1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #ifndef EIGEN_DOT_H 11 #define EIGEN_DOT_H 12 13 namespace Eigen { 14 15 namespace internal { 16 17 // helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot 18 // with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE 19 // looking at the static assertions. Thus this is a trick to get better compile errors. 20 template<typename T, typename U, 21 // the NeedToTranspose condition here is taken straight from Assign.h 22 bool NeedToTranspose = T::IsVectorAtCompileTime 23 && U::IsVectorAtCompileTime 24 && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1) 25 | // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&". 26 // revert to || as soon as not needed anymore. 27 (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1)) 28 > 29 struct dot_nocheck 30 { 31 typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar; 32 static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b) 33 { 34 return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum(); 35 } 36 }; 37 38 template<typename T, typename U> 39 struct dot_nocheck<T, U, true> 40 { 41 typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar; 42 static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b) 43 { 44 return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum(); 45 } 46 }; 47 48 } // end namespace internal 49 50 /** \returns the dot product of *this with other. 51 * 52 * \only_for_vectors 53 * 54 * \note If the scalar type is complex numbers, then this function returns the hermitian 55 * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the 56 * second variable. 57 * 58 * \sa squaredNorm(), norm() 59 */ 60 template<typename Derived> 61 template<typename OtherDerived> 62 typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType 63 MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const 64 { 65 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 66 EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived) 67 EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived) 68 typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func; 69 EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar); 70 71 eigen_assert(size() == other.size()); 72 73 return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other); 74 } 75 76 #ifdef EIGEN2_SUPPORT 77 /** \returns the dot product of *this with other, with the Eigen2 convention that the dot product is linear in the first variable 78 * (conjugating the second variable). Of course this only makes a difference in the complex case. 79 * 80 * This method is only available in EIGEN2_SUPPORT mode. 81 * 82 * \only_for_vectors 83 * 84 * \sa dot() 85 */ 86 template<typename Derived> 87 template<typename OtherDerived> 88 typename internal::traits<Derived>::Scalar 89 MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const 90 { 91 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 92 EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived) 93 EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived) 94 EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value), 95 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) 96 97 eigen_assert(size() == other.size()); 98 99 return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this); 100 } 101 #endif 102 103 104 //---------- implementation of L2 norm and related functions ---------- 105 106 /** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the Frobenius norm. 107 * In both cases, it consists in the sum of the square of all the matrix entries. 108 * For vectors, this is also equals to the dot product of \c *this with itself. 109 * 110 * \sa dot(), norm() 111 */ 112 template<typename Derived> 113 EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const 114 { 115 return internal::real((*this).cwiseAbs2().sum()); 116 } 117 118 /** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm. 119 * In both cases, it consists in the square root of the sum of the square of all the matrix entries. 120 * For vectors, this is also equals to the square root of the dot product of \c *this with itself. 121 * 122 * \sa dot(), squaredNorm() 123 */ 124 template<typename Derived> 125 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const 126 { 127 return internal::sqrt(squaredNorm()); 128 } 129 130 /** \returns an expression of the quotient of *this by its own norm. 131 * 132 * \only_for_vectors 133 * 134 * \sa norm(), normalize() 135 */ 136 template<typename Derived> 137 inline const typename MatrixBase<Derived>::PlainObject 138 MatrixBase<Derived>::normalized() const 139 { 140 typedef typename internal::nested<Derived>::type Nested; 141 typedef typename internal::remove_reference<Nested>::type _Nested; 142 _Nested n(derived()); 143 return n / n.norm(); 144 } 145 146 /** Normalizes the vector, i.e. divides it by its own norm. 147 * 148 * \only_for_vectors 149 * 150 * \sa norm(), normalized() 151 */ 152 template<typename Derived> 153 inline void MatrixBase<Derived>::normalize() 154 { 155 *this /= norm(); 156 } 157 158 //---------- implementation of other norms ---------- 159 160 namespace internal { 161 162 template<typename Derived, int p> 163 struct lpNorm_selector 164 { 165 typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar; 166 static inline RealScalar run(const MatrixBase<Derived>& m) 167 { 168 return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p); 169 } 170 }; 171 172 template<typename Derived> 173 struct lpNorm_selector<Derived, 1> 174 { 175 static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) 176 { 177 return m.cwiseAbs().sum(); 178 } 179 }; 180 181 template<typename Derived> 182 struct lpNorm_selector<Derived, 2> 183 { 184 static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) 185 { 186 return m.norm(); 187 } 188 }; 189 190 template<typename Derived> 191 struct lpNorm_selector<Derived, Infinity> 192 { 193 static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) 194 { 195 return m.cwiseAbs().maxCoeff(); 196 } 197 }; 198 199 } // end namespace internal 200 201 /** \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 202 * of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$ 203 * norm, that is the maximum of the absolute values of the coefficients of *this. 204 * 205 * \sa norm() 206 */ 207 template<typename Derived> 208 template<int p> 209 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real 210 MatrixBase<Derived>::lpNorm() const 211 { 212 return internal::lpNorm_selector<Derived, p>::run(*this); 213 } 214 215 //---------- implementation of isOrthogonal / isUnitary ---------- 216 217 /** \returns true if *this is approximately orthogonal to \a other, 218 * within the precision given by \a prec. 219 * 220 * Example: \include MatrixBase_isOrthogonal.cpp 221 * Output: \verbinclude MatrixBase_isOrthogonal.out 222 */ 223 template<typename Derived> 224 template<typename OtherDerived> 225 bool MatrixBase<Derived>::isOrthogonal 226 (const MatrixBase<OtherDerived>& other, RealScalar prec) const 227 { 228 typename internal::nested<Derived,2>::type nested(derived()); 229 typename internal::nested<OtherDerived,2>::type otherNested(other.derived()); 230 return internal::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm(); 231 } 232 233 /** \returns true if *this is approximately an unitary matrix, 234 * within the precision given by \a prec. In the case where the \a Scalar 235 * type is real numbers, a unitary matrix is an orthogonal matrix, whence the name. 236 * 237 * \note This can be used to check whether a family of vectors forms an orthonormal basis. 238 * Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an 239 * orthonormal basis. 240 * 241 * Example: \include MatrixBase_isUnitary.cpp 242 * Output: \verbinclude MatrixBase_isUnitary.out 243 */ 244 template<typename Derived> 245 bool MatrixBase<Derived>::isUnitary(RealScalar prec) const 246 { 247 typename Derived::Nested nested(derived()); 248 for(Index i = 0; i < cols(); ++i) 249 { 250 if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec)) 251 return false; 252 for(Index j = 0; j < i; ++j) 253 if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec)) 254 return false; 255 } 256 return true; 257 } 258 259 } // end namespace Eigen 260 261 #endif // EIGEN_DOT_H 262
