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RedHat 9 (Linux i386) - man page for zgesdd (redhat section l)

ZGESDD(l)					)					ZGESDD(l)

NAME
       ZGESDD  -  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 ZGESDD( 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( * )

	   DOUBLE	  PRECISION RWORK( * ), S( * )

	   COMPLEX*16	  A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

PURPOSE
       ZGESDD 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
       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  arith-
       metic.  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*16 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) otherwise.  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) 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)
	       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) 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*16 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 singu-
	       lar  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*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.   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 performance, LWORK should  gener-
	       ally be larger.	If LWORK < 0 but other input arguments are legal, WORK(1) returns
	       the optimal LWORK.

       RWORK   (workspace) DOUBLE PRECISION 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 DBDSDC 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 				ZGESDD(l)


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