Anasazi Version of the Day
BlockKrylovSchur/BlockKrylovSchurEpetraEx.cpp

This is an example of how to use the Anasazi::BlockKrylovSchurSolMgr solver manager, using Epetra data structures.

```//  This example computes the specified eigenvalues of the discretized 2D Convection-Diffusion
//  equation using the block Krylov-Schur method.  This discretized operator is constructed as an
//  Epetra matrix, then passed into the Anasazi::EpetraOp to be used in the construction of the
//  Krylov decomposition.  The specifics of the block Krylov-Schur method can be set by the user.
#include "AnasaziBlockKrylovSchurSolMgr.hpp"
#include "AnasaziBasicEigenproblem.hpp"
#include "AnasaziConfigDefs.hpp"
#include "AnasaziBasicSort.hpp"
#include "Epetra_CrsMatrix.h"

#include "Teuchos_LAPACK.hpp"
#include "Teuchos_CommandLineProcessor.hpp"

#ifdef EPETRA_MPI
#include "Epetra_MpiComm.h"
#else
#include "Epetra_SerialComm.h"
#endif
#include "Epetra_Map.h"

int main(int argc, char *argv[]) {

using std::cout;

#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif

bool boolret;
int MyPID = Comm.MyPID();

bool verbose = true;
bool debug = false;
bool dynXtraNev = false;
std::string which("SM");
int nx = 10;        // Discretization points in any one direction.
int nev = 4;
int blockSize = 1;
int numBlocks = 20;

Teuchos::CommandLineProcessor cmdp(false,true);
cmdp.setOption("verbose","quiet",&verbose,"Print messages and results.");
cmdp.setOption("debug","nodebug",&debug,"Print debugging information.");
cmdp.setOption("sort",&which,"Targetted eigenvalues (SM,LM,SR,LR,SI,or LI).");
cmdp.setOption("nx",&nx,"Number of discretization points in each direction; n=nx*nx.");
cmdp.setOption("nev",&nev,"Number of eigenvalues to compute.");
cmdp.setOption("blocksize",&blockSize,"Block Size.");
cmdp.setOption("numblocks",&numBlocks,"Number of blocks for the Krylov-Schur form.");
cmdp.setOption("dynrestart","nodynrestart",&dynXtraNev,"Use dynamic restart boundary to accelerate convergence.");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}

typedef double ScalarType;
typedef Teuchos::ScalarTraits<ScalarType>          SCT;
typedef SCT::magnitudeType               MagnitudeType;
typedef Epetra_MultiVector                          MV;
typedef Epetra_Operator                             OP;
typedef Anasazi::MultiVecTraits<ScalarType,MV>     MVT;
typedef Anasazi::OperatorTraits<ScalarType,MV,OP>  OPT;

//  Dimension of the matrix
int NumGlobalElements = nx*nx;  // Size of matrix nx*nx

// Construct a Map that puts approximately the same number of
// equations on each processor.

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 term for the ith global equation
// on this processor
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

Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Copy, Map, &NumNz[0]) );

// Diffusion coefficient, can be set by user.
// When rho*h/2 <= 1, the discrete convection-diffusion operator has real eigenvalues.
// When rho*h/2 > 1, the operator has complex eigenvalues.
//double rho = 2*nx+1;
double rho = 0.0;

// Compute coefficients for discrete convection-diffution operator
const double one = 1.0;
std::vector<double> Values(4);
std::vector<int> Indices(4);
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, info;

for (int i=0; i<NumMyElements; i++)
{
if (MyGlobalElements[i]==0)
{
Indices[0] = 1;
Indices[1] = nx;
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == nx*(nx-1))
{
Indices[0] = nx*(nx-1)+1;
Indices[1] = nx*(nx-2);
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == nx-1)
{
Indices[0] = nx-2;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
Indices[0] = 2*nx-1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == NumGlobalElements-1)
{
Indices[0] = NumGlobalElements-2;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
Indices[0] = nx*(nx-1)-1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] < nx)
{
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]+nx;
NumEntries = 3;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( 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;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( 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;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if ((MyGlobalElements[i]+1)%nx == 0)
{
Indices[0] = MyGlobalElements[i]-nx;
Indices[1] = MyGlobalElements[i]+nx;
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
Indices[0] = MyGlobalElements[i]-1;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( 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;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
// Put in the diagonal entry
info = A->InsertGlobalValues(MyGlobalElements[i], 1, &diag, &MyGlobalElements[i]);
assert( info==0 );
}

// Finish up
info = A->FillComplete();
assert( info==0 );
A->SetTracebackMode(1); // Shutdown Epetra Warning tracebacks

//************************************
// Start the block Arnoldi iteration
//***********************************
//
//  Variables used for the Block Krylov Schur Method
//
int maxRestarts = 500;
//int stepSize = 5;
double tol = 1e-8;

// Create a sort manager to pass into the block Krylov-Schur solver manager
// -->  Make sure the reference-counted pointer is of type Anasazi::SortManager<>
// -->  The block Krylov-Schur solver manager uses Anasazi::BasicSort<> by default,
//      so you can also pass in the parameter "Which", instead of a sort manager.
Teuchos::RCP<Anasazi::SortManager<MagnitudeType> > MySort =
Teuchos::rcp( new Anasazi::BasicSort<MagnitudeType>( which ) );

// Set verbosity level
int verbosity = Anasazi::Errors + Anasazi::Warnings;
if (verbose) {
verbosity += Anasazi::FinalSummary + Anasazi::TimingDetails;
}
if (debug) {
verbosity += Anasazi::Debug;
}
//
// Create parameter list to pass into solver manager
//
Teuchos::ParameterList MyPL;
MyPL.set( "Verbosity", verbosity );
MyPL.set( "Sort Manager", MySort );
//MyPL.set( "Which", which );
MyPL.set( "Block Size", blockSize );
MyPL.set( "Num Blocks", numBlocks );
MyPL.set( "Maximum Restarts", maxRestarts );
//MyPL.set( "Step Size", stepSize );
MyPL.set( "Convergence Tolerance", tol );
MyPL.set("Dynamic Extra NEV",dynXtraNev);

// 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> > MyProblem =
Teuchos::rcp( new Anasazi::BasicEigenproblem<double, MV, OP>(A, ivec) );

// Inform the eigenproblem that the operator A is symmetric
MyProblem->setHermitian(rho==0.0);

// Set the number of eigenvalues requested
MyProblem->setNEV( nev );

// Inform the eigenproblem that you are finishing passing it information
boolret = MyProblem->setProblem();
if (boolret != true) {
if (verbose && MyPID == 0) {
std::cout << "Anasazi::BasicEigenproblem::setProblem() returned with error." << std::endl;
}
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return -1;
}

// Initialize the Block Arnoldi solver
Anasazi::BlockKrylovSchurSolMgr<double, MV, OP> MySolverMgr(MyProblem, MyPL);

// Solve the problem to the specified tolerances or length
Anasazi::ReturnType returnCode = MySolverMgr.solve();
if (returnCode != Anasazi::Converged && MyPID==0 && verbose) {
std::cout << "Anasazi::EigensolverMgr::solve() returned unconverged." << std::endl;
}

// Get the Ritz values from the eigensolver
std::vector<Anasazi::Value<double> > ritzValues = MySolverMgr.getRitzValues();

// Output computed eigenvalues and their direct residuals
if (verbose && MyPID==0) {
int numritz = (int)ritzValues.size();
std::cout<<std::endl<< "Computed Ritz Values"<< std::endl;
if (MyProblem->isHermitian()) {
std::cout<< std::setw(16) << "Real Part"
<< std::endl;
std::cout<<"-----------------------------------------------------------"<<std::endl;
for (int i=0; i<numritz; i++) {
std::cout<< std::setw(16) << ritzValues[i].realpart
<< std::endl;
}
std::cout<<"-----------------------------------------------------------"<<std::endl;
}
else {
std::cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< std::endl;
std::cout<<"-----------------------------------------------------------"<<std::endl;
for (int i=0; i<numritz; i++) {
std::cout<< std::setw(16) << ritzValues[i].realpart
<< std::setw(16) << ritzValues[i].imagpart
<< std::endl;
}
std::cout<<"-----------------------------------------------------------"<<std::endl;
}
}

// Get the eigenvalues and eigenvectors from the eigenproblem
Anasazi::Eigensolution<ScalarType,MV> sol = MyProblem->getSolution();
std::vector<Anasazi::Value<ScalarType> > evals = sol.Evals;
Teuchos::RCP<MV> evecs = sol.Evecs;
std::vector<int> index = sol.index;
int numev = sol.numVecs;

if (numev > 0) {
// Compute residuals.
Teuchos::LAPACK<int,double> lapack;
std::vector<double> normA(numev);

if (MyProblem->isHermitian()) {
// Get storage
Epetra_MultiVector Aevecs(Map,numev);
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( *A, *evecs, Aevecs );

// Compute A*evecs - lambda*evecs and its norm
MVT::MvTimesMatAddMv( -1.0, *evecs, B, 1.0, Aevecs );
MVT::MvNorm( Aevecs, normA );

// Scale the norms by the eigenvalue
for (int i=0; i<numev; i++) {
normA[i] /= Teuchos::ScalarTraits<double>::magnitude( evals[i].realpart );
}
} else {
// The problem is non-Hermitian.
int i=0;
std::vector<int> curind(1);
std::vector<double> resnorm(1), tempnrm(1);
Teuchos::RCP<MV> tempAevec;
Teuchos::RCP<const MV> evecr, eveci;
Epetra_MultiVector Aevec(Map,numev);

// Compute A*evecs
OPT::Apply( *A, *evecs, Aevec );

Teuchos::SerialDenseMatrix<int,double> Breal(1,1), Bimag(1,1);
while (i<numev) {
if (index[i]==0) {
// Get a view of the current eigenvector (evecr)
curind[0] = i;
evecr = MVT::CloneView( *evecs, curind );

// Get a copy of A*evecr
tempAevec = MVT::CloneCopy( Aevec, curind );

// Compute A*evecr - lambda*evecr
Breal(0,0) = evals[i].realpart;
MVT::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );

// Compute the norm of the residual and increment counter
MVT::MvNorm( *tempAevec, resnorm );
normA[i] = resnorm[0]/Teuchos::ScalarTraits<MagnitudeType>::magnitude( evals[i].realpart );
i++;
} else {
// Get a view of the real part of the eigenvector (evecr)
curind[0] = i;
evecr = MVT::CloneView( *evecs, curind );

// Get a copy of A*evecr
tempAevec = MVT::CloneCopy( Aevec, curind );

// Get a view of the imaginary part of the eigenvector (eveci)
curind[0] = i+1;
eveci = MVT::CloneView( *evecs, curind );

// Set the eigenvalue into Breal and Bimag
Breal(0,0) = evals[i].realpart;
Bimag(0,0) = evals[i].imagpart;

// Compute A*evecr - evecr*lambdar + eveci*lambdai
MVT::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );
MVT::MvTimesMatAddMv( 1.0, *eveci, Bimag, 1.0, *tempAevec );
MVT::MvNorm( *tempAevec, tempnrm );

// Get a copy of A*eveci
tempAevec = MVT::CloneCopy( Aevec, curind );

// Compute A*eveci - eveci*lambdar - evecr*lambdai
MVT::MvTimesMatAddMv( -1.0, *evecr, Bimag, 1.0, *tempAevec );
MVT::MvTimesMatAddMv( -1.0, *eveci, Breal, 1.0, *tempAevec );
MVT::MvNorm( *tempAevec, resnorm );

// Compute the norms and scale by magnitude of eigenvalue
normA[i] = lapack.LAPY2( tempnrm[0], resnorm[0] ) /
lapack.LAPY2( evals[i].realpart, evals[i].imagpart );
normA[i+1] = normA[i];

i=i+2;
}
}
}

// Output computed eigenvalues and their direct residuals
if (verbose && MyPID==0) {
std::cout<<std::endl<< "Actual Residuals"<<std::endl;
if (MyProblem->isHermitian()) {
std::cout<< std::setw(16) << "Real Part"
<< std::setw(20) << "Direct Residual"<< std::endl;
std::cout<<"-----------------------------------------------------------"<<std::endl;
for (int i=0; i<numev; i++) {
std::cout<< std::setw(16) << evals[i].realpart
<< std::setw(20) << normA[i] << std::endl;
}
std::cout<<"-----------------------------------------------------------"<<std::endl;
}
else {
std::cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< std::setw(20) << "Direct Residual"<< std::endl;
std::cout<<"-----------------------------------------------------------"<<std::endl;
for (int i=0; i<numev; i++) {
std::cout<< std::setw(16) << evals[i].realpart
<< std::setw(16) << evals[i].imagpart
<< std::setw(20) << normA[i] << std::endl;
}
std::cout<<"-----------------------------------------------------------"<<std::endl;
}
}
}

#ifdef EPETRA_MPI
MPI_Finalize();
#endif

return 0;
}
```