int
main (int argc, char *argv[])
{
using namespace Anasazi;
using Teuchos::RCP;
using Teuchos::rcp;
using std::endl;
#ifdef HAVE_MPI
// Initialize MPI
MPI_Init (&argc, &argv);
#endif // HAVE_MPI
// Create an Epetra communicator
#ifdef HAVE_MPI
Epetra_MpiComm Comm (MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif // HAVE_MPI
// Create an Anasazi output manager
BasicOutputManager<double> printer;
printer.stream(Errors) << Anasazi_Version() << std::endl << std::endl;
// Get the sorting std::string from the command line
std::string which ("LM");
Teuchos::CommandLineProcessor cmdp (false, true);
cmdp.setOption("sort", &which, "Targetted eigenvalues (SM or LM).");
if (cmdp.parse (argc, argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
#ifdef HAVE_MPI
MPI_Finalize ();
#endif // HAVE_MPI
return -1;
}
// Dimension of the matrix
//
// Discretization points in any one direction.
const int nx = 10;
// Size of matrix nx*nx
const int NumGlobalElements = nx*nx;
// Construct a Map that puts approximately the same number of
// equations on each process.
Epetra_Map Map (NumGlobalElements, 0, Comm);
// Get update list and number of local equations from newly created Map.
int NumMyElements = Map.NumMyElements ();
std::vector<int> MyGlobalElements (NumMyElements);
Map.MyGlobalElements (&MyGlobalElements[0]);
// Create an integer vector NumNz that is used to build the Petra
// matrix. NumNz[i] is the number of OFF-DIAGONAL terms for the
// i-th global equation on this process.
std::vector<int> NumNz (NumMyElements);
/* We are building a matrix of block structure:
| T -I |
|-I T -I |
| -I T |
| ... -I|
| -I T|
where each block is dimension nx by nx and the matrix is on the order of
nx*nx. The block T is a tridiagonal matrix.
*/
for (int i=0; i<NumMyElements; ++i) {
if (MyGlobalElements[i] == 0 || MyGlobalElements[i] == NumGlobalElements-1 ||
MyGlobalElements[i] == nx-1 || MyGlobalElements[i] == nx*(nx-1) ) {
NumNz[i] = 3;
}
else if (MyGlobalElements[i] < nx || MyGlobalElements[i] > nx*(nx-1) ||
MyGlobalElements[i]%nx == 0 || (MyGlobalElements[i]+1)%nx == 0) {
NumNz[i] = 4;
}
else {
NumNz[i] = 5;
}
}
// Create an Epetra_Matrix
RCP<Epetra_CrsMatrix> A = rcp (new Epetra_CrsMatrix (Epetra_DataAccess::Copy, Map, &NumNz[0]));
// Compute coefficients for discrete convection-diffution operator
const double one = 1.0;
std::vector<double> Values(4);
std::vector<int> Indices(4);
double rho = 0.0;
double h = one /(nx+1);
double h2 = h*h;
double c = 5.0e-01*rho/ h;
Values[0] = -one/h2 - c; Values[1] = -one/h2 + c; Values[2] = -one/h2; Values[3]= -one/h2;
double diag = 4.0 / h2;
int NumEntries;
for (int i=0; i<NumMyElements; ++i) {
if (MyGlobalElements[i]==0) {
Indices[0] = 1;
Indices[1] = nx;
NumEntries = 2;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
else if (MyGlobalElements[i] == nx*(nx-1)) {
Indices[0] = nx*(nx-1)+1;
Indices[1] = nx*(nx-2);
NumEntries = 2;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
else if (MyGlobalElements[i] == nx-1) {
Indices[0] = nx-2;
NumEntries = 1;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
Indices[0] = 2*nx-1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
else if (MyGlobalElements[i] == NumGlobalElements-1) {
Indices[0] = NumGlobalElements-2;
NumEntries = 1;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
Indices[0] = nx*(nx-1)-1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
else if (MyGlobalElements[i] < nx) {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]+nx;
NumEntries = 3;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
else if (MyGlobalElements[i] > nx*(nx-1)) {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]-nx;
NumEntries = 3;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
else if (MyGlobalElements[i]%nx == 0) {
Indices[0] = MyGlobalElements[i]+1;
Indices[1] = MyGlobalElements[i]-nx;
Indices[2] = MyGlobalElements[i]+nx;
NumEntries = 3;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
else if ((MyGlobalElements[i]+1)%nx == 0) {
Indices[0] = MyGlobalElements[i]-nx;
Indices[1] = MyGlobalElements[i]+nx;
NumEntries = 2;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
Indices[0] = MyGlobalElements[i]-1;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
else {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]-nx;
Indices[3] = MyGlobalElements[i]+nx;
NumEntries = 4;
int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
// Put in the diagonal entry
int info = A->InsertGlobalValues(MyGlobalElements[i], 1, &diag, &MyGlobalElements[i]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "InsertGlobalValues returned info = "
<< info << " != 0." );
}
// Finish up
int info = A->FillComplete ();
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "A->FillComplete() returned info = "
<< info << " != 0." );
A->SetTracebackMode (1); // Shutdown Epetra Warning tracebacks
// Create a identity matrix for the temporary mass matrix
RCP<Epetra_CrsMatrix> M = rcp (new Epetra_CrsMatrix (Epetra_DataAccess::Copy, Map, 1));
for (int i=0; i<NumMyElements; i++) {
Values[0] = one;
Indices[0] = i;
NumEntries = 1;
info = M->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "M->InsertGlobalValues() returned info = "
<< info << " != 0." );
}
// Finish up
info = M->FillComplete ();
TEUCHOS_TEST_FOR_EXCEPTION
(info != 0, std::runtime_error, "M->FillComplete() returned info = "
<< info << " != 0." );
M->SetTracebackMode (1); // Shutdown Epetra Warning tracebacks
//************************************
// Call the LOBPCG solver manager
//***********************************
//
// Variables used for the LOBPCG Method
const int nev = 10;
const int blockSize = 5;
const int maxIters = 500;
const double tol = 1.0e-8;
typedef Epetra_MultiVector MV;
typedef Epetra_Operator OP;
typedef 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.
RCP<Epetra_MultiVector> ivec = rcp (new Epetra_MultiVector (Map, blockSize));
ivec->Random (); // fill the initial vector with random values
// Create the eigenproblem.
RCP<BasicEigenproblem<double, MV, OP> > MyProblem =
rcp (new BasicEigenproblem<double, MV, OP> (A, ivec));
// Inform the eigenproblem that the operator A is symmetric
MyProblem->setHermitian (true);
// Set the number of eigenvalues requested
MyProblem->setNEV (nev);
// Tell the eigenproblem that you are finishing passing it information.
const bool success = MyProblem->setProblem ();
if (! success) {
printer.print (Errors, "Anasazi::BasicEigenproblem::setProblem() reported an error.\n");
#ifdef HAVE_MPI
MPI_Finalize ();
#endif // HAVE_MPI
return -1;
}
// Create parameter list to pass into the solver manager
Teuchos::ParameterList MyPL;
MyPL.set ("Which", which);
MyPL.set ("Block Size", blockSize);
MyPL.set ("Maximum Iterations", maxIters);
MyPL.set ("Convergence Tolerance", tol);
MyPL.set ("Full Ortho", true);
MyPL.set ("Use Locking", true);
// Create the solver manager
LOBPCGSolMgr<double, MV, OP> MySolverMan (MyProblem, MyPL);
// Solve the problem
ReturnType returnCode = MySolverMan.solve ();
// Get the eigenvalues and eigenvectors from the eigenproblem
Eigensolution<double,MV> sol = MyProblem->getSolution ();
std::vector<Value<double> > evals = sol.Evals;
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::ostringstream os;
os.setf (std::ios_base::right, std::ios_base::adjustfield);
os << "Solver manager returned "
<< (returnCode == Converged ? "converged." : "unconverged.") << endl;
os << endl;
os << "------------------------------------------------------" << endl;
os << std::setw(16) << "Eigenvalue"
<< std::setw(18) << "Direct Residual"
<< endl;
os << "------------------------------------------------------" << endl;
for (int i = 0; i < sol.numVecs; ++i) {
os << std::setw(16) << evals[i].realpart
<< std::setw(18) << normR[i] / evals[i].realpart
<< endl;
}
os << "------------------------------------------------------" << endl;
printer.print (Errors, os.str ());
#ifdef HAVE_MPI
MPI_Finalize ();
#endif // HAVE_MPI
return 0;
}
void
factorExplicit (Kokkos::MultiVector<Scalar, NodeType>& A,
Kokkos::MultiVector<Scalar, NodeType>& Q,
Teuchos::SerialDenseMatrix<LocalOrdinal, Scalar>& R,
const bool contiguousCacheBlocks,
const bool forceNonnegativeDiagonal=false)
{
using Teuchos::asSafe;
typedef Kokkos::MultiVector<Scalar, NodeType> KMV;
// Tsqr currently likes LocalOrdinal ordinals, but
// Kokkos::MultiVector has size_t ordinals. Do conversions
// here.
//
// Teuchos::asSafe() can do safe conversion (e.g., checking for
// overflow when casting to a narrower integer type), if a
// custom specialization is defined for
// Teuchos::ValueTypeConversionTraits<size_t, LocalOrdinal>.
// Otherwise, this has the same (potentially) unsafe effect as
// static_cast<LocalOrdinal>(...) would have.
const LocalOrdinal A_numRows = asSafe<LocalOrdinal> (A.getNumRows());
const LocalOrdinal A_numCols = asSafe<LocalOrdinal> (A.getNumCols());
const LocalOrdinal A_stride = asSafe<LocalOrdinal> (A.getStride());
const LocalOrdinal Q_numRows = asSafe<LocalOrdinal> (Q.getNumRows());
const LocalOrdinal Q_numCols = asSafe<LocalOrdinal> (Q.getNumCols());
const LocalOrdinal Q_stride = asSafe<LocalOrdinal> (Q.getStride());
// Sanity checks for matrix dimensions
if (A_numRows < A_numCols) {
std::ostringstream os;
os << "In Tsqr::factorExplicit: input matrix A has " << A_numRows
<< " local rows, and " << A_numCols << " columns. The input "
"matrix must have at least as many rows on each processor as "
"there are columns.";
throw std::invalid_argument(os.str());
} else if (A_numRows != Q_numRows) {
std::ostringstream os;
os << "In Tsqr::factorExplicit: input matrix A and output matrix Q "
"must have the same number of rows. A has " << A_numRows << " rows"
" and Q has " << Q_numRows << " rows.";
throw std::invalid_argument(os.str());
} else if (R.numRows() < R.numCols()) {
std::ostringstream os;
os << "In Tsqr::factorExplicit: output matrix R must have at least "
"as many rows as columns. R has " << R.numRows() << " rows and "
<< R.numCols() << " columns.";
throw std::invalid_argument(os.str());
} else if (A_numCols != R.numCols()) {
std::ostringstream os;
os << "In Tsqr::factorExplicit: input matrix A and output matrix R "
"must have the same number of columns. A has " << A_numCols
<< " columns and R has " << R.numCols() << " columns.";
throw std::invalid_argument(os.str());
}
// Check for quick exit, based on matrix dimensions
if (Q_numCols == 0)
return;
// Hold on to nonconst views of A and Q. This will make TSQR
// correct (if perhaps inefficient) for all possible Kokkos Node
// types, even GPU nodes.
Teuchos::ArrayRCP<scalar_type> A_ptr = A.getValuesNonConst();
Teuchos::ArrayRCP<scalar_type> Q_ptr = Q.getValuesNonConst();
R.putScalar (STS::zero());
NodeOutput nodeResults =
nodeTsqr_->factor (A_numRows, A_numCols, A_ptr.getRawPtr(), A_stride,
R.values(), R.stride(), contiguousCacheBlocks);
// FIXME (mfh 19 Oct 2010) Replace actions on raw pointer with
// actions on the Kokkos::MultiVector or at least the ArrayRCP.
nodeTsqr_->fill_with_zeros (Q_numRows, Q_numCols,
Q_ptr.getRawPtr(), Q_stride,
contiguousCacheBlocks);
matview_type Q_rawView (Q_numRows, Q_numCols,
Q_ptr.getRawPtr(), Q_stride);
matview_type Q_top_block =
nodeTsqr_->top_block (Q_rawView, contiguousCacheBlocks);
if (Q_top_block.nrows() < R.numCols()) {
std::ostringstream os;
os << "The top block of Q has too few rows. This means that the "
<< "the intranode TSQR implementation has a bug in its top_block"
<< "() method. The top block should have at least " << R.numCols()
<< " rows, but instead has only " << Q_top_block.ncols()
<< " rows.";
throw std::logic_error (os.str());
}
{
matview_type Q_top (R.numCols(), Q_numCols, Q_top_block.get(),
Q_top_block.lda());
matview_type R_view (R.numRows(), R.numCols(), R.values(), R.stride());
distTsqr_->factorExplicit (R_view, Q_top, forceNonnegativeDiagonal);
}
nodeTsqr_->apply (ApplyType::NoTranspose,
A_numRows, A_numCols, A_ptr.getRawPtr(), A_stride,
nodeResults, Q_numCols, Q_ptr.getRawPtr(), Q_stride,
contiguousCacheBlocks);
// If necessary, force the R factor to have a nonnegative diagonal.
if (forceNonnegativeDiagonal &&
! QR_produces_R_factor_with_nonnegative_diagonal()) {
details::NonnegDiagForcer<LocalOrdinal, Scalar, STS::isComplex> forcer;
matview_type Q_mine (Q_numRows, Q_numCols, Q_ptr.getRawPtr(), Q_stride);
matview_type R_mine (R.numRows(), R.numCols(), R.values(), R.stride());
forcer.force (Q_mine, R_mine);
}
// "Commit" the changes to the multivector.
A_ptr = Teuchos::null;
Q_ptr = Teuchos::null;
}