completed as...

1 files changed, 6 insertions, 2 deletions

diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein.py
index ba0f7343..aab0cb3c 100644
--- a/src/python/gudhi/wasserstein.py
+++ b/src/python/gudhi/wasserstein.py
@@ -30,7 +30,9 @@ def _build_dist_matrix(X, Y, order=2., internal_p=2.):
     :param order: exponent for the Wasserstein metric.
     :param internal_p: Ground metric (i.e. norm L^p).
     :returns: (n+1) x (m+1) np.array encoding the cost matrix C. 
-                For 1 <= i <= n, 1 <= j <= m, C[i,j] encodes the distance between X[i] and Y[j], while C[i, m+1] (resp. C[n+1, j]) encodes the distance (to the p) between X[i] (resp Y[j]) and its orthogonal proj onto the diagonal.
+                For 1 <= i <= n, 1 <= j <= m, C[i,j] encodes the distance between X[i] and Y[j], 
+                while C[i, m+1] (resp. C[n+1, j]) encodes the distance (to the p) between X[i] (resp Y[j]) 
+                and its orthogonal proj onto the diagonal.
                 note also that C[n+1, m+1] = 0  (it costs nothing to move from the diagonal to the diagonal).
     '''
     Xdiag = _proj_on_diag(X)
@@ -88,7 +90,9 @@ def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2.):
     :param X: (n x 2) numpy.array encoding the (finite points of the) first diagram. Must not contain essential points 
                 (i.e. with infinite coordinate).
     :param Y: (m x 2) numpy.array encoding the second diagram.
-    :param matching: if True, computes and returns the optimal matching between X and Y, encoded as...
+    :param matching: if True, computes and returns the optimal matching between X and Y, encoded as
+                        a list of tuple [...(i,j)...], meaning the i-th point in X is matched to
+                        the j-th point in Y, with the convention (-1) represents the diagonal.
     :param order: exponent for Wasserstein; Default value is 2.
     :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2); 
                         Default value is 2 (Euclidean norm).