zgesdd(3P) Sun Performance Library zgesdd(3P)NAMEzgesdd - compute the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right singular vec‐
tors, by using divide-and-conquer method
SYNOPSIS
SUBROUTINE ZGESDD(JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
LWORK, RWORK, IWORK, INFO)
CHARACTER * 1 JOBZ
DOUBLE COMPLEX A(LDA,*), U(LDU,*), VT(LDVT,*), WORK(*)
INTEGER M, N, LDA, LDU, LDVT, LWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION S(*), RWORK(*)
SUBROUTINE ZGESDD_64(JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
LWORK, RWORK, IWORK, INFO)
CHARACTER * 1 JOBZ
DOUBLE COMPLEX A(LDA,*), U(LDU,*), VT(LDVT,*), WORK(*)
INTEGER*8 M, N, LDA, LDU, LDVT, LWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION S(*), RWORK(*)
F95 INTERFACE
SUBROUTINE GESDD(JOBZ, [M], [N], A, [LDA], S, U, [LDU], VT, [LDVT],
[WORK], [LWORK], [RWORK], [IWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, U, VT
INTEGER :: M, N, LDA, LDU, LDVT, LWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: S, RWORK
SUBROUTINE GESDD_64(JOBZ, [M], [N], A, [LDA], S, U, [LDU], VT, [LDVT],
[WORK], [LWORK], [RWORK], [IWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, U, VT
INTEGER(8) :: M, N, LDA, LDU, LDVT, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: S, RWORK
C INTERFACE
#include <sunperf.h>
void zgesdd(char jobz, int m, int n, doublecomplex *a, int lda, double
*s, doublecomplex *u, int ldu, doublecomplex *vt, int ldvt,
int *info);
void zgesdd_64(char jobz, long m, long n, doublecomplex *a, long lda,
double *s, doublecomplex *u, long ldu, doublecomplex *vt,
long ldvt, long *info);
PURPOSEzgesdd computes the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right singular vec‐
tors, by using divide-and-conquer method. 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 VT = V**H, not V.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard digit
in add/subtract, or on those binary machines without guard digits which
subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
conceivably fail on hexadecimal or decimal machines without guard dig‐
its, but we know of none.
ARGUMENTS
JOBZ (input)
Specifies options for computing all or part of the matrix U:
= 'A': all M columns of U and all N rows of V**H are
returned in the arrays U and VT; = 'S': the first min(M,N)
columns of U and the first min(M,N) rows of V**H are returned
in the arrays U and VT; = 'O': If M >= N, the first N col‐
umns of U are overwritten on the array A and all rows of V**H
are returned in the array VT; otherwise, all columns of U are
returned in the array U and the first M rows of V**H are
overwritten on the array A; = 'N': no columns of U or rows
of V**H are computed.
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 JOBZ = 'O', A is
overwritten with the first N columns of U (the left singular
vectors, stored columnwise) if M >= N; A is overwritten with
the first M rows of V**H (the right singular vectors, stored
rowwise) otherwise. if JOBZ .ne. 'O', the contents of A are
destroyed.
LDA (input)
The leading dimension of the array A. LDA >= max(1,M).
S (output)
The singular values of A, sorted so that S(i) >= S(i+1).
U (output)
UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL =
min(M,N) if JOBZ = 'S'. If JOBZ = 'A' or JOBZ = 'O' and M <
N, U contains the M-by-M unitary matrix U; if JOBZ = 'S', U
contains the first min(M,N) columns of U (the left singular
vectors, stored columnwise); if JOBZ = 'O' and M >= N, or
JOBZ = 'N', U is not referenced.
LDU (input)
The leading dimension of the array U. LDU >= 1; if JOBZ =
'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
VT (output)
If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-
N unitary matrix V**H; if JOBZ = 'S', VT contains the first
min(M,N) rows of V**H (the right singular vectors, stored
rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not
referenced.
LDVT (input)
The leading dimension of the array VT. LDVT >= 1; if JOBZ =
'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT
>= min(M,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >= 1. If LWORK = -1,
then a workspace query is assumed. In this case, 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 LWORK is issued. The minimum workspace
size requirement is as follows:
If M is much larger than N such that M >= (N*17/9)):
if JOBZ = 'N', LWORK >= 3*N
if JOBZ = 'O', LWORK >= 2*N*N + 3*N
if JOBZ = 'S', LWORK >= N*N + 3*N
if JOBZ = 'A', LWORK >= N*N + 2*N + M Else if ((N*17/9) > M
>= N):
if JOBZ = 'N', LWORK >= 2*N + M
if JOBZ = 'O', LWORK >= 2*N + M + N*N
if JOBZ = 'S', LWORK >= 2*N + M
if JOBZ = 'A', LWORK >= 2*N + M Else if N is much larger
than M such that N >= (M*17/9)):
if JOBZ = 'N', LWORK >= 3*M
if JOBZ = 'O', LWORK >= 2*M*M + 3*M
if JOBZ = 'S', LWORK >= M*M + 3*M
if JOBZ = 'A', LWORK >= M*M + 2*M + N Else if ((M*17/9) > N
>= M):
if JOBZ = 'N', LWORK >= 2*M + N
if JOBZ = 'O', LWORK >= 2*M+N + M*M
if JOBZ = 'S', LWORK >= 2*M + N
if JOBZ = 'A', LWORK >= 2*M + N
RWORK (workspace)
If JOBZ = 'N', RWORK must be at least 7*min(M,N). Otherwise,
RWORK must be at least 5*min(M,N)*min(M,N) + 5*min(M,N)
IWORK (workspace)
dimension(8*MIN(M,N))
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The updating process of SBDSDC did not converge.
FURTHER DETAILS
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
6 Mar 2009 zgesdd(3P)
