Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  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

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 routine (version 3.2)               April 2011                            SGGBAK(3lapack)