Newtons_Method.py

from scipy.misc import derivative
#from sympy import diff

def NewtonsMethod(f, initial, tolerance = 1e-10, max_iterations = 100, debug = False):
  """
  Parameters
      ----------
      f : function name
          input of function(x)
      initial : float
          Inital guess for Newton's Method
      tolerance : float, optional
          The tolerance for Newton's Method. The default is 1e-10.
      max_iterations : int, optional
          Maximum number of iterations for Newton's Method. The default is 100.
      debug : boolean, optional
          Toggles several print statements. The default is False.

      Returns
      -------
      x0 : float
        Calculated root found
  """
  it = 0
  x0 = initial

  while True:
      x1 = x0 - f(x0) / derivative(f, x0)
      difference = abs(x1 - x0)
      if (difference < tolerance) or it >= max_iterations:
          break
      it += 1
      x0 = x1
  return x0

def f(x):
  return x**2 + 1

#initial = -2
#approx_root = NewtonsMethod(f, initial)

#print('x: ', initial)
#print('approx root: ', approx_root)
#print("f(approx root) = ", (f(approx_root)))