ORTHES(3F)

NAME
     ORTHES, SORTHES  -  EISPACK routine.  Given a REAL GENERAL matrix, this
     subroutine reduces a submatrix situated in rows and columns LOW through
     IGH to upper Hessenberg form by orthogonal similarity transformations.


SYNOPSYS
          subroutine  orthes(nm, n, low, igh, a, ort)
          integer          nm, n, low, igh
          double precision a(nm,n), ort(igh)

          subroutine sorthes(nm, n, low, igh, a, ort)
          integer          nm, n, low, igh
          real             a(nm,n), ort(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.

     N is the order of the matrix.

     LOW and IGH are integers determined by the balancing subroutine  BALANC.
     If  BALANC  has not been used, set LOW=1, IGH=N.

     A contains the input matrix. On OUTPUT

     A contains the Hessenberg matrix.  Information about the orthogonal
     transformations used in the reduction is stored in the remaining triangle
     under the Hessenberg matrix.

     ORT contains further information about the transformations. only elements
     LOW through IGH are used.  Questions and comments should be directed to
     B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY