BlockDavidson/BlockDavidsonEpetraEx.cpp

This is an example of how to use the Anasazi::BlockDavidsonSolMgr solver manager to solve a standard eigenvalue problem.

#include "AnasaziConfigDefs.hpp"
#include "AnasaziBasicEigenproblem.hpp"
#include "AnasaziBlockDavidsonSolMgr.hpp"
#include "AnasaziBasicOutputManager.hpp"
#include "AnasaziEpetraAdapter.hpp"
#include "Epetra_CrsMatrix.h"
#include "Teuchos_CommandLineProcessor.hpp"

#ifdef HAVE_MPI
#include "Epetra_MpiComm.h"
#include <mpi.h>
#else
#include "Epetra_SerialComm.h"
#endif
#include "Epetra_Map.h"

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

#ifdef HAVE_MPI
  // Initialize MPI
  //
  MPI_Init(&argc,&argv);
#endif

  // Create an Epetra communicator
  //
#ifdef HAVE_MPI
  Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
  Epetra_SerialComm Comm;
#endif

  // Create an Anasazi output manager
  //
  Anasazi::BasicOutputManager<double> printer;
  printer.stream(Anasazi::Errors) << Anasazi::Anasazi_Version() << endl << endl;

  // Get the sorting 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
    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 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::RefCountPtr<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(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]);
      assert( 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]);
      assert( 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]);
      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;
      int 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;
      int 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;
      int 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;
      int 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;
      int 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;
      int info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
      assert( info==0 );
    }
    // Put in the diagonal entry
    int info = A->InsertGlobalValues(MyGlobalElements[i], 1, &diag, &MyGlobalElements[i]);
    assert( info==0 );
  }

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

  // Create a identity matrix for the temporary mass matrix
  Teuchos::RefCountPtr<Epetra_CrsMatrix> M = Teuchos::rcp( new Epetra_CrsMatrix(Copy, Map, 1) );
  for (int i=0; i<NumMyElements; i++)
  {
    Values[0] = one;
    Indices[0] = i;
    NumEntries = 1;
    int info = M->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
    assert( info==0 );
  }
  // Finish up
  info = M->FillComplete();
  assert( info==0 );
  M->SetTracebackMode(1); // Shutdown Epetra Warning tracebacks
  
  //************************************
  // Call the Block Davidson solver manager
  //***********************************
  //
  //  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::RefCountPtr<Epetra_MultiVector> ivec = Teuchos::rcp( new Epetra_MultiVector(Map, blockSize) );
  ivec->Random();

  // Create the eigenproblem.
  //
  Teuchos::RefCountPtr<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(true);

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

  // Inform the eigenproblem that you are finishing passing it information
  //
  bool boolret = MyProblem->setProblem();
  if (boolret != true) {
    printer.print(Anasazi::Errors,"Anasazi::BasicEigenproblem::setProblem() returned an error.\n");
#ifdef HAVE_MPI
    MPI_Finalize();
#endif
    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( "Num Blocks", numBlocks );
  MyPL.set( "Maximum Restarts", maxRestarts );
  MyPL.set( "Convergence Tolerance", tol );
  //
  // Create the solver manager
  Anasazi::BlockDavidsonSolMgr<double, MV, OP> MySolverMan(MyProblem, MyPL);

  // Solve the problem
  //
  Anasazi::ReturnType returnCode = MySolverMan.solve();

  // Get the eigenvalues and eigenvectors from the eigenproblem
  //
  Anasazi::Eigensolution<double,MV> sol = MyProblem->getSolution();
  std::vector<Anasazi::Value<double> > evals = sol.Evals;
  Teuchos::RefCountPtr<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
  //
  ostringstream os;
  os.setf(ios_base::right, ios_base::adjustfield);
  os<<"Solver manager returned " << (returnCode == Anasazi::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(Anasazi::Errors,os.str());

#ifdef HAVE_MPI
  MPI_Finalize();
#endif
  return 0;
}

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