| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com> |
| // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> |
| // |
| // Eigen is free software; you can redistribute it and/or |
| // modify it under the terms of the GNU Lesser General Public |
| // License as published by the Free Software Foundation; either |
| // version 3 of the License, or (at your option) any later version. |
| // |
| // Alternatively, you can redistribute it and/or |
| // modify it under the terms of the GNU General Public License as |
| // published by the Free Software Foundation; either version 2 of |
| // the License, or (at your option) any later version. |
| // |
| // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY |
| // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
| // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the |
| // GNU General Public License for more details. |
| // |
| // You should have received a copy of the GNU Lesser General Public |
| // License and a copy of the GNU General Public License along with |
| // Eigen. If not, see <http://www.gnu.org/licenses/>. |
| |
| #ifndef EIGEN_FUZZY_H |
| #define EIGEN_FUZZY_H |
| |
| // TODO support small integer types properly i.e. do exact compare on coeffs --- taking a HS norm is guaranteed to cause integer overflow. |
| |
| #ifndef EIGEN_LEGACY_COMPARES |
| |
| /** \returns \c true if \c *this is approximately equal to \a other, within the precision |
| * determined by \a prec. |
| * |
| * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$ |
| * are considered to be approximately equal within precision \f$ p \f$ if |
| * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f] |
| * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm |
| * L2 norm). |
| * |
| * \note Because of the multiplicativeness of this comparison, one can't use this function |
| * to check whether \c *this is approximately equal to the zero matrix or vector. |
| * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix |
| * or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const |
| * RealScalar&, RealScalar) instead. |
| * |
| * \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const |
| */ |
| template<typename Derived> |
| template<typename OtherDerived> |
| bool DenseBase<Derived>::isApprox( |
| const DenseBase<OtherDerived>& other, |
| RealScalar prec |
| ) const |
| { |
| const typename ei_nested<Derived,2>::type nested(derived()); |
| const typename ei_nested<OtherDerived,2>::type otherNested(other.derived()); |
| // std::cerr << typeid(Derived).name() << " => " << typeid(typename ei_nested<Derived,2>::type).name() << "\n"; |
| // std::cerr << typeid(OtherDerived).name() << " => " << typeid(typename ei_nested<OtherDerived,2>::type).name() << "\n"; |
| // return false; |
| return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * std::min(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum()); |
| } |
| |
| /** \returns \c true if the norm of \c *this is much smaller than \a other, |
| * within the precision determined by \a prec. |
| * |
| * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is |
| * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if |
| * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f] |
| * |
| * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, |
| * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm |
| * of a reference matrix of same dimensions. |
| * |
| * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const |
| */ |
| template<typename Derived> |
| bool DenseBase<Derived>::isMuchSmallerThan( |
| const typename NumTraits<Scalar>::Real& other, |
| RealScalar prec |
| ) const |
| { |
| return derived().cwiseAbs2().sum() <= prec * prec * other * other; |
| } |
| |
| /** \returns \c true if the norm of \c *this is much smaller than the norm of \a other, |
| * within the precision determined by \a prec. |
| * |
| * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is |
| * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if |
| * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f] |
| * For matrices, the comparison is done using the Hilbert-Schmidt norm. |
| * |
| * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const |
| */ |
| template<typename Derived> |
| template<typename OtherDerived> |
| bool DenseBase<Derived>::isMuchSmallerThan( |
| const DenseBase<OtherDerived>& other, |
| RealScalar prec |
| ) const |
| { |
| return derived().cwiseAbs2().sum() <= prec * prec * other.derived().cwiseAbs2().sum(); |
| } |
| |
| #else |
| |
| template<typename Derived, typename OtherDerived=Derived, bool IsVector=Derived::IsVectorAtCompileTime> |
| struct ei_fuzzy_selector; |
| |
| /** \returns \c true if \c *this is approximately equal to \a other, within the precision |
| * determined by \a prec. |
| * |
| * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$ |
| * are considered to be approximately equal within precision \f$ p \f$ if |
| * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f] |
| * For matrices, the comparison is done on all columns. |
| * |
| * \note Because of the multiplicativeness of this comparison, one can't use this function |
| * to check whether \c *this is approximately equal to the zero matrix or vector. |
| * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix |
| * or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const |
| * RealScalar&, RealScalar) instead. |
| * |
| * \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const |
| */ |
| template<typename Derived> |
| template<typename OtherDerived> |
| bool DenseBase<Derived>::isApprox( |
| const DenseBase<OtherDerived>& other, |
| RealScalar prec |
| ) const |
| { |
| return ei_fuzzy_selector<Derived,OtherDerived>::isApprox(derived(), other.derived(), prec); |
| } |
| |
| /** \returns \c true if the norm of \c *this is much smaller than \a other, |
| * within the precision determined by \a prec. |
| * |
| * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is |
| * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if |
| * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f] |
| * For matrices, the comparison is done on all columns. |
| * |
| * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const |
| */ |
| template<typename Derived> |
| bool DenseBase<Derived>::isMuchSmallerThan( |
| const typename NumTraits<Scalar>::Real& other, |
| RealScalar prec |
| ) const |
| { |
| return ei_fuzzy_selector<Derived>::isMuchSmallerThan(derived(), other, prec); |
| } |
| |
| /** \returns \c true if the norm of \c *this is much smaller than the norm of \a other, |
| * within the precision determined by \a prec. |
| * |
| * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is |
| * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if |
| * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f] |
| * For matrices, the comparison is done on all columns. |
| * |
| * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const |
| */ |
| template<typename Derived> |
| template<typename OtherDerived> |
| bool DenseBase<Derived>::isMuchSmallerThan( |
| const DenseBase<OtherDerived>& other, |
| RealScalar prec |
| ) const |
| { |
| return ei_fuzzy_selector<Derived,OtherDerived>::isMuchSmallerThan(derived(), other.derived(), prec); |
| } |
| |
| |
| template<typename Derived, typename OtherDerived> |
| struct ei_fuzzy_selector<Derived,OtherDerived,true> |
| { |
| typedef typename Derived::RealScalar RealScalar; |
| static bool isApprox(const Derived& self, const OtherDerived& other, RealScalar prec) |
| { |
| EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived) |
| ei_assert(self.size() == other.size()); |
| return((self - other).squaredNorm() <= std::min(self.squaredNorm(), other.squaredNorm()) * prec * prec); |
| } |
| static bool isMuchSmallerThan(const Derived& self, const RealScalar& other, RealScalar prec) |
| { |
| return(self.squaredNorm() <= ei_abs2(other * prec)); |
| } |
| static bool isMuchSmallerThan(const Derived& self, const OtherDerived& other, RealScalar prec) |
| { |
| EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived) |
| ei_assert(self.size() == other.size()); |
| return(self.squaredNorm() <= other.squaredNorm() * prec * prec); |
| } |
| }; |
| |
| template<typename Derived, typename OtherDerived> |
| struct ei_fuzzy_selector<Derived,OtherDerived,false> |
| { |
| typedef typename Derived::RealScalar RealScalar; |
| static bool isApprox(const Derived& self, const OtherDerived& other, RealScalar prec) |
| { |
| EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived) |
| ei_assert(self.rows() == other.rows() && self.cols() == other.cols()); |
| typename Derived::Nested nested(self); |
| typename OtherDerived::Nested otherNested(other); |
| for(int i = 0; i < self.cols(); ++i) |
| if((nested.col(i) - otherNested.col(i)).squaredNorm() |
| > std::min(nested.col(i).squaredNorm(), otherNested.col(i).squaredNorm()) * prec * prec) |
| return false; |
| return true; |
| } |
| static bool isMuchSmallerThan(const Derived& self, const RealScalar& other, RealScalar prec) |
| { |
| typename Derived::Nested nested(self); |
| for(int i = 0; i < self.cols(); ++i) |
| if(nested.col(i).squaredNorm() > ei_abs2(other * prec)) |
| return false; |
| return true; |
| } |
| static bool isMuchSmallerThan(const Derived& self, const OtherDerived& other, RealScalar prec) |
| { |
| EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived) |
| ei_assert(self.rows() == other.rows() && self.cols() == other.cols()); |
| typename Derived::Nested nested(self); |
| typename OtherDerived::Nested otherNested(other); |
| for(int i = 0; i < self.cols(); ++i) |
| if(nested.col(i).squaredNorm() > otherNested.col(i).squaredNorm() * prec * prec) |
| return false; |
| return true; |
| } |
| }; |
| |
| #endif |
| |
| #endif // EIGEN_FUZZY_H |