Contents
sbdsqr - compute the singular value decomposition (SVD) of a
real N-by-N (upper or lower) bidiagonal matrix B.
SUBROUTINE SBDSQR(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C,
LDC, WORK, INFO)
CHARACTER * 1 UPLO
INTEGER N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL D(*), E(*), VT(LDVT,*), U(LDU,*), C(LDC,*), WORK(*)
SUBROUTINE SBDSQR_64(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU,
C, LDC, WORK, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL D(*), E(*), VT(LDVT,*), U(LDU,*), C(LDC,*), WORK(*)
F95 INTERFACE
SUBROUTINE BDSQR(UPLO, [N], [NCVT], [NRU], [NCC], D, E, VT, [LDVT],
U, [LDU], C, [LDC], [WORK], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL, DIMENSION(:) :: D, E, WORK
REAL, DIMENSION(:,:) :: VT, U, C
SUBROUTINE BDSQR_64(UPLO, [N], [NCVT], [NRU], [NCC], D, E, VT, [LDVT],
U, [LDU], C, [LDC], [WORK], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL, DIMENSION(:) :: D, E, WORK
REAL, DIMENSION(:,:) :: VT, U, C
C INTERFACE
#include <sunperf.h>
void sbdsqr(char uplo, int n, int ncvt, int nru, int ncc,
float *d, float *e, float *vt, int ldvt, float *u,
int ldu, float *c, int ldc, int *info);
void sbdsqr_64(char uplo, long n, long ncvt, long nru, long
ncc, float *d, float *e, float *vt, long ldvt,
float *u, long ldu, float *c, long ldc, long
*info);
sbdsqr computes the singular value decomposition (SVD) of a
real N-by-N (upper or lower) bidiagonal matrix B: B = Q * S
* P' (P' denotes the transpose of P), where S is a diagonal
matrix with non-negative diagonal elements (the singular
values of B), and Q and P are orthogonal matrices.
The routine computes S, and optionally computes U * Q, P' *
VT, or Q' * C, for given real input matrices U, VT, and C.
See "Computing Small Singular Values of Bidiagonal Matrices
With Guaranteed High Relative Accuracy," by J. Demmel and W.
Kahan, LAPACK Working Note #3 (or SIAM J. Sci. Statist. Com-
put. vol. 11, no. 5, pp. 873-912, Sept 1990) and
"Accurate singular values and differential qd algorithms,"
by B. Parlett and V. Fernando, Technical Report CPAM-554,
Mathematics Department, University of California at Berke-
ley, July 1992 for a detailed description of the algorithm.
UPLO (input)
= 'U': B is upper bidiagonal;
= 'L': B is lower bidiagonal.
N (input) The order of the matrix B. N >= 0.
NCVT (input)
The number of columns of the matrix VT. NCVT >= 0.
NRU (input)
The number of rows of the matrix U. NRU >= 0.
NCC (input)
The number of columns of the matrix C. NCC >= 0.
D (input/output)
On entry, the n diagonal elements of the bidiago-
nal matrix B. On exit, if INFO=0, the singular
values of B in decreasing order.
E (input/output)
On entry, the elements of E contain the offdiago-
nal elements of the bidiagonal matrix whose SVD is
desired. On normal exit (INFO = 0), E is
destroyed. If the algorithm does not converge
(INFO > 0), D and E will contain the diagonal and
superdiagonal elements of a bidiagonal matrix
orthogonally equivalent to the one given as input.
E(N) is used for workspace.
VT (input/output)
On entry, an N-by-NCVT matrix VT. On exit, VT is
overwritten by P' * VT. VT is not referenced if
NCVT = 0.
LDVT (input)
The leading dimension of the array VT. LDVT >=
max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0.
U (input/output)
On entry, an NRU-by-N matrix U. On exit, U is
overwritten by U * Q. U is not referenced if NRU
= 0.
LDU (input)
The leading dimension of the array U. LDU >=
max(1,NRU).
C (input/output)
On entry, an N-by-NCC matrix C. On exit, C is
overwritten by Q' * C. C is not referenced if NCC
= 0.
LDC (input)
The leading dimension of the array C. LDC >=
max(1,N) if NCC > 0; LDC >=1 if NCC = 0.
WORK (workspace)
dimension(4*N)
INFO (output)
= 0: successful exit
< 0: If INFO = -i, the i-th argument had an ille-
gal value
> 0: the algorithm did not converge; D and E con-
tain the elements of a bidiagonal matrix which is
orthogonally similar to the input matrix B; if
INFO = i, i elements of E have not converged to
zero.