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;
}
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!!
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!!
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;
}
