def test_unscented_transform_linear_transformation():
"""Test unscented transform with a linear transformation."""
mvn = MVN(mean=np.zeros(2), covariance=np.eye(2), random_state=42)
points = mvn.sigma_points()
new_points = np.copy(points)
new_points[:, 1] *= 10
new_points += np.array([0.5, -3.0])
transformed_mvn = mvn.estimate_from_sigma_points(new_points)
assert_array_almost_equal(transformed_mvn.mean, np.array([0.5, -3.0]))
assert_array_almost_equal(transformed_mvn.covariance,
np.array([[1.0, 0.0], [0.0, 100.0]]))
sample1 = transformed_mvn.sample(1)
sample2 = mvn.estimate_from_sigma_points(new_points,
random_state=42).sample(1)
assert_array_almost_equal(sample1, sample2)
def test_unscented_transform_linear_combination():
"""Test unscented transform with a linear combination."""
mvn = MVN(mean=np.zeros(2), covariance=np.eye(2), random_state=42)
points = mvn.sigma_points()
new_points = np.empty_like(points)
new_points[:, 0] = points[:, 1]
new_points[:, 1] = points[:, 0] - 0.5 * points[:, 1]
new_points += np.array([-0.5, 3.0])
transformed_mvn = mvn.estimate_from_sigma_points(new_points)
assert_array_almost_equal(transformed_mvn.mean, np.array([-0.5, 3.0]))
assert_array_almost_equal(transformed_mvn.covariance,
np.array([[1.0, -0.5], [-0.5, 1.25]]))
def test_unscented_transform_quadratic():
"""Test unscented transform with a quadratic transformation."""
mvn = MVN(mean=np.zeros(2), covariance=np.eye(2), random_state=42)
points = mvn.sigma_points(alpha=0.67, kappa=5.0)
def f(points):
new_points = np.empty_like(points)
new_points[:, 0] = points[:, 0] ** 2 * np.sign(points[:, 0])
new_points[:, 1] = points[:, 1] ** 2 * np.sign(points[:, 1])
new_points += np.array([5.0, -3.0])
return new_points
transformed_mvn = mvn.estimate_from_sigma_points(f(points), alpha=0.67, kappa=5.0)
assert_array_almost_equal(transformed_mvn.mean, np.array([5.0, -3.0]))
assert_array_almost_equal(
transformed_mvn.covariance,
np.array([[3.1, 0.0], [0.0, 3.1]]),
decimal=1
)
def test_unscented_transform_projection_to_more_dimensions():
"""Test unscented transform with a projection to 3D."""
mvn = MVN(mean=np.zeros(2), covariance=np.eye(2), random_state=42)
points = mvn.sigma_points()
def f(points):
new_points = np.empty((len(points), 3))
new_points[:, 0] = points[:, 0]
new_points[:, 1] = points[:, 1]
new_points[:, 2] = -0.5 * points[:, 0] + 0.5 * points[:, 1]
new_points += np.array([-0.5, 3.0, 10.0])
return new_points
transformed_mvn = mvn.estimate_from_sigma_points(f(points))
assert_array_almost_equal(transformed_mvn.mean, np.array([-0.5, 3.0,
10.0]))
assert_array_almost_equal(
transformed_mvn.covariance,
np.array([[1.0, 0.0, -0.5], [0.0, 1.0, 0.5], [-0.5, 0.5, 0.5]]))
mean=np.array([2.5, 1.3]),
covariance=np.array([[1.0, -1.5], [-1.5, 4.0]]),
random_state=0)
plot_error_ellipse(ax, mvn_cartesian)
samples_cartesian = mvn_cartesian.sample(1000)
ax.scatter(samples_cartesian[:, 0], samples_cartesian[:, 1], s=1)
ax = plt.subplot(132)
ax.set_title("(2) Polar coordinates")
ax.set_xlabel("$r$")
ax.set_ylabel("$\phi$")
ax.set_xlim((-8, 8))
ax.set_ylim((-8, 8))
sigma_points_cartesian = mvn_cartesian.sigma_points(alpha=alpha, kappa=kappa)
sigma_points_polar = cartesian_to_polar(sigma_points_cartesian)
mvn_polar = mvn_cartesian.estimate_from_sigma_points(sigma_points_polar, alpha=alpha, beta=beta, kappa=kappa)
plot_error_ellipse(ax, mvn_polar)
samples_polar = cartesian_to_polar(samples_cartesian)
ax.scatter(samples_polar[:, 0], samples_polar[:, 1], s=1)
ax = plt.subplot(133)
ax.set_title("(3) Cartesian coordinates")
ax.set_xlabel("$x_1$")
ax.set_ylabel("$x_2$")
ax.set_xlim((-8, 8))
ax.set_ylim((-8, 8))
sigma_points_polar2 = mvn_polar.sigma_points(alpha=alpha, kappa=kappa)
sigma_points_cartesian2 = polar_to_cartesian(sigma_points_polar2)
mvn_cartesian2 = mvn_polar.estimate_from_sigma_points(sigma_points_cartesian2, alpha=alpha, beta=beta, kappa=kappa)
plot_error_ellipse(ax, mvn_cartesian2)
samples_cartesian2 = polar_to_cartesian(samples_polar)
