COMQR(3F)

NAME
     COMQR, SCOMQR   -  EISPACK routine.  This subroutine finds the
     eigenvalues of a COMPLEX upper Hessenberg matrix by the QR method.


SYNOPSYS
          subroutine  comqr(nm, n, low, igh, hr, hi, wr, wi, ierr)
          integer          nm, n, low, igh, ierr
          double precision hr(nm,n), hi(nm,n), wr(n), wi(n)

          subroutine scomqr(nm, n, low, igh, hr, hi, wr, wi, ierr)
          integer          nm, n, low, igh, ierr
          real             hr(nm,n), hi(nm,n), wr(n), wi(n)



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.

     HR and HI contain the real and imaginary parts, respectively, of the
     complex upper Hessenberg matrix.  Their lower triangles below the
     subdiagonal contain information about the unitary transformations used in
     the reduction by  CORTH, if performed.  On OUTPUT The upper Hessenberg
     portions of HR and HI have been destroyed.  Therefore, they must be saved
     before calling  COMQR  if subsequent calculation of eigenvectors is to be
     performed.

     WR and WI contain the real and imaginary parts, respectively, of the
     eigenvalues.  If an error exit is made, the eigenvalues should be correct
     for indices IERR+1,...,N.

     IERR is set to ZERO       for normal return, J          if the J-th
     eigenvalue has not been
        determined after a total of 30*N iterations.  Calls CSROOT for complex
     square root.  Calls PYTHAG(A,B) for sqrt(A**2 + B**2).  Calls CDIV for
     complex division.  Questions and comments should be directed to B. S.
     Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY