n dimensional grid in Python / numpy

Question

I have an unknown number n of variables that can range from 0 to 1 with some known step s, with the condition that they sum up to 1. I want to create a

Answer 1

This method will also work for an arbitrary sum (total):

import numpy as np
import itertools as it
import scipy.special

n = 3
s = 1/3.
total = 1.00

interval = int(total/s)
n_combs = scipy.special.comb(n+interval-1, interval, exact=True)
counts = np.zeros((n_combs, n), dtype=int)

def count_elements(elements, n):
    count = np.zeros(n, dtype=int)
    for elem in elements:
        count[elem] += 1
    return count

for i, comb in enumerate(it.combinations_with_replacement(range(n), interval)):
    counts[i] = count_elements(comb, n)

ratios = counts*s
print(ratios)