ELMBAK(3F)

NAME
     ELMBAK, SELMBAK  -  EISPACK routine.  This subroutine forms the
     eigenvectors of a REAL GENERAL matrix by back transforming those of the
     corresponding upper Hessenberg matrix determined by  ELMHES.


SYNOPSYS
          subroutine  elmbak(nm, low, igh, a, int, m, z)
          integer          nm, low, igh, m, int(igh)
          double precision a(nm,igh), z(nm,m)

          subroutine selmbak(nm, low, igh, a, int, m, z)
          integer          nm, low, igh, m, int(igh)
          real             a(nm,igh), z(nm,m)



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  BALANC.
     If  BALANC  has not been used, set LOW=1 and IGH equal to the order of
     the matrix.

     A contains the multipliers which were used in the reduction by  ELMHES
     in its lower triangle below the subdiagonal.

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

     M is the number of columns of Z to be back transformed.

     Z contains the real and imaginary parts of the eigen- vectors to be back
     transformed in its first M columns.  On OUTPUT

     Z contains the real and imaginary parts of the transformed eigenvectors
     in its first M columns.  Questions and comments should be directed to B.
     S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY