def test_aux_differential_srv_transform_vectorization(
self, dim, n_sampling_points, curve_a, curve_b
):
"""Test differential of square root velocity transform.
Check vectorization.
"""
dim = 3
curves = gs.stack((curve_a, curve_b))
tangent_vecs = gs.random.rand(2, n_sampling_points, dim)
srv_metric_r3 = SRVMetric(r3)
result = srv_metric_r3.aux_differential_srv_transform(tangent_vecs, curves)
res_a = srv_metric_r3.aux_differential_srv_transform(tangent_vecs[0], curve_a)
res_b = srv_metric_r3.aux_differential_srv_transform(tangent_vecs[1], curve_b)
expected = gs.stack([res_a, res_b])
self.assertAllClose(result, expected)
def test_aux_differential_srv_transform_inverse(
self, dim, n_sampling_points, curve_a
):
"""Test inverse of differential of square root velocity transform.
Check that it is the inverse of aux_differential_srv_transform.
"""
tangent_vec = gs.transpose(
gs.tile(gs.linspace(0.0, 1.0, n_sampling_points), (dim, 1))
)
srv_metric_r3 = SRVMetric(r3)
d_srv = srv_metric_r3.aux_differential_srv_transform(tangent_vec, curve_a)
result = srv_metric_r3.aux_differential_srv_transform_inverse(d_srv, curve_a)
expected = tangent_vec
self.assertAllClose(result, expected, atol=1e-3, rtol=1e-3)
def test_aux_differential_srv_transform(self, dim, n_sampling_points,
n_curves, curve_fun_a):
"""Test differential of square root velocity transform.
Check that its value at (curve, tangent_vec) coincides
with the derivative at zero of the square root velocity
transform of a path of curves starting at curve with
initial derivative tangent_vec.
"""
srv_metric_r3 = SRVMetric(r3)
sampling_times = gs.linspace(0.0, 1.0, n_sampling_points)
curve_a = curve_fun_a(sampling_times)
tangent_vec = gs.transpose(
gs.tile(gs.linspace(1.0, 2.0, n_sampling_points), (dim, 1)))
result = srv_metric_r3.aux_differential_srv_transform(
tangent_vec, curve_a)
times = gs.linspace(0.0, 1.0, n_curves)
path_of_curves = curve_a + gs.einsum("i,jk->ijk", times, tangent_vec)
srv_path = srv_metric_r3.srv_transform(path_of_curves)
expected = n_curves * (srv_path[1] - srv_path[0])
self.assertAllClose(result, expected, atol=1e-3, rtol=1e-3)
