mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +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>
64 lines
1.2 KiB
Python
64 lines
1.2 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 = 1e-14
|
|
) -> float:
|
|
"""
|
|
Square root approximated using Newton's method.
|
|
https://en.wikipedia.org/wiki/Newton%27s_method
|
|
|
|
>>> all(abs(square_root_iterative(i) - math.sqrt(i)) <= 1e-14 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 _ 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()
|