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<div id="projectname">Boost.uBlas&#160;<span id="projectnumber">1.49</span></div>
<div id="projectbrief">Linear Algebra in C++: matrices, vectors and numeric algorithms</div>
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<h1>lu.hpp</h1> </div>
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<a href="a00618.html">Go to the documentation of this file.</a><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_LU_</span>
<a name="l00014"></a>00014 <span class="preprocessor"></span><span class="preprocessor">#define _BOOST_UBLAS_LU_</span>
<a name="l00015"></a>00015 <span class="preprocessor"></span>
<a name="l00016"></a>00016 <span class="preprocessor">#include &lt;boost/numeric/ublas/operation.hpp&gt;</span>
<a name="l00017"></a>00017 <span class="preprocessor">#include &lt;boost/numeric/ublas/vector_proxy.hpp&gt;</span>
<a name="l00018"></a>00018 <span class="preprocessor">#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;</span>
<a name="l00019"></a>00019 <span class="preprocessor">#include &lt;boost/numeric/ublas/vector.hpp&gt;</span>
<a name="l00020"></a>00020 <span class="preprocessor">#include &lt;boost/numeric/ublas/triangular.hpp&gt;</span>
<a name="l00021"></a>00021
<a name="l00022"></a>00022 <span class="comment">// LU factorizations in the spirit of LAPACK and Golub &amp; van Loan</span>
<a name="l00023"></a>00023
<a name="l00024"></a>00024 <span class="keyword">namespace </span>boost { <span class="keyword">namespace </span>numeric { <span class="keyword">namespace </span>ublas {
<a name="l00025"></a>00025
<a name="l00031"></a>00031 <span class="keyword">template</span>&lt;<span class="keyword">class</span> T = std::<span class="keywordtype">size_t</span>, <span class="keyword">class</span> A = unbounded_array&lt;T&gt; &gt;
<a name="l00032"></a><a class="code" href="a00363.html">00032</a> <span class="keyword">class </span><a class="code" href="a00363.html">permutation_matrix</a>:
<a name="l00033"></a>00033 <span class="keyword">public</span> <a class="code" href="a00481.html" title="A dense vector of values of type T.">vector</a>&lt;T, A&gt; {
<a name="l00034"></a>00034 <span class="keyword">public</span>:
<a name="l00035"></a><a class="code" href="a00363.html#a918e3c7132db9391baac020582036771">00035</a> <span class="keyword">typedef</span> <a class="code" href="a00481.html" title="A dense vector of values of type T.">vector&lt;T, A&gt;</a> <a class="code" href="a00363.html#a918e3c7132db9391baac020582036771">vector_type</a>;
<a name="l00036"></a><a class="code" href="a00363.html#a532c3f8a21b43b78c664f857b01c7ad0">00036</a> <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="a00481.html#a738b42501164c4bf04477aeb866f2928">vector_type::size_type</a> <a class="code" href="a00363.html#a532c3f8a21b43b78c664f857b01c7ad0">size_type</a>;
<a name="l00037"></a>00037
<a name="l00038"></a>00038 <span class="comment">// Construction and destruction</span>
<a name="l00039"></a>00039 <a class="code" href="a00603.html#a578c14139742374e9a04e5afcb6cd24c">BOOST_UBLAS_INLINE</a>
<a name="l00040"></a>00040 <span class="keyword">explicit</span>
<a name="l00041"></a><a class="code" href="a00363.html#a29da30627bbc65500be69ba6489da6b9">00041</a> <a class="code" href="a00363.html#a29da30627bbc65500be69ba6489da6b9">permutation_matrix</a> (<a class="code" href="a00363.html#a532c3f8a21b43b78c664f857b01c7ad0">size_type</a> <a class="code" href="a00481.html#a1b9ef7522219d74ebd27bab25e4b6841" title="Return the size of the vector.">size</a>):
<a name="l00042"></a>00042 <a class="code" href="a00481.html" title="A dense vector of values of type T.">vector</a>&lt;T, A&gt; (size) {
<a name="l00043"></a>00043 <span class="keywordflow">for</span> (<a class="code" href="a00363.html#a532c3f8a21b43b78c664f857b01c7ad0">size_type</a> i = 0; i &lt; <a class="code" href="a00481.html#a1b9ef7522219d74ebd27bab25e4b6841" title="Return the size of the vector.">size</a>; ++ i)
<a name="l00044"></a>00044 (*<span class="keyword">this</span>) (i) = i;
<a name="l00045"></a>00045 }
<a name="l00046"></a>00046 <a class="code" href="a00603.html#a578c14139742374e9a04e5afcb6cd24c">BOOST_UBLAS_INLINE</a>
<a name="l00047"></a>00047 <span class="keyword">explicit</span>
<a name="l00048"></a><a class="code" href="a00363.html#a2745817a058634cf27528577438d8240">00048</a> <a class="code" href="a00363.html#a29da30627bbc65500be69ba6489da6b9">permutation_matrix</a> (<span class="keyword">const</span> <a class="code" href="a00481.html" title="A dense vector of values of type T.">vector_type</a> &amp; init)
<a name="l00049"></a>00049 : <a class="code" href="a00481.html" title="A dense vector of values of type T.">vector_type</a>(init)
<a name="l00050"></a>00050 { }
<a name="l00051"></a>00051 <a class="code" href="a00603.html#a578c14139742374e9a04e5afcb6cd24c">BOOST_UBLAS_INLINE</a>
<a name="l00052"></a><a class="code" href="a00363.html#a0307d13fa766e3843ed8449aaf9d55cf">00052</a> <a class="code" href="a00363.html#a0307d13fa766e3843ed8449aaf9d55cf">~permutation_matrix</a> () {}
<a name="l00053"></a>00053
<a name="l00054"></a>00054 <span class="comment">// Assignment</span>
<a name="l00055"></a>00055 <a class="code" href="a00603.html#a578c14139742374e9a04e5afcb6cd24c">BOOST_UBLAS_INLINE</a>
<a name="l00056"></a><a class="code" href="a00363.html#aa240d3636599dccd87e7c17d62e3c96f">00056</a> <a class="code" href="a00363.html">permutation_matrix</a> &amp;<a class="code" href="a00363.html#aa240d3636599dccd87e7c17d62e3c96f">operator = </a>(<span class="keyword">const</span> <a class="code" href="a00363.html">permutation_matrix</a> &amp;m) {
<a name="l00057"></a>00057 <a class="code" href="a00481.html#a1724d353e3006619a995342bc6be134e" title="Assign a full vector (RHS-vector) to the current vector (LHS-vector)">vector_type::operator = </a>(m);
<a name="l00058"></a>00058 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00059"></a>00059 }
<a name="l00060"></a>00060 };
<a name="l00061"></a>00061
<a name="l00062"></a>00062 <span class="keyword">template</span>&lt;<span class="keyword">class</span> PM, <span class="keyword">class</span> MV&gt;
<a name="l00063"></a>00063 <a class="code" href="a00603.html#a578c14139742374e9a04e5afcb6cd24c">BOOST_UBLAS_INLINE</a>
<a name="l00064"></a><a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">00064</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">swap_rows</a> (<span class="keyword">const</span> PM &amp;pm, MV &amp;mv, <a class="code" href="a00547.html">vector_tag</a>) {
<a name="l00065"></a>00065 <span class="keyword">typedef</span> <span class="keyword">typename</span> PM::size_type size_type;
<a name="l00066"></a>00066 <span class="keyword">typedef</span> <span class="keyword">typename</span> MV::value_type value_type;
<a name="l00067"></a>00067
<a name="l00068"></a>00068 size_type <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a> = pm.size ();
<a name="l00069"></a>00069 <span class="keywordflow">for</span> (size_type i = 0; i &lt; <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a>; ++ i) {
<a name="l00070"></a>00070 <span class="keywordflow">if</span> (i != pm (i))
<a name="l00071"></a>00071 <a class="code" href="a00651.html#a7359c42bdbf22249101e062d45c8fec6">std::swap</a> (mv (i), mv (pm (i)));
<a name="l00072"></a>00072 }
<a name="l00073"></a>00073 }
<a name="l00074"></a>00074 <span class="keyword">template</span>&lt;<span class="keyword">class</span> PM, <span class="keyword">class</span> MV&gt;
<a name="l00075"></a>00075 <a class="code" href="a00603.html#a578c14139742374e9a04e5afcb6cd24c">BOOST_UBLAS_INLINE</a>
<a name="l00076"></a><a class="code" href="a00595.html#a78b94f903ddf016f9dee9b735fd529a1">00076</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">swap_rows</a> (<span class="keyword">const</span> PM &amp;pm, MV &amp;mv, <a class="code" href="a00290.html">matrix_tag</a>) {
<a name="l00077"></a>00077 <span class="keyword">typedef</span> <span class="keyword">typename</span> PM::size_type size_type;
<a name="l00078"></a>00078 <span class="keyword">typedef</span> <span class="keyword">typename</span> MV::value_type value_type;
<a name="l00079"></a>00079
<a name="l00080"></a>00080 size_type <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a> = pm.size ();
<a name="l00081"></a>00081 <span class="keywordflow">for</span> (size_type i = 0; i &lt; <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a>; ++ i) {
<a name="l00082"></a>00082 <span class="keywordflow">if</span> (i != pm (i))
<a name="l00083"></a>00083 <a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (mv, i).swap (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (mv, pm (i)));
<a name="l00084"></a>00084 }
<a name="l00085"></a>00085 }
<a name="l00086"></a>00086 <span class="comment">// Dispatcher</span>
<a name="l00087"></a>00087 <span class="keyword">template</span>&lt;<span class="keyword">class</span> PM, <span class="keyword">class</span> MV&gt;
<a name="l00088"></a>00088 <a class="code" href="a00603.html#a578c14139742374e9a04e5afcb6cd24c">BOOST_UBLAS_INLINE</a>
<a name="l00089"></a><a class="code" href="a00595.html#a65c1ef5d24c4fecfed509888bbd36f6e">00089</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">swap_rows</a> (<span class="keyword">const</span> PM &amp;pm, MV &amp;mv) {
<a name="l00090"></a>00090 <a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">swap_rows</a> (pm, mv, <span class="keyword">typename</span> MV::type_category ());
<a name="l00091"></a>00091 }
<a name="l00092"></a>00092
<a name="l00093"></a>00093 <span class="comment">// LU factorization without pivoting</span>
<a name="l00094"></a>00094 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M&gt;
<a name="l00095"></a><a class="code" href="a00595.html#ab84672d39f8c6b5c759fe732edc0e31f">00095</a> <span class="keyword">typename</span> M::size_type <a class="code" href="a00595.html#ab84672d39f8c6b5c759fe732edc0e31f">lu_factorize</a> (M &amp;m) {
<a name="l00096"></a>00096 <span class="keyword">typedef</span> M matrix_type;
<a name="l00097"></a>00097 <span class="keyword">typedef</span> <span class="keyword">typename</span> M::size_type size_type;
<a name="l00098"></a>00098 <span class="keyword">typedef</span> <span class="keyword">typename</span> M::value_type value_type;
<a name="l00099"></a>00099
<a name="l00100"></a>00100 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00101"></a>00101 <span class="preprocessor"></span> matrix_type cm (m);
<a name="l00102"></a>00102 <span class="preprocessor">#endif</span>
<a name="l00103"></a>00103 <span class="preprocessor"></span> size_type <a class="code" href="a00407.html">singular</a> = 0;
<a name="l00104"></a>00104 size_type <a class="code" href="a00658.html#a979596ba6e2373d596e34c2a73809cf6">size1</a> = m.size1 ();
<a name="l00105"></a>00105 size_type <a class="code" href="a00658.html#a981c2ed31bf42bd03499d4ee32444141">size2</a> = m.size2 ();
<a name="l00106"></a>00106 size_type <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a> = (std::min) (size1, size2);
<a name="l00107"></a>00107 <span class="keywordflow">for</span> (size_type i = 0; i &lt; <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a>; ++ i) {
<a name="l00108"></a>00108 <a class="code" href="a00247.html">matrix_column&lt;M&gt;</a> mci (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (m, i));
<a name="l00109"></a>00109 <a class="code" href="a00276.html">matrix_row&lt;M&gt;</a> mri (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (m, i));
<a name="l00110"></a>00110 <span class="keywordflow">if</span> (m (i, i) != value_type<span class="comment">/*zero*/</span>()) {
<a name="l00111"></a>00111 value_type m_inv = value_type (1) / m (i, i);
<a name="l00112"></a>00112 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mci, <a class="code" href="a00001.html">range</a> (i + 1, size1)) *= m_inv;
<a name="l00113"></a>00113 } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (singular == 0) {
<a name="l00114"></a>00114 singular = i + 1;
<a name="l00115"></a>00115 }
<a name="l00116"></a>00116 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (m, <a class="code" href="a00001.html">range</a> (i + 1, size1), <a class="code" href="a00001.html">range</a> (i + 1, size2)).minus_assign (
<a name="l00117"></a>00117 <a class="code" href="a00595.html#a1ec699972aadfd0a7323cd130fca8fa3">outer_prod</a> (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mci, <a class="code" href="a00001.html">range</a> (i + 1, size1)),
<a name="l00118"></a>00118 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mri, <a class="code" href="a00001.html">range</a> (i + 1, size2))));
<a name="l00119"></a>00119 }
<a name="l00120"></a>00120 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00121"></a>00121 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (singular != 0 ||
<a name="l00122"></a>00122 <a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (<a class="code" href="a00453.html">triangular_adaptor&lt;matrix_type, unit_lower&gt;</a> (m),
<a name="l00123"></a>00123 <a class="code" href="a00453.html">triangular_adaptor&lt;matrix_type, upper&gt;</a> (m)),
<a name="l00124"></a>00124 cm), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00125"></a>00125 <span class="preprocessor">#endif</span>
<a name="l00126"></a>00126 <span class="preprocessor"></span> <span class="keywordflow">return</span> singular;
<a name="l00127"></a>00127 }
<a name="l00128"></a>00128
<a name="l00129"></a>00129 <span class="comment">// LU factorization with partial pivoting</span>
<a name="l00130"></a>00130 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> PM&gt;
<a name="l00131"></a><a class="code" href="a00595.html#a1f84fd06cf633165ae26000345d104eb">00131</a> <span class="keyword">typename</span> M::size_type <a class="code" href="a00595.html#ab84672d39f8c6b5c759fe732edc0e31f">lu_factorize</a> (M &amp;m, PM &amp;pm) {
<a name="l00132"></a>00132 <span class="keyword">typedef</span> M matrix_type;
<a name="l00133"></a>00133 <span class="keyword">typedef</span> <span class="keyword">typename</span> M::size_type size_type;
<a name="l00134"></a>00134 <span class="keyword">typedef</span> <span class="keyword">typename</span> M::value_type value_type;
<a name="l00135"></a>00135
<a name="l00136"></a>00136 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00137"></a>00137 <span class="preprocessor"></span> matrix_type cm (m);
<a name="l00138"></a>00138 <span class="preprocessor">#endif</span>
<a name="l00139"></a>00139 <span class="preprocessor"></span> size_type <a class="code" href="a00407.html">singular</a> = 0;
<a name="l00140"></a>00140 size_type <a class="code" href="a00658.html#a979596ba6e2373d596e34c2a73809cf6">size1</a> = m.size1 ();
<a name="l00141"></a>00141 size_type <a class="code" href="a00658.html#a981c2ed31bf42bd03499d4ee32444141">size2</a> = m.size2 ();
<a name="l00142"></a>00142 size_type <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a> = (std::min) (size1, size2);
<a name="l00143"></a>00143 <span class="keywordflow">for</span> (size_type i = 0; i &lt; <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a>; ++ i) {
<a name="l00144"></a>00144 <a class="code" href="a00247.html">matrix_column&lt;M&gt;</a> mci (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (m, i));
<a name="l00145"></a>00145 <a class="code" href="a00276.html">matrix_row&lt;M&gt;</a> mri (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (m, i));
<a name="l00146"></a>00146 size_type i_norm_inf = i + <a class="code" href="a00595.html#a86ddb4076691133a54d03bfc2dbca1d0">index_norm_inf</a> (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mci, <a class="code" href="a00001.html">range</a> (i, size1)));
<a name="l00147"></a>00147 <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (i_norm_inf &lt; size1, <a class="code" href="a00132.html">external_logic</a> ());
<a name="l00148"></a>00148 <span class="keywordflow">if</span> (m (i_norm_inf, i) != value_type<span class="comment">/*zero*/</span>()) {
<a name="l00149"></a>00149 <span class="keywordflow">if</span> (i_norm_inf != i) {
<a name="l00150"></a>00150 pm (i) = i_norm_inf;
<a name="l00151"></a>00151 <a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (m, i_norm_inf).swap (mri);
<a name="l00152"></a>00152 } <span class="keywordflow">else</span> {
<a name="l00153"></a>00153 <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (pm (i) == i_norm_inf, <a class="code" href="a00132.html">external_logic</a> ());
<a name="l00154"></a>00154 }
<a name="l00155"></a>00155 value_type m_inv = value_type (1) / m (i, i);
<a name="l00156"></a>00156 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mci, <a class="code" href="a00001.html">range</a> (i + 1, size1)) *= m_inv;
<a name="l00157"></a>00157 } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (singular == 0) {
<a name="l00158"></a>00158 singular = i + 1;
<a name="l00159"></a>00159 }
<a name="l00160"></a>00160 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (m, <a class="code" href="a00001.html">range</a> (i + 1, size1), <a class="code" href="a00001.html">range</a> (i + 1, size2)).minus_assign (
<a name="l00161"></a>00161 <a class="code" href="a00595.html#a1ec699972aadfd0a7323cd130fca8fa3">outer_prod</a> (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mci, <a class="code" href="a00001.html">range</a> (i + 1, size1)),
<a name="l00162"></a>00162 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mri, <a class="code" href="a00001.html">range</a> (i + 1, size2))));
<a name="l00163"></a>00163 }
<a name="l00164"></a>00164 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00165"></a>00165 <span class="preprocessor"></span> <a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">swap_rows</a> (pm, cm);
<a name="l00166"></a>00166 <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (singular != 0 ||
<a name="l00167"></a>00167 <a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (<a class="code" href="a00453.html">triangular_adaptor&lt;matrix_type, unit_lower&gt;</a> (m),
<a name="l00168"></a>00168 <a class="code" href="a00453.html">triangular_adaptor&lt;matrix_type, upper&gt;</a> (m)), cm), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00169"></a>00169 <span class="preprocessor">#endif</span>
<a name="l00170"></a>00170 <span class="preprocessor"></span> <span class="keywordflow">return</span> singular;
<a name="l00171"></a>00171 }
<a name="l00172"></a>00172
<a name="l00173"></a>00173 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> PM&gt;
<a name="l00174"></a><a class="code" href="a00595.html#af7c3251ed329652ad3967405d28690e2">00174</a> <span class="keyword">typename</span> M::size_type <a class="code" href="a00595.html#af7c3251ed329652ad3967405d28690e2">axpy_lu_factorize</a> (M &amp;m, PM &amp;pm) {
<a name="l00175"></a>00175 <span class="keyword">typedef</span> M matrix_type;
<a name="l00176"></a>00176 <span class="keyword">typedef</span> <span class="keyword">typename</span> M::size_type size_type;
<a name="l00177"></a>00177 <span class="keyword">typedef</span> <span class="keyword">typename</span> M::value_type value_type;
<a name="l00178"></a>00178 <span class="keyword">typedef</span> <a class="code" href="a00481.html" title="A dense vector of values of type T.">vector&lt;value_type&gt;</a> vector_type;
<a name="l00179"></a>00179
<a name="l00180"></a>00180 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00181"></a>00181 <span class="preprocessor"></span> matrix_type cm (m);
<a name="l00182"></a>00182 <span class="preprocessor">#endif</span>
<a name="l00183"></a>00183 <span class="preprocessor"></span> size_type <a class="code" href="a00407.html">singular</a> = 0;
<a name="l00184"></a>00184 size_type <a class="code" href="a00658.html#a979596ba6e2373d596e34c2a73809cf6">size1</a> = m.size1 ();
<a name="l00185"></a>00185 size_type <a class="code" href="a00658.html#a981c2ed31bf42bd03499d4ee32444141">size2</a> = m.size2 ();
<a name="l00186"></a>00186 size_type <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a> = (std::min) (size1, size2);
<a name="l00187"></a>00187 <span class="preprocessor">#ifndef BOOST_UBLAS_LU_WITH_INPLACE_SOLVE</span>
<a name="l00188"></a>00188 <span class="preprocessor"></span> matrix_type mr (m);
<a name="l00189"></a>00189 mr.assign (<a class="code" href="a00587.html" title="A matrix with all values of type T equal to zero.">zero_matrix&lt;value_type&gt;</a> (size1, size2));
<a name="l00190"></a>00190 vector_type v (size1);
<a name="l00191"></a>00191 <span class="keywordflow">for</span> (size_type i = 0; i &lt; <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a>; ++ i) {
<a name="l00192"></a>00192 <a class="code" href="a00270.html">matrix_range&lt;matrix_type&gt;</a> lrr (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mr, <a class="code" href="a00001.html">range</a> (0, i), <a class="code" href="a00001.html">range</a> (0, i)));
<a name="l00193"></a>00193 <a class="code" href="a00528.html" title="A vector referencing a continuous subvector of elements of vector v containing all elements specified...">vector_range&lt;matrix_column&lt;matrix_type&gt;</a> &gt; urr (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (mr, i), <a class="code" href="a00001.html">range</a> (0, i)));
<a name="l00194"></a>00194 urr.<a class="code" href="a00528.html#a8c9035097ac15f67bc3c543fe162f40a">assign</a> (<a class="code" href="a00595.html#a8377d6eca1abae4087e4d5c085f2cef7">solve</a> (lrr, <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (m, i), <a class="code" href="a00001.html">range</a> (0, i)), <a class="code" href="a00474.html">unit_lower_tag</a> ()));
<a name="l00195"></a>00195 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (v, <a class="code" href="a00001.html">range</a> (i, size1)).assign (
<a name="l00196"></a>00196 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (m, i), <a class="code" href="a00001.html">range</a> (i, size1)) -
<a name="l00197"></a>00197 axpy_prod&lt;vector_type&gt; (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (mr, <a class="code" href="a00001.html">range</a> (i, size1), <a class="code" href="a00001.html">range</a> (0, i)), urr));
<a name="l00198"></a>00198 size_type i_norm_inf = i + <a class="code" href="a00595.html#a86ddb4076691133a54d03bfc2dbca1d0">index_norm_inf</a> (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (v, <a class="code" href="a00001.html">range</a> (i, size1)));
<a name="l00199"></a>00199 <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (i_norm_inf &lt; size1, <a class="code" href="a00132.html">external_logic</a> ());
<a name="l00200"></a>00200 <span class="keywordflow">if</span> (v (i_norm_inf) != value_type<span class="comment">/*zero*/</span>()) {
<a name="l00201"></a>00201 <span class="keywordflow">if</span> (i_norm_inf != i) {
<a name="l00202"></a>00202 pm (i) = i_norm_inf;
<a name="l00203"></a>00203 <a class="code" href="a00651.html#a7359c42bdbf22249101e062d45c8fec6">std::swap</a> (v (i_norm_inf), v (i));
<a name="l00204"></a>00204 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (m, i_norm_inf), <a class="code" href="a00001.html">range</a> (i + 1, size2)).swap (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (m, i), <a class="code" href="a00001.html">range</a> (i + 1, size2)));
<a name="l00205"></a>00205 } <span class="keywordflow">else</span> {
<a name="l00206"></a>00206 <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (pm (i) == i_norm_inf, <a class="code" href="a00132.html">external_logic</a> ());
<a name="l00207"></a>00207 }
<a name="l00208"></a>00208 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (mr, i), <a class="code" href="a00001.html">range</a> (i + 1, size1)).assign (
<a name="l00209"></a>00209 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (v, <a class="code" href="a00001.html">range</a> (i + 1, size1)) / v (i));
<a name="l00210"></a>00210 <span class="keywordflow">if</span> (i_norm_inf != i) {
<a name="l00211"></a>00211 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (mr, i_norm_inf), <a class="code" href="a00001.html">range</a> (0, i)).swap (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (mr, i), <a class="code" href="a00001.html">range</a> (0, i)));
<a name="l00212"></a>00212 }
<a name="l00213"></a>00213 } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (singular == 0) {
<a name="l00214"></a>00214 singular = i + 1;
<a name="l00215"></a>00215 }
<a name="l00216"></a>00216 mr (i, i) = v (i);
<a name="l00217"></a>00217 }
<a name="l00218"></a>00218 m.assign (mr);
<a name="l00219"></a>00219 <span class="preprocessor">#else</span>
<a name="l00220"></a>00220 <span class="preprocessor"></span> matrix_type lr (m);
<a name="l00221"></a>00221 matrix_type ur (m);
<a name="l00222"></a>00222 lr.assign (<a class="code" href="a00155.html" title="An identity matrix with values of type T.">identity_matrix&lt;value_type&gt;</a> (size1, size2));
<a name="l00223"></a>00223 ur.assign (<a class="code" href="a00587.html" title="A matrix with all values of type T equal to zero.">zero_matrix&lt;value_type&gt;</a> (size1, size2));
<a name="l00224"></a>00224 vector_type v (size1);
<a name="l00225"></a>00225 <span class="keywordflow">for</span> (size_type i = 0; i &lt; <a class="code" href="a00595.html#a21019ef1d90c1854094dffa247fe1daf" title="Return the number of columns.">size</a>; ++ i) {
<a name="l00226"></a>00226 <a class="code" href="a00270.html">matrix_range&lt;matrix_type&gt;</a> lrr (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (lr, <a class="code" href="a00001.html">range</a> (0, i), <a class="code" href="a00001.html">range</a> (0, i)));
<a name="l00227"></a>00227 <a class="code" href="a00528.html" title="A vector referencing a continuous subvector of elements of vector v containing all elements specified...">vector_range&lt;matrix_column&lt;matrix_type&gt;</a> &gt; urr (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (ur, i), <a class="code" href="a00001.html">range</a> (0, i)));
<a name="l00228"></a>00228 urr.<a class="code" href="a00528.html#a8c9035097ac15f67bc3c543fe162f40a">assign</a> (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (m, i), <a class="code" href="a00001.html">range</a> (0, i)));
<a name="l00229"></a>00229 <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (lrr, urr, <a class="code" href="a00474.html">unit_lower_tag</a> ());
<a name="l00230"></a>00230 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (v, <a class="code" href="a00001.html">range</a> (i, size1)).assign (
<a name="l00231"></a>00231 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (m, i), <a class="code" href="a00001.html">range</a> (i, size1)) -
<a name="l00232"></a>00232 axpy_prod&lt;vector_type&gt; (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (lr, <a class="code" href="a00001.html">range</a> (i, size1), <a class="code" href="a00001.html">range</a> (0, i)), urr));
<a name="l00233"></a>00233 size_type i_norm_inf = i + <a class="code" href="a00595.html#a86ddb4076691133a54d03bfc2dbca1d0">index_norm_inf</a> (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (v, <a class="code" href="a00001.html">range</a> (i, size1)));
<a name="l00234"></a>00234 <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (i_norm_inf &lt; size1, <a class="code" href="a00132.html">external_logic</a> ());
<a name="l00235"></a>00235 <span class="keywordflow">if</span> (v (i_norm_inf) != value_type<span class="comment">/*zero*/</span>()) {
<a name="l00236"></a>00236 <span class="keywordflow">if</span> (i_norm_inf != i) {
<a name="l00237"></a>00237 pm (i) = i_norm_inf;
<a name="l00238"></a>00238 <a class="code" href="a00651.html#a7359c42bdbf22249101e062d45c8fec6">std::swap</a> (v (i_norm_inf), v (i));
<a name="l00239"></a>00239 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (m, i_norm_inf), <a class="code" href="a00001.html">range</a> (i + 1, size2)).swap (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (m, i), <a class="code" href="a00001.html">range</a> (i + 1, size2)));
<a name="l00240"></a>00240 } <span class="keywordflow">else</span> {
<a name="l00241"></a>00241 <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (pm (i) == i_norm_inf, <a class="code" href="a00132.html">external_logic</a> ());
<a name="l00242"></a>00242 }
<a name="l00243"></a>00243 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#a401950b707ff8a1209616085404065c8">column</a> (lr, i), <a class="code" href="a00001.html">range</a> (i + 1, size1)).assign (
<a name="l00244"></a>00244 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (v, <a class="code" href="a00001.html">range</a> (i + 1, size1)) / v (i));
<a name="l00245"></a>00245 <span class="keywordflow">if</span> (i_norm_inf != i) {
<a name="l00246"></a>00246 <a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (lr, i_norm_inf), <a class="code" href="a00001.html">range</a> (0, i)).swap (<a class="code" href="a00595.html#a4725b73798dad3ab53e7a4f4fdd964fb">project</a> (<a class="code" href="a00595.html#af8da104f49e2652e2c036c431dec2879">row</a> (lr, i), <a class="code" href="a00001.html">range</a> (0, i)));
<a name="l00247"></a>00247 }
<a name="l00248"></a>00248 } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (singular == 0) {
<a name="l00249"></a>00249 singular = i + 1;
<a name="l00250"></a>00250 }
<a name="l00251"></a>00251 ur (i, i) = v (i);
<a name="l00252"></a>00252 }
<a name="l00253"></a>00253 m.assign (<a class="code" href="a00453.html">triangular_adaptor&lt;matrix_type, strict_lower&gt;</a> (lr) +
<a name="l00254"></a>00254 <a class="code" href="a00453.html">triangular_adaptor&lt;matrix_type, upper&gt;</a> (ur));
<a name="l00255"></a>00255 <span class="preprocessor">#endif</span>
<a name="l00256"></a>00256 <span class="preprocessor"></span><span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00257"></a>00257 <span class="preprocessor"></span> <a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">swap_rows</a> (pm, cm);
<a name="l00258"></a>00258 <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (singular != 0 ||
<a name="l00259"></a>00259 <a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (<a class="code" href="a00453.html">triangular_adaptor&lt;matrix_type, unit_lower&gt;</a> (m),
<a name="l00260"></a>00260 <a class="code" href="a00453.html">triangular_adaptor&lt;matrix_type, upper&gt;</a> (m)), cm), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00261"></a>00261 <span class="preprocessor">#endif</span>
<a name="l00262"></a>00262 <span class="preprocessor"></span> <span class="keywordflow">return</span> singular;
<a name="l00263"></a>00263 }
<a name="l00264"></a>00264
<a name="l00265"></a>00265 <span class="comment">// LU substitution</span>
<a name="l00266"></a>00266 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> E&gt;
<a name="l00267"></a><a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">00267</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">lu_substitute</a> (<span class="keyword">const</span> M &amp;m, <a class="code" href="a00507.html" title="Base class for Vector Expression models.">vector_expression&lt;E&gt;</a> &amp;e) {
<a name="l00268"></a>00268 <span class="keyword">typedef</span> <span class="keyword">const</span> M const_matrix_type;
<a name="l00269"></a>00269 <span class="keyword">typedef</span> <a class="code" href="a00481.html" title="A dense vector of values of type T.">vector&lt;typename E::value_type&gt;</a> vector_type;
<a name="l00270"></a>00270
<a name="l00271"></a>00271 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00272"></a>00272 <span class="preprocessor"></span> vector_type cv1 (e);
<a name="l00273"></a>00273 <span class="preprocessor">#endif</span>
<a name="l00274"></a>00274 <span class="preprocessor"></span> <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (m, e, <a class="code" href="a00474.html">unit_lower_tag</a> ());
<a name="l00275"></a>00275 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00276"></a>00276 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (<a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (<a class="code" href="a00453.html">triangular_adaptor&lt;const_matrix_type, unit_lower&gt;</a> (m), e), cv1), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00277"></a>00277 vector_type cv2 (e);
<a name="l00278"></a>00278 <span class="preprocessor">#endif</span>
<a name="l00279"></a>00279 <span class="preprocessor"></span> <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (m, e, <a class="code" href="a00480.html">upper_tag</a> ());
<a name="l00280"></a>00280 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00281"></a>00281 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (<a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (<a class="code" href="a00453.html">triangular_adaptor&lt;const_matrix_type, upper&gt;</a> (m), e), cv2), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00282"></a>00282 <span class="preprocessor">#endif</span>
<a name="l00283"></a>00283 <span class="preprocessor"></span> }
<a name="l00284"></a>00284 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> E&gt;
<a name="l00285"></a><a class="code" href="a00595.html#a0844146d84d0fb875544262ae2bd43ac">00285</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">lu_substitute</a> (<span class="keyword">const</span> M &amp;m, <a class="code" href="a00251.html" title="Base class for Matrix Expression models.">matrix_expression&lt;E&gt;</a> &amp;e) {
<a name="l00286"></a>00286 <span class="keyword">typedef</span> <span class="keyword">const</span> M const_matrix_type;
<a name="l00287"></a>00287 <span class="keyword">typedef</span> <a class="code" href="a00218.html" title="A dense matrix of values of type T.">matrix&lt;typename E::value_type&gt;</a> matrix_type;
<a name="l00288"></a>00288
<a name="l00289"></a>00289 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00290"></a>00290 <span class="preprocessor"></span> matrix_type cm1 (e);
<a name="l00291"></a>00291 <span class="preprocessor">#endif</span>
<a name="l00292"></a>00292 <span class="preprocessor"></span> <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (m, e, <a class="code" href="a00474.html">unit_lower_tag</a> ());
<a name="l00293"></a>00293 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00294"></a>00294 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (<a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (<a class="code" href="a00453.html">triangular_adaptor&lt;const_matrix_type, unit_lower&gt;</a> (m), e), cm1), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00295"></a>00295 matrix_type cm2 (e);
<a name="l00296"></a>00296 <span class="preprocessor">#endif</span>
<a name="l00297"></a>00297 <span class="preprocessor"></span> <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (m, e, <a class="code" href="a00480.html">upper_tag</a> ());
<a name="l00298"></a>00298 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00299"></a>00299 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (<a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (<a class="code" href="a00453.html">triangular_adaptor&lt;const_matrix_type, upper&gt;</a> (m), e), cm2), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00300"></a>00300 <span class="preprocessor">#endif</span>
<a name="l00301"></a>00301 <span class="preprocessor"></span> }
<a name="l00302"></a>00302 <span class="keyword">template</span>&lt;<span class="keyword">class</span> M, <span class="keyword">class</span> PMT, <span class="keyword">class</span> PMA, <span class="keyword">class</span> MV&gt;
<a name="l00303"></a><a class="code" href="a00595.html#a682301a5b24de966ad16f2bacf2f87b6">00303</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">lu_substitute</a> (<span class="keyword">const</span> M &amp;m, <span class="keyword">const</span> <a class="code" href="a00363.html">permutation_matrix&lt;PMT, PMA&gt;</a> &amp;pm, MV &amp;mv) {
<a name="l00304"></a>00304 <a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">swap_rows</a> (pm, mv);
<a name="l00305"></a>00305 <a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">lu_substitute</a> (m, mv);
<a name="l00306"></a>00306 }
<a name="l00307"></a>00307 <span class="keyword">template</span>&lt;<span class="keyword">class</span> E, <span class="keyword">class</span> M&gt;
<a name="l00308"></a><a class="code" href="a00595.html#ac551bcf3348225974ed9ad405a23e278">00308</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">lu_substitute</a> (<a class="code" href="a00507.html" title="Base class for Vector Expression models.">vector_expression&lt;E&gt;</a> &amp;e, <span class="keyword">const</span> M &amp;m) {
<a name="l00309"></a>00309 <span class="keyword">typedef</span> <span class="keyword">const</span> M const_matrix_type;
<a name="l00310"></a>00310 <span class="keyword">typedef</span> <a class="code" href="a00481.html" title="A dense vector of values of type T.">vector&lt;typename E::value_type&gt;</a> vector_type;
<a name="l00311"></a>00311
<a name="l00312"></a>00312 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00313"></a>00313 <span class="preprocessor"></span> vector_type cv1 (e);
<a name="l00314"></a>00314 <span class="preprocessor">#endif</span>
<a name="l00315"></a>00315 <span class="preprocessor"></span> <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (e, m, <a class="code" href="a00480.html">upper_tag</a> ());
<a name="l00316"></a>00316 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00317"></a>00317 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (<a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (e, <a class="code" href="a00453.html">triangular_adaptor&lt;const_matrix_type, upper&gt;</a> (m)), cv1), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00318"></a>00318 vector_type cv2 (e);
<a name="l00319"></a>00319 <span class="preprocessor">#endif</span>
<a name="l00320"></a>00320 <span class="preprocessor"></span> <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (e, m, <a class="code" href="a00474.html">unit_lower_tag</a> ());
<a name="l00321"></a>00321 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00322"></a>00322 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (<a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (e, <a class="code" href="a00453.html">triangular_adaptor&lt;const_matrix_type, unit_lower&gt;</a> (m)), cv2), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00323"></a>00323 <span class="preprocessor">#endif</span>
<a name="l00324"></a>00324 <span class="preprocessor"></span> }
<a name="l00325"></a>00325 <span class="keyword">template</span>&lt;<span class="keyword">class</span> E, <span class="keyword">class</span> M&gt;
<a name="l00326"></a><a class="code" href="a00595.html#a973c1c142d05b5c1dcf996d965f83130">00326</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">lu_substitute</a> (<a class="code" href="a00251.html" title="Base class for Matrix Expression models.">matrix_expression&lt;E&gt;</a> &amp;e, <span class="keyword">const</span> M &amp;m) {
<a name="l00327"></a>00327 <span class="keyword">typedef</span> <span class="keyword">const</span> M const_matrix_type;
<a name="l00328"></a>00328 <span class="keyword">typedef</span> <a class="code" href="a00218.html" title="A dense matrix of values of type T.">matrix&lt;typename E::value_type&gt;</a> matrix_type;
<a name="l00329"></a>00329
<a name="l00330"></a>00330 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00331"></a>00331 <span class="preprocessor"></span> matrix_type cm1 (e);
<a name="l00332"></a>00332 <span class="preprocessor">#endif</span>
<a name="l00333"></a>00333 <span class="preprocessor"></span> <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (e, m, <a class="code" href="a00480.html">upper_tag</a> ());
<a name="l00334"></a>00334 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00335"></a>00335 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (<a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (e, <a class="code" href="a00453.html">triangular_adaptor&lt;const_matrix_type, upper&gt;</a> (m)), cm1), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00336"></a>00336 matrix_type cm2 (e);
<a name="l00337"></a>00337 <span class="preprocessor">#endif</span>
<a name="l00338"></a>00338 <span class="preprocessor"></span> <a class="code" href="a00595.html#a698df21f7016a3bc612c952018264179">inplace_solve</a> (e, m, <a class="code" href="a00474.html">unit_lower_tag</a> ());
<a name="l00339"></a>00339 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00340"></a>00340 <span class="preprocessor"></span> <a class="code" href="a00610.html#aada705f9d1fd36fc1af3b703217ec69e">BOOST_UBLAS_CHECK</a> (<a class="code" href="a00653.html#a43a1eab42456d66c868af16c340e8246">detail::expression_type_check</a> (<a class="code" href="a00595.html#a80a491b0d654ad0d661a7ed3b272db88">prod</a> (e, <a class="code" href="a00453.html">triangular_adaptor&lt;const_matrix_type, unit_lower&gt;</a> (m)), cm2), <a class="code" href="a00178.html" title="Expception raised when some interal errors occurs like computations errors, zeros values where you sh...">internal_logic</a> ());
<a name="l00341"></a>00341 <span class="preprocessor">#endif</span>
<a name="l00342"></a>00342 <span class="preprocessor"></span> }
<a name="l00343"></a>00343 <span class="keyword">template</span>&lt;<span class="keyword">class</span> MV, <span class="keyword">class</span> M, <span class="keyword">class</span> PMT, <span class="keyword">class</span> PMA&gt;
<a name="l00344"></a><a class="code" href="a00595.html#a5ab8456644f59cfe4fb9b51390120820">00344</a> <span class="keywordtype">void</span> <a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">lu_substitute</a> (MV &amp;mv, <span class="keyword">const</span> M &amp;m, <span class="keyword">const</span> <a class="code" href="a00363.html">permutation_matrix&lt;PMT, PMA&gt;</a> &amp;pm) {
<a name="l00345"></a>00345 <a class="code" href="a00595.html#a9c80cd7830f001e9d7116317f0d1a888">swap_rows</a> (pm, mv);
<a name="l00346"></a>00346 <a class="code" href="a00595.html#aa175eceb7973bfe8ced6f92fe566a2be">lu_substitute</a> (mv, m);
<a name="l00347"></a>00347 }
<a name="l00348"></a>00348
<a name="l00349"></a>00349 }}}
<a name="l00350"></a>00350
<a name="l00351"></a>00351 <span class="preprocessor">#endif</span>
</pre></div></div>
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