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 EIGEN_DEVICE_FUNC
23 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
31template<typename Derived, typename OtherDerived>
32struct 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
41template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
42struct 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
51template<typename Derived, typename OtherDerived>
52struct 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
61template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
62struct 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
71template<typename Derived>
72struct 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 */
101template<typename Derived>
102template<typename OtherDerived>
103bool 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 */
124template<typename Derived>
125bool 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 */
143template<typename Derived>
144template<typename OtherDerived>
145bool 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