def test_fisher_rao_invariance(self):
"""Test invariance of fisher rao metric: d(f,g)= d(foh, goh)"""
t = np.linspace(0, np.pi)
id = FDataGrid([t], t)
cos = np.cos(id)
sin = np.sin(id)
gamma = normalize_warping(np.sqrt(id), (0, np.pi))
gamma2 = normalize_warping(np.square(id), (0, np.pi))
distance_original = fisher_rao_distance(cos, sin)
# Construction of 2 warpings
distance_warping = fisher_rao_distance(cos.compose(gamma),
sin.compose(gamma))
distance_warping2 = fisher_rao_distance(cos.compose(gamma2),
sin.compose(gamma2))
# The error ~0.001 due to the derivation
np.testing.assert_almost_equal(distance_original,
distance_warping,
decimal=2)
np.testing.assert_almost_equal(distance_original,
distance_warping2,
decimal=2)
def test_amplitude_distance_limit(self):
"""Test limit of amplitude distance penalty"""
f = make_multimodal_samples(n_samples=1, random_state=1)
g = make_multimodal_samples(n_samples=1, random_state=9999)
amplitude_limit = amplitude_distance(f, g, lam=1000)
fr_distance = fisher_rao_distance(f, g)
np.testing.assert_almost_equal(amplitude_limit, fr_distance)