SUBROUTINE TSTURM(NM,N,EPS1,D,E,E2,LB,UB,MM,M,W,Z,IERR,RV1,RV2,
     1   RV3,RV4,RV5,RV6)
C***BEGIN PROLOGUE  TSTURM
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
C            given interval and eigenvectors by Sturm sequencing.
C            This subroutine is a translation of the ALGOL procedure
C            TRISTURM by Peters and Wilkinson. HANDBOOK
C            FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 418-439(1971).
C***DESCRIPTION
C
C     This subroutine finds those eigenvalues of a TRIDIAGONAL
C     SYMMETRIC matrix which lie in a specified interval and their
C     associated eigenvectors, using bisection and inverse iteration.
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        EPS1 is an absolute error tolerance for the computed
C          eigenvalues.  It should be chosen commensurate with
C          relative perturbations in the matrix elements of the
C          order of the relative machine precision.  If the
C          input EPS1 is non-positive, it is reset for each
C          submatrix to a default value, namely, minus the
C          product of the relative machine precision and the
C          1-norm of the submatrix.
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        LB and UB define the interval to be searched for eigenvalues.
C          If LB is not less than UB, no eigenvalues will be found.
C
C        MM should be set to an upper bound for the number of
C          eigenvalues in the interval.  WARNING. If more than
C          MM eigenvalues are determined to lie in the interval,
C          an error return is made with no values or vectors found.
C
C     On Output
C
C        EPS1 is unaltered unless it has been reset to its
C          (last) default value.
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C          as negligible, have been replaced by zero causing the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        M is the number of eigenvalues determined to lie in (LB,UB).
C
C        W contains the M eigenvalues in ascending order if the matrix
C          does not split.  If the matrix splits, the eigenvalues are
C          in ascending order for each submatrix.  If a vector error
C          exit is made, W contains those values already found.
C
C        Z contains the associated set of orthonormal eigenvectors.
C          If an error exit is made, Z contains those vectors
C          already found.
C
C        IERR is set to
C          Zero       for normal return,
C          3*N+1      if M exceeds MM.
C          4*N+R      if the eigenvector corresponding to the R-th
C                     eigenvalue fails to converge in 5 iterations.
C
C        RV1, RV2, RV3, RV4, RV5, and RV6 are temporary storage arrays.
C
C     The ALGOL procedure STURMCNT contained in TRISTURM
C     appears in TSTURM in-line.
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  TSTURM