def test_specify_support_twice(self):
#
# TODO: Haven't done it for precision yet
#
oort = 1 / np.sqrt(2)
V = np.array([[0.5, oort, 0, 0.5], [0.5, 0, -oort, -0.5],
[0.5, -oort, 0, 0.5], [0.5, 0, oort, -0.5]])
# Eigenvalues
d = np.array([4, 0, 2, 0], dtype=float)
Lmd = np.diag(d)
# Covariance matrix
K = V.dot(Lmd.dot(V.T))
#
# Restrict subspace in two steps
#
# Field with predefined subspace
u = GaussianField(4, K=K, mode='covariance', support=V[:, 0:3])
# Further restrict subspace (automatically)
u.update_support()
#
# Reduce subspace at once
#
v = GaussianField(4, K=K, mode='covariance', support=V[:, [0, 2]])
# Check that the supports are the same
U = u.support()
V = v.support()
self.assertTrue(np.allclose(U - V.dot(V.T.dot(U)), np.zeros(U.shape)))
self.assertTrue(np.allclose(V - U.dot(U.T.dot(V)), np.zeros(V.shape)))
def test_degenerate_sample(self):
"""
Test support and reduced covariance
"""
oort = 1 / np.sqrt(2)
V = np.array([[0.5, oort, 0, 0.5], [0.5, 0, -oort, -0.5],
[0.5, -oort, 0, 0.5], [0.5, 0, oort, -0.5]])
# Eigenvalues
d = np.array([4, 3, 2, 0], dtype=float)
Lmd = np.diag(d)
# Covariance matrix
K = V.dot(Lmd.dot(V.T))
# Zero mean Gaussian field
u_ex = GaussianField(4, K=K, mode='covariance', support=V[:, 0:3])
u_im = GaussianField(4, K=K, mode='covariance')
u_im.update_support()
# Check reduced covariances
self.assertTrue(
np.allclose(u_ex.covariance().get_matrix(),
u_im.covariance().get_matrix().toarray()))
# Check supports
V_ex = u_ex.support()
V_im = u_im.support()
# Ensure they have the same sign
for i in range(V_ex.shape[1]):
if V_ex[0, i] < 0:
V_ex[:, i] = -V_ex[:, i]
if V_im[0, i] < 0:
V_im[:, i] = -V_im[:, i]
self.assertTrue(np.allclose(V_ex, V_im))
u_ex.set_support(V_ex)
u_im.set_support(V_im)
# Compare samples
z = u_ex.iid_gauss(n_samples=1)
u_ex_smp = u_ex.sample(z=z, decomposition='chol')
u_im_smp = u_im.sample(z=z, decomposition='chol')
self.assertTrue(np.allclose(u_ex_smp, u_im_smp))