def test_von_mises_3d_gof(scale):
concentration = torch.randn(3)
concentration = concentration * (scale / concentration.norm(2))
d = VonMises3D(concentration, validate_args=True)
with xfail_if_not_implemented():
samples = d.sample(torch.Size([2000]))
probs = d.log_prob(samples).exp()
gof = auto_goodness_of_fit(samples, probs, dim=2)
assert gof > TEST_FAILURE_RATE
def test_von_mises_3d(scale):
concentration = torch.randn(3)
concentration = concentration * (scale / concentration.norm(2))
num_samples = 100000
samples = torch.randn(num_samples, 3)
samples = samples / samples.norm(2, dim=-1, keepdim=True)
d = VonMises3D(concentration, validate_args=True)
actual_total = d.log_prob(samples).exp().mean()
expected_total = 1 / (4 * math.pi)
ratio = actual_total / expected_total
assert torch.abs(ratio - 1) < 0.01, ratio