uniroot                package:stats                R Documentation

_O_n_e _D_i_m_e_n_s_i_o_n_a_l _R_o_o_t (_Z_e_r_o) _F_i_n_d_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     The function 'uniroot' searches the interval from 'lower' to
     'upper' for a root (i.e., zero) of the function 'f' with respect
     to its first argument.

_U_s_a_g_e:

     uniroot(f, interval, lower = min(interval), upper = max(interval),
             tol = .Machine$double.eps^0.25, maxiter = 1000, ...)

_A_r_g_u_m_e_n_t_s:

       f: the function for which the root is sought.

interval: a vector containing the end-points of the interval to be
          searched for the root.

   lower: the lower end point of the interval to be searched.

   upper: the upper end point of the interval to be searched.

     tol: the desired accuracy (convergence tolerance).

 maxiter: the maximum number of iterations.

     ...: additional arguments to 'f'.

_D_e_t_a_i_l_s:

     Either 'interval' or both 'lower' and 'upper' must be specified. 
     The function uses Fortran subroutine '"zeroin"' (from Netlib)
     based on algorithms given in the reference below.

     Convergence is declared either if 'f(x) == 0' or the change in 'x'
     for one step of the algorithm is less than 'tol' (plus an
     allowance for representation error in 'x').

     If the algorithm does not converge in 'maxiter' steps, a warning
     is printed and the current approximation is returned.

_V_a_l_u_e:

     A list with four components: 'root' and 'f.root' give the location
     of the root and the value of the function evaluated at that point.
     'iter' and 'estim.prec' give the number of iterations used and an
     approximate estimated precision for 'root'.

_R_e_f_e_r_e_n_c_e_s:

     Brent, R. (1973) _Algorithms for Minimization without
     Derivatives._ Englewood Cliffs, NJ: Prentice-Hall.

_S_e_e _A_l_s_o:

     'polyroot' for all complex roots of a polynomial; 'optimize',
     'nlm'.

_E_x_a_m_p_l_e_s:

     f <- function (x,a) x - a
     str(xmin <- uniroot(f, c(0, 1), tol = 0.0001, a = 1/3))
     str(uniroot(function(x) x*(x^2-1) + .5, low = -2, up = 2, tol = 0.0001),
         dig = 10)
     str(uniroot(function(x) x*(x^2-1) + .5, low = -2, up = 2, tol = 1e-10 ),
         dig = 10)

     ## Find the smallest value x for which exp(x) > 0 (numerically):
     r <- uniroot(function(x) 1e80*exp(x)-1e-300, c(-1000,0), tol = 1e-15)
     str(r, digits= 15) ##> around -745, depending on the platform.

     exp(r$r)        # = 0, but not for r$r * 0.999...
     minexp <- r$r * (1 - 10*.Machine$double.eps)
     exp(minexp)     # typically denormalized

