def test_cholesky_update(spdmat1, spdmat2):
expected = np.linalg.cholesky(spdmat1 + spdmat2)
S1 = np.linalg.cholesky(spdmat1)
S2 = np.linalg.cholesky(spdmat2)
received = utlin.cholesky_update(S1, S2)
np.testing.assert_allclose(expected, received)
def _forward_rv_sqrt(
self,
rv,
t,
compute_gain=False,
_diffusion=1.0) -> Tuple[randvars.RandomVariable, typing.Dict]:
if config.matrix_free:
raise NotImplementedError(
"Sqrt-implementation does not work with linops for now.")
H = self.transition_matrix_fun(t)
noise = self.noise_fun(t)
shift, SR = noise.mean, noise.cov_cholesky
new_mean = H @ rv.mean + shift
new_cov_cholesky = cholesky_update(H @ rv.cov_cholesky,
np.sqrt(_diffusion) * SR)
new_cov = new_cov_cholesky @ new_cov_cholesky.T
crosscov = rv.cov @ H.T
info = {"crosscov": crosscov}
if compute_gain:
info["gain"] = scipy.linalg.cho_solve((new_cov_cholesky, True),
crosscov.T).T
return (
randvars.Normal(new_mean,
cov=new_cov,
cov_cholesky=new_cov_cholesky),
info,
)
def _forward_rv_sqrt(
self,
rv,
t,
compute_gain=False,
_diffusion=1.0) -> (randvars.RandomVariable, typing.Dict):
H = self.state_trans_mat_fun(t)
SR = self.proc_noise_cov_cholesky_fun(t)
shift = self.shift_vec_fun(t)
new_mean = H @ rv.mean + shift
new_cov_cholesky = cholesky_update(H @ rv.cov_cholesky,
np.sqrt(_diffusion) * SR)
new_cov = new_cov_cholesky @ new_cov_cholesky.T
crosscov = rv.cov @ H.T
info = {"crosscov": crosscov}
if compute_gain:
info["gain"] = scipy.linalg.cho_solve((new_cov_cholesky, True),
crosscov.T).T
return (
randvars.Normal(new_mean,
cov=new_cov,
cov_cholesky=new_cov_cholesky),
info,
)
def test_cholesky_optional(spdmat1, even_ndim):
"""Assert that cholesky_update() transforms a non-square matrix square-root into a
correct Cholesky factor."""
H = np.random.rand(even_ndim // 2, even_ndim)
expected = np.linalg.cholesky(H @ spdmat1 @ H.T)
S1 = np.linalg.cholesky(spdmat1)
received = utlin.cholesky_update(H @ S1)
np.testing.assert_allclose(expected, received)
def _project_rv(projmat, rv):
# There is no way of checking whether `rv` has its Cholesky factor computed already or not.
# Therefore, since we need to update the Cholesky factor for square-root filtering,
# we also update the Cholesky factor for non-square-root algorithms here,
# which implies additional cost.
# See Issues #319 and #329.
# When they are resolved, this function here will hopefully be superfluous.
new_mean = projmat @ rv.mean
new_cov = projmat @ rv.cov @ projmat.T
new_cov_cholesky = cholesky_update(projmat @ rv.cov_cholesky)
return randvars.Normal(new_mean, new_cov, cov_cholesky=new_cov_cholesky)
def _forward_rv_sqrt(self,
rv,
t,
compute_gain=False,
_diffusion=1.0) -> (pnrv.RandomVariable, typing.Dict):
H = self.state_trans_mat_fun(t)
SR = self.proc_noise_cov_cholesky_fun(t)
shift = self.shift_vec_fun(t)
new_mean = H @ rv.mean + shift
new_cov_cholesky = cholesky_update(H @ rv.cov_cholesky,
np.sqrt(_diffusion) * SR)
new_cov = new_cov_cholesky @ new_cov_cholesky.T
crosscov = rv.cov @ H.T
info = {"crosscov": crosscov}
if compute_gain:
gain = crosscov @ np.linalg.inv(new_cov)
info["gain"] = gain
return pnrv.Normal(new_mean,
cov=new_cov,
cov_cholesky=new_cov_cholesky), info