cgesvd - by-N matrix A, optionally computing the left and/or right singular vec- tors
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, complex *a, long lda, float *sing, complex *u, long ldu, complex *vt, long ldvt, long *info);
Oracle Solaris Studio Performance Library cgesvd(3P)
NAME
cgesvd - compute the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right singular vec-
tors
SYNOPSIS
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, complex *a, long
lda, float *sing, complex *u, long ldu, complex *vt, long
ldvt, long *info);
PURPOSE
cgesvd computes the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right singular vec-
tors. 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.
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**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 over-
written on the array A; = 'N': no rows of V**H (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**H (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 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 (output)
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 performance, LDWORK should gen-
erally 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.
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 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.
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if CBDSQR did not converge, INFO specifies how many
superdiagonals of an intermediate bidiagonal form B did not
converge to zero. See the description of WORK2 above for
details.
7 Nov 2015 cgesvd(3P)