
ZGESVD(l) ) ZGESVD(l)
NAME
ZGESVD  compute the singular value decomposition (SVD) of a complex MbyN matrix A,
optionally computing the left and/or right singular vectors
SYNOPSIS
SUBROUTINE ZGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK,
INFO )
CHARACTER JOBU, JOBVT
INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
DOUBLE PRECISION RWORK( * ), S( * )
COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
ZGESVD computes the singular value decomposition (SVD) of a complex MbyN matrix A,
optionally computing the left and/or right singular vectors. The SVD is written
A = U * SIGMA * conjugatetranspose(V)
where SIGMA is an MbyN matrix which is zero except for its min(m,n) diagonal elements, U
is an MbyM unitary matrix, and V is an NbyN unitary matrix. The diagonal elements of
SIGMA are the singular values of A; they are real and nonnegative, 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) CHARACTER*1
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 vec
tors) are overwritten on the array A; = 'N': no columns of U (no left singular
vectors) are computed.
JOBVT (input) CHARACTER*1
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 vec
tors) 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'.
M (input) INTEGER
The number of rows of the input matrix A. M >= 0.
N (input) INTEGER
The number of columns of the input matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the MbyN 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 sin
gular vectors, stored rowwise); if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents
of A are destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
S (output) DOUBLE PRECISION array, dimension (min(M,N))
The singular values of A, sorted so that S(i) >= S(i+1).
U (output) COMPLEX*16 array, dimension (LDU,UCOL)
(LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If JOBU = 'A', U contains
the MbyM 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) INTEGER
The leading dimension of the array U. LDU >= 1; if JOBU = 'S' or 'A', LDU >= M.
VT (output) COMPLEX*16 array, dimension (LDVT,N)
If JOBVT = 'A', VT contains the NbyN unitary matrix V**H; if JOBVT = 'S', VT
contains the first min(m,n) rows of V**H (the right singular vectors, stored row
wise); if JOBVT = 'N' or 'O', VT is not referenced.
LDVT (input) INTEGER
The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'A', LDVT >= N; if
JOBVT = 'S', LDVT >= min(M,N).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1. LWORK >= 2*MIN(M,N)+MAX(M,N). For
good performance, LWORK should generally be larger.
If LWORK = 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 LWORK is issued by XERBLA.
RWORK (workspace) DOUBLE PRECISION array, dimension (5*min(M,N))
On exit, if INFO > 0, RWORK(1:MIN(M,N)1) contains the unconverged superdiagonal
elements of an upper bidiagonal matrix B whose diagonal is in S (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) INTEGER
= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
> 0: if ZBDSQR did not converge, INFO specifies how many superdiagonals of an
intermediate bidiagonal form B did not converge to zero. See the description of
RWORK above for details.
LAPACK version 3.0 15 June 2000 ZGESVD(l) 
