def test_project_to_psd_cone(self):
""" Tests projection onto PSD cone. """
self.report('Testing projection to PSD cone.')
M1 = np.random.random((10, 10))
M1 = M1 + M1.T
M2 = M1.dot(M1.T)
M1_proj = general_utils.project_symmetric_to_psd_cone(M1)
M2_proj = general_utils.project_symmetric_to_psd_cone(M2)
eigvals_M1, _ = np.linalg.eigh(M1_proj)
assert np.all(eigvals_M1 > -1e-10)
assert np.linalg.norm(M2_proj - M2) < 1e-5
def _get_cholesky_decomp(K_trtr_wo_noise, noise_var, handle_non_psd_kernels):
""" Computes cholesky decomposition after checking how to handle non-psd kernels. """
if handle_non_psd_kernels == 'try_before_project':
K_trtr_w_noise = K_trtr_wo_noise + noise_var * np.eye(
K_trtr_wo_noise.shape[0])
try:
# If the cholesky decomposition on the (noise added) matrix succeeds, return!
L = stable_cholesky(K_trtr_w_noise, add_to_diag_till_psd=False)
return L
except np.linalg.linalg.LinAlgError:
# otherwise, project and return
return _get_cholesky_decomp(K_trtr_wo_noise, noise_var,
'project_first')
elif handle_non_psd_kernels == 'project_first':
# project the Kernel (without noise) to the PSD cone and return
K_trtr_wo_noise = project_symmetric_to_psd_cone(K_trtr_wo_noise)
return _get_cholesky_decomp(K_trtr_wo_noise, noise_var,
'guaranteed_psd')
elif handle_non_psd_kernels == 'guaranteed_psd':
K_trtr_w_noise = K_trtr_wo_noise + noise_var * np.eye(
K_trtr_wo_noise.shape[0])
return stable_cholesky(K_trtr_w_noise)
else:
raise ValueError('Unknown option for handle_non_psd_kernels: %s' %
(handle_non_psd_kernels))
def _get_post_covar_from_raw_covar(raw_post_covar, noise_var, is_guaranteed_psd):
""" Computes the posterior covariance from the raw_post_covar. This is mostly to
account for the fact that the kernel may not be psd.
"""
if is_guaranteed_psd:
return raw_post_covar
else:
epsilon = 0.05 * noise_var
return project_symmetric_to_psd_cone(raw_post_covar, epsilon=epsilon)