// ======================================================================
bool BasicTest(string PrecType, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A,bool backward, bool reorder=false)
{
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
LHS.PutScalar(0.0); RHS.Random();
double starting_residual = Galeri::ComputeNorm(&*A, &LHS, &RHS);
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
// Set up the list
Teuchos::ParameterList List;
List.set("relaxation: damping factor", 1.0);
List.set("relaxation: sweeps",2550);
List.set("relaxation: type", PrecType);
if(backward) List.set("relaxation: backward mode",backward);
// Reordering if needed
int NumRows=A->NumMyRows();
std::vector<int> RowList(NumRows);
if(reorder) {
for(int i=0; i<NumRows; i++)
RowList[i]=i;
List.set("relaxation: number of local smoothing indices",NumRows);
List.set("relaxation: local smoothing indices",RowList.size()>0? &RowList[0] : (int*)0);
}
Ifpack_PointRelaxation Point(&*A);
Point.SetParameters(List);
Point.Compute();
// use the preconditioner as solver, with 1550 iterations
Point.ApplyInverse(RHS,LHS);
// compute the real residual
double residual = Galeri::ComputeNorm(&*A, &LHS, &RHS);
if (A->Comm().MyPID() == 0 && verbose)
cout << "||A * x - b||_2 (scaled) = " << residual / starting_residual << endl;
// Jacobi is very slow to converge here
if (residual / starting_residual < 1e-2) {
if (verbose)
cout << "BasicTest Test passed" << endl;
return(true);
}
else {
if (verbose)
cout << "BasicTest Test failed!" << endl;
return(false);
}
}
// ======================================================================
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
verbose = (Comm.MyPID() == 0);
for (int i = 1 ; i < argc ; ++i) {
if (strcmp(argv[i],"-s") == 0) {
SymmetricGallery = true;
Solver = AZ_cg;
}
}
// size of the global matrix.
Teuchos::ParameterList GaleriList;
int nx = 30;
GaleriList.set("nx", nx);
GaleriList.set("ny", nx * Comm.NumProc());
GaleriList.set("mx", 1);
GaleriList.set("my", Comm.NumProc());
Teuchos::RefCountPtr<Epetra_Map> Map = Teuchos::rcp( Galeri::CreateMap("Cartesian2D", Comm, GaleriList) );
Teuchos::RefCountPtr<Epetra_CrsMatrix> A;
if (SymmetricGallery)
A = Teuchos::rcp( Galeri::CreateCrsMatrix("Laplace2D", &*Map, GaleriList) );
else
A = Teuchos::rcp( Galeri::CreateCrsMatrix("Recirc2D", &*Map, GaleriList) );
// coordinates
Teuchos::RCP<Epetra_MultiVector> coord = Teuchos::rcp( Galeri::CreateCartesianCoordinates("2D",&*Map,GaleriList));
// test the preconditioner
int TestPassed = true;
// ======================================== //
// first verify that we can get convergence //
// with all point relaxation methods //
// ======================================== //
if(!BasicTest("Jacobi",A,false))
TestPassed = false;
if(!BasicTest("symmetric Gauss-Seidel",A,false))
TestPassed = false;
if(!BasicTest("symmetric Gauss-Seidel",A,false,true))
TestPassed = false;
if (!SymmetricGallery) {
if(!BasicTest("Gauss-Seidel",A,false))
TestPassed = false;
if(!BasicTest("Gauss-Seidel",A,true))
TestPassed = false;
if(!BasicTest("Gauss-Seidel",A,false,true))
TestPassed = false;
if(!BasicTest("Gauss-Seidel",A,true,true))
TestPassed = false;
}
// ============================= //
// check uses as preconditioners //
// ============================= //
if(!KrylovTest("symmetric Gauss-Seidel",A,false))
TestPassed = false;
if(!KrylovTest("symmetric Gauss-Seidel",A,false,true))
TestPassed = false;
if (!SymmetricGallery) {
if(!KrylovTest("Gauss-Seidel",A,false))
TestPassed = false;
if(!KrylovTest("Gauss-Seidel",A,true))
TestPassed = false;
if(!KrylovTest("Gauss-Seidel",A,false,true))
TestPassed = false;
if(!KrylovTest("Gauss-Seidel",A,true,true))
TestPassed = false;
}
// ================================== //
// compare point and block relaxation //
// ================================== //
//TestPassed = TestPassed &&
// ComparePointAndBlock("Jacobi",A,1);
TestPassed = TestPassed &&
ComparePointAndBlock("Jacobi",A,10);
//TestPassed = TestPassed &&
//ComparePointAndBlock("symmetric Gauss-Seidel",A,1);
TestPassed = TestPassed &&
ComparePointAndBlock("symmetric Gauss-Seidel",A,10);
if (!SymmetricGallery) {
//TestPassed = TestPassed &&
//ComparePointAndBlock("Gauss-Seidel",A,1);
TestPassed = TestPassed &&
ComparePointAndBlock("Gauss-Seidel",A,10);
}
// ============================ //
// verify effect of # of blocks //
// ============================ //
{
int Iters4, Iters8, Iters16;
Iters4 = CompareBlockSizes("Jacobi",A,4);
Iters8 = CompareBlockSizes("Jacobi",A,8);
Iters16 = CompareBlockSizes("Jacobi",A,16);
if ((Iters16 > Iters8) && (Iters8 > Iters4)) {
if (verbose)
cout << "CompareBlockSizes Test passed" << endl;
}
else {
if (verbose)
cout << "CompareBlockSizes TEST FAILED!" << endl;
TestPassed = TestPassed && false;
}
}
// ================================== //
// verify effect of overlap in Jacobi //
// ================================== //
{
int Iters0, Iters2, Iters4;
Iters0 = CompareBlockOverlap(A,0);
Iters2 = CompareBlockOverlap(A,2);
Iters4 = CompareBlockOverlap(A,4);
if ((Iters4 < Iters2) && (Iters2 < Iters0)) {
if (verbose)
cout << "CompareBlockOverlap Test passed" << endl;
}
else {
if (verbose)
cout << "CompareBlockOverlap TEST FAILED!" << endl;
TestPassed = TestPassed && false;
}
}
// ================================== //
// check if line smoothing works //
// ================================== //
{
int Iters1=
CompareLineSmoother(A,coord);
printf(" comparelinesmoother iters %d \n",Iters1);
}
// ================================== //
// check if All singleton version of CompareLineSmoother //
// ================================== //
{
AllSingle(A,coord);
}
// ================================== //
// test variable blocking //
// ================================== //
{
TestPassed = TestPassed && TestVariableBlocking(A->Comm());
}
// ================================== //
// test variable blocking //
// ================================== //
{
TestPassed = TestPassed && TestTriDiVariableBlocking(A->Comm());
}
// ============ //
// final output //
// ============ //
if (!TestPassed) {
cout << "Test `TestRelaxation.exe' failed!" << endl;
exit(EXIT_FAILURE);
}
#ifdef HAVE_MPI
MPI_Finalize();
#endif
cout << endl;
cout << "Test `TestRelaxation.exe' passed!" << endl;
cout << endl;
return(EXIT_SUCCESS);
}
// ======================================================================
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);
}