Пример #1
0
int SchwarzSolver::solve()
{
  // compute some statistics for the original problem
  double condest = -1;
  Epetra_LinearProblem problem(_stiffnessMatrix.get(), _lhs.get(), _rhs.get());
  AztecOO solverForConditionEstimate(problem);
  solverForConditionEstimate.SetAztecOption(AZ_solver, AZ_cg_condnum);
  solverForConditionEstimate.ConstructPreconditioner(condest);
  Epetra_RowMatrix *A = problem.GetMatrix();
  double norminf = A->NormInf();
  double normone = A->NormOne();
  if (_printToConsole)
  {
    cout << "\n Inf-norm of stiffness matrix before scaling = " << norminf;
    cout << "\n One-norm of stiffness matrix before scaling = " << normone << endl << endl;
    cout << "Condition number estimate: " << condest << endl;
  }

  AztecOO solver(problem);

  int otherRows = A->NumGlobalRows() - A->NumMyRows();
  int overlapLevel = std::min(otherRows,_overlapLevel);

  solver.SetAztecOption(AZ_precond, AZ_dom_decomp);   // additive schwarz
  solver.SetAztecOption(AZ_overlap, overlapLevel);   // level of overlap for schwarz
  solver.SetAztecOption(AZ_type_overlap, AZ_symmetric);
  solver.SetAztecOption(AZ_solver, AZ_cg_condnum); // more expensive than AZ_cg, but allows estimate of condition #
  solver.SetAztecOption(AZ_subdomain_solve, AZ_ilut); // TODO: look these up (copied from example)
  solver.SetAztecParam(AZ_ilut_fill, 1.0);            // TODO: look these up (copied from example)
  solver.SetAztecParam(AZ_drop, 0.0);                 // TODO: look these up (copied from example)


  int solveResult = solver.Iterate(_maxIters,_tol);
//  int solveResult = solver.AdaptiveIterate(_maxIters,1,_tol); // an experiment (was Iterate())

  norminf = A->NormInf();
  normone = A->NormOne();
  condest = solver.Condest();
  int numIters = solver.NumIters();

  if (_printToConsole)
  {
    cout << "\n Inf-norm of stiffness matrix after scaling = " << norminf;
    cout << "\n One-norm of stiffness matrix after scaling = " << normone << endl << endl;
    cout << "Condition number estimate: " << condest << endl;
    cout << "Num iterations: " << numIters << endl;
  }

  return solveResult;
}
Пример #2
0
int check(Epetra_RowMatrix& A, Epetra_RowMatrix & B, bool verbose)  {

  int ierr = 0;
  EPETRA_TEST_ERR(!A.Comm().NumProc()==B.Comm().NumProc(),ierr);
  EPETRA_TEST_ERR(!A.Comm().MyPID()==B.Comm().MyPID(),ierr);
  EPETRA_TEST_ERR(!A.Filled()==B.Filled(),ierr);
  EPETRA_TEST_ERR(!A.HasNormInf()==B.HasNormInf(),ierr);
  EPETRA_TEST_ERR(!A.LowerTriangular()==B.LowerTriangular(),ierr);
  EPETRA_TEST_ERR(!A.Map().SameAs(B.Map()),ierr);
  EPETRA_TEST_ERR(!A.MaxNumEntries()==B.MaxNumEntries(),ierr);
  EPETRA_TEST_ERR(!A.NumGlobalCols64()==B.NumGlobalCols64(),ierr);
  EPETRA_TEST_ERR(!A.NumGlobalDiagonals64()==B.NumGlobalDiagonals64(),ierr);
  EPETRA_TEST_ERR(!A.NumGlobalNonzeros64()==B.NumGlobalNonzeros64(),ierr);
  EPETRA_TEST_ERR(!A.NumGlobalRows64()==B.NumGlobalRows64(),ierr);
  EPETRA_TEST_ERR(!A.NumMyCols()==B.NumMyCols(),ierr);
  EPETRA_TEST_ERR(!A.NumMyDiagonals()==B.NumMyDiagonals(),ierr);
  EPETRA_TEST_ERR(!A.NumMyNonzeros()==B.NumMyNonzeros(),ierr);
  for (int i=0; i<A.NumMyRows(); i++) {
    int nA, nB;
    A.NumMyRowEntries(i,nA); B.NumMyRowEntries(i,nB);
    EPETRA_TEST_ERR(!nA==nB,ierr);
  }
  EPETRA_TEST_ERR(!A.NumMyRows()==B.NumMyRows(),ierr);
  EPETRA_TEST_ERR(!A.OperatorDomainMap().SameAs(B.OperatorDomainMap()),ierr);
  EPETRA_TEST_ERR(!A.OperatorRangeMap().SameAs(B.OperatorRangeMap()),ierr);
  EPETRA_TEST_ERR(!A.RowMatrixColMap().SameAs(B.RowMatrixColMap()),ierr);
  EPETRA_TEST_ERR(!A.RowMatrixRowMap().SameAs(B.RowMatrixRowMap()),ierr);
  EPETRA_TEST_ERR(!A.UpperTriangular()==B.UpperTriangular(),ierr);
  EPETRA_TEST_ERR(!A.UseTranspose()==B.UseTranspose(),ierr);

  int NumVectors = 5;
  { // No transpose case
    Epetra_MultiVector X(A.OperatorDomainMap(), NumVectors);
    Epetra_MultiVector YA1(A.OperatorRangeMap(), NumVectors);
    Epetra_MultiVector YA2(YA1);
    Epetra_MultiVector YB1(YA1);
    Epetra_MultiVector YB2(YA1);
    X.Random();

    bool transA = false;
    A.SetUseTranspose(transA);
    B.SetUseTranspose(transA);
    A.Apply(X,YA1);
    A.Multiply(transA, X, YA2);
    EPETRA_TEST_ERR(checkMultiVectors(YA1,YA2,"A Multiply and A Apply", verbose),ierr);
    B.Apply(X,YB1);
    EPETRA_TEST_ERR(checkMultiVectors(YA1,YB1,"A Multiply and B Multiply", verbose),ierr);
    B.Multiply(transA, X, YB2);
    EPETRA_TEST_ERR(checkMultiVectors(YA1,YB2,"A Multiply and B Apply", verbose), ierr);

  }
  {// transpose case
    Epetra_MultiVector X(A.OperatorRangeMap(), NumVectors);
    Epetra_MultiVector YA1(A.OperatorDomainMap(), NumVectors);
    Epetra_MultiVector YA2(YA1);
    Epetra_MultiVector YB1(YA1);
    Epetra_MultiVector YB2(YA1);
    X.Random();

    bool transA = true;
    A.SetUseTranspose(transA);
    B.SetUseTranspose(transA);
    A.Apply(X,YA1);
    A.Multiply(transA, X, YA2);
    EPETRA_TEST_ERR(checkMultiVectors(YA1,YA2, "A Multiply and A Apply (transpose)", verbose),ierr);
    B.Apply(X,YB1);
    EPETRA_TEST_ERR(checkMultiVectors(YA1,YB1, "A Multiply and B Multiply (transpose)", verbose),ierr);
    B.Multiply(transA, X,YB2);
    EPETRA_TEST_ERR(checkMultiVectors(YA1,YB2, "A Multiply and B Apply (transpose)", verbose),ierr);

  }

  Epetra_Vector diagA(A.RowMatrixRowMap());
  EPETRA_TEST_ERR(A.ExtractDiagonalCopy(diagA),ierr);
  Epetra_Vector diagB(B.RowMatrixRowMap());
  EPETRA_TEST_ERR(B.ExtractDiagonalCopy(diagB),ierr);
  EPETRA_TEST_ERR(checkMultiVectors(diagA,diagB, "ExtractDiagonalCopy", verbose),ierr);

  Epetra_Vector rowA(A.RowMatrixRowMap());
  EPETRA_TEST_ERR(A.InvRowSums(rowA),ierr);
  Epetra_Vector rowB(B.RowMatrixRowMap());
  EPETRA_TEST_ERR(B.InvRowSums(rowB),ierr)
  EPETRA_TEST_ERR(checkMultiVectors(rowA,rowB, "InvRowSums", verbose),ierr);

  Epetra_Vector colA(A.RowMatrixColMap());
  EPETRA_TEST_ERR(A.InvColSums(colA),ierr);
  Epetra_Vector colB(B.RowMatrixColMap());
  EPETRA_TEST_ERR(B.InvColSums(colB),ierr);
  EPETRA_TEST_ERR(checkMultiVectors(colA,colB, "InvColSums", verbose),ierr);

  EPETRA_TEST_ERR(checkValues(A.NormInf(), B.NormInf(), "NormInf before scaling", verbose), ierr);
  EPETRA_TEST_ERR(checkValues(A.NormOne(), B.NormOne(), "NormOne before scaling", verbose),ierr);

  EPETRA_TEST_ERR(A.RightScale(colA),ierr);
  EPETRA_TEST_ERR(B.RightScale(colB),ierr);


  EPETRA_TEST_ERR(A.LeftScale(rowA),ierr);
  EPETRA_TEST_ERR(B.LeftScale(rowB),ierr);


  EPETRA_TEST_ERR(checkValues(A.NormInf(), B.NormInf(), "NormInf after scaling", verbose), ierr);
  EPETRA_TEST_ERR(checkValues(A.NormOne(), B.NormOne(), "NormOne after scaling", verbose),ierr);

  vector<double> valuesA(A.MaxNumEntries());
  vector<int> indicesA(A.MaxNumEntries());
  vector<double> valuesB(B.MaxNumEntries());
  vector<int> indicesB(B.MaxNumEntries());
  return(0);
  for (int i=0; i<A.NumMyRows(); i++) {
    int nA, nB;
    EPETRA_TEST_ERR(A.ExtractMyRowCopy(i, A.MaxNumEntries(), nA, &valuesA[0], &indicesA[0]),ierr);
    EPETRA_TEST_ERR(B.ExtractMyRowCopy(i, B.MaxNumEntries(), nB, &valuesB[0], &indicesB[0]),ierr);
    EPETRA_TEST_ERR(!nA==nB,ierr);
    for (int j=0; j<nA; j++) {
      double curVal = valuesA[j];
      int curIndex = indicesA[j];
      bool notfound = true;
      int jj = 0;
      while (notfound && jj< nB) {
	if (!checkValues(curVal, valuesB[jj])) notfound = false;
	jj++;
      }
      EPETRA_TEST_ERR(notfound, ierr);
      vector<int>::iterator p = find(indicesB.begin(),indicesB.end(),curIndex);  // find curIndex in indicesB
      EPETRA_TEST_ERR(p==indicesB.end(), ierr);
    }

  }
  if (verbose) cout << "RowMatrix Methods check OK" << endl;

  return (ierr);
}
Пример #3
0
void AZOO_iterate(double * xsolve, double * b, 
		  int * options, double * params, 
		  double * status, int *proc_config,
		  AZ_MATRIX * Amat,
		  AZ_PRECOND *precond, struct AZ_SCALING *scaling)
{
  (void)precond;
  (void)scaling;
  bool verbose = (options[AZ_output]!=AZ_none); // Print info unless all output is turned off

  Epetra_Comm * comm;
  Epetra_BlockMap * map;
  Epetra_RowMatrix * A;
  Epetra_Vector * px;
  Epetra_Vector * pb;
  int * global_indices;

  int ierr = Aztec2Petra(proc_config, Amat, xsolve, b, comm, map, A, px, pb, &global_indices);
  if (ierr!=0) {
    cerr << "Error detected in Aztec2Petra. Value = " << ierr << endl;
    exit(1);
  }


  Epetra_LinearProblem problem(A, px, pb);

  Epetra_Vector * leftScaleVec = 0;
  Epetra_Vector * rightScaleVec = 0;
  bool doRowScaling = false;
  bool doColScaling = false;
  
  if ((options[AZ_scaling]==AZ_Jacobi) || options[AZ_scaling]==AZ_BJacobi) {
    doRowScaling = true;
    leftScaleVec = new Epetra_Vector(*map);
    A->ExtractDiagonalCopy(*leftScaleVec); // Extract diagonal of matrix
    leftScaleVec->Reciprocal(*leftScaleVec); // invert it
  }

  else if (options[AZ_scaling]==AZ_row_sum) {
    doRowScaling = true;
    leftScaleVec = new Epetra_Vector(*map);
    A->InvRowSums(*leftScaleVec);
  }
  else if (options[AZ_scaling]==AZ_sym_diag) {
    doRowScaling = true;
    doColScaling = true;
    leftScaleVec = new Epetra_Vector(*map);
    A->ExtractDiagonalCopy(*leftScaleVec); // Extract diagonal of matrix

    int length = leftScaleVec->MyLength();
    for (int i=0; i<length; i++) (*leftScaleVec)[i] = sqrt(fabs((*leftScaleVec)[i])); // Take its sqrt

    rightScaleVec = leftScaleVec; // symmetric, so left and right the same
    leftScaleVec->Reciprocal(*leftScaleVec); // invert it
  }
  else if (options[AZ_scaling]==AZ_sym_row_sum) {
    doRowScaling = true;
    doColScaling = true;
    leftScaleVec = new Epetra_Vector(*map);
    A->InvRowSums(*leftScaleVec);
    int length = leftScaleVec->MyLength();
    for (int i=0; i<length; i++) (*leftScaleVec)[i] = sqrt(fabs((*leftScaleVec)[i])); // Take its sqrt

    rightScaleVec = leftScaleVec; // symmetric, so left and right the same
  }
  if ((doRowScaling || doColScaling) && verbose) {
    double norminf = A->NormInf();
    double normone = A->NormOne();
    if (comm->MyPID()==0) 
      cout << "\n Inf-norm of A before scaling = " << norminf 
	   << "\n One-norm of A before scaling = " << normone<< endl << endl;
  }
  if (doRowScaling) problem.LeftScale(*leftScaleVec);
  if (doColScaling) problem.RightScale(*rightScaleVec);

  if ((doRowScaling || doColScaling) && verbose) {
    double norminf = A->NormInf();
    double normone = A->NormOne();
    if (comm->MyPID()==0) 
      cout << "\n Inf-norm of A after  scaling = " << norminf  
	   << "\n One-norm of A after  scaling = " << normone << endl << endl;
  }



  AztecOO solver(problem);

  solver.SetAllAztecParams(params); // set all AztecOO params with user-provided params
  solver.SetAllAztecOptions(options); // set all AztecOO options with user-provided options

  solver.CheckInput();
  solver.SetAztecOption(AZ_scaling, AZ_none); // Always must have scaling off
  solver.Iterate(options[AZ_max_iter], params[AZ_tol]);
  solver.GetAllAztecStatus(status);
  
  if (doColScaling) {
    rightScaleVec->Reciprocal(*rightScaleVec);
    problem.RightScale(*rightScaleVec);
  }
  if (doRowScaling) {
    leftScaleVec->Reciprocal(*leftScaleVec);
    problem.LeftScale(*leftScaleVec);
  }

  if ((rightScaleVec!=0) && (rightScaleVec!=leftScaleVec)) delete rightScaleVec;
  if (leftScaleVec!=0) delete leftScaleVec;

  delete pb; // These are all objects created here and we have to delete them
  delete px;
  delete A;
  delete map;
  delete comm;
  if (global_indices!=0) AZ_free((void *) global_indices); // Note: we used a special version of free here

  return;
}
Пример #4
0
int Ifpack_Analyze(const Epetra_RowMatrix& A, const bool Cheap,
                   const int NumPDEEqns)
{

  int NumMyRows = A.NumMyRows();
  long long NumGlobalRows = A.NumGlobalRows64();
  long long NumGlobalCols = A.NumGlobalCols64();
  long long MyBandwidth = 0, GlobalBandwidth;
  long long MyLowerNonzeros = 0, MyUpperNonzeros = 0;
  long long GlobalLowerNonzeros, GlobalUpperNonzeros;
  long long MyDiagonallyDominant = 0, GlobalDiagonallyDominant;
  long long MyWeaklyDiagonallyDominant = 0, GlobalWeaklyDiagonallyDominant;
  double MyMin, MyAvg, MyMax;
  double GlobalMin, GlobalAvg, GlobalMax;
  long long GlobalStorage;

  bool verbose = (A.Comm().MyPID() == 0);

  GlobalStorage = sizeof(int*) * NumGlobalRows +
    sizeof(int) * A.NumGlobalNonzeros64() +
    sizeof(double) * A.NumGlobalNonzeros64();

  if (verbose) {
    print();
    Ifpack_PrintLine();
    print<const char*>("Label", A.Label());
    print<long long>("Global rows", NumGlobalRows);
    print<long long>("Global columns", NumGlobalCols);
    print<long long>("Stored nonzeros", A.NumGlobalNonzeros64());
    print<long long>("Nonzeros / row", A.NumGlobalNonzeros64() / NumGlobalRows);
    print<double>("Estimated storage (Mbytes)", 1.0e-6 * GlobalStorage);
  }

  long long NumMyActualNonzeros = 0, NumGlobalActualNonzeros;
  long long NumMyEmptyRows = 0, NumGlobalEmptyRows;
  long long NumMyDirichletRows = 0, NumGlobalDirichletRows;

  std::vector<int> colInd(A.MaxNumEntries());
  std::vector<double> colVal(A.MaxNumEntries());

  Epetra_Vector Diag(A.RowMatrixRowMap());
  Epetra_Vector RowSum(A.RowMatrixRowMap());
  Diag.PutScalar(0.0);
  RowSum.PutScalar(0.0);

  for (int i = 0 ; i < NumMyRows ; ++i) {

    long long GRID = A.RowMatrixRowMap().GID64(i);
    int Nnz;
    IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
                                      &colVal[0],&colInd[0]));

    if (Nnz == 0)
      NumMyEmptyRows++;

    if (Nnz == 1)
      NumMyDirichletRows++;

    for (int j = 0 ; j < Nnz ; ++j) {

      double v = colVal[j];
      if (v < 0) v = -v;
      if (colVal[j] != 0.0)
        NumMyActualNonzeros++;

      long long GCID = A.RowMatrixColMap().GID64(colInd[j]);

      if (GCID != GRID)
        RowSum[i] += v;
      else
        Diag[i] = v;

      if (GCID < GRID)
        MyLowerNonzeros++;
      else if (GCID > GRID)
        MyUpperNonzeros++;
      long long b = GCID - GRID;
      if (b < 0) b = -b;
      if (b > MyBandwidth)
        MyBandwidth = b;
    }

    if (Diag[i] > RowSum[i])
      MyDiagonallyDominant++;

    if (Diag[i] >= RowSum[i])
      MyWeaklyDiagonallyDominant++;

    RowSum[i] += Diag[i];
  }

  // ======================== //
  // summing up global values //
  // ======================== //

  A.Comm().SumAll(&MyDiagonallyDominant,&GlobalDiagonallyDominant,1);
  A.Comm().SumAll(&MyWeaklyDiagonallyDominant,&GlobalWeaklyDiagonallyDominant,1);
  A.Comm().SumAll(&NumMyActualNonzeros, &NumGlobalActualNonzeros, 1);
  A.Comm().SumAll(&NumMyEmptyRows, &NumGlobalEmptyRows, 1);
  A.Comm().SumAll(&NumMyDirichletRows, &NumGlobalDirichletRows, 1);
  A.Comm().SumAll(&MyBandwidth, &GlobalBandwidth, 1);
  A.Comm().SumAll(&MyLowerNonzeros, &GlobalLowerNonzeros, 1);
  A.Comm().SumAll(&MyUpperNonzeros, &GlobalUpperNonzeros, 1);
  A.Comm().SumAll(&MyDiagonallyDominant, &GlobalDiagonallyDominant, 1);
  A.Comm().SumAll(&MyWeaklyDiagonallyDominant, &GlobalWeaklyDiagonallyDominant, 1);

  double NormOne = A.NormOne();
  double NormInf = A.NormInf();
  double NormF   = Ifpack_FrobeniusNorm(A);

  if (verbose) {
    print();
    print<long long>("Actual nonzeros", NumGlobalActualNonzeros);
    print<long long>("Nonzeros in strict lower part", GlobalLowerNonzeros);
    print<long long>("Nonzeros in strict upper part", GlobalUpperNonzeros);
    print();
    print<long long>("Empty rows", NumGlobalEmptyRows,
               100.0 * NumGlobalEmptyRows / NumGlobalRows);
    print<long long>("Dirichlet rows", NumGlobalDirichletRows,
               100.0 * NumGlobalDirichletRows / NumGlobalRows);
    print<long long>("Diagonally dominant rows", GlobalDiagonallyDominant,
               100.0 * GlobalDiagonallyDominant / NumGlobalRows);
    print<long long>("Weakly diag. dominant rows",
               GlobalWeaklyDiagonallyDominant,
               100.0 * GlobalWeaklyDiagonallyDominant / NumGlobalRows);
    print();
    print<long long>("Maximum bandwidth", GlobalBandwidth);

    print();
    print("", "one-norm", "inf-norm", "Frobenius", false);
    print("", "========", "========", "=========", false);
    print();

    print<double>("A", NormOne, NormInf, NormF);
  }

  if (Cheap == false) {

    // create A + A^T and A - A^T

    Epetra_FECrsMatrix AplusAT(Copy, A.RowMatrixRowMap(), 0);
    Epetra_FECrsMatrix AminusAT(Copy, A.RowMatrixRowMap(), 0);

#ifndef EPETRA_NO_32BIT_GLOBAL_INDICES
    if(A.RowMatrixRowMap().GlobalIndicesInt()) {
      for (int i = 0 ; i < NumMyRows ; ++i) {

        int GRID = A.RowMatrixRowMap().GID(i);
        assert (GRID != -1);

        int Nnz;
        IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
                                          &colVal[0],&colInd[0]));

        for (int j = 0 ; j < Nnz ; ++j) {

          int GCID         = A.RowMatrixColMap().GID(colInd[j]);
          assert (GCID != -1);

          double plus_val  = colVal[j];
          double minus_val = -colVal[j];

          if (AplusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) {
            IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val));
          }

          if (AplusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&plus_val) != 0) {
            IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GCID,1,&GRID,&plus_val));
          }

          if (AminusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) {
            IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val));
          }

          if (AminusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&minus_val) != 0) {
            IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GCID,1,&GRID,&minus_val));
          }

        }
      }
    }
        else
#endif
#ifndef EPETRA_NO_64BIT_GLOBAL_INDICES
    if(A.RowMatrixRowMap().GlobalIndicesLongLong()) {
      for (int i = 0 ; i < NumMyRows ; ++i) {

        long long GRID = A.RowMatrixRowMap().GID64(i);
        assert (GRID != -1);

        int Nnz;
        IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
                                          &colVal[0],&colInd[0]));

        for (int j = 0 ; j < Nnz ; ++j) {

          long long GCID         = A.RowMatrixColMap().GID64(colInd[j]);
          assert (GCID != -1);

          double plus_val  = colVal[j];
          double minus_val = -colVal[j];

          if (AplusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) {
            IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val));
          }

          if (AplusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&plus_val) != 0) {
            IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GCID,1,&GRID,&plus_val));
          }

          if (AminusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) {
            IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val));
          }

          if (AminusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&minus_val) != 0) {
            IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GCID,1,&GRID,&minus_val));
          }

        }
      }
        }
        else
#endif
      throw "Ifpack_Analyze: GlobalIndices type unknown";

    AplusAT.FillComplete();
    AminusAT.FillComplete();

    AplusAT.Scale(0.5);
    AminusAT.Scale(0.5);

    NormOne = AplusAT.NormOne();
    NormInf = AplusAT.NormInf();
    NormF   = Ifpack_FrobeniusNorm(AplusAT);

    if (verbose) {
      print<double>("A + A^T", NormOne, NormInf, NormF);
    }

    NormOne = AminusAT.NormOne();
    NormInf = AminusAT.NormInf();
    NormF   = Ifpack_FrobeniusNorm(AminusAT);

    if (verbose) {
      print<double>("A - A^T", NormOne, NormInf, NormF);
    }
  }

  if (verbose) {
    print();
    print<const char*>("", "min", "avg", "max", false);
    print<const char*>("", "===", "===", "===", false);
  }

  MyMax = -DBL_MAX;
  MyMin = DBL_MAX;
  MyAvg = 0.0;

  for (int i = 0 ; i < NumMyRows ; ++i) {

    int Nnz;
    IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
                                      &colVal[0],&colInd[0]));

    for (int j = 0 ; j < Nnz ; ++j) {
      MyAvg += colVal[j];
      if (colVal[j] > MyMax) MyMax = colVal[j];
      if (colVal[j] < MyMin) MyMin = colVal[j];
    }
  }

  A.Comm().MaxAll(&MyMax, &GlobalMax, 1);
  A.Comm().MinAll(&MyMin, &GlobalMin, 1);
  A.Comm().SumAll(&MyAvg, &GlobalAvg, 1);
  GlobalAvg /= A.NumGlobalNonzeros64();

  if (verbose) {
    print();
    print<double>(" A(i,j)", GlobalMin, GlobalAvg, GlobalMax);
  }

  MyMax = 0.0;
  MyMin = DBL_MAX;
  MyAvg = 0.0;

  for (int i = 0 ; i < NumMyRows ; ++i) {

    int Nnz;
    IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
                                      &colVal[0],&colInd[0]));

    for (int j = 0 ; j < Nnz ; ++j) {
      double v = colVal[j];
      if (v < 0) v = -v;
      MyAvg += v;
      if (colVal[j] > MyMax) MyMax = v;
      if (colVal[j] < MyMin) MyMin = v;
    }
  }

  A.Comm().MaxAll(&MyMax, &GlobalMax, 1);
  A.Comm().MinAll(&MyMin, &GlobalMin, 1);
  A.Comm().SumAll(&MyAvg, &GlobalAvg, 1);
  GlobalAvg /= A.NumGlobalNonzeros64();

  if (verbose) {
    print<double>("|A(i,j)|", GlobalMin, GlobalAvg, GlobalMax);
  }

  // ================= //
  // diagonal elements //
  // ================= //

  Diag.MinValue(&GlobalMin);
  Diag.MaxValue(&GlobalMax);
  Diag.MeanValue(&GlobalAvg);

  if (verbose) {
    print();
    print<double>(" A(k,k)", GlobalMin, GlobalAvg, GlobalMax);
  }

  Diag.Abs(Diag);
  Diag.MinValue(&GlobalMin);
  Diag.MaxValue(&GlobalMax);
  Diag.MeanValue(&GlobalAvg);
  if (verbose) {
    print<double>("|A(k,k)|", GlobalMin, GlobalAvg, GlobalMax);
  }

  // ============================================== //
  // cycle over all equations for diagonal elements //
  // ============================================== //

  if (NumPDEEqns > 1 ) {

    if (verbose) print();

    for (int ie = 0 ; ie < NumPDEEqns ; ie++) {

      MyMin = DBL_MAX;
      MyMax = -DBL_MAX;
      MyAvg = 0.0;

      for (int i = ie ; i < Diag.MyLength() ; i += NumPDEEqns) {
        double d = Diag[i];
        MyAvg += d;
        if (d < MyMin)
          MyMin = d;
        if (d > MyMax)
          MyMax = d;
      }
      A.Comm().MinAll(&MyMin, &GlobalMin, 1);
      A.Comm().MaxAll(&MyMax, &GlobalMax, 1);
      A.Comm().SumAll(&MyAvg, &GlobalAvg, 1);
      // does not really work fine if the number of global
      // elements is not a multiple of NumPDEEqns
          GlobalAvg /= (Diag.GlobalLength64() / NumPDEEqns);

      if (verbose) {
        char str[80];
        sprintf(str, " A(k,k), eq %d", ie);
        print<double>(str, GlobalMin, GlobalAvg, GlobalMax);
      }
    }
  }

  // ======== //
  // row sums //
  // ======== //

  RowSum.MinValue(&GlobalMin);
  RowSum.MaxValue(&GlobalMax);
  RowSum.MeanValue(&GlobalAvg);

  if (verbose) {
    print();
    print<double>(" sum_j A(k,j)", GlobalMin, GlobalAvg, GlobalMax);
  }

  // ===================================== //
  // cycle over all equations for row sums //
  // ===================================== //

  if (NumPDEEqns > 1 ) {

    if (verbose) print();

    for (int ie = 0 ; ie < NumPDEEqns ; ie++) {

      MyMin = DBL_MAX;
      MyMax = -DBL_MAX;
      MyAvg = 0.0;

      for (int i = ie ; i < Diag.MyLength() ; i += NumPDEEqns) {
        double d = RowSum[i];
        MyAvg += d;
        if (d < MyMin)
          MyMin = d;
        if (d > MyMax)
          MyMax = d;
      }
      A.Comm().MinAll(&MyMin, &GlobalMin, 1);
      A.Comm().MaxAll(&MyMax, &GlobalMax, 1);
      A.Comm().SumAll(&MyAvg, &GlobalAvg, 1);
      // does not really work fine if the number of global
      // elements is not a multiple of NumPDEEqns
          GlobalAvg /= (Diag.GlobalLength64() / NumPDEEqns);

      if (verbose) {
        char str[80];
        sprintf(str, " sum_j A(k,j), eq %d", ie);
        print<double>(str, GlobalMin, GlobalAvg, GlobalMax);
      }
    }
  }

  if (verbose)
    Ifpack_PrintLine();

  return(0);
}