def test_covariance(self): gc = GaussianCovariance() x = np.array([[x1,x2] for x1 in range(10) for x2 in range(10)]) #np.atleast_2d(np.linspace(0, 10, 30)).T theta = np.log(np.array([2,0.01,0.04,0.04])) cov = gc.cov_matrix(x,theta) cov_super = Covariance.cov_matrix(gc,x,theta) self.assertLessEqual(np.abs((cov-cov_super-0.01*np.eye(100))).sum(),1e-10) dcov = gc._d_cov_matrix_d_theta(x,theta,2) dcov_super = Covariance._d_cov_matrix_d_theta(gc,x,theta,2) self.assertLessEqual(np.abs((dcov-dcov_super)).sum(),1e-10) #np.count_nonzero(cov-cov_super) t = GaussianProcess.get_realisation(x, GaussianCovariance(), theta) #t = y + 0.1 * np.random.randn(len(x)) #-> vt = 0.01 dndt = gc._d_nll_d_theta(x,t,theta) print(dndt) dndt_est = [] for j in range(len(theta)): d = np.zeros(len(theta)) d[j] = 1e-5 #d = np.log(1+d/np.exp(theta)) # Addition of log: log(x+y) = log(x) + log(1+y/x) dndt_est.append( (gc._negativeloglikelihood(x,t,theta+d) - gc._negativeloglikelihood(x,t,theta-d))/2e-5 ) dndt_est = np.array(dndt_est) print(dndt_est) print(np.abs(dndt_est - dndt)) self.assertTrue((np.abs(dndt_est - dndt) < 5e-1).all())
def test_spgp_nll(self):
x = np.array([[x1,x2] for x1 in range(10) for x2 in range(10)]) #np.atleast_2d(np.linspace(0, 10, 30)).T
w = np.array([0.04,0.04])
v = 2
vt = 0#.01
theta = np.zeros(2+len(w))
theta[0] = np.log(v)
theta[1] = np.log(vt)
theta[2:2+len(w)] = np.log(w)
y = GaussianProcess.get_realisation(x, GaussianCovariance(), theta)
t = y + 0.1 * np.random.randn(len(x)) #-> vt = 0.01
spgpcov = SPGPCovariance(10)
gc = GaussianCovariance()
theta = spgpcov.get_theta(x,t)
theta_gc = gc.get_theta(x,t)
start = time.time()
res_g = gc._negativeloglikelihood(x,t,theta_gc)
print("Gaussian NLL: ",res_g)
print("Time: ",time.time()-start)
start = time.time()
res = Covariance._negativeloglikelihood(spgpcov,x,t,theta)
print("My NLL: ",res)
print("Time: ",time.time()-start)
res_s = spgpcov._negativeloglikelihood(x,t,theta)
print("Snelson NLL: ", res_s)
print("Time: ", time.time()-start)
self.assertAlmostEqual(res,res_s,delta=2e-1)