Newton's Method

newton.py

import numpy as np
import sympy as sym
import math


class NewtonsMethod:
  """
  Newton's Method to find zeros and optimize functions.
  """
  def __init__(self, f):
    self.x = sym.Symbol("x")
    self.f = f
   
  def zeros(self, value):
    """
    Recursively performs Newton's Method with initial guess to find zeros.
    :param value: initial guess
    """
    if math.isclose(self.f(value), 0):
      return value
    df = sym.lambdify(self.x, sym.diff(self.f, self.x))
    next_value -= self.f(value)/df(value)
    return self.zeros(self.f, next_value)
  
  def optimize(self, value, max_iter=100):
    """
    Performs Newton's Method with initial guess to optimize function.
    :param value: initial guess
    """
    for _ in range(max_iter):
      df = sym.lambdify(self.x, sym.diff(self.f, self.x))
      d2f = sym.lambdify(self.x, sym.diff(df, self.x))
      value -= df(value)/d2f(value)
    return value
  
  
if __name__ == "__main__":
  function = x**2 - 9
  newtons = NewtonsMethod(function)
  guess = 4
  optimized = newtons.optimize(function, guess)
  print(optimized)