SUBROUTINE HQR(NM,N,LOW,IGH,H,WR,WI,IERR)
C***BEGIN PROLOGUE  HQR
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 a real upper Hessenberg matrix
C            using the QR method.
C***DESCRIPTION
C
C     This subroutine is a translation of the ALGOL procedure HQR,
C     NUM. MATH. 14, 219-231(1970) by Martin, Peters, and Wilkinson.
C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 359-371(1971).
C
C     This subroutine finds the eigenvalues of a REAL
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  BALANC.  If  BALANC  has not been used,
C          set LOW=1, IGH=N.
C
C        H contains the upper Hessenberg matrix.  Information about
C          the transformations used in the reduction to Hessenberg
C          form by  ELMHES  or  ORTHES, if performed, is stored
C          in the remaining triangle under the Hessenberg matrix.
C
C     On OUTPUT
C
C        H has been destroyed.  Therefore, it must be saved
C          before calling  HQR  if subsequent calculation and
C          back transformation of eigenvectors is to be performed.
C
C        WR and WI contain the real and imaginary parts,
C          respectively, of the eigenvalues.  The eigenvalues
C          are unordered except that complex conjugate pairs
C          of values appear consecutively with the eigenvalue
C          having the positive imaginary part first.  If an
C          error 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     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  (NONE)
C***END PROLOGUE  HQR