Skip to content

Adds Gaussian Function in maths section #1054

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 8 commits into from
Jul 20, 2019
Merged

Adds Gaussian Function in maths section #1054

Show file tree
Hide file tree
Changes from 6 commits
Commits
Show all changes
8 commits
Select commit Hold shift + click to select a range
f5498e3
Create gaussian.py
QuantumNovice Jul 20, 2019
024d5fd
Update gaussian.py
QuantumNovice Jul 20, 2019
3993f96
Update gaussian.py
QuantumNovice Jul 20, 2019
6a4748f
Create gaussian.png
QuantumNovice Jul 20, 2019
f3b4401
Add files via upload
QuantumNovice Jul 20, 2019
dd6b25a
Create prime_factors.py
QuantumNovice Jul 20, 2019
ae99fff
Update prime_factors.py
QuantumNovice Jul 20, 2019
0382832
Update prime_factors.py
QuantumNovice Jul 20, 2019
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
61 changes: 61 additions & 0 deletions maths/gaussian.py
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -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()
Binary file added maths/images/gaussian.png
View file
Open in desktop
Loading
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
50 changes: 50 additions & 0 deletions maths/prime_factors.py
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,50 @@
"""
python/black : True
"""


def prime_factors(n: int) -> list:
"""
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)
[]
>>> prime_factors(10**241)
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]
Copy link
Member

@cclauss cclauss Jul 20, 2019 •
edited
Loading

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

My last request on this PR... I promise.

>>> prime_factors(10**241)  # doctest: NORMALIZE_WHITESPACE
<and then wrap the next line so it is readable in GitHub editor without left-right scrolling>

https://docs.python.org/3/library/doctest.html#doctest.NORMALIZE_WHITESPACE

Copy link
Contributor Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Done. Thank you for your time. This is educational for me.

>>> 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()