
SLASDQ(l) ) SLASDQ(l)
NAME
SLASDQ  compute the singular value decomposition (SVD) of a real (upper or lower) bidiag
onal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired
SYNOPSIS
SUBROUTINE SLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK,
INFO )
CHARACTER UPLO
INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE
REAL C( LDC, * ), D( * ), E( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
SLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiago
nal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired.
Letting B denote the input bidiagonal matrix, the algorithm computes orthogonal matrices Q
and P such that B = Q * S * P' (P' denotes the transpose of P). The singular values S are
overwritten on D.
The input matrix U is changed to U * Q if desired.
The input matrix VT is changed to P' * VT if desired.
The input matrix C is changed to Q' * C if desired.
See "Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative
Accuracy," by J. Demmel and W. Kahan, LAPACK Working Note #3, for a detailed description
of the algorithm.
ARGUMENTS
UPLO (input) CHARACTER*1
On entry, UPLO specifies whether the input bidiagonal matrix is upper or lower bidi
agonal, and wether it is square are not. UPLO = 'U' or 'u' B is upper bidiagonal.
UPLO = 'L' or 'l' B is lower bidiagonal.
SQRE (input) INTEGER
= 0: then the input matrix is NbyN.
= 1: then the input matrix is Nby(N+1) if UPLU = 'U' and (N+1)byN if UPLU = 'L'.
The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.
N (input) INTEGER
On entry, N specifies the number of rows and columns in the matrix. N must be at
least 0.
NCVT (input) INTEGER
On entry, NCVT specifies the number of columns of the matrix VT. NCVT must be at
least 0.
NRU (input) INTEGER
On entry, NRU specifies the number of rows of the matrix U. NRU must be at least 0.
NCC (input) INTEGER
On entry, NCC specifies the number of columns of the matrix C. NCC must be at least
0.
D (input/output) REAL array, dimension (N)
On entry, D contains the diagonal entries of the bidiagonal matrix whose SVD is
desired. On normal exit, D contains the singular values in ascending order.
E (input/output) REAL array.
dimension is (N1) if SQRE = 0 and N if SQRE = 1. On entry, the entries of E con
tain the offdiagonal entries of the bidiagonal matrix whose SVD is desired. On nor
mal exit, E will contain 0. If the algorithm does not converge, D and E will contain
the diagonal and superdiagonal entries of a bidiagonal matrix orthogonally equiva
lent to the one given as input.
VT (input/output) REAL array, dimension (LDVT, NCVT)
On entry, contains a matrix which on exit has been premultiplied by P', dimension N
byNCVT if SQRE = 0 and (N+1)byNCVT if SQRE = 1 (not referenced if NCVT=0).
LDVT (input) INTEGER
On entry, LDVT specifies the leading dimension of VT as declared in the calling
(sub) program. LDVT must be at least 1. If NCVT is nonzero LDVT must also be at
least N.
U (input/output) REAL array, dimension (LDU, N)
On entry, contains a matrix which on exit has been postmultiplied by Q, dimension
NRUbyN if SQRE = 0 and NRUby(N+1) if SQRE = 1 (not referenced if NRU=0).
LDU (input) INTEGER
On entry, LDU specifies the leading dimension of U as declared in the calling (sub)
program. LDU must be at least max( 1, NRU ) .
C (input/output) REAL array, dimension (LDC, NCC)
On entry, contains an NbyNCC matrix which on exit has been premultiplied by Q'
dimension NbyNCC if SQRE = 0 and (N+1)byNCC if SQRE = 1 (not referenced if
NCC=0).
LDC (input) INTEGER
On entry, LDC specifies the leading dimension of C as declared in the calling (sub)
program. LDC must be at least 1. If NCC is nonzero, LDC must also be at least N.
WORK (workspace) REAL array, dimension (4*N)
Workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero, and if N is at
least 2.
INFO (output) INTEGER
On exit, a value of 0 indicates a successful exit. If INFO < 0, argument number
INFO is illegal. If INFO > 0, the algorithm did not converge, and INFO specifies
how many superdiagonals 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 SLASDQ(l) 
