SVDInfo GolubReinsch
( Matrix<Field>& A,
Matrix<Base<Field>>& s,
const SVDCtrl<Base<Field>>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
SVDInfo info;
// Bidiagonalize A
Timer timer;
Matrix<Field> householderScalarsP, householderScalarsQ;
if( ctrl.time )
timer.Start();
Bidiag( A, householderScalarsP, householderScalarsQ );
if( ctrl.time )
Output("Reduction to bidiagonal: ",timer.Stop()," seconds");
// Compute the singular values of the bidiagonal matrix
const UpperOrLower uplo = ( m>=n ? UPPER : LOWER );
const Int offdiagonal = ( uplo==UPPER ? 1 : -1 );
auto mainDiag = GetRealPartOfDiagonal( A );
auto offDiag = GetRealPartOfDiagonal( A, offdiagonal );
if( ctrl.time )
timer.Start();
info.bidiagSVDInfo =
BidiagSVD( uplo, mainDiag, offDiag, s, ctrl.bidiagSVDCtrl );
if( ctrl.time )
Output("Bidiag SVD: ",timer.Stop()," seconds");
return info;
}
SVDInfo GolubReinsch
( DistMatrix<Field>& A,
AbstractDistMatrix<Base<Field>>& s,
const SVDCtrl<Base<Field>>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Grid& g = A.Grid();
SVDInfo info;
// Bidiagonalize A
Timer timer;
DistMatrix<Field,STAR,STAR> householderScalarsP(g), householderScalarsQ(g);
if( ctrl.time && g.Rank() == 0 )
timer.Start();
Bidiag( A, householderScalarsP, householderScalarsQ );
if( ctrl.time && g.Rank() == 0 )
Output("Reduction to bidiagonal: ",timer.Stop()," seconds");
// Grab copies of the diagonal and sub/super-diagonal of A
const UpperOrLower uplo = ( m>=n ? UPPER : LOWER );
const Int offdiagonal = ( uplo==UPPER ? 1 : -1 );
auto mainDiag = GetRealPartOfDiagonal(A);
auto offDiag = GetRealPartOfDiagonal(A,offdiagonal);
if( ctrl.time && g.Rank() == 0 )
timer.Start();
info.bidiagSVDInfo =
BidiagSVD( uplo, mainDiag, offDiag, s, ctrl.bidiagSVDCtrl );
if( ctrl.time && g.Rank() == 0 )
Output("Bidiag SVD: ",timer.Stop()," seconds");
return info;
}
inline void
SimpleSingularValuesUpper
( DistMatrix<Complex<Real> >& A,
DistMatrix<Real,VR,STAR>& s )
{
#ifndef RELEASE
PushCallStack("svd::SimpleSingularValuesUpper");
#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 );
// In order to use serial QR kernels, we need the full bidiagonal matrix
// on each process
//
// 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;
// Compute the singular values of the bidiagonal matrix
lapack::BidiagQRAlg
( uplo, k, 0, 0,
d_STAR_STAR.LocalBuffer(), e_STAR_STAR.LocalBuffer(),
(C*)0, 1, (C*)0, 1 );
// Copy out the appropriate subset of the singular values
s = d_STAR_STAR;
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
GolubReinschUpper
( DistMatrix<F>& A,
DistMatrix<BASE(F),VR,STAR>& s )
{
#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 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 );
// In order to use serial DQDS kernels, we need the full bidiagonal matrix
// on each process
//
// NOTE: lapack::BidiagDQDS 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;
// Compute the singular values of the bidiagonal matrix via DQDS
lapack::BidiagDQDS( k, d_STAR_STAR.Buffer(), e_STAR_STAR.Buffer() );
// Copy out the appropriate subset of the singular values
s = d_STAR_STAR;
}
SVDInfo GolubReinsch
( DistMatrix<Field>& A,
DistMatrix<Field>& U,
AbstractDistMatrix<Base<Field>>& s,
DistMatrix<Field>& V,
const SVDCtrl<Base<Field>>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const bool avoidU = !ctrl.bidiagSVDCtrl.wantU;
const bool avoidV = !ctrl.bidiagSVDCtrl.wantV;
const Grid& g = A.Grid();
if( avoidU && avoidV )
{
return SVD( A, s, ctrl );
}
SVDInfo info;
// Bidiagonalize A
Timer timer;
DistMatrix<Field,STAR,STAR> householderScalarsP(g), householderScalarsQ(g);
if( ctrl.time && g.Rank() == 0 )
timer.Start();
Bidiag( A, householderScalarsP, householderScalarsQ );
if( ctrl.time && g.Rank() == 0 )
Output("Reduction to bidiagonal: ",timer.Stop()," seconds");
// Grab copies of the diagonal and sub/super-diagonal of A
const UpperOrLower uplo = ( m>=n ? UPPER : LOWER );
const Int offdiagonal = ( m>=n ? 1 : -1 );
auto mainDiag = GetRealPartOfDiagonal(A);
auto offDiag = GetRealPartOfDiagonal(A,offdiagonal);
// Run the bidiagonal SVD
if( ctrl.time && g.Rank() == 0 )
timer.Start();
if( m == n || (m > n && avoidU) || (m < n && avoidV) )
{
// There is no need to work on a subset of U or V
info.bidiagSVDInfo =
BidiagSVD( uplo, mainDiag, offDiag, U, s, V, ctrl.bidiagSVDCtrl );
}
else if( m > n )
{
// We need to work on a subset of U
DistMatrix<Field> USub(g);
info.bidiagSVDInfo =
BidiagSVD( uplo, mainDiag, offDiag, USub, s, V, ctrl.bidiagSVDCtrl );
// Copy USub into U
const Int UWidth = USub.Width();
Identity( U, m, UWidth );
auto UTop = U( IR(0,n), ALL );
UTop = USub;
}
else if( m < n )
{
// We need to work on a subset of V
DistMatrix<Field> VSub(g);
info.bidiagSVDInfo =
BidiagSVD( uplo, mainDiag, offDiag, U, s, VSub, ctrl.bidiagSVDCtrl );
// Copy VSub into V
const Int VWidth = VSub.Width();
Identity( V, n, VWidth );
auto VTop = V( IR(0,m), ALL );
VTop = VSub;
}
if( ctrl.time )
{
mpi::Barrier( g.Comm() );
if( g.Rank() == 0 )
Output("Bidiag SVD: ",timer.Stop()," seconds");
}
// Backtransform U and V
if( ctrl.time && g.Rank() == 0 )
timer.Start();
if( !avoidU ) bidiag::ApplyQ( LEFT, NORMAL, A, householderScalarsQ, U );
if( !avoidV ) bidiag::ApplyP( LEFT, NORMAL, A, householderScalarsP, V );
if( ctrl.time && g.Rank() == 0 )
Output("GolubReinsch backtransformation: ",timer.Stop()," seconds");
return info;
}
SVDInfo GolubReinsch
( Matrix<Field>& A,
Matrix<Field>& U,
Matrix<Base<Field>>& s,
Matrix<Field>& V,
const SVDCtrl<Base<Field>>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const bool avoidU = !ctrl.bidiagSVDCtrl.wantU;
const bool avoidV = !ctrl.bidiagSVDCtrl.wantV;
if( avoidU && avoidV )
{
return SVD( A, s, ctrl );
}
SVDInfo info;
// Bidiagonalize A
Timer timer;
Matrix<Field> householderScalarsP, householderScalarsQ;
if( ctrl.time )
timer.Start();
Bidiag( A, householderScalarsP, householderScalarsQ );
if( ctrl.time )
Output("Reduction to bidiagonal: ",timer.Stop()," seconds");
// Compute the SVD of the bidiagonal matrix.
// (We can guarantee that accumulation was not requested.)
const Int offdiagonal = ( m>=n ? 1 : -1 );
const UpperOrLower uplo = ( m>=n ? UPPER : LOWER );
auto mainDiag = GetRealPartOfDiagonal( A );
auto offDiag = GetRealPartOfDiagonal( A, offdiagonal );
if( ctrl.time )
timer.Start();
if( m == n || (m > n && avoidU) || (m < n && avoidV) )
{
// There is no need to work on a subset of U or V
info.bidiagSVDInfo =
BidiagSVD( uplo, mainDiag, offDiag, U, s, V, ctrl.bidiagSVDCtrl );
}
else if( m > n )
{
// We need to work on a subset of U
Matrix<Field> USub;
info.bidiagSVDInfo =
BidiagSVD( uplo, mainDiag, offDiag, USub, s, V, ctrl.bidiagSVDCtrl );
// Copy USub into U
const Int UWidth = USub.Width();
Identity( U, m, UWidth );
auto UTop = U( IR(0,n), ALL );
UTop = USub;
}
else if( m < n )
{
// We need to work on a subset of V
Matrix<Field> VSub;
info.bidiagSVDInfo =
BidiagSVD( uplo, mainDiag, offDiag, U, s, VSub, ctrl.bidiagSVDCtrl );
// Copy VSub into V
const Int VWidth = VSub.Width();
Identity( V, n, VWidth );
auto VTop = V( IR(0,m), ALL );
VTop = VSub;
}
if( ctrl.time )
Output("Bidiag SVD: ",timer.Stop()," seconds");
// Backtransform U and V
if( ctrl.time )
timer.Start();
if( !avoidU ) bidiag::ApplyQ( LEFT, NORMAL, A, householderScalarsQ, U );
if( !avoidV ) bidiag::ApplyP( LEFT, NORMAL, A, householderScalarsP, V );
if( ctrl.time )
Output("GolubReinsch backtransformation: ",timer.Stop()," seconds");
return info;
}
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
GolubReinschUpper_FLA
( DistMatrix<F>& A, DistMatrix<BASE(F),VR,STAR>& s, DistMatrix<F>& V )
{
#ifndef RELEASE
CallStackEntry entry("svd::GolubReinschUpper_FLA");
#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 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 );
// In order to use serial QR kernels, we need the full bidiagonal matrix
// on each process
DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR ),
e_STAR_STAR( e_MD_STAR );
// Initialize U and VAdj to the appropriate identity matrices
DistMatrix<F,VC,STAR> U_VC_STAR(g), V_VC_STAR(g);
U_VC_STAR.AlignWith( A );
V_VC_STAR.AlignWith( V );
Identity( U_VC_STAR, m, k );
Identity( V_VC_STAR, n, k );
FlaSVD
( k, U_VC_STAR.LocalHeight(), V_VC_STAR.LocalHeight(),
d_STAR_STAR.Buffer(), e_STAR_STAR.Buffer(),
U_VC_STAR.Buffer(), U_VC_STAR.LDim(),
V_VC_STAR.Buffer(), V_VC_STAR.LDim() );
// Make a copy of A (for the Householder vectors) and pull the necessary
// portions of U and V 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 );
V = V_VC_STAR;
}
else
{
DistMatrix<F> VT(g), VB(g);
DistMatrix<F,VC,STAR> VT_VC_STAR(g), VB_VC_STAR(g);
PartitionDown( V, VT, VB, m );
PartitionDown( V_VC_STAR, VT_VC_STAR, VB_VC_STAR, m );
VT = VT_VC_STAR;
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<double> >& A,
DistMatrix<double,VR,STAR>& s,
DistMatrix<Complex<double> >& V )
{
#ifndef RELEASE
PushCallStack("svd::SimpleSVDUpper");
#endif
typedef double Real;
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 );
// In order to use serial QR kernels, we need the full bidiagonal matrix
// on each process
DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR ),
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,VC,STAR> V_VC_STAR( g );
U_VC_STAR.AlignWith( A );
V_VC_STAR.AlignWith( V );
Identity( m, k, U_VC_STAR );
Identity( n, k, V_VC_STAR );
// Compute the SVD of the bidiagonal matrix and accumulate the Givens
// rotations into our local portion of U and V
// NOTE: This _only_ works in the case where m >= n
const int numAccum = 32;
const int maxNumIts = 30;
const int bAlg = 512;
std::vector<C> GBuffer( (k-1)*numAccum ),
HBuffer( (k-1)*numAccum );
FLA_Bsvd_v_opz_var1
( k, U_VC_STAR.LocalHeight(), V_VC_STAR.LocalHeight(),
numAccum, maxNumIts,
d_STAR_STAR.LocalBuffer(), 1,
e_STAR_STAR.LocalBuffer(), 1,
&GBuffer[0], 1, k-1,
&HBuffer[0], 1, k-1,
U_VC_STAR.LocalBuffer(), 1, U_VC_STAR.LocalLDim(),
V_VC_STAR.LocalBuffer(), 1, V_VC_STAR.LocalLDim(),
bAlg );
// Make a copy of A (for the Householder vectors) and pull the necessary
// portions of U and V 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 );
V = V_VC_STAR;
}
else
{
DistMatrix<C> VT( g ),
VB( g );
DistMatrix<C,VC,STAR> VT_VC_STAR( g ),
VB_VC_STAR( g );
PartitionDown( V, VT,
VB, m );
PartitionDown
( V_VC_STAR, VT_VC_STAR,
VB_VC_STAR, m );
VT = VT_VC_STAR;
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
}
inline void
SimpleSVDUpper
( DistMatrix<Real>& A,
DistMatrix<Real,VR,STAR>& s,
DistMatrix<Real>& V )
{
#ifndef RELEASE
PushCallStack("svd::SimpleSVDUpper");
#endif
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
Bidiag( A );
// Grab copies of the diagonal and sub/super-diagonal of A
DistMatrix<Real,MD,STAR> d_MD_STAR( g ),
e_MD_STAR( g );
A.GetDiagonal( d_MD_STAR );
A.GetDiagonal( e_MD_STAR, offdiagonal );
// In order to use serial QR kernels, we need the full bidiagonal matrix
// on each process.
//
// 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 VTrans to the appropriate identity matrices.
DistMatrix<Real,VC,STAR> U_VC_STAR( g );
DistMatrix<Real,STAR,VC> VTrans_STAR_VC( g );
U_VC_STAR.AlignWith( A );
VTrans_STAR_VC.AlignWith( V );
Identity( m, k, U_VC_STAR );
Identity( k, n, VTrans_STAR_VC );
// Compute the SVD of the bidiagonal matrix and accumulate the Givens
// rotations into our local portion of U and VTrans
Matrix<Real>& ULocal = U_VC_STAR.LocalMatrix();
Matrix<Real>& VTransLocal = VTrans_STAR_VC.LocalMatrix();
lapack::BidiagQRAlg
( uplo, k, VTransLocal.Width(), ULocal.Height(),
d_STAR_STAR.LocalBuffer(), e_STAR_STAR.LocalBuffer(),
VTransLocal.Buffer(), VTransLocal.LDim(),
ULocal.Buffer(), ULocal.LDim() );
// Make a copy of A (for the Householder vectors) and pull the necessary
// portions of U and VTrans into a standard matrix dist.
DistMatrix<Real> B( A );
if( m >= n )
{
DistMatrix<Real> AT( g ),
AB( g );
DistMatrix<Real,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 );
Transpose( VTrans_STAR_VC, V );
}
else
{
DistMatrix<Real> VT( g ),
VB( g );
DistMatrix<Real,STAR,VC>
VTransL_STAR_VC( g ), VTransR_STAR_VC( g );
PartitionDown( V, VT,
VB, m );
PartitionRight( VTrans_STAR_VC, VTransL_STAR_VC, VTransR_STAR_VC, m );
Transpose( VTransL_STAR_VC, VT );
MakeZeros( VB );
}
// Backtransform U and V
if( m >= n )
{
ApplyPackedReflectors
( LEFT, LOWER, VERTICAL, BACKWARD, 0, B, A );
ApplyPackedReflectors
( LEFT, UPPER, HORIZONTAL, BACKWARD, 1, B, V );
}
else
{
ApplyPackedReflectors
( LEFT, LOWER, VERTICAL, BACKWARD, -1, B, A );
ApplyPackedReflectors
( LEFT, UPPER, HORIZONTAL, BACKWARD, 0, B, V );
}
// Copy out the appropriate subset of the singular values
s = d_STAR_STAR;
#ifndef RELEASE
PopCallStack();
#endif
}
