CGESDD(l)								 )								 CGESDD(l)

NAME

       CGESDD  -  compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular
       vectors, by using divide-and-conquer method

SYNOPSIS

       SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO )

	   CHARACTER	  JOBZ

	   INTEGER	  INFO, LDA, LDU, LDVT, LWORK, M, N

	   INTEGER	  IWORK( * )

	   REAL 	  RWORK( * ), S( * )

	   COMPLEX	  A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

PURPOSE

       CGESDD computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left  and/or  right  singular
       vectors, by using divide-and-conquer method. 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 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 digits, but we know of none.

ARGUMENTS

       JOBZ    (input) CHARACTER*1
	       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 columns 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 in the array VT; = 'N':  no columns of U or rows of V**H are computed.

       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 array, dimension (LDA,N)
	       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) other-
	       wise.  if JOBZ .ne. 'O', the contents of A are destroyed.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,M).

       S       (output) REAL array, dimension (min(M,N))
	       The singular values of A, sorted so that S(i) >= S(i+1).

       U       (output) COMPLEX array, dimension (LDU,UCOL)
	       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 column-
	       wise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.

       LDU     (input) INTEGER
	       The leading dimension of the array U.  LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.

       VT      (output) COMPLEX array, dimension (LDVT,N)
	       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) INTEGER
	       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/output) COMPLEX 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.	 if  JOBZ  =  'N',  LWORK  >=  2*min(M,N)+max(M,N).   if  JOBZ	=  'O',  LWORK	>=
	       2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).   if  JOBZ = 'S' or 'A', LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).  For good perfor-
	       mance, LWORK should generally be larger.  If LWORK < 0 but other input arguments are legal, WORK(1) returns the optimal LWORK.

       RWORK   (workspace) REAL array, dimension (LRWORK)
	       If JOBZ = 'N', LRWORK >= 7*min(M,N).  Otherwise, LRWORK >= 5*min(M,N)*min(M,N) + 5*min(M,N)

       IWORK   (workspace) INTEGER array, dimension (8*min(M,N))

       INFO    (output) INTEGER
	       = 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

LAPACK version 3.0						   15 June 2000 							 CGESDD(l)