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_standard_normalize_warping(self):
"""Test normalization to (0, 1)"""
normalized = normalize_warping(self.polynomial, (0, 1))
# Test new domain range (0, 1)
np.testing.assert_array_equal(normalized.domain_range, [(0, 1)])
np.testing.assert_array_almost_equal(normalized.sample_points[0],
np.linspace(0, 1, 50))
np.testing.assert_array_almost_equal(normalized(0), [[0.], [0.]])
np.testing.assert_array_almost_equal(normalized(1), [[1.], [1.]])
def test_normalize_warping(self):
"""Test normalization to (a, b)"""
a = -4
b = 3
domain = (a, b)
normalized = normalize_warping(self.polynomial, domain)
# Test new domain range (0, 1)
np.testing.assert_array_equal(normalized.domain_range, [domain])
np.testing.assert_array_almost_equal(normalized.grid_points[0],
np.linspace(*domain, 50))
np.testing.assert_array_equal(normalized(a)[..., 0], [[a], [a]])
np.testing.assert_array_equal(normalized(b)[..., 0], [[b], [b]])
def test_standard_normalize_warping_default_value(self):
"""Test normalization """
normalized = normalize_warping(self.polynomial)
# Test new domain range (0, 1)
np.testing.assert_array_equal(normalized.domain_range, [(-1, 1)])
np.testing.assert_array_almost_equal(normalized.grid_points[0],
np.linspace(-1, 1, 50))
np.testing.assert_array_almost_equal(
normalized(-1)[..., 0], [[-1], [-1]])
np.testing.assert_array_almost_equal(
normalized(1)[..., 0], [[1.], [1.]])