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Diffstat (limited to 'extern/Eigen2/Eigen/src/Core/Fuzzy.h')
| -rw-r--r-- | extern/Eigen2/Eigen/src/Core/Fuzzy.h | 234 |
1 files changed, 234 insertions, 0 deletions
diff --git a/extern/Eigen2/Eigen/src/Core/Fuzzy.h b/extern/Eigen2/Eigen/src/Core/Fuzzy.h new file mode 100644 index 00000000000..1285542966c --- /dev/null +++ b/extern/Eigen2/Eigen/src/Core/Fuzzy.h @@ -0,0 +1,234 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. Eigen itself is part of the KDE project. +// +// 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 + +#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 MatrixBase<Derived>::isApprox( + const MatrixBase<OtherDerived>& other, + typename NumTraits<Scalar>::Real prec +) const +{ + const typename ei_nested<Derived,2>::type nested(derived()); + const typename ei_nested<OtherDerived,2>::type otherNested(other.derived()); + return (nested - otherNested).cwise().abs2().sum() <= prec * prec * std::min(nested.cwise().abs2().sum(), otherNested.cwise().abs2().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 MatrixBase<OtherDerived>&, RealScalar) const + */ +template<typename Derived> +bool MatrixBase<Derived>::isMuchSmallerThan( + const typename NumTraits<Scalar>::Real& other, + typename NumTraits<Scalar>::Real prec +) const +{ + return cwise().abs2().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 MatrixBase<Derived>::isMuchSmallerThan( + const MatrixBase<OtherDerived>& other, + typename NumTraits<Scalar>::Real prec +) const +{ + return this->cwise().abs2().sum() <= prec * prec * other.cwise().abs2().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 MatrixBase<Derived>::isApprox( + const MatrixBase<OtherDerived>& other, + typename NumTraits<Scalar>::Real 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 MatrixBase<OtherDerived>&, RealScalar) const + */ +template<typename Derived> +bool MatrixBase<Derived>::isMuchSmallerThan( + const typename NumTraits<Scalar>::Real& other, + typename NumTraits<Scalar>::Real 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 MatrixBase<Derived>::isMuchSmallerThan( + const MatrixBase<OtherDerived>& other, + typename NumTraits<Scalar>::Real 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 |