SGGBAK(l)								 )								 SGGBAK(l)

NAME

       SGGBAK  -  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 SGGBAL

SYNOPSIS

       SUBROUTINE SGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO )

	   CHARACTER	  JOB, SIDE

	   INTEGER	  IHI, ILO, INFO, LDV, M, N

	   REAL 	  LSCALE( * ), RSCALE( * ), V( LDV, * )

PURPOSE

       SGGBAK 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 SGGBAL.

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 SGGBAL.

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

       LSCALE  (input) REAL array, dimension (N)
	       Details of the permutations and/or scaling factors applied to the left side of A and B, as returned by SGGBAL.

       RSCALE  (input) REAL array, dimension (N)
	       Details of the permutations and/or scaling factors applied to the right side of A and B, as returned by SGGBAL.

       M       (input) INTEGER
	       The number of columns of the matrix V.  M >= 0.

       V       (input/output) REAL array, dimension (LDV,M)
	       On  entry,  the	matrix	of  right or left eigenvectors to be transformed, as returned by STGEVC.  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 version 3.0						   15 June 2000 							 SGGBAK(l)