def test_is_in_tangent_space():
p = np.array([
[np.cosh(0.), np.sinh(0.)],
[np.cosh(0.), np.sinh(0.)],
[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.],
[1., 0.],
[0., 1.],
[0., -1.],
[0.478393040868114, 0.521606959131886],
[0.499066278634146, 0.500933721365854]
])
expected = np.array([
[True],
[False],
[True],
[True],
[True],
[True],
])
hyperb = Hyperboloid(1)
assert_array_almost_equal(hyperb.is_in_tangent_space(p, v), expected)
def test_project_to_tangent_space():
p = np.array([
[np.cosh(0.), np.sinh(0.)],
[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.],
[1., 0.],
[1., 1.],
[1., 1.],
[1., 1.]
])
expected = np.array([
[0., 0.],
[0., 0.],
[0., 1.],
[0.478393040868114, 0.521606959131886],
[0.499066278634146, 0.500933721365854]
])
hyperb = Hyperboloid(1)
v_TpM = hyperb.project_to_tangent_space(p, v)
assert_array_almost_equal(v_TpM, expected)
# projection(projection(v)) should equal projection(v)
assert_array_almost_equal(
hyperb.project_to_tangent_space(p, v_TpM),
expected
)
def test_parallel_transport():
# Test relies on fact that parallel transporting vector from p0->p1->p0 along
# same path should yield the same vector in Tp0M
p0 = 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)]
])
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)]
])
v_Tp0M = np.array([
[0., 0.],
[0., 1.],
[0.478393040868114, 0.521606959131886],
[0.499066278634146, 0.500933721365854]
])
hyperb = Hyperboloid(1)
print("")
v_Tp1M = hyperb.parallel_transport(v_Tp0M, p0, p1)
print(v_Tp1M)
v_Tp0M_ptd = hyperb.parallel_transport(v_Tp1M, p1, p0)
print(v_Tp0M_ptd)
assert_array_almost_equal(v_Tp0M, v_Tp0M_ptd)
def test_distance():
u = np.array([
[np.cosh(0.), np.sinh(0.)],
[np.cosh(0.5), np.sinh(0.5)],
[np.cosh(10.), np.sinh(10.)]
])
v = np.array([
[np.cosh(0.5), np.sinh(0.5)],
[np.cosh(0.5), np.sinh(0.5)],
[np.cosh(0.5), np.sinh(0.5)]
])
expected = np.array([[0.5], [0.], [9.5]])
hyperb = Hyperboloid(1)
assert_array_almost_equal(hyperb.distance(u, v), expected)
def test_is_on_manifold():
p = np.array([
[np.cosh(0.), np.sinh(0.)],
[-1., 0],
[np.cosh(0.), np.sinh(0.)],
[3.14, 1.59],
[np.cosh(0.25*np.pi), np.sinh(0.25*np.pi)],
[np.cos(0.25 * np.pi), np.sin(0.25 * np.pi)],
])
expected = np.array([
[True],
[False],
[True],
[False],
[True],
[False],
])
hyperb = Hyperboloid(1)
assert_array_almost_equal(hyperb.is_on_manifold(p), 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)
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)