Possible unintended behavior of vector_vector boundary matrix specification

[apizzimenti]

I've been using PHAT's Python bindings to detect the births of essential cycles on a cubical 2-torus. I've noticed that changing the order in which the indices of a cell's faces are listed — e.g. (2, [9, 10, 14, 18]) to (2, [10, 14, 9, 18]) — causes different/incorrect persistence pairs to be reported. Here's a MWE:

from random import sample
import phat

vertices = [(0, [])]*9

edges = [
    (1, [0, 1]),
    (1, [0, 3]),
    (1, [0, 2]),
    (1, [0, 6]),
    (1, [1, 2]),
    (1, [1, 4]),
    (1, [1, 7]),
    (1, [2, 5]),
    (1, [2, 8]),
    (1, [3, 4]),
    (1, [3, 6]),
    (1, [3, 5]),
    (1, [4, 5]),
    (1, [4, 7]),
    (1, [5, 8]),
    (1, [6, 7]),
    (1, [6, 8]),
    (1, [7, 8]),
]

squares = [
    (2, [9, 10, 14, 18]),
    (2, [13, 14, 16, 21]),
    (2, [18, 19, 22, 24]),
    (2, [21, 22, 23, 26]),
    (2, [10, 11, 16, 20]),
    (2, [9, 12, 15, 24]),
    (2, [19, 20, 23, 25]),
    (2, [13, 15, 17, 26]),
    (2, [11, 12, 17, 25]),
]


# To compare the resultant persistence pairs, we shuffle the order in which the
# indices of each square's faces are listed. These indices are listed in increasing
# order by default.
for question, shuffler in zip(["original", "shuffled"], [lambda A: A, lambda B: sample(B, len(B))]):
    # Shuffle the ordering of the squares' faces and construct the cubical complex.
    squares = [(d, shuffler(faces)) for d, faces in squares]
    complex = vertices + edges + squares

    # Construct the boundary matrix and compute the persistence pairs.
    boundary = phat.boundary_matrix()
    boundary.columns = complex
    pairs = boundary.compute_persistence_pairs()
    pairs.sort()
    pairs = list(pairs)

    # Determine the births of essential cycles; these should be invariant under
    # re-orderings of the squares' faces in the specification.
    deaths = set([d for b, d in pairs])
    births = set([b for b, d in pairs])
    times = set(range(len(complex)))
    essential = times-(births|deaths)

    print(question)
    print(f"births @ {births}")
    print(f"deaths @ {deaths}")
    print(f"essential @ {essential}")
    print()

which outputs

>>> original
    births @ {1, 2, 3, 4, 5, 6, 7, 8, 18, 20, 21, 22, 23, 24, 25, 26}
    deaths @ {32, 33, 34, 9, 10, 11, 12, 14, 15, 16, 17, 27, 28, 29, 30, 31}
    essential @ {0, 35, 19, 13}

    shuffled
    births @ {1, 2, 3, 4, 5, 6, 7, 8, 12, 13, 17, 18, 19, 20, 22, 24, 26}
    deaths @ {32, 33, 34, 35, 9, 10, 11, 14, 15, 16, 23, 25, 27, 28, 29, 30, 31}
    essential @ {0, 21}

which are correct and incorrect, respectively. Is this behavior intended?