Contents
dgesvd - compute the singular value decomposition (SVD) of a
real M-by-N matrix A, optionally computing the left and/or
right singular vectors
SUBROUTINE DGESVD(JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT, LDVT,
WORK, LDWORK, INFO)
CHARACTER * 1 JOBU, JOBVT
INTEGER M, N, LDA, LDU, LDVT, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), SING(*), U(LDU,*), VT(LDVT,*),
WORK(*)
SUBROUTINE DGESVD_64(JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT,
LDVT, WORK, LDWORK, INFO)
CHARACTER * 1 JOBU, JOBVT
INTEGER*8 M, N, LDA, LDU, LDVT, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), SING(*), U(LDU,*), VT(LDVT,*),
WORK(*)
F95 INTERFACE
SUBROUTINE GESVD(JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU], VT,
[LDVT], [WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBVT
INTEGER :: M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL(8), DIMENSION(:) :: SING, WORK
REAL(8), DIMENSION(:,:) :: A, U, VT
SUBROUTINE GESVD_64(JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU],
VT, [LDVT], [WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBVT
INTEGER(8) :: M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL(8), DIMENSION(:) :: SING, WORK
REAL(8), DIMENSION(:,:) :: A, U, VT
C INTERFACE
#include <sunperf.h>
void dgesvd(char jobu, char jobvt, int m, int n, double *a,
int lda, double *sing, double *u, int ldu, double
*vt, int ldvt, int *info);
void dgesvd_64(char jobu, char jobvt, long m, long n, double
*a, long lda, double *sing, double *u, long ldu,
double *vt, long ldvt, long *info);
dgesvd computes the singular value decomposition (SVD) of a
real M-by-N matrix A, optionally computing the left and/or
right singular vectors. The SVD is written
= U * SIGMA * transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M orthogonal
matrix, and V is an N-by-N orthogonal matrix. The diagonal
elements of SIGMA are the singular values of A; they are
real and non-negative, and are returned in descending order.
The first min(m,n) columns of U and V are the left and right
singular vectors of A.
Note that the routine returns V**T, not V.
JOBU (input)
Specifies options for computing all or part of the
matrix U:
= 'A': all M columns of U are returned in array
U:
= 'S': the first min(m,n) columns of U (the left
singular vectors) are returned in the array U; =
'O': the first min(m,n) columns of U (the left
singular vectors) are overwritten on the array A;
= 'N': no columns of U (no left singular vectors)
are computed.
JOBVT (input)
Specifies options for computing all or part of the
matrix V**T:
= 'A': all N rows of V**T are returned in the
array VT;
= 'S': the first min(m,n) rows of V**T (the right
singular vectors) are returned in the array VT; =
'O': the first min(m,n) rows of V**T (the right
singular vectors) are overwritten on the array A;
= 'N': no rows of V**T (no right singular vec-
tors) are computed.
JOBVT and JOBU cannot both be 'O'.
M (input) The number of rows of the input matrix A. M >= 0.
N (input) The number of columns of the input matrix A. N >=
0.
A (input/output)
On entry, the M-by-N matrix A. On exit, if JOBU =
'O', A is overwritten with the first min(m,n)
columns of U (the left singular vectors, stored
columnwise); if JOBVT = 'O', A is overwritten with
the first min(m,n) rows of V**T (the right singu-
lar vectors, stored rowwise); if JOBU .ne. 'O' and
JOBVT .ne. 'O', the contents of A are destroyed.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
SING (output)
The singular values of A, sorted so that SING(i)
>= SING(i+1).
U (input) (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU =
'S'. If JOBU = 'A', U contains the M-by-M orthog-
onal matrix U; if JOBU = 'S', U contains the first
min(m,n) columns of U (the left singular vectors,
stored columnwise); if JOBU = 'N' or 'O', U is not
referenced.
LDU (input)
The leading dimension of the array U. LDU >= 1;
if JOBU = 'S' or 'A', LDU >= M.
VT (input)
If JOBVT = 'A', VT contains the N-by-N orthogonal
matrix V**T; if JOBVT = 'S', VT contains the first
min(m,n) rows of V**T (the right singular vectors,
stored rowwise); if JOBVT = 'N' or 'O', VT is not
referenced.
LDVT (input)
The leading dimension of the array VT. LDVT >= 1;
if JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >=
min(M,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK; if INFO > 0, WORK(2:MIN(M,N)) contains the
unconverged superdiagonal elements of an upper
bidiagonal matrix B whose diagonal is in SING (not
necessarily sorted). B satisfies A = U * B * VT,
so it has the same singular values as A, and
singular vectors related by U and VT.
LDWORK (input)
The dimension of the array WORK. LDWORK >= 1.
LDWORK >= MAX(3*MIN(M,N)+MAX(M,N),5*MIN(M,N)).
For good performance, LDWORK should generally be
larger.
If LDWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LDWORK is issued by XERBLA.
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
> 0: if SBDSQR did not converge, INFO specifies
how many superdiagonals of an intermediate bidiag-
onal form B did not converge to zero. See the
description of WORK above for details.