mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-05 02:40:16 +00:00
bc8df6de31
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
117 lines
3.4 KiB
Python
117 lines
3.4 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
|
|
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
|
|
Python's Standard Library math.gamma() function overflows around gamma(171.624).
|
|
"""
|
|
|
|
import math
|
|
|
|
from numpy import inf
|
|
from scipy.integrate import quad
|
|
|
|
|
|
def gamma_iterative(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 ...).
|
|
|
|
>>> gamma_iterative(-1)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma_iterative(0)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma_iterative(9)
|
|
40320.0
|
|
>>> from math import gamma as math_gamma
|
|
>>> all(.99999999 < gamma_iterative(i) / math_gamma(i) <= 1.000000001
|
|
... for i in range(1, 50))
|
|
True
|
|
>>> gamma_iterative(-1)/math_gamma(-1) <= 1.000000001
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma_iterative(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)
|
|
|
|
|
|
def gamma_recursive(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_recursive(0.5)
|
|
1.7724538509055159
|
|
>>> gamma_recursive(1)
|
|
1.0
|
|
>>> gamma_recursive(2)
|
|
1.0
|
|
>>> gamma_recursive(3.5)
|
|
3.3233509704478426
|
|
>>> gamma_recursive(171.5)
|
|
9.483367566824795e+307
|
|
>>> all(isclose(gamma_recursive(num), math_gamma(num))
|
|
... for num in (0.5, 2, 3.5, 171.5))
|
|
True
|
|
>>> gamma_recursive(0)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma_recursive(-1.1)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma_recursive(-4)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> gamma_recursive(172)
|
|
Traceback (most recent call last):
|
|
...
|
|
OverflowError: math range error
|
|
>>> gamma_recursive(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 math.sqrt(math.pi)
|
|
else:
|
|
return 1.0 if num == 1 else (num - 1) * gamma_recursive(num - 1)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
from doctest import testmod
|
|
|
|
testmod()
|
|
num = 1.0
|
|
while num:
|
|
num = float(input("Gamma of: "))
|
|
print(f"gamma_iterative({num}) = {gamma_iterative(num)}")
|
|
print(f"gamma_recursive({num}) = {gamma_recursive(num)}")
|
|
print("\nEnter 0 to exit...")
|