Add id_interpolation to sparse mappings transforms

src/fugw/mappings/sparse.py

@@ -305,7 +305,9 @@ def fit(
 
         return self
 
-    def transform(self, source_features, device="auto"):
+    def transform(
+        self, source_features, id_interpolation=False, device="auto"
+    ):
         """
         Transport source feature maps using fitted OT plan.
         Use GPUs if available.
@@ -314,6 +316,9 @@ def transform(self, source_features, device="auto"):
         ----------
         source_features: ndarray(n_samples, n) or ndarray(n)
             Contrast map for source subject
+        id_interpolation: bool, optional, defaults to False
+            If True and source/target share the same geometry,
+            interpolate the transport plan with the identity.
         device: "auto" or torch.device
             If "auto": use first available GPU if it's available,
             CPU otherwise.
@@ -346,23 +351,51 @@ def transform(self, source_features, device="auto"):
             )
 
         # Transform data
-        transformed_data = (
-            (
-                torch.sparse.mm(
-                    self.pi.to(device).transpose(0, 1),
-                    source_features_tensor.T,
-                ).to_dense()
-                / (
-                    torch.sparse.sum(self.pi.to(device), dim=0)
-                    .to_dense()
-                    .reshape(-1, 1)
-                    # Add very small value to handle null rows
-                    + 1e-16
+        if id_interpolation:
+            if self.pi.shape[0] != self.pi.shape[1]:
+                raise ValueError(
+                    "Cannot interpolate with identity if source and target"
+                    " have different geometries."
+                )
+            transformed_data = (
+                (
+                    (
+                        torch.sparse.mm(
+                            self.pi.to(device).transpose(0, 1),
+                            source_features_tensor.T,
+                        ).to_dense()
+                        / (
+                            torch.sparse.sum(self.pi.to(device), dim=0)
+                            .to_dense()
+                            .reshape(-1, 1)
+                            # Add very small value to handle null rows
+                            + 1e-16
+                        )
+                        + source_features_tensor.T
+                    )
+                    / 2
                 )
+                .T.detach()
+                .cpu()
+            )
+        else:
+            transformed_data = (
+                (
+                    torch.sparse.mm(
+                        self.pi.to(device).transpose(0, 1),
+                        source_features_tensor.T,
+                    ).to_dense()
+                    / (
+                        torch.sparse.sum(self.pi.to(device), dim=0)
+                        .to_dense()
+                        .reshape(-1, 1)
+                        # Add very small value to handle null rows
+                        + 1e-16
+                    )
+                )
+                .T.detach()
+                .cpu()
             )
-            .T.detach()
-            .cpu()
-        )
 
         # Free allocated GPU memory
         del source_features_tensor