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;
}
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", ¶mListFile,
"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 );
}