doc/html/BlockDavidson_2BlockDavidsonEpetraEx_8cpp-example.html

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//                 Anasazi: Block Eigensolvers Package

//                 Copyright 2004 Sandia Corporation

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#include "AnasaziConfigDefs.hpp"

#include "AnasaziBasicEigenproblem.hpp"

#include "AnasaziBlockDavidsonSolMgr.hpp"

#include "AnasaziBasicOutputManager.hpp"

#include "AnasaziEpetraAdapter.hpp"

#include "Epetra_CrsMatrix.h"

#include "Teuchos_CommandLineProcessor.hpp"

#include "Teuchos_StandardCatchMacros.hpp"

#include "Teuchos_Assert.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


  bool success = false;

  try {

    // 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() << std::endl << std::endl;


    // Get the sorting string from the command line

    //

    std::string which("SM");

    Teuchos::CommandLineProcessor cmdp(false,true);

    cmdp.setOption("sort",&which,"Targetted eigenvalues (SM or LM).");

    if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {

      throw -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::RCP<Epetra_CrsMatrix> A = Teuchos::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, "Failure in InsertGlobalValues()" );

      }

      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, "Failure in InsertGlobalValues()" );

      }

      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]);

        TEUCHOS_TEST_FOR_EXCEPTION( info != 0, std::runtime_error, "Failure in InsertGlobalValues()" );

      }

      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]);

        TEUCHOS_TEST_FOR_EXCEPTION( info != 0, std::runtime_error, "Failure in InsertGlobalValues()" );

      }

      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, "Failure in InsertGlobalValues()" );

      }

      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, "Failure in InsertGlobalValues()" );

      }

      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, "Failure in InsertGlobalValues()" );

      }

      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]);

        TEUCHOS_TEST_FOR_EXCEPTION( info != 0, std::runtime_error, "Failure in InsertGlobalValues()" );

      }

      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, "Failure in InsertGlobalValues()" );

      }

      // Put in the diagonal entry

      int info = A->InsertGlobalValues(MyGlobalElements[i], 1, &diag, &MyGlobalElements[i]);

      TEUCHOS_TEST_FOR_EXCEPTION( info != 0, std::runtime_error, "Failure in InsertGlobalValues()" );

    }


    // Finish up

    int info = A->FillComplete();

    TEUCHOS_ASSERT( info==0 );

    A->SetTracebackMode(1); // Shutdown Epetra Warning tracebacks


    // Create a identity matrix for the temporary mass matrix

    Teuchos::RCP<Epetra_CrsMatrix> M = Teuchos::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_ASSERT( info==0 );

    }

    // Finish up

    info = M->FillComplete();

    TEUCHOS_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;

    const int verbosity = Anasazi::Errors + Anasazi::Warnings + Anasazi::FinalSummary;


    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> > 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");

      throw -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 );

    MyPL.set( "Verbosity", verbosity );

    //

    // 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::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 == Anasazi::Converged ? "converged." : "unconverged.") << std::endl;

    os<<std::endl;

    os<<"------------------------------------------------------"<<std::endl;

    os<<std::setw(16)<<"Eigenvalue"

      <<std::setw(18)<<"Direct Residual"

      <<std::endl;

    os<<"------------------------------------------------------"<<std::endl;

    for (int i=0; i<sol.numVecs; i++) {

      os<<std::setw(16)<<evals[i].realpart

        <<std::setw(18)<<normR[i]/evals[i].realpart

        <<std::endl;

    }

    os<<"------------------------------------------------------"<<std::endl;

    printer.print(Anasazi::Errors,os.str());

    success = true;

  }

  TEUCHOS_STANDARD_CATCH_STATEMENTS(true, std::cerr, success);


#ifdef HAVE_MPI

  MPI_Finalize();

#endif

  return ( success ? EXIT_SUCCESS : EXIT_FAILURE );

}