add test free support barycenter algorithm + cleaning

1 files changed, 1 insertions, 81 deletions

diff --git a/ot/lp/cvx.py b/ot/lp/cvx.py
index c097f58..8e763be 100644
--- a/ot/lp/cvx.py
+++ b/ot/lp/cvx.py
@@ -10,7 +10,7 @@ LP solvers for optimal transport using cvxopt
 import numpy as np
 import scipy as sp
 import scipy.sparse as sps
-import ot
+
 
 try:
     import cvxopt
@@ -145,83 +145,3 @@ def barycenter(A, M, weights=None, verbose=False, log=False, solver='interior-po
         return b, sol
     else:
         return b
-
-
-def free_support_barycenter(measures_locations, measures_weights, X_init, b, weights=None, numItermax=100, stopThr=1e-6, verbose=False):
-    """
-    Solves the free support (locations of the barycenters are optimized, not the weights) Wasserstein barycenter problem (i.e. the weighted Frechet mean for the 2-Wasserstein distance)
-
-    The function solves the Wasserstein barycenter problem when the barycenter measure is constrained to be supported on k atoms.
-    This problem is considered in [1] (Algorithm 2). There are two differences with the following codes:
-    - we do not optimize over the weights
-    - we do not do line search for the locations updates, we use i.e. theta = 1 in [1] (Algorithm 2). This can be seen as a discrete implementation of the fixed-point algorithm of [2] proposed in the continuous setting.
-
-    Parameters
-    ----------
-    data_positions : list of (k_i,d) np.ndarray
-        The discrete support of a measure supported on k_i locations of a d-dimensional space (k_i can be different for each element of the list)
-    data_weights : list of (k_i,) np.ndarray
-        Numpy arrays where each numpy array has k_i non-negatives values summing to one representing the weights of each discrete input measure
-
-    X_init : (k,d) np.ndarray
-        Initialization of the support locations (on k atoms) of the barycenter
-    b : (k,) np.ndarray
-        Initialization of the weights of the barycenter (non-negatives, sum to 1)
-    weights : (k,) np.ndarray
-        Initialization of the coefficients of the barycenter (non-negatives, sum to 1)
-
-    numItermax : int, optional
-        Max number of iterations
-    stopThr : float, optional
-        Stop threshol on error (>0)
-    verbose : bool, optional
-        Print information along iterations
-    log : bool, optional
-        record log if True
-
-    Returns
-    -------
-    X : (k,d) np.ndarray
-        Support locations (on k atoms) of the barycenter
-
-    References
-    ----------
-
-    .. [1] Cuturi, Marco, and Arnaud Doucet. "Fast computation of Wasserstein barycenters." International Conference on Machine Learning. 2014.
-
-    .. [2]  Álvarez-Esteban, Pedro C., et al. "A fixed-point approach to barycenters in Wasserstein space." Journal of Mathematical Analysis and Applications 441.2 (2016): 744-762.
-
-    """
-
-    iter_count = 0
-
-    d = X_init.shape[1]
-    k = b.size
-    N = len(measures_locations)
-
-    if not weights:
-        weights = np.ones((N,)) / N
-
-    X = X_init
-
-    displacement_square_norm = stopThr + 1.
-
-    while (displacement_square_norm > stopThr and iter_count < numItermax):
-
-        T_sum = np.zeros((k, d))
-
-        for (measure_locations_i, measure_weights_i, weight_i) in zip(measures_locations, measures_weights, weights.tolist()):
-
-            M_i = ot.dist(X, measure_locations_i)
-            T_i = ot.emd(b, measure_weights_i, M_i)
-            T_sum = T_sum + weight_i * np.reshape(1. / b, (-1, 1)) * np.matmul(T_i, measure_locations_i)
-
-        displacement_square_norm = np.sum(np.square(X - T_sum))
-        X = T_sum
-
-        if verbose:
-            print('iteration %d, displacement_square_norm=%f\n', iter_count, displacement_square_norm)
-
-        iter_count += 1
-
-    return X