Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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@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 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 115 | return numext::real((*this).cwiseAbs2().sum()); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 127 | using std::sqrt; |
| 128 | return sqrt(squaredNorm()); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 129 | } |
| 130 | |
| 131 | /** \returns an expression of the quotient of *this by its own norm. |
| 132 | * |
| 133 | * \only_for_vectors |
| 134 | * |
| 135 | * \sa norm(), normalize() |
| 136 | */ |
| 137 | template<typename Derived> |
| 138 | inline const typename MatrixBase<Derived>::PlainObject |
| 139 | MatrixBase<Derived>::normalized() const |
| 140 | { |
| 141 | typedef typename internal::nested<Derived>::type Nested; |
| 142 | typedef typename internal::remove_reference<Nested>::type _Nested; |
| 143 | _Nested n(derived()); |
| 144 | return n / n.norm(); |
| 145 | } |
| 146 | |
| 147 | /** Normalizes the vector, i.e. divides it by its own norm. |
| 148 | * |
| 149 | * \only_for_vectors |
| 150 | * |
| 151 | * \sa norm(), normalized() |
| 152 | */ |
| 153 | template<typename Derived> |
| 154 | inline void MatrixBase<Derived>::normalize() |
| 155 | { |
| 156 | *this /= norm(); |
| 157 | } |
| 158 | |
| 159 | //---------- implementation of other norms ---------- |
| 160 | |
| 161 | namespace internal { |
| 162 | |
| 163 | template<typename Derived, int p> |
| 164 | struct lpNorm_selector |
| 165 | { |
| 166 | typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar; |
| 167 | static inline RealScalar run(const MatrixBase<Derived>& m) |
| 168 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 169 | using std::pow; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 170 | return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p); |
| 171 | } |
| 172 | }; |
| 173 | |
| 174 | template<typename Derived> |
| 175 | struct lpNorm_selector<Derived, 1> |
| 176 | { |
| 177 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) |
| 178 | { |
| 179 | return m.cwiseAbs().sum(); |
| 180 | } |
| 181 | }; |
| 182 | |
| 183 | template<typename Derived> |
| 184 | struct lpNorm_selector<Derived, 2> |
| 185 | { |
| 186 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) |
| 187 | { |
| 188 | return m.norm(); |
| 189 | } |
| 190 | }; |
| 191 | |
| 192 | template<typename Derived> |
| 193 | struct lpNorm_selector<Derived, Infinity> |
| 194 | { |
| 195 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) |
| 196 | { |
| 197 | return m.cwiseAbs().maxCoeff(); |
| 198 | } |
| 199 | }; |
| 200 | |
| 201 | } // end namespace internal |
| 202 | |
| 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 |
| 204 | * of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$ |
| 205 | * norm, that is the maximum of the absolute values of the coefficients of *this. |
| 206 | * |
| 207 | * \sa norm() |
| 208 | */ |
| 209 | template<typename Derived> |
| 210 | template<int p> |
| 211 | inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real |
| 212 | MatrixBase<Derived>::lpNorm() const |
| 213 | { |
| 214 | return internal::lpNorm_selector<Derived, p>::run(*this); |
| 215 | } |
| 216 | |
| 217 | //---------- implementation of isOrthogonal / isUnitary ---------- |
| 218 | |
| 219 | /** \returns true if *this is approximately orthogonal to \a other, |
| 220 | * within the precision given by \a prec. |
| 221 | * |
| 222 | * Example: \include MatrixBase_isOrthogonal.cpp |
| 223 | * Output: \verbinclude MatrixBase_isOrthogonal.out |
| 224 | */ |
| 225 | template<typename Derived> |
| 226 | template<typename OtherDerived> |
| 227 | bool MatrixBase<Derived>::isOrthogonal |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 228 | (const MatrixBase<OtherDerived>& other, const RealScalar& prec) const |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 229 | { |
| 230 | typename internal::nested<Derived,2>::type nested(derived()); |
| 231 | typename internal::nested<OtherDerived,2>::type otherNested(other.derived()); |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 232 | return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm(); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 233 | } |
| 234 | |
| 235 | /** \returns true if *this is approximately an unitary matrix, |
| 236 | * within the precision given by \a prec. In the case where the \a Scalar |
| 237 | * type is real numbers, a unitary matrix is an orthogonal matrix, whence the name. |
| 238 | * |
| 239 | * \note This can be used to check whether a family of vectors forms an orthonormal basis. |
| 240 | * Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an |
| 241 | * orthonormal basis. |
| 242 | * |
| 243 | * Example: \include MatrixBase_isUnitary.cpp |
| 244 | * Output: \verbinclude MatrixBase_isUnitary.out |
| 245 | */ |
| 246 | template<typename Derived> |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 247 | bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 248 | { |
| 249 | typename Derived::Nested nested(derived()); |
| 250 | for(Index i = 0; i < cols(); ++i) |
| 251 | { |
| 252 | if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec)) |
| 253 | return false; |
| 254 | for(Index j = 0; j < i; ++j) |
| 255 | if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec)) |
| 256 | return false; |
| 257 | } |
| 258 | return true; |
| 259 | } |
| 260 | |
| 261 | } // end namespace Eigen |
| 262 | |
| 263 | #endif // EIGEN_DOT_H |