SUBROUTINE COMQR(NM,N,LOW,IGH,HR,HI,WR,WI,IERR)
C***BEGIN PROLOGUE  COMQR
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C2B
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Computes eigenvalues of complex upper Hessenberg matrix
C            using the QR method.
C***DESCRIPTION
C
C     This subroutine is a translation of a unitary analogue of the
C     ALGOL procedure  COMLR, NUM. MATH. 12, 369-376(1968) by Martin
C     and Wilkinson.
C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 396-403(1971).
C     The unitary analogue substitutes the QR algorithm of Francis
C     (COMP. JOUR. 4, 332-345(1962)) for the LR algorithm.
C
C     This subroutine finds the eigenvalues of a COMPLEX
C     upper Hessenberg matrix by the QR method.
C
C     On INPUT
C
C        NM must be set to the row dimension of two-dimensional
C          array parameters as declared in the calling program
C          dimension statement.
C
C        N is the order of the matrix.
C
C        LOW and IGH are integers determined by the balancing
C          subroutine  CBAL.  If  CBAL  has not been used,
C          set LOW=1, IGH=N.
C
C        HR and HI contain the real and imaginary parts,
C          respectively, of the complex upper Hessenberg matrix.
C          Their lower triangles below the subdiagonal contain
C          information about the unitary transformations used in
C          the reduction by  CORTH, if performed.
C
C     On OUTPUT
C
C        The upper Hessenberg portions of HR and HI have been
C          destroyed.  Therefore, they must be saved before
C          calling  COMQR  if subsequent calculation of
C          eigenvectors is to be performed.
C
C        WR and WI contain the real and imaginary parts,
C          respectively, of the eigenvalues.  If an error
C          exit is made, the eigenvalues should be correct
C          for indices IERR+1,...,N.
C
C        IERR is set to
C          ZERO       for normal return,
C          J          if the J-th eigenvalue has not been
C                     determined after a total of 30*N iterations.
C
C     Calls CSROOT for complex square root.
C     Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
C     Calls CDIV for complex division.
C
C     Questions and comments should be directed to B. S. Garbow,
C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C***REFERENCES  B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW,
C                 Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN-
C                 SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG,
C                 1976.
C***ROUTINES CALLED  CDIV,CSROOT,PYTHAG
C***END PROLOGUE  COMQR