Python/maths/entropy.py
Maxim Smolskiy 4700297b3e
Enable ruff RUF002 rule ()
* Enable ruff RUF002 rule

* Fix

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
2024-04-22 21:51:47 +02:00

133 lines
4.7 KiB
Python

#!/usr/bin/env python3
"""
Implementation of entropy of information
https://en.wikipedia.org/wiki/Entropy_(information_theory)
"""
from __future__ import annotations
import math
from collections import Counter
from string import ascii_lowercase
def calculate_prob(text: str) -> None:
"""
This method takes path and two dict as argument
and than calculates entropy of them.
:param dict:
:param dict:
:return: Prints
1) Entropy of information based on 1 alphabet
2) Entropy of information based on couples of 2 alphabet
3) print Entropy of H(X n|Xn-1)
Text from random books. Also, random quotes.
>>> text = ("Behind Winston's back the voice "
... "from the telescreen was still "
... "babbling and the overfulfilment")
>>> calculate_prob(text)
4.0
6.0
2.0
>>> text = ("The Ministry of Truth—Minitrue, in Newspeak [Newspeak was the official"
... "face in elegant lettering, the three")
>>> calculate_prob(text)
4.0
5.0
1.0
>>> text = ("Had repulsive dashwoods suspicion sincerity but advantage now him. "
... "Remark easily garret nor nay. Civil those mrs enjoy shy fat merry. "
... "You greatest jointure saw horrible. He private he on be imagine "
... "suppose. Fertile beloved evident through no service elderly is. Blind "
... "there if every no so at. Own neglected you preferred way sincerity "
... "delivered his attempted. To of message cottage windows do besides "
... "against uncivil. Delightful unreserved impossible few estimating "
... "men favourable see entreaties. She propriety immediate was improving. "
... "He or entrance humoured likewise moderate. Much nor game son say "
... "feel. Fat make met can must form into gate. Me we offending prevailed "
... "discovery.")
>>> calculate_prob(text)
4.0
7.0
3.0
"""
single_char_strings, two_char_strings = analyze_text(text)
my_alphas = list(" " + ascii_lowercase)
# what is our total sum of probabilities.
all_sum = sum(single_char_strings.values())
# one length string
my_fir_sum = 0
# for each alpha we go in our dict and if it is in it we calculate entropy
for ch in my_alphas:
if ch in single_char_strings:
my_str = single_char_strings[ch]
prob = my_str / all_sum
my_fir_sum += prob * math.log2(prob) # entropy formula.
# print entropy
print(f"{round(-1 * my_fir_sum):.1f}")
# two len string
all_sum = sum(two_char_strings.values())
my_sec_sum = 0
# for each alpha (two in size) calculate entropy.
for ch0 in my_alphas:
for ch1 in my_alphas:
sequence = ch0 + ch1
if sequence in two_char_strings:
my_str = two_char_strings[sequence]
prob = int(my_str) / all_sum
my_sec_sum += prob * math.log2(prob)
# print second entropy
print(f"{round(-1 * my_sec_sum):.1f}")
# print the difference between them
print(f"{round((-1 * my_sec_sum) - (-1 * my_fir_sum)):.1f}")
def analyze_text(text: str) -> tuple[dict, dict]:
"""
Convert text input into two dicts of counts.
The first dictionary stores the frequency of single character strings.
The second dictionary stores the frequency of two character strings.
"""
single_char_strings = Counter() # type: ignore[var-annotated]
two_char_strings = Counter() # type: ignore[var-annotated]
single_char_strings[text[-1]] += 1
# first case when we have space at start.
two_char_strings[" " + text[0]] += 1
for i in range(len(text) - 1):
single_char_strings[text[i]] += 1
two_char_strings[text[i : i + 2]] += 1
return single_char_strings, two_char_strings
def main():
import doctest
doctest.testmod()
# text = (
# "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
# "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
# "jointure saw horrible. He private he on be imagine suppose. Fertile "
# "beloved evident through no service elderly is. Blind there if every no so "
# "at. Own neglected you preferred way sincerity delivered his attempted. To "
# "of message cottage windows do besides against uncivil. Delightful "
# "unreserved impossible few estimating men favourable see entreaties. She "
# "propriety immediate was improving. He or entrance humoured likewise "
# "moderate. Much nor game son say feel. Fat make met can must form into "
# "gate. Me we offending prevailed discovery. "
# )
# calculate_prob(text)
if __name__ == "__main__":
main()