# rst.f

          SUBROUTINE RST (NM, N, W, E, MATZ, Z, IERR)
    C***BEGIN PROLOGUE  RST
    C***PURPOSE  Compute the eigenvalues and, optionally, the eigenvectors
    C            of a real symmetric tridiagonal matrix.
    C***LIBRARY   SLATEC (EISPACK)
    C***CATEGORY  D4A5
    C***TYPE      SINGLE PRECISION (RST-S)
    C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
    C***AUTHOR  Smith, B. T., et al.
    C***DESCRIPTION
    C
    C     This subroutine calls the recommended sequence of
    C     subroutines from the eigensystem subroutine package (EISPACK)
    C     to find the eigenvalues and eigenvectors (if desired)
    C     of a REAL SYMMETRIC TRIDIAGONAL matrix.
    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        W contains the diagonal elements of the real symmetric
    C          tridiagonal matrix.  W is a one-dimensional REAL array,
    C          dimensioned W(N).
    C
    C        E contains the subdiagonal elements of the matrix in its last
    C          N-1 positions.  E(1) is arbitrary.  E is a one-dimensional
    C          REAL array, dimensioned E(N).
    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.
    C
    C        Z contains the eigenvectors if MATZ is not zero.  The eigen-
    C          vectors are orthonormal.  Z is a two-dimensional REAL array,
    C          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          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     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  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  RST