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CGGEV(1)	      LAPACK driver routine (version 3.2)	      CGGEV(1)

NAME
       CGGEV  -	 computes  for	a pair of N-by-N complex nonsymmetric matrices
       (A,B), the generalized eigenvalues, and	optionally,  the  left	and/or
       right generalized eigenvectors

SYNOPSIS
       SUBROUTINE CGGEV( JOBVL,	 JOBVR,	 N,  A,	 LDA, B, LDB, ALPHA, BETA, VL,
			 LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )

	   CHARACTER	 JOBVL, JOBVR

	   INTEGER	 INFO, LDA, LDB, LDVL, LDVR, LWORK, N

	   REAL		 RWORK( * )

	   COMPLEX	 A( LDA, * ), ALPHA( * ), B( LDB, * ), BETA( * ),  VL(
			 LDVL, * ), VR( LDVR, * ), WORK( * )

PURPOSE
       CGGEV  computes	for  a	pair  of  N-by-N complex nonsymmetric matrices
       (A,B), the generalized eigenvalues, and	optionally,  the  left	and/or
       right generalized eigenvectors.	A generalized eigenvalue for a pair of
       matrices (A,B) is a scalar lambda or a ratio alpha/beta = lambda,  such
       that  A	-  lambda*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.
       The right generalized eigenvector v(j) corresponding to the generalized
       eigenvalue lambda(j) of (A,B) satisfies
		    A * v(j) = lambda(j) * B * v(j).
       The left generalized eigenvector u(j) corresponding to the  generalized
       eigenvalues lambda(j) of (A,B) satisfies
		    u(j)**H * A = lambda(j) * u(j)**H * B
       where u(j)**H is the conjugate-transpose of u(j).

ARGUMENTS
       JOBVL   (input) CHARACTER*1
	       = 'N':  do not compute the left generalized eigenvectors;
	       = 'V':  compute the left generalized eigenvectors.

       JOBVR   (input) CHARACTER*1
	       = 'N':  do not compute the right generalized eigenvectors;
	       = 'V':  compute the right generalized eigenvectors.

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

       A       (input/output) COMPLEX array, dimension (LDA, N)
	       On  entry, the matrix A in the pair (A,B).  On exit, A has been
	       overwritten.

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

       B       (input/output) COMPLEX array, dimension (LDB, N)
	       On entry, the matrix B in the pair (A,B).  On exit, B has  been
	       overwritten.

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

       ALPHA   (output) COMPLEX array, dimension (N)
	       BETA	 (output)   COMPLEX  array,  dimension	(N)  On	 exit,
	       ALPHA(j)/BETA(j), j=1,...,N, will be the generalized  eigenval‐
	       ues.   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).

       VL      (output) COMPLEX array, dimension (LDVL,N)
	       If JOBVL = 'V', the  left  generalized  eigenvectors  u(j)  are
	       stored  one  after  another  in	the columns of VL, in the same
	       order as their eigenvalues.  Each eigenvector is scaled so  the
	       largest	component  has	abs(real  part) + abs(imag. part) = 1.
	       Not referenced if JOBVL = 'N'.

       LDVL    (input) INTEGER
	       The leading dimension of the matrix VL. LDVL >= 1, and if JOBVL
	       = 'V', LDVL >= N.

       VR      (output) COMPLEX array, dimension (LDVR,N)
	       If  JOBVR  =  'V',  the right generalized eigenvectors v(j) are
	       stored one after another in the columns	of  VR,	 in  the  same
	       order  as their eigenvalues.  Each eigenvector is scaled so the
	       largest component has abs(real part) +  abs(imag.  part)	 =  1.
	       Not referenced if JOBVR = 'N'.

       LDVR    (input) INTEGER
	       The leading dimension of the matrix VR. LDVR >= 1, and if JOBVR
	       = 'V', LDVR >= N.

       WORK    (workspace/output) COMPLEX array, dimension (MAX(1,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.  If LWORK =
	       -1, then a workspace query is assumed; the routine only	calcu‐
	       lates 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/output) REAL array, dimension (8*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.  No eigenvectors have been
	       calculated, but ALPHA(j) and  BETA(j)  should  be  correct  for
	       j=INFO+1,...,N.	 > N:  =N+1: other then QZ iteration failed in
	       SHGEQZ,
	       =N+2: error return from STGEVC.

 LAPACK driver routine (version 3November 2008			      CGGEV(1)
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