Python/maths/square_root.py
Christian Clauss 9316e7c014
Set the Python file maximum line length to 88 characters (#2122)
* flake8 --max-line-length=88

* fixup! Format Python code with psf/black push

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
2020-06-16 10:09:19 +02:00

65 lines
1.3 KiB
Python

import math
def fx(x: float, a: float) -> float:
return math.pow(x, 2) - a
def fx_derivative(x: float) -> float:
return 2 * x
def get_initial_point(a: float) -> float:
start = 2.0
while start <= a:
start = math.pow(start, 2)
return start
def square_root_iterative(
a: float, max_iter: int = 9999, tolerance: float = 0.00000000000001
) -> float:
"""
Square root is aproximated using Newtons method.
https://en.wikipedia.org/wiki/Newton%27s_method
>>> all(abs(square_root_iterative(i)-math.sqrt(i)) <= .00000000000001
... for i in range(500))
True
>>> square_root_iterative(-1)
Traceback (most recent call last):
...
ValueError: math domain error
>>> square_root_iterative(4)
2.0
>>> square_root_iterative(3.2)
1.788854381999832
>>> square_root_iterative(140)
11.832159566199232
"""
if a < 0:
raise ValueError("math domain error")
value = get_initial_point(a)
for i in range(max_iter):
prev_value = value
value = value - fx(value, a) / fx_derivative(value)
if abs(prev_value - value) < tolerance:
return value
return value
if __name__ == "__main__":
from doctest import testmod
testmod()