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* flake8 --max-line-length=88
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
65 lines
1.3 KiB
Python
65 lines
1.3 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 = 0.00000000000001
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) -> float:
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"""
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Square root is aproximated using Newtons 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)) <= .00000000000001
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... 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 i 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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