CORTH(3F)

NAME
     CORTH, SCORTH   -  EISPACK routine.  Given a COMPLEX GENERAL matrix, this
     subroutine reduces a submatrix situated in rows and columns LOW through
     IGH to upper Hessenberg form by unitary similarity transformations.


SYNOPSYS
          subroutine  corth(nm, n, low, igh, ar, ai, ortr, orti)
          integer          nm, n, low, igh
          double precision ar(nm,n), ai(nm,n), ortr(igh), orti(igh)

          subroutine scorth(nm, n, low, igh, ar, ai, ortr, orti)
          integer          nm, n, low, igh
          real             ar(nm,n), ai(nm,n), ortr(igh), orti(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  CBAL.
     If  CBAL  has not been used, set LOW=1, IGH=N.

     AR and AI contain the real and imaginary parts, respectively, of the
     complex input matrix.  On OUTPUT

     AR and AI contain the real and imaginary parts, respectively, of the
     Hessenberg matrix.  Information about the unitary transformations used in
     the reduction is stored in the remaining triangles under the Hessenberg
     matrix.

     ORTR and ORTI contain further information about the transformations.
     Only elements LOW through IGH are used.  Calls PYTHAG(A,B) for sqrt(A**2
     + B**2).  Questions and comments should be directed to B. S. Garbow,
     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY