Stokhos_KL_OneDExponentialCovarianceFunction.hpp

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// @HEADER
// *****************************************************************************
//                           Stokhos Package
//
// Copyright 2009 NTESS and the Stokhos contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#ifndef STOKHOS_KL_ONE_D_EXPONENTIAL_COVARIANCE_FUNCTION_HPP
#define STOKHOS_KL_ONE_D_EXPONENTIAL_COVARIANCE_FUNCTION_HPP

#include <string>
#include <cmath>
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_ScalarTraits.hpp"
#include "Stokhos_KL_OneDExponentialEigenPair.hpp"

namespace Stokhos {

  namespace KL {

    template <typename value_type>
    class OneDExponentialCovarianceFunction {
    public:

      typedef ExponentialOneDEigenFunction<value_type> eigen_function_type;
      typedef OneDEigenPair<eigen_function_type> eigen_pair_type;

      OneDExponentialCovarianceFunction(int M,
                                        const value_type& a,
                                        const value_type& b,
                                        const value_type& L,
                                        const int dim_name,
                                        Teuchos::ParameterList& solverParams);

      ~OneDExponentialCovarianceFunction() {}

      value_type evaluateCovariance(const value_type& x,
                                    const value_type& xp) const {
        return std::exp(-std::abs(x-xp)/L);
      }

      const Teuchos::Array<eigen_pair_type>& getEigenPairs() const {
        return eig_pair;
      }

    private:

      OneDExponentialCovarianceFunction(const OneDExponentialCovarianceFunction&);

      OneDExponentialCovarianceFunction& operator=(const OneDExponentialCovarianceFunction&);

    protected:

      typedef typename Teuchos::ScalarTraits<value_type>::magnitudeType magnitude_type;

      value_type L;

      Teuchos::Array<eigen_pair_type> eig_pair;

      template <class Func>
      value_type newton(const Func& func, const value_type& a,
                        const value_type& b, magnitude_type tol,
                        int max_num_its);

      template <class Func>
      value_type bisection(const Func& func, const value_type& a,
                           const value_type& b, magnitude_type tol,
                           int max_num_its);

      struct EigFuncSin {
        const value_type& alpha;
        EigFuncSin(const value_type& alpha_) : alpha(alpha_) {}
        value_type eval(const value_type& u) const {
          return alpha*std::tan(u) + u; }
        value_type deriv(const value_type& u) const {
          return alpha/(std::cos(u)*std::cos(u)) + 1.0; }
      };

      struct EigFuncCos {
        const value_type& alpha;
        EigFuncCos(const value_type& alpha_) : alpha(alpha_) {}
        value_type eval(const value_type& u) const {
          return alpha - u*std::tan(u); }
        value_type deriv(const value_type& u) const {
          return -std::tan(u) - u/(std::cos(u)*std::cos(u)); }
      };

    }; // class OneDExponentialCovarianceFunction

  } // namespace KL

} // namespace Stokhos

// Include template definitions
#include "Stokhos_KL_OneDExponentialCovarianceFunctionImp.hpp"

#endif // STOKHOS_KL_ONE_D_EXPONENTIAL_COVARIANCE_FUNCTION_HPP