dgesvd(3P) Sun Performance Library dgesvd(3P)NAMEdgesvd - compute the singular value decomposition (SVD) of a real M-by-
N matrix A, optionally computing the left and/or right singular vectors
SYNOPSIS
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);
PURPOSEdgesvd 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.
ARGUMENTS
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 over‐
written on the array A; = 'N': no columns of U (no left sin‐
gular 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 over‐
written on the array A; = 'N': no rows of V**T (no right
singular vectors) 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
singular 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 (output)
(LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If
JOBU = 'A', U contains the M-by-M orthogonal 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 (output)
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 super‐
diagonal elements of an upper bidiagonal matrix B whose diag‐
onal 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 rou‐
tine 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 illegal value.
> 0: if SBDSQR did not converge, INFO specifies how many
superdiagonals of an intermediate bidiagonal form B did not
converge to zero. See the description of WORK above for
details.
6 Mar 2009 dgesvd(3P)
