maths/gaussian.py · python/Python

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Python

maths

gaussian.py

gaussian.py 1.56 KB

"""
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()

一键复制编辑原始数据按行查看历史

aryan26roy 提交于 2020年07月30日 03:32 +08:00 . Correcting the Gaussian Formula (#2249)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61

"""
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()