Fuzzy.h revision c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd
1// This file is part of Eigen, a lightweight C++ template library 2// for linear algebra. 3// 4// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com> 5// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> 6// 7// This Source Code Form is subject to the terms of the Mozilla 8// Public License v. 2.0. If a copy of the MPL was not distributed 9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11#ifndef EIGEN_FUZZY_H 12#define EIGEN_FUZZY_H 13 14namespace Eigen { 15 16namespace internal 17{ 18 19template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> 20struct isApprox_selector 21{ 22 static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar prec) 23 { 24 using std::min; 25 typename internal::nested<Derived,2>::type nested(x); 26 typename internal::nested<OtherDerived,2>::type otherNested(y); 27 return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * (min)(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum()); 28 } 29}; 30 31template<typename Derived, typename OtherDerived> 32struct isApprox_selector<Derived, OtherDerived, true> 33{ 34 static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar) 35 { 36 return x.matrix() == y.matrix(); 37 } 38}; 39 40template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> 41struct isMuchSmallerThan_object_selector 42{ 43 static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar prec) 44 { 45 return x.cwiseAbs2().sum() <= abs2(prec) * y.cwiseAbs2().sum(); 46 } 47}; 48 49template<typename Derived, typename OtherDerived> 50struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true> 51{ 52 static bool run(const Derived& x, const OtherDerived&, typename Derived::RealScalar) 53 { 54 return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); 55 } 56}; 57 58template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> 59struct isMuchSmallerThan_scalar_selector 60{ 61 static bool run(const Derived& x, const typename Derived::RealScalar& y, typename Derived::RealScalar prec) 62 { 63 return x.cwiseAbs2().sum() <= abs2(prec * y); 64 } 65}; 66 67template<typename Derived> 68struct isMuchSmallerThan_scalar_selector<Derived, true> 69{ 70 static bool run(const Derived& x, const typename Derived::RealScalar&, typename Derived::RealScalar) 71 { 72 return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); 73 } 74}; 75 76} // end namespace internal 77 78 79/** \returns \c true if \c *this is approximately equal to \a other, within the precision 80 * determined by \a prec. 81 * 82 * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$ 83 * are considered to be approximately equal within precision \f$ p \f$ if 84 * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f] 85 * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm 86 * L2 norm). 87 * 88 * \note Because of the multiplicativeness of this comparison, one can't use this function 89 * to check whether \c *this is approximately equal to the zero matrix or vector. 90 * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix 91 * or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const 92 * RealScalar&, RealScalar) instead. 93 * 94 * \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const 95 */ 96template<typename Derived> 97template<typename OtherDerived> 98bool DenseBase<Derived>::isApprox( 99 const DenseBase<OtherDerived>& other, 100 RealScalar prec 101) const 102{ 103 return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec); 104} 105 106/** \returns \c true if the norm of \c *this is much smaller than \a other, 107 * within the precision determined by \a prec. 108 * 109 * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is 110 * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if 111 * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f] 112 * 113 * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, 114 * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm 115 * of a reference matrix of same dimensions. 116 * 117 * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const 118 */ 119template<typename Derived> 120bool DenseBase<Derived>::isMuchSmallerThan( 121 const typename NumTraits<Scalar>::Real& other, 122 RealScalar prec 123) const 124{ 125 return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec); 126} 127 128/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other, 129 * within the precision determined by \a prec. 130 * 131 * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is 132 * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if 133 * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f] 134 * For matrices, the comparison is done using the Hilbert-Schmidt norm. 135 * 136 * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const 137 */ 138template<typename Derived> 139template<typename OtherDerived> 140bool DenseBase<Derived>::isMuchSmallerThan( 141 const DenseBase<OtherDerived>& other, 142 RealScalar prec 143) const 144{ 145 return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec); 146} 147 148} // end namespace Eigen 149 150#endif // EIGEN_FUZZY_H 151