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LAPACK version 3.0
dggbak(3)

PURPOSE
  DGGBAK - form 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 DGGBAL

SYNTAX
  SUBROUTINE DGGBAK( 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( * ), V( LDV, * )

DESCRIPTION
  DGGBAK 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 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 permutation and
	  scaling.  JOB must be the same as the argument JOB supplied to
	  DGGBAL.

  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
	  DGGBAL.  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 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 V.  M >= 0.

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