TRIDIB(3F)

NAME
     TRIDIB, STRIDIB  -  EISPACK routine.  This subroutine finds those
     eigenvalues of a TRIDIAGONAL SYMMETRIC matrix between specified boundary
     indices, using bisection.


SYNOPSYS
          subroutine  tridib(n,eps1,d,e,e2,lb,ub,m11,m,w,ind,ierr,rv4,rv5)
          integer          n, m11, m, ierr, ind(m)
          double precision eps1, lb, ub
          double precision d(n), e(n), e2(n), w(m), rv4(n), rv5(n)

          subroutine stridib(n,eps1,d,e,e2,lb,ub,m11,m,w,ind,ierr,rv4,rv5)
          integer          n, m11, m, ierr, ind(m)
          real             eps1, lb, ub
          real             d(n), e(n), e2(n), w(m), rv4(n), rv5(n)



DESCRIPTION
     On Input

     N is the order of the matrix.

     EPS1 is an absolute error tolerance for the computed eigenvalues.  If the
     input EPS1 is non-positive, it is reset for each submatrix to a default
     value, namely, minus the product of the relative machine precision and
     the 1-norm of the submatrix.

     D contains the diagonal elements of the input matrix.

     E contains the subdiagonal elements of the input matrix in its last N-1
     positions.  E(1) is arbitrary.

     E2 contains the squares of the corresponding elements of E. E2(1) is
     arbitrary.

     M11 specifies the lower boundary index for the desired eigenvalues.

     M specifies the number of eigenvalues desired.  The upper boundary index
     M22 is then obtained as M22=M11+M-1.  On Output

     EPS1 is unaltered unless it has been reset to its (last) default value.

     D and E are unaltered. ELEMENTS of E2, corresponding to elements of E
     regarded as negligible, have been replaced by zero causing the matrix to
     split into a direct sum of submatrices.  E2(1) is also set to zero.

     LB and UB DEFINE an interval containing exactly the desired eigenvalues.

     W contains, in its first M positions, the eigenvalues between indices M11
     and M22 in ascending order.
     IND contains in its first M positions the submatrix indices associated
     with the corresponding eigenvalues in W -- 1 for eigenvalues belonging to
     the first submatrix from the top, 2 for those belonging to the second
     submatrix, etc.

     IERR is set to Zero       for normal return, 3*N+1      if multiple
     eigenvalues at index M11 make
        unique selection impossible, 3*N+2      if multiple eigenvalues at
     index M22 make
        unique selection impossible.

     RV4 and RV5 are temporary storage arrays. Note that subroutine TQL1,
     IMTQL1, or TQLRAT is generally faster than TRIDIB, if more than N/4
     eigenvalues are to be found.  Questions and comments should be directed
     to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL
     LABORATORY