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nest-open-source / nest-learning-thermostat / 5.0 / boost / 317601cb979f96545d0e892ce7cfdf59f676ee0a / . / boost_1_45_0 / libs / numeric / ublas / doc / html / blas_8hpp_source.html
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<h1>blas.hpp</h1><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">//</span>
<a name="l00002"></a>00002 <span class="comment">// Copyright (c) 2000-2002</span>
<a name="l00003"></a>00003 <span class="comment">// Joerg Walter, Mathias Koch</span>
<a name="l00004"></a>00004 <span class="comment">//</span>
<a name="l00005"></a>00005 <span class="comment">// Distributed under the Boost Software License, Version 1.0. (See</span>
<a name="l00006"></a>00006 <span class="comment">// accompanying file LICENSE_1_0.txt or copy at</span>
<a name="l00007"></a>00007 <span class="comment">// http://www.boost.org/LICENSE_1_0.txt)</span>
<a name="l00008"></a>00008 <span class="comment">//</span>
<a name="l00009"></a>00009 <span class="comment">// The authors gratefully acknowledge the support of</span>
<a name="l00010"></a>00010 <span class="comment">// GeNeSys mbH &amp; Co. KG in producing this work.</span>
<a name="l00011"></a>00011 <span class="comment">//</span>
<a name="l00012"></a>00012
<a name="l00013"></a>00013 <span class="preprocessor">#ifndef _BOOST_UBLAS_BLAS_</span>
<a name="l00014"></a>00014 <span class="preprocessor"></span><span class="preprocessor">#define _BOOST_UBLAS_BLAS_</span>
<a name="l00015"></a>00015 <span class="preprocessor"></span>
<a name="l00016"></a>00016 <span class="preprocessor">#include &lt;boost/numeric/ublas/traits.hpp&gt;</span>
<a name="l00017"></a>00017
<a name="l00018"></a>00018 <span class="keyword">namespace </span>boost { <span class="keyword">namespace </span>numeric { <span class="keyword">namespace </span>ublas {
<a name="l00019"></a>00019
<a name="l00020"></a>00020
<a name="l00026"></a>00026 <span class="keyword">namespace </span>blas_1 {
<a name="l00027"></a>00027
<a name="l00035"></a>00035 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V&gt;
<a name="l00036"></a>00036 <span class="keyword">typename</span> type_traits&lt;typename V::value_type&gt;::real_type
<a name="l00037"></a>00037 asum (<span class="keyword">const</span> V &amp;v) {
<a name="l00038"></a>00038 <span class="keywordflow">return</span> norm_1 (v);
<a name="l00039"></a>00039 }
<a name="l00040"></a>00040
<a name="l00048"></a>00048 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V&gt;
<a name="l00049"></a>00049 <span class="keyword">typename</span> type_traits&lt;typename V::value_type&gt;::real_type
<a name="l00050"></a>00050 nrm2 (<span class="keyword">const</span> V &amp;v) {
<a name="l00051"></a>00051 <span class="keywordflow">return</span> norm_2 (v);
<a name="l00052"></a>00052 }
<a name="l00053"></a>00053
<a name="l00061"></a>00061 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V&gt;
<a name="l00062"></a>00062 <span class="keyword">typename</span> type_traits&lt;typename V::value_type&gt;::real_type
<a name="l00063"></a>00063 amax (<span class="keyword">const</span> V &amp;v) {
<a name="l00064"></a>00064 <span class="keywordflow">return</span> norm_inf (v);
<a name="l00065"></a>00065 }
<a name="l00066"></a>00066
<a name="l00076"></a>00076 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V1, <span class="keyword">class</span> V2&gt;
<a name="l00077"></a>00077 <span class="keyword">typename</span> promote_traits&lt;typename V1::value_type, typename V2::value_type&gt;::promote_type
<a name="l00078"></a>00078 dot (<span class="keyword">const</span> V1 &amp;v1, <span class="keyword">const</span> V2 &amp;v2) {
<a name="l00079"></a>00079 <span class="keywordflow">return</span> inner_prod (v1, v2);
<a name="l00080"></a>00080 }
<a name="l00081"></a>00081
<a name="l00091"></a>00091 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V1, <span class="keyword">class</span> V2&gt;
<a name="l00092"></a>00092 V1 &amp; copy (V1 &amp;v1, <span class="keyword">const</span> V2 &amp;v2)
<a name="l00093"></a>00093 {
<a name="l00094"></a>00094 <span class="keywordflow">return</span> v1.assign (v2);
<a name="l00095"></a>00095 }
<a name="l00096"></a>00096
<a name="l00105"></a>00105 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V1, <span class="keyword">class</span> V2&gt;
<a name="l00106"></a>00106 <span class="keywordtype">void</span> swap (V1 &amp;v1, V2 &amp;v2)
<a name="l00107"></a>00107 {
<a name="l00108"></a>00108 v1.swap (v2);
<a name="l00109"></a>00109 }
<a name="l00110"></a>00110
<a name="l00120"></a>00120 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V, <span class="keyword">class</span> T&gt;
<a name="l00121"></a>00121 V &amp; scal (V &amp;v, <span class="keyword">const</span> T &amp;t)
<a name="l00122"></a>00122 {
<a name="l00123"></a>00123 <span class="keywordflow">return</span> v *= t;
<a name="l00124"></a>00124 }
<a name="l00125"></a>00125
<a name="l00137"></a>00137 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V1, <span class="keyword">class</span> T, <span class="keyword">class</span> V2&gt;
<a name="l00138"></a>00138 V1 &amp; axpy (V1 &amp;v1, <span class="keyword">const</span> T &amp;t, <span class="keyword">const</span> V2 &amp;v2)
<a name="l00139"></a>00139 {
<a name="l00140"></a>00140 <span class="keywordflow">return</span> v1.plus_assign (t * v2);
<a name="l00141"></a>00141 }
<a name="l00142"></a>00142
<a name="l00160"></a>00160 <span class="keyword">template</span>&lt;<span class="keyword">class</span> T1, <span class="keyword">class</span> V1, <span class="keyword">class</span> T2, <span class="keyword">class</span> V2&gt;
<a name="l00161"></a>00161 <span class="keywordtype">void</span> rot (<span class="keyword">const</span> T1 &amp;t1, V1 &amp;v1, <span class="keyword">const</span> T2 &amp;t2, V2 &amp;v2)
<a name="l00162"></a>00162 {
<a name="l00163"></a>00163 <span class="keyword">typedef</span> <span class="keyword">typename</span> promote_traits&lt;typename V1::value_type, typename V2::value_type&gt;::promote_type promote_type;
<a name="l00164"></a>00164 vector&lt;promote_type&gt; vt (t1 * v1 + t2 * v2);
<a name="l00165"></a>00165 v2.assign (- t2 * v1 + t1 * v2);
<a name="l00166"></a>00166 v1.assign (vt);
<a name="l00167"></a>00167 }
<a name="l00168"></a>00168
<a name="l00169"></a>00169 }
<a name="l00170"></a>00170
<a name="l00176"></a>00176 <span class="keyword">namespace </span>blas_2 {
<a name="l00177"></a>00177
<a name="l00187"></a>00187 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V, <span class="keyword">class</span> M&gt;
<a name="l00188"></a>00188 V &amp; tmv (V &amp;v, <span class="keyword">const</span> M &amp;m)
<a name="l00189"></a>00189 {
<a name="l00190"></a>00190 <span class="keywordflow">return</span> v = prod (m, v);
<a name="l00191"></a>00191 }
<a name="l00192"></a>00192
<a name="l00204"></a>00204 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V, <span class="keyword">class</span> M, <span class="keyword">class</span> C&gt;
<a name="l00205"></a>00205 V &amp; tsv (V &amp;v, <span class="keyword">const</span> M &amp;m, C)
<a name="l00206"></a>00206 {
<a name="l00207"></a>00207 <span class="keywordflow">return</span> v = solve (m, v, C ());
<a name="l00208"></a>00208 }
<a name="l00209"></a>00209
<a name="l00225"></a>00225 <span class="keyword">template</span>&lt;<span class="keyword">class</span> V1, <span class="keyword">class</span> T1, <span class="keyword">class</span> T2, <span class="keyword">class</span> M, <span class="keyword">class</span> V2&gt;
<a name="l00226"></a>00226 V1 &amp; gmv (V1 &amp;v1, <span class="keyword">const</span> T1 &amp;t1, <span class="keyword">const</span> T2 &amp;t2, <span class="keyword">const</span> M &amp;m, <span class="keyword">const</span> V2 &amp;v2)
<a name="l00227"></a>00227 {
<a name="l00228"></a>00228 <span class="keywordflow">return</span> v1 = t1 * v1 + t2 * prod (m, v2);
<a name="l00229"></a>00229 }
<a name="l00230"></a>00230
<a name="l00244"></a>00244 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> T, <span class="keyword">class</span> V1, <span class="keyword">class</span> V2&gt;
<a name="l00245"></a>00245 M &amp; gr (M &amp;m, <span class="keyword">const</span> T &amp;t, <span class="keyword">const</span> V1 &amp;v1, <span class="keyword">const</span> V2 &amp;v2)
<a name="l00246"></a>00246 {
<a name="l00247"></a>00247 <span class="preprocessor">#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG</span>
<a name="l00248"></a>00248 <span class="preprocessor"></span> <span class="keywordflow">return</span> m += t * outer_prod (v1, v2);
<a name="l00249"></a>00249 <span class="preprocessor">#else</span>
<a name="l00250"></a>00250 <span class="preprocessor"></span> <span class="keywordflow">return</span> m = m + t * outer_prod (v1, v2);
<a name="l00251"></a>00251 <span class="preprocessor">#endif</span>
<a name="l00252"></a>00252 <span class="preprocessor"></span> }
<a name="l00253"></a>00253
<a name="l00265"></a>00265 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> T, <span class="keyword">class</span> V&gt;
<a name="l00266"></a>00266 M &amp; sr (M &amp;m, <span class="keyword">const</span> T &amp;t, <span class="keyword">const</span> V &amp;v)
<a name="l00267"></a>00267 {
<a name="l00268"></a>00268 <span class="preprocessor">#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG</span>
<a name="l00269"></a>00269 <span class="preprocessor"></span> <span class="keywordflow">return</span> m += t * outer_prod (v, v);
<a name="l00270"></a>00270 <span class="preprocessor">#else</span>
<a name="l00271"></a>00271 <span class="preprocessor"></span> <span class="keywordflow">return</span> m = m + t * outer_prod (v, v);
<a name="l00272"></a>00272 <span class="preprocessor">#endif</span>
<a name="l00273"></a>00273 <span class="preprocessor"></span> }
<a name="l00274"></a>00274
<a name="l00286"></a>00286 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> T, <span class="keyword">class</span> V&gt;
<a name="l00287"></a>00287 M &amp; hr (M &amp;m, <span class="keyword">const</span> T &amp;t, <span class="keyword">const</span> V &amp;v)
<a name="l00288"></a>00288 {
<a name="l00289"></a>00289 <span class="preprocessor">#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG</span>
<a name="l00290"></a>00290 <span class="preprocessor"></span> <span class="keywordflow">return</span> m += t * outer_prod (v, conj (v));
<a name="l00291"></a>00291 <span class="preprocessor">#else</span>
<a name="l00292"></a>00292 <span class="preprocessor"></span> <span class="keywordflow">return</span> m = m + t * outer_prod (v, conj (v));
<a name="l00293"></a>00293 <span class="preprocessor">#endif</span>
<a name="l00294"></a>00294 <span class="preprocessor"></span> }
<a name="l00295"></a>00295
<a name="l00309"></a>00309 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> T, <span class="keyword">class</span> V1, <span class="keyword">class</span> V2&gt;
<a name="l00310"></a>00310 M &amp; sr2 (M &amp;m, <span class="keyword">const</span> T &amp;t, <span class="keyword">const</span> V1 &amp;v1, <span class="keyword">const</span> V2 &amp;v2)
<a name="l00311"></a>00311 {
<a name="l00312"></a>00312 <span class="preprocessor">#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG</span>
<a name="l00313"></a>00313 <span class="preprocessor"></span> <span class="keywordflow">return</span> m += t * (outer_prod (v1, v2) + outer_prod (v2, v1));
<a name="l00314"></a>00314 <span class="preprocessor">#else</span>
<a name="l00315"></a>00315 <span class="preprocessor"></span> <span class="keywordflow">return</span> m = m + t * (outer_prod (v1, v2) + outer_prod (v2, v1));
<a name="l00316"></a>00316 <span class="preprocessor">#endif</span>
<a name="l00317"></a>00317 <span class="preprocessor"></span> }
<a name="l00318"></a>00318
<a name="l00332"></a>00332 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> T, <span class="keyword">class</span> V1, <span class="keyword">class</span> V2&gt;
<a name="l00333"></a>00333 M &amp; hr2 (M &amp;m, <span class="keyword">const</span> T &amp;t, <span class="keyword">const</span> V1 &amp;v1, <span class="keyword">const</span> V2 &amp;v2)
<a name="l00334"></a>00334 {
<a name="l00335"></a>00335 <span class="preprocessor">#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG</span>
<a name="l00336"></a>00336 <span class="preprocessor"></span> <span class="keywordflow">return</span> m += t * outer_prod (v1, conj (v2)) + type_traits&lt;T&gt;::conj (t) * outer_prod (v2, conj (v1));
<a name="l00337"></a>00337 <span class="preprocessor">#else</span>
<a name="l00338"></a>00338 <span class="preprocessor"></span> <span class="keywordflow">return</span> m = m + t * outer_prod (v1, conj (v2)) + type_traits&lt;T&gt;::conj (t) * outer_prod (v2, conj (v1));
<a name="l00339"></a>00339 <span class="preprocessor">#endif</span>
<a name="l00340"></a>00340 <span class="preprocessor"></span> }
<a name="l00341"></a>00341
<a name="l00342"></a>00342 }
<a name="l00343"></a>00343
<a name="l00349"></a>00349 <span class="keyword">namespace </span>blas_3 {
<a name="l00350"></a>00350
<a name="l00365"></a>00365 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M1, <span class="keyword">class</span> T, <span class="keyword">class</span> M2, <span class="keyword">class</span> M3&gt;
<a name="l00366"></a>00366 M1 &amp; tmm (M1 &amp;m1, <span class="keyword">const</span> T &amp;t, <span class="keyword">const</span> M2 &amp;m2, <span class="keyword">const</span> M3 &amp;m3)
<a name="l00367"></a>00367 {
<a name="l00368"></a>00368 <span class="keywordflow">return</span> m1 = t * prod (m2, m3);
<a name="l00369"></a>00369 }
<a name="l00370"></a>00370
<a name="l00384"></a>00384 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M1, <span class="keyword">class</span> T, <span class="keyword">class</span> M2, <span class="keyword">class</span> C&gt;
<a name="l00385"></a>00385 M1 &amp; tsm (M1 &amp;m1, <span class="keyword">const</span> T &amp;t, <span class="keyword">const</span> M2 &amp;m2, C)
<a name="l00386"></a>00386 {
<a name="l00387"></a>00387 <span class="keywordflow">return</span> m1 = solve (m2, t * m1, C ());
<a name="l00388"></a>00388 }
<a name="l00389"></a>00389
<a name="l00405"></a>00405 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M1, <span class="keyword">class</span> T1, <span class="keyword">class</span> T2, <span class="keyword">class</span> M2, <span class="keyword">class</span> M3&gt;
<a name="l00406"></a>00406 M1 &amp; gmm (M1 &amp;m1, <span class="keyword">const</span> T1 &amp;t1, <span class="keyword">const</span> T2 &amp;t2, <span class="keyword">const</span> M2 &amp;m2, <span class="keyword">const</span> M3 &amp;m3)
<a name="l00407"></a>00407 {
<a name="l00408"></a>00408 <span class="keywordflow">return</span> m1 = t1 * m1 + t2 * prod (m2, m3);
<a name="l00409"></a>00409 }
<a name="l00410"></a>00410
<a name="l00425"></a>00425 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M1, <span class="keyword">class</span> T1, <span class="keyword">class</span> T2, <span class="keyword">class</span> M2&gt;
<a name="l00426"></a>00426 M1 &amp; srk (M1 &amp;m1, <span class="keyword">const</span> T1 &amp;t1, <span class="keyword">const</span> T2 &amp;t2, <span class="keyword">const</span> M2 &amp;m2)
<a name="l00427"></a>00427 {
<a name="l00428"></a>00428 <span class="keywordflow">return</span> m1 = t1 * m1 + t2 * prod (m2, trans (m2));
<a name="l00429"></a>00429 }
<a name="l00430"></a>00430
<a name="l00445"></a>00445 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M1, <span class="keyword">class</span> T1, <span class="keyword">class</span> T2, <span class="keyword">class</span> M2&gt;
<a name="l00446"></a>00446 M1 &amp; hrk (M1 &amp;m1, <span class="keyword">const</span> T1 &amp;t1, <span class="keyword">const</span> T2 &amp;t2, <span class="keyword">const</span> M2 &amp;m2)
<a name="l00447"></a>00447 {
<a name="l00448"></a>00448 <span class="keywordflow">return</span> m1 = t1 * m1 + t2 * prod (m2, herm (m2));
<a name="l00449"></a>00449 }
<a name="l00450"></a>00450
<a name="l00467"></a>00467 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M1, <span class="keyword">class</span> T1, <span class="keyword">class</span> T2, <span class="keyword">class</span> M2, <span class="keyword">class</span> M3&gt;
<a name="l00468"></a>00468 M1 &amp; sr2k (M1 &amp;m1, <span class="keyword">const</span> T1 &amp;t1, <span class="keyword">const</span> T2 &amp;t2, <span class="keyword">const</span> M2 &amp;m2, <span class="keyword">const</span> M3 &amp;m3)
<a name="l00469"></a>00469 {
<a name="l00470"></a>00470 <span class="keywordflow">return</span> m1 = t1 * m1 + t2 * (prod (m2, trans (m3)) + prod (m3, trans (m2)));
<a name="l00471"></a>00471 }
<a name="l00472"></a>00472
<a name="l00489"></a>00489 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M1, <span class="keyword">class</span> T1, <span class="keyword">class</span> T2, <span class="keyword">class</span> M2, <span class="keyword">class</span> M3&gt;
<a name="l00490"></a>00490 M1 &amp; hr2k (M1 &amp;m1, <span class="keyword">const</span> T1 &amp;t1, <span class="keyword">const</span> T2 &amp;t2, <span class="keyword">const</span> M2 &amp;m2, <span class="keyword">const</span> M3 &amp;m3)
<a name="l00491"></a>00491 {
<a name="l00492"></a>00492 <span class="keywordflow">return</span> m1 =
<a name="l00493"></a>00493 t1 * m1
<a name="l00494"></a>00494 + t2 * prod (m2, herm (m3))
<a name="l00495"></a>00495 + type_traits&lt;T2&gt;::conj (t2) * prod (m3, herm (m2));
<a name="l00496"></a>00496 }
<a name="l00497"></a>00497
<a name="l00498"></a>00498 }
<a name="l00499"></a>00499
<a name="l00500"></a>00500 }}}
<a name="l00501"></a>00501
<a name="l00502"></a>00502 <span class="preprocessor">#endif</span>
</pre></div></div>
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