ZGGBAK(l)		LAPACK routine (version	1.1)		    ZGGBAK(l)

NAME
  ZGGBAK - form	the right or left eigenvectors of the generalized eigenvalue
  problem by backward transformation on	the computed eigenvectors of the bal-
  anced	matrix output by ZGGBAL

SYNOPSIS

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

      CHARACTER	     JOB, SIDE

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

      DOUBLE	     PRECISION LSCALE( * ), RSCALE( * )

      COMPLEX*16     E(	LDE, * )

PURPOSE
  ZGGBAK forms the right or left eigenvectors of the generalized eigenvalue
  problem by backward transformation on	the computed eigenvectors of the bal-
  anced	matrix 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 scal-
	  ing.	JOB must be the	same as	the argument JOB supplied to ZGGBAL.

  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
	  ZGGBAL.

  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 E.

  E	  (input/output) COMPLEX*16 array, dimension (LDE,M)
	  On entry, the	matrix of right	or left	eigenvectors to	be
	  transformed, as returned by ZTGEVC.  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.