SUBROUTINE BISECT(N,EPS1,D,E,E2,LB,UB,MM,M,W,IND,IERR,RV4,RV5)
C***BEGIN PROLOGUE  BISECT
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 of symmetric tridiagonal matrix
C            given interval using Sturm sequencing.
C***DESCRIPTION
C
C     This subroutine is a translation of the bisection technique
C     in the ALGOL procedure TRISTURM by Peters and Wilkinson.
C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 418-439(1971).
C
C     This subroutine finds those eigenvalues of a TRIDIAGONAL
C     SYMMETRIC matrix which lie in a specified interval,
C     using bisection.
C
C     On INPUT
C
C        N is the order of the matrix.
C
C        EPS1 is an absolute error tolerance for the computed
C          eigenvalues.  If the input EPS1 is non-positive,
C          it is reset for each submatrix to a default value,
C          namely, minus the product of the relative machine
C          precision and the 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 eigenvalues 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C          as negligible, have been replaced by zero causing the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.
C
C        IND contains in its first M positions the submatrix indices
C          associated with the corresponding eigenvalues in W --
C          1 for eigenvalues belonging to the first submatrix from
C          the top, 2 for those belonging to the second submatrix, etc.
C
C        IERR is set to
C          Zero       for normal return,
C          3*N+1      if M exceeds MM.
C
C        RV4 and RV5 are temporary storage arrays.
C
C     The ALGOL procedure STURMCNT contained in TRISTURM
C     appears in BISECT in-line.
C
C     Note that subroutine TQL1 or IMTQL1 is generally faster than
C     BISECT, if more than N/4 eigenvalues are to be found.
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  BISECT