int main(int narg, char *arg[])
{
using std::cout;
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&narg,&arg);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
int MyPID = Comm.MyPID();
bool verbose = true;
int verbosity = 1;
bool testEpetra64 = true;
// Matrix properties
bool isHermitian = true;
// Multivector properties
std::string initvec = "random";
// Eigenvalue properties
std::string which = "SR";
std::string method = "LOBPCG";
std::string precond = "none";
std::string ortho = "SVQB";
bool lock = true;
bool relconvtol = false;
bool rellocktol = false;
int nev = 5;
// Block-Arnoldi properties
int blockSize = -1;
int numblocks = -1;
int maxrestarts = -1;
int maxiterations = -1;
int extrablocks = 0;
int gensize = 25; // Needs to be long long to test with > INT_MAX rows
double tol = 1.0e-5;
// Echo the command line
if (MyPID == 0) {
for (int i = 0; i < narg; i++)
cout << arg[i] << " ";
cout << endl;
}
// Command-line processing
Teuchos::CommandLineProcessor cmdp(false,true);
cmdp.setOption("Epetra64", "no-Epetra64", &testEpetra64,
"Force code to use Epetra64, even if the problem size does "
"not require it. (Epetra64 will be used automatically for "
"sufficiently large problems, or not used if Epetra does not have built in support.)");
cmdp.setOption("gen",&gensize,
"Generate a simple Laplacian matrix of size n.");
cmdp.setOption("verbosity", &verbosity, "0=quiet, 1=low, 2=medium, 3=high.");
cmdp.setOption("method",&method,
"Solver method to use: LOBPCG, BD, BKS or IRTR.");
cmdp.setOption("nev",&nev,"Number of eigenvalues to find.");
cmdp.setOption("which",&which,"Targetted eigenvalues (SM,LM,SR,or LR).");
cmdp.setOption("tol",&tol,"Solver convergence tolerance.");
cmdp.setOption("blocksize",&blockSize,"Block size to use in solver.");
cmdp.setOption("numblocks",&numblocks,"Number of blocks to allocate.");
cmdp.setOption("extrablocks",&extrablocks,
"Number of extra NEV blocks to allocate in BKS.");
cmdp.setOption("maxrestarts",&maxrestarts,
"Maximum number of restarts in BKS or BD.");
cmdp.setOption("maxiterations",&maxiterations,
"Maximum number of iterations in LOBPCG.");
cmdp.setOption("lock","no-lock",&lock,
"Use Locking parameter (deflate for converged eigenvalues)");
cmdp.setOption("initvec", &initvec,
"Initial vectors (random, unit, zero, random2)");
cmdp.setOption("ortho", &ortho,
"Orthogonalization method (DGKS, SVQB, TSQR).");
cmdp.setOption("relative-convergence-tol","no-relative-convergence-tol",
&relconvtol,
"Use Relative convergence tolerance "
"(normalized by eigenvalue)");
cmdp.setOption("relative-lock-tol","no-relative-lock-tol",&rellocktol,
"Use Relative locking tolerance (normalized by eigenvalue)");
if (cmdp.parse(narg,arg)!=Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
FINALIZE;
return -1;
}
// Print the most essential options (not in the MyPL parameters later)
verbose = (verbosity>0);
if (verbose && MyPID==0){
cout << "verbosity = " << verbosity << endl;
cout << "method = " << method << endl;
cout << "initvec = " << initvec << endl;
cout << "nev = " << nev << endl;
}
// We need blockSize to be set so we can allocate memory with it.
// If it wasn't set on the command line, set it to the Anasazi defaults here.
// Defaults are those given in the documentation.
if (blockSize < 0)
if (method == "BKS")
blockSize = 1;
else // other methods: LOBPCG, BD, IRTR
blockSize = nev;
// Make sure Epetra was built with 64-bit global indices enabled.
#ifdef EPETRA_NO_64BIT_GLOBAL_INDICES
if (testEpetra64)
testEpetra64 = false;
#endif
Epetra_CrsMatrix *K = NULL;
// Read matrix from file or generate a matrix
if ((gensize > 0 && testEpetra64)) {
// Generate the matrix using long long for global indices
build_simple_matrix<long long>(Comm, K, (long long)gensize, true, verbose);
}
else if (gensize) {
// Generate the matrix using int for global indices
build_simple_matrix<int>(Comm, K, gensize, false, verbose);
}
else {
printf("YOU SHOULDN'T BE HERE \n");
exit(-1);
}
if (verbose && (K->NumGlobalRows64() < TINYMATRIX)) {
if (MyPID == 0) cout << "Input matrix: " << endl;
K->Print(cout);
}
Teuchos::RCP<Epetra_CrsMatrix> rcpK = Teuchos::rcp( K );
// Set Anasazi verbosity level
if (MyPID == 0) cout << "Setting up the problem..." << endl;
int anasazi_verbosity = Anasazi::Errors + Anasazi::Warnings;
if (verbosity >= 1) // low
anasazi_verbosity += Anasazi::FinalSummary + Anasazi::TimingDetails;
if (verbosity >= 2) // medium
anasazi_verbosity += Anasazi::IterationDetails;
if (verbosity >= 3) // high
anasazi_verbosity += Anasazi::StatusTestDetails
+ Anasazi::OrthoDetails
+ Anasazi::Debug;
// Create parameter list to pass into solver
Teuchos::ParameterList MyPL;
MyPL.set("Verbosity", anasazi_verbosity);
MyPL.set("Which", which);
MyPL.set("Convergence Tolerance", tol);
MyPL.set("Relative Convergence Tolerance", relconvtol);
MyPL.set("Orthogonalization", ortho);
// For the following, use Anasazi's defaults unless explicitly specified.
if (numblocks > 0) MyPL.set( "Num Blocks", numblocks);
if (maxrestarts > 0) MyPL.set( "Maximum Restarts", maxrestarts);
if (maxiterations > 0) MyPL.set( "Maximum Iterations", maxiterations);
if (blockSize > 0) MyPL.set( "Block Size", blockSize );
typedef Epetra_MultiVector MV;
typedef Epetra_Operator OP;
typedef Anasazi::MultiVecTraits<double, MV> MVT;
typedef Anasazi::OperatorTraits<double, MV, OP> OPT;
// Create the eigenproblem to be solved.
// Dummy initial vectors - will be set later.
Teuchos::RCP<Epetra_MultiVector> ivec =
Teuchos::rcp(new Epetra_MultiVector(K->Map(), blockSize));
Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > MyProblem;
MyProblem =
Teuchos::rcp(new Anasazi::BasicEigenproblem<double, MV, OP>(rcpK, ivec) );
// Inform the eigenproblem whether K is Hermitian
MyProblem->setHermitian(isHermitian);
// Set the number of eigenvalues requested
MyProblem->setNEV(nev);
// Loop to solve the same eigenproblem numtrial times (different initial vectors)
int numfailed = 0;
int iter = 0;
double solvetime = 0;
// Set random seed to have consistent initial vectors between
// experiments. Different seed in each loop iteration.
ivec->SetSeed(2*(MyPID) +1); // Odd seed
// Set up initial vectors
// Using random values as the initial guess.
if (initvec == "random"){
MVT::MvRandom(*ivec);
}
else if (initvec == "zero"){
// All zero initial vector should be essentially the same,
// but appears slightly worse in practice.
ivec->PutScalar(0.);
}
else if (initvec == "unit"){
// Orthogonal unit initial vectors.
ivec->PutScalar(0.);
for (int i = 0; i < blockSize; i++)
ivec->ReplaceGlobalValue(i,i,1.);
}
else if (initvec == "random2"){
// Partially random but orthogonal (0,1) initial vectors.
// ivec(i,*) is zero in all but one column (for each i)
// Inefficient implementation but this is only done once...
double rowmax;
int col;
ivec->Random();
for (int i = 0; i < ivec->MyLength(); i++){
rowmax = -1;
col = -1;
for (int j = 0; j < blockSize; j++){
// Make ivec(i,j) = 1 for largest random value in row i
if ((*ivec)[j][i] > rowmax){
rowmax = (*ivec)[j][i];
col = j;
}
ivec->ReplaceMyValue(i,j,0.);
}
ivec->ReplaceMyValue(i,col,1.);
}
}
else
cout << "ERROR: Unknown value for initial vectors." << endl;
if (verbose && (ivec->GlobalLength64() < TINYMATRIX))
ivec->Print(std::cout);
// Inform the eigenproblem that you are finished passing it information
bool boolret = MyProblem->setProblem();
if (boolret != true) {
if (verbose && MyPID == 0) {
cout << "Anasazi::BasicEigenproblem::setProblem() returned with error."
<< endl;
}
FINALIZE;
return -1;
}
Teuchos::RCP<Anasazi::SolverManager<double, MV, OP> > MySolverMgr;
if (method == "BKS") {
// Initialize the Block Arnoldi solver
MyPL.set("Extra NEV Blocks", extrablocks);
MySolverMgr = Teuchos::rcp( new Anasazi::BlockKrylovSchurSolMgr<double, MV, OP>(MyProblem,MyPL) );
}
else if (method == "BD") {
// Initialize the Block Davidson solver
MyPL.set("Use Locking", lock);
MyPL.set("Relative Locking Tolerance", rellocktol);
MySolverMgr = Teuchos::rcp( new Anasazi::BlockDavidsonSolMgr<double, MV, OP>(MyProblem, MyPL) );
}
else if (method == "LOBPCG") {
// Initialize the LOBPCG solver
MyPL.set("Use Locking", lock);
MyPL.set("Relative Locking Tolerance", rellocktol);
MySolverMgr = Teuchos::rcp( new Anasazi::LOBPCGSolMgr<double, MV, OP>(MyProblem, MyPL) );
}
else if (method == "IRTR") {
// Initialize the IRTR solver
MySolverMgr = Teuchos::rcp( new Anasazi::RTRSolMgr<double, MV, OP>(MyProblem, MyPL) );
}
else
cout << "Unknown solver method!" << endl;
if (verbose && MyPID==0) MyPL.print(cout);
// Solve the problem to the specified tolerances or length
if (MyPID == 0) cout << "Beginning the " << method << " solve..." << endl;
Anasazi::ReturnType returnCode = MySolverMgr->solve();
if (returnCode != Anasazi::Converged && MyPID==0) {
++numfailed;
cout << "Anasazi::SolverManager::solve() returned unconverged." << endl;
}
iter = MySolverMgr->getNumIters();
solvetime = (MySolverMgr->getTimers()[0])->totalElapsedTime();
if (MyPID == 0) {
cout << "Iterations in this solve: " << iter << endl;
cout << "Solve complete; beginning post-processing..."<< endl;
}
// Get the eigenvalues and eigenvectors from the eigenproblem
Anasazi::Eigensolution<double,MV> sol = MyProblem->getSolution();
std::vector<Anasazi::Value<double> > evals = sol.Evals;
Teuchos::RCP<MV> evecs = sol.Evecs;
std::vector<int> index = sol.index;
int numev = sol.numVecs;
// Compute residuals.
if (numev > 0) {
Teuchos::LAPACK<int,double> lapack;
std::vector<double> normR(numev);
if (MyProblem->isHermitian()) {
// Get storage
Epetra_MultiVector Kevecs(K->Map(),numev);
Teuchos::RCP<Epetra_MultiVector> Mevecs;
Teuchos::SerialDenseMatrix<int,double> B(numev,numev);
B.putScalar(0.0);
for (int i=0; i<numev; i++) {B(i,i) = evals[i].realpart;}
// Compute A*evecs
OPT::Apply( *rcpK, *evecs, Kevecs );
Mevecs = evecs;
// Compute A*evecs - lambda*evecs and its norm
MVT::MvTimesMatAddMv( -1.0, *Mevecs, B, 1.0, Kevecs );
MVT::MvNorm( Kevecs, normR );
// Scale the norms by the eigenvalue if relative convergence tol was used
if (relconvtol) {
for (int i=0; i<numev; i++)
normR[i] /= Teuchos::ScalarTraits<double>::magnitude(evals[i].realpart);
}
} else {
printf("The problem isn't non-Hermitian; sorry.\n");
exit(-1);
}
if (verbose && MyPID==0) {
cout.setf(std::ios_base::right, std::ios_base::adjustfield);
cout<<endl<< "Actual Results"<<endl;
if (MyProblem->isHermitian()) {
cout<< std::setw(16) << "Eigenvalue "
<< std::setw(20) << "Direct Residual"
<< (relconvtol?" (normalized by eigenvalue)":" (no normalization)")
<< endl;
cout<<"--------------------------------------------------------"<<endl;
for (int i=0; i<numev; i++) {
cout<< "EV" << i << std::setw(16) << evals[i].realpart
<< std::setw(20) << normR[i] << endl;
}
cout<<"--------------------------------------------------------"<<endl;
}
else {
cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< std::setw(20) << "Direct Residual"<< endl;
cout<<"--------------------------------------------------------"<<endl;
for (int i=0; i<numev; i++) {
cout<< std::setw(16) << evals[i].realpart
<< std::setw(16) << evals[i].imagpart
<< std::setw(20) << normR[i] << endl;
}
cout<<"--------------------------------------------------------"<<endl;
}
}
}
// Summarize iteration counts and solve time
if (MyPID == 0) {
cout << endl;
cout << "DRIVER SUMMARY" << endl;
cout << "Failed to converge: " << numfailed << endl;
cout << "Solve time: " << solvetime << endl;
}
FINALIZE;
if (numfailed) {
if (MyPID == 0) {
cout << "End Result: TEST FAILED" << endl;
}
return -1;
}
//
// Default return value
//
if (MyPID == 0) {
cout << "End Result: TEST PASSED" << endl;
}
return 0;
}
