SGGBAK forms the right or left eigenvectors of a real generalized
 eigenvalue problem A*x = lambda*B*x, by backward transformation on
 the computed eigenvectors of the balanced pair of matrices output by
 SGGBAL.

          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 SGGBAL.

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

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

          ILO is INTEGER

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

          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 SGGBAL.

          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 SGGBAL.

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

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

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

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

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