NR.py

from random import *

def NR(func, deriv, epsilon=10**(-8),n=100,x0=None):
   """ Given a real valued func and its real value derivative,
   deriv, NR attempts to find a zero of func, using the
   Newton-Raphson method.
   NR starts with a an initial x0 (default value is None
   which is replaced upon execusion by a random number distributed
   uniformly in (-100.,100.)), and performs n=100 iterations.
   If the absolute value derivative on some x_i is smaller
   than epsilon, None is the returned value. """
   if x0 is None:
    x0 = uniform(-100.,100.)
   x = x0
   y = func(x)
   for i in range(n):
      if abs(y) < epsilon:
         return x
      elif abs(deriv(x)) < epsilon:
         print ("zero derivative, x0=", x0, " i=", i, " xi=", x)
         return None
      else:
         x = x - func(x) / deriv(x)
         y = func(x)
   print("no convergence, x0=", x0," i=", i, " xi=", x)
   return None