def test_1d_kriging1(self): x = array([[0.05], [.25], [0.61], [0.95]]) y = array([0.738513784857542, -0.210367746201974, -0.489015457891476, 12.3033138316612]) krig1 = KrigingSurrogate() krig1.train(x, y) self.assertAlmostEqual(.4771, krig1.thetas[0], places=4)
def test_one_pt(self): surrogate = KrigingSurrogate() x = [[0.]] y = [[1.]] with self.assertRaises(ValueError) as cm: surrogate.train(x, y) self.assertEqual(str(cm.exception), 'KrigingSurrogate require at least' ' 2 training points.')
def test_vector_derivs(self): surrogate = KrigingSurrogate() x = array([[a, b] for a, b in itertools.product(linspace(0, 1, 10), repeat=2)]) y = array([[a+b, a-b] for a, b in x]) surrogate.train(x, y) jac = surrogate.jacobian(array([[0.5, 0.5]])) assert_rel_error(self, jac, array([[1, 1], [1, -1]]), 1e-5)
def test_scalar_derivs(self): surrogate = KrigingSurrogate() x = array([[0.], [1.], [2.], [3.]]) y = x.copy() surrogate.train(x, y) jac = surrogate.jacobian(array([[0.]])) assert_rel_error(self, jac[0][0], 1., 1e-3)
def test_1d_kriging3(self): # Test for least squares solver utilization when ill-conditioned x = [[case] for case in linspace(0., 1., 40)] y = sin(x).flatten() krig1 = KrigingSurrogate() krig1.train(x, y) new_x = array([0.5]) mu, sigma = krig1.predict(new_x) self.assertAlmostEqual(8.7709e-09, sigma, places=7) self.assertAlmostEqual(0.479425538688, mu, places=7)
def test_1d_kriging_predictor(self): x = array([[0.05], [.25], [0.61], [0.95]]) y = array([0.738513784857542, -0.210367746201974, -0.489015457891476, 12.3033138316612]) krig1 = KrigingSurrogate() krig1.train(x, y) new_x = array([0.5]) mu, sigma = krig1.predict(new_x) self.assertAlmostEqual(.41552, sigma, places=3) self.assertAlmostEqual( -1.725, mu, places=3)
def test_1d_ill_conditioned(self): # Test for least squares solver utilization when ill-conditioned x = array([[case] for case in linspace(0., 1., 40)]) y = sin(x) surrogate = KrigingSurrogate() surrogate.train(x, y) new_x = array([0.5]) mu, sigma = surrogate.predict(new_x) self.assertTrue(sigma < 1.1e-8) assert_rel_error(self, mu, sin(0.5), 1e-6)
def test_1d_training(self): x = array([[0.0], [2.0], [3.0], [4.0], [6.0]]) y = array([[branin_1d(case)] for case in x]) surrogate = KrigingSurrogate() surrogate.train(x, y) for x0, y0 in zip(x, y): mu, sigma = surrogate.predict(x0) assert_rel_error(self, mu, y0, 1e-9) assert_rel_error(self, sigma, 0, 1e-6)
def test_1d_predictor(self): x = array([[0.0], [2.0], [3.0], [4.0], [6.0]]) y = array([[branin_1d(case)] for case in x]) surrogate = KrigingSurrogate() surrogate.train(x, y) new_x = array([pi]) mu, sigma = surrogate.predict(new_x) assert_rel_error(self, mu, 0.397887, 1e-1) assert_rel_error(self, sigma, 0.0294172, 1e-2)
def test_vector_output(self): surrogate = KrigingSurrogate() y = array([[0., 0.], [1., 1.], [2., 0.]]) x = array([[0.], [2.], [4.]]) surrogate.train(x, y) for x0, y0 in zip(x, y): mu, sigma = surrogate.predict(x0) assert_rel_error(self, mu, y0, 1e-9) assert_rel_error(self, sigma, 0, 1e-6)
def test_2d_kriging(self): def bran(x): y = (x[1]-(5.1/(4.*pi**2.))*x[0]**2.+5.*x[0]/pi-6.)**2.+10.*(1.-1./(8.*pi))*cos(x[0])+10. return y x = array([[-2., 0.], [-0.5, 1.5], [1., 3.], [8.5, 4.5], [-3.5, 6.], [4., 7.5], [-5., 9.], [5.5, 10.5], [10., 12.], [7., 13.5], [2.5, 15.]]) y = array([bran(case) for case in x]) krig1 = KrigingSurrogate() krig1.train(x, y) mu, sigma = krig1.predict([-2., 0.]) self.assertAlmostEqual(bran(x[0]), mu, places=5) mu, sigma = krig1.predict([5., 5.]) self.assertAlmostEqual(5.79, sigma, places=0) self.assertAlmostEqual(25.34, mu, places=1)
def test_2d(self): x = array([[-2., 0.], [-0.5, 1.5], [1., 3.], [8.5, 4.5], [-3.5, 6.], [4., 7.5], [-5., 9.], [5.5, 10.5], [10., 12.], [7., 13.5], [2.5, 15.]]) y = array([[branin(case)] for case in x]) surrogate = KrigingSurrogate() surrogate.train(x, y) for x0, y0 in zip(x, y): mu, sigma = surrogate.predict(x0) assert_rel_error(self, mu, y0, 1e-9) assert_rel_error(self, sigma, 0, 1e-6) mu, sigma = surrogate.predict([5., 5.]) assert_rel_error(self, mu, branin([5., 5.]), 1e-1) assert_rel_error(self, sigma, 5.79, 1e-2)