Beispiel #1
0
int main(int argc, char *argv[])
{
  int n = 100;
  double alpha = 0.0;
  double beta = 0.0;
  double scale = 1.0;
  int maxNewtonIters = 20;
  int ierr = 0;

  alpha = alpha / scale;

  try {

    bool verbose = false;
    // Check for verbose output
    if (argc>1)
      if (argv[1][0]=='-' && argv[1][1]=='v') 
	verbose = true;

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    stepperList.set("Continuation Parameter", "alpha");
    stepperList.set("Initial Value", alpha);
    stepperList.set("Max Value", 5.0/scale);
    stepperList.set("Min Value", 0.0/scale);
    stepperList.set("Max Steps", 50);
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters);

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Initial Step Size", 0.1/scale);
    stepSizeList.set("Min Step Size", 1.0e-3/scale);
    stepSizeList.set("Max Step Size", 10.0/scale);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    if (verbose)
       nlPrintParams.set("Output Information", 
			 NOX::Utils::Error +
			 NOX::Utils::Details +
			 NOX::Utils::OuterIteration + 
			 NOX::Utils::InnerIteration + 
			 NOX::Utils::Warning +
			 NOX::Utils::TestDetails + 
			 NOX::Utils::StepperIteration +
			 NOX::Utils::StepperDetails +
			 NOX::Utils::StepperParameters);
     else
       nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList);

    // Set up the problem interface
    ChanProblemInterface chan(globalData, n, alpha, beta, scale);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("scale",scale);
  
    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    Teuchos::RCP<LOCA::MultiContinuation::AbstractGroup> grp =
      Teuchos::rcp(new LOCA::LAPACK::Group(globalData, chan));
    
    grp->setParams(p);

    // Set up the status tests
    Teuchos::RCP<NOX::StatusTest::NormF> normF = 
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxIters =
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Generic> comboOR =
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR,
					      normF,
					      maxIters));

    // Create the stepper  
    LOCA::Stepper stepper(globalData, grp, comboOR, paramList);

    // Perform continuation run
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    // Check for convergence
    if (status != LOCA::Abstract::Iterator::Finished) {
      ierr = 1;
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() 
	  << "Stepper failed to converge!" << std::endl;
    }

    // Get the final solution from the stepper
    Teuchos::RCP<const LOCA::LAPACK::Group> finalGroup =
      Teuchos::rcp_dynamic_cast<const LOCA::LAPACK::Group>(stepper.getSolutionGroup());
    const NOX::LAPACK::Vector& finalSolution = 
      dynamic_cast<const NOX::LAPACK::Vector&>(finalGroup->getX());

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    // Check some statistics on the solution
    NOX::TestCompare testCompare(globalData->locaUtils->out(), 
				 *(globalData->locaUtils));

    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() 
	<< std::endl 
	<< "***** Checking solution statistics *****" 
	<< std::endl;
  
    // Check number of steps
    int numSteps = stepper.getStepNumber();
    int numSteps_expected = 32;
    ierr += testCompare.testValue(numSteps, numSteps_expected, 0.0,
				  "number of continuation steps",
				  NOX::TestCompare::Absolute);

    // Check number of failed steps
    int numFailedSteps = stepper.getNumFailedSteps();
    int numFailedSteps_expected = 0;
    ierr += testCompare.testValue(numFailedSteps, numFailedSteps_expected, 0.0,
				  "number of failed continuation steps",
				  NOX::TestCompare::Absolute);

    // Check final value of continuation parameter
    double alpha_final = finalGroup->getParam("alpha");
    double alpha_expected = 5.0;
    ierr += testCompare.testValue(alpha_final, alpha_expected, 1.0e-14,
				  "final value of continuation parameter", 
				  NOX::TestCompare::Relative);
 
    // Check norm of solution
    double norm_x = finalSolution.norm();
    double norm_x_expected = 203.1991024;
    ierr += testCompare.testValue(norm_x, norm_x_expected, 1.0e-7,
				  "norm of final solution",
				  NOX::TestCompare::Relative);

    LOCA::destroyGlobalData(globalData);
  }

  catch (std::exception& e) {
    cout << e.what() << endl;
    ierr = 1;
  }
  catch (const char *s) {
    cout << s << endl;
    ierr = 1;
  }
  catch (...) {
    cout << "Caught unknown exception!" << endl;
    ierr = 1;
  }

  if (ierr == 0)
    cout << "All tests passed!" << endl;
  else
    cout << ierr << " test(s) failed!" << endl;

  return ierr;
}
int main()
{
  double pi = 4.0*atan(1.0);
  int n = 100;
  double alpha = 0.25;
  double D1 = 1.0/40.0;
  double D2 = 1.0/40.0;
  double beta = 2.0*pi*pi*D1 + 1.0 + alpha*alpha;
  int maxNewtonIters = 10;

  try {
    // Create output file to save solutions
    ofstream outFile("BrusselatorHopfContinuation.dat");
    outFile.setf(ios::scientific, ios::floatfield);
    outFile.precision(14);

    // Save size of discretizations
    outFile << n << endl;

    // Create initial guess for the real and imaginary eigenvectors
    NOX::LAPACK::Vector y(2*n), z(2*n);
    double h = 1.0 / double(n-1);
    double lambda_real = (beta - 1.0 - alpha*alpha)/2.0;
    double lambda_imag = sqrt(alpha*alpha - lambda_real*lambda_real);
    double v1_real = -alpha*alpha;
    double v1_imag = 0.0;
    double v2_real = beta - 1.0 - lambda_real;
    double v2_imag = -lambda_imag;
    double x;
    for (int i=0; i<n; i++) {
      x = sin(pi*h*i);
      y(i) = v1_real*x;
      z(i) = v1_imag*x;

      y(i+n) = v2_real*x;
      z(i+n) = v2_imag*x;
    }

    // Initial guess for frequency (valid for |alpha| > (pi^2)*|D1|)
    double w = lambda_imag;

    // Create length scaling vector (phi)
    NOX::LAPACK::Vector phi(2*n);
    phi.init(1.0);

    Teuchos::RCP<NOX::Abstract::Vector> y_vec =
      Teuchos::rcp(&y,false);
    Teuchos::RCP<NOX::Abstract::Vector> z_vec =
      Teuchos::rcp(&z,false);
    Teuchos::RCP<NOX::Abstract::Vector> phi_vec =
      Teuchos::rcp(&phi,false);

    // Create initial values for a and b for minimally augmented method
    Teuchos::RCP<NOX::Abstract::Vector> a_vec_real = 
      Teuchos::rcp(new NOX::LAPACK::Vector(2*n));
    Teuchos::RCP<NOX::Abstract::Vector> a_vec_imag = 
      Teuchos::rcp(new NOX::LAPACK::Vector(2*n));
    Teuchos::RCP<NOX::Abstract::Vector> b_vec_real = 
      Teuchos::rcp(new NOX::LAPACK::Vector(2*n));
    Teuchos::RCP<NOX::Abstract::Vector> b_vec_imag = 
      Teuchos::rcp(new NOX::LAPACK::Vector(2*n));
    *a_vec_real = *y_vec;
    *a_vec_imag = *z_vec;
    *b_vec_real = *y_vec;
    *b_vec_imag = *z_vec;

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList = 
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    stepperList.set("Continuation Method", "Arc Length");   // Default
    //stepperList.set("Continuation Method", "Natural");   // Default
    stepperList.set("Continuation Parameter", "alpha");
    stepperList.set("Initial Value", alpha);
    stepperList.set("Max Value", 1.0);
    stepperList.set("Min Value", 0.24);
    stepperList.set("Max Steps", 100);
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters);

    // Create bifurcation sublist
    Teuchos::ParameterList& bifurcationList = 
      locaParamsList.sublist("Bifurcation");
    bifurcationList.set("Type", "Hopf");
    bifurcationList.set("Bifurcation Parameter", "beta");        // Must set
    bifurcationList.set("Initial Frequency", w);                 // Must set

//     // For Moore-Spence Formulation
//     bifurcationList.set("Formulation", "Moore-Spence");          // Default
//     bifurcationList.set("Solver Method", "Salinger Bordering");  // Default    
//     bifurcationList.set("Length Normalization Vector", phi_vec); // Must set
//     bifurcationList.set("Initial Real Eigenvector", y_vec);      // Must set
//     bifurcationList.set("Initial Imaginary Eigenvector", z_vec); // Must set

    // For minimally augmented formulation
    bifurcationList.set("Formulation", "Minimally Augmented");
    bifurcationList.set("Initial Real A Vector", a_vec_real);       // Must set
    bifurcationList.set("Initial Imaginary A Vector", a_vec_imag);  // Must set
    bifurcationList.set("Initial Real B Vector", b_vec_real);       // Must set
    bifurcationList.set("Initial Imaginary B Vector", b_vec_imag);  // Must set
    bifurcationList.set("Update Null Vectors Every Continuation Step", true);

    // For minimally augmented method, should set these for good performance
    // Direct solve of bordered equations
    bifurcationList.set("Bordered Solver Method",  "LAPACK Direct Solve");
    // Combine arc-length and turning point bordered rows & columns
    stepperList.set("Bordered Solver Method", "Nested");
    Teuchos::ParameterList& nestedList = 
      stepperList.sublist("Nested Bordered Solver");
    // Direct solve of combined bordered system
    nestedList.set("Bordered Solver Method", "LAPACK Direct Solve");

    // Create predictor sublist
    Teuchos::ParameterList& predictorList = 
      locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Secant");     // Default

//     // Should use w/Secant predictor & Moore-Spence formulation
//     Teuchos::ParameterList& firstStepPredictor 
//       = predictorList.sublist("First Step Predictor");
//     firstStepPredictor.set("Method", "Random");
//     firstStepPredictor.set("Epsilon", 1.0e-3);

//     // Should use w/Secant predictor & Moore-Spence fomulation
//     Teuchos::ParameterList& lastStepPredictor 
//       = predictorList.sublist("Last Step Predictor");
//     lastStepPredictor.set("Method", "Random");
//     lastStepPredictor.set("Epsilon", 1.0e-3);

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Method", "Adaptive");      // Default
    stepSizeList.set("Initial Step Size", 0.02);
    stepSizeList.set("Min Step Size", 1.0e-3);
    stepSizeList.set("Max Step Size", 0.1);
    stepSizeList.set("Aggressiveness", 0.5);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("Output Precision", 3);
    nlPrintParams.set("Output Information", 
		      NOX::Utils::OuterIteration + 
		      NOX::Utils::OuterIterationStatusTest + 
		      NOX::Utils::InnerIteration +
		      NOX::Utils::Details + 
		      NOX::Utils::Warning + 
		      NOX::Utils::StepperIteration +
		      NOX::Utils::StepperDetails +
		      NOX::Utils::StepperParameters);

    // Create the "Line Search" sublist for the "Line Search Based" solver
    Teuchos::ParameterList& searchParams = nlParams.sublist("Line Search");
    searchParams.set("Method", "Full Step");

    // Create LAPACK Factory
    Teuchos::RCP<LOCA::LAPACK::Factory> lapackFactory = 
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, lapackFactory);

     // Set up the problem interface
    BrusselatorProblemInterface brus(globalData, n, alpha, beta, D1, D2, 
				     outFile);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("D1",D1);
    p.addParameter("D2",D2);

    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    Teuchos::RCP<LOCA::LAPACK::Group> grp = 
      Teuchos::rcp(new LOCA::LAPACK::Group(globalData, brus));

    grp->setParams(p);

    // Set up the status tests
    Teuchos::RCP<NOX::StatusTest::NormF> statusTestA = 
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-10, 
					      NOX::StatusTest::NormF::Scaled));
    Teuchos::RCP<NOX::StatusTest::MaxIters> statusTestB = 
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Combo> combo = 
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR, 
					      statusTestA, statusTestB));

    // Create the stepper  
    LOCA::Stepper stepper(globalData, grp, combo, paramList);

    // Solve the nonlinear system
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    if (status == LOCA::Abstract::Iterator::Finished) 
      cout << "All examples passed" << endl;
    else {
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() 
	  << "Stepper failed to converge!" << std::endl;
    }

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    outFile.close();

    LOCA::destroyGlobalData(globalData);
  }

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

  return 0;
}
Beispiel #3
0
int main( int argc, char **argv )
{

// check for parallel computation
#ifdef HAVE_MPI
  MPI_Init(&argc, &argv);
  Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
  Epetra_SerialComm Comm;
#endif


// define main parameters

  double c = 0.25;             // continuation parameter
  int N = 50;                  // number of grid points
  int maxNewtonIters = 20;     // max number of Newton iterations
  int maxSteps = 75;           // max number of continuation steps taken

// Set flag for whether the computations will be Matrix-free (true) or will use a computed
//   Jacobian (false)
  bool doMatFree = false;      
      
// Create output file to save solutions
  ofstream outFile("Heq4.dat");
  outFile.setf(ios::scientific, ios::floatfield);
  outFile.precision(10);

// Define the problem class
  HeqProblem Problem(N,&Comm,outFile);
  
// Create the initial guess vector and set it to all ones
  Epetra_Vector InitialGuess(Problem.GetMap());
  InitialGuess.PutScalar(1.0);     

// Create the top level parameter list
  Teuchos::RCP<Teuchos::ParameterList> ParamList = Teuchos::rcp(new Teuchos::ParameterList);

  // Create LOCA sublist
  Teuchos::ParameterList& locaParamsList = ParamList->sublist("LOCA");

  // Create the sublist for continuation and set the stepper parameters
  Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
  stepperList.set("Continuation Method", "Arc Length");// Default
  // stepperList.set("Continuation Method", "Natural");
  stepperList.set("Continuation Parameter", "c");  // Must set
  stepperList.set("Initial Value", c);             // Must set
  stepperList.set("Max Value", 100.0);             // Must set
  stepperList.set("Min Value", 0.0);             // Must set
  stepperList.set("Max Steps", maxSteps);                    // Should set
  stepperList.set("Max Nonlinear Iterations", maxNewtonIters); // Should set

// Set up parameters to compute Eigenvalues
#ifdef HAVE_LOCA_ANASAZI
  // Create Anasazi Eigensolver sublist (needs --with-loca-anasazi)
  stepperList.set("Compute Eigenvalues",true);
  Teuchos::ParameterList& aList = stepperList.sublist("Eigensolver");
  aList.set("Method", "Anasazi");
  aList.set("Block Size", 1);        // Size of blocks
  aList.set("Num Blocks", 20);       // Size of Arnoldi factorization
  aList.set("Num Eigenvalues", 5);   // Number of eigenvalues
  //  aList.set("Sorting Order", "SR");
  aList.set("Convergence Tolerance", 2.0e-7);          // Tolerance
  aList.set("Step Size", 1);         // How often to check convergence
  aList.set("Maximum Restarts",2);   // Maximum number of restarts
  aList.set("Verbosity",  
	    Anasazi::Errors + 
	    Anasazi::Warnings +
	    Anasazi::FinalSummary);        // Verbosity
#else
    stepperList.set("Compute Eigenvalues",false);
#endif
 
    stepperList.set("Bordered Solver Method", "Householder");
//    stepperList.set("Bordered Solver Method", "Bordering");

  //  Teuchos::ParameterList& nestedList = 
  //    stepperList.sublist("Nested Bordered Solver");
  //  nestedList.set("Bordered Solver Method", "Householder");
  //  nestedList.set("Include UV In Preconditioner", true);
  //  //nestedList.set("Use P For Preconditioner", true);
  //  nestedList.set("Preconditioner Method", "SMW");

 
// Create bifurcation sublist -- use if not doing turning point
  Teuchos::ParameterList& bifurcationList = locaParamsList.sublist("Bifurcation");
  bifurcationList.set("Type", "None");                 // Default

  // Create predictor sublist
  Teuchos::ParameterList& predictorList = locaParamsList.sublist("Predictor");
  predictorList.set("Method", "Secant");               // Default
  // predictorList.set("Method", "Constant");     // Other options
  // predictorList.set("Method", "Tangent");      // Other options

  // Create step size sublist
  Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
  stepSizeList.set("Method", "Adaptive");             // Default
  stepSizeList.set("Initial Step Size", 0.1);   // Should set
  stepSizeList.set("Min Step Size", 1.0e-4);    // Should set
  stepSizeList.set("Max Step Size", 1.0);      // Should set
  stepSizeList.set("Aggressiveness", 0.1);

  // Set up NOX info
  Teuchos::ParameterList& nlParams = ParamList->sublist("NOX");

  // Set the nonlinear solver method
  nlParams.set("Nonlinear Solver", "Line Search Based");

  // Set the printing parameters in the "Printing" sublist
  Teuchos::ParameterList& printParams = nlParams.sublist("Printing");
  printParams.set("MyPID", Comm.MyPID()); 
  printParams.set("Output Precision", 5);
  printParams.set("Output Processor", 0);
  printParams.set("Output Information", 
			NOX::Utils::OuterIteration + 
			NOX::Utils::OuterIterationStatusTest + 
			NOX::Utils::InnerIteration +
			NOX::Utils::LinearSolverDetails +
			NOX::Utils::Parameters + 
			NOX::Utils::Details + 
			NOX::Utils::Warning +
         NOX::Utils::StepperIteration +
         NOX::Utils::StepperDetails +
         NOX::Utils::StepperParameters);


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

  // Sublist for direction
  Teuchos::ParameterList& dirParams = nlParams.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", 800);  
  lsParams.set("Tolerance", 1e-8);
  lsParams.set("Output Frequency", 1);    
  lsParams.set("Preconditioner", "None");
//  lsParams.set("Preconditioner", "AztecOO");
//  lsParams.set("Aztec Preconditioner", "ilu"); 
//  lsParams.set("Preconditioner", "Ifpack");
//  lsParams.set("Ifpack Preconditioner", "ILU");
//  lsParams.set("Preconditioner", "New Ifpack");
//  Teuchos::ParameterList& ifpackParams = lsParams.sublist("Ifpack");
//    ifpackParams.set("fact: level-of-fill", 1);


  // set up the continuation parameter vector
  LOCA::ParameterVector p;
  p.addParameter("c",c);  

  // Set up the problem interface
  Teuchos::RCP<SimpleProblemInterface> interface = 
    Teuchos::rcp(new SimpleProblemInterface(&Problem,c) );

  Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;

// Create the operator to hold either the Jacobian matrix or the Matrix-free operator
  Teuchos::RCP<Epetra_Operator> A;
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac;

  // Need a NOX::Epetra::Vector for constructor
  // This becomes the initial guess vector that is used for the nonlinear solves
  NOX::Epetra::Vector noxInitGuess(InitialGuess, NOX::DeepCopy);   

  if (doMatFree) {
    // Matrix Free application (Epetra Operator):
    Teuchos::RCP<NOX::Epetra::MatrixFree> MF = 
      Teuchos::rcp(new NOX::Epetra::MatrixFree(printParams, interface, noxInitGuess)); 
    A = MF;
    iJac = MF;
  }
  else  {  // Computed Jacobian application
    A = Teuchos::rcp( Problem.GetMatrix(), false );
    iJac = interface;
  }
 
// Build the linear system solver
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linSys = 
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
						      iReq,
						      iJac, A, 
						      noxInitGuess));

// Create the Loca (continuation) vector
  NOX::Epetra::Vector locaSoln(noxInitGuess);
  
  // Create Epetra Factory
  Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory = Teuchos::rcp(new LOCA::Epetra::Factory);

  // Create global data object
  Teuchos::RCP<LOCA::GlobalData> globalData = LOCA::createGlobalData(ParamList, epetraFactory);
 
  // Create the Group - must be LOCA group
  Teuchos::RCP<LOCA::Epetra::Group> grpPtr = 
    Teuchos::rcp(new LOCA::Epetra::Group(globalData, printParams, 
					iReq, locaSoln, 
					linSys, p)); 

  // Calculate the first F(x0) as a starting point.  This is only needed for
  // certain status tests, to ensure that an initial residual (|r0|) is calculated
  grpPtr->computeF();

// Set up the status tests to check for convergence
  // Determines the error tolerance for the Newton solves 
  Teuchos::RCP<NOX::StatusTest::NormF> testNormF = 
    Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-4));
  // Sets the max number of nonlinear (Newton) iterations that will be taken.  If this is not
  //   already set, it will default to the '20' given 
  Teuchos::RCP<NOX::StatusTest::MaxIters> testMaxIters = 
    Teuchos::rcp(new NOX::StatusTest::MaxIters(stepperList.get("Max Nonlinear Iterations", 20)));
// This combination of tests will be used by NOX to determine whether the step converged
  Teuchos::RCP<NOX::StatusTest::Combo> combo = 
    Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR, 
					    testNormF, testMaxIters));

// This is sample code to write and read parameters to/from a file.  Currently not activated! 
// To use, change the 'XXXHAVE_TEUCHOS_EXTENDED' TO 'HAVE_TEUCHOS_EXTENDED'
#ifdef XXXHAVE_TEUCHOS_EXTENDED
  // Write the parameter list to a file
  cout << "Writing parameter list to \"input.xml\"" << endl;
  Teuchos::writeParameterListToXmlFile(*ParamList, "input.xml");

  // Read in the parameter list from a file
  cout << "Reading parameter list from \"input.xml\"" << endl;
  Teuchos::RCP<Teuchos::ParameterList> paramList2 = 
    Teuchos::rcp(new Teuchos::ParameterList);
  Teuchos::updateParametersFromXmlFile("input.xml", paramList2.get());
  ParamList = paramList2;
#endif


// Create the stepper
  LOCA::Stepper stepper(globalData, grpPtr, combo, ParamList);
  LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

  // Check if the stepper completed  
  if  (status == LOCA::Abstract::Iterator::Finished)
    globalData->locaUtils->out() << "\nAll tests passed!" << endl;
  else 
    if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
      globalData->locaUtils->out() << "\nStepper failed to converge!"  << endl;

// Output the stepper parameter list info
  if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
    globalData->locaUtils->out() << endl << "Final Parameters" << endl
    << "*******************" << endl;
    stepper.getList()->print(globalData->locaUtils->out());
    globalData->locaUtils->out() << endl;
  }

// Make sure all processors are done and close the output file
Comm.Barrier();
outFile.close();

// Deallocate memory
LOCA::destroyGlobalData(globalData);

#ifdef HAVE_MPI
  MPI_Finalize();
#endif
  return(EXIT_SUCCESS);
}  // DONE!!
Beispiel #4
0
int main(int argc, char *argv[])
{
  // Initialize MPI
  Teuchos::GlobalMPISession mpiSession(&argc,&argv);

  // Get the number of elements from the command line
  int NumGlobalNodes = 100 + 1;

#ifdef DO_XYZT
  // MPI MANIPULATION FOR XYZT PROBLEMS
  int spatialProcs = 1; // default
  if (argc>2) { spatialProcs = atoi(argv[2]);}
  int numTimeSteps= 1; // default
  if (argc>3) { numTimeSteps = atoi(argv[3]);}

  Teuchos::RCP<EpetraExt::MultiMpiComm> globalComm = 
    Teuchos::rcp(new EpetraExt::MultiMpiComm(MPI_COMM_WORLD, spatialProcs, numTimeSteps));
  Epetra_Comm& Comm = globalComm->SubDomainComm();

#else
  // Create a communicator for Epetra objects
#ifdef HAVE_MPI
  Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
  Epetra_SerialComm Comm();
#endif

#endif

  // Create and reset the Timer
  Epetra_Time myTimer(Comm);
  double startWallTime = myTimer.WallTime();

  // Get the process ID and the total number of processors
  int MyPID = Comm.MyPID();
  int NumProc = Comm.NumProc();

  // The number of unknowns must be at least equal to the 
  // number of processors.
  if (NumGlobalNodes < NumProc) {
    std::cout << "numGlobalNodes = " << NumGlobalNodes 
	 << " cannot be < number of processors = " << NumProc << std::endl;
    exit(1);
  }

  // Create the Brusselator problem class.  This creates all required
  // Epetra objects for the problem and allows calls to the 
  // function (F) and Jacobian evaluation routines.
  Brusselator::OverlapType OType = Brusselator::ELEMENTS;
  Brusselator Problem(NumGlobalNodes, Comm, OType);
  double dt = 0.5;

  // Get the vector from the Problem
  Epetra_Vector& soln = Problem.getSolution();
  Epetra_Vector& initCond = soln;

  // Begin Nonlinear Solver ************************************

  // Create the top level parameter list

  Teuchos::RCP<Teuchos::ParameterList> paramList =
       Teuchos::rcp(new Teuchos::ParameterList);

  // Create LOCA sublist
  Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

  // Create the stepper sublist and set the stepper parameters
  Teuchos::ParameterList& locaStepperList = locaParamsList.sublist("Stepper");
  locaStepperList.set("Continuation Method", "Natural");
  //locaStepperList.set("Continuation Method", "Arc Length");
  //locaStepperList.set("Continuation Method", "Householder Arc Length");
  locaStepperList.set("Continuation Parameter", "alpha");
  locaStepperList.set("Initial Value", 0.6);
  locaStepperList.set("Max Value", 100.0);
  locaStepperList.set("Min Value", 0.05);
#ifdef DO_XYZT
  locaStepperList.set("Max Steps", 7);
#else
  locaStepperList.set("Max Steps", 0);// must be 0 so just a nonlinear solver
#endif
  locaStepperList.set("Max Nonlinear Iterations", 15);
  locaStepperList.set("Enable Arc Length Scaling", true);
  locaStepperList.set("Goal Arc Length Parameter Contribution", 0.5);
  locaStepperList.set("Max Arc Length Parameter Contribution", 0.7);
  locaStepperList.set("Initial Scale Factor", 1.0);
  locaStepperList.set("Min Scale Factor", 1.0e-8);
  locaStepperList.set("Enable Tangent Factor Step Size Scaling",false);
  locaStepperList.set("Min Tangent Factor", 0.8);
  locaStepperList.set("Tangent Factor Exponent",1.5);

  // Create step size sublist
  Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
  stepSizeList.set("Method", "Constant");
 // stepSizeList.set("Method", "Adaptive");
  stepSizeList.set("Initial Step Size", -0.1);
  stepSizeList.set("Min Step Size", 1.0e-3);
  stepSizeList.set("Max Step Size", 2000.0);
  stepSizeList.set("Aggressiveness", 0.1);
  stepSizeList.set("Failed Step Reduction Factor", 0.5);
  stepSizeList.set("Successful Step Increase Factor", 1.00); // for constant

  // Create predictor sublist
  Teuchos::ParameterList& predictorList = locaParamsList.sublist("Predictor");
  //predictorList.set("Method", "Constant");
  //predictorList.set("Method", "Tangent");
  predictorList.set("Method", "Secant");

  // Create bifurcation sublist
    Teuchos::ParameterList& bifurcationList = 
      locaParamsList.sublist("Bifurcation");
    bifurcationList.set("Type", "None");

  // Create Anasazi Eigensolver sublist (needs --with-loca-anasazi)
  locaStepperList.set("Compute Eigenvalues",false);
#ifdef HAVE_LOCA_ANASAZI
  Teuchos::ParameterList& aList = locaStepperList.sublist("Eigensolver");
  aList.set("Method", "Anasazi");
  aList.set("Block Size", 1);
  aList.set("Num Blocks", 10);
  aList.set("Num Eigenvalues", 3);
  aList.set("Convergence Tolerance", 2.0e-7);
  aList.set("Convergence Check", 1);
  aList.set("Maximum Restarts",2);
  aList.set("Step Size",1);
  aList.set("Verbosity",
	    Anasazi::Errors + 
	    Anasazi::Warnings +
	    Anasazi::FinalSummary);
#endif

  // Create the "Solver" parameters sublist to be used with NOX Solvers
  Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
  // Set the nonlinear solver method
  nlParams.set("Nonlinear Solver", "Line Search Based");
  //nlParams.set("Nonlinear Solver", "Trust Region Based");

  // Set the printing parameters in the "Printing" sublist
  Teuchos::ParameterList& printParams = nlParams.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::Warning + 
			   NOX::Utils::StepperIteration +
			   NOX::Utils::StepperDetails);

  // Sublist for line search 
  Teuchos::ParameterList& searchParams = nlParams.sublist("Line Search");
  searchParams.set("Method", "Full Step");
  //searchParams.set("Method", "Interval Halving");
  //searchParams.set("Method", "Polynomial");
  //searchParams.set("Method", "NonlinearCG");
  //searchParams.set("Method", "Quadratic");
  //searchParams.set("Method", "More'-Thuente");

  // Sublist for direction
  Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
  dirParams.set("Method", "Newton");
  Teuchos::ParameterList& newtonParams = dirParams.sublist("Newton");
    newtonParams.set("Forcing Term Method", "Constant");
    //newtonParams.set("Forcing Term Method", "Type 1");
    //newtonParams.set("Forcing Term Method", "Type 2");
    //newtonParams.set("Forcing Term Minimum Tolerance", 1.0e-4);
    //newtonParams.set("Forcing Term Maximum Tolerance", 0.1);
  //dirParams.set("Method", "Steepest Descent");
  //Teuchos::ParameterList& sdParams = dirParams.sublist("Steepest Descent");
    //sdParams.set("Scaling Type", "None");
    //sdParams.set("Scaling Type", "2-Norm");
    //sdParams.set("Scaling Type", "Quadratic Model Min");
  //dirParams.set("Method", "NonlinearCG");
  //Teuchos::ParameterList& nlcgParams = dirParams.sublist("Nonlinear CG");
    //nlcgParams.set("Restart Frequency", 2000);
    //nlcgParams.set("Precondition", "On");
    //nlcgParams.set("Orthogonalize", "Polak-Ribiere");
    //nlcgParams.set("Orthogonalize", "Fletcher-Reeves");

  // Sublist for linear solver for the Newton method
  Teuchos::ParameterList& lsParams = newtonParams.sublist("Linear Solver");
  lsParams.set("Aztec Solver", "GMRES");  
  lsParams.set("Max Iterations", 800);  
  lsParams.set("Tolerance", 1e-6);
  lsParams.set("Output Frequency", 50);    
#ifdef DO_XYZT_PREC
  lsParams.set("Preconditioner", "User Defined"); 
#else
  lsParams.set("Preconditioner", "Ifpack"); 
  //lsParams.set("Preconditioner", "AztecOO"); 
  //lsParams.set("Aztec Preconditioner", "ilu"); 
  //lsParams.set("Overlap", 2);  
  //lsParams.set("Graph Fill", 2); 
  //lsParams.set("Aztec Preconditioner", "ilut"); 
  //lsParams.set("Overlap", 2);   
  //lsParams.set("Fill Factor", 2);   
  //lsParams.set("Drop Tolerance", 1.0e-12);   
  //lsParams.set("Aztec Preconditioner", "Polynomial"); 
  //lsParams.set("Polynomial Order", 6); 
#endif

  // Create the interface between the test problem and the nonlinear solver
  Teuchos::RCP<Problem_Interface> interface = 
    Teuchos::rcp(new Problem_Interface(Problem));

  // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
  Teuchos::RCP<Epetra_RowMatrix> A = 
    Teuchos::rcp(&Problem.getJacobian(),false);

#ifdef DO_XYZT
  Epetra_MultiVector initGuess(soln.Map(), globalComm->NumTimeStepsOnDomain());
  for (int i=0; i<globalComm->NumTimeStepsOnDomain(); i++) *(initGuess(i)) = soln;

#ifdef DO_XYZT_PREC
  // Sublist for linear solver of the preconditioner
  Teuchos::RCP<Teuchos::ParameterList> precLSParams =
       Teuchos::rcp(new Teuchos::ParameterList(lsParams));
  precLSParams->set("Aztec Solver", "GMRES");  
  precLSParams->set("Preconditioner", "Ifpack");  
  //precLSParams->set("Preconditioner", "AztecOO");  
  precLSParams->set("Max Iterations", 800);  
  precLSParams->set("Tolerance", 1e-6);
  precLSParams->set("Output Frequency", 50);    
  //precLSParams->set("XYZTPreconditioner", "None"); 
  precLSParams->set("XYZTPreconditioner", "Global"); 
  //precLSParams->set("XYZTPreconditioner", "Sequential"); 
  //precLSParams->set("XYZTPreconditioner", "Parallel"); 
  //precLSParams->set("XYZTPreconditioner", "Parareal"); 
  //precLSParams->set("XYZTPreconditioner", "BlockDiagonal"); 

  Teuchos::RCP<Teuchos::ParameterList> precPrintParams =
       Teuchos::rcp(new Teuchos::ParameterList(printParams));
  precPrintParams->set("MyPID", MyPID); 
  precPrintParams->set("Output Precision", 3);
  precPrintParams->set("Output Processor", 0);
  precPrintParams->set("Output Information", 
			NOX::Utils::OuterIteration + 
			NOX::Utils::OuterIterationStatusTest + 
			NOX::Utils::InnerIteration +
			NOX::Utils::Parameters + 
			NOX::Utils::Details + 
			NOX::Utils::Warning);

  Teuchos::RCP<LOCA::Epetra::Interface::xyzt> ixyzt = 
    Teuchos::rcp(new LOCA::Epetra::Interface::xyzt(interface, 
						   initGuess, A,
						   globalComm, 
                                                   initCond, dt,
						   precPrintParams.get(), precLSParams.get()));

  Teuchos::RCP<Epetra_RowMatrix> Axyzt =
     Teuchos::rcp(&(ixyzt->getJacobian()),false);
  Epetra_Vector& solnxyzt = ixyzt->getSolution();
  Teuchos::RCP<Epetra_Operator> Mxyzt = 
     Teuchos::rcp(&(ixyzt->getPreconditioner()),false);

  Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = ixyzt;

  // Create the Linear System
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = ixyzt;
  Teuchos::RCP<NOX::Epetra::Interface::Preconditioner> iPrec = 
    Teuchos::rcp(&(ixyzt->getPreconditioner()),false);
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linSys =
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
						      iJac, Axyzt, iPrec, Mxyzt, 
						      solnxyzt));
#else
  Teuchos::RCP<LOCA::Epetra::Interface::xyzt> ixyzt = 
    Teuchos::rcp(new LOCA::Epetra::Interface::xyzt(interface, 
						   initGuess, A,
                                                   initCond, dt,
						   globalComm));

  Teuchos::RCP<Epetra_RowMatrix> Axyzt =
     Teuchos::rcp(&(ixyzt->getJacobian()),false);
  Epetra_Vector& solnxyzt = ixyzt->getSolution();

  Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = ixyzt;

  // Create the Linear System
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = ixyzt;
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linSys =
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
						      iReq, iJac, Axyzt, 
						      solnxyzt));
#endif
  NOX::Epetra::Vector initialGuess(solnxyzt);
#else
  // Use an Epetra Scaling object if desired
  Teuchos::RCP<Epetra_Vector> scaleVec = 
    Teuchos::rcp(new Epetra_Vector(soln));
  NOX::Epetra::Scaling scaling;
  scaling.addRowSumScaling(NOX::Epetra::Scaling::Left, scaleVec);

  Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;

  // Create the Linear System
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linSys = 
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
						      iReq, iJac, A, soln));
		                                      //&scaling);

  // Create the Group
  NOX::Epetra::Vector initialGuess(Teuchos::rcp(&soln,false), 
				   NOX::Epetra::Vector::CreateView,
				   NOX::DeepCopy);
#endif

  // Create and initialize the parameter vector
  LOCA::ParameterVector pVector;
  pVector.addParameter("alpha",0.6);
  pVector.addParameter("beta",2.0);

  // Create Epetra factory
  Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
    Teuchos::rcp(new LOCA::Epetra::Factory);

  // Create global data object
  Teuchos::RCP<LOCA::GlobalData> globalData = 
    LOCA::createGlobalData(paramList, epetraFactory);

  Teuchos::RCP<LOCA::Epetra::Group> grp =
    Teuchos::rcp(new LOCA::Epetra::Group(globalData, printParams,
                 iReq, initialGuess, linSys, pVector));

  grp->computeF();

  // Create the convergence tests
  Teuchos::RCP<NOX::StatusTest::NormF> absresid = 
    Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8, 
					    NOX::StatusTest::NormF::Unscaled));
  //NOX::StatusTest::NormF relresid(*grp.get(), 1.0e-2);
  //NOX::StatusTest::NormUpdate update(1.0e-5);
  //NOX::StatusTest::NormWRMS wrms(1.0e-2, 1.0e-8);
  //NOX::StatusTest::Combo converged(NOX::StatusTest::Combo::AND);
  //converged.addStatusTest(absresid);
  //converged.addStatusTest(relresid);
  //converged.addStatusTest(wrms);
  //converged.addStatusTest(update);
  Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters = 
    Teuchos::rcp(new NOX::StatusTest::MaxIters(50));
  Teuchos::RCP<NOX::StatusTest::Combo> combo =
    Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
  combo->addStatusTest(absresid);
  combo->addStatusTest(maxiters);

  // Create the method
  //NOX::Solver::Manager solver(grp, combo, nlParams);
  LOCA::Stepper stepper(globalData, grp, combo, paramList);

  // Initialize time integration parameters
#ifdef DO_XYZT
  int maxTimeSteps = 1; // No longer need a time integration loop
#else
  int maxTimeSteps = 2;
#endif
  int timeStep = 0;
  double time = 0.;
  
  // Time integration loop
  while(timeStep < maxTimeSteps) {

    timeStep++;
    time += dt;
  
    globalData->locaUtils->out() 
      << "Time Step: " << timeStep << ",\tTime: " << time << std::endl;
  
//    NOX::StatusTest::StatusType status = solver.solve();
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    if (status == LOCA::Abstract::Iterator::Finished)
      globalData->locaUtils->out() << "All tests passed" << std::endl;
    else
       globalData->locaUtils->out() << "Stepper failed to converge!" << std::endl;


    // Get the Epetra_Vector with the final solution from the solver
    const LOCA::Epetra::Group& finalGroup = 
      dynamic_cast<const LOCA::Epetra::Group&>(*(stepper.getSolutionGroup()));
    const Epetra_Vector& finalSolution = 
      (dynamic_cast<const NOX::Epetra::Vector&>(finalGroup.getX())).getEpetraVector();

    // End Nonlinear Solver **************************************

#ifndef DO_XYZT

    //Problem.reset(finalSolution);
    grp->setX(finalSolution);
    stepper.reset(globalData, grp, combo, paramList);
    grp->computeF();
#endif

  } // end time step while loop

  // Output the parameter list
  if (globalData->locaUtils->isPrintType(NOX::Utils::Parameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

  // Output timing info
  globalData->locaUtils->out() << "\nTimings :\n\tWallTime --> " << 
    myTimer.WallTime() - startWallTime << " sec."
	      << "\n\tElapsedTime --> " << myTimer.ElapsedTime() 
	      << " sec." << std::endl << std::endl;

  LOCA::destroyGlobalData(globalData);

return 0 ;
}
Beispiel #5
0
int main(int argc, char *argv[])
{
  int n = 100;
  double alpha = 10.0;
  double beta = 0.0;
  double scale = 1.0;
  int maxNewtonIters = 20;
  int ierr = 0;

  alpha = alpha / scale;

  try {

    bool verbose = false;
    // Check for verbose output
    if (argc>1) 
      if (argv[1][0]=='-' && argv[1][1]=='v') 
	verbose = true;

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList = 
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    if (verbose)
       nlPrintParams.set("Output Information", 
			 NOX::Utils::Error +
			 NOX::Utils::Details +
			 NOX::Utils::OuterIterationStatusTest + 
			 NOX::Utils::OuterIteration +
			 NOX::Utils::InnerIteration + 
			 NOX::Utils::Warning +
			 NOX::Utils::TestDetails + 
			 NOX::Utils::StepperIteration +
			 NOX::Utils::StepperDetails +
			 NOX::Utils::StepperParameters);
     else
       nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create LAPACK Factory
    Teuchos::RCP<LOCA::LAPACK::Factory> lapackFactory = 
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, lapackFactory);

    // Set up the problem interface
    ChanProblemInterface chan(globalData, n, alpha, beta, scale);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("scale",scale);
  
    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    Teuchos::RCP<LOCA::LAPACK::Group> grp = 
      Teuchos::rcp(new LOCA::LAPACK::Group(globalData, chan));
    grp->setParams(p);

    // Set up the status tests
    grp->computeF();
    double size = sqrt(static_cast<double>(grp->getX().length()));
    double normF_0 = grp->getNormF() / size;
    double tolerance = 1.0e-8 / normF_0 / normF_0;
    Teuchos::RCP<NOX::StatusTest::NormF> statusTestA = 
      Teuchos::rcp(new NOX::StatusTest::NormF(*grp, tolerance));
    Teuchos::RCP<NOX::StatusTest::MaxIters> statusTestB = 
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Combo> combo = 
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR, 
					       statusTestA, statusTestB));

    // Create the homotopy group
    Teuchos::RCP<LOCA::Homotopy::Group> hGrp = 
      Teuchos::rcp(new LOCA::Homotopy::Group(locaParamsList, globalData, grp));

    // Override default parameters
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters);

    // Create the stepper  
    LOCA::Stepper stepper(globalData, hGrp, combo, paramList);

    // Solve the nonlinear system
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    if (status != LOCA::Abstract::Iterator::Finished) {
      ierr = 1;
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() << "Stepper failed to converge!" 
				     << std::endl;
    }

    // Get the final solution from the stepper
    Teuchos::RCP<const LOCA::LAPACK::Group> finalGroup = 
      Teuchos::rcp_dynamic_cast<const LOCA::LAPACK::Group>(stepper.getSolutionGroup());
    const NOX::LAPACK::Vector& finalSolution = 
      dynamic_cast<const NOX::LAPACK::Vector&>(finalGroup->getX());

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    // Check some statistics on the solution
    NOX::Utils utils(nlPrintParams);
    NOX::TestCompare testCompare(cout, utils);

    if (utils.isPrintType(NOX::Utils::TestDetails))
      cout << endl << "***** Checking solutions statistics *****" << endl;
  
    // Check number of steps
    int numSteps = stepper.getStepNumber();
    int numSteps_expected = 14;
    ierr += testCompare.testValue(numSteps, numSteps_expected, 0.0,
				  "number of continuation steps", 
				  NOX::TestCompare::Absolute);

    // Check number of failed steps
    int numFailedSteps = stepper.getNumFailedSteps();
    int numFailedSteps_expected = 3;
    ierr += testCompare.testValue(numFailedSteps, numFailedSteps_expected, 
				  0.0, "number of failed continuation steps", 
				  NOX::TestCompare::Absolute);

    // Check final value of continuation parameter
    double alpha_final = 
      finalGroup->getParam("Homotopy Continuation Parameter");
    double alpha_expected = 1.0;
    ierr += testCompare.testValue(alpha_final, alpha_expected, 1.0e-14,
				  "final value of continuation parameter", 
				  NOX::TestCompare::Relative);
 
    // Check norm of solution
    double norm_x = finalSolution.norm();
    double norm_x_expected =  456.0303417;
    ierr += testCompare.testValue(norm_x, norm_x_expected, 1.0e-7,
				  "norm of final solution", 
				  NOX::TestCompare::Relative);

    LOCA::destroyGlobalData(globalData);
  }

  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  }
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

  if (ierr == 0)
    std::cout << "All tests passed!" << std::endl;
  else
    std::cout << ierr << " test(s) failed!" << std::endl;

  return 0;
}
Beispiel #6
0
int testTransposeSolve(
         int NumGlobalElements,
         int nRHS,
         double reltol,
         double abstol,
         Epetra_Comm& Comm,
         const Teuchos::RCP<LOCA::GlobalData>& globalData,
         const Teuchos::RCP<Teuchos::ParameterList>& paramList)
{
  int ierr = 0;

  double left_bc = 0.0;
  double right_bc = 1.0;
  double nonlinear_factor = 1.0;

  // Create the FiniteElementProblem class.  This creates all required
  // Epetra objects for the problem and allows calls to the
  // function (RHS) and Jacobian evaluation routines.
  Tcubed_FiniteElementProblem Problem(NumGlobalElements, Comm);

  // Get the vector from the Problem
  Epetra_Vector& soln = Problem.getSolution();

  // Initialize Solution
  soln.PutScalar(0.0);

  // Create and initialize the parameter vector
  LOCA::ParameterVector pVector;
  pVector.addParameter("Nonlinear Factor",nonlinear_factor);
  pVector.addParameter("Left BC", left_bc);
  pVector.addParameter("Right BC", right_bc);

  // Create the interface between the test problem and the nonlinear solver
  // This is created by the user using inheritance of the abstract base
  // class:
  Teuchos::RCP<Problem_Interface> interface =
    Teuchos::rcp(new Problem_Interface(Problem));
  Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;

  // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
  Teuchos::RCP<Epetra_RowMatrix> Amat =
    Teuchos::rcp(&Problem.getJacobian(),false);

  // Get sublists
  Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
  Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
  Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
  Teuchos::ParameterList& newParams = dirParams.sublist("Newton");
  Teuchos::ParameterList& lsParams = newParams.sublist("Linear Solver");

  // Create the linear systems
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys =
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams,
                              lsParams, iReq, iJac,
                              Amat, soln));

  // Create the loca vector
  NOX::Epetra::Vector locaSoln(soln);

  // Create the Group
  Teuchos::RCP<LOCA::Epetra::Group> grp_tp =
    Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams,
                     iReq, locaSoln,
                     linsys, pVector));

  // Create the Group
  Teuchos::RCP<LOCA::Epetra::Group> grp_lp =
    Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams,
                     iReq, locaSoln,
                     linsys, pVector));

  // Create the Group
  Teuchos::RCP<LOCA::Epetra::Group> grp_ep =
    Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams,
                     iReq, locaSoln,
                     linsys, pVector));

  // Change initial guess to a random vector
  Teuchos::RCP<NOX::Abstract::Vector> xnew =
    grp_tp->getX().clone();
  xnew->random();
  grp_tp->setX(*xnew);
  grp_lp->setX(*xnew);
  grp_ep->setX(*xnew);

  // Check some statistics on the solution
  Teuchos::RCP<NOX::TestCompare> testCompare =
    Teuchos::rcp(new NOX::TestCompare(globalData->locaUtils->out(),
                      *(globalData->locaUtils)));

  // Evaluate blocks
  grp_tp->computeF();
  grp_lp->computeF();
  grp_ep->computeF();
  grp_tp->computeJacobian();
  grp_lp->computeJacobian();
  grp_ep->computeJacobian();

    // Set up left- and right-hand sides
  Teuchos::RCP<NOX::Abstract::MultiVector> F =
    grp_tp->getX().createMultiVector(nRHS);
  F->random();
  Teuchos::RCP<NOX::Abstract::MultiVector> X_tp =
    F->clone(NOX::ShapeCopy);
  X_tp->init(0.0);
  Teuchos::RCP<NOX::Abstract::MultiVector> X_lp =
    F->clone(NOX::ShapeCopy);
  X_lp->init(0.0);
  Teuchos::RCP<NOX::Abstract::MultiVector> X_ep =
    F->clone(NOX::ShapeCopy);
  X_ep->init(0.0);

  // Set up residuals
  Teuchos::RCP<NOX::Abstract::MultiVector> R_tp =
    F->clone(NOX::ShapeCopy);
  Teuchos::RCP<NOX::Abstract::MultiVector> R_lp =
    F->clone(NOX::ShapeCopy);
  Teuchos::RCP<NOX::Abstract::MultiVector> R_ep =
    F->clone(NOX::ShapeCopy);

  // Set up linear solver lists
  Teuchos::ParameterList lsParams_tp = lsParams;
  Teuchos::ParameterList lsParams_lp = lsParams;
  Teuchos::ParameterList lsParams_ep = lsParams;
  lsParams_tp.set("Transpose Solver Method",
               "Transpose Preconditioner");
  lsParams_lp.set("Transpose Solver Method",
               "Left Preconditioning");
  lsParams_ep.set("Transpose Solver Method",
               "Explicit Transpose");

  NOX::Abstract::Group::ReturnType status;

  // Test transpose solve with transposed preconditioner
  if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
    globalData->locaUtils->out() << std::endl <<
      "\t***** " <<
      "Testing Transposed Preconditioner Residual" <<
      " *****" << std::endl;

  status = grp_tp->applyJacobianTransposeInverseMultiVector(lsParams_tp, *F,
                                *X_tp);
  if (status == NOX::Abstract::Group::Failed)
    ++ierr;
  status = grp_tp->applyJacobianTransposeMultiVector(*X_tp, *R_tp);
  ierr += testCompare->testMultiVector(*R_tp, *F, reltol, abstol,
                       "Residual");

  // Test transpose solve with transposed left-preconditioner
  if (lsParams.get("Preconditioner", "None") != "None") {
    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() << std::endl <<
    "\t***** " <<
    "Testing Transposed Left Preconditioner Residual" <<
    " *****" << std::endl;

    status = grp_lp->applyJacobianTransposeInverseMultiVector(lsParams_lp, *F,
                                  *X_lp);
    if (status == NOX::Abstract::Group::Failed)
      ++ierr;
    status = grp_lp->applyJacobianTransposeMultiVector(*X_lp, *R_lp);
    ierr += testCompare->testMultiVector(*R_lp, *F, reltol, abstol,
                     "Residual");
  }

#ifdef HAVE_NOX_EPETRAEXT
  // Test transpose solve with explicit preconditioner
  if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
    globalData->locaUtils->out() << std::endl <<
      "\t***** " <<
      "Testing Explicit Preconditioner Residual" <<
      " *****" << std::endl;

  status = grp_ep->applyJacobianTransposeInverseMultiVector(lsParams_ep, *F,
                                *X_ep);
  if (status == NOX::Abstract::Group::Failed)
    ++ierr;
  status = grp_ep->applyJacobianTransposeMultiVector(*X_ep, *R_ep);
  ierr += testCompare->testMultiVector(*R_ep, *F, reltol, abstol,
                       "Residual");
#endif


  // Compare solutions
  if (lsParams.get("Preconditioner", "None") != "None") {
    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() << std::endl <<
    "\t***** " <<
    "Comparing Transposed Preconditioner and Left Preconditioner Solutions"
                   <<
    " *****" << std::endl;
    ierr += testCompare->testMultiVector(*X_lp, *X_tp,
                     reltol, abstol, "Solution");
  }

#ifdef HAVE_NOX_EPETRAEXT
  if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
    globalData->locaUtils->out() << std::endl <<
      "\t***** " <<
      "Comparing Transposed Preconditioner and Explicit Preconditioner Solutions"
                 <<
      " *****" << std::endl;
  ierr += testCompare->testMultiVector(*X_ep, *X_tp,
                       reltol, abstol, "Solution");
#endif

  return ierr;
}
Beispiel #7
0
int tcubed_test(int NumGlobalElements, bool verbose, Epetra_Comm& Comm,
		bool includeUV, bool useP, const std::string& prec,
		const std::string& prec_method)
{
  int ierr = 0;
  int MyPID = Comm.MyPID();

  if (MyPID == 0) {
    std::cout << "********** " 
	 << "Testing includeUV = " << includeUV << " useP = " << useP
	 << " Preconditioner = " << prec 
	 << " Preconditioner method = " << prec_method
	 << " **********" << std::endl;
  }

  try {

    double nonlinear_factor = 1.0;
    double left_bc = 0.0;
    double right_bc = 2.07;

    // Create the FiniteElementProblem class.  This creates all required
    // Epetra objects for the problem and allows calls to the 
    // function (RHS) and Jacobian evaluation routines.
    Tcubed_FiniteElementProblem Problem(NumGlobalElements, Comm);

    // Get the vector from the Problem
    Epetra_Vector& soln = Problem.getSolution();

    // Initialize Solution
    soln.PutScalar(1.0);

    // Create initial guess for the null vector of jacobian
    // Only needed for Moore-Spence
    Teuchos::RCP<NOX::Abstract::Vector> nullVec = 
      Teuchos::rcp(new NOX::Epetra::Vector(soln));  
    nullVec->init(1.0);             // initial value 1.0
  
    // Begin LOCA Solver ************************************

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList = 
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& locaStepperList = 
      locaParamsList.sublist("Stepper");
    locaStepperList.set("Continuation Method", "Arc Length");
    locaStepperList.set("Continuation Parameter", "Nonlinear Factor");
    locaStepperList.set("Initial Value", nonlinear_factor);
    locaStepperList.set("Max Value", 2.0);
    locaStepperList.set("Min Value", 0.05);
    locaStepperList.set("Max Steps", 20);
    locaStepperList.set("Max Nonlinear Iterations", 15);

    locaStepperList.set("Bordered Solver Method", "Nested");
    Teuchos::ParameterList& nestedList = 
      locaStepperList.sublist("Nested Bordered Solver");
    nestedList.set("Bordered Solver Method", "Householder");
    nestedList.set("Include UV In Preconditioner", includeUV);
    nestedList.set("Use P For Preconditioner", useP);

    // Create bifurcation sublist
    Teuchos::ParameterList& bifurcationList = 
      locaParamsList.sublist("Bifurcation");
    bifurcationList.set("Type", "Turning Point");
    bifurcationList.set("Bifurcation Parameter", "Right BC");

    bifurcationList.set("Formulation", "Minimally Augmented");
    bifurcationList.set("Symmetric Jacobian", false); 
    bifurcationList.set("Update Null Vectors Every Continuation Step", true);
    bifurcationList.set("Update Null Vectors Every Nonlinear Iteration", 
			false);
    bifurcationList.set("Transpose Solver Method",prec);
    bifurcationList.set("Multiply Null Vectors by Mass Matrix", true);

    // The others don't seem to work with "Solve df/dp"
    if (prec == "Explicit Transpose")
      bifurcationList.set("Initial Null Vector Computation", "Solve df/dp");
    else {
      bifurcationList.set("Initial A Vector", nullVec);
      bifurcationList.set("Initial B Vector", nullVec);
    }

    bifurcationList.set("Bordered Solver Method", "Householder");
    bifurcationList.set("Include UV In Preconditioner", includeUV);
    bifurcationList.set("Use P For Preconditioner", useP);
    bifurcationList.set("Preconditioner Method", prec_method);

    //bifurcationList.set("Formulation", "Moore-Spence");
    //bifurcationList.set("Solver Method", "Phipps Bordering");
    //bifurcationList.set("Solver Method", "Salinger Bordering");
    //bifurcationList.set("Initial Null Vector", nullVec);
    //bifurcationList.set("Length Normalization Vector", nullVec);

    // Create predictor sublist
    Teuchos::ParameterList& predictorList = 
      locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Secant");

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Method", "Adaptive");
    stepSizeList.set("Initial Step Size", 0.1);
    stepSizeList.set("Min Step Size", 1.0e-3);
    stepSizeList.set("Max Step Size", 2000.0);
    stepSizeList.set("Aggressiveness", 0.1);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

    // Create the NOX printing parameter list
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("MyPID", MyPID); 
    nlPrintParams.set("Output Precision", 4); 
    if (verbose)
      nlPrintParams.set("Output Information", 
			NOX::Utils::OuterIteration + 
			NOX::Utils::OuterIterationStatusTest + 
			NOX::Utils::InnerIteration +
			NOX::Utils::Details + 
			NOX::Utils::LinearSolverDetails +
			NOX::Utils::Warning + 
			NOX::Utils::TestDetails + 
			NOX::Utils::Error +
			NOX::Utils::StepperIteration +
			NOX::Utils::StepperDetails +
			NOX::Utils::StepperParameters);
    else
      nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create the "Linear Solver" sublist for Newton's method
    Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
    Teuchos::ParameterList& newParams = dirParams.sublist("Newton");
    Teuchos::ParameterList& lsParams = newParams.sublist("Linear Solver");
    lsParams.set("Aztec Solver", "GMRES");  
    lsParams.set("Max Iterations", 200);  
    lsParams.set("Tolerance", 1e-6);
    lsParams.set("Output Frequency", 50);    
    //lsParams.set("Scaling", "None");             
    //lsParams.set("Scaling", "Row Sum");  
    lsParams.set("Compute Scaling Manually", false);
    //lsParams.set("Preconditioner", "Ifpack");
    lsParams.set("Preconditioner", "New Ifpack");
    lsParams.set("Ifpack Preconditioner", "ILU");

    // Create and initialize the parameter vector
    LOCA::ParameterVector pVector;
    pVector.addParameter("Nonlinear Factor",nonlinear_factor);
    pVector.addParameter("Left BC", left_bc);
    pVector.addParameter("Right BC", right_bc);

    // Create the interface between the test problem and the nonlinear solver
    // This is created by the user using inheritance of the abstract base class
    Teuchos::RCP<Problem_Interface> interface = 
      Teuchos::rcp(new Problem_Interface(Problem));
    Teuchos::RCP<LOCA::Epetra::Interface::TimeDependent> iReq = interface;
    Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;
    
    // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
    Teuchos::RCP<Epetra_RowMatrix> Amat = 
      Teuchos::rcp(&Problem.getJacobian(),false);

    // Create scaling object
    Teuchos::RCP<NOX::Epetra::Scaling> scaling = Teuchos::null;
//       scaling = Teuchos::rcp(new NOX::Epetra::Scaling);
//       Teuchos::RCP<Epetra_Vector> scalingVector = 
// 	Teuchos::rcp(new Epetra_Vector(soln.Map()));
//       //scaling->addRowSumScaling(NOX::Epetra::Scaling::Left, scalingVector);
//       scaling->addColSumScaling(NOX::Epetra::Scaling::Right, scalingVector);

    // Create transpose scaling object
//     Teuchos::RCP<NOX::Epetra::Scaling> trans_scaling = Teuchos::null;
//     trans_scaling = Teuchos::rcp(new NOX::Epetra::Scaling);
//     Teuchos::RCP<Epetra_Vector> transScalingVector = 
//       Teuchos::rcp(new Epetra_Vector(soln.Map()));
//     trans_scaling->addRowSumScaling(NOX::Epetra::Scaling::Right, 
// 				    transScalingVector);
//     trans_scaling->addColSumScaling(NOX::Epetra::Scaling::Left, 
// 				    transScalingVector);
//     //bifurcationList.set("Transpose Scaling", trans_scaling);

    // Create the linear systems
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys = 
      Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams, 
							lsParams,
							iReq, iJac, Amat, soln,
							scaling));

    // Create the loca vector
    NOX::Epetra::Vector locaSoln(soln);

    // Create Epetra factory
    Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
      Teuchos::rcp(new LOCA::Epetra::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData = 
      LOCA::createGlobalData(paramList, epetraFactory);

    // Create the Group
    Teuchos::RCP<LOCA::Epetra::Group> grp = 
      Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams, iReq, 
					   locaSoln, linsys, linsys,
					   pVector));
    grp->computeF();
  
    // Create the Solver convergence test
    //NOX::StatusTest::NormWRMS wrms(1.0e-2, 1.0e-8);
    Teuchos::RCP<NOX::StatusTest::NormF> wrms = 
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-12));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters = 
      Teuchos::rcp(new NOX::StatusTest::MaxIters(locaStepperList.get("Max Nonlinear Iterations", 10)));
    Teuchos::RCP<NOX::StatusTest::Combo> combo = 
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
    combo->addStatusTest(wrms);
    combo->addStatusTest(maxiters);
  
    // Create the stepper  
    LOCA::Stepper stepper(globalData, grp, combo, paramList);
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();
  
    if (status != LOCA::Abstract::Iterator::Finished) {
      ierr = 1;
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() 
	  << "Stepper failed to converge!" << std::endl;
    }

    // Get the final solution from the stepper
    Teuchos::RCP<const LOCA::Epetra::Group> finalGroup = 
      Teuchos::rcp_dynamic_cast<const LOCA::Epetra::Group>(stepper.getSolutionGroup());
    const NOX::Epetra::Vector& finalSolution = 
      dynamic_cast<const NOX::Epetra::Vector&>(finalGroup->getX());

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    // Check some statistics on the solution
    NOX::TestCompare testCompare(globalData->locaUtils->out(), 
				 *(globalData->locaUtils));
  
    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() 
	<< std::endl 
	<< "***** Checking solution statistics *****" 
	<< std::endl;

    // Check number of steps
    int numSteps = stepper.getStepNumber();
    int numSteps_expected = 7;
    ierr += testCompare.testValue(numSteps, numSteps_expected, 0.0,
				  "number of continuation steps",
				  NOX::TestCompare::Absolute);

    // Check number of failed steps
    int numFailedSteps = stepper.getNumFailedSteps();
    int numFailedSteps_expected = 0;
    ierr += testCompare.testValue(numFailedSteps, numFailedSteps_expected, 0.0,
				  "number of failed continuation steps",
				  NOX::TestCompare::Absolute);

    // Check final value of continuation parameter
    double factor_final = finalGroup->getParam("Nonlinear Factor");
    double factor_expected = 2.0;
    ierr += testCompare.testValue(factor_final, factor_expected, 1.0e-14,
				  "final value of continuation parameter", 
				  NOX::TestCompare::Relative);

    // Check final value of bifurcation parameter
    double right_bc_final = finalGroup->getParam("Right BC");
    double right_bc_expected = 1.47241293;
    ierr += testCompare.testValue(right_bc_final, right_bc_expected, 1.0e-7,
				  "final value of bifurcation parameter", 
				  NOX::TestCompare::Relative);

    // Check norm of solution
    double norm_x = finalSolution.norm();
    double norm_x_expected = 12.038464;
    ierr += testCompare.testValue(norm_x, norm_x_expected, 1.0e-7,
				  "norm of final solution",
				  NOX::TestCompare::Relative);

    LOCA::destroyGlobalData(globalData);

  }

  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  }
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

  return ierr ;
}
int main(int argc, char *argv[])
{
  Teuchos::GlobalMPISession mpi_session(&argc, &argv);

  int n = 100;
  double alpha = 0.0;
  double beta = 0.0;
  double scale = 1.0;
  int ierr = 0;
  int nev = 10;
  int narn = 20;
  double arntol = 1.0e-12;

  alpha = alpha / scale;

  try {

    bool verbose = false;
    // Check for verbose output
    if (argc>1)
      if (argv[1][0]=='-' && argv[1][1]=='v') 
	verbose = true;

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList = 
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");

    // Create Anasazi Eigensolver sublist (needs --with-loca-anasazi)
    Teuchos::ParameterList& aList = stepperList.sublist("Eigensolver");
    aList.set("Method", "Anasazi");
    aList.set("Operator", "Jacobian Inverse");
    aList.set("Block Size", 1);
    aList.set("Num Blocks", narn);
    aList.set("Num Eigenvalues", nev);
    aList.set("Convergence Tolerance", arntol);
    aList.set("Step Size", 1);
    aList.set("Maximum Restarts",2);
    aList.set("Sorting Order","LM");
    if (verbose)
      aList.set("Debug Level",
		Anasazi::Errors + 
		Anasazi::Warnings +
		Anasazi::FinalSummary);
    else
      aList.set("Debug Level", Anasazi::Errors);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    if (verbose)
       nlPrintParams.set("Output Information", 
				  NOX::Utils::Error +
				  NOX::Utils::Details +
				  NOX::Utils::OuterIteration + 
				  NOX::Utils::InnerIteration + 
				  NOX::Utils::Warning +
				  NOX::Utils::TestDetails + 
				  NOX::Utils::StepperIteration +
				  NOX::Utils::StepperDetails);
     else
       nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create LAPACK factory
    Teuchos::RCP<LOCA::Abstract::Factory> lapackFactory =
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, lapackFactory);

    // Create parsed parameter list
    Teuchos::RCP<LOCA::Parameter::SublistParser> parsedParams = 
      Teuchos::rcp(new LOCA::Parameter::SublistParser(globalData));
    parsedParams->parseSublists(paramList);

    // Set up the problem interface
    ChanProblemInterface chan(globalData, n, alpha, beta, scale);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("scale",scale);
  
    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    LOCA::LAPACK::Group grp(globalData, chan);
    
    grp.setParams(p);

    grp.computeF();
    grp.computeJacobian();

    // Create Anasazi eigensolver
    Teuchos::RCP<LOCA::Eigensolver::AbstractStrategy> anasaziStrategy
      = globalData->locaFactory->createEigensolverStrategy(
				     parsedParams, 
				     parsedParams->getSublist("Eigensolver"));

    Teuchos::RCP< std::vector<double> > anasazi_evals_r;
    Teuchos::RCP< std::vector<double> > anasazi_evals_i;
    Teuchos::RCP< NOX::Abstract::MultiVector > anasazi_evecs_r;
    Teuchos::RCP< NOX::Abstract::MultiVector > anasazi_evecs_i;
    NOX::Abstract::Group::ReturnType anasaziStatus = 
      anasaziStrategy->computeEigenvalues(grp, 
					  anasazi_evals_r, 
					  anasazi_evals_i,
					  anasazi_evecs_r,
					  anasazi_evecs_i);

    if (anasaziStatus != NOX::Abstract::Group::Ok)
      ++ierr;

    // Change strategy to DGGEV
    aList.set("Method", "DGGEV");
    aList.set("Sorting Order","SM");

    // Create DGGEV eigensolver
    Teuchos::RCP<LOCA::Eigensolver::AbstractStrategy> dggevStrategy
      = globalData->locaFactory->createEigensolverStrategy(
				      parsedParams,
				      parsedParams->getSublist("Eigensolver"));

    Teuchos::RCP< std::vector<double> > dggev_evals_r;
    Teuchos::RCP< std::vector<double> > dggev_evals_i;
    Teuchos::RCP< NOX::Abstract::MultiVector > dggev_evecs_r;
    Teuchos::RCP< NOX::Abstract::MultiVector > dggev_evecs_i;
    NOX::Abstract::Group::ReturnType dggevStatus = 
      dggevStrategy->computeEigenvalues(grp, 
					dggev_evals_r, 
					dggev_evals_i,
					dggev_evecs_r,
					dggev_evecs_i);

    if (dggevStatus != NOX::Abstract::Group::Ok)
      ++ierr;

    // Check some statistics on the solution
    NOX::TestCompare testCompare(globalData->locaUtils->out(), 
				 *(globalData->locaUtils));

    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() 
	<< std::endl 
	<< "***** Checking solution statistics *****" 
	<< std::endl;

    // Check eigenvalues
    for (int i=0; i<nev; i++) {
      std::stringstream sstr;
      sstr << "Eigenvalue " << i;
      ierr += testCompare.testValue((*anasazi_evals_r)[i], 
				    (*dggev_evals_r)[i], arntol*1e3,
				    sstr.str(),
				    NOX::TestCompare::Relative);
    }

    LOCA::destroyGlobalData(globalData);

  }

 catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  } 
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

   if (ierr == 0)
     std::cout << "All tests passed!" << std::endl;
   else
     std::cout << ierr << " test(s) failed!" << std::endl;

  return ierr;
}
int main(int argc, char *argv[])
{
  int n = 10;
  int ierr = 0;
  double reltol = 1.0e-14;
  double abstol = 1.0e-14;
  int MyPID = 0;

  try {

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

    // Create a communicator for Epetra objects
#ifdef HAVE_MPI
    Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
    Epetra_SerialComm Comm;
#endif

    MyPID = Comm.MyPID();

    // Create the map
    Epetra_Map map(n, 0, Comm);

    bool verbose = false;
    // Check for verbose output
    if (argc>1)
      if (argv[1][0]=='-' && argv[1][1]=='v')
    verbose = true;

    // Seed the random number generator in Teuchos.  We create random
    // bordering matrices and it is possible different processors might generate
    // different matrices.  By setting the seed, this shouldn't happen.
    Teuchos::ScalarTraits<double>::seedrandom(12345);

    // Create and initialize the parameter vector
    LOCA::ParameterVector pVector;
    pVector.addParameter("Param 1",  1.69);
    pVector.addParameter("Param 2", -9.7);
    pVector.addParameter("Param 3",  0.35);
    pVector.addParameter("Param 4", -0.78);
    pVector.addParameter("Param 5",  2.53);

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("MyPID", MyPID);
    if (verbose)
       nlPrintParams.set("Output Information",
                  NOX::Utils::Error +
                  NOX::Utils::Details +
                  NOX::Utils::OuterIteration +
                  NOX::Utils::InnerIteration +
                  NOX::Utils::Warning +
                  NOX::Utils::TestDetails +
                  NOX::Utils::StepperIteration +
                  NOX::Utils::StepperDetails);
     else
       nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList);

    Epetra_Vector clone_vec(map);
    NOX::Epetra::Vector nox_clone_vec(clone_vec);

    Teuchos::RCP<NOX::Abstract::Vector> x =
      nox_clone_vec.clone(NOX::ShapeCopy);
    x->random();

    Teuchos::RCP<NOX::Abstract::MultiVector> dx1 =
      nox_clone_vec.createMultiVector(3);
    Teuchos::RCP<NOX::Abstract::MultiVector> dx2 =
      nox_clone_vec.createMultiVector(1);
    Teuchos::RCP<NOX::Abstract::MultiVector> dx3 =
      nox_clone_vec.createMultiVector(2);
    Teuchos::RCP<NOX::Abstract::MultiVector> dx4 =
      nox_clone_vec.createMultiVector(2);
    dx1->random();
    dx2->random();
    dx3->init(0.0);
    dx4->random();

    Teuchos::RCP<NOX::Abstract::MultiVector> dx_all =
      dx1->clone(NOX::DeepCopy);
    dx_all->augment(*dx2);
    dx_all->augment(*dx3);
    dx_all->augment(*dx4);

    NOX::Abstract::MultiVector::DenseMatrix dp1(dx1->numVectors(),
                        pVector.length());
    NOX::Abstract::MultiVector::DenseMatrix dp2(dx2->numVectors(),
                        pVector.length());
    NOX::Abstract::MultiVector::DenseMatrix dp3(dx3->numVectors(),
                        pVector.length());
    NOX::Abstract::MultiVector::DenseMatrix dp4(dx4->numVectors(),
                        pVector.length());
    dp1.random();
    dp2.random();
    dp3.random();
    dp4.random();

    NOX::Abstract::MultiVector::DenseMatrix dp_all(dx_all->numVectors(),
                           pVector.length());
    for (int j=0; j<dp_all.numCols(); j++) {
      for (int i=0; i<dp1.numRows(); i++)
    dp_all(i,j) = dp1(i,j);
      for (int i=0; i<dp2.numRows(); i++)
    dp_all(dp1.numRows()+i,j) = dp2(i,j);
      for (int i=0; i<dp3.numRows(); i++)
    dp_all(dp1.numRows()+dp2.numRows()+i,j) = dp3(i,j);
      for (int i=0; i<dp4.numRows(); i++)
    dp_all(dp1.numRows()+dp2.numRows()+dp3.numRows()+i,j) = dp4(i,j);
    }


    std::vector< Teuchos::RCP<LOCA::MultiContinuation::ConstraintInterface> > constraintObjs(4);
    Teuchos::RCP<LinearConstraint> linear_constraint;

    linear_constraint = Teuchos::rcp(new LinearConstraint(dx1->numVectors(),
                              pVector,
                              nox_clone_vec));
    linear_constraint->setDgDx(*dx1);
    linear_constraint->setDgDp(dp1);
    linear_constraint->setIsZeroDX(false);
    constraintObjs[0] = linear_constraint;

    linear_constraint = Teuchos::rcp(new LinearConstraint(dx2->numVectors(),
                              pVector,
                              nox_clone_vec));
    linear_constraint->setDgDx(*dx2);
    linear_constraint->setDgDp(dp2);
    linear_constraint->setIsZeroDX(false);
    constraintObjs[1] = linear_constraint;

    linear_constraint = Teuchos::rcp(new LinearConstraint(dx3->numVectors(),
                              pVector,
                              nox_clone_vec));
    linear_constraint->setDgDx(*dx3);
    linear_constraint->setDgDp(dp3);
    linear_constraint->setIsZeroDX(true);
    constraintObjs[2] = linear_constraint;

    linear_constraint = Teuchos::rcp(new LinearConstraint(dx4->numVectors(),
                              pVector,
                              nox_clone_vec));
    linear_constraint->setDgDx(*dx4);
    linear_constraint->setDgDp(dp4);
    linear_constraint->setIsZeroDX(false);
    constraintObjs[3] = linear_constraint;

    // Check some statistics on the solution
    NOX::TestCompare testCompare(globalData->locaUtils->out(),
                 *(globalData->locaUtils));

    LOCA::MultiContinuation::CompositeConstraint composite(globalData,
                               constraintObjs);
    composite.setX(*x);

    LinearConstraint combined(dx_all->numVectors(), pVector, nox_clone_vec);
    combined.setDgDx(*dx_all);
    combined.setDgDp(dp_all);
    combined.setX(*x);

    //
    // test computeConstraints()
    //

    composite.computeConstraints();
    combined.computeConstraints();

    int numConstraints = dx_all->numVectors();
    const NOX::Abstract::MultiVector::DenseMatrix& g_composite =
      composite.getConstraints();
    const NOX::Abstract::MultiVector::DenseMatrix& g_combined =
      combined.getConstraints();

    ierr += testCompare.testMatrix(
                 g_composite, g_combined, reltol, abstol,
                 "CompositeConstraint::computeConstraints()");

    //
    // test computeDP()
    //

    std::vector<int> paramIDs(3);
    paramIDs[0] = 1;
    paramIDs[1] = 2;
    paramIDs[2] = 4;
    NOX::Abstract::MultiVector::DenseMatrix dgdp_composite(
                            numConstraints,
                            paramIDs.size()+1);
    NOX::Abstract::MultiVector::DenseMatrix dgdp_combined(
                            numConstraints,
                            paramIDs.size()+1);
    dgdp_composite.putScalar(0.0);
    dgdp_combined.putScalar(0.0);
    composite.computeDP(paramIDs, dgdp_composite, false);
    combined.computeDP(paramIDs, dgdp_combined, false);

    ierr += testCompare.testMatrix(
                 dgdp_composite, dgdp_combined, reltol, abstol,
                 "CompositeConstraint::computeDP()");

    //
    // test multiplyDX()
    //

    composite.computeDX();
    combined.computeDX();

    int numMultiply = 5;
    Teuchos::RCP<NOX::Abstract::MultiVector> A =
      nox_clone_vec.createMultiVector(numMultiply);
    A->random();
    NOX::Abstract::MultiVector::DenseMatrix composite_multiply(numConstraints,
                                   numMultiply);
    NOX::Abstract::MultiVector::DenseMatrix combined_multiply(numConstraints,
                                  numMultiply);
    composite.multiplyDX(2.65, *A, composite_multiply);
    combined.multiplyDX(2.65, *A, combined_multiply);

    ierr += testCompare.testMatrix(composite_multiply, combined_multiply,
                    reltol, abstol,
                    "CompositeConstraint::multiplyDX()");

    //
    // test addDX() (No Trans)
    //

    int numAdd = 5;
    NOX::Abstract::MultiVector::DenseMatrix B1(numConstraints, numAdd);
    B1.random();
    NOX::Abstract::MultiVector::DenseMatrix B2(numAdd, numConstraints);
    B2.random();

    Teuchos::RCP<NOX::Abstract::MultiVector> composite_add1 =
      nox_clone_vec.createMultiVector(numAdd);
    composite_add1->random();
    Teuchos::RCP<NOX::Abstract::MultiVector> composite_add2 =
      nox_clone_vec.createMultiVector(numAdd);
    composite_add2->random();

    Teuchos::RCP<NOX::Abstract::MultiVector> combined_add1 =
      composite_add1->clone(NOX::DeepCopy);
    Teuchos::RCP<NOX::Abstract::MultiVector> combined_add2 =
      composite_add2->clone(NOX::DeepCopy);

    composite.addDX(Teuchos::NO_TRANS, 1.45, B1, 2.78, *composite_add1);
    combined.addDX(Teuchos::NO_TRANS, 1.45, B1, 2.78, *combined_add1);

    ierr += testCompare.testMultiVector(
                   *composite_add1, *combined_add1,
                   reltol, abstol,
                   "CompositeConstraint::addDX() (No Trans)");

    //
    // test addDX() (Trans)
    //

    composite.addDX(Teuchos::TRANS, 1.45, B2, 2.78, *composite_add2);
    combined.addDX(Teuchos::TRANS, 1.45, B2, 2.78, *combined_add2);

    ierr += testCompare.testMultiVector(
                   *composite_add2, *combined_add2,
                   reltol, abstol,
                   "CompositeConstraint::addDX() (Trans)");

    LOCA::destroyGlobalData(globalData);
  }

  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  }
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

  if (MyPID == 0) {
    if (ierr == 0)
      std::cout << "All tests passed!" << std::endl;
    else
      std::cout << ierr << " test(s) failed!" << std::endl;
  }

#ifdef HAVE_MPI
  MPI_Finalize() ;
#endif

  return ierr;
}
int main(int argc, char *argv[])
{
  int nConstraints = 10;
  int nRHS = 7;

  double left_bc = 0.0;
  double right_bc = 1.0;
  double nonlinear_factor = 1.0;
  int ierr = 0;
  double reltol = 1.0e-8;
  double abstol = 1.0e-8;
  double lstol = 1.0e-11;

  int MyPID = 0;

  try {

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

    // Create a communicator for Epetra objects
#ifdef HAVE_MPI
    Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
    Epetra_SerialComm Comm;
#endif

    // Get the total number of processors
    MyPID = Comm.MyPID();
    int NumProc = Comm.NumProc();

    bool verbose = false;
    // Check for verbose output
    if (argc>1)
      if (argv[1][0]=='-' && argv[1][1]=='v')
    verbose = true;

    // Get the number of elements from the command line
    int NumGlobalElements = 0;
    if ((argc > 2) && (verbose))
      NumGlobalElements = atoi(argv[2]) + 1;
    else if ((argc > 1) && (!verbose))
      NumGlobalElements = atoi(argv[1]) + 1;
    else
      NumGlobalElements = 101;

    // The number of unknowns must be at least equal to the
    // number of processors.
    if (NumGlobalElements < NumProc) {
      std::cout << "numGlobalBlocks = " << NumGlobalElements
       << " cannot be < number of processors = " << NumProc << std::endl;
      exit(1);
    }

    // Seed the random number generator in Teuchos.  We create random
    // bordering matrices and it is possible different processors might generate
    // different matrices.  By setting the seed, this shouldn't happen.
    Teuchos::ScalarTraits<double>::seedrandom(12345);

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the constraints list
    Teuchos::ParameterList& constraintsList =
      locaParamsList.sublist("Constraints");
    constraintsList.set("Bordered Solver Method", "Bordering");

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("MyPID", MyPID);
    if (verbose)
       nlPrintParams.set("Output Information",
                  NOX::Utils::Error +
                  NOX::Utils::Details +
                      NOX::Utils::LinearSolverDetails +
                  NOX::Utils::OuterIteration +
                  NOX::Utils::InnerIteration +
                  NOX::Utils::Warning +
                  NOX::Utils::TestDetails +
                  NOX::Utils::StepperIteration +
                  NOX::Utils::StepperDetails);
     else
       nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create the "Direction" sublist for the "Line Search Based" solver
    Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
    Teuchos::ParameterList& newParams = dirParams.sublist("Newton");
    Teuchos::ParameterList& lsParams = newParams.sublist("Linear Solver");
    lsParams.set("Aztec Solver", "GMRES");
    lsParams.set("Max Iterations", 100);
    lsParams.set("Tolerance", lstol);
    if (verbose)
      lsParams.set("Output Frequency", 1);
    else
      lsParams.set("Output Frequency", 0);
    lsParams.set("Scaling", "None");
    lsParams.set("Preconditioner", "Ifpack");
    //lsParams.set("Preconditioner", "AztecOO");
    //lsParams.set("Jacobian Operator", "Matrix-Free");
    //lsParams.set("Preconditioner Operator", "Finite Difference");
    lsParams.set("Aztec Preconditioner", "ilut");
    //lsParams.set("Overlap", 2);
    //lsParams.set("Fill Factor", 2.0);
    //lsParams.set("Drop Tolerance", 1.0e-12);
    lsParams.set("Max Age Of Prec", -2);

    // Create the FiniteElementProblem class.  This creates all required
    // Epetra objects for the problem and allows calls to the
    // function (RHS) and Jacobian evaluation routines.
    Tcubed_FiniteElementProblem Problem(NumGlobalElements, Comm);

    // Get the vector from the Problem
    Epetra_Vector& soln = Problem.getSolution();

    // Initialize Solution
    soln.PutScalar(0.0);

    // Create and initialize the parameter vector
    LOCA::ParameterVector pVector;
    pVector.addParameter("Nonlinear Factor",nonlinear_factor);
    pVector.addParameter("Left BC", left_bc);
    pVector.addParameter("Right BC", right_bc);

    // Create the interface between the test problem and the nonlinear solver
    // This is created by the user using inheritance of the abstract base
    // class:
    Teuchos::RCP<Problem_Interface> interface =
      Teuchos::rcp(new Problem_Interface(Problem));
    Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;
    Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;

    // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
    Teuchos::RCP<Epetra_RowMatrix> Amat =
      Teuchos::rcp(&Problem.getJacobian(),false);

    // Create the linear systems
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys =
      Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams,
                            lsParams, iReq, iJac,
                            Amat, soln));

    // Create the loca vector
    NOX::Epetra::Vector locaSoln(soln);

    // Create Epetra factory
    Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
      Teuchos::rcp(new LOCA::Epetra::Factory);

     // Create global data object
    globalData = LOCA::createGlobalData(paramList, epetraFactory);

    // Create parsed parameter list
    parsedParams =
      Teuchos::rcp(new LOCA::Parameter::SublistParser(globalData));
    parsedParams->parseSublists(paramList);

    // Create the Group
    grp = Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams,
                           iReq, locaSoln,
                           linsys, pVector));

    // Create Jacobian operator
    op = Teuchos::rcp(new LOCA::BorderedSolver::JacobianOperator(grp));

    // Change initial guess to a random vector
    Teuchos::RCP<NOX::Abstract::Vector> xnew =
      grp->getX().clone();
    xnew->random();
    grp->setX(*xnew);

    // Create the constraints object & constraint param IDs list
    constraints =
      Teuchos::rcp(new LinearConstraint(nConstraints, LOCA::ParameterVector(),
                    locaSoln));

    // Create bordering solver
    bordering
      = globalData->locaFactory->createBorderedSolverStrategy(
                     parsedParams,
                     parsedParams->getSublist("Constraints"));

    // Change strategy to Householder
    constraintsList.set("Bordered Solver Method",
                 "Householder");

    // Create householder solver
    householder
      = globalData->locaFactory->createBorderedSolverStrategy(
                     parsedParams,
                     parsedParams->getSublist("Constraints"));

    // Check some statistics on the solution
    testCompare = Teuchos::rcp(new NOX::TestCompare(
                                 globalData->locaUtils->out(),
                         *(globalData->locaUtils)));

    // Evaluate blocks
    grp->computeF();
    grp->computeJacobian();

    // A
    A = grp->getX().createMultiVector(nConstraints);
    A->random();

    // B
    constraints->setX(grp->getX());
    B = grp->getX().createMultiVector(nConstraints);
    B->random();
    constraints->setDgDx(*B);
    constraints->computeConstraints();
    constraints->computeDX();

    // C
    C = Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(nConstraints,
                                 nConstraints));
    C->random();

    // Set up left- and right-hand sides
    F = grp->getX().createMultiVector(nRHS);
    F->random();
    G = Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(nConstraints,
                                 nRHS));
    G->random();
    X_bordering = F->clone(NOX::ShapeCopy);
    Y_bordering =
      Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(nConstraints,
                                   nRHS));
    X_householder = F->clone(NOX::ShapeCopy);
    Y_householder =
      Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(nConstraints,
                                   nRHS));

    std::string testName;

    // Test all nonzero
    testName = "Testing all nonzero";
    ierr += testSolve(false, false, false, false, false,
              reltol, abstol, testName);

    // Test A = 0
    testName = "Testing A=0";
    ierr += testSolve(true, false, false, false, false,
              reltol, abstol, testName);

    // Test B = 0
    testName = "Testing B=0";
    ierr += testSolve(false, true, false, false, false,
              reltol, abstol, testName);

    // Test C = 0
    testName = "Testing C=0";
    ierr += testSolve(false, false, true, false, false,
              reltol, abstol, testName);

    // Test F = 0
    testName = "Testing F=0";
    ierr += testSolve(false, false, false, true, false,
              reltol, abstol, testName);

    // Test G = 0
    testName = "Testing G=0";
    ierr += testSolve(false, false, false, false, true,
              reltol, abstol, testName);

    // Test A,B = 0
    testName = "Testing A,B=0";
    ierr += testSolve(true, true, false, false, false,
              reltol, abstol, testName);

    // Test A,F = 0
    testName = "Testing A,F=0";
    ierr += testSolve(true, false, false, true, false,
              reltol, abstol, testName);

    // Test A,G = 0
    testName = "Testing A,G=0";
    ierr += testSolve(true, false, false, false, true,
              reltol, abstol, testName);

    // Test B,F = 0
    testName = "Testing B,F=0";
    ierr += testSolve(false, true, false, true, false,
              reltol, abstol, testName);

    // Test B,G = 0
    testName = "Testing B,G=0";
    ierr += testSolve(false, true, false, false, true,
              reltol, abstol, testName);

    // Test C,F = 0
    testName = "Testing C,F=0";
    ierr += testSolve(false, false, true, true, false,
              reltol, abstol, testName);

    // Test C,G = 0
    testName = "Testing C,G=0";
    ierr += testSolve(false, false, true, false, true,
              reltol, abstol, testName);

    // Test F,G = 0
    testName = "Testing F,G=0";
    ierr += testSolve(false, false, false, true, true,
              reltol, abstol, testName);

    // Test A,B,F = 0
    testName = "Testing A,B,F=0";
    ierr += testSolve(true, true, false, true, false,
              reltol, abstol, testName);

    // Test A,B,G = 0
    testName = "Testing A,B,G=0";
    ierr += testSolve(true, true, false, false, true,
              reltol, abstol, testName);

    // Test A,F,G = 0
    testName = "Testing A,F,G=0";
    ierr += testSolve(true, false, false, true, true,
              reltol, abstol, testName);

    // Test B,F,G = 0
    testName = "Testing B,F,G=0";
    ierr += testSolve(false, true, false, true, true,
              reltol, abstol, testName);

    // Test C,F,G = 0
    testName = "Testing C,F,G=0";
    ierr += testSolve(false, false, true, true, true,
              reltol, abstol, testName);

    // Test A,B,F,G = 0
    testName = "Testing A,B,F,G=0";
    ierr += testSolve(true, true, false, true, true,
              reltol, abstol, testName);

    LOCA::destroyGlobalData(globalData);

  }

  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  }
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

  if (MyPID == 0) {
    if (ierr == 0)
      std::cout << "All tests passed!" << std::endl;
    else
      std::cout << ierr << " test(s) failed!" << std::endl;
  }

#ifdef HAVE_MPI
  MPI_Finalize() ;
#endif

  return ierr;
}
Beispiel #11
0
int main()
{
  int n = 100;
  double alpha = 0.25;
  double beta = 0.0;
  double D1 = 1.0/40.0;
  double D2 = 1.0/40.0;
  int maxNewtonIters = 10;

  try {

    // Create output file to save solutions
    ofstream outFile("BrusselatorContinuation.dat");
    outFile.setf(ios::scientific, ios::floatfield);
    outFile.precision(14);

    // Save size of discretizations
    outFile << n << endl;

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList = 
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    stepperList.set("Continuation Method", "Arc Length");    // Default
    stepperList.set("Continuation Parameter", "beta");
    stepperList.set("Initial Value", beta);
    stepperList.set("Max Value", 2.0);
    stepperList.set("Min Value", 0.0);
    stepperList.set("Max Steps", 100);
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters);
    
    // Use LAPACK solver for arclength bordered solves for efficiency
    stepperList.set("Bordered Solver Method", "LAPACK Direct Solve");

    // Create Eigensolver list using LAPACK eigensolver
    stepperList.set("Compute Eigenvalues",true);
    Teuchos::ParameterList& eigenList = stepperList.sublist("Eigensolver");
    eigenList.set("Method", "DGGEV");     // LAPACK eigensolver
    eigenList.set("NEV", 10);             // Show 10 eigenvalues
    eigenList.set("Sorting Order", "LR"); // Sort by largest real component

    // Create predictor sublist.  We use the constant predictor because the
    // solution is linear in the continuation parameter.  Using Secant or
    // Tangent is not very interesting, but are perfectly valid
    Teuchos::ParameterList& predictorList = 
      locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Constant");
    //predictorList.set("Method", "Tangent");
    //predictorList.set("Method", "Secant");

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Method", "Adaptive");    // Default
    stepSizeList.set("Initial Step Size", 0.1);
    stepSizeList.set("Min Step Size", 1.0e-3);
    stepSizeList.set("Max Step Size", 10.0);
    stepSizeList.set("Aggressiveness", 0.1);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("Output Information", 
		      NOX::Utils::Details +
		      NOX::Utils::OuterIteration + 
		      NOX::Utils::InnerIteration + 
		      NOX::Utils::Warning + 
		      NOX::Utils::StepperIteration +
		      NOX::Utils::StepperDetails +
		      NOX::Utils::StepperParameters);

    // Create LAPACK Factory (necessary for LAPACK eigensolver)
    Teuchos::RCP<LOCA::LAPACK::Factory> lapackFactory = 
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, lapackFactory);

    // Set up the problem interface
    BrusselatorProblemInterface brus(globalData, n, alpha, beta, D1, D2, 
				     outFile);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("D1",D1);
    p.addParameter("D2",D2);
  
    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    Teuchos::RCP<LOCA::MultiContinuation::AbstractGroup> grp = 
      Teuchos::rcp(new LOCA::LAPACK::Group(globalData, brus));

    grp->setParams(p);

    // Set up the status tests
    Teuchos::RCP<NOX::StatusTest::NormF> normF = 
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxIters = 
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Generic> comboOR = 
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR, 
					      normF, 
					      maxIters));

    // Create the stepper  
    LOCA::Stepper stepper(globalData, grp, comboOR, paramList);

    // Perform continuation run
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    // Check for convergence
    if (status == LOCA::Abstract::Iterator::Finished) 
      cout << "All examples passed" << endl;
    else {
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() 
	  << "Stepper failed to converge!" << std::endl;
    }

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    outFile.close();

    LOCA::destroyGlobalData(globalData);
  }

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

  return 0;
}
Beispiel #12
0
int main(int argc, char *argv[])
{
  // Initialize MPI
#ifdef HAVE_MPI
  MPI_Init(&argc,&argv);
#endif

  // Create a communicator for Epetra objects
#ifdef HAVE_MPI
  Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
  Epetra_SerialComm Comm;
#endif

  bool verbose = false;
  bool success = false;
  try {
    // scale factor to test arc-length scaling
    double scale = 1.0;

    // Create output file to save solutions
    std::ofstream outFile("t3.dat");
    outFile.setf(ios::scientific, ios::floatfield);
    outFile.precision(14);

    int ierr = 0;

    // Get the process ID and the total number of processors
    int MyPID = Comm.MyPID();
    int NumProc = Comm.NumProc();

    // Get the number of elements from the command line
    int NumGlobalElements = 100 + 1;

    // The number of unknowns must be at least equal to the
    // number of processors.
    if (NumGlobalElements < NumProc) {
      std::cout << "numGlobalBlocks = " << NumGlobalElements
        << " cannot be < number of processors = " << NumProc << std::endl;
      exit(1);
    }

    // Create the FiniteElementProblem class.  This creates all required
    // Epetra objects for the problem and allows calls to the
    // function (RHS) and Jacobian evaluation routines.
    FiniteElementProblem Problem(NumGlobalElements, Comm, scale, &outFile);

    // Get the vector from the Problem
    Epetra_Vector& soln = Problem.getSolution();

    // Initialize Solution
    soln.PutScalar(1.0);

    // Begin LOCA Solver ************************************

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& locaStepperList = locaParamsList.sublist("Stepper");
    locaStepperList.set("Continuation Method", "Arc Length");      // Default
    locaStepperList.set("Continuation Parameter", "Right BC");
    locaStepperList.set("Initial Value", 0.1/scale);
    locaStepperList.set("Max Value", 100.0/scale);
    locaStepperList.set("Min Value", 0.05/scale);
    locaStepperList.set("Max Steps", 30);
    locaStepperList.set("Max Nonlinear Iterations", 15);

    // Use Housholder method for solving bordered arclength equations
    locaStepperList.set("Bordered Solver Method", "Householder");

#ifdef HAVE_LOCA_ANASAZI
    // Create Anasazi Eigensolver sublist (needs --with-loca-anasazi)
    locaStepperList.set("Compute Eigenvalues",true);
    Teuchos::ParameterList& aList = locaStepperList.sublist("Eigensolver");
    aList.set("Method", "Anasazi");
    aList.set("Block Size", 1);        // Size of blocks
    aList.set("Num Blocks", 10);       // Size of Arnoldi factorization
    aList.set("Num Eigenvalues", 3);   // Number of eigenvalues
    aList.set("Convergence Tolerance", 2.0e-7);          // Tolerance
    aList.set("Step Size", 1);         // How often to check convergence
    aList.set("Maximum Restarts",2);   // Maximum number of restarts
    aList.set("Verbosity",
        Anasazi::Errors +
        Anasazi::Warnings +
        Anasazi::FinalSummary);        // Verbosity
#else
    locaStepperList.set("Compute Eigenvalues",false);
#endif

    // Create predictor sublist
    Teuchos::ParameterList& predictorList = locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Secant");      // Default

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Method", "Adaptive");    // Dfault
    stepSizeList.set("Initial Step Size", 0.1/scale);
    stepSizeList.set("Min Step Size", 1.0e-3/scale);
    stepSizeList.set("Max Step Size", 2000.0/scale);
    stepSizeList.set("Aggressiveness", 0.1);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

    // Create the NOX printing parameter list
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("MyPID", MyPID);
    nlPrintParams.set("Output Information",
        NOX::Utils::OuterIteration +
        NOX::Utils::OuterIterationStatusTest +
        NOX::Utils::InnerIteration +
        NOX::Utils::Details +
        NOX::Utils::Warning +
        NOX::Utils::StepperIteration +
        NOX::Utils::StepperDetails +
        NOX::Utils::StepperParameters);

    // Create the "Linear Solver" sublist for Newton's method
    Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
    Teuchos::ParameterList& newParams = dirParams.sublist("Newton");
    Teuchos::ParameterList& lsParams = newParams.sublist("Linear Solver");
    lsParams.set("Aztec Solver", "GMRES");
    lsParams.set("Max Iterations", 100);
    lsParams.set("Tolerance", 1e-4);
    lsParams.set("Output Frequency", 1);
    lsParams.set("Scaling", "None");
    lsParams.set("Preconditioner", "Ifpack");
    //lsParams.set("Preconditioner", "AztecOO");
    //lsParams.set("Jacobian Operator", "Matrix-Free");
    //lsParams.set("Preconditioner Operator", "Finite Difference");
    //lsParams.set("Aztec Preconditioner", "ilut");
    //lsParams.set("Overlap", 2);
    //lsParams.set("Fill Factor", 2.0);
    //lsParams.set("Drop Tolerance", 1.0e-12);

    // Create and initialize the parameter vector
    LOCA::ParameterVector pVector;
    pVector.addParameter("Nonlinear Factor",1.0);
    pVector.addParameter("Left BC", 0.0);
    pVector.addParameter("Right BC", 0.1);

    // Create the interface between the test problem and the nonlinear solver
    // This is created by the user using inheritance of the abstract base class:
    Teuchos::RCP<Problem_Interface> interface =
      Teuchos::rcp(new Problem_Interface(Problem));
    Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;
    Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;

    // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
    Teuchos::RCP<Epetra_RowMatrix> Amat =
      Teuchos::rcp(&Problem.getJacobian(),false);

    // Create the linear systems
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys =
      Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams, lsParams,
            iReq, iJac, Amat, soln));

    // Create the loca vector
    NOX::Epetra::Vector locaSoln(soln);

    // Create Epetra factory
    Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
      Teuchos::rcp(new LOCA::Epetra::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, epetraFactory);

    // Create the Group
    Teuchos::RCP<LOCA::Epetra::Group> grp =
      Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams,
            iReq, locaSoln, linsys,
            pVector));
    grp->computeF();

    // Create the Solver convergence test
    Teuchos::RCP<NOX::StatusTest::NormF> wrms =
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters =
      Teuchos::rcp(new NOX::StatusTest::MaxIters(locaStepperList.get("Max Nonlinear Iterations", 10)));
    Teuchos::RCP<NOX::StatusTest::Combo> combo =
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
    combo->addStatusTest(wrms);
    combo->addStatusTest(maxiters);

#ifdef HAVE_TEUCHOS_EXTENDED
    // Write the parameter list to a file
    std::cout << "Writing parameter list to \"input.xml\"" << std::endl;
    Teuchos::writeParameterListToXmlFile(*paramList, "input.xml");

    // Read in the parameter list from a file
    std::cout << "Reading parameter list from \"input.xml\"" << std::endl;
    Teuchos::RCP<Teuchos::ParameterList> paramList2 =
      Teuchos::rcp(new Teuchos::ParameterList);
    Teuchos::updateParametersFromXmlFile("input.xml", paramList2.ptr());
    paramList = paramList2;
#endif

    // Create the stepper
    LOCA::Stepper stepper(globalData, grp, combo, paramList);
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    if (status == LOCA::Abstract::Iterator::Finished)
      globalData->locaUtils->out() << "\nAll tests passed" << std::endl;
    else {
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
        globalData->locaUtils->out()
          << "Stepper failed to converge!" << std::endl;
    }

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out()
        << std::endl << "Final Parameters" << std::endl
        << "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    LOCA::destroyGlobalData(globalData);

    success = ierr==0;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(verbose, std::cerr, success);

#ifdef HAVE_MPI
  MPI_Finalize() ;
#endif

  return ( success ? EXIT_SUCCESS : EXIT_FAILURE );
}
Beispiel #13
0
void cnoxinit(int* nelems, double* statevector, int* mpi_comm_ignored,
              void* blackbox_res, void* blackbox_prec,
              void (*residualFunction)(double *, double *, int, void *),
              void (*precFunction)(double *, double *, int, double*, void *))
{
  try {
    TEST_FOR_EXCEPTION(!is_null(solver), logic_error,
         "Exception: cnoxinit() called with solver!=null: "
      << "did not cnoxfinish() since last cnoxinit() call!!");
 
    // Create a communicator for Epetra objects
    Epetra_MpiComm Comm( MPI_COMM_WORLD );

    // Get the process ID and the total number of processors
    int MyPID = Comm.MyPID();

    // Begin LOCA Solver ************************************
    //
    // Create and initialize the continuation/bifurcation parameter vector
    LOCA::ParameterVector pVector;
    pVector.addParameter("ContinuationParam", 0.0);

    // Create parameter (options) list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Read in the parameter list from a file
    cout << "Reading parameter list from \"input.xml\"" << endl;
    Teuchos::updateParametersFromXmlFile("input.xml", paramList.get());

    // Set some default parameters
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");
    Teuchos::ParameterList& locaStepperList = locaParamsList.sublist("Stepper");
    locaStepperList.set("Continuation Parameter", "ContinuationParam");

    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlDir = nlParams.sublist("Direction");
    Teuchos::ParameterList& nlNewton = nlDir.sublist("Newton");
    Teuchos::ParameterList& lsParams = nlNewton.sublist("Linear Solver");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("MyPID", MyPID);
     if (!nlPrintParams.isParameter("Output Information"))
        nlPrintParams.set("Output Information",
                          NOX::Utils::OuterIteration  +
//                        NOX::Utils::OuterIterationStatusTest +
//                        NOX::Utils::InnerIteration +
//                        NOX::Utils::Details +
                          NOX::Utils::LinearSolverDetails
//                        NOX::Utils::Warning +
//                        NOX::Utils::StepperIteration +
//                        NOX::Utils::StepperDetails +
//                        NOX::Utils::StepperParameters
                                );


    // Create the interface between the test problem and the nonlinear solver
  // This is created by the user using inheritance of the abstract base class:
    interface = Teuchos::rcp(new CNOX_Interface(nelems, statevector, pVector, Comm,
                                                blackbox_res, blackbox_prec,
                                                residualFunction, precFunction));
    Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;

    // Interface is inherited from these 2 classes as well for user prec
    Teuchos::RCP<NOX::Epetra::Interface::Preconditioner> iPrec = interface;
    Teuchos::RCP<Epetra_Operator> precOperator = interface;

    // Create the Epetra_Vector for the  state vector
    Teuchos::RCP<Epetra_Vector> soln = interface->getVector();

// The next 2 statements need to be changed if your interface can
// supply a Jacobian matrix!!! See nox examples epetra .....
    Teuchos::RCP<NOX::Epetra::MatrixFree> FD =
      Teuchos::rcp(new NOX::Epetra::MatrixFree(nlPrintParams, interface, soln));

    Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = FD;

    // Create the linear systems
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys =
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams, lsParams,
                                         iJac, FD, iPrec, precOperator, soln));

/* With a Jacobian, and no user-define preconditioner the previous 3 calls should be:

  Teuchos::RCP<Epetra_RowMatrix> Amat = Teuchos::rcp(interface->getJacobian(),false)
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;
  // Create the linear systems
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys =
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams, lsParams,
                                                      iReq, iJac, Amat, soln))
*/

    // Create the loca vector
    initialGuess = Teuchos::RCP<NOX::Epetra::Vector>(new NOX::Epetra::Vector(soln));

    // Create Epetra factory
    Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
      Teuchos::rcp(new LOCA::Epetra::Factory);

    // Create global data object
    globalData = LOCA::createGlobalData(paramList, epetraFactory);

    // Create the Group
    Teuchos::RCP<LOCA::Epetra::Group> grp =
      Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams,
                                           iReq, *initialGuess, linsys,
                                           pVector));
    grp->computeF();

    // Create the Solver convergence test
    Teuchos::RCP<NOX::StatusTest::NormF> wrms =
      Teuchos::rcp(new NOX::StatusTest::NormF(nlParams.get("Convergence Tolerance",1.0e-8)));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters =
      Teuchos::rcp(new NOX::StatusTest::MaxIters(10));
    Teuchos::RCP<NOX::StatusTest::Combo> combo =
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
    combo->addStatusTest(wrms);
    combo->addStatusTest(maxiters);

    Teuchos::RCP<Teuchos::ParameterList> nlParamsRCP = Teuchos::rcp(&nlParams, false);
    solver = NOX::Solver::buildSolver(grp, combo, nlParamsRCP);

  } //end try block

  catch (std::exception& e) {
    cout << e.what() << endl;
  }
  catch (const char *s) {
    cout << s << endl;
  }
  catch (...) {
    cout << "Caught unknown exception!" << endl;
  }
}
int main(int argc, char *argv[])
{
  int ierr = 0;

  try {
    int n = 100;
    double alpha = 4.0;
    double beta = 0.0;
    double scale = 1.0;
    int maxNewtonIters = 10;

    NOX::Random::setSeed(1);

    bool verbose = false;
    // Check for verbose output
    if (argc>1) 
      if (argv[1][0]=='-' && argv[1][1]=='v') 
	verbose = true;

    // Create initial guess for the null vector of jacobian
    Teuchos::RCP<NOX::Abstract::Vector> nullVec = 
      Teuchos::rcp(new NOX::LAPACK::Vector(n));
    nullVec->init(1.0);               // initial value 1.0

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList = 
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    stepperList.set("Continuation Parameter", "beta");
    stepperList.set("Initial Value", beta);
    stepperList.set("Max Value", 1.0);
    stepperList.set("Min Value", 0.0);
    stepperList.set("Max Steps", 20);
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters);

    // Create bifurcation sublist
    Teuchos::ParameterList& bifurcationList = 
      locaParamsList.sublist("Bifurcation");
    bifurcationList.set("Type", "Turning Point");
    bifurcationList.set("Bifurcation Parameter", "alpha");
    bifurcationList.set("Length Normalization Vector", nullVec);
    bifurcationList.set("Initial Null Vector", nullVec);

    // Create predictor sublist
    Teuchos::ParameterList& predictorList = 
      locaParamsList.sublist("Predictor");
    Teuchos::ParameterList& firstStepPredictor 
      = predictorList.sublist("First Step Predictor");
    firstStepPredictor.set("Method", "Random");
    firstStepPredictor.set("Epsilon", 1.0e-3);
    Teuchos::ParameterList& lastStepPredictor 
      = predictorList.sublist("Last Step Predictor");
    lastStepPredictor.set("Method", "Random");
    lastStepPredictor.set("Epsilon", 1.0e-3);

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Initial Step Size", 0.1);
    stepSizeList.set("Min Step Size", 1.0e-3);
    stepSizeList.set("Max Step Size", 1.0);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    if (verbose)
      nlPrintParams.set("Output Information", 
			NOX::Utils::Error +
			NOX::Utils::OuterIteration + 
			NOX::Utils::InnerIteration +
			NOX::Utils::Details + 
			NOX::Utils::Warning +
			NOX::Utils::TestDetails + 
			NOX::Utils::StepperIteration +
			NOX::Utils::StepperDetails +
			NOX::Utils::StepperParameters);
    else
       nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create LAPACK Factory
    Teuchos::RCP<LOCA::LAPACK::Factory> lapackFactory = 
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, lapackFactory);

    // Set up the problem interface
    ChanProblemInterface chan(globalData, n, alpha, beta, scale);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("scale",scale);

    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    Teuchos::RCP<LOCA::MultiContinuation::AbstractGroup> grp = 
      Teuchos::rcp(new LOCA::LAPACK::Group(globalData, chan));
    
    grp->setParams(p);

    // Set up the status tests
    Teuchos::RCP<NOX::StatusTest::NormF> statusTestA =
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-5, 
					      NOX::StatusTest::NormF::Scaled));
    Teuchos::RCP<NOX::StatusTest::MaxIters> statusTestB =
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Combo> combo = 
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR, 
					      statusTestA, statusTestB));

    // Create the stepper  
    LOCA::Stepper stepper(globalData, grp, combo, paramList);

    // Solve the nonlinear system
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    if (status != LOCA::Abstract::Iterator::Finished) {
      ierr = 1;
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() 
	  << "Stepper failed to converge!" << std::endl;
    }

    // Get the final solution from the stepper
    Teuchos::RCP<const LOCA::LAPACK::Group> finalGroup = 
      Teuchos::rcp_dynamic_cast<const LOCA::LAPACK::Group>(stepper.getSolutionGroup());
    const NOX::LAPACK::Vector& finalSolution = 
      dynamic_cast<const NOX::LAPACK::Vector&>(finalGroup->getX());

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    // Check some statistics on the solution
     NOX::TestCompare testCompare(globalData->locaUtils->out(), 
				 *(globalData->locaUtils));

    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() 
	<< std::endl 
	<< "***** Checking solution statistics *****" 
	<< std::endl;
  
    // Check number of steps
    int numSteps = stepper.getStepNumber();
    int numSteps_expected = 10;
    ierr += testCompare.testValue(numSteps, numSteps_expected, 0.0,
				  "number of continuation steps", 
				  NOX::TestCompare::Absolute);

    // Check number of failed steps
    int numFailedSteps = stepper.getNumFailedSteps();
    int numFailedSteps_expected = 0;
    ierr += testCompare.testValue(numFailedSteps, numFailedSteps_expected, 
				  0.0, "number of failed continuation steps", 
				  NOX::TestCompare::Absolute);

    // Check final value of continuation parameter
    double beta_final = finalGroup->getParam("beta");
    double beta_expected = 0.0;
    ierr += testCompare.testValue(beta_final, beta_expected, 1.0e-14,
				  "final value of continuation parameter", 
				  NOX::TestCompare::Relative);

    // Check final value of turning point parameter
    double alpha_final = finalGroup->getParam("alpha");
    double alpha_expected = 3.1601952;
    ierr += testCompare.testValue(alpha_final, alpha_expected, 1.0e-5,
				  "final value of turning point parameter", 
				  NOX::TestCompare::Relative);

    // Check norm of solution
    double norm_x = finalSolution.norm();
    double norm_x_expected = 63.1872045;
    ierr += testCompare.testValue(norm_x, norm_x_expected, 1.0e-4,
				  "norm of final solution", 
				  NOX::TestCompare::Relative);

    LOCA::destroyGlobalData(globalData);
  }

  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  }
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

  if (ierr == 0)
    std::cout << "All tests passed!" << std::endl;
  else
    std::cout << ierr << " test(s) failed!" << std::endl;

  return ierr;
}
Beispiel #15
0
int main()
{

  try {
    int n = 100;
    double alpha = 4.0;
    double beta = 0.0;
    double scale = 1.0;
    int maxNewtonIters = 10;

    // Create output file to save solutions
    std::ofstream outFile("ChanTPContinuation.dat");
    outFile.setf(std::ios::scientific, std::ios::floatfield);
    outFile.precision(14);

    // Save size of discretizations
    outFile << n << std::endl;

    // Create initial guess for the null vector of jacobian
    Teuchos::RCP<NOX::Abstract::Vector> nullVec =
      Teuchos::rcp(new NOX::LAPACK::Vector(n));
    nullVec->init(1.0);               // initial value 1.0

    // Create initial values for a and b for minimally augmented method
    Teuchos::RCP<NOX::Abstract::Vector> a_vec =
      Teuchos::rcp(new NOX::LAPACK::Vector(n));
    a_vec->init(1.0);

    Teuchos::RCP<NOX::Abstract::Vector> b_vec =
      Teuchos::rcp(new NOX::LAPACK::Vector(n));
    b_vec->init(1.0);

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    stepperList.set("Continuation Method", "Arc Length");  // Default
    stepperList.set("Continuation Parameter", "beta");     // Must set
    stepperList.set("Initial Value", beta);                // Must set
    stepperList.set("Max Value", 1.0);                     // Must set
    stepperList.set("Min Value", 0.0);                     // Must set
    stepperList.set("Max Steps", 20);                      // Should set
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters); // Should set

    // Create bifurcation sublist
    Teuchos::ParameterList& bifurcationList =
      locaParamsList.sublist("Bifurcation");
    bifurcationList.set("Type", "Turning Point");          // For turning point
    bifurcationList.set("Bifurcation Parameter", "alpha"); // Must set

    // For Moore-Spence formulation w/bordering
    //bifurcationList.set("Formulation", "Moore-Spence");          // Default
    //bifurcationList.set("Solver Method", "Salinger Bordering");  // Default
    //bifurcationList.set("Solver Method", "Phipps Bordering");
    //bifurcationList.set("Bordered Solver Method",
    //                    "LAPACK Direct Solve");   // For Phipps Bordering
    //bifurcationList.set("Length Normalization Vector", nullVec); // Must set
    //bifurcationList.set("Initial Null Vector", nullVec);         // Must set

    // For minimally augmented formulation
    bifurcationList.set("Formulation", "Minimally Augmented");
    bifurcationList.set("Initial A Vector", a_vec);                // Must set
    bifurcationList.set("Initial B Vector", b_vec);                // Must set

    // For minimally augmented method, should set these for good performance
    // Direct solve of bordered equations
    bifurcationList.set("Bordered Solver Method",  "LAPACK Direct Solve");
    // Combine arc-length and turning point bordered rows & columns
    stepperList.set("Bordered Solver Method", "Nested");
    Teuchos::ParameterList& nestedList =
      stepperList.sublist("Nested Bordered Solver");
    // Direct solve of combined bordered system
    nestedList.set("Bordered Solver Method", "LAPACK Direct Solve");

    // Create predictor sublist
    Teuchos::ParameterList& predictorList =
      locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Secant");                         // Default

    // Should use for Moore-Spence w/Salinger Bordering & Secant predictor
    //Teuchos::ParameterList& firstStepPredictor
    //  = predictorList.sublist("First Step Predictor");
    //firstStepPredictor.set("Method", "Random");
    //firstStepPredictor.set("Epsilon", 1.0e-3);

    // Should use for Moore-Spence w/Salinger Bordering & Secant predictor
    //Teuchos::ParameterList& lastStepPredictor
    //  = predictorList.sublist("Last Step Predictor");
    //lastStepPredictor.set("Method", "Random");
    //lastStepPredictor.set("Epsilon", 1.0e-3);

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Method", "Adaptive");                      // Default
    stepSizeList.set("Initial Step Size", 0.1);                  // Should set
    stepSizeList.set("Min Step Size", 1.0e-3);                   // Should set
    stepSizeList.set("Max Step Size", 1.0);                      // Should set

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("Output Information",
              NOX::Utils::OuterIteration +
              NOX::Utils::OuterIterationStatusTest +
              NOX::Utils::InnerIteration +
              NOX::Utils::Details +
              NOX::Utils::Warning +
              NOX::Utils::StepperIteration +
              NOX::Utils::StepperDetails +
              NOX::Utils::StepperParameters);            // Should set

    // Create LAPACK Factory
    Teuchos::RCP<LOCA::LAPACK::Factory> lapackFactory =
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, lapackFactory);

    // Set up the problem interface
    ChanProblemInterface chan(globalData, n, alpha, beta, scale, outFile);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("scale",scale);

    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    Teuchos::RCP<LOCA::MultiContinuation::AbstractGroup> grp =
      Teuchos::rcp(new LOCA::LAPACK::Group(globalData, chan));

    grp->setParams(p);

    // Set up the status tests
    Teuchos::RCP<NOX::StatusTest::NormF> statusTestA =
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-10,
                          NOX::StatusTest::NormF::Scaled));
    Teuchos::RCP<NOX::StatusTest::MaxIters> statusTestB =
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Combo> combo =
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR,
                          statusTestA, statusTestB));

    // Create the stepper
    LOCA::Stepper stepper(globalData, grp, combo, paramList);

    // Solve the nonlinear system
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    if (status == LOCA::Abstract::Iterator::Finished)
      std::cout << "All examples passed" << std::endl;
    else {
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
    globalData->locaUtils->out()
      << "Stepper failed to converge!" << std::endl;
    }

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out()
    << std::endl << "Final Parameters" << std::endl
    << "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    outFile.close();

    LOCA::destroyGlobalData(globalData);
  }

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

  return 0;
}
int main(int argc, char *argv[])
{
  int nConstraints = 10;
  int nRHS = 7;

  int n = 100;
  double alpha = 1.0;
  double beta = 0.0;
  double gamma = 2.0;
  double scale = 1.0;
  int ierr = 0;
  double reltol = 1.0e-9;
  double abstol = 1.0e-9;

  alpha = alpha / scale;

  try {

    bool verbose = false;
    // Check for verbose output
    if (argc>1)
      if (argv[1][0]=='-' && argv[1][1]=='v')
    verbose = true;

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the constraints list
    Teuchos::ParameterList& constraintsList =
      locaParamsList.sublist("Constraints");
    constraintsList.set("Bordered Solver Method", "Bordering");

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    if (verbose)
       nlPrintParams.set("Output Information",
                  NOX::Utils::Error +
                  NOX::Utils::Details +
                  NOX::Utils::OuterIteration +
                  NOX::Utils::InnerIteration +
                  NOX::Utils::Warning +
                  NOX::Utils::TestDetails +
                  NOX::Utils::StepperIteration +
                  NOX::Utils::StepperDetails);
     else
       nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create LAPACK factory
    Teuchos::RCP<LOCA::Abstract::Factory> lapackFactory =
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    globalData = LOCA::createGlobalData(paramList, lapackFactory);

    // Create parsed parameter list
    parsedParams =
      Teuchos::rcp(new LOCA::Parameter::SublistParser(globalData));
    parsedParams->parseSublists(paramList);

    // Set up the problem interface
    ChanProblemInterface chan(globalData, n, alpha, beta, scale);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("gamma",gamma);
    p.addParameter("scale",scale);

    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    grp = Teuchos::rcp(new LOCA::LAPACK::Group(globalData, chan));
    grp->setParams(p);

    // Create Jacobian operator
    op = Teuchos::rcp(new LOCA::BorderedSolver::JacobianOperator(grp));

    // Change initial guess to a random vector
    Teuchos::RCP<NOX::Abstract::Vector> xnew = grp->getX().clone();
    xnew->random();
    grp->setX(*xnew);

    // Create the constraints object & constraint param IDs list
    constraints = Teuchos::rcp(new LinearConstraint(nConstraints, p, *xnew));
    Teuchos::RCP< std::vector<int> > constraintParamIDs =
      Teuchos::rcp(new std::vector<int>(1));
    (*constraintParamIDs)[0] = p.getIndex("alpha");

    // Create bordering solver
    bordering
      = globalData->locaFactory->createBorderedSolverStrategy(
                     parsedParams,
                     parsedParams->getSublist("Constraints"));

    // Change strategy to LAPACK Direct Solve
    constraintsList.set("Bordered Solver Method",
                 "LAPACK Direct Solve");

    // Create direct solver
    direct
      = globalData->locaFactory->createBorderedSolverStrategy(
                     parsedParams,
                     parsedParams->getSublist("Constraints"));

    // Check some statistics on the solution
    testCompare = Teuchos::rcp(new NOX::TestCompare(
                                 globalData->locaUtils->out(),
                         *(globalData->locaUtils)));

    // Evaluate blocks
    grp->computeF();
    grp->computeJacobian();

    // A
    A = grp->getX().createMultiVector(nConstraints);
    A->random();

    // B
    constraints->setX(grp->getX());
    B = grp->getX().createMultiVector(nConstraints);
    B->random();
    constraints->setDgDx(*B);
    constraints->computeConstraints();
    constraints->computeDX();

    // C
    C =
      Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(nConstraints,
                                   nConstraints));
    C->random();

    // Set up left- and right-hand sides
    F = grp->getX().createMultiVector(nRHS);
    F->random();
    G = Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(nConstraints,
                                 nRHS));
    G->random();
    X_bordering = F->clone(NOX::ShapeCopy);
    Y_bordering =
      Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(nConstraints,
                                   nRHS));
    X_direct = F->clone(NOX::ShapeCopy);
    Y_direct =
      Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(nConstraints,
                                   nRHS));

    std::string testName;

    // Test all nonzero
    testName = "Testing all nonzero";
    ierr += testSolve(false, false, false, false, false,
              reltol, abstol, testName);

    // Test A = 0
    testName = "Testing A=0";
    ierr += testSolve(true, false, false, false, false,
              reltol, abstol, testName);

    // Test B = 0
    testName = "Testing B=0";
    ierr += testSolve(false, true, false, false, false,
              reltol, abstol, testName);

    // Test C = 0
    testName = "Testing C=0";
    ierr += testSolve(false, false, true, false, false,
              reltol, abstol, testName);

    // Test F = 0
    testName = "Testing F=0";
    ierr += testSolve(false, false, false, true, false,
              reltol, abstol, testName);

    // Test G = 0
    testName = "Testing G=0";
    ierr += testSolve(false, false, false, false, true,
              reltol, abstol, testName);

    // Test A,B = 0
    testName = "Testing A,B=0";
    ierr += testSolve(true, true, false, false, false,
              reltol, abstol, testName);

    // Test A,F = 0
    testName = "Testing A,F=0";
    ierr += testSolve(true, false, false, true, false,
              reltol, abstol, testName);

    // Test A,G = 0
    testName = "Testing A,G=0";
    ierr += testSolve(true, false, false, false, true,
              reltol, abstol, testName);

    // Test B,F = 0
    testName = "Testing B,F=0";
    ierr += testSolve(false, true, false, true, false,
              reltol, abstol, testName);

    // Test B,G = 0
    testName = "Testing B,G=0";
    ierr += testSolve(false, true, false, false, true,
              reltol, abstol, testName);

    // Test C,F = 0
    testName = "Testing C,F=0";
    ierr += testSolve(false, false, true, true, false,
              reltol, abstol, testName);

    // Test C,G = 0
    testName = "Testing C,G=0";
    ierr += testSolve(false, false, true, false, true,
              reltol, abstol, testName);

    // Test F,G = 0
    testName = "Testing F,G=0";
    ierr += testSolve(false, false, false, true, true,
              reltol, abstol, testName);

    // Test A,B,F = 0
    testName = "Testing A,B,F=0";
    ierr += testSolve(true, true, false, true, false,
              reltol, abstol, testName);

    // Test A,B,G = 0
    testName = "Testing A,B,G=0";
    ierr += testSolve(true, true, false, false, true,
              reltol, abstol, testName);

    // Test A,F,G = 0
    testName = "Testing A,F,G=0";
    ierr += testSolve(true, false, false, true, true,
              reltol, abstol, testName);

    // Test B,F,G = 0
    testName = "Testing B,F,G=0";
    ierr += testSolve(false, true, false, true, true,
              reltol, abstol, testName);

    // Test C,F,G = 0
    testName = "Testing C,F,G=0";
    ierr += testSolve(false, false, true, true, true,
              reltol, abstol, testName);

    // Test A,B,F,G = 0
    testName = "Testing A,B,F,G=0";
    ierr += testSolve(true, true, false, true, true,
              reltol, abstol, testName);

    LOCA::destroyGlobalData(globalData);
  }

  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  }
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

  if (ierr == 0)
    std::cout << "All tests passed!" << std::endl;
  else
    std::cout << ierr << " test(s) failed!" << std::endl;

  return ierr;
}
Beispiel #17
0
int main(int argc, char *argv[])
{
  int ierr = 0;

  double nonlinear_factor = 1.0;
  double left_bc = 0.0;
  double right_bc = 0.40;

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

  // Create a communicator for Epetra objects
#ifdef HAVE_MPI
  Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
  Epetra_SerialComm Comm;
#endif

  // Get the process ID and the total number of processors
  int MyPID = Comm.MyPID();
  int NumProc = Comm.NumProc();

  // Get the number of elements from the command line
  int NumGlobalElements = 100 + 1;

  // The number of unknowns must be at least equal to the 
  // number of processors.
  if (NumGlobalElements < NumProc) {
    cout << "numGlobalBlocks = " << NumGlobalElements 
	 << " cannot be < number of processors = " << NumProc << endl;
    exit(1);
  }

  // Create the FiniteElementProblem class.  This creates all required
  // Epetra objects for the problem and allows calls to the 
  // function (RHS) and Jacobian evaluation routines.
  FiniteElementProblem Problem(NumGlobalElements, Comm);

  // Get the vector from the Problem
  Epetra_Vector& soln = Problem.getSolution();

  // Initialize Solution
  soln.PutScalar(0.1);

  // Create initial guess for the null vector of jacobian
  Teuchos::RCP<NOX::Abstract::Vector> solnTwo = 
    Teuchos::rcp(new NOX::Epetra::Vector(soln));  
  solnTwo->init(2.5);             // initial value 1.0
  
  // Begin LOCA Solver ************************************

  // Create parameter list
  Teuchos::RCP<Teuchos::ParameterList> paramList = 
    Teuchos::rcp(new Teuchos::ParameterList);

  // Create LOCA sublist
  Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

  // Create the stepper sublist and set the stepper parameters
  Teuchos::ParameterList& locaStepperList = locaParamsList.sublist("Stepper");
  locaStepperList.set("Continuation Method", "Natural");
  //locaStepperList.set("Bordered Solver Method", "Nested");
  //locaStepperList.set("Bordered Solver Method", "Householder");
  locaStepperList.set("Continuation Parameter", "Nonlinear Factor");
  locaStepperList.set("Initial Value", nonlinear_factor);
  locaStepperList.set("Max Value", 1.6);
  locaStepperList.set("Min Value", 0.00);
  locaStepperList.set("Max Steps", 20);
  locaStepperList.set("Max Nonlinear Iterations", 15);

  // Create bifurcation sublist
  Teuchos::ParameterList& bifurcationList = 
    locaParamsList.sublist("Bifurcation");
  bifurcationList.set("Type", "Phase Transition");
  bifurcationList.set("Bifurcation Parameter", "Right BC");

  bifurcationList.set("Second Solution Vector", solnTwo);
  
  // Create predictor sublist
  Teuchos::ParameterList& predictorList = locaParamsList.sublist("Predictor");
  predictorList.set("Method", "Secant");

  // Create step size sublist
  Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
  stepSizeList.set("Method", "Constant");
  stepSizeList.set("Initial Step Size", 0.1);
  stepSizeList.set("Min Step Size", 1.0e-3);
  stepSizeList.set("Max Step Size", 2000.0);
  stepSizeList.set("Aggressiveness", 0.1);

  // Create the "Solver" parameters sublist to be used with NOX Solvers
  Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

  // Create the NOX printing parameter list
  Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
  nlPrintParams.set("MyPID", MyPID); 
  nlPrintParams.set("Output Precision", 6); 
  nlPrintParams.set("Output Information", 
		    NOX::Utils::OuterIteration + 
		    NOX::Utils::OuterIterationStatusTest + 
		    NOX::Utils::InnerIteration +
		    NOX::Utils::Details + 
		    NOX::Utils::LinearSolverDetails +
		    NOX::Utils::Warning + 
		    NOX::Utils::StepperIteration +
		    NOX::Utils::StepperDetails +
		    NOX::Utils::StepperParameters);

  // Create the "Linear Solver" sublist for Newton's method
  Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
  Teuchos::ParameterList& newParams = dirParams.sublist("Newton");
  Teuchos::ParameterList& lsParams = newParams.sublist("Linear Solver");
  lsParams.set("Aztec Solver", "GMRES");  
  lsParams.set("Max Iterations", 200);  
  lsParams.set("Tolerance", 1e-6);
  lsParams.set("Output Frequency", 50);    
  //lsParams.set("Scaling", "None");             
  //lsParams.set("Scaling", "Row Sum");  
  lsParams.set("Compute Scaling Manually", false);
  lsParams.set("Preconditioner", "Ifpack");
  lsParams.set("Ifpack Preconditioner", "ILU");

  //lsParams.set("Preconditioner", "New Ifpack");
  //Teuchos::ParameterList& ifpackParams = lsParams.sublist("Ifpack");
  //ifpackParams.set("fact: level-of-fill", 1);

  // Create and initialize the parameter vector
  LOCA::ParameterVector pVector;
  pVector.addParameter("Nonlinear Factor",nonlinear_factor);
  pVector.addParameter("Left BC", left_bc);
  pVector.addParameter("Right BC", right_bc);

  // Create the interface between the test problem and the nonlinear solver
  // This is created by the user using inheritance of the abstract base class:
  Teuchos::RCP<Problem_Interface> interface = 
    Teuchos::rcp(new Problem_Interface(Problem));
  Teuchos::RCP<LOCA::Epetra::Interface::TimeDependent> iReq = interface;
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;
  
  // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
  Teuchos::RCP<Epetra_RowMatrix> Amat = 
    Teuchos::rcp(&Problem.getJacobian(),false);

  // Create scaling object
  Teuchos::RCP<NOX::Epetra::Scaling> scaling = Teuchos::null;
//   scaling = Teuchos::rcp(new NOX::Epetra::Scaling);
//   Teuchos::RCP<Epetra_Vector> scalingVector = 
//     Teuchos::rcp(new Epetra_Vector(soln.Map()));
//   //scaling->addRowSumScaling(NOX::Epetra::Scaling::Left, scalingVector);
//   scaling->addColSumScaling(NOX::Epetra::Scaling::Right, scalingVector);

  // Create transpose scaling object
  Teuchos::RCP<NOX::Epetra::Scaling> trans_scaling = Teuchos::null;
//   trans_scaling = Teuchos::rcp(new NOX::Epetra::Scaling);
//   Teuchos::RCP<Epetra_Vector> transScalingVector = 
//     Teuchos::rcp(new Epetra_Vector(soln.Map()));
//   trans_scaling->addRowSumScaling(NOX::Epetra::Scaling::Right, 
// 				  transScalingVector);
//   trans_scaling->addColSumScaling(NOX::Epetra::Scaling::Left, 
// 				  transScalingVector);
  //bifurcationList.set("Transpose Scaling", trans_scaling);

  // Create the linear systems
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys = 
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams, lsParams,
						      iReq, iJac, Amat, soln,
						      scaling));

  // Create the loca vector
  NOX::Epetra::Vector locaSoln(soln);

  // Create Epetra factory
  Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
    Teuchos::rcp(new LOCA::Epetra::Factory);

  // Create global data object
  Teuchos::RCP<LOCA::GlobalData> globalData = 
    LOCA::createGlobalData(paramList, epetraFactory);

  // Create the Group
  Teuchos::RCP<LOCA::Epetra::Group> grp = 
    Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams, iReq, 
					 locaSoln, linsys, linsys,
					 pVector));

  // Inject FreeEnergy interface into the group
  Teuchos::RCP<LOCA::Epetra::Interface::FreeEnergy> iFE = interface;
  grp->setFreeEnergyInterface(iFE);

  grp->computeF();

  // Create the Solver convergence test
  //NOX::StatusTest::NormWRMS wrms(1.0e-2, 1.0e-8);
  Teuchos::RCP<NOX::StatusTest::NormF> wrms = 
    Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-12));
  Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters = 
    Teuchos::rcp(new NOX::StatusTest::MaxIters(locaStepperList.get("Max Nonlinear Iterations", 10)));
  Teuchos::RCP<NOX::StatusTest::Combo> combo = 
    Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
  combo->addStatusTest(wrms);
  combo->addStatusTest(maxiters);
  
  // Create the stepper  
  LOCA::Stepper stepper(globalData, grp, combo, paramList);
  LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();
  
  if (status == LOCA::Abstract::Iterator::Finished) 
    globalData->locaUtils->out() << "All tests passed" << endl;
  else {
    if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
      globalData->locaUtils->out() 
	<< "Stepper failed to converge!" << std::endl;
  }

  // Output the parameter list
  if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
    globalData->locaUtils->out() 
      << std::endl << "Final Parameters" << std::endl
      << "****************" << std::endl;
    stepper.getList()->print(globalData->locaUtils->out());
    globalData->locaUtils->out() << std::endl;
  }

  LOCA::destroyGlobalData(globalData);

#ifdef HAVE_MPI
  MPI_Finalize() ;
#endif

/* end main
*/
return ierr ;
}
Beispiel #18
0
int main(int argc, char *argv[])
{
  int ierr = 0;
  int MyPID = 0;
  double alpha = 0.25;
  double beta = 1.5;
  double D1 = 1.0/40.0;
  double D2 = 1.0/40.0;
  int maxNewtonIters = 10;

  try {

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

    // Create a communicator for Epetra objects
#ifdef HAVE_MPI
    Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
    Epetra_SerialComm Comm;
#endif

    // Get the process ID and the total number of processors
    MyPID = Comm.MyPID();
    int NumProc = Comm.NumProc();

    // Check for verbose output
    bool verbose = false;
    if (argc>1) 
      if (argv[1][0]=='-' && argv[1][1]=='v') 
	verbose = true;

    // Get the number of elements from the command line
    int NumGlobalNodes = 0;
    if ((argc > 2) && (verbose))
      NumGlobalNodes = atoi(argv[2]) + 1;
    else if ((argc > 1) && (!verbose))
      NumGlobalNodes = atoi(argv[1]) + 1;
    else 
      NumGlobalNodes = 101;

    // The number of unknowns must be at least equal to the 
    // number of processors.
    if (NumGlobalNodes < NumProc) {
      std::cout << "numGlobalNodes = " << NumGlobalNodes 
		<< " cannot be < number of processors = " << NumProc 
		<< std::endl;
      exit(1);
    }

    // Create the Brusselator problem class.  This creates all required
    // Epetra objects for the problem and allows calls to the 
    // function (F) and Jacobian evaluation routines.
    Brusselator Problem(NumGlobalNodes, Comm);

    // Get the vector from the Problem
    Epetra_Vector& soln = Problem.getSolution();

    // Begin LOCA Solver ************************************

    // Create the top level parameter list

    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    stepperList.set("Bordered Solver Method", "Householder");
    stepperList.set("Continuation Parameter", "beta");
    stepperList.set("Initial Value", beta);
    stepperList.set("Max Value", 1.6);
    stepperList.set("Min Value", 0.0);
    stepperList.set("Max Steps", 100);
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters);

#ifdef HAVE_LOCA_ANASAZI
    // Create Anasazi Eigensolver sublist (needs --with-loca-anasazi)
    stepperList.set("Compute Eigenvalues",true);
    Teuchos::ParameterList& aList = stepperList.sublist("Eigensolver");
    aList.set("Method", "Anasazi");
    if (!verbose)
      aList.set("Verbosity", Anasazi::Errors);
    aList.set("Block Size", 1);        // Size of blocks
    aList.set("Num Blocks", 50);       // Size of Arnoldi factorization
    aList.set("Num Eigenvalues", 3);   // Number of eigenvalues
    aList.set("Convergence Tolerance", 1.0e-7);          // Tolerance
    aList.set("Step Size", 1);         // How often to check convergence
    aList.set("Maximum Restarts",1);   // Maximum number of restarts
    aList.set("Operator", "Cayley");
    aList.set("Cayley Pole", 0.1);
    aList.set("Cayley Zero", -0.1);
    aList.set("Sorting Order", "CA");
#else
    stepperList.set("Compute Eigenvalues",false);
#endif

    // Create predictor sublist
    Teuchos::ParameterList& predictorList = 
      locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Constant");

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Initial Step Size", 0.01);
    stepSizeList.set("Min Step Size", 1.0e-3);
    stepSizeList.set("Max Step Size", 0.01);
    stepSizeList.set("Aggressiveness", 0.1);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

    // Set the printing parameters in the "Printing" sublist
    Teuchos::ParameterList& printParams = nlParams.sublist("Printing");
    printParams.set("MyPID", MyPID); 
    printParams.set("Output Precision", 3);
    printParams.set("Output Processor", 0);
     if (verbose)
      printParams.set("Output Information", 
		      NOX::Utils::OuterIteration + 
		      NOX::Utils::OuterIterationStatusTest + 
		      NOX::Utils::InnerIteration +
		      NOX::Utils::Details + 
		      NOX::Utils::Warning +
		      NOX::Utils::TestDetails + 
		      NOX::Utils::Error + 
		      NOX::Utils::StepperIteration +
		      NOX::Utils::StepperDetails +
		      NOX::Utils::StepperParameters);
     else
       printParams.set("Output Information", NOX::Utils::Error);

    // Sublist for "Linear Solver"
    Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
    Teuchos::ParameterList& newtonParams = dirParams.sublist("Newton");
    Teuchos::ParameterList& lsParams = newtonParams.sublist("Linear Solver");
    lsParams.set("Aztec Solver", "GMRES");  
    lsParams.set("Max Iterations", 800);  
    lsParams.set("Tolerance", 1e-6);
    lsParams.set("Output Frequency", 50);    
    lsParams.set("Preconditioner", "Ifpack"); 

    // Create the interface between the test problem and the nonlinear solver
    Teuchos::RCP<Problem_Interface> interface = 
      Teuchos::rcp(new Problem_Interface(Problem));

    // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
    Teuchos::RCP<Epetra_RowMatrix> A = 
      Teuchos::rcp(&Problem.getJacobian(),false);


    // Use an Epetra Scaling object if desired
    Teuchos::RCP<Epetra_Vector> scaleVec = 
      Teuchos::rcp(new Epetra_Vector(soln));
    NOX::Epetra::Scaling scaling;
    scaling.addRowSumScaling(NOX::Epetra::Scaling::Left, scaleVec);

    Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;

    // Create the Linear System
    Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linSys = 
      Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
							iReq, iJac, A, soln));
                                                        //&scaling);
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> shiftedLinSys = 
      Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
							iReq, iJac, A, soln));

    // Create initial guess
    NOX::Epetra::Vector initialGuess(Teuchos::rcp(&soln,false), 
				     NOX::Epetra::Vector::CreateView,
				     NOX::DeepCopy);

    // Create and initialize the parameter vector
    LOCA::ParameterVector pVector;
    pVector.addParameter("alpha",alpha);
    pVector.addParameter("beta",beta);
    pVector.addParameter("D1",D1);
    pVector.addParameter("D2",D2);

    // Create Epetra factory
    Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
      Teuchos::rcp(new LOCA::Epetra::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData = 
      LOCA::createGlobalData(paramList, epetraFactory);

    // Create the Group
    Teuchos::RCP<LOCA::Epetra::Interface::TimeDependent> iTime = interface;
    Teuchos::RCP<LOCA::Epetra::Group> grp =
      Teuchos::rcp(new LOCA::Epetra::Group(globalData, printParams,
					   iTime, initialGuess, linSys, 
					   shiftedLinSys, pVector));

    grp->computeF();

    // Create the convergence tests
    Teuchos::RCP<NOX::StatusTest::NormF> absresid = 
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8, 
					   NOX::StatusTest::NormF::Unscaled));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters = 
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Combo> combo =
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
    combo->addStatusTest(absresid);
    combo->addStatusTest(maxiters);

    // Create stepper
    LOCA::Stepper stepper(globalData, grp, combo, paramList);

    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    if (status != LOCA::Abstract::Iterator::Finished) {
      ierr = 1;
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() 
	  << "Stepper failed to converge!" << std::endl;
    }

    // Get the final solution from the stepper
    Teuchos::RCP<const LOCA::Epetra::Group> finalGroup = 
      Teuchos::rcp_dynamic_cast<const LOCA::Epetra::Group>(stepper.getSolutionGroup());
    const NOX::Epetra::Vector& finalSolution = 
      dynamic_cast<const NOX::Epetra::Vector&>(finalGroup->getX());

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    // Check some statistics on the solution
    NOX::TestCompare testCompare(globalData->locaUtils->out(), 
				 *(globalData->locaUtils));
  
    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() 
	<< std::endl 
	<< "***** Checking solution statistics *****" 
	<< std::endl;

    // Check number of continuation steps
    int numSteps = stepper.getStepNumber();
    int numSteps_expected = 11;
    ierr += testCompare.testValue(numSteps, numSteps_expected, 0.0,
				  "number of continuation steps",
				  NOX::TestCompare::Absolute);

    // Check number of failed steps
    int numFailedSteps = stepper.getNumFailedSteps();
    int numFailedSteps_expected = 0;
    ierr += testCompare.testValue(numFailedSteps, numFailedSteps_expected, 0.0,
				  "number of failed continuation steps",
				  NOX::TestCompare::Absolute);

    // Check final value of continuation parameter
    double beta_final = finalGroup->getParam("beta");
    double beta_expected = 1.6;
    ierr += testCompare.testValue(beta_final, beta_expected, 1.0e-14,
				  "final value of continuation parameter", 
				  NOX::TestCompare::Relative);

    // Check final of solution
    NOX::Epetra::Vector final_x_expected(finalSolution);
    int n = final_x_expected.getEpetraVector().MyLength()/2;
    for (int i=0; i<n; i++) {
      final_x_expected.getEpetraVector()[2*i] = alpha;
      final_x_expected.getEpetraVector()[2*i+1] = beta_final/alpha;
    }
    ierr += testCompare.testVector(finalSolution, final_x_expected, 
				   1.0e-6, 1.0e-6,
				   "value of final solution");

    LOCA::destroyGlobalData(globalData);
  }
  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  }
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

  if (MyPID == 0) {
    if (ierr == 0)
      std::cout << "All tests passed!" << std::endl;
    else
      std::cout << ierr << " test(s) failed!" << std::endl;
  }

#ifdef HAVE_MPI
  MPI_Finalize() ;
#endif

return ierr;
}
Beispiel #19
0
int main(int argc, char *argv[])
{
  
  // Initialize MPI
  Teuchos::GlobalMPISession mpiSession(&argc,&argv);

  int ierr = 0;
  int MyPID = 0;
  double alpha = 1.00; // stable steady state
  double beta = BETA_INIT;
  double D1 = 1.0/40.0;
  double D2 = 1.0/40.0;
  int NumGlobalNodes = 10;  // default
  int spatialProcs   = 1;   // default
  int numTimeSteps   = 100;  // default
  
  try {

    // Check for verbose output
    bool verbose = false;
    if (argc>1) 
      if (argv[1][0]=='-' && argv[1][1]=='v') 
	verbose = true;

    // Get the number of elements from the command line
    if ((argc > 2) && (verbose))
      NumGlobalNodes = atoi(argv[2]) + 1;
    else if ((argc > 1) && (!verbose))
      NumGlobalNodes = atoi(argv[1]) + 1;

    // Get the number of processors to use for the spatial problem
    if ((argc > 3) && (verbose))
      spatialProcs = atoi(argv[3]);
    else if ((argc > 2) && (!verbose))
      spatialProcs = atoi(argv[2]);

    // Get the number of processors to use for the spatial problem
    if ((argc > 4) && (verbose))
      numTimeSteps = atoi(argv[4]);
    else if ((argc > 3) && (!verbose))
      numTimeSteps = atoi(argv[3]);

    // MPI MANIPULATION FOR XYZT PROBLEMS
#ifdef HAVE_MPI
    Teuchos::RCP<EpetraExt::MultiMpiComm> globalComm = 
      Teuchos::rcp(new EpetraExt::MultiMpiComm(MPI_COMM_WORLD, 
					       spatialProcs, numTimeSteps));
#else
    Teuchos::RCP<EpetraExt::MultiSerialComm> globalComm = 
      Teuchos::rcp(new EpetraExt::MultiSerialComm(numTimeSteps));
#endif
    Epetra_Comm& Comm = globalComm->SubDomainComm();
    MyPID = globalComm->MyPID();

    // Get the total number of processors
    int NumProc = Comm.NumProc();

    // The number of unknowns must be at least equal to the 
    // number of processors.
    if (NumGlobalNodes < NumProc) {
      std::cout << "numGlobalNodes = " << NumGlobalNodes 
		<< " cannot be < number of processors = " << NumProc 
		<< std::endl;
      exit(1);
    }

    // Create the Brusselator problem class.  This creates all required
    // Epetra objects for the problem and allows calls to the 
    // function (F) and Jacobian evaluation routines.
    Brusselator::OverlapType OType = Brusselator::ELEMENTS;
    Brusselator Problem(NumGlobalNodes, Comm, OType);
    
    // Get the vector from the Problem
    Epetra_Vector& soln = Problem.getSolution();
    
    // Begin Nonlinear Solver ************************************
    
    // Create the top level parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);
    getParamList(&(*paramList), MyPID);
    
    // Sublist for "Linear Solver"
    Teuchos::ParameterList& lsParams = 
      paramList->sublist("NOX").sublist("Direction").sublist("Newton").sublist("Linear Solver");
    
    // Sublist for "Printing"
    Teuchos::ParameterList& printParams = 
      paramList->sublist("NOX").sublist("Printing");
    
    // Change NOX priting settings if "-verbose" not requested
    if (!verbose)
      printParams.set("Output Information", NOX::Utils::Error);
      
    // Create the interface between the test problem and the nonlinear solver
    Teuchos::RCP<Problem_Interface> interface = 
      Teuchos::rcp(new Problem_Interface(Problem));
      
    // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
    Teuchos::RCP<Epetra_RowMatrix> A = 
      Teuchos::rcp(&Problem.getJacobian(),false);
      
    // Create initial guess
    Epetra_MultiVector initGuess(soln.Map(), 
				 globalComm->NumTimeStepsOnDomain());
    for (int i=0; i<globalComm->NumTimeStepsOnDomain(); i++) 
      *(initGuess(i)) = soln;
      
    // Get XYZT preconditioner linear solver parameters
    Teuchos::RCP<Teuchos::ParameterList> precLSParams = 
      Teuchos::rcp(new Teuchos::ParameterList);
    getPrecLSParams(&(*precLSParams), MyPID);

    // Get XYZT preconditioner print parameters
    Teuchos::RCP<Teuchos::ParameterList> precPrintParams = 
      Teuchos::rcp(new Teuchos::ParameterList);
    getPrecPrintParams(&(*precPrintParams), MyPID);
      
    // Change xyztPrec priting settings if "-verbose" not requested
    if (!verbose)
      precPrintParams->set("Output Information", NOX::Utils::Error);
	
    // Create the XYZT object
    Teuchos::RCP<LOCA::Epetra::Interface::xyzt> ixyzt = 
      Teuchos::rcp(new LOCA::Epetra::Interface::xyzt(interface,
                                                     initGuess, A,
                                                     globalComm,
                                                     soln, 0.5,
                                                     precPrintParams.get(),
                                                     precLSParams.get()));

    // Create the XYZT operator, solution, and preconditioner
    Teuchos::RCP<Epetra_RowMatrix> Axyzt =
      Teuchos::rcp(&(ixyzt->getJacobian()),false);
    Epetra_Vector& solnxyzt = ixyzt->getSolution();
    Teuchos::RCP<Epetra_Operator> Mxyzt = 
      Teuchos::rcp(&(ixyzt->getPreconditioner()),false);
    
    // Create the Linear System
    Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = ixyzt;
    Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = ixyzt;
    Teuchos::RCP<NOX::Epetra::Interface::Preconditioner> iPrec = 
      Teuchos::rcp(&(ixyzt->getPreconditioner()),false);
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linSys =
      Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
							iJac, Axyzt, 
							iPrec, Mxyzt, 
							solnxyzt));

    // Create full xyzt initial guess
    NOX::Epetra::Vector initialGuess(solnxyzt);
      
    // Create and initialize the parameter vector
    LOCA::ParameterVector pVector;
    pVector.addParameter("alpha",alpha);
    pVector.addParameter("beta",beta);
    pVector.addParameter("D1",D1);
    pVector.addParameter("D2",D2);
      
    // Create Epetra factory
    Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
      Teuchos::rcp(new LOCA::Epetra::Factory);
      
    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData = 
      LOCA::createGlobalData(paramList, epetraFactory);
      
    Teuchos::RCP<LOCA::Epetra::Group> grp =
      Teuchos::rcp(new LOCA::Epetra::Group(globalData, printParams,
					   iReq, initialGuess, linSys, 
					   pVector));
      
    grp->computeF();
      
    // Create the convergence tests
    Teuchos::RCP<NOX::StatusTest::NormF> absresid = 
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8, 
					      NOX::StatusTest::NormF::Unscaled));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters = 
      Teuchos::rcp(new NOX::StatusTest::MaxIters(MAX_NEWTON_ITERS));
    Teuchos::RCP<NOX::StatusTest::Combo> combo =
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
    combo->addStatusTest(absresid);
    combo->addStatusTest(maxiters);
      
    // Create stepper
    LOCA::Stepper stepper(globalData, grp, combo, paramList);
      
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();
      
    if (status != LOCA::Abstract::Iterator::Finished) {
      ierr =1;
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() 
	  << "Stepper failed to converge!" << std::endl;
    }
      
    // Get the final solution from the stepper
    Teuchos::RCP<const LOCA::Epetra::Group> finalGroup = 
      Teuchos::rcp_dynamic_cast<const LOCA::Epetra::Group>(stepper.getSolutionGroup());
    const NOX::Epetra::Vector& finalSolution = 
      dynamic_cast<const NOX::Epetra::Vector&>(finalGroup->getX());
      
    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }
      
    // Check some statistics on the solution
    NOX::TestCompare testCompare(globalData->locaUtils->out(), 
				 *(globalData->locaUtils));
      
    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() 
	<< std::endl 
	<< "***** Checking solution statistics *****" 
	<< std::endl;
      
    // Check number of continuation steps
    int numSteps = stepper.getStepNumber();
    int numSteps_expected = 3;
    ierr += testCompare.testValue(numSteps, numSteps_expected, 0.0,
				  "number of continuation steps",
				  NOX::TestCompare::Absolute);
      
    // Check number of failed steps
    int numFailedSteps = stepper.getNumFailedSteps();
    int numFailedSteps_expected = 0;
    ierr += testCompare.testValue(numFailedSteps, numFailedSteps_expected, 0.0,
				  "number of failed continuation steps",
				  NOX::TestCompare::Absolute);
      
    // Check final value of continuation parameter
    double beta_final = finalGroup->getParam("beta");
    double beta_expected = 2.0;
    ierr += testCompare.testValue(beta_final, beta_expected, 1.0e-14,
				  "final value of continuation parameter", 
				  NOX::TestCompare::Relative);
      
    // Check final value of ||F||
    double Fnorm_final = (const_cast<Teuchos::ParameterList&>(*stepper.getList()).sublist("NOX").sublist("Output").get("2-Norm of Residual",1.0e+10));
    double Fnorm_expected = 0.0;
    ierr += testCompare.testValue(Fnorm_final, Fnorm_expected, 1.0e-8,
				  "final value of ||F||", 
				  NOX::TestCompare::Absolute);
      
    // Check number of nonlinear iterations on last continuation step
    int nonlin_final = (const_cast<Teuchos::ParameterList&>(*stepper.getList()).sublist("NOX").
			sublist("Output").get("Nonlinear Iterations",MAX_NEWTON_ITERS));
    int nonlin_expected = 4;
    ierr += testCompare.testValue(nonlin_final, nonlin_expected, 0.0,
				  "number of nonlinear iterations on last continuation step", 
				  NOX::TestCompare::Absolute);
      
      
    // initialize solution comparison norm on all procs
    double solution_diff_norm = 0.0;
      
    // Compute norm of difference of computed solution - expected solution
    if (globalComm->MyPID() == (globalComm->NumProc()-1)) {
      // Get solution at last time step
      ixyzt->getSolution().ExtractBlockValues(soln, 
					      (globalComm->NumTimeStepsOnDomain() + 
					       globalComm->FirstTimeStepOnDomain() - 1));
	
      // Check final solution at final time step
      NOX::Epetra::Vector final_solution(soln);
      NOX::Epetra::Vector final_x_expected(final_solution);
      for (int i=0; i<NumGlobalNodes; i++) {
	final_x_expected.getEpetraVector()[2*i] = alpha;
	final_x_expected.getEpetraVector()[2*i+1] = beta_final/alpha;
      }
      solution_diff_norm = testCompare.computeVectorNorm(final_solution, 
							 final_x_expected, 
							 1.0e-4, 
							 1.0e-4);
	
    }
      
    // Check final solution at final time step on all procs
    globalComm->Broadcast(&solution_diff_norm, 1, globalComm->NumProc()-1);
    double solution_diff_norm_expected = 0.0;
    ierr += testCompare.testValue(solution_diff_norm, solution_diff_norm_expected, 1.0e-4,
				  "inf norm of (solution_final - solution_expected) at last time step", 
				  NOX::TestCompare::Absolute);
            
    LOCA::destroyGlobalData(globalData);
        
  }
  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
    ierr = 1;
  }
  catch (const char *s) {
    std::cout << s << std::endl;
    ierr = 1;
  }
  catch (...) {
    std::cout << "Caught unknown exception!" << std::endl;
    ierr = 1;
  }

  if (MyPID == 0) {
    if (ierr == 0)
      std::cout << "All tests passed!" << std::endl;
    else
      std::cout << ierr << " test(s) failed!" << std::endl;
  }

  return ierr;
}
Beispiel #20
0
int main( int argc, char **argv )
{

// check for parallel computation
#ifdef HAVE_MPI
  MPI_Init(&argc, &argv);
  Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
  Epetra_SerialComm Comm;
#endif


// define main parameters

  double c = 0.9999;           // continuation parameter
  int N = 50;                  // number of grid points
  int maxNewtonIters = 20;     // max number of Newton iterations
  int maxSteps = 50;           // max number of continuation steps taken
  int ilocal, iglobal;         // counter variables used for loops:
                               //   ilocal = counter for local elements on this processor;
                               //   iglobal = counter to signify global position across all procs 
  int Myele;                   // holds the number of elements on the processor

// Set flag for whether the computations will be Matrix-free (true) or will use a computed
//   Jacobian (false)
  bool doMatFree = false;      
   
// Create output file to save solutions
  ofstream outFile("Heq5.dat");
  outFile.setf(ios::scientific, ios::floatfield);
  outFile.precision(10);

// Define the problem class
  HeqProblem Problem(N,&Comm,outFile);
  
// Build initial guess.  The initial guess should be a solution vector x close to the 
//   bifurcation point.

  // Create the initial guess vector
  Epetra_Vector InitialGuess(Problem.GetMap());

  // Get the number of elements on this processor  
  Myele = Problem.GetMap().NumMyElements();

  // Compute the initial guess.  For this example, it is a line from (0,1) to (1,8/3)
  for (ilocal=0; ilocal<Myele; ilocal++) {
     iglobal=Problem.GetMap().GID(ilocal);
     InitialGuess[ilocal]= 1.0 + (5.0*iglobal)/(3.0*(N-1));
  }

// Create the null vector for the Jacobian (ie, J*v=0, used to solve the system of equations
//   f(x,p)=0; J*v=0; v0*v=1.  The solution of the system is [x*,v*,p*]. )
  Teuchos::RCP<NOX::Abstract::Vector> nullVec =
    Teuchos::rcp(new NOX::Epetra::Vector(InitialGuess));

  // Initialize to all ones
  nullVec->init(1.0);  
    // NOTE:  init is a function within the NOX::Abstract:Vector class which initializes every
    // value of the vector to the value within the parentheses (must be in 'double' format) 

// Create the top level parameter list
  Teuchos::RCP<Teuchos::ParameterList> ParamList = Teuchos::rcp(new Teuchos::ParameterList);

  // Create LOCA sublist
  Teuchos::ParameterList& locaParamsList = ParamList->sublist("LOCA");

  // Create the sublist for continuation and set the stepper parameters
  Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    //stepperList.set("Continuation Method", "Arc Length");// Default
    stepperList.set("Continuation Method", "Natural");
    stepperList.set("Continuation Parameter", "dummy");  // Must set
    stepperList.set("Initial Value", 999.0);             // Must set
    stepperList.set("Max Value", 50.0e4);             // Must set
    stepperList.set("Min Value", 0.0);             // Must set
    stepperList.set("Max Steps", maxSteps);                    // Should set
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters); // Should set
    stepperList.set("Bordered Solver Method", "Bordering");

  //  Teuchos::ParameterList& nestedList = 
  //    stepperList.sublist("Nested Bordered Solver");
  //  nestedList.set("Bordered Solver Method", "Householder");
  //  nestedList.set("Include UV In Preconditioner", true);
  //  //nestedList.set("Use P For Preconditioner", true);
  //  nestedList.set("Preconditioner Method", "SMW");

// Set up parameters to compute Eigenvalues
#ifdef HAVE_LOCA_ANASAZI
  // Create Anasazi Eigensolver sublist (needs --with-loca-anasazi)
  stepperList.set("Compute Eigenvalues",true);
  Teuchos::ParameterList& aList = stepperList.sublist("Eigensolver");
  aList.set("Method", "Anasazi");
  aList.set("Block Size", 1);        // Size of blocks
  aList.set("Num Blocks", 20);       // Size of Arnoldi factorization
  aList.set("Num Eigenvalues", 5);   // Number of eigenvalues
  //  aList.set("Sorting Order", "SR");
  aList.set("Convergence Tolerance", 2.0e-7);          // Tolerance
  aList.set("Step Size", 1);         // How often to check convergence
  aList.set("Maximum Restarts",2);   // Maximum number of restarts
  aList.set("Verbosity",  
	    Anasazi::Errors + 
	    Anasazi::Warnings +
	    Anasazi::FinalSummary);        // Verbosity
#else
    stepperList.set("Compute Eigenvalues",false);
#endif
  
  // Create bifurcation sublist.  Note that for turning point continuation, the "type"
  //   is set to "Turning Point".  If not doing TP, type should be "None".
  Teuchos::ParameterList& bifurcationList = locaParamsList.sublist("Bifurcation");
  bifurcationList.set("Type", "Turning Point");
  bifurcationList.set("Bifurcation Parameter", "c");
  //  bifurcationList.set("Formulation", "Minimally Augmented");
  bifurcationList.set("Symmetric Jacobian", false); 
  bifurcationList.set("Update Null Vectors Every Continuation Step", true);
  bifurcationList.set("Update Null Vectors Every Nonlinear Iteration", false);
  bifurcationList.set("Transpose Solver Method","Explicit Transpose");
  //  bifurcationList.set("Transpose Solver Method","Transpose Preconditioner");
  //  bifurcationList.set("Transpose Solver Method","Left Preconditioning");
  bifurcationList.set("Initial Null Vector Computation", "Solve df/dp");
  //  bifurcationList.set("Initial A Vector", nullVec);      // minimally augmented
  //  bifurcationList.set("Initial B Vector", nullVec);      //minimally augmented
  
  //  bifurcationList.set("Bordered Solver Method", "Householder");
  //  bifurcationList.set("Include UV In Preconditioner", true);
  //  //bifurcationList.set("Use P For Preconditioner", true);
  //  bifurcationList.set("Preconditioner Method", "SMW");

  bifurcationList.set("Formulation", "Moore-Spence");
  bifurcationList.set("Solver Method", "Phipps Bordering"); // better for nearly singular matrices
  //  bifurcationList.set("Solver Method", "Salinger Bordering");   
  bifurcationList.set("Initial Null Vector", nullVec);
  bifurcationList.set("Length Normalization Vector", nullVec);

    // Create the sublist for the predictor
    Teuchos::ParameterList& predictorList = locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Secant");         // Default
    // predictorList.set("Method", "Constant");     // Other options
    // predictorList.set("Method", "Tangent");      // Other options

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Method", "Adaptive");             // Default
    stepSizeList.set("Initial Step Size", 0.1);   // Should set
    stepSizeList.set("Min Step Size", 1.0e-6);    // Should set
    stepSizeList.set("Max Step Size", 1.0);      // Should set
    stepSizeList.set("Aggressiveness", 0.1);

// Set up NOX info
  Teuchos::ParameterList& nlParams = ParamList->sublist("NOX");

// Set the nonlinear solver method
  nlParams.set("Nonlinear Solver", "Line Search Based");

// Set the printing parameters in the "Printing" sublist.  This list determines how much
//   of the NOX information is output
  Teuchos::ParameterList& printParams = nlParams.sublist("Printing");
  printParams.set("MyPID", Comm.MyPID()); 
  printParams.set("Output Precision", 5);
  printParams.set("Output Processor", 0);
  printParams.set("Output Information", 
			NOX::Utils::OuterIteration + 
			NOX::Utils::OuterIterationStatusTest + 
			NOX::Utils::InnerIteration +
			NOX::Utils::LinearSolverDetails +
			NOX::Utils::Parameters + 
			NOX::Utils::Details + 
			NOX::Utils::Warning +
         NOX::Utils::StepperIteration +
         NOX::Utils::StepperDetails +
         NOX::Utils::StepperParameters);

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

  // Sublist for direction
  Teuchos::ParameterList& dirParams = nlParams.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", 800);  
  lsParams.set("Tolerance", 1e-8);
  lsParams.set("Output Frequency", 1);    
  lsParams.set("Preconditioner", "None");
  //  lsParams.set("Preconditioner", "AztecOO");
  //  lsParams.set("Aztec Preconditioner", "ilu"); 
  //  lsParams.set("Scaling", "None");
  //  lsParams.set("Scaling", "Row Sum");  
  lsParams.set("Compute Scaling Manually", false);
  //  lsParams.set("Preconditioner", "Ifpack");
  //  lsParams.set("Ifpack Preconditioner", "ILU");
  //  lsParams.set("Preconditioner", "New Ifpack");
  //  Teuchos::ParameterList& ifpackParams = lsParams.sublist("Ifpack");
  //  ifpackParams.set("fact: level-of-fill", 1);

// Set up the continuation parameter vector
  LOCA::ParameterVector p;
  p.addParameter("c",c);  
  p.addParameter("dummy",999.0);  

// Create the problem interface
  Teuchos::RCP<SimpleProblemInterface> interface = 
    Teuchos::rcp(new SimpleProblemInterface(&Problem,c) );

  Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;

// Create the operator to hold either the Jacobian matrix or the Matrix-free operator
  Teuchos::RCP<Epetra_Operator> A;
  //  Teuchos::RCP<Epetra_RowMatrix> A;
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac;

  // Need a NOX::Epetra::Vector for constructor
  // This becomes the initial guess vector that is used for the nonlinear solves
  NOX::Epetra::Vector noxInitGuess(InitialGuess, NOX::DeepCopy);   

  if (doMatFree) {
    // Matrix Free application (Epetra Operator):
    Teuchos::RCP<NOX::Epetra::MatrixFree> MF = 
      Teuchos::rcp(new NOX::Epetra::MatrixFree(printParams, interface, noxInitGuess)); 
    A = MF;
    iJac = MF;
  }
  else  {  // Computed Jacobian application
    A = Teuchos::rcp( Problem.GetMatrix(), false );
    iJac = interface;
  }
 
  // Create scaling object
  Teuchos::RCP<NOX::Epetra::Scaling> scaling = Teuchos::null;
  //   scaling = Teuchos::rcp(new NOX::Epetra::Scaling);
  //   Teuchos::RCP<Epetra_Vector> scalingVector = 
  //     Teuchos::rcp(new Epetra_Vector(soln.Map()));
  //   //scaling->addRowSumScaling(NOX::Epetra::Scaling::Left, scalingVector);
  //   scaling->addColSumScaling(NOX::Epetra::Scaling::Right, scalingVector);

  // Create transpose scaling object
  Teuchos::RCP<NOX::Epetra::Scaling> trans_scaling = Teuchos::null;
  //   trans_scaling = Teuchos::rcp(new NOX::Epetra::Scaling);
  //   Teuchos::RCP<Epetra_Vector> transScalingVector = 
  //     Teuchos::rcp(new Epetra_Vector(soln.Map()));
  //   trans_scaling->addRowSumScaling(NOX::Epetra::Scaling::Right, 
  // 				  transScalingVector);
  //   trans_scaling->addColSumScaling(NOX::Epetra::Scaling::Left, 
  // 				  transScalingVector);
    //bifurcationList.set("Transpose Scaling", trans_scaling);

// Build the linear system solver
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linSys = 
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
						      iReq,
						      iJac, A, 
                        noxInitGuess, scaling));            // use if scaling
//                        noxInitGuess));                     // use if no scaling

// Create the Loca (continuation) vector
  NOX::Epetra::Vector locaSoln(noxInitGuess);
  
  // Create Epetra Factory
  Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory = Teuchos::rcp(new LOCA::Epetra::Factory);

  // Create global data object
  Teuchos::RCP<LOCA::GlobalData> globalData = LOCA::createGlobalData(ParamList, epetraFactory);
 
  // Create the Group - must be LOCA group
  Teuchos::RCP<LOCA::Epetra::Group> grpPtr = 
    Teuchos::rcp(new LOCA::Epetra::Group(globalData, printParams, 
					iReq, locaSoln, 
					linSys, p)); 

  // Calculate the first F(x0) as a starting point.  This is only needed for
  // certain status tests, to ensure that an initial residual (|r0|) is calculated
  grpPtr->computeF();

// Set up the status tests to check for convergence
  // Determines the error tolerance for the Newton solves 
  Teuchos::RCP<NOX::StatusTest::NormF> testNormF = 
    Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-4));
  // Sets the max number of nonlinear (Newton) iterations that will be taken.  If this is not
  //   already set, it will default to the '20' given 
  Teuchos::RCP<NOX::StatusTest::MaxIters> testMaxIters = 
    Teuchos::rcp(new NOX::StatusTest::MaxIters(stepperList.get("Max Nonlinear Iterations", 20)));
// This combination of tests will be used by NOX to determine whether the step converged
  Teuchos::RCP<NOX::StatusTest::Combo> combo = 
    Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR, 
					    testNormF, testMaxIters));

// This is sample code to write and read parameters to/from a file.  Currently not activated! 
// To use, change the 'XXXHAVE_TEUCHOS_EXTENDED' TO 'HAVE_TEUCHOS_EXTENDED'
#ifdef XXXHAVE_TEUCHOS_EXTENDED
  // Write the parameter list to a file
  cout << "Writing parameter list to \"input.xml\"" << endl;
  Teuchos::writeParameterListToXmlFile(*ParamList, "input.xml");

  // Read in the parameter list from a file
  cout << "Reading parameter list from \"input.xml\"" << endl;
  Teuchos::RCP<Teuchos::ParameterList> paramList2 = 
    Teuchos::rcp(new Teuchos::ParameterList);
  Teuchos::updateParametersFromXmlFile("input.xml", paramList2.get());
  ParamList = paramList2;
#endif


// Create the stepper
  LOCA::Stepper stepper(globalData, grpPtr, combo, ParamList);
  LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();
  
  // Check if the stepper completed
  if  (status == LOCA::Abstract::Iterator::Finished)
    globalData->locaUtils->out() << "\nAll tests passed!" << endl;
  else 
    if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
      globalData->locaUtils->out() << "\nStepper failed to converge!"  << endl;

// Output the stepper parameter list info
  if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
    globalData->locaUtils->out() << endl << "Final Parameters" << endl
    << "*******************" << endl;
    stepper.getList()->print(globalData->locaUtils->out());
    globalData->locaUtils->out() << endl;
  }

// Make sure all processors are done and close the output file
Comm.Barrier();
outFile.close();

// Deallocate memory
LOCA::destroyGlobalData(globalData);

#ifdef HAVE_MPI
  MPI_Finalize();
#endif
  return(EXIT_SUCCESS);
}  // DONE!!
Beispiel #21
0
int main()
{
  int n = 100;
  double alpha = 3.5;
  double beta = 0.0;
  double scale = 1.0;
  int maxNewtonIters = 10;

  alpha = alpha / scale;

  // These seeds were found to work -- not the first try
  int seed1 = 3;
  int seed2 = 4; //Subsequent seeds keep incrementing by seed2-seed1
  double homScale = -1.0;

  /* Uncomment for interactive mode 
  std::cout << "Input first seed" << endl;     std::cin >> seed1;
  std::cout << "Input second seed" << endl;    std::cin >> seed2;
  std::cout << "Input identity-scale" << endl; std::cin >> homScale;
  */

  try {

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList = 
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("Output Information", 
		      NOX::Utils::Details +
		      NOX::Utils::OuterIteration + 
		      NOX::Utils::InnerIteration + 
		      NOX::Utils::Warning +
		      NOX::Utils::Error + 
		      NOX::Utils::Parameters +
		      NOX::Utils::StepperIteration +
		      NOX::Utils::StepperDetails +
		      NOX::Utils::StepperParameters);

    // Create LAPACK Factory
    Teuchos::RCP<LOCA::LAPACK::Factory> lapackFactory = 
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, lapackFactory);

    // Set up the problem interface
    ChanProblemInterface chan(globalData, n, alpha, beta, scale);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("scale",scale);
  
    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    Teuchos::RCP<LOCA::LAPACK::Group> grp = 
      Teuchos::rcp(new LOCA::LAPACK::Group(globalData, chan));
    grp->setParams(p);

    // Set up the status tests
    Teuchos::RCP<NOX::StatusTest::NormF> statusTestA = 
      Teuchos::rcp(new NOX::StatusTest::NormF(*grp, 1.0e-8));
    Teuchos::RCP<NOX::StatusTest::MaxIters> statusTestB = 
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Combo> combo = 
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR, 
					       statusTestA, statusTestB));

    // Create the homotopy group
//     Teuchos::RCP<LOCA::Homotopy::Group> hGrp = 
//       Teuchos::rcp(new LOCA::Homotopy::Group(locaParamsList, globalData, grp));

    Teuchos::RCP<Teuchos::ParameterList> hParams = 
      Teuchos::rcp(&locaParamsList.sublist("Homotopy"),false);
    hParams->set("Bordered Solver Method", "LAPACK Direct Solve");
    Teuchos::RCP<NOX::Abstract::Vector> startVec = 
      grp->getX().clone(NOX::ShapeCopy);
    startVec->random(true, seed1); /* Always use same seed for testing */
    startVec->abs(*startVec);
    std::vector< Teuchos::RCP<const NOX::Abstract::Vector> > solns;

    LOCA::Abstract::Iterator::IteratorStatus status
         = LOCA::Abstract::Iterator::Finished;

    int deflationIter = 0;
    const int maxDeflationIters = 4;

    while (deflationIter < maxDeflationIters
           &&  status==LOCA::Abstract::Iterator::Finished) {

      // ToDo:  Add deflateAndReset(vec) to Homotopy group,
      //        including option to perturb startVec

      Teuchos::RCP<LOCA::Homotopy::DeflatedGroup> hGrp = 
        Teuchos::rcp(new LOCA::Homotopy::DeflatedGroup(globalData,
                        paramList, hParams, grp, startVec, solns,homScale)); 

      // Override default parameters
      stepperList.set("Max Nonlinear Iterations", maxNewtonIters);
      stepperList.set("Continuation Method", "Arc Length");
      stepperList.set("Max Steps", 100);

      stepSizeList.set("Min Step Size", 1.0e-5);


      // Create the stepper  
      LOCA::Stepper stepper(globalData, hGrp, combo, paramList);

      // Solve the nonlinear system
      status = stepper.run();

      if (status != LOCA::Abstract::Iterator::Finished) 
        globalData->locaUtils->out() << "Stepper failed to converge!" 
				   << std::endl;
      else {
        // Deflate with soln vector just solved for
        solns.push_back(grp->getX().clone(NOX::DeepCopy));
 
        // If seed1=seed2, then all seeds the same. Otherwise, keep incrementing seed
        startVec->random(true, seed2 + deflationIter*(seed2-seed1)); 
      }

      deflationIter++;

      // Output the parameter list
      if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
        globalData->locaUtils->out() 
  	<< std::endl << "Final Parameters for deflation iter " 
        << deflationIter << std::endl
  	<< "****************" << std::endl;
        stepper.getList()->print(globalData->locaUtils->out());
        globalData->locaUtils->out() << std::endl;
      }

    } //End While loop over delfation iters

    LOCA::destroyGlobalData(globalData);
  }

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

  cout << "All examples passed" << endl;

  return 0;
}
Beispiel #22
0
int main()
{
  int n = 100;
  double alpha = 0.0;
  double beta = 0.0;
  double scale = 1.0;
  int maxNewtonIters = 20;

  alpha = alpha / scale;

  try {

    // Create output file to save solutions
    std::ofstream outFile("ChanContinuation.dat");
    outFile.setf(std::ios::scientific, std::ios::floatfield);
    outFile.precision(14);

    // Save size of discretizations
    outFile << n << std::endl;

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList =
      Teuchos::rcp(new Teuchos::ParameterList);

    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& stepperList = locaParamsList.sublist("Stepper");
    stepperList.set("Continuation Method", "Arc Length");// Default
    //stepperList.set("Continuation Method", "Natural");
    stepperList.set("Continuation Parameter", "alpha");  // Must set
    stepperList.set("Initial Value", alpha);             // Must set
    stepperList.set("Max Value", 5.0/scale);             // Must set
    stepperList.set("Min Value", 0.0/scale);             // Must set
    stepperList.set("Max Steps", 50);                    // Should set
    stepperList.set("Max Nonlinear Iterations", maxNewtonIters); // Should set
    stepperList.set("Compute Eigenvalues",false);        // Default

    // Create bifurcation sublist
    Teuchos::ParameterList& bifurcationList =
      locaParamsList.sublist("Bifurcation");
    bifurcationList.set("Type", "None");                 // Default

    // Create predictor sublist
    Teuchos::ParameterList& predictorList =
      locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Secant");               // Default
    //predictorList.set("Method", "Constant");
    //predictorList.set("Method", "Tangent");

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Method", "Adaptive");             // Default
    stepSizeList.set("Initial Step Size", 0.1/scale);   // Should set
    stepSizeList.set("Min Step Size", 1.0e-3/scale);    // Should set
    stepSizeList.set("Max Step Size", 10.0/scale);      // Should set

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("Output Information",
              NOX::Utils::Details +
              NOX::Utils::OuterIteration +
              NOX::Utils::InnerIteration +
              NOX::Utils::Warning +
              NOX::Utils::StepperIteration +
              NOX::Utils::StepperDetails +
              NOX::Utils::StepperParameters);  // Should set

    // Create LAPACK Factory
    Teuchos::RCP<LOCA::LAPACK::Factory> lapackFactory =
      Teuchos::rcp(new LOCA::LAPACK::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData =
      LOCA::createGlobalData(paramList, lapackFactory);

    // Set up the problem interface
    ChanProblemInterface chan(globalData, n, alpha, beta, scale, outFile);
    LOCA::ParameterVector p;
    p.addParameter("alpha",alpha);
    p.addParameter("beta",beta);
    p.addParameter("scale",scale);

    // Create a group which uses that problem interface. The group will
    // be initialized to contain the default initial guess for the
    // specified problem.
    Teuchos::RCP<LOCA::MultiContinuation::AbstractGroup> grp =
      Teuchos::rcp(new LOCA::LAPACK::Group(globalData, chan));

    grp->setParams(p);

    // Set up the status tests
    Teuchos::RCP<NOX::StatusTest::NormF> normF =
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxIters =
      Teuchos::rcp(new NOX::StatusTest::MaxIters(maxNewtonIters));
    Teuchos::RCP<NOX::StatusTest::Generic> comboOR =
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR,
                          normF,
                          maxIters));

    // Create the stepper
    LOCA::Stepper stepper(globalData, grp, comboOR, paramList);

    // Perform continuation run
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    // Check for convergence
    if (status == LOCA::Abstract::Iterator::Finished)
      std::cout << "All examples passed" << std::endl;
    else {
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
    globalData->locaUtils->out()
      << "Stepper failed to converge!" << std::endl;
    }

    // Get the final solution from the stepper
    Teuchos::RCP<const LOCA::LAPACK::Group> finalGroup =
      Teuchos::rcp_dynamic_cast<const LOCA::LAPACK::Group>(stepper.getSolutionGroup());
    const NOX::LAPACK::Vector& finalSolution =
      dynamic_cast<const NOX::LAPACK::Vector&>(finalGroup->getX());

    // Print final solution
    globalData->locaUtils->out()
                << std::endl << "Final solution is " << std::endl;
    finalGroup->printSolution(finalSolution,
                      finalGroup->getParam("alpha"));

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out()
    << std::endl << "Final Parameters" << std::endl
    << "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    outFile.close();

    LOCA::destroyGlobalData(globalData);
  }

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

  return 0;
}
Beispiel #23
0
int main(int argc, char *argv[])
{
  int ierr = 0;
  int MyPID = 0;

  try {
  
    // scale factor to test arc-length scaling
    double scale = 1.0;

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

    // Create a communicator for Epetra objects
#ifdef HAVE_MPI
    Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
    Epetra_SerialComm Comm;
#endif

    // Get the process ID and the total number of processors
    MyPID = Comm.MyPID();
    int NumProc = Comm.NumProc();

    // Check for verbose output
    bool verbose = false;
    if (argc>1) 
      if (argv[1][0]=='-' && argv[1][1]=='v') 
	verbose = true;

    // Get the number of elements from the command line
    int NumGlobalElements = 0;
    if ((argc > 2) && (verbose))
      NumGlobalElements = atoi(argv[2]) + 1;
    else if ((argc > 1) && (!verbose))
      NumGlobalElements = atoi(argv[1]) + 1;
    else 
      NumGlobalElements = 101;

    // The number of unknowns must be at least equal to the 
    // number of processors.
    if (NumGlobalElements < NumProc) {
      cout << "numGlobalBlocks = " << NumGlobalElements 
	   << " cannot be < number of processors = " << NumProc << endl;
      exit(1);
    }

    // Create the FiniteElementProblem class.  This creates all required
    // Epetra objects for the problem and allows calls to the 
    // function (RHS) and Jacobian evaluation routines.
    Tcubed_FiniteElementProblem Problem(NumGlobalElements, Comm, scale);

    // Get the vector from the Problem
    Epetra_Vector& soln = Problem.getSolution();

    // Initialize Solution
    soln.PutScalar(1.0);
  
    // Begin LOCA Solver ************************************

    // Create parameter list
    Teuchos::RCP<Teuchos::ParameterList> paramList = 
      Teuchos::rcp(new Teuchos::ParameterList);
  
    // Create LOCA sublist
    Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

    // Create the stepper sublist and set the stepper parameters
    Teuchos::ParameterList& locaStepperList = 
      locaParamsList.sublist("Stepper");
    locaStepperList.set("Bordered Solver Method", "Householder");
    locaStepperList.set("Continuation Parameter", "Right BC");
    locaStepperList.set("Initial Value", 0.1/scale);
    locaStepperList.set("Max Value", 100.0/scale);
    locaStepperList.set("Min Value", 0.05/scale);
    locaStepperList.set("Max Steps", 30);
    locaStepperList.set("Max Nonlinear Iterations", 15);

#ifdef HAVE_LOCA_ANASAZI
    // Create Anasazi Eigensolver sublist (needs --with-loca-anasazi)
    locaStepperList.set("Compute Eigenvalues",true);
    Teuchos::ParameterList& aList = locaStepperList.sublist("Eigensolver");
    aList.set("Method", "Anasazi");
    if (!verbose)
      aList.set("Verbosity", Anasazi::Errors);
#else
    locaStepperList.set("Compute Eigenvalues",false);
#endif

    // Create predictor sublist
    Teuchos::ParameterList& predictorList = 
      locaParamsList.sublist("Predictor");
    predictorList.set("Method", "Tangent");

    // Create step size sublist
    Teuchos::ParameterList& stepSizeList = locaParamsList.sublist("Step Size");
    stepSizeList.set("Initial Step Size", 0.1/scale);
    stepSizeList.set("Min Step Size", 1.0e-3/scale);
    stepSizeList.set("Max Step Size", 2000.0/scale);
    stepSizeList.set("Aggressiveness", 0.1);

    // Create the "Solver" parameters sublist to be used with NOX Solvers
    Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

    // Create the NOX printing parameter list
    Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
    nlPrintParams.set("MyPID", MyPID); 
    if (verbose)
      nlPrintParams.set("Output Information", 
			NOX::Utils::OuterIteration + 
			NOX::Utils::OuterIterationStatusTest + 
			NOX::Utils::InnerIteration +
			//NOX::Utils::Details + 
			NOX::Utils::Warning +
			NOX::Utils::TestDetails + 
			NOX::Utils::Error + 
			NOX::Utils::StepperIteration +
			NOX::Utils::StepperDetails +
			NOX::Utils::StepperParameters);
    else
      nlPrintParams.set("Output Information", NOX::Utils::Error);

    // Create the "Linear Solver" sublist
    Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
    Teuchos::ParameterList& newParams = dirParams.sublist("Newton");
    Teuchos::ParameterList& lsParams = newParams.sublist("Linear Solver");
    lsParams.set("Aztec Solver", "GMRES");  
    lsParams.set("Max Iterations", 100);  
    lsParams.set("Tolerance", 1e-4);
    if (verbose)
      lsParams.set("Output Frequency", 1);
    else
      lsParams.set("Output Frequency", 0);
    lsParams.set("Scaling", "None");             
    lsParams.set("Preconditioner", "Ifpack");

    // Create and initialize the parameter vector
    LOCA::ParameterVector pVector;
    pVector.addParameter("Nonlinear Factor",1.0);
    pVector.addParameter("Left BC", 0.0);
    pVector.addParameter("Right BC", 0.1);

    // Create the interface between the test problem and the nonlinear solver
    // This is created by the user using inheritance of the abstract base 
    // class:
    Teuchos::RCP<Problem_Interface> interface = 
      Teuchos::rcp(new Problem_Interface(Problem));
    Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;
    Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;
    
    // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
    Teuchos::RCP<Epetra_RowMatrix> Amat = 
      Teuchos::rcp(&Problem.getJacobian(),false);
    
    // Create the linear systems
    Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys = 
      Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams, 
							lsParams, iReq, iJac, 
							Amat, soln));

    // Create the loca vector
    NOX::Epetra::Vector locaSoln(soln);

    // Create Epetra factory
    Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
      Teuchos::rcp(new LOCA::Epetra::Factory);

    // Create global data object
    Teuchos::RCP<LOCA::GlobalData> globalData = 
      LOCA::createGlobalData(paramList, epetraFactory);

    // Create the Group
    Teuchos::RCP<LOCA::Epetra::Group> grp = 
      Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams, 
					   iReq, locaSoln, 
					   linsys, pVector));
    grp->computeF();

    // Create the Solver convergence test
    Teuchos::RCP<NOX::StatusTest::NormF> wrms = 
      Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8));
    Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters = 
      Teuchos::rcp(new NOX::StatusTest::MaxIters(15));
    Teuchos::RCP<NOX::StatusTest::Combo> combo = 
      Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
    combo->addStatusTest(wrms);
    combo->addStatusTest(maxiters);

    // Create the stepper  
    LOCA::Stepper stepper(globalData, grp, combo, paramList);
    LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

    if (status != LOCA::Abstract::Iterator::Finished) {
      ierr = 1;
      if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
	globalData->locaUtils->out() 
	  << "Stepper failed to converge!" << std::endl;
    }

    // Get the final solution from the stepper
    Teuchos::RCP<const LOCA::Epetra::Group> finalGroup = 
      Teuchos::rcp_dynamic_cast<const LOCA::Epetra::Group>(stepper.getSolutionGroup());
    const NOX::Epetra::Vector& finalSolution = 
      dynamic_cast<const NOX::Epetra::Vector&>(finalGroup->getX());

    // Output the parameter list
    if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
      globalData->locaUtils->out() 
	<< std::endl << "Final Parameters" << std::endl
	<< "****************" << std::endl;
      stepper.getList()->print(globalData->locaUtils->out());
      globalData->locaUtils->out() << std::endl;
    }

    // Check some statistics on the solution
    NOX::TestCompare testCompare(globalData->locaUtils->out(), 
				 *(globalData->locaUtils));
  
    if (globalData->locaUtils->isPrintType(NOX::Utils::TestDetails))
      globalData->locaUtils->out() 
	<< std::endl 
	<< "***** Checking solution statistics *****" 
	<< std::endl;

    // Check number of steps
    int numSteps = stepper.getStepNumber();
    int numSteps_expected = 23;
    ierr += testCompare.testValue(numSteps, numSteps_expected, 0.0,
				  "number of continuation steps",
				  NOX::TestCompare::Absolute);

    // Check number of failed steps
    int numFailedSteps = stepper.getNumFailedSteps();
    int numFailedSteps_expected = 0;
    ierr += testCompare.testValue(numFailedSteps, numFailedSteps_expected, 0.0,
				  "number of failed continuation steps",
				  NOX::TestCompare::Absolute);

    // Check final value of continuation parameter
    double right_bc_final = finalGroup->getParam("Right BC");
    double right_bc_expected = 0.05;
    ierr += testCompare.testValue(right_bc_final, right_bc_expected, 1.0e-14,
				  "final value of continuation parameter", 
				  NOX::TestCompare::Relative);
 
    // Check norm of solution
    double norm_x = finalSolution.norm();
    double norm_x_expected = 25.00498021;
    ierr += testCompare.testValue(norm_x, norm_x_expected, 1.0e-7,
				  "norm of final solution",
				  NOX::TestCompare::Relative);

    LOCA::destroyGlobalData(globalData);
  }

  catch (std::exception& e) {
    cout << e.what() << endl;
    ierr = 1;
  }
  catch (const char *s) {
    cout << s << endl;
    ierr = 1;
  }
  catch (...) {
    cout << "Caught unknown exception!" << endl;
    ierr = 1;
  }

  if (MyPID == 0) {
    if (ierr == 0)
      cout << "All tests passed!" << endl;
    else
      cout << ierr << " test(s) failed!" << endl;
  }

#ifdef HAVE_MPI
  MPI_Finalize() ;
#endif

/* end main
*/
  return ierr ;
}
int main(int argc, char *argv[])
{
  int ierr = 0;
  
  // scale factor to test arc-length scaling
  double scale = 1.0;

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

  // Create a communicator for Epetra objects
#ifdef HAVE_MPI
  Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
  Epetra_SerialComm Comm;
#endif

  // Get the process ID and the total number of processors
  int MyPID = Comm.MyPID();
  int NumProc = Comm.NumProc();

  // Get the number of elements from the command line
  int NumGlobalElements = 100 + 1;

  // The number of unknowns must be at least equal to the 
  // number of processors.
  if (NumGlobalElements < NumProc) {
    cout << "numGlobalBlocks = " << NumGlobalElements 
	 << " cannot be < number of processors = " << NumProc << endl;
    exit(1);
  }

  // Create the FiniteElementProblem class.  This creates all required
  // Epetra objects for the problem and allows calls to the 
  // function (RHS) and Jacobian evaluation routines.
  FiniteElementProblem Problem(NumGlobalElements, Comm, scale);

  // Get the vector from the Problem
  Epetra_Vector& soln = Problem.getSolution();

  // Initialize Solution
  soln.PutScalar(1.0);
  
  // Begin LOCA Solver ************************************

  // Create parameter list
  Teuchos::RCP<Teuchos::ParameterList> paramList = 
    Teuchos::rcp(new Teuchos::ParameterList);

  // Create LOCA sublist
  Teuchos::ParameterList& locaParamsList = paramList->sublist("LOCA");

  // Create the stepper sublist and set the stepper parameters
  Teuchos::ParameterList& locaStepperList = locaParamsList.sublist("Stepper");
  locaStepperList.set("Continuation Method", "Arc Length");
  locaStepperList.set("Bordered Solver Method", "Householder");
  locaStepperList.set("Number of Continuation Parameters", 2);
  locaStepperList.set("Epsilon", 0.1);
  locaStepperList.set("Max Charts", 10000);
  locaStepperList.set("Verbosity", 1);
  locaStepperList.set("Page Charts", 1);
  locaStepperList.set("Dump Polyhedra", true);
  locaStepperList.set("Dump Centers", false);
  locaStepperList.set("Filename", "MFresults");
  locaStepperList.set("Enable Arc Length Scaling", false);
  locaStepperList.set("Max Nonlinear Iterations", 15);
  locaStepperList.set("Aggressiveness", 0.0);
  locaStepperList.set("Max Solution Component", 6.0);

  // Create sublist for each continuation parameter
  Teuchos::ParameterList& paramList1 = 
    locaStepperList.sublist("Continuation Parameter 1");
  paramList1.set("Parameter Name", "Right BC");
  paramList1.set("Initial Value", 0.1);
  paramList1.set("Max Value", 4.0);
  paramList1.set("Min Value", 0.0);
  paramList1.set("Initial Step Size", 0.1);
  paramList1.set("Max Step Size", 0.2);
  paramList1.set("Min Step Size", 1.0e-3);

  Teuchos::ParameterList& paramList2 = 
    locaStepperList.sublist("Continuation Parameter 2");
  paramList2.set("Parameter Name", "Nonlinear Factor");
  paramList2.set("Initial Value", 1.0);
  paramList2.set("Max Value", 4.0);
  paramList2.set("Min Value", 0.0);
  paramList2.set("Initial Step Size", 0.1);
  paramList2.set("Max Step Size", 0.2);
  paramList2.set("Min Step Size", 1.0e-3);

  // Create predictor sublist
  Teuchos::ParameterList& predictorList = locaParamsList.sublist("Predictor");
  predictorList.set("Method", "Tangent");

  // Create the "Solver" parameters sublist to be used with NOX Solvers
  Teuchos::ParameterList& nlParams = paramList->sublist("NOX");

  // Create the NOX printing parameter list
  Teuchos::ParameterList& nlPrintParams = nlParams.sublist("Printing");
  nlPrintParams.set("MyPID", MyPID); 
  nlPrintParams.set("Output Information", 
		    NOX::Utils::OuterIteration + 
		    NOX::Utils::OuterIterationStatusTest + 
		    NOX::Utils::InnerIteration +
		    NOX::Utils::LinearSolverDetails +
		    NOX::Utils::Details + 
		    NOX::Utils::Warning + 
		    NOX::Utils::StepperIteration +
		    NOX::Utils::StepperDetails +
		    NOX::Utils::StepperParameters);

  // Create the "Linear Solver" sublist for Newton's method
  Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
  Teuchos::ParameterList& newParams = dirParams.sublist("Newton");
  Teuchos::ParameterList& lsParams = newParams.sublist("Linear Solver");
  lsParams.set("Aztec Solver", "GMRES");  
  lsParams.set("Max Iterations", 100);  
  lsParams.set("Tolerance", 1e-4);
  lsParams.set("Output Frequency", 50);    
  lsParams.set("Scaling", "None");             
  lsParams.set("Preconditioner", "Ifpack");

  // Create and initialize the parameter vector
  LOCA::ParameterVector pVector;
  pVector.addParameter("Right BC", 0.1);
  pVector.addParameter("Nonlinear Factor",1.0);
  pVector.addParameter("Left BC", 0.0);

  // Create the interface between the test problem and the nonlinear solver
  // This is created by the user using inheritance of the abstract base class:
  Teuchos::RCP<Problem_Interface> interface = 
    Teuchos::rcp(new Problem_Interface(Problem));
  Teuchos::RCP<LOCA::Epetra::Interface::Required> iReq = interface;
  Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;
  
  // Create the Epetra_RowMatrixfor the Jacobian/Preconditioner
  Teuchos::RCP<Epetra_RowMatrix> Amat = 
    Teuchos::rcp(&Problem.getJacobian(),false);

  // Create the linear systems
  Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linsys = 
    Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(nlPrintParams, lsParams,
						      iReq, iJac, Amat, soln));

  // Create the loca vector
  NOX::Epetra::Vector locaSoln(soln);

  // Create Epetra factory
  Teuchos::RCP<LOCA::Abstract::Factory> epetraFactory =
    Teuchos::rcp(new LOCA::Epetra::Factory);

  // Create global data object
  Teuchos::RCP<LOCA::GlobalData> globalData = 
    LOCA::createGlobalData(paramList, epetraFactory);

  // Create the Group
  Teuchos::RCP<LOCA::Epetra::Group> grp = 
    Teuchos::rcp(new LOCA::Epetra::Group(globalData, nlPrintParams, iReq, 
					 locaSoln, linsys,
					 pVector));
  grp->computeF();

  // Create the Solver convergence test
  //NOX::StatusTest::NormWRMS wrms(1.0e-2, 1.0e-8);
  Teuchos::RCP<NOX::StatusTest::NormF> wrms = 
    Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-8));
  Teuchos::RCP<NOX::StatusTest::MaxIters> maxiters = 
    Teuchos::rcp(new NOX::StatusTest::MaxIters(locaStepperList.get("Max Nonlinear Iterations", 10)));
  Teuchos::RCP<NOX::StatusTest::Combo> combo = 
    Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR));
  combo->addStatusTest(wrms);
  combo->addStatusTest(maxiters);

  // Create the stepper  
  LOCA::MultiStepper stepper(globalData, grp, combo, paramList);
  LOCA::Abstract::Iterator::IteratorStatus status = stepper.run();

  if (status == LOCA::Abstract::Iterator::Finished) 
    globalData->locaUtils->out() << "All tests passed" << endl;
  else {
    if (globalData->locaUtils->isPrintType(NOX::Utils::Error))
      globalData->locaUtils->out() 
	<< "Stepper failed to converge!" << std::endl;
    }

  // Output the parameter list
  if (globalData->locaUtils->isPrintType(NOX::Utils::StepperParameters)) {
    globalData->locaUtils->out() 
      << std::endl << "Final Parameters" << std::endl
      << "****************" << std::endl;
    stepper.getList()->print(globalData->locaUtils->out());
    globalData->locaUtils->out() << std::endl;
  }

  LOCA::destroyGlobalData(globalData);

#ifdef HAVE_MPI
  MPI_Finalize() ;
#endif

/* end main
*/
return ierr ;
}