numba-safe version of itertools.combinations?

Question

I have some code which loops through a large set of itertools.combinations, which is now a performance bottleneck. I'm trying to turn to numba's @jit(nopython=True) to speed it up, but I'm running into some issues.

First, it seems numba can't handle itertools.combinations itself, per this small example:

import itertools
import numpy as np
from numba import jit

arr = [1, 2, 3]
c = 2

@jit(nopython=True)
def using_it(arr, c):
    return itertools.combinations(arr, c)

for i in using_it(arr, c):
    print(i)

throw error: numba.errors.TypingError: Failed in nopython mode pipeline (step: nopython frontend) Unknown attribute 'combinations' of type Module(<module 'itertools' (built-in)>)

After some googling, I found this github issue where the questioner proposed this numba-safe function for calculating permutations:

@jit(nopython=True)
def permutations(A, k):
    r = [[i for i in range(0)]]
    for i in range(k):
        r = [[a] + b for a in A for b in r if (a in b)==False]
    return r

Leveraging that, I can then easily filter down to combinations:

@jit(nopython=True)
def combinations(A, k):
    return [item for item in permutations(A, k) if sorted(item) == item]

Now I can run that combinations function without errors and get the correct result. However, this is now dramatically slower with the @jit(nopython=True) than without it. Running this timing test:

A = list(range(20))  # numba throws 'cannot determine numba type of range' w/o list
k = 2
start = pd.Timestamp.utcnow()
print(combinations(A, k))
print(f"took {pd.Timestamp.utcnow() - start}")

clocks in at 2.6 seconds with the numba @jit(nopython=True) decorators, and under 1/000 of a second with them commented out. So that's not really a workable solution for me either.

Answer 1

There is not much to gain with Numba in this case as itertools.combinations is written in C.

If you want to benchmark it, here is a Numba / Python implementation of what itertools.combinatiions does:

@jit(nopython=True)
def using_numba(pool, r):
    n = len(pool)
    indices = list(range(r))
    empty = not(n and (0 < r <= n))

    if not empty:
        result = [pool[i] for i in indices]
        yield result

    while not empty:
        i = r - 1
        while i >= 0 and indices[i] == i + n - r:
            i -= 1
        if i < 0:
            empty = True
        else:
            indices[i] += 1
            for j in range(i+1, r):
                indices[j] = indices[j-1] + 1

            result = [pool[i] for i in indices]
            yield result

On my machine, this is about 15 times slower than itertools.combinations. Getting the permutations and filtering the combinations would certainly be even slower.