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 | /** \internal like variable_if_dynamic but for DynamicIndex
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69 | */
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70 | template<typename T, int Value> class variable_if_dynamicindex
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71 | {
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72 | public:
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73 | EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamicindex)
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74 | explicit variable_if_dynamicindex(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); assert(v == T(Value)); }
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75 | static T value() { return T(Value); }
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76 | void setValue(T) {}
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77 | };
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78 |
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79 | template<typename T> class variable_if_dynamicindex<T, DynamicIndex>
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80 | {
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81 | T m_value;
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82 | variable_if_dynamicindex() { assert(false); }
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83 | public:
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84 | explicit variable_if_dynamicindex(T value) : m_value(value) {}
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85 | T value() const { return m_value; }
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86 | void setValue(T value) { m_value = value; }
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87 | };
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88 |
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89 | template<typename T> struct functor_traits
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90 | {
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91 | enum
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92 | {
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93 | Cost = 10,
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94 | PacketAccess = false,
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95 | IsRepeatable = false
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96 | };
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97 | };
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98 |
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99 | template<typename T> struct packet_traits;
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100 |
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101 | template<typename T> struct unpacket_traits
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102 | {
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103 | typedef T type;
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104 | enum {size=1};
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105 | };
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106 |
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107 | template<typename _Scalar, int _Rows, int _Cols,
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108 | int _Options = AutoAlign |
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109 | ( (_Rows==1 && _Cols!=1) ? RowMajor
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110 | : (_Cols==1 && _Rows!=1) ? ColMajor
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111 | : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
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112 | int _MaxRows = _Rows,
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113 | int _MaxCols = _Cols
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114 | > class make_proper_matrix_type
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115 | {
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116 | enum {
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117 | IsColVector = _Cols==1 && _Rows!=1,
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118 | IsRowVector = _Rows==1 && _Cols!=1,
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119 | Options = IsColVector ? (_Options | ColMajor) & ~RowMajor
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120 | : IsRowVector ? (_Options | RowMajor) & ~ColMajor
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121 | : _Options
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122 | };
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123 | public:
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124 | typedef Matrix<_Scalar, _Rows, _Cols, Options, _MaxRows, _MaxCols> type;
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125 | };
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126 |
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127 | template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
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128 | class compute_matrix_flags
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129 | {
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130 | enum {
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131 | row_major_bit = Options&RowMajor ? RowMajorBit : 0,
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132 | is_dynamic_size_storage = MaxRows==Dynamic || MaxCols==Dynamic,
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133 |
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134 | aligned_bit =
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135 | (
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136 | ((Options&DontAlign)==0)
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137 | && (
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138 | #if EIGEN_ALIGN_STATICALLY
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139 | ((!is_dynamic_size_storage) && (((MaxCols*MaxRows*int(sizeof(Scalar))) % 16) == 0))
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140 | #else
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141 | 0
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142 | #endif
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143 |
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144 | ||
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145 |
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146 | #if EIGEN_ALIGN
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147 | is_dynamic_size_storage
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148 | #else
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149 | 0
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150 | #endif
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151 |
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152 | )
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153 | ) ? AlignedBit : 0,
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154 | packet_access_bit = packet_traits<Scalar>::Vectorizable && aligned_bit ? PacketAccessBit : 0
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155 | };
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156 |
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157 | public:
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158 | enum { ret = LinearAccessBit | LvalueBit | DirectAccessBit | NestByRefBit | packet_access_bit | row_major_bit | aligned_bit };
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159 | };
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160 |
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161 | template<int _Rows, int _Cols> struct size_at_compile_time
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162 | {
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163 | enum { ret = (_Rows==Dynamic || _Cols==Dynamic) ? Dynamic : _Rows * _Cols };
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164 | };
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165 |
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166 | /* plain_matrix_type : the difference from eval is that plain_matrix_type is always a plain matrix type,
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167 | * whereas eval is a const reference in the case of a matrix
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168 | */
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169 |
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170 | template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_matrix_type;
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171 | template<typename T, typename BaseClassType> struct plain_matrix_type_dense;
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172 | template<typename T> struct plain_matrix_type<T,Dense>
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173 | {
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174 | typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind>::type type;
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175 | };
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176 |
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177 | template<typename T> struct plain_matrix_type_dense<T,MatrixXpr>
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178 | {
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179 | typedef Matrix<typename traits<T>::Scalar,
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180 | traits<T>::RowsAtCompileTime,
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181 | traits<T>::ColsAtCompileTime,
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182 | AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
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183 | traits<T>::MaxRowsAtCompileTime,
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184 | traits<T>::MaxColsAtCompileTime
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185 | > type;
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186 | };
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187 |
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188 | template<typename T> struct plain_matrix_type_dense<T,ArrayXpr>
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189 | {
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190 | typedef Array<typename traits<T>::Scalar,
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191 | traits<T>::RowsAtCompileTime,
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192 | traits<T>::ColsAtCompileTime,
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193 | AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
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194 | traits<T>::MaxRowsAtCompileTime,
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195 | traits<T>::MaxColsAtCompileTime
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196 | > type;
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197 | };
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198 |
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199 | /* eval : the return type of eval(). For matrices, this is just a const reference
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200 | * in order to avoid a useless copy
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201 | */
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202 |
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203 | template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct eval;
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204 |
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205 | template<typename T> struct eval<T,Dense>
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206 | {
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207 | typedef typename plain_matrix_type<T>::type type;
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208 | // typedef typename T::PlainObject type;
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209 | // typedef T::Matrix<typename traits<T>::Scalar,
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210 | // traits<T>::RowsAtCompileTime,
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211 | // traits<T>::ColsAtCompileTime,
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212 | // AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
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213 | // traits<T>::MaxRowsAtCompileTime,
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214 | // traits<T>::MaxColsAtCompileTime
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215 | // > type;
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216 | };
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217 |
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218 | // for matrices, no need to evaluate, just use a const reference to avoid a useless copy
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219 | template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
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220 | struct eval<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
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221 | {
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222 | typedef const Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;
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223 | };
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224 |
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225 | template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
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226 | struct eval<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
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227 | {
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228 | typedef const Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;
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229 | };
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230 |
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231 |
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232 |
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233 | /* plain_matrix_type_column_major : same as plain_matrix_type but guaranteed to be column-major
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234 | */
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235 | template<typename T> struct plain_matrix_type_column_major
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236 | {
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237 | enum { Rows = traits<T>::RowsAtCompileTime,
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238 | Cols = traits<T>::ColsAtCompileTime,
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239 | MaxRows = traits<T>::MaxRowsAtCompileTime,
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240 | MaxCols = traits<T>::MaxColsAtCompileTime
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241 | };
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242 | typedef Matrix<typename traits<T>::Scalar,
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243 | Rows,
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244 | Cols,
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245 | (MaxRows==1&&MaxCols!=1) ? RowMajor : ColMajor,
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246 | MaxRows,
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247 | MaxCols
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248 | > type;
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249 | };
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250 |
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251 | /* plain_matrix_type_row_major : same as plain_matrix_type but guaranteed to be row-major
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252 | */
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253 | template<typename T> struct plain_matrix_type_row_major
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254 | {
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255 | enum { Rows = traits<T>::RowsAtCompileTime,
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256 | Cols = traits<T>::ColsAtCompileTime,
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257 | MaxRows = traits<T>::MaxRowsAtCompileTime,
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258 | MaxCols = traits<T>::MaxColsAtCompileTime
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259 | };
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260 | typedef Matrix<typename traits<T>::Scalar,
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261 | Rows,
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262 | Cols,
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263 | (MaxCols==1&&MaxRows!=1) ? RowMajor : ColMajor,
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264 | MaxRows,
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265 | MaxCols
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266 | > type;
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267 | };
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268 |
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269 | // we should be able to get rid of this one too
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270 | template<typename T> struct must_nest_by_value { enum { ret = false }; };
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271 |
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272 | /** \internal The reference selector for template expressions. The idea is that we don't
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273 | * need to use references for expressions since they are light weight proxy
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274 | * objects which should generate no copying overhead. */
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275 | template <typename T>
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276 | struct ref_selector
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277 | {
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278 | typedef typename conditional<
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279 | bool(traits<T>::Flags & NestByRefBit),
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280 | T const&,
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281 | const T
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282 | >::type type;
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283 | };
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284 |
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285 | /** \internal Adds the const qualifier on the value-type of T2 if and only if T1 is a const type */
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286 | template<typename T1, typename T2>
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287 | struct transfer_constness
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288 | {
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289 | typedef typename conditional<
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290 | bool(internal::is_const<T1>::value),
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291 | typename internal::add_const_on_value_type<T2>::type,
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292 | T2
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293 | >::type type;
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294 | };
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295 |
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296 | /** \internal Determines how a given expression should be nested into another one.
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297 | * For example, when you do a * (b+c), Eigen will determine how the expression b+c should be
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298 | * nested into the bigger product expression. The choice is between nesting the expression b+c as-is, or
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299 | * evaluating that expression b+c into a temporary variable d, and nest d so that the resulting expression is
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300 | * a*d. Evaluating can be beneficial for example if every coefficient access in the resulting expression causes
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301 | * many coefficient accesses in the nested expressions -- as is the case with matrix product for example.
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302 | *
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303 | * \param T the type of the expression being nested
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304 | * \param n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression.
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305 | *
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306 | * Note that if no evaluation occur, then the constness of T is preserved.
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307 | *
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308 | * Example. Suppose that a, b, and c are of type Matrix3d. The user forms the expression a*(b+c).
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309 | * 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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310 | * the Product expression uses: nested<S, 3>::ret, which turns out to be Matrix3d because the internal logic of
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311 | * 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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312 | * 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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313 | * const Matrix3d&, because the internal logic of nested determined that since a was already a matrix, there was no point
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314 | * in copying it into another matrix.
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315 | */
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316 | template<typename T, int n=1, typename PlainObject = typename eval<T>::type> struct nested
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317 | {
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318 | enum {
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319 | // for the purpose of this test, to keep it reasonably simple, we arbitrarily choose a value of Dynamic values.
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320 | // the choice of 10000 makes it larger than any practical fixed value and even most dynamic values.
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321 | // in extreme cases where these assumptions would be wrong, we would still at worst suffer performance issues
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322 | // (poor choice of temporaries).
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323 | // it's important that this value can still be squared without integer overflowing.
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324 | DynamicAsInteger = 10000,
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325 | ScalarReadCost = NumTraits<typename traits<T>::Scalar>::ReadCost,
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326 | ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? int(DynamicAsInteger) : int(ScalarReadCost),
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327 | CoeffReadCost = traits<T>::CoeffReadCost,
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328 | CoeffReadCostAsInteger = CoeffReadCost == Dynamic ? int(DynamicAsInteger) : int(CoeffReadCost),
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329 | NAsInteger = n == Dynamic ? int(DynamicAsInteger) : n,
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330 | CostEvalAsInteger = (NAsInteger+1) * ScalarReadCostAsInteger + CoeffReadCostAsInteger,
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331 | CostNoEvalAsInteger = NAsInteger * CoeffReadCostAsInteger
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332 | };
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333 |
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334 | typedef typename conditional<
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335 | ( (int(traits<T>::Flags) & EvalBeforeNestingBit) ||
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336 | int(CostEvalAsInteger) < int(CostNoEvalAsInteger)
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337 | ),
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338 | PlainObject,
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339 | typename ref_selector<T>::type
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340 | >::type type;
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341 | };
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342 |
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343 | template<typename T>
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344 | inline T* const_cast_ptr(const T* ptr)
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345 | {
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346 | return const_cast<T*>(ptr);
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347 | }
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348 |
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349 | template<typename Derived, typename XprKind = typename traits<Derived>::XprKind>
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350 | struct dense_xpr_base
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351 | {
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352 | /* 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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353 | };
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354 |
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355 | template<typename Derived>
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356 | struct dense_xpr_base<Derived, MatrixXpr>
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357 | {
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358 | typedef MatrixBase<Derived> type;
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359 | };
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360 |
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361 | template<typename Derived>
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362 | struct dense_xpr_base<Derived, ArrayXpr>
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363 | {
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364 | typedef ArrayBase<Derived> type;
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365 | };
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366 |
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367 | /** \internal Helper base class to add a scalar multiple operator
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368 | * overloads for complex types */
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369 | template<typename Derived, typename Scalar, typename OtherScalar, typename BaseType,
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370 | bool EnableIt = !is_same<Scalar,OtherScalar>::value >
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371 | struct special_scalar_op_base : public BaseType
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372 | {
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373 | // dummy operator* so that the
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374 | // "using special_scalar_op_base::operator*" compiles
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375 | void operator*() const;
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376 | };
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377 |
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378 | template<typename Derived,typename Scalar,typename OtherScalar, typename BaseType>
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379 | struct special_scalar_op_base<Derived,Scalar,OtherScalar,BaseType,true> : public BaseType
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380 | {
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381 | const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
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382 | operator*(const OtherScalar& scalar) const
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383 | {
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384 | return CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
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385 | (*static_cast<const Derived*>(this), scalar_multiple2_op<Scalar,OtherScalar>(scalar));
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386 | }
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387 |
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388 | inline friend const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
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389 | operator*(const OtherScalar& scalar, const Derived& matrix)
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390 | { return static_cast<const special_scalar_op_base&>(matrix).operator*(scalar); }
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391 | };
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392 |
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393 | template<typename XprType, typename CastType> struct cast_return_type
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394 | {
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395 | typedef typename XprType::Scalar CurrentScalarType;
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396 | typedef typename remove_all<CastType>::type _CastType;
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397 | typedef typename _CastType::Scalar NewScalarType;
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398 | typedef typename conditional<is_same<CurrentScalarType,NewScalarType>::value,
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399 | const XprType&,CastType>::type type;
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400 | };
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401 |
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402 | template <typename A, typename B> struct promote_storage_type;
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403 |
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404 | template <typename A> struct promote_storage_type<A,A>
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405 | {
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406 | typedef A ret;
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407 | };
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408 |
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409 | /** \internal gives the plain matrix or array type to store a row/column/diagonal of a matrix type.
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410 | * \param Scalar optional parameter allowing to pass a different scalar type than the one of the MatrixType.
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411 | */
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412 | template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
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413 | struct plain_row_type
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414 | {
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415 | typedef Matrix<Scalar, 1, ExpressionType::ColsAtCompileTime,
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416 | ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> MatrixRowType;
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417 | typedef Array<Scalar, 1, ExpressionType::ColsAtCompileTime,
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418 | ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> ArrayRowType;
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419 |
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420 | typedef typename conditional<
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421 | is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
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422 | MatrixRowType,
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423 | ArrayRowType
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424 | >::type type;
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425 | };
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426 |
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427 | template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
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428 | struct plain_col_type
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429 | {
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430 | typedef Matrix<Scalar, ExpressionType::RowsAtCompileTime, 1,
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431 | ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> MatrixColType;
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432 | typedef Array<Scalar, ExpressionType::RowsAtCompileTime, 1,
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433 | ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> ArrayColType;
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434 |
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435 | typedef typename conditional<
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436 | is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
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437 | MatrixColType,
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438 | ArrayColType
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439 | >::type type;
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440 | };
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441 |
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442 | template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
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443 | struct plain_diag_type
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444 | {
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445 | enum { diag_size = EIGEN_SIZE_MIN_PREFER_DYNAMIC(ExpressionType::RowsAtCompileTime, ExpressionType::ColsAtCompileTime),
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446 | max_diag_size = EIGEN_SIZE_MIN_PREFER_FIXED(ExpressionType::MaxRowsAtCompileTime, ExpressionType::MaxColsAtCompileTime)
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447 | };
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448 | typedef Matrix<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> MatrixDiagType;
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449 | typedef Array<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> ArrayDiagType;
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450 |
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451 | typedef typename conditional<
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452 | is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
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453 | MatrixDiagType,
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454 | ArrayDiagType
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455 | >::type type;
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456 | };
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457 |
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458 | template<typename ExpressionType>
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459 | struct is_lvalue
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460 | {
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461 | enum { value = !bool(is_const<ExpressionType>::value) &&
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462 | bool(traits<ExpressionType>::Flags & LvalueBit) };
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463 | };
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464 |
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465 | } // end namespace internal
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466 |
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467 | } // end namespace Eigen
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468 |
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469 | #endif // EIGEN_XPRHELPER_H
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