mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 05:39:30 +00:00
a8b6bda993
* Remove eval from arithmetic_analysis/newton_raphson.py
* Relocate contents of arithmetic_analysis/
Delete the arithmetic_analysis/ directory and relocate its files because
the purpose of the directory was always ill-defined. "Arithmetic
analysis" isn't a field of math, and the directory's files contained
algorithms for linear algebra, numerical analysis, and physics.
Relocated the directory's linear algebra algorithms to linear_algebra/,
its numerical analysis algorithms to a new subdirectory called
maths/numerical_analysis/, and its single physics algorithm to physics/.
* updating DIRECTORY.md
---------
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
46 lines
1.5 KiB
Python
46 lines
1.5 KiB
Python
# 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 sympy import diff, lambdify, symbols
|
|
|
|
|
|
def newton_raphson(func: str, a: float | Decimal, precision: float = 1e-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 = symbols("x")
|
|
f = lambdify(x, func, "math")
|
|
f_derivative = lambdify(x, diff(func), "math")
|
|
x_curr = a
|
|
while True:
|
|
x_curr = Decimal(x_curr) - Decimal(f(x_curr)) / Decimal(f_derivative(x_curr))
|
|
if abs(f(x_curr)) < precision:
|
|
return float(x_curr)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|
|
|
|
# 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 value of e
|
|
print(f"The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}")
|
|
# Find root of exponential function
|
|
print(f"The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}")
|