1 | // This file is part of Eigen, a lightweight C++ template library |
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2 | // for linear algebra. |
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3 | // |
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4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> |
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5 | // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com> |
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6 | // |
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7 | // This Source Code Form is subject to the terms of the Mozilla |
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8 | // Public License v. 2.0. If a copy of the MPL was not distributed |
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9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
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10 | |
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11 | #ifndef EIGEN_XPRHELPER_H |
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12 | #define EIGEN_XPRHELPER_H |
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13 | |
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14 | // just a workaround because GCC seems to not really like empty structs |
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15 | // FIXME: gcc 4.3 generates bad code when strict-aliasing is enabled |
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16 | // so currently we simply disable this optimization for gcc 4.3 |
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17 | #if (defined __GNUG__) && !((__GNUC__==4) && (__GNUC_MINOR__==3)) |
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18 | #define EIGEN_EMPTY_STRUCT_CTOR(X) \ |
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19 | EIGEN_STRONG_INLINE X() {} \ |
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20 | EIGEN_STRONG_INLINE X(const X& ) {} |
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21 | #else |
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22 | #define EIGEN_EMPTY_STRUCT_CTOR(X) |
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23 | #endif |
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24 | |
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25 | namespace Eigen { |
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26 | |
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27 | typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex; |
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28 | |
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29 | namespace internal { |
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30 | |
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31 | //classes inheriting no_assignment_operator don't generate a default operator=. |
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32 | class no_assignment_operator |
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33 | { |
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34 | private: |
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35 | no_assignment_operator& operator=(const no_assignment_operator&); |
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36 | }; |
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37 | |
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38 | /** \internal return the index type with the largest number of bits */ |
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39 | template<typename I1, typename I2> |
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40 | struct promote_index_type |
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41 | { |
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42 | typedef typename conditional<(sizeof(I1)<sizeof(I2)), I2, I1>::type type; |
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43 | }; |
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44 | |
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45 | /** \internal If the template parameter Value is Dynamic, this class is just a wrapper around a T variable that |
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46 | * can be accessed using value() and setValue(). |
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47 | * Otherwise, this class is an empty structure and value() just returns the template parameter Value. |
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48 | */ |
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49 | template<typename T, int Value> class variable_if_dynamic |
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50 | { |
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51 | public: |
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52 | EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamic) |
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53 | explicit variable_if_dynamic(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); assert(v == T(Value)); } |
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54 | static T value() { return T(Value); } |
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55 | void setValue(T) {} |
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56 | }; |
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57 | |
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58 | template<typename T> class variable_if_dynamic<T, Dynamic> |
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59 | { |
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60 | T m_value; |
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61 | variable_if_dynamic() { assert(false); } |
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62 | public: |
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63 | explicit variable_if_dynamic(T value) : m_value(value) {} |
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64 | T value() const { return m_value; } |
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65 | void setValue(T value) { m_value = value; } |
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66 | }; |
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67 | |
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68 | template<typename T> struct functor_traits |
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69 | { |
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70 | enum |
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71 | { |
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72 | Cost = 10, |
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73 | PacketAccess = false |
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74 | }; |
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75 | }; |
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76 | |
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77 | template<typename T> struct packet_traits; |
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78 | |
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79 | template<typename T> struct unpacket_traits |
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80 | { |
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81 | typedef T type; |
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82 | enum {size=1}; |
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83 | }; |
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84 | |
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85 | template<typename _Scalar, int _Rows, int _Cols, |
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86 | int _Options = AutoAlign | |
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87 | ( (_Rows==1 && _Cols!=1) ? RowMajor |
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88 | : (_Cols==1 && _Rows!=1) ? ColMajor |
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89 | : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ), |
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90 | int _MaxRows = _Rows, |
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91 | int _MaxCols = _Cols |
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92 | > class make_proper_matrix_type |
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93 | { |
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94 | enum { |
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95 | IsColVector = _Cols==1 && _Rows!=1, |
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96 | IsRowVector = _Rows==1 && _Cols!=1, |
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97 | Options = IsColVector ? (_Options | ColMajor) & ~RowMajor |
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98 | : IsRowVector ? (_Options | RowMajor) & ~ColMajor |
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99 | : _Options |
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100 | }; |
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101 | public: |
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102 | typedef Matrix<_Scalar, _Rows, _Cols, Options, _MaxRows, _MaxCols> type; |
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103 | }; |
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104 | |
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105 | template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols> |
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106 | class compute_matrix_flags |
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107 | { |
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108 | enum { |
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109 | row_major_bit = Options&RowMajor ? RowMajorBit : 0, |
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110 | is_dynamic_size_storage = MaxRows==Dynamic || MaxCols==Dynamic, |
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111 | |
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112 | aligned_bit = |
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113 | ( |
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114 | ((Options&DontAlign)==0) |
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115 | && ( |
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116 | #if EIGEN_ALIGN_STATICALLY |
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117 | ((!is_dynamic_size_storage) && (((MaxCols*MaxRows*int(sizeof(Scalar))) % 16) == 0)) |
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118 | #else |
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119 | 0 |
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120 | #endif |
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121 | |
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122 | || |
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123 | |
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124 | #if EIGEN_ALIGN |
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125 | is_dynamic_size_storage |
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126 | #else |
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127 | 0 |
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128 | #endif |
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129 | |
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130 | ) |
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131 | ) ? AlignedBit : 0, |
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132 | packet_access_bit = packet_traits<Scalar>::Vectorizable && aligned_bit ? PacketAccessBit : 0 |
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133 | }; |
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134 | |
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135 | public: |
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136 | enum { ret = LinearAccessBit | LvalueBit | DirectAccessBit | NestByRefBit | packet_access_bit | row_major_bit | aligned_bit }; |
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137 | }; |
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138 | |
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139 | template<int _Rows, int _Cols> struct size_at_compile_time |
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140 | { |
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141 | enum { ret = (_Rows==Dynamic || _Cols==Dynamic) ? Dynamic : _Rows * _Cols }; |
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142 | }; |
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143 | |
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144 | /* plain_matrix_type : the difference from eval is that plain_matrix_type is always a plain matrix type, |
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145 | * whereas eval is a const reference in the case of a matrix |
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146 | */ |
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147 | |
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148 | template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_matrix_type; |
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149 | template<typename T, typename BaseClassType> struct plain_matrix_type_dense; |
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150 | template<typename T> struct plain_matrix_type<T,Dense> |
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151 | { |
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152 | typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind>::type type; |
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153 | }; |
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154 | |
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155 | template<typename T> struct plain_matrix_type_dense<T,MatrixXpr> |
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156 | { |
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157 | typedef Matrix<typename traits<T>::Scalar, |
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158 | traits<T>::RowsAtCompileTime, |
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159 | traits<T>::ColsAtCompileTime, |
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160 | AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor), |
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161 | traits<T>::MaxRowsAtCompileTime, |
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162 | traits<T>::MaxColsAtCompileTime |
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163 | > type; |
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164 | }; |
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165 | |
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166 | template<typename T> struct plain_matrix_type_dense<T,ArrayXpr> |
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167 | { |
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168 | typedef Array<typename traits<T>::Scalar, |
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169 | traits<T>::RowsAtCompileTime, |
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170 | traits<T>::ColsAtCompileTime, |
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171 | AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor), |
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172 | traits<T>::MaxRowsAtCompileTime, |
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173 | traits<T>::MaxColsAtCompileTime |
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174 | > type; |
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175 | }; |
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176 | |
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177 | /* eval : the return type of eval(). For matrices, this is just a const reference |
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178 | * in order to avoid a useless copy |
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179 | */ |
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180 | |
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181 | template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct eval; |
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182 | |
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183 | template<typename T> struct eval<T,Dense> |
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184 | { |
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185 | typedef typename plain_matrix_type<T>::type type; |
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186 | // typedef typename T::PlainObject type; |
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187 | // typedef T::Matrix<typename traits<T>::Scalar, |
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188 | // traits<T>::RowsAtCompileTime, |
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189 | // traits<T>::ColsAtCompileTime, |
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190 | // AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor), |
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191 | // traits<T>::MaxRowsAtCompileTime, |
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192 | // traits<T>::MaxColsAtCompileTime |
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193 | // > type; |
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194 | }; |
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195 | |
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196 | // for matrices, no need to evaluate, just use a const reference to avoid a useless copy |
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197 | template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols> |
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198 | struct eval<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense> |
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199 | { |
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200 | typedef const Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type; |
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201 | }; |
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202 | |
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203 | template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols> |
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204 | struct eval<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense> |
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205 | { |
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206 | typedef const Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type; |
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207 | }; |
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208 | |
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209 | |
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210 | |
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211 | /* plain_matrix_type_column_major : same as plain_matrix_type but guaranteed to be column-major |
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212 | */ |
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213 | template<typename T> struct plain_matrix_type_column_major |
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214 | { |
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215 | enum { Rows = traits<T>::RowsAtCompileTime, |
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216 | Cols = traits<T>::ColsAtCompileTime, |
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217 | MaxRows = traits<T>::MaxRowsAtCompileTime, |
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218 | MaxCols = traits<T>::MaxColsAtCompileTime |
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219 | }; |
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220 | typedef Matrix<typename traits<T>::Scalar, |
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221 | Rows, |
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222 | Cols, |
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223 | (MaxRows==1&&MaxCols!=1) ? RowMajor : ColMajor, |
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224 | MaxRows, |
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225 | MaxCols |
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226 | > type; |
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227 | }; |
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228 | |
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229 | /* plain_matrix_type_row_major : same as plain_matrix_type but guaranteed to be row-major |
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230 | */ |
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231 | template<typename T> struct plain_matrix_type_row_major |
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232 | { |
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233 | enum { Rows = traits<T>::RowsAtCompileTime, |
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234 | Cols = traits<T>::ColsAtCompileTime, |
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235 | MaxRows = traits<T>::MaxRowsAtCompileTime, |
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236 | MaxCols = traits<T>::MaxColsAtCompileTime |
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237 | }; |
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238 | typedef Matrix<typename traits<T>::Scalar, |
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239 | Rows, |
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240 | Cols, |
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241 | (MaxCols==1&&MaxRows!=1) ? RowMajor : ColMajor, |
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242 | MaxRows, |
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243 | MaxCols |
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244 | > type; |
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245 | }; |
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246 | |
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247 | // we should be able to get rid of this one too |
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248 | template<typename T> struct must_nest_by_value { enum { ret = false }; }; |
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249 | |
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250 | /** \internal The reference selector for template expressions. The idea is that we don't |
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251 | * need to use references for expressions since they are light weight proxy |
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252 | * objects which should generate no copying overhead. */ |
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253 | template <typename T> |
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254 | struct ref_selector |
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255 | { |
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256 | typedef typename conditional< |
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257 | bool(traits<T>::Flags & NestByRefBit), |
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258 | T const&, |
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259 | const T |
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260 | >::type type; |
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261 | }; |
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262 | |
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263 | /** \internal Adds the const qualifier on the value-type of T2 if and only if T1 is a const type */ |
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264 | template<typename T1, typename T2> |
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265 | struct transfer_constness |
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266 | { |
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267 | typedef typename conditional< |
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268 | bool(internal::is_const<T1>::value), |
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269 | typename internal::add_const_on_value_type<T2>::type, |
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270 | T2 |
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271 | >::type type; |
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272 | }; |
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273 | |
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274 | /** \internal Determines how a given expression should be nested into another one. |
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275 | * For example, when you do a * (b+c), Eigen will determine how the expression b+c should be |
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276 | * nested into the bigger product expression. The choice is between nesting the expression b+c as-is, or |
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277 | * evaluating that expression b+c into a temporary variable d, and nest d so that the resulting expression is |
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278 | * a*d. Evaluating can be beneficial for example if every coefficient access in the resulting expression causes |
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279 | * many coefficient accesses in the nested expressions -- as is the case with matrix product for example. |
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280 | * |
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281 | * \param T the type of the expression being nested |
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282 | * \param n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression. |
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283 | * |
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284 | * Note that if no evaluation occur, then the constness of T is preserved. |
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285 | * |
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286 | * Example. Suppose that a, b, and c are of type Matrix3d. The user forms the expression a*(b+c). |
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287 | * b+c is an expression "sum of matrices", which we will denote by S. In order to determine how to nest it, |
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288 | * the Product expression uses: nested<S, 3>::ret, which turns out to be Matrix3d because the internal logic of |
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289 | * nested determined that in this case it was better to evaluate the expression b+c into a temporary. On the other hand, |
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290 | * since a is of type Matrix3d, the Product expression nests it as nested<Matrix3d, 3>::ret, which turns out to be |
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291 | * const Matrix3d&, because the internal logic of nested determined that since a was already a matrix, there was no point |
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292 | * in copying it into another matrix. |
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293 | */ |
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294 | template<typename T, int n=1, typename PlainObject = typename eval<T>::type> struct nested |
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295 | { |
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296 | enum { |
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297 | // for the purpose of this test, to keep it reasonably simple, we arbitrarily choose a value of Dynamic values. |
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298 | // the choice of 10000 makes it larger than any practical fixed value and even most dynamic values. |
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299 | // in extreme cases where these assumptions would be wrong, we would still at worst suffer performance issues |
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300 | // (poor choice of temporaries). |
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301 | // it's important that this value can still be squared without integer overflowing. |
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302 | DynamicAsInteger = 10000, |
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303 | ScalarReadCost = NumTraits<typename traits<T>::Scalar>::ReadCost, |
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304 | ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? int(DynamicAsInteger) : int(ScalarReadCost), |
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305 | CoeffReadCost = traits<T>::CoeffReadCost, |
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306 | CoeffReadCostAsInteger = CoeffReadCost == Dynamic ? int(DynamicAsInteger) : int(CoeffReadCost), |
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307 | NAsInteger = n == Dynamic ? int(DynamicAsInteger) : n, |
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308 | CostEvalAsInteger = (NAsInteger+1) * ScalarReadCostAsInteger + CoeffReadCostAsInteger, |
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309 | CostNoEvalAsInteger = NAsInteger * CoeffReadCostAsInteger |
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310 | }; |
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311 | |
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312 | typedef typename conditional< |
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313 | ( (int(traits<T>::Flags) & EvalBeforeNestingBit) || |
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314 | int(CostEvalAsInteger) < int(CostNoEvalAsInteger) |
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315 | ), |
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316 | PlainObject, |
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317 | typename ref_selector<T>::type |
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318 | >::type type; |
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319 | }; |
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320 | |
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321 | template<typename T> |
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322 | T* const_cast_ptr(const T* ptr) |
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323 | { |
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324 | return const_cast<T*>(ptr); |
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325 | } |
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326 | |
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327 | template<typename Derived, typename XprKind = typename traits<Derived>::XprKind> |
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328 | struct dense_xpr_base |
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329 | { |
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330 | /* dense_xpr_base should only ever be used on dense expressions, thus falling either into the MatrixXpr or into the ArrayXpr cases */ |
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331 | }; |
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332 | |
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333 | template<typename Derived> |
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334 | struct dense_xpr_base<Derived, MatrixXpr> |
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335 | { |
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336 | typedef MatrixBase<Derived> type; |
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337 | }; |
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338 | |
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339 | template<typename Derived> |
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340 | struct dense_xpr_base<Derived, ArrayXpr> |
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341 | { |
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342 | typedef ArrayBase<Derived> type; |
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343 | }; |
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344 | |
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345 | /** \internal Helper base class to add a scalar multiple operator |
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346 | * overloads for complex types */ |
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347 | template<typename Derived,typename Scalar,typename OtherScalar, |
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348 | bool EnableIt = !is_same<Scalar,OtherScalar>::value > |
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349 | struct special_scalar_op_base : public DenseCoeffsBase<Derived> |
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350 | { |
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351 | // dummy operator* so that the |
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352 | // "using special_scalar_op_base::operator*" compiles |
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353 | void operator*() const; |
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354 | }; |
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355 | |
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356 | template<typename Derived,typename Scalar,typename OtherScalar> |
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357 | struct special_scalar_op_base<Derived,Scalar,OtherScalar,true> : public DenseCoeffsBase<Derived> |
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358 | { |
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359 | const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived> |
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360 | operator*(const OtherScalar& scalar) const |
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361 | { |
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362 | return CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived> |
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363 | (*static_cast<const Derived*>(this), scalar_multiple2_op<Scalar,OtherScalar>(scalar)); |
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364 | } |
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365 | |
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366 | inline friend const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived> |
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367 | operator*(const OtherScalar& scalar, const Derived& matrix) |
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368 | { return static_cast<const special_scalar_op_base&>(matrix).operator*(scalar); } |
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369 | }; |
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370 | |
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371 | template<typename XprType, typename CastType> struct cast_return_type |
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372 | { |
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373 | typedef typename XprType::Scalar CurrentScalarType; |
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374 | typedef typename remove_all<CastType>::type _CastType; |
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375 | typedef typename _CastType::Scalar NewScalarType; |
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376 | typedef typename conditional<is_same<CurrentScalarType,NewScalarType>::value, |
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377 | const XprType&,CastType>::type type; |
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378 | }; |
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379 | |
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380 | template <typename A, typename B> struct promote_storage_type; |
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381 | |
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382 | template <typename A> struct promote_storage_type<A,A> |
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383 | { |
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384 | typedef A ret; |
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385 | }; |
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386 | |
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387 | /** \internal gives the plain matrix or array type to store a row/column/diagonal of a matrix type. |
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388 | * \param Scalar optional parameter allowing to pass a different scalar type than the one of the MatrixType. |
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389 | */ |
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390 | template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar> |
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391 | struct plain_row_type |
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392 | { |
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393 | typedef Matrix<Scalar, 1, ExpressionType::ColsAtCompileTime, |
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394 | ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> MatrixRowType; |
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395 | typedef Array<Scalar, 1, ExpressionType::ColsAtCompileTime, |
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396 | ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> ArrayRowType; |
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397 | |
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398 | typedef typename conditional< |
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399 | is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value, |
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400 | MatrixRowType, |
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401 | ArrayRowType |
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402 | >::type type; |
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403 | }; |
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404 | |
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405 | template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar> |
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406 | struct plain_col_type |
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407 | { |
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408 | typedef Matrix<Scalar, ExpressionType::RowsAtCompileTime, 1, |
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409 | ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> MatrixColType; |
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410 | typedef Array<Scalar, ExpressionType::RowsAtCompileTime, 1, |
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411 | ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> ArrayColType; |
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412 | |
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413 | typedef typename conditional< |
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414 | is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value, |
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415 | MatrixColType, |
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416 | ArrayColType |
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417 | >::type type; |
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418 | }; |
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419 | |
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420 | template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar> |
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421 | struct plain_diag_type |
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422 | { |
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423 | enum { diag_size = EIGEN_SIZE_MIN_PREFER_DYNAMIC(ExpressionType::RowsAtCompileTime, ExpressionType::ColsAtCompileTime), |
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424 | max_diag_size = EIGEN_SIZE_MIN_PREFER_FIXED(ExpressionType::MaxRowsAtCompileTime, ExpressionType::MaxColsAtCompileTime) |
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425 | }; |
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426 | typedef Matrix<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> MatrixDiagType; |
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427 | typedef Array<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> ArrayDiagType; |
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428 | |
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429 | typedef typename conditional< |
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430 | is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value, |
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431 | MatrixDiagType, |
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432 | ArrayDiagType |
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433 | >::type type; |
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434 | }; |
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435 | |
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436 | template<typename ExpressionType> |
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437 | struct is_lvalue |
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438 | { |
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439 | enum { value = !bool(is_const<ExpressionType>::value) && |
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440 | bool(traits<ExpressionType>::Flags & LvalueBit) }; |
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441 | }; |
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442 | |
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443 | } // end namespace internal |
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444 | |
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445 | } // end namespace Eigen |
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446 | |
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447 | #endif // EIGEN_XPRHELPER_H |
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