def test_forward(self):
precise_guess_loss = PreciseGuessLoss()
predicted_cubes = (torch.stack([
Magma(FOUR_GROUP).probabilistic_cube,
CyclicGroup(4).probabilistic_cube,
]).to(CURRENT_DEVICE).view(-1, 4, 4, 4))
target_cubes = (torch.stack([
Magma(FOUR_GROUP).probabilistic_cube,
Magma(FOUR_GROUP).probabilistic_cube,
]).to(CURRENT_DEVICE).view(-1, 4, 4, 4))
self.assertEqual(precise_guess_loss(predicted_cubes, target_cubes),
0.5)
self.assertEqual(precise_guess_loss(target_cubes, target_cubes), 1.0)
def test_forward(self):
cayley_cube = (torch.stack([
Magma(FOUR_GROUP).probabilistic_cube,
Magma(FOUR_GROUP).probabilistic_cube,
]).view(-1, 4, 4, 4).to(CURRENT_DEVICE))
self.assertEqual(
self.magma_dae(cayley_cube).detach().sum().item(),
32.0,
)
self.assertEqual(
self.magma_vae(cayley_cube).detach().sum().item(),
32.0,
)
def random_semigroup(dim: int,
maximal_tries: int) -> Tuple[bool, torch.Tensor]:
"""
randomly search for a semigroup Cayley table.
Not recommended to use with dim > 4
:param dim: number of elements in a semigroup
:param maximal_tries: how many times to try at most
:returns: a pair (whether the Cayley table is associative, a Cayley table of a magma)
"""
associative = False
try_count = 0
magma = Magma(cardinality=dim)
while not associative and try_count <= maximal_tries:
magma = Magma(cardinality=dim)
associative = magma.is_associative
try_count += 1
return associative, magma.cayley_table
def get_magma_by_index(cardinality: int, index: int) -> Magma:
"""
find a magma from a lexicographical order by its index
:param cardinality: the number of elements in a magma
:param index: an index of magma in a lexicographical order
:returns: a magma with a given index
"""
square = cardinality**2
if index < 0 or index >= cardinality**square:
raise ValueError("""
An index must be non negative and less than $n^(n^2)$""")
cayley_table = list()
residual = index
for _ in range(square):
cayley_table.append(residual % cardinality)
residual = residual // cardinality
return Magma(
torch.tensor(list(reversed(cayley_table))).reshape(
cardinality, cardinality))
def test_guessed_ratio(self):
ratio = guessed_ratio(
Magma(FOUR_GROUP).probabilistic_cube.view(-1, 4, 4, 4),
Magma(FOUR_GROUP).probabilistic_cube.view(-1, 4, 4, 4),
)
self.assertTrue(torch.tensor(1.0).allclose(ratio))
def test_associate_ratio(self):
ratio = associative_ratio(
Magma(FOUR_GROUP).probabilistic_cube.view(-1, 4, 4, 4),
torch.tensor(0.0),
)
self.assertTrue(torch.tensor(1.0).allclose(ratio))
def test_is_associative(self):
self.assertFalse(Magma(torch.tensor([[0, 0], [1, 0]])).is_associative)
self.assertTrue(self.klein_group.is_associative)
self.assertFalse(self.some_magma.is_associative)
def setUp(self):
torch.manual_seed(777)
self.some_magma = Magma(NON_ASSOCIATIVE_MAGMA)
self.klein_group = Magma(FOUR_GROUP)