TEUCHOS_UNIT_TEST_TEMPLATE_1_DECL( SimpleDenseLinearOp, basic,
  Scalar )
{

  using Teuchos::rcp_dynamic_cast;
  typedef ScalarTraits<Scalar> ST;

  const RCP<MultiVectorBase<Scalar> > mv =
    createSerialMultiVector<Scalar>(g_dim, g_dim/2, ST::one());
  const RCP<LinearOpBase<Scalar> > op =
    createNonconstSimpleDenseLinearOp<Scalar>(mv);

  TEST_EQUALITY(
    mv,
    rcp_dynamic_cast<SimpleDenseLinearOp<Scalar> >(op)->getNonconstMultiVector()
    );

  Thyra::LinearOpTester<Scalar> linearOpTester;
  linearOpTester.dump_all(g_dumpAll);
  TEST_ASSERT(linearOpTester.check(*op, ptrFromRef(out)));

}
Ejemplo n.º 2
0
bool runCgSolveExample(
  const int dim,
  const Scalar diagScale,
  const bool symOp,
  const bool showAllTests,
  const typename Teuchos::ScalarTraits<Scalar>::magnitudeType tolerance,
  const int maxNumIters
  )
{

  using Teuchos::as;
  using Teuchos::null;
  using Teuchos::RCP;
  using Teuchos::rcp;
  using Teuchos::OSTab;
  typedef Teuchos::ScalarTraits<Scalar> ST;
  using Thyra::multiply;
  using Thyra::scale;
  typedef typename ST::magnitudeType  ScalarMag;
  bool success = true;
  bool result;
  Teuchos::RCP<Teuchos::FancyOStream> out =
    Teuchos::VerboseObjectBase::getDefaultOStream();
  *out << "\n***\n*** Running silly CG solver using scalar type = \'"
       << ST::name() << "\' ...\n***\n";
  Teuchos::Time timer("");
  timer.start(true);

  //
  // (A) Setup a simple linear system with tridiagonal operator:
  //
  //       [   a*2   -1                         ]
  //       [ -r(1)  a*2       -1                ]
  //  A =  [          .        .        .       ]
  //       [             -r(n-2)      a*2    -1 ]
  //       [                      -r(n-1)   a*2 ]
  //

  // (A.1) Create the tridiagonal matrix operator
  *out << "\nConstructing tridiagonal matrix A of dimension = " << dim
       << " and diagonal multiplier = " << diagScale << " ...\n";
  Teuchos::Array<Scalar> lower(dim-1), diag(dim), upper(dim-1);
  const Scalar
    up = -ST::one(),
    diagTerm = as<Scalar>(2.0) * diagScale * ST::one(),
    low = -(symOp ? ST::one() : ST::random());
  int k = 0;
  // First row
  diag[k] = diagTerm; upper[k] = up;
  // Middle rows
  for( k = 1; k < dim - 1; ++k ) {
    lower[k-1] = low; diag[k] = diagTerm; upper[k] = up;
  }
  // Last row
  lower[k-1] = low; diag[k] = diagTerm;
  RCP<const Thyra::LinearOpBase<Scalar> > A =
    rcp(new ExampleTridiagSerialLinearOp<Scalar>(dim, lower, diag, upper));

  // (A.2) Testing the linear operator constructed linear operator
  *out << "\nTesting the constructed linear operator A ...\n";
  Thyra::LinearOpTester<Scalar> linearOpTester;
  linearOpTester.enable_all_tests(false);
  linearOpTester.check_linear_properties(true);
  linearOpTester.set_all_error_tol(tolerance);
  linearOpTester.set_all_warning_tol(1e-2*tolerance);
  linearOpTester.show_all_tests(showAllTests);
  result = linearOpTester.check(*A, out.ptr());
  if(!result) success = false;

  // (A.3) Create RHS vector b and set to a random value
  RCP<Thyra::VectorBase<Scalar> > b = createMember(A->range());
  Thyra::seed_randomize<Scalar>(0);
  Thyra::randomize( -ST::one(), +ST::one(), b.ptr() );

  // (A.4) Create LHS vector x and set to zero
  RCP<Thyra::VectorBase<Scalar> > x = createMember(A->domain());
  Thyra::V_S( x.ptr(), ST::zero() );

  // (A.5) Create the final linear system
  if(!symOp) {
    *out << "\nSetting up normal equations for unsymmetric system A^H*(A*x-b) => new A*x = b ...\n";
    // A^H*A
    RCP<const Thyra::LinearOpBase<Scalar> > AtA = multiply(adjoint(A), A);
    // A^H*b
    RCP<Thyra::VectorBase<Scalar> > nb = createMember(AtA->range());
    Thyra::apply<Scalar>(*A, Thyra::CONJTRANS, *b, nb.ptr());
    A = AtA;
    b = nb;
  }

  // (A.6) Testing the linear operator used with the solve
  *out << "\nTesting the linear operator used with the solve ...\n";
  linearOpTester.check_for_symmetry(true);
  result = linearOpTester.check(*A, out.ptr());
  if(!result) success = false;

  //
  // (B) Solve the linear system with the silly CG solver
  //
  *out << "\nSolving the linear system with sillyCgSolve(...) ...\n";
  {
    OSTab tab2(out);
    result = sillyCgSolve(*A, *b, maxNumIters, tolerance, x.ptr(), *out);
  }
  if(!result) success = false;

  //
  // (C) Check that the linear system was solved to the specified tolerance
  //
  RCP<Thyra::VectorBase<Scalar> > r = createMember(A->range());                     
  // r = b
  Thyra::V_V(r.ptr(), *b);
   // r = -A*x + r
  Thyra::apply<Scalar>(*A, Thyra::NOTRANS, *x, r.ptr(), -ST::one(), ST::one());
  const ScalarMag r_nrm = Thyra::norm(*r), b_nrm = Thyra::norm(*b);
  const ScalarMag rel_err = r_nrm/b_nrm, relaxTol = 10.0*tolerance;
  result = rel_err <= relaxTol;
  if(!result) success = false;
  *out << "\nChecking the residual ourselves ...\n";
  {
    OSTab tab(out);
    *out
      << "\n||b-A*x||/||b|| = "<<r_nrm<<"/"<<b_nrm<<" = "<<rel_err<<(result?" <= ":" > ")
      <<"10.0*tolerance = "<<relaxTol<<": "<<(result?"passed":"failed")<<std::endl;
  }
  timer.stop();
  *out << "\nTotal time = " << timer.totalElapsedTime() << " sec\n";
  
  return success;

} // end runCgSolveExample()
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;

}
Ejemplo n.º 4
0
bool run_composite_linear_ops_tests(
  const Teuchos::RCP<const Teuchos::Comm<Thyra::Ordinal> > comm,
  const int n,
  const bool useSpmd,
  const typename Teuchos::ScalarTraits<Scalar>::magnitudeType &tol,
  const bool dumpAll,
  Teuchos::FancyOStream *out_arg
  )
{

  using Teuchos::as;
  typedef Teuchos::ScalarTraits<Scalar> ST;
  typedef typename ST::magnitudeType    ScalarMag;
  typedef Teuchos::ScalarTraits<ScalarMag> STM;
  using Teuchos::RCP;
  using Teuchos::rcp;
  using Teuchos::null;
  using Teuchos::rcp_const_cast;
  using Teuchos::rcp_dynamic_cast;
  using Teuchos::dyn_cast;
  using Teuchos::OSTab;
  using Thyra::relErr;
  using Thyra::passfail;

  RCP<Teuchos::FancyOStream>
    out = rcp(new Teuchos::FancyOStream(rcp(out_arg,false)));

  const Teuchos::EVerbosityLevel
    verbLevel = dumpAll?Teuchos::VERB_EXTREME:Teuchos::VERB_HIGH;

  if (nonnull(out)) *out
    << "\n*** Entering run_composite_linear_ops_tests<"<<ST::name()<<">(...) ...\n";

  bool success = true, result;

  const ScalarMag warning_tol = ScalarMag(1e-2)*tol, error_tol = tol;
  Thyra::LinearOpTester<Scalar> linearOpTester;
  linearOpTester.linear_properties_warning_tol(warning_tol);
  linearOpTester.linear_properties_error_tol(error_tol);
  linearOpTester.adjoint_warning_tol(warning_tol);
  linearOpTester.adjoint_error_tol(error_tol);
  linearOpTester.dump_all(dumpAll);
  Thyra::LinearOpTester<Scalar> symLinearOpTester(linearOpTester);
  symLinearOpTester.check_for_symmetry(true);
  symLinearOpTester.symmetry_warning_tol(STM::squareroot(warning_tol));
  symLinearOpTester.symmetry_error_tol(STM::squareroot(error_tol));

  RCP<const Thyra::VectorSpaceBase<Scalar> > space;
  if(useSpmd) space = Thyra::defaultSpmdVectorSpace<Scalar>(comm,n,-1);
  else space = Thyra::defaultSpmdVectorSpace<Scalar>(n);
  if (nonnull(out)) *out
    << "\nUsing a basic vector space described as " << describe(*space,verbLevel) << " ...\n";

  if (nonnull(out)) *out << "\nCreating random n x (n/2) multi-vector origA ...\n";
  RCP<Thyra::MultiVectorBase<Scalar> >
    mvOrigA = createMembers(space,n/2,"origA");
  Thyra::seed_randomize<Scalar>(0);
  //RTOpPack::show_spmd_apply_op_dump = true;
  Thyra::randomize( as<Scalar>(as<Scalar>(-1)*ST::one()), as<Scalar>(as<Scalar>(+1)*ST::one()),
    mvOrigA.ptr() );
  RCP<const Thyra::LinearOpBase<Scalar> >
    origA = mvOrigA;
  if (nonnull(out)) *out << "\norigA =\n" << describe(*origA,verbLevel);
  //RTOpPack::show_spmd_apply_op_dump = false;

  if (nonnull(out)) *out << "\nTesting origA ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*origA, out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out
    << "\nCreating implicit scaled linear operator A1 = scale(0.5,origA) ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A1 = scale(as<Scalar>(0.5),origA);
  if (nonnull(out)) *out << "\nA1 =\n" << describe(*A1,verbLevel);

  if (nonnull(out)) *out << "\nTesting A1 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A1,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nTesting that A1.getOp() == origA ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.compare(
    *dyn_cast<const Thyra::DefaultScaledAdjointLinearOp<Scalar> >(*A1).getOp(),
    *origA,out.ptr());
  if(!result) success = false;

  {

    if (nonnull(out)) *out
      << "\nUnwrapping origA to get non-persisting pointer to origA_1, scalar and transp ...\n";
    Scalar  scalar;
    Thyra::EOpTransp transp;
    const Thyra::LinearOpBase<Scalar> *origA_1 = NULL;
    unwrap( *origA, &scalar, &transp, &origA_1 );
    TEUCHOS_TEST_FOR_EXCEPT( origA_1 == NULL );

    if (nonnull(out)) *out << "\nscalar = " << scalar << " == 1 ? ";
    result = (scalar == ST::one());
    if(!result) success = false;
    if (nonnull(out))	*out << passfail(result) << std::endl;

    if (nonnull(out)) *out << "\ntransp = " << toString(transp) << " == NOTRANS ? ";
    result = (transp == Thyra::NOTRANS);
    if(!result) success = false;
    if (nonnull(out))	*out << passfail(result) << std::endl;

    if (nonnull(out)) *out << "\nTesting that origA_1 == origA ...\n";
    Thyra::seed_randomize<Scalar>(0);
    result = linearOpTester.compare(*origA_1,*origA,out.ptr());
    if(!result) success = false;

  }

  {

    if (nonnull(out)) *out << "\nUnwrapping A1 to get non-persisting pointer to origA_2 ...\n";
    Scalar  scalar;
    Thyra::EOpTransp transp;
    const Thyra::LinearOpBase<Scalar> *origA_2 = NULL;
    unwrap( *A1, &scalar, &transp, &origA_2 );
    TEUCHOS_TEST_FOR_EXCEPT( origA_2 == NULL );

    if (nonnull(out)) *out << "\nscalar = " << scalar << " == 0.5 ? ";
    result = (scalar == as<Scalar>(0.5));
    if(!result) success = false;
    if (nonnull(out))	*out << passfail(result) << std::endl;

    if (nonnull(out)) *out << "\ntransp = " << toString(transp) << " == NOTRANS ? ";
    result = (transp == Thyra::NOTRANS);
    if(!result) success = false;
    if (nonnull(out))	*out << passfail(result) << std::endl;

    if (nonnull(out)) *out << "\nTesting that origA_2 == origA ...\n";
    Thyra::seed_randomize<Scalar>(0);
    result = linearOpTester.compare(*origA_2,*origA,out.ptr());
    if(!result) success = false;

  }

  if (nonnull(out)) *out << "\nCreating implicit scaled linear operator A2 = adjoint(A1) ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A2 = adjoint(A1);
  if (nonnull(out)) *out << "\nA2 =\n" << describe(*A2,verbLevel);

  if (nonnull(out)) *out << "\nTesting A2 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A2,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nTesting that A2.getOp() == A1 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.compare(*dyn_cast<const Thyra::DefaultScaledAdjointLinearOp<Scalar> >(*A2).getOp(),*A1,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating implicit scaled, adjoined linear operator A3 = adjoint(scale(2.0,(A2)) ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A3 = adjoint(scale(as<Scalar>(2.0),A2));
  if (nonnull(out)) *out << "\nA3 =\n" << describe(*A3,verbLevel);

  if (nonnull(out)) *out << "\nTesting A3 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A3,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nTesting that A3 == origA ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.compare(*A3,*origA,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCalling all of the rest of the functions for non-const just to test them ...\n";
  RCP<Thyra::LinearOpBase<Scalar> >
    A4 = nonconstScale(
      as<Scalar>(0.25)
      ,nonconstAdjoint(
        nonconstTranspose(
          nonconstAdjoint(
            nonconstScaleAndAdjoint(
              as<Scalar>(4.0)
              ,Thyra::TRANS
              ,Teuchos::rcp_const_cast<Thyra::LinearOpBase<Scalar> >(origA)
              )
            )
          )
        )
      );
  if(!ST::isComplex) A4 = nonconstTranspose(nonconstAdjoint(A4)); // Should result in CONJ
  if (nonnull(out)) *out << "\nA4 =\n" << describe(*A4,verbLevel);

  if (nonnull(out)) *out << "\nTesting A4 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A4,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCalling all of the rest of the functions for const just to test them ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A5 = scale(
      as<Scalar>(0.25)
      ,adjoint(
        transpose(
          adjoint(
            scaleAndAdjoint(
              as<Scalar>(4.0)
              ,Thyra::TRANS
              ,origA
              )
            )
          )
        )
      );
  if(!ST::isComplex) A5 = transpose(adjoint(A5)); // Should result in CONJ
  if (nonnull(out)) *out << "\nA5 =\n" << describe(*A5,verbLevel);

  if (nonnull(out)) *out << "\nTesting A5 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A5,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating a multiplied operator A6 = origA^H*A1 ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A6 = multiply(adjoint(origA),A1);
  if (nonnull(out)) *out << "\nA6 =\n" << describe(*A6,verbLevel);

  if (nonnull(out)) *out << "\nTesting A6 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = symLinearOpTester.check(*A6,out.ptr());
  if(!result) success = false;
  // Note that testing the symmetry above helps to check the transpose mode
  // against the non-transpose mode!

#ifdef TEUCHOS_DEBUG
  if (nonnull(out)) *out << "\nCreating an invalid multiplied operator A6b = origA*origA (should throw an exception) ...\n\n";
  try {
    RCP<const Thyra::LinearOpBase<Scalar> >
      A6b = multiply(origA,origA);
    result = true;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(true,out.get()?*out:std::cerr,result)
  if (nonnull(out))
    *out << "\nCaught expected exception : " << (result?"failed\n":"passed\n");
  if(result) success = false;
#endif // TEUCHOS_DEBUG

  if (nonnull(out)) *out << "\nCreating a non-const multiplied operator A7 = origA^H*A1 ...\n";
  RCP<Thyra::LinearOpBase<Scalar> >
    A7 = nonconstMultiply(
      rcp_const_cast<Thyra::LinearOpBase<Scalar> >(adjoint(origA))
      ,rcp_const_cast<Thyra::LinearOpBase<Scalar> >(A1)
      );
  if (nonnull(out)) *out << "\nA7 =\n" << describe(*A7,verbLevel);

  if (nonnull(out)) *out << "\nTesting A7 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = symLinearOpTester.check(*A7,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating an added operator A8 = origA + A1 ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A8 = add(origA,A1);
  if (nonnull(out)) *out << "\nA8 =\n" << describe(*A8,verbLevel);

  if (nonnull(out)) *out << "\nTesting A8 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A8,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating a symmetric subtracted operator A8b = A6 + adjoint(origA)*origA ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A8b = subtract(A6,multiply(adjoint(origA),origA));
  if (nonnull(out)) *out << "\nA8b =\n" << describe(*A8b,verbLevel);

  if (nonnull(out)) *out << "\nTesting A8b ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = symLinearOpTester.check(*A8b,out.ptr());
  if(!result) success = false;

#ifdef TEUCHOS_DEBUG
  if (nonnull(out)) *out << "\nCreating an invalid added operator A8c = origA + adjoint(origA) (should throw an exception) ...\n\n";
  try {
    RCP<const Thyra::LinearOpBase<Scalar> >
      A8c = add(origA,adjoint(origA));
    result = true;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(true,out.get()?*out:std::cerr,result)
  if (nonnull(out))
    *out << "\nCaught expected exception : " << (result?"failed\n":"passed\n");
  if(result) success = false;
#endif // TEUCHOS_DEBUG

  RCP<const Thyra::LinearOpBase<Scalar> >
    nullOp = null;

  if (nonnull(out)) *out << "\nCreating a blocked 2x2 linear operator A9 = [ A6, A1^H; A1, null ] ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A9 = Thyra::block2x2<Scalar>(
      A6,  adjoint(A1)
      ,A1, nullOp
      );
  if (nonnull(out)) *out << "\nA9 =\n" << describe(*A9,verbLevel);

  if (nonnull(out)) *out << "\nTesting A9 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = symLinearOpTester.check(*A9,out.ptr());
  if(!result) success = false;
  // Note that testing the symmetry above helps to check the transpose mode
  // against the non-transpose mode!

  if (nonnull(out)) *out << "\nCreating a blocked 2x2 linear operator A9_a = [ A6, A1^H; A1, null ] using pre-formed range and domain product spaces ...\n";
  RCP<Thyra::PhysicallyBlockedLinearOpBase<Scalar> >
    A9_a = rcp(new Thyra::DefaultBlockedLinearOp<Scalar>());
  A9_a->beginBlockFill(
    rcp_dynamic_cast<const Thyra::BlockedLinearOpBase<Scalar> >(A9,true)->productRange()
    ,rcp_dynamic_cast<const Thyra::BlockedLinearOpBase<Scalar> >(A9,true)->productDomain()
    );
  A9_a->setBlock(0,0,A6);
  A9_a->setBlock(0,1,adjoint(A1));
  A9_a->setBlock(1,0,A1);
  A9_a->endBlockFill();
  if (nonnull(out)) *out << "\nA9_a =\n" << describe(*A9_a,verbLevel);

  if (nonnull(out)) *out << "\nTesting A9_a ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = symLinearOpTester.check(*A9_a,out.ptr());
  if(!result) success = false;
  // Note that testing the symmetry above helps to check the transpose mode
  // against the non-transpose mode!

  if (nonnull(out)) *out << "\nComparing A9 == A9_a ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.compare(*A9,*A9_a,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating a blocked 2x2 linear operator A9_b = [ A6, A1^H; A1, null ] using flexible fill ...\n";
  RCP<Thyra::PhysicallyBlockedLinearOpBase<Scalar> >
    A9_b = rcp(new Thyra::DefaultBlockedLinearOp<Scalar>());
  A9_b->beginBlockFill();
  A9_b->setBlock(0,0,A6);
  A9_b->setBlock(0,1,adjoint(A1));
  A9_b->setBlock(1,0,A1);
  A9_b->endBlockFill();
  if (nonnull(out)) *out << "\nA9_b =\n" << describe(*A9_b,verbLevel);

  if (nonnull(out)) *out << "\nTesting A9_b ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = symLinearOpTester.check(*A9_b,out.ptr());
  if(!result) success = false;
  // Note that testing the symmetry above helps to check the transpose mode
  // against the non-transpose mode!

  if (nonnull(out)) *out << "\nComparing A9 == A9_b ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.compare(*A9,*A9_b,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating a blocked 2x2 linear operator A9a = [ null, A1^H; A1, null ] ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A9a = Thyra::block2x2<Scalar>(
      nullOp,  adjoint(A1),
      A1,      nullOp
      );
  if (nonnull(out)) *out << "\nA9a =\n" << describe(*A9a,verbLevel);

  if (nonnull(out)) *out << "\nTesting A9a ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = symLinearOpTester.check(*A9a,out.ptr());
  if(!result) success = false;
  // Note that testing the symmetry above helps to check the transpose mode
  // against the non-transpose mode!

#ifdef TEUCHOS_DEBUG
  if (nonnull(out)) *out << "\nCreating an invalid blocked 2x2 operator A9b = [ A6, A1^H; A1, A1 ] (should throw an exception) ...\n\n";
  try {
    RCP<const Thyra::LinearOpBase<Scalar> >
      A9b = Thyra::block2x2<Scalar>(
        A6,  adjoint(A1),
        A1,  A1
        );
    result = true;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(true,out.get()?*out:std::cerr,result)
  if (nonnull(out))
    *out << "\nCaught expected exception : " << (result?"failed\n":"passed\n");
  if(result) success = false;
#endif // TEUCHOS_DEBUG

#ifdef TEUCHOS_DEBUG
  if (nonnull(out)) *out << "\nCreating an invalid blocked 2x2 operator A9c = [ A1, A1 ; null, null ] (should throw an exception) ...\n\n";
  try {
    RCP<const Thyra::LinearOpBase<Scalar> >
      A9c = Thyra::block2x2<Scalar>(
        A1,       A1,
        nullOp,   nullOp
        );
    result = true;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(true,out.get()?*out:std::cerr,result)
  if (nonnull(out))
    *out << "\nCaught expected exception : " << (result?"failed\n":"passed\n");
  if(result) success = false;
#endif // TEUCHOS_DEBUG

#ifdef TEUCHOS_DEBUG
  if (nonnull(out)) *out << "\nCreating an invalid blocked 2x2 operator A9d = [ A1, null; A1, null ] (should throw an exception) ...\n\n";
  try {
    RCP<const Thyra::LinearOpBase<Scalar> >
      A9d = Thyra::block2x2<Scalar>(
        A1,  nullOp,
        A1,  nullOp
        );
    result = true;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(true,out.get()?*out:std::cerr,result)
  if (nonnull(out))
    *out << "\nCaught expected exception : " << (result?"failed\n":"passed\n");
  if(result) success = false;
#endif // TEUCHOS_DEBUG

  if (nonnull(out)) *out << "\nCreating a blocked 2x1 linear operator A10 = [ A6; A1 ] ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A10 = Thyra::block2x1<Scalar>(
      A6,
      A1
      );
  if (nonnull(out)) *out << "\nA10 =\n" << describe(*A10,verbLevel);

  if (nonnull(out)) *out << "\nTesting A10 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A10,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating a blocked 1x2 linear operator A11 = [ A9, A10 ] ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A11 = Thyra::block1x2<Scalar>( A9, A10 );
  if (nonnull(out)) *out << "\nA11 =\n" << describe(*A11,verbLevel);

  if (nonnull(out)) *out << "\nTesting A11 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A11,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating a zero linear operator A12 = 0 (range and domain spaces of origA) ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A12 = Thyra::zero(origA->range(),origA->domain());
  if (nonnull(out)) *out << "\nA12 =\n" << describe(*A12,verbLevel);

  if (nonnull(out)) *out << "\nTesting A12 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.check(*A12,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating a blocked 2x2 linear operator A13 = [ zero, A1^H; A1, zero ] ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A13 = Thyra::block2x2<Scalar>(
      Thyra::zero(A1->domain(),A1->domain()),   adjoint(A1),
      A1,                                       Thyra::zero(A1->range(),A1->range())
      );
  if (nonnull(out)) *out << "\nA13 =\n" << describe(*A13,verbLevel);

  if (nonnull(out)) *out << "\nComparing A9a == A13 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = linearOpTester.compare(*A9a,*A13,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\nCreating a zero linear operator A14 = I (range space of origA) ...\n";
  RCP<const Thyra::LinearOpBase<Scalar> >
    A14 = Thyra::identity(origA->range());
  if (nonnull(out)) *out << "\nA14 =\n" << describe(*A14,verbLevel);

  if (nonnull(out)) *out << "\nTesting A14 ...\n";
  Thyra::seed_randomize<Scalar>(0);
  result = symLinearOpTester.check(*A14,out.ptr());
  if(!result) success = false;

  if (nonnull(out)) *out << "\n*** Leaving run_composite_linear_ops_tests<"<<ST::name()<<">(...) ...\n";

  return success;

} // end run_composite_linear_ops_tests() [Doxygen looks for this!]
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 );
}