[MRG] Regularized OT (optim.cg) bug solve (#286)

* Line search stops when derphi is 0 instead of bugging out like in some instances

* pep8 compliance

* Tests

Author: ncassereau

ot/optim.py

@@ -178,9 +178,9 @@ def cg(a, b, M, reg, f, df, G0=None, numItermax=200, numItermaxEmd=100000,
     numItermaxEmd : int, optional
         Max number of iterations for emd
     stopThr : float, optional
-        Stop threshol on the relative variation (>0)
+        Stop threshold on the relative variation (>0)
     stopThr2 : float, optional
-        Stop threshol on the absolute variation (>0)
+        Stop threshold on the absolute variation (>0)
     verbose : bool, optional
         Print information along iterations
     log : bool, optional
@@ -249,6 +249,8 @@ def cost(G):
 
         # line search
         alpha, fc, f_val = solve_linesearch(cost, G, deltaG, Mi, f_val, reg=reg, M=M, Gc=Gc, **kwargs)
+        if alpha is None:
+            alpha = 0.0
 
         G = G + alpha * deltaG
 
@@ -320,9 +322,9 @@ def gcg(a, b, M, reg1, reg2, f, df, G0=None, numItermax=10,
     numInnerItermax : int, optional
         Max number of iterations of Sinkhorn
     stopThr : float, optional
-        Stop threshol on the relative variation (>0)
+        Stop threshold on the relative variation (>0)
     stopThr2 : float, optional
-        Stop threshol on the absolute variation (>0)
+        Stop threshold on the absolute variation (>0)
     verbose : bool, optional
         Print information along iterations
     log : bool, optional

test/test_da.py

@@ -565,6 +565,14 @@ def test_mapping_transport_class():
     otda.fit(Xs=Xs, Xt=Xt)
     assert len(otda.log_.keys()) != 0
 
+    # check that it does not crash when derphi is very close to 0
+    np.random.seed(39)
+    Xs, ys = make_data_classif('3gauss', ns)
+    Xt, yt = make_data_classif('3gauss2', nt)
+    otda = ot.da.MappingTransport(kernel="gaussian", bias=False)
+    otda.fit(Xs=Xs, Xt=Xt)
+    np.random.seed(None)
+
 
 def test_linear_mapping():
     ns = 150

test/test_optim.py

@@ -114,3 +114,28 @@ def test_line_search_armijo():
     # Should not throw an exception and return None for alpha
     alpha, _, _ = ot.optim.line_search_armijo(lambda x: 1, xk, pk, gfk, old_fval)
     assert alpha is None
+
+    # check line search armijo
+    def f(x):
+        return np.sum((x - 5.0) ** 2)
+
+    def grad(x):
+        return 2 * (x - 5.0)
+
+    xk = np.array([[[-5.0, -5.0]]])
+    pk = np.array([[[100.0, 100.0]]])
+    gfk = grad(xk)
+    old_fval = f(xk)
+
+    # chech the case where the optimum is on the direction
+    alpha, _, _ = ot.optim.line_search_armijo(f, xk, pk, gfk, old_fval)
+    np.testing.assert_allclose(alpha, 0.1)
+
+    # check the case where the direction is not far enough
+    pk = np.array([[[3.0, 3.0]]])
+    alpha, _, _ = ot.optim.line_search_armijo(f, xk, pk, gfk, old_fval, alpha0=1.0)
+    np.testing.assert_allclose(alpha, 1.0)
+
+    # check the case where the checking the wrong direction
+    alpha, _, _ = ot.optim.line_search_armijo(f, xk, -pk, gfk, old_fval)
+    assert alpha <= 0