Tempus_NumericalUtils.hpp

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// @HEADER
// ****************************************************************************
//                Tempus: Copyright (2017) Sandia Corporation
//
// Distributed under BSD 3-clause license (See accompanying file Copyright.txt)
// ****************************************************************************
// @HEADER

#ifndef Tempus_NumericalUtils_hpp
#define Tempus_NumericalUtils_hpp

#include "Teuchos_ScalarTraits.hpp"

#include "Tempus_config.hpp"

namespace Tempus {

template <typename Scalar>
const Scalar numericalTol()
{
  const Scalar numericalTol =
      Teuchos::ScalarTraits<Scalar>::eps() *
      typename Teuchos::ScalarTraits<Scalar>::magnitudeType(100.0);
  return numericalTol;
}

template <typename Scalar>
bool approxZero(Scalar value,
                Scalar tol = Teuchos::ScalarTraits<Scalar>::sfmin())
{
  typedef Teuchos::ScalarTraits<Scalar> ST;
  return ST::magnitude(value) <= ST::magnitude(tol);
}

template <typename Scalar>
bool approxEqualAbsTol(Scalar a, Scalar b, Scalar absTol)
{
  return Teuchos::ScalarTraits<Scalar>::magnitude(a - b) < std::abs(absTol);
}

template <typename Scalar>
bool approxEqual(Scalar a, Scalar b, Scalar relTol = numericalTol<Scalar>())
{
  const Scalar min = std::min(std::abs(a), std::abs(b));
  Scalar absTol    = min * std::abs(relTol);
  if (absTol == Scalar(0.0)) absTol = Teuchos::ScalarTraits<Scalar>::sfmin();
  return approxEqualAbsTol(a, b, absTol);
}

template <typename Scalar>
bool approxEqualScale(Scalar a, Scalar b, Scalar scale,
                      Scalar relTol = numericalTol<Scalar>())
{
  return approxEqualAbsTol(a, b, scale * relTol);
}

}  // namespace Tempus

#endif  // Tempus_NumericalUtils_hpp