Resolve "(Learner1D) add possibility to use the direct neighbors in the loss"

Closes #119 (closed)

Currently works for one R^1 \to R^1

Still have to make it work for R^1 \to R^N

Also performance is actually quite good. As in: the learner slows down about 1.5 times. Going (on my laptop) from 3 seconds per 1000 points to 4.5 seconds per 1000 points.

Which, I believe, will be more than compensated by the fact that the chosen points are generally better

adaptive/learner/learner1D.py

@@ -15,7 +15,7 @@ from ..notebook_integration import ensure_holoviews
 from ..utils import cache_latest
 
 
-def uniform_loss(interval, scale, function_values):
+def uniform_loss(interval, scale, function_values, neighbors):
     """Loss function that samples the domain uniformly.
 
     Works with `~adaptive.Learner1D` only.
@@ -36,7 +36,7 @@ def uniform_loss(interval, scale, function_values):
     return dx
 
 
-def default_loss(interval, scale, function_values):
+def default_loss(interval, scale, function_values, neighbors):
     """Calculate loss on a single interval.
 
     Currently returns the rescaled length of the interval. If one of the
@@ -70,13 +70,13 @@ def _loss_of_multi_interval(xs, ys):
     return sum(vol(pts[i:i+3]) for i in range(N)) / N
 
 
-def triangle_loss(interval, neighbours, scale, function_values):
+def triangle_loss(interval, scale, function_values, neighbors):
     x_left, x_right = interval
-    neighbour_left, neighbour_right = neighbours
-    xs = [neighbour_left, x_left, x_right, neighbour_right]
-    # The neighbours could be None if we are at the boundary, in that case we
-    # have to filter this out
-    xs = [x for x in xs if x is not None]
+    xs = [x_left, x_right]
+    if x_left in neighbors:
+        xs.insert(0, neighbors[x_left][1])
+    if x_right in neighbors:
+        xs.append(neighbors[x_right][0])
 
     if len(xs) <= 2:
         return (x_right - x_left) / scale[0]
@@ -88,9 +88,9 @@ def triangle_loss(interval, neighbours, scale, function_values):
 
 
 def get_curvature_loss(area_factor=1, euclid_factor=0.02, horizontal_factor=0.02):
-    def curvature_loss(interval, neighbours, scale, function_values):
-        triangle_loss_ = triangle_loss(interval, neighbours, scale, function_values)
-        default_loss_ = default_loss(interval, scale, function_values)
+    def curvature_loss(interval, scale, function_values, neighbors):
+        triangle_loss_ = triangle_loss(interval, scale, function_values, neighbors)
+        default_loss_ = default_loss(interval, scale, function_values, neighbors)
         dx = (interval[1] - interval[0]) / scale[0]
         return (area_factor * (triangle_loss_**0.5)
                 + euclid_factor * default_loss_
@@ -121,6 +121,13 @@ def _get_neighbors_from_list(xs):
     return sortedcontainers.SortedDict(neighbors)
 
 
+def _get_interval(x, neighbors, nn_neighbors):
+    n = nn_neighbors
+    index = neighbors.bisect_left(x)
+    return [neighbors.iloc[i] for i in range(index - n - 1, index + 2 + n)
+            if 0 <= i < len(neighbors)]
+
+
 class Learner1D(BaseLearner):
     """Learns and predicts a function 'f:ℝ → ℝ^N'.
 
@@ -156,16 +163,18 @@ class Learner1D(BaseLearner):
     function_values : dict(float → float)
         A map containing evaluated function values. It is guaranteed
         to have values for both of the points in 'interval'.
+    neighbors : dict(float → (float, float))
+        A map containing points as keys to its neighbors as a tuple.
     """
 
-    def __init__(self, function, bounds, loss_per_interval=None, loss_depends_on_neighbours=False):
+    def __init__(self, function, bounds, loss_per_interval=None, nn_neighbors=0):
         self.function = function
-        self._loss_depends_on_neighbours = loss_depends_on_neighbours
+        self.nn_neighbors = nn_neighbors
 
-        if loss_depends_on_neighbours:
-            self.loss_per_interval = loss_per_interval or get_curvature_loss()
-        else:
+        if nn_neighbors == 0:
             self.loss_per_interval = loss_per_interval or default_loss
+        else:
+            self.loss_per_interval = loss_per_interval or get_curvature_loss()
 
         # A dict storing the loss function for each interval x_n.
         self.losses = {}
@@ -231,14 +240,8 @@ class Learner1D(BaseLearner):
 
         # we need to compute the loss for this interval
         interval = (x_left, x_right)
-        if self._loss_depends_on_neighbours:
-            neighbour_left = self.neighbors.get(x_left, (None, None))[0]
-            neighbour_right = self.neighbors.get(x_right, (None, None))[1]
-            neighbours = neighbour_left, neighbour_right
-            return self.loss_per_interval(interval, neighbours,
-                                          self._scale, self.data)
-        else:
-            return self.loss_per_interval(interval, self._scale, self.data)
+        return self.loss_per_interval(
+            interval, self._scale, self.data, self.neighbors)
 
 
     def _update_interpolated_loss_in_interval(self, x_left, x_right):
@@ -271,17 +274,12 @@ class Learner1D(BaseLearner):
 
         if real:
             # We need to update all interpolated losses in the interval
-            # (x_left, x) and (x, x_right). Since the addition of the point
-            # 'x' could change their loss.
-            self._update_interpolated_loss_in_interval(x_left, x)
-            self._update_interpolated_loss_in_interval(x, x_right)
-
-            # if the loss depends on the neighbors we should also update those losses
-            if self._loss_depends_on_neighbours:
-                neighbour_left = self.neighbors.get(x_left, (None, None))[0]
-                neighbour_right = self.neighbors.get(x_right, (None, None))[1]
-                self._update_interpolated_loss_in_interval(neighbour_left, x_left)
-                self._update_interpolated_loss_in_interval(x_right, neighbour_right)
+            # (x_left, x), (x, x_right) and the nn_neighbors nearest
+            # neighboring intervals. Since the addition of the
+            # point 'x' could change their loss.
+            points = _get_interval(x, self.neighbors, self.nn_neighbors)
+            for ival in zip(points, points[1:]):
+                self._update_interpolated_loss_in_interval(*ival)
 
             # Since 'x' is in between (x_left, x_right),
             # we get rid of the interval.