
DLASDA(l) ) DLASDA(l)
NAME
DLASDA  a divide and conquer approach, DLASDA computes the singular value decomposition
(SVD) of a real upper bidiagonal NbyM matrix B with diagonal D and offdiagonal E, where
M = N + SQRE
SYNOPSIS
SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES,
GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO )
INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE
INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), K( * ), PERM( LDGCOL, * )
DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), E( * ),
GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), U( LDU, * ), VT( LDU, * ),
WORK( * ), Z( LDU, * )
PURPOSE
Using a divide and conquer approach, DLASDA computes the singular value decomposition
(SVD) of a real upper bidiagonal NbyM matrix B with diagonal D and offdiagonal E, where
M = N + SQRE. The algorithm computes the singular values in the SVD B = U * S * VT. The
orthogonal matrices U and VT are optionally computed in compact form.
A related subroutine, DLASD0, computes the singular values and the singular vectors in
explicit form.
ARGUMENTS
ICOMPQ (input) INTEGER Specifies whether singular vectors are to be computed in compact
form, as follows = 0: Compute singular values only.
= 1: Compute singular vectors of upper bidiagonal matrix in compact form.
SMLSIZ (input) INTEGER The maximum size of the subproblems at the bottom of the computa
tion tree.
N (input) INTEGER
The row dimension of the upper bidiagonal matrix. This is also the dimension of the
main diagonal array D.
SQRE (input) INTEGER
Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal
matrix has column dimension M = N;
= 1: The bidiagonal matrix has column dimension M = N + 1.
D (input/output) DOUBLE PRECISION array, dimension ( N )
On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO
= 0, contains its singular values.
E (input) DOUBLE PRECISION array, dimension ( M1 )
Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been
destroyed.
U (output) DOUBLE PRECISION array,
dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If
ICOMPQ = 1, on exit, U contains the left singular vector matrices of all subprob
lems at the bottom level.
LDU (input) INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.
VT (output) DOUBLE PRECISION array,
dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If
ICOMPQ = 1, on exit, VT' contains the right singular vector matrices of all sub
problems at the bottom level.
K (output) INTEGER array,
dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1, on
exit, K(I) is the dimension of the Ith secular equation on the computation tree.
DIFL (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ),
where NLVL = floor(log_2 (N/SMLSIZ))).
DIFR (output) DOUBLE PRECISION array,
dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. If
ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I  1) record distances between
singular values on the Ith level and singular values on the (I 1)th level, and
DIFR(1:N, 2 * I ) contains the normalizing factors for the right singular vector
matrix. See DLASD8 for details.
Z (output) DOUBLE PRECISION array,
dimension ( LDU, NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. The first
K elements of Z(1, I) contain the components of the deflationadjusted updating row
vector for subproblems on the Ith level.
POLES (output) DOUBLE PRECISION array,
dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If
ICOMPQ = 1, on exit, POLES(1, 2*I  1) and POLES(1, 2*I) contain the new and old
singular values involved in the secular equations on the Ith level.
GIVPTR (output) INTEGER array, dimension ( N ) if ICOMPQ = 1, and not referenced if
ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records the number of Givens rota
tions performed on the Ith problem on the computation tree.
GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and
not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVCOL(1, 2 *I 
1) and GIVCOL(1, 2 *I) record the locations of Givens rotations performed on the I
th level on the computation tree.
LDGCOL (input) INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and
PERM.
PERM (output) INTEGER array,
dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If
ICOMPQ = 1, on exit, PERM(1, I) records permutations done on the Ith level of the
computation tree.
GIVNUM (output) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1,
and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVNUM(1, 2
*I  1) and GIVNUM(1, 2 *I) record the C and S values of Givens rotations per
formed on the Ith level on the computation tree.
C (output) DOUBLE PRECISION array,
dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and
the Ith subproblem is not square, on exit, C( I ) contains the Cvalue of a Givens
rotation related to the right null space of the Ith subproblem.
S (output) DOUBLE PRECISION array, dimension ( N ) if
ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the Ith subproblem is
not square, on exit, S( I ) contains the Svalue of a Givens rotation related to
the right null space of the Ith subproblem.
WORK (workspace) DOUBLE PRECISION array, dimension
(6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
IWORK (workspace) INTEGER array.
Dimension must be at least (7 * N).
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
> 0: if INFO = 1, an singular value did not converge
FURTHER DETAILS
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
LAPACK version 3.0 15 June 2000 DLASDA(l) 
