[MRG] Fix entropic regularization in gcg

RELEASES.md

@@ -45,6 +45,7 @@ This new release adds support for sparse cost matrices and a new lazy EMD solver
 - Reverting the openmp fix on macOS (PR #789) for macOS (PR #797)
 - Align documentation build dependencies and doc extras (PR #801)
 - Debug Debug linux test core dump (PR #815)
+- Fix entropic regularization in `gcg`(PR #817, Issue #758)
 - Fix documentation build on master with submodules (PR #818)
 
 ## 0.9.6.post1

ot/optim.py

@@ -910,7 +910,7 @@ def line_search(cost, G, deltaG, Mi, cost_G, df_G, **kwargs):
         f,
         df,
         reg2,
-        reg1,
+        None,
         lp_solver,
         line_search,
         G0=G0,

test/test_optim.py

@@ -123,6 +123,37 @@ def fb(G):
     np.testing.assert_allclose(b, Gb.sum(0), atol=1e-05)
 
 
+def test_gcg_no_reg():
+    n = 100
+    X = ot.datasets.make_2D_samples_gauss(n, m=[0, 0], sigma=np.eye(2))
+    Y = ot.datasets.make_2D_samples_gauss(n, m=[1, 1], sigma=np.eye(2))
+
+    a = ot.unif(n)
+    b = ot.unif(n)
+
+    M = ot.dist(X, Y)
+    M /= M.max()
+
+    eps = 1e-2
+
+    G_gcg = ot.optim.gcg(
+        a,
+        b,
+        M,
+        eps,
+        0.0,
+        lambda x: 0.0,
+        lambda x: np.zeros(x.shape),
+        numInnerItermax=1000,
+        numItermax=10,
+    )
+    G_sinkhorn = ot.sinkhorn(a, b, M, eps, numItermax=1000)
+
+    np.testing.assert_allclose(G_gcg, G_sinkhorn, atol=1e-12)
+    np.testing.assert_allclose(a, G_gcg.sum(1), atol=1e-5)
+    np.testing.assert_allclose(b, G_gcg.sum(0), atol=1e-5)
+
+
 def test_solve_1d_linesearch_quad_funct():
     np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(1, -1), 0.5)
     np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(-1, 5), 0)