C++ Epetra_LinearProblem::GetRHS方法代码示例

void show_matrix(const char *txt, const Epetra_LinearProblem &problem, const Epetra_Comm &comm)
{
  int me = comm.MyPID();

  if (comm.NumProc() > 10){
    if (me == 0){
      std::cout << txt << std::endl;
      std::cout << "Printed matrix format only works for 10 or fewer processes" << std::endl;
    }
    return;
  }

  Epetra_RowMatrix *matrix = problem.GetMatrix();
  Epetra_MultiVector *lhs = problem.GetLHS();
  Epetra_MultiVector *rhs = problem.GetRHS();

  int numRows = matrix->NumGlobalRows();
  int numCols = matrix->NumGlobalCols();

  if ((numRows > 200) || (numCols > 500)){
    if (me == 0){
      std::cerr << txt << std::endl;
      std::cerr << "show_matrix: problem is too large to display" << std::endl;
    }
    return;
  }

  int *myA = new int [numRows * numCols];

  make_my_A(*matrix, myA, comm);

  int *myX = new int [numCols];
  int *myB = new int [numRows];

  memset(myX, 0, sizeof(int) * numCols);
  memset(myB, 0, sizeof(int) * numRows);

  const Epetra_BlockMap &lhsMap = lhs->Map();
  const Epetra_BlockMap &rhsMap = rhs->Map();

  int base = lhsMap.IndexBase();

  for (int j=0; j < lhsMap.NumMyElements(); j++){
    int colGID = lhsMap.GID(j);
    myX[colGID - base] = me + 1;
  }

  for (int i=0; i < rhsMap.NumMyElements(); i++){
    int rowGID = rhsMap.GID(i);
    myB[rowGID - base] = me + 1;
  }

  printMatrix(txt, myA, myX, myB, numRows, numCols, comm);

  delete [] myA;
  delete [] myX;
  delete [] myB;
}

int TestMultiLevelPreconditioner(char ProblemType[],
				 Teuchos::ParameterList & MLList,
				 Epetra_LinearProblem & Problem, double & TotalErrorResidual,
				 double & TotalErrorExactSol,bool cg=false)
{

  Epetra_MultiVector* lhs = Problem.GetLHS();
  Epetra_MultiVector* rhs = Problem.GetRHS();
  Epetra_RowMatrix* A = Problem.GetMatrix();

  // ======================================== //
  // create a rhs corresponding to lhs or 1's //
  // ======================================== //

  lhs->PutScalar(1.0);
  A->Multiply(false,*lhs,*rhs);

  lhs->PutScalar(0.0);

  Epetra_Time Time(A->Comm());

  // =================== //
  // call ML and AztecOO //
  // =================== //

  AztecOO solver(Problem);

  MLList.set("ML output", 10);

  ML_Epetra::MultiLevelPreconditioner * MLPrec = new ML_Epetra::MultiLevelPreconditioner(*A, MLList, true);

  // tell AztecOO to use this preconditioner, then solve
  solver.SetPrecOperator(MLPrec);

  if(cg) solver.SetAztecOption(AZ_solver, AZ_cg);
  else solver.SetAztecOption(AZ_solver, AZ_gmres);
  solver.SetAztecOption(AZ_output, 32);
  solver.SetAztecOption(AZ_kspace, 160);

  solver.Iterate(1550, 1e-12);

  delete MLPrec;

  // ==================================================== //
  // compute difference between exact solution and ML one //
  // ==================================================== //

  double d = 0.0, d_tot = 0.0;

  for( int i=0 ; i<lhs->Map().NumMyElements() ; ++i )
    d += ((*lhs)[0][i] - 1.0) * ((*lhs)[0][i] - 1.0);

  A->Comm().SumAll(&d,&d_tot,1);

  // ================== //
  // compute ||Ax - b|| //
  // ================== //

  double Norm;
  Epetra_Vector Ax(rhs->Map());
  A->Multiply(false, *lhs, Ax);
  Ax.Update(1.0, *rhs, -1.0);
  Ax.Norm2(&Norm);

  string msg = ProblemType;

  if (A->Comm().MyPID() == 0) {
    cout << msg << "......Using " << A->Comm().NumProc() << " processes" << endl;
    cout << msg << "......||A x - b||_2 = " << Norm << endl;
    cout << msg << "......||x_exact - x||_2 = " << sqrt(d_tot) << endl;
    cout << msg << "......Total Time = " << Time.ElapsedTime() << endl;
  }

  TotalErrorExactSol += sqrt(d_tot);
  TotalErrorResidual += Norm;

  return( solver.NumIters() );

}

int TestMultiLevelPreconditioner(char ProblemType[],
				 Teuchos::ParameterList & MLList,
				 Epetra_LinearProblem & Problem, double & TotalErrorResidual,
				 double & TotalErrorExactSol)
{
  
  Epetra_MultiVector* lhs = Problem.GetLHS();
  Epetra_MultiVector* rhs = Problem.GetRHS();
  Epetra_CrsMatrix* A = dynamic_cast<Epetra_CrsMatrix*>(Problem.GetMatrix());
  int PID = A->Comm().MyPID();
  int numProcs = A->Comm().NumProc();
  RCP<const Epetra_RowMatrix> Arcp = Teuchos::rcp(A, false);
  double n1, n2,nf;
  
  // ======================================== //
  // create a rhs corresponding to lhs or 1's //
  // ======================================== //
  
  lhs->PutScalar(1.0);
  A->Multiply(false,*lhs,*rhs);

  lhs->PutScalar(0.0);
  MLList.set("ML output", 0);

  RowMatrixToMatlabFile("mat_f.dat",*A);  
  MultiVectorToMatrixMarketFile("lhs_f.dat",*lhs,0,0,false);
  MultiVectorToMatrixMarketFile("rhs_f.dat",*rhs,0,0,false);

  
  Epetra_Time Time(A->Comm());
  /* Build the Zoltan list - Group #1 */
  ParameterList Zlist1,Sublist1;
  Sublist1.set("DEBUG_LEVEL","0");
  Sublist1.set("NUM_GLOBAL_PARTITIONS","2");
  Zlist1.set("Zoltan",Sublist1);
  
  /* Start Isorropia's Ninja Magic - Group #1 */
  RefCountPtr<Isorropia::Epetra::Partitioner> partitioner1 =
    Isorropia::Epetra::create_partitioner(Arcp, Zlist1);
  Isorropia::Epetra::Redistributor rd1(partitioner1);

  Teuchos::RCP<Epetra_CrsMatrix> ResA1=rd1.redistribute(*A);
  Teuchos::RCP<Epetra_MultiVector> ResX1=rd1.redistribute(*lhs);
  Teuchos::RCP<Epetra_MultiVector> ResB1=rd1.redistribute(*rhs);

  RestrictedCrsMatrixWrapper RW1;
  RW1.restrict_comm(ResA1);
  RestrictedMultiVectorWrapper RX1,RB1;
  RX1.restrict_comm(ResX1);
  RB1.restrict_comm(ResB1);

  /* Build the Zoltan list - Group #2 */
  ParameterList Zlist2,Sublist2;
  Sublist2.set("DEBUG_LEVEL","0");
  if(PID > 1) Sublist2.set("NUM_LOCAL_PARTITIONS","1");
  else Sublist2.set("NUM_LOCAL_PARTITIONS","0");
  Zlist2.set("Zoltan",Sublist2);
    
  /* Start Isorropia's Ninja Magic - Group #2 */
  RefCountPtr<Isorropia::Epetra::Partitioner> partitioner2 =
    Isorropia::Epetra::create_partitioner(Arcp, Zlist2);
  Isorropia::Epetra::Redistributor rd2(partitioner2);

  Teuchos::RCP<Epetra_CrsMatrix> ResA2=rd2.redistribute(*A);
  Teuchos::RCP<Epetra_MultiVector> ResX2=rd2.redistribute(*lhs);
  Teuchos::RCP<Epetra_MultiVector> ResB2=rd2.redistribute(*rhs);

  RestrictedCrsMatrixWrapper RW2;
  RW2.restrict_comm(ResA2);
  RestrictedMultiVectorWrapper RX2,RB2;
  RX2.restrict_comm(ResX2);
  RB2.restrict_comm(ResB2);

  if(RW1.RestrictedProcIsActive()){
    Teuchos::RCP<Epetra_CrsMatrix> SubA1 = RW1.RestrictedMatrix();
    Teuchos::RCP<Epetra_MultiVector> SubX1 = RX1.RestrictedMultiVector();
    Teuchos::RCP<Epetra_MultiVector> SubB1 = RB1.RestrictedMultiVector();    
    ML_Epetra::MultiLevelPreconditioner * SubPrec1 = new ML_Epetra::MultiLevelPreconditioner(*SubA1, MLList, true);        

    Epetra_LinearProblem Problem1(&*SubA1,&*SubX1,&*SubB1);
    AztecOO solver1(Problem1);
    solver1.SetPrecOperator(SubPrec1);  
    solver1.SetAztecOption(AZ_solver, AZ_gmres);
    solver1.SetAztecOption(AZ_output, 32);
    solver1.SetAztecOption(AZ_kspace, 160);  
    solver1.Iterate(1550, 1e-12);
    delete SubPrec1;

  }
  else{
    Teuchos::RCP<Epetra_CrsMatrix> SubA2 = RW2.RestrictedMatrix();
    Teuchos::RCP<Epetra_MultiVector> SubX2 = RX2.RestrictedMultiVector();
    Teuchos::RCP<Epetra_MultiVector> SubB2 = RB2.RestrictedMultiVector();        
    ML_Epetra::MultiLevelPreconditioner * SubPrec2 = new ML_Epetra::MultiLevelPreconditioner(*SubA2, MLList, true);        
    
    Epetra_LinearProblem Problem2(&*SubA2,&*SubX2,&*SubB2);
    AztecOO solver2(Problem2);
    solver2.SetPrecOperator(SubPrec2);  
    solver2.SetAztecOption(AZ_solver, AZ_gmres);
    solver2.SetAztecOption(AZ_output, 32);
//.........这里部分代码省略.........

bool CompareWithAztecOO(Epetra_LinearProblem& Problem, const std::string what,
                       int Overlap, int ival)
{
  using std::cout;
  using std::endl;

  AztecOO AztecOOSolver(Problem);
  AztecOOSolver.SetAztecOption(AZ_solver,AZ_gmres);
  AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
  AztecOOSolver.SetAztecOption(AZ_overlap,Overlap);
  AztecOOSolver.SetAztecOption(AZ_graph_fill,ival);
  AztecOOSolver.SetAztecOption(AZ_poly_ord, ival);
  AztecOOSolver.SetAztecParam(AZ_drop, 0.0);
  AztecOOSolver.SetAztecParam(AZ_athresh, 0.0);
  AztecOOSolver.SetAztecParam(AZ_rthresh, 0.0);

  Epetra_MultiVector& RHS = *(Problem.GetRHS());
  Epetra_MultiVector& LHS = *(Problem.GetLHS());
  Teuchos::RefCountPtr<Epetra_RowMatrix> A = Teuchos::rcp(Problem.GetMatrix(), false);

  LHS.Random();
  A->Multiply(false,LHS,RHS);

  Teuchos::ParameterList List;
  List.set("fact: level-of-fill", ival);
  List.set("relaxation: sweeps", ival);
  List.set("relaxation: damping factor", 1.0);
  List.set("relaxation: zero starting solution", true);

  //default combine mode is as for AztecOO
  List.set("schwarz: combine mode", Zero);

  Epetra_Time Time(A->Comm());

  Teuchos::RefCountPtr<Ifpack_Preconditioner> Prec;

  if (what == "Jacobi") {
    Prec = Teuchos::rcp( new Ifpack_PointRelaxation(&*A) );
    List.set("relaxation: type", "Jacobi");
    AztecOOSolver.SetAztecOption(AZ_precond,AZ_Jacobi);
    AztecOOSolver.SetAztecOption(AZ_reorder,0);
  }
  else if (what == "IC no reord") {
    Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_IC>(&*A,Overlap) );
    AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
    AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_icc);
    AztecOOSolver.SetAztecOption(AZ_reorder,0);
  }
  else if (what == "IC reord") {
    Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_IC>(&*A,Overlap) );
    List.set("schwarz: use reordering", true);
    AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
    AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_icc);
    AztecOOSolver.SetAztecOption(AZ_reorder,1);
  }
  else if (what == "ILU no reord") {
    Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_ILU>(&*A,Overlap) );
    AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
    AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_ilu);
    AztecOOSolver.SetAztecOption(AZ_reorder,0);
  }
  else if (what == "ILU reord") {
    Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_ILU>(&*A,Overlap) );
    List.set("schwarz: use reordering", true);
    AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
    AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_ilu);
    AztecOOSolver.SetAztecOption(AZ_reorder,1);
  }
#ifdef HAVE_IFPACK_AMESOS
  else if (what == "LU") {
    Prec = Teuchos::rcp( new Ifpack_AdditiveSchwarz<Ifpack_Amesos>(&*A,Overlap) );
    List.set("amesos: solver type", "Klu");
    AztecOOSolver.SetAztecOption(AZ_precond,AZ_dom_decomp);
    AztecOOSolver.SetAztecOption(AZ_subdomain_solve,AZ_lu);
  }
#endif
  else {
    cerr << "Option not recognized" << endl;
    exit(EXIT_FAILURE);
  }

  // ==================================== //
  // Solve with AztecOO's preconditioners //
  // ==================================== //

  LHS.PutScalar(0.0);

  Time.ResetStartTime();
  AztecOOSolver.Iterate(150,1e-5);

  if (verbose) {
    cout << endl;
    cout << "==================================================" << endl;
    cout << "Testing `" << what << "', Overlap = "
         << Overlap << ", ival = " << ival << endl;
    cout << endl;
    cout << "[AztecOO] Total time = " << Time.ElapsedTime() << " (s)" << endl;
    cout << "[AztecOO] Residual   = " << AztecOOSolver.TrueResidual() << " (s)" << endl;
    cout << "[AztecOO] Iterations = " << AztecOOSolver.NumIters() << endl;
    cout << endl;
//.........这里部分代码省略.........

// ============================================================================
void
Solve(const Epetra_LinearProblem Problem)
{
  Solve(Problem.GetMatrix(), Problem.GetLHS(), Problem.GetRHS());
}

//.........这里部分代码省略.........

  Comm.Barrier();

  int NumMyElements = 3;
 
  Epetra_Map Map( NumMyElements, 0, Comm );
  
  Epetra_CrsGraph Graph( Copy, Map, 1 );

  int index[2];
  index[0] = 2;
  Graph.InsertGlobalIndices( 0, 1, &index[0] );
  index[0] = 0;
  index[1] = 2;
  Graph.InsertGlobalIndices( 1, 2, &index[0] );
  index[0] = 1;
  Graph.InsertGlobalIndices( 2, 1, &index[0] );

  Graph.FillComplete();
  if (verbose) {
    cout << "***************** PERFORMING BTF TRANSFORM ON CRS_GRAPH *****************" <<endl<<endl;
    cout << "CrsGraph *before* BTF transform: " << endl << endl;
    cout << Graph << endl;
  }

  EpetraExt::AmesosBTF_CrsGraph BTFTrans( true, verbose );
  Epetra_CrsGraph & NewBTFGraph = BTFTrans( Graph );

  if (verbose) {
    cout << "CrsGraph *after* BTF transform: " << endl << endl;
    cout << NewBTFGraph << endl;
  }
	
  // Use BTF graph transformation to solve linear system.
  // Create an Epetra::CrsMatrix
  Epetra_CrsMatrix Matrix( Copy, Graph );
  double value[2];
  index[0] = 2; value[0] = 3.0;
  Matrix.ReplaceMyValues( 0, 1, &value[0], &index[0] );
  index[0] = 0; index[1] = 2;
  value[0] = 2.0; value[1] = 2.5;
  Matrix.ReplaceMyValues( 1, 2, &value[0], &index[0] );
  index[0] = 1; value[0] = 1.0;
  Matrix.ReplaceMyValues( 2, 1, &value[0], &index[0] );
  Matrix.FillComplete();

  // Create the solution and right-hand side vectors.
  Epetra_MultiVector RHS( Map, 1 ), LHS( Map, 1 );
  LHS.PutScalar( 0.0 );
  RHS.ReplaceMyValue( 0, 0, 3.0 );
  RHS.ReplaceMyValue( 1, 0, 4.5 );
  RHS.ReplaceMyValue( 2, 0, 1.0 );
  Epetra_LinearProblem problem( &Matrix, &LHS, &RHS );

  if (verbose) {
    cout << "*************** PERFORMING BTF TRANSFORM ON LINEAR_PROBLEM **************" <<endl<<endl;
    cout << "CrsMatrix *before* BTF transform: " << endl << endl;
    cout << Matrix << endl;
    cout << "MultiVector RHS *before* BTF transform: " << endl << endl;
    RHS.Print( cout );
  }

  // Create the linear problem transform.
  EpetraExt::LinearProblem_GraphTrans * LPTrans =
        new EpetraExt::LinearProblem_GraphTrans(
        *(dynamic_cast<EpetraExt::StructuralSameTypeTransform<Epetra_CrsGraph>*>(&BTFTrans)) );
  Epetra_LinearProblem* tProblem = &((*LPTrans)( problem ));
  LPTrans->fwd();

  if (verbose) {
    cout << "CrsMatrix *after* BTF transform: " << endl << endl;
    dynamic_cast<Epetra_CrsMatrix*>(tProblem->GetMatrix())->Print( cout );
    cout << "MultiVector RHS *after* BTF transform: " << endl << endl;
    tProblem->GetRHS()->Print( cout );
  }

  if (verbose) {
    cout << endl << "*************** PERFORMING REINDEXING ON LINEAR_PROBLEM **************" <<endl<<endl;
  }
  EpetraExt::ViewTransform<Epetra_LinearProblem> * ReIdx_LPTrans =
        new EpetraExt::LinearProblem_Reindex( 0 );

  Epetra_LinearProblem* tProblem2 = &((*ReIdx_LPTrans)( *tProblem ));
  ReIdx_LPTrans->fwd();

  if (verbose) {
    cout << endl << "CrsMatrix *after* BTF transform *and* reindexing: " << endl << endl;
    dynamic_cast<Epetra_CrsMatrix*>(tProblem2->GetMatrix())->Print( cout );
    cout << endl <<"Column Map *before* reindexing: " << endl << endl;
    cout << dynamic_cast<Epetra_CrsMatrix*>(tProblem->GetMatrix())->ColMap() << endl;
    cout << "Column Map *after* reindexing: " << endl << endl;
    cout << dynamic_cast<Epetra_CrsMatrix*>(tProblem2->GetMatrix())->ColMap() << endl;
  }
  
#ifdef EPETRA_MPI
  MPI_Finalize();
#endif
  
  return returnierr;
}

//.........这里部分代码省略.........
  
  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();

int TestMultiLevelPreconditioner(char ProblemType[],
				 Teuchos::ParameterList & MLList,
				 Epetra_LinearProblem & Problem, double & TotalErrorResidual,
				 double & TotalErrorExactSol)
{
  
  Epetra_MultiVector* lhs = Problem.GetLHS();
  Epetra_MultiVector* rhs = Problem.GetRHS();
  Epetra_RowMatrix* A = Problem.GetMatrix();
  
  // ======================================== //
  // create a rhs corresponding to lhs or 1's //
  // ======================================== //
  
  lhs->PutScalar(1.0);
  A->Multiply(false,*lhs,*rhs);

  lhs->PutScalar(0.0);
  
  Epetra_Time Time(A->Comm());

  Epetra_MultiVector lhs2(*lhs);
  Epetra_MultiVector rhs2(*rhs);
  
  // =================== //
  // call ML and AztecOO //
  // =================== //

  AztecOO solver(Problem);
  
  MLList.set("ML output", 0);
  ML_set_random_seed(24601);
  ML_Epetra::MultiLevelPreconditioner * MLPrec = new ML_Epetra::MultiLevelPreconditioner(*A, MLList, true);
  
  // tell AztecOO to use this preconditioner, then solve
  solver.SetPrecOperator(MLPrec);
  
  solver.SetAztecOption(AZ_solver, AZ_gmres);
  solver.SetAztecOption(AZ_output, 32);
  solver.SetAztecOption(AZ_kspace, 160);
  
  solver.Iterate(1550, 1e-12);
  
  delete MLPrec;



  // ================================= //
  // call ML and AztecOO a second time //
  // ================================= // 
  Epetra_LinearProblem Problem2(A,&lhs2,&rhs2);

  AztecOO solver2(Problem2);
  ML_set_random_seed(24601);  
  ML_Epetra::MultiLevelPreconditioner * MLPrec2 = new ML_Epetra::MultiLevelPreconditioner(*A, MLList, true);
  
  // tell AztecOO to use this preconditioner, then solve
  solver2.SetPrecOperator(MLPrec2);
  
  solver2.SetAztecOption(AZ_solver, AZ_gmres);
  solver2.SetAztecOption(AZ_output, 32);
  solver2.SetAztecOption(AZ_kspace, 160);
  
  solver2.Iterate(1550, 1e-12);
  
  
  
  // ==================================================== //
  // compute difference between the two ML solutions //
  // ==================================================== //
  
  double d = 0.0, d_tot = 0.0;
  
  for( int i=0 ; i<lhs->Map().NumMyElements() ; ++i )
    d += ((*lhs)[0][i] - lhs2[0][i]) * ((*lhs)[0][i] - lhs2[0][i]);
  
  A->Comm().SumAll(&d,&d_tot,1);
  string msg = ProblemType;
  if (A->Comm().MyPID() == 0) {
    cout << msg << "......Using " << A->Comm().NumProc() << " processes" << endl;
    cout << msg << "......||x_1 - x_2||_2 = " << sqrt(d_tot) << endl;
    cout << msg << "......Total Time = " << Time.ElapsedTime() << endl;
  }
  
  TotalErrorExactSol += sqrt(d_tot);
  
  return( solver.NumIters() );
  
}

int main(int argc, char** argv) {
#if defined(HAVE_MPI) && defined(HAVE_EPETRA)

  int p, numProcs = 1;
  int localProc = 0;

  //first, set up our MPI environment...
  MPI_Init(&argc, &argv);
  MPI_Comm_rank(MPI_COMM_WORLD, &localProc);
  MPI_Comm_size(MPI_COMM_WORLD, &numProcs);

  int local_n = 600;

  //Create a Epetra_LinearProblem object.

  Epetra_LinearProblem* linprob = 0;
  try {
    linprob = create_epetra_problem(numProcs, localProc, local_n);
  }
  catch(std::exception& exc) {
    std::cout << "linsys example: create_epetra_problem threw exception '"
          << exc.what() << "' on proc " << localProc << std::endl;
    MPI_Finalize();
    return(-1);
  }

  //We'll need a Teuchos::ParameterList object to pass to the
  //Isorropia::Epetra::Partitioner class.
  Teuchos::ParameterList paramlist;

  // If Zoltan is available, the Zoltan package will be used for
  // the partitioning operation. By default, Isorropia selects Zoltan's
  // Hypergraph partitioner. If a method other than Hypergraph is
  // desired, it can be specified by first creating a parameter sublist
  // named "Zoltan", and then setting appropriate Zoltan parameters in
  // that sublist. A sublist is created like this:
  //      Teuchos::ParameterList& sublist = paramlist.sublist("Zoltan");
  //

  // If Zoltan is not available, a simple linear partitioner will be
  // used to partition such that the number of nonzeros is equal (or
  // close to equal) on each processor.


  Epetra_RowMatrix* rowmatrix = linprob->GetMatrix();
  Teuchos::RCP<const Epetra_RowMatrix> rowmat =
    Teuchos::rcp(rowmatrix, false);


  //Now create the partitioner 

  Teuchos::RCP<Isorropia::Epetra::Partitioner> partitioner =
    Teuchos::rcp(new Isorropia::Epetra::Partitioner(rowmat, paramlist));

  //Next create a Redistributor object and use it to create balanced
  //copies of the objects in linprob.

  Isorropia::Epetra::Redistributor rd(partitioner);

  Teuchos::RCP<Epetra_CrsMatrix> bal_matrix;
  Teuchos::RCP<Epetra_MultiVector> bal_x;
  Teuchos::RCP<Epetra_MultiVector> bal_b;

  //Use a try-catch block because Isorropia will throw an exception
  //if it encounters an error.

  if (localProc == 0) {
    std::cout << " calling Isorropia::Epetra::Redistributor::redistribute..."
        << std::endl;
  }

  try {
    bal_matrix = rd.redistribute(*linprob->GetMatrix());
    bal_x = rd.redistribute(*linprob->GetLHS());
    bal_b = rd.redistribute(*linprob->GetRHS());
  }
  catch(std::exception& exc) {
    std::cout << "linsys example: Isorropia::Epetra::Redistributor threw "
         << "exception '" << exc.what() << "' on proc "
         << localProc << std::endl;
    MPI_Finalize();
    return(-1);
  }

  Epetra_LinearProblem balanced_problem(bal_matrix.get(),
                                        bal_x.get(), bal_b.get());


  // Results

  double goalWeight = 1.0 / (double)numProcs;
  double bal0, bal1, cutn0, cutn1, cutl0, cutl1;
  Isorropia::Epetra::CostDescriber default_costs;

  // Balance and cut quality before partitioning

  ispatest::compute_hypergraph_metrics(*(linprob->GetMatrix()), default_costs, goalWeight,
                     bal0, cutn0, cutl0);

  // Balance and cut quality after partitioning
//.........这里部分代码省略.........