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