Eigen/src/Core/Fuzzy.h - mirror - Git at Google

 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
 //
 // Eigen is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
 // License as published by the Free Software Foundation; either
 // version 3 of the License, or (at your option) any later version.
 //
 // Alternatively, you can redistribute it and/or
 // modify it under the terms of the GNU General Public License as
 // published by the Free Software Foundation; either version 2 of
 // the License, or (at your option) any later version.
 //
 // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
 // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
 // GNU General Public License for more details.
 //
 // You should have received a copy of the GNU Lesser General Public
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.

 #ifndef EIGEN_FUZZY_H
 #define EIGEN_FUZZY_H

 // TODO support small integer types properly i.e. do exact compare on coeffs --- taking a HS norm is guaranteed to cause integer overflow.

 #ifndef EIGEN_LEGACY_COMPARES

 /** \returns \c true if \c *this is approximately equal to \a other, within the precision
   * determined by \a prec.
   *
   * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
   * are considered to be approximately equal within precision \f$ p \f$ if
   * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
   * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
   * L2 norm).
   *
   * \note Because of the multiplicativeness of this comparison, one can't use this function
   * to check whether \c *this is approximately equal to the zero matrix or vector.
   * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
   * or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const
   * RealScalar&, RealScalar) instead.
   *
   * \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const
   */
 template<typename Derived>
 template<typename OtherDerived>
 bool DenseBase<Derived>::isApprox(
   const DenseBase<OtherDerived>& other,
   RealScalar prec
 ) const
 {
   const typename ei_nested<Derived,2>::type nested(derived());
   const typename ei_nested<OtherDerived,2>::type otherNested(other.derived());
 //   std::cerr << typeid(Derived).name() << " => " << typeid(typename ei_nested<Derived,2>::type).name() << "\n";
 //   std::cerr << typeid(OtherDerived).name() << " => " << typeid(typename ei_nested<OtherDerived,2>::type).name() << "\n";
 //   return false;
   return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * std::min(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
 }

 /** \returns \c true if the norm of \c *this is much smaller than \a other,
   * within the precision determined by \a prec.
   *
   * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
   * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
   * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
   *
   * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
   * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
   * of a reference matrix of same dimensions.
   *
   * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
   */
 template<typename Derived>
 bool DenseBase<Derived>::isMuchSmallerThan(
   const typename NumTraits<Scalar>::Real& other,
   RealScalar prec
 ) const
 {
   return derived().cwiseAbs2().sum() <= prec * prec * other * other;
 }

 /** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
   * within the precision determined by \a prec.
   *
   * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
   * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
   * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
   * For matrices, the comparison is done using the Hilbert-Schmidt norm.
   *
   * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
   */
 template<typename Derived>
 template<typename OtherDerived>
 bool DenseBase<Derived>::isMuchSmallerThan(
   const DenseBase<OtherDerived>& other,
   RealScalar prec
 ) const
 {
   return derived().cwiseAbs2().sum() <= prec * prec * other.derived().cwiseAbs2().sum();
 }

 #else

 template<typename Derived, typename OtherDerived=Derived, bool IsVector=Derived::IsVectorAtCompileTime>
 struct ei_fuzzy_selector;

 /** \returns \c true if \c *this is approximately equal to \a other, within the precision
   * determined by \a prec.
   *
   * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
   * are considered to be approximately equal within precision \f$ p \f$ if
   * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
   * For matrices, the comparison is done on all columns.
   *
   * \note Because of the multiplicativeness of this comparison, one can't use this function
   * to check whether \c *this is approximately equal to the zero matrix or vector.
   * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
   * or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const
   * RealScalar&, RealScalar) instead.
   *
   * \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const
   */
 template<typename Derived>
 template<typename OtherDerived>
 bool DenseBase<Derived>::isApprox(
   const DenseBase<OtherDerived>& other,
   RealScalar prec
 ) const
 {
   return ei_fuzzy_selector<Derived,OtherDerived>::isApprox(derived(), other.derived(), prec);
 }

 /** \returns \c true if the norm of \c *this is much smaller than \a other,
   * within the precision determined by \a prec.
   *
   * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
   * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
   * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
   * For matrices, the comparison is done on all columns.
   *
   * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
   */
 template<typename Derived>
 bool DenseBase<Derived>::isMuchSmallerThan(
   const typename NumTraits<Scalar>::Real& other,
   RealScalar prec
 ) const
 {
   return ei_fuzzy_selector<Derived>::isMuchSmallerThan(derived(), other, prec);
 }

 /** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
   * within the precision determined by \a prec.
   *
   * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
   * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
   * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
   * For matrices, the comparison is done on all columns.
   *
   * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
   */
 template<typename Derived>
 template<typename OtherDerived>
 bool DenseBase<Derived>::isMuchSmallerThan(
   const DenseBase<OtherDerived>& other,
   RealScalar prec
 ) const
 {
   return ei_fuzzy_selector<Derived,OtherDerived>::isMuchSmallerThan(derived(), other.derived(), prec);
 }


 template<typename Derived, typename OtherDerived>
 struct ei_fuzzy_selector<Derived,OtherDerived,true>
 {
   typedef typename Derived::RealScalar RealScalar;
   static bool isApprox(const Derived& self, const OtherDerived& other, RealScalar prec)
   {
     EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
     ei_assert(self.size() == other.size());
     return((self - other).squaredNorm() <= std::min(self.squaredNorm(), other.squaredNorm()) * prec * prec);
   }
   static bool isMuchSmallerThan(const Derived& self, const RealScalar& other, RealScalar prec)
   {
     return(self.squaredNorm() <= ei_abs2(other * prec));
   }
   static bool isMuchSmallerThan(const Derived& self, const OtherDerived& other, RealScalar prec)
   {
     EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
     ei_assert(self.size() == other.size());
     return(self.squaredNorm() <= other.squaredNorm() * prec * prec);
   }
 };

 template<typename Derived, typename OtherDerived>
 struct ei_fuzzy_selector<Derived,OtherDerived,false>
 {
   typedef typename Derived::RealScalar RealScalar;
   typedef typename Derived::Index Index;
   static bool isApprox(const Derived& self, const OtherDerived& other, RealScalar prec)
   {
     EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
     ei_assert(self.rows() == other.rows() && self.cols() == other.cols());
     typename Derived::Nested nested(self);
     typename OtherDerived::Nested otherNested(other);
     for(Index i = 0; i < self.cols(); ++i)
       if((nested.col(i) - otherNested.col(i)).squaredNorm()
           > std::min(nested.col(i).squaredNorm(), otherNested.col(i).squaredNorm()) * prec * prec)
         return false;
     return true;
   }
   static bool isMuchSmallerThan(const Derived& self, const RealScalar& other, RealScalar prec)
   {
     typename Derived::Nested nested(self);
     for(Index i = 0; i < self.cols(); ++i)
       if(nested.col(i).squaredNorm() > ei_abs2(other * prec))
         return false;
     return true;
   }
   static bool isMuchSmallerThan(const Derived& self, const OtherDerived& other, RealScalar prec)
   {
     EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
     ei_assert(self.rows() == other.rows() && self.cols() == other.cols());
     typename Derived::Nested nested(self);
     typename OtherDerived::Nested otherNested(other);
     for(Index i = 0; i < self.cols(); ++i)
       if(nested.col(i).squaredNorm() > otherNested.col(i).squaredNorm() * prec * prec)
         return false;
     return true;
   }
 };

 #endif

 #endif // EIGEN_FUZZY_H
	// This file is part of Eigen, a lightweight C++ template library
	// for linear algebra.
	//
	// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
	// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
	//
	// Eigen is free software; you can redistribute it and/or
	// modify it under the terms of the GNU Lesser General Public
	// License as published by the Free Software Foundation; either
	// version 3 of the License, or (at your option) any later version.
	//
	// Alternatively, you can redistribute it and/or
	// modify it under the terms of the GNU General Public License as
	// published by the Free Software Foundation; either version 2 of
	// the License, or (at your option) any later version.
	//
	// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
	// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
	// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
	// GNU General Public License for more details.
	//
	// You should have received a copy of the GNU Lesser General Public
	// License and a copy of the GNU General Public License along with
	// Eigen. If not, see <http://www.gnu.org/licenses/>.

	#ifndef EIGEN_FUZZY_H
	#define EIGEN_FUZZY_H

	// TODO support small integer types properly i.e. do exact compare on coeffs --- taking a HS norm is guaranteed to cause integer overflow.

	#ifndef EIGEN_LEGACY_COMPARES

	/** \returns \c true if \c *this is approximately equal to \a other, within the precision
	* determined by \a prec.
	*
	* \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
	* are considered to be approximately equal within precision \f$ p \f$ if
	* \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
	* For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
	* L2 norm).
	*
	* \note Because of the multiplicativeness of this comparison, one can't use this function
	* to check whether \c *this is approximately equal to the zero matrix or vector.
	* Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
	* or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const
	* RealScalar&, RealScalar) instead.
	*
	* \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const
	*/
	template<typename Derived>
	template<typename OtherDerived>
	bool DenseBase<Derived>::isApprox(
	const DenseBase<OtherDerived>& other,
	RealScalar prec
	) const
	{
	const typename ei_nested<Derived,2>::type nested(derived());
	const typename ei_nested<OtherDerived,2>::type otherNested(other.derived());
	// std::cerr << typeid(Derived).name() << " => " << typeid(typename ei_nested<Derived,2>::type).name() << "\n";
	// std::cerr << typeid(OtherDerived).name() << " => " << typeid(typename ei_nested<OtherDerived,2>::type).name() << "\n";
	// return false;
	return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * std::min(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
	}

	/** \returns \c true if the norm of \c *this is much smaller than \a other,
	* within the precision determined by \a prec.
	*
	* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
	* considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
	* \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
	*
	* For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
	* the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
	* of a reference matrix of same dimensions.
	*
	* \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
	*/
	template<typename Derived>
	bool DenseBase<Derived>::isMuchSmallerThan(
	const typename NumTraits<Scalar>::Real& other,
	RealScalar prec
	) const
	{
	return derived().cwiseAbs2().sum() <= prec * prec * other * other;
	}

	/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
	* within the precision determined by \a prec.
	*
	* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
	* considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
	* \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
	* For matrices, the comparison is done using the Hilbert-Schmidt norm.
	*
	* \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
	*/
	template<typename Derived>
	template<typename OtherDerived>
	bool DenseBase<Derived>::isMuchSmallerThan(
	const DenseBase<OtherDerived>& other,
	RealScalar prec
	) const
	{
	return derived().cwiseAbs2().sum() <= prec * prec * other.derived().cwiseAbs2().sum();
	}

	#else

	template<typename Derived, typename OtherDerived=Derived, bool IsVector=Derived::IsVectorAtCompileTime>
	struct ei_fuzzy_selector;

	/** \returns \c true if \c *this is approximately equal to \a other, within the precision
	* determined by \a prec.
	*
	* \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
	* are considered to be approximately equal within precision \f$ p \f$ if
	* \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
	* For matrices, the comparison is done on all columns.
	*
	* \note Because of the multiplicativeness of this comparison, one can't use this function
	* to check whether \c *this is approximately equal to the zero matrix or vector.
	* Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
	* or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const
	* RealScalar&, RealScalar) instead.
	*
	* \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const
	*/
	template<typename Derived>
	template<typename OtherDerived>
	bool DenseBase<Derived>::isApprox(
	const DenseBase<OtherDerived>& other,
	RealScalar prec
	) const
	{
	return ei_fuzzy_selector<Derived,OtherDerived>::isApprox(derived(), other.derived(), prec);
	}

	/** \returns \c true if the norm of \c *this is much smaller than \a other,
	* within the precision determined by \a prec.
	*
	* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
	* considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
	* \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
	* For matrices, the comparison is done on all columns.
	*
	* \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
	*/
	template<typename Derived>
	bool DenseBase<Derived>::isMuchSmallerThan(
	const typename NumTraits<Scalar>::Real& other,
	RealScalar prec
	) const
	{
	return ei_fuzzy_selector<Derived>::isMuchSmallerThan(derived(), other, prec);
	}

	/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
	* within the precision determined by \a prec.
	*
	* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
	* considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
	* \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
	* For matrices, the comparison is done on all columns.
	*
	* \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
	*/
	template<typename Derived>
	template<typename OtherDerived>
	bool DenseBase<Derived>::isMuchSmallerThan(
	const DenseBase<OtherDerived>& other,
	RealScalar prec
	) const
	{
	return ei_fuzzy_selector<Derived,OtherDerived>::isMuchSmallerThan(derived(), other.derived(), prec);
	}


	template<typename Derived, typename OtherDerived>
	struct ei_fuzzy_selector<Derived,OtherDerived,true>
	{
	typedef typename Derived::RealScalar RealScalar;
	static bool isApprox(const Derived& self, const OtherDerived& other, RealScalar prec)
	{
	EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
	ei_assert(self.size() == other.size());
	return((self - other).squaredNorm() <= std::min(self.squaredNorm(), other.squaredNorm()) * prec * prec);
	}
	static bool isMuchSmallerThan(const Derived& self, const RealScalar& other, RealScalar prec)
	{
	return(self.squaredNorm() <= ei_abs2(other * prec));
	}
	static bool isMuchSmallerThan(const Derived& self, const OtherDerived& other, RealScalar prec)
	{
	EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
	ei_assert(self.size() == other.size());
	return(self.squaredNorm() <= other.squaredNorm() * prec * prec);
	}
	};

	template<typename Derived, typename OtherDerived>
	struct ei_fuzzy_selector<Derived,OtherDerived,false>
	{
	typedef typename Derived::RealScalar RealScalar;
	typedef typename Derived::Index Index;
	static bool isApprox(const Derived& self, const OtherDerived& other, RealScalar prec)
	{
	EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
	ei_assert(self.rows() == other.rows() && self.cols() == other.cols());
	typename Derived::Nested nested(self);
	typename OtherDerived::Nested otherNested(other);
	for(Index i = 0; i < self.cols(); ++i)
	if((nested.col(i) - otherNested.col(i)).squaredNorm()
	> std::min(nested.col(i).squaredNorm(), otherNested.col(i).squaredNorm()) * prec * prec)
	return false;
	return true;
	}
	static bool isMuchSmallerThan(const Derived& self, const RealScalar& other, RealScalar prec)
	{
	typename Derived::Nested nested(self);
	for(Index i = 0; i < self.cols(); ++i)
	if(nested.col(i).squaredNorm() > ei_abs2(other * prec))
	return false;
	return true;
	}
	static bool isMuchSmallerThan(const Derived& self, const OtherDerived& other, RealScalar prec)
	{
	EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
	ei_assert(self.rows() == other.rows() && self.cols() == other.cols());
	typename Derived::Nested nested(self);
	typename OtherDerived::Nested otherNested(other);
	for(Index i = 0; i < self.cols(); ++i)
	if(nested.col(i).squaredNorm() > otherNested.col(i).squaredNorm() * prec * prec)
	return false;
	return true;
	}
	};

	#endif

	#endif // EIGEN_FUZZY_H