DLASDQ(3S)DLASDQ(3S)NAMEDLASDQ - 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( * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSEDLASDQ 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 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 bidiagonal, and wether it is square are not. UPLO =
'U' or 'u' B is upper bidiagonal. UPLO = 'L' or 'l' B is lower
bidiagonal.
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DLASDQ(3S)DLASDQ(3S)
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.
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) 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 bidiagonal 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).
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DLASDQ(3S)DLASDQ(3S)
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) 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 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) 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, University of
California at Berkeley, USA
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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