ZGGBAK 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
 ZGGBAL.

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 ZGGBAL.

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 ZGGBAL.
          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

LSCALE

          LSCALE is DOUBLE PRECISION array, dimension (N)
          Details of the permutations and/or scaling factors applied
          to the left side of A and B, as returned by ZGGBAL.

RSCALE

          RSCALE is DOUBLE PRECISION array, dimension (N)
          Details of the permutations and/or scaling factors applied
          to the right side of A and B, as returned by ZGGBAL.

M

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

V

          V is COMPLEX*16 array, dimension (LDV,M)
          On entry, the matrix of right or left eigenvectors to be
          transformed, as returned by ZTGEVC.
          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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