cbdsqr(3P) Sun Performance Library cbdsqr(3P)NAMEcbdsqr - compute the singular value decomposition (SVD) of a real N-by-
N (upper or lower) bidiagonal matrix B.
SYNOPSIS
SUBROUTINE CBDSQR(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C,
LDC, WORK, INFO)
CHARACTER * 1 UPLO
COMPLEX VT(LDVT,*), U(LDU,*), C(LDC,*)
INTEGER N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL D(*), E(*), WORK(*)
SUBROUTINE CBDSQR_64(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU,
C, LDC, WORK, INFO)
CHARACTER * 1 UPLO
COMPLEX VT(LDVT,*), U(LDU,*), C(LDC,*)
INTEGER*8 N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL 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, DIMENSION(:,:) :: VT, U, C
INTEGER :: N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL, 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, DIMENSION(:,:) :: VT, U, C
INTEGER(8) :: N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
REAL, DIMENSION(:) :: D, E, WORK
C INTERFACE
#include <sunperf.h>
void cbdsqr(char uplo, int n, int ncvt, int nru, int ncc, float *d,
float *e, complex *vt, int ldvt, complex *u, int ldu, complex
*c, int ldc, int *info);
void cbdsqr_64(char uplo, long n, long ncvt, long nru, long ncc, float
*d, float *e, complex *vt, long ldvt, complex *u, long ldu,
complex *c, long ldc, long *info);
PURPOSEcbdsqr 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 diago‐
nal 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 Guar‐
anteed High Relative Accuracy," by J. Demmel and W. Kahan, LAPACK Work‐
ing Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, no. 5, pp.
873-912, Sept 1990) and
"Accurate singular values and differential qd algorithms," by B. Par‐
lett and V. Fernando, Technical Report CPAM-554, Mathematics Depart‐
ment, University of California at Berkeley, July 1992 for a detailed
description of the algorithm.
ARGUMENTS
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 bidiagonal 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 offdiagonal elements
of 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 illegal value
> 0: the algorithm did not converge; D and E contain 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.
6 Mar 2009 cbdsqr(3P)
