int
AmesosGenOp::Apply (const Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{
if (problem_ == NULL) {
throw std::logic_error ("AmesosGenOp::Apply: problem_ is NULL");
}
if (massMtx_.is_null ()) {
throw std::logic_error ("AmesosGenOp::Apply: massMtx_ is null");
}
if (solver_.is_null ()) {
throw std::logic_error ("AmesosGenOp::Apply: solver_ is null");
}
if (! useTranspose_) {
// Storage for M*X
Epetra_MultiVector MX (X.Map (), X.NumVectors ());
// Apply M*X
massMtx_->Apply (X, MX);
Y.PutScalar (0.0);
// Set the LHS and RHS
problem_->SetRHS (&MX);
problem_->SetLHS (&Y);
// Solve the linear system A*Y = MX
solver_->Solve ();
}
else { // apply the transposed operator
// Storage for A^{-T}*X
Epetra_MultiVector ATX (X.Map (), X.NumVectors ());
Epetra_MultiVector tmpX = const_cast<Epetra_MultiVector&> (X);
// Set the LHS and RHS
problem_->SetRHS (&tmpX);
problem_->SetLHS (&ATX);
// Solve the linear system A^T*Y = X
solver_->Solve ();
// Apply M*ATX
massMtx_->Apply (ATX, Y);
}
return 0; // the method completed correctly
}
// ======================================================================
void Krylov(const Operator& A, const MultiVector& LHS,
const MultiVector& RHS, const BaseOperator& Prec,
Teuchos::ParameterList& List)
{
#ifndef HAVE_ML_AZTECOO
std::cerr << "Please configure ML with --enable-aztecoo to use" << std::endl;
std::cerr << "MLAPI Krylov solvers" << std::endl;
exit(EXIT_FAILURE);
#else
if (LHS.GetNumVectors() != 1)
ML_THROW("FIXME: only one vector is currently supported", -1);
Epetra_LinearProblem Problem;
const Epetra_RowMatrix& A_Epetra = *(A.GetRowMatrix());
Epetra_Vector LHS_Epetra(View,A_Epetra.OperatorDomainMap(),
(double*)&(LHS(0)));
Epetra_Vector RHS_Epetra(View,A_Epetra.OperatorRangeMap(),
(double*)&(RHS(0)));
// FIXME: this works only for Epetra-based operators
Problem.SetOperator((const_cast<Epetra_RowMatrix*>(&A_Epetra)));
Problem.SetLHS(&LHS_Epetra);
Problem.SetRHS(&RHS_Epetra);
AztecOO solver(Problem);
EpetraBaseOperator Prec_Epetra(A_Epetra.OperatorDomainMap(),Prec);
solver.SetPrecOperator(&Prec_Epetra);
// get options from List
int NumIters = List.get("krylov: max iterations", 1550);
double Tol = List.get("krylov: tolerance", 1e-9);
std::string type = List.get("krylov: type", "gmres");
int output = List.get("krylov: output level", GetPrintLevel());
// set options in `solver'
if (type == "cg")
solver.SetAztecOption(AZ_solver, AZ_cg);
else if (type == "cg_condnum")
solver.SetAztecOption(AZ_solver, AZ_cg_condnum);
else if (type == "gmres")
solver.SetAztecOption(AZ_solver, AZ_gmres);
else if (type == "gmres_condnum")
solver.SetAztecOption(AZ_solver, AZ_gmres_condnum);
else if (type == "fixed point")
solver.SetAztecOption(AZ_solver, AZ_fixed_pt);
else
ML_THROW("krylov: type has incorrect value (" +
type + ")", -1);
solver.SetAztecOption(AZ_output, output);
solver.Iterate(NumIters, Tol);
#endif
}
int AmesosGenOp::Apply(const Epetra_MultiVector& X, Epetra_MultiVector& Y ) const
{
if (!useTranspose_) {
// Storage for M*X
Epetra_MultiVector MX(X.Map(),X.NumVectors());
// Apply M*X
massMtx_->Apply(X, MX);
Y.PutScalar(0.0);
// Set the LHS and RHS
problem_->SetRHS(&MX);
problem_->SetLHS(&Y);
// Solve the linear system A*Y = MX
solver_->Solve();
}
else {
// Storage for A^{-T}*X
Epetra_MultiVector ATX(X.Map(),X.NumVectors());
Epetra_MultiVector tmpX = const_cast<Epetra_MultiVector&>(X);
// Set the LHS and RHS
problem_->SetRHS(&tmpX);
problem_->SetLHS(&ATX);
// Solve the linear system A^T*Y = X
solver_->Solve();
// Apply M*ATX
massMtx_->Apply(ATX, Y);
}
return 0;
}
int AmesosBucklingOp::Apply(const Epetra_MultiVector& X, Epetra_MultiVector& Y ) const
{
// Storage for A*X
Epetra_MultiVector AX(X.Map(),X.NumVectors());
// Apply A*X
stiffMtx_->Apply(X, AX);
Y.PutScalar(0.0);
// Set the LHS and RHS
problem_->SetRHS(&AX);
problem_->SetLHS(&Y);
// Solve the linear system (A-sigma*M)*Y = AX
solver_->Solve();
return 0;
}
int PartialFactorizationOneStep( const char* AmesosClass,
const Epetra_Comm &Comm,
bool transpose,
bool verbose,
Teuchos::ParameterList ParamList,
Epetra_CrsMatrix *& Amat,
double Rcond,
int Steps )
{
assert( Steps >= 0 && Steps < MaxNumSteps ) ;
int iam = Comm.MyPID() ;
int errors = 0 ;
const Epetra_Map *RangeMap =
transpose?&Amat->OperatorDomainMap():&Amat->OperatorRangeMap() ;
const Epetra_Map *DomainMap =
transpose?&Amat->OperatorRangeMap():&Amat->OperatorDomainMap() ;
Epetra_Vector xexact(*DomainMap);
Epetra_Vector x(*DomainMap);
Epetra_Vector b(*RangeMap);
Epetra_Vector bcheck(*RangeMap);
Epetra_Vector difference(*DomainMap);
Epetra_LinearProblem Problem;
Amesos_BaseSolver* Abase ;
Amesos Afactory;
Abase = Afactory.Create( AmesosClass, Problem ) ;
std::string AC = AmesosClass ;
if ( AC == "Amesos_Mumps" ) {
ParamList.set( "NoDestroy", true );
Abase->SetParameters( ParamList ) ;
}
double relresidual = 0 ;
if ( Steps > 0 ) {
//
// Phase 1: Compute b = A' A' A xexact
//
Problem.SetOperator( Amat );
//
// We only set transpose if we have to - this allows valgrind to check
// that transpose is set to a default value before it is used.
//
if ( transpose ) OUR_CHK_ERR( Abase->SetUseTranspose( transpose ) );
// if (verbose) ParamList.set( "DebugLevel", 1 );
// if (verbose) ParamList.set( "OutputLevel", 1 );
if ( Steps > 1 ) {
OUR_CHK_ERR( Abase->SetParameters( ParamList ) );
if ( Steps > 2 ) {
xexact.Random();
xexact.PutScalar(1.0);
//
// Compute cAx = A' xexact
//
Amat->Multiply( transpose, xexact, b ) ; // b = A x2 = A A' A'' xexact
#if 0
std::cout << __FILE__ << "::" << __LINE__ << "b = " << std::endl ;
b.Print( std::cout ) ;
std::cout << __FILE__ << "::" << __LINE__ << "xexact = " << std::endl ;
xexact.Print( std::cout ) ;
std::cout << __FILE__ << "::" << __LINE__ << "x = " << std::endl ;
x.Print( std::cout ) ;
#endif
//
// Phase 2: Solve A' A' A x = b
//
//
// Solve A sAAx = b
//
Problem.SetLHS( &x );
Problem.SetRHS( &b );
OUR_CHK_ERR( Abase->SymbolicFactorization( ) );
if ( Steps > 2 ) {
OUR_CHK_ERR( Abase->SymbolicFactorization( ) );
if ( Steps > 3 ) {
OUR_CHK_ERR( Abase->NumericFactorization( ) );
if ( Steps > 4 ) {
OUR_CHK_ERR( Abase->NumericFactorization( ) );
if ( Steps > 5 ) {
OUR_CHK_ERR( Abase->Solve( ) );
if ( Steps > 6 ) {
OUR_CHK_ERR( Abase->Solve( ) );
Amat->Multiply( transpose, x, bcheck ) ; // temp = A" x2
double norm_diff ;
double norm_one ;
difference.Update( 1.0, x, -1.0, xexact, 0.0 ) ;
difference.Norm2( &norm_diff ) ;
x.Norm2( &norm_one ) ;
relresidual = norm_diff / norm_one ;
if (iam == 0 ) {
if ( relresidual * Rcond > 1e-16 ) {
if (verbose) std::cout << __FILE__ << "::"<< __LINE__
<< " norm( x - xexact ) / norm(x) = "
<< norm_diff /norm_one << std::endl ;
errors += 1 ;
}
}
}
}
}
}
}
}
}
}
delete Abase;
return errors;
}
double Ifpack_Condest(const Ifpack_Preconditioner& IFP,
const Ifpack_CondestType CT,
const int MaxIters,
const double Tol,
Epetra_RowMatrix* Matrix)
{
double ConditionNumberEstimate = -1.0;
if (CT == Ifpack_Cheap) {
// Create a vector with all values equal to one
Epetra_Vector Ones(IFP.OperatorDomainMap());
Ones.PutScalar(1.0);
// Create the vector of results
Epetra_Vector OnesResult(IFP.OperatorRangeMap());
// Compute the effect of the solve on the vector of ones
IFPACK_CHK_ERR(IFP.ApplyInverse(Ones, OnesResult));
// Make all values non-negative
IFPACK_CHK_ERR(OnesResult.Abs(OnesResult));
// Get the maximum value across all processors
IFPACK_CHK_ERR(OnesResult.MaxValue(&ConditionNumberEstimate));
}
else if (CT == Ifpack_CG) {
#ifdef HAVE_IFPACK_AZTECOO
if (Matrix == 0)
Matrix = (Epetra_RowMatrix*)&(IFP.Matrix());
Epetra_Vector LHS(IFP.OperatorDomainMap());
LHS.PutScalar(0.0);
Epetra_Vector RHS(IFP.OperatorRangeMap());
RHS.Random();
Epetra_LinearProblem Problem;
Problem.SetOperator(Matrix);
Problem.SetLHS(&LHS);
Problem.SetRHS(&RHS);
AztecOO Solver(Problem);
Solver.SetAztecOption(AZ_output,AZ_none);
Solver.SetAztecOption(AZ_solver,AZ_cg_condnum);
Solver.Iterate(MaxIters,Tol);
const double* status = Solver.GetAztecStatus();
ConditionNumberEstimate = status[AZ_condnum];
#endif
} else if (CT == Ifpack_GMRES) {
#ifdef HAVE_IFPACK_AZTECOO
if (Matrix == 0)
Matrix = (Epetra_RowMatrix*)&(IFP.Matrix());
Epetra_Vector LHS(IFP.OperatorDomainMap());
LHS.PutScalar(0.0);
Epetra_Vector RHS(IFP.OperatorRangeMap());
RHS.Random();
Epetra_LinearProblem Problem;
Problem.SetOperator(Matrix);
Problem.SetLHS(&LHS);
Problem.SetRHS(&RHS);
AztecOO Solver(Problem);
Solver.SetAztecOption(AZ_solver,AZ_gmres_condnum);
Solver.SetAztecOption(AZ_output,AZ_none);
// the following can be problematic for large problems,
// but any restart would destroy useful information about
// the condition number.
Solver.SetAztecOption(AZ_kspace,MaxIters);
Solver.Iterate(MaxIters,Tol);
const double* status = Solver.GetAztecStatus();
ConditionNumberEstimate = status[AZ_condnum];
#endif
}
return(ConditionNumberEstimate);
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv, 0);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
int nProcs, myPID ;
Teuchos::ParameterList pLUList ; // ParaLU parameters
Teuchos::ParameterList isoList ; // Isorropia parameters
string ipFileName = "ShyLU.xml"; // TODO : Accept as i/p
nProcs = mpiSession.getNProc();
myPID = Comm.MyPID();
if (myPID == 0)
{
cout <<"Parallel execution: nProcs="<< nProcs << endl;
}
// =================== Read input xml file =============================
Teuchos::updateParametersFromXmlFile(ipFileName, &pLUList);
isoList = pLUList.sublist("Isorropia Input");
// Get matrix market file name
string MMFileName = Teuchos::getParameter<string>(pLUList, "mm_file");
string prec_type = Teuchos::getParameter<string>(pLUList, "preconditioner");
if (myPID == 0)
{
cout << "Input :" << endl;
cout << "ParaLU params " << endl;
pLUList.print(std::cout, 2, true, true);
cout << "Matrix market file name: " << MMFileName << endl;
}
// ==================== Read input Matrix ==============================
Epetra_CrsMatrix *A;
int err = EpetraExt::MatrixMarketFileToCrsMatrix(MMFileName.c_str(), Comm, A);
//EpetraExt::MatlabFileToCrsMatrix(MMFileName.c_str(), Comm, A);
//assert(err != 0);
cout <<"Done reading the matrix"<< endl;
int n = A->NumGlobalRows();
cout <<"n="<< n << endl;
// Create input vectors
Epetra_Map vecMap(n, 0, Comm);
Epetra_MultiVector x(vecMap, 1);
Epetra_MultiVector b(vecMap, 1, false);
b.PutScalar(1.0); // TODO : Accept it as input
// Partition the matrix with hypergraph partitioning and redisstribute
Isorropia::Epetra::Partitioner *partitioner = new
Isorropia::Epetra::Partitioner(A, isoList, false);
partitioner->partition();
Isorropia::Epetra::Redistributor rd(partitioner);
Epetra_CrsMatrix *newA;
Epetra_MultiVector *newX, *newB;
rd.redistribute(*A, newA);
delete A;
A = newA;
rd.redistribute(x, newX);
rd.redistribute(b, newB);
Epetra_LinearProblem problem(A, newX, newB);
Amesos Factory;
char* SolverType = "Amesos_Klu";
bool IsAvailable = Factory.Query(SolverType);
Epetra_LinearProblem *LP = new Epetra_LinearProblem();
LP->SetOperator(A);
LP->SetLHS(newX);
LP->SetRHS(newB);
Amesos_BaseSolver *Solver = Factory.Create(SolverType, *LP);
Solver->SymbolicFactorization();
Teuchos::Time ftime("setup time");
ftime.start();
Solver->NumericFactorization();
cout << "Numeric Factorization" << endl;
Solver->Solve();
cout << "Solve done" << endl;
ftime.stop();
cout << "Time to setup" << ftime.totalElapsedTime() << endl;
// compute ||Ax - b||
double Norm;
Epetra_MultiVector Ax(vecMap, 1);
Epetra_MultiVector *newAx;
rd.redistribute(Ax, newAx);
A->Multiply(false, *newX, *newAx);
newAx->Update(1.0, *newB, -1.0);
newAx->Norm2(&Norm);
double ANorm = A->NormOne();
cout << "|Ax-b |/|A| = " << Norm/ANorm << endl;
delete newAx;
delete newX;
delete newB;
delete A;
delete partitioner;
}
