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41 lines
1.4 KiB
Python
41 lines
1.4 KiB
Python
# Implementing Newton Raphson method in Python
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# Author: Syed Haseeb Shah (github.com/QuantumNovice)
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# The Newton-Raphson method (also known as Newton's method) is a way to
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# quickly find a good approximation for the root of a real-valued function
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from decimal import Decimal
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from math import * # noqa: F401, F403
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from sympy import diff
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def newton_raphson(func: str, a: int, precision: int = 10 ** -10) -> float:
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"""Finds root from the point 'a' onwards by Newton-Raphson method
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>>> newton_raphson("sin(x)", 2)
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3.1415926536808043
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>>> newton_raphson("x**2 - 5*x +2", 0.4)
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0.4384471871911695
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>>> newton_raphson("x**2 - 5", 0.1)
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2.23606797749979
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>>> newton_raphson("log(x)- 1", 2)
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2.718281828458938
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"""
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x = a
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while True:
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x = Decimal(x) - (Decimal(eval(func)) / Decimal(eval(str(diff(func)))))
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# This number dictates the accuracy of the answer
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if abs(eval(func)) < precision:
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return float(x)
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# Let's Execute
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if __name__ == "__main__":
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# Find root of trigonometric function
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# Find value of pi
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print(f"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")
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# Find root of polynomial
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print(f"The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}")
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# Find Square Root of 5
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print(f"The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}")
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# Exponential Roots
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print(f"The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}")
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