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_no_training_data(self):
krig1 = KrigingSurrogate()
try:
krig1.predict([0., 1.])
except RuntimeError as err:
self.assertEqual(str(err),
"KrigingSurrogate has not been trained, so no prediction can be made")
else:
self.fail("RuntimeError Expected")
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_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_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_no_training_data(self):
surrogate = KrigingSurrogate()
try:
surrogate.predict([0., 1.])
except RuntimeError as err:
self.assertEqual(str(err),
"KrigingSurrogate has not been trained, "
"so no prediction can be made.")
else:
self.fail("RuntimeError Expected")
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)
def test_sin_metamodel_obj_return(self):
# create a MetaModel for Sin and add it to a Problem
sin_mm = MetaModel()
sin_mm.add_param('x', 0.)
sin_mm.add_output('f_x', (0., 0.))
prob = Problem(Group())
prob.root.add('sin_mm', sin_mm)
# check that missing surrogate is detected in check_setup
stream = cStringIO()
prob.setup(out_stream=stream)
msg = ("No default surrogate model is defined and the "
"following outputs do not have a surrogate model:\n"
"['f_x']\n"
"Either specify a default_surrogate, or specify a "
"surrogate model for all outputs.")
self.assertTrue(msg in stream.getvalue())
# check that output with no specified surrogate gets the default
sin_mm.default_surrogate = KrigingSurrogate()
prob.setup(check=False)
surrogate = prob.root.unknowns.metadata('sin_mm.f_x').get('surrogate')
self.assertTrue(isinstance(surrogate, KrigingSurrogate),
'sin_mm.f_x should get the default surrogate')
# train the surrogate and check predicted value
prob['sin_mm.train:x'] = np.linspace(0, 10, 20)
prob['sin_mm.train:f_x'] = np.sin(prob['sin_mm.train:x'])
prob['sin_mm.x'] = 2.1
prob.run()
assert_rel_error(self, prob['sin_mm.f_x'][0], 0.86323233, 1e-4) # mean
self.assertTrue(self, prob['sin_mm.f_x'][1] < 1e-5) #std deviation