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_BLAS_ |
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14 | #define _BOOST_UBLAS_BLAS_ |
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15 | |
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16 | #include <boost/numeric/ublas/traits.hpp> |
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17 | |
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18 | namespace boost { namespace numeric { namespace ublas { |
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19 | |
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20 | |
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21 | /** Interface and implementation of BLAS level 1 |
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22 | * This includes functions which perform \b vector-vector operations. |
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23 | * More information about BLAS can be found at |
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24 | * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a> |
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25 | */ |
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26 | namespace blas_1 { |
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27 | |
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28 | /** 1-Norm: \f$\sum_i |x_i|\f$ (also called \f$\mathcal{L}_1\f$ or Manhattan norm) |
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29 | * |
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30 | * \param v a vector or vector expression |
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31 | * \return the 1-Norm with type of the vector's type |
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32 | * |
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33 | * \tparam V type of the vector (not needed by default) |
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34 | */ |
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35 | template<class V> |
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36 | typename type_traits<typename V::value_type>::real_type |
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37 | asum (const V &v) { |
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38 | return norm_1 (v); |
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39 | } |
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40 | |
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41 | /** 2-Norm: \f$\sum_i |x_i|^2\f$ (also called \f$\mathcal{L}_2\f$ or Euclidean norm) |
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42 | * |
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43 | * \param v a vector or vector expression |
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44 | * \return the 2-Norm with type of the vector's type |
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45 | * |
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46 | * \tparam V type of the vector (not needed by default) |
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47 | */ |
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48 | template<class V> |
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49 | typename type_traits<typename V::value_type>::real_type |
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50 | nrm2 (const V &v) { |
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51 | return norm_2 (v); |
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52 | } |
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53 | |
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54 | /** Infinite-norm: \f$\max_i |x_i|\f$ (also called \f$\mathcal{L}_\infty\f$ norm) |
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55 | * |
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56 | * \param v a vector or vector expression |
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57 | * \return the Infinite-Norm with type of the vector's type |
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58 | * |
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59 | * \tparam V type of the vector (not needed by default) |
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60 | */ |
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61 | template<class V> |
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62 | typename type_traits<typename V::value_type>::real_type |
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63 | amax (const V &v) { |
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64 | return norm_inf (v); |
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65 | } |
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66 | |
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67 | /** Inner product of vectors \f$v_1\f$ and \f$v_2\f$ |
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68 | * |
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69 | * \param v1 first vector of the inner product |
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70 | * \param v2 second vector of the inner product |
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71 | * \return the inner product of the type of the most generic type of the 2 vectors |
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72 | * |
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73 | * \tparam V1 type of first vector (not needed by default) |
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74 | * \tparam V2 type of second vector (not needed by default) |
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75 | */ |
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76 | template<class V1, class V2> |
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77 | typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type |
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78 | dot (const V1 &v1, const V2 &v2) { |
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79 | return inner_prod (v1, v2); |
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80 | } |
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81 | |
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82 | /** Copy vector \f$v_2\f$ to \f$v_1\f$ |
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83 | * |
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84 | * \param v1 target vector |
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85 | * \param v2 source vector |
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86 | * \return a reference to the target vector |
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87 | * |
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88 | * \tparam V1 type of first vector (not needed by default) |
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89 | * \tparam V2 type of second vector (not needed by default) |
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90 | */ |
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91 | template<class V1, class V2> |
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92 | V1 & copy (V1 &v1, const V2 &v2) |
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93 | { |
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94 | return v1.assign (v2); |
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95 | } |
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96 | |
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97 | /** Swap vectors \f$v_1\f$ and \f$v_2\f$ |
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98 | * |
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99 | * \param v1 first vector |
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100 | * \param v2 second vector |
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101 | * |
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102 | * \tparam V1 type of first vector (not needed by default) |
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103 | * \tparam V2 type of second vector (not needed by default) |
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104 | */ |
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105 | template<class V1, class V2> |
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106 | void swap (V1 &v1, V2 &v2) |
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107 | { |
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108 | v1.swap (v2); |
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109 | } |
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110 | |
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111 | /** scale vector \f$v\f$ with scalar \f$t\f$ |
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112 | * |
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113 | * \param v vector to be scaled |
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114 | * \param t the scalar |
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115 | * \return \c t*v |
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116 | * |
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117 | * \tparam V type of the vector (not needed by default) |
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118 | * \tparam T type of the scalar (not needed by default) |
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119 | */ |
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120 | template<class V, class T> |
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121 | V & scal (V &v, const T &t) |
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122 | { |
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123 | return v *= t; |
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124 | } |
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125 | |
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126 | /** Compute \f$v_1= v_1 + t.v_2\f$ |
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127 | * |
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128 | * \param v1 target and first vector |
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129 | * \param t the scalar |
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130 | * \param v2 second vector |
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131 | * \return a reference to the first and target vector |
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132 | * |
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133 | * \tparam V1 type of the first vector (not needed by default) |
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134 | * \tparam T type of the scalar (not needed by default) |
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135 | * \tparam V2 type of the second vector (not needed by default) |
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136 | */ |
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137 | template<class V1, class T, class V2> |
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138 | V1 & axpy (V1 &v1, const T &t, const V2 &v2) |
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139 | { |
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140 | return v1.plus_assign (t * v2); |
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141 | } |
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142 | |
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143 | /** Performs rotation of points in the plane and assign the result to the first vector |
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144 | * |
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145 | * Each point is defined as a pair \c v1(i) and \c v2(i), being respectively |
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146 | * the \f$x\f$ and \f$y\f$ coordinates. The parameters \c t1 and \t2 are respectively |
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147 | * the cosine and sine of the angle of the rotation. |
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148 | * Results are not returned but directly written into \c v1. |
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149 | * |
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150 | * \param t1 cosine of the rotation |
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151 | * \param v1 vector of \f$x\f$ values |
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152 | * \param t2 sine of the rotation |
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153 | * \param v2 vector of \f$y\f$ values |
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154 | * |
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155 | * \tparam T1 type of the cosine value (not needed by default) |
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156 | * \tparam V1 type of the \f$x\f$ vector (not needed by default) |
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157 | * \tparam T2 type of the sine value (not needed by default) |
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158 | * \tparam V2 type of the \f$y\f$ vector (not needed by default) |
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159 | */ |
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160 | template<class T1, class V1, class T2, class V2> |
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161 | void rot (const T1 &t1, V1 &v1, const T2 &t2, V2 &v2) |
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162 | { |
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163 | typedef typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type promote_type; |
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164 | vector<promote_type> vt (t1 * v1 + t2 * v2); |
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165 | v2.assign (- t2 * v1 + t1 * v2); |
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166 | v1.assign (vt); |
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167 | } |
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168 | |
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169 | } |
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170 | |
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171 | /** \brief Interface and implementation of BLAS level 2 |
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172 | * This includes functions which perform \b matrix-vector operations. |
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173 | * More information about BLAS can be found at |
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174 | * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a> |
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175 | */ |
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176 | namespace blas_2 { |
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177 | |
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178 | /** \brief multiply vector \c v with triangular matrix \c m |
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179 | * |
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180 | * \param v a vector |
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181 | * \param m a triangular matrix |
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182 | * \return the result of the product |
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183 | * |
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184 | * \tparam V type of the vector (not needed by default) |
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185 | * \tparam M type of the matrix (not needed by default) |
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186 | */ |
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187 | template<class V, class M> |
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188 | V & tmv (V &v, const M &m) |
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189 | { |
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190 | return v = prod (m, v); |
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191 | } |
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192 | |
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193 | /** \brief solve \f$m.x = v\f$ in place, where \c m is a triangular matrix |
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194 | * |
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195 | * \param v a vector |
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196 | * \param m a matrix |
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197 | * \param C (this parameter is not needed) |
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198 | * \return a result vector from the above operation |
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199 | * |
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200 | * \tparam V type of the vector (not needed by default) |
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201 | * \tparam M type of the matrix (not needed by default) |
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202 | * \tparam C n/a |
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203 | */ |
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204 | template<class V, class M, class C> |
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205 | V & tsv (V &v, const M &m, C) |
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206 | { |
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207 | return v = solve (m, v, C ()); |
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208 | } |
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209 | |
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210 | /** \brief compute \f$ v_1 = t_1.v_1 + t_2.(m.v_2)\f$, a general matrix-vector product |
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211 | * |
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212 | * \param v1 a vector |
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213 | * \param t1 a scalar |
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214 | * \param t2 another scalar |
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215 | * \param m a matrix |
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216 | * \param v2 another vector |
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217 | * \return the vector \c v1 with the result from the above operation |
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218 | * |
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219 | * \tparam V1 type of first vector (not needed by default) |
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220 | * \tparam T1 type of first scalar (not needed by default) |
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221 | * \tparam T2 type of second scalar (not needed by default) |
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222 | * \tparam M type of matrix (not needed by default) |
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223 | * \tparam V2 type of second vector (not needed by default) |
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224 | */ |
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225 | template<class V1, class T1, class T2, class M, class V2> |
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226 | V1 & gmv (V1 &v1, const T1 &t1, const T2 &t2, const M &m, const V2 &v2) |
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227 | { |
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228 | return v1 = t1 * v1 + t2 * prod (m, v2); |
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229 | } |
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230 | |
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231 | /** \brief Rank 1 update: \f$ m = m + t.(v_1.v_2^T)\f$ |
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232 | * |
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233 | * \param m a matrix |
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234 | * \param t a scalar |
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235 | * \param v1 a vector |
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236 | * \param v2 another vector |
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237 | * \return a matrix with the result from the above operation |
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238 | * |
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239 | * \tparam M type of matrix (not needed by default) |
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240 | * \tparam T type of scalar (not needed by default) |
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241 | * \tparam V1 type of first vector (not needed by default) |
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242 | * \tparam V2type of second vector (not needed by default) |
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243 | */ |
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244 | template<class M, class T, class V1, class V2> |
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245 | M & gr (M &m, const T &t, const V1 &v1, const V2 &v2) |
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246 | { |
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247 | #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG |
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248 | return m += t * outer_prod (v1, v2); |
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249 | #else |
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250 | return m = m + t * outer_prod (v1, v2); |
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251 | #endif |
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252 | } |
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253 | |
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254 | /** \brief symmetric rank 1 update: \f$m = m + t.(v.v^T)\f$ |
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255 | * |
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256 | * \param m a matrix |
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257 | * \param t a scalar |
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258 | * \param v a vector |
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259 | * \return a matrix with the result from the above operation |
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260 | * |
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261 | * \tparam M type of matrix (not needed by default) |
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262 | * \tparam T type of scalar (not needed by default) |
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263 | * \tparam V type of vector (not needed by default) |
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264 | */ |
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265 | template<class M, class T, class V> |
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266 | M & sr (M &m, const T &t, const V &v) |
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267 | { |
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268 | #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG |
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269 | return m += t * outer_prod (v, v); |
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270 | #else |
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271 | return m = m + t * outer_prod (v, v); |
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272 | #endif |
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273 | } |
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274 | |
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275 | /** \brief hermitian rank 1 update: \f$m = m + t.(v.v^H)\f$ |
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276 | * |
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277 | * \param m a matrix |
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278 | * \param t a scalar |
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279 | * \param v a vector |
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280 | * \return a matrix with the result from the above operation |
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281 | * |
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282 | * \tparam M type of matrix (not needed by default) |
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283 | * \tparam T type of scalar (not needed by default) |
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284 | * \tparam V type of vector (not needed by default) |
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285 | */ |
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286 | template<class M, class T, class V> |
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287 | M & hr (M &m, const T &t, const V &v) |
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288 | { |
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289 | #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG |
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290 | return m += t * outer_prod (v, conj (v)); |
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291 | #else |
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292 | return m = m + t * outer_prod (v, conj (v)); |
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293 | #endif |
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294 | } |
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295 | |
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296 | /** \brief symmetric rank 2 update: \f$ m=m+ t.(v_1.v_2^T + v_2.v_1^T)\f$ |
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297 | * |
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298 | * \param m a matrix |
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299 | * \param t a scalar |
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300 | * \param v1 a vector |
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301 | * \param v2 another vector |
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302 | * \return a matrix with the result from the above operation |
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303 | * |
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304 | * \tparam M type of matrix (not needed by default) |
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305 | * \tparam T type of scalar (not needed by default) |
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306 | * \tparam V1 type of first vector (not needed by default) |
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307 | * \tparam V2type of second vector (not needed by default) |
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308 | */ |
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309 | template<class M, class T, class V1, class V2> |
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310 | M & sr2 (M &m, const T &t, const V1 &v1, const V2 &v2) |
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311 | { |
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312 | #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG |
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313 | return m += t * (outer_prod (v1, v2) + outer_prod (v2, v1)); |
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314 | #else |
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315 | return m = m + t * (outer_prod (v1, v2) + outer_prod (v2, v1)); |
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316 | #endif |
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317 | } |
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318 | |
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319 | /** \brief hermitian rank 2 update: \f$m=m+t.(v_1.v_2^H) + v_2.(t.v_1)^H)\f$ |
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320 | * |
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321 | * \param m a matrix |
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322 | * \param t a scalar |
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323 | * \param v1 a vector |
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324 | * \param v2 another vector |
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325 | * \return a matrix with the result from the above operation |
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326 | * |
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327 | * \tparam M type of matrix (not needed by default) |
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328 | * \tparam T type of scalar (not needed by default) |
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329 | * \tparam V1 type of first vector (not needed by default) |
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330 | * \tparam V2type of second vector (not needed by default) |
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331 | */ |
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332 | template<class M, class T, class V1, class V2> |
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333 | M & hr2 (M &m, const T &t, const V1 &v1, const V2 &v2) |
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334 | { |
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335 | #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG |
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336 | return m += t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1)); |
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337 | #else |
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338 | return m = m + t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1)); |
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339 | #endif |
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340 | } |
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341 | |
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342 | } |
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343 | |
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344 | /** \brief Interface and implementation of BLAS level 3 |
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345 | * This includes functions which perform \b matrix-matrix operations. |
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346 | * More information about BLAS can be found at |
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347 | * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a> |
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348 | */ |
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349 | namespace blas_3 { |
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350 | |
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351 | /** \brief triangular matrix multiplication \f$m_1=t.m_2.m_3\f$ where \f$m_2\f$ and \f$m_3\f$ are triangular |
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352 | * |
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353 | * \param m1 a matrix for storing result |
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354 | * \param t a scalar |
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355 | * \param m2 a triangular matrix |
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356 | * \param m3 a triangular matrix |
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357 | * \return the matrix \c m1 |
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358 | * |
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359 | * \tparam M1 type of the result matrix (not needed by default) |
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360 | * \tparam T type of the scalar (not needed by default) |
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361 | * \tparam M2 type of the first triangular matrix (not needed by default) |
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362 | * \tparam M3 type of the second triangular matrix (not needed by default) |
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363 | * |
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364 | */ |
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365 | template<class M1, class T, class M2, class M3> |
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366 | M1 & tmm (M1 &m1, const T &t, const M2 &m2, const M3 &m3) |
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367 | { |
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368 | return m1 = t * prod (m2, m3); |
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369 | } |
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370 | |
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371 | /** \brief triangular solve \f$ m_2.x = t.m_1\f$ in place, \f$m_2\f$ is a triangular matrix |
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372 | * |
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373 | * \param m1 a matrix |
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374 | * \param t a scalar |
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375 | * \param m2 a triangular matrix |
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376 | * \param C (not used) |
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377 | * \return the \f$m_1\f$ matrix |
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378 | * |
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379 | * \tparam M1 type of the first matrix (not needed by default) |
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380 | * \tparam T type of the scalar (not needed by default) |
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381 | * \tparam M2 type of the triangular matrix (not needed by default) |
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382 | * \tparam C (n/a) |
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383 | */ |
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384 | template<class M1, class T, class M2, class C> |
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385 | M1 & tsm (M1 &m1, const T &t, const M2 &m2, C) |
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386 | { |
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387 | return m1 = solve (m2, t * m1, C ()); |
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388 | } |
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389 | |
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390 | /** \brief general matrix multiplication \f$m_1=t_1.m_1 + t_2.m_2.m_3\f$ |
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391 | * |
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392 | * \param m1 first matrix |
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393 | * \param t1 first scalar |
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394 | * \param t2 second scalar |
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395 | * \param m2 second matrix |
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396 | * \param m3 third matrix |
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397 | * \return the matrix \c m1 |
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398 | * |
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399 | * \tparam M1 type of the first matrix (not needed by default) |
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400 | * \tparam T1 type of the first scalar (not needed by default) |
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401 | * \tparam T2 type of the second scalar (not needed by default) |
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402 | * \tparam M2 type of the second matrix (not needed by default) |
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403 | * \tparam M3 type of the third matrix (not needed by default) |
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404 | */ |
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405 | template<class M1, class T1, class T2, class M2, class M3> |
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406 | M1 & gmm (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) |
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407 | { |
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408 | return m1 = t1 * m1 + t2 * prod (m2, m3); |
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409 | } |
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410 | |
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411 | /** \brief symmetric rank \a k update: \f$m_1=t.m_1+t_2.(m_2.m_2^T)\f$ |
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412 | * |
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413 | * \param m1 first matrix |
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414 | * \param t1 first scalar |
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415 | * \param t2 second scalar |
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416 | * \param m2 second matrix |
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417 | * \return matrix \c m1 |
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418 | * |
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419 | * \tparam M1 type of the first matrix (not needed by default) |
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420 | * \tparam T1 type of the first scalar (not needed by default) |
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421 | * \tparam T2 type of the second scalar (not needed by default) |
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422 | * \tparam M2 type of the second matrix (not needed by default) |
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423 | * \todo use opb_prod() |
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424 | */ |
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425 | template<class M1, class T1, class T2, class M2> |
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426 | M1 & srk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2) |
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427 | { |
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428 | return m1 = t1 * m1 + t2 * prod (m2, trans (m2)); |
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429 | } |
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430 | |
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431 | /** \brief hermitian rank \a k update: \f$m_1=t.m_1+t_2.(m_2.m2^H)\f$ |
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432 | * |
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433 | * \param m1 first matrix |
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434 | * \param t1 first scalar |
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435 | * \param t2 second scalar |
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436 | * \param m2 second matrix |
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437 | * \return matrix \c m1 |
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438 | * |
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439 | * \tparam M1 type of the first matrix (not needed by default) |
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440 | * \tparam T1 type of the first scalar (not needed by default) |
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441 | * \tparam T2 type of the second scalar (not needed by default) |
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442 | * \tparam M2 type of the second matrix (not needed by default) |
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443 | * \todo use opb_prod() |
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444 | */ |
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445 | template<class M1, class T1, class T2, class M2> |
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446 | M1 & hrk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2) |
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447 | { |
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448 | return m1 = t1 * m1 + t2 * prod (m2, herm (m2)); |
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449 | } |
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450 | |
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451 | /** \brief generalized symmetric rank \a k update: \f$m_1=t_1.m_1+t_2.(m_2.m3^T)+t_2.(m_3.m2^T)\f$ |
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452 | * |
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453 | * \param m1 first matrix |
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454 | * \param t1 first scalar |
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455 | * \param t2 second scalar |
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456 | * \param m2 second matrix |
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457 | * \param m3 third matrix |
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458 | * \return matrix \c m1 |
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459 | * |
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460 | * \tparam M1 type of the first matrix (not needed by default) |
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461 | * \tparam T1 type of the first scalar (not needed by default) |
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462 | * \tparam T2 type of the second scalar (not needed by default) |
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463 | * \tparam M2 type of the second matrix (not needed by default) |
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464 | * \tparam M3 type of the third matrix (not needed by default) |
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465 | * \todo use opb_prod() |
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466 | */ |
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467 | template<class M1, class T1, class T2, class M2, class M3> |
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468 | M1 & sr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) |
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469 | { |
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470 | return m1 = t1 * m1 + t2 * (prod (m2, trans (m3)) + prod (m3, trans (m2))); |
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471 | } |
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472 | |
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473 | /** \brief generalized hermitian rank \a k update: * \f$m_1=t_1.m_1+t_2.(m_2.m_3^H)+(m_3.(t_2.m_2)^H)\f$ |
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474 | * |
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475 | * \param m1 first matrix |
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476 | * \param t1 first scalar |
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477 | * \param t2 second scalar |
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478 | * \param m2 second matrix |
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479 | * \param m3 third matrix |
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480 | * \return matrix \c m1 |
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481 | * |
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482 | * \tparam M1 type of the first matrix (not needed by default) |
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483 | * \tparam T1 type of the first scalar (not needed by default) |
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484 | * \tparam T2 type of the second scalar (not needed by default) |
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485 | * \tparam M2 type of the second matrix (not needed by default) |
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486 | * \tparam M3 type of the third matrix (not needed by default) |
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487 | * \todo use opb_prod() |
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488 | */ |
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489 | template<class M1, class T1, class T2, class M2, class M3> |
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490 | M1 & hr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) |
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491 | { |
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492 | return m1 = |
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493 | t1 * m1 |
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494 | + t2 * prod (m2, herm (m3)) |
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495 | + type_traits<T2>::conj (t2) * prod (m3, herm (m2)); |
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496 | } |
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497 | |
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498 | } |
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499 | |
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500 | }}} |
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501 | |
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502 | #endif |
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