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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).