!>
!> CGGBAK forms the right or left eigenvectors of a complex generalized
!> eigenvalue problem A*x = lambda*B*x, by backward transformation on
!> the computed eigenvectors of the balanced pair of matrices output by
!> CGGBAL.
!> 

JOB

!>          JOB is CHARACTER*1
!>          Specifies the type of backward transformation required:
!>          = 'N':  do nothing, return immediately;
!>          = 'P':  do backward transformation for permutation only;
!>          = 'S':  do backward transformation for scaling only;
!>          = 'B':  do backward transformations for both permutation and
!>                  scaling.
!>          JOB must be the same as the argument JOB supplied to CGGBAL.
!> 

SIDE

!>          SIDE is CHARACTER*1
!>          = 'R':  V contains right eigenvectors;
!>          = 'L':  V contains left eigenvectors.
!> 

N

!>          N is INTEGER
!>          The number of rows of the matrix V.  N >= 0.
!> 

ILO

!>          ILO is INTEGER
!> 

IHI

!>          IHI is INTEGER
!>          The integers ILO and IHI determined by CGGBAL.
!>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
!> 

LSCALE

!>          LSCALE is REAL array, dimension (N)
!>          Details of the permutations and/or scaling factors applied
!>          to the left side of A and B, as returned by CGGBAL.
!> 

RSCALE

!>          RSCALE is REAL array, dimension (N)
!>          Details of the permutations and/or scaling factors applied
!>          to the right side of A and B, as returned by CGGBAL.
!> 

M

!>          M is INTEGER
!>          The number of columns of the matrix V.  M >= 0.
!> 

V

!>          V is COMPLEX array, dimension (LDV,M)
!>          On entry, the matrix of right or left eigenvectors to be
!>          transformed, as returned by CTGEVC.
!>          On exit, V is overwritten by the transformed eigenvectors.
!> 

LDV

!>          LDV is INTEGER
!>          The leading dimension of the matrix V. LDV >= max(1,N).
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!> 

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!>
!>  See R.C. Ward, Balancing the generalized eigenvalue problem,
!>                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
!>