SUBROUTINE IMTQLV(N,D,E,E2,W,IND,IERR,RV1)
C***BEGIN PROLOGUE  IMTQLV
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  Computes eigenvalues of symmetric tridiagonal matrix by the
C            implicit QL method. Eigenvectors may be computed later.
C***DESCRIPTION
C
C     This subroutine is a variant of  IMTQL1  which is a translation of
C     ALGOL procedure IMTQL1, NUM. MATH. 12, 377-383(1968) by Martin and
C     Wilkinson, as modified in NUM. MATH. 15, 450(1970) by Dubrulle.
C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 241-248(1971).
C
C     This subroutine finds the eigenvalues of a SYMMETRIC TRIDIAGONAL
C     matrix by the implicit QL method and associates with them
C     their corresponding submatrix indices.
C
C     On INPUT
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        E2 contains the squares of the corresponding elements of E.
C          E2(1) is arbitrary.
C
C     On OUTPUT
C
C        D and E are unaltered.
C
C        Elements of E2, corresponding to elements of E regarded
C          as negligible, have been replaced by zero causing the
C          matrix to split into a direct sum of submatrices.
C          E2(1) is also set to zero.
C
C        W contains the eigenvalues in ascending order.  If an
C          error exit is made, the eigenvalues are correct and
C          ordered for indices 1,2,...IERR-1, but may not be
C          the smallest eigenvalues.
C
C        IND contains the submatrix indices associated with the
C          corresponding eigenvalues in W -- 1 for eigenvalues
C          belonging to the first submatrix from the top,
C          2 for those belonging to the second submatrix, etc.
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        RV1 is a temporary storage array.
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  IMTQLV