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 14 namespace Eigen { 15 16 namespace internal 17 { 18 19 template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> 20 struct isApprox_selector 21 { 22 EIGEN_DEVICE_FUNC runisApprox_selector23 static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) 24 { 25 typename internal::nested_eval<Derived,2>::type nested(x); 26 typename internal::nested_eval<OtherDerived,2>::type otherNested(y); 27 return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * numext::mini(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum()); 28 } 29 }; 30 31 template<typename Derived, typename OtherDerived> 32 struct isApprox_selector<Derived, OtherDerived, true> 33 { 34 EIGEN_DEVICE_FUNC 35 static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&) 36 { 37 return x.matrix() == y.matrix(); 38 } 39 }; 40 41 template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> 42 struct isMuchSmallerThan_object_selector 43 { 44 EIGEN_DEVICE_FUNC 45 static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) 46 { 47 return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum(); 48 } 49 }; 50 51 template<typename Derived, typename OtherDerived> 52 struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true> 53 { 54 EIGEN_DEVICE_FUNC 55 static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&) 56 { 57 return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); 58 } 59 }; 60 61 template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> 62 struct isMuchSmallerThan_scalar_selector 63 { 64 EIGEN_DEVICE_FUNC 65 static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec) 66 { 67 return x.cwiseAbs2().sum() <= numext::abs2(prec * y); 68 } 69 }; 70 71 template<typename Derived> 72 struct isMuchSmallerThan_scalar_selector<Derived, true> 73 { 74 EIGEN_DEVICE_FUNC 75 static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&) 76 { 77 return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); 78 } 79 }; 80 81 } // end namespace internal 82 83 84 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 85 * determined by \a prec. 86 * 87 * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$ 88 * are considered to be approximately equal within precision \f$ p \f$ if 89 * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f] 90 * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm 91 * L2 norm). 92 * 93 * \note Because of the multiplicativeness of this comparison, one can't use this function 94 * to check whether \c *this is approximately equal to the zero matrix or vector. 95 * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix 96 * or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const 97 * RealScalar&, RealScalar) instead. 98 * 99 * \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const 100 */ 101 template<typename Derived> 102 template<typename OtherDerived> 103 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApprox( 104 const DenseBase<OtherDerived>& other, 105 const RealScalar& prec 106 ) const 107 { 108 return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec); 109 } 110 111 /** \returns \c true if the norm of \c *this is much smaller than \a other, 112 * within the precision determined by \a prec. 113 * 114 * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is 115 * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if 116 * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f] 117 * 118 * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, 119 * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm 120 * of a reference matrix of same dimensions. 121 * 122 * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const 123 */ 124 template<typename Derived> 125 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan( 126 const typename NumTraits<Scalar>::Real& other, 127 const RealScalar& prec 128 ) const 129 { 130 return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec); 131 } 132 133 /** \returns \c true if the norm of \c *this is much smaller than the norm of \a other, 134 * within the precision determined by \a prec. 135 * 136 * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is 137 * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if 138 * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f] 139 * For matrices, the comparison is done using the Hilbert-Schmidt norm. 140 * 141 * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const 142 */ 143 template<typename Derived> 144 template<typename OtherDerived> 145 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan( 146 const DenseBase<OtherDerived>& other, 147 const RealScalar& prec 148 ) const 149 { 150 return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec); 151 } 152 153 } // end namespace Eigen 154 155 #endif // EIGEN_FUZZY_H 156