def backward_rv(
self,
rv_obtained,
rv,
rv_forwarded=None,
gain=None,
t=None,
dt=None,
_diffusion=1.0,
**kwargs,
):
if dt is None:
raise ValueError(
"Continuous-time transitions require a time-increment ``dt``."
)
# Fetch things into preconditioned space
rv_obtained = _preconditioner.apply_precon(self.precon.inverse(dt), rv_obtained)
rv = _preconditioner.apply_precon(self.precon.inverse(dt), rv)
rv_forwarded = (
_preconditioner.apply_precon(self.precon.inverse(dt), rv_forwarded)
if rv_forwarded is not None
else None
)
gain = (
self.precon.inverse(dt) @ gain @ self.precon.inverse(dt).T
if gain is not None
else None
)
# Apply preconditioning to system matrices
new_drift_matrix = self.precon.inverse(dt) @ self.drift_matrix @ self.precon(dt)
new_force_vector = self.precon.inverse(dt) @ self.force_vector
new_dispersion_matrix = self.precon.inverse(dt) @ self.dispersion_matrix
new_lti_sde = continuous.LTISDE(
drift_matrix=new_drift_matrix,
force_vector=new_force_vector,
dispersion_matrix=new_dispersion_matrix,
forward_implementation=self.forward_implementation,
backward_implementation=self.backward_implementation,
)
# Discretise and propagate
discretised_model = new_lti_sde.discretise(dt=dt)
rv, info = discretised_model.backward_rv(
rv_obtained=rv_obtained,
rv=rv,
rv_forwarded=rv_forwarded,
gain=gain,
t=t,
_diffusion=_diffusion,
)
# Undo preconditioning and return
rv = _preconditioner.apply_precon(self.precon(dt), rv)
return rv, info
def forward_rv(
self,
rv,
t,
dt=None,
compute_gain=False,
_diffusion=1.0,
**kwargs,
):
if dt is None:
raise ValueError(
"Continuous-time transitions require a time-increment ``dt``.")
# Fetch things into preconditioned space
rv = _preconditioner.apply_precon(self.precon.inverse(dt), rv)
# Apply preconditioning to system matrices
new_drift_matrix = self.precon.inverse(
dt) @ self.drift_matrix @ self.precon(dt)
new_force_vector = self.precon.inverse(dt) @ self.force_vector
new_dispersion_matrix = self.precon.inverse(
dt) @ self.dispersion_matrix
new_lti_sde = continuous.LTISDE(
drift_matrix=new_drift_matrix,
force_vector=new_force_vector,
dispersion_matrix=new_dispersion_matrix,
forward_implementation=self.forward_implementation,
backward_implementation=self.backward_implementation,
)
# Discretise and propagate
discretised_model = new_lti_sde.discretise(dt=dt)
rv, info = discretised_model.forward_rv(rv,
t,
compute_gain=compute_gain,
_diffusion=_diffusion)
# Undo preconditioning and return
rv = _preconditioner.apply_precon(self.precon(dt), rv)
info["crosscov"] = self.precon(dt) @ info["crosscov"] @ self.precon(
dt).T
if "gain" in info:
info["gain"] = self.precon(
dt) @ info["gain"] @ self.precon.inverse(dt).T
return rv, info