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) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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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 | #ifndef EIGEN_DOT_H
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11 | #define EIGEN_DOT_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | namespace internal {
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16 |
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17 | // helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
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18 | // with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
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19 | // looking at the static assertions. Thus this is a trick to get better compile errors.
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20 | template<typename T, typename U,
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21 | // the NeedToTranspose condition here is taken straight from Assign.h
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22 | bool NeedToTranspose = T::IsVectorAtCompileTime
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23 | && U::IsVectorAtCompileTime
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24 | && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)
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25 | | // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
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26 | // revert to || as soon as not needed anymore.
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27 | (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))
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28 | >
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29 | struct dot_nocheck
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30 | {
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31 | typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
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32 | static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
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33 | {
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34 | return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
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35 | }
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36 | };
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37 |
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38 | template<typename T, typename U>
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39 | struct dot_nocheck<T, U, true>
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40 | {
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41 | typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
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42 | static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
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43 | {
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44 | return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
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45 | }
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46 | };
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47 |
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48 | } // end namespace internal
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49 |
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50 | /** \returns the dot product of *this with other.
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51 | *
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52 | * \only_for_vectors
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53 | *
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54 | * \note If the scalar type is complex numbers, then this function returns the hermitian
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55 | * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the
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56 | * second variable.
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57 | *
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58 | * \sa squaredNorm(), norm()
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59 | */
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60 | template<typename Derived>
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61 | template<typename OtherDerived>
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62 | inline typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
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63 | MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
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64 | {
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65 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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66 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
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67 | EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
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68 | typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
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69 | EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
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70 |
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71 | eigen_assert(size() == other.size());
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72 |
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73 | return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
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74 | }
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75 |
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76 | #ifdef EIGEN2_SUPPORT
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77 | /** \returns the dot product of *this with other, with the Eigen2 convention that the dot product is linear in the first variable
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78 | * (conjugating the second variable). Of course this only makes a difference in the complex case.
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79 | *
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80 | * This method is only available in EIGEN2_SUPPORT mode.
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81 | *
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82 | * \only_for_vectors
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83 | *
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84 | * \sa dot()
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85 | */
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86 | template<typename Derived>
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87 | template<typename OtherDerived>
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88 | typename internal::traits<Derived>::Scalar
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89 | MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const
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90 | {
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91 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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92 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
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93 | EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
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94 | EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
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95 | YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
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96 |
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97 | eigen_assert(size() == other.size());
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98 |
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99 | return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this);
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100 | }
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101 | #endif
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102 |
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103 |
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104 | //---------- implementation of L2 norm and related functions ----------
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105 |
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106 | /** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the Frobenius norm.
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107 | * In both cases, it consists in the sum of the square of all the matrix entries.
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108 | * For vectors, this is also equals to the dot product of \c *this with itself.
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109 | *
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110 | * \sa dot(), norm()
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111 | */
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112 | template<typename Derived>
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113 | EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
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114 | {
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115 | return numext::real((*this).cwiseAbs2().sum());
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116 | }
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117 |
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118 | /** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
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119 | * In both cases, it consists in the square root of the sum of the square of all the matrix entries.
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120 | * For vectors, this is also equals to the square root of the dot product of \c *this with itself.
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121 | *
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122 | * \sa dot(), squaredNorm()
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123 | */
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124 | template<typename Derived>
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125 | inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
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126 | {
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127 | using std::sqrt;
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128 | return sqrt(squaredNorm());
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129 | }
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130 |
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131 | /** \returns an expression of the quotient of *this by its own norm.
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132 | *
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133 | * \only_for_vectors
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134 | *
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135 | * \sa norm(), normalize()
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136 | */
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137 | template<typename Derived>
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138 | inline const typename MatrixBase<Derived>::PlainObject
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139 | MatrixBase<Derived>::normalized() const
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140 | {
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141 | typedef typename internal::nested<Derived>::type Nested;
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142 | typedef typename internal::remove_reference<Nested>::type _Nested;
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143 | _Nested n(derived());
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144 | return n / n.norm();
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145 | }
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146 |
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147 | /** Normalizes the vector, i.e. divides it by its own norm.
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148 | *
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149 | * \only_for_vectors
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150 | *
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151 | * \sa norm(), normalized()
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152 | */
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153 | template<typename Derived>
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154 | inline void MatrixBase<Derived>::normalize()
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155 | {
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156 | *this /= norm();
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157 | }
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158 |
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159 | //---------- implementation of other norms ----------
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160 |
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161 | namespace internal {
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162 |
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163 | template<typename Derived, int p>
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164 | struct lpNorm_selector
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165 | {
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166 | typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
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167 | static inline RealScalar run(const MatrixBase<Derived>& m)
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168 | {
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169 | using std::pow;
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170 | return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
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171 | }
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172 | };
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173 |
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174 | template<typename Derived>
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175 | struct lpNorm_selector<Derived, 1>
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176 | {
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177 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
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178 | {
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179 | return m.cwiseAbs().sum();
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180 | }
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181 | };
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182 |
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183 | template<typename Derived>
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184 | struct lpNorm_selector<Derived, 2>
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185 | {
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186 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
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187 | {
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188 | return m.norm();
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189 | }
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190 | };
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191 |
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192 | template<typename Derived>
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193 | struct lpNorm_selector<Derived, Infinity>
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194 | {
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195 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
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196 | {
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197 | return m.cwiseAbs().maxCoeff();
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198 | }
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199 | };
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200 |
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201 | } // end namespace internal
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202 |
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203 | /** \returns the \f$ \ell^p \f$ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
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204 | * of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
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205 | * norm, that is the maximum of the absolute values of the coefficients of *this.
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206 | *
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207 | * \sa norm()
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208 | */
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209 | template<typename Derived>
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210 | template<int p>
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211 | inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
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212 | MatrixBase<Derived>::lpNorm() const
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213 | {
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214 | return internal::lpNorm_selector<Derived, p>::run(*this);
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215 | }
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216 |
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217 | //---------- implementation of isOrthogonal / isUnitary ----------
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218 |
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219 | /** \returns true if *this is approximately orthogonal to \a other,
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220 | * within the precision given by \a prec.
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221 | *
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222 | * Example: \include MatrixBase_isOrthogonal.cpp
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223 | * Output: \verbinclude MatrixBase_isOrthogonal.out
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224 | */
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225 | template<typename Derived>
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226 | template<typename OtherDerived>
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227 | bool MatrixBase<Derived>::isOrthogonal
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228 | (const MatrixBase<OtherDerived>& other, const RealScalar& prec) const
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229 | {
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230 | typename internal::nested<Derived,2>::type nested(derived());
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231 | typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
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232 | return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
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233 | }
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234 |
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235 | /** \returns true if *this is approximately an unitary matrix,
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236 | * within the precision given by \a prec. In the case where the \a Scalar
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237 | * type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
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238 | *
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239 | * \note This can be used to check whether a family of vectors forms an orthonormal basis.
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240 | * Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an
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241 | * orthonormal basis.
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242 | *
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243 | * Example: \include MatrixBase_isUnitary.cpp
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244 | * Output: \verbinclude MatrixBase_isUnitary.out
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245 | */
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246 | template<typename Derived>
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247 | bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const
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248 | {
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249 | typename Derived::Nested nested(derived());
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250 | for(Index i = 0; i < cols(); ++i)
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251 | {
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252 | if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
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253 | return false;
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254 | for(Index j = 0; j < i; ++j)
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255 | if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
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256 | return false;
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257 | }
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258 | return true;
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259 | }
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260 |
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261 | } // end namespace Eigen
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262 |
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263 | #endif // EIGEN_DOT_H
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