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<h1>lu.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 & 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 <boost/numeric/ublas/operation.hpp></span>
<a name="l00017"></a>00017 <span class="preprocessor">#include <boost/numeric/ublas/vector_proxy.hpp></span>
<a name="l00018"></a>00018 <span class="preprocessor">#include <boost/numeric/ublas/matrix_proxy.hpp></span>
<a name="l00019"></a>00019 <span class="preprocessor">#include <boost/numeric/ublas/vector.hpp></span>
<a name="l00020"></a>00020 <span class="preprocessor">#include <boost/numeric/ublas/triangular.hpp></span>
<a name="l00021"></a>00021
<a name="l00022"></a>00022 <span class="comment">// LU factorizations in the spirit of LAPACK and Golub & 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><<span class="keyword">class</span> T = std::<span class="keywordtype">size_t</span>, <span class="keyword">class</span> A = unbounded_array<T> >
<a name="l00032"></a><a class="code" href="classboost_1_1numeric_1_1ublas_1_1permutation__matrix.html">00032</a> <span class="keyword">class </span><a class="code" href="classboost_1_1numeric_1_1ublas_1_1permutation__matrix.html">permutation_matrix</a>:
<a name="l00033"></a>00033 <span class="keyword">public</span> <a class="code" href="classboost_1_1numeric_1_1ublas_1_1vector.html" title="A dense vector of values of type T.">vector</a><T, A> {
<a name="l00034"></a>00034 <span class="keyword">public</span>:
<a name="l00035"></a>00035 <span class="keyword">typedef</span> <a class="code" href="classboost_1_1numeric_1_1ublas_1_1vector.html" title="A dense vector of values of type T.">vector<T, A></a> <a class="code" href="classboost_1_1numeric_1_1ublas_1_1vector.html" title="A dense vector of values of type T.">vector_type</a>;
<a name="l00036"></a>00036 <span class="keyword">typedef</span> <span class="keyword">typename</span> vector_type::size_type size_type;
<a name="l00037"></a>00037
<a name="l00038"></a>00038 <span class="comment">// Construction and destruction</span>
<a name="l00039"></a>00039 BOOST_UBLAS_INLINE
<a name="l00040"></a>00040 <span class="keyword">explicit</span>
<a name="l00041"></a>00041 <a class="code" href="classboost_1_1numeric_1_1ublas_1_1permutation__matrix.html">permutation_matrix</a> (size_type <a class="code" href="classboost_1_1numeric_1_1ublas_1_1vector.html#a1b9ef7522219d74ebd27bab25e4b6841" title="Return the size of the vector.">size</a>):
<a name="l00042"></a>00042 <a class="code" href="classboost_1_1numeric_1_1ublas_1_1vector.html" title="A dense vector of values of type T.">vector<T, A></a> (size) {
<a name="l00043"></a>00043 <span class="keywordflow">for</span> (size_type i = 0; i < size; ++ i)
<a name="l00044"></a>00044 (*<span class="keyword">this</span>) (i) = i;
<a name="l00045"></a>00045 }
<a name="l00046"></a>00046 BOOST_UBLAS_INLINE
<a name="l00047"></a>00047 <span class="keyword">explicit</span>
<a name="l00048"></a>00048 permutation_matrix (<span class="keyword">const</span> <a class="code" href="classboost_1_1numeric_1_1ublas_1_1vector.html" title="A dense vector of values of type T.">vector_type</a> & init)
<a name="l00049"></a>00049 : <a class="code" href="classboost_1_1numeric_1_1ublas_1_1vector.html" title="A dense vector of values of type T.">vector_type</a>(init)
<a name="l00050"></a>00050 { }
<a name="l00051"></a>00051 BOOST_UBLAS_INLINE
<a name="l00052"></a>00052 ~permutation_matrix () {}
<a name="l00053"></a>00053
<a name="l00054"></a>00054 <span class="comment">// Assignment</span>
<a name="l00055"></a>00055 BOOST_UBLAS_INLINE
<a name="l00056"></a><a class="code" href="classboost_1_1numeric_1_1ublas_1_1permutation__matrix.html#aa240d3636599dccd87e7c17d62e3c96f">00056</a> permutation_matrix &<a class="code" href="classboost_1_1numeric_1_1ublas_1_1permutation__matrix.html#aa240d3636599dccd87e7c17d62e3c96f" title="Assign a full vector (RHS-vector) to the current vector (LHS-vector).">operator = </a>(<span class="keyword">const</span> permutation_matrix &m) {
<a name="l00057"></a>00057 <a class="code" href="classboost_1_1numeric_1_1ublas_1_1vector.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><<span class="keyword">class</span> PM, <span class="keyword">class</span> MV>
<a name="l00063"></a>00063 BOOST_UBLAS_INLINE
<a name="l00064"></a>00064 <span class="keywordtype">void</span> swap_rows (<span class="keyword">const</span> PM &pm, MV &mv, vector_tag) {
<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 size = pm.size ();
<a name="l00069"></a>00069 <span class="keywordflow">for</span> (size_type i = 0; i < size; ++ i) {
<a name="l00070"></a>00070 <span class="keywordflow">if</span> (i != pm (i))
<a name="l00071"></a>00071 std::swap (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><<span class="keyword">class</span> PM, <span class="keyword">class</span> MV>
<a name="l00075"></a>00075 BOOST_UBLAS_INLINE
<a name="l00076"></a>00076 <span class="keywordtype">void</span> swap_rows (<span class="keyword">const</span> PM &pm, MV &mv, matrix_tag) {
<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 size = pm.size ();
<a name="l00081"></a>00081 <span class="keywordflow">for</span> (size_type i = 0; i < size; ++ i) {
<a name="l00082"></a>00082 <span class="keywordflow">if</span> (i != pm (i))
<a name="l00083"></a>00083 row (mv, i).swap (row (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><<span class="keyword">class</span> PM, <span class="keyword">class</span> MV>
<a name="l00088"></a>00088 BOOST_UBLAS_INLINE
<a name="l00089"></a>00089 <span class="keywordtype">void</span> swap_rows (<span class="keyword">const</span> PM &pm, MV &mv) {
<a name="l00090"></a>00090 swap_rows (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><<span class="keyword">class</span> M>
<a name="l00095"></a>00095 <span class="keyword">typename</span> M::size_type lu_factorize (M &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 singular = 0;
<a name="l00104"></a>00104 size_type size1 = m.size1 ();
<a name="l00105"></a>00105 size_type size2 = m.size2 ();
<a name="l00106"></a>00106 size_type size = (std::min) (size1, size2);
<a name="l00107"></a>00107 <span class="keywordflow">for</span> (size_type i = 0; i < size; ++ i) {
<a name="l00108"></a>00108 matrix_column<M> mci (column (m, i));
<a name="l00109"></a>00109 matrix_row<M> mri (row (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 project (mci, range (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 project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign (
<a name="l00117"></a>00117 outer_prod (project (mci, range (i + 1, size1)),
<a name="l00118"></a>00118 project (mri, range (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> BOOST_UBLAS_CHECK (singular != 0 ||
<a name="l00122"></a>00122 detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
<a name="l00123"></a>00123 triangular_adaptor<matrix_type, upper> (m)),
<a name="l00124"></a>00124 cm), internal_logic ());
<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><<span class="keyword">class</span> M, <span class="keyword">class</span> PM>
<a name="l00131"></a>00131 <span class="keyword">typename</span> M::size_type lu_factorize (M &m, PM &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 singular = 0;
<a name="l00140"></a>00140 size_type size1 = m.size1 ();
<a name="l00141"></a>00141 size_type size2 = m.size2 ();
<a name="l00142"></a>00142 size_type size = (std::min) (size1, size2);
<a name="l00143"></a>00143 <span class="keywordflow">for</span> (size_type i = 0; i < size; ++ i) {
<a name="l00144"></a>00144 matrix_column<M> mci (column (m, i));
<a name="l00145"></a>00145 matrix_row<M> mri (row (m, i));
<a name="l00146"></a>00146 size_type i_norm_inf = i + index_norm_inf (project (mci, range (i, size1)));
<a name="l00147"></a>00147 BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
<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 row (m, i_norm_inf).swap (mri);
<a name="l00152"></a>00152 } <span class="keywordflow">else</span> {
<a name="l00153"></a>00153 BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
<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 project (mci, range (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 project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign (
<a name="l00161"></a>00161 outer_prod (project (mci, range (i + 1, size1)),
<a name="l00162"></a>00162 project (mri, range (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> swap_rows (pm, cm);
<a name="l00166"></a>00166 BOOST_UBLAS_CHECK (singular != 0 ||
<a name="l00167"></a>00167 detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
<a name="l00168"></a>00168 triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ());
<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><<span class="keyword">class</span> M, <span class="keyword">class</span> PM>
<a name="l00174"></a>00174 <span class="keyword">typename</span> M::size_type axpy_lu_factorize (M &m, PM &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> vector<value_type> 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 singular = 0;
<a name="l00184"></a>00184 size_type size1 = m.size1 ();
<a name="l00185"></a>00185 size_type size2 = m.size2 ();
<a name="l00186"></a>00186 size_type size = (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 (zero_matrix<value_type> (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 < size; ++ i) {
<a name="l00192"></a>00192 matrix_range<matrix_type> lrr (project (mr, range (0, i), range (0, i)));
<a name="l00193"></a>00193 vector_range<matrix_column<matrix_type> > urr (project (column (mr, i), range (0, i)));
<a name="l00194"></a>00194 urr.assign (solve (lrr, project (column (m, i), range (0, i)), unit_lower_tag ()));
<a name="l00195"></a>00195 project (v, range (i, size1)).assign (
<a name="l00196"></a>00196 project (column (m, i), range (i, size1)) -
<a name="l00197"></a>00197 axpy_prod<vector_type> (project (mr, range (i, size1), range (0, i)), urr));
<a name="l00198"></a>00198 size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1)));
<a name="l00199"></a>00199 BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
<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 std::swap (v (i_norm_inf), v (i));
<a name="l00204"></a>00204 project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2)));
<a name="l00205"></a>00205 } <span class="keywordflow">else</span> {
<a name="l00206"></a>00206 BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
<a name="l00207"></a>00207 }
<a name="l00208"></a>00208 project (column (mr, i), range (i + 1, size1)).assign (
<a name="l00209"></a>00209 project (v, range (i + 1, size1)) / v (i));
<a name="l00210"></a>00210 <span class="keywordflow">if</span> (i_norm_inf != i) {
<a name="l00211"></a>00211 project (row (mr, i_norm_inf), range (0, i)).swap (project (row (mr, i), range (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 (identity_matrix<value_type> (size1, size2));
<a name="l00223"></a>00223 ur.assign (zero_matrix<value_type> (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 < size; ++ i) {
<a name="l00226"></a>00226 matrix_range<matrix_type> lrr (project (lr, range (0, i), range (0, i)));
<a name="l00227"></a>00227 vector_range<matrix_column<matrix_type> > urr (project (column (ur, i), range (0, i)));
<a name="l00228"></a>00228 urr.assign (project (column (m, i), range (0, i)));
<a name="l00229"></a>00229 inplace_solve (lrr, urr, unit_lower_tag ());
<a name="l00230"></a>00230 project (v, range (i, size1)).assign (
<a name="l00231"></a>00231 project (column (m, i), range (i, size1)) -
<a name="l00232"></a>00232 axpy_prod<vector_type> (project (lr, range (i, size1), range (0, i)), urr));
<a name="l00233"></a>00233 size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1)));
<a name="l00234"></a>00234 BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
<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 std::swap (v (i_norm_inf), v (i));
<a name="l00239"></a>00239 project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2)));
<a name="l00240"></a>00240 } <span class="keywordflow">else</span> {
<a name="l00241"></a>00241 BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
<a name="l00242"></a>00242 }
<a name="l00243"></a>00243 project (column (lr, i), range (i + 1, size1)).assign (
<a name="l00244"></a>00244 project (v, range (i + 1, size1)) / v (i));
<a name="l00245"></a>00245 <span class="keywordflow">if</span> (i_norm_inf != i) {
<a name="l00246"></a>00246 project (row (lr, i_norm_inf), range (0, i)).swap (project (row (lr, i), range (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 (triangular_adaptor<matrix_type, strict_lower> (lr) +
<a name="l00254"></a>00254 triangular_adaptor<matrix_type, upper> (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> swap_rows (pm, cm);
<a name="l00258"></a>00258 BOOST_UBLAS_CHECK (singular != 0 ||
<a name="l00259"></a>00259 detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
<a name="l00260"></a>00260 triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ());
<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><<span class="keyword">class</span> M, <span class="keyword">class</span> E>
<a name="l00267"></a>00267 <span class="keywordtype">void</span> lu_substitute (<span class="keyword">const</span> M &m, vector_expression<E> &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> vector<typename E::value_type> 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> inplace_solve (m, e, unit_lower_tag ());
<a name="l00275"></a>00275 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00276"></a>00276 <span class="preprocessor"></span> BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cv1), internal_logic ());
<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> inplace_solve (m, e, upper_tag ());
<a name="l00280"></a>00280 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00281"></a>00281 <span class="preprocessor"></span> BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cv2), internal_logic ());
<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><<span class="keyword">class</span> M, <span class="keyword">class</span> E>
<a name="l00285"></a>00285 <span class="keywordtype">void</span> lu_substitute (<span class="keyword">const</span> M &m, matrix_expression<E> &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> matrix<typename E::value_type> 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> inplace_solve (m, e, unit_lower_tag ());
<a name="l00293"></a>00293 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00294"></a>00294 <span class="preprocessor"></span> BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cm1), internal_logic ());
<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> inplace_solve (m, e, upper_tag ());
<a name="l00298"></a>00298 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00299"></a>00299 <span class="preprocessor"></span> BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cm2), internal_logic ());
<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><<span class="keyword">class</span> M, <span class="keyword">class</span> PMT, <span class="keyword">class</span> PMA, <span class="keyword">class</span> MV>
<a name="l00303"></a>00303 <span class="keywordtype">void</span> lu_substitute (<span class="keyword">const</span> M &m, <span class="keyword">const</span> permutation_matrix<PMT, PMA> &pm, MV &mv) {
<a name="l00304"></a>00304 swap_rows (pm, mv);
<a name="l00305"></a>00305 lu_substitute (m, mv);
<a name="l00306"></a>00306 }
<a name="l00307"></a>00307 <span class="keyword">template</span><<span class="keyword">class</span> E, <span class="keyword">class</span> M>
<a name="l00308"></a>00308 <span class="keywordtype">void</span> lu_substitute (vector_expression<E> &e, <span class="keyword">const</span> M &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> vector<typename E::value_type> 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> inplace_solve (e, m, upper_tag ());
<a name="l00316"></a>00316 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00317"></a>00317 <span class="preprocessor"></span> BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cv1), internal_logic ());
<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> inplace_solve (e, m, unit_lower_tag ());
<a name="l00321"></a>00321 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00322"></a>00322 <span class="preprocessor"></span> BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cv2), internal_logic ());
<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><<span class="keyword">class</span> E, <span class="keyword">class</span> M>
<a name="l00326"></a>00326 <span class="keywordtype">void</span> lu_substitute (matrix_expression<E> &e, <span class="keyword">const</span> M &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> matrix<typename E::value_type> 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> inplace_solve (e, m, upper_tag ());
<a name="l00334"></a>00334 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00335"></a>00335 <span class="preprocessor"></span> BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cm1), internal_logic ());
<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> inplace_solve (e, m, unit_lower_tag ());
<a name="l00339"></a>00339 <span class="preprocessor">#if BOOST_UBLAS_TYPE_CHECK</span>
<a name="l00340"></a>00340 <span class="preprocessor"></span> BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cm2), internal_logic ());
<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><<span class="keyword">class</span> MV, <span class="keyword">class</span> M, <span class="keyword">class</span> PMT, <span class="keyword">class</span> PMA>
<a name="l00344"></a>00344 <span class="keywordtype">void</span> lu_substitute (MV &mv, <span class="keyword">const</span> M &m, <span class="keyword">const</span> permutation_matrix<PMT, PMA> &pm) {
<a name="l00345"></a>00345 swap_rows (pm, mv);
<a name="l00346"></a>00346 lu_substitute (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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