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In my Uni, my scientific professor asked me to make some researches about the extreme points of polyhedrals. And I did them. I found that there is still no code in public for searching extreme points for polyhedral with n dimensions (n - x's), but polyhedrons are everywhere (CV, game theories, etc.). I wrote a function for this task and made a python library (also there are matrix and array combination maker functions).

All I want is to make this code more optimal and compatible for all python versions (I have some troubles that some times happen when I install it by "pip install lin", but other times no). I want to make the life of people easier and make it more comfortable.

I am asking for you to test this function on your computer and write if you have any bugs, fails or thoughts on how to make it better. I am open to constructive criticism and non-constructive too (it will help to understand if somebody needs it or that is just a waste of time).

All the examples, instructions and code on my GitHub: https://github.com/r4ndompuff/polyhedral_set

import numpy as np
import itertools as it
import math
import re

def permutation(m,n):
 return math.factorial(n)/(math.factorial(n-m)*math.factorial(m))

def matrix_combinations(matr,n):
 timed = list(map(list, it.combinations(matr, n)))
 for i in range(n):
 timed[i][i][i] = np.asscalar(timed[i][i][i])
 all = np.array(list(timed))
 return all

def array_combinations(arr,n):
 timed = list(map(list, it.combinations(arr, n)))
 for i in range(n):
 timed[i][i] = np.asscalar(timed[i][i])
 all = np.array(list(timed))
 return all

def check_extreme(matr, arr, x, sym_comb, m):
 sym_comb = sym_comb.replace(']', '')
 sym_comb = sym_comb.replace('[', '')
 sym_comb = re.split("[ ,]", sym_comb)
 for i in range(m):
 td_answer = sum(matr[i]*x)
 if sym_comb[i] == '>':
 if td_answer <= arr[i]:
 return 0
 elif sym_comb[i] == '>=':
 if td_answer < arr[i]:
 return 0
 elif sym_comb[i] == '<':
 if td_answer >= arr[i]:
 return 0
 elif sym_comb[i] == '<=':
 if td_answer > arr[i]:
 return 0
 elif sym_comb[i] == '=':
 if td_answer != arr[i]:
 return 0
 elif sym_comb[i] == '!=':
 if td_answer == arr[i]:
 return 0
 else:
 return 0
 return 1

def extreme_points(m,n,A,b,sym_comb):
 # Input
 A = np.array(A).reshape(m,n)
 b = np.array(b).reshape(m,1)
 # Proccess
 ans_comb = np.zeros((1,n))
 arr_comb = array_combinations(b,n)
 matr_comb = matrix_combinations(A,n)
 for i in range(int(permutation(n,m))):
 if np.linalg.det(matr_comb[i]) != 0:
 x = np.linalg.solve(matr_comb[i],arr_comb[i])
 ans_comb = np.vstack([ans_comb,x])
 ans_comb = np.delete(ans_comb, (0), axis=0)
 j = 0
 for i in range(len(ans_comb)):
 if check_extreme(A, b, ans_comb[j], sym_comb, m):
 ans_comb = ans_comb
 j = j + 1
 else:
 ans_comb = np.delete(ans_comb, (j), axis=0)
 # Output
 return ans_comb

And I am uploading some more tests. https://imgur.com/mjweDyy

I created a rudimentary pull request to your GitHub repo. I won't show all of the content here except for the main file:

import numpy as np
import itertools as it
import math
import re


def permutation(m, n):
 return math.factorial(n) / (math.factorial(n - m) * math.factorial(m))


def matrix_combinations(matr, n):
 timed = list(map(list, it.combinations(matr, n)))
 for i in range(n):
 timed[i][i][i] = np.asscalar(timed[i][i][i])
 return np.array(list(timed))


def array_combinations(arr, n):
 timed = list(map(list, it.combinations(arr, n)))
 for i in range(n):
 timed[i][i] = np.asscalar(timed[i][i])
 return np.array(list(timed))


def check_extreme(matr, arr, x, sym_comb, m):
 sym_comb = sym_comb.replace(']', '')
 sym_comb = sym_comb.replace('[', '')
 sym_comb = re.split("[ ,]", sym_comb)
 for i in range(m):
 td_answer = sum(matr[i] * x)
 if sym_comb[i] == '>':
 if td_answer <= arr[i]:
 return 0
 elif sym_comb[i] == '>=':
 if td_answer < arr[i]:
 return 0
 elif sym_comb[i] == '<':
 if td_answer >= arr[i]:
 return 0
 elif sym_comb[i] == '<=':
 if td_answer > arr[i]:
 return 0
 elif sym_comb[i] == '=':
 if td_answer != arr[i]:
 return 0
 elif sym_comb[i] == '!=':
 if td_answer == arr[i]:
 return 0
 else:
 return 0
 return 1


def extreme_points(m, n, A, b, sym_comb):
 # Input
 A = np.array(A).reshape(m, n)
 b = np.array(b).reshape(m, 1)
 # Process
 ans_comb = np.zeros((1, n))
 arr_comb = array_combinations(b, n)
 matr_comb = matrix_combinations(A, n)
 for i in range(int(permutation(n, m))):
 if np.linalg.det(matr_comb[i]) != 0:
 x = np.linalg.solve(matr_comb[i], arr_comb[i])
 ans_comb = np.vstack([ans_comb, x])
 ans_comb = np.delete(ans_comb, 0, axis=0)
 j = 0
 for i in range(len(ans_comb)):
 if check_extreme(A, b, ans_comb[j], sym_comb, m):
 ans_comb = ans_comb
 j = j + 1
 else:
 ans_comb = np.delete(ans_comb, j, axis=0)
 # Output
 return ans_comb

This is a first cut mainly for PEP8 compliance, and doesn't solve the bigger issue that you should replace 99% of this with a call to scipy. I'll do that separately (I suspect that @vnp is, as well).