ZGESVD(l)								 )								 ZGESVD(l)

NAME

       ZGESVD  -  compute the singular value decomposition (SVD) of a complex M-by-N 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 M-by-N matrix A, optionally computing the left  and/or  right  singular
       vectors. The SVD is written
	    A = 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  descend-
       ing 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 vectors) 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 vectors) are overwritten on the array A; = 'N':  no rows of V**H (no right singular vectors) are com-
	       puted.

	       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 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) 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 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) 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 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) 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 vec-
	       tors related by U and VT.

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th 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)