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5d5831bdd0
* added gamma_function * Add files via upload * Resolved issue with str.format And also changed output to math notation * Update gamma_function.py * Rename physics/gamma_function.py to maths/gamma_recursive.py * Fixes: #4709 Fixed issues for pre-commit test * Fixes: #4709 solved issues with doctests And comments * Fixes: #4709 Added failed tests to doctest * Align with Python's Standard Library math.gamma() Replicate the exceptions of https://docs.python.org/3/library/math.html#math.gamma * Update gamma_recursive.py * Update gamma_recursive.py * Update gamma_recursive.py * Update gamma_recursive.py Co-authored-by: Christian Clauss <cclauss@me.com>
79 lines
2.1 KiB
Python
79 lines
2.1 KiB
Python
"""
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Gamma function is a very useful tool in math and physics.
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It helps calculating complex integral in a convenient way.
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for more info: https://en.wikipedia.org/wiki/Gamma_function
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Python's Standard Library math.gamma() function overflows around gamma(171.624).
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"""
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from math import pi, sqrt
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def gamma(num: float) -> float:
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"""
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Calculates the value of Gamma function of num
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where num is either an integer (1, 2, 3..) or a half-integer (0.5, 1.5, 2.5 ...).
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Implemented using recursion
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Examples:
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>>> from math import isclose, gamma as math_gamma
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>>> gamma(0.5)
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1.7724538509055159
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>>> gamma(2)
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1.0
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>>> gamma(3.5)
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3.3233509704478426
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>>> gamma(171.5)
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9.483367566824795e+307
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>>> all(isclose(gamma(num), math_gamma(num)) for num in (0.5, 2, 3.5, 171.5))
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True
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>>> gamma(0)
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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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>>> gamma(-1.1)
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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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>>> gamma(-4)
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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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>>> gamma(172)
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Traceback (most recent call last):
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...
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OverflowError: math range error
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>>> gamma(1.1)
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Traceback (most recent call last):
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...
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NotImplementedError: num must be an integer or a half-integer
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"""
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if num <= 0:
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raise ValueError("math domain error")
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if num > 171.5:
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raise OverflowError("math range error")
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elif num - int(num) not in (0, 0.5):
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raise NotImplementedError("num must be an integer or a half-integer")
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elif num == 0.5:
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return sqrt(pi)
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else:
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return 1.0 if num == 1 else (num - 1) * gamma(num - 1)
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def test_gamma() -> None:
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"""
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>>> test_gamma()
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"""
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assert gamma(0.5) == sqrt(pi)
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assert gamma(1) == 1.0
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assert gamma(2) == 1.0
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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num = 1
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while num:
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num = float(input("Gamma of: "))
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print(f"gamma({num}) = {gamma(num)}")
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print("\nEnter 0 to exit...")
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