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 +15,65 @@ from ..notebook_integration import ensure_holoviews
 from ..utils import cache_latest
 
 
+def use_nn_neighbors(n):
+    """Decorator to specify how many neighboring intervals the loss function uses.
+    
+    This decorator can wrap around a loss function to let `~adaptive.Learner1D` 
+    know that you would like to look at the N-nearest neighboring intervals.
+    
+    The loss function is then guaranteed to receive the data of at least the 
+    nn-neighbors and a dict that tells you what the neighboring points of these 
+    are. And the Learner1D will then make sure that the loss is updated whenever 
+    on of the nn-neighbours changes.
+
+    Examples
+    --------
+
+    This is a part of the curvature loss function
+
+    >>> @use_nn_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, neighbours[<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.
+
+    >>>@use_nn_neighbors(1)
+    ...def loss(interval, scale, data, neighbors):
+    ...    x_left, x_right = interval
+    ...    n_left = neighbors[x_left][0]
+    ...    n_right = neighbors[x_right][1]
+    ...    is_min = True
+    ...    
+    ...    if n_left is not None and data[x_left] > data[n_left]:
+    ...        is_min = False
+    ...    if n_right is not None and data[x_right] > data[n_right]:
+    ...        is_min = False
+    ...    
+    ...    loss = (x_right - x_left) / scale[0]
+    ...    
+    ...    if is_min: 
+    ...        return loss * 100
+    ...    return loss
+    """
+    def _wrapped(loss_per_interval):
+        loss_per_interval.nn_neighbors = n
+        return loss_per_interval
+    return _wrapped
+
+
+@use_nn_neighbors(0)
 def uniform_loss(interval, scale, data, neighbors):
     """Loss function that samples the domain uniformly.
 
@@ -36,6 +95,7 @@ def uniform_loss(interval, scale, data, neighbors):
     return dx
 
 
+@use_nn_neighbors(0)
 def default_loss(interval, scale, data, neighbors):
     """Calculate loss on a single interval.
 
@@ -70,6 +130,7 @@ def _loss_of_multi_interval(xs, ys):
     return sum(vol(pts[i:i+3]) for i in range(N)) / N
 
 
+@use_nn_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 +146,7 @@ def triangle_loss(interval, scale, data, neighbors):
 
 
 def get_curvature_loss(area_factor=1, euclid_factor=0.02, horizontal_factor=0.02):
+    @use_nn_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)
@@ -141,10 +203,12 @@ 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
+    nn_neighbors : int, optional, default: None
         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.
+        at all, then it should be 0. By default we try to access the
+        ``loss_per_interval.nn_neighbors`` attribute which is set for all
+        implemented loss functions.
 
     Attributes
     ----------
@@ -170,14 +234,15 @@ class Learner1D(BaseLearner):
         A map containing points as keys to its neighbors as a tuple.
     """
 
-    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, 'nn_neighbors'):
+            self.nn_neighbors = loss_per_interval.nn_neighbors
         else:
-            self.loss_per_interval = loss_per_interval or get_curvature_loss()
+            self.nn_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 = {}