def test_exp_log_inv_0():
tol = 1e-4
c = 2.0
x = tf.constant([[1.6970563, -1.5, 0.3, 0.2], [3.4278274, 3., -1.5, 0.]])
M = Lorentz()
v = M.logmap0(x, c)
expv = M.expmap0(v, c)
assert tf.reduce_max(tf.abs(expv - x)) < tol
def test_proj_tan_orthogonal(c):
x = tf.constant([[1.0, -3.0, 0.2, -0.3], [0.0, 0.3, -30., 1.]])
M = Lorentz()
y = M.proj(x, c)
v = tf.constant([[4.0, 4.0, -1.0, 0.0], [20., 20., 0.0, -1.]])
p = M.proj_tan(v, y, c)
assert is_in_tangent(p, y)
def test_proj_on_manifold(c):
tol = 1e-5
x = tf.constant([[0.5, 1.0, -2.0, 10.0], [1.0, -2.0, 3.0, 4.0],
[2.4, -1.5, 0.3, 0.2]])
M = Lorentz()
y = M.proj(x, c)
dot = M.minkowski_dot(y, y)
targ = -tf.ones_like(dot)
assert tf.reduce_max(tf.abs(dot - targ))
def test_exp_log_inv():
tol = 1e-4
c = 1.0
x = tf.constant([[4.690416, 1., -2., 4.], [5.477226, -2., 3., 4.]])
y = tf.constant([[1.8384776, -1.5, 0.3, 0.2], [3.5, 3., -1.5, 0.]])
M = Lorentz()
v = M.logmap(y, x, c)
assert is_in_tangent(v, x)
expv = M.expmap(v, x, c)
assert tf.reduce_max(tf.abs(expv - y)) < tol
def test_parallel_transport():
tol = 1e-4
c = 1.0
x = tf.constant([[4.690416, 1., -2., 4.], [5.477226, -2., 3., 4.]])
y = tf.constant([[1.8384776, -1.5, 0.3, 0.2], [3.5, 3., -1.5, 0.]])
M = Lorentz()
v = M.proj_tan(
tf.constant([[-3.0, -2.0, 1.0, 0.0], [0.5, -3.4, 4.0, 1.0]]), x, c)
assert is_in_tangent(v, x, tol=tol)
tr_v = M.ptransp(x, y, v, c)
assert is_in_tangent(tr_v, y, tol=tol)
def test_parallel_transport_0():
tol = 1e-4
c = 1.0
zero = tf.constant([[1., 0., 0, 0.], [1., 0., 0., 0.]])
x = tf.constant([[4.690416, 1., -2., 4.], [5.477226, -2., 3., 4.]])
M = Lorentz()
v = M.proj_tan0(
tf.constant([[-3.0, -2.0, 1.0, 0.0], [0.5, -3.4, 4.0, 1.0]]), c)
M = Lorentz()
assert is_in_tangent(v, zero, tol=tol)
tr_v = M.ptransp0(x, v, c)
assert is_in_tangent(tr_v, x, tol=tol)
def is_in_tangent(v, x, tol=1e-5):
dot = Lorentz().minkowski_dot(v, x)
return tf.reduce_max(dot) < tol
def test_proj_tan_orthogonal_0(c):
K = 1. / c
zero = tf.constant([[K**0.5, 0., 0., 0.], [K**0.5, 0., 0., 0.]])
v = tf.constant([[4.0, 2.0, -1.0, -0.4], [20., 20., 0.0, -1.]])
v = Lorentz().proj_tan0(v, c)
assert is_in_tangent(v, zero)