From 61fec83242bb00766141ffa2571414bbba68ab6e Mon Sep 17 00:00:00 2001 From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com> Date: Sat, 20 Jul 2019 17:32:40 +0500 Subject: [PATCH] Adds Gaussian Function in maths section (#1054) * Create gaussian.py * Update gaussian.py * Update gaussian.py * Create gaussian.png * Add files via upload * Create prime_factors.py * Update prime_factors.py * Update prime_factors.py --- maths/gaussian.py | 61 ++++++++++++++++++++++++++++++++++++++ maths/images/gaussian.png | Bin 0 -> 53511 bytes maths/prime_factors.py | 52 ++++++++++++++++++++++++++++++++ 3 files changed, 113 insertions(+) create mode 100644 maths/gaussian.py create mode 100644 maths/images/gaussian.png create mode 100644 maths/prime_factors.py diff --git a/maths/gaussian.py b/maths/gaussian.py new file mode 100644 index 000000000..f3a47a3f6 --- /dev/null +++ b/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() diff --git a/maths/images/gaussian.png b/maths/images/gaussian.png new file mode 100644 index 0000000000000000000000000000000000000000..eb007c7e21b2296c17a11ebf4dee30cfa2e2f6b1 GIT binary patch literal 53511 zcmeFYgM-b?gVeyNaeEG4>Te{3aTEOyZ*P${h!X()yo2+!Dp&_t=xt9%?2Y2F~w1 zysh2d;y7A+xO{N-`0(C_%j>P1`+H}nM9F_7{0y73_VF;iBsQxuy8-7o5Pea?7H0%fQcz zemlZ`cUS1GN4ZyIw;hx>I4$QWRHT!W6LQIMe*Evm-0hT^M(Zg)--yj$0h>8=de9`#<9=3Wb4FCN@lT(>P@+TMt~#If|>lk`K& zEx}P6BqMQs9`YA_WWACKvKM?qk!u8qJFu&|HyRN>>!K}n8~Y@3n&bD5=w{zPJxJtK z1YNw%CTO9=?fY#?#7lX!ImY96y15eY84w8`+laW%B5g&nWwIMq`Dy&MNcU+cK95i+ 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@@ +""" +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()