def test_srv_transform_and_srv_transform_inverse(self, rtol, atol):
"""Test that srv and its inverse are inverse."""
metric = SRVMetric(ambient_manifold=r3)
curve = DiscreteCurves(r3).random_point(n_samples=2)
srv = metric.srv_transform(curve)
srv_inverse = metric.srv_transform_inverse(srv, curve[:, 0])
result = srv.shape
expected = (curve.shape[0], curve.shape[1] - 1, 3)
self.assertAllClose(result, expected)
result = srv_inverse
expected = curve
self.assertAllClose(result, expected, rtol, atol)
def test_srv_transform_and_inverse(self, times, curve_a, curve_b):
"""Test of SRVT and its inverse.
N.B: Here curves_ab are seen as curves in R3 and not S2.
"""
l2_metric_s2 = L2CurvesMetric(ambient_manifold=s2)
srv_metric_r3 = SRVMetric(ambient_manifold=r3)
curves_ab = l2_metric_s2.geodesic(curve_a, curve_b)
curves_ab = curves_ab(times)
curves = curves_ab
srv_curves = srv_metric_r3.srv_transform(curves)
starting_points = curves[:, 0, :]
result = srv_metric_r3.srv_transform_inverse(srv_curves, starting_points)
expected = curves
self.assertAllClose(result, expected)
def test_srv_norm(self, curve_a, curve_b, times):
l2_metric_s2 = L2CurvesMetric(ambient_manifold=s2)
srv_metric_r3 = SRVMetric(ambient_manifold=r3)
curves_ab = l2_metric_s2.geodesic(curve_a, curve_b)
curves_ab = curves_ab(times)
srvs_ab = srv_metric_r3.srv_transform(curves_ab)
result = srv_metric_r3.l2_curves_metric.norm(srvs_ab)
products = srvs_ab * srvs_ab
sums = [gs.sum(product) for product in products]
squared_norm = gs.array(sums) / (srvs_ab.shape[-2] + 1)
expected = gs.sqrt(squared_norm)
self.assertAllClose(result, expected)
result = result.shape
expected = [srvs_ab.shape[0]]
self.assertAllClose(result, expected)
def test_srv_inner_product(self, curve_a, curve_b, curve_c, times):
l2_metric_s2 = L2CurvesMetric(ambient_manifold=s2)
srv_metric_r3 = SRVMetric(ambient_manifold=r3)
curves_ab = l2_metric_s2.geodesic(curve_a, curve_b)
curves_bc = l2_metric_s2.geodesic(curve_b, curve_c)
curves_ab = curves_ab(times)
curves_bc = curves_bc(times)
srvs_ab = srv_metric_r3.srv_transform(curves_ab)
srvs_bc = srv_metric_r3.srv_transform(curves_bc)
result = srv_metric_r3.l2_curves_metric.inner_product(srvs_ab, srvs_bc)
products = srvs_ab * srvs_bc
expected = [gs.sum(product) for product in products]
expected = gs.array(expected) / (srvs_ab.shape[-2] + 1)
self.assertAllClose(result, expected)
result = result.shape
expected = [srvs_ab.shape[0]]
self.assertAllClose(result, expected)
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)