Brute force FCA concepts by trying all combinations with NumPy

fca_numpy.py

"""Generate concepts by trying all combinations with NumPy."""

from collections.abc import Iterator, Sequence
import itertools

import numpy as np

OBJECTS = ('1s', '1de', '1pe', '1di', '1pi',
           '2s', '2d', '2p',
           '3s.m', '3s.f', '3s.n',
           '3d.m', '3d.f', '3d.n',
           '3p.m', '3p.f', '3p.n')

PROPERTIES = ('+1', '-1', '+2', '-2', '+3', '-3',
              '+sg', '+du', '+pl', '-sg', '-du', '-pl',
              '+masc', '+fem', '+neut', '-masc', '-fem', '-neut')

BOOLS = [(1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0),
         (1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0),
         (1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0),
         (1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0),
         (1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0),
         (0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0),
         (0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0),
         (0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0),
         (0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1),
         (0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1),
         (0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0),
         (0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1),
         (0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1),
         (0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0),
         (0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1),
         (0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1),
         (0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0)]


def concepts(objects: Sequence[str],
             properties: Sequence[str],
             bools: Sequence[Sequence[int]]
             ) -> Iterator[tuple[Sequence[str], Sequence[str]]]:
    """Yield all (extent, intent) pairs in shortlex order."""
    X = np.array(bools, dtype=bool)
    Y = X.transpose().copy()

    indexes = range(len(objects))
    for r in range(len(objects) + 1):
        for idx in itertools.combinations(indexes, r):
            P = X.take(idx, axis=0)
            prime = np.logical_and.reduce(P)

            O = Y.compress(prime, axis=0)
            double = np.logical_and.reduce(O)

            if np.count_nonzero(double) == r:
                intent = tuple(np.compress(prime, properties))
                extent = tuple(np.compress(double, objects))

                yield extent, intent


for extent, intent in concepts(OBJECTS, PROPERTIES, BOOLS):
    print(f"{{{', '.join(extent)}}} <-> [{' '.join(intent)}]")