def test_triu():
"""Check that conversion from and to to the triangular form works."""
fn = TreeMarginals(4, False)
matrix = torch.Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12],
[13, 14, 15, 16]])
triu = fn.triu(Variable(matrix))
assert np.allclose(triu.data.numpy(), np.array([2, 3, 4, 7, 8, 12]))
matrix_recovered = fn.to_mat(triu).data
assert np.allclose(
matrix_recovered.numpy(),
np.array([[0, 2, 3, 4], [0, 0, 7, 8], [0, 0, 0, 12], [0, 0, 0, 0]]))
def test_dumbbell():
"""Test that on the dumbbell graph two complete graphs connected using a
single edge, the single edge gets a probability of one and the ones
in the complete graphs get uniform probabilities."""
for m in range(3, 51):
n = 2 * m
fn = TreeMarginals(n, False)
unaries = -10000 * torch.ones(n * (n - 1) // 2)
k = 0
indices = np.zeros(n * (n - 1) // 2, dtype=np.bool)
for i in range(n):
for j in range(i + 1, n):
if i < m and j < m or i >= m and j >= m:
unaries[k] = 1
indices[k] = 1
elif i + 1 == m == j:
unaries[k] = 1
dumbbell_idx = k
k += 1
margs = fn(Variable(unaries)).cpu().data.numpy()
indices = np.asarray(indices, dtype=np.bool)
assert np.allclose(margs[indices], (m - 1) / (m * (m - 1) // 2),
rtol=1e-3)
assert np.allclose(margs[dumbbell_idx], 1., rtol=1e-3)
def test_cardinality():
"""Check that the sum of all edges is always n-1."""
torch.manual_seed(0)
for n in range(5, 51):
fn = TreeMarginals(n, False)
unaries = torch.randn(1, n * (n - 1) // 2)
margs = fn(Variable(unaries))
assert np.isclose(margs.sum().data.item(), n - 1)
def test_cycle():
"""Test that on a cycle graph the edges present in the cycle have marginals
close to n / (n - 1) and the other have marginals close to zero."""
for n in range(3, 51):
fn = TreeMarginals(n, False)
unaries = -10000 * torch.ones(n * (n - 1) // 2)
k = 0
indices = []
for i in range(n):
for j in range(i + 1, n):
if j == i + 1 or i == 0 and j + 1 == n:
unaries[k] = 1
indices.append(1)
else:
indices.append(0)
k += 1
margs = fn(Variable(unaries)).cpu().data.numpy()
indices = np.asarray(indices, dtype=np.bool)
assert np.allclose(margs[indices], (n - 1) / n)
assert np.allclose(margs[~indices], 0)