# rt.f

          SUBROUTINE RT (NM, N, A, W, MATZ, Z, FV1, IERR)
    C***BEGIN PROLOGUE  RT
    C***PURPOSE  Compute the eigenvalues and eigenvectors of a special real
    C            tridiagonal matrix.
    C***LIBRARY   SLATEC (EISPACK)
    C***CATEGORY  D4A5
    C***TYPE      SINGLE PRECISION (RT-S)
    C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
    C***AUTHOR  Smith, B. T., et al.
    C***DESCRIPTION
    C
    C     This subroutine calls the recommended sequence of subroutines
    C     from the eigensystem subroutine package (EISPACK) to find the
    C     eigenvalues and eigenvectors (if desired) of a special REAL
    C     TRIDIAGONAL matrix.  The property of the matrix required for use
    C     of this subroutine is that the products of pairs of corresponding
    C     off-diagonal elements be all non-negative.  If eigenvectors are
    C     desired, no product can be zero unless both factors are zero.
    C
    C     On Input
    C
    C        NM must be set to the row dimension of the two-dimensional
    C          array parameter, A and Z, as declared in the calling
    C          program dimension statement.  NM is an INTEGER variable.
    C
    C        N is the order of the matrix A.  N is an INTEGER variable.
    C          N must be less than or equal to NM.
    C
    C        A contains the special real tridiagonal matrix in its first
    C          three columns.  The subdiagonal elements are stored in the
    C          last N-1 positions of the first column, the diagonal elements
    C          in the second column, and the superdiagonal elements in the
    C          first N-1 positions of the third column.  Elements A(1,1) and
    C          A(N,3) are arbitrary.  A is a two-dimensional REAL array,
    C          dimensioned A(NM,3).
    C
    C        MATZ is an INTEGER variable set equal to zero if only
    C          eigenvalues are desired.  Otherwise, it is set to any
    C          non-zero integer for both eigenvalues and eigenvectors.
    C
    C     On Output
    C
    C        W contains the eigenvalues in ascending order.  W is a
    C          one-dimensional REAL array, dimensioned W(N).
    C
    C        Z contains the eigenvectors if MATZ is not zero.  The eigen-
    C          vectors are not normalized.  Z is a two-dimensional REAL
    C          array, dimensioned Z(NM,N).
    C
    C        IERR is an INTEGER flag set to
    C          Zero       for normal return,
    C          10*N       if N is greater than NM,
    C          N+J        if A(J,1)*A(J-1,3) is negative,
    C          2*N+J      if the product is zero with one factor non-zero,
    C                     and MATZ is non-zero;
    C          J          if the J-th eigenvalue has not been
    C                     determined after 30 iterations.
    C                     The eigenvalues and eigenvectors in the W and Z
    C                     arrays should be correct for indices
    C                     1, 2, ..., IERR-1.
    C
    C        FV1 is a one-dimensional REAL array used for temporary storage,
    C          dimensioned FV1(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  FIGI, FIGI2, IMTQL1, IMTQL2
    C***REVISION HISTORY  (YYMMDD)
    C   760101  DATE WRITTEN
    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  RT