From f93c403b81b4ccb98bfad8e4ef30cdf0e7333f6c Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Sat, 18 Apr 2020 23:52:12 +0200 Subject: enable_autodiff for POT wasserstein_distance --- src/python/gudhi/wasserstein/wasserstein.py | 64 ++++++++++++++++++++++++----- 1 file changed, 53 insertions(+), 11 deletions(-) (limited to 'src/python/gudhi/wasserstein') diff --git a/src/python/gudhi/wasserstein/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py index 5df66cf9..9660b99b 100644 --- a/src/python/gudhi/wasserstein/wasserstein.py +++ b/src/python/gudhi/wasserstein/wasserstein.py @@ -53,17 +53,30 @@ def _build_dist_matrix(X, Y, order, internal_p): return Cf -def _perstot(X, order, internal_p): +def _perstot_autodiff(X, order, internal_p): + ''' + Version of _perstot that works on eagerpy tensors. + ''' + return _dist_to_diag(X, internal_p).norms.lp(order) + +def _perstot(X, order, internal_p, enable_autodiff): ''' :param X: (n x 2) numpy.array (points of a given diagram). :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). + :param enable_autodiff: If X is torch.tensor, tensorflow.Tensor or jax.numpy.ndarray, make the computation + transparent to automatic differentiation. + :type enable_autodiff: bool :returns: float, the total persistence of the diagram (that is, its distance to the empty diagram). ''' - return np.linalg.norm(_dist_to_diag(X, internal_p), ord=order) + if enable_autodiff: + import eagerpy as ep + return _perstot_autodiff(ep.astensor(X), order, internal_p).raw + else: + return np.linalg.norm(_dist_to_diag(X, internal_p), ord=order) -def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2.): +def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2., enable_autodiff=False): ''' :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). @@ -74,6 +87,9 @@ def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2.): :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). + :param enable_autodiff: If X and Y are torch.tensor, tensorflow.Tensor or jax.numpy.ndarray, make the computation + transparent to automatic differentiation. + :type enable_autodiff: bool :returns: the Wasserstein distance of order q (1 <= q < infinity) between persistence diagrams with respect to the internal_p-norm as ground metric. If matching is set to True, also returns the optimal matching between X and Y. @@ -82,23 +98,30 @@ def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2.): m = len(Y) # handle empty diagrams - if X.size == 0: - if Y.size == 0: + if n == 0: + if m == 0: if not matching: + # What if enable_autodiff? return 0. else: return 0., np.array([]) else: if not matching: - return _perstot(Y, order, internal_p) + return _perstot(Y, order, internal_p, enable_autodiff) else: - return _perstot(Y, order, internal_p), np.array([[-1, j] for j in range(m)]) - elif Y.size == 0: + return _perstot(Y, order, internal_p, enable_autodiff), np.array([[-1, j] for j in range(m)]) + elif m == 0: if not matching: - return _perstot(X, order, internal_p) + return _perstot(X, order, internal_p, enable_autodiff) else: - return _perstot(X, order, internal_p), np.array([[i, -1] for i in range(n)]) - + return _perstot(X, order, internal_p, enable_autodiff), np.array([[i, -1] for i in range(n)]) + + if enable_autodiff: + import eagerpy as ep + X_orig = ep.astensor(X) + Y_orig = ep.astensor(Y) + X = X_orig.numpy() + Y = Y_orig.numpy() M = _build_dist_matrix(X, Y, order=order, internal_p=internal_p) a = np.ones(n+1) # weight vector of the input diagram. Uniform here. a[-1] = m @@ -106,6 +129,7 @@ def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2.): b[-1] = n if matching: + assert not enable_autodiff, "matching and enable_autodiff are currently incompatible" P = ot.emd(a=a,b=b,M=M, numItermax=2000000) ot_cost = np.sum(np.multiply(P,M)) P[-1, -1] = 0 # Remove matching corresponding to the diagonal @@ -115,6 +139,24 @@ def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2.): match[:,1][match[:,1] >= m] = -1 return ot_cost ** (1./order) , match + if enable_autodiff: + P = ot.emd(a=a,b=b,M=M, numItermax=2000000) + pairs = np.argwhere(P[:-1, :-1]) + diag2 = np.nonzero(P[-1, :-1]) + diag1 = np.nonzero(P[:-1, -1]) + dists = [] + # empty arrays are not handled properly by the helpers, so we avoid calling them + if len(pairs): + dists.append((Y_orig[pairs[:, 1]] - X_orig[pairs[:, 0]]).norms.lp(internal_p, axis=-1).norms.lp(order)) + if len(diag1): + dists.append(_perstot_autodiff(X_orig[diag1], order, internal_p)) + if len(diag2): + dists.append(_perstot_autodiff(Y_orig[diag2], order, internal_p)) + dists = [ dist.reshape(1) for dist in dists ] + return ep.concatenate(dists).norms.lp(order) + # Should just compute the L^order norm manually? + # We can also concatenate the 3 vectors to compute just one norm. + # Comptuation of the otcost using the ot.emd2 library. # Note: it is the Wasserstein distance to the power q. # The default numItermax=100000 is not sufficient for some examples with 5000 points, what is a good value? -- cgit v1.2.3