## Python, math, gaussian.py

``````"""
Reference: https://en.wikipedia.org/wiki/Gaussian_function
"""
from numpy import exp, pi, sqrt

def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> int:
"""
>>> gaussian(1)
0.24197072451914337

>>> gaussian(24)
3.342714441794458e-126

>>> gaussian(1, 4, 2)
0.06475879783294587

>>> gaussian(1, 5, 3)
0.05467002489199788

Supports NumPy Arrays
Use numpy.meshgrid with this to generate gaussian blur on images.
>>> import numpy as np
>>> x = np.arange(15)
>>> gaussian(x)
array([3.98942280e-01, 2.41970725e-01, 5.39909665e-02, 4.43184841e-03,
1.33830226e-04, 1.48671951e-06, 6.07588285e-09, 9.13472041e-12,
5.05227108e-15, 1.02797736e-18, 7.69459863e-23, 2.11881925e-27,
2.14638374e-32, 7.99882776e-38, 1.09660656e-43])

>>> gaussian(15)
5.530709549844416e-50

>>> gaussian([1,2, 'string'])
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for -: 'list' and 'float'

>>> gaussian('hello world')
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for -: 'str' and 'float'

>>> gaussian(10**234) # doctest: +IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
...
OverflowError: (34, 'Result too large')

>>> gaussian(10**-326)
0.3989422804014327

>>> gaussian(2523, mu=234234, sigma=3425)
0.0
"""
return 1 / sqrt(2 * pi * sigma**2) * exp(-((x - mu) ** 2) / (2 * sigma**2))

if __name__ == "__main__":
import doctest

doctest.testmod()
``````