Contents
cgesvd - compute the singular value decomposition (SVD) of a
complex M-by-N matrix A, optionally computing the left
and/or right singular vectors
SUBROUTINE CGESVD(JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT, LDVT,
WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBU, JOBVT
COMPLEX A(LDA,*), U(LDU,*), VT(LDVT,*), WORK(*)
INTEGER M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL SING(*), WORK2(*)
SUBROUTINE CGESVD_64(JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT,
LDVT, WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBU, JOBVT
COMPLEX A(LDA,*), U(LDU,*), VT(LDVT,*), WORK(*)
INTEGER*8 M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL SING(*), WORK2(*)
F95 INTERFACE
SUBROUTINE GESVD(JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU], VT,
[LDVT], [WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBVT
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, U, VT
INTEGER :: M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL, DIMENSION(:) :: SING, WORK2
SUBROUTINE GESVD_64(JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU],
VT, [LDVT], [WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBVT
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, U, VT
INTEGER(8) :: M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL, DIMENSION(:) :: SING, WORK2
C INTERFACE
#include <sunperf.h>
void cgesvd(char jobu, char jobvt, int m, int n, complex *a,
int lda, float *sing, complex *u, int ldu, complex
*vt, int ldvt, int *info);
void cgesvd_64(char jobu, char jobvt, long m, long n, com-
plex *a, long lda, float *sing, complex *u, long
ldu, complex *vt, long ldvt, long *info);
cgesvd computes the singular value decomposition (SVD) of a
complex M-by-N matrix A, optionally computing the left
and/or right singular vectors. The SVD is written
= U * SIGMA * conjugate-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 unitary matrix,
and V is an N-by-N unitary 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**H, 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**H:
= 'A': all N rows of V**H are returned in the
array VT;
= 'S': the first min(m,n) rows of V**H (the right
singular vectors) are returned in the array VT; =
'O': the first min(m,n) rows of V**H (the right
singular vectors) are overwritten on the array A;
= 'N': no rows of V**H (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**H (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 unitary
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 unitary
matrix V**H; if JOBVT = 'S', VT contains the first
min(m,n) rows of V**H (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.
LDWORK (input)
The dimension of the array WORK. LDWORK >= 1.
LDWORK >= 2*MIN(M,N)+MAX(M,N) For good perfor-
mance, 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.
WORK2 (workspace)
DIMENSION(5*MIN(M,N)). On exit, if INFO > 0,
WORK2(1:MIN(M,N)-1) contains the unconverged
superdiagonal elements of an upper bidiagonal
matrix B whose diagonal is in SING (not neces-
sarily sorted). B satisfies A = U * B * VT, so it
has the same singular values as A, and singular
vectors related by U and VT.
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
> 0: if CBDSQR did not converge, INFO specifies
how many superdiagonals of an intermediate bidiag-
onal form B did not converge to zero. See the
description of WORK2 above for details.