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

@@ -15,6 +15,61 @@ from ..notebook_integration import ensure_holoviews
 from ..utils import cache_latest
 
 
+def uses_nth_neighbors(n):
+    """Decorator to specify how many neighboring intervals the loss function uses.
+
+    Wraps loss functions to indicate that they expect intervals together
+    with ``n`` nearest neighbors
+
+    The loss function is then guaranteed to receive the data of at least the
+    N nearest neighbors (``nth_neighbors``) in a dict that tells you what the
+    neighboring points of these are. And the `~adaptive.Learner1D` will
+    then make sure that the loss is updated whenever one of the
+    ``nth_neighbors`` changes.
+
+    Examples
+    --------
+
+    The next function is a part of the `get_curvature_loss` function.
+
+    >>> @uses_nth_neighbors(1)
+    ... def triangle_loss(interval, scale, data, neighbors):
+    ...     x_left, x_right = interval
+    ...     xs = [neighbors[x_left][0], x_left, x_right, neighbors[x_right][1]]
+    ...     # at the boundary, neighbors[<left boundary x>] is (None, <some other x>)
+    ...     xs = [x for x in xs if x is not None]
+    ...     if len(xs) <= 2:
+    ...         return (x_right - x_left) / scale[0]
+    ...
+    ...     y_scale = scale[1] or 1
+    ...     ys_scaled = [data[x] / y_scale for x in xs]
+    ...     xs_scaled = [x / scale[0] for x in xs]
+    ...     N = len(xs) - 2
+    ...     pts = [(x, y) for x, y in zip(xs_scaled, ys_scaled)]
+    ...     return sum(volume(pts[i:i+3]) for i in range(N)) / N
+
+    Or you may define a loss that favours the (local) minima of a function.
+
+    >>> @uses_nth_neighbors(1)
+    ... def local_minima_resolving_loss(interval, scale, data, neighbors):
+    ...     x_left, x_right = interval
+    ...     n_left = neighbors[x_left][0]
+    ...     n_right = neighbors[x_right][1]
+    ...     loss = (x_right - x_left) / scale[0]
+    ...
+    ...     if not ((n_left is not None and data[x_left] > data[n_left])
+    ...         or (n_right is not None and data[x_right] > data[n_right])):
+    ...         return loss * 100
+    ...
+    ...     return loss
+    """
+    def _wrapped(loss_per_interval):
+        loss_per_interval.nth_neighbors = n
+        return loss_per_interval
+    return _wrapped
+
+
+@uses_nth_neighbors(0)
 def uniform_loss(interval, scale, data, neighbors):
     """Loss function that samples the domain uniformly.
 
@@ -36,6 +91,7 @@ def uniform_loss(interval, scale, data, neighbors):
     return dx
 
 
+@uses_nth_neighbors(0)
 def default_loss(interval, scale, data, neighbors):
     """Calculate loss on a single interval.
 
@@ -70,6 +126,7 @@ def _loss_of_multi_interval(xs, ys):
     return sum(vol(pts[i:i+3]) for i in range(N)) / N
 
 
+@uses_nth_neighbors(1)
 def triangle_loss(interval, scale, data, neighbors):
     x_left, x_right = interval
     xs = [neighbors[x_left][0], x_left, x_right, neighbors[x_right][1]]
@@ -85,6 +142,7 @@ def triangle_loss(interval, scale, data, neighbors):
 
 
 def get_curvature_loss(area_factor=1, euclid_factor=0.02, horizontal_factor=0.02):
+    @uses_nth_neighbors(1)
     def curvature_loss(interval, scale, data, neighbors):
         triangle_loss_ = triangle_loss(interval, scale, data, neighbors)
         default_loss_ = default_loss(interval, scale, data, neighbors)
@@ -118,8 +176,8 @@ def _get_neighbors_from_list(xs):
     return sortedcontainers.SortedDict(neighbors)
 
 
-def _get_intervals(x, neighbors, nn_neighbors):
-    nn = nn_neighbors
+def _get_intervals(x, neighbors, nth_neighbors):
+    nn = nth_neighbors
     i = neighbors.index(x)
     start = max(0, i - nn - 1)
     end = min(len(neighbors), i + nn + 2)
@@ -141,10 +199,6 @@ class Learner1D(BaseLearner):
         A function that returns the loss for a single interval of the domain.
         If not provided, then a default is used, which uses the scaled distance
         in the x-y plane as the loss. See the notes for more details.
-    nn_neighbors : int, default: 0
-        The number of neighboring intervals that the loss function
-        takes into account. If ``loss_per_interval`` doesn't use the neighbors
-        at all, then it should be 0.
 
     Attributes
     ----------
@@ -168,16 +222,27 @@ class Learner1D(BaseLearner):
         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.
+        At the left ``x_left`` and right ``x_left`` most boundary it has
+        ``x_left: (None, float)`` and ``x_right: (float, None)``.
+
+    The `loss_per_interval` function should also have
+    an attribute `nth_neighbors` that indicates how many of the neighboring
+    intervals to `interval` are used. If `loss_per_interval` doesn't
+    have such an attribute, it's assumed that is uses **no** neighboring
+    intervals. Also see the `uses_nth_neighbors` decorator.
+    **WARNING**: When modifying the `data` and `neighbors` datastructures
+    the learner will behave in an undefined way.
     """
 
-    def __init__(self, function, bounds, loss_per_interval=None, nn_neighbors=0):
+    def __init__(self, function, bounds, loss_per_interval=None):
         self.function = function
-        self.nn_neighbors = nn_neighbors
 
-        if nn_neighbors == 0:
-            self.loss_per_interval = loss_per_interval or default_loss
+        if hasattr(loss_per_interval, 'nth_neighbors'):
+            self.nth_neighbors = loss_per_interval.nth_neighbors
         else:
-            self.loss_per_interval = loss_per_interval or get_curvature_loss()
+            self.nth_neighbors = 0
+
+        self.loss_per_interval = loss_per_interval or default_loss
 
         # A dict storing the loss function for each interval x_n.
         self.losses = {}
@@ -276,10 +341,10 @@ class Learner1D(BaseLearner):
 
         if real:
             # We need to update all interpolated losses in the interval
-            # (x_left, x), (x, x_right) and the nn_neighbors nearest
+            # (x_left, x), (x, x_right) and the nth_neighbors nearest
             # neighboring intervals. Since the addition of the
             # point 'x' could change their loss.
-            for ival in _get_intervals(x, self.neighbors, self.nn_neighbors):
+            for ival in _get_intervals(x, self.neighbors, self.nth_neighbors):
                 self._update_interpolated_loss_in_interval(*ival)
 
             # Since 'x' is in between (x_left, x_right),