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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>
50 lines
1.5 KiB
Python
50 lines
1.5 KiB
Python
import math
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from collections.abc import Callable
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def intersection(function: Callable[[float], float], x0: float, x1: float) -> float:
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"""
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function is the f we want to find its root
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x0 and x1 are two random starting points
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>>> intersection(lambda x: x ** 3 - 1, -5, 5)
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0.9999999999954654
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>>> intersection(lambda x: x ** 3 - 1, 5, 5)
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Traceback (most recent call last):
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...
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ZeroDivisionError: float division by zero, could not find root
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>>> intersection(lambda x: x ** 3 - 1, 100, 200)
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1.0000000000003888
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>>> intersection(lambda x: x ** 2 - 4 * x + 3, 0, 2)
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0.9999999998088019
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>>> intersection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
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2.9999999998088023
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>>> intersection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
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3.0000000001786042
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>>> intersection(math.sin, -math.pi, math.pi)
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0.0
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>>> intersection(math.cos, -math.pi, math.pi)
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Traceback (most recent call last):
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...
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ZeroDivisionError: float division by zero, could not find root
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"""
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x_n: float = x0
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x_n1: float = x1
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while True:
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if x_n == x_n1 or function(x_n1) == function(x_n):
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raise ZeroDivisionError("float division by zero, could not find root")
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x_n2: float = x_n1 - (
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function(x_n1) / ((function(x_n1) - function(x_n)) / (x_n1 - x_n))
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)
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if abs(x_n2 - x_n1) < 10**-5:
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return x_n2
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x_n = x_n1
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x_n1 = x_n2
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def f(x: float) -> float:
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return math.pow(x, 3) - (2 * x) - 5
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if __name__ == "__main__":
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print(intersection(f, 3, 3.5))
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