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ZGEGS(l)					)					 ZGEGS(l)

NAME
       ZGEGS - routine is deprecated and has been replaced by routine ZGGES

SYNOPSIS
       SUBROUTINE ZGEGS( JOBVSL,  JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR,
			 WORK, LWORK, RWORK, INFO )

	   CHARACTER	 JOBVSL, JOBVSR

	   INTEGER	 INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N

	   DOUBLE	 PRECISION RWORK( * )

	   COMPLEX*16	 A( LDA, * ), ALPHA( * ), B( LDB, * ), BETA( * ), VSL( LDVSL, *  ),  VSR(
			 LDVSR, * ), WORK( * )

PURPOSE
       This  routine  is deprecated and has been replaced by routine ZGGES.  ZGEGS computes for a
       pair of N-by-N complex nonsymmetric matrices A, B:  the	generalized  eigenvalues  (alpha,
       beta),  the complex Schur form (A, B), and optionally left and/or right Schur vectors (VSL
       and VSR).

       (If only the generalized eigenvalues are needed, use the driver ZGEGV instead.)

       A generalized eigenvalue for a pair of matrices (A,B) is, roughly speaking, a scalar w  or
       a ratio	alpha/beta = w, such that  A - w*B is singular.  It is usually represented as the
       pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even	for  both
       being  zero.  A good beginning reference is the book, "Matrix Computations", by G. Golub &
       C. van Loan (Johns Hopkins U. Press)

       The (generalized) Schur form of a pair of matrices  is  the  result  of	multiplying  both
       matrices  on  the  left	by  one  unitary  matrix and both on the right by another unitary
       matrix, these two unitary matrices being chosen so as to bring the pair of  matrices  into
       upper  triangular  form	with  the  diagonal elements of B being non-negative real numbers
       (this is also called complex Schur form.)

       The left and right Schur vectors are the columns of VSL and VSR, respectively,  where  VSL
       and VSR are the unitary matrices
       which reduce A and B to Schur form:

       Schur form of (A,B) = ( (VSL)**H A (VSR), (VSL)**H B (VSR) )

ARGUMENTS
       JOBVSL	(input) CHARACTER*1
		= 'N':	do not compute the left Schur vectors;
		= 'V':	compute the left Schur vectors.

       JOBVSR	(input) CHARACTER*1
		= 'N':	do not compute the right Schur vectors;
		= 'V':	compute the right Schur vectors.

       N       (input) INTEGER
	       The order of the matrices A, B, VSL, and VSR.  N >= 0.

       A       (input/output) COMPLEX*16 array, dimension (LDA, N)
	       On  entry,  the	first  of  the pair of matrices whose generalized eigenvalues and
	       (optionally) Schur vectors are to be computed.  On  exit,  the  generalized  Schur
	       form of A.

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

       B       (input/output) COMPLEX*16 array, dimension (LDB, N)
	       On  entry,  the	second	of the pair of matrices whose generalized eigenvalues and
	       (optionally) Schur vectors are to be computed.  On  exit,  the  generalized  Schur
	       form of B.

       LDB     (input) INTEGER
	       The leading dimension of B.  LDB >= max(1,N).

       ALPHA   (output) COMPLEX*16 array, dimension (N)
	       BETA	(output)  COMPLEX*16  array,  dimension  (N)  On exit,	ALPHA(j)/BETA(j),
	       j=1,...,N,  will  be  the  generalized  eigenvalues.   ALPHA(j),  j=1,...,N    and
	       BETA(j),  j=1,...,N   are  the diagonals of the complex Schur form (A,B) output by
	       ZGEGS.  The  BETA(j) will be non-negative real.

	       Note: the quotients ALPHA(j)/BETA(j) may easily over- or  underflow,  and  BETA(j)
	       may  even  be  zero.   Thus,  the  user	should	avoid naively computing the ratio
	       alpha/beta.  However, ALPHA will be always less than and usually  comparable  with
	       norm(A)	in  magnitude,	and  BETA  always  less  than and usually comparable with
	       norm(B).

       VSL     (output) COMPLEX*16 array, dimension (LDVSL,N)
	       If JOBVSL = 'V', VSL will contain the left Schur vectors.  (See "Purpose", above.)
	       Not referenced if JOBVSL = 'N'.

       LDVSL   (input) INTEGER
	       The leading dimension of the matrix VSL. LDVSL >= 1, and if JOBVSL = 'V', LDVSL >=
	       N.

       VSR     (output) COMPLEX*16 array, dimension (LDVSR,N)
	       If JOBVSR = 'V', VSR will  contain  the	right  Schur  vectors.	 (See  "Purpose",
	       above.)	Not referenced if JOBVSR = 'N'.

       LDVSR   (input) INTEGER
	       The leading dimension of the matrix VSR. LDVSR >= 1, and if JOBVSR = 'V', LDVSR >=
	       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	>=  max(1,2*N).   For  good  performance,
	       LWORK  must  generally  be  larger.   To  compute the optimal value of LWORK, call
	       ILAENV to get blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute:  NB   --
	       MAX  of	the  blocksizes  for  ZGEQRF,  ZUNMQR,	and  CUNGQR; the optimal LWORK is
	       N*(NB+1).

	       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 (3*N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       =1,...,N: The QZ iteration failed.  (A,B) are not in Schur form, but ALPHA(j)  and
	       BETA(j)	should be correct for j=INFO+1,...,N.  > N:  errors that usually indicate
	       LAPACK problems:
	       =N+1: error return from ZGGBAL
	       =N+2: error return from ZGEQRF
	       =N+3: error return from ZUNMQR
	       =N+4: error return from ZUNGQR
	       =N+5: error return from ZGGHRD
	       =N+6: error return from ZHGEQZ (other than failed iteration)  =N+7:  error  return
	       from ZGGBAK (computing VSL)
	       =N+8: error return from ZGGBAK (computing VSR)
	       =N+9: error return from ZLASCL (various places)

LAPACK version 3.0			   15 June 2000 				 ZGEGS(l)
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