Remove error in hessian if gradient is constant

theano/gradient.py

@@ -1636,12 +1636,17 @@ def hessian(cost, wrt, consider_constant=None,
         assert input.ndim == 1, \
                 "tensor.hessian expects a (list of) 1 dimensional variable "\
                 "as `wrt`"
-        expr = grad(cost, input)
+        expr = grad(cost, input, consider_constant=consider_constant,
+                    disconnected_inputs=disconnected_inputs)
+
+        # It is possible that the inputs are disconnected from expr,
+        # even if they are connected to cost.
+        # This should not be an error.
         hess, updates = theano.scan(lambda i, y, x: grad(
                             y[i],
                             x,
                             consider_constant=consider_constant,
-                            disconnected_inputs=disconnected_inputs),
+                            disconnected_inputs='ignore'),
                        sequences=arange(expr.shape[0]),
                        non_sequences=[expr, input])
         assert not updates, \

theano/tensor/tests/test_basic.py

@@ -3086,6 +3086,28 @@ class T_Join_and_Split(unittest.TestCase):
         assert numpy.allclose(Ha_v, 2.)
         assert numpy.allclose(Hb_v, 2.)
 
+    def test_stack_hessian2(self):
+        # Test the hessian macro when the gradient itself does not depend
+        # on the input (but the cost does)
+        a = tensor.dvector('a')
+        b = tensor.dvector('b')
+        A = stack([a, b])
+        Ha, Hb = hessian(A.sum(), [a, b])
+
+        # Try some values
+        a_v = numpy.random.rand(4)
+        b_v = numpy.random.rand(4)
+        f = theano.function([a, b], [Ha, Hb])
+        Ha_v, Hb_v = f(a_v, b_v)
+        print Ha_v
+        print Hb_v
+        # The Hessian is always a matrix full of 0
+        assert Ha_v.shape == (4, 4)
+        assert Hb_v.shape == (4, 4)
+        assert numpy.allclose(Ha_v, 0.)
+        assert numpy.allclose(Hb_v, 0.)
+
+
     def test_join_concatenate_one_element(self):
         ''' Fast test of concatenate as this is an alias for join.
         also test that we remove the Join op if there is only 1 input'''