Don't introduce useless prod op

theano/tensor/opt.py

@@ -4081,28 +4081,29 @@ def local_sum_prod_mul_by_scalar(node):
     """
     # TODO: if the the thing inside the Sum is a division,
     # we should get at the numerator....
-    if isinstance(node.op, T.Sum) or isinstance(node.op, T.elemwise.Prod):
+    if isinstance(node.op, (T.Sum, T.elemwise.Prod)):
         node_inps, = node.inputs
         if node_inps.owner and node_inps.owner.op == T.mul:
             terms = node_inps.owner.inputs
             scalars = [t.dimshuffle() for t in terms if
                        numpy.all(t.type.broadcastable)]
-            non_scalars = [t for t in terms if not numpy.all(t.broadcastable)]
 
             if len(scalars) == 0:
                 # Nothing to optimize here
                 return
 
+            non_scalars = [t for t in terms if not numpy.all(t.broadcastable)]
+
             # Perform the op only on the non-scalar inputs, if applicable
             if len(non_scalars) == 0:
                 new_op_input_nb_elements = 1
                 new_op_output = 1
             elif len(non_scalars) == 1:
-                new_op_input_nb_elements = T.prod(non_scalars[0].shape)
+                new_op_input_nb_elements = non_scalars[0].size
                 new_op_output = node.op(non_scalars[0])
             else:
                 new_op_input = T.mul(*non_scalars)
-                new_op_input_nb_elements = T.prod(new_op_input.shape)
+                new_op_input_nb_elements = new_op_input.size
                 new_op_output = node.op(new_op_input)
 
             # If node.op is a T.elemwise.Prod, then the scalars need to be

theano/tensor/tests/test_opt.py

@@ -4568,7 +4568,7 @@ class T_local_sum_prod(unittest.TestCase):
 
         # Case 2
         test_reduction_opt([vect, scalar1], [v_val, s1_val], T.elemwise.Prod,
-                           (s1_val * v_val).prod(), 2)
+                           (s1_val * v_val).prod(), 1)
 
         # Case 3
         test_reduction_opt([vect, mat, scalar1], [v_val, m_val, s1_val],
@@ -4581,7 +4581,7 @@ class T_local_sum_prod(unittest.TestCase):
         # Case 5
         test_reduction_opt([vect, scalar1, scalar2], [v_val, s1_val, s2_val],
                            T.elemwise.Prod, (s1_val * s2_val * v_val).prod(),
-                           2)
+                           1)
 
         # Case 6
         test_reduction_opt([vect, mat, scalar1, scalar2],

theano/tensor/var.py

@@ -280,7 +280,8 @@ class _tensor_py_operators:
 
     shape = property(lambda self: theano.tensor.basic.shape(self))
 
-    size = property(lambda self: theano.tensor.basic.prod(self.shape))
+    size = property(lambda self: self.shape[0] if self.ndim == 1 else
+                    theano.tensor.basic.prod(self.shape))
 
     # We can't implement __len__ to provide a better error message.
     def any(self, axis=None, keepdims=False):