def test_sigma_plot(): """ Test to make sure sigma's correctly mirror the shape and orientation of the covariance array.""" x = np.array([[1, 2]]) P = np.array([[2, 1.2], [1.2, 2]]) kappa = .1 # if kappa is larger, than points shoudld be closer together sp0 = JulierSigmaPoints(n=2, kappa=kappa) sp1 = JulierSigmaPoints(n=2, kappa=kappa * 1000) w0, _ = sp0.weights() w1, _ = sp1.weights() Xi0 = sp0.sigma_points(x, P) Xi1 = sp1.sigma_points(x, P) assert max(Xi1[:, 0]) > max(Xi0[:, 0]) assert max(Xi1[:, 1]) > max(Xi0[:, 1]) if DO_PLOT: plt.figure() for i in range(Xi0.shape[0]): plt.scatter((Xi0[i, 0] - x[0, 0]) * w0[i] + x[0, 0], (Xi0[i, 1] - x[0, 1]) * w0[i] + x[0, 1], color='blue') for i in range(Xi1.shape[0]): plt.scatter((Xi1[i, 0] - x[0, 0]) * w1[i] + x[0, 0], (Xi1[i, 1] - x[0, 1]) * w1[i] + x[0, 1], color='green') stats.plot_covariance_ellipse([1, 2], P)
def test_sigma_plot(): """ Test to make sure sigma's correctly mirror the shape and orientation of the covariance array.""" x = np.array([[1, 2]]) P = np.array([[2, 1.2], [1.2, 2]]) kappa = .1 # if kappa is larger, than points shoudld be closer together sp0 = JulierSigmaPoints(n=2, kappa=kappa) sp1 = JulierSigmaPoints(n=2, kappa=kappa * 1000) sp2 = MerweScaledSigmaPoints(n=2, kappa=0, beta=2, alpha=1e-3) sp3 = SimplexSigmaPoints(n=2) # test __repr__ doesn't crash str(sp0) str(sp1) str(sp2) str(sp3) w0, _ = sp0.weights() w1, _ = sp1.weights() w2, _ = sp2.weights() w3, _ = sp3.weights() Xi0 = sp0.sigma_points(x, P) Xi1 = sp1.sigma_points(x, P) Xi2 = sp2.sigma_points(x, P) Xi3 = sp3.sigma_points(x, P) assert max(Xi1[:, 0]) > max(Xi0[:, 0]) assert max(Xi1[:, 1]) > max(Xi0[:, 1]) if DO_PLOT: plt.figure() for i in range(Xi0.shape[0]): plt.scatter((Xi0[i, 0] - x[0, 0]) * w0[i] + x[0, 0], (Xi0[i, 1] - x[0, 1]) * w0[i] + x[0, 1], color='blue', label='Julier low $\kappa$') for i in range(Xi1.shape[0]): plt.scatter((Xi1[i, 0] - x[0, 0]) * w1[i] + x[0, 0], (Xi1[i, 1] - x[0, 1]) * w1[i] + x[0, 1], color='green', label='Julier high $\kappa$') # for i in range(Xi2.shape[0]): # plt.scatter((Xi2[i, 0] - x[0, 0]) * w2[i] + x[0, 0], # (Xi2[i, 1] - x[0, 1]) * w2[i] + x[0, 1], # color='red') for i in range(Xi3.shape[0]): plt.scatter((Xi3[i, 0] - x[0, 0]) * w3[i] + x[0, 0], (Xi3[i, 1] - x[0, 1]) * w3[i] + x[0, 1], color='black', label='Simplex') stats.plot_covariance_ellipse([1, 2], P)
def test_sigma_plot(): """ Test to make sure sigma's correctly mirror the shape and orientation of the covariance array.""" x = np.array([[1, 2]]) P = np.array([[2, 1.2], [1.2, 2]]) kappa = .1 # if kappa is larger, than points shoudld be closer together sp0 = JulierSigmaPoints(n=2, kappa=kappa) sp1 = JulierSigmaPoints(n=2, kappa=kappa*1000) sp2 = MerweScaledSigmaPoints(n=2, kappa=0, beta=2, alpha=1e-3) sp3 = SimplexSigmaPoints(n=2) w0, _ = sp0.weights() w1, _ = sp1.weights() w2, _ = sp2.weights() w3, _ = sp3.weights() Xi0 = sp0.sigma_points(x, P) Xi1 = sp1.sigma_points(x, P) Xi2 = sp2.sigma_points(x, P) Xi3 = sp3.sigma_points(x, P) assert max(Xi1[:,0]) > max(Xi0[:,0]) assert max(Xi1[:,1]) > max(Xi0[:,1]) if DO_PLOT: plt.figure() for i in range(Xi0.shape[0]): plt.scatter((Xi0[i,0]-x[0, 0])*w0[i] + x[0, 0], (Xi0[i,1]-x[0, 1])*w0[i] + x[0, 1], color='blue', label='Julier low $\kappa$') for i in range(Xi1.shape[0]): plt.scatter((Xi1[i, 0]-x[0, 0]) * w1[i] + x[0,0], (Xi1[i, 1]-x[0, 1]) * w1[i] + x[0,1], color='green', label='Julier high $\kappa$') # for i in range(Xi2.shape[0]): # plt.scatter((Xi2[i, 0] - x[0, 0]) * w2[i] + x[0, 0], # (Xi2[i, 1] - x[0, 1]) * w2[i] + x[0, 1], # color='red') for i in range(Xi3.shape[0]): plt.scatter((Xi3[i, 0] - x[0, 0]) * w3[i] + x[0, 0], (Xi3[i, 1] - x[0, 1]) * w3[i] + x[0, 1], color='black', label='Simplex') stats.plot_covariance_ellipse([1, 2], P)
def test_sigma_points_1D(): """ tests passing 1D data into sigma_points""" kappa = 0. sp = JulierSigmaPoints(1, kappa) #ukf = UKF(dim_x=1, dim_z=1, dt=0.1, hx=None, fx=None, kappa=kappa) Wm, Wc = sp.weights() assert np.allclose(Wm, Wc, 1e-12) assert len(Wm) == 3 mean = 5 cov = 9 Xi = sp.sigma_points(mean, cov) xm, ucov = unscented_transform(Xi, Wm, Wc, 0) # sum of weights*sigma points should be the original mean m = 0.0 for x, w in zip(Xi, Wm): m += x * w assert abs(m - mean) < 1.e-12 assert abs(xm[0] - mean) < 1.e-12 assert abs(ucov[0, 0] - cov) < 1.e-12 assert Xi.shape == (3, 1)
def test_sigma_points_1D(): """ tests passing 1D data into sigma_points""" kappa = 0. sp = JulierSigmaPoints(1, kappa) #ukf = UKF(dim_x=1, dim_z=1, dt=0.1, hx=None, fx=None, kappa=kappa) Wm, Wc = sp.weights() assert np.allclose(Wm, Wc, 1e-12) assert len(Wm) == 3 mean = 5 cov = 9 Xi = sp.sigma_points (mean, cov) xm, ucov = unscented_transform(Xi,Wm, Wc, 0) # sum of weights*sigma points should be the original mean m = 0.0 for x, w in zip(Xi, Wm): m += x*w assert abs(m-mean) < 1.e-12 assert abs(xm[0] - mean) < 1.e-12 assert abs(ucov[0,0]-cov) < 1.e-12 assert Xi.shape == (3,1)
def test_sigma_plot(): """ Test to make sure sigma's correctly mirror the shape and orientation of the covariance array.""" x = np.array([[1, 2]]) P = np.array([[2, 1.2], [1.2, 2]]) kappa = .1 # if kappa is larger, than points shoudld be closer together sp0 = JulierSigmaPoints(n=2, kappa=kappa) sp1 = JulierSigmaPoints(n=2, kappa=kappa*1000) w0, _ = sp0.weights() w1, _ = sp1.weights() Xi0 = sp0.sigma_points (x, P) Xi1 = sp1.sigma_points (x, P) assert max(Xi1[:,0]) > max(Xi0[:,0]) assert max(Xi1[:,1]) > max(Xi0[:,1])
def test_sigma_plot(): """ Test to make sure sigma's correctly mirror the shape and orientation of the covariance array.""" x = np.array([[1, 2]]) P = np.array([[2, 1.2], [1.2, 2]]) kappa = .1 # if kappa is larger, than points shoudld be closer together sp0 = JulierSigmaPoints(n=2, kappa=kappa) sp1 = JulierSigmaPoints(n=2, kappa=kappa*1000) w0, _ = sp0.weights() w1, _ = sp1.weights() Xi0 = sp0.sigma_points (x, P) Xi1 = sp1.sigma_points (x, P) assert max(Xi1[:,0]) > max(Xi0[:,0]) assert max(Xi1[:,1]) > max(Xi0[:,1]) if DO_PLOT: plt.figure() for i in range(Xi0.shape[0]): plt.scatter((Xi0[i,0]-x[0, 0])*w0[i] + x[0, 0], (Xi0[i,1]-x[0, 1])*w0[i] + x[0, 1], color='blue') for i in range(Xi1.shape[0]): plt.scatter((Xi1[i, 0]-x[0, 0]) * w1[i] + x[0,0], (Xi1[i, 1]-x[0, 1]) * w1[i] + x[0,1], color='green') stats.plot_covariance_ellipse([1, 2], P)