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dggbak

 NAME
      DGGBAK - form the right or left eigenvectors of the general-
      ized eigenvalue problem by backward transformation on the
      computed eigenvectors of the balanced matrix output by
      DGGBAL

 SYNOPSIS
      SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE,
                         M, E, LDE, INFO )

          CHARACTER      JOB, SIDE

          INTEGER        IHI, ILO, INFO, LDE, M, N

          DOUBLE         PRECISION E( LDE, * ), LSCALE( * ),
                         RSCALE( * )

 PURPOSE
      DGGBAK forms the right or left eigenvectors of the general-
      ized eigenvalue problem by backward transformation on the
      computed eigenvectors of the balanced matrix output by
      DGGBAL.

 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 permu-
              tation and scaling.  JOB must be the same as the
              argument JOB supplied to DGGBAL.

      SIDE    (input) CHARACTER*1
              = 'R':  E contains right eigenvectors;
              = 'L':  E contains left eigenvectors.

      N       (input) INTEGER
              The number of rows of the matrix E.  N >= 0.

      ILO     (input) INTEGER
              IHI     (input) INTEGER The integers ILO and IHI
              determined by DGGBAL.

      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
              DGGBAL.

      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
              DGGBAL.

      M       (input) INTEGER
              The number of columns of the matrix E.

      E       (input/output) DOUBLE PRECISION array, dimension (LDE,M)
              On entry, the matrix of right or left eigenvectors
              to be transformed, as returned by DTGEVC.  On exit,
              E is overwritten by the transformed eigenvectors.

      LDE     (input) INTEGER
              The leading dimension of the matrix E. LDE >=
              max(1,N).

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

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