SUBROUTINE TINVIT(NM,N,D,E,E2,M,W,IND,Z,IERR,RV1,RV2,RV3,RV4,RV6)
C***BEGIN PROLOGUE  TINVIT
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C3
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Eigenvectors of symmetric tridiagonal matrix corresponding
C            to some specified eigenvalues, using inverse iteration
C***DESCRIPTION
C
C     This subroutine is a translation of the inverse iteration tech-
C     nique 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 eigenvectors of a TRIDIAGONAL
C     SYMMETRIC matrix corresponding to specified eigenvalues,
C     using 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        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          with zeros corresponding to negligible elements of E.
C          E(I) is considered negligible if it is not larger than
C          the product of the relative machine precision and the sum
C          of the magnitudes of D(I) and D(I-1).  E2(1) must contain
C          0.0e0 if the eigenvalues are in ascending order, or 2.0e0
C          if the eigenvalues are in descending order.  If  BISECT,
C          TRIDIB, or  IMTQLV  has been used to find the eigenvalues,
C          their output E2 array is exactly what is expected here.
C
C        M is the number of specified eigenvalues.
C
C        W CONTAINS the M eigenvalues in ascending or descending 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     On Output
C
C       ** All input arrays are unaltered.**
C
C        Z contains the associated set of orthonormal eigenvectors.
C          any vector which fails to converge is set to zero.
C
C        IERR is set to
C          Zero       for normal return,
C          -R         if the eigenvector corresponding to the R-th
C                     eigenvalue fails to converge in 5 iterations.
C
C        RV1, RV2, RV3, RV4, and RV6 are temporary storage arrays.
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  TINVIT