def test_forward_difference(self):
result = FiniteDifferences.forward_difference(self.f, self.x, self.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 result:
new_x = deepcopy(self.x)
new_x[i] += self.h[0]
new_eval = \
Matern52.evaluate_cov_defined_by_params(
new_x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)
for j in range(2):
for h in range(2):
assert result[i][j, h] == (new_eval[j, h] - base_eval[j, h]) / self.h[0]
def test_evaluate_cov_defined_by_params(self):
result = Matern52.evaluate_cov_defined_by_params(
np.array([1, 3, 5]), np.array([[4, 5]]), 2)
kernel = Matern52.define_kernel_from_array(2, np.array([1, 3, 5]))
assert result == kernel.cov(np.array([[4, 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)
def f(x):
return Matern52.evaluate_cov_defined_by_params(x, np.array([[2.0, 0.0], [0.0, 2.0]]), 2)