ORTBAK(3F)

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


SYNOPSYS
          subroutine  ortbak(nm, low, igh, a, ort, m, z)
          integer          nm, low, igh, m
          double precision a(nm,igh), ort(igh), z(nm,m)

          subroutine sortbak(nm, low, igh, a, ort, m, z)
          integer          nm, low, igh, m
          real             a(nm,igh), ort(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 information about the orthogonal trans- formations used in the
     reduction by  ORTHES in its strict lower triangle.

     ORT contains further information about the trans- formations used in the
     reduction by  ORTHES.  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.

     ORT has been altered. NOTE that ORTBAK preserves vector Euclidean norms.
     Questions and comments should be directed to B. S. Garbow, APPLIED
     MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY