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//
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
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//
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA
// Questions? Contact Michael A. Heroux (maherou@sandia.gov)
//
// ***********************************************************************

// Print out some information about a CRS matrix

#include "float.h"
#include "Epetra_ConfigDefs.h"
#ifdef HAVE_MPI
#include "mpi.h"
#include "Epetra_MpiComm.h"
#else
#include "Epetra_SerialComm.h"
#endif
#include "Epetra_Map.h"
#include "Epetra_Vector.h"
#include "Epetra_CrsMatrix.h"

// ============================================================
// define a class, derived from Epetra_CrsMatrix, which
// initializes the matrix entires. User has to provide
// a valid Epetra_Map in the constructor, plus the diagonal
// value, and the sub- and super-diagonal values.
// ============================================================

class TridiagonalCrsMatrix : public Epetra_CrsMatrix {

public:

TridiagonalCrsMatrix(const Epetra_Map & Map,
double a,
double diag, double c) :
Epetra_CrsMatrix(Copy,Map,3)
{

// global number of rows
int NumGlobalElements = Map.NumGlobalElements();
// local number of rows
int NumMyElements = Map.NumMyElements();
// get update list
int * MyGlobalElements = new int [NumMyElements];
Map.MyGlobalElements( MyGlobalElements );

// Need some vectors to help
// Off diagonal Values will always be -1

double *Values = new double[2];
Values[0] = a; Values[1] = c;
int *Indices = new int[2];
int NumEntries;

for( int i=0 ; i<NumMyElements; ++i ) {
if (MyGlobalElements[i]==0) {
Indices[0] = 1;
NumEntries = 1;
} else if (MyGlobalElements[i] == NumGlobalElements-1) {
Indices[0] = NumGlobalElements-2;
NumEntries = 1;
} else {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
NumEntries = 2;
}
InsertGlobalValues(MyGlobalElements[i], NumEntries, Values, Indices);
// Put in the diagonal entry
InsertGlobalValues(MyGlobalElements[i], 1, &diag, MyGlobalElements+i);
}

// Finish up
FillComplete();

}

};

// =============================================================
// This function print out some information about the input
// matrix. This includes number of rows and columns, some norms,
// few statistics about the nonzero structure of the matrix.
// Some details about the Trilinos storage of the matrix
// are also reported.
//
// Return code:        true if matrix has been printed out
// -----------         false otherwise
//
// Parameters:
// ----------
//
// - Epetra_CrsMatrix  reference to the ditributed CrsMatrix to
//                     print out
// - os                output stream (can be cout)
//===============================================================

bool CrsMatrixInfo( const Epetra_CrsMatrix & A,
ostream & os )

{

int MyPID = A.Comm().MyPID();

// take care that matrix is already trasformed
bool IndicesAreGlobal = A.IndicesAreGlobal();
if( IndicesAreGlobal == true ) {
if( MyPID == 0 ) {
os << "WARNING : matrix must be transformed to local\n";
os << "          before calling CrsMatrixInfo\n";
os << "          Now returning...\n";
}
return false;
}

int NumGlobalRows = A.NumGlobalRows();
int NumGlobalNonzeros = A.NumGlobalNonzeros();
int NumGlobalCols = A.NumGlobalCols();
double NormInf = A.NormInf();
double NormOne = A.NormOne();
int NumGlobalDiagonals = A.NumGlobalDiagonals();
int GlobalMaxNumEntries = A.GlobalMaxNumEntries();
int IndexBase = A.IndexBase();
bool StorageOptimized = A.StorageOptimized();
bool LowerTriangular = A.LowerTriangular();
bool UpperTriangular = A.UpperTriangular();
bool NoDiagonal = A.NoDiagonal();

// these variables identifies quantities I have to compute,
// since not provided by Epetra_CrsMatrix

double MyFrobeniusNorm( 0.0 ), FrobeniusNorm( 0.0 );
double MyMinElement( DBL_MAX ), MinElement( DBL_MAX );
double MyMaxElement( DBL_MIN ), MaxElement( DBL_MIN );
double MyMinAbsElement( DBL_MAX ), MinAbsElement( DBL_MAX );
double MyMaxAbsElement( 0.0 ), MaxAbsElement( 0.0 );

int NumMyRows = A.NumMyRows();
int * NzPerRow = new int[NumMyRows];
int Row; // iterator on rows
int Col; // iterator on cols
int MaxNumEntries = A.MaxNumEntries();
double * Values = new double[MaxNumEntries];
int * Indices = new int[MaxNumEntries];
double Element, AbsElement; // generic nonzero element and its abs value
int NumEntries;
double * Diagonal = new double [NumMyRows];
// SumOffDiagonal is the sum of absolute values for off-diagonals
double * SumOffDiagonal = new double [NumMyRows];
for( Row=0 ;  Row<NumMyRows ; ++Row ) {
SumOffDiagonal[Row] = 0.0;
}
int * IsDiagonallyDominant = new int [NumMyRows];
int GlobalRow;

// cycle over all matrix elements
for( Row=0 ; Row<NumMyRows ; ++Row ) {
GlobalRow = A.GRID(Row);
NzPerRow[Row] = A.NumMyEntries(Row);
A.ExtractMyRowCopy(Row,NzPerRow[Row],NumEntries,Values,Indices);
for( Col=0 ; Col<NumEntries ; ++Col ) {
Element = Values[Col];
AbsElement = abs(Element);
if( Element<MyMinElement ) MyMinElement = Element;
if( Element>MyMaxElement ) MyMaxElement = Element;
if( AbsElement<MyMinAbsElement ) MyMinAbsElement = AbsElement;
if( AbsElement>MyMaxAbsElement ) MyMaxAbsElement = AbsElement;
if( Indices[Col] == Row ) Diagonal[Row] = Element;
else
SumOffDiagonal[Row] += abs(Element);
MyFrobeniusNorm += pow(Element,2);
}
}

// analise storage per row
int MyMinNzPerRow( NumMyRows ), MinNzPerRow( NumMyRows );
int MyMaxNzPerRow( 0 ), MaxNzPerRow( 0 );

for( Row=0 ; Row<NumMyRows ; ++Row ) {
if( NzPerRow[Row]<MyMinNzPerRow ) MyMinNzPerRow=NzPerRow[Row];
if( NzPerRow[Row]>MyMaxNzPerRow ) MyMaxNzPerRow=NzPerRow[Row];
}

// a test to see if matrix is diagonally-dominant

int MyDiagonalDominance( 0 ), DiagonalDominance( 0 );
int MyWeakDiagonalDominance( 0 ), WeakDiagonalDominance( 0 );

for( Row=0 ; Row<NumMyRows ; ++Row ) {
if( abs(Diagonal[Row])>SumOffDiagonal[Row] )
++MyDiagonalDominance;
else if( abs(Diagonal[Row])==SumOffDiagonal[Row] )
++MyWeakDiagonalDominance;
}

// reduction operations

A.Comm().SumAll(&MyFrobeniusNorm, &FrobeniusNorm, 1);
A.Comm().MinAll(&MyMinElement, &MinElement, 1);
A.Comm().MaxAll(&MyMaxElement, &MaxElement, 1);
A.Comm().MinAll(&MyMinAbsElement, &MinAbsElement, 1);
A.Comm().MaxAll(&MyMaxAbsElement, &MaxAbsElement, 1);
A.Comm().MinAll(&MyMinNzPerRow, &MinNzPerRow, 1);
A.Comm().MaxAll(&MyMaxNzPerRow, &MaxNzPerRow, 1);
A.Comm().SumAll(&MyDiagonalDominance, &DiagonalDominance, 1);
A.Comm().SumAll(&MyWeakDiagonalDominance, &WeakDiagonalDominance, 1);

// free memory

delete Values;
delete Indices;
delete Diagonal;
delete SumOffDiagonal;
delete IsDiagonallyDominant;
delete NzPerRow;

// simply no output for MyPID>0, only proc 0 write on os
if( MyPID != 0 ) return true;

os << "*** general Information about the matrix\n";
os << "Number of Global Rows = " << NumGlobalRows << endl;
os << "Number of Global Cols = " << NumGlobalCols << endl;
os << "is the matrix square  = " <<
((NumGlobalRows==NumGlobalCols)?"yes":"no") << endl;
os << "||A||_\\infty          = " << NormInf << endl;
os << "||A||_1               = " << NormOne << endl;
os << "||A||_F               = " << sqrt(FrobeniusNorm) << endl;
os << "Number of nonzero diagonal entries = "
<< NumGlobalDiagonals
<< "( " << 1.0* NumGlobalDiagonals/NumGlobalRows*100
<< " %)\n";
os << "Nonzero per row : min = " << MinNzPerRow
<< " average = " << 1.0*NumGlobalNonzeros/NumGlobalRows
<< " max = " << MaxNzPerRow << endl;
os << "Maximum number of nonzero elements/row = "
<< GlobalMaxNumEntries << endl;
os << "min( a_{i,j} )      = " << MinElement << endl;
os << "max( a_{i,j} )      = " << MaxElement << endl;
os << "min( abs(a_{i,j}) ) = " << MinAbsElement << endl;
os << "max( abs(a_{i,j}) ) = " << MaxAbsElement << endl;
os << "Number of diagonal dominant rows        = " << DiagonalDominance
<< " (" << 100.0*DiagonalDominance/NumGlobalRows << " % of total)\n";
os << "Number of weakly diagonal dominant rows = "
<< WeakDiagonalDominance
<< " (" << 100.0*WeakDiagonalDominance/NumGlobalRows << " % of total)\n";

os << "*** Information about the Trilinos storage\n";
os << "Base Index                 = " << IndexBase << endl;
os << "is storage optimized       = "
<< ((StorageOptimized==true)?"yes":"no") << endl;
os << "are indices global         = "
<< ((IndicesAreGlobal==true)?"yes":"no") << endl;
os << "is matrix lower triangular = "
<< ((LowerTriangular==true)?"yes":"no") << endl;
os << "is matrix upper triangular = "
<< ((UpperTriangular==true)?"yes":"no") << endl;
os << "are there diagonal entries = "
<<  ((NoDiagonal==false)?"yes":"no") << endl;

return true;

}

// =========== //
// Main driver //
// =========== //

int main(int argc, char *argv[])
{

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

// set global dimension to 5, could be any number
int NumGlobalElements = 5;

// create a map
Epetra_Map Map(NumGlobalElements,0,Comm);

TridiagonalCrsMatrix A( Map, -1.0, 2.0, -1.0);

// query the matrix
CrsMatrixInfo(A, cout);

#ifdef HAVE_MPI
MPI_Finalize();
#endif

return(EXIT_SUCCESS);

}

#else

#include <stdlib.h>
#include <stdio.h>

int main(int argc, char *argv[])
{