def _backward_sampling_ON2(self, M, idx):
"""O(N^2) version of backward sampling.
not meant to be called directly, see backward_sampling
"""
for m in range(M):
for t in reversed(range(self.T - 1)):
lwm = (self.wgts[t].lw + self.fk.logpt(
t + 1, self.X[t], self.X[t + 1][idx[t + 1, m]]))
idx[t, m] = rs.multinomial_once(rs.exp_and_normalise(lwm))
def multinomial_sampling(W: np.ndarray) -> Tuple:
# tested
"""Multinomial sampling for multi-dimensional numpy arrays.
:param W: a numpy array of weights, summing to 1
:returns: a tuple of indices indicating the chosen element
"""
W_raveled = np.ravel(W)
#chosen_raveled_index = np.random.choice(len(W_raveled), p=W_raveled)
chosen_raveled_index = rs.multinomial_once(W_raveled)
return np.unravel_index(chosen_raveled_index, W.shape)
def extract_one_trajectory(self):
"""Extract a single trajectory from the particle history.
The final state is chosen randomly, then the corresponding trajectory
is constructed backwards, until time t=0.
"""
traj = []
for t in reversed(range(self.T)):
if t == self.T - 1:
n = rs.multinomial_once(self.wgts[-1].W)
else:
n = self.A[t + 1][n]
traj.append(self.X[t][n])
return traj[::-1]
def sample(self, N=1):
"""Sample N trajectories from the posterior.
Note
----
Performs the forward step in case it has not been performed.
"""
if not self.filt:
self.forward()
paths = np.empty((len(self.filt), N), np.int)
paths[-1, :] = rs.multinomial(self.filt[-1], M=N)
log_trans = np.log(self.hmm.trans_mat)
for t, f in reversed(list(enumerate(self.filt[:-1]))):
for n in range(N):
probs = rs.exp_and_normalise(log_trans[:, paths[t + 1, n]] + np.log(f))
paths[t, n] = rs.multinomial_once(probs)
return paths