mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
4d0a8f2355
* optimized recursive_bubble_sort
* Fixed doctest error due whitespace
* reduce loop times for optimization
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
55 lines
1.5 KiB
Python
55 lines
1.5 KiB
Python
"""Newton's Method."""
|
|
|
|
# Newton's Method - https://en.wikipedia.org/wiki/Newton%27s_method
|
|
from typing import Callable
|
|
|
|
RealFunc = Callable[[float], float] # type alias for a real -> real function
|
|
|
|
|
|
# function is the f(x) and derivative is the f'(x)
|
|
def newton(
|
|
function: RealFunc,
|
|
derivative: RealFunc,
|
|
starting_int: int,
|
|
) -> float:
|
|
"""
|
|
>>> newton(lambda x: x ** 3 - 2 * x - 5, lambda x: 3 * x ** 2 - 2, 3)
|
|
2.0945514815423474
|
|
>>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -2)
|
|
1.0
|
|
>>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -4)
|
|
1.0000000000000102
|
|
>>> import math
|
|
>>> newton(math.sin, math.cos, 1)
|
|
0.0
|
|
>>> newton(math.sin, math.cos, 2)
|
|
3.141592653589793
|
|
>>> newton(math.cos, lambda x: -math.sin(x), 2)
|
|
1.5707963267948966
|
|
>>> newton(math.cos, lambda x: -math.sin(x), 0)
|
|
Traceback (most recent call last):
|
|
...
|
|
ZeroDivisionError: Could not find root
|
|
"""
|
|
prev_guess = float(starting_int)
|
|
while True:
|
|
try:
|
|
next_guess = prev_guess - function(prev_guess) / derivative(prev_guess)
|
|
except ZeroDivisionError:
|
|
raise ZeroDivisionError("Could not find root")
|
|
if abs(prev_guess - next_guess) < 10 ** -5:
|
|
return next_guess
|
|
prev_guess = next_guess
|
|
|
|
|
|
def f(x: float) -> float:
|
|
return (x ** 3) - (2 * x) - 5
|
|
|
|
|
|
def f1(x: float) -> float:
|
|
return 3 * (x ** 2) - 2
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(newton(f, f1, 3))
|