diff options
Diffstat (limited to 'src/python/gudhi/wasserstein.py')
| -rw-r--r-- | src/python/gudhi/wasserstein.py | 34 |
1 files changed, 17 insertions, 17 deletions
diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein.py index 2acf93d6..aef54f64 100644 --- a/src/python/gudhi/wasserstein.py +++ b/src/python/gudhi/wasserstein.py @@ -23,12 +23,12 @@ def _proj_on_diag(X): return np.array([Z , Z]).T -def _build_dist_matrix(X, Y, q=2., internal_p=2.): +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_q). - :param q: exponent for the Wasserstein metric. + :param order: exponent for the Wasserstein metric. :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). @@ -36,13 +36,13 @@ def _build_dist_matrix(X, Y, q=2., internal_p=2.): Xdiag = _proj_on_diag(X) Ydiag = _proj_on_diag(Y) if np.isinf(internal_p): - C = sc.cdist(X,Y, metric='chebyshev')**q - Cxd = np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**q - Cdy = np.linalg.norm(Y - Ydiag, ord=internal_p, axis=1)**q + 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)**q - Cxd = np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**q - Cdy = np.linalg.norm(Y - Ydiag, ord=internal_p, axis=1)**q + 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) @@ -51,23 +51,23 @@ def _build_dist_matrix(X, Y, q=2., internal_p=2.): return Cf -def _perstot(X, q, internal_p): +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 q: exponent for Wasserstein; Default value is 2. + :param order: exponent for Wasserstein; Default value is 2. :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)**q))**(1./q) + return (np.sum(np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order))**(1./order) -def wasserstein_distance(X, Y, q=2., internal_p=2.): +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 q: exponent for Wasserstein; Default value is 2. + :param order: exponent for Wasserstein; Default value is 2. :returns: the q-Wasserstein distance (1 <= q < infinity) with respect to the internal_p-norm as ground metric. :rtype: float ''' @@ -79,11 +79,11 @@ def wasserstein_distance(X, Y, q=2., internal_p=2.): if Y.size == 0: return 0. else: - return _perstot(Y, q, internal_p) + return _perstot(Y, order, internal_p) elif Y.size == 0: - return _perstot(X, q, internal_p) + return _perstot(X, order, internal_p) - M = _build_dist_matrix(X, Y, q=q, internal_p=internal_p) + M = _build_dist_matrix(X, Y, order=order, internal_p=internal_p) a = np.full(n+1, 1. / (n + m) ) # weight vector of the input diagram. Uniform here. a[-1] = a[-1] * m # normalized so that we have a probability measure, required by POT b = np.full(m+1, 1. / (n + m) ) # weight vector of the input diagram. Uniform here. @@ -94,5 +94,5 @@ def wasserstein_distance(X, Y, q=2., internal_p=2.): # The default numItermax=100000 is not sufficient for some examples with 5000 points, what is a good value? ot_cost = (n+m) * ot.emd2(a, b, M, numItermax=2000000) - return ot_cost ** (1./q) + return ot_cost ** (1./order) |