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 (at) gmail.com> 5 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) 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 static bool run(const Derived& x, const OtherDerived& y, const 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 31 template<typename Derived, typename OtherDerived> 32 struct isApprox_selector<Derived, OtherDerived, true> 33 { 34 static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&) 35 { 36 return x.matrix() == y.matrix(); 37 } 38 }; 39 40 template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> 41 struct isMuchSmallerThan_object_selector 42 { 43 static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) 44 { 45 return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum(); 46 } 47 }; 48 49 template<typename Derived, typename OtherDerived> 50 struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true> 51 { 52 static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&) 53 { 54 return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); 55 } 56 }; 57 58 template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger> 59 struct isMuchSmallerThan_scalar_selector 60 { 61 static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec) 62 { 63 return x.cwiseAbs2().sum() <= numext::abs2(prec * y); 64 } 65 }; 66 67 template<typename Derived> 68 struct isMuchSmallerThan_scalar_selector<Derived, true> 69 { 70 static bool run(const Derived& x, const typename Derived::RealScalar&, const 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 */ 96 template<typename Derived> 97 template<typename OtherDerived> 98 bool DenseBase<Derived>::isApprox( 99 const DenseBase<OtherDerived>& other, 100 const 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 */ 119 template<typename Derived> 120 bool DenseBase<Derived>::isMuchSmallerThan( 121 const typename NumTraits<Scalar>::Real& other, 122 const 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 */ 138 template<typename Derived> 139 template<typename OtherDerived> 140 bool DenseBase<Derived>::isMuchSmallerThan( 141 const DenseBase<OtherDerived>& other, 142 const 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
