| // 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 <gael.guennebaud@inria.fr> |
| // |
| // 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_FUZZY_H |
| #define EIGEN_FUZZY_H |
| |
| namespace Eigen { |
| |
| namespace internal |
| { |
| |
| template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> |
| struct isApprox_selector |
| { |
| static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) |
| { |
| using std::min; |
| typename internal::nested<Derived,2>::type nested(x); |
| typename internal::nested<OtherDerived,2>::type otherNested(y); |
| return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * (min)(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum()); |
| } |
| }; |
| |
| template<typename Derived, typename OtherDerived> |
| struct isApprox_selector<Derived, OtherDerived, true> |
| { |
| static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&) |
| { |
| return x.matrix() == y.matrix(); |
| } |
| }; |
| |
| template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> |
| struct isMuchSmallerThan_object_selector |
| { |
| static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) |
| { |
| return x.cwiseAbs2().sum() <= abs2(prec) * y.cwiseAbs2().sum(); |
| } |
| }; |
| |
| template<typename Derived, typename OtherDerived> |
| struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true> |
| { |
| static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&) |
| { |
| return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); |
| } |
| }; |
| |
| template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> |
| struct isMuchSmallerThan_scalar_selector |
| { |
| static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec) |
| { |
| return x.cwiseAbs2().sum() <= abs2(prec * y); |
| } |
| }; |
| |
| template<typename Derived> |
| struct isMuchSmallerThan_scalar_selector<Derived, true> |
| { |
| static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&) |
| { |
| return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); |
| } |
| }; |
| |
| } // end namespace internal |
| |
| |
| /** \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 internal::isMuchSmallerThan(const |
| * RealScalar&, RealScalar) instead. |
| * |
| * \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const |
| */ |
| template<typename Derived> |
| template<typename OtherDerived> |
| bool DenseBase<Derived>::isApprox( |
| const DenseBase<OtherDerived>& other, |
| const RealScalar& prec |
| ) const |
| { |
| return internal::isApprox_selector<Derived, OtherDerived>::run(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 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, |
| const RealScalar& prec |
| ) const |
| { |
| return internal::isMuchSmallerThan_scalar_selector<Derived>::run(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 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, |
| const RealScalar& prec |
| ) const |
| { |
| return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec); |
| } |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_FUZZY_H |