コード例 #1
0
int exampleImplicitlyComposedLinearOperators(
  const int n0,
  const int n1,
  const int n2,
  Teuchos::FancyOStream &out,
  const Teuchos::EVerbosityLevel verbLevel,
  typename Teuchos::ScalarTraits<Scalar>::magnitudeType errorTol,
  const bool testAdjoint
  )
{

  // Using and other declarations
  typedef Teuchos::ScalarTraits<Scalar> ST;
  using Teuchos::as;
  using Teuchos::RCP;
  using Teuchos::OSTab;
  using Thyra::VectorSpaceBase;
  using Thyra::VectorBase;
  using Thyra::MultiVectorBase;
  using Thyra::LinearOpBase;
  using Thyra::defaultSpmdVectorSpace;
  using Thyra::randomize;
  using Thyra::identity;
  using Thyra::diagonal;
  using Thyra::multiply;
  using Thyra::add;
  using Thyra::subtract;
  using Thyra::scale;
  using Thyra::adjoint;
  using Thyra::block1x2;
  using Thyra::block2x2;
  using Thyra::block2x2;

  out << "\n***"
      << "\n*** Demonstrating building linear operators for scalar type "
      << ST::name()
      << "\n***\n";

  OSTab tab(out);

  //
  // A) Set up the basic objects and other inputs to build the implicitly
  // composed linear operators.
  //
  
  // Create serial vector spaces in this case
  const RCP<const VectorSpaceBase<Scalar> >
    space0 = defaultSpmdVectorSpace<Scalar>(n0),
    space1 = defaultSpmdVectorSpace<Scalar>(n1),
    space2 = defaultSpmdVectorSpace<Scalar>(n2);

  // Create the component linear operators first as multi-vectors
  const RCP<MultiVectorBase<Scalar> >
    mvA = createMembers(space2, n0, "A"),
    mvB = createMembers(space0, n2, "B"),
    mvC = createMembers(space0, n0, "C"),
    mvE = createMembers(space0, n1, "E"),
    mvF = createMembers(space0, n1, "F"),
    mvJ = createMembers(space2, n1, "J"),
    mvK = createMembers(space1, n2, "K"),
    mvL = createMembers(space2, n1, "L"),
    mvN = createMembers(space0, n1, "N"),
    mvP = createMembers(space2, n1, "P"),
    mvQ = createMembers(space0, n2, "Q");

  // Create the vector diagonal for D
  const RCP<VectorBase<Scalar> > d = createMember(space2);

  // Get the constants
  const Scalar
    one = 1.0,
    beta = 2.0,
    gamma = 3.0,
    eta = 4.0;

  // Randomize the values in the Multi-Vector
  randomize( -one, +one, mvA.ptr() );
  randomize( -one, +one, mvB.ptr() );
  randomize( -one, +one, mvC.ptr() );
  randomize( -one, +one, d.ptr() );
  randomize( -one, +one, mvE.ptr() );
  randomize( -one, +one, mvF.ptr() );
  randomize( -one, +one, mvJ.ptr() );
  randomize( -one, +one, mvK.ptr() );
  randomize( -one, +one, mvL.ptr() );
  randomize( -one, +one, mvN.ptr() );
  randomize( -one, +one, mvP.ptr() );
  randomize( -one, +one, mvQ.ptr() );

  // Get the linear operator forms of the basic component linear operators
  const RCP<const LinearOpBase<Scalar> >
    A = mvA,
    B = mvB,
    C = mvC,
    E = mvE,
    F = mvF,
    J = mvJ,
    K = mvK,
    L = mvL,
    N = mvN,
    P = mvP,
    Q = mvQ;

  out << describe(*A, verbLevel);
  out << describe(*B, verbLevel);
  out << describe(*C, verbLevel);
  out << describe(*E, verbLevel);
  out << describe(*F, verbLevel);
  out << describe(*J, verbLevel);
  out << describe(*K, verbLevel);
  out << describe(*L, verbLevel);
  out << describe(*N, verbLevel);
  out << describe(*P, verbLevel);
  out << describe(*Q, verbLevel);

  //
  // B) Create the composed linear operators
  //

  // I
  const RCP<const LinearOpBase<Scalar> > I = identity(space1, "I");

  // D = diag(d)
  const RCP<const LinearOpBase<Scalar> > D = diagonal(d, "D");

  // M00 = [ gama*B*A + C,  E + F ] ^H
  //       [ J^H * A,       I     ]
  const RCP<const LinearOpBase<Scalar> > M00 =
    adjoint(
      block2x2(
        add( scale(gamma,multiply(B,A)), C ),  add( E, F ),
        multiply(adjoint(J),A),                I
        ),
      "M00"
      );

  out << "\nM00 = " << describe(*M00, verbLevel);

  // M01 = beta * [ Q ]
  //              [ K ]
  const RCP<const LinearOpBase<Scalar> > M01 =
    scale(
      beta,
      block2x1( Q, K ),
      "M01"
      );

  out << "\nM01 = "  << describe(*M01, verbLevel);
            
  // M10 = [ L * N^H,  eta*P ]
  const RCP<const LinearOpBase<Scalar> > M10 =
    block1x2(
      multiply(L,adjoint(N)),  scale(eta,P),
      "M10"
      );

  out << "\nM10 = " << describe(*M10, verbLevel);

  // M11 = D - Q^H*Q
  const RCP<const LinearOpBase<Scalar> > M11 =
    subtract( D, multiply(adjoint(Q),Q), "M11" );

  out << "\nM11 = "  << describe(*M11, verbLevel);
  

  // M = [ M00, M01 ]
  //     [ M10, M11 ]
  const RCP<const LinearOpBase<Scalar> > M =
    block2x2(
      M00, M01,
      M10, M11,
      "M"
      );

  out << "\nM = " << describe(*M, verbLevel);

  
  //
  // C) Test the final composed operator
  //

  Thyra::LinearOpTester<Scalar> linearOpTester;
  linearOpTester.set_all_error_tol(errorTol);
  linearOpTester.check_adjoint(testAdjoint);
  if (as<int>(verbLevel) >= as<int>(Teuchos::VERB_HIGH))
    linearOpTester.show_all_tests(true);
  if (as<int>(verbLevel) >= as<int>(Teuchos::VERB_EXTREME))
    linearOpTester.dump_all(true);

  const bool result = linearOpTester.check(*M,&out);

  return result;

}
コード例 #2
0
int main(int argc, char* argv[])
{

    using Teuchos::describe;
    using Teuchos::rcp;
    using Teuchos::rcp_dynamic_cast;
    using Teuchos::rcp_const_cast;
    using Teuchos::RCP;
    using Teuchos::CommandLineProcessor;
    using Teuchos::ParameterList;
    using Teuchos::sublist;
    using Teuchos::getParametersFromXmlFile;
    typedef ParameterList::PrintOptions PLPrintOptions;
    using Thyra::inverse;
    using Thyra::initializePreconditionedOp;
    using Thyra::initializeOp;
    using Thyra::unspecifiedPrec;
    using Thyra::solve;
    typedef RCP<const Thyra::LinearOpBase<double> > LinearOpPtr;
    typedef RCP<Thyra::VectorBase<double> > VectorPtr;

    bool success = true;
    bool verbose = true;

    Teuchos::GlobalMPISession mpiSession(&argc,&argv);

    Teuchos::RCP<Teuchos::FancyOStream>
    out = Teuchos::VerboseObjectBase::getDefaultOStream();

    try {

        //
        // Read in options from the command line
        //

        CommandLineProcessor clp(false); // Don't throw exceptions

        const int numVerbLevels = 6;
        Teuchos::EVerbosityLevel
        verbLevelValues[] =
        {
            Teuchos::VERB_DEFAULT, Teuchos::VERB_NONE,
            Teuchos::VERB_LOW, Teuchos::VERB_MEDIUM,
            Teuchos::VERB_HIGH, Teuchos::VERB_EXTREME
        };
        const char*
        verbLevelNames[] =
        { "default", "none", "low", "medium", "high", "extreme" };

        Teuchos::EVerbosityLevel verbLevel = Teuchos::VERB_MEDIUM;
        clp.setOption( "verb-level", &verbLevel,
                       numVerbLevels, verbLevelValues, verbLevelNames,
                       "Verbosity level used for all objects."
                     );

        std::string matrixFile = ".";
        clp.setOption( "matrix-file", &matrixFile,
                       "Matrix file."
                     );

        std::string paramListFile = "";
        clp.setOption( "param-list-file", &paramListFile,
                       "Parameter list for preconditioner and solver blocks."
                     );

        bool showParams = false;
        clp.setOption( "show-params", "no-show-params", &showParams,
                       "Show the parameter list or not."
                     );

        bool testPrecIsLinearOp = true;
        clp.setOption( "test-prec-is-linear-op", "test-prec-is-linear-op", &testPrecIsLinearOp,
                       "Test if the preconditioner is a linear operator or not."
                     );

        double solveTol = 1e-8;
        clp.setOption( "solve-tol", &solveTol,
                       "Tolerance for the solution to determine success or failure!"
                     );

        clp.setDocString(
            "This example program shows how to use one linear solver (e.g. AztecOO)\n"
            "as a preconditioner for another iterative solver (e.g. Belos).\n"
        );

        // Note: Use --help on the command line to see the above documentation

        CommandLineProcessor::EParseCommandLineReturn parse_return = clp.parse(argc,argv);
        if( parse_return != CommandLineProcessor::PARSE_SUCCESSFUL ) return parse_return;


        //
        *out << "\nA) Reading in the matrix ...\n";
        //

#ifdef HAVE_MPI
        Epetra_MpiComm comm(MPI_COMM_WORLD);
#else
        Epetra_SerialComm comm;
#endif

        const LinearOpPtr A = readEpetraCrsMatrixFromMatrixMarketAsLinearOp(
                                  matrixFile, comm, "A");
        *out << "\nA = " << describe(*A,verbLevel) << "\n";

        const RCP<ParameterList> paramList = getParametersFromXmlFile(paramListFile);
        if (showParams) {
            *out << "\nRead in parameter list:\n\n";
            paramList->print(*out, PLPrintOptions().indent(2).showTypes(true));
        }

        //
        *out << "\nB) Get the preconditioner as a forward solver\n";
        //

        const RCP<ParameterList> precParamList = sublist(paramList, "Preconditioner Solver");
        Stratimikos::DefaultLinearSolverBuilder precSolverBuilder;
        precSolverBuilder.setParameterList(precParamList);
        const RCP<const Thyra::LinearOpWithSolveFactoryBase<double> > precSolverStrategy
            = createLinearSolveStrategy(precSolverBuilder);
        //precSolverStrategy->setVerbLevel(verbLevel);

        const LinearOpPtr A_inv_prec = inverse<double>(*precSolverStrategy, A,
                                       Thyra::SUPPORT_SOLVE_FORWARD_ONLY,
                                       Teuchos::null, // Use internal solve criteria
                                       Thyra::IGNORE_SOLVE_FAILURE // Ignore solve failures since this is just a prec
                                                      );
        *out << "\nA_inv_prec = " << describe(*A_inv_prec, verbLevel) << "\n";

        if (testPrecIsLinearOp) {
            *out << "\nTest that the preconditioner A_inv_prec is indeed a linear operator.\n";
            Thyra::LinearOpTester<double> linearOpTester;
            linearOpTester.check_adjoint(false);
            const bool linearOpCheck = linearOpTester.check(*A_inv_prec, out.ptr());
            if (!linearOpCheck) {
                success = false;
            }
        }

        //
        *out << "\nC) Create the forward solver using the created preconditioner ...\n";
        //

        const RCP<ParameterList> fwdSolverParamList = sublist(paramList, "Forward Solver");
        Stratimikos::DefaultLinearSolverBuilder fwdSolverSolverBuilder;
        fwdSolverSolverBuilder.setParameterList(fwdSolverParamList);
        const RCP<const Thyra::LinearOpWithSolveFactoryBase<double> > fwdSolverSolverStrategy
            = createLinearSolveStrategy(fwdSolverSolverBuilder);

        const RCP<Thyra::LinearOpWithSolveBase<double> >
        A_lows = fwdSolverSolverStrategy->createOp();

        initializePreconditionedOp<double>( *fwdSolverSolverStrategy, A,
                                            unspecifiedPrec(A_inv_prec), A_lows.ptr());
        //A_lows->setVerbLevel(verbLevel);
        *out << "\nA_lows = " << describe(*A_lows, verbLevel) << "\n";

        //
        *out << "\nD) Solve the linear system for a random RHS ...\n";
        //

        VectorPtr x = createMember(A->domain());
        VectorPtr b = createMember(A->range());
        Thyra::randomize(-1.0, +1.0, b.ptr());
        Thyra::assign(x.ptr(), 0.0); // Must give an initial guess!

        Thyra::SolveStatus<double>
        solveStatus = solve<double>( *A_lows, Thyra::NOTRANS, *b, x.ptr() );

        *out << "\nSolve status:\n" << solveStatus;

        *out << "\nSolution ||x|| = " << Thyra::norm(*x) << "\n";

        if(showParams) {
            *out << "\nParameter list after use:\n\n";
            paramList->print(*out, PLPrintOptions().indent(2).showTypes(true));
        }

        //
        *out << "\nF) Checking the error in the solution of r=b-A*x ...\n";
        //

        VectorPtr Ax = Thyra::createMember(b->space());
        Thyra::apply( *A, Thyra::NOTRANS, *x, Ax.ptr() );
        VectorPtr r = Thyra::createMember(b->space());
        Thyra::V_VmV<double>(r.ptr(), *b, *Ax);

        double
        Ax_nrm = Thyra::norm(*Ax),
        r_nrm = Thyra::norm(*r),
        b_nrm = Thyra::norm(*b),
        r_nrm_over_b_nrm = r_nrm / b_nrm;

        bool resid_tol_check = ( r_nrm_over_b_nrm <= solveTol );
        if(!resid_tol_check) success = false;

        *out
                << "\n||A*x|| = " << Ax_nrm << "\n";

        *out
                << "\n||A*x-b||/||b|| = " << r_nrm << "/" << b_nrm
                << " = " << r_nrm_over_b_nrm << " <= " << solveTol
                << " : " << Thyra::passfail(resid_tol_check) << "\n";

        Teuchos::TimeMonitor::summarize(*out<<"\n");
    }
    TEUCHOS_STANDARD_CATCH_STATEMENTS(verbose, std::cerr, success)

    if (verbose) {
        if(success)  *out << "\nCongratulations! All of the tests checked out!\n";
        else         *out << "\nOh no! At least one of the tests failed!\n";
    }

    return ( success ? EXIT_SUCCESS : EXIT_FAILURE );
}