This routine is deprecated and has been replaced by routine ZGGEV.
 ZGEGV computes the eigenvalues and, optionally, the left and/or right
 eigenvectors of a complex matrix pair (A,B).
 Given two square matrices A and B,
 the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
 eigenvalues lambda and corresponding (non-zero) eigenvectors x such
 that
    A*x = lambda*B*x.
 An alternate form is to find the eigenvalues mu and corresponding
 eigenvectors y such that
    mu*A*y = B*y.
 These two forms are equivalent with mu = 1/lambda and x = y if
 neither lambda nor mu is zero.  In order to deal with the case that
 lambda or mu is zero or small, two values alpha and beta are returned
 for each eigenvalue, such that lambda = alpha/beta and
 mu = beta/alpha.
 The vectors x and y in the above equations are right eigenvectors of
 the matrix pair (A,B).  Vectors u and v satisfying
    u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
 are left eigenvectors of (A,B).
 Note: this routine performs 'full balancing' on A and B

JOBVL

          JOBVL is CHARACTER*1
          = 'N':  do not compute the left generalized eigenvectors;
          = 'V':  compute the left generalized eigenvectors (returned
                  in VL).

JOBVR

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

N

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

A

          A is COMPLEX*16 array, dimension (LDA, N)
          On entry, the matrix A.
          If JOBVL = 'V' or JOBVR = 'V', then on exit A
          contains the Schur form of A from the generalized Schur
          factorization of the pair (A,B) after balancing.  If no
          eigenvectors were computed, then only the diagonal elements
          of the Schur form will be correct.  See ZGGHRD and ZHGEQZ
          for details.

LDA

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

B

          B is COMPLEX*16 array, dimension (LDB, N)
          On entry, the matrix B.
          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
          upper triangular matrix obtained from B in the generalized
          Schur factorization of the pair (A,B) after balancing.
          If no eigenvectors were computed, then only the diagonal
          elements of B will be correct.  See ZGGHRD and ZHGEQZ for
          details.

LDB

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

ALPHA

          ALPHA is COMPLEX*16 array, dimension (N)
          The complex scalars alpha that define the eigenvalues of
          GNEP.

BETA

          BETA is COMPLEX*16 array, dimension (N)
          The complex scalars beta that define the eigenvalues of GNEP.
          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
          represent the j-th eigenvalue of the matrix pair (A,B), in
          one of the forms lambda = alpha/beta or mu = beta/alpha.
          Since either lambda or mu may overflow, they should not,
          in general, be computed.

VL

          VL is COMPLEX*16 array, dimension (LDVL,N)
          If JOBVL = 'V', the left eigenvectors u(j) are stored
          in the columns of VL, in the same order as their eigenvalues.
          Each eigenvector is scaled so that its largest component has
          abs(real part) + abs(imag. part) = 1, except for eigenvectors
          corresponding to an eigenvalue with alpha = beta = 0, which
          are set to zero.
          Not referenced if JOBVL = 'N'.

LDVL

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

VR

          VR is COMPLEX*16 array, dimension (LDVR,N)
          If JOBVR = 'V', the right eigenvectors x(j) are stored
          in the columns of VR, in the same order as their eigenvalues.
          Each eigenvector is scaled so that its largest component has
          abs(real part) + abs(imag. part) = 1, except for eigenvectors
          corresponding to an eigenvalue with alpha = beta = 0, which
          are set to zero.
          Not referenced if JOBVR = 'N'.

LDVR

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

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is 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 ZUNGQR.)  Then compute:
          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and ZUNGQR;
          The optimal LWORK is  MAX( 2*N, 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

          RWORK is DOUBLE PRECISION array, dimension (8*N)

INFO

          INFO is 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:  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 ZTGEVC
                =N+8: error return from ZGGBAK (computing VL)
                =N+9: error return from ZGGBAK (computing VR)
                =N+10: error return from ZLASCL (various calls)

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  Balancing
  ---------
  This driver calls ZGGBAL to both permute and scale rows and columns
  of A and B.  The permutations PL and PR are chosen so that PL*A*PR
  and PL*B*R will be upper triangular except for the diagonal blocks
  A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
  possible.  The diagonal scaling matrices DL and DR are chosen so
  that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
  one (except for the elements that start out zero.)
  After the eigenvalues and eigenvectors of the balanced matrices
  have been computed, ZGGBAK transforms the eigenvectors back to what
  they would have been (in perfect arithmetic) if they had not been
  balanced.
  Contents of A and B on Exit
  -------- -- - --- - -- ----
  If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
  both), then on exit the arrays A and B will contain the complex Schur
  form[*] of the 'balanced' versions of A and B.  If no eigenvectors
  are computed, then only the diagonal blocks will be correct.
  [*] In other words, upper triangular form.