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
