update documenation

Author: rflamary

ot/gromov.py

@@ -338,6 +338,10 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', log=False, armijo=F
     - :math:`\mathbf{q}`: distribution in the target space
     - `L`: loss function to account for the misfit between the similarity matrices
 
+    .. note:: This function is backend-compatible and will work on arrays
+        from all compatible backends. But the algorithm uses the C++ CPU backend
+        which can lead to copy overhead on GPU arrays.
+
     Parameters
     ----------
     C1 : array-like, shape (ns, ns)
@@ -436,6 +440,10 @@ def gromov_wasserstein2(C1, C2, p, q, loss_fun='square_loss', log=False, armijo=
     Note that when using backends, this loss function is differentiable wrt the
     marices and weights for quadratic loss using the gradients from [38]_.
 
+    .. note:: This function is backend-compatible and will work on arrays
+        from all compatible backends. But the algorithm uses the C++ CPU backend
+        which can lead to copy overhead on GPU arrays.
+
     Parameters
     ----------
     C1 : array-like, shape (ns, ns)
@@ -545,6 +553,10 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5,
     - :math:`\mathbf{p}` and :math:`\mathbf{q}` are source and target weights (sum to 1)
     - `L` is a loss function to account for the misfit between the similarity matrices
 
+    .. note:: This function is backend-compatible and will work on arrays
+        from all compatible backends. But the algorithm uses the C++ CPU backend
+        which can lead to copy overhead on GPU arrays.
+
     The algorithm used for solving the problem is conditional gradient as discussed in :ref:`[24] <references-fused-gromov-wasserstein>`
 
     Parameters
@@ -645,6 +657,10 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5
     The algorithm used for solving the problem is conditional gradient as
     discussed in :ref:`[24] <references-fused-gromov-wasserstein2>`
 
+    .. note:: This function is backend-compatible and will work on arrays
+        from all compatible backends. But the algorithm uses the C++ CPU backend
+        which can lead to copy overhead on GPU arrays.
+
     Note that when using backends, this loss function is differentiable wrt the
     marices and weights for quadratic loss using the gradients from [38]_.
 

ot/lp/__init__.py

@@ -222,7 +222,8 @@ def emd(a, b, M, numItermax=100000, log=False, center_dual=True, numThreads=1):
         format
 
     .. note:: This function is backend-compatible and will work on arrays
-        from all compatible backends.
+        from all compatible backends. But the algorithm uses the C++ CPU backend
+        which can lead to copy overhead on GPU arrays.
 
     Uses the algorithm proposed in :ref:`[1] <references-emd>`.
 
@@ -360,7 +361,8 @@ def emd2(a, b, M, processes=1,
     - :math:`\mathbf{a}` and :math:`\mathbf{b}` are the sample weights
 
     .. note:: This function is backend-compatible and will work on arrays
-        from all compatible backends.
+        from all compatible backends. But the algorithm uses the C++ CPU backend
+        which can lead to copy overhead on GPU arrays.
 
     Uses the algorithm proposed in :ref:`[1] <references-emd2>`.
 

ot/weak.py

@@ -33,7 +33,8 @@ def weak_optimal_transport(Xa, Xb, a=None, b=None, verbose=False, log=False, G0=
 
 
     .. note:: This function is backend-compatible and will work on arrays
-        from all compatible backends.
+        from all compatible backends. But the algorithm uses the C++ CPU backend
+        which can lead to copy overhead on GPU arrays.
 
     Uses the conditional gradient algorithm to solve the problem proposed
     in :ref:`[39] <references-weak>`.