def test_predict_output(self): d, n = (3, 10) sx = LHS( xlimits=np.repeat(np.atleast_2d([0.0, 1.0]), d, axis=0), criterion="m", random_state=42, ) x = sx(n) sy = LHS( xlimits=np.repeat(np.atleast_2d([0.0, 1.0]), 1, axis=0), criterion="m", random_state=42, ) y = sy(n) y = y.flatten() kriging = MGP(n_comp=2) kriging.set_training_values(x, y) kriging.train() x_fail_1 = np.asarray([0, 0, 0, 0]) x_fail_2 = np.asarray([0]) self.assertRaises(ValueError, lambda: kriging.predict_values(x_fail_1)) self.assertRaises(ValueError, lambda: kriging.predict_values(x_fail_2)) self.assertRaises(ValueError, lambda: kriging.predict_variances(x_fail_1)) self.assertRaises(ValueError, lambda: kriging.predict_variances(x_fail_2)) x_1 = np.atleast_2d([0, 0, 0]) var = kriging.predict_variances(x_1) var_1 = kriging.predict_variances(x_1, True) self.assertEqual(var, var_1[0])
def test_likelihood_hessian(self): for corr_str in [ "abs_exp", "squar_exp", "act_exp", "matern32", "matern52", ]: # For every kernel for poly_str in ["constant", "linear", "quadratic"]: # For every method if corr_str == "act_exp": kr = MGP(print_global=False) theta = self.random.rand(4) else: kr = KRG(print_global=False) theta = self.theta kr.options["poly"] = poly_str kr.options["corr"] = corr_str kr.set_training_values(self.X, self.y) kr.train() grad_red, dpar = kr._reduced_likelihood_gradient(theta) hess, hess_ij, _ = kr._reduced_likelihood_hessian(theta) Hess = np.zeros((theta.shape[0], theta.shape[0])) Hess[hess_ij[:, 0], hess_ij[:, 1]] = hess[:, 0] Hess[hess_ij[:, 1], hess_ij[:, 0]] = hess[:, 0] grad_norm_all = [] diff_norm_all = [] ind_theta = [] for j, omega_j in enumerate(theta): eps_omega = theta.copy() eps_omega[j] += self.eps grad_red_eps, _ = kr._reduced_likelihood_gradient( eps_omega) for i, theta_i in enumerate(theta): hess_eps = (grad_red_eps[i] - grad_red[i]) / self.eps grad_norm_all.append( np.linalg.norm(Hess[i, j]) / np.linalg.norm(Hess)) diff_norm_all.append( np.linalg.norm(hess_eps) / np.linalg.norm(Hess)) ind_theta.append(r"$x_%d,x_%d$" % (j, i)) self.assert_error( np.array(grad_norm_all), np.array(diff_norm_all), atol=1e-5, rtol=1e-3, ) # from utils/smt_test_case.py
def test_likelihood_derivatives(self): for corr_str in [ "abs_exp", "squar_exp", "act_exp", "matern32", "matern52", ]: # For every kernel for poly_str in ["constant", "linear", "quadratic"]: # For every method if corr_str == "act_exp": kr = MGP(print_global=False) theta = self.random.rand(4) else: kr = KRG(print_global=False) theta = self.theta kr.options["poly"] = poly_str kr.options["corr"] = corr_str kr.set_training_values(self.X, self.y) kr.train() grad_red, dpar = kr._reduced_likelihood_gradient(theta) red, par = kr._reduced_likelihood_function(theta) grad_norm_all = [] diff_norm_all = [] ind_theta = [] for i, theta_i in enumerate(theta): eps_theta = theta.copy() eps_theta[i] = eps_theta[i] + self.eps red_dk, par_dk = kr._reduced_likelihood_function(eps_theta) dred_dk = (red_dk - red) / self.eps grad_norm_all.append(grad_red[i]) diff_norm_all.append(float(dred_dk)) ind_theta.append(r"$x_%d$" % i) grad_norm_all = np.atleast_2d(grad_norm_all) diff_norm_all = np.atleast_2d(diff_norm_all).T self.assert_error(grad_norm_all, diff_norm_all, atol=1e-5, rtol=1e-3) # from utils/smt_test_case.py
def test_predict_output(self): x = np.random.random((10, 3)) y = np.random.random((10)) kriging = MGP(n_comp=2) kriging.set_training_values(x, y) kriging.train() x_fail_1 = np.asarray([0, 0, 0, 0]) x_fail_2 = np.asarray([0]) self.assertRaises(ValueError, lambda: kriging.predict_values(x_fail_1)) self.assertRaises(ValueError, lambda: kriging.predict_values(x_fail_2)) self.assertRaises(ValueError, lambda: kriging.predict_variances(x_fail_1)) self.assertRaises(ValueError, lambda: kriging.predict_variances(x_fail_2)) x_1 = np.atleast_2d([0, 0, 0]) var = kriging.predict_variances(x_1) var_1 = kriging.predict_variances(x_1, True) self.assertEqual(var, var_1[0])
def test_mgp(self): import numpy as np import matplotlib.pyplot as plt from smt.surrogate_models import MGP from smt.sampling_methods import LHS # Construction of the DOE dim = 3 def fun(x): import numpy as np res = (np.sum(x, axis=1)**2 - np.sum(x, axis=1) + 0.2 * (np.sum(x, axis=1) * 1.2)**3) return res sampling = LHS(xlimits=np.asarray([(-1, 1)] * dim), criterion="m") xt = sampling(8) yt = np.atleast_2d(fun(xt)).T # Build the MGP model sm = MGP( theta0=[1e-2], print_prediction=False, n_comp=1, ) sm.set_training_values(xt, yt[:, 0]) sm.train() # Get the transfert matrix A emb = sm.embedding["C"] # Compute the smallest box containing all points of A upper = np.sum(np.abs(emb), axis=0) lower = -upper # Test the model u_plot = np.atleast_2d(np.arange(lower, upper, 0.01)).T x_plot = sm.get_x_from_u(u_plot) # Get corresponding points in Omega y_plot_true = fun(x_plot) y_plot_pred = sm.predict_values(u_plot) sigma_MGP, sigma_KRG = sm.predict_variances(u_plot, True) u_train = sm.get_u_from_x(xt) # Get corresponding points in A # Plots fig, ax = plt.subplots() ax.plot(u_plot, y_plot_pred, label="Predicted") ax.plot(u_plot, y_plot_true, "k--", label="True") ax.plot(u_train, yt, "k+", mew=3, ms=10, label="Train") ax.fill_between( u_plot[:, 0], y_plot_pred - 3 * sigma_MGP, y_plot_pred + 3 * sigma_MGP, color="r", alpha=0.5, label="Variance with hyperparameters uncertainty", ) ax.fill_between( u_plot[:, 0], y_plot_pred - 3 * sigma_KRG, y_plot_pred + 3 * sigma_KRG, color="b", alpha=0.5, label="Variance without hyperparameters uncertainty", ) ax.set(xlabel="x", ylabel="y", title="MGP") fig.legend(loc="upper center", ncol=2) fig.tight_layout() fig.subplots_adjust(top=0.74) plt.show()