2, class M2, class M3&gt; M1 &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="#ga2">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>
    32. 

  32. 

  33. <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">general matrix multiplication  <a href="#ga2"></a><br /><br /></td></tr>
    34. 

  34. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M1, class T1, class T2, class M2&gt; M1 &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="#ga3">boost::numeric::ublas::blas_3::srk</a> (M1 &amp;m1, const T1 &amp;t1, const T2 &amp;t2, const M2 &amp;m2)</td></tr>
    35. 

  35. 

  36. <tr><td class="mdescLeft">&nbsp;</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>
    37. 

  37. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M1, class T1, class T2, class M2&gt; M1 &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="#ga4">boost::numeric::ublas::blas_3::hrk</a> (M1 &amp;m1, const T1 &amp;t1, const T2 &amp;t2, const M2 &amp;m2)</td></tr>
    38. 

  38. 

  39. <tr><td class="mdescLeft">&nbsp;</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>
    40. 

  40. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M1, class T1, class T2, class M2, class M3&gt; M1 &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="#ga5">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>
    41. 

  41. 

  42. <tr><td class="mdescLeft">&nbsp;</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>
    43. 

  43. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M1, class T1, class T2, class M2, class M3&gt; M1 &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="#ga6">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>
    44. 

  44. 

  45. <tr><td class="mdescLeft">&nbsp;</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>
    46. 

  46. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M, class E1, class E2&gt; BOOST_UBLAS_INLINE M &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="products.html#ga7">boost::numeric::ublas::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>
    47. 

  47. 

  48. <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion.  <a href="products.html#ga7"></a><br /><br /></td></tr>
    49. 

  49. <tr><td class="memItemLeft" nowrap align=right valign=top>template&lt;class M, class E1, class E2&gt; BOOST_UBLAS_INLINE M &amp;&nbsp;</td><td class="memItemRight" valign=bottom><a class="el" href="products.html#ga8">boost::numeric::ublas::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>
    50. 

  50. 

  51. <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">computes <code>M += A X</code> or <code>M = A X</code> in an optimized fashion.  <a href="products.html#ga8"></a><br /><br /></td></tr>
    52. 

  52. </table>
    53. 

  53. 

  54. <hr />
    55. 

  55. 

  56. <h2>Function Documentation</h2>
    57. 

  57. 

  58. <a class="anchor" name="ga0" doxytag="boost::numeric::ublas::blas_3::tmm" ></a>
    59. 

  59. <table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
    60. 

  60.   <tr>
    61. 

  61.     <td class="mdRow">
    62. 

  62.       <table summary="" cellpadding="0" cellspacing="0" border="0">
    63. 

  63.         <tr>
    64. 

  64.           <td class="md" nowrap valign="top"> M1&amp; tmm           </td>
    65. 

  65.           <td class="md" valign="top">(&nbsp;</td>
    66. 

  66.           <td class="md" nowrap valign="top">M1 &amp;&nbsp;</td>
    67. 

  67.           <td class="mdname" nowrap> <em>m1</em>, </td>
    68. 

  68.         </tr>
    69. 

  69.         <tr>
    70. 

  70.           <td class="md" nowrap align="right"></td>
    71. 

  71.           <td></td>
    72. 

  72.           <td class="md" nowrap>const T &amp;&nbsp;</td>
    73. 

  73.           <td class="mdname" nowrap> <em>t</em>, </td>
    74. 

  74.         </tr>
    75. 

  75.         <tr>
    76. 

  76.           <td class="md" nowrap align="right"></td>
    77. 

  77.           <td></td>
    78. 

  78.           <td class="md" nowrap>const M2 &amp;&nbsp;</td>
    79. 

  79.           <td class="mdname" nowrap> <em>m2</em>, </td>
    80. 

  80.         </tr>
    81. 

  81.         <tr>
    82. 

  82.           <td class="md" nowrap align="right"></td>
    83. 

  83.           <td></td>
    84. 

  84.           <td class="md" nowrap>const M3 &amp;&nbsp;</td>
    85. 

  85.           <td class="mdname" nowrap> <em>m3</em></td>
    86. 

  86.         </tr>
    87. 

  87.         <tr>
    88. 

  88.           <td></td>
    89. 

  89.           <td class="md">)&nbsp;</td>
    90. 

  90.           <td class="md" colspan="2"></td>
    91. 

  91.         </tr>
    92. 

  92.       </table>
    93. 

  93.     </td>
    94. 

  94.   </tr>
    95. 

  95. </table>
    96. 

  96. <table summary="" cellspacing=5 cellpadding=0 border=0>
    97. 

  97.   <tr>
    98. 

  98.     <td>
    99. 

  99.       &nbsp;
    100. 

  100.     </td>
    101. 

  101.     <td>
    102. 

  102. <p>triangular matrix multiplication </p>
    103. 

  103.     </td>
    104. 

  104.   </tr>
    105. 

  105. </table>
    106. 

  106. <a class="anchor" name="ga1" doxytag="boost::numeric::ublas::blas_3::tsm" ></a>
    107. 

  107. <table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
    108. 

  108.   <tr>
    109. 

  109.     <td class="mdRow">
    110. 

  110.       <table summary="" cellpadding="0" cellspacing="0" border="0">
    111. 

  111.         <tr>
    112. 

  112.           <td class="md" nowrap valign="top"> M1&amp; tsm           </td>
    113. 

  113.           <td class="md" valign="top">(&nbsp;</td>
    114. 

  114.           <td class="md" nowrap valign="top">M1 &amp;&nbsp;</td>
    115. 

  115.           <td class="mdname" nowrap> <em>m1</em>, </td>
    116. 

  116.         </tr>
    117. 

  117.         <tr>
    118. 

  118.           <td class="md" nowrap align="right"></td>
    119. 

  119.           <td></td>
    120. 

  120.           <td class="md" nowrap>const T &amp;&nbsp;</td>
    121. 

  121.           <td class="mdname" nowrap> <em>t</em>, </td>
    122. 

  122.         </tr>
    123. 

  123.         <tr>
    124. 

  124.           <td class="md" nowrap align="right"></td>
    125. 

  125.           <td></td>
    126. 

  126.           <td class="md" nowrap>const M2 &amp;&nbsp;</td>
    127. 

  127.           <td class="mdname" nowrap> <em>m2</em>, </td>
    128. 

  128.         </tr>
    129. 

  129.         <tr>
    130. 

  130.           <td class="md" nowrap align="right"></td>
    131. 

  131.           <td></td>
    132. 

  132.           <td class="md" nowrap>C&nbsp;</td>
    133. 

  133.           <td class="mdname" nowrap></td>
    134. 

  134.         </tr>
    135. 

  135.         <tr>
    136. 

  136.           <td></td>
    137. 

  137.           <td class="md">)&nbsp;</td>
    138. 

  138.           <td class="md" colspan="2"></td>
    139. 

  139.         </tr>
    140. 

  140.       </table>
    141. 

  141.     </td>
    142. 

  142.   </tr>
    143. 

  143. </table>
    144. 

  144. <table summary="" cellspacing=5 cellpadding=0 border=0>
    145. 

  145.   <tr>
    146. 

  146.     <td>
    147. 

  147.       &nbsp;
    148. 

  148.     </td>
    149. 

  149.     <td>
    150. 

  150. 

  151. <p>
    152. 

  152. triangular solve <em>m2</em> * <em>x</em> = <em>t</em> * <em>m1</em> in place, <em>m2</em> is a triangular matrix 
    153. 

  153. </p>
    154. 

  154.     </td>
    155. 

  155.   </tr>
    156. 

  156. </table>
    157. 

  157. <a class="anchor" name="ga2" doxytag="boost::numeric::ublas::blas_3::gmm" ></a>
    158. 

  158. <table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
    159. 

  159.   <tr>
    160. 

  160.     <td class="mdRow">
    161. 

  161.       <table summary="" cellpadding="0" cellspacing="0" border="0">
    162. 

  162.         <tr>
    163. 

  163.           <td class="md" nowrap valign="top"> M1&amp; gmm           </td>
    164. 

  164.           <td class="md" valign="top">(&nbsp;</td>
    165. 

  165.           <td class="md" nowrap valign="top">M1 &amp;&nbsp;</td>
    166. 

  166.           <td class="mdname" nowrap> <em>m1</em>, </td>
    167. 

  167.         </tr>
    168. 

  168.         <tr>
    169. 

  169.           <td class="md" nowrap align="right"></td>
    170. 

  170.           <td></td>
    171. 

  171.           <td class="md" nowrap>const T1 &amp;&nbsp;</td>
    172. 

  172.           <td class="mdname" nowrap> <em>t1</em>, </td>
    173. 

  173.         </tr>
    174. 

  174.         <tr>
    175. 

  175.           <td class="md" nowrap align="right"></td>
    176. 

  176.           <td></td>
    177. 

  177.           <td class="md" nowrap>const T2 &amp;&nbsp;</td>
    178. 

  178.           <td class="mdname" nowrap> <em>t2</em>, </td>
    179. 

  179.         </tr>
    180. 

  180.         <tr>
    181. 

  181.           <td class="md" nowrap align="right"></td>
    182. 

  182.           <td></td>
    183. 

  183.           <td class="md" nowrap>const M2 &amp;&nbsp;</td>
    184. 

  184.           <td class="mdname" nowrap> <em>m2</em>, </td>
    185. 

  185.         </tr>
    186. 

  186.         <tr>
    187. 

  187.           <td class="md" nowrap align="right"></td>
    188. 

  188.           <td></td>
    189. 

  189.           <td class="md" nowrap>const M3 &amp;&nbsp;</td>
    190. 

  190.           <td class="mdname" nowrap> <em>m3</em></td>
    191. 

  191.         </tr>
    192. 

  192.         <tr>
    193. 

  193.           <td></td>
    194. 

  194.           <td class="md">)&nbsp;</td>
    195. 

  195.           <td class="md" colspan="2"></td>
    196. 

  196.         </tr>
    197. 

  197.       </table>
    198. 

  198.     </td>
    199. 

  199.   </tr>
    200. 

  200. </table>
    201. 

  201. <table summary="" cellspacing=5 cellpadding=0 border=0>
    202. 

  202.   <tr>
    203. 

  203.     <td>
    204. 

  204.       &nbsp;
    205. 

  205.     </td>
    206. 

  206.     <td>
    207. 

  207. 

  208. <p>
    209. 

  209. general matrix multiplication 
    210. 

  210. </p>
    211. 

  211.     </td>
    212. 

  212.   </tr>
    213. 

  213. </table>
    214. 

  214. <a class="anchor" name="ga3" doxytag="boost::numeric::ublas::blas_3::srk" ></a>
    215. 

  215. <table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
    216. 

  216.   <tr>
    217. 

  217.     <td class="mdRow">
    218. 

  218.       <table summary="" cellpadding="0" cellspacing="0" border="0">
    219. 

  219.         <tr>
    220. 

  220.           <td class="md" nowrap valign="top"> M1&amp; srk           </td>
    221. 

  221.           <td class="md" valign="top">(&nbsp;</td>
    222. 

  222.           <td class="md" nowrap valign="top">M1 &amp;&nbsp;</td>
    223. 

  223.           <td class="mdname" nowrap> <em>m1</em>, </td>
    224. 

  224.         </tr>
    225. 

  225.         <tr>
    226. 

  226.           <td class="md" nowrap align="right"></td>
    227. 

  227.           <td></td>
    228. 

  228.           <td class="md" nowrap>const T1 &amp;&nbsp;</td>
    229. 

  229.           <td class="mdname" nowrap> <em>t1</em>, </td>
    230. 

  230.         </tr>
    231. 

  231.         <tr>
    232. 

  232.           <td class="md" nowrap align="right"></td>
    233. 

  233.           <td></td>
    234. 

  234.           <td class="md" nowrap>const T2 &amp;&nbsp;</td>
    235. 

  235.           <td class="mdname" nowrap> <em>t2</em>, </td>
    236. 

  236.         </tr>
    237. 

  237.         <tr>
    238. 

  238.           <td class="md" nowrap align="right"></td>
    239. 

  239.           <td></td>
    240. 

  240.           <td class="md" nowrap>const M2 &amp;&nbsp;</td>
    241. 

  241.           <td class="mdname" nowrap> <em>m2</em></td>
    242. 

  242.         </tr>
    243. 

  243.         <tr>
    244. 

  244.           <td></td>
    245. 

  245.           <td class="md">)&nbsp;</td>
    246. 

  246.           <td class="md" colspan="2"></td>
    247. 

  247.         </tr>
    248. 

  248.       </table>
    249. 

  249.     </td>
    250. 

  250.   </tr>
    251. 

  251. </table>
    252. 

  252. <table summary="" cellspacing=5 cellpadding=0 border=0>
    253. 

  253.   <tr>
    254. 

  254.     <td>
    255. 

  255.       &nbsp;
    256. 

  256.     </td>
    257. 

  257.     <td>
    258. 

  258. 

  259. <p>
    260. 

  260. 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>) 
    261. 

  261. </p>
    262. 

  262. <dl compact><dt><b>Todo:</b></dt><dd>use opb_prod() </dd></dl>
    263. 

  263.     </td>
    264. 

  264.   </tr>
    265. 

  265. </table>
    266. 

  266. <a class="anchor" name="ga4" doxytag="boost::numeric::ublas::blas_3::hrk" ></a>
    267. 

  267. <table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
    268. 

  268.   <tr>
    269. 

  269.     <td class="mdRow">
    270. 

  270.       <table summary="" cellpadding="0" cellspacing="0" border="0">
    271. 

  271.         <tr>
    272. 

  272.           <td class="md" nowrap valign="top"> M1&amp; hrk           </td>
    273. 

  273.           <td class="md" valign="top">(&nbsp;</td>
    274. 

  274.           <td class="md" nowrap valign="top">M1 &amp;&nbsp;</td>
    275. 

  275.           <td class="mdname" nowrap> <em>m1</em>, </td>
    276. 

  276.         </tr>
    277. 

  277.         <tr>
    278. 

  278.           <td class="md" nowrap align="right"></td>
    279. 

  279.           <td></td>
    280. 

  280.           <td class="md" nowrap>const T1 &amp;&nbsp;</td>
    281. 

  281.           <td class="mdname" nowrap> <em>t1</em>, </td>
    282. 

  282.         </tr>
    283. 

  283.         <tr>
    284. 

  284.           <td class="md" nowrap align="right"></td>
    285. 

  285.           <td></td>
    286. 

  286.           <td class="md" nowrap>const T2 &amp;&nbsp;</td>
    287. 

  287.           <td class="mdname" nowrap> <em>t2</em>, </td>
    288. 

  288.         </tr>
    289. 

  289.         <tr>
    290. 

  290.           <td class="md" nowrap align="right"></td>
    291. 

  291.           <td></td>
    292. 

  292.           <td class="md" nowrap>const M2 &amp;&nbsp;</td>
    293. 

  293.           <td class="mdname" nowrap> <em>m2</em></td>
    294. 

  294.         </tr>
    295. 

  295.         <tr>
    296. 

  296.           <td></td>
    297. 

  297.           <td class="md">)&nbsp;</td>
    298. 

  298.           <td class="md" colspan="2"></td>
    299. 

  299.         </tr>
    300. 

  300.       </table>
    301. 

  301.     </td>
    302. 

  302.   </tr>
    303. 

  303. </table>
    304. 

  304. <table summary="" cellspacing=5 cellpadding=0 border=0>
    305. 

  305.   <tr>
    306. 

  306.     <td>
    307. 

  307.       &nbsp;
    308. 

  308.     </td>
    309. 

  309.     <td>
    310. 

  310. 

  311. <p>
    312. 

  312. 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>) 
    313. 

  313. </p>
    314. 

  314. <dl compact><dt><b>Todo:</b></dt><dd>use opb_prod()</dd></dl>
    315. 

  315.     </td>
    316. 

  316.   </tr>
    317. 

  317. </table>
    318. 

  318. <a class="anchor" name="ga5" doxytag="boost::numeric::ublas::blas_3::sr2k" ></a>
    319. 

  319. <table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
    320. 

  320.   <tr>
    321. 

  321.     <td class="mdRow">
    322. 

  322.       <table summary="" cellpadding="0" cellspacing="0" border="0">
    323. 

  323.         <tr>
    324. 

  324.           <td class="md" nowrap valign="top"> M1&amp; sr2k           </td>
    325. 

  325.           <td class="md" valign="top">(&nbsp;</td>
    326. 

  326.           <td class="md" nowrap valign="top">M1 &amp;&nbsp;</td>
    327. 

  327.           <td class="mdname" nowrap> <em>m1</em>, </td>
    328. 

  328.         </tr>
    329. 

  329.         <tr>
    330. 

  330.           <td class="md" nowrap align="right"></td>
    331. 

  331.           <td></td>
    332. 

  332.           <td class="md" nowrap>const T1 &amp;&nbsp;</td>
    333. 

  333.           <td class="mdname" nowrap> <em>t1</em>, </td>
    334. 

  334.         </tr>
    335. 

  335.         <tr>
    336. 

  336.           <td class="md" nowrap align="right"></td>
    337. 

  337.           <td></td>
    338. 

  338.           <td class="md" nowrap>const T2 &amp;&nbsp;</td>
    339. 

  339.           <td class="mdname" nowrap> <em>t2</em>, </td>
    340. 

  340.         </tr>
    341. 

  341.         <tr>
    342. 

  342.           <td class="md" nowrap align="right"></td>
    343. 

  343.           <td></td>
    344. 

  344.           <td class="md" nowrap>const M2 &amp;&nbsp;</td>
    345. 

  345.           <td class="mdname" nowrap> <em>m2</em>, </td>
    346. 

  346.         </tr>
    347. 

  347.         <tr>
    348. 

  348.           <td class="md" nowrap align="right"></td>
    349. 

  349.           <td></td>
    350. 

  350.           <td class="md" nowrap>const M3 &amp;&nbsp;</td>
    351. 

  351.           <td class="mdname" nowrap> <em>m3</em></td>
    352. 

  352.         </tr>
    353. 

  353.         <tr>
    354. 

  354.           <td></td>
    355. 

  355.           <td class="md">)&nbsp;</td>
    356. 

  356.           <td class="md" colspan="2"></td>
    357. 

  357.         </tr>
    358. 

  358.       </table>
    359. 

  359.     </td>
    360. 

  360.   </tr>
    361. 

  361. </table>
    362. 

  362. <table summary="" cellspacing=5 cellpadding=0 border=0>
    363. 

  363.   <tr>
    364. 

  364.     <td>
    365. 

  365.       &nbsp;
    366. 

  366.     </td>
    367. 

  367.     <td>
    368. 

  368. 

  369. <p>
    370. 

  370. 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>) 
    371. 

  371. </p>
    372. 

  372. <dl compact><dt><b>Todo:</b></dt><dd>use opb_prod()</dd></dl>
    373. 

  373.     </td>
    374. 

  374.   </tr>
    375. 

  375. </table>
    376. 

  376. <a class="anchor" name="ga6" doxytag="boost::numeric::ublas::blas_3::hr2k" ></a>
    377. 

  377. <table summary="" class="mdTable" width="100%" cellpadding="2" cellspacing="0">
    378. 

  378.   <tr>
    379. 

  379.     <td class="mdRow">
    380. 

  380.       <table summary="" cellpadding="0" cellspacing="0" border="0">
    381. 

  381.         <tr>
    382. 

  382.           <td class="md" nowrap valign="top"> M1&amp; hr2k           </td>
    383. 

  383.           <td class="md" valign="top">(&nbsp;</td>
    384. 

  384.           <td class="md" nowrap valign="top">M1 &amp;&nbsp;</td>
    385. 

  385.           <td class="mdname" nowrap> <em>m1</em>, </td>
    386. 

  386.         </tr>
    387. 

  387.         <tr>
    388. 

  388.           <td class="md" nowrap align="right"></td>
    389. 

  389.           <td></td>
    390. 

  390.           <td class="md" nowrap>const T1 &amp;&nbsp;</td>
    391. 

  391.           <td class="mdname" nowrap> <em>t1</em>, </td>
    392. 

  392.         </tr>
    393. 

  393.         <tr>
    394. 

  394.           <td class="md" nowrap align="right"></td>
    395. 

  395.           <td></td>
    396. 

  396.           <td class="md" nowrap>const T2 &amp;&nbsp;</td>
    397. 

  397.           <td class="mdname" nowrap> <em>t2</em>, </td>
    398. 

  398.         </tr>
    399. 

  399.         <tr>
    400. 

  400.           <td class="md" nowrap align="right"></td>
    401. 

  401.           <td></td>
    402. 

  402.           <td class="md" nowrap>const M2 &amp;&nbsp;</td>
    403. 

  403.           <td class="mdname" nowrap> <em>m2</em>, </td>
    404. 

  404.         </tr>
    405. 

  405.         <tr>
    406. 

  406.           <td class="md" nowrap align="right"></td>
    407. 

  407.           <td></td>
    408. 

  408.           <td class="md" nowrap>const M3 &amp;&nbsp;</td>
    409. 

  409.           <td class="mdname" nowrap> <em>m3</em></td>
    410. 

  410.         </tr>
    411. 

  411.         <tr>
    412. 

  412.           <td></td>
    413. 

  413.           <td class="md">)&nbsp;</td>
    414. 

  414.           <td class="md" colspan="2"></td>
    415. 

  415.         </tr>
    416. 

  416.       </table>
    417. 

  417.     </td>
    418. 

  418.   </tr>
    419. 

  419. </table>
    420. 

  420. <table summary="" cellspacing=5 cellpadding=0 border=0>
    421. 

  421.   <tr>
    422. 

  422.     <td>
    423. 

  423.       &nbsp;
    424. 

  424.     </td>
    425. 

  425.     <td>
    426. 

  426. 

  427. <p>
    428. 

  428. 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>) 
    429. 

  429. </p>
    430. 

  430. <dl compact><dt><b>Todo:</b></dt><dd>use opb_prod()</dd></dl>
    431. 

  431.     </td>
    432. 

  432.   </tr>
    433. 

  433. </table>
    434. 

  434. 

  435. 

  436. 

  437. <hr />
    438. 

  438. <p>Copyright (&copy;) 2000-2004 Michael Stevens, Mathias Koch, 
    439. 

  439. Joerg Walter, Gunter Winkler<br />
    440. 

  440. Use, modification and distribution are subject to the
    441. 

  441. Boost Software License, Version 1.0.
    442. 

  442. (See accompanying file LICENSE_1_0.txt
    443. 

  443. or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
    444. 

  444. http://www.boost.org/LICENSE_1_0.txt</a>).
    445. 

  445. </p>
    446. 

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    447. 

  447. (function($) {
    448. 

  448.     $('#toc').toc();
    449. 

  449. })(jQuery);
    450. 

  450. </script>
    451. 

  451. </body>
    452. 

  452. </html>
    453.