Update notebooks and scripts

sliced_wasserstein.py

@@ -3,6 +3,13 @@ import dionysus as d
 
 
 def diagram_array(dgm):
+    """Convert a Dionysus diagram to a Numpy array.
+
+    :param dgm: Dionysus Diagram
+
+    :return: a Numpy array of tuples representing the points in the
+             diagram.
+    """
     res = []
     for p in dgm:
         if p.death != np.inf:
@@ -11,8 +18,19 @@ def diagram_array(dgm):
 
 
 def SW_approx(dgm1, dgm2, M):
+    """Approximate computation of the Sliced Wasserstein kernel.
+
+    :param dgm1: first Diagram
+    :param dgm2: second Diagram
+    :param M int: number of directions
+
+    :return: The approximate value of the Sliced Wasserstein kernel of
+             dgm1 and dgm2, sampled over M dimensions.
+    """
     dgm1 = diagram_array(dgm1)
     dgm2 = diagram_array(dgm2)
+    if dgm1.size == 0 or dgm2.size == 0:
+        return 0
     # Add \pi_\delta(dgm1) to dgm2 and vice-versa
     proj1 = dgm1.dot([1, 1])/np.sqrt(2)
     proj2 = dgm2.dot([1, 1])/np.sqrt(2)