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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
1.4 KiB
Python
64 lines
1.4 KiB
Python
"""
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Given a function on floating number f(x) and two floating numbers ‘a’ and ‘b’ such that
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f(a) * f(b) < 0 and f(x) is continuous in [a, b].
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Here f(x) represents algebraic or transcendental equation.
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Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)
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https://en.wikipedia.org/wiki/Bisection_method
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"""
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def equation(x: float) -> float:
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"""
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>>> equation(5)
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-15
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>>> equation(0)
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10
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>>> equation(-5)
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-15
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>>> equation(0.1)
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9.99
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>>> equation(-0.1)
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9.99
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"""
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return 10 - x * x
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def bisection(a: float, b: float) -> float:
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"""
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>>> bisection(-2, 5)
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3.1611328125
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>>> bisection(0, 6)
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3.158203125
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>>> bisection(2, 3)
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Traceback (most recent call last):
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...
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ValueError: Wrong space!
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"""
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# Bolzano theory in order to find if there is a root between a and b
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if equation(a) * equation(b) >= 0:
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raise ValueError("Wrong space!")
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c = a
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while (b - a) >= 0.01:
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# Find middle point
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c = (a + b) / 2
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# Check if middle point is root
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if equation(c) == 0.0:
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break
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# Decide the side to repeat the steps
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if equation(c) * equation(a) < 0:
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b = c
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else:
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a = c
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return c
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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print(bisection(-2, 5))
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print(bisection(0, 6))
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