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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
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def fx(x: float, a: float) -> float:
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return math.pow(x, 2) - a
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def fx_derivative(x: float) -> float:
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return 2 * x
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def get_initial_point(a: float) -> float:
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start = 2.0
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while start <= a:
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start = math.pow(start, 2)
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return start
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def square_root_iterative(
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a: float, max_iter: int = 9999, tolerance: float = 1e-14
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) -> float:
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"""
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Square root approximated using Newton's method.
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https://en.wikipedia.org/wiki/Newton%27s_method
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>>> all(abs(square_root_iterative(i) - math.sqrt(i)) <= 1e-14 for i in range(500))
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True
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>>> square_root_iterative(-1)
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Traceback (most recent call last):
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...
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ValueError: math domain error
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>>> square_root_iterative(4)
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2.0
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>>> square_root_iterative(3.2)
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1.788854381999832
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>>> square_root_iterative(140)
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11.832159566199232
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"""
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if a < 0:
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raise ValueError("math domain error")
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value = get_initial_point(a)
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for _ in range(max_iter):
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prev_value = value
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value = value - fx(value, a) / fx_derivative(value)
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if abs(prev_value - value) < tolerance:
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return value
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return value
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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