COMBAK(3F)

NAME
     COMBAK, SCOMBAK  -  EISPACK routine.  This subroutine forms the
     eigenvectors of a COMPLEX GENERAL matrix by back transforming those of
     the corresponding upper Hessenberg matrix determined by  COMHES.


SYNOPSYS
          subroutine  combak(nm, low, igh, ar, ai, int, m, zr, zi)
            integer          nm, low, igh, m
            double precision ar(nm,igh),ai(nm,igh),zr(nm,m),zi(nm,m)
            integer          int(igh)

          subroutine scombak(nm, low, igh, ar, ai, int, m, zr, zi)
            integer          nm, low, igh, m
            real             ar(nm,igh),ai(nm,igh),zr(nm,m),zi(nm,m)
            integer          int(igh)



DESCRIPTION
     On INPUT

     NM must be set to the row dimension of two-dimensional array parameters
     as declared in the calling program dimension statement.

     LOW and IGH are integers determined by the balancing subroutine  CBAL.
     If  CBAL  has not been used, set LOW=1 and IGH equal to the order of the
     matrix.

     AR and AI contain the multipliers which were used in the reduction by
     COMHES  in their lower triangles below the subdiagonal.

     INT contains information on the rows and columns interchanged in the
     reduction by  COMHES.  Only elements LOW through IGH are used.

     M is the number of eigenvectors to be back transformed.

     ZR and ZI contain the real and imaginary parts, respectively, of the
     eigenvectors to be back transformed in their first M columns.  On OUTPUT

     ZR and ZI contain the real and imaginary parts, respectively, of the
     transformed eigenvectors in their first M columns.  Questions and
     comments should be directed to B. S. Garbow, APPLIED MATHEMATICS
     DIVISION, ARGONNE NATIONAL LABORATORY