def test_exp_jacobian(self):
np.random.seed(0)
x0 = np.random.randn(3)
j_numerical = numeric_jacobian(lambda x: rotation.exp(x), x0,
output_atlas=rotation.RotationAtlas)
j_analytic = rotation.exp_jacobian(x0)
np.testing.assert_array_almost_equal(j_numerical, j_analytic)
def test_exp_jacobian(self):
np.random.seed(0)
x0 = np.random.randn(3)
j_numerical = numeric_jacobian(lambda x: rotation.exp(x),
x0,
output_atlas=rotation.RotationAtlas)
j_analytic = rotation.exp_jacobian(x0)
np.testing.assert_array_almost_equal(j_numerical, j_analytic)
def test_displacement_left_jacobian_wrt_lhs(self):
np.random.seed(0)
r1 = rotation.exp(np.random.randn(3))
r2 = rotation.exp(np.random.randn(3))
j_numerical = numeric_jacobian(lambda r: rotation.displacement_left(r, r2),
r1,
atlas=rotation.RotationAtlas)
j_analytic = rotation.displacement_left_jacobian_wrt_lhs(r1, r2)
assert_arrays_almost_equal(j_numerical, j_analytic, xlabel='analytic', ylabel='numerical')
def test_jacobian(self):
np.random.seed(0)
p = np.random.randn(3)
print(homography.exp(np.zeros(8)))
j_numerical = numeric_jacobian(lambda x: np.dot(homography.exp(x), p),
np.zeros(8))
j_analytic = homography.multiply_generators(p).T
np.testing.assert_array_almost_equal(j_numerical, j_analytic)
def test_displacement_left_jacobian_wrt_lhs(self):
np.random.seed(0)
r1 = rotation.exp(np.random.randn(3))
r2 = rotation.exp(np.random.randn(3))
j_numerical = numeric_jacobian(
lambda r: rotation.displacement_left(r, r2),
r1,
atlas=rotation.RotationAtlas)
j_analytic = rotation.displacement_left_jacobian_wrt_lhs(r1, r2)
assert_arrays_almost_equal(j_numerical,
j_analytic,
xlabel='analytic',
ylabel='numerical')
def displacement_left_jacobian_wrt_rhs(r1, r2):
# TODO: implement analytically
from manifolds import numeric_jacobian
return numeric_jacobian(lambda q: displacement_left(r1, q), r2, atlas=RotationAtlas)
def displacement_left_jacobian_wrt_rhs(r1, r2):
# TODO: implement analytically
from manifolds import numeric_jacobian
return numeric_jacobian(lambda q: displacement_left(r1, q),
r2,
atlas=RotationAtlas)