test/CrsMatrix/cxx_main.cpp

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//               Epetra: Linear Algebra Services Package
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#include "Epetra_Map.h"
#include "Epetra_Time.h"
#include "Epetra_CrsMatrix.h"
#include "Epetra_Vector.h"
#include "Epetra_Flops.h"
#ifdef EPETRA_MPI
#include "Epetra_MpiComm.h"
#include "mpi.h"
#else
#include "Epetra_SerialComm.h"
#endif
#include "../epetra_test_err.h"
#include "Epetra_Version.h"
 
// prototypes
 
int check(Epetra_CrsMatrix& A, int NumMyRows1, int NumGlobalRows1, int NumMyNonzeros1,
    int NumGlobalNonzeros1, int * MyGlobalElements, bool verbose);
 
int power_method(bool TransA, Epetra_CrsMatrix& A,
     Epetra_Vector& q,
     Epetra_Vector& z,
     Epetra_Vector& resid,
     double * lambda, int niters, double tolerance,
     bool verbose);
 
int check_graph_sharing(Epetra_Comm& Comm);
 
int main(int argc, char *argv[])
{
  int ierr = 0, forierr = 0;
  bool debug = false;
 
#ifdef EPETRA_MPI
 
  // Initialize MPI
 
  MPI_Init(&argc,&argv);
  int rank; // My process ID
 
  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
  Epetra_MpiComm Comm( MPI_COMM_WORLD );
 
#else
 
  int rank = 0;
  Epetra_SerialComm Comm;
 
#endif
 
  bool verbose = false;
 
  // Check if we should print results to standard out
  if (argc>1) if (argv[1][0]=='-' && argv[1][1]=='v') verbose = true;
 
  int verbose_int = verbose ? 1 : 0;
  Comm.Broadcast(&verbose_int, 1, 0);
  verbose = verbose_int==1 ? true : false;
 
 
  //  char tmp;
  //  if (rank==0) cout << "Press any key to continue..."<< std::endl;
  //  if (rank==0) cin >> tmp;
  //  Comm.Barrier();
 
  Comm.SetTracebackMode(0); // This should shut down any error traceback reporting
  int MyPID = Comm.MyPID();
  int NumProc = Comm.NumProc();
 
  if(verbose && MyPID==0)
    cout << Epetra_Version() << std::endl << std::endl;
 
  if (verbose) cout << "Processor "<<MyPID<<" of "<< NumProc
        << " is alive."<<endl;
 
  bool verbose1 = verbose;
 
  // Redefine verbose to only print on PE 0
  if(verbose && rank!=0)
    verbose = false;
 
  int NumMyEquations = 10000;
  int NumGlobalEquations = (NumMyEquations * NumProc) + EPETRA_MIN(NumProc,3);
  if(MyPID < 3)
    NumMyEquations++;
 
  // Construct a Map that puts approximately the same Number of equations on each processor
 
  Epetra_Map Map(NumGlobalEquations, NumMyEquations, 0, Comm);
 
  // Get update list and number of local equations from newly created Map
  int* MyGlobalElements = new int[Map.NumMyElements()];
  Map.MyGlobalElements(MyGlobalElements);
 
  // Create an integer vector NumNz that is used to build the Petra Matrix.
  // NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation on this processor
 
  int* NumNz = new int[NumMyEquations];
 
  // We are building a tridiagonal matrix where each row has (-1 2 -1)
  // So we need 2 off-diagonal terms (except for the first and last equation)
 
  for (int i = 0; i < NumMyEquations; i++)
    if((MyGlobalElements[i] == 0) || (MyGlobalElements[i] == NumGlobalEquations - 1))
      NumNz[i] = 1;
    else
      NumNz[i] = 2;
 
  // Create a Epetra_Matrix
 
  Epetra_CrsMatrix A(Copy, Map, NumNz);
  EPETRA_TEST_ERR(A.IndicesAreGlobal(),ierr);
  EPETRA_TEST_ERR(A.IndicesAreLocal(),ierr);
 
  // Add  rows one-at-a-time
  // Need some vectors to help
  // Off diagonal Values will always be -1
 
 
  double* Values = new double[2];
  Values[0] = -1.0;
  Values[1] = -1.0;
  int* Indices = new int[2];
  double two = 2.0;
  int NumEntries;
 
  forierr = 0;
  for (int i = 0; i < NumMyEquations; i++) {
    if(MyGlobalElements[i] == 0) {
      Indices[0] = 1;
      NumEntries = 1;
    }
    else if (MyGlobalElements[i] == NumGlobalEquations-1) {
      Indices[0] = NumGlobalEquations-2;
      NumEntries = 1;
    }
    else {
      Indices[0] = MyGlobalElements[i]-1;
      Indices[1] = MyGlobalElements[i]+1;
      NumEntries = 2;
    }
    forierr += !(A.InsertGlobalValues(MyGlobalElements[i], NumEntries, Values, Indices)==0);
    forierr += !(A.InsertGlobalValues(MyGlobalElements[i], 1, &two, MyGlobalElements+i)>0); // Put in the diagonal entry
  }
  EPETRA_TEST_ERR(forierr,ierr);
 
  int * indexOffsetTmp;
  int * indicesTmp;
  double * valuesTmp;
  // Finish up
  EPETRA_TEST_ERR(!(A.IndicesAreGlobal()),ierr);
  EPETRA_TEST_ERR(!(A.ExtractCrsDataPointers(indexOffsetTmp, indicesTmp, valuesTmp)==-1),ierr);  // Should fail
  EPETRA_TEST_ERR(!(A.FillComplete(false)==0),ierr);
  EPETRA_TEST_ERR(!(A.ExtractCrsDataPointers(indexOffsetTmp, indicesTmp, valuesTmp)==-1),ierr);  // Should fail
  EPETRA_TEST_ERR(!(A.IndicesAreLocal()),ierr);
  EPETRA_TEST_ERR(A.StorageOptimized(),ierr);
  A.OptimizeStorage();
  EPETRA_TEST_ERR(!(A.StorageOptimized()),ierr);
  EPETRA_TEST_ERR(!(A.ExtractCrsDataPointers(indexOffsetTmp, indicesTmp, valuesTmp)==0),ierr);  // Should succeed
  const Epetra_CrsGraph & GofA = A.Graph();
  EPETRA_TEST_ERR((indicesTmp!=GofA[0] || valuesTmp!=A[0]),ierr); // Extra check to see if operator[] is consistent
  EPETRA_TEST_ERR(A.UpperTriangular(),ierr);
  EPETRA_TEST_ERR(A.LowerTriangular(),ierr);
  
  int NumMyNonzeros = 3 * NumMyEquations;
  if(A.LRID(0) >= 0)
    NumMyNonzeros--; // If I own first global row, then there is one less nonzero
  if(A.LRID(NumGlobalEquations-1) >= 0)
    NumMyNonzeros--; // If I own last global row, then there is one less nonzero
  EPETRA_TEST_ERR(check(A, NumMyEquations, NumGlobalEquations, NumMyNonzeros, 3*NumGlobalEquations-2,
         MyGlobalElements, verbose),ierr);
  forierr = 0;
  for (int i = 0; i < NumMyEquations; i++)
    forierr += !(A.NumGlobalEntries(MyGlobalElements[i])==NumNz[i]+1);
  EPETRA_TEST_ERR(forierr,ierr);
  forierr = 0;
  for (int i = 0; i < NumMyEquations; i++)
    forierr += !(A.NumMyEntries(i)==NumNz[i]+1);
  EPETRA_TEST_ERR(forierr,ierr);
 
  if (verbose) cout << "\n\nNumEntries function check OK" << std::endl<< std::endl;
 
  EPETRA_TEST_ERR(check_graph_sharing(Comm),ierr);
 
  // Create vectors for Power method
 
  Epetra_Vector q(Map);
  Epetra_Vector z(Map);
  Epetra_Vector resid(Map);
 
  // variable needed for iteration
  double lambda = 0.0;
  // int niters = 10000;
  int niters = 200;
  double tolerance = 1.0e-1;
 
  
  // Iterate
 
  Epetra_Flops flopcounter;
  A.SetFlopCounter(flopcounter);
  q.SetFlopCounter(A);
  z.SetFlopCounter(A);
  resid.SetFlopCounter(A);
  
 
  Epetra_Time timer(Comm);
  EPETRA_TEST_ERR(power_method(false, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
  double elapsed_time = timer.ElapsedTime();
  double total_flops = A.Flops() + q.Flops() + z.Flops() + resid.Flops();
  double MFLOPs = total_flops/elapsed_time/1000000.0;
 
  if (verbose) cout << "\n\nTotal MFLOPs for first solve = " << MFLOPs << std::endl<< std::endl;
 
  
  // Solve transpose problem
 
  if (verbose) cout << "\n\nUsing transpose of matrix and solving again (should give same result).\n\n"
        << std::endl;
  // Iterate
  lambda = 0.0;
  flopcounter.ResetFlops();
  timer.ResetStartTime();
  EPETRA_TEST_ERR(power_method(true, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
  elapsed_time = timer.ElapsedTime();
  total_flops = A.Flops() + q.Flops() + z.Flops() + resid.Flops();
  MFLOPs = total_flops/elapsed_time/1000000.0;
 
  if (verbose) cout << "\n\nTotal MFLOPs for transpose solve = " << MFLOPs << std::endl<< endl;
 
 
  // Increase diagonal dominance
 
  if (verbose) cout << "\n\nIncreasing the magnitude of first diagonal term and solving again\n\n"
        << endl;
 
 
  if (A.MyGlobalRow(0)) {
    int numvals = A.NumGlobalEntries(0);
    double * Rowvals = new double [numvals];
    int    * Rowinds = new int    [numvals];
    A.ExtractGlobalRowCopy(0, numvals, numvals, Rowvals, Rowinds); // Get A[0,0]
 
    for (int i=0; i<numvals; i++) if (Rowinds[i] == 0) Rowvals[i] *= 10.0;
 
    A.ReplaceGlobalValues(0, numvals, Rowvals, Rowinds);
    delete [] Rowvals;
    delete [] Rowinds;
  }
  // Iterate (again)
  lambda = 0.0;
  flopcounter.ResetFlops();
  timer.ResetStartTime();
  EPETRA_TEST_ERR(power_method(false, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
  elapsed_time = timer.ElapsedTime();
  total_flops = A.Flops() + q.Flops() + z.Flops() + resid.Flops();
  MFLOPs = total_flops/elapsed_time/1000000.0;
 
  if (verbose) cout << "\n\nTotal MFLOPs for second solve = " << MFLOPs << endl<< endl;
 
 
  // Solve transpose problem
 
  if (verbose) cout << "\n\nUsing transpose of matrix and solving again (should give same result).\n\n"
        << endl;
 
  // Iterate (again)
  lambda = 0.0;
  flopcounter.ResetFlops();
  timer.ResetStartTime();
  EPETRA_TEST_ERR(power_method(true, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
  elapsed_time = timer.ElapsedTime();
  total_flops = A.Flops() + q.Flops() + z.Flops() + resid.Flops();
  MFLOPs = total_flops/elapsed_time/1000000.0;
 
 
  if (verbose) cout << "\n\nTotal MFLOPs for tranpose of second solve = " << MFLOPs << endl<< endl;
 
  if (verbose) cout << "\n\n*****Testing constant entry constructor" << endl<< endl;
 
  Epetra_CrsMatrix AA(Copy, Map, 5);
 
  if (debug) Comm.Barrier();
 
  double dble_one = 1.0;
  for (int i=0; i< NumMyEquations; i++) AA.InsertGlobalValues(MyGlobalElements[i], 1, &dble_one, MyGlobalElements+i);
 
  // Note:  All processors will call the following Insert routines, but only the processor
  //        that owns it will actually do anything
 
  int One = 1;
  if (AA.MyGlobalRow(0)) {
    EPETRA_TEST_ERR(!(AA.InsertGlobalValues(0, 0, &dble_one, &One)==0),ierr);
  }
  else EPETRA_TEST_ERR(!(AA.InsertGlobalValues(0, 1, &dble_one, &One)==-1),ierr);
  EPETRA_TEST_ERR(!(AA.FillComplete(false)==0),ierr);
  EPETRA_TEST_ERR(AA.StorageOptimized(),ierr);
  EPETRA_TEST_ERR(!(AA.UpperTriangular()),ierr);
  EPETRA_TEST_ERR(!(AA.LowerTriangular()),ierr);
 
  if (debug) Comm.Barrier();
  EPETRA_TEST_ERR(check(AA, NumMyEquations, NumGlobalEquations, NumMyEquations, NumGlobalEquations,
         MyGlobalElements, verbose),ierr);
 
  if (debug) Comm.Barrier();
 
  forierr = 0;
  for (int i=0; i<NumMyEquations; i++) forierr += !(AA.NumGlobalEntries(MyGlobalElements[i])==1);
  EPETRA_TEST_ERR(forierr,ierr);
 
  if (verbose) cout << "\n\nNumEntries function check OK" << endl<< endl;
 
  if (debug) Comm.Barrier();
 
  if (verbose) cout << "\n\n*****Testing copy constructor" << endl<< endl;
 
  Epetra_CrsMatrix B(AA);
  EPETRA_TEST_ERR(check(B, NumMyEquations, NumGlobalEquations, NumMyEquations, NumGlobalEquations,
         MyGlobalElements, verbose),ierr);
 
  forierr = 0;
  for (int i=0; i<NumMyEquations; i++) forierr += !(B.NumGlobalEntries(MyGlobalElements[i])==1);
  EPETRA_TEST_ERR(forierr,ierr);
 
  if (verbose) cout << "\n\nNumEntries function check OK" << endl<< endl;
 
  if (debug) Comm.Barrier();
 
  if (verbose) cout << "\n\n*****Testing local view constructor" << endl<< endl;
 
  Epetra_CrsMatrix BV(View, AA.RowMap(), AA.ColMap(), 0);
 
  forierr = 0;
  int* Inds;
  double* Vals;
  for (int i = 0; i < NumMyEquations; i++) {
    forierr += !(AA.ExtractMyRowView(i, NumEntries, Vals, Inds)==0);
    forierr += !(BV.InsertMyValues(i, NumEntries, Vals, Inds)==0);
  }
  BV.FillComplete(false);
  EPETRA_TEST_ERR(check(BV, NumMyEquations, NumGlobalEquations, NumMyEquations, NumGlobalEquations,
                        MyGlobalElements, verbose),ierr);
 
  forierr = 0;
  for (int i=0; i<NumMyEquations; i++) forierr += !(BV.NumGlobalEntries(MyGlobalElements[i])==1);
  EPETRA_TEST_ERR(forierr,ierr);
 
  if (verbose) cout << "\n\nNumEntries function check OK" << endl<< endl;
 
  if (debug) Comm.Barrier();
  if (verbose) cout << "\n\n*****Testing post construction modifications" << endl<< endl;
 
  EPETRA_TEST_ERR(!(B.InsertGlobalValues(0, 1, &dble_one, &One)==-2),ierr);
 
 
  // Release all objects
  delete [] NumNz;
  delete [] Values;
  delete [] Indices;
  delete [] MyGlobalElements;
      
 
  if (verbose1) {
    // Test ostream << operator (if verbose1)
    // Construct a Map that puts 2 equations on each PE
 
    int NumMyElements1 = 2;
    int NumMyEquations1 = NumMyElements1;
    int NumGlobalEquations1 = NumMyEquations1*NumProc;
 
    Epetra_Map Map1(-1, NumMyElements1, 0, Comm);
 
    // Get update list and number of local equations from newly created Map
    int * MyGlobalElements1 = new int[Map1.NumMyElements()];
    Map1.MyGlobalElements(MyGlobalElements1);
 
    // Create an integer vector NumNz that is used to build the Petra Matrix.
    // NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation on this processor
 
    int * NumNz1 = new int[NumMyEquations1];
 
    // We are building a tridiagonal matrix where each row has (-1 2 -1)
    // So we need 2 off-diagonal terms (except for the first and last equation)
 
    for (int i=0; i<NumMyEquations1; i++)
      if (MyGlobalElements1[i]==0 || MyGlobalElements1[i] == NumGlobalEquations1-1)
  NumNz1[i] = 1;
      else
  NumNz1[i] = 2;
 
    // Create a Epetra_Matrix
 
    Epetra_CrsMatrix A1(Copy, Map1, NumNz1);
 
    // Add  rows one-at-a-time
    // Need some vectors to help
    // Off diagonal Values will always be -1
 
 
    double *Values1 = new double[2];
    Values1[0] = -1.0; Values1[1] = -1.0;
    int *Indices1 = new int[2];
    double two1 = 2.0;
    int NumEntries1;
 
    forierr = 0;
    for (int i=0; i<NumMyEquations1; i++)
      {
  if (MyGlobalElements1[i]==0)
    {
      Indices1[0] = 1;
      NumEntries1 = 1;
    }
  else if (MyGlobalElements1[i] == NumGlobalEquations1-1)
    {
      Indices1[0] = NumGlobalEquations1-2;
      NumEntries1 = 1;
    }
  else
    {
      Indices1[0] = MyGlobalElements1[i]-1;
      Indices1[1] = MyGlobalElements1[i]+1;
      NumEntries1 = 2;
    }
  forierr += !(A1.InsertGlobalValues(MyGlobalElements1[i], NumEntries1, Values1, Indices1)==0);
  forierr += !(A1.InsertGlobalValues(MyGlobalElements1[i], 1, &two1, MyGlobalElements1+i)>0); // Put in the diagonal entry
      }
    EPETRA_TEST_ERR(forierr,ierr);
    delete [] Indices1;
    delete [] Values1;
 
    // Finish up
    EPETRA_TEST_ERR(!(A1.FillComplete(false)==0),ierr);
 
    // Test diagonal extraction function
 
    Epetra_Vector checkDiag(Map1);
    EPETRA_TEST_ERR(!(A1.ExtractDiagonalCopy(checkDiag)==0),ierr);
 
    forierr = 0;
    for (int i=0; i<NumMyEquations1; i++) forierr += !(checkDiag[i]==two1);
    EPETRA_TEST_ERR(forierr,ierr);
 
    // Test diagonal replacement method
 
    forierr = 0;
    for (int i=0; i<NumMyEquations1; i++) checkDiag[i]=two1*two1;
    EPETRA_TEST_ERR(forierr,ierr);
 
    EPETRA_TEST_ERR(!(A1.ReplaceDiagonalValues(checkDiag)==0),ierr);
 
    Epetra_Vector checkDiag1(Map1);
    EPETRA_TEST_ERR(!(A1.ExtractDiagonalCopy(checkDiag1)==0),ierr);
 
    forierr = 0;
    for (int i=0; i<NumMyEquations1; i++) forierr += !(checkDiag[i]==checkDiag1[i]);
    EPETRA_TEST_ERR(forierr,ierr);
 
    if (verbose) cout << "\n\nDiagonal extraction and replacement OK.\n\n" << endl;
 
    double orignorm = A1.NormOne();
    EPETRA_TEST_ERR(!(A1.Scale(4.0)==0),ierr);
    EPETRA_TEST_ERR(!(A1.NormOne()!=orignorm),ierr);
 
    if (verbose) cout << "\n\nMatrix scale OK.\n\n" << endl;
 
    if (verbose) cout << "\n\nPrint out tridiagonal matrix, each part on each processor.\n\n" << endl;
    cout << A1 << endl;
 
 
  // Release all objects
  delete [] NumNz1;
  delete [] MyGlobalElements1;
 
  }
 
  if (verbose) cout << "\n\n*****Testing LeftScale and RightScale" << endl << endl;
 
  int NumMyElements2 = 7;
  int NumMyRows2 = 1;//This value should not be changed without editing the
    // code below.
  Epetra_Map RowMap(-1,NumMyRows2,0,Comm);
  Epetra_Map ColMap(NumMyElements2,NumMyElements2,0,Comm);
  // The DomainMap needs to be different from the ColMap for the test to
  // be meaningful.
  Epetra_Map DomainMap(NumMyElements2,0,Comm);
  int NumMyRangeElements2 = 0;
  // We need to distribute the elements differently for the range map also.
  if (MyPID % 2 == 0)
    NumMyRangeElements2 = NumMyRows2*2; //put elements on even number procs
  if (NumProc % 2 == 1 && MyPID == NumProc-1)
    NumMyRangeElements2 = NumMyRows2; //If number of procs is odd, put
      // the last NumMyElements2 elements on the last proc
  Epetra_Map RangeMap(-1,NumMyRangeElements2,0,Comm);
  Epetra_CrsMatrix A2(Copy,RowMap,ColMap,NumMyElements2);
  double * Values2 = new double[NumMyElements2];
  int * Indices2 = new int[NumMyElements2];
 
  for (int i=0; i<NumMyElements2; i++) {
    Values2[i] = i+MyPID;
    Indices2[i]=i;
  }
 
  A2.InsertMyValues(0,NumMyElements2,Values2,Indices2);
  A2.FillComplete(DomainMap,RangeMap,false);
  Epetra_CrsMatrix A2copy(A2);
 
  double * RowLeftScaleValues = new double[NumMyRows2];
  double * ColRightScaleValues = new double[NumMyElements2];
  int RowLoopLength = RowMap.MaxMyGID()-RowMap.MinMyGID()+1;
  for (int i=0; i<RowLoopLength; i++)
    RowLeftScaleValues[i] = (i + RowMap.MinMyGID() ) % 2 + 1;
  // For the column map, all procs own all elements
  for (int  i=0; i<NumMyElements2;i++)
    ColRightScaleValues[i] = i % 2 + 1;
 
  int RangeLoopLength = RangeMap.MaxMyGID()-RangeMap.MinMyGID()+1;
  double * RangeLeftScaleValues = new double[RangeLoopLength];
  int DomainLoopLength = DomainMap.MaxMyGID()-DomainMap.MinMyGID()+1;
   double * DomainRightScaleValues = new double[DomainLoopLength];
  for (int i=0; i<RangeLoopLength; i++)
    RangeLeftScaleValues[i] = 1.0/((i + RangeMap.MinMyGID() ) % 2 + 1);
  for (int  i=0; i<DomainLoopLength;i++)
    DomainRightScaleValues[i] = 1.0/((i + DomainMap.MinMyGID() ) % 2 + 1);
 
  Epetra_Vector xRow(View,RowMap,RowLeftScaleValues);
  Epetra_Vector xCol(View,ColMap,ColRightScaleValues);
  Epetra_Vector xRange(View,RangeMap,RangeLeftScaleValues);
  Epetra_Vector xDomain(View,DomainMap,DomainRightScaleValues);
 
  double A2infNorm = A2.NormInf();
  double A2oneNorm = A2.NormOne();
 
  if (verbose1) cout << A2;
  EPETRA_TEST_ERR(A2.LeftScale(xRow),ierr);
  double A2infNorm1 = A2.NormInf();
  double A2oneNorm1 = A2.NormOne();
  bool ScalingBroke = false;
  if (A2infNorm1>2*A2infNorm||A2infNorm1<A2infNorm) {
    EPETRA_TEST_ERR(-31,ierr);
    ScalingBroke = true;
  }
  if (A2oneNorm1>2*A2oneNorm||A2oneNorm1<A2oneNorm) {
 
    EPETRA_TEST_ERR(-32,ierr);
    ScalingBroke = true;
  }
  if (verbose1) cout << A2;
  EPETRA_TEST_ERR(A2.RightScale(xCol),ierr);
  double A2infNorm2 = A2.NormInf();
  double A2oneNorm2 = A2.NormOne();
  if (A2infNorm2>=2*A2infNorm1||A2infNorm2<=A2infNorm1) {
    EPETRA_TEST_ERR(-33,ierr);
    ScalingBroke = true;
  }
  if (A2oneNorm2>2*A2oneNorm1||A2oneNorm2<=A2oneNorm1) {
    EPETRA_TEST_ERR(-34,ierr);
    ScalingBroke = true;
  }
  if (verbose1) cout << A2;
  EPETRA_TEST_ERR(A2.RightScale(xDomain),ierr);
  double A2infNorm3 = A2.NormInf();
  double A2oneNorm3 = A2.NormOne();
  // The last two scaling ops cancel each other out
  if (A2infNorm3!=A2infNorm1) {
    EPETRA_TEST_ERR(-35,ierr)
    ScalingBroke = true;
  }
  if (A2oneNorm3!=A2oneNorm1) {
    EPETRA_TEST_ERR(-36,ierr)
    ScalingBroke = true;
  }
  if (verbose1) cout << A2;
  EPETRA_TEST_ERR(A2.LeftScale(xRange),ierr);
  double A2infNorm4 = A2.NormInf();
  double A2oneNorm4 = A2.NormOne();
  // The 4 scaling ops all cancel out
  if (A2infNorm4!=A2infNorm) {
    EPETRA_TEST_ERR(-37,ierr)
    ScalingBroke = true;
  }
  if (A2oneNorm4!=A2oneNorm) {
    EPETRA_TEST_ERR(-38,ierr)
    ScalingBroke = true;
  }
 
  //
  //  Now try changing the values underneath and make sure that
  //  telling one process about the change causes NormInf() and
  //  NormOne() to recompute the norm on all processes.
  //
 
  double *values;
  int num_my_rows = A2.NumMyRows() ;
  int num_entries;
 
  for ( int  i=0 ; i< num_my_rows; i++ ) {
    EPETRA_TEST_ERR( A2.ExtractMyRowView( i, num_entries, values ), ierr );
    for ( int j = 0 ; j <num_entries; j++ ) {
      values[j] *= 2.0;
    }
  }
 
 
  if ( MyPID == 0 )
    A2.SumIntoGlobalValues( 0, 0, 0, 0 ) ;
 
  double A2infNorm5 = A2.NormInf();
  double A2oneNorm5 = A2.NormOne();
 
  if (A2infNorm5!=2.0 * A2infNorm4) {
    EPETRA_TEST_ERR(-39,ierr)
    ScalingBroke = true;
  }
  if (A2oneNorm5!= 2.0 * A2oneNorm4) {
    EPETRA_TEST_ERR(-40,ierr)
    ScalingBroke = true;
  }
 
  //
  //  Restore the values underneath
  //
  for ( int  i=0 ; i< num_my_rows; i++ ) {
    EPETRA_TEST_ERR( A2.ExtractMyRowView( i, num_entries, values ), ierr );
    for ( int j = 0 ; j <num_entries; j++ ) {
      values[j] /= 2.0;
    }
  }
 
  if (verbose1) cout << A2;
 
  if (ScalingBroke) {
    if (verbose) cout << endl << "LeftScale and RightScale tests FAILED" << endl << endl;
  }
  else {
    if (verbose) cout << endl << "LeftScale and RightScale tests PASSED" << endl << endl;
  }
 
  Comm.Barrier();
 
  if (verbose) cout << "\n\n*****Testing InvRowMaxs and InvColMaxs" << endl << endl;
 
  if (verbose1) cout << A2 << endl;
  EPETRA_TEST_ERR(A2.InvRowMaxs(xRow),ierr);
  EPETRA_TEST_ERR(A2.InvRowMaxs(xRange),ierr);
  if (verbose1) cout << xRow << endl << xRange << endl;
 
  if (verbose) cout << "\n\n*****Testing InvRowSums and InvColSums" << endl << endl;
  bool InvSumsBroke = false;
// Works!
  EPETRA_TEST_ERR(A2.InvRowSums(xRow),ierr);
  if (verbose1) cout << xRow;
  EPETRA_TEST_ERR(A2.LeftScale(xRow),ierr);
  float A2infNormFloat = A2.NormInf();
  if (verbose1) cout << A2 << endl;
  if (fabs(1.0-A2infNormFloat) > 1.e-5) {
    EPETRA_TEST_ERR(-41,ierr);
    InvSumsBroke = true;
  }
 
  // Works
  int expectedcode = 1;
  if (Comm.NumProc()>1) expectedcode = 0;
  EPETRA_TEST_ERR(!(A2.InvColSums(xDomain)==expectedcode),ierr); // This matrix has a single row, the first column has a zero, so a warning is issued.
  if (verbose1) cout << xDomain << endl;
  EPETRA_TEST_ERR(A2.RightScale(xDomain),ierr);
  float A2oneNormFloat2 = A2.NormOne();
  if (verbose1) cout << A2;
  if (fabs(1.0-A2oneNormFloat2)>1.e-5) {
    EPETRA_TEST_ERR(-42,ierr)
    InvSumsBroke = true;
  }
 
// Works!
  EPETRA_TEST_ERR(A2.InvRowSums(xRange),ierr);
 
  if (verbose1) cout << xRange;
  EPETRA_TEST_ERR(A2.LeftScale(xRange),ierr);
  float A2infNormFloat2 = A2.NormInf(); // We use a float so that rounding error
  // will not prevent the sum from being 1.0.
  if (verbose1) cout << A2;
  if (fabs(1.0-A2infNormFloat2)>1.e-5) {
    cout << "InfNorm should be = 1, but InfNorm = " << A2infNormFloat2 << endl;
    EPETRA_TEST_ERR(-43,ierr);
    InvSumsBroke = true;
  }
 
  // Doesn't work - may not need this test because column ownership is not unique
  /*  EPETRA_TEST_ERR(A2.InvColSums(xCol),ierr);
cout << xCol;
  EPETRA_TEST_ERR(A2.RightScale(xCol),ierr);
  float A2oneNormFloat = A2.NormOne();
cout << A2;
  if (fabs(1.0-A2oneNormFloat)>1.e-5) {
    EPETRA_TEST_ERR(-44,ierr);
    InvSumsBroke = true;
  }
  */
  delete [] ColRightScaleValues;
  delete [] DomainRightScaleValues;
  if (verbose) cout << "Begin partial sum testing." << endl;
  // Test with a matrix that has partial sums for a subset of the rows
  // on multiple processors. (Except for the serial case, of course.)
  int NumMyRows3 = 2; // Changing this requires further changes below
  int * myGlobalElements = new int[NumMyRows3];
  for (int i=0; i<NumMyRows3; i++) myGlobalElements[i] = MyPID+i;
  Epetra_Map RowMap3(NumProc*2, NumMyRows3, myGlobalElements, 0, Comm);
  int NumMyElements3 = 5;
  Epetra_CrsMatrix A3(Copy, RowMap3, NumMyElements3);
  double * Values3 = new double[NumMyElements3];
  int * Indices3 = new int[NumMyElements3];
  for (int i=0; i < NumMyElements3; i++) {
    Values3[i] = (int) (MyPID + (i+1));
    Indices3[i]=i;
  }
  for (int i=0; i<NumMyRows3; i++) {
    A3.InsertGlobalValues(myGlobalElements[i],NumMyElements3,Values3,Indices3);
  }
  Epetra_Map RangeMap3(NumProc+1, 0, Comm);
  Epetra_Map DomainMap3(NumMyElements3, 0, Comm);
  EPETRA_TEST_ERR(A3.FillComplete(DomainMap3, RangeMap3,false),ierr);
  if (verbose1) cout << A3;
  Epetra_Vector xRange3(RangeMap3,false);
  Epetra_Vector xDomain3(DomainMap3,false);
 
  EPETRA_TEST_ERR(A3.InvRowSums(xRange3),ierr);
 
  if (verbose1) cout << xRange3;
  EPETRA_TEST_ERR(A3.LeftScale(xRange3),ierr);
  float A3infNormFloat = A3.NormInf();
  if (verbose1) cout << A3;
  if (1.0!=A3infNormFloat) {
    cout << "InfNorm should be = 1, but InfNorm = " << A3infNormFloat <<endl;
    EPETRA_TEST_ERR(-61,ierr);
    InvSumsBroke = true;
  }
  // we want to take the transpose of our matrix and fill in different values.
  int NumMyColumns3 = NumMyRows3;
  Epetra_Map ColMap3cm(RowMap3);
  Epetra_Map RowMap3cm(A3.ColMap());
 
  Epetra_CrsMatrix A3cm(Copy,RowMap3cm,ColMap3cm,NumProc+1);
  double *Values3cm = new double[NumMyColumns3];
  int * Indices3cm = new int[NumMyColumns3];
  for (int i=0; i<NumMyColumns3; i++) {
    Values3cm[i] = MyPID + i + 1;
    Indices3cm[i]= i + MyPID;
  }
  for (int ii=0; ii<NumMyElements3; ii++) {
    A3cm.InsertGlobalValues(ii, NumMyColumns3, Values3cm, Indices3cm);
  }
 
  // The DomainMap and the RangeMap from the last test will work fine for
  // the RangeMap and DomainMap, respectively, but I will make copies to
  // avaoid confusion when passing what looks like a DomainMap where we
  // need a RangeMap and vice vera.
  Epetra_Map RangeMap3cm(DomainMap3);
  Epetra_Map DomainMap3cm(RangeMap3);
  EPETRA_TEST_ERR(A3cm.FillComplete(DomainMap3cm,RangeMap3cm),ierr);
  if (verbose1) cout << A3cm << endl;
 
  // Again, we can copy objects from the last example.
  //Epetra_Vector xRange3cm(xDomain3); //Don't use at this time
  Epetra_Vector xDomain3cm(DomainMap3cm,false);
 
  EPETRA_TEST_ERR(A3cm.InvColSums(xDomain3cm),ierr);
 
  if (verbose1) cout << xDomain3cm << endl;
 
  EPETRA_TEST_ERR(A3cm.RightScale(xDomain3cm),ierr);
  float A3cmOneNormFloat  = A3cm.NormOne();
  if (verbose1) cout << A3cm << endl;
  if (1.0!=A3cmOneNormFloat) {
    cout << "OneNorm should be = 1, but OneNorm = " << A3cmOneNormFloat << endl;
    EPETRA_TEST_ERR(-62,ierr);
    InvSumsBroke = true;
  }
 
  if (verbose) cout << "End partial sum testing" << endl;
  if (verbose) cout << "Begin replicated testing" << endl;
 
  // We will now view the shared row as a repliated row, rather than one
  // that has partial sums of its entries on mulitple processors.
  // We will reuse much of the data used for the partial sum tesitng.
  Epetra_Vector xRow3(RowMap3,false);
  Epetra_CrsMatrix A4(Copy, RowMap3, NumMyElements3);
  for (int ii=0; ii < NumMyElements3; ii++) {
    Values3[ii] = (int)((ii*.6)+1.0);
  }
  for (int ii=0; ii<NumMyRows3; ii++) {
    A4.InsertGlobalValues(myGlobalElements[ii],NumMyElements3,Values3,Indices3);
  }
  EPETRA_TEST_ERR(A4.FillComplete(DomainMap3, RangeMap3,false),ierr);
  if (verbose1) cout << A4 << endl;
  // The next two lines should be expanded into a verifiable test.
  EPETRA_TEST_ERR(A4.InvRowMaxs(xRow3),ierr);
  EPETRA_TEST_ERR(A4.InvRowMaxs(xRange3),ierr);
  if (verbose1) cout << xRow3 << xRange3;
 
  EPETRA_TEST_ERR(A4.InvRowSums(xRow3),ierr);
  if (verbose1) cout << xRow3;
  EPETRA_TEST_ERR(A4.LeftScale(xRow3),ierr);
  float A4infNormFloat = A4.NormInf();
  if (verbose1) cout << A4;
  if (2.0!=A4infNormFloat && NumProc != 1) {
    if (verbose1) cout << "InfNorm should be = 2 (because one column is replicated on two processors and NormOne() does not handle replication), but InfNorm = " << A4infNormFloat <<endl;
    EPETRA_TEST_ERR(-63,ierr);
    InvSumsBroke = true;
  }
  else if (1.0!=A4infNormFloat && NumProc == 1) {
    if (verbose1) cout << "InfNorm should be = 1, but InfNorm = " << A4infNormFloat <<endl;
    EPETRA_TEST_ERR(-63,ierr);
    InvSumsBroke = true;
  }
 
  Epetra_Vector xCol3cm(ColMap3cm,false);
  Epetra_CrsMatrix A4cm(Copy, RowMap3cm, ColMap3cm, NumProc+1);
  //Use values from A3cm
  for (int ii=0; ii<NumMyElements3; ii++) {
    A4cm.InsertGlobalValues(ii,NumMyColumns3,Values3cm,Indices3cm);
  }
  EPETRA_TEST_ERR(A4cm.FillComplete(DomainMap3cm, RangeMap3cm,false),ierr);
  if (verbose1) cout << A4cm << endl;
  // The next two lines should be expanded into a verifiable test.
  EPETRA_TEST_ERR(A4cm.InvColMaxs(xCol3cm),ierr);
  EPETRA_TEST_ERR(A4cm.InvColMaxs(xDomain3cm),ierr);
  if (verbose1) cout << xCol3cm << xDomain3cm;
 
  EPETRA_TEST_ERR(A4cm.InvColSums(xCol3cm),ierr);
 
  if (verbose1) cout << xCol3cm << endl;
  EPETRA_TEST_ERR(A4cm.RightScale(xCol3cm),ierr);
  float A4cmOneNormFloat = A4cm.NormOne();
  if (verbose1) cout << A4cm << endl;
  if (2.0!=A4cmOneNormFloat && NumProc != 1) {
    if (verbose1) cout << "OneNorm should be = 2 (because one column is replicated on two processors and NormOne() does not handle replication), but OneNorm = " << A4cmOneNormFloat << endl;
    EPETRA_TEST_ERR(-64,ierr);
    InvSumsBroke = true;
  }
  else if (1.0!=A4cmOneNormFloat && NumProc == 1) {
    if (verbose1) cout << "OneNorm should be = 1, but OneNorm = " << A4infNormFloat <<endl;
    EPETRA_TEST_ERR(-64,ierr);
    InvSumsBroke = true;
  }
 
  if (verbose) cout << "End replicated testing" << endl;
 
  if (InvSumsBroke) {
    if (verbose) cout << endl << "InvRowSums tests FAILED" << endl << endl;
  }
  else
    if (verbose) cout << endl << "InvRowSums tests PASSED" << endl << endl;
 
  A3cm.PutScalar(2.0);
  int nnz_A3cm = A3cm.Graph().NumGlobalNonzeros();
  double check_frobnorm = sqrt(nnz_A3cm*4.0);
  double frobnorm = A3cm.NormFrobenius();
 
  bool frobnorm_test_failed = false;
  if (fabs(check_frobnorm-frobnorm) > 5.e-5) {
    frobnorm_test_failed = true;
  }
 
  if (frobnorm_test_failed) {
    if (verbose) std::cout << "Frobenius-norm test FAILED."<<std::endl;
    EPETRA_TEST_ERR(-65, ierr);
  }
 
  // Subcommunicator test - only processor 1 has unknowns
  {
    int rv=0;
    int NumMyRows = (MyPID==0) ? NumGlobalEquations : 0;
    Epetra_Map Map1(-1,NumMyRows, 0, Comm);
 
    Epetra_CrsMatrix *A1 = new Epetra_CrsMatrix(Copy, Map1,0);
    double value = 1.0;
    for(int i=0; i<NumMyRows; i++) {
      int GID = Map1.GID(i);
      EPETRA_TEST_ERR(A1->InsertGlobalValues(GID, 1,&value,&GID),ierr);
    }
    EPETRA_TEST_ERR(A1->FillComplete(),ierr);
 
    Epetra_BlockMap *Map2 = Map1.RemoveEmptyProcesses();
    rv=A1->RemoveEmptyProcessesInPlace(Map2);
    if(rv!=0) {
      if (verbose) std::cout << "Subcommunicator test FAILED."<<std::endl;
      EPETRA_TEST_ERR(-66, ierr);
    }
 
    delete Map2;
  }
 
  delete [] Values2;
  delete [] Indices2;
  delete [] myGlobalElements;
  delete [] Values3;
  delete [] Indices3;
  delete [] Values3cm;
  delete [] Indices3cm;
  delete [] RangeLeftScaleValues;
  delete [] RowLeftScaleValues;
#ifdef EPETRA_MPI
  MPI_Finalize() ;
#endif
 
/* end main
*/
return ierr ;
}
 
int power_method(bool TransA, Epetra_CrsMatrix& A, Epetra_Vector& q, Epetra_Vector& z,
                 Epetra_Vector& resid, double* lambda, int niters, double tolerance, bool verbose)
{
  
  // Fill z with random Numbers
  z.Random();
  
  // variable needed for iteration
  double normz, residual;
 
  int ierr = 1;
  
  for(int iter = 0; iter < niters; iter++) {
    z.Norm2(&normz); // Compute 2-norm of z
    q.Scale(1.0/normz, z);
    A.Multiply(TransA, q, z); // Compute z = A*q // SEGFAULT HAPPENS HERE
    q.Dot(z, lambda); // Approximate maximum eigenvaluE
    if(iter%100==0 || iter+1==niters) {
      resid.Update(1.0, z, -(*lambda), q, 0.0); // Compute A*q - lambda*q
      resid.Norm2(&residual);
      if(verbose) cout << "Iter = " << iter << "  Lambda = " << *lambda
                       << "  Residual of A*q - lambda*q = " << residual << endl;
    }
    if(residual < tolerance) {
      ierr = 0;
      break;
    }
  }
  return(ierr);
}
 
int check(Epetra_CrsMatrix& A, int NumMyRows1, int NumGlobalRows1, int NumMyNonzeros1,
          int NumGlobalNonzeros1, int* MyGlobalElements, bool verbose)
{
  (void)MyGlobalElements;
  int ierr = 0, forierr = 0;
  int NumGlobalIndices;
  int NumMyIndices;
  int* MyViewIndices = 0;
  int* GlobalViewIndices = 0;
  double* MyViewValues = 0;
  double* GlobalViewValues = 0;
  int MaxNumIndices = A.Graph().MaxNumIndices();
  int* MyCopyIndices = new int[MaxNumIndices];
  int* GlobalCopyIndices = new int[MaxNumIndices];
  double* MyCopyValues = new double[MaxNumIndices];
  double* GlobalCopyValues = new double[MaxNumIndices];
 
  // Test query functions
 
  int NumMyRows = A.NumMyRows();
  if (verbose) cout << "\n\nNumber of local Rows = " << NumMyRows << endl<< endl;
 
  EPETRA_TEST_ERR(!(NumMyRows==NumMyRows1),ierr);
 
  int NumMyNonzeros = A.NumMyNonzeros();
  if (verbose) cout << "\n\nNumber of local Nonzero entries = " << NumMyNonzeros << endl<< endl;
 
  EPETRA_TEST_ERR(!(NumMyNonzeros==NumMyNonzeros1),ierr);
 
  int NumGlobalRows = A.NumGlobalRows();
  if (verbose) cout << "\n\nNumber of global Rows = " << NumGlobalRows << endl<< endl;
 
  EPETRA_TEST_ERR(!(NumGlobalRows==NumGlobalRows1),ierr);
 
  int NumGlobalNonzeros = A.NumGlobalNonzeros();
  if (verbose) cout << "\n\nNumber of global Nonzero entries = " << NumGlobalNonzeros << endl<< endl;
 
  EPETRA_TEST_ERR(!(NumGlobalNonzeros==NumGlobalNonzeros1),ierr);
 
  // GlobalRowView should be illegal (since we have local indices)
 
  EPETRA_TEST_ERR(!(A.ExtractGlobalRowView(A.RowMap().MaxMyGID(), NumGlobalIndices, GlobalViewValues, GlobalViewIndices)==-2),ierr);
 
  // Other binary tests
 
  EPETRA_TEST_ERR(A.NoDiagonal(),ierr);
  EPETRA_TEST_ERR(!(A.Filled()),ierr);
  EPETRA_TEST_ERR(!(A.MyGRID(A.RowMap().MaxMyGID())),ierr);
  EPETRA_TEST_ERR(!(A.MyGRID(A.RowMap().MinMyGID())),ierr);
  EPETRA_TEST_ERR(A.MyGRID(1+A.RowMap().MaxMyGID()),ierr);
  EPETRA_TEST_ERR(A.MyGRID(-1+A.RowMap().MinMyGID()),ierr);
  EPETRA_TEST_ERR(!(A.MyLRID(0)),ierr);
  EPETRA_TEST_ERR(!(A.MyLRID(NumMyRows-1)),ierr);
  EPETRA_TEST_ERR(A.MyLRID(-1),ierr);
  EPETRA_TEST_ERR(A.MyLRID(NumMyRows),ierr);
 
  forierr = 0;
  for (int i = 0; i < NumMyRows; i++) {
    int Row = A.GRID(i);
    A.ExtractGlobalRowCopy(Row, MaxNumIndices, NumGlobalIndices, GlobalCopyValues, GlobalCopyIndices);
    A.ExtractMyRowView(i, NumMyIndices, MyViewValues, MyViewIndices); // this is where the problem comes from
    forierr += !(NumGlobalIndices == NumMyIndices);
    for(int j = 1; j < NumMyIndices; j++) {
      forierr += !(MyViewIndices[j-1] < MyViewIndices[j]); // this is where the test fails
    }
    for(int j = 0; j < NumGlobalIndices; j++) {
      forierr += !(GlobalCopyIndices[j] == A.GCID(MyViewIndices[j]));
      forierr += !(A.LCID(GlobalCopyIndices[j]) == MyViewIndices[j]);
      forierr += !(GlobalCopyValues[j] == MyViewValues[j]);
    }
  }
  EPETRA_TEST_ERR(forierr,ierr);
 
  forierr = 0;
  for (int i = 0; i < NumMyRows; i++) {
    int Row = A.GRID(i);
    A.ExtractGlobalRowCopy(Row, MaxNumIndices, NumGlobalIndices, GlobalCopyValues, GlobalCopyIndices);
    A.ExtractMyRowCopy(i, MaxNumIndices, NumMyIndices, MyCopyValues, MyCopyIndices);
    forierr += !(NumGlobalIndices == NumMyIndices);
    for (int j = 1; j < NumMyIndices; j++)
      forierr += !(MyCopyIndices[j-1] < MyCopyIndices[j]);
    for (int j = 0; j < NumGlobalIndices; j++) {
      forierr += !(GlobalCopyIndices[j] == A.GCID(MyCopyIndices[j]));
      forierr += !(A.LCID(GlobalCopyIndices[j]) == MyCopyIndices[j]);
      forierr += !(GlobalCopyValues[j] == MyCopyValues[j]);
    }
 
  }
  EPETRA_TEST_ERR(forierr,ierr);
 
  delete [] MyCopyIndices;
  delete [] GlobalCopyIndices;
  delete [] MyCopyValues;
  delete [] GlobalCopyValues;
 
  if (verbose) cout << "\n\nRows sorted check OK" << endl<< endl;
 
  return (ierr);
}
 
int check_graph_sharing(Epetra_Comm& Comm)
{
  int numLocalElems = 5;
  int localProc = Comm.MyPID();
  int firstElem = localProc*numLocalElems;
  int err;
  Epetra_Map map(-1, numLocalElems, 0, Comm);
 
  Epetra_CrsMatrix* A = new Epetra_CrsMatrix(Copy, map, 1);
 
  for (int i=0; i<numLocalElems; ++i) {
    int row = firstElem+i;
    int col = row;
    double val = 1.0;
 
    err = A->InsertGlobalValues(row, 1, &val, &col);
    if (err != 0) {
      cerr << "A->InsertGlobalValues("<<row<<") returned err="<<err<<endl;
      return(err);
    }
  }
 
  A->FillComplete(false);
 
  Epetra_CrsMatrix B(Copy, A->Graph());
 
  delete A;
 
  for (int i=0; i<numLocalElems; ++i) {
    int row = firstElem+i;
    int col = row;
    double val = 1.0;
 
    err = B.ReplaceGlobalValues(row, 1, &val, &col);
    if (err != 0) {
      cerr << "B.InsertGlobalValues("<<row<<") returned err="<<err<<endl;
      return(err);
    }
  }
 
  return(0);
}