CGGEV(l)								 )								  CGGEV(l)

NAME

       CGGEV  -  compute  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 eigenvalues.

	       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 will be scaled so the largest component will have 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 will be scaled so the largest component will have 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 (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 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/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 version 3.0						   15 June 2000 							  CGGEV(l)