Base<F> HermitianNorm( UpperOrLower uplo, const Matrix<F>& A, NormType type )
{
DEBUG_ONLY(CSE cse("HermitianNorm"))
Base<F> norm = 0;
switch( type )
{
// The following norms are rather cheap to compute
case FROBENIUS_NORM:
norm = HermitianFrobeniusNorm( uplo, A );
break;
case ENTRYWISE_ONE_NORM:
norm = HermitianEntrywiseNorm( uplo, A, Base<F>(1) );
break;
case INFINITY_NORM:
norm = HermitianInfinityNorm( uplo, A );
break;
case MAX_NORM:
norm = HermitianMaxNorm( uplo, A );
break;
case ONE_NORM:
norm = HermitianOneNorm( uplo, A );
break;
// The following norms make use of an SVD
case NUCLEAR_NORM:
norm = HermitianNuclearNorm( uplo, A );
break;
case TWO_NORM:
norm = HermitianTwoNorm( uplo, A );
break;
}
return norm;
}
Base<F> Coherence( const ElementalMatrix<F>& A )
{
DEBUG_ONLY(CSE cse("Coherence"))
DistMatrix<F> B( A );
DistMatrix<Base<F>,MR,STAR> norms(B.Grid());
ColumnTwoNorms( B, norms );
DiagonalSolve( RIGHT, NORMAL, norms, B, true );
DistMatrix<F> C(B.Grid());
Identity( C, A.Width(), A.Width() );
Herk( UPPER, ADJOINT, Base<F>(-1), B, Base<F>(1), C );
return HermitianMaxNorm( UPPER, C );
}
Base<F> Coherence( const Matrix<F>& A )
{
DEBUG_ONLY(CallStackEntry cse("Coherence"))
Matrix<F> B( A );
Matrix<Base<F>> norms;
ColumnNorms( B, norms );
DiagonalSolve( RIGHT, NORMAL, norms, B, true );
Matrix<F> C;
Identity( C, A.Width(), A.Width() );
Herk( UPPER, ADJOINT, Base<F>(-1), B, Base<F>(1), C );
return HermitianMaxNorm( UPPER, C );
}
bool CheckScale( UpperOrLower uplo, DistMatrix<F>& A, Base<F>& scale )
{
typedef Base<F> Real;
scale = 1;
const Real maxNormOfA = HermitianMaxNorm( uplo, A );
const Real underflowThreshold = lapack::MachineUnderflowThreshold<Real>();
const Real overflowThreshold = lapack::MachineOverflowThreshold<Real>();
if( maxNormOfA > 0 && maxNormOfA < underflowThreshold )
{
scale = underflowThreshold / maxNormOfA;
return true;
}
else if( maxNormOfA > overflowThreshold )
{
scale = overflowThreshold / maxNormOfA;
return true;
}
else
return false;
}