[WIP] Sparse emd implementation

ot/lp/_network_simplex.py

@@ -10,6 +10,7 @@
 
 import numpy as np
 import warnings
+from scipy.sparse import issparse as scipy_issparse
 
 from ..utils import list_to_array, check_number_threads
 from ..backend import get_backend
@@ -298,10 +299,20 @@ def emd(
     a, b = list_to_array(a, b)
     nx = get_backend(a, b)
 
-    # Check if M is sparse using backend's issparse method
-    is_sparse = nx.issparse(M)
+    # Check if M is sparse (either backend sparse or scipy.sparse)
+    is_sparse = nx.issparse(M) or scipy_issparse(M)
 
     if is_sparse:
+        # Check if backend supports sparse matrices
+        backend_name = nx.__class__.__name__
+        if backend_name in ["JaxBackend", "TensorflowBackend"]:
+            raise NotImplementedError(
+                f"Sparse optimal transport is not supported for {backend_name}. "
+                "JAX does not have native sparse matrix support, and TensorFlow's "
+                "sparse implementation is incomplete. Please convert your sparse "
+                "matrix to dense format using M.toarray() or equivalent before calling emd()."
+            )
+
         # Extract COO data using backend method - returns numpy arrays
         edge_sources, edge_targets, edge_costs, (n1, n2) = nx.sparse_coo_data(M)
 
@@ -572,10 +583,22 @@ def emd2(
     a, b = list_to_array(a, b)
     nx = get_backend(a, b)
 
-    # Check if M is sparse using backend's issparse method
-    is_sparse = nx.issparse(M)
+    # Check if M is sparse (either backend sparse or scipy.sparse)
+    from scipy.sparse import issparse as scipy_issparse
+
+    is_sparse = nx.issparse(M) or scipy_issparse(M)
 
     if is_sparse:
+        # Check if backend supports sparse matrices
+        backend_name = nx.__class__.__name__
+        if backend_name in ["JaxBackend", "TensorflowBackend"]:
+            raise NotImplementedError(
+                f"Sparse optimal transport is not supported for {backend_name}. "
+                "JAX does not have native sparse matrix support, and TensorFlow's "
+                "sparse implementation is incomplete. Please convert your sparse "
+                "matrix to dense format using M.toarray() or equivalent before calling emd2()."
+            )
+
         # Extract COO data using backend method - returns numpy arrays
         edge_sources, edge_targets, edge_costs, (n1, n2) = nx.sparse_coo_data(M)