Merge branch '126--speed-up-learner1D' into 'master'

Resolve "(Learner1D) improve time complexity"

Closes #126 and #104

See merge request !139

adaptive/learner/learner1D.py

@@ -8,6 +8,7 @@ from collections import Iterable
 
 import numpy as np
 import sortedcontainers
+import sortedcollections
 
 from adaptive.learner.base_learner import BaseLearner
 from adaptive.learner.learnerND import volume
@@ -225,9 +226,6 @@ class Learner1D(BaseLearner):
 
         self.loss_per_interval = loss_per_interval or default_loss
 
-        # A dict storing the loss function for each interval x_n.
-        self.losses = {}
-        self.losses_combined = {}
 
         # When the scale changes by a factor 2, the losses are
         # recomputed. This is tunable such that we can test
@@ -249,6 +247,10 @@ class Learner1D(BaseLearner):
         self._scale = [bounds[1] - bounds[0], 0]
         self._oldscale = deepcopy(self._scale)
 
+        # A LossManager storing the loss function for each interval x_n.
+        self.losses = loss_manager(self._scale[0])
+        self.losses_combined = loss_manager(self._scale[0])
+
         # The precision in 'x' below which we set losses to 0.
         self._dx_eps = 2 * max(np.abs(bounds)) * np.finfo(float).eps
 
@@ -284,7 +286,10 @@ class Learner1D(BaseLearner):
     @cache_latest
     def loss(self, real=True):
         losses = self.losses if real else self.losses_combined
-        return max(losses.values()) if len(losses) > 0 else float('inf')
+        if not losses:
+            return np.inf
+        max_interval, max_loss = losses.peekitem(0)
+        return max_loss
 
     def _scale_x(self, x):
         if x is None:
@@ -454,8 +459,7 @@ class Learner1D(BaseLearner):
 
         # If the scale has increased enough, recompute all losses.
         if self._scale[1] > self._recompute_losses_factor * self._oldscale[1]:
-
-            for interval in self.losses:
+            for interval in reversed(self.losses):
                 self._update_interpolated_loss_in_interval(*interval)
 
             self._oldscale = deepcopy(self._scale)
@@ -504,18 +508,18 @@ class Learner1D(BaseLearner):
             for neighbors in (self.neighbors, self.neighbors_combined)]
 
         # The the losses for the "real" intervals.
-        self.losses = {}
+        self.losses = loss_manager(self._scale[0])
         for ival in intervals:
             self.losses[ival] = self._get_loss_in_interval(*ival)
 
         # List with "real" intervals that have interpolated intervals inside
         to_interpolate = []
 
-        self.losses_combined = {}
+        self.losses_combined = loss_manager(self._scale[0])
         for ival in intervals_combined:
             # If this interval exists in 'losses' then copy it otherwise
             # calculate it.
-            if ival in self.losses:
+            if ival in reversed(self.losses):
                 self.losses_combined[ival] = self.losses[ival]
             else:
                 # Set all losses to inf now, later they might be udpdated if the
@@ -530,7 +534,7 @@ class Learner1D(BaseLearner):
                     to_interpolate.append((x_left, x_right))
 
         for ival in to_interpolate:
-            if ival in self.losses:
+            if ival in reversed(self.losses):
                 # If this interval does not exist it should already
                 # have an inf loss.
                 self._update_interpolated_loss_in_interval(*ival)
@@ -566,64 +570,57 @@ class Learner1D(BaseLearner):
         if len(missing_bounds) >= n:
             return missing_bounds[:n], [np.inf] * n
 
-        def finite_loss(loss, xs):
-            # If the loss is infinite we return the
-            # distance between the two points.
-            if math.isinf(loss):
-                loss = (xs[1] - xs[0]) / self._scale[0]
-
-            # We round the loss to 12 digits such that losses
-            # are equal up to numerical precision will be considered
-            # equal.
-            return round(loss, ndigits=12)
-
-        quals = [(-finite_loss(loss, x), x, 1)
-                 for x, loss in self.losses_combined.items()]
-
         # Add bound intervals to quals if bounds were missing.
         if len(self.data) + len(self.pending_points) == 0:
             # We don't have any points, so return a linspace with 'n' points.
             return np.linspace(*self.bounds, n).tolist(), [np.inf] * n
-        elif len(missing_bounds) > 0:
+
+        quals = loss_manager(self._scale[0])
+        if len(missing_bounds) > 0:
             # There is at least one point in between the bounds.
             all_points = list(self.data.keys()) + list(self.pending_points)
             intervals = [(self.bounds[0], min(all_points)),
                          (max(all_points), self.bounds[1])]
             for interval, bound in zip(intervals, self.bounds):
                 if bound in missing_bounds:
-                    qual = (-finite_loss(np.inf, interval), interval, 1)
-                    quals.append(qual)
-
-        # Calculate how many points belong to each interval.
-        points, loss_improvements = self._subdivide_quals(
-            quals, n - len(missing_bounds))
-
-        points = missing_bounds + points
-        loss_improvements = [np.inf] * len(missing_bounds) + loss_improvements
+                    quals[(*interval, 1)] = np.inf
 
-        return points, loss_improvements
+        points_to_go = n - len(missing_bounds)
 
-    def _subdivide_quals(self, quals, n):
         # Calculate how many points belong to each interval.
-        heapq.heapify(quals)
-
-        for _ in range(n):
-            quality, x, n = quals[0]
-            if abs(x[1] - x[0]) / (n + 1) <= self._dx_eps:
-                # The interval is too small and should not be subdivided.
-                quality = np.inf
-                # XXX: see https://gitlab.kwant-project.org/qt/adaptive/issues/104
-            heapq.heapreplace(quals, (quality * n / (n + 1), x, n + 1))
+        i, i_max = 0, len(self.losses_combined)
+        for _ in range(points_to_go):
+            qual, loss_qual = quals.peekitem(0) if quals else (None, 0)
+            ival, loss_ival = self.losses_combined.peekitem(i) if i < i_max else (None, 0)
+
+            if (qual is None
+                or (ival is not None
+                    and self._loss(self.losses_combined, ival)
+                        >= self._loss(quals, qual))):
+                i += 1
+                quals[(*ival, 2)] = loss_ival / 2
+            else:
+                quals.pop(qual, None)
+                *xs, n = qual
+                quals[(*xs, n+1)] = loss_qual * n / (n+1)
 
         points = list(itertools.chain.from_iterable(
-            linspace(*interval, n) for quality, interval, n in quals))
+            linspace(*ival, n) for (*ival, n) in quals))
 
         loss_improvements = list(itertools.chain.from_iterable(
-            itertools.repeat(-quality, n - 1)
-            for quality, interval, n in quals))
+            itertools.repeat(quals[x0, x1, n], n - 1)
+            for (x0, x1, n)  in quals))
+
+        # add the missing bounds
+        points = missing_bounds + points
+        loss_improvements = [np.inf] * len(missing_bounds) + loss_improvements
 
         return points, loss_improvements
 
+    def _loss(self, mapping, ival):
+        loss = mapping[ival]
+        return finite_loss(ival, loss, self._scale[0])
+
     def plot(self):
         """Returns a plot of the evaluated data.
 
@@ -658,3 +655,42 @@ class Learner1D(BaseLearner):
 
     def _set_data(self, data):
         self.tell_many(*zip(*data.items()))
+
+
+def _fix_deepcopy(sorted_dict, x_scale):
+    # XXX: until https://github.com/grantjenks/sortedcollections/issues/5 is fixed
+    import types
+    def __deepcopy__(self, memo):
+        items = deepcopy(list(self.items()))
+        lm = loss_manager(self.x_scale)
+        lm.update(items)
+        return lm
+    sorted_dict.x_scale = x_scale
+    sorted_dict.__deepcopy__ = types.MethodType(__deepcopy__, sorted_dict)
+
+
+def loss_manager(x_scale):
+    def sort_key(ival, loss):
+        loss, ival = finite_loss(ival, loss, x_scale)
+        return -loss, ival
+    sorted_dict = sortedcollections.ItemSortedDict(sort_key)
+    _fix_deepcopy(sorted_dict, x_scale)
+    return sorted_dict
+
+
+def finite_loss(ival, loss, x_scale):
+    """Get the socalled finite_loss of an interval in order to be able to
+    sort intervals that have infinite loss."""
+    # If the loss is infinite we return the
+    # distance between the two points.
+    if math.isinf(loss):
+        loss = (ival[1] - ival[0]) / x_scale
+        if len(ival) == 3:
+            # Used when constructing quals. Last item is
+            # the number of points inside the qual.
+            loss /= ival[2]
+
+    # We round the loss to 12 digits such that losses
+    # are equal up to numerical precision will be considered
+    # equal.
+    return round(loss, ndigits=12), ival

environment.yml

@@ -6,6 +6,7 @@ channels:
 dependencies:
   - python=3.6
   - sortedcontainers
+  - sortedcollections
   - scipy
   - holoviews
   - ipyparallel

setup.py

@@ -26,6 +26,7 @@ version, cmdclass = get_version_and_cmdclass('adaptive')
 
 install_requires = [
     'scipy',
+    'sortedcollections',
     'sortedcontainers',
 ]