mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
61 lines
1.3 KiB
Python
61 lines
1.3 KiB
Python
import math
|
|
from scipy.integrate import quad
|
|
from numpy import inf
|
|
|
|
|
|
def gamma(num: float) -> float:
|
|
"""
|
|
https://en.wikipedia.org/wiki/Gamma_function
|
|
In mathematics, the gamma function is one commonly
|
|
used extension of the factorial function to complex numbers.
|
|
The gamma function is defined for all complex numbers except the non-positive integers
|
|
|
|
|
|
>>> gamma(-1)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
|
|
|
|
|
|
>>> gamma(0)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
|
|
|
|
>>> gamma(9)
|
|
40320.0
|
|
|
|
>>> from math import gamma as math_gamma
|
|
>>> all(gamma(i)/math_gamma(i) <= 1.000000001 and abs(gamma(i)/math_gamma(i)) > .99999999 for i in range(1, 50))
|
|
True
|
|
|
|
|
|
>>> from math import gamma as math_gamma
|
|
>>> gamma(-1)/math_gamma(-1) <= 1.000000001
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
|
|
|
|
>>> from math import gamma as math_gamma
|
|
>>> gamma(3.3) - math_gamma(3.3) <= 0.00000001
|
|
True
|
|
"""
|
|
|
|
if num <= 0:
|
|
raise ValueError("math domain error")
|
|
|
|
return quad(integrand, 0, inf, args=(num))[0]
|
|
|
|
|
|
def integrand(x: float, z: float) -> float:
|
|
return math.pow(x, z - 1) * math.exp(-x)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
from doctest import testmod
|
|
|
|
testmod()
|