BlockGmres/BlockGmresPolyEpetraExFile.cpp

"Hybrid block GMRES" means that the solver first runs block GMRES.It stores the resulting coefficients, which form a matrix polynomial. It then can reuse this polynomial for subsequent solves. This avoids the cost of the inner products and norms in GMRES. However, the resulting polynomial is not necessarily as effective as the equivalent number of GMRES iterations.

We call solvers that take this approach "seed solvers." Belos implements both a Block GMRES seed solver (this class) and a CG-based seed solver (Belos::PCPGSolMgr).

Here is a list of all the parameters that this solver accepts:

• "Convergence Tolerance" (MagnitudeType): The level that residual norms must reach to decide convergence. Default: 1e-8.
• "Block Size" (int): The block size to be used by the underlying block GMRES solver. Default: 1 (which means don't use blocks).
• "Num Blocks" (int): The restart length; that is, the number of blocks allocated for the Krylov basis. Default: 300.
• "Maximum Iterations" (int): The maximum number of iterations GMRES is allowed to perform, across all restarts. Default: 1000.
• "Maximum Restarts" (int): The maximum number of restarts the underlying solver is allowed to perform. This does not include the first restart cycle. Default: 20.
• "Orthogonalization" (std::string): The desired orthogonalization method. Default: "DGKS".
• "Verbosity" (Belos::MsgType): A sum of Belos::MsgType values specifying what kinds of messages to print. Default: Belos::Errors.
• "Output Style" (Belos::OutputType): The output style. Default: Belos::General.

Like all Belos solvers, parameters have relative or "delta" semantics. This means the following:

• Any parameter that was never set has its default value
• Any parameter not explicitly set in the input ParameterList retains its current value

//@HEADER
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//
//                 Belos: Block Linear Solvers Package
//                  Copyright 2004 Sandia Corporation
//
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//@HEADER
//
// This driver reads a problem from a file, which can be in Harwell-Boeing (*.hb),
// Matrix Market (*.mtx), or triplet format (*.triU, *.triS).  The right-hand side
// from the problem, if it exists, will be used instead of multiple
// random right-hand-sides.  The initial guesses are all set to zero.
//
// NOTE: No preconditioner is used in this example.
//
#include "BelosConfigDefs.hpp"
#include "BelosLinearProblem.hpp"
#include "BelosEpetraAdapter.hpp"
#include "BelosGmresPolySolMgr.hpp"
#include "BelosBlockGmresSolMgr.hpp"

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

#include "Ifpack.h"

#include "Teuchos_CommandLineProcessor.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_StandardCatchMacros.hpp"

int main(int argc, char *argv[]) {
  //
  int MyPID = 0;
#ifdef EPETRA_MPI
  // Initialize MPI
  MPI_Init(&argc,&argv);
  Epetra_MpiComm Comm(MPI_COMM_WORLD);
  MyPID = Comm.MyPID();
#else
  Epetra_SerialComm Comm;
#endif
  //
  typedef double                            ST;
  typedef Teuchos::ScalarTraits<ST>        SCT;
  typedef SCT::magnitudeType                MT;
  typedef Epetra_MultiVector                MV;
  typedef Epetra_Operator                   OP;
  typedef Belos::MultiVecTraits<ST,MV>     MVT;
  typedef Belos::OperatorTraits<ST,MV,OP>  OPT;

  using Teuchos::ParameterList;
  using Teuchos::RCP;
  using Teuchos::rcp;

  bool verbose = false;
  bool success = true;
  try {
    bool proc_verbose = false;
    bool debug = false;
    bool userandomrhs = true;
    int frequency = -1;        // frequency of status test output.
    int blocksize = 1;         // blocksize
    int numrhs = 1;            // number of right-hand sides to solve for
    int maxiters = -1;         // maximum number of iterations allowed per linear system
    int maxdegree = 25;        // maximum degree of polynomial
    int maxsubspace = 50;      // maximum number of blocks the solver can use for the subspace
    int maxrestarts = 15;      // number of restarts allowed
    std::string outersolver("Block Gmres");
    std::string polytype("Arnoldi");
    std::string filename("orsirr1.hb");
    std::string precond("right");
    MT tol = 1.0e-5;           // relative residual tolerance
    MT polytol = tol/10;       // relative residual tolerance for polynomial construction

    Teuchos::CommandLineProcessor cmdp(false,true);
    cmdp.setOption("verbose","quiet",&verbose,"Print messages and results.");
    cmdp.setOption("debug","nondebug",&debug,"Print debugging information from solver.");
    cmdp.setOption("use-random-rhs","use-rhs",&userandomrhs,"Use linear system RHS or random RHS to generate polynomial.");
    cmdp.setOption("frequency",&frequency,"Solvers frequency for printing residuals (#iters).");
    cmdp.setOption("filename",&filename,"Filename for test matrix.  Acceptable file extensions: *.hb,*.mtx,*.triU,*.triS");
    cmdp.setOption("outersolver",&outersolver,"Name of outer solver to be used with GMRES poly");
    cmdp.setOption("poly-type",&polytype,"Name of the polynomial to be generated.");
    cmdp.setOption("precond",&precond,"Preconditioning type (none, left, right).");
    cmdp.setOption("tol",&tol,"Relative residual tolerance used by GMRES solver.");
    cmdp.setOption("poly-tol",&polytol,"Relative residual tolerance used to construct the GMRES polynomial.");
    cmdp.setOption("num-rhs",&numrhs,"Number of right-hand sides to be solved for.");
    cmdp.setOption("block-size",&blocksize,"Block size used by GMRES.");
    cmdp.setOption("max-iters",&maxiters,"Maximum number of iterations per linear system (-1 = adapted to problem/block size).");
    cmdp.setOption("max-degree",&maxdegree,"Maximum degree of the GMRES polynomial.");
    cmdp.setOption("max-subspace",&maxsubspace,"Maximum number of blocks the solver can use for the subspace.");
    cmdp.setOption("max-restarts",&maxrestarts,"Maximum number of restarts allowed for GMRES solver.");
    if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
      return -1;
    }
    if (!verbose)
      frequency = -1;  // reset frequency if test is not verbose
    //
    // Get the problem
    //
    RCP<Epetra_Map> Map;
    RCP<Epetra_CrsMatrix> A;
    RCP<Epetra_MultiVector> B, X;
    RCP<Epetra_Vector> vecB, vecX;
    EpetraExt::readEpetraLinearSystem(filename, Comm, &A, &Map, &vecX, &vecB);
    A->OptimizeStorage();
    proc_verbose = verbose && (MyPID==0);  /* Only print on the zero processor */

    // Check to see if the number of right-hand sides is the same as requested.
    if (numrhs>1) {
      X = rcp( new Epetra_MultiVector( *Map, numrhs ) );
      B = rcp( new Epetra_MultiVector( *Map, numrhs ) );
      X->Random();
      OPT::Apply( *A, *X, *B );
      X->PutScalar( 0.0 );
    }
    else {
      X = Teuchos::rcp_implicit_cast<Epetra_MultiVector>(vecX);
      B = Teuchos::rcp_implicit_cast<Epetra_MultiVector>(vecB);
    }
    //
    // ************Construct preconditioner*************
    //
    RCP<Belos::EpetraPrecOp> belosPrec;

    if (precond != "none") {
      ParameterList ifpackList;

      // allocates an IFPACK factory. No data is associated
      // to this object (only method Create()).
      Ifpack Factory;

      // create the preconditioner. For valid PrecType values,
      // please check the documentation
      std::string PrecType = "ILU"; // incomplete LU
      int OverlapLevel = 1; // must be >= 0. If Comm.NumProc() == 1,
      // it is ignored.

      RCP<Ifpack_Preconditioner> Prec = Teuchos::rcp( Factory.Create(PrecType, &*A, OverlapLevel) );
      assert(Prec != Teuchos::null);

      // specify parameters for ILU
      ifpackList.set("fact: level-of-fill", 1);
      // the combine mode is on the following:
      // "Add", "Zero", "Insert", "InsertAdd", "Average", "AbsMax"
      // Their meaning is as defined in file Epetra_CombineMode.h
      ifpackList.set("schwarz: combine mode", "Add");
      // sets the parameters
      IFPACK_CHK_ERR(Prec->SetParameters(ifpackList));

      // initialize the preconditioner. At this point the matrix must
      // have been FillComplete()'d, but actual values are ignored.
      IFPACK_CHK_ERR(Prec->Initialize());

      // Builds the preconditioners, by looking for the values of
      // the matrix.
      IFPACK_CHK_ERR(Prec->Compute());

      // Create the Belos preconditioned operator from the Ifpack preconditioner.
      // NOTE:  This is necessary because Belos expects an operator to apply the
      //        preconditioner with Apply() NOT ApplyInverse().
      belosPrec = rcp( new Belos::EpetraPrecOp( Prec ) );
    }
    //
    // ********Other information used by block solver***********
    // *****************(can be user specified)******************
    //
    const int NumGlobalElements = B->GlobalLength();
    if (maxiters == -1)
      maxiters = NumGlobalElements/blocksize - 1; // maximum number of iterations to run
    //
    ParameterList belosList;
    belosList.set( "Num Blocks", maxsubspace);             // Maximum number of blocks in Krylov factorization
    belosList.set( "Block Size", blocksize );              // Blocksize to be used by iterative solver
    belosList.set( "Maximum Iterations", maxiters );       // Maximum number of iterations allowed
    belosList.set( "Maximum Restarts", maxrestarts );      // Maximum number of restarts allowed
    belosList.set( "Convergence Tolerance", tol );         // Relative convergence tolerance requested
    int verbosity = Belos::Errors + Belos::Warnings;
    if (verbose) {
      verbosity += Belos::FinalSummary + Belos::TimingDetails + Belos::StatusTestDetails;
      if (frequency > 0)
        belosList.set( "Output Frequency", frequency );
    }
    if (debug) {
      verbosity += Belos::Debug;
    }
    belosList.set( "Verbosity", verbosity );

    ParameterList polyList;
    polyList.set( "Polynomial Type", polytype );          // Type of polynomial to be generated
    polyList.set( "Maximum Degree", maxdegree );          // Maximum degree of the GMRES polynomial
    polyList.set( "Polynomial Tolerance", polytol );      // Polynomial convergence tolerance requested
    polyList.set( "Verbosity", verbosity );               // Verbosity for polynomial construction
    polyList.set( "Random RHS", userandomrhs );           // Use RHS from linear system or random vector
    if ( outersolver != "" ) {
      polyList.set( "Outer Solver", outersolver );
      polyList.set( "Outer Solver Params", belosList );
    }
    //
    // Construct an unpreconditioned linear problem instance.
    //
    Belos::LinearProblem<double,MV,OP> problem( A, X, B );
    problem.setInitResVec( B );
    if (precond == "left") {
      problem.setLeftPrec( belosPrec );
    }
    if (precond == "right") {
      problem.setRightPrec( belosPrec );
    }
    bool set = problem.setProblem();
    if (set == false) {
      if (proc_verbose)
        std::cout << std::endl << "ERROR:  Belos::LinearProblem failed to set up correctly!" << std::endl;
      return -1;
    }
    //
    // *******************************************************************
    // *************Start the block Gmres iteration*************************
    // *******************************************************************
    //
    // Create an iterative solver manager.
    RCP< Belos::SolverManager<double,MV,OP> > newSolver
      = rcp( new Belos::GmresPolySolMgr<double,MV,OP>(rcp(&problem,false), rcp(&polyList,false)));

    //
    // **********Print out information about problem*******************
    //
    if (proc_verbose) {
      std::cout << std::endl << std::endl;
      std::cout << "Dimension of matrix: " << NumGlobalElements << std::endl;
      std::cout << "Number of right-hand sides: " << numrhs << std::endl;
      std::cout << "Block size used by solver: " << blocksize << std::endl;
      std::cout << "Max number of restarts allowed: " << maxrestarts << std::endl;
      std::cout << "Max number of Gmres iterations per restart cycle: " << maxiters << std::endl;
      std::cout << "Relative residual tolerance: " << tol << std::endl;
      std::cout << std::endl;
    }
    //
    // Perform solve
    //
    Belos::ReturnType ret = newSolver->solve();
    //
    // Compute actual residuals.
    //
    bool badRes = false;
    std::vector<double> actual_resids( numrhs );
    std::vector<double> rhs_norm( numrhs );
    Epetra_MultiVector resid(*Map, numrhs);
    OPT::Apply( *A, *X, resid );
    MVT::MvAddMv( -1.0, resid, 1.0, *B, resid );
    MVT::MvNorm( resid, actual_resids );
    MVT::MvNorm( *B, rhs_norm );
    if (proc_verbose) {
      std::cout<< "---------- Actual Residuals (normalized) ----------"<<std::endl<<std::endl;
      for ( int i=0; i<numrhs; i++) {
        double actRes = actual_resids[i]/rhs_norm[i];
        std::cout<<"Problem "<<i<<" : \t"<< actRes <<std::endl;
        if (actRes > tol) badRes = true;
      }
    }

    if (ret!=Belos::Converged || badRes) {
      success = false;
      if (proc_verbose)
        std::cout << std::endl << "ERROR:  Belos did not converge!" << std::endl;
    } else {
      success = true;
      if (proc_verbose)
        std::cout << std::endl << "SUCCESS:  Belos converged!" << std::endl;
    }
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(verbose, std::cerr, success);

#ifdef EPETRA_MPI
  MPI_Finalize();
#endif

  return success ? EXIT_SUCCESS : EXIT_FAILURE;
}