maths/gamma.py · napole/Python

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Python

maths

gamma.py

gamma.py 1.21 KB

import math

from numpy import inf
from scipy.integrate import quad

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(.99999999 < gamma(i) / math_gamma(i) <= 1.000000001
 ... for i in range(1, 50))
 True
 >>> gamma(-1)/math_gamma(-1) <= 1.000000001
 Traceback (most recent call last):
 ...
 ValueError: math domain error
 >>> 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()

一键复制编辑原始数据按行查看历史

Tianyi Zheng 提交于 2022年12月30日 01:06 +08:00 . Remove extra imports in gamma.py doctests (#8060)

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import math

from numpy import inf
from scipy.integrate import quad


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(.99999999 < gamma(i) / math_gamma(i) <= 1.000000001
 ... for i in range(1, 50))
 True
 >>> gamma(-1)/math_gamma(-1) <= 1.000000001
 Traceback (most recent call last):
 ...
 ValueError: math domain error
 >>> 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()