def test_pt_cache(self):
test_x = np.array([[0.5]])
self.surrogate.predict(test_x)
# Mess with internals to ensure cache is being used.
self.surrogate.interpolant._KData = None
mu = self.surrogate.linearize(test_x)
assert_rel_error(self, mu, np.array([[2.34609214]]), 1e-6)
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.fit(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_vector_derivs(self):
surrogate = RSurfaceSurrogate()
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.fit(x, y)
jac = surrogate.linearize(array([[0.5, 0.5]]))
assert_rel_error(self, jac, array([[1, 1], [1, -1]]), 1e-5)
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.fit(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 = RSurfaceSurrogate()
surrogate.fit(x, y)
new_x = array([pi])
mu = surrogate.predict(new_x)
assert_rel_error(self, mu, 1.73114, 1e-4)
def test_vector_output(self):
surrogate = RSurfaceSurrogate()
x = array([[0.], [2.], [4.]])
y = array([[0., 0.], [1., 1.], [2., 0.]])
surrogate.fit(x, y)
for x0, y0 in zip(x, y):
mu = surrogate.predict(x0)
assert_rel_error(self, mu, y0, 1e-9)
def test_vector_output(self):
surrogate = KrigingSurrogate()
y = array([[0., 0.], [1., 1.], [2., 0.]])
x = array([[0.], [2.], [4.]])
surrogate.fit(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.fit(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_2d(self):
x = array([[-2., 0.], [-0.5, 1.5], [1., 1.], [0., .25], [.25, 0.], [.66, .33]])
y = array([[branin(case)] for case in x])
surrogate = RSurfaceSurrogate()
surrogate.fit(x, y)
for x0, y0 in zip(x, y):
mu = surrogate.predict(x0)
assert_rel_error(self, mu, y0, 1e-9)
mu = surrogate.predict(array([.5, .5]))
assert_rel_error(self, mu, branin([.5, .5]), 1e-1)
def test_bulk_prediction(self):
test_x = np.array([[1., 0.5], [0.5, 1.0], [1.0, 1.5], [1.5, 1.],
[0., 1.], [.5, .5]])
a = 0.05453616
b = 0.5013363
c = 0.33860606
d = 0.13507662
expected_y = np.array([[a, b, 0.5, a], [a, b, 0.5, a], [a, b, 0.5, a],
[a, b, 0.5, a], [c, d, 0.5, c],
[0.37840446, 0.336283, 0.5, 0.37840446]])
mu = self.surrogate.predict(test_x)
assert_rel_error(self, mu, expected_y, 1e-6)
def test_jacobian(self):
test_x = np.array([[0.5, 0.5], [0.5, 1.5], [1.5, 1.5], [1.5, 0.5]])
a = -0.97153433
b = -0.97153433
c = 0.59055939
d = 0.59055939
expected_deriv = np.array([[[a, b], [c, d], [0., 0.], [a, b]],
[[a, -b], [c, -d], [0., 0.], [a, -b]],
[[-a, -b], [-c, -d], [0., 0.], [-a, -b]],
[[-a, b], [-c, d], [0., 0.], [-a, b]]])
for x0, y0 in zip(test_x, expected_deriv):
mu = self.surrogate.linearize(x0)
assert_rel_error(self, mu, y0, 1e-6)
def test_jacobian(self):
test_x = np.array([[1., 0.5],
[0.5, 1.],
[1., 1.5],
[1.5, 1.]
])
expected_deriv = np.array([
[[0., -1.], [0., 1.], [0., 0.], [0., -1.]],
[[-1., 0.], [1., 0.], [0., 0.], [-1., 0.]],
[[0., 1.], [0., -1.], [0., 0.], [0., 1.]],
[[1., 0.], [-1., 0.], [0., 0.], [1., 0.]]
])
for x0, y0 in zip(test_x, expected_deriv):
mu = self.surrogate.linearize(x0)
assert_rel_error(self, mu, y0, 1e-9)
def test_bulk_prediction(self):
test_x = np.array([[1., 0.5], [0.5, 1.0], [1.0, 1.5], [1.5, 1.],
[0., 1.], [.5, .5]])
a = ((16. / (5 * np.sqrt(5.)) + 16. / (13. * np.sqrt(13.))) /
(16. / (5 * np.sqrt(5.)) + 16. / (13. * np.sqrt(13.)) + 8.))
b = 8. / (8. + 16. / (5 * np.sqrt(5.)) + 16. / (13. * np.sqrt(13.)))
c = (2. + 2. / (5. * np.sqrt(5))) / (3. + 2. / (5. * np.sqrt(5)))
d = 1. / (3. + 2. / (5. * np.sqrt(5)))
expected_y = np.array([[a, b, 0.5, a], [a, b, 0.5, a], [a, b, 0.5, a],
[a, b, 0.5, a], [c, d, 0.5, c],
[0.54872067, 0.45127933, 0.5, 0.54872067]])
mu = self.surrogate.predict(test_x, n=5, dist_eff=3)
assert_rel_error(self, mu, expected_y, 1e-6)
def test_bulk_prediction(self):
test_x = np.array([[1., 0.5],
[0.5, 1.0],
[1.0, 1.5],
[1.5, 1.],
[0., 1.],
[.5, .5]
])
expected_y = np.array([[0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5],
[1., 0., 0.5, 1.],
[0.5, 0.5, 0.5, 0.5]
])
mu = self.surrogate.predict(test_x)
assert_rel_error(self, mu, expected_y, 1e-9)
def test_prediction(self):
test_x = np.array([[1., 0.5],
[0.5, 1.0],
[1.0, 1.5],
[1.5, 1.],
[0., 1.],
[.5, .5]
])
expected_y = np.array([[0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5],
[0.5, 0.5, 0.5, 0.5],
[1., 0., 0.5, 1.],
[0.5, 0.5, 0.5, 0.5]
])
for x0, y0 in zip(test_x, expected_y):
mu = self.surrogate.predict(x0)
assert_rel_error(self, mu, y0, 1e-9)
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.fit(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_training(self):
for x0, y0 in zip(self.x, self.y):
mu = self.surrogate.predict(x0)
assert_rel_error(self, mu, y0, 1e-9)
