def test_compute_hessian_parameters_for_sample(self):
point = np.array([[95.0]])
candidate_point = np.array([[99.15, 0]])
val = self.gp_complete_2.compute_hessian_parameters_for_sample(
point, candidate_point)
dh = 0.01
finite_diff = FiniteDifferences.second_order_central(
lambda x: self.gp_complete_2.compute_parameters_for_sample(
x.reshape(
(1, len(point))), candidate_point, clear_cache=False)['a'],
point[0, :], np.array([dh]))
npt.assert_almost_equal(finite_diff[(0, 0)], val['a'][0, :], decimal=5)
dh = 0.1
finite_diff = FiniteDifferences.second_order_central(
lambda x: self.gp_complete_2.compute_parameters_for_sample(
x.reshape(
(1, len(point))), candidate_point, clear_cache=False)['b'],
point[0, :], np.array([dh]))
npt.assert_almost_equal(finite_diff[(0, 0)], val['b'], decimal=5)
def test_hessian_posterior_mean(self):
gp = self.gp_complete
point = np.array([[80.5]])
# Test evaluate_grad_quadrature_cross_cov
hessian = gp.hessian_posterior_mean(point)
dh = 0.1
finite_diff = FiniteDifferences.second_order_central(
lambda points: gp.compute_posterior_parameters(
points.reshape((1, len(points))), only_mean=True)['mean'],
point[0, :], np.array([dh]))
npt.assert_almost_equal(finite_diff[(0, 0)], hessian[0, 0])
def test_evaluate_hessian_respect_point(self):
point = np.array([[4.5, 7.5]])
inputs = np.array([[5.0, 6.0], [8.0, 9.0]])
params = np.array([1.0, 5.0])
result = Matern52.evaluate_hessian_respect_point(
params, point, inputs, 2)
dh = 0.00001
finite_diff = FiniteDifferences.second_order_central(
lambda x: Matern52.evaluate_cross_cov_defined_by_params(
params, x.reshape((1, len(x))), inputs, 2), point[0, :],
np.array([dh]))
for i in xrange(2):
for j in xrange(2):
print i, j
npt.assert_almost_equal(
finite_diff[i, j],
np.array([[result[0, i, j], result[1, i, j]]]),
decimal=5)
def test_hessian_distance_length_scale_respect_point(self):
params = np.array([1.0, 5.0])
point = np.array([[4.5, 7.5]])
inputs = np.array([[5.0, 6.0], [8.0, 9.0]])
result = Distances.gradient_distance_length_scale_respect_point(
params, point, inputs, second=True)
result = result['second']
dh = 0.00001
finite_diff = FiniteDifferences.second_order_central(
lambda x: np.sqrt(
Distances.dist_square_length_scale(
params, x.reshape((1, len(x))), inputs)), point[0, :],
np.array([dh]))
for i in xrange(2):
for j in xrange(2):
print i, j
npt.assert_almost_equal(
finite_diff[i, j],
np.array([[result[0, i, j], result[1, i, j]]]),
decimal=5)
def test_second_order_central(self):
self.x = np.array([1.5, 1.5, 1.5])
h = np.array([0.1])
result = FiniteDifferences.second_order_central(self.f, self.x, h)
base_eval = \
Matern52.evaluate_cov_defined_by_params(self.x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)
for i in xrange(3):
val = result[(i, i)]
new_x = deepcopy(self.x)
new_x[i] += h[0]
new_eval = \
Matern52.evaluate_cov_defined_by_params(
new_x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)
new_x = deepcopy(self.x)
new_x[i] -= h[0]
new_eval_2 = \
Matern52.evaluate_cov_defined_by_params(
new_x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)
assert np.all(val == (new_eval + new_eval_2 - 2.0 * base_eval) / (h[0] ** 2))
for i in xrange(3):
for j in xrange(3):
if j == i:
continue
val = result[(i, j)]
new_x = deepcopy(self.x)
new_x[i] += h[0]
new_x[j] += h[0]
new_eval = \
Matern52.evaluate_cov_defined_by_params(
new_x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)
val_2 = new_eval
new_x = deepcopy(self.x)
new_x[i] -= h[0]
new_x[j] -= h[0]
new_eval_2 = \
Matern52.evaluate_cov_defined_by_params(
new_x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)
val_2 += new_eval_2
new_x = deepcopy(self.x)
new_x[i] += h[0]
new_x[j] -= h[0]
new_eval = \
Matern52.evaluate_cov_defined_by_params(
new_x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)
val_2 -= new_eval
new_x = deepcopy(self.x)
new_x[i] -= h[0]
new_x[j] += h[0]
new_eval_2 = \
Matern52.evaluate_cov_defined_by_params(
new_x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)
val_2 -= new_eval_2
val_2 /= (4.0 * h * h)
assert np.all(val_2 == val)