Avoid invalid assumptions about particle ordering

When starting from a cached state, we cannot assume that the initial
particle ordering is consistent with previous time-steps.

src/pypfilt/obs.py

@@ -30,7 +30,7 @@ def expect(ctx, time, unit, period, prev, curr):
         raise ValueError("Unknown observation type '{}'".format(unit))
 
 
-def log_llhd_of(ctx, hist, hist_ix, obs, max_back=None):
+def log_llhd_of(ctx, hist, hist_ix, obs, max_back=0):
     """Return the log-likelihood of obtaining observations from each particle.
 
     :param ctx: The simulation context.
@@ -39,7 +39,7 @@ def log_llhd_of(ctx, hist, hist_ix, obs, max_back=None):
     :param obs: The observation(s) that have been made.
     :param max_back: The number of time-steps into the past when the most
         recent resampling occurred (i.e., how far back the current particle
-        ordering is guaranteed to persist; default is ``None``, no limit).
+        ordering is guaranteed to persist; default is 0, no guarantee).
 
     :returns: An array containing the log-likelihood for each particle.
     """
@@ -58,7 +58,7 @@ def log_llhd_of(ctx, hist, hist_ix, obs, max_back=None):
     def hist_for(period):
         """Return past state vectors in the appropriate order."""
         steps_back = steps_per_unit * period
-        same_ixs = max_back is None or max_back >= steps_back
+        same_ixs = max_back >= steps_back
         if same_ixs:
             if steps_back > hist_ix:
                 # If the observation period starts before the beginning of the

src/pypfilt/pfilter.py

@@ -8,7 +8,7 @@ from . import obs as obs_mod
 from . import state as state_mod
 
 
-def reweight(ctx, hist, hist_ix, obs, max_back=None):
+def reweight(ctx, hist, hist_ix, obs, max_back):
     """Adjust particle weights in response to some observation(s).
 
     :param params: The simulation parameters.
@@ -17,7 +17,7 @@ def reweight(ctx, hist, hist_ix, obs, max_back=None):
     :param obs: The observation(s) that have been made.
     :param max_back: The number of time-steps into the past when the most
         recent resampling occurred (i.e., how far back the current particle
-        ordering is guaranteed to persist; default is ``None``, no limit).
+        ordering is guaranteed to persist).
 
     :returns: A tuple; the first element (*bool*) indicates whether resampling
         is required, the second element (*float*) is the **effective** number
@@ -200,7 +200,12 @@ def run(ctx, start, end, streams, state=None,
     # The time of the previous time-step (if any).
     most_recent = None
     # The time-step number of the most recent resampling (if any).
-    last_rs = None
+    # NOTE: the first time-step is number 1 and updates hist[1] given hist[0].
+    # So we set this value to zero to indicate that we can step back as far as
+    # the beginning of this simulation; this is important when resuming from
+    # cached states where we cannot assume anything about the history prior to
+    # the first time-step.
+    last_rs = 0
     # The index of the current time-step in the state matrix.
     hist_ix = None
 
@@ -237,10 +242,7 @@ def run(ctx, start, end, streams, state=None,
             hist[hist_ix, :, :-2] = 0
 
         # Determine how many time-steps back the most recent resampling was.
-        if last_rs is None:
-            max_back = None
-        else:
-            max_back = (step_num - last_rs)
+        max_back = (step_num - last_rs)
 
         # Simulate the current time-step.
         resampled = step(ctx, hist, hist_ix, step_num, when, obs,