Stokhos_KL_OneDExponentialCovarianceFunction.hpp

Go to the documentation of this file.

// @HEADER
// ***********************************************************************
//
//                           Stokhos Package
//                 Copyright (2009) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Questions? Contact Eric T. Phipps (etphipp@sandia.gov).
//
// ***********************************************************************
// @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