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CGESVD(l)			       )			     CGESVD(l)

NAME
       CGESVD - compute the singular value decomposition (SVD) of a complex M-
       by-N matrix A, optionally computing the left and/or right singular vec‐
       tors

SYNOPSIS
       SUBROUTINE CGESVD( 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

	   REAL		  RWORK( * ), S( * )

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

PURPOSE
       CGESVD computes the singular value decomposition (SVD) of a complex  M-
       by-N matrix A, optionally computing the left and/or right singular vec‐
       tors. 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 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 vec‐
	       tors) 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 over‐
	       written on the array A; = 'N':  no rows of V**H (no right  sin‐
	       gular 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 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 sin‐
	       gular  vectors,	stored columnwise); if JOBVT = 'O', A is over‐
	       written with the first min(m,n) rows of V**H (the right	singu‐
	       lar  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) 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)
	       (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 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 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 gener‐
	       ally 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) REAL array, dimension (5*min(M,N))
	       On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains  the	uncon‐
	       verged  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 sin‐
	       gular vectors 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 CBDSQR 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			     CGESVD(l)
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