# Implementing Newton Raphson method in Python
# Author: Syed Haseeb Shah (github.com/QuantumNovice)
# The Newton-Raphson method (also known as Newton's method) is a way to
# quickly find a good approximation for the root of a real-valued function
from sympy import diff
from decimal import Decimal


def NewtonRaphson(func, a):
    """ Finds root from the point 'a' onwards by Newton-Raphson method """
    while True:
        c = Decimal(a) - (Decimal(eval(func)) / Decimal(eval(str(diff(func)))))

        a = c

        # This number dictates the accuracy of the answer
        if abs(eval(func)) < 10 ** -15:
            return c


# Let's Execute
if __name__ == "__main__":
    # Find root of trigonometric function
    # Find value of pi
    print("sin(x) = 0", NewtonRaphson("sin(x)", 2))

    # Find root of polynomial
    print("x**2 - 5*x +2 = 0", NewtonRaphson("x**2 - 5*x +2", 0.4))

    # Find Square Root of 5
    print("x**2 - 5 = 0", NewtonRaphson("x**2 - 5", 0.1))

    # Exponential Roots
    print("exp(x) - 1 = 0", NewtonRaphson("exp(x) - 1", 0))