def test_split_horizontal_vertical(
self, times, n_discretized_curves, curve_a, curve_b
):
"""Test split horizontal vertical.
Check that horizontal and vertical parts of any tangent
vector are othogonal with respect to the SRVMetric inner
product, and check vectorization.
"""
srv_metric_r3 = SRVMetric(r3)
quotient_srv_metric_r3 = DiscreteCurves(ambient_manifold=r3).quotient_srv_metric
geod = srv_metric_r3.geodesic(initial_curve=curve_a, end_curve=curve_b)
geod = geod(times)
tangent_vec = n_discretized_curves * (geod[1, :, :] - geod[0, :, :])
(
tangent_vec_hor,
tangent_vec_ver,
_,
) = quotient_srv_metric_r3.split_horizontal_vertical(tangent_vec, curve_a)
result = srv_metric_r3.inner_product(tangent_vec_hor, tangent_vec_ver, curve_a)
expected = 0.0
self.assertAllClose(result, expected, atol=1e-4)
tangent_vecs = n_discretized_curves * (geod[1:] - geod[:-1])
_, _, result = quotient_srv_metric_r3.split_horizontal_vertical(
tangent_vecs, geod[:-1]
)
expected = []
for i in range(n_discretized_curves - 1):
_, _, res = quotient_srv_metric_r3.split_horizontal_vertical(
tangent_vecs[i], geod[i]
)
expected.append(res)
expected = gs.stack(expected)
self.assertAllClose(result, expected)
def test_horizontal_geodesic(self, n_sampling_points, curve_a, n_times):
"""Test horizontal geodesic.
Check that the time derivative of the geodesic is
horizontal at all time.
"""
curve_b = gs.transpose(
gs.stack(
(
gs.zeros(n_sampling_points),
gs.zeros(n_sampling_points),
gs.linspace(1.0, 0.5, n_sampling_points),
)
)
)
quotient_srv_metric_r3 = DiscreteCurves(ambient_manifold=r3).quotient_srv_metric
horizontal_geod_fun = quotient_srv_metric_r3.horizontal_geodesic(
curve_a, curve_b
)
times = gs.linspace(0.0, 1.0, n_times)
horizontal_geod = horizontal_geod_fun(times)
velocity_vec = n_times * (horizontal_geod[1:] - horizontal_geod[:-1])
_, _, vertical_norms = quotient_srv_metric_r3.split_horizontal_vertical(
velocity_vec, horizontal_geod[:-1]
)
result = gs.sum(vertical_norms**2, axis=1) ** (1 / 2)
expected = gs.zeros(n_times - 1)
self.assertAllClose(result, expected, atol=1e-3)