class TestGaussian(unittest.TestCase): def setUp(self): self.g1f = Gaussian(1, False) self.g2f = Gaussian(2, False) self.g4t = Gaussian(4, True) self.param1f = np.array([0,2]) self.param2f = np.array([np.arange(6), 2*np.arange(6)]) self.param4t = np.array([np.arange(8), -np.arange(8)]) def test_reparam(self): t1f = {"g_mu":np.array([0]), "g_Sig":np.array([4]), "g_Siginv":np.array([0.25])} theta1f = self.g1f.reparam(self.param1f) self.assertDictEqual(t1f, theta1f) t2f = {"g_mu":np.array([[0,1],[0,2]]), "g_Sig":np.array([[[13,23],[23,41]],[[52,92],[92,164]]]), "g_Siginv":np.array([[[10.25,-5.75],[-5.75,3.25]],[[2.5625,-1.4375],[-1.4375,0.8125]]])} theta2f = self.g2f.reparam(self.param2f) for key in t2f.keys(): with self.subTest(key=key): self.assertTrue(np.all(np.round(t2f[key],2)==np.round(theta2f[key],2))) t4t = {"g_mu":np.array([[0,1,2,3],[0,-1,-2,-3]]), "g_Sig":np.array([np.exp([4,5,6,7]),np.exp([-4,-5,-6,-7])])} theta4t = self.g4t.reparam(self.param4t) for key in t4t.keys(): with self.subTest(key=key): self.assertTrue(np.all(t4t[key]==theta4t[key])) def test_logpdf(self): X1f = np.random.randn(5) p1f = norm.logpdf(X1f, 0, 2) logp1f = self.g1f.logpdf(self.param1f, X1f) self.assertTrue(np.all(np.round(p1f[:,np.newaxis],5)==np.round(logp1f,5))) X2f = np.random.randn(2) p2f1 = multivariate_normal.logpdf(X2f, np.array([0,1]), np.array([[13,23],[23,41]])) p2f2 = multivariate_normal.logpdf(X2f, np.array([0,2]), np.array([[52,92],[92,164]])) p2f = np.array([p2f1, p2f2]) logp2f = self.g2f.logpdf(self.param2f, X2f) self.assertTrue(np.all(np.round(p2f[np.newaxis,:],5)==np.round(logp2f,5))) X4t = np.random.randn(8).reshape((2,4)) p4t1 = multivariate_normal.logpdf(X4t, np.array([0,1,2,3]),np.diag(np.exp(np.array([4,5,6,7])))) p4t2 = multivariate_normal.logpdf(X4t, np.array([0,-1,-2,-3]),np.diag(np.exp(np.array([-4,-5,-6,-7])))) p4t = np.hstack((p4t1[:,np.newaxis], p4t2[:,np.newaxis])) logp4t = self.g4t.logpdf(self.param4t, X4t) self.assertTrue(np.all(np.around(p4t,5)==np.around(logp4t,5))) def test_sample(self): np.random.seed(1) x1 = 0 + 2* np.random.randn(5) x2 = np.array([0,1]) + np.dot(np.random.randn(1,2), np.array([[2,3],[4,5]])) x4 = np.array([0,1,2,3]) + np.dot(np.random.randn(10,4), np.diag(np.exp(np.array([4,5,6,7])/2))) np.random.seed(1) samp1 = self.g1f.sample(self.param1f, 5) samp2 = self.g2f.sample(self.param2f[0,:], 1) samp4 = self.g4t.sample(self.param4t[0,:], 10) self.assertTrue(np.all(np.round(x1[:,np.newaxis],3)==np.round(samp1,3))) self.assertTrue(np.all(np.round(x2,3)==np.round(samp2,3))) self.assertTrue(np.all(np.round(x4,3)==np.round(samp4,3))) def test_cross_sample(self): var1f = 2 / np.array([1/4+1/25]) mu1f = np.array([0]) cov2f = 2 * np.linalg.inv(np.array([[10.25,-5.75],[-5.75,3.25]])+np.array([[2.5625,-1.4375],[-1.4375,0.8125]])) mu2f = 0.5*np.dot(cov2f, np.dot(np.array([[10.25,-5.75],[-5.75,3.25]]),np.array([0,1])) + np.dot(np.array([[2.5625,-1.4375],[-1.4375,0.8125]]),np.array([0,2]))) cov4t = 2 /(np.exp(np.arange(-4,-8,-1)) + np.exp(np.arange(4,8))) mu4t = 0.5*(cov4t*(np.arange(4)*np.exp(np.arange(-4,-8,-1))+np.arange(0,-4,-1)*np.exp(np.arange(4,8)))) np.random.seed(1) x1 = np.random.multivariate_normal(mu1f, np.atleast_2d(var1f), 5) np.random.seed(2) x2 = np.random.multivariate_normal(mu2f, cov2f, 1) np.random.seed(0) x4 = mu4t + np.sqrt(cov4t)*np.random.randn(10, 4) np.random.seed(1) samp1 = self.g1f.cross_sample(self.param1f, -2.5*self.param1f, 5) np.random.seed(2) samp2 = self.g2f.cross_sample(self.param2f[0,:], self.param2f[1,:], 1) np.random.seed(0) samp4 = self.g4t.cross_sample(self.param4t[0,:], self.param4t[1,:], 10) self.assertTrue(np.all(np.round(x1,3)==np.round(samp1,3))) self.assertTrue(np.all(np.round(x2,3)==np.round(samp2,3))) self.assertTrue(np.all(np.round(x4,3)==np.round(samp4,3))) def test_log_sqrt_pair_integral(self): l1 = -0.5*np.log(10/(2*4)) difmu2 = np.array([0,1]) s = np.array([[13,23],[23,41]]) S = np.array([[52,92],[92,164]]) S2 = np.array([[32.5,57.5],[57.5,102.5]]) l21 = -0.125*(difmu2*np.linalg.solve(S2,difmu2)).sum()- 0.5*np.linalg.slogdet(S2)[1] + 0.25*np.linalg.slogdet(s)[1] + 0.25*np.linalg.slogdet(S)[1] l2 = np.array([0,l21]) difmu4 = np.array([[0,-0.5,-1,-1.5],[0,2.5,5,7.5]]) lsig = self.param4t[0, 4:] Lsig = self.param4t[:,4:]*1.5 lSig2 = np.log(0.5)+np.logaddexp(lsig, Lsig) l4 = -0.125*np.sum(np.exp(-lSig2)*difmu4**2, axis=1) - 0.5*np.sum(lSig2, axis=1) + 0.25*np.sum(lsig) + 0.25*np.sum(Lsig, axis=1) la1f = self.g1f.log_sqrt_pair_integral(self.param1f, -2*self.param1f) la2f = self.g2f.log_sqrt_pair_integral(self.param2f[0,:], self.param2f) la4t = self.g4t.log_sqrt_pair_integral(self.param4t[0,:], 1.5*self.param4t) self.assertTrue(np.all(np.round(l1,5)==np.round(la1f,5))) self.assertTrue(np.all(np.round(l2,5)==np.round(la2f,5))) self.assertTrue(np.all(np.round(l4,5)==np.round(la4t,5))) def test_params_init(self): np.random.seed(1) m0 = np.random.multivariate_normal(np.zeros(2), 4*np.eye(2)) prm0f = np.concatenate((m0, np.array([1,0,0,1]))) np.random.seed(2) m0 = np.random.multivariate_normal(np.zeros(2), 4*np.eye(2)) prm0t = np.concatenate((m0, np.zeros(2))) np.random.seed(4) mu = np.array([[0,1,2,3],[0,-1,-2,-3]]) k = np.random.choice(2, p=np.array([0.5,0.5])) lsig = np.array([[4,5,6,7],[-4,-5,-6,-7]]) mu0 = mu[k]+np.random.randn(4)*np.sqrt(10)*np.exp(lsig[k,:]) LSig = np.random.randn(4)+lsig[k] prm4t = np.hstack((mu0, LSig)) g2t = Gaussian(2, True) np.random.seed(1) par0f = self.g2f.params_init(np.empty((0,6)), np.empty((0,1)), 4) np.random.seed(2) par0t = g2t.params_init(np.empty((0,6)), np.empty((0,1)), 4) np.random.seed(4) par4t = self.g4t.params_init(self.param4t, np.array([0.1, 0.9]), 10) self.assertTrue(np.all(np.round(par0f,3)==np.round(prm0f,3))) self.assertTrue(np.all(np.round(par0t,3)==np.round(prm0t,3))) self.assertTrue(np.all(np.round(par4t,3)==np.round(prm4t,3)))