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Diffstat (limited to 'Eigen/src/Core/Dot.h')
| -rw-r--r-- | Eigen/src/Core/Dot.h | 261 |
1 files changed, 261 insertions, 0 deletions
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h new file mode 100644 index 000000000..ae9274e36 --- /dev/null +++ b/Eigen/src/Core/Dot.h @@ -0,0 +1,261 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DOT_H +#define EIGEN_DOT_H + +namespace Eigen { + +namespace internal { + +// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot +// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE +// looking at the static assertions. Thus this is a trick to get better compile errors. +template<typename T, typename U, +// the NeedToTranspose condition here is taken straight from Assign.h + bool NeedToTranspose = T::IsVectorAtCompileTime + && U::IsVectorAtCompileTime + && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1) + | // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&". + // revert to || as soon as not needed anymore. + (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1)) +> +struct dot_nocheck +{ + typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar; + static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b) + { + return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum(); + } +}; + +template<typename T, typename U> +struct dot_nocheck<T, U, true> +{ + typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar; + static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b) + { + return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum(); + } +}; + +} // end namespace internal + +/** \returns the dot product of *this with other. + * + * \only_for_vectors + * + * \note If the scalar type is complex numbers, then this function returns the hermitian + * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the + * second variable. + * + * \sa squaredNorm(), norm() + */ +template<typename Derived> +template<typename OtherDerived> +typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType +MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived) + EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived) + typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func; + EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar); + + eigen_assert(size() == other.size()); + + return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other); +} + +#ifdef EIGEN2_SUPPORT +/** \returns the dot product of *this with other, with the Eigen2 convention that the dot product is linear in the first variable + * (conjugating the second variable). Of course this only makes a difference in the complex case. + * + * This method is only available in EIGEN2_SUPPORT mode. + * + * \only_for_vectors + * + * \sa dot() + */ +template<typename Derived> +template<typename OtherDerived> +typename internal::traits<Derived>::Scalar +MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived) + EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived) + EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value), + YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) + + eigen_assert(size() == other.size()); + + return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this); +} +#endif + + +//---------- implementation of L2 norm and related functions ---------- + +/** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the Frobenius norm. + * In both cases, it consists in the sum of the square of all the matrix entries. + * For vectors, this is also equals to the dot product of \c *this with itself. + * + * \sa dot(), norm() + */ +template<typename Derived> +EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const +{ + return internal::real((*this).cwiseAbs2().sum()); +} + +/** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm. + * In both cases, it consists in the square root of the sum of the square of all the matrix entries. + * For vectors, this is also equals to the square root of the dot product of \c *this with itself. + * + * \sa dot(), squaredNorm() + */ +template<typename Derived> +inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const +{ + return internal::sqrt(squaredNorm()); +} + +/** \returns an expression of the quotient of *this by its own norm. + * + * \only_for_vectors + * + * \sa norm(), normalize() + */ +template<typename Derived> +inline const typename MatrixBase<Derived>::PlainObject +MatrixBase<Derived>::normalized() const +{ + typedef typename internal::nested<Derived>::type Nested; + typedef typename internal::remove_reference<Nested>::type _Nested; + _Nested n(derived()); + return n / n.norm(); +} + +/** Normalizes the vector, i.e. divides it by its own norm. + * + * \only_for_vectors + * + * \sa norm(), normalized() + */ +template<typename Derived> +inline void MatrixBase<Derived>::normalize() +{ + *this /= norm(); +} + +//---------- implementation of other norms ---------- + +namespace internal { + +template<typename Derived, int p> +struct lpNorm_selector +{ + typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar; + static inline RealScalar run(const MatrixBase<Derived>& m) + { + return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p); + } +}; + +template<typename Derived> +struct lpNorm_selector<Derived, 1> +{ + static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) + { + return m.cwiseAbs().sum(); + } +}; + +template<typename Derived> +struct lpNorm_selector<Derived, 2> +{ + static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) + { + return m.norm(); + } +}; + +template<typename Derived> +struct lpNorm_selector<Derived, Infinity> +{ + static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m) + { + return m.cwiseAbs().maxCoeff(); + } +}; + +} // end namespace internal + +/** \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 + * of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$ + * norm, that is the maximum of the absolute values of the coefficients of *this. + * + * \sa norm() + */ +template<typename Derived> +template<int p> +inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real +MatrixBase<Derived>::lpNorm() const +{ + return internal::lpNorm_selector<Derived, p>::run(*this); +} + +//---------- implementation of isOrthogonal / isUnitary ---------- + +/** \returns true if *this is approximately orthogonal to \a other, + * within the precision given by \a prec. + * + * Example: \include MatrixBase_isOrthogonal.cpp + * Output: \verbinclude MatrixBase_isOrthogonal.out + */ +template<typename Derived> +template<typename OtherDerived> +bool MatrixBase<Derived>::isOrthogonal +(const MatrixBase<OtherDerived>& other, RealScalar prec) const +{ + typename internal::nested<Derived,2>::type nested(derived()); + typename internal::nested<OtherDerived,2>::type otherNested(other.derived()); + return internal::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm(); +} + +/** \returns true if *this is approximately an unitary matrix, + * within the precision given by \a prec. In the case where the \a Scalar + * type is real numbers, a unitary matrix is an orthogonal matrix, whence the name. + * + * \note This can be used to check whether a family of vectors forms an orthonormal basis. + * Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an + * orthonormal basis. + * + * Example: \include MatrixBase_isUnitary.cpp + * Output: \verbinclude MatrixBase_isUnitary.out + */ +template<typename Derived> +bool MatrixBase<Derived>::isUnitary(RealScalar prec) const +{ + typename Derived::Nested nested(derived()); + for(Index i = 0; i < cols(); ++i) + { + if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec)) + return false; + for(Index j = 0; j < i; ++j) + if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec)) + return false; + } + return true; +} + +} // end namespace Eigen + +#endif // EIGEN_DOT_H |