From dd96965e521313b6210391f511c82cced9b2a950 Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 6 Apr 2020 19:37:58 +0200 Subject: Remove trailing whitespace --- src/python/gudhi/wasserstein/barycenter.py | 42 ++++++++++++++--------------- src/python/gudhi/wasserstein/wasserstein.py | 14 +++++----- 2 files changed, 28 insertions(+), 28 deletions(-) (limited to 'src/python/gudhi/wasserstein') diff --git a/src/python/gudhi/wasserstein/barycenter.py b/src/python/gudhi/wasserstein/barycenter.py index 99f29a1e..de7aea81 100644 --- a/src/python/gudhi/wasserstein/barycenter.py +++ b/src/python/gudhi/wasserstein/barycenter.py @@ -18,7 +18,7 @@ from gudhi.wasserstein import wasserstein_distance def _mean(x, m): ''' :param x: a list of 2D-points, off diagonal, x_0... x_{k-1} - :param m: total amount of points taken into account, + :param m: total amount of points taken into account, that is we have (m-k) copies of diagonal :returns: the weighted mean of x with (m-k) copies of the diagonal ''' @@ -33,14 +33,14 @@ def _mean(x, m): def lagrangian_barycenter(pdiagset, init=None, verbose=False): ''' - :param pdiagset: a list of ``numpy.array`` of shape `(n x 2)` - (`n` can variate), encoding a set of - persistence diagrams with only finite coordinates. - :param init: The initial value for barycenter estimate. - If ``None``, init is made on a random diagram from the dataset. - Otherwise, it can be an ``int`` + :param pdiagset: a list of ``numpy.array`` of shape `(n x 2)` + (`n` can variate), encoding a set of + persistence diagrams with only finite coordinates. + :param init: The initial value for barycenter estimate. + If ``None``, init is made on a random diagram from the dataset. + Otherwise, it can be an ``int`` (then initialization is made on ``pdiagset[init]``) - or a `(n x 2)` ``numpy.array`` enconding + or a `(n x 2)` ``numpy.array`` enconding a persistence diagram with `n` points. :type init: ``int``, or (n x 2) ``np.array`` :param verbose: if ``True``, returns additional information about the @@ -48,16 +48,16 @@ def lagrangian_barycenter(pdiagset, init=None, verbose=False): :type verbose: boolean :returns: If not verbose (default), a ``numpy.array`` encoding the barycenter estimate of pdiagset - (local minimum of the energy function). + (local minimum of the energy function). If ``pdiagset`` is empty, returns ``None``. If verbose, returns a couple ``(Y, log)`` where ``Y`` is the barycenter estimate, and ``log`` is a ``dict`` that contains additional informations: - `"groupings"`, a list of list of pairs ``(i,j)``. - Namely, ``G[k] = [...(i, j)...]``, where ``(i,j)`` indicates + Namely, ``G[k] = [...(i, j)...]``, where ``(i,j)`` indicates that ``pdiagset[k][i]`` is matched to ``Y[j]`` - if ``i = -1`` or ``j = -1``, it means they + if ``i = -1`` or ``j = -1``, it means they represent the diagonal. - `"energy"`, ``float`` representing the Frechet energy value obtained. @@ -70,13 +70,13 @@ def lagrangian_barycenter(pdiagset, init=None, verbose=False): if m == 0: print("Warning: computing barycenter of empty diag set. Returns None") return None - + # store the number of off-diagonal point for each of the X_i - nb_off_diag = np.array([len(X_i) for X_i in X]) + nb_off_diag = np.array([len(X_i) for X_i in X]) # Initialisation of barycenter if init is None: i0 = np.random.randint(m) # Index of first state for the barycenter - Y = X[i0].copy() + Y = X[i0].copy() else: if type(init)==int: Y = X[init].copy() @@ -90,8 +90,8 @@ def lagrangian_barycenter(pdiagset, init=None, verbose=False): nb_iter += 1 K = len(Y) # current nb of points in Y (some might be on diagonal) G = np.full((K, m), -1, dtype=int) # will store for each j, the (index) - # point matched in each other diagram - #(might be the diagonal). + # point matched in each other diagram + #(might be the diagonal). # that is G[j, i] = k <=> y_j is matched to # x_k in the diagram i-th diagram X[i] updated_points = np.zeros((K, 2)) # will store the new positions of @@ -111,7 +111,7 @@ def lagrangian_barycenter(pdiagset, init=None, verbose=False): else: # ...which is a diagonal point G[y_j, i] = -1 # -1 stands for the diagonal (mask) else: # We matched a diagonal point to x_i_j... - if x_i_j >= 0: # which is a off-diag point ! + if x_i_j >= 0: # which is a off-diag point ! # need to create new point in Y new_y = _mean(np.array([X[i][x_i_j]]), m) # Average this point with (m-1) copies of Delta @@ -123,19 +123,19 @@ def lagrangian_barycenter(pdiagset, init=None, verbose=False): matched_points = [X[i][G[j, i]] for i in range(m) if G[j, i] > -1] new_y_j = _mean(matched_points, m) if not np.array_equal(new_y_j, np.array([0,0])): - updated_points[j] = new_y_j + updated_points[j] = new_y_j else: # this points is no longer of any use. to_delete.append(j) # we remove the point to be deleted now. - updated_points = np.delete(updated_points, to_delete, axis=0) + updated_points = np.delete(updated_points, to_delete, axis=0) # we cannot converge if there have been new created points. - if new_created_points: + if new_created_points: Y = np.concatenate((updated_points, new_created_points)) else: # Step 3 : we check convergence if np.array_equal(updated_points, Y): - converged = True + converged = True Y = updated_points diff --git a/src/python/gudhi/wasserstein/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py index e1233eec..35315939 100644 --- a/src/python/gudhi/wasserstein/wasserstein.py +++ b/src/python/gudhi/wasserstein/wasserstein.py @@ -30,9 +30,9 @@ def _build_dist_matrix(X, Y, order=2., internal_p=2.): :param Y: (m x 2) numpy.array encoding the second diagram. :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 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], - while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) + :returns: (n+1) x (m+1) np.array encoding the cost matrix C. + For 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], + while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) 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). ''' @@ -59,7 +59,7 @@ def _perstot(X, order, internal_p): :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). - :returns: float, the total persistence of the diagram (that is, its distance to the empty diagram). + :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) @@ -67,16 +67,16 @@ def _perstot(X, order, internal_p): 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 + :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 a (n x 2) np.array [...[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); + :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 + :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. ''' -- cgit v1.2.3