nox_example.cpp

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#include <iostream>
#include <sstream>

// NOX
#include "NOX.H"
#include "NOX_Epetra.H"

// Epetra communicator
#ifdef HAVE_MPI
#include "Epetra_MpiComm.h"
#else
#include "Epetra_SerialComm.h"
#endif

// Stokhos Stochastic Galerkin
#include "Stokhos_Epetra.hpp"

// Timing utilities
#include "Teuchos_TimeMonitor.hpp"

// Our model
#include "SimpleME.hpp"

int main(int argc, char *argv[]) {

// Initialize MPI
#ifdef HAVE_MPI
  MPI_Init(&argc,&argv);
#endif

  int MyPID;

  try {

    // Create a communicator for Epetra objects
    Teuchos::RCP<const Epetra_Comm> globalComm;
#ifdef HAVE_MPI
    globalComm = Teuchos::rcp(new Epetra_MpiComm(MPI_COMM_WORLD));
#else
    globalComm = Teuchos::rcp(new Epetra_SerialComm);
#endif
    MyPID = globalComm->MyPID();
    
    // Create Stochastic Galerkin basis and expansion
    int p = 5;
    Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > bases(1); 
    bases[0] = Teuchos::rcp(new Stokhos::LegendreBasis<int,double>(p));
    Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> > basis = 
      Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(bases));
    int sz = basis->size();
    Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > Cijk;
    Cijk = basis->computeTripleProductTensor();
    Teuchos::RCP<Stokhos::OrthogPolyExpansion<int,double> > expansion = 
      Teuchos::rcp(new Stokhos::AlgebraicOrthogPolyExpansion<int,double>(basis,
                   Cijk));
    if (MyPID == 0)
      std::cout << "Stochastic Galerkin expansion size = " << sz << std::endl;

    // Create stochastic parallel distribution
    int num_spatial_procs = -1;
    Teuchos::ParameterList parallelParams;
    parallelParams.set("Number of Spatial Processors", num_spatial_procs);
    Teuchos::RCP<Stokhos::ParallelData> sg_parallel_data =
      Teuchos::rcp(new Stokhos::ParallelData(basis, Cijk, globalComm,
               parallelParams));
    Teuchos::RCP<const EpetraExt::MultiComm> sg_comm = 
      sg_parallel_data->getMultiComm();
    Teuchos::RCP<const Epetra_Comm> app_comm = 
      sg_parallel_data->getSpatialComm();
    
    // Create application model evaluator
    Teuchos::RCP<EpetraExt::ModelEvaluator> model = 
      Teuchos::rcp(new SimpleME(app_comm));
    
    // Setup stochastic Galerkin algorithmic parameters
    Teuchos::RCP<Teuchos::ParameterList> sgParams = 
      Teuchos::rcp(new Teuchos::ParameterList);
    sgParams->set("Jacobian Method", "Matrix Free");
    sgParams->set("Mean Preconditioner Type", "Ifpack");

    // Create stochastic Galerkin model evaluator
    Teuchos::RCP<Stokhos::SGModelEvaluator> sg_model =
      Teuchos::rcp(new Stokhos::SGModelEvaluator(model, basis, Teuchos::null,
                 expansion, sg_parallel_data, 
             sgParams));

    // Stochastic Galerkin initial guess
    // Set the mean to the deterministic initial guess, higher-order terms
    // to zero
    Teuchos::RCP<Stokhos::EpetraVectorOrthogPoly> x_init_sg = 
      sg_model->create_x_sg();
    x_init_sg->init(0.0);
    (*x_init_sg)[0] = *(model->get_x_init());
    sg_model->set_x_sg_init(*x_init_sg);

    // Stochastic Galerkin parameters
    // Linear expansion with the mean given by the deterministic initial
    // parameter values, linear terms equal to 1, and higher order terms
    // equal to zero.
    Teuchos::RCP<Stokhos::EpetraVectorOrthogPoly> p_init_sg =
      sg_model->create_p_sg(0);
    p_init_sg->init(0.0);
    (*p_init_sg)[0] = *(model->get_p_init(0));
    for (int i=0; i<model->get_p_map(0)->NumMyElements(); i++)
      (*p_init_sg)[i+1][i] = 1.0;
    sg_model->set_p_sg_init(0, *p_init_sg);
    std::cout << "Stochatic Galerkin parameter expansion = " << std::endl
        << *p_init_sg << std::endl;

    // Set up NOX parameters
    Teuchos::RCP<Teuchos::ParameterList> noxParams =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Set the nonlinear solver method
    noxParams->set("Nonlinear Solver", "Line Search Based");

    // Set the printing parameters in the "Printing" sublist
    Teuchos::ParameterList& printParams = noxParams->sublist("Printing");
    printParams.set("MyPID", MyPID); 
    printParams.set("Output Precision", 3);
    printParams.set("Output Processor", 0);
    printParams.set("Output Information", 
                    NOX::Utils::OuterIteration + 
                    NOX::Utils::OuterIterationStatusTest + 
                    NOX::Utils::InnerIteration +
                    //NOX::Utils::Parameters + 
                    //NOX::Utils::Details + 
                    NOX::Utils::LinearSolverDetails +
                    NOX::Utils::Warning + 
                    NOX::Utils::Error);

    // Create printing utilities
    NOX::Utils utils(printParams);

    // Sublist for line search 
    Teuchos::ParameterList& searchParams = noxParams->sublist("Line Search");
    searchParams.set("Method", "Full Step");

    // Sublist for direction
    Teuchos::ParameterList& dirParams = noxParams->sublist("Direction");
    dirParams.set("Method", "Newton");
    Teuchos::ParameterList& newtonParams = dirParams.sublist("Newton");
    newtonParams.set("Forcing Term Method", "Constant");

    // Sublist for linear solver for the Newton method
    Teuchos::ParameterList& lsParams = newtonParams.sublist("Linear Solver");
    lsParams.set("Aztec Solver", "GMRES");  
    lsParams.set("Max Iterations", 100);
    lsParams.set("Size of Krylov Subspace", 100);
    lsParams.set("Tolerance", 1e-4); 
    lsParams.set("Output Frequency", 10);
    lsParams.set("Preconditioner", "Ifpack");

    // Sublist for convergence tests
    Teuchos::ParameterList& statusParams = noxParams->sublist("Status Tests");
    statusParams.set("Test Type", "Combo");
    statusParams.set("Number of Tests", 2);
    statusParams.set("Combo Type", "OR");
    Teuchos::ParameterList& normF = statusParams.sublist("Test 0");
    normF.set("Test Type", "NormF");
    normF.set("Tolerance", 1e-10);
    normF.set("Scale Type", "Scaled");
    Teuchos::ParameterList& maxIters = statusParams.sublist("Test 1");
    maxIters.set("Test Type", "MaxIters");
    maxIters.set("Maximum Iterations", 10);

    // Create NOX interface
    Teuchos::RCP<NOX::Epetra::ModelEvaluatorInterface> nox_interface = 
       Teuchos::rcp(new NOX::Epetra::ModelEvaluatorInterface(sg_model));

    // Create NOX linear system object
    Teuchos::RCP<const Epetra_Vector> u = sg_model->get_x_init();
    Teuchos::RCP<Epetra_Operator> A = sg_model->create_W();
    Teuchos::RCP<NOX::Epetra::Interface::Required> iReq = nox_interface;
    Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = nox_interface;
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys;
    Teuchos::RCP<Epetra_Operator> M = sg_model->create_WPrec()->PrecOp;
    Teuchos::RCP<NOX::Epetra::Interface::Preconditioner> iPrec = nox_interface;
    lsParams.set("Preconditioner", "User Defined");
    linsys = 
      Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
                  iJac, A, iPrec, M,
                  *u));
    // linsys = 
    //   Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
    //              iReq, iJac, A, *u));

    // Build NOX group
    Teuchos::RCP<NOX::Epetra::Group> grp = 
      Teuchos::rcp(new NOX::Epetra::Group(printParams, iReq, *u, linsys));

    // Create the Solver convergence test
    Teuchos::RCP<NOX::StatusTest::Generic> statusTests =
      NOX::StatusTest::buildStatusTests(statusParams, utils);

    // Create the solver
    Teuchos::RCP<NOX::Solver::Generic> solver = 
      NOX::Solver::buildSolver(grp, statusTests, noxParams);

    // Solve the system
    NOX::StatusTest::StatusType status = solver->solve();

    // Get final solution
    const NOX::Epetra::Group& finalGroup = 
      dynamic_cast<const NOX::Epetra::Group&>(solver->getSolutionGroup());
    const Epetra_Vector& finalSolution = 
      (dynamic_cast<const NOX::Epetra::Vector&>(finalGroup.getX())).getEpetraVector();

    // Convert block Epetra_Vector to orthogonal polynomial of Epetra_Vector's
    Teuchos::RCP<Stokhos::EpetraVectorOrthogPoly> x_sg =
      sg_model->create_x_sg(View, &finalSolution);

    utils.out() << "Final Solution (block vector) = " << std::endl;
    std::cout << finalSolution << std::endl;
    utils.out() << "Final Solution (polynomial) = " << std::endl;
    std::cout << *x_sg << std::endl;

    if (status == NOX::StatusTest::Converged && MyPID == 0) 
      utils.out() << "Example Passed!" << std::endl;

  }
  
  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
  }
  catch (std::string& s) {
    std::cout << s << std::endl;
  }
  catch (char *s) {
    std::cout << s << std::endl;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
  }

#ifdef HAVE_MPI
  MPI_Finalize() ;
#endif

}