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 <g.gael@free.fr>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
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11 |
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12 | namespace Eigen {
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13 |
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14 | /** \geometry_module \ingroup Geometry_Module
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15 | *
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16 | * \class Translation
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17 | *
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18 | * \brief Represents a translation transformation
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19 | *
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20 | * \param _Scalar the scalar type, i.e., the type of the coefficients.
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21 | * \param _Dim the dimension of the space, can be a compile time value or Dynamic
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22 | *
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23 | * \note This class is not aimed to be used to store a translation transformation,
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24 | * but rather to make easier the constructions and updates of Transform objects.
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25 | *
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26 | * \sa class Scaling, class Transform
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27 | */
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28 | template<typename _Scalar, int _Dim>
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29 | class Translation
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30 | {
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31 | public:
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32 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
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33 | /** dimension of the space */
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34 | enum { Dim = _Dim };
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35 | /** the scalar type of the coefficients */
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36 | typedef _Scalar Scalar;
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37 | /** corresponding vector type */
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38 | typedef Matrix<Scalar,Dim,1> VectorType;
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39 | /** corresponding linear transformation matrix type */
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40 | typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
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41 | /** corresponding scaling transformation type */
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42 | typedef Scaling<Scalar,Dim> ScalingType;
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43 | /** corresponding affine transformation type */
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44 | typedef Transform<Scalar,Dim> TransformType;
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45 |
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46 | protected:
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47 |
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48 | VectorType m_coeffs;
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49 |
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50 | public:
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51 |
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52 | /** Default constructor without initialization. */
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53 | Translation() {}
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54 | /** */
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55 | inline Translation(const Scalar& sx, const Scalar& sy)
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56 | {
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57 | ei_assert(Dim==2);
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58 | m_coeffs.x() = sx;
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59 | m_coeffs.y() = sy;
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60 | }
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61 | /** */
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62 | inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
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63 | {
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64 | ei_assert(Dim==3);
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65 | m_coeffs.x() = sx;
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66 | m_coeffs.y() = sy;
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67 | m_coeffs.z() = sz;
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68 | }
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69 | /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */
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70 | explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
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71 |
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72 | const VectorType& vector() const { return m_coeffs; }
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73 | VectorType& vector() { return m_coeffs; }
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74 |
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75 | /** Concatenates two translation */
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76 | inline Translation operator* (const Translation& other) const
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77 | { return Translation(m_coeffs + other.m_coeffs); }
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78 |
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79 | /** Concatenates a translation and a scaling */
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80 | inline TransformType operator* (const ScalingType& other) const;
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81 |
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82 | /** Concatenates a translation and a linear transformation */
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83 | inline TransformType operator* (const LinearMatrixType& linear) const;
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84 |
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85 | template<typename Derived>
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86 | inline TransformType operator*(const RotationBase<Derived,Dim>& r) const
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87 | { return *this * r.toRotationMatrix(); }
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88 |
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89 | /** Concatenates a linear transformation and a translation */
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90 | // its a nightmare to define a templated friend function outside its declaration
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91 | friend inline TransformType operator* (const LinearMatrixType& linear, const Translation& t)
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92 | {
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93 | TransformType res;
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94 | res.matrix().setZero();
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95 | res.linear() = linear;
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96 | res.translation() = linear * t.m_coeffs;
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97 | res.matrix().row(Dim).setZero();
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98 | res(Dim,Dim) = Scalar(1);
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99 | return res;
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100 | }
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101 |
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102 | /** Concatenates a translation and an affine transformation */
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103 | inline TransformType operator* (const TransformType& t) const;
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104 |
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105 | /** Applies translation to vector */
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106 | inline VectorType operator* (const VectorType& other) const
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107 | { return m_coeffs + other; }
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108 |
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109 | /** \returns the inverse translation (opposite) */
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110 | Translation inverse() const { return Translation(-m_coeffs); }
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111 |
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112 | Translation& operator=(const Translation& other)
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113 | {
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114 | m_coeffs = other.m_coeffs;
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115 | return *this;
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116 | }
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117 |
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118 | /** \returns \c *this with scalar type casted to \a NewScalarType
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119 | *
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120 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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121 | * then this function smartly returns a const reference to \c *this.
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122 | */
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123 | template<typename NewScalarType>
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124 | inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const
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125 | { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
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126 |
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127 | /** Copy constructor with scalar type conversion */
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128 | template<typename OtherScalarType>
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129 | inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
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130 | { m_coeffs = other.vector().template cast<Scalar>(); }
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131 |
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132 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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133 | * determined by \a prec.
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134 | *
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135 | * \sa MatrixBase::isApprox() */
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136 | bool isApprox(const Translation& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
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137 | { return m_coeffs.isApprox(other.m_coeffs, prec); }
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138 |
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139 | };
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140 |
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141 | /** \addtogroup Geometry_Module */
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142 | //@{
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143 | typedef Translation<float, 2> Translation2f;
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144 | typedef Translation<double,2> Translation2d;
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145 | typedef Translation<float, 3> Translation3f;
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146 | typedef Translation<double,3> Translation3d;
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147 | //@}
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148 |
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149 |
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150 | template<typename Scalar, int Dim>
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151 | inline typename Translation<Scalar,Dim>::TransformType
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152 | Translation<Scalar,Dim>::operator* (const ScalingType& other) const
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153 | {
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154 | TransformType res;
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155 | res.matrix().setZero();
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156 | res.linear().diagonal() = other.coeffs();
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157 | res.translation() = m_coeffs;
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158 | res(Dim,Dim) = Scalar(1);
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159 | return res;
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160 | }
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161 |
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162 | template<typename Scalar, int Dim>
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163 | inline typename Translation<Scalar,Dim>::TransformType
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164 | Translation<Scalar,Dim>::operator* (const LinearMatrixType& linear) const
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165 | {
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166 | TransformType res;
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167 | res.matrix().setZero();
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168 | res.linear() = linear;
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169 | res.translation() = m_coeffs;
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170 | res.matrix().row(Dim).setZero();
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171 | res(Dim,Dim) = Scalar(1);
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172 | return res;
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173 | }
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174 |
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175 | template<typename Scalar, int Dim>
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176 | inline typename Translation<Scalar,Dim>::TransformType
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177 | Translation<Scalar,Dim>::operator* (const TransformType& t) const
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178 | {
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179 | TransformType res = t;
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180 | res.pretranslate(m_coeffs);
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181 | return res;
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182 | }
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183 |
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184 | } // end namespace Eigen
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