void HermitianSign
( UpperOrLower uplo,
AbstractDistMatrix<Field>& APre,
AbstractDistMatrix<Field>& NPre,
const HermitianEigCtrl<Field>& ctrl )
{
EL_DEBUG_CSE
DistMatrixReadWriteProxy<Field,Field,MC,MR> AProx( APre );
DistMatrixWriteProxy<Field,Field,MC,MR> NProx( NPre );
auto& A = AProx.Get();
auto& N = NProx.Get();
// Get the EVD of A
typedef Base<Field> Real;
const Grid& g = A.Grid();
DistMatrix<Real,VR,STAR> w(g);
DistMatrix<Field> Q(g);
auto ctrlMod( ctrl );
ctrlMod.tridiagEigCtrl.sort = UNSORTED;
HermitianEig( uplo, A, w, Q, ctrlMod );
const Int n = A.Height();
const Int numLocalEigs = w.LocalHeight();
DistMatrix<Real,VR,STAR> wSgn(g), wAbs(g);
wSgn.AlignWith( w );
wAbs.AlignWith( w );
wSgn.Resize( n, 1 );
wAbs.Resize( n, 1 );
for( Int iLoc=0; iLoc<numLocalEigs; ++iLoc )
{
const Real omega = w.GetLocal(iLoc,0);
if( omega >= 0 )
{
wSgn.SetLocal(iLoc,0,Real(1));
wAbs.SetLocal(iLoc,0,omega);
}
else
{
wSgn.SetLocal(iLoc,0,Real(-1));
wAbs.SetLocal(iLoc,0,-omega);
}
}
// Form the Hermitian matrix with the modified eigenvalues
HermitianFromEVD( uplo, A, wSgn, Q );
HermitianFromEVD( uplo, N, wAbs, Q );
}
void HermitianPseudoinverse
( UpperOrLower uplo, Matrix<F>& A, Base<F> tolerance )
{
DEBUG_CSE
typedef Base<F> Real;
// Get the EVD of A
// TODO: Use a relative eigenvalue lower bound
Matrix<Real> w;
Matrix<F> Z;
HermitianEig( uplo, A, w, Z );
if( tolerance == Real(0) )
{
// Set the tolerance equal to n ||A||_2 eps
const Int n = Z.Height();
const Real eps = limits::Epsilon<Real>();
const Real twoNorm = MaxNorm( w );
tolerance = n*twoNorm*eps;
}
// Invert above the tolerance
auto omegaMap =
[=]( Real omega ) { return ( omega < tolerance ? Real(0) : 1/omega ); };
EntrywiseMap( w, function<Real(Real)>(omegaMap) );
// Form the pseudoinverse
HermitianFromEVD( uplo, A, w, Z );
}
void HermitianSign
( UpperOrLower uplo, Matrix<Field>& A, const HermitianEigCtrl<Field>& ctrl )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
// Get the EVD of A
Matrix<Real> w;
Matrix<Field> Q;
auto ctrlMod( ctrl );
ctrlMod.tridiagEigCtrl.sort = UNSORTED;
HermitianEig( uplo, A, w, Q, ctrlMod );
const Int n = A.Height();
for( Int i=0; i<n; ++i )
{
const Real omega = w(i);
if( omega >= 0 )
w(i) = Real(1);
else
w(i) = Real(-1);
}
// Reform the Hermitian matrix with the modified eigenvalues
HermitianFromEVD( uplo, A, w, Q );
}
void HermitianPseudoinverse
( UpperOrLower uplo, ElementalMatrix<F>& APre, Base<F> tolerance )
{
DEBUG_CSE
typedef Base<F> Real;
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
auto& A = AProx.Get();
const Grid& g = A.Grid();
// Get the EVD of A
// TODO: Use a relative eigenvalue lower-bound
DistMatrix<Real,VR,STAR> w(g);
DistMatrix<F> Z(g);
HermitianEig( uplo, A, w, Z );
if( tolerance == Real(0) )
{
// Set the tolerance equal to n ||A||_2 eps
const Int n = Z.Height();
const Real eps = limits::Epsilon<Real>();
const Real twoNorm = MaxNorm( w );
tolerance = n*twoNorm*eps;
}
// Invert above the tolerance
auto omegaMap =
[=]( Real omega ) { return ( omega < tolerance ? Real(0) : 1/omega ); };
EntrywiseMap( w, function<Real(Real)>(omegaMap) );
// Form the pseudoinverse
HermitianFromEVD( uplo, A, w, Z );
}
void HermitianSign
( UpperOrLower uplo,
ElementalMatrix<F>& APre,
const HermitianEigCtrl<F>& ctrl )
{
DEBUG_CSE
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
auto& A = AProx.Get();
// Get the EVD of A
typedef Base<F> Real;
const Grid& g = A.Grid();
DistMatrix<Real,VR,STAR> w(g);
DistMatrix<F> Q(g);
auto ctrlMod( ctrl );
ctrlMod.tridiagEigCtrl.sort = UNSORTED;
HermitianEig( uplo, A, w, Q, ctrlMod );
const Int numLocalEigs = w.LocalHeight();
for( Int iLoc=0; iLoc<numLocalEigs; ++iLoc )
{
const Real omega = w.GetLocal(iLoc,0);
if( omega >= 0 )
w.SetLocal(iLoc,0,Real(1));
else
w.SetLocal(iLoc,0,Real(-1));
}
// Reform the Hermitian matrix with the modified eigenvalues
HermitianFromEVD( uplo, A, w, Q );
}
inline Matrix<F>
HermitianFromEVD
( UpperOrLower uplo,
const Matrix<BASE(F)>& w,
const Matrix<F>& Z )
{
Matrix<F> A;
HermitianFromEVD( uplo, A, w, Z );
return A;
}
void HermitianSign
( UpperOrLower uplo,
Matrix<Field>& A,
Matrix<Field>& N,
const HermitianEigCtrl<Field>& ctrl )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
// Get the EVD of A
Matrix<Real> w;
Matrix<Field> Q;
auto ctrlMod( ctrl );
ctrlMod.tridiagEigCtrl.sort = UNSORTED;
HermitianEig( uplo, A, w, Q, ctrlMod );
const Int n = A.Height();
Matrix<Real> wSgn( n, 1 ), wAbs( n, 1 );
for( Int i=0; i<n; ++i )
{
const Real omega = w(i);
if( omega >= 0 )
{
wSgn(i) = Real(1);
wAbs(i) = omega;
}
else
{
wSgn(i) = Real(-1);
wAbs(i) = -omega;
}
}
// Form the Hermitian matrices with modified eigenvalues
HermitianFromEVD( uplo, A, wSgn, Q );
HermitianFromEVD( uplo, N, wAbs, Q );
}
void SVD( Matrix<F>& A, Matrix<F>& P )
{
DEBUG_CSE
typedef Base<F> Real;
// Get the SVD of A
Matrix<Real> s;
Matrix<F> U, V;
SVDCtrl<Real> ctrl;
ctrl.overwrite = true;
El::SVD( A, U, s, V, ctrl );
// Form Q := U V^H in A
Gemm( NORMAL, ADJOINT, F(1), U, V, A );
// Form P := V Sigma V^H in P
HermitianFromEVD( LOWER, P, s, V );
}
void SVD( ElementalMatrix<F>& APre, ElementalMatrix<F>& PPre )
{
DEBUG_CSE
typedef Base<F> Real;
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
DistMatrixWriteProxy<F,F,MC,MR> PProx( PPre );
auto& A = AProx.Get();
auto& P = PProx.Get();
const Grid& g = A.Grid();
// Get the SVD of A
DistMatrix<Real,VR,STAR> s(g);
DistMatrix<F> U(g), V(g);
SVDCtrl<Real> ctrl;
ctrl.overwrite = true;
El::SVD( A, U, s, V, ctrl );
// Form Q := U V^H in A
Gemm( NORMAL, ADJOINT, F(1), U, V, A );
// Form P := V Sigma V^H in P
HermitianFromEVD( LOWER, P, s, V );
}