Thyra ANA Operator/VectorBase Interfaces and Related Software: sillyCgSolve

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// ***********************************************************************
// 
//    Thyra: Interfaces and Support for Abstract Numerical Algorithms
//                 Copyright (2004) Sandia Corporation
// 
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
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// This library is free software; you can redistribute it and/or modify
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// Lesser General Public License for more details.
//  
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// License along with this library; if not, write to the Free Software
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// Questions? Contact Michael A. Heroux (maherou@sandia.gov) 
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#include "MPITridiagLinearOp.hpp"
#include "sillyCgSolve.hpp"
#include "Thyra_VectorStdOps.hpp"
#include "Thyra_TestingTools.hpp"
#include "Thyra_LinearOpTester.hpp"
#include "Teuchos_CommandLineProcessor.hpp"
#include "Teuchos_Time.hpp"
#include "Teuchos_oblackholestream.hpp"

//
// This example program is meant to show how easy it is to create MPI
// Thyra objects and use them with an ANA (CG in this case).
//
// This example uses a silly concrete tridiagonal matrix class called
// MPITridiagLinearOp that demonstrates how to write such
// subclasses.
//
template<class Scalar>
bool runCgSolveExample(
  MPI_Comm                                                       mpiComm
  ,const int                                                     procRank
  ,const int                                                     numProc
  ,const int                                                     localDim
  ,const Scalar                                                  diagScale
  ,const bool                                                    verbose
  ,const bool                                                    dumpAll
  ,const typename Teuchos::ScalarTraits<Scalar>::magnitudeType   tolerance
  ,const int                                                     maxNumIters
  )
{
  using Teuchos::RefCountPtr;
  using Teuchos::rcp;
  typedef Teuchos::ScalarTraits<Scalar> ST;
  typedef typename ST::magnitudeType    ScalarMag;
  bool success = true;
  bool result;
  // Setup the output stream (do output only on root process!)
  Teuchos::oblackholestream black_hole_out;
  std::ostream &out = ( procRank == 0 ? std::cout : black_hole_out );
  if(verbose)
    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                ]
  //       [ -1    a*2  -1            ]
  //  A =  [         .   .    .       ]
  //       [            -1  a*2    -1 ]
  //       [                 -1   a*2 ]
  //
  // (A.1) Create the tridiagonal matrix operator
  if(verbose) out << "\nConstructing tridiagonal matrix A of local dimension = " << localDim
                        << " and diagonal multiplier = " << diagScale << " ...\n";
  const Thyra::Index
    lowerDim = ( procRank == 0         ? localDim - 1 : localDim ),
    upperDim = ( procRank == numProc-1 ? localDim - 1 : localDim );
  std::vector<Scalar> lower(lowerDim), diag(localDim), upper(upperDim);
  const Scalar one = ST::one(), diagTerm = Scalar(2)*diagScale*ST::one();
  int k = 0, kl = 0;
  if(procRank > 0) { lower[kl] = -one; ++kl; };  diag[k] = diagTerm; upper[k] = -one; // First local row
  for( k = 1; k < localDim - 1; ++k, ++kl ) {
    lower[kl] = -one; diag[k] = diagTerm; upper[k] = -one;                            // Middle local rows
  }
  lower[kl] = -one; diag[k] = diagTerm; if(procRank < numProc-1) upper[k] = -one;     // Last local row
  RefCountPtr<const Thyra::LinearOpBase<Scalar> >
    A = rcp(new MPITridiagLinearOp<Scalar>(mpiComm,localDim,&lower[0],&diag[0],&upper[0]));
  if(verbose) out << "\nGlobal dimension of A = " << A->domain()->dim() << std::endl;
  // (A.2) Testing the linear operator constructed linear operator
  if(verbose) out << "\nTesting the constructed linear operator A ...\n";
  Thyra::LinearOpTester<Scalar> linearOpTester;
  linearOpTester.dump_all(dumpAll);
  linearOpTester.set_all_error_tol(tolerance);
  linearOpTester.set_all_warning_tol(ScalarMag(ScalarMag(1e-2)*tolerance));
  linearOpTester.show_all_tests(true);
  linearOpTester.check_adjoint(false);
  linearOpTester.check_for_symmetry(true);
  result = linearOpTester.check(*A,verbose?&out:0);
  if(!result) success = false;
  // (A.3) Create RHS vector b and set to a random value
  RefCountPtr<Thyra::VectorBase<Scalar> > b = createMember(A->range());
  Thyra::seed_randomize<Scalar>(0);
  Thyra::randomize( Scalar(-ST::one()), Scalar(+ST::one()), &*b );
  // (A.4) Create LHS vector x and set to zero
  RefCountPtr<Thyra::VectorBase<Scalar> > x = createMember(A->domain());
  Thyra::assign( &*x, ST::zero() );
  //
  // (B) Solve the linear system with the silly CG solver
  //
  result = sillyCgSolve(*A,*b,maxNumIters,tolerance,&*x,verbose?&out:0);
  if(!result) success = false;
  //
  // (C) Check that the linear system was solved to the specified tolerance
  //
  RefCountPtr<Thyra::VectorBase<Scalar> > r = createMember(A->range());                     
  Thyra::assign(&*r,*b);                                               // r = b
  Thyra::apply(*A,Thyra::NOTRANS,*x,&*r,Scalar(-ST::one()),ST::one()); // r = -A*x + r
  const ScalarMag r_nrm = Thyra::norm(*r), b_nrm = Thyra::norm(*b);
  const ScalarMag rel_err = r_nrm/b_nrm, relaxTol = ScalarMag(10.0)*tolerance;
  result = rel_err <= relaxTol;
  if(!result) success = false;
  if(verbose)
    out
      << "\n||b-A*x||/||b|| = "<<r_nrm<<"/"<<b_nrm<<" = "<<rel_err<<(result?" <= ":" > ")
      <<"10.0*tolerance = "<<relaxTol<<": "<<(result?"passed":"failed")<<std::endl;
  timer.stop();
  if(verbose) out << "\nTotal time = " << timer.totalElapsedTime() << " sec\n";

  return success;
} // end runCgSolveExample()

//
// Actual main driver program
//
int main(int argc, char *argv[])
{

  using Teuchos::CommandLineProcessor;

  bool success = true;
  bool verbose = true;
  bool result;

  MPI_Init(&argc,&argv);

  MPI_Comm mpiComm = MPI_COMM_WORLD;
  int procRank, numProc;
  MPI_Comm_size( mpiComm, &numProc );
  MPI_Comm_rank( mpiComm, &procRank );

  try {

    //
    // Read in command-line options
    //

    int    localDim    = 500;
    double diagScale   = 1.001;
    double tolerance   = 1e-4;
    int    maxNumIters = 300;
    bool   dumpAll     = false;

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

    clp.setOption( "verbose", "quiet", &verbose, "Determines if any output is printed or not." );
    clp.setOption( "local-dim", &localDim, "Local dimension of the linear system." );
    clp.setOption( "diag-scale", &diagScale, "Scaling of the diagonal to improve conditioning." );
    clp.setOption( "tol", &tolerance, "Relative tolerance for linear system solve." );
    clp.setOption( "max-num-iters", &maxNumIters, "Maximum of CG iterations." );
    clp.setOption( "dump-all", "no-dump-all", &dumpAll, "Determines if vectors are printed or not." );

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

    TEST_FOR_EXCEPTION( localDim < 2, std::logic_error, "Error, localDim=" << localDim << " < 2 is not allowed!" );

    // Run using float
    result = runCgSolveExample<float>(mpiComm,procRank,numProc,localDim,diagScale,verbose,dumpAll,tolerance,maxNumIters);
    if(!result) success = false;

    // Run using double
    result = runCgSolveExample<double>(mpiComm,procRank,numProc,localDim,diagScale,verbose,dumpAll,tolerance,maxNumIters);
    if(!result) success = false;

#if defined(HAVE_COMPLEX) && defined(HAVE_TEUCHOS_COMPLEX)

    // Run using std::complex<float>
    result = runCgSolveExample<std::complex<float> >(mpiComm,procRank,numProc,localDim,diagScale,verbose,dumpAll,tolerance,maxNumIters);
    if(!result) success = false;

    // Run using std::complex<double>
    result = runCgSolveExample<std::complex<double> >(mpiComm,procRank,numProc,localDim,diagScale,verbose,dumpAll,tolerance,maxNumIters);
    if(!result) success = false;

#endif    

  }
  catch( const std::exception &excpt ) {
    std::cerr << "*** p="<<procRank<<": Caught standard exception : " << excpt.what() << std::endl;
    success = false;
  }
  catch( ... ) {
    std::cerr << "*** p="<<procRank<<":Caught an unknown exception\n";
    success = false;
  }

  if( verbose && procRank==0 ) {
    if(success) std::cout << "\nAll of the tests seem to have run successfully!\n";
    else        std::cout << "\nOh no! at least one of the tests failed!\n";  
  }
  
  MPI_Finalize();
  
  return success ? 0 : 1;

} // end main()
sillyCgSolve_mpi.cpp
