sggbak(3F)

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.