Contents
zbdsqr - compute the singular value decomposition (SVD) of a
real N-by-N (upper or lower) bidiagonal matrix B.
SUBROUTINE ZBDSQR(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C,
LDC, WORK, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX VT(LDVT,*), U(LDU,*), C(LDC,*)
INTEGER N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
DOUBLE PRECISION D(*), E(*), WORK(*)
SUBROUTINE ZBDSQR_64(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU,
C, LDC, WORK, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX VT(LDVT,*), U(LDU,*), C(LDC,*)
INTEGER*8 N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
DOUBLE PRECISION D(*), E(*), WORK(*)
F95 INTERFACE
SUBROUTINE BDSQR(UPLO, [N], [NCVT], [NRU], [NCC], D, E, VT, [LDVT],
U, [LDU], C, [LDC], [WORK], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:,:) :: VT, U, C
INTEGER :: N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL(8), DIMENSION(:) :: D, E, WORK
SUBROUTINE BDSQR_64(UPLO, [N], [NCVT], [NRU], [NCC], D, E, VT, [LDVT],
U, [LDU], C, [LDC], [WORK], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:,:) :: VT, U, C
INTEGER(8) :: N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL(8), DIMENSION(:) :: D, E, WORK
C INTERFACE
#include <sunperf.h>
void zbdsqr(char uplo, int n, int ncvt, int nru, int ncc,
double *d, double *e, doublecomplex *vt, int ldvt,
doublecomplex *u, int ldu, doublecomplex *c, int
ldc, int *info);
void zbdsqr_64(char uplo, long n, long ncvt, long nru, long
ncc, double *d, double *e, doublecomplex *vt, long
ldvt, doublecomplex *u, long ldu, doublecomplex
*c, long ldc, long *info);
zbdsqr 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 complex 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 of the bidiagonal matrix whose SVD
is desired. On normal exit (INFO = 0), E is des-
troyed. If the algorithm does not converge (INFO
> 0), D and E will contain the diagonal and super-
diagonal elements of a bidiagonal matrix orthogo-
nally 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.