add test free support barycenter algorithm + cleaning

1 files changed, 91 insertions, 1 deletions

diff --git a/ot/lp/__init__.py b/ot/lp/__init__.py
index 4c0d170..96bf6de 100644
--- a/ot/lp/__init__.py
+++ b/ot/lp/__init__.py
@@ -17,8 +17,9 @@ from .import cvx
 from .emd_wrap import emd_c, check_result
 from ..utils import parmap
 from .cvx import barycenter
+from ..utils import dist
 
-__all__=['emd', 'emd2', 'barycenter', 'cvx']
+__all__=['emd', 'emd2', 'barycenter', 'free_support_barycenter', 'cvx']
 
 
 def emd(a, b, M, numItermax=100000, log=False):
@@ -216,3 +217,92 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(),
 
     res = parmap(f, [b[:, i] for i in range(nb)], processes)
     return res
+
+
+
+def free_support_barycenter(measures_locations, measures_weights, X_init, b=None, weights=None, numItermax=100, stopThr=1e-7, verbose=False, log=None):
+    """
+    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
+    ----------
+    measures_locations : 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)
+    measures_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
+
+    N = len(measures_locations)
+    k = X_init.shape[0]
+    d = X_init.shape[1]
+    if b is None:
+        b = np.ones((k,))/k
+    if weights is None:
+        weights = np.ones((N,)) / N
+
+    X = X_init
+
+    displacement_square_norms = []
+    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 = dist(X, measure_locations_i)
+            T_i = 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(T_sum-X))
+        if log:
+            displacement_square_norms.append(displacement_square_norm)
+
+        X = T_sum
+
+        if verbose:
+            print('iteration %d, displacement_square_norm=%f\n', iter_count, displacement_square_norm)
+
+        iter_count += 1
+
+    if log:
+        return X, displacement_square_norms
+    else:
+        return X
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