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"""

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()

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