1 | // |
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2 | // Copyright (c) 2000-2009 |
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3 | // Joerg Walter, Mathias Koch, Gunter Winkler |
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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_FUNCTIONAL_ |
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14 | #define _BOOST_UBLAS_FUNCTIONAL_ |
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15 | |
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16 | #include <functional> |
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17 | |
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18 | #include <boost/numeric/ublas/traits.hpp> |
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19 | #ifdef BOOST_UBLAS_USE_DUFF_DEVICE |
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20 | #include <boost/numeric/ublas/detail/duff.hpp> |
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21 | #endif |
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22 | #ifdef BOOST_UBLAS_USE_SIMD |
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23 | #include <boost/numeric/ublas/detail/raw.hpp> |
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24 | #else |
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25 | namespace boost { namespace numeric { namespace ublas { namespace raw { |
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26 | }}}} |
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27 | #endif |
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28 | #ifdef BOOST_UBLAS_HAVE_BINDINGS |
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29 | #include <boost/numeric/bindings/traits/std_vector.hpp> |
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30 | #include <boost/numeric/bindings/traits/ublas_vector.hpp> |
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31 | #include <boost/numeric/bindings/traits/ublas_matrix.hpp> |
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32 | #include <boost/numeric/bindings/atlas/cblas.hpp> |
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33 | #endif |
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34 | |
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35 | #include <boost/numeric/ublas/detail/definitions.hpp> |
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36 | |
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37 | |
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38 | |
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39 | namespace boost { namespace numeric { namespace ublas { |
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40 | |
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41 | // Scalar functors |
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42 | |
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43 | // Unary |
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44 | template<class T> |
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45 | struct scalar_unary_functor { |
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46 | typedef T value_type; |
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47 | typedef typename type_traits<T>::const_reference argument_type; |
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48 | typedef typename type_traits<T>::value_type result_type; |
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49 | }; |
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50 | |
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51 | template<class T> |
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52 | struct scalar_identity: |
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53 | public scalar_unary_functor<T> { |
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54 | typedef typename scalar_unary_functor<T>::argument_type argument_type; |
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55 | typedef typename scalar_unary_functor<T>::result_type result_type; |
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56 | |
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57 | static BOOST_UBLAS_INLINE |
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58 | result_type apply (argument_type t) { |
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59 | return t; |
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60 | } |
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61 | }; |
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62 | template<class T> |
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63 | struct scalar_negate: |
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64 | public scalar_unary_functor<T> { |
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65 | typedef typename scalar_unary_functor<T>::argument_type argument_type; |
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66 | typedef typename scalar_unary_functor<T>::result_type result_type; |
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67 | |
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68 | static BOOST_UBLAS_INLINE |
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69 | result_type apply (argument_type t) { |
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70 | return - t; |
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71 | } |
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72 | }; |
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73 | template<class T> |
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74 | struct scalar_conj: |
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75 | public scalar_unary_functor<T> { |
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76 | typedef typename scalar_unary_functor<T>::value_type value_type; |
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77 | typedef typename scalar_unary_functor<T>::argument_type argument_type; |
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78 | typedef typename scalar_unary_functor<T>::result_type result_type; |
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79 | |
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80 | static BOOST_UBLAS_INLINE |
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81 | result_type apply (argument_type t) { |
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82 | return type_traits<value_type>::conj (t); |
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83 | } |
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84 | }; |
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85 | |
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86 | // Unary returning real |
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87 | template<class T> |
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88 | struct scalar_real_unary_functor { |
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89 | typedef T value_type; |
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90 | typedef typename type_traits<T>::const_reference argument_type; |
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91 | typedef typename type_traits<T>::real_type result_type; |
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92 | }; |
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93 | |
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94 | template<class T> |
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95 | struct scalar_real: |
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96 | public scalar_real_unary_functor<T> { |
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97 | typedef typename scalar_real_unary_functor<T>::value_type value_type; |
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98 | typedef typename scalar_real_unary_functor<T>::argument_type argument_type; |
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99 | typedef typename scalar_real_unary_functor<T>::result_type result_type; |
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100 | |
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101 | static BOOST_UBLAS_INLINE |
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102 | result_type apply (argument_type t) { |
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103 | return type_traits<value_type>::real (t); |
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104 | } |
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105 | }; |
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106 | template<class T> |
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107 | struct scalar_imag: |
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108 | public scalar_real_unary_functor<T> { |
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109 | typedef typename scalar_real_unary_functor<T>::value_type value_type; |
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110 | typedef typename scalar_real_unary_functor<T>::argument_type argument_type; |
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111 | typedef typename scalar_real_unary_functor<T>::result_type result_type; |
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112 | |
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113 | static BOOST_UBLAS_INLINE |
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114 | result_type apply (argument_type t) { |
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115 | return type_traits<value_type>::imag (t); |
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116 | } |
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117 | }; |
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118 | |
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119 | // Binary |
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120 | template<class T1, class T2> |
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121 | struct scalar_binary_functor { |
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122 | typedef typename type_traits<T1>::const_reference argument1_type; |
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123 | typedef typename type_traits<T2>::const_reference argument2_type; |
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124 | typedef typename promote_traits<T1, T2>::promote_type result_type; |
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125 | }; |
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126 | |
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127 | template<class T1, class T2> |
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128 | struct scalar_plus: |
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129 | public scalar_binary_functor<T1, T2> { |
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130 | typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type; |
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131 | typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type; |
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132 | typedef typename scalar_binary_functor<T1, T2>::result_type result_type; |
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133 | |
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134 | static BOOST_UBLAS_INLINE |
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135 | result_type apply (argument1_type t1, argument2_type t2) { |
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136 | return t1 + t2; |
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137 | } |
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138 | }; |
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139 | template<class T1, class T2> |
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140 | struct scalar_minus: |
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141 | public scalar_binary_functor<T1, T2> { |
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142 | typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type; |
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143 | typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type; |
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144 | typedef typename scalar_binary_functor<T1, T2>::result_type result_type; |
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145 | |
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146 | static BOOST_UBLAS_INLINE |
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147 | result_type apply (argument1_type t1, argument2_type t2) { |
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148 | return t1 - t2; |
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149 | } |
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150 | }; |
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151 | template<class T1, class T2> |
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152 | struct scalar_multiplies: |
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153 | public scalar_binary_functor<T1, T2> { |
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154 | typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type; |
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155 | typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type; |
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156 | typedef typename scalar_binary_functor<T1, T2>::result_type result_type; |
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157 | |
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158 | static BOOST_UBLAS_INLINE |
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159 | result_type apply (argument1_type t1, argument2_type t2) { |
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160 | return t1 * t2; |
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161 | } |
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162 | }; |
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163 | template<class T1, class T2> |
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164 | struct scalar_divides: |
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165 | public scalar_binary_functor<T1, T2> { |
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166 | typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type; |
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167 | typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type; |
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168 | typedef typename scalar_binary_functor<T1, T2>::result_type result_type; |
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169 | |
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170 | static BOOST_UBLAS_INLINE |
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171 | result_type apply (argument1_type t1, argument2_type t2) { |
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172 | return t1 / t2; |
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173 | } |
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174 | }; |
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175 | |
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176 | template<class T1, class T2> |
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177 | struct scalar_binary_assign_functor { |
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178 | // ISSUE Remove reference to avoid reference to reference problems |
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179 | typedef typename type_traits<typename boost::remove_reference<T1>::type>::reference argument1_type; |
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180 | typedef typename type_traits<T2>::const_reference argument2_type; |
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181 | }; |
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182 | |
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183 | struct assign_tag {}; |
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184 | struct computed_assign_tag {}; |
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185 | |
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186 | template<class T1, class T2> |
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187 | struct scalar_assign: |
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188 | public scalar_binary_assign_functor<T1, T2> { |
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189 | typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; |
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190 | typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; |
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191 | #if BOOST_WORKAROUND( __IBMCPP__, <=600 ) |
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192 | static const bool computed ; |
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193 | #else |
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194 | static const bool computed = false ; |
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195 | #endif |
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196 | |
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197 | static BOOST_UBLAS_INLINE |
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198 | void apply (argument1_type t1, argument2_type t2) { |
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199 | t1 = t2; |
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200 | } |
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201 | |
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202 | template<class U1, class U2> |
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203 | struct rebind { |
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204 | typedef scalar_assign<U1, U2> other; |
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205 | }; |
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206 | }; |
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207 | |
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208 | #if BOOST_WORKAROUND( __IBMCPP__, <=600 ) |
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209 | template<class T1, class T2> |
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210 | const bool scalar_assign<T1,T2>::computed = false; |
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211 | #endif |
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212 | |
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213 | template<class T1, class T2> |
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214 | struct scalar_plus_assign: |
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215 | public scalar_binary_assign_functor<T1, T2> { |
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216 | typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; |
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217 | typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; |
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218 | #if BOOST_WORKAROUND( __IBMCPP__, <=600 ) |
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219 | static const bool computed ; |
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220 | #else |
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221 | static const bool computed = true ; |
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222 | #endif |
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223 | |
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224 | static BOOST_UBLAS_INLINE |
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225 | void apply (argument1_type t1, argument2_type t2) { |
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226 | t1 += t2; |
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227 | } |
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228 | |
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229 | template<class U1, class U2> |
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230 | struct rebind { |
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231 | typedef scalar_plus_assign<U1, U2> other; |
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232 | }; |
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233 | }; |
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234 | |
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235 | #if BOOST_WORKAROUND( __IBMCPP__, <=600 ) |
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236 | template<class T1, class T2> |
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237 | const bool scalar_plus_assign<T1,T2>::computed = true; |
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238 | #endif |
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239 | |
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240 | template<class T1, class T2> |
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241 | struct scalar_minus_assign: |
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242 | public scalar_binary_assign_functor<T1, T2> { |
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243 | typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; |
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244 | typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; |
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245 | #if BOOST_WORKAROUND( __IBMCPP__, <=600 ) |
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246 | static const bool computed ; |
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247 | #else |
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248 | static const bool computed = true ; |
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249 | #endif |
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250 | |
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251 | static BOOST_UBLAS_INLINE |
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252 | void apply (argument1_type t1, argument2_type t2) { |
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253 | t1 -= t2; |
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254 | } |
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255 | |
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256 | template<class U1, class U2> |
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257 | struct rebind { |
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258 | typedef scalar_minus_assign<U1, U2> other; |
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259 | }; |
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260 | }; |
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261 | |
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262 | #if BOOST_WORKAROUND( __IBMCPP__, <=600 ) |
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263 | template<class T1, class T2> |
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264 | const bool scalar_minus_assign<T1,T2>::computed = true; |
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265 | #endif |
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266 | |
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267 | template<class T1, class T2> |
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268 | struct scalar_multiplies_assign: |
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269 | public scalar_binary_assign_functor<T1, T2> { |
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270 | typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; |
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271 | typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; |
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272 | static const bool computed = true; |
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273 | |
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274 | static BOOST_UBLAS_INLINE |
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275 | void apply (argument1_type t1, argument2_type t2) { |
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276 | t1 *= t2; |
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277 | } |
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278 | |
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279 | template<class U1, class U2> |
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280 | struct rebind { |
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281 | typedef scalar_multiplies_assign<U1, U2> other; |
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282 | }; |
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283 | }; |
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284 | template<class T1, class T2> |
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285 | struct scalar_divides_assign: |
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286 | public scalar_binary_assign_functor<T1, T2> { |
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287 | typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; |
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288 | typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; |
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289 | static const bool computed ; |
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290 | |
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291 | static BOOST_UBLAS_INLINE |
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292 | void apply (argument1_type t1, argument2_type t2) { |
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293 | t1 /= t2; |
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294 | } |
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295 | |
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296 | template<class U1, class U2> |
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297 | struct rebind { |
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298 | typedef scalar_divides_assign<U1, U2> other; |
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299 | }; |
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300 | }; |
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301 | template<class T1, class T2> |
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302 | const bool scalar_divides_assign<T1,T2>::computed = true; |
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303 | |
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304 | template<class T1, class T2> |
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305 | struct scalar_binary_swap_functor { |
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306 | typedef typename type_traits<typename boost::remove_reference<T1>::type>::reference argument1_type; |
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307 | typedef typename type_traits<typename boost::remove_reference<T2>::type>::reference argument2_type; |
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308 | }; |
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309 | |
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310 | template<class T1, class T2> |
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311 | struct scalar_swap: |
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312 | public scalar_binary_swap_functor<T1, T2> { |
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313 | typedef typename scalar_binary_swap_functor<T1, T2>::argument1_type argument1_type; |
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314 | typedef typename scalar_binary_swap_functor<T1, T2>::argument2_type argument2_type; |
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315 | |
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316 | static BOOST_UBLAS_INLINE |
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317 | void apply (argument1_type t1, argument2_type t2) { |
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318 | std::swap (t1, t2); |
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319 | } |
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320 | |
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321 | template<class U1, class U2> |
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322 | struct rebind { |
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323 | typedef scalar_swap<U1, U2> other; |
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324 | }; |
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325 | }; |
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326 | |
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327 | // Vector functors |
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328 | |
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329 | // Unary returning scalar |
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330 | template<class V> |
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331 | struct vector_scalar_unary_functor { |
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332 | typedef typename V::value_type value_type; |
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333 | typedef typename V::value_type result_type; |
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334 | }; |
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335 | |
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336 | template<class V> |
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337 | struct vector_sum: |
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338 | public vector_scalar_unary_functor<V> { |
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339 | typedef typename vector_scalar_unary_functor<V>::value_type value_type; |
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340 | typedef typename vector_scalar_unary_functor<V>::result_type result_type; |
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341 | |
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342 | template<class E> |
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343 | static BOOST_UBLAS_INLINE |
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344 | result_type apply (const vector_expression<E> &e) { |
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345 | result_type t = result_type (0); |
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346 | typedef typename E::size_type vector_size_type; |
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347 | vector_size_type size (e ().size ()); |
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348 | for (vector_size_type i = 0; i < size; ++ i) |
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349 | t += e () (i); |
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350 | return t; |
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351 | } |
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352 | // Dense case |
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353 | template<class D, class I> |
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354 | static BOOST_UBLAS_INLINE |
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355 | result_type apply (D size, I it) { |
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356 | result_type t = result_type (0); |
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357 | while (-- size >= 0) |
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358 | t += *it, ++ it; |
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359 | return t; |
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360 | } |
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361 | // Sparse case |
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362 | template<class I> |
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363 | static BOOST_UBLAS_INLINE |
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364 | result_type apply (I it, const I &it_end) { |
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365 | result_type t = result_type (0); |
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366 | while (it != it_end) |
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367 | t += *it, ++ it; |
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368 | return t; |
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369 | } |
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370 | }; |
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371 | |
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372 | // Unary returning real scalar |
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373 | template<class V> |
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374 | struct vector_scalar_real_unary_functor { |
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375 | typedef typename V::value_type value_type; |
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376 | typedef typename type_traits<value_type>::real_type real_type; |
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377 | typedef real_type result_type; |
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378 | }; |
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379 | |
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380 | template<class V> |
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381 | struct vector_norm_1: |
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382 | public vector_scalar_real_unary_functor<V> { |
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383 | typedef typename vector_scalar_real_unary_functor<V>::value_type value_type; |
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384 | typedef typename vector_scalar_real_unary_functor<V>::real_type real_type; |
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385 | typedef typename vector_scalar_real_unary_functor<V>::result_type result_type; |
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386 | |
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387 | template<class E> |
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388 | static BOOST_UBLAS_INLINE |
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389 | result_type apply (const vector_expression<E> &e) { |
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390 | real_type t = real_type (); |
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391 | typedef typename E::size_type vector_size_type; |
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392 | vector_size_type size (e ().size ()); |
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393 | for (vector_size_type i = 0; i < size; ++ i) { |
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394 | real_type u (type_traits<value_type>::type_abs (e () (i))); |
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395 | t += u; |
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396 | } |
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397 | return t; |
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398 | } |
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399 | // Dense case |
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400 | template<class D, class I> |
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401 | static BOOST_UBLAS_INLINE |
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402 | result_type apply (D size, I it) { |
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403 | real_type t = real_type (); |
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404 | while (-- size >= 0) { |
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405 | real_type u (type_traits<value_type>::norm_1 (*it)); |
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406 | t += u; |
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407 | ++ it; |
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408 | } |
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409 | return t; |
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410 | } |
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411 | // Sparse case |
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412 | template<class I> |
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413 | static BOOST_UBLAS_INLINE |
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414 | result_type apply (I it, const I &it_end) { |
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415 | real_type t = real_type (); |
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416 | while (it != it_end) { |
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417 | real_type u (type_traits<value_type>::norm_1 (*it)); |
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418 | t += u; |
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419 | ++ it; |
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420 | } |
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421 | return t; |
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422 | } |
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423 | }; |
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424 | template<class V> |
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425 | struct vector_norm_2: |
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426 | public vector_scalar_real_unary_functor<V> { |
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427 | typedef typename vector_scalar_real_unary_functor<V>::value_type value_type; |
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428 | typedef typename vector_scalar_real_unary_functor<V>::real_type real_type; |
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429 | typedef typename vector_scalar_real_unary_functor<V>::result_type result_type; |
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430 | |
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431 | template<class E> |
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432 | static BOOST_UBLAS_INLINE |
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433 | result_type apply (const vector_expression<E> &e) { |
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434 | #ifndef BOOST_UBLAS_SCALED_NORM |
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435 | real_type t = real_type (); |
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436 | typedef typename E::size_type vector_size_type; |
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437 | vector_size_type size (e ().size ()); |
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438 | for (vector_size_type i = 0; i < size; ++ i) { |
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439 | real_type u (type_traits<value_type>::norm_2 (e () (i))); |
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440 | t += u * u; |
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441 | } |
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442 | return type_traits<real_type>::type_sqrt (t); |
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443 | #else |
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444 | real_type scale = real_type (); |
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445 | real_type sum_squares (1); |
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446 | size_type size (e ().size ()); |
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447 | for (size_type i = 0; i < size; ++ i) { |
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448 | real_type u (type_traits<value_type>::norm_2 (e () (i))); |
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449 | if ( real_type () /* zero */ == u ) continue; |
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450 | if (scale < u) { |
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451 | real_type v (scale / u); |
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452 | sum_squares = sum_squares * v * v + real_type (1); |
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453 | scale = u; |
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454 | } else { |
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455 | real_type v (u / scale); |
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456 | sum_squares += v * v; |
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457 | } |
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458 | } |
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459 | return scale * type_traits<real_type>::type_sqrt (sum_squares); |
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460 | #endif |
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461 | } |
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462 | // Dense case |
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463 | template<class D, class I> |
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464 | static BOOST_UBLAS_INLINE |
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465 | result_type apply (D size, I it) { |
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466 | #ifndef BOOST_UBLAS_SCALED_NORM |
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467 | real_type t = real_type (); |
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468 | while (-- size >= 0) { |
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469 | real_type u (type_traits<value_type>::norm_2 (*it)); |
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470 | t += u * u; |
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471 | ++ it; |
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472 | } |
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473 | return type_traits<real_type>::type_sqrt (t); |
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474 | #else |
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475 | real_type scale = real_type (); |
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476 | real_type sum_squares (1); |
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477 | while (-- size >= 0) { |
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478 | real_type u (type_traits<value_type>::norm_2 (*it)); |
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479 | if (scale < u) { |
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480 | real_type v (scale / u); |
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481 | sum_squares = sum_squares * v * v + real_type (1); |
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482 | scale = u; |
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483 | } else { |
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484 | real_type v (u / scale); |
---|
485 | sum_squares += v * v; |
---|
486 | } |
---|
487 | ++ it; |
---|
488 | } |
---|
489 | return scale * type_traits<real_type>::type_sqrt (sum_squares); |
---|
490 | #endif |
---|
491 | } |
---|
492 | // Sparse case |
---|
493 | template<class I> |
---|
494 | static BOOST_UBLAS_INLINE |
---|
495 | result_type apply (I it, const I &it_end) { |
---|
496 | #ifndef BOOST_UBLAS_SCALED_NORM |
---|
497 | real_type t = real_type (); |
---|
498 | while (it != it_end) { |
---|
499 | real_type u (type_traits<value_type>::norm_2 (*it)); |
---|
500 | t += u * u; |
---|
501 | ++ it; |
---|
502 | } |
---|
503 | return type_traits<real_type>::type_sqrt (t); |
---|
504 | #else |
---|
505 | real_type scale = real_type (); |
---|
506 | real_type sum_squares (1); |
---|
507 | while (it != it_end) { |
---|
508 | real_type u (type_traits<value_type>::norm_2 (*it)); |
---|
509 | if (scale < u) { |
---|
510 | real_type v (scale / u); |
---|
511 | sum_squares = sum_squares * v * v + real_type (1); |
---|
512 | scale = u; |
---|
513 | } else { |
---|
514 | real_type v (u / scale); |
---|
515 | sum_squares += v * v; |
---|
516 | } |
---|
517 | ++ it; |
---|
518 | } |
---|
519 | return scale * type_traits<real_type>::type_sqrt (sum_squares); |
---|
520 | #endif |
---|
521 | } |
---|
522 | }; |
---|
523 | template<class V> |
---|
524 | struct vector_norm_inf: |
---|
525 | public vector_scalar_real_unary_functor<V> { |
---|
526 | typedef typename vector_scalar_real_unary_functor<V>::value_type value_type; |
---|
527 | typedef typename vector_scalar_real_unary_functor<V>::real_type real_type; |
---|
528 | typedef typename vector_scalar_real_unary_functor<V>::result_type result_type; |
---|
529 | |
---|
530 | template<class E> |
---|
531 | static BOOST_UBLAS_INLINE |
---|
532 | result_type apply (const vector_expression<E> &e) { |
---|
533 | real_type t = real_type (); |
---|
534 | typedef typename E::size_type vector_size_type; |
---|
535 | vector_size_type size (e ().size ()); |
---|
536 | for (vector_size_type i = 0; i < size; ++ i) { |
---|
537 | real_type u (type_traits<value_type>::norm_inf (e () (i))); |
---|
538 | if (u > t) |
---|
539 | t = u; |
---|
540 | } |
---|
541 | return t; |
---|
542 | } |
---|
543 | // Dense case |
---|
544 | template<class D, class I> |
---|
545 | static BOOST_UBLAS_INLINE |
---|
546 | result_type apply (D size, I it) { |
---|
547 | real_type t = real_type (); |
---|
548 | while (-- size >= 0) { |
---|
549 | real_type u (type_traits<value_type>::norm_inf (*it)); |
---|
550 | if (u > t) |
---|
551 | t = u; |
---|
552 | ++ it; |
---|
553 | } |
---|
554 | return t; |
---|
555 | } |
---|
556 | // Sparse case |
---|
557 | template<class I> |
---|
558 | static BOOST_UBLAS_INLINE |
---|
559 | result_type apply (I it, const I &it_end) { |
---|
560 | real_type t = real_type (); |
---|
561 | while (it != it_end) { |
---|
562 | real_type u (type_traits<value_type>::norm_inf (*it)); |
---|
563 | if (u > t) |
---|
564 | t = u; |
---|
565 | ++ it; |
---|
566 | } |
---|
567 | return t; |
---|
568 | } |
---|
569 | }; |
---|
570 | |
---|
571 | // Unary returning index |
---|
572 | template<class V> |
---|
573 | struct vector_scalar_index_unary_functor { |
---|
574 | typedef typename V::value_type value_type; |
---|
575 | typedef typename type_traits<value_type>::real_type real_type; |
---|
576 | typedef typename V::size_type result_type; |
---|
577 | }; |
---|
578 | |
---|
579 | template<class V> |
---|
580 | struct vector_index_norm_inf: |
---|
581 | public vector_scalar_index_unary_functor<V> { |
---|
582 | typedef typename vector_scalar_index_unary_functor<V>::value_type value_type; |
---|
583 | typedef typename vector_scalar_index_unary_functor<V>::real_type real_type; |
---|
584 | typedef typename vector_scalar_index_unary_functor<V>::result_type result_type; |
---|
585 | |
---|
586 | template<class E> |
---|
587 | static BOOST_UBLAS_INLINE |
---|
588 | result_type apply (const vector_expression<E> &e) { |
---|
589 | // ISSUE For CBLAS compatibility return 0 index in empty case |
---|
590 | result_type i_norm_inf (0); |
---|
591 | real_type t = real_type (); |
---|
592 | typedef typename E::size_type vector_size_type; |
---|
593 | vector_size_type size (e ().size ()); |
---|
594 | for (vector_size_type i = 0; i < size; ++ i) { |
---|
595 | real_type u (type_traits<value_type>::norm_inf (e () (i))); |
---|
596 | if (u > t) { |
---|
597 | i_norm_inf = i; |
---|
598 | t = u; |
---|
599 | } |
---|
600 | } |
---|
601 | return i_norm_inf; |
---|
602 | } |
---|
603 | // Dense case |
---|
604 | template<class D, class I> |
---|
605 | static BOOST_UBLAS_INLINE |
---|
606 | result_type apply (D size, I it) { |
---|
607 | // ISSUE For CBLAS compatibility return 0 index in empty case |
---|
608 | result_type i_norm_inf (0); |
---|
609 | real_type t = real_type (); |
---|
610 | while (-- size >= 0) { |
---|
611 | real_type u (type_traits<value_type>::norm_inf (*it)); |
---|
612 | if (u > t) { |
---|
613 | i_norm_inf = it.index (); |
---|
614 | t = u; |
---|
615 | } |
---|
616 | ++ it; |
---|
617 | } |
---|
618 | return i_norm_inf; |
---|
619 | } |
---|
620 | // Sparse case |
---|
621 | template<class I> |
---|
622 | static BOOST_UBLAS_INLINE |
---|
623 | result_type apply (I it, const I &it_end) { |
---|
624 | // ISSUE For CBLAS compatibility return 0 index in empty case |
---|
625 | result_type i_norm_inf (0); |
---|
626 | real_type t = real_type (); |
---|
627 | while (it != it_end) { |
---|
628 | real_type u (type_traits<value_type>::norm_inf (*it)); |
---|
629 | if (u > t) { |
---|
630 | i_norm_inf = it.index (); |
---|
631 | t = u; |
---|
632 | } |
---|
633 | ++ it; |
---|
634 | } |
---|
635 | return i_norm_inf; |
---|
636 | } |
---|
637 | }; |
---|
638 | |
---|
639 | // Binary returning scalar |
---|
640 | template<class V1, class V2, class TV> |
---|
641 | struct vector_scalar_binary_functor { |
---|
642 | typedef TV value_type; |
---|
643 | typedef TV result_type; |
---|
644 | }; |
---|
645 | |
---|
646 | template<class V1, class V2, class TV> |
---|
647 | struct vector_inner_prod: |
---|
648 | public vector_scalar_binary_functor<V1, V2, TV> { |
---|
649 | typedef typename vector_scalar_binary_functor<V1, V2, TV>::value_type value_type; |
---|
650 | typedef typename vector_scalar_binary_functor<V1, V2, TV>::result_type result_type; |
---|
651 | |
---|
652 | template<class C1, class C2> |
---|
653 | static BOOST_UBLAS_INLINE |
---|
654 | result_type apply (const vector_container<C1> &c1, |
---|
655 | const vector_container<C2> &c2) { |
---|
656 | #ifdef BOOST_UBLAS_USE_SIMD |
---|
657 | using namespace raw; |
---|
658 | typedef typename C1::size_type vector_size_type; |
---|
659 | vector_size_type size (BOOST_UBLAS_SAME (c1 ().size (), c2 ().size ())); |
---|
660 | const typename V1::value_type *data1 = data_const (c1 ()); |
---|
661 | const typename V1::value_type *data2 = data_const (c2 ()); |
---|
662 | vector_size_type s1 = stride (c1 ()); |
---|
663 | vector_size_type s2 = stride (c2 ()); |
---|
664 | result_type t = result_type (0); |
---|
665 | if (s1 == 1 && s2 == 1) { |
---|
666 | for (vector_size_type i = 0; i < size; ++ i) |
---|
667 | t += data1 [i] * data2 [i]; |
---|
668 | } else if (s2 == 1) { |
---|
669 | for (vector_size_type i = 0, i1 = 0; i < size; ++ i, i1 += s1) |
---|
670 | t += data1 [i1] * data2 [i]; |
---|
671 | } else if (s1 == 1) { |
---|
672 | for (vector_size_type i = 0, i2 = 0; i < size; ++ i, i2 += s2) |
---|
673 | t += data1 [i] * data2 [i2]; |
---|
674 | } else { |
---|
675 | for (vector_size_type i = 0, i1 = 0, i2 = 0; i < size; ++ i, i1 += s1, i2 += s2) |
---|
676 | t += data1 [i1] * data2 [i2]; |
---|
677 | } |
---|
678 | return t; |
---|
679 | #elif defined(BOOST_UBLAS_HAVE_BINDINGS) |
---|
680 | return boost::numeric::bindings::atlas::dot (c1 (), c2 ()); |
---|
681 | #else |
---|
682 | return apply (static_cast<const vector_expression<C1> > (c1), static_cast<const vector_expression<C2> > (c2)); |
---|
683 | #endif |
---|
684 | } |
---|
685 | template<class E1, class E2> |
---|
686 | static BOOST_UBLAS_INLINE |
---|
687 | result_type apply (const vector_expression<E1> &e1, |
---|
688 | const vector_expression<E2> &e2) { |
---|
689 | typedef typename E1::size_type vector_size_type; |
---|
690 | vector_size_type size (BOOST_UBLAS_SAME (e1 ().size (), e2 ().size ())); |
---|
691 | result_type t = result_type (0); |
---|
692 | #ifndef BOOST_UBLAS_USE_DUFF_DEVICE |
---|
693 | for (vector_size_type i = 0; i < size; ++ i) |
---|
694 | t += e1 () (i) * e2 () (i); |
---|
695 | #else |
---|
696 | vector_size_type i (0); |
---|
697 | DD (size, 4, r, (t += e1 () (i) * e2 () (i), ++ i)); |
---|
698 | #endif |
---|
699 | return t; |
---|
700 | } |
---|
701 | // Dense case |
---|
702 | template<class D, class I1, class I2> |
---|
703 | static BOOST_UBLAS_INLINE |
---|
704 | result_type apply (D size, I1 it1, I2 it2) { |
---|
705 | result_type t = result_type (0); |
---|
706 | #ifndef BOOST_UBLAS_USE_DUFF_DEVICE |
---|
707 | while (-- size >= 0) |
---|
708 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
709 | #else |
---|
710 | DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2)); |
---|
711 | #endif |
---|
712 | return t; |
---|
713 | } |
---|
714 | // Packed case |
---|
715 | template<class I1, class I2> |
---|
716 | static BOOST_UBLAS_INLINE |
---|
717 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) { |
---|
718 | result_type t = result_type (0); |
---|
719 | typedef typename I1::difference_type vector_difference_type; |
---|
720 | vector_difference_type it1_size (it1_end - it1); |
---|
721 | vector_difference_type it2_size (it2_end - it2); |
---|
722 | vector_difference_type diff (0); |
---|
723 | if (it1_size > 0 && it2_size > 0) |
---|
724 | diff = it2.index () - it1.index (); |
---|
725 | if (diff != 0) { |
---|
726 | vector_difference_type size = (std::min) (diff, it1_size); |
---|
727 | if (size > 0) { |
---|
728 | it1 += size; |
---|
729 | it1_size -= size; |
---|
730 | diff -= size; |
---|
731 | } |
---|
732 | size = (std::min) (- diff, it2_size); |
---|
733 | if (size > 0) { |
---|
734 | it2 += size; |
---|
735 | it2_size -= size; |
---|
736 | diff += size; |
---|
737 | } |
---|
738 | } |
---|
739 | vector_difference_type size ((std::min) (it1_size, it2_size)); |
---|
740 | while (-- size >= 0) |
---|
741 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
742 | return t; |
---|
743 | } |
---|
744 | // Sparse case |
---|
745 | template<class I1, class I2> |
---|
746 | static BOOST_UBLAS_INLINE |
---|
747 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, sparse_bidirectional_iterator_tag) { |
---|
748 | result_type t = result_type (0); |
---|
749 | if (it1 != it1_end && it2 != it2_end) { |
---|
750 | while (true) { |
---|
751 | if (it1.index () == it2.index ()) { |
---|
752 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
753 | if (it1 == it1_end || it2 == it2_end) |
---|
754 | break; |
---|
755 | } else if (it1.index () < it2.index ()) { |
---|
756 | increment (it1, it1_end, it2.index () - it1.index ()); |
---|
757 | if (it1 == it1_end) |
---|
758 | break; |
---|
759 | } else if (it1.index () > it2.index ()) { |
---|
760 | increment (it2, it2_end, it1.index () - it2.index ()); |
---|
761 | if (it2 == it2_end) |
---|
762 | break; |
---|
763 | } |
---|
764 | } |
---|
765 | } |
---|
766 | return t; |
---|
767 | } |
---|
768 | }; |
---|
769 | |
---|
770 | // Matrix functors |
---|
771 | |
---|
772 | // Binary returning vector |
---|
773 | template<class M1, class M2, class TV> |
---|
774 | struct matrix_vector_binary_functor { |
---|
775 | typedef typename M1::size_type size_type; |
---|
776 | typedef typename M1::difference_type difference_type; |
---|
777 | typedef TV value_type; |
---|
778 | typedef TV result_type; |
---|
779 | }; |
---|
780 | |
---|
781 | template<class M1, class M2, class TV> |
---|
782 | struct matrix_vector_prod1: |
---|
783 | public matrix_vector_binary_functor<M1, M2, TV> { |
---|
784 | typedef typename matrix_vector_binary_functor<M1, M2, TV>::size_type size_type; |
---|
785 | typedef typename matrix_vector_binary_functor<M1, M2, TV>::difference_type difference_type; |
---|
786 | typedef typename matrix_vector_binary_functor<M1, M2, TV>::value_type value_type; |
---|
787 | typedef typename matrix_vector_binary_functor<M1, M2, TV>::result_type result_type; |
---|
788 | |
---|
789 | template<class C1, class C2> |
---|
790 | static BOOST_UBLAS_INLINE |
---|
791 | result_type apply (const matrix_container<C1> &c1, |
---|
792 | const vector_container<C2> &c2, |
---|
793 | size_type i) { |
---|
794 | #ifdef BOOST_UBLAS_USE_SIMD |
---|
795 | using namespace raw; |
---|
796 | size_type size = BOOST_UBLAS_SAME (c1 ().size2 (), c2 ().size ()); |
---|
797 | const typename M1::value_type *data1 = data_const (c1 ()) + i * stride1 (c1 ()); |
---|
798 | const typename M2::value_type *data2 = data_const (c2 ()); |
---|
799 | size_type s1 = stride2 (c1 ()); |
---|
800 | size_type s2 = stride (c2 ()); |
---|
801 | result_type t = result_type (0); |
---|
802 | if (s1 == 1 && s2 == 1) { |
---|
803 | for (size_type j = 0; j < size; ++ j) |
---|
804 | t += data1 [j] * data2 [j]; |
---|
805 | } else if (s2 == 1) { |
---|
806 | for (size_type j = 0, j1 = 0; j < size; ++ j, j1 += s1) |
---|
807 | t += data1 [j1] * data2 [j]; |
---|
808 | } else if (s1 == 1) { |
---|
809 | for (size_type j = 0, j2 = 0; j < size; ++ j, j2 += s2) |
---|
810 | t += data1 [j] * data2 [j2]; |
---|
811 | } else { |
---|
812 | for (size_type j = 0, j1 = 0, j2 = 0; j < size; ++ j, j1 += s1, j2 += s2) |
---|
813 | t += data1 [j1] * data2 [j2]; |
---|
814 | } |
---|
815 | return t; |
---|
816 | #elif defined(BOOST_UBLAS_HAVE_BINDINGS) |
---|
817 | return boost::numeric::bindings::atlas::dot (c1 ().row (i), c2 ()); |
---|
818 | #else |
---|
819 | return apply (static_cast<const matrix_expression<C1> > (c1), static_cast<const vector_expression<C2> > (c2, i)); |
---|
820 | #endif |
---|
821 | } |
---|
822 | template<class E1, class E2> |
---|
823 | static BOOST_UBLAS_INLINE |
---|
824 | result_type apply (const matrix_expression<E1> &e1, |
---|
825 | const vector_expression<E2> &e2, |
---|
826 | size_type i) { |
---|
827 | size_type size = BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size ()); |
---|
828 | result_type t = result_type (0); |
---|
829 | #ifndef BOOST_UBLAS_USE_DUFF_DEVICE |
---|
830 | for (size_type j = 0; j < size; ++ j) |
---|
831 | t += e1 () (i, j) * e2 () (j); |
---|
832 | #else |
---|
833 | size_type j (0); |
---|
834 | DD (size, 4, r, (t += e1 () (i, j) * e2 () (j), ++ j)); |
---|
835 | #endif |
---|
836 | return t; |
---|
837 | } |
---|
838 | // Dense case |
---|
839 | template<class I1, class I2> |
---|
840 | static BOOST_UBLAS_INLINE |
---|
841 | result_type apply (difference_type size, I1 it1, I2 it2) { |
---|
842 | result_type t = result_type (0); |
---|
843 | #ifndef BOOST_UBLAS_USE_DUFF_DEVICE |
---|
844 | while (-- size >= 0) |
---|
845 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
846 | #else |
---|
847 | DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2)); |
---|
848 | #endif |
---|
849 | return t; |
---|
850 | } |
---|
851 | // Packed case |
---|
852 | template<class I1, class I2> |
---|
853 | static BOOST_UBLAS_INLINE |
---|
854 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) { |
---|
855 | result_type t = result_type (0); |
---|
856 | difference_type it1_size (it1_end - it1); |
---|
857 | difference_type it2_size (it2_end - it2); |
---|
858 | difference_type diff (0); |
---|
859 | if (it1_size > 0 && it2_size > 0) |
---|
860 | diff = it2.index () - it1.index2 (); |
---|
861 | if (diff != 0) { |
---|
862 | difference_type size = (std::min) (diff, it1_size); |
---|
863 | if (size > 0) { |
---|
864 | it1 += size; |
---|
865 | it1_size -= size; |
---|
866 | diff -= size; |
---|
867 | } |
---|
868 | size = (std::min) (- diff, it2_size); |
---|
869 | if (size > 0) { |
---|
870 | it2 += size; |
---|
871 | it2_size -= size; |
---|
872 | diff += size; |
---|
873 | } |
---|
874 | } |
---|
875 | difference_type size ((std::min) (it1_size, it2_size)); |
---|
876 | while (-- size >= 0) |
---|
877 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
878 | return t; |
---|
879 | } |
---|
880 | // Sparse case |
---|
881 | template<class I1, class I2> |
---|
882 | static BOOST_UBLAS_INLINE |
---|
883 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, |
---|
884 | sparse_bidirectional_iterator_tag, sparse_bidirectional_iterator_tag) { |
---|
885 | result_type t = result_type (0); |
---|
886 | if (it1 != it1_end && it2 != it2_end) { |
---|
887 | size_type it1_index = it1.index2 (), it2_index = it2.index (); |
---|
888 | while (true) { |
---|
889 | difference_type compare = it1_index - it2_index; |
---|
890 | if (compare == 0) { |
---|
891 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
892 | if (it1 != it1_end && it2 != it2_end) { |
---|
893 | it1_index = it1.index2 (); |
---|
894 | it2_index = it2.index (); |
---|
895 | } else |
---|
896 | break; |
---|
897 | } else if (compare < 0) { |
---|
898 | increment (it1, it1_end, - compare); |
---|
899 | if (it1 != it1_end) |
---|
900 | it1_index = it1.index2 (); |
---|
901 | else |
---|
902 | break; |
---|
903 | } else if (compare > 0) { |
---|
904 | increment (it2, it2_end, compare); |
---|
905 | if (it2 != it2_end) |
---|
906 | it2_index = it2.index (); |
---|
907 | else |
---|
908 | break; |
---|
909 | } |
---|
910 | } |
---|
911 | } |
---|
912 | return t; |
---|
913 | } |
---|
914 | // Sparse packed case |
---|
915 | template<class I1, class I2> |
---|
916 | static BOOST_UBLAS_INLINE |
---|
917 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &/* it2_end */, |
---|
918 | sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag) { |
---|
919 | result_type t = result_type (0); |
---|
920 | while (it1 != it1_end) { |
---|
921 | t += *it1 * it2 () (it1.index2 ()); |
---|
922 | ++ it1; |
---|
923 | } |
---|
924 | return t; |
---|
925 | } |
---|
926 | // Packed sparse case |
---|
927 | template<class I1, class I2> |
---|
928 | static BOOST_UBLAS_INLINE |
---|
929 | result_type apply (I1 it1, const I1 &/* it1_end */, I2 it2, const I2 &it2_end, |
---|
930 | packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag) { |
---|
931 | result_type t = result_type (0); |
---|
932 | while (it2 != it2_end) { |
---|
933 | t += it1 () (it1.index1 (), it2.index ()) * *it2; |
---|
934 | ++ it2; |
---|
935 | } |
---|
936 | return t; |
---|
937 | } |
---|
938 | // Another dispatcher |
---|
939 | template<class I1, class I2> |
---|
940 | static BOOST_UBLAS_INLINE |
---|
941 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, |
---|
942 | sparse_bidirectional_iterator_tag) { |
---|
943 | typedef typename I1::iterator_category iterator1_category; |
---|
944 | typedef typename I2::iterator_category iterator2_category; |
---|
945 | return apply (it1, it1_end, it2, it2_end, iterator1_category (), iterator2_category ()); |
---|
946 | } |
---|
947 | }; |
---|
948 | |
---|
949 | template<class M1, class M2, class TV> |
---|
950 | struct matrix_vector_prod2: |
---|
951 | public matrix_vector_binary_functor<M1, M2, TV> { |
---|
952 | typedef typename matrix_vector_binary_functor<M1, M2, TV>::size_type size_type; |
---|
953 | typedef typename matrix_vector_binary_functor<M1, M2, TV>::difference_type difference_type; |
---|
954 | typedef typename matrix_vector_binary_functor<M1, M2, TV>::value_type value_type; |
---|
955 | typedef typename matrix_vector_binary_functor<M1, M2, TV>::result_type result_type; |
---|
956 | |
---|
957 | template<class C1, class C2> |
---|
958 | static BOOST_UBLAS_INLINE |
---|
959 | result_type apply (const vector_container<C1> &c1, |
---|
960 | const matrix_container<C2> &c2, |
---|
961 | size_type i) { |
---|
962 | #ifdef BOOST_UBLAS_USE_SIMD |
---|
963 | using namespace raw; |
---|
964 | size_type size = BOOST_UBLAS_SAME (c1 ().size (), c2 ().size1 ()); |
---|
965 | const typename M1::value_type *data1 = data_const (c1 ()); |
---|
966 | const typename M2::value_type *data2 = data_const (c2 ()) + i * stride2 (c2 ()); |
---|
967 | size_type s1 = stride (c1 ()); |
---|
968 | size_type s2 = stride1 (c2 ()); |
---|
969 | result_type t = result_type (0); |
---|
970 | if (s1 == 1 && s2 == 1) { |
---|
971 | for (size_type j = 0; j < size; ++ j) |
---|
972 | t += data1 [j] * data2 [j]; |
---|
973 | } else if (s2 == 1) { |
---|
974 | for (size_type j = 0, j1 = 0; j < size; ++ j, j1 += s1) |
---|
975 | t += data1 [j1] * data2 [j]; |
---|
976 | } else if (s1 == 1) { |
---|
977 | for (size_type j = 0, j2 = 0; j < size; ++ j, j2 += s2) |
---|
978 | t += data1 [j] * data2 [j2]; |
---|
979 | } else { |
---|
980 | for (size_type j = 0, j1 = 0, j2 = 0; j < size; ++ j, j1 += s1, j2 += s2) |
---|
981 | t += data1 [j1] * data2 [j2]; |
---|
982 | } |
---|
983 | return t; |
---|
984 | #elif defined(BOOST_UBLAS_HAVE_BINDINGS) |
---|
985 | return boost::numeric::bindings::atlas::dot (c1 (), c2 ().column (i)); |
---|
986 | #else |
---|
987 | return apply (static_cast<const vector_expression<C1> > (c1), static_cast<const matrix_expression<C2> > (c2, i)); |
---|
988 | #endif |
---|
989 | } |
---|
990 | template<class E1, class E2> |
---|
991 | static BOOST_UBLAS_INLINE |
---|
992 | result_type apply (const vector_expression<E1> &e1, |
---|
993 | const matrix_expression<E2> &e2, |
---|
994 | size_type i) { |
---|
995 | size_type size = BOOST_UBLAS_SAME (e1 ().size (), e2 ().size1 ()); |
---|
996 | result_type t = result_type (0); |
---|
997 | #ifndef BOOST_UBLAS_USE_DUFF_DEVICE |
---|
998 | for (size_type j = 0; j < size; ++ j) |
---|
999 | t += e1 () (j) * e2 () (j, i); |
---|
1000 | #else |
---|
1001 | size_type j (0); |
---|
1002 | DD (size, 4, r, (t += e1 () (j) * e2 () (j, i), ++ j)); |
---|
1003 | #endif |
---|
1004 | return t; |
---|
1005 | } |
---|
1006 | // Dense case |
---|
1007 | template<class I1, class I2> |
---|
1008 | static BOOST_UBLAS_INLINE |
---|
1009 | result_type apply (difference_type size, I1 it1, I2 it2) { |
---|
1010 | result_type t = result_type (0); |
---|
1011 | #ifndef BOOST_UBLAS_USE_DUFF_DEVICE |
---|
1012 | while (-- size >= 0) |
---|
1013 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
1014 | #else |
---|
1015 | DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2)); |
---|
1016 | #endif |
---|
1017 | return t; |
---|
1018 | } |
---|
1019 | // Packed case |
---|
1020 | template<class I1, class I2> |
---|
1021 | static BOOST_UBLAS_INLINE |
---|
1022 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) { |
---|
1023 | result_type t = result_type (0); |
---|
1024 | difference_type it1_size (it1_end - it1); |
---|
1025 | difference_type it2_size (it2_end - it2); |
---|
1026 | difference_type diff (0); |
---|
1027 | if (it1_size > 0 && it2_size > 0) |
---|
1028 | diff = it2.index1 () - it1.index (); |
---|
1029 | if (diff != 0) { |
---|
1030 | difference_type size = (std::min) (diff, it1_size); |
---|
1031 | if (size > 0) { |
---|
1032 | it1 += size; |
---|
1033 | it1_size -= size; |
---|
1034 | diff -= size; |
---|
1035 | } |
---|
1036 | size = (std::min) (- diff, it2_size); |
---|
1037 | if (size > 0) { |
---|
1038 | it2 += size; |
---|
1039 | it2_size -= size; |
---|
1040 | diff += size; |
---|
1041 | } |
---|
1042 | } |
---|
1043 | difference_type size ((std::min) (it1_size, it2_size)); |
---|
1044 | while (-- size >= 0) |
---|
1045 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
1046 | return t; |
---|
1047 | } |
---|
1048 | // Sparse case |
---|
1049 | template<class I1, class I2> |
---|
1050 | static BOOST_UBLAS_INLINE |
---|
1051 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, |
---|
1052 | sparse_bidirectional_iterator_tag, sparse_bidirectional_iterator_tag) { |
---|
1053 | result_type t = result_type (0); |
---|
1054 | if (it1 != it1_end && it2 != it2_end) { |
---|
1055 | size_type it1_index = it1.index (), it2_index = it2.index1 (); |
---|
1056 | while (true) { |
---|
1057 | difference_type compare = it1_index - it2_index; |
---|
1058 | if (compare == 0) { |
---|
1059 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
1060 | if (it1 != it1_end && it2 != it2_end) { |
---|
1061 | it1_index = it1.index (); |
---|
1062 | it2_index = it2.index1 (); |
---|
1063 | } else |
---|
1064 | break; |
---|
1065 | } else if (compare < 0) { |
---|
1066 | increment (it1, it1_end, - compare); |
---|
1067 | if (it1 != it1_end) |
---|
1068 | it1_index = it1.index (); |
---|
1069 | else |
---|
1070 | break; |
---|
1071 | } else if (compare > 0) { |
---|
1072 | increment (it2, it2_end, compare); |
---|
1073 | if (it2 != it2_end) |
---|
1074 | it2_index = it2.index1 (); |
---|
1075 | else |
---|
1076 | break; |
---|
1077 | } |
---|
1078 | } |
---|
1079 | } |
---|
1080 | return t; |
---|
1081 | } |
---|
1082 | // Packed sparse case |
---|
1083 | template<class I1, class I2> |
---|
1084 | static BOOST_UBLAS_INLINE |
---|
1085 | result_type apply (I1 it1, const I1 &/* it1_end */, I2 it2, const I2 &it2_end, |
---|
1086 | packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag) { |
---|
1087 | result_type t = result_type (0); |
---|
1088 | while (it2 != it2_end) { |
---|
1089 | t += it1 () (it2.index1 ()) * *it2; |
---|
1090 | ++ it2; |
---|
1091 | } |
---|
1092 | return t; |
---|
1093 | } |
---|
1094 | // Sparse packed case |
---|
1095 | template<class I1, class I2> |
---|
1096 | static BOOST_UBLAS_INLINE |
---|
1097 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &/* it2_end */, |
---|
1098 | sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag) { |
---|
1099 | result_type t = result_type (0); |
---|
1100 | while (it1 != it1_end) { |
---|
1101 | t += *it1 * it2 () (it1.index (), it2.index2 ()); |
---|
1102 | ++ it1; |
---|
1103 | } |
---|
1104 | return t; |
---|
1105 | } |
---|
1106 | // Another dispatcher |
---|
1107 | template<class I1, class I2> |
---|
1108 | static BOOST_UBLAS_INLINE |
---|
1109 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, |
---|
1110 | sparse_bidirectional_iterator_tag) { |
---|
1111 | typedef typename I1::iterator_category iterator1_category; |
---|
1112 | typedef typename I2::iterator_category iterator2_category; |
---|
1113 | return apply (it1, it1_end, it2, it2_end, iterator1_category (), iterator2_category ()); |
---|
1114 | } |
---|
1115 | }; |
---|
1116 | |
---|
1117 | // Binary returning matrix |
---|
1118 | template<class M1, class M2, class TV> |
---|
1119 | struct matrix_matrix_binary_functor { |
---|
1120 | typedef typename M1::size_type size_type; |
---|
1121 | typedef typename M1::difference_type difference_type; |
---|
1122 | typedef TV value_type; |
---|
1123 | typedef TV result_type; |
---|
1124 | }; |
---|
1125 | |
---|
1126 | template<class M1, class M2, class TV> |
---|
1127 | struct matrix_matrix_prod: |
---|
1128 | public matrix_matrix_binary_functor<M1, M2, TV> { |
---|
1129 | typedef typename matrix_matrix_binary_functor<M1, M2, TV>::size_type size_type; |
---|
1130 | typedef typename matrix_matrix_binary_functor<M1, M2, TV>::difference_type difference_type; |
---|
1131 | typedef typename matrix_matrix_binary_functor<M1, M2, TV>::value_type value_type; |
---|
1132 | typedef typename matrix_matrix_binary_functor<M1, M2, TV>::result_type result_type; |
---|
1133 | |
---|
1134 | template<class C1, class C2> |
---|
1135 | static BOOST_UBLAS_INLINE |
---|
1136 | result_type apply (const matrix_container<C1> &c1, |
---|
1137 | const matrix_container<C2> &c2, |
---|
1138 | size_type i, size_type j) { |
---|
1139 | #ifdef BOOST_UBLAS_USE_SIMD |
---|
1140 | using namespace raw; |
---|
1141 | size_type size = BOOST_UBLAS_SAME (c1 ().size2 (), c2 ().sizc1 ()); |
---|
1142 | const typename M1::value_type *data1 = data_const (c1 ()) + i * stride1 (c1 ()); |
---|
1143 | const typename M2::value_type *data2 = data_const (c2 ()) + j * stride2 (c2 ()); |
---|
1144 | size_type s1 = stride2 (c1 ()); |
---|
1145 | size_type s2 = stride1 (c2 ()); |
---|
1146 | result_type t = result_type (0); |
---|
1147 | if (s1 == 1 && s2 == 1) { |
---|
1148 | for (size_type k = 0; k < size; ++ k) |
---|
1149 | t += data1 [k] * data2 [k]; |
---|
1150 | } else if (s2 == 1) { |
---|
1151 | for (size_type k = 0, k1 = 0; k < size; ++ k, k1 += s1) |
---|
1152 | t += data1 [k1] * data2 [k]; |
---|
1153 | } else if (s1 == 1) { |
---|
1154 | for (size_type k = 0, k2 = 0; k < size; ++ k, k2 += s2) |
---|
1155 | t += data1 [k] * data2 [k2]; |
---|
1156 | } else { |
---|
1157 | for (size_type k = 0, k1 = 0, k2 = 0; k < size; ++ k, k1 += s1, k2 += s2) |
---|
1158 | t += data1 [k1] * data2 [k2]; |
---|
1159 | } |
---|
1160 | return t; |
---|
1161 | #elif defined(BOOST_UBLAS_HAVE_BINDINGS) |
---|
1162 | return boost::numeric::bindings::atlas::dot (c1 ().row (i), c2 ().column (j)); |
---|
1163 | #else |
---|
1164 | return apply (static_cast<const matrix_expression<C1> > (c1), static_cast<const matrix_expression<C2> > (c2, i)); |
---|
1165 | #endif |
---|
1166 | } |
---|
1167 | template<class E1, class E2> |
---|
1168 | static BOOST_UBLAS_INLINE |
---|
1169 | result_type apply (const matrix_expression<E1> &e1, |
---|
1170 | const matrix_expression<E2> &e2, |
---|
1171 | size_type i, size_type j) { |
---|
1172 | size_type size = BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ()); |
---|
1173 | result_type t = result_type (0); |
---|
1174 | #ifndef BOOST_UBLAS_USE_DUFF_DEVICE |
---|
1175 | for (size_type k = 0; k < size; ++ k) |
---|
1176 | t += e1 () (i, k) * e2 () (k, j); |
---|
1177 | #else |
---|
1178 | size_type k (0); |
---|
1179 | DD (size, 4, r, (t += e1 () (i, k) * e2 () (k, j), ++ k)); |
---|
1180 | #endif |
---|
1181 | return t; |
---|
1182 | } |
---|
1183 | // Dense case |
---|
1184 | template<class I1, class I2> |
---|
1185 | static BOOST_UBLAS_INLINE |
---|
1186 | result_type apply (difference_type size, I1 it1, I2 it2) { |
---|
1187 | result_type t = result_type (0); |
---|
1188 | #ifndef BOOST_UBLAS_USE_DUFF_DEVICE |
---|
1189 | while (-- size >= 0) |
---|
1190 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
1191 | #else |
---|
1192 | DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2)); |
---|
1193 | #endif |
---|
1194 | return t; |
---|
1195 | } |
---|
1196 | // Packed case |
---|
1197 | template<class I1, class I2> |
---|
1198 | static BOOST_UBLAS_INLINE |
---|
1199 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, packed_random_access_iterator_tag) { |
---|
1200 | result_type t = result_type (0); |
---|
1201 | difference_type it1_size (it1_end - it1); |
---|
1202 | difference_type it2_size (it2_end - it2); |
---|
1203 | difference_type diff (0); |
---|
1204 | if (it1_size > 0 && it2_size > 0) |
---|
1205 | diff = it2.index1 () - it1.index2 (); |
---|
1206 | if (diff != 0) { |
---|
1207 | difference_type size = (std::min) (diff, it1_size); |
---|
1208 | if (size > 0) { |
---|
1209 | it1 += size; |
---|
1210 | it1_size -= size; |
---|
1211 | diff -= size; |
---|
1212 | } |
---|
1213 | size = (std::min) (- diff, it2_size); |
---|
1214 | if (size > 0) { |
---|
1215 | it2 += size; |
---|
1216 | it2_size -= size; |
---|
1217 | diff += size; |
---|
1218 | } |
---|
1219 | } |
---|
1220 | difference_type size ((std::min) (it1_size, it2_size)); |
---|
1221 | while (-- size >= 0) |
---|
1222 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
1223 | return t; |
---|
1224 | } |
---|
1225 | // Sparse case |
---|
1226 | template<class I1, class I2> |
---|
1227 | static BOOST_UBLAS_INLINE |
---|
1228 | result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, sparse_bidirectional_iterator_tag) { |
---|
1229 | result_type t = result_type (0); |
---|
1230 | if (it1 != it1_end && it2 != it2_end) { |
---|
1231 | size_type it1_index = it1.index2 (), it2_index = it2.index1 (); |
---|
1232 | while (true) { |
---|
1233 | difference_type compare = difference_type (it1_index - it2_index); |
---|
1234 | if (compare == 0) { |
---|
1235 | t += *it1 * *it2, ++ it1, ++ it2; |
---|
1236 | if (it1 != it1_end && it2 != it2_end) { |
---|
1237 | it1_index = it1.index2 (); |
---|
1238 | it2_index = it2.index1 (); |
---|
1239 | } else |
---|
1240 | break; |
---|
1241 | } else if (compare < 0) { |
---|
1242 | increment (it1, it1_end, - compare); |
---|
1243 | if (it1 != it1_end) |
---|
1244 | it1_index = it1.index2 (); |
---|
1245 | else |
---|
1246 | break; |
---|
1247 | } else if (compare > 0) { |
---|
1248 | increment (it2, it2_end, compare); |
---|
1249 | if (it2 != it2_end) |
---|
1250 | it2_index = it2.index1 (); |
---|
1251 | else |
---|
1252 | break; |
---|
1253 | } |
---|
1254 | } |
---|
1255 | } |
---|
1256 | return t; |
---|
1257 | } |
---|
1258 | }; |
---|
1259 | |
---|
1260 | // Unary returning scalar norm |
---|
1261 | template<class M> |
---|
1262 | struct matrix_scalar_real_unary_functor { |
---|
1263 | typedef typename M::value_type value_type; |
---|
1264 | typedef typename type_traits<value_type>::real_type real_type; |
---|
1265 | typedef real_type result_type; |
---|
1266 | }; |
---|
1267 | |
---|
1268 | template<class M> |
---|
1269 | struct matrix_norm_1: |
---|
1270 | public matrix_scalar_real_unary_functor<M> { |
---|
1271 | typedef typename matrix_scalar_real_unary_functor<M>::value_type value_type; |
---|
1272 | typedef typename matrix_scalar_real_unary_functor<M>::real_type real_type; |
---|
1273 | typedef typename matrix_scalar_real_unary_functor<M>::result_type result_type; |
---|
1274 | |
---|
1275 | template<class E> |
---|
1276 | static BOOST_UBLAS_INLINE |
---|
1277 | result_type apply (const matrix_expression<E> &e) { |
---|
1278 | real_type t = real_type (); |
---|
1279 | typedef typename E::size_type matrix_size_type; |
---|
1280 | matrix_size_type size2 (e ().size2 ()); |
---|
1281 | for (matrix_size_type j = 0; j < size2; ++ j) { |
---|
1282 | real_type u = real_type (); |
---|
1283 | matrix_size_type size1 (e ().size1 ()); |
---|
1284 | for (matrix_size_type i = 0; i < size1; ++ i) { |
---|
1285 | real_type v (type_traits<value_type>::norm_1 (e () (i, j))); |
---|
1286 | u += v; |
---|
1287 | } |
---|
1288 | if (u > t) |
---|
1289 | t = u; |
---|
1290 | } |
---|
1291 | return t; |
---|
1292 | } |
---|
1293 | }; |
---|
1294 | |
---|
1295 | template<class M> |
---|
1296 | struct matrix_norm_frobenius: |
---|
1297 | public matrix_scalar_real_unary_functor<M> { |
---|
1298 | typedef typename matrix_scalar_real_unary_functor<M>::value_type value_type; |
---|
1299 | typedef typename matrix_scalar_real_unary_functor<M>::real_type real_type; |
---|
1300 | typedef typename matrix_scalar_real_unary_functor<M>::result_type result_type; |
---|
1301 | |
---|
1302 | template<class E> |
---|
1303 | static BOOST_UBLAS_INLINE |
---|
1304 | result_type apply (const matrix_expression<E> &e) { |
---|
1305 | real_type t = real_type (); |
---|
1306 | typedef typename E::size_type matrix_size_type; |
---|
1307 | matrix_size_type size1 (e ().size1 ()); |
---|
1308 | for (matrix_size_type i = 0; i < size1; ++ i) { |
---|
1309 | matrix_size_type size2 (e ().size2 ()); |
---|
1310 | for (matrix_size_type j = 0; j < size2; ++ j) { |
---|
1311 | real_type u (type_traits<value_type>::norm_2 (e () (i, j))); |
---|
1312 | t += u * u; |
---|
1313 | } |
---|
1314 | } |
---|
1315 | return type_traits<real_type>::type_sqrt (t); |
---|
1316 | } |
---|
1317 | }; |
---|
1318 | |
---|
1319 | template<class M> |
---|
1320 | struct matrix_norm_inf: |
---|
1321 | public matrix_scalar_real_unary_functor<M> { |
---|
1322 | typedef typename matrix_scalar_real_unary_functor<M>::value_type value_type; |
---|
1323 | typedef typename matrix_scalar_real_unary_functor<M>::real_type real_type; |
---|
1324 | typedef typename matrix_scalar_real_unary_functor<M>::result_type result_type; |
---|
1325 | |
---|
1326 | template<class E> |
---|
1327 | static BOOST_UBLAS_INLINE |
---|
1328 | result_type apply (const matrix_expression<E> &e) { |
---|
1329 | real_type t = real_type (); |
---|
1330 | typedef typename E::size_type matrix_size_type; |
---|
1331 | matrix_size_type size1 (e ().size1 ()); |
---|
1332 | for (matrix_size_type i = 0; i < size1; ++ i) { |
---|
1333 | real_type u = real_type (); |
---|
1334 | matrix_size_type size2 (e ().size2 ()); |
---|
1335 | for (matrix_size_type j = 0; j < size2; ++ j) { |
---|
1336 | real_type v (type_traits<value_type>::norm_inf (e () (i, j))); |
---|
1337 | u += v; |
---|
1338 | } |
---|
1339 | if (u > t) |
---|
1340 | t = u; |
---|
1341 | } |
---|
1342 | return t; |
---|
1343 | } |
---|
1344 | }; |
---|
1345 | |
---|
1346 | // forward declaration |
---|
1347 | template <class Z, class D> struct basic_column_major; |
---|
1348 | |
---|
1349 | // This functor defines storage layout and it's properties |
---|
1350 | // matrix (i,j) -> storage [i * size_i + j] |
---|
1351 | template <class Z, class D> |
---|
1352 | struct basic_row_major { |
---|
1353 | typedef Z size_type; |
---|
1354 | typedef D difference_type; |
---|
1355 | typedef row_major_tag orientation_category; |
---|
1356 | typedef basic_column_major<Z,D> transposed_layout; |
---|
1357 | |
---|
1358 | static |
---|
1359 | BOOST_UBLAS_INLINE |
---|
1360 | size_type storage_size (size_type size_i, size_type size_j) { |
---|
1361 | // Guard against size_type overflow |
---|
1362 | BOOST_UBLAS_CHECK (size_j == 0 || size_i <= (std::numeric_limits<size_type>::max) () / size_j, bad_size ()); |
---|
1363 | return size_i * size_j; |
---|
1364 | } |
---|
1365 | |
---|
1366 | // Indexing conversion to storage element |
---|
1367 | static |
---|
1368 | BOOST_UBLAS_INLINE |
---|
1369 | size_type element (size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1370 | BOOST_UBLAS_CHECK (i < size_i, bad_index ()); |
---|
1371 | BOOST_UBLAS_CHECK (j < size_j, bad_index ()); |
---|
1372 | detail::ignore_unused_variable_warning(size_i); |
---|
1373 | // Guard against size_type overflow |
---|
1374 | BOOST_UBLAS_CHECK (i <= ((std::numeric_limits<size_type>::max) () - j) / size_j, bad_index ()); |
---|
1375 | return i * size_j + j; |
---|
1376 | } |
---|
1377 | static |
---|
1378 | BOOST_UBLAS_INLINE |
---|
1379 | size_type address (size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1380 | BOOST_UBLAS_CHECK (i <= size_i, bad_index ()); |
---|
1381 | BOOST_UBLAS_CHECK (j <= size_j, bad_index ()); |
---|
1382 | // Guard against size_type overflow - address may be size_j past end of storage |
---|
1383 | BOOST_UBLAS_CHECK (size_j == 0 || i <= ((std::numeric_limits<size_type>::max) () - j) / size_j, bad_index ()); |
---|
1384 | detail::ignore_unused_variable_warning(size_i); |
---|
1385 | return i * size_j + j; |
---|
1386 | } |
---|
1387 | |
---|
1388 | // Storage element to index conversion |
---|
1389 | static |
---|
1390 | BOOST_UBLAS_INLINE |
---|
1391 | difference_type distance_i (difference_type k, size_type /* size_i */, size_type size_j) { |
---|
1392 | return size_j != 0 ? k / size_j : 0; |
---|
1393 | } |
---|
1394 | static |
---|
1395 | BOOST_UBLAS_INLINE |
---|
1396 | difference_type distance_j (difference_type k, size_type /* size_i */, size_type /* size_j */) { |
---|
1397 | return k; |
---|
1398 | } |
---|
1399 | static |
---|
1400 | BOOST_UBLAS_INLINE |
---|
1401 | size_type index_i (difference_type k, size_type /* size_i */, size_type size_j) { |
---|
1402 | return size_j != 0 ? k / size_j : 0; |
---|
1403 | } |
---|
1404 | static |
---|
1405 | BOOST_UBLAS_INLINE |
---|
1406 | size_type index_j (difference_type k, size_type /* size_i */, size_type size_j) { |
---|
1407 | return size_j != 0 ? k % size_j : 0; |
---|
1408 | } |
---|
1409 | static |
---|
1410 | BOOST_UBLAS_INLINE |
---|
1411 | bool fast_i () { |
---|
1412 | return false; |
---|
1413 | } |
---|
1414 | static |
---|
1415 | BOOST_UBLAS_INLINE |
---|
1416 | bool fast_j () { |
---|
1417 | return true; |
---|
1418 | } |
---|
1419 | |
---|
1420 | // Iterating storage elements |
---|
1421 | template<class I> |
---|
1422 | static |
---|
1423 | BOOST_UBLAS_INLINE |
---|
1424 | void increment_i (I &it, size_type /* size_i */, size_type size_j) { |
---|
1425 | it += size_j; |
---|
1426 | } |
---|
1427 | template<class I> |
---|
1428 | static |
---|
1429 | BOOST_UBLAS_INLINE |
---|
1430 | void increment_i (I &it, difference_type n, size_type /* size_i */, size_type size_j) { |
---|
1431 | it += n * size_j; |
---|
1432 | } |
---|
1433 | template<class I> |
---|
1434 | static |
---|
1435 | BOOST_UBLAS_INLINE |
---|
1436 | void decrement_i (I &it, size_type /* size_i */, size_type size_j) { |
---|
1437 | it -= size_j; |
---|
1438 | } |
---|
1439 | template<class I> |
---|
1440 | static |
---|
1441 | BOOST_UBLAS_INLINE |
---|
1442 | void decrement_i (I &it, difference_type n, size_type /* size_i */, size_type size_j) { |
---|
1443 | it -= n * size_j; |
---|
1444 | } |
---|
1445 | template<class I> |
---|
1446 | static |
---|
1447 | BOOST_UBLAS_INLINE |
---|
1448 | void increment_j (I &it, size_type /* size_i */, size_type /* size_j */) { |
---|
1449 | ++ it; |
---|
1450 | } |
---|
1451 | template<class I> |
---|
1452 | static |
---|
1453 | BOOST_UBLAS_INLINE |
---|
1454 | void increment_j (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) { |
---|
1455 | it += n; |
---|
1456 | } |
---|
1457 | template<class I> |
---|
1458 | static |
---|
1459 | BOOST_UBLAS_INLINE |
---|
1460 | void decrement_j (I &it, size_type /* size_i */, size_type /* size_j */) { |
---|
1461 | -- it; |
---|
1462 | } |
---|
1463 | template<class I> |
---|
1464 | static |
---|
1465 | BOOST_UBLAS_INLINE |
---|
1466 | void decrement_j (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) { |
---|
1467 | it -= n; |
---|
1468 | } |
---|
1469 | |
---|
1470 | // Triangular access |
---|
1471 | static |
---|
1472 | BOOST_UBLAS_INLINE |
---|
1473 | size_type triangular_size (size_type size_i, size_type size_j) { |
---|
1474 | size_type size = (std::max) (size_i, size_j); |
---|
1475 | // Guard against size_type overflow - simplified |
---|
1476 | BOOST_UBLAS_CHECK (size == 0 || size / 2 < (std::numeric_limits<size_type>::max) () / size /* +1/2 */, bad_size ()); |
---|
1477 | return ((size + 1) * size) / 2; |
---|
1478 | } |
---|
1479 | static |
---|
1480 | BOOST_UBLAS_INLINE |
---|
1481 | size_type lower_element (size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1482 | BOOST_UBLAS_CHECK (i < size_i, bad_index ()); |
---|
1483 | BOOST_UBLAS_CHECK (j < size_j, bad_index ()); |
---|
1484 | BOOST_UBLAS_CHECK (i >= j, bad_index ()); |
---|
1485 | detail::ignore_unused_variable_warning(size_i); |
---|
1486 | detail::ignore_unused_variable_warning(size_j); |
---|
1487 | // FIXME size_type overflow |
---|
1488 | // sigma_i (i + 1) = (i + 1) * i / 2 |
---|
1489 | // i = 0 1 2 3, sigma = 0 1 3 6 |
---|
1490 | return ((i + 1) * i) / 2 + j; |
---|
1491 | } |
---|
1492 | static |
---|
1493 | BOOST_UBLAS_INLINE |
---|
1494 | size_type upper_element (size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1495 | BOOST_UBLAS_CHECK (i < size_i, bad_index ()); |
---|
1496 | BOOST_UBLAS_CHECK (j < size_j, bad_index ()); |
---|
1497 | BOOST_UBLAS_CHECK (i <= j, bad_index ()); |
---|
1498 | // FIXME size_type overflow |
---|
1499 | // sigma_i (size - i) = size * i - i * (i - 1) / 2 |
---|
1500 | // i = 0 1 2 3, sigma = 0 4 7 9 |
---|
1501 | return (i * (2 * (std::max) (size_i, size_j) - i + 1)) / 2 + j - i; |
---|
1502 | } |
---|
1503 | |
---|
1504 | // Major and minor indices |
---|
1505 | static |
---|
1506 | BOOST_UBLAS_INLINE |
---|
1507 | size_type index_M (size_type index1, size_type /* index2 */) { |
---|
1508 | return index1; |
---|
1509 | } |
---|
1510 | static |
---|
1511 | BOOST_UBLAS_INLINE |
---|
1512 | size_type index_m (size_type /* index1 */, size_type index2) { |
---|
1513 | return index2; |
---|
1514 | } |
---|
1515 | static |
---|
1516 | BOOST_UBLAS_INLINE |
---|
1517 | size_type size_M (size_type size_i, size_type /* size_j */) { |
---|
1518 | return size_i; |
---|
1519 | } |
---|
1520 | static |
---|
1521 | BOOST_UBLAS_INLINE |
---|
1522 | size_type size_m (size_type /* size_i */, size_type size_j) { |
---|
1523 | return size_j; |
---|
1524 | } |
---|
1525 | }; |
---|
1526 | |
---|
1527 | // This functor defines storage layout and it's properties |
---|
1528 | // matrix (i,j) -> storage [i + j * size_i] |
---|
1529 | template <class Z, class D> |
---|
1530 | struct basic_column_major { |
---|
1531 | typedef Z size_type; |
---|
1532 | typedef D difference_type; |
---|
1533 | typedef column_major_tag orientation_category; |
---|
1534 | typedef basic_row_major<Z,D> transposed_layout; |
---|
1535 | |
---|
1536 | static |
---|
1537 | BOOST_UBLAS_INLINE |
---|
1538 | size_type storage_size (size_type size_i, size_type size_j) { |
---|
1539 | // Guard against size_type overflow |
---|
1540 | BOOST_UBLAS_CHECK (size_i == 0 || size_j <= (std::numeric_limits<size_type>::max) () / size_i, bad_size ()); |
---|
1541 | return size_i * size_j; |
---|
1542 | } |
---|
1543 | |
---|
1544 | // Indexing conversion to storage element |
---|
1545 | static |
---|
1546 | BOOST_UBLAS_INLINE |
---|
1547 | size_type element (size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1548 | BOOST_UBLAS_CHECK (i < size_i, bad_index ()); |
---|
1549 | BOOST_UBLAS_CHECK (j < size_j, bad_index ()); |
---|
1550 | detail::ignore_unused_variable_warning(size_j); |
---|
1551 | // Guard against size_type overflow |
---|
1552 | BOOST_UBLAS_CHECK (j <= ((std::numeric_limits<size_type>::max) () - i) / size_i, bad_index ()); |
---|
1553 | return i + j * size_i; |
---|
1554 | } |
---|
1555 | static |
---|
1556 | BOOST_UBLAS_INLINE |
---|
1557 | size_type address (size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1558 | BOOST_UBLAS_CHECK (i <= size_i, bad_index ()); |
---|
1559 | BOOST_UBLAS_CHECK (j <= size_j, bad_index ()); |
---|
1560 | detail::ignore_unused_variable_warning(size_j); |
---|
1561 | // Guard against size_type overflow - address may be size_i past end of storage |
---|
1562 | BOOST_UBLAS_CHECK (size_i == 0 || j <= ((std::numeric_limits<size_type>::max) () - i) / size_i, bad_index ()); |
---|
1563 | return i + j * size_i; |
---|
1564 | } |
---|
1565 | |
---|
1566 | // Storage element to index conversion |
---|
1567 | static |
---|
1568 | BOOST_UBLAS_INLINE |
---|
1569 | difference_type distance_i (difference_type k, size_type /* size_i */, size_type /* size_j */) { |
---|
1570 | return k; |
---|
1571 | } |
---|
1572 | static |
---|
1573 | BOOST_UBLAS_INLINE |
---|
1574 | difference_type distance_j (difference_type k, size_type size_i, size_type /* size_j */) { |
---|
1575 | return size_i != 0 ? k / size_i : 0; |
---|
1576 | } |
---|
1577 | static |
---|
1578 | BOOST_UBLAS_INLINE |
---|
1579 | size_type index_i (difference_type k, size_type size_i, size_type /* size_j */) { |
---|
1580 | return size_i != 0 ? k % size_i : 0; |
---|
1581 | } |
---|
1582 | static |
---|
1583 | BOOST_UBLAS_INLINE |
---|
1584 | size_type index_j (difference_type k, size_type size_i, size_type /* size_j */) { |
---|
1585 | return size_i != 0 ? k / size_i : 0; |
---|
1586 | } |
---|
1587 | static |
---|
1588 | BOOST_UBLAS_INLINE |
---|
1589 | bool fast_i () { |
---|
1590 | return true; |
---|
1591 | } |
---|
1592 | static |
---|
1593 | BOOST_UBLAS_INLINE |
---|
1594 | bool fast_j () { |
---|
1595 | return false; |
---|
1596 | } |
---|
1597 | |
---|
1598 | // Iterating |
---|
1599 | template<class I> |
---|
1600 | static |
---|
1601 | BOOST_UBLAS_INLINE |
---|
1602 | void increment_i (I &it, size_type /* size_i */, size_type /* size_j */) { |
---|
1603 | ++ it; |
---|
1604 | } |
---|
1605 | template<class I> |
---|
1606 | static |
---|
1607 | BOOST_UBLAS_INLINE |
---|
1608 | void increment_i (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) { |
---|
1609 | it += n; |
---|
1610 | } |
---|
1611 | template<class I> |
---|
1612 | static |
---|
1613 | BOOST_UBLAS_INLINE |
---|
1614 | void decrement_i (I &it, size_type /* size_i */, size_type /* size_j */) { |
---|
1615 | -- it; |
---|
1616 | } |
---|
1617 | template<class I> |
---|
1618 | static |
---|
1619 | BOOST_UBLAS_INLINE |
---|
1620 | void decrement_i (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) { |
---|
1621 | it -= n; |
---|
1622 | } |
---|
1623 | template<class I> |
---|
1624 | static |
---|
1625 | BOOST_UBLAS_INLINE |
---|
1626 | void increment_j (I &it, size_type size_i, size_type /* size_j */) { |
---|
1627 | it += size_i; |
---|
1628 | } |
---|
1629 | template<class I> |
---|
1630 | static |
---|
1631 | BOOST_UBLAS_INLINE |
---|
1632 | void increment_j (I &it, difference_type n, size_type size_i, size_type /* size_j */) { |
---|
1633 | it += n * size_i; |
---|
1634 | } |
---|
1635 | template<class I> |
---|
1636 | static |
---|
1637 | BOOST_UBLAS_INLINE |
---|
1638 | void decrement_j (I &it, size_type size_i, size_type /* size_j */) { |
---|
1639 | it -= size_i; |
---|
1640 | } |
---|
1641 | template<class I> |
---|
1642 | static |
---|
1643 | BOOST_UBLAS_INLINE |
---|
1644 | void decrement_j (I &it, difference_type n, size_type size_i, size_type /* size_j */) { |
---|
1645 | it -= n* size_i; |
---|
1646 | } |
---|
1647 | |
---|
1648 | // Triangular access |
---|
1649 | static |
---|
1650 | BOOST_UBLAS_INLINE |
---|
1651 | size_type triangular_size (size_type size_i, size_type size_j) { |
---|
1652 | size_type size = (std::max) (size_i, size_j); |
---|
1653 | // Guard against size_type overflow - simplified |
---|
1654 | BOOST_UBLAS_CHECK (size == 0 || size / 2 < (std::numeric_limits<size_type>::max) () / size /* +1/2 */, bad_size ()); |
---|
1655 | return ((size + 1) * size) / 2; |
---|
1656 | } |
---|
1657 | static |
---|
1658 | BOOST_UBLAS_INLINE |
---|
1659 | size_type lower_element (size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1660 | BOOST_UBLAS_CHECK (i < size_i, bad_index ()); |
---|
1661 | BOOST_UBLAS_CHECK (j < size_j, bad_index ()); |
---|
1662 | BOOST_UBLAS_CHECK (i >= j, bad_index ()); |
---|
1663 | // FIXME size_type overflow |
---|
1664 | // sigma_j (size - j) = size * j - j * (j - 1) / 2 |
---|
1665 | // j = 0 1 2 3, sigma = 0 4 7 9 |
---|
1666 | return i - j + (j * (2 * (std::max) (size_i, size_j) - j + 1)) / 2; |
---|
1667 | } |
---|
1668 | static |
---|
1669 | BOOST_UBLAS_INLINE |
---|
1670 | size_type upper_element (size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1671 | BOOST_UBLAS_CHECK (i < size_i, bad_index ()); |
---|
1672 | BOOST_UBLAS_CHECK (j < size_j, bad_index ()); |
---|
1673 | BOOST_UBLAS_CHECK (i <= j, bad_index ()); |
---|
1674 | // FIXME size_type overflow |
---|
1675 | // sigma_j (j + 1) = (j + 1) * j / 2 |
---|
1676 | // j = 0 1 2 3, sigma = 0 1 3 6 |
---|
1677 | return i + ((j + 1) * j) / 2; |
---|
1678 | } |
---|
1679 | |
---|
1680 | // Major and minor indices |
---|
1681 | static |
---|
1682 | BOOST_UBLAS_INLINE |
---|
1683 | size_type index_M (size_type /* index1 */, size_type index2) { |
---|
1684 | return index2; |
---|
1685 | } |
---|
1686 | static |
---|
1687 | BOOST_UBLAS_INLINE |
---|
1688 | size_type index_m (size_type index1, size_type /* index2 */) { |
---|
1689 | return index1; |
---|
1690 | } |
---|
1691 | static |
---|
1692 | BOOST_UBLAS_INLINE |
---|
1693 | size_type size_M (size_type /* size_i */, size_type size_j) { |
---|
1694 | return size_j; |
---|
1695 | } |
---|
1696 | static |
---|
1697 | BOOST_UBLAS_INLINE |
---|
1698 | size_type size_m (size_type size_i, size_type /* size_j */) { |
---|
1699 | return size_i; |
---|
1700 | } |
---|
1701 | }; |
---|
1702 | |
---|
1703 | |
---|
1704 | template <class Z> |
---|
1705 | struct basic_full { |
---|
1706 | typedef Z size_type; |
---|
1707 | |
---|
1708 | template<class L> |
---|
1709 | static |
---|
1710 | BOOST_UBLAS_INLINE |
---|
1711 | size_type packed_size (L, size_type size_i, size_type size_j) { |
---|
1712 | return L::storage_size (size_i, size_j); |
---|
1713 | } |
---|
1714 | |
---|
1715 | static |
---|
1716 | BOOST_UBLAS_INLINE |
---|
1717 | bool zero (size_type /* i */, size_type /* j */) { |
---|
1718 | return false; |
---|
1719 | } |
---|
1720 | static |
---|
1721 | BOOST_UBLAS_INLINE |
---|
1722 | bool one (size_type /* i */, size_type /* j */) { |
---|
1723 | return false; |
---|
1724 | } |
---|
1725 | static |
---|
1726 | BOOST_UBLAS_INLINE |
---|
1727 | bool other (size_type /* i */, size_type /* j */) { |
---|
1728 | return true; |
---|
1729 | } |
---|
1730 | // FIXME: this should not be used at all |
---|
1731 | static |
---|
1732 | BOOST_UBLAS_INLINE |
---|
1733 | size_type restrict1 (size_type i, size_type /* j */) { |
---|
1734 | return i; |
---|
1735 | } |
---|
1736 | static |
---|
1737 | BOOST_UBLAS_INLINE |
---|
1738 | size_type restrict2 (size_type /* i */, size_type j) { |
---|
1739 | return j; |
---|
1740 | } |
---|
1741 | static |
---|
1742 | BOOST_UBLAS_INLINE |
---|
1743 | size_type mutable_restrict1 (size_type i, size_type /* j */) { |
---|
1744 | return i; |
---|
1745 | } |
---|
1746 | static |
---|
1747 | BOOST_UBLAS_INLINE |
---|
1748 | size_type mutable_restrict2 (size_type /* i */, size_type j) { |
---|
1749 | return j; |
---|
1750 | } |
---|
1751 | }; |
---|
1752 | |
---|
1753 | namespace detail { |
---|
1754 | template < class L > |
---|
1755 | struct transposed_structure { |
---|
1756 | typedef typename L::size_type size_type; |
---|
1757 | |
---|
1758 | template<class LAYOUT> |
---|
1759 | static |
---|
1760 | BOOST_UBLAS_INLINE |
---|
1761 | size_type packed_size (LAYOUT l, size_type size_i, size_type size_j) { |
---|
1762 | return L::packed_size(l, size_j, size_i); |
---|
1763 | } |
---|
1764 | |
---|
1765 | static |
---|
1766 | BOOST_UBLAS_INLINE |
---|
1767 | bool zero (size_type i, size_type j) { |
---|
1768 | return L::zero(j, i); |
---|
1769 | } |
---|
1770 | static |
---|
1771 | BOOST_UBLAS_INLINE |
---|
1772 | bool one (size_type i, size_type j) { |
---|
1773 | return L::one(j, i); |
---|
1774 | } |
---|
1775 | static |
---|
1776 | BOOST_UBLAS_INLINE |
---|
1777 | bool other (size_type i, size_type j) { |
---|
1778 | return L::other(j, i); |
---|
1779 | } |
---|
1780 | template<class LAYOUT> |
---|
1781 | static |
---|
1782 | BOOST_UBLAS_INLINE |
---|
1783 | size_type element (LAYOUT /* l */, size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1784 | return L::element(typename LAYOUT::transposed_layout(), j, size_j, i, size_i); |
---|
1785 | } |
---|
1786 | |
---|
1787 | static |
---|
1788 | BOOST_UBLAS_INLINE |
---|
1789 | size_type restrict1 (size_type i, size_type j, size_type size1, size_type size2) { |
---|
1790 | return L::restrict2(j, i, size2, size1); |
---|
1791 | } |
---|
1792 | static |
---|
1793 | BOOST_UBLAS_INLINE |
---|
1794 | size_type restrict2 (size_type i, size_type j, size_type size1, size_type size2) { |
---|
1795 | return L::restrict1(j, i, size2, size1); |
---|
1796 | } |
---|
1797 | static |
---|
1798 | BOOST_UBLAS_INLINE |
---|
1799 | size_type mutable_restrict1 (size_type i, size_type j, size_type size1, size_type size2) { |
---|
1800 | return L::mutable_restrict2(j, i, size2, size1); |
---|
1801 | } |
---|
1802 | static |
---|
1803 | BOOST_UBLAS_INLINE |
---|
1804 | size_type mutable_restrict2 (size_type i, size_type j, size_type size1, size_type size2) { |
---|
1805 | return L::mutable_restrict1(j, i, size2, size1); |
---|
1806 | } |
---|
1807 | |
---|
1808 | static |
---|
1809 | BOOST_UBLAS_INLINE |
---|
1810 | size_type global_restrict1 (size_type index1, size_type size1, size_type index2, size_type size2) { |
---|
1811 | return L::global_restrict2(index2, size2, index1, size1); |
---|
1812 | } |
---|
1813 | static |
---|
1814 | BOOST_UBLAS_INLINE |
---|
1815 | size_type global_restrict2 (size_type index1, size_type size1, size_type index2, size_type size2) { |
---|
1816 | return L::global_restrict1(index2, size2, index1, size1); |
---|
1817 | } |
---|
1818 | static |
---|
1819 | BOOST_UBLAS_INLINE |
---|
1820 | size_type global_mutable_restrict1 (size_type index1, size_type size1, size_type index2, size_type size2) { |
---|
1821 | return L::global_mutable_restrict2(index2, size2, index1, size1); |
---|
1822 | } |
---|
1823 | static |
---|
1824 | BOOST_UBLAS_INLINE |
---|
1825 | size_type global_mutable_restrict2 (size_type index1, size_type size1, size_type index2, size_type size2) { |
---|
1826 | return L::global_mutable_restrict1(index2, size2, index1, size1); |
---|
1827 | } |
---|
1828 | }; |
---|
1829 | } |
---|
1830 | |
---|
1831 | template <class Z> |
---|
1832 | struct basic_lower { |
---|
1833 | typedef Z size_type; |
---|
1834 | typedef lower_tag triangular_type; |
---|
1835 | |
---|
1836 | template<class L> |
---|
1837 | static |
---|
1838 | BOOST_UBLAS_INLINE |
---|
1839 | size_type packed_size (L, size_type size_i, size_type size_j) { |
---|
1840 | return L::triangular_size (size_i, size_j); |
---|
1841 | } |
---|
1842 | |
---|
1843 | static |
---|
1844 | BOOST_UBLAS_INLINE |
---|
1845 | bool zero (size_type i, size_type j) { |
---|
1846 | return j > i; |
---|
1847 | } |
---|
1848 | static |
---|
1849 | BOOST_UBLAS_INLINE |
---|
1850 | bool one (size_type /* i */, size_type /* j */) { |
---|
1851 | return false; |
---|
1852 | } |
---|
1853 | static |
---|
1854 | BOOST_UBLAS_INLINE |
---|
1855 | bool other (size_type i, size_type j) { |
---|
1856 | return j <= i; |
---|
1857 | } |
---|
1858 | template<class L> |
---|
1859 | static |
---|
1860 | BOOST_UBLAS_INLINE |
---|
1861 | size_type element (L, size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1862 | return L::lower_element (i, size_i, j, size_j); |
---|
1863 | } |
---|
1864 | |
---|
1865 | // return nearest valid index in column j |
---|
1866 | static |
---|
1867 | BOOST_UBLAS_INLINE |
---|
1868 | size_type restrict1 (size_type i, size_type j, size_type size1, size_type size2) { |
---|
1869 | return (std::max)(j, (std::min) (size1, i)); |
---|
1870 | } |
---|
1871 | // return nearest valid index in row i |
---|
1872 | static |
---|
1873 | BOOST_UBLAS_INLINE |
---|
1874 | size_type restrict2 (size_type i, size_type j, size_type /* size1 */, size_type /* size2 */) { |
---|
1875 | return (std::max)(size_type(0), (std::min) (i+1, j)); |
---|
1876 | } |
---|
1877 | // return nearest valid mutable index in column j |
---|
1878 | static |
---|
1879 | BOOST_UBLAS_INLINE |
---|
1880 | size_type mutable_restrict1 (size_type i, size_type j, size_type size1, size_type /* size2 */) { |
---|
1881 | return (std::max)(j, (std::min) (size1, i)); |
---|
1882 | } |
---|
1883 | // return nearest valid mutable index in row i |
---|
1884 | static |
---|
1885 | BOOST_UBLAS_INLINE |
---|
1886 | size_type mutable_restrict2 (size_type i, size_type j, size_type /* size1 */, size_type /* size2 */) { |
---|
1887 | return (std::max)(size_type(0), (std::min) (i+1, j)); |
---|
1888 | } |
---|
1889 | |
---|
1890 | // return an index between the first and (1+last) filled row |
---|
1891 | static |
---|
1892 | BOOST_UBLAS_INLINE |
---|
1893 | size_type global_restrict1 (size_type index1, size_type size1, size_type /* index2 */, size_type /* size2 */) { |
---|
1894 | return (std::max)(size_type(0), (std::min)(size1, index1) ); |
---|
1895 | } |
---|
1896 | // return an index between the first and (1+last) filled column |
---|
1897 | static |
---|
1898 | BOOST_UBLAS_INLINE |
---|
1899 | size_type global_restrict2 (size_type /* index1 */, size_type /* size1 */, size_type index2, size_type size2) { |
---|
1900 | return (std::max)(size_type(0), (std::min)(size2, index2) ); |
---|
1901 | } |
---|
1902 | |
---|
1903 | // return an index between the first and (1+last) filled mutable row |
---|
1904 | static |
---|
1905 | BOOST_UBLAS_INLINE |
---|
1906 | size_type global_mutable_restrict1 (size_type index1, size_type size1, size_type /* index2 */, size_type /* size2 */) { |
---|
1907 | return (std::max)(size_type(0), (std::min)(size1, index1) ); |
---|
1908 | } |
---|
1909 | // return an index between the first and (1+last) filled mutable column |
---|
1910 | static |
---|
1911 | BOOST_UBLAS_INLINE |
---|
1912 | size_type global_mutable_restrict2 (size_type /* index1 */, size_type /* size1 */, size_type index2, size_type size2) { |
---|
1913 | return (std::max)(size_type(0), (std::min)(size2, index2) ); |
---|
1914 | } |
---|
1915 | }; |
---|
1916 | |
---|
1917 | // the first row only contains a single 1. Thus it is not stored. |
---|
1918 | template <class Z> |
---|
1919 | struct basic_unit_lower : public basic_lower<Z> { |
---|
1920 | typedef Z size_type; |
---|
1921 | typedef unit_lower_tag triangular_type; |
---|
1922 | |
---|
1923 | template<class L> |
---|
1924 | static |
---|
1925 | BOOST_UBLAS_INLINE |
---|
1926 | size_type packed_size (L, size_type size_i, size_type size_j) { |
---|
1927 | // Zero size strict triangles are bad at this point |
---|
1928 | BOOST_UBLAS_CHECK (size_i != 0 && size_j != 0, bad_index ()); |
---|
1929 | return L::triangular_size (size_i - 1, size_j - 1); |
---|
1930 | } |
---|
1931 | |
---|
1932 | static |
---|
1933 | BOOST_UBLAS_INLINE |
---|
1934 | bool one (size_type i, size_type j) { |
---|
1935 | return j == i; |
---|
1936 | } |
---|
1937 | static |
---|
1938 | BOOST_UBLAS_INLINE |
---|
1939 | bool other (size_type i, size_type j) { |
---|
1940 | return j < i; |
---|
1941 | } |
---|
1942 | template<class L> |
---|
1943 | static |
---|
1944 | BOOST_UBLAS_INLINE |
---|
1945 | size_type element (L, size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
1946 | // Zero size strict triangles are bad at this point |
---|
1947 | BOOST_UBLAS_CHECK (size_i != 0 && size_j != 0 && i != 0, bad_index ()); |
---|
1948 | return L::lower_element (i-1, size_i - 1, j, size_j - 1); |
---|
1949 | } |
---|
1950 | |
---|
1951 | static |
---|
1952 | BOOST_UBLAS_INLINE |
---|
1953 | size_type mutable_restrict1 (size_type i, size_type j, size_type size1, size_type /* size2 */) { |
---|
1954 | return (std::max)(j+1, (std::min) (size1, i)); |
---|
1955 | } |
---|
1956 | static |
---|
1957 | BOOST_UBLAS_INLINE |
---|
1958 | size_type mutable_restrict2 (size_type i, size_type j, size_type /* size1 */, size_type /* size2 */) { |
---|
1959 | return (std::max)(size_type(0), (std::min) (i, j)); |
---|
1960 | } |
---|
1961 | |
---|
1962 | // return an index between the first and (1+last) filled mutable row |
---|
1963 | static |
---|
1964 | BOOST_UBLAS_INLINE |
---|
1965 | size_type global_mutable_restrict1 (size_type index1, size_type size1, size_type /* index2 */, size_type /* size2 */) { |
---|
1966 | return (std::max)(size_type(1), (std::min)(size1, index1) ); |
---|
1967 | } |
---|
1968 | // return an index between the first and (1+last) filled mutable column |
---|
1969 | static |
---|
1970 | BOOST_UBLAS_INLINE |
---|
1971 | size_type global_mutable_restrict2 (size_type /* index1 */, size_type /* size1 */, size_type index2, size_type size2) { |
---|
1972 | BOOST_UBLAS_CHECK( size2 >= 1 , external_logic() ); |
---|
1973 | return (std::max)(size_type(0), (std::min)(size2-1, index2) ); |
---|
1974 | } |
---|
1975 | }; |
---|
1976 | |
---|
1977 | // the first row only contains no element. Thus it is not stored. |
---|
1978 | template <class Z> |
---|
1979 | struct basic_strict_lower : public basic_unit_lower<Z> { |
---|
1980 | typedef Z size_type; |
---|
1981 | typedef strict_lower_tag triangular_type; |
---|
1982 | |
---|
1983 | template<class L> |
---|
1984 | static |
---|
1985 | BOOST_UBLAS_INLINE |
---|
1986 | size_type packed_size (L, size_type size_i, size_type size_j) { |
---|
1987 | // Zero size strict triangles are bad at this point |
---|
1988 | BOOST_UBLAS_CHECK (size_i != 0 && size_j != 0, bad_index ()); |
---|
1989 | return L::triangular_size (size_i - 1, size_j - 1); |
---|
1990 | } |
---|
1991 | |
---|
1992 | static |
---|
1993 | BOOST_UBLAS_INLINE |
---|
1994 | bool zero (size_type i, size_type j) { |
---|
1995 | return j >= i; |
---|
1996 | } |
---|
1997 | static |
---|
1998 | BOOST_UBLAS_INLINE |
---|
1999 | bool one (size_type /*i*/, size_type /*j*/) { |
---|
2000 | return false; |
---|
2001 | } |
---|
2002 | static |
---|
2003 | BOOST_UBLAS_INLINE |
---|
2004 | bool other (size_type i, size_type j) { |
---|
2005 | return j < i; |
---|
2006 | } |
---|
2007 | template<class L> |
---|
2008 | static |
---|
2009 | BOOST_UBLAS_INLINE |
---|
2010 | size_type element (L, size_type i, size_type size_i, size_type j, size_type size_j) { |
---|
2011 | // Zero size strict triangles are bad at this point |
---|
2012 | BOOST_UBLAS_CHECK (size_i != 0 && size_j != 0 && i != 0, bad_index ()); |
---|
2013 | return L::lower_element (i-1, size_i - 1, j, size_j - 1); |
---|
2014 | } |
---|
2015 | |
---|
2016 | static |
---|
2017 | BOOST_UBLAS_INLINE |
---|
2018 | size_type restrict1 (size_type i, size_type j, size_type size1, size_type size2) { |
---|
2019 | return basic_unit_lower<Z>::mutable_restrict1(i, j, size1, size2); |
---|
2020 | } |
---|
2021 | static |
---|
2022 | BOOST_UBLAS_INLINE |
---|
2023 | size_type restrict2 (size_type i, size_type j, size_type size1, size_type size2) { |
---|
2024 | return basic_unit_lower<Z>::mutable_restrict2(i, j, size1, size2); |
---|
2025 | } |
---|
2026 | |
---|
2027 | // return an index between the first and (1+last) filled row |
---|
2028 | static |
---|
2029 | BOOST_UBLAS_INLINE |
---|
2030 | size_type global_restrict1 (size_type index1, size_type size1, size_type index2, size_type size2) { |
---|
2031 | return basic_unit_lower<Z>::global_mutable_restrict1(index1, size1, index2, size2); |
---|
2032 | } |
---|
2033 | // return an index between the first and (1+last) filled column |
---|
2034 | static |
---|
2035 | BOOST_UBLAS_INLINE |
---|
2036 | size_type global_restrict2 (size_type index1, size_type size1, size_type index2, size_type size2) { |
---|
2037 | return basic_unit_lower<Z>::global_mutable_restrict2(index1, size1, index2, size2); |
---|
2038 | } |
---|
2039 | }; |
---|
2040 | |
---|
2041 | |
---|
2042 | template <class Z> |
---|
2043 | struct basic_upper : public detail::transposed_structure<basic_lower<Z> > |
---|
2044 | { |
---|
2045 | typedef upper_tag triangular_type; |
---|
2046 | }; |
---|
2047 | |
---|
2048 | template <class Z> |
---|
2049 | struct basic_unit_upper : public detail::transposed_structure<basic_unit_lower<Z> > |
---|
2050 | { |
---|
2051 | typedef unit_upper_tag triangular_type; |
---|
2052 | }; |
---|
2053 | |
---|
2054 | template <class Z> |
---|
2055 | struct basic_strict_upper : public detail::transposed_structure<basic_strict_lower<Z> > |
---|
2056 | { |
---|
2057 | typedef strict_upper_tag triangular_type; |
---|
2058 | }; |
---|
2059 | |
---|
2060 | |
---|
2061 | }}} |
---|
2062 | |
---|
2063 | #endif |
---|