inline typename Base<F>::type
SymmetricSchattenNorm
( UpperOrLower uplo, const DistMatrix<F,U,V>& A, typename Base<F>::type p )
{
#ifndef RELEASE
PushCallStack("SymmetricSchattenNorm");
#endif
typedef typename Base<F>::type R;
DistMatrix<F> B( A );
DistMatrix<R,VR,STAR> s( A.Grid() );
MakeSymmetric( uplo, B );
SVD( B, s );
// TODO: Think of how to make this more stable
const int kLocal = s.LocalHeight();
R localSum = 0;
for( int j=0; j<kLocal; ++j )
localSum += Pow( s.GetLocal(j,0), p );
R sum;
mpi::AllReduce( &localSum, &sum, 1, mpi::SUM, A.Grid().VRComm() );
const R norm = Pow( sum, 1/p );
#ifndef RELEASE
PopCallStack();
#endif
return norm;
}
Base<F> SymmetricTwoNorm( UpperOrLower uplo, const AbstractDistMatrix<F>& A )
{
DEBUG_ONLY(CSE cse("SymmetricTwoNorm"))
DistMatrix<F> B( A );
DistMatrix<Base<F>,VR,STAR> s( A.Grid() );
MakeSymmetric( uplo, B );
SVD( B, s );
return MaxNorm( s );
}
Base<F> SymmetricTwoNorm( UpperOrLower uplo, const Matrix<F>& A )
{
DEBUG_ONLY(CSE cse("SymmetricTwoNorm"))
Matrix<F> B( A );
Matrix<Base<F>> s;
MakeSymmetric( uplo, B );
SVD( B, s );
return MaxNorm( s );
}
void
QuasiDiagonalSolve
( LeftOrRight side, UpperOrLower uplo,
const Matrix<FMain>& d,
const Matrix<F>& dSub,
Matrix<F>& X,
bool conjugated )
{
DEBUG_CSE
const Int m = X.Height();
const Int n = X.Width();
Matrix<F> D( 2, 2 );
if( side == LEFT && uplo == LOWER )
{
if( m == 0 )
return;
DEBUG_ONLY(
if( d.Height() != m )
LogicError
("d was the wrong size: m=",m,",n=",n,", d ~ ",
d.Height()," x ",d.Width());
if( dSub.Height() != m-1 )
LogicError
("dSub was the wrong size: m=",m,",n=",n,", dSub ~ ",
dSub.Height()," x ",dSub.Width());
)
Int i=0;
while( i < m )
{
Int nb;
if( i < m-1 && Abs(dSub.Get(i,0)) > 0 )
nb = 2;
else
nb = 1;
auto XRow = X( IR(i,i+nb), IR(0,n) );
if( nb == 1 )
{
Scale( F(1)/d.Get(i,0), XRow );
}
else
{
D.Set(0,0,d.Get(i,0));
D.Set(1,1,d.Get(i+1,0));
D.Set(1,0,dSub.Get(i,0));
Symmetric2x2Inv( LOWER, D, conjugated );
MakeSymmetric( LOWER, D, conjugated );
Transform2x2Rows( D, X, i, i+1 );
}
i += nb;
}
}
Base<F> SymmetricTwoNorm( UpperOrLower uplo, const ElementalMatrix<F>& A )
{
DEBUG_ONLY(CSE cse("SymmetricTwoNorm"))
DistMatrix<F> B( A );
DistMatrix<Base<F>,VR,STAR> s( A.Grid() );
MakeSymmetric( uplo, B );
SVDCtrl<Base<F>> ctrl;
ctrl.overwrite = true;
SVD( B, s, ctrl );
return MaxNorm( s );
}
Base<F> SymmetricTwoNorm( UpperOrLower uplo, const Matrix<F>& A )
{
DEBUG_ONLY(CSE cse("SymmetricTwoNorm"))
Matrix<F> B( A );
Matrix<Base<F>> s;
MakeSymmetric( uplo, B );
SVDCtrl<Base<F>> ctrl;
ctrl.overwrite = true;
SVD( B, s, ctrl );
return MaxNorm( s );
}
inline void
MakeHermitian( UpperOrLower uplo, DistMatrix<T>& A )
{
#ifndef RELEASE
PushCallStack("MakeHermitian");
#endif
MakeSymmetric( uplo, A, true );
#ifndef RELEASE
PopCallStack();
#endif
}
SymmetricTwoNorm( UpperOrLower uplo, const DistMatrix<F,U,V>& A )
{
#ifndef RELEASE
CallStackEntry entry("SymmetricTwoNorm");
#endif
typedef BASE(F) R;
DistMatrix<F,U,V> B( A );
DistMatrix<R,VR,STAR> s( A.Grid() );
MakeSymmetric( uplo, B );
SVD( B, s );
return MaxNorm( s );
}
SymmetricTwoNorm( UpperOrLower uplo, const Matrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("SymmetricTwoNorm");
#endif
typedef BASE(F) R;
Matrix<F> B( A );
Matrix<R> s;
MakeSymmetric( uplo, B );
SVD( B, s );
return MaxNorm( s );
}
inline typename Base<F>::type
SymmetricSchattenNorm
( UpperOrLower uplo, const Matrix<F>& A, typename Base<F>::type p )
{
#ifndef RELEASE
PushCallStack("SymmetricSchattenNorm");
#endif
typedef typename Base<F>::type R;
Matrix<F> B( A );
Matrix<R> s;
MakeSymmetric( uplo, B );
SVD( B, s );
// TODO: Think of how to make this more stable
const int k = s.Height();
R sum = 0;
for( int j=0; j<k; ++j )
sum += Pow( s.Get(j,0), p );
const R norm = Pow( sum, 1/p );
#ifndef RELEASE
PopCallStack();
#endif
return norm;
}
void QuasiDiagonalScale
( LeftOrRight side,
UpperOrLower uplo,
const Matrix<FMain>& d,
const Matrix<F>& dSub,
Matrix<F>& X,
bool conjugated )
{
DEBUG_CSE
const Int m = X.Height();
const Int n = X.Width();
Matrix<F> D( 2, 2 );
if( side == LEFT && uplo == LOWER )
{
Int i=0;
while( i < m )
{
Int nb;
if( i < m-1 && Abs(dSub.Get(i,0)) > 0 )
nb = 2;
else
nb = 1;
if( nb == 1 )
{
auto xRow = View( X, i, 0, nb, n );
Scale( d.Get(i,0), xRow );
}
else
{
D.Set(0,0,d.Get(i,0));
D.Set(1,1,d.Get(i+1,0));
D.Set(1,0,dSub.Get(i,0));
MakeSymmetric( LOWER, D, conjugated );
Transform2x2Rows( D, X, i, i+1 );
}
i += nb;
}
}
else if( side == RIGHT && uplo == LOWER )
{
Int j=0;
while( j < n )
{
Int nb;
if( j < n-1 && Abs(dSub.Get(j,0)) > 0 )
nb = 2;
else
nb = 1;
if( nb == 1 )
{
auto xCol = View( X, 0, j, m, nb );
Scale( d.Get(j,0), xCol );
}
else
{
D.Set(0,0,d.Get(j,0));
D.Set(1,1,d.Get(j+1,0));
D.Set(1,0,dSub.Get(j,0));
MakeSymmetric( LOWER, D, conjugated );
Transform2x2Cols( D, X, j, j+1 );
}
j += nb;
}
}
else
LogicError("This option not yet supported");
}
void MakeHermitian( UpperOrLower uplo, DistSparseMatrix<T>& A )
{
DEBUG_ONLY(CallStackEntry cse("MakeHermitian"))
MakeSymmetric( uplo, A, true );
}
