dbdsqr
dbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B.
SUBROUTINE DBDSQR( 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
DOUBLE PRECISION D(*), E(*), VT(LDVT,*), U(LDU,*), C(LDC,*), WORK(*)
SUBROUTINE DBDSQR_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
DOUBLE PRECISION D(*), E(*), VT(LDVT,*), U(LDU,*), C(LDC,*), WORK(*)
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(8), DIMENSION(:) :: D, E, WORK
REAL(8), 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(8), DIMENSION(:) :: D, E, WORK
REAL(8), DIMENSION(:,:) :: VT, U, C
#include <sunperf.h>
void dbdsqr(char uplo, int n, int ncvt, int nru, int ncc, double *d, double *e, double *vt, int ldvt, double *u, int ldu, double *c, int ldc, int *info);
void dbdsqr_64(char uplo, long n, long ncvt, long nru, long ncc, double *d, double *e, double *vt, long ldvt, double *u, long ldu, double *c, long ldc, long *info);
dbdsqr 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. Comput. 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 Berkeley, July 1992
for a detailed description of the algorithm.
-
* UPLO (input)
-
-
* 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 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)
-