def backward_sampling_qmc(self, M):
"""QMC version of backward sampling.
Parameters
----------
M : int
number of trajectories
Note
----
Use this only on the history of a SQMC algorithm.
"""
self._check_h_orders()
u = qmc.sobol(M, self.T)
# the final particles have not been sorted
hT = hilbert.hilbert_sort(self.X[-1])
# searchsorted to avoid having to sort in place u according to u[:,T-1]
idx = np.searchsorted(np.cumsum(self.wgts[-1].W[hT]), u[:, -1])
paths = [
self.X[-1][hT][idx],
]
for t in reversed(range(self.T - 1)):
idx = np.empty(M, 'int')
for m, xn in enumerate(paths[-1]):
lwm = self.wgts[t].lw + self.fk.logpt(t + 1, self.X[t], xn)
# use ordered version here
cw = np.cumsum(rs.exp_and_normalise(lwm[self.h_orders[t]]))
idx[m] = np.searchsorted(cw, u[m, t])
paths.append(self.X[t][self.h_orders[t]][idx])
paths.reverse()
return paths
def resample_move_qmc(self):
self.rs_flag = True # we *always* resample in SQMC
u = qmc.sobol(self.N, self.fk.du + 1)
tau = np.argsort(u[:, 0])
self.h_order = hilbert.hilbert_sort(self.X)
self.A = self.h_order[rs.inverse_cdf(u[tau, 0],
self.aux.W[self.h_order])]
self.Xp = self.X[self.A]
v = u[tau, 1:].squeeze()
# v is (N,) if du=1, (N,d) otherwise
self.X = self.fk.Gamma(self.t, self.Xp, v)
self.reset_weights()