(* Newton-Raphson example from Kennedy's dissertation (p. 11). *)

val newton : -all d1,d2:dim-
  (* f, a function *)              (real[d1] -> real[d2])
  (* f', its derivative *)       * (real[d1] -> real[(d1 ^ ~1) * d2])
  (* x, the initial guess *)     * real[d1]
  (* xacc, relative accuracy *)  * real
                                -> real[d1]

fun newton (f, f', x, xacc) =
  let val dx = f x / f' x
      val x' = x - dx
  in
      if abs dx / x' < xacc
      then x'
      else newton (f, f', x', xacc)
  end


val result = newton (fn x => x * x - (12345.678 * 12345.678),
                     fn x => 2.0 * x,
                     2350.0,
                     0.001)

val _ = print ("result = " ^ Real.toString result ^ "\n")