mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-07 14:19:31 +00:00
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
"""
|
|
Gamma function is a very useful tool in math and physics.
|
|
It helps calculating complex integral in a convenient way.
|
|
for more info: https://en.wikipedia.org/wiki/Gamma_function
|
|
|
|
Python's Standard Library math.gamma() function overflows around gamma(171.624).
|
|
"""
|
|
from math import pi, sqrt
|
|
|
|
|
|
def gamma(num: float) -> float:
|
|
"""
|
|
Calculates the value of Gamma function of num
|
|
where num is either an integer (1, 2, 3..) or a half-integer (0.5, 1.5, 2.5 ...).
|
|
Implemented using recursion
|
|
Examples:
|
|
>>> from math import isclose, gamma as math_gamma
|
|
>>> gamma(0.5)
|
|
1.7724538509055159
|
|
>>> gamma(2)
|
|
1.0
|
|
>>> gamma(3.5)
|
|
3.3233509704478426
|
|
>>> gamma(171.5)
|
|
9.483367566824795e+307
|
|
>>> all(isclose(gamma(num), math_gamma(num)) for num in (0.5, 2, 3.5, 171.5))
|
|
True
|
|
>>> gamma(0)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma(-1.1)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma(-4)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma(172)
|
|
Traceback (most recent call last):
|
|
...
|
|
OverflowError: math range error
|
|
>>> gamma(1.1)
|
|
Traceback (most recent call last):
|
|
...
|
|
NotImplementedError: num must be an integer or a half-integer
|
|
"""
|
|
if num <= 0:
|
|
raise ValueError("math domain error")
|
|
if num > 171.5:
|
|
raise OverflowError("math range error")
|
|
elif num - int(num) not in (0, 0.5):
|
|
raise NotImplementedError("num must be an integer or a half-integer")
|
|
elif num == 0.5:
|
|
return sqrt(pi)
|
|
else:
|
|
return 1.0 if num == 1 else (num - 1) * gamma(num - 1)
|
|
|
|
|
|
def test_gamma() -> None:
|
|
"""
|
|
>>> test_gamma()
|
|
"""
|
|
assert gamma(0.5) == sqrt(pi)
|
|
assert gamma(1) == 1.0
|
|
assert gamma(2) == 1.0
|
|
|
|
|
|
if __name__ == "__main__":
|
|
from doctest import testmod
|
|
|
|
testmod()
|
|
num = 1
|
|
while num:
|
|
num = float(input("Gamma of: "))
|
|
print(f"gamma({num}) = {gamma(num)}")
|
|
print("\nEnter 0 to exit...")
|