Add comparison to POT

tests/mappings/test_barycenter.py

@@ -3,6 +3,7 @@
 import numpy as np
 import pytest
 import torch
+import ot
 
 from fugw.mappings import FUGWBarycenter
 from fugw.utils import _init_mock_distribution
@@ -121,3 +122,66 @@ def test_identity_case(alpha):
         # by the number of voxels
         for plan in plans:
             assert torch.allclose(plan, torch.eye(n_voxels) / n_voxels)
+
+
+@pytest.mark.parametrize(
+    "alpha",
+    alphas,
+)
+def test_fgw_barycenter(alpha):
+    """Tests the FUGW barycenter in the case rho=inf and compare with POT."""
+    torch.manual_seed(0)
+    n_subjects = 3
+    n_features = 1
+    n_voxels = 5
+    nits_barycenter = 2
+
+    geometry = _init_mock_distribution(
+        n_features, n_voxels, should_normalize=True
+    )[2]
+    geometry_list = [geometry for _ in range(n_subjects)]
+    weights_list = [torch.ones(n_voxels) / n_voxels] * n_subjects
+    features_list = [torch.tensor([[1.0, 2.0, 3.0, 4.0, 5.0]])] * n_subjects
+
+    fugw_barycenter = FUGWBarycenter(
+        alpha=alpha,
+        rho=float("inf"),
+        eps=1e-6,
+    )
+
+    fugw_barycenter = FUGWBarycenter(alpha=alpha, eps=1e-6, rho=float("inf"))
+    (
+        fugw_bary_weights,
+        fugw_bary_features,
+        fugw_bary_geometry,
+        _,
+        _,
+        _,
+    ) = fugw_barycenter.fit(
+        weights_list,
+        features_list,
+        geometry_list,
+        solver_params={"nits_bcd": 5, "nits_uot": 100},
+        nits_barycenter=nits_barycenter,
+        device=torch.device("cpu"),
+        init_barycenter_geometry=geometry_list[0],
+        init_barycenter_features=features_list[0],
+    )
+
+    # Compare the barycenter with the one obtained with POT
+    pot_bary_features, pot_bary_geometry, log = ot.gromov.fgw_barycenters(
+        n_voxels,
+        [features.T for features in features_list],
+        geometry_list,
+        weights_list,
+        alpha=1 - alpha,
+        log=True,
+        fixed_structure=True,
+        init_C=geometry_list[0],
+    )
+
+    assert torch.allclose(fugw_bary_geometry, pot_bary_geometry)
+    assert torch.allclose(fugw_bary_weights, log["p"])
+
+    if alpha != 1.0:
+        assert torch.allclose(fugw_bary_features, pot_bary_features.T)