DGEBAK forms the right or left eigenvectors of a real general matrix
 by backward transformation on the computed eigenvectors of the
 balanced matrix output by DGEBAL.

          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 DGEBAL.

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

          SCALE is DOUBLE PRECISION array, dimension (N)
          Details of the permutation and scaling factors, as returned
          by DGEBAL.

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

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

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

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