bool Test(const Teuchos::RefCountPtr<Epetra_RowMatrix>& Matrix, Teuchos::ParameterList& List)
{
int NumVectors = 1;
bool UseTranspose = false;
Epetra_MultiVector LHS(Matrix->OperatorDomainMap(),NumVectors);
Epetra_MultiVector RHS(Matrix->OperatorRangeMap(),NumVectors);
Epetra_MultiVector LHSexact(Matrix->OperatorDomainMap(),NumVectors);
LHS.PutScalar(0.0);
LHSexact.Random();
Matrix->Multiply(UseTranspose,LHSexact,RHS);
Epetra_LinearProblem Problem(&*Matrix,&LHS,&RHS);
Teuchos::RefCountPtr<T> Prec;
Prec = Teuchos::rcp( new T(&*Matrix) );
assert(Prec != Teuchos::null);
IFPACK_CHK_ERR(Prec->SetParameters(List));
IFPACK_CHK_ERR(Prec->Initialize());
IFPACK_CHK_ERR(Prec->Compute());
// create the AztecOO solver
AztecOO AztecOOSolver(Problem);
// specify solver
AztecOOSolver.SetAztecOption(AZ_solver,AZ_gmres);
AztecOOSolver.SetAztecOption(AZ_output,32);
AztecOOSolver.SetPrecOperator(&*Prec);
// solver. The solver should converge in one iteration,
// or maximum two (numerical errors)
AztecOOSolver.Iterate(1550,1e-8);
cout << *Prec;
vector<double> Norm(NumVectors);
LHS.Update(1.0,LHSexact,-1.0);
LHS.Norm2(&Norm[0]);
for (int i = 0 ; i < NumVectors ; ++i) {
cout << "Norm[" << i << "] = " << Norm[i] << endl;
if (Norm[i] > 1e-3)
return(false);
}
return(true);
}
// ======================================================================
bool TestContainer(std::string Type, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A)
{
using std::cout;
using std::endl;
int NumVectors = 3;
int NumMyRows = A->NumMyRows();
Epetra_MultiVector LHS_exact(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
LHS_exact.Random(); LHS.PutScalar(0.0);
A->Multiply(false, LHS_exact, RHS);
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
if (verbose) {
cout << "Container type = " << Type << endl;
cout << "NumMyRows = " << NumMyRows << ", NumVectors = " << NumVectors << endl;
}
LHS.PutScalar(0.0);
Teuchos::RefCountPtr<Ifpack_Container> Container;
if (Type == "dense")
Container = Teuchos::rcp( new Ifpack_DenseContainer(A->NumMyRows(), NumVectors) );
else
Container = Teuchos::rcp( new Ifpack_SparseContainer<Ifpack_Amesos>(A->NumMyRows(), NumVectors) );
assert (Container != Teuchos::null);
IFPACK_CHK_ERR(Container->Initialize());
// set as ID all the local rows of A
for (int i = 0 ; i < A->NumMyRows() ; ++i)
Container->ID(i) = i;
// extract submatrix (in this case, the entire matrix)
// and complete setup
IFPACK_CHK_ERR(Container->Compute(*A));
// set the RHS and LHS
for (int i = 0 ; i < A->NumMyRows() ; ++i)
for (int j = 0 ; j < NumVectors ; ++j) {
Container->RHS(i,j) = RHS[j][i];
Container->LHS(i,j) = LHS[j][i];
}
// set parameters (empty for dense containers)
Teuchos::ParameterList List;
List.set("amesos: solver type", Type);
IFPACK_CHK_ERR(Container->SetParameters(List));
// solve the linear system
IFPACK_CHK_ERR(Container->ApplyInverse());
// get the computed solution, store it in LHS
for (int i = 0 ; i < A->NumMyRows() ; ++i)
for (int j = 0 ; j < NumVectors ; ++j) {
LHS[j][i] = Container->LHS(i,j);
}
double residual = Galeri::ComputeNorm(&LHS, &LHS_exact);
if (A->Comm().MyPID() == 0 && verbose) {
cout << "||x_exact - x||_2 = " << residual << endl;
cout << *Container;
}
bool passed = false;
if (residual < 1e-5)
passed = true;
return(passed);
}
bool CompareWithAztecOO(Epetra_LinearProblem& Problem, const std::string what,
int Overlap, int ival)
{
using std::cout;
using std::endl;
AztecOO AztecOOSolver(Problem);
AztecOOSolver.SetAztecOption(AZ_solver,AZ_gmres);
AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
AztecOOSolver.SetAztecOption(AZ_overlap,Overlap);
AztecOOSolver.SetAztecOption(AZ_graph_fill,ival);
AztecOOSolver.SetAztecOption(AZ_poly_ord, ival);
AztecOOSolver.SetAztecParam(AZ_drop, 0.0);
AztecOOSolver.SetAztecParam(AZ_athresh, 0.0);
AztecOOSolver.SetAztecParam(AZ_rthresh, 0.0);
Epetra_MultiVector& RHS = *(Problem.GetRHS());
Epetra_MultiVector& LHS = *(Problem.GetLHS());
Teuchos::RefCountPtr<Epetra_RowMatrix> A = Teuchos::rcp(Problem.GetMatrix(), false);
LHS.Random();
A->Multiply(false,LHS,RHS);
Teuchos::ParameterList List;
List.set("fact: level-of-fill", ival);
List.set("relaxation: sweeps", ival);
List.set("relaxation: damping factor", 1.0);
List.set("relaxation: zero starting solution", true);
//default combine mode is as for AztecOO
List.set("schwarz: combine mode", Zero);
Epetra_Time Time(A->Comm());
Teuchos::RefCountPtr<Ifpack_Preconditioner> Prec;
if (what == "Jacobi") {
Prec = Teuchos::rcp( new Ifpack_PointRelaxation(&*A) );
List.set("relaxation: type", "Jacobi");
AztecOOSolver.SetAztecOption(AZ_precond,AZ_Jacobi);
AztecOOSolver.SetAztecOption(AZ_reorder,0);
}
else if (what == "IC no reord") {
Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_IC>(&*A,Overlap) );
AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_icc);
AztecOOSolver.SetAztecOption(AZ_reorder,0);
}
else if (what == "IC reord") {
Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_IC>(&*A,Overlap) );
List.set("schwarz: use reordering", true);
AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_icc);
AztecOOSolver.SetAztecOption(AZ_reorder,1);
}
else if (what == "ILU no reord") {
Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_ILU>(&*A,Overlap) );
AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_ilu);
AztecOOSolver.SetAztecOption(AZ_reorder,0);
}
else if (what == "ILU reord") {
Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_ILU>(&*A,Overlap) );
List.set("schwarz: use reordering", true);
AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_ilu);
AztecOOSolver.SetAztecOption(AZ_reorder,1);
}
#ifdef HAVE_IFPACK_AMESOS
else if (what == "LU") {
Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_Amesos>(&*A,Overlap) );
List.set("amesos: solver type", "Klu");
AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_lu);
}
#endif
else {
cerr << "Option not recognized" << endl;
exit(EXIT_FAILURE);
}
// ==================================== //
// Solve with AztecOO's preconditioners //
// ==================================== //
LHS.PutScalar(0.0);
Time.ResetStartTime();
AztecOOSolver.Iterate(150,1e-5);
if (verbose) {
cout << endl;
cout << "==================================================" << endl;
cout << "Testing `" << what << "', Overlap = "
<< Overlap << ", ival = " << ival << endl;
cout << endl;
cout << "[AztecOO] Total time = " << Time.ElapsedTime() << " (s)" << endl;
cout << "[AztecOO] Residual = " << AztecOOSolver.TrueResidual() << " (s)" << endl;
cout << "[AztecOO] Iterations = " << AztecOOSolver.NumIters() << endl;
cout << endl;
}
int AztecOOPrecIters = AztecOOSolver.NumIters();
// =========================================== //
// Create the IFPACK preconditioner and solver //
// =========================================== //
Epetra_Time Time2(A->Comm());
assert(Prec != Teuchos::null);
IFPACK_CHK_ERR(Prec->SetParameters(List));
Time.ResetStartTime();
IFPACK_CHK_ERR(Prec->Initialize());
if (verbose)
cout << "[IFPACK] Time for Initialize() = "
<< Time.ElapsedTime() << " (s)" << endl;
Time.ResetStartTime();
IFPACK_CHK_ERR(Prec->Compute());
if (verbose)
cout << "[IFPACK] Time for Compute() = "
<< Time.ElapsedTime() << " (s)" << endl;
AztecOOSolver.SetPrecOperator(&*Prec);
LHS.PutScalar(0.0);
Time.ResetStartTime();
AztecOOSolver.Iterate(150,1e-5);
if (verbose) {
cout << "[IFPACK] Total time = " << Time2.ElapsedTime() << " (s)" << endl;
cout << "[IFPACK] Residual = " << AztecOOSolver.TrueResidual() << " (s)" << endl;
cout << "[IFPACK] Iterations = " << AztecOOSolver.NumIters() << endl;
cout << endl;
}
int IFPACKPrecIters = AztecOOSolver.NumIters();
if (IFPACK_ABS(AztecOOPrecIters - IFPACKPrecIters) > 3) {
cerr << "TEST FAILED (" << AztecOOPrecIters << " != "
<< IFPACKPrecIters << ")" << endl;
return(false);
}
else
return(true);
}