correct emd2 and add centering for dual potentials

Author: rflamary

ot/lp/__init__.py

@@ -264,13 +264,19 @@ def emd(a, b, M, numItermax=100000, log=False, dense=True, center_dual=True):
     if dense:
         G, cost, u, v, result_code = emd_c(a, b, M, numItermax, dense)
 
+        if center_dual:
+            u, v = center_ot_dual(u, v, a, b)
+
         if np.any(~asel) or np.any(~bsel):
             u, v = estimate_dual_null_weights(u, v, a, b, M)
 
     else:
         Gv, iG, jG, cost, u, v, result_code = emd_c(a, b, M, numItermax, dense)
         G = coo_matrix((Gv, (iG, jG)), shape=(a.shape[0], b.shape[0]))
 
+        if center_dual:
+            u, v = center_ot_dual(u, v, a, b)
+
         if np.any(~asel) or np.any(~bsel):
             u, v = estimate_dual_null_weights(u, v, a, b, M)
 
@@ -287,7 +293,8 @@ def emd(a, b, M, numItermax=100000, log=False, dense=True, center_dual=True):
 
 
 def emd2(a, b, M, processes=multiprocessing.cpu_count(),
-         numItermax=100000, log=False, dense=True, return_matrix=False):
+         numItermax=100000, log=False, dense=True, return_matrix=False,
+         center_dual=True):
     r"""Solves the Earth Movers distance problem and returns the loss
 
     .. math::
@@ -329,6 +336,9 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(),
         If True, returns math:`\gamma` as a dense ndarray of shape (ns, nt).
         Otherwise returns a sparse representation using scipy's `coo_matrix`
         format.
+    center_dual: boolean, optional (default=True)
+        If True, centers the dual potential using function
+        :ref:`center_ot_dual`.
 
     Returns
     -------
@@ -383,14 +393,23 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(),
     assert (a.shape[0] == M.shape[0] and b.shape[0] == M.shape[1]), \
         "Dimension mismatch, check dimensions of M with a and b"
 
+    asel = a != 0
+
     if log or return_matrix:
         def f(b):
+            bsel = b != 0
             if dense:
                 G, cost, u, v, result_code = emd_c(a, b, M, numItermax, dense)
             else:
                 Gv, iG, jG, cost, u, v, result_code = emd_c(a, b, M, numItermax, dense)
                 G = coo_matrix((Gv, (iG, jG)), shape=(a.shape[0], b.shape[0]))
 
+            if center_dual:
+                u, v = center_ot_dual(u, v, a, b)
+
+            if np.any(~asel) or np.any(~bsel):
+                u, v = estimate_dual_null_weights(u, v, a, b, M)
+
             result_code_string = check_result(result_code)
             log = {}
             if return_matrix:
@@ -402,12 +421,19 @@ def f(b):
             return [cost, log]
     else:
         def f(b):
+            bsel = b != 0
             if dense:
                 G, cost, u, v, result_code = emd_c(a, b, M, numItermax, dense)
             else:
                 Gv, iG, jG, cost, u, v, result_code = emd_c(a, b, M, numItermax, dense)
                 G = coo_matrix((Gv, (iG, jG)), shape=(a.shape[0], b.shape[0]))
 
+            if center_dual:
+                u, v = center_ot_dual(u, v, a, b)
+
+            if np.any(~asel) or np.any(~bsel):
+                u, v = estimate_dual_null_weights(u, v, a, b, M)
+
             result_code_string = check_result(result_code)
             check_result(result_code)
             return cost