diff options
| -rw-r--r-- | src/python/gudhi/wasserstein.py | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein.py index db5ddff2..b1cfd588 100644 --- a/src/python/gudhi/wasserstein.py +++ b/src/python/gudhi/wasserstein.py @@ -27,8 +27,8 @@ def _build_dist_matrix(X, Y, order=2., internal_p=2.): ''' :param X: (n x 2) numpy.array encoding the (points of the) first diagram. :param Y: (m x 2) numpy.array encoding the second diagram. - :param internal_p: Ground metric (i.e. norm l_p). :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. note also that C[n+1, m+1] = 0 (it costs nothing to move from the diagonal to the diagonal). @@ -54,8 +54,8 @@ def _build_dist_matrix(X, Y, order=2., internal_p=2.): def _perstot(X, order, internal_p): ''' :param X: (n x 2) numpy.array (points of a given diagram). - :param internal_p: Ground metric on the (upper-half) plane (i.e. norm l_p in R^2); Default value is 2 (Euclidean norm). :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). :returns: float, the total persistence of the diagram (that is, its distance to the empty diagram). ''' Xdiag = _proj_on_diag(X) @@ -66,8 +66,8 @@ def wasserstein_distance(X, Y, 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 internal_p: Ground metric on the (upper-half) plane (i.e. norm l_p in R^2); Default value is 2 (euclidean norm). :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). :returns: the Wasserstein distance of order q (1 <= q < infinity) between persistence diagrams with respect to the internal_p-norm as ground metric. :rtype: float ''' |