cbdsqr - N (upper or lower) bidiagonal matrix B
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);
Oracle Solaris Studio Performance Library cbdsqr(3P)
NAME
cbdsqr - 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);
PURPOSE
cbdsqr 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.
7 Nov 2015 cbdsqr(3P)