int
powerMethod (double & lambda, 
             Epetra_CrsMatrix& A, 
             const int niters, 
             const double tolerance,
             const bool verbose)
{
  // In the power iteration, z = A*q.  Thus, q must be in the domain
  // of A, and z must be in the range of A.  The residual vector is of
  // course in the range of A.
  Epetra_Vector q (A.OperatorDomainMap ());
  Epetra_Vector z (A.OperatorRangeMap ());
  Epetra_Vector resid (A.OperatorRangeMap ());

  Epetra_Flops* counter = A.GetFlopCounter();
  if (counter != 0) {
    q.SetFlopCounter(A);
    z.SetFlopCounter(A);
    resid.SetFlopCounter(A);
  }

  // Initialize the starting vector z with random data.
  z.Random();

  double normz, residual;
  int ierr = 1;
  for (int iter = 0; iter < niters; ++iter)
    {
      z.Norm2 (&normz);        // normz  := ||z||_2
      q.Scale (1.0/normz, z);  // q      := z / normz
      A.Multiply(false, q, z); // z      := A * q
      q.Dot(z, &lambda);       // lambda := dot (q, z)

      // Compute the residual vector and display status output every
      // 100 iterations, or if we have reached the maximum number of
      // iterations.
      if (iter % 100 == 0 || iter + 1 == niters)
        {
          resid.Update (1.0, z, -lambda, q, 0.0); // resid := A*q - lambda*q
          resid.Norm2 (&residual);                // residual := ||resid||_2
          if (verbose) 
            cout << "Iter = " << iter << "  Lambda = " << lambda 
                 << "  Residual of A*q - lambda*q = " << residual << endl;
        } 
      if (residual < tolerance) { // We've converged!
        ierr = 0;
        break;
      }
    }
  return ierr;
}
Beispiel #2
0
int main(int argc, char *argv[]) {

#ifdef EPETRA_MPI
  MPI_Init(&argc,&argv);
  Epetra_MpiComm Comm (MPI_COMM_WORLD);
#else
  Epetra_SerialComm Comm;
#endif

  cout << Comm << endl;

  int MyPID = Comm.MyPID();

  bool verbose = false;
  bool verbose1 = true;
  if (MyPID==0) verbose = true;

  if(argc < 2 && verbose) {
    cerr << "Usage: " << argv[0] 
	 << " HB_filename [level_fill [level_overlap [absolute_threshold [ relative_threshold]]]]" << endl
	 << "where:" << endl
	 << "HB_filename        - filename and path of a Harwell-Boeing data set" << endl
	 << "level_fill         - The amount of fill to use for ILU(k) preconditioner (default 0)" << endl
	 << "level_overlap      - The amount of overlap used for overlapping Schwarz subdomains (default 0)" << endl
	 << "absolute_threshold - The minimum value to place on the diagonal prior to factorization (default 0.0)" << endl
	 << "relative_threshold - The relative amount to perturb the diagonal prior to factorization (default 1.0)" << endl << endl
	 << "To specify a non-default value for one of these parameters, you must specify all" << endl
	 << " preceding values but not any subsequent parameters. Example:" << endl
	 << "ifpackHpcSerialMsr.exe mymatrix.hpc 1  - loads mymatrix.hpc, uses level fill of one, all other values are defaults" << endl
	 << endl;
    return(1);

  }

  // Uncomment the next three lines to debug in mpi mode
  //int tmp;
  //if (MyPID==0) cin >> tmp;
  //Comm.Barrier();

  Epetra_Map * readMap;
  Epetra_CrsMatrix * readA; 
  Epetra_Vector * readx; 
  Epetra_Vector * readb;
  Epetra_Vector * readxexact;
   
  // Call routine to read in HB problem
  Trilinos_Util_ReadHb2Epetra(argv[1], Comm, readMap, readA, readx, readb, readxexact);

  // Create uniform distributed map
  Epetra_Map map(readMap->NumGlobalElements(), 0, Comm);

  // Create Exporter to distribute read-in matrix and vectors

  Epetra_Export exporter(*readMap, map);
  Epetra_CrsMatrix A(Copy, map, 0);
  Epetra_Vector x(map);
  Epetra_Vector b(map);
  Epetra_Vector xexact(map);

  Epetra_Time FillTimer(Comm);
  x.Export(*readx, exporter, Add);
  b.Export(*readb, exporter, Add);
  xexact.Export(*readxexact, exporter, Add);
  Comm.Barrier();
  double vectorRedistributeTime = FillTimer.ElapsedTime();
  A.Export(*readA, exporter, Add);
  Comm.Barrier();
  double matrixRedistributeTime = FillTimer.ElapsedTime() - vectorRedistributeTime;
  assert(A.FillComplete()==0);    
  Comm.Barrier();
  double fillCompleteTime = FillTimer.ElapsedTime() - matrixRedistributeTime;
  if (Comm.MyPID()==0)	{
    cout << "\n\n****************************************************" << endl;
    cout << "\n Vector redistribute  time (sec) = " << vectorRedistributeTime<< endl;
    cout << "    Matrix redistribute time (sec) = " << matrixRedistributeTime << endl;
    cout << "    Transform to Local  time (sec) = " << fillCompleteTime << endl<< endl;
  }
  Epetra_Vector tmp1(*readMap);
  Epetra_Vector tmp2(map);
  readA->Multiply(false, *readxexact, tmp1);

  A.Multiply(false, xexact, tmp2);
  double residual;
  tmp1.Norm2(&residual);
  if (verbose) cout << "Norm of Ax from file            = " << residual << endl;
  tmp2.Norm2(&residual);
  if (verbose) cout << "Norm of Ax after redistribution = " << residual << endl << endl << endl;

  //cout << "A from file = " << *readA << endl << endl << endl;

  //cout << "A after dist = " << A << endl << endl << endl;

  delete readA;
  delete readx;
  delete readb;
  delete readxexact;
  delete readMap;

  Comm.Barrier();

  bool smallProblem = false;
  if (A.RowMap().NumGlobalElements()<100) smallProblem = true;

  if (smallProblem)
    cout << "Original Matrix = " << endl << A   << endl;

  x.PutScalar(0.0);

  Epetra_LinearProblem FullProblem(&A, &x, &b);
  double normb, norma;
  b.NormInf(&normb);
  norma = A.NormInf();
  if (verbose)
    cout << "Inf norm of Original Matrix = " << norma << endl
	 << "Inf norm of Original RHS    = " << normb << endl;
  
  Epetra_Time ReductionTimer(Comm);
  Epetra_CrsSingletonFilter SingletonFilter;
  Comm.Barrier();
  double reduceInitTime = ReductionTimer.ElapsedTime();
  SingletonFilter.Analyze(&A);
  Comm.Barrier();
  double reduceAnalyzeTime = ReductionTimer.ElapsedTime() - reduceInitTime;

  if (SingletonFilter.SingletonsDetected())
    cout << "Singletons found" << endl;
  else {
    cout << "Singletons not found" << endl;
    exit(1);
  }
  SingletonFilter.ConstructReducedProblem(&FullProblem);
  Comm.Barrier();
  double reduceConstructTime = ReductionTimer.ElapsedTime() - reduceInitTime;

  double totalReduceTime = ReductionTimer.ElapsedTime();

  if (verbose)
    cout << "\n\n****************************************************" << endl
	 << "    Reduction init  time (sec)           = " << reduceInitTime<< endl
	 << "    Reduction Analyze time (sec)         = " << reduceAnalyzeTime << endl
	 << "    Construct Reduced Problem time (sec) = " << reduceConstructTime << endl
	 << "    Reduction Total time (sec)           = " << totalReduceTime << endl<< endl;

  Statistics(SingletonFilter);

  Epetra_LinearProblem * ReducedProblem = SingletonFilter.ReducedProblem();

  Epetra_CrsMatrix * Ap = dynamic_cast<Epetra_CrsMatrix *>(ReducedProblem->GetMatrix());
  Epetra_Vector * bp = (*ReducedProblem->GetRHS())(0);
  Epetra_Vector * xp = (*ReducedProblem->GetLHS())(0);
  

  if (smallProblem)
    cout << " Reduced Matrix = " << endl << *Ap << endl
	 << " LHS before sol = " << endl << *xp << endl
	 << " RHS            = " << endl << *bp << endl;

  // Construct ILU preconditioner

  double elapsed_time, total_flops, MFLOPs;
  Epetra_Time timer(Comm);

  int LevelFill = 0;
  if (argc > 2)  LevelFill = atoi(argv[2]);
  if (verbose) cout << "Using Level Fill = " << LevelFill << endl;
  int Overlap = 0;
  if (argc > 3) Overlap = atoi(argv[3]);
  if (verbose) cout << "Using Level Overlap = " << Overlap << endl;
  double Athresh = 0.0;
  if (argc > 4) Athresh = atof(argv[4]);
  if (verbose) cout << "Using Absolute Threshold Value of = " << Athresh << endl;

  double Rthresh = 1.0;
  if (argc > 5) Rthresh = atof(argv[5]);
  if (verbose) cout << "Using Relative Threshold Value of = " << Rthresh << endl;

  Ifpack_IlukGraph * IlukGraph = 0;
  Ifpack_CrsRiluk * ILUK = 0;

  if (LevelFill>-1) {
    elapsed_time = timer.ElapsedTime();
    IlukGraph = new Ifpack_IlukGraph(Ap->Graph(), LevelFill, Overlap);
    assert(IlukGraph->ConstructFilledGraph()==0);
    elapsed_time = timer.ElapsedTime() - elapsed_time;
    if (verbose) cout << "Time to construct ILUK graph = " << elapsed_time << endl;


    Epetra_Flops fact_counter;
  
    elapsed_time = timer.ElapsedTime();
    ILUK = new Ifpack_CrsRiluk(*IlukGraph);
    ILUK->SetFlopCounter(fact_counter);
    ILUK->SetAbsoluteThreshold(Athresh);
    ILUK->SetRelativeThreshold(Rthresh);
    //assert(ILUK->InitValues()==0);
    int initerr = ILUK->InitValues(*Ap);
    if (initerr!=0) {
      cout << endl << Comm << endl << "  InitValues error = " << initerr;
      if (initerr==1) cout << "  Zero diagonal found, warning error only";
      cout << endl << endl;
    }
    assert(ILUK->Factor()==0);
    elapsed_time = timer.ElapsedTime() - elapsed_time;
    total_flops = ILUK->Flops();
    MFLOPs = total_flops/elapsed_time/1000000.0;
    if (verbose) cout << "Time to compute preconditioner values = " 
		    << elapsed_time << endl
		    << "MFLOPS for Factorization = " << MFLOPs << endl;
    //cout << *ILUK << endl;
  double Condest;
  ILUK->Condest(false, Condest);

  if (verbose) cout << "Condition number estimate for this preconditioner = " << Condest << endl;
  }
  int Maxiter = 100;
  double Tolerance = 1.0E-8;

  Epetra_Flops counter;
  Ap->SetFlopCounter(counter);
  xp->SetFlopCounter(*Ap);
  bp->SetFlopCounter(*Ap);
  if (ILUK!=0) ILUK->SetFlopCounter(*Ap);

  elapsed_time = timer.ElapsedTime();

  double normreducedb, normreduceda;
  bp->NormInf(&normreducedb);
  normreduceda = Ap->NormInf();
  if (verbose) 
    cout << "Inf norm of Reduced Matrix = " << normreduceda << endl
	 << "Inf norm of Reduced RHS    = " << normreducedb << endl;

  BiCGSTAB(*Ap, *xp, *bp, ILUK, Maxiter, Tolerance, &residual, verbose);

  elapsed_time = timer.ElapsedTime() - elapsed_time;
  total_flops = counter.Flops();
  MFLOPs = total_flops/elapsed_time/1000000.0;
  if (verbose) cout << "Time to compute solution = " 
		    << elapsed_time << endl
		    << "Number of operations in solve = " << total_flops << endl
		    << "MFLOPS for Solve = " << MFLOPs<< endl << endl;

  SingletonFilter.ComputeFullSolution();

  if (smallProblem)
  cout << " Reduced LHS after sol = " << endl << *xp << endl
       << " Full    LHS after sol = " << endl << x << endl
       << " Full  Exact LHS         = " << endl << xexact << endl;

  Epetra_Vector resid(x);

  resid.Update(1.0, x, -1.0, xexact, 0.0); // resid = xcomp - xexact

  resid.Norm2(&residual);
  double normx, normxexact;
  x.Norm2(&normx);
  xexact.Norm2(&normxexact);

  if (verbose) 
    cout << "2-norm of computed solution                               = " << normx << endl
	 << "2-norm of exact solution                                  = " << normxexact << endl
	 << "2-norm of difference between computed and exact solution  = " << residual << endl;
    
  if (verbose1 && residual>1.0e-5) {
    if (verbose)
      cout << "Difference between computed and exact solution appears large..." << endl
	   << "Computing norm of A times this difference.  If this norm is small, then matrix is singular"
	   << endl;
    Epetra_Vector bdiff(b);
    assert(A.Multiply(false, resid, bdiff)==0);
    assert(bdiff.Norm2(&residual)==0);
    if (verbose) 
      cout << "2-norm of A times difference between computed and exact solution  = " << residual << endl;
    
  }
  if (verbose) 
    cout << "********************************************************" << endl
	 << "              Solving again with 2*Ax=2*b" << endl
	 << "********************************************************" << endl;

  A.Scale(1.0); // A = 2*A
  b.Scale(1.0); // b = 2*b
  x.PutScalar(0.0);
  b.NormInf(&normb);
  norma = A.NormInf();
  if (verbose)
    cout << "Inf norm of Original Matrix = " << norma << endl
	 << "Inf norm of Original RHS    = " << normb << endl;
  double updateReducedProblemTime = ReductionTimer.ElapsedTime();
  SingletonFilter.UpdateReducedProblem(&FullProblem);
  Comm.Barrier();
  updateReducedProblemTime = ReductionTimer.ElapsedTime() - updateReducedProblemTime;
  if (verbose)
    cout << "\n\n****************************************************" << endl
	 << "    Update Reduced Problem time (sec)           = " << updateReducedProblemTime<< endl
	 << "****************************************************" << endl;
  Statistics(SingletonFilter);

  if (LevelFill>-1) {

    Epetra_Flops fact_counter;
  
    elapsed_time = timer.ElapsedTime();

    int initerr = ILUK->InitValues(*Ap);
    if (initerr!=0) {
      cout << endl << Comm << endl << "  InitValues error = " << initerr;
      if (initerr==1) cout << "  Zero diagonal found, warning error only";
      cout << endl << endl;
    }
    assert(ILUK->Factor()==0);
    elapsed_time = timer.ElapsedTime() - elapsed_time;
    total_flops = ILUK->Flops();
    MFLOPs = total_flops/elapsed_time/1000000.0;
    if (verbose) cout << "Time to compute preconditioner values = " 
		    << elapsed_time << endl
		    << "MFLOPS for Factorization = " << MFLOPs << endl;
    double Condest;
    ILUK->Condest(false, Condest);
    
    if (verbose) cout << "Condition number estimate for this preconditioner = " << Condest << endl;
  }
  bp->NormInf(&normreducedb);
  normreduceda = Ap->NormInf();
  if (verbose) 
    cout << "Inf norm of Reduced Matrix = " << normreduceda << endl
	 << "Inf norm of Reduced RHS    = " << normreducedb << endl;

  BiCGSTAB(*Ap, *xp, *bp, ILUK, Maxiter, Tolerance, &residual, verbose);

  elapsed_time = timer.ElapsedTime() - elapsed_time;
  total_flops = counter.Flops();
  MFLOPs = total_flops/elapsed_time/1000000.0;
  if (verbose) cout << "Time to compute solution = " 
		    << elapsed_time << endl
		    << "Number of operations in solve = " << total_flops << endl
		    << "MFLOPS for Solve = " << MFLOPs<< endl << endl;

  SingletonFilter.ComputeFullSolution();

  if (smallProblem)
  cout << " Reduced LHS after sol = " << endl << *xp << endl
       << " Full    LHS after sol = " << endl << x << endl
       << " Full  Exact LHS         = " << endl << xexact << endl;

  resid.Update(1.0, x, -1.0, xexact, 0.0); // resid = xcomp - xexact

  resid.Norm2(&residual);
  x.Norm2(&normx);
  xexact.Norm2(&normxexact);

  if (verbose) 
    cout << "2-norm of computed solution                               = " << normx << endl
	 << "2-norm of exact solution                                  = " << normxexact << endl
	 << "2-norm of difference between computed and exact solution  = " << residual << endl;
    
  if (verbose1 && residual>1.0e-5) {
    if (verbose)
      cout << "Difference between computed and exact solution appears large..." << endl
	   << "Computing norm of A times this difference.  If this norm is small, then matrix is singular"
	   << endl;
    Epetra_Vector bdiff(b);
    assert(A.Multiply(false, resid, bdiff)==0);
    assert(bdiff.Norm2(&residual)==0);
    if (verbose) 
      cout << "2-norm of A times difference between computed and exact solution  = " << residual << endl;
    
  }
 


  if (ILUK!=0) delete ILUK;
  if (IlukGraph!=0) delete IlukGraph;
				       
#ifdef EPETRA_MPI
  MPI_Finalize() ;
#endif

return 0 ;
}