pair<Base<F>,Base<F>>
Helper( const SparseMatrix<F>& A, Int basisSize )
{
typedef Base<F> Real;
Matrix<Real> T;
ProductLanczos( A, T, basisSize );
const Int k = T.Height();
if( k == 0 )
return pair<Real,Real>(0,0);
Matrix<Real> d, dSub;
d = GetDiagonal( T );
dSub = GetDiagonal( T, -1 );
Matrix<Real> w;
HermitianTridiagEig( d, dSub, w, ASCENDING );
pair<Real,Real> extremal;
extremal.first = Sqrt( Max(w.Get(0,0),Real(0)) );
extremal.second = Sqrt( Max(w.Get(k-1,0),Real(0)) );
return extremal;
}
pair<Base<F>,Base<F>>
Helper( const DistSparseMatrix<F>& A, Int basisSize )
{
typedef Base<F> Real;
Grid grid( A.Comm() );
DistMatrix<Real,STAR,STAR> T(grid);
ProductLanczos( A, T, basisSize );
const Int k = T.Height();
if( k == 0 )
return pair<Real,Real>(0,0);
auto d = GetDiagonal( T.Matrix() );
auto dSub = GetDiagonal( T.Matrix(), -1 );
Matrix<Real> w;
HermitianTridiagEig( d, dSub, w, ASCENDING );
pair<Real,Real> extremal;
extremal.first = Sqrt( Max(w.Get(0,0),Real(0)) );
extremal.second = Sqrt( Max(w.Get(k-1,0),Real(0)) );
return extremal;
}
pair<Base<F>,Base<F>>
ExtremalSingValEst( const SparseMatrix<F>& A, Int basisSize )
{
EL_DEBUG_CSE
typedef Base<F> Real;
Matrix<Real> T;
ProductLanczos( A, T, basisSize );
const Int k = T.Height();
if( k == 0 )
return pair<Real,Real>(0,0);
Matrix<Real> d, dSub;
d = GetDiagonal( T );
dSub = GetDiagonal( T, -1 );
Matrix<Real> w;
HermitianTridiagEig( d, dSub, w );
pair<Real,Real> extremal;
extremal.first = Sqrt( Max(w(0),Real(0)) );
extremal.second = Sqrt( Max(w(k-1),Real(0)) );
return extremal;
}