# 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))