Base<F> HermitianTwoNorm( UpperOrLower uplo, const ElementalMatrix<F>& A )
{
DEBUG_ONLY(CSE cse("HermitianTwoNorm"))
DistMatrix<Base<F>,VR,STAR> s( A.Grid() );
HermitianSVD( uplo, A, s );
return InfinityNorm( s );
}
Base<F> Norm( const Matrix<F>& A, NormType type )
{
DEBUG_ONLY(CSE cse("Norm"))
Base<F> norm = 0;
switch( type )
{
// The following norms are rather cheap to compute
case ENTRYWISE_ONE_NORM:
norm = EntrywiseNorm( A, Base<F>(1) );
break;
case FROBENIUS_NORM:
norm = FrobeniusNorm( A );
break;
case INFINITY_NORM:
norm = InfinityNorm( A );
break;
case MAX_NORM:
norm = MaxNorm( A );
break;
case ONE_NORM:
norm = OneNorm( A );
break;
// The following two norms make use of an SVD
case NUCLEAR_NORM:
norm = NuclearNorm( A );
break;
case TWO_NORM:
norm = TwoNorm( A );
break;
}
return norm;
}
Base<F> TwoNorm( const ElementalMatrix<F>& A )
{
DEBUG_ONLY(CSE cse("TwoNorm"))
DistMatrix<Base<F>,VR,STAR> s( A.Grid() );
SVD( A, s );
return InfinityNorm( s );
}
Base<F> HermitianTwoNorm( UpperOrLower uplo, const Matrix<F>& A )
{
DEBUG_ONLY(CSE cse("HermitianTwoNorm"))
Matrix<Base<F>> s;
HermitianSVD( uplo, A, s );
return InfinityNorm( s );
}
Base<F> TwoNorm( const Matrix<F>& A )
{
DEBUG_ONLY(CSE cse("TwoNorm"))
Matrix<Base<F>> s;
SVD( A, s );
return InfinityNorm( s );
}
Base<F> TwoNorm( const Matrix<F>& A )
{
DEBUG_CSE
Matrix<Base<F>> s;
SVD( A, s );
return InfinityNorm( s );
}
Base<F> TwoNorm( const AbstractDistMatrix<F>& A )
{
DEBUG_ONLY(CSE cse("TwoNorm"))
DistMatrix<F> B( A );
DistMatrix<Base<F>,VR,STAR> s( A.Grid() );
SVD( B, s );
return InfinityNorm( s );
}
HermitianTwoNorm( UpperOrLower uplo, const DistMatrix<F,U,V>& A )
{
#ifndef RELEASE
CallStackEntry entry("HermitianTwoNorm");
#endif
typedef BASE(F) R;
DistMatrix<F,U,V> B( A );
DistMatrix<R,VR,STAR> s( A.Grid() );
HermitianSVD( uplo, B, s );
return InfinityNorm( s );
}
TwoNorm( const DistMatrix<F,U,V>& A )
{
#ifndef RELEASE
CallStackEntry entry("TwoNorm");
#endif
typedef BASE(F) R;
DistMatrix<F> B( A );
DistMatrix<R,VR,STAR> s( A.Grid() );
SVD( B, s );
return InfinityNorm( s );
}
HermitianTwoNorm( UpperOrLower uplo, const Matrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("HermitianTwoNorm");
#endif
typedef BASE(F) R;
Matrix<F> B( A );
Matrix<R> s;
HermitianSVD( uplo, B, s );
return InfinityNorm( s );
}
TwoNorm( const Matrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("TwoNorm");
#endif
typedef BASE(F) R;
Matrix<F> B( A );
Matrix<R> s;
SVD( B, s );
return InfinityNorm( s );
}
TwoNormUpperBound( const DistMatrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("TwoNormUpperBound");
#endif
typedef BASE(F) R;
const R m = A.Height();
const R n = A.Width();
const R maxNorm = MaxNorm( A );
const R oneNorm = OneNorm( A );
const R infNorm = InfinityNorm( A );
R upperBound = std::min( Sqrt(m*n)*maxNorm, Sqrt(m)*infNorm );
upperBound = std::min( upperBound, Sqrt(n)*oneNorm );
upperBound = std::min( upperBound, Sqrt( oneNorm*infNorm ) );
return upperBound;
}
which can be found in the LICENSE file in the root directory, or at
http://opensource.org/licenses/BSD-2-Clause
*/
#pragma once
#ifndef EL_CONDITION_INFINITY_HPP
#define EL_CONDITION_INFINITY_HPP
namespace El {
template<typename F>
Base<F> InfinityCondition( const Matrix<F>& A )
{
DEBUG_ONLY(CallStackEntry cse("InfinityCondition"))
typedef Base<F> Real;
Matrix<F> B( A );
const Real infNorm = InfinityNorm( B );
try { Inverse( B ); }
catch( SingularMatrixException& e )
{ return std::numeric_limits<Real>::infinity(); }
const Real infNormInv = InfinityNorm( B );
return infNorm*infNormInv;
}
template<typename F>
Base<F> InfinityCondition( const AbstractDistMatrix<F>& A )
{
DEBUG_ONLY(CallStackEntry cse("InfinityCondition"))
typedef Base<F> Real;
DistMatrix<F> B( A );
const Real infNorm = InfinityNorm( B );
try { Inverse( B ); }
