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