From 17aaa979e4cdfe5faed9b2750d452171de4b67e1 Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Fri, 17 Apr 2020 22:13:29 +0200 Subject: Simplify distance-to-diagonal in Wasserstein --- src/python/gudhi/wasserstein/wasserstein.py | 24 +++++++++++------------- 1 file changed, 11 insertions(+), 13 deletions(-) (limited to 'src/python/gudhi/wasserstein') diff --git a/src/python/gudhi/wasserstein/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py index 35315939..5df66cf9 100644 --- a/src/python/gudhi/wasserstein/wasserstein.py +++ b/src/python/gudhi/wasserstein/wasserstein.py @@ -15,16 +15,19 @@ try: except ImportError: print("POT (Python Optimal Transport) package is not installed. Try to run $ conda install -c conda-forge pot ; or $ pip install POT") -def _proj_on_diag(X): +def _dist_to_diag(X, internal_p): ''' :param X: (n x 2) array encoding the points of a persistent diagram. - :returns: (n x 2) array encoding the (respective orthogonal) projections of the points onto the diagonal + :param internal_p: Ground metric (i.e. norm L^p). + :returns: (n) array encoding the (respective orthogonal) distances of the points to the diagonal + + .. note:: + Assumes that the points are above the diagonal. ''' - Z = (X[:,0] + X[:,1]) / 2. - return np.array([Z , Z]).T + return (X[:, 1] - X[:, 0]) * 2 ** (1.0 / internal_p - 1) -def _build_dist_matrix(X, Y, order=2., internal_p=2.): +def _build_dist_matrix(X, Y, order, internal_p): ''' :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. @@ -36,16 +39,12 @@ def _build_dist_matrix(X, Y, order=2., internal_p=2.): and its orthogonal projection onto the diagonal. note also that C[n, m] = 0 (it costs nothing to move from the diagonal to the diagonal). ''' - Xdiag = _proj_on_diag(X) - Ydiag = _proj_on_diag(Y) + Cxd = _dist_to_diag(X, internal_p)**order + Cdy = _dist_to_diag(Y, internal_p)**order if np.isinf(internal_p): C = sc.cdist(X,Y, metric='chebyshev')**order - Cxd = np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order - Cdy = np.linalg.norm(Y - Ydiag, ord=internal_p, axis=1)**order else: C = sc.cdist(X,Y, metric='minkowski', p=internal_p)**order - Cxd = np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order - Cdy = np.linalg.norm(Y - Ydiag, ord=internal_p, axis=1)**order Cf = np.hstack((C, Cxd[:,None])) Cdy = np.append(Cdy, 0) @@ -61,8 +60,7 @@ def _perstot(X, order, internal_p): :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) - return (np.sum(np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order))**(1./order) + return np.linalg.norm(_dist_to_diag(X, internal_p), ord=order) def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2.): -- cgit v1.2.3