inline void
GolubReinschUpper
( DistMatrix<F>& A, DistMatrix<BASE(F),VR,STAR>& s, DistMatrix<F>& V )
{
#ifndef RELEASE
CallStackEntry entry("svd::GolubReinschUpper");
#endif
typedef BASE(F) Real;
const Int m = A.Height();
const Int n = A.Width();
const Int k = Min( m, n );
const Int offdiagonal = ( m>=n ? 1 : -1 );
const char uplo = ( m>=n ? 'U' : 'L' );
const Grid& g = A.Grid();
// Bidiagonalize A
DistMatrix<F,STAR,STAR> tP( g ), tQ( g );
Bidiag( A, tP, tQ );
// Grab copies of the diagonal and sub/super-diagonal of A
DistMatrix<Real,MD,STAR> d_MD_STAR(g), e_MD_STAR(g);
A.GetRealPartOfDiagonal( d_MD_STAR );
A.GetRealPartOfDiagonal( e_MD_STAR, offdiagonal );
// NOTE: lapack::BidiagQRAlg expects e to be of length k
DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR ),
eHat_STAR_STAR( k, 1, g ),
e_STAR_STAR( g );
View( e_STAR_STAR, eHat_STAR_STAR, 0, 0, k-1, 1 );
e_STAR_STAR = e_MD_STAR;
// Initialize U and VAdj to the appropriate identity matrices
DistMatrix<F,VC,STAR> U_VC_STAR( g );
DistMatrix<F,STAR,VC> VAdj_STAR_VC( g );
U_VC_STAR.AlignWith( A );
VAdj_STAR_VC.AlignWith( V );
Identity( U_VC_STAR, m, k );
Identity( VAdj_STAR_VC, k, n );
// Compute the SVD of the bidiagonal matrix and accumulate the Givens
// rotations into our local portion of U and VAdj
Matrix<F>& ULoc = U_VC_STAR.Matrix();
Matrix<F>& VAdjLoc = VAdj_STAR_VC.Matrix();
lapack::BidiagQRAlg
( uplo, k, VAdjLoc.Width(), ULoc.Height(),
d_STAR_STAR.Buffer(), e_STAR_STAR.Buffer(),
VAdjLoc.Buffer(), VAdjLoc.LDim(),
ULoc.Buffer(), ULoc.LDim() );
// Make a copy of A (for the Householder vectors) and pull the necessary
// portions of U and VAdj into a standard matrix dist.
DistMatrix<F> B( A );
if( m >= n )
{
DistMatrix<F> AT(g), AB(g);
DistMatrix<F,VC,STAR> UT_VC_STAR(g), UB_VC_STAR(g);
PartitionDown( A, AT, AB, n );
PartitionDown( U_VC_STAR, UT_VC_STAR, UB_VC_STAR, n );
AT = UT_VC_STAR;
MakeZeros( AB );
Adjoint( VAdj_STAR_VC, V );
}
else
{
DistMatrix<F> VT(g), VB(g);
DistMatrix<F,STAR,VC> VAdjL_STAR_VC(g), VAdjR_STAR_VC(g);
PartitionDown( V, VT, VB, m );
PartitionRight( VAdj_STAR_VC, VAdjL_STAR_VC, VAdjR_STAR_VC, m );
Adjoint( VAdjL_STAR_VC, VT );
MakeZeros( VB );
}
// Backtransform U and V
bidiag::ApplyU( LEFT, NORMAL, B, tQ, A );
bidiag::ApplyV( LEFT, NORMAL, B, tP, V );
// Copy out the appropriate subset of the singular values
s = d_STAR_STAR;
}
inline void
SimpleSVDUpper
( DistMatrix<Complex<Real> >& A,
DistMatrix<Real,VR,STAR>& s,
DistMatrix<Complex<Real> >& V )
{
#ifndef RELEASE
PushCallStack("svd::SimpleSVDUpper");
#endif
typedef Complex<Real> C;
const int m = A.Height();
const int n = A.Width();
const int k = std::min( m, n );
const int offdiagonal = ( m>=n ? 1 : -1 );
const char uplo = ( m>=n ? 'U' : 'L' );
const Grid& g = A.Grid();
// Bidiagonalize A
DistMatrix<C,STAR,STAR> tP( g ), tQ( g );
Bidiag( A, tP, tQ );
// Grab copies of the diagonal and sub/super-diagonal of A
DistMatrix<Real,MD,STAR> d_MD_STAR( g ),
e_MD_STAR( g );
A.GetRealPartOfDiagonal( d_MD_STAR );
A.GetRealPartOfDiagonal( e_MD_STAR, offdiagonal );
// NOTE: lapack::BidiagQRAlg expects e to be of length k
DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR );
DistMatrix<Real,STAR,STAR> eHat_STAR_STAR( k, 1, g );
DistMatrix<Real,STAR,STAR> e_STAR_STAR( g );
e_STAR_STAR.View( eHat_STAR_STAR, 0, 0, k-1, 1 );
e_STAR_STAR = e_MD_STAR;
// Initialize U and VAdj to the appropriate identity matrices
DistMatrix<C,VC,STAR> U_VC_STAR( g );
DistMatrix<C,STAR,VC> VAdj_STAR_VC( g );
U_VC_STAR.AlignWith( A );
VAdj_STAR_VC.AlignWith( V );
Identity( m, k, U_VC_STAR );
Identity( k, n, VAdj_STAR_VC );
// Compute the SVD of the bidiagonal matrix and accumulate the Givens
// rotations into our local portion of U and VAdj
Matrix<C>& ULocal = U_VC_STAR.LocalMatrix();
Matrix<C>& VAdjLocal = VAdj_STAR_VC.LocalMatrix();
lapack::BidiagQRAlg
( uplo, k, VAdjLocal.Width(), ULocal.Height(),
d_STAR_STAR.LocalBuffer(), e_STAR_STAR.LocalBuffer(),
VAdjLocal.Buffer(), VAdjLocal.LDim(),
ULocal.Buffer(), ULocal.LDim() );
// Make a copy of A (for the Householder vectors) and pull the necessary
// portions of U and VAdj into a standard matrix dist.
DistMatrix<C> B( A );
if( m >= n )
{
DistMatrix<C> AT( g ),
AB( g );
DistMatrix<C,VC,STAR> UT_VC_STAR( g ),
UB_VC_STAR( g );
PartitionDown( A, AT,
AB, n );
PartitionDown( U_VC_STAR, UT_VC_STAR,
UB_VC_STAR, n );
AT = UT_VC_STAR;
MakeZeros( AB );
Adjoint( VAdj_STAR_VC, V );
}
else
{
DistMatrix<C> VT( g ),
VB( g );
DistMatrix<C,STAR,VC> VAdjL_STAR_VC( g ), VAdjR_STAR_VC( g );
PartitionDown( V, VT,
VB, m );
PartitionRight( VAdj_STAR_VC, VAdjL_STAR_VC, VAdjR_STAR_VC, m );
Adjoint( VAdjL_STAR_VC, VT );
MakeZeros( VB );
}
// Backtransform U and V
if( m >= n )
{
ApplyPackedReflectors
( LEFT, LOWER, VERTICAL, BACKWARD, UNCONJUGATED, 0, B, tQ, A );
ApplyPackedReflectors
( LEFT, UPPER, HORIZONTAL, BACKWARD, UNCONJUGATED, 1, B, tP, V );
}
else
{
ApplyPackedReflectors
( LEFT, LOWER, VERTICAL, BACKWARD, UNCONJUGATED, -1, B, tQ, A );
ApplyPackedReflectors
( LEFT, UPPER, HORIZONTAL, BACKWARD, UNCONJUGATED, 0, B, tP, V );
}
// Copy out the appropriate subset of the singular values
s = d_STAR_STAR;
#ifndef RELEASE
PopCallStack();
#endif
}
