Adds Gaussian Function in maths section

maths/gaussian.py

@@ -0,0 +1,61 @@
+
+"""
+Reference: https://en.wikipedia.org/wiki/Gaussian_function
+
+python/black : True
+python : 3.7.3
+
+"""
+from numpy import pi, sqrt, exp
+
+
+
+def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> int:
+    """
+    >>> gaussian(1)
+    0.24197072451914337
+
+    >>> gaussian(24)
+    3.342714441794458e-126
+
+    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()

maths/prime_factors.py

@@ -0,0 +1,52 @@
+"""
+python/black : True
+"""
+from typing import List
+
+
+def prime_factors(n: int) -> List[int]:
+    """
+    Returns prime factors of n as a list.
+
+    >>> prime_factors(0)
+    []
+    >>> prime_factors(100)
+    [2, 2, 5, 5]
+    >>> prime_factors(2560)
+    [2, 2, 2, 2, 2, 2, 2, 2, 2, 5]
+    >>> prime_factors(10**-2)
+    []
+    >>> prime_factors(0.02)
+    []
+    >>> x = prime_factors(10**241) # doctest: +NORMALIZE_WHITESPACE
+    >>> x == [2]*241 + [5]*241
+    True
+    >>> prime_factors(10**-354)
+    []
+    >>> prime_factors('hello')
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'str'
+    >>> prime_factors([1,2,'hello'])
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'list'
+
+    """
+    i = 2
+    factors = []
+    while i * i <= n:
+        if n % i:
+            i += 1
+        else:
+            n //= i
+            factors.append(i)
+    if n > 1:
+        factors.append(n)
+    return factors
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()