Tempus_DIRK_ASA.cpp

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

#include "Teuchos_UnitTestHarness.hpp"
#include "Teuchos_XMLParameterListHelpers.hpp"
#include "Teuchos_TimeMonitor.hpp"
#include "Teuchos_DefaultComm.hpp"

#include "Thyra_VectorStdOps.hpp"
#include "Thyra_MultiVectorStdOps.hpp"

#include "Tempus_IntegratorBasic.hpp"
#include "Tempus_IntegratorAdjointSensitivity.hpp"

#include "Thyra_DefaultMultiVectorProductVector.hpp"
#include "Thyra_DefaultProductVector.hpp"

#include "../TestModels/SinCosModel.hpp"
#include "../TestUtils/Tempus_ConvergenceTestUtils.hpp"

#include <fstream>
#include <vector>

namespace Tempus_Test {

using Teuchos::RCP;
using Teuchos::ParameterList;
using Teuchos::sublist;
using Teuchos::getParametersFromXmlFile;

using Tempus::IntegratorBasic;
using Tempus::SolutionHistory;
using Tempus::SolutionState;

// ************************************************************
// ************************************************************
TEUCHOS_UNIT_TEST(DIRK, SinCos_ASA)
{
  std::vector<std::string> RKMethods;
  RKMethods.push_back("RK Backward Euler");
  RKMethods.push_back("IRK 1 Stage Theta Method");
  RKMethods.push_back("SDIRK 1 Stage 1st order");
  RKMethods.push_back("SDIRK 2 Stage 2nd order");
  RKMethods.push_back("SDIRK 2 Stage 3rd order");
  RKMethods.push_back("EDIRK 2 Stage 3rd order");
  RKMethods.push_back("EDIRK 2 Stage Theta Method");
  RKMethods.push_back("SDIRK 3 Stage 4th order");
  RKMethods.push_back("SDIRK 5 Stage 4th order");
  RKMethods.push_back("SDIRK 5 Stage 5th order");

  std::vector<double> RKMethodErrors;
  RKMethodErrors.push_back(0.0383339);
  RKMethodErrors.push_back(0.000221028);
  RKMethodErrors.push_back(0.0383339);
  RKMethodErrors.push_back(8.48235e-05);
  RKMethodErrors.push_back(4.87848e-06);
  RKMethodErrors.push_back(7.30827e-07);
  RKMethodErrors.push_back(0.0144662);
  RKMethodErrors.push_back(3.10132e-07);
  RKMethodErrors.push_back(7.56838e-10);
  RKMethodErrors.push_back(1.32374e-10);

  Teuchos::RCP<const Teuchos::Comm<int> > comm =
    Teuchos::DefaultComm<int>::getComm();
  Teuchos::RCP<Teuchos::FancyOStream> my_out =
    Teuchos::fancyOStream(Teuchos::rcpFromRef(std::cout));
  my_out->setProcRankAndSize(comm->getRank(), comm->getSize());
  my_out->setOutputToRootOnly(0);

  for(std::vector<std::string>::size_type m = 0; m != RKMethods.size(); m++) {

    std::string RKMethod_ = RKMethods[m];
    std::replace(RKMethod_.begin(), RKMethod_.end(), ' ', '_');
    std::replace(RKMethod_.begin(), RKMethod_.end(), '/', '.');
    std::vector<double> StepSize;
    std::vector<double> ErrorNorm;
    const int nTimeStepSizes = 3; // 7 for error plots
    double dt = 0.05;
    double order = 0.0;
    for (int n=0; n<nTimeStepSizes; n++) {

      // Read params from .xml file
      RCP<ParameterList> pList =
        getParametersFromXmlFile("Tempus_DIRK_SinCos.xml");

      // Setup the SinCosModel
      RCP<ParameterList> scm_pl = sublist(pList, "SinCosModel", true);
      RCP<SinCosModel<double> > model =
        Teuchos::rcp(new SinCosModel<double>(scm_pl));

      // Set the Stepper
      RCP<ParameterList> pl = sublist(pList, "Tempus", true);
      pl->sublist("Default Stepper").set("Stepper Type", RKMethods[m]);
      if (RKMethods[m] == "IRK 1 Stage Theta Method" ||
          RKMethods[m] == "EDIRK 2 Stage Theta Method") {
        pl->sublist("Default Stepper").set<double>("theta", 0.5);
      } else if (RKMethods[m] == "SDIRK 2 Stage 2nd order") {
        pl->sublist("Default Stepper").set("gamma", 0.2928932188134524);
      } else if (RKMethods[m] == "SDIRK 2 Stage 3rd order") {
        pl->sublist("Default Stepper").set("3rd Order A-stable", true);
        pl->sublist("Default Stepper").set("2nd Order L-stable", false);
        pl->sublist("Default Stepper").set("gamma", 0.7886751345948128);
      }

      dt /= 2;

      // Setup sensitivities
      ParameterList& sens_pl = pl->sublist("Sensitivities");
      sens_pl.set("Mass Matrix Is Identity", true); // Necessary for explicit
      ParameterList& interp_pl =
        pl->sublist("Default Integrator").sublist("Solution History").sublist("Interpolator");
      interp_pl.set("Interpolator Type", "Lagrange");
      interp_pl.set("Order", 4); // All RK methods here are at most 5th order

      // Setup the Integrator and reset initial time step
      pl->sublist("Default Integrator")
         .sublist("Time Step Control").set("Initial Time Step", dt);
      RCP<Tempus::IntegratorAdjointSensitivity<double> > integrator =
        Tempus::integratorAdjointSensitivity<double>(pl, model);
      order = integrator->getStepper()->getOrder();

      // Fixme - order should be 2, but only gets first order?
      if (RKMethods[m] == "EDIRK 2 Stage Theta Method") order = 1.0;

      // Initial Conditions
      // During the Integrator construction, the initial SolutionState
      // is set by default to model->getNominalVales().get_x().  However,
      // the application can set it also by integrator->initializeSolutionHistory.
      RCP<Thyra::VectorBase<double> > x0 =
        model->getNominalValues().get_x()->clone_v();
      const int num_param = model->get_p_space(0)->dim();
      RCP<Thyra::MultiVectorBase<double> > DxDp0 =
        Thyra::createMembers(model->get_x_space(), num_param);
      for (int i=0; i<num_param; ++i)
        Thyra::assign(DxDp0->col(i).ptr(),
                      *(model->getExactSensSolution(i, 0.0).get_x()));
      integrator->initializeSolutionHistory(0.0, x0, Teuchos::null, Teuchos::null,
                                  DxDp0, Teuchos::null, Teuchos::null);

      // Integrate to timeMax
      bool integratorStatus = integrator->advanceTime();
      TEST_ASSERT(integratorStatus)

      // Test if at 'Final Time'
      double time = integrator->getTime();
      double timeFinal = pl->sublist("Default Integrator")
        .sublist("Time Step Control").get<double>("Final Time");
      double tol = 100.0 * std::numeric_limits<double>::epsilon();
      TEST_FLOATING_EQUALITY(time, timeFinal, tol);

      // Time-integrated solution and the exact solution along with
      // sensitivities (relying on response g(x) = x).  Note we must transpose
      // dg/dp since the integrator returns it in gradient form.
      RCP<const Thyra::VectorBase<double> > x = integrator->getX();
      RCP<const Thyra::MultiVectorBase<double> > DgDp = integrator->getDgDp();
      RCP<Thyra::MultiVectorBase<double> > DxDp =
        Thyra::createMembers(model->get_x_space(), num_param);
      {
        Thyra::ConstDetachedMultiVectorView<double> dgdp_view(*DgDp);
        Thyra::DetachedMultiVectorView<double> dxdp_view(*DxDp);
        const int num_g = DgDp->domain()->dim();
        for (int i=0; i<num_g; ++i)
          for (int j=0; j<num_param; ++j)
            dxdp_view(i,j) = dgdp_view(j,i);
      }
      RCP<const Thyra::VectorBase<double> > x_exact =
        model->getExactSolution(time).get_x();
      RCP<Thyra::MultiVectorBase<double> > DxDp_exact =
        Thyra::createMembers(model->get_x_space(), num_param);
      for (int i=0; i<num_param; ++i)
        Thyra::assign(DxDp_exact->col(i).ptr(),
                      *(model->getExactSensSolution(i, time).get_x()));

      // Plot sample solution and exact solution
      if (comm->getRank() == 0 && n == nTimeStepSizes-1) {
        typedef Thyra::DefaultProductVector<double> DPV;
        typedef Thyra::DefaultMultiVectorProductVector<double> DMVPV;

        std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_AdjSens.dat");
        RCP<const SolutionHistory<double> > solutionHistory =
          integrator->getSolutionHistory();
        for (int i=0; i<solutionHistory->getNumStates(); i++) {
          RCP<const SolutionState<double> > solutionState =
            (*solutionHistory)[i];
          const double time_i = solutionState->getTime();
          RCP<const DPV> x_prod_plot =
            Teuchos::rcp_dynamic_cast<const DPV>(solutionState->getX());
          RCP<const Thyra::VectorBase<double> > x_plot =
            x_prod_plot->getVectorBlock(0);
          RCP<const DMVPV > adjoint_prod_plot =
            Teuchos::rcp_dynamic_cast<const DMVPV>(x_prod_plot->getVectorBlock(1));
          RCP<const Thyra::MultiVectorBase<double> > adjoint_plot =
            adjoint_prod_plot->getMultiVector();
          RCP<const Thyra::VectorBase<double> > x_exact_plot =
            model->getExactSolution(time_i).get_x();
          ftmp << std::fixed << std::setprecision(7)
               << time_i
               << std::setw(11) << get_ele(*(x_plot), 0)
               << std::setw(11) << get_ele(*(x_plot), 1)
               << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 0)
               << std::setw(11) << get_ele(*(adjoint_plot->col(0)), 1)
               << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 0)
               << std::setw(11) << get_ele(*(adjoint_plot->col(1)), 1)
               << std::setw(11) << get_ele(*(x_exact_plot), 0)
               << std::setw(11) << get_ele(*(x_exact_plot), 1)
               << std::endl;
        }
        ftmp.close();
      }

      // Calculate the error
      RCP<Thyra::VectorBase<double> > xdiff = x->clone_v();
      RCP<Thyra::MultiVectorBase<double> > DxDpdiff = DxDp->clone_mv();
      Thyra::V_StVpStV(xdiff.ptr(), 1.0, *x_exact, -1.0, *(x));
      Thyra::V_VmV(DxDpdiff.ptr(), *DxDp_exact, *DxDp);
      StepSize.push_back(dt);
      double L2norm = Thyra::norm_2(*xdiff);
      L2norm *= L2norm;
      Teuchos::Array<double> L2norm_DxDp(num_param);
      Thyra::norms_2(*DxDpdiff, L2norm_DxDp());
      for (int i=0; i<num_param; ++i)
        L2norm += L2norm_DxDp[i]*L2norm_DxDp[i];
      L2norm = std::sqrt(L2norm);
      ErrorNorm.push_back(L2norm);

      *my_out << " n = " << n << " dt = " << dt << " error = " << L2norm
              << std::endl;
    }

    if (comm->getRank() == 0) {
      std::ofstream ftmp("Tempus_"+RKMethod_+"_SinCos_AdjSens-Error.dat");
      double error0 = 0.8*ErrorNorm[0];
      for (int n=0; n<(int)StepSize.size(); n++) {
        ftmp << StepSize[n]  << "   " << ErrorNorm[n] << "   "
             << error0*(pow(StepSize[n]/StepSize[0],order)) << std::endl;
      }
      ftmp.close();
    }

    //if (RKMethods[m] == "SDIRK 5 Stage 4th order") {
    //  StepSize.pop_back();  StepSize.pop_back();
    //  ErrorNorm.pop_back(); ErrorNorm.pop_back();
    //} else if (RKMethods[m] == "SDIRK 5 Stage 5th order") {
    //  StepSize.pop_back();  StepSize.pop_back();  StepSize.pop_back();
    //  ErrorNorm.pop_back(); ErrorNorm.pop_back(); ErrorNorm.pop_back();
    //}

    // Check the order and intercept
    double slope = computeLinearRegressionLogLog<double>(StepSize, ErrorNorm);
    *my_out << "  Stepper = " << RKMethods[m] << std::endl;
    *my_out << "  =========================" << std::endl;
    *my_out << "  Expected order: " << order << std::endl;
    *my_out << "  Observed order: " << slope << std::endl;
    *my_out << "  =========================" << std::endl;
    TEST_FLOATING_EQUALITY( slope, order, 0.03 );
    TEST_FLOATING_EQUALITY( ErrorNorm[0], RKMethodErrors[m], 5.0e-4 );

  }
  Teuchos::TimeMonitor::summarize();
}

} // namespace Tempus_Test