speed up scan forced_replace by not recursing and making less objects.

theano/scan_module/scan_utils.py

@@ -1329,6 +1329,9 @@ def forced_replace(out, x, y):
     x := sigmoid(wu)
     forced_replace(out, x, y) := y*(1-y)
 
+    Note
+    ----
+    When it find a match, it don't continue on the corresponding inputs.
     """
     if out is None:
         return None
@@ -1336,18 +1339,18 @@ def forced_replace(out, x, y):
     # ``visited`` is a set of nodes that are already known and don't need to be
     # checked again, speeding up the traversal of multiply-connected graphs.
     visited = set()
-    def local_traverse(graph, x):
+    from collections import deque
+    q = deque()
+    q.append(out)
+    to_replace = []
+    while q:
+        graph = q.popleft()
         if graph in visited:
-            return []
+            continue
         visited.add(graph)
         if equal_computations([graph], [x]):
-            return [graph]
-        elif not graph.owner:
-            return []
-        else:
-            rval = []
-            for inp in graph.owner.inputs:
-                rval += local_traverse(inp, x)
-            return rval
-    to_replace = local_traverse(out, x)
-    return clone(out, replace=OrderedDict((v, y) for v in to_replace))
+            to_replace.append((graph, y))
+        elif graph.owner:
+            q.extendleft(graph.owner.inputs)
+
+    return clone(out, replace=to_replace)