From 570a9b83eb3f714bc52735dae289a5195874bf41 Mon Sep 17 00:00:00 2001 From: tlacombe Date: Thu, 5 Mar 2020 15:40:45 +0100 Subject: completed as... --- src/python/gudhi/wasserstein.py | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) (limited to 'src/python/gudhi/wasserstein.py') 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). -- cgit v1.2.3