SLATEC Routines --- BISECT ---

*DECK BISECT
      SUBROUTINE BISECT (N, EPS1, D, E, E2, LB, UB, MM, M, W, IND, IERR,
     +   RV4, RV5)
C***BEGIN PROLOGUE  BISECT
C***PURPOSE  Compute the eigenvalues of a symmetric tridiagonal matrix
C            in a given interval using Sturm sequencing.
C***LIBRARY   SLATEC (EISPACK)
C***CATEGORY  D4A5, D4C2A
C***TYPE      SINGLE PRECISION (BISECT-S)
C***KEYWORDS  EIGENVALUES, EISPACK
C***AUTHOR  Smith, B. T., et al.
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.  N is an INTEGER variable.
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          EPS1 is a REAL variable.
C
C        D contains the diagonal elements of the input matrix.
C          D is a one-dimensional REAL array, dimensioned D(N).
C
C        E contains the subdiagonal elements of the input matrix
C          in its last N-1 positions.  E(1) is arbitrary.
C          E is a one-dimensional REAL array, dimensioned E(N).
C
C        E2 contains the squares of the corresponding elements of E.
C          E2(1) is arbitrary.  E2 is a one-dimensional REAL array,
C          dimensioned E2(N).
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          LB and UB are REAL variables.
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          MM is an INTEGER variable.
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C          as negligible, have been replaced by zero causing the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          M is an INTEGER variable.
C
C        W contains the M eigenvalues in ascending order.
C          W is a one-dimensional REAL array, dimensioned W(MM).
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          IND is an one-dimensional INTEGER array, dimensioned IND(MM).
C
C        IERR is an INTEGER flag set to
C          Zero       for normal return,
C          3*N+1      if M exceeds MM.  In this case, M contains the
C                     number of eigenvalues determined to lie in
C                     (LB,UB).
C
C        RV4 and RV5 are one-dimensional REAL arrays used for temporary
C          storage, dimensioned RV4(N) and RV5(N).
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
C***REFERENCES  B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
C                 Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
C                 system Routines - EISPACK Guide, Springer-Verlag,
C                 1976.
C***ROUTINES CALLED  R1MACH
C***REVISION HISTORY  (YYMMDD)
C   760101  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  BISECT