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;
}
