SUBROUTINE TQL2(NM,N,D,E,Z,IERR)
C***BEGIN PROLOGUE  TQL2
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4A5,D4C2A
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Compute eigenvalues and eigenvectors of symmetric
C            tridiagonal matrix.
C***DESCRIPTION
C
C     This subroutine is a translation of the ALGOL procedure TQL2,
C     NUM. MATH. 11, 293-306(1968) by Bowdler, Martin, Reinsch, and
C     Wilkinson.
C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 227-240(1971).
C
C     This subroutine finds the eigenvalues and eigenvectors
C     of a SYMMETRIC TRIDIAGONAL matrix by the QL method.
C     The eigenvectors of a FULL SYMMETRIC matrix can also
C     be found if  TRED2  has been used to reduce this
C     full matrix to tridiagonal form.
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        D contains the diagonal elements of the input matrix.
C
C        E contains the subdiagonal elements of the input matrix
C          in its last N-1 positions.  E(1) is arbitrary.
C
C        Z contains the transformation matrix produced in the
C          reduction by  TRED2, if performed.  If the eigenvectors
C          of the tridiagonal matrix are desired, Z must contain
C          the identity matrix.
C
C      On Output
C
C        D contains the eigenvalues in ascending order.  If an
C          error exit is made, the eigenvalues are correct but
C          unordered for indices 1,2,...,IERR-1.
C
C        E has been destroyed.
C
C        Z contains orthonormal eigenvectors of the symmetric
C          tridiagonal (or full) matrix.  If an error exit is made,
C          Z contains the eigenvectors associated with the stored
C          eigenvalues.
C
C        IERR is set to
C          Zero       for normal return,
C          J          if the J-th eigenvalue has not been
C                     determined after 30 iterations.
C
C     Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
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  PYTHAG
C***END PROLOGUE  TQL2