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