int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
// Initialize MPI and setup an Epetra communicator
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
// If we aren't using MPI, then setup a serial communicator.
Epetra_SerialComm Comm;
#endif
// Some typedefs for oft-used data types
typedef Epetra_MultiVector MV;
typedef Epetra_Operator OP;
typedef Belos::MultiVecTraits<double, Epetra_MultiVector> MVT;
bool ierr;
// Get our processor ID (0 if running serial)
int MyPID = Comm.MyPID();
// Verbose flag: only processor 0 should print
bool verbose = (MyPID==0);
// Initialize a Gallery object, from which we will select a matrix
// Select a 2-D laplacian, of order 100
Trilinos_Util::CrsMatrixGallery Gallery("laplace_2d", Comm);
Gallery.Set("problem_size", 100);
// Say hello and print some information about the gallery matrix
if (verbose) {
cout << "Belos Example: Block CG" << endl;
cout << "Problem info:" << endl;
cout << Gallery;
cout << endl;
}
// Setup some more problem/solver parameters:
// Block size
int blocksize = 4;
// Get a pointer to the system matrix, inside of a Teuchos::RCP
// The Teuchos::RCP is a reference counting pointer that handles
// garbage collection for us, so that we can perform memory allocation without
// having to worry about freeing memory manually.
Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( Gallery.GetMatrix(), false );
// Create an Belos MultiVector, based on Epetra MultiVector
const Epetra_Map * Map = &(A->RowMap());
Teuchos::RCP<Epetra_MultiVector> B =
Teuchos::rcp( new Epetra_MultiVector(*Map,blocksize) );
Teuchos::RCP<Epetra_MultiVector> X =
Teuchos::rcp( new Epetra_MultiVector(*Map,blocksize) );
// Initialize the solution with zero and right-hand side with random entries
X->PutScalar( 0.0 );
B->Random();
// Setup the linear problem, with the matrix A and the vectors X and B
Teuchos::RCP< Belos::LinearProblem<double,MV,OP> > myProblem =
Teuchos::rcp( new Belos::LinearProblem<double,MV,OP>(A, X, B) );
// The 2-D laplacian is symmetric. Specify this in the linear problem.
myProblem->setHermitian();
// Signal that we are done setting up the linear problem
ierr = myProblem->setProblem();
// Check the return from setProblem(). If this is true, there was an
// error. This probably means we did not specify enough information for
// the eigenproblem.
assert(ierr == true);
// Specify the verbosity level. Options include:
// Belos::Errors
// This option is always set
// Belos::Warnings
// Warnings (less severe than errors)
// Belos::IterationDetails
// Details at each iteration, such as the current eigenvalues
// Belos::OrthoDetails
// Details about orthogonality
// Belos::TimingDetails
// A summary of the timing info for the solve() routine
// Belos::FinalSummary
// A final summary
// Belos::Debug
// Debugging information
int verbosity = Belos::Warnings + Belos::Errors + Belos::FinalSummary + Belos::TimingDetails;
// Create the parameter list for the eigensolver
Teuchos::RCP<Teuchos::ParameterList> myPL = Teuchos::rcp( new Teuchos::ParameterList() );
myPL->set( "Verbosity", verbosity );
myPL->set( "Block Size", blocksize );
myPL->set( "Maximum Iterations", 100 );
myPL->set( "Convergence Tolerance", 1.0e-8 );
// Create the Block CG solver
// This takes as inputs the linear problem and the solver parameters
Belos::BlockCGSolMgr<double,MV,OP> mySolver(myProblem, myPL);
// Solve the linear problem, and save the return code
Belos::ReturnType solverRet = mySolver.solve();
// Check return code of the solver: Unconverged, Failed, or OK
switch (solverRet) {
// UNCONVERGED
case Belos::Unconverged:
if (verbose)
cout << "Belos::BlockCGSolMgr::solve() did not converge!" << endl;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return 0;
break;
// CONVERGED
case Belos::Converged:
if (verbose)
cout << "Belos::BlockCGSolMgr::solve() converged!" << endl;
break;
}
// Test residuals
Epetra_MultiVector R( B->Map(), blocksize );
// R = A*X
A->Apply( *X, R );
// R -= B
MVT::MvAddMv( -1.0, *B, 1.0, R, R );
// Compute the 2-norm of each vector in the MultiVector
// and store them to a std::vector<double>
std::vector<double> normR(blocksize), normB(blocksize);
MVT::MvNorm( R, normR );
MVT::MvNorm( *B, normB );
// Output results to screen
if(verbose) {
cout << scientific << setprecision(6) << showpoint;
cout << "******************************************************\n"
<< " Results (outside of linear solver) \n"
<< "------------------------------------------------------\n"
<< " Linear System\t\tRelative Residual\n"
<< "------------------------------------------------------\n";
for( int i=0 ; i<blocksize ; ++i ) {
cout << " " << i+1 << "\t\t\t" << normR[i]/normB[i] << endl;
}
cout << "******************************************************\n" << endl;
}
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return(EXIT_SUCCESS);
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
Teuchos::ParameterList GaleriList;
// The problem is defined on a 2D grid, global size is nx * nx.
int nx = 30;
GaleriList.set("n", nx * nx);
GaleriList.set("nx", nx);
GaleriList.set("ny", nx);
Teuchos::RCP<Epetra_Map> Map = Teuchos::rcp( Galeri::CreateMap("Linear", Comm, GaleriList) );
Teuchos::RCP<Epetra_RowMatrix> A = Teuchos::rcp( Galeri::CreateCrsMatrix("Laplace2D", &*Map, GaleriList) );
// Variables used for the Block Davidson Method
const int nev = 4;
const int blockSize = 5;
const int numBlocks = 8;
const int maxRestarts = 100;
const double tol = 1.0e-8;
typedef Epetra_MultiVector MV;
typedef Epetra_Operator OP;
typedef Anasazi::MultiVecTraits<double, Epetra_MultiVector> MVT;
// Create an Epetra_MultiVector for an initial vector to start the solver.
// Note: This needs to have the same number of columns as the blocksize.
//
Teuchos::RCP<Epetra_MultiVector> ivec = Teuchos::rcp( new Epetra_MultiVector(*Map, blockSize) );
ivec->Random();
// Create the eigenproblem.
Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > problem =
Teuchos::rcp( new Anasazi::BasicEigenproblem<double, MV, OP>(A, ivec) );
// Inform the eigenproblem that the operator A is symmetric
problem->setHermitian(true);
// Set the number of eigenvalues requested
problem->setNEV( nev );
// Inform the eigenproblem that you are finishing passing it information
bool boolret = problem->setProblem();
if (boolret != true) {
std::cout<<"Anasazi::BasicEigenproblem::setProblem() returned an error." << std::endl;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
// Create parameter list to pass into the solver manager
Teuchos::ParameterList anasaziPL;
anasaziPL.set( "Which", "LM" );
anasaziPL.set( "Block Size", blockSize );
anasaziPL.set( "Maximum Iterations", 500 );
anasaziPL.set( "Convergence Tolerance", tol );
anasaziPL.set( "Verbosity", Anasazi::Errors+Anasazi::Warnings+Anasazi::TimingDetails+Anasazi::FinalSummary );
// Create the solver manager
Anasazi::LOBPCGSolMgr<double, MV, OP> anasaziSolver(problem, anasaziPL);
// Solve the problem
Anasazi::ReturnType returnCode = anasaziSolver.solve();
// Get the eigenvalues and eigenvectors from the eigenproblem
Anasazi::Eigensolution<double,MV> sol = problem->getSolution();
std::vector<Anasazi::Value<double> > evals = sol.Evals;
Teuchos::RCP<MV> evecs = sol.Evecs;
// Compute residuals.
std::vector<double> normR(sol.numVecs);
if (sol.numVecs > 0) {
Teuchos::SerialDenseMatrix<int,double> T(sol.numVecs, sol.numVecs);
Epetra_MultiVector tempAevec( *Map, sol.numVecs );
T.putScalar(0.0);
for (int i=0; i<sol.numVecs; i++) {
T(i,i) = evals[i].realpart;
}
A->Apply( *evecs, tempAevec );
MVT::MvTimesMatAddMv( -1.0, *evecs, T, 1.0, tempAevec );
MVT::MvNorm( tempAevec, normR );
}
// Print the results
std::cout<<"Solver manager returned " << (returnCode == Anasazi::Converged ? "converged." : "unconverged.") << std::endl;
std::cout<<std::endl;
std::cout<<"------------------------------------------------------"<<std::endl;
std::cout<<std::setw(16)<<"Eigenvalue"
<<std::setw(18)<<"Direct Residual"
<<std::endl;
std::cout<<"------------------------------------------------------"<<std::endl;
for (int i=0; i<sol.numVecs; i++) {
std::cout<<std::setw(16)<<evals[i].realpart
<<std::setw(18)<<normR[i]/evals[i].realpart
<<std::endl;
}
std::cout<<"------------------------------------------------------"<<std::endl;
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return 0;
}
