def test_exponential_map():
p = np.array([
[np.cosh(0.), np.sinh(0.)],
[np.cosh(0.), np.sinh(0.)],
[np.cosh(0.5*np.pi), np.sinh(0.5*np.pi)],
# [np.cosh(np.pi), np.sinh(np.pi)]
])
v = np.array([
[0., 0.],
[0., 0.25*np.pi],
[0.478393040868114, 0.521606959131886],
# [0.499066278634146, 0.500933721365854]
])
expected = np.array([
[1., 0.],
[1.324609089252006, 0.86867096148601],
[3.04543575, 2.87657416],
])
hyperb = Hyperboloid(1)
print("")
print(hyperb.exponential_map(p, v))
print(expected)
assert_array_almost_equal(hyperb.exponential_map(p, v), expected)
def test_logarithmic_map():
# Leverage trusted exponential map to verify logarithmic map
p0 = np.array([
[np.cosh(0.), np.sinh(0.)],
[np.cosh(0.), np.sinh(0.)],
[np.cosh(1), np.sinh(1)],
[np.cosh(1), np.sinh(1)],
])
p1 = np.array([
[np.cosh(0.), np.sinh(0.)],
[np.cosh(1.), np.sinh(1.)],
[np.cosh(-1.), np.sinh(-1.)],
[np.cosh(-np.pi), np.sinh(-np.pi)]
])
hyperb = Hyperboloid(1)
vectors = hyperb.logarithmic_map(p0, p1)
p1_from_v = hyperb.exponential_map(p0, vectors)
assert_array_equal(
hyperb.is_on_manifold(p1_from_v),
np.ones((p1_from_v.shape[0], 1), dtype=bool)
)
assert_array_almost_equal(p1, p1_from_v)