1 | // |
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2 | // Copyright (c) 2000-2002 |
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3 | // Joerg Walter, Mathias Koch |
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4 | // |
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5 | // Distributed under the Boost Software License, Version 1.0. (See |
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6 | // accompanying file LICENSE_1_0.txt or copy at |
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7 | // http://www.boost.org/LICENSE_1_0.txt) |
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8 | // |
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9 | // The authors gratefully acknowledge the support of |
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10 | // GeNeSys mbH & Co. KG in producing this work. |
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11 | // |
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12 | |
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13 | #ifndef _BOOST_UBLAS_OPERATION_ |
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14 | #define _BOOST_UBLAS_OPERATION_ |
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15 | |
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16 | #include <boost/numeric/ublas/matrix_proxy.hpp> |
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17 | |
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18 | /** \file operation.hpp |
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19 | * \brief This file contains some specialized products. |
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20 | */ |
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21 | |
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22 | // axpy-based products |
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23 | // Alexei Novakov had a lot of ideas to improve these. Thanks. |
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24 | // Hendrik Kueck proposed some new kernel. Thanks again. |
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25 | |
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26 | namespace boost { namespace numeric { namespace ublas { |
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27 | |
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28 | template<class V, class T1, class L1, class IA1, class TA1, class E2> |
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29 | BOOST_UBLAS_INLINE |
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30 | V & |
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31 | axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1, |
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32 | const vector_expression<E2> &e2, |
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33 | V &v, row_major_tag) { |
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34 | typedef typename V::size_type size_type; |
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35 | typedef typename V::value_type value_type; |
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36 | |
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37 | for (size_type i = 0; i < e1.filled1 () -1; ++ i) { |
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38 | size_type begin = e1.index1_data () [i]; |
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39 | size_type end = e1.index1_data () [i + 1]; |
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40 | value_type t (v (i)); |
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41 | for (size_type j = begin; j < end; ++ j) |
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42 | t += e1.value_data () [j] * e2 () (e1.index2_data () [j]); |
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43 | v (i) = t; |
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44 | } |
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45 | return v; |
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46 | } |
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47 | |
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48 | template<class V, class T1, class L1, class IA1, class TA1, class E2> |
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49 | BOOST_UBLAS_INLINE |
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50 | V & |
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51 | axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1, |
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52 | const vector_expression<E2> &e2, |
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53 | V &v, column_major_tag) { |
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54 | typedef typename V::size_type size_type; |
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55 | |
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56 | for (size_type j = 0; j < e1.filled1 () -1; ++ j) { |
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57 | size_type begin = e1.index1_data () [j]; |
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58 | size_type end = e1.index1_data () [j + 1]; |
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59 | for (size_type i = begin; i < end; ++ i) |
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60 | v (e1.index2_data () [i]) += e1.value_data () [i] * e2 () (j); |
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61 | } |
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62 | return v; |
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63 | } |
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64 | |
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65 | // Dispatcher |
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66 | template<class V, class T1, class L1, class IA1, class TA1, class E2> |
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67 | BOOST_UBLAS_INLINE |
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68 | V & |
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69 | axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1, |
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70 | const vector_expression<E2> &e2, |
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71 | V &v, bool init = true) { |
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72 | typedef typename V::value_type value_type; |
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73 | typedef typename L1::orientation_category orientation_category; |
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74 | |
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75 | if (init) |
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76 | v.assign (zero_vector<value_type> (e1.size1 ())); |
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77 | #if BOOST_UBLAS_TYPE_CHECK |
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78 | vector<value_type> cv (v); |
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79 | typedef typename type_traits<value_type>::real_type real_type; |
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80 | real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2)); |
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81 | indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2)); |
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82 | #endif |
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83 | axpy_prod (e1, e2, v, orientation_category ()); |
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84 | #if BOOST_UBLAS_TYPE_CHECK |
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85 | BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ()); |
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86 | #endif |
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87 | return v; |
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88 | } |
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89 | template<class V, class T1, class L1, class IA1, class TA1, class E2> |
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90 | BOOST_UBLAS_INLINE |
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91 | V |
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92 | axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1, |
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93 | const vector_expression<E2> &e2) { |
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94 | typedef V vector_type; |
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95 | |
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96 | vector_type v (e1.size1 ()); |
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97 | return axpy_prod (e1, e2, v, true); |
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98 | } |
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99 | |
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100 | template<class V, class T1, class L1, class IA1, class TA1, class E2> |
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101 | BOOST_UBLAS_INLINE |
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102 | V & |
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103 | axpy_prod (const coordinate_matrix<T1, L1, 0, IA1, TA1> &e1, |
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104 | const vector_expression<E2> &e2, |
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105 | V &v, bool init = true) { |
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106 | typedef typename V::size_type size_type; |
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107 | typedef typename V::value_type value_type; |
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108 | typedef L1 layout_type; |
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109 | |
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110 | size_type size1 = e1.size1(); |
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111 | size_type size2 = e1.size2(); |
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112 | |
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113 | if (init) { |
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114 | noalias(v) = zero_vector<value_type>(size1); |
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115 | } |
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116 | |
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117 | for (size_type i = 0; i < e1.nnz(); ++i) { |
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118 | size_type row_index = layout_type::index_M( e1.index1_data () [i], e1.index2_data () [i] ); |
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119 | size_type col_index = layout_type::index_m( e1.index1_data () [i], e1.index2_data () [i] ); |
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120 | v( row_index ) += e1.value_data () [i] * e2 () (col_index); |
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121 | } |
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122 | return v; |
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123 | } |
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124 | |
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125 | template<class V, class E1, class E2> |
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126 | BOOST_UBLAS_INLINE |
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127 | V & |
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128 | axpy_prod (const matrix_expression<E1> &e1, |
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129 | const vector_expression<E2> &e2, |
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130 | V &v, packed_random_access_iterator_tag, row_major_tag) { |
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131 | typedef const E1 expression1_type; |
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132 | typedef const E2 expression2_type; |
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133 | typedef typename V::size_type size_type; |
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134 | |
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135 | typename expression1_type::const_iterator1 it1 (e1 ().begin1 ()); |
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136 | typename expression1_type::const_iterator1 it1_end (e1 ().end1 ()); |
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137 | while (it1 != it1_end) { |
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138 | size_type index1 (it1.index1 ()); |
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139 | #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION |
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140 | typename expression1_type::const_iterator2 it2 (it1.begin ()); |
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141 | typename expression1_type::const_iterator2 it2_end (it1.end ()); |
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142 | #else |
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143 | typename expression1_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ())); |
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144 | typename expression1_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ())); |
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145 | #endif |
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146 | while (it2 != it2_end) { |
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147 | v (index1) += *it2 * e2 () (it2.index2 ()); |
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148 | ++ it2; |
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149 | } |
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150 | ++ it1; |
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151 | } |
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152 | return v; |
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153 | } |
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154 | |
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155 | template<class V, class E1, class E2> |
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156 | BOOST_UBLAS_INLINE |
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157 | V & |
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158 | axpy_prod (const matrix_expression<E1> &e1, |
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159 | const vector_expression<E2> &e2, |
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160 | V &v, packed_random_access_iterator_tag, column_major_tag) { |
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161 | typedef const E1 expression1_type; |
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162 | typedef const E2 expression2_type; |
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163 | typedef typename V::size_type size_type; |
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164 | |
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165 | typename expression1_type::const_iterator2 it2 (e1 ().begin2 ()); |
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166 | typename expression1_type::const_iterator2 it2_end (e1 ().end2 ()); |
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167 | while (it2 != it2_end) { |
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168 | size_type index2 (it2.index2 ()); |
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169 | #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION |
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170 | typename expression1_type::const_iterator1 it1 (it2.begin ()); |
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171 | typename expression1_type::const_iterator1 it1_end (it2.end ()); |
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172 | #else |
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173 | typename expression1_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ())); |
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174 | typename expression1_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ())); |
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175 | #endif |
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176 | while (it1 != it1_end) { |
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177 | v (it1.index1 ()) += *it1 * e2 () (index2); |
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178 | ++ it1; |
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179 | } |
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180 | ++ it2; |
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181 | } |
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182 | return v; |
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183 | } |
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184 | |
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185 | template<class V, class E1, class E2> |
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186 | BOOST_UBLAS_INLINE |
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187 | V & |
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188 | axpy_prod (const matrix_expression<E1> &e1, |
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189 | const vector_expression<E2> &e2, |
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190 | V &v, sparse_bidirectional_iterator_tag) { |
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191 | typedef const E1 expression1_type; |
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192 | typedef const E2 expression2_type; |
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193 | typedef typename V::size_type size_type; |
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194 | |
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195 | typename expression2_type::const_iterator it (e2 ().begin ()); |
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196 | typename expression2_type::const_iterator it_end (e2 ().end ()); |
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197 | while (it != it_end) { |
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198 | v.plus_assign (column (e1 (), it.index ()) * *it); |
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199 | ++ it; |
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200 | } |
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201 | return v; |
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202 | } |
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203 | |
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204 | // Dispatcher |
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205 | template<class V, class E1, class E2> |
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206 | BOOST_UBLAS_INLINE |
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207 | V & |
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208 | axpy_prod (const matrix_expression<E1> &e1, |
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209 | const vector_expression<E2> &e2, |
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210 | V &v, packed_random_access_iterator_tag) { |
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211 | typedef typename E1::orientation_category orientation_category; |
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212 | return axpy_prod (e1, e2, v, packed_random_access_iterator_tag (), orientation_category ()); |
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213 | } |
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214 | |
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215 | |
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216 | /** \brief computes <tt>v += A x</tt> or <tt>v = A x</tt> in an |
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217 | optimized fashion. |
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218 | |
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219 | \param e1 the matrix expression \c A |
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220 | \param e2 the vector expression \c x |
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221 | \param v the result vector \c v |
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222 | \param init a boolean parameter |
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223 | |
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224 | <tt>axpy_prod(A, x, v, init)</tt> implements the well known |
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225 | axpy-product. Setting \a init to \c true is equivalent to call |
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226 | <tt>v.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init |
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227 | defaults to \c true, but this may change in the future. |
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228 | |
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229 | Up to now there are some specialisation for compressed |
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230 | matrices that give a large speed up compared to prod. |
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231 | |
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232 | \ingroup blas2 |
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233 | |
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234 | \internal |
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235 | |
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236 | template parameters: |
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237 | \param V type of the result vector \c v |
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238 | \param E1 type of a matrix expression \c A |
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239 | \param E2 type of a vector expression \c x |
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240 | */ |
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241 | template<class V, class E1, class E2> |
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242 | BOOST_UBLAS_INLINE |
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243 | V & |
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244 | axpy_prod (const matrix_expression<E1> &e1, |
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245 | const vector_expression<E2> &e2, |
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246 | V &v, bool init = true) { |
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247 | typedef typename V::value_type value_type; |
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248 | typedef typename E2::const_iterator::iterator_category iterator_category; |
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249 | |
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250 | if (init) |
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251 | v.assign (zero_vector<value_type> (e1 ().size1 ())); |
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252 | #if BOOST_UBLAS_TYPE_CHECK |
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253 | vector<value_type> cv (v); |
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254 | typedef typename type_traits<value_type>::real_type real_type; |
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255 | real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2)); |
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256 | indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2)); |
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257 | #endif |
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258 | axpy_prod (e1, e2, v, iterator_category ()); |
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259 | #if BOOST_UBLAS_TYPE_CHECK |
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260 | BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ()); |
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261 | #endif |
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262 | return v; |
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263 | } |
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264 | template<class V, class E1, class E2> |
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265 | BOOST_UBLAS_INLINE |
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266 | V |
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267 | axpy_prod (const matrix_expression<E1> &e1, |
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268 | const vector_expression<E2> &e2) { |
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269 | typedef V vector_type; |
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270 | |
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271 | vector_type v (e1 ().size1 ()); |
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272 | return axpy_prod (e1, e2, v, true); |
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273 | } |
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274 | |
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275 | template<class V, class E1, class T2, class IA2, class TA2> |
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276 | BOOST_UBLAS_INLINE |
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277 | V & |
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278 | axpy_prod (const vector_expression<E1> &e1, |
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279 | const compressed_matrix<T2, column_major, 0, IA2, TA2> &e2, |
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280 | V &v, column_major_tag) { |
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281 | typedef typename V::size_type size_type; |
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282 | typedef typename V::value_type value_type; |
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283 | |
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284 | for (size_type j = 0; j < e2.filled1 () -1; ++ j) { |
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285 | size_type begin = e2.index1_data () [j]; |
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286 | size_type end = e2.index1_data () [j + 1]; |
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287 | value_type t (v (j)); |
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288 | for (size_type i = begin; i < end; ++ i) |
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289 | t += e2.value_data () [i] * e1 () (e2.index2_data () [i]); |
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290 | v (j) = t; |
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291 | } |
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292 | return v; |
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293 | } |
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294 | |
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295 | template<class V, class E1, class T2, class IA2, class TA2> |
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296 | BOOST_UBLAS_INLINE |
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297 | V & |
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298 | axpy_prod (const vector_expression<E1> &e1, |
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299 | const compressed_matrix<T2, row_major, 0, IA2, TA2> &e2, |
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300 | V &v, row_major_tag) { |
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301 | typedef typename V::size_type size_type; |
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302 | |
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303 | for (size_type i = 0; i < e2.filled1 () -1; ++ i) { |
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304 | size_type begin = e2.index1_data () [i]; |
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305 | size_type end = e2.index1_data () [i + 1]; |
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306 | for (size_type j = begin; j < end; ++ j) |
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307 | v (e2.index2_data () [j]) += e2.value_data () [j] * e1 () (i); |
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308 | } |
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309 | return v; |
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310 | } |
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311 | |
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312 | // Dispatcher |
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313 | template<class V, class E1, class T2, class L2, class IA2, class TA2> |
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314 | BOOST_UBLAS_INLINE |
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315 | V & |
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316 | axpy_prod (const vector_expression<E1> &e1, |
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317 | const compressed_matrix<T2, L2, 0, IA2, TA2> &e2, |
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318 | V &v, bool init = true) { |
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319 | typedef typename V::value_type value_type; |
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320 | typedef typename L2::orientation_category orientation_category; |
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321 | |
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322 | if (init) |
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323 | v.assign (zero_vector<value_type> (e2.size2 ())); |
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324 | #if BOOST_UBLAS_TYPE_CHECK |
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325 | vector<value_type> cv (v); |
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326 | typedef typename type_traits<value_type>::real_type real_type; |
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327 | real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2)); |
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328 | indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2)); |
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329 | #endif |
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330 | axpy_prod (e1, e2, v, orientation_category ()); |
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331 | #if BOOST_UBLAS_TYPE_CHECK |
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332 | BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ()); |
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333 | #endif |
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334 | return v; |
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335 | } |
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336 | template<class V, class E1, class T2, class L2, class IA2, class TA2> |
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337 | BOOST_UBLAS_INLINE |
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338 | V |
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339 | axpy_prod (const vector_expression<E1> &e1, |
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340 | const compressed_matrix<T2, L2, 0, IA2, TA2> &e2) { |
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341 | typedef V vector_type; |
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342 | |
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343 | vector_type v (e2.size2 ()); |
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344 | return axpy_prod (e1, e2, v, true); |
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345 | } |
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346 | |
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347 | template<class V, class E1, class E2> |
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348 | BOOST_UBLAS_INLINE |
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349 | V & |
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350 | axpy_prod (const vector_expression<E1> &e1, |
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351 | const matrix_expression<E2> &e2, |
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352 | V &v, packed_random_access_iterator_tag, column_major_tag) { |
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353 | typedef const E1 expression1_type; |
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354 | typedef const E2 expression2_type; |
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355 | typedef typename V::size_type size_type; |
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356 | |
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357 | typename expression2_type::const_iterator2 it2 (e2 ().begin2 ()); |
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358 | typename expression2_type::const_iterator2 it2_end (e2 ().end2 ()); |
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359 | while (it2 != it2_end) { |
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360 | size_type index2 (it2.index2 ()); |
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361 | #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION |
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362 | typename expression2_type::const_iterator1 it1 (it2.begin ()); |
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363 | typename expression2_type::const_iterator1 it1_end (it2.end ()); |
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364 | #else |
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365 | typename expression2_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ())); |
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366 | typename expression2_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ())); |
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367 | #endif |
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368 | while (it1 != it1_end) { |
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369 | v (index2) += *it1 * e1 () (it1.index1 ()); |
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370 | ++ it1; |
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371 | } |
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372 | ++ it2; |
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373 | } |
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374 | return v; |
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375 | } |
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376 | |
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377 | template<class V, class E1, class E2> |
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378 | BOOST_UBLAS_INLINE |
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379 | V & |
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380 | axpy_prod (const vector_expression<E1> &e1, |
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381 | const matrix_expression<E2> &e2, |
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382 | V &v, packed_random_access_iterator_tag, row_major_tag) { |
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383 | typedef const E1 expression1_type; |
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384 | typedef const E2 expression2_type; |
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385 | typedef typename V::size_type size_type; |
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386 | |
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387 | typename expression2_type::const_iterator1 it1 (e2 ().begin1 ()); |
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388 | typename expression2_type::const_iterator1 it1_end (e2 ().end1 ()); |
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389 | while (it1 != it1_end) { |
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390 | size_type index1 (it1.index1 ()); |
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391 | #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION |
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392 | typename expression2_type::const_iterator2 it2 (it1.begin ()); |
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393 | typename expression2_type::const_iterator2 it2_end (it1.end ()); |
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394 | #else |
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395 | typename expression2_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ())); |
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396 | typename expression2_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ())); |
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397 | #endif |
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398 | while (it2 != it2_end) { |
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399 | v (it2.index2 ()) += *it2 * e1 () (index1); |
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400 | ++ it2; |
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401 | } |
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402 | ++ it1; |
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403 | } |
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404 | return v; |
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405 | } |
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406 | |
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407 | template<class V, class E1, class E2> |
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408 | BOOST_UBLAS_INLINE |
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409 | V & |
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410 | axpy_prod (const vector_expression<E1> &e1, |
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411 | const matrix_expression<E2> &e2, |
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412 | V &v, sparse_bidirectional_iterator_tag) { |
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413 | typedef const E1 expression1_type; |
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414 | typedef const E2 expression2_type; |
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415 | typedef typename V::size_type size_type; |
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416 | |
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417 | typename expression1_type::const_iterator it (e1 ().begin ()); |
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418 | typename expression1_type::const_iterator it_end (e1 ().end ()); |
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419 | while (it != it_end) { |
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420 | v.plus_assign (*it * row (e2 (), it.index ())); |
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421 | ++ it; |
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422 | } |
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423 | return v; |
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424 | } |
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425 | |
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426 | // Dispatcher |
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427 | template<class V, class E1, class E2> |
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428 | BOOST_UBLAS_INLINE |
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429 | V & |
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430 | axpy_prod (const vector_expression<E1> &e1, |
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431 | const matrix_expression<E2> &e2, |
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432 | V &v, packed_random_access_iterator_tag) { |
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433 | typedef typename E2::orientation_category orientation_category; |
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434 | return axpy_prod (e1, e2, v, packed_random_access_iterator_tag (), orientation_category ()); |
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435 | } |
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436 | |
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437 | |
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438 | /** \brief computes <tt>v += A<sup>T</sup> x</tt> or <tt>v = A<sup>T</sup> x</tt> in an |
---|
439 | optimized fashion. |
---|
440 | |
---|
441 | \param e1 the vector expression \c x |
---|
442 | \param e2 the matrix expression \c A |
---|
443 | \param v the result vector \c v |
---|
444 | \param init a boolean parameter |
---|
445 | |
---|
446 | <tt>axpy_prod(x, A, v, init)</tt> implements the well known |
---|
447 | axpy-product. Setting \a init to \c true is equivalent to call |
---|
448 | <tt>v.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init |
---|
449 | defaults to \c true, but this may change in the future. |
---|
450 | |
---|
451 | Up to now there are some specialisation for compressed |
---|
452 | matrices that give a large speed up compared to prod. |
---|
453 | |
---|
454 | \ingroup blas2 |
---|
455 | |
---|
456 | \internal |
---|
457 | |
---|
458 | template parameters: |
---|
459 | \param V type of the result vector \c v |
---|
460 | \param E1 type of a vector expression \c x |
---|
461 | \param E2 type of a matrix expression \c A |
---|
462 | */ |
---|
463 | template<class V, class E1, class E2> |
---|
464 | BOOST_UBLAS_INLINE |
---|
465 | V & |
---|
466 | axpy_prod (const vector_expression<E1> &e1, |
---|
467 | const matrix_expression<E2> &e2, |
---|
468 | V &v, bool init = true) { |
---|
469 | typedef typename V::value_type value_type; |
---|
470 | typedef typename E1::const_iterator::iterator_category iterator_category; |
---|
471 | |
---|
472 | if (init) |
---|
473 | v.assign (zero_vector<value_type> (e2 ().size2 ())); |
---|
474 | #if BOOST_UBLAS_TYPE_CHECK |
---|
475 | vector<value_type> cv (v); |
---|
476 | typedef typename type_traits<value_type>::real_type real_type; |
---|
477 | real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2)); |
---|
478 | indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2)); |
---|
479 | #endif |
---|
480 | axpy_prod (e1, e2, v, iterator_category ()); |
---|
481 | #if BOOST_UBLAS_TYPE_CHECK |
---|
482 | BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ()); |
---|
483 | #endif |
---|
484 | return v; |
---|
485 | } |
---|
486 | template<class V, class E1, class E2> |
---|
487 | BOOST_UBLAS_INLINE |
---|
488 | V |
---|
489 | axpy_prod (const vector_expression<E1> &e1, |
---|
490 | const matrix_expression<E2> &e2) { |
---|
491 | typedef V vector_type; |
---|
492 | |
---|
493 | vector_type v (e2 ().size2 ()); |
---|
494 | return axpy_prod (e1, e2, v, true); |
---|
495 | } |
---|
496 | |
---|
497 | template<class M, class E1, class E2, class TRI> |
---|
498 | BOOST_UBLAS_INLINE |
---|
499 | M & |
---|
500 | axpy_prod (const matrix_expression<E1> &e1, |
---|
501 | const matrix_expression<E2> &e2, |
---|
502 | M &m, TRI, |
---|
503 | dense_proxy_tag, row_major_tag) { |
---|
504 | typedef M matrix_type; |
---|
505 | typedef const E1 expression1_type; |
---|
506 | typedef const E2 expression2_type; |
---|
507 | typedef typename M::size_type size_type; |
---|
508 | typedef typename M::value_type value_type; |
---|
509 | |
---|
510 | #if BOOST_UBLAS_TYPE_CHECK |
---|
511 | matrix<value_type, row_major> cm (m); |
---|
512 | typedef typename type_traits<value_type>::real_type real_type; |
---|
513 | real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); |
---|
514 | indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ()); |
---|
515 | #endif |
---|
516 | size_type size1 (e1 ().size1 ()); |
---|
517 | size_type size2 (e1 ().size2 ()); |
---|
518 | for (size_type i = 0; i < size1; ++ i) |
---|
519 | for (size_type j = 0; j < size2; ++ j) |
---|
520 | row (m, i).plus_assign (e1 () (i, j) * row (e2 (), j)); |
---|
521 | #if BOOST_UBLAS_TYPE_CHECK |
---|
522 | BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); |
---|
523 | #endif |
---|
524 | return m; |
---|
525 | } |
---|
526 | template<class M, class E1, class E2, class TRI> |
---|
527 | BOOST_UBLAS_INLINE |
---|
528 | M & |
---|
529 | axpy_prod (const matrix_expression<E1> &e1, |
---|
530 | const matrix_expression<E2> &e2, |
---|
531 | M &m, TRI, |
---|
532 | sparse_proxy_tag, row_major_tag) { |
---|
533 | typedef M matrix_type; |
---|
534 | typedef TRI triangular_restriction; |
---|
535 | typedef const E1 expression1_type; |
---|
536 | typedef const E2 expression2_type; |
---|
537 | typedef typename M::size_type size_type; |
---|
538 | typedef typename M::value_type value_type; |
---|
539 | |
---|
540 | #if BOOST_UBLAS_TYPE_CHECK |
---|
541 | matrix<value_type, row_major> cm (m); |
---|
542 | typedef typename type_traits<value_type>::real_type real_type; |
---|
543 | real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); |
---|
544 | indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ()); |
---|
545 | #endif |
---|
546 | typename expression1_type::const_iterator1 it1 (e1 ().begin1 ()); |
---|
547 | typename expression1_type::const_iterator1 it1_end (e1 ().end1 ()); |
---|
548 | while (it1 != it1_end) { |
---|
549 | #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION |
---|
550 | typename expression1_type::const_iterator2 it2 (it1.begin ()); |
---|
551 | typename expression1_type::const_iterator2 it2_end (it1.end ()); |
---|
552 | #else |
---|
553 | typename expression1_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ())); |
---|
554 | typename expression1_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ())); |
---|
555 | #endif |
---|
556 | while (it2 != it2_end) { |
---|
557 | // row (m, it1.index1 ()).plus_assign (*it2 * row (e2 (), it2.index2 ())); |
---|
558 | matrix_row<expression2_type> mr (e2 (), it2.index2 ()); |
---|
559 | typename matrix_row<expression2_type>::const_iterator itr (mr.begin ()); |
---|
560 | typename matrix_row<expression2_type>::const_iterator itr_end (mr.end ()); |
---|
561 | while (itr != itr_end) { |
---|
562 | if (triangular_restriction::other (it1.index1 (), itr.index ())) |
---|
563 | m (it1.index1 (), itr.index ()) += *it2 * *itr; |
---|
564 | ++ itr; |
---|
565 | } |
---|
566 | ++ it2; |
---|
567 | } |
---|
568 | ++ it1; |
---|
569 | } |
---|
570 | #if BOOST_UBLAS_TYPE_CHECK |
---|
571 | BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); |
---|
572 | #endif |
---|
573 | return m; |
---|
574 | } |
---|
575 | |
---|
576 | template<class M, class E1, class E2, class TRI> |
---|
577 | BOOST_UBLAS_INLINE |
---|
578 | M & |
---|
579 | axpy_prod (const matrix_expression<E1> &e1, |
---|
580 | const matrix_expression<E2> &e2, |
---|
581 | M &m, TRI, |
---|
582 | dense_proxy_tag, column_major_tag) { |
---|
583 | typedef M matrix_type; |
---|
584 | typedef const E1 expression1_type; |
---|
585 | typedef const E2 expression2_type; |
---|
586 | typedef typename M::size_type size_type; |
---|
587 | typedef typename M::value_type value_type; |
---|
588 | |
---|
589 | #if BOOST_UBLAS_TYPE_CHECK |
---|
590 | matrix<value_type, column_major> cm (m); |
---|
591 | typedef typename type_traits<value_type>::real_type real_type; |
---|
592 | real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); |
---|
593 | indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ()); |
---|
594 | #endif |
---|
595 | size_type size1 (e2 ().size1 ()); |
---|
596 | size_type size2 (e2 ().size2 ()); |
---|
597 | for (size_type j = 0; j < size2; ++ j) |
---|
598 | for (size_type i = 0; i < size1; ++ i) |
---|
599 | column (m, j).plus_assign (e2 () (i, j) * column (e1 (), i)); |
---|
600 | #if BOOST_UBLAS_TYPE_CHECK |
---|
601 | BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); |
---|
602 | #endif |
---|
603 | return m; |
---|
604 | } |
---|
605 | template<class M, class E1, class E2, class TRI> |
---|
606 | BOOST_UBLAS_INLINE |
---|
607 | M & |
---|
608 | axpy_prod (const matrix_expression<E1> &e1, |
---|
609 | const matrix_expression<E2> &e2, |
---|
610 | M &m, TRI, |
---|
611 | sparse_proxy_tag, column_major_tag) { |
---|
612 | typedef M matrix_type; |
---|
613 | typedef TRI triangular_restriction; |
---|
614 | typedef const E1 expression1_type; |
---|
615 | typedef const E2 expression2_type; |
---|
616 | typedef typename M::size_type size_type; |
---|
617 | typedef typename M::value_type value_type; |
---|
618 | |
---|
619 | #if BOOST_UBLAS_TYPE_CHECK |
---|
620 | matrix<value_type, column_major> cm (m); |
---|
621 | typedef typename type_traits<value_type>::real_type real_type; |
---|
622 | real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); |
---|
623 | indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ()); |
---|
624 | #endif |
---|
625 | typename expression2_type::const_iterator2 it2 (e2 ().begin2 ()); |
---|
626 | typename expression2_type::const_iterator2 it2_end (e2 ().end2 ()); |
---|
627 | while (it2 != it2_end) { |
---|
628 | #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION |
---|
629 | typename expression2_type::const_iterator1 it1 (it2.begin ()); |
---|
630 | typename expression2_type::const_iterator1 it1_end (it2.end ()); |
---|
631 | #else |
---|
632 | typename expression2_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ())); |
---|
633 | typename expression2_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ())); |
---|
634 | #endif |
---|
635 | while (it1 != it1_end) { |
---|
636 | // column (m, it2.index2 ()).plus_assign (*it1 * column (e1 (), it1.index1 ())); |
---|
637 | matrix_column<expression1_type> mc (e1 (), it1.index1 ()); |
---|
638 | typename matrix_column<expression1_type>::const_iterator itc (mc.begin ()); |
---|
639 | typename matrix_column<expression1_type>::const_iterator itc_end (mc.end ()); |
---|
640 | while (itc != itc_end) { |
---|
641 | if(triangular_restriction::other (itc.index (), it2.index2 ())) |
---|
642 | m (itc.index (), it2.index2 ()) += *it1 * *itc; |
---|
643 | ++ itc; |
---|
644 | } |
---|
645 | ++ it1; |
---|
646 | } |
---|
647 | ++ it2; |
---|
648 | } |
---|
649 | #if BOOST_UBLAS_TYPE_CHECK |
---|
650 | BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); |
---|
651 | #endif |
---|
652 | return m; |
---|
653 | } |
---|
654 | |
---|
655 | // Dispatcher |
---|
656 | template<class M, class E1, class E2, class TRI> |
---|
657 | BOOST_UBLAS_INLINE |
---|
658 | M & |
---|
659 | axpy_prod (const matrix_expression<E1> &e1, |
---|
660 | const matrix_expression<E2> &e2, |
---|
661 | M &m, TRI, bool init = true) { |
---|
662 | typedef typename M::value_type value_type; |
---|
663 | typedef typename M::storage_category storage_category; |
---|
664 | typedef typename M::orientation_category orientation_category; |
---|
665 | typedef TRI triangular_restriction; |
---|
666 | |
---|
667 | if (init) |
---|
668 | m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ())); |
---|
669 | return axpy_prod (e1, e2, m, triangular_restriction (), storage_category (), orientation_category ()); |
---|
670 | } |
---|
671 | template<class M, class E1, class E2, class TRI> |
---|
672 | BOOST_UBLAS_INLINE |
---|
673 | M |
---|
674 | axpy_prod (const matrix_expression<E1> &e1, |
---|
675 | const matrix_expression<E2> &e2, |
---|
676 | TRI) { |
---|
677 | typedef M matrix_type; |
---|
678 | typedef TRI triangular_restriction; |
---|
679 | |
---|
680 | matrix_type m (e1 ().size1 (), e2 ().size2 ()); |
---|
681 | return axpy_prod (e1, e2, m, triangular_restriction (), true); |
---|
682 | } |
---|
683 | |
---|
684 | /** \brief computes <tt>M += A X</tt> or <tt>M = A X</tt> in an |
---|
685 | optimized fashion. |
---|
686 | |
---|
687 | \param e1 the matrix expression \c A |
---|
688 | \param e2 the matrix expression \c X |
---|
689 | \param m the result matrix \c M |
---|
690 | \param init a boolean parameter |
---|
691 | |
---|
692 | <tt>axpy_prod(A, X, M, init)</tt> implements the well known |
---|
693 | axpy-product. Setting \a init to \c true is equivalent to call |
---|
694 | <tt>M.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init |
---|
695 | defaults to \c true, but this may change in the future. |
---|
696 | |
---|
697 | Up to now there are no specialisations. |
---|
698 | |
---|
699 | \ingroup blas3 |
---|
700 | |
---|
701 | \internal |
---|
702 | |
---|
703 | template parameters: |
---|
704 | \param M type of the result matrix \c M |
---|
705 | \param E1 type of a matrix expression \c A |
---|
706 | \param E2 type of a matrix expression \c X |
---|
707 | */ |
---|
708 | template<class M, class E1, class E2> |
---|
709 | BOOST_UBLAS_INLINE |
---|
710 | M & |
---|
711 | axpy_prod (const matrix_expression<E1> &e1, |
---|
712 | const matrix_expression<E2> &e2, |
---|
713 | M &m, bool init = true) { |
---|
714 | typedef typename M::value_type value_type; |
---|
715 | typedef typename M::storage_category storage_category; |
---|
716 | typedef typename M::orientation_category orientation_category; |
---|
717 | |
---|
718 | if (init) |
---|
719 | m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ())); |
---|
720 | return axpy_prod (e1, e2, m, full (), storage_category (), orientation_category ()); |
---|
721 | } |
---|
722 | template<class M, class E1, class E2> |
---|
723 | BOOST_UBLAS_INLINE |
---|
724 | M |
---|
725 | axpy_prod (const matrix_expression<E1> &e1, |
---|
726 | const matrix_expression<E2> &e2) { |
---|
727 | typedef M matrix_type; |
---|
728 | |
---|
729 | matrix_type m (e1 ().size1 (), e2 ().size2 ()); |
---|
730 | return axpy_prod (e1, e2, m, full (), true); |
---|
731 | } |
---|
732 | |
---|
733 | |
---|
734 | template<class M, class E1, class E2> |
---|
735 | BOOST_UBLAS_INLINE |
---|
736 | M & |
---|
737 | opb_prod (const matrix_expression<E1> &e1, |
---|
738 | const matrix_expression<E2> &e2, |
---|
739 | M &m, |
---|
740 | dense_proxy_tag, row_major_tag) { |
---|
741 | typedef M matrix_type; |
---|
742 | typedef const E1 expression1_type; |
---|
743 | typedef const E2 expression2_type; |
---|
744 | typedef typename M::size_type size_type; |
---|
745 | typedef typename M::value_type value_type; |
---|
746 | |
---|
747 | #if BOOST_UBLAS_TYPE_CHECK |
---|
748 | matrix<value_type, row_major> cm (m); |
---|
749 | typedef typename type_traits<value_type>::real_type real_type; |
---|
750 | real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); |
---|
751 | indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ()); |
---|
752 | #endif |
---|
753 | size_type size (BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ())); |
---|
754 | for (size_type k = 0; k < size; ++ k) { |
---|
755 | vector<value_type> ce1 (column (e1 (), k)); |
---|
756 | vector<value_type> re2 (row (e2 (), k)); |
---|
757 | m.plus_assign (outer_prod (ce1, re2)); |
---|
758 | } |
---|
759 | #if BOOST_UBLAS_TYPE_CHECK |
---|
760 | BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); |
---|
761 | #endif |
---|
762 | return m; |
---|
763 | } |
---|
764 | |
---|
765 | template<class M, class E1, class E2> |
---|
766 | BOOST_UBLAS_INLINE |
---|
767 | M & |
---|
768 | opb_prod (const matrix_expression<E1> &e1, |
---|
769 | const matrix_expression<E2> &e2, |
---|
770 | M &m, |
---|
771 | dense_proxy_tag, column_major_tag) { |
---|
772 | typedef M matrix_type; |
---|
773 | typedef const E1 expression1_type; |
---|
774 | typedef const E2 expression2_type; |
---|
775 | typedef typename M::size_type size_type; |
---|
776 | typedef typename M::value_type value_type; |
---|
777 | |
---|
778 | #if BOOST_UBLAS_TYPE_CHECK |
---|
779 | matrix<value_type, column_major> cm (m); |
---|
780 | typedef typename type_traits<value_type>::real_type real_type; |
---|
781 | real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); |
---|
782 | indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ()); |
---|
783 | #endif |
---|
784 | size_type size (BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ())); |
---|
785 | for (size_type k = 0; k < size; ++ k) { |
---|
786 | vector<value_type> ce1 (column (e1 (), k)); |
---|
787 | vector<value_type> re2 (row (e2 (), k)); |
---|
788 | m.plus_assign (outer_prod (ce1, re2)); |
---|
789 | } |
---|
790 | #if BOOST_UBLAS_TYPE_CHECK |
---|
791 | BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); |
---|
792 | #endif |
---|
793 | return m; |
---|
794 | } |
---|
795 | |
---|
796 | // Dispatcher |
---|
797 | |
---|
798 | /** \brief computes <tt>M += A X</tt> or <tt>M = A X</tt> in an |
---|
799 | optimized fashion. |
---|
800 | |
---|
801 | \param e1 the matrix expression \c A |
---|
802 | \param e2 the matrix expression \c X |
---|
803 | \param m the result matrix \c M |
---|
804 | \param init a boolean parameter |
---|
805 | |
---|
806 | <tt>opb_prod(A, X, M, init)</tt> implements the well known |
---|
807 | axpy-product. Setting \a init to \c true is equivalent to call |
---|
808 | <tt>M.clear()</tt> before <tt>opb_prod</tt>. Currently \a init |
---|
809 | defaults to \c true, but this may change in the future. |
---|
810 | |
---|
811 | This function may give a speedup if \c A has less columns than |
---|
812 | rows, because the product is computed as a sum of outer |
---|
813 | products. |
---|
814 | |
---|
815 | \ingroup blas3 |
---|
816 | |
---|
817 | \internal |
---|
818 | |
---|
819 | template parameters: |
---|
820 | \param M type of the result matrix \c M |
---|
821 | \param E1 type of a matrix expression \c A |
---|
822 | \param E2 type of a matrix expression \c X |
---|
823 | */ |
---|
824 | template<class M, class E1, class E2> |
---|
825 | BOOST_UBLAS_INLINE |
---|
826 | M & |
---|
827 | opb_prod (const matrix_expression<E1> &e1, |
---|
828 | const matrix_expression<E2> &e2, |
---|
829 | M &m, bool init = true) { |
---|
830 | typedef typename M::value_type value_type; |
---|
831 | typedef typename M::storage_category storage_category; |
---|
832 | typedef typename M::orientation_category orientation_category; |
---|
833 | |
---|
834 | if (init) |
---|
835 | m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ())); |
---|
836 | return opb_prod (e1, e2, m, storage_category (), orientation_category ()); |
---|
837 | } |
---|
838 | template<class M, class E1, class E2> |
---|
839 | BOOST_UBLAS_INLINE |
---|
840 | M |
---|
841 | opb_prod (const matrix_expression<E1> &e1, |
---|
842 | const matrix_expression<E2> &e2) { |
---|
843 | typedef M matrix_type; |
---|
844 | |
---|
845 | matrix_type m (e1 ().size1 (), e2 ().size2 ()); |
---|
846 | return opb_prod (e1, e2, m, true); |
---|
847 | } |
---|
848 | |
---|
849 | }}} |
---|
850 | |
---|
851 | #endif |
---|