SYNOPSIS
 SUBROUTINE ZGGBAK(
 JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO )
 CHARACTER JOB, SIDE
 INTEGER IHI, ILO, INFO, LDV, M, N
 DOUBLE PRECISION LSCALE( * ), RSCALE( * )
 COMPLEX*16 V( LDV, * )
PURPOSE
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.ARGUMENTS
 JOB (input) 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 (input) CHARACTER*1

= 'R': V contains right eigenvectors;
= 'L': V contains left eigenvectors.  N (input) INTEGER
 The number of rows of the matrix V. N >= 0.
 ILO (input) INTEGER
 IHI (input) 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 (input) 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 (input) 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 (input) INTEGER
 The number of columns of the matrix V. M >= 0.
 V (input/output) 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 (input) INTEGER
 The leading dimension of the matrix V. LDV >= max(1,N).
 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
FURTHER DETAILS
See R.C. Ward, Balancing the generalized eigenvalue problem,SIAM J. Sci. Stat. Comp. 2 (1981), 141152.