COMLR2(3F)

NAME
     COMLR2, SCOMLR2  -  EISPACK routine.  This subroutine finds the
     eigenvalues and eigenvectors of a COMPLEX UPPER Hessenberg matrix by the
     modified LR method.  The eigenvectors of a COMPLEX GENERAL matrix can
     also be found if  COMHES  has been used to reduce this general matrix to
     Hessenberg form.


SYNOPSYS
          subroutine  comlr2(nm, n, low, igh, int, hr, hi, wr, wi, zr, zi,
     ierr)
          integer           nm, n, low, igh, ierr
          integer           int(igh)
          double precision  hr(nm,n),hi(nm,n),wr(n),wi(n),zr(nm,n),zi(nm,n)

          subroutine scomlr2(nm, n, low, igh, int, hr, hi, wr, wi, zr, zi,
     ierr)
          integer           nm, n, low, igh, ierr
          integer           int(igh)
          real              hr(nm,n),hi(nm,n),wr(n),wi(n),zr(nm,n),zi(nm,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.

     INT contains information on the rows and columns interchanged in the
     reduction by  COMHES, if performed.  Only elements LOW through IGH are
     used.  If the eigenvectors of the HESSEN- BERG matrix are desired, set
     INT(J)=J for these elements.

     HR and HI contain the real and imaginary parts, respectively, of the
     complex upper Hessenberg matrix.  Their lower triangles below the
     subdiagonal contain the multipliers which were used in the reduction by
     COMHES, if performed.  If the eigenvectors of the Hessenberg matrix are
     desired, these elements must be set to zero.  On OUTPUT The upper
     Hessenberg portions of HR and HI have been destroyed, but the location
     HR(1,1) contains the norm of the triangularized matrix.

     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.

     ZR and ZI contain the real and imaginary parts, respectively, of the
     eigenvectors.  The eigenvectors are unnormalized.  If an error exit is
     made, none of the eigenvectors has been found.

     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 CDIV for complex division.  Questions and comments
     should be directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE
     NATIONAL LABORATORY