BlockKrylovSchur/BlockKrylovSchurEpetraExSVD.cpp

Use Anasazi::BlockKrylovSchurSolMgr to compute a singular value decomposition (SVD), using Epetra data structures.

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//                 Anasazi: Block Eigensolvers Package
//                 Copyright 2004 Sandia Corporation
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// @HEADER
//  This example shows how to use the block Krylov-Schur method to compute a few
//  of the largest singular values (sigma) and corresponding right singular
//  vectors (v) for the matrix A by solving the symmetric problem:
//
//                             (A'*A)*v = sigma*v
//
//  where A is an m by n real matrix that is derived from the simplest finite
//  difference discretization of the 2-dimensional kernel K(s,t)dt where
//
//                    K(s,t) = s(t-1)   if 0 <= s <= t <= 1
//                             t(s-1)   if 0 <= t <= s <= 1
//
//  NOTE:  This example came from the ARPACK SVD driver dsvd.f
//
#include "AnasaziBlockKrylovSchurSolMgr.hpp"
#include "AnasaziBasicEigenproblem.hpp"
#include "AnasaziConfigDefs.hpp"
#include "AnasaziEpetraAdapter.hpp"

#include "Epetra_CrsMatrix.h"
#include "Teuchos_LAPACK.hpp"
#include "Teuchos_StandardCatchMacros.hpp"

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

  bool success = false;
  try {
#ifdef EPETRA_MPI
    Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
    Epetra_SerialComm Comm;
#endif
    int i, j, info;
    const double one = 1.0;
    const double zero = 0.0;
    Teuchos::LAPACK<int,double> lapack;

    int MyPID = Comm.MyPID();

    //  Dimension of the matrix
    int m = 500;
    int n = 100;

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

    Epetra_Map RowMap(m, 0, Comm);
    Epetra_Map ColMap(n, 0, Comm);

    // Get update list and number of local equations from newly created Map.

    int NumMyRowElements = RowMap.NumMyElements();

    std::vector<int> MyGlobalRowElements(NumMyRowElements);
    RowMap.MyGlobalElements(&MyGlobalRowElements[0]);

    /* We are building an m by n matrix with entries

       A(i,j) = k*(si)*(tj - 1) if i <= j
       = k*(tj)*(si - 1) if i  > j

       where si = i/(m+1) and tj = j/(n+1) and k = 1/(n+1).
       */

    // Create an Epetra_Matrix
    Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Epetra_DataAccess::Copy, RowMap, n) );

    // Compute coefficients for discrete integral operator
    std::vector<double> Values(n);
    std::vector<int> Indices(n);
    double inv_mp1 = one/(m+1);
    double inv_np1 = one/(n+1);
    for (i=0; i<n; i++) { Indices[i] = i; }

    for (i=0; i<NumMyRowElements; i++) {
      //
      for (j=0; j<n; j++) {
        //
        if ( MyGlobalRowElements[i] <= j ) {
          Values[j] = inv_np1 * ( (MyGlobalRowElements[i]+one)*inv_mp1 ) * ( (j+one)*inv_np1 - one );  // k*(si)*(tj-1)
        }
        else {
          Values[j] = inv_np1 * ( (j+one)*inv_np1 ) * ( (MyGlobalRowElements[i]+one)*inv_mp1 - one );  // k*(tj)*(si-1)
        }
      }
      info = A->InsertGlobalValues(MyGlobalRowElements[i], n, &Values[0], &Indices[0]);
      assert( info==0 );
    }

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

    //************************************
    // Start the block Arnoldi iteration
    //***********************************
    //
    //  Variables used for the Block Arnoldi Method
    //
    int nev = 4;
    int blockSize = 1;
    int numBlocks = 10;
    int maxRestarts = 20;
    int verbosity = Anasazi::Errors + Anasazi::Warnings + Anasazi::FinalSummary;
    double tol = lapack.LAMCH('E');
    std::string which = "LM";
    //
    // Create parameter list to pass into solver
    //
    Teuchos::ParameterList MyPL;
    MyPL.set( "Verbosity", verbosity );
    MyPL.set( "Which", which );
    MyPL.set( "Block Size", blockSize );
    MyPL.set( "Num Blocks", numBlocks );
    MyPL.set( "Maximum Restarts", maxRestarts );
    MyPL.set( "Convergence Tolerance", tol );

    typedef Anasazi::MultiVec<double> MV;
    typedef Anasazi::Operator<double> OP;

    // Create an Anasazi::EpetraMultiVec for an initial vector to start the solver.
    // Note:  This needs to have the same number of columns as the blocksize.
    Teuchos::RCP<Anasazi::EpetraMultiVec> ivec = Teuchos::rcp( new Anasazi::EpetraMultiVec(ColMap, blockSize) );
    ivec->MvRandom();

    // Call the constructor for the (A^T*A) operator
    Teuchos::RCP<Anasazi::EpetraSymOp>  Amat = Teuchos::rcp( new Anasazi::EpetraSymOp(A) );
    Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > MyProblem =
      Teuchos::rcp( new Anasazi::BasicEigenproblem<double, MV, OP>(Amat, ivec) );

    // Inform the eigenproblem that the matrix A is symmetric
    MyProblem->setHermitian(true);

    // Set the number of eigenvalues requested and the blocksize the solver should use
    MyProblem->setNEV( nev );

    // Inform the eigenproblem that you are finished passing it information
    bool boolret = MyProblem->setProblem();
    if (!boolret) {
      throw "Anasazi::BasicEigenproblem::setProblem() returned with error.";
    }

    // 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) {
      std::cout << "Anasazi::EigensolverMgr::solve() returned unconverged." << std::endl;
    }

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

    if (numev > 0) {

      // Compute singular values/vectors and direct residuals.
      //
      // Compute singular values which are the square root of the eigenvalues
      if (MyPID==0) {
        std::cout<<"------------------------------------------------------"<<std::endl;
        std::cout<<"Computed Singular Values: "<<std::endl;
        std::cout<<"------------------------------------------------------"<<std::endl;
      }
      for (i=0; i<numev; i++) { evals[i].realpart = Teuchos::ScalarTraits<double>::squareroot( evals[i].realpart ); }
      //
      // Compute left singular vectors :  u = Av/sigma
      //
      std::vector<double> tempnrm(numev), directnrm(numev);
      std::vector<int> index(numev);
      for (i=0; i<numev; i++) { index[i] = i; }
      Anasazi::EpetraMultiVec Av(RowMap,numev), u(RowMap,numev);
      Anasazi::EpetraMultiVec* evecs = dynamic_cast<Anasazi::EpetraMultiVec* >(sol.Evecs->CloneViewNonConst( index ));
      Teuchos::SerialDenseMatrix<int,double> S(numev,numev);
      A->Apply( *evecs, Av );
      Av.MvNorm( tempnrm );
      for (i=0; i<numev; i++) { S(i,i) = one/tempnrm[i]; };
      u.MvTimesMatAddMv( one, Av, S, zero );
      //
      // Compute direct residuals : || Av - sigma*u ||
      //
      for (i=0; i<numev; i++) { S(i,i) = evals[i].realpart; }
      Av.MvTimesMatAddMv( -one, u, S, one );
      Av.MvNorm( directnrm );
      if (MyPID==0) {
        std::cout.setf(std::ios_base::right, std::ios_base::adjustfield);
        std::cout<<std::setw(16)<<"Singular Value"
          <<std::setw(20)<<"Direct Residual"
          <<std::endl;
        std::cout<<"------------------------------------------------------"<<std::endl;
        for (i=0; i<numev; i++) {
          std::cout<<std::setw(16)<<evals[i].realpart
            <<std::setw(20)<<directnrm[i]
            <<std::endl;
        }
        std::cout<<"------------------------------------------------------"<<std::endl;
      }
    }
    success = true;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(true, std::cerr, success);

#ifdef EPETRA_MPI
  MPI_Finalize() ;
#endif

  return ( success ? EXIT_SUCCESS : EXIT_FAILURE );
}