DLASDQ - compute the singular value decomposition (SVD) of
a real (upper or lower) bidiagonal matrix with diagonal D
and offdiagonal E, accumulating the transformations if
desired
SYNOPSIS
SUBROUTINE DLASDQ( 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
DOUBLE PRECISION C( LDC, * ), D( * ), E( * ),
U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
DLASDQ computes the singular value decomposition (SVD) of
a real (upper or lower) bidiagonal 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 Matri
ces 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 bidiago
nal matrix is upper or lower bidiagonal, 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 N-by-N.
= 1: then the input matrix is N-by-(N+1) if UPLU =
'U' and (N+1)-by-N if UPLU = 'L'.
The bidiagonal matrix has N = NL + NR + 1 rows and M
= N + SQRE >= N columns.
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) DOUBLE PRECISION 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) DOUBLE PRECISION array.
dimension is (N-1) if SQRE = 0 and N if SQRE = 1.
On entry, the entries of E contain the offdiagonal
entries of the bidiagonal matrix whose SVD is
desired. On normal exit, E will contain 0. If the
algorithm does not converge, D and E will contain
the diagonal and superdiagonal entries of a bidiago
nal matrix orthogonally equivalent to the one given
as input.
VT (input/output) DOUBLE PRECISION array, dimension
(LDVT, NCVT)
On entry, contains a matrix which on exit has been
premultiplied by P', dimension N-by-NCVT if SQRE = 0
and (N+1)-by-NCVT 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) DOUBLE PRECISION array, dimension
(LDU, N)
On entry, contains a matrix which on exit has been
postmultiplied by Q, dimension NRU-by-N if SQRE = 0
and NRU-by-(N+1) if SQRE = 1 (not referenced if
NRU=0).
LDU (input) INTEGER
On entry, LDU specifies the leading dimension of U
be at least max( 1, NRU ) .
C (input/output) DOUBLE PRECISION array, dimension
(LDC, NCC)
On entry, contains an N-by-NCC matrix which on exit
has been premultiplied by Q' dimension N-by-NCC if
SQRE = 0 and (N+1)-by-NCC if SQRE = 1 (not refer
enced 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) DOUBLE PRECISION 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, Uni
versity of
California at Berkeley, USA
Man(1) output converted with
man2html