SLATEC Routines --- TSTURM ---

*DECK TSTURM
      SUBROUTINE TSTURM (NM, N, EPS1, D, E, E2, LB, UB, MM, M, W, Z,
     +   IERR, RV1, RV2, RV3, RV4, RV5, RV6)
C***BEGIN PROLOGUE  TSTURM
C***PURPOSE  Find those eigenvalues of a symmetric tridiagonal matrix
C            in a given interval and their associated eigenvectors by
C            Sturm sequencing.
C***LIBRARY   SLATEC (EISPACK)
C***CATEGORY  D4A5, D4C2A
C***TYPE      SINGLE PRECISION (TSTURM-S)
C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR  Smith, B. T., et al.
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 the two-dimensional
C          array parameter, Z, as declared in the calling program
C          dimension statement.  NM is an INTEGER variable.
C
C        N is the order of the matrix.  N is an INTEGER variable.
C          N must be less than or equal to NM.
C
C        EPS1 is an absolute error tolerance for the computed eigen-
C          values.  It should be chosen so that the accuracy of these
C          eigenvalues is commensurate with relative perturbations of
C          the order of the relative machine precision in the matrix
C          elements.  If the input EPS1 is non-positive, it is reset
C          for each submatrix to a default value, namely, minus the
C          product of the relative machine precision and the 1-norm of
C          the submatrix.  EPS1 is a REAL variable.
C
C        D contains the diagonal elements of the symmetric tridiagonal
C          matrix.  D is a one-dimensional REAL array, dimensioned D(N).
C
C        E contains the subdiagonal elements of the symmetric
C          tridiagonal matrix in its last N-1 positions.  E(1) is
C          arbitrary.  E is a one-dimensional REAL array, dimensioned
C          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.  MM is an INTEGER variable.
C          WARNING -  If more than MM eigenvalues are determined to lie
C          in the interval, an error return is made with no values or
C          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 as
C          negligible, have been replaced by zero causing the matrix to
C          split into a direct sum of submatrices.  E2(1) is also set
C          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 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.  W is a
C          one-dimensional REAL array, dimensioned W(MM).
C
C        Z contains the associated set of orthonormal eigenvectors.
C          If an error exit is made, Z contains those vectors already
C          found.  Z is a one-dimensional REAL array, dimensioned
C          Z(NM,MM).
C
C        IERR is an INTEGER flag set to
C          Zero       for normal return,
C          3*N+1      if M exceeds MM no eigenvalues or eigenvectors
C                     are computed,
C          4*N+J      if the eigenvector corresponding to the J-th
C                     eigenvalue fails to converge in 5 iterations, then
C                     the eigenvalues and eigenvectors in W and Z should
C                     be correct for indices 1, 2, ..., J-1.
C
C        RV1, RV2, RV3, RV4, RV5, and RV6 are temporary storage arrays,
C          dimensioned RV1(N), RV2(N), RV3(N), RV4(N), RV5(N), and
C          RV6(N).
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
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   890531  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  TSTURM