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(*)
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
#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);
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.
= '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.
= '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 vectors) are computed.
JOBVT and JOBU cannot both be 'O'.
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.
SING(i)
> = SING(i+1).
min(m,n)
columns of U
(the left singular vectors, stored columnwise);
if JOBU = 'N' or 'O', U is not referenced.
min(m,n)
rows of
V**H (the right singular vectors, stored rowwise);
if JOBVT = 'N' or 'O', VT is not referenced.
WORK(1)
returns the optimal LDWORK.
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(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.
= 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.