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# 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 __future__ import annotations

from decimal import Decimal

from math import * # noqa: F401, F403

from sympy import diff

def newton_raphson(

func: str, a: float | Decimal, precision: float = 10 ** -10

) -> float:

"""Finds root from the point 'a' onwards by Newton-Raphson method

>>> newton_raphson("sin(x)", 2)

3.1415926536808043

>>> newton_raphson("x**2 - 5*x +2", 0.4)

0.4384471871911695

>>> newton_raphson("x**2 - 5", 0.1)

2.23606797749979

>>> newton_raphson("log(x)- 1", 2)

2.718281828458938

"""

x = a

while True:

x = Decimal(x) - (Decimal(eval(func)) / Decimal(eval(str(diff(func)))))

# This number dictates the accuracy of the answer

if abs(eval(func)) < precision:

return float(x)

# Let's Execute

if __name__ == "__main__":

# Find root of trigonometric function

# Find value of pi

print(f"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")

# Find root of polynomial

print(f"The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}")

# Find Square Root of 5

print(f"The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}")

# Exponential Roots

print(f"The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}")

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