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DGGBAK(1)		 LAPACK routine (version 3.2)		     DGGBAK(1)

NAME
       DGGBAK - forms the right or left eigenvectors of a real generalized ei‐
       genvalue problem A*x = lambda*B*x, by backward  transformation  on  the
       computed eigenvectors of the balanced pair of matrices output by DGGBAL

SYNOPSIS
       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, * )

PURPOSE
       DGGBAK forms the right or left eigenvectors of a real  generalized  ei‐
       genvalue	 problem  A*x  = lambda*B*x, by backward transformation on the
       computed eigenvectors of the balanced pair of matrices output  by  DGG‐
       BAL.

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 trans‐
	       formed, 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.

 LAPACK routine (version 3.2)	 November 2008			     DGGBAK(1)
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