// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
//
// Eigen is free software; 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 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 General Public License for more
// details.
//
// You should have received a copy of the GNU General Public License along
// with Eigen; if not, write to the Free Software Foundation, Inc., 51
// Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
//
// As a special exception, if other files instantiate templates or use macros
// or functions from this file, or you compile this file and link it
// with other works to produce a work based on this file, this file does not
// by itself cause the resulting work to be covered by the GNU General Public
// License. This exception does not invalidate any other reasons why a work
// based on this file might be covered by the GNU General Public License.

#ifndef EIGEN_FUZZY_H
#define EIGEN_FUZZY_H

/** \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 isMuchSmallerThan(const
  * RealScalar&, RealScalar) instead.
  *
  * \sa isMuchSmallerThan(const RealScalar&, RealScalar) const
  */
template<typename Scalar, typename Derived>
template<typename OtherDerived>
bool MatrixBase<Scalar, Derived>::isApprox(
  const OtherDerived& other,
  typename NumTraits<Scalar>::Real prec
) const
{
  assert(rows() == other.rows() && cols() == other.cols());
  if(Traits::IsVectorAtCompileTime)
  {
    return((*this - other).norm2() <= std::min(norm2(), other.norm2()) * prec * prec);
  }
  else
  {
    for(int i = 0; i < cols(); i++)
      if((col(i) - other.col(i)).norm2()
         > std::min(col(i).norm2(), other.col(i).norm2()) * prec * prec)
        return false;
    return true;
  }
}

/** \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 MatrixBase<Scalar, OtherDerived>&, RealScalar) const
  */
template<typename Scalar, typename Derived>
bool MatrixBase<Scalar, Derived>::isMuchSmallerThan(
  const typename NumTraits<Scalar>::Real& other,
  typename NumTraits<Scalar>::Real prec
) const
{
  if(Traits::IsVectorAtCompileTime)
  {
    return(norm2() <= abs2(other * prec));
  }
  else
  {
    for(int i = 0; i < cols(); i++)
      if(col(i).norm2() > abs2(other * prec))
        return false;
    return true;
  }
}

/** \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 Scalar, typename Derived>
template<typename OtherDerived>
bool MatrixBase<Scalar, Derived>::isMuchSmallerThan(
  const MatrixBase<Scalar, OtherDerived>& other,
  typename NumTraits<Scalar>::Real prec
) const
{
  assert(rows() == other.rows() && cols() == other.cols());
  if(Traits::IsVectorAtCompileTime)
  {
    return(norm2() <= other.norm2() * prec * prec);
  }
  else
  {
    for(int i = 0; i < cols(); i++)
      if(col(i).norm2() > other.col(i).norm2() * prec * prec)
        return false;
    return true;
  }
}

#endif // EIGEN_FUZZY_H