Rythmos_HermiteInterpolator.hpp

//@HEADER
// ***********************************************************************
//
//                           Rythmos Package
//                 Copyright (2006) 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.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//
// This library 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
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA
// Questions? Contact Todd S. Coffey (tscoffe@sandia.gov)
//
// ***********************************************************************
//@HEADER

#ifndef Rythmos_HERMITE_INTERPOLATOR_H
#define Rythmos_HERMITE_INTERPOLATOR_H

#include "Rythmos_InterpolatorBase.hpp"

namespace Rythmos {
template<class Scalar>
class HermiteInterpolator : virtual public InterpolatorBase<Scalar>
{
  public:

    ~HermiteInterpolator() {};

    HermiteInterpolator();


    void interpolate(
        const typename DataStore<Scalar>::DataStoreVector_t &data_in
        ,const Array<Scalar> &t_values
        ,typename DataStore<Scalar>::DataStoreVector_t *data_out
        ) const;

    int order() const; 


    std::string description() const;

    void describe(
      Teuchos::FancyOStream       &out
      ,const Teuchos::EVerbosityLevel      verbLevel
      ) const;


    void setParameterList(Teuchos::RCP<Teuchos::ParameterList> const& paramList);

    Teuchos::RCP<Teuchos::ParameterList> getParameterList();

    Teuchos::RCP<Teuchos::ParameterList> unsetParameterList();

    void assertInterpolatePreconditions(
        const typename DataStore<Scalar>::DataStoreVector_t &data_in
        ,const Array<Scalar> &t_values
        ,typename DataStore<Scalar>::DataStoreVector_t *data_out
        ) const;

  private:

    Teuchos::RCP<Teuchos::ParameterList> parameterList;

};

template<class Scalar>
HermiteInterpolator<Scalar>::HermiteInterpolator()
{
}

template<class Scalar>
void HermiteInterpolator<Scalar>::interpolate(
    const typename DataStore<Scalar>::DataStoreVector_t &data_in
    ,const Array<Scalar> &t_values
    ,typename DataStore<Scalar>::DataStoreVector_t *data_out ) const
{
  typedef Teuchos::ScalarTraits<Scalar> ST;
#ifdef TEUCHOS_DEBUG
  assertInterpolatePreconditions(data_in,t_values,data_out);
#endif // TEUCHOS_DEBUG
  Teuchos::RCP<Teuchos::FancyOStream> out = this->getOStream();
  Teuchos::OSTab ostab(out,1,"HI::interpolator");
  if ( Teuchos::as<int>(this->getVerbLevel()) >= Teuchos::as<int>(Teuchos::VERB_HIGH) ) {
    *out << "data_in:" << std::endl;
    for (unsigned int i=0 ; i<data_in.size() ; ++i) {
      *out << "data_in[" << i << "] = " << std::endl;
      data_in[i].describe(*out,Teuchos::VERB_EXTREME);
    }
    *out << "t_values = " << std::endl;
    for (unsigned int i=0 ; i<t_values.size() ; ++i) {
      *out << "t_values[" << i << "] = " << t_values[i] << std::endl;
    }
    for (unsigned int i=0; i<data_out->size() ; ++i) {
      *out << "data_out[" << i << "] = " << std::endl;
      (*data_out)[i].describe(*out,Teuchos::VERB_EXTREME);
    }
  }
  data_out->clear();
  if (t_values.size() == 0) {
    return;
  }
  
  if (data_in.size() == 1) {
    // trivial case of one node
    // preconditions assert that t_values[0] == data_in[0].time so we can just pass it out
    DataStore<Scalar> DS(data_in[0]);
    data_out->push_back(DS);
  } else {
    // data_in.size() >= 2
    int n = 0;
    for (int i=0 ; i<Teuchos::as<int>(data_in.size())-1 ; ++i) {
      const Scalar& ti = data_in[i].time;
      const Scalar& tip1 = data_in[i+1].time;
      while ((ti <= t_values[n]) && (t_values[n] <= tip1)) {
        const Scalar& t = t_values[n];
        // First we check for exact node matches:
        if (t == ti) {
          DataStore<Scalar> DS(data_in[i]);
          data_out->push_back(DS);
        } else if (t == tip1) {
          DataStore<Scalar> DS(data_in[i+1]);
          data_out->push_back(DS);
        } else {
          Teuchos::RCP<const Thyra::VectorBase<Scalar> > xi =      data_in[i  ].x;
          Teuchos::RCP<const Thyra::VectorBase<Scalar> > xip1 =    data_in[i+1].x;
          Teuchos::RCP<const Thyra::VectorBase<Scalar> > xdoti =   data_in[i  ].xdot;
          Teuchos::RCP<const Thyra::VectorBase<Scalar> > xdotip1 = data_in[i+1].xdot;
          
          // 10/10/06 tscoffe:  this could be expensive:
          Teuchos::RCP<Thyra::VectorBase<Scalar> > tmp_vec = xi->clone_v(); 
          Teuchos::RCP<Thyra::VectorBase<Scalar> > xdot_temp = xip1->clone_v(); 
          Scalar dt = tip1-ti;
          Scalar dt2 = dt*dt;
          Scalar t_t0 = t - ti;
          Scalar t_t1 = t - tip1;
          Scalar tmp_t;

          // Compute numerical divided difference:
          Thyra::Vt_S(&*xdot_temp,Scalar(ST::one()/dt));
          Thyra::Vp_StV(&*xdot_temp,Scalar(-ST::one()/dt),*xi);

          // interpolate this point
          DataStore<Scalar> DS;
          DS.time = t;

          //  H_3(x) = f(x0) + f'(x0)(x-x0) + ((f(x1)-f(x0))/(x1-x0) - f'(x0))(x-x0)^2/(x1-x0)
          //           +(f'(x1) - 2(f(x1)-f(x0))/(x1-x0) + f'(x0))(x-x0)^2(x-x1)/(x1-x0)^2
          Teuchos::RCP<Thyra::VectorBase<Scalar> > x_vec = xi->clone_v(); 
          Thyra::Vp_StV(&*x_vec,t_t0,*xdoti);
          tmp_t = t_t0*t_t0/dt;
          Thyra::V_StVpStV(&*tmp_vec,tmp_t,*xdot_temp,Scalar(-ST::one()*tmp_t),*xdoti);
          Thyra::Vp_V(&*x_vec,*tmp_vec);
          tmp_t = t_t0*t_t0*t_t1/dt2;
          Thyra::V_StVpStV(&*tmp_vec,tmp_t,*xdotip1,Scalar(-2*tmp_t),*xdot_temp);
          Thyra::Vp_StV(&*tmp_vec,tmp_t,*xdoti);
          Thyra::Vp_V(&*x_vec,*tmp_vec);
          DS.x = x_vec;

          //  H_3'(x) =        f'(x0) + 2*((f(x1)-f(x0))/(x1-x0) - f'(x0))(x-x0)/(x1-x0)
          //           +(f'(x1) - 2(f(x1)-f(x0))/(x1-x0) + f'(x0))[2*(x-x0)(x-x1) + (x-x0)^2]/(x1-x0)^2
          Teuchos::RCP<Thyra::VectorBase<Scalar> > xdot_vec = xdoti->clone_v(); 
          tmp_t = t_t0/dt;
          Thyra::Vp_StV(&*xdot_vec,Scalar(2*tmp_t),*xdot_temp);
          Thyra::Vp_StV(&*xdot_vec,Scalar(-ST::one()*tmp_t),*xdoti);
          tmp_t = Scalar((2*t_t0*t_t1+t_t0*t_t0)/dt2);
          Thyra::V_StVpStV(&*tmp_vec,tmp_t,*xdotip1,Scalar(-2*tmp_t),*xdot_temp);
          Thyra::Vp_StV(&*tmp_vec,tmp_t,*xdoti);
          Thyra::Vp_V(&*xdot_vec,*tmp_vec);
          DS.xdot = xdot_vec;
          
          // Accuracy:
          // f(x) - H_3(x) = (f^{(3)}(\xi(x))/(4!))(x-x0)^2(x-x1)^2
          DS.accuracy = (t_t0)*(t_t0)*(t_t1)*(t_t1);

          // Push DataStore object onto vector:
          data_out->push_back(DS);
        }
        n++;
        if (n == Teuchos::as<int>(t_values.size())) {
          return;
        }
      }
    }
  } // data_in.size() == 1
}

template<class Scalar>
int HermiteInterpolator<Scalar>::order() const
{
  return(2);
}

template<class Scalar>
std::string HermiteInterpolator<Scalar>::description() const
{
  std::string name = "Rythmos::HermiteInterpolator";
  return(name);
}

template<class Scalar>
void HermiteInterpolator<Scalar>::describe(
      Teuchos::FancyOStream       &out
      ,const Teuchos::EVerbosityLevel      verbLevel
      ) const
{
  if ( (Teuchos::as<int>(verbLevel) == Teuchos::as<int>(Teuchos::VERB_DEFAULT) ) ||
       (Teuchos::as<int>(verbLevel) >= Teuchos::as<int>(Teuchos::VERB_LOW)     )
     ) {
    out << description() << "::describe" << std::endl;
  } else if (Teuchos::as<int>(verbLevel) >= Teuchos::as<int>(Teuchos::VERB_LOW)) {
  } else if (Teuchos::as<int>(verbLevel) >= Teuchos::as<int>(Teuchos::VERB_MEDIUM)) {
  } else if (Teuchos::as<int>(verbLevel) >= Teuchos::as<int>(Teuchos::VERB_HIGH)) {
  }
}

template <class Scalar>
void HermiteInterpolator<Scalar>::setParameterList(Teuchos::RCP<Teuchos::ParameterList> const& paramList)
{
  parameterList = paramList;
  int outputLevel = parameterList->get( "outputLevel", int(-1) );
  outputLevel = std::min(std::max(outputLevel,-1),4);
  this->setVerbLevel(static_cast<Teuchos::EVerbosityLevel>(outputLevel));
}

template <class Scalar>
Teuchos::RCP<Teuchos::ParameterList> HermiteInterpolator<Scalar>::getParameterList()
{
  return(parameterList);
}

template <class Scalar>
Teuchos::RCP<Teuchos::ParameterList> HermiteInterpolator<Scalar>::unsetParameterList()
{
  Teuchos::RCP<Teuchos::ParameterList> temp_param_list = parameterList;
  parameterList = Teuchos::null;
  return(temp_param_list);
}

template<class Scalar>
void HermiteInterpolator<Scalar>::assertInterpolatePreconditions(
        const typename DataStore<Scalar>::DataStoreVector_t &data_in
        ,const Array<Scalar> &t_values
        ,typename DataStore<Scalar>::DataStoreVector_t *data_out
        ) const
{
  assertBaseInterpolatePreconditions(data_in,t_values,data_out);
  for (int i=0; i<Teuchos::as<int>(data_in.size()) ; ++i) {
    TEST_FOR_EXCEPTION(
        data_in[i].xdot == Teuchos::null, std::logic_error,
        "Error, data_in[" << i << "].xdot == Teuchos::null.\n"
        );
  }
}

} // namespace Rythmos

#endif // Rythmos_HERMITE_INTERPOLATOR_H

---