151 lines
5.5 KiB
C++
151 lines
5.5 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_FUZZY_H
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#define EIGEN_FUZZY_H
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namespace Eigen {
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namespace internal
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{
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template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
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struct isApprox_selector
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{
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static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
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{
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using std::min;
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typename internal::nested<Derived,2>::type nested(x);
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typename internal::nested<OtherDerived,2>::type otherNested(y);
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return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * (min)(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
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}
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};
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template<typename Derived, typename OtherDerived>
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struct isApprox_selector<Derived, OtherDerived, true>
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{
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static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&)
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{
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return x.matrix() == y.matrix();
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}
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};
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template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
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struct isMuchSmallerThan_object_selector
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{
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static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
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{
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return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
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}
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};
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template<typename Derived, typename OtherDerived>
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struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
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{
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static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&)
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{
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return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
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}
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};
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template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
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struct isMuchSmallerThan_scalar_selector
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{
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static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
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{
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return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
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}
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};
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template<typename Derived>
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struct isMuchSmallerThan_scalar_selector<Derived, true>
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{
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static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&)
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{
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return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
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}
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};
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} // end namespace internal
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/** \returns \c true if \c *this is approximately equal to \a other, within the precision
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* determined by \a prec.
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*
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* \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
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* are considered to be approximately equal within precision \f$ p \f$ if
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* \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
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* For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
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* L2 norm).
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*
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* \note Because of the multiplicativeness of this comparison, one can't use this function
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* to check whether \c *this is approximately equal to the zero matrix or vector.
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* Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
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* or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const
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* RealScalar&, RealScalar) instead.
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*
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* \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
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*/
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template<typename Derived>
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template<typename OtherDerived>
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bool DenseBase<Derived>::isApprox(
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const DenseBase<OtherDerived>& other,
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const RealScalar& prec
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) const
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{
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return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
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}
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/** \returns \c true if the norm of \c *this is much smaller than \a other,
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* within the precision determined by \a prec.
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*
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* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
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* considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
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* \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
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*
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* For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
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* the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
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* of a reference matrix of same dimensions.
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*
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* \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
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*/
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template<typename Derived>
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bool DenseBase<Derived>::isMuchSmallerThan(
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const typename NumTraits<Scalar>::Real& other,
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const RealScalar& prec
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) const
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{
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return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
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}
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/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
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* within the precision determined by \a prec.
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*
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* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
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* considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
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* \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
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* For matrices, the comparison is done using the Hilbert-Schmidt norm.
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*
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* \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
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*/
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template<typename Derived>
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template<typename OtherDerived>
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bool DenseBase<Derived>::isMuchSmallerThan(
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const DenseBase<OtherDerived>& other,
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const RealScalar& prec
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) const
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{
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return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
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}
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} // end namespace Eigen
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#endif // EIGEN_FUZZY_H
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