TQLRAT(3F)

NAME
     TQLRAT, STQLRAT  -  EISPACK routine.  This subroutine finds the
     eigenvalues of a SYMMETRIC TRIDIAGONAL matrix by the rational QL method.


SYNOPSYS
          subroutine  tqlrat(n, d, e2, ierr)
          integer          n, ierr
          double precision d(n), e2(n)

          subroutine stqlrat(n, d, e2, ierr)
          integer          n, ierr
          real             d(n), e2(n)



DESCRIPTION
     On Input

     N is the order of the matrix.

     D contains the diagonal elements of the input matrix.

     E2 contains the squares of the subdiagonal elements of the input matrix
     in its last N-1 positions.  E2(1) is arbitrary.  On Output

     D contains the eigenvalues in ascending order.  If an error exit is made,
     the eigenvalues are correct and ordered for indices 1,2,...IERR-1, but
     may not be the smallest eigenvalues.

     E2 has been destroyed.

     IERR is set to Zero       for normal return, J          if the J-th
     eigenvalue has not been
        determined after 30 iterations.  Calls PYTHAG(A,B) for sqrt(A**2 +
     B**2).  Questions and comments should be directed to B. S. Garbow,
     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY