SLATEC Routines --- TINVIT ---

*DECK TINVIT
      SUBROUTINE TINVIT (NM, N, D, E, E2, M, W, IND, Z, IERR, RV1, RV2,
     +   RV3, RV4, RV6)
C***BEGIN PROLOGUE  TINVIT
C***PURPOSE  Compute the eigenvectors of symmetric tridiagonal matrix
C            corresponding to specified eigenvalues, using inverse
C            iteration.
C***LIBRARY   SLATEC (EISPACK)
C***CATEGORY  D4C3
C***TYPE      SINGLE PRECISION (TINVIT-S)
C***KEYWORDS  EIGENVECTORS, EISPACK
C***AUTHOR  Smith, B. T., et al.
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 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        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          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          E2 is a one-dimensional REAL array, dimensioned E2(N).
C
C        M is the number of specified eigenvalues for which eigenvectors
C          are to be determined.  M is an INTEGER variable.
C
C        W contains the M eigenvalues in ascending or descending order.
C          W is a one-dimensional REAL array, dimensioned W(M).
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          If  BISECT  or  TRIDIB  has been used to determine the
C          eigenvalues, their output IND array is suitable for input
C          to TINVIT.  IND is a one-dimensional INTEGER array,
C          dimensioned IND(M).
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          Z is a two-dimensional REAL array, dimensioned Z(NM,M).
C
C        IERR is an INTEGER flag set to
C          Zero       for normal return,
C          -J         if the eigenvector corresponding to the J-th
C                     eigenvalue fails to converge in 5 iterations.
C
C        RV1, RV2 and RV3 are one-dimensional REAL arrays used for
C          temporary storage.  They are used to store the main diagonal
C          and the two adjacent diagonals of the triangular matrix
C          produced in the inverse iteration process.  RV1, RV2 and
C          RV3 are dimensioned RV1(N), RV2(N) and RV3(N).
C
C        RV4 and RV6 are one-dimensional REAL arrays used for temporary
C          storage.  RV4 holds the multipliers of the Gaussian
C          elimination process.  RV6 holds the approximate eigenvectors
C          in this process.  RV4 and RV6 are dimensioned RV4(N) and
C          RV6(N).
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  (NONE)
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  TINVIT