more optimizer doc

doc/tutorials/advanced/optimization.txt

@@ -211,12 +211,49 @@ for this somewhere in the future.
 Local optimization
 ------------------
 
+The local version of the above code would be the following:
 
 
+.. code-block:: python
+   
+   class LocalSimplify(gof.LocalOptimizer):
+       def transform(self, node):
+           if node.op == div:
+               x, y = node.inputs
+               if x.owner and x.owner.op == mul:
+                   a, b = x.owner.inputs
+                   if y == a:
+                       return [b]
+                   elif y == b:
+                       return [a]
+           return False
+   
+   local_simplify = LocalSimplify()
 
+The definition of transform is the inner loop of the global optimizer,
+where the node is given as argument. If no changes are to be made,
+False must be returned. Else, a list of what to replace the node's
+outputs with must be returned.
 
+In order to apply the local optimizer we must use it in conjunction
+with a :ref:`navigator`. You can follow this :ref:`link <navigator>`
+for further documentation, but basically a Navigator is a global
+optimizer that loops through all nodes in the graph (or a well-defined
+subset of them) and applies one or several local optimizers on them.
 
+>>> x = double('x')
+>>> y = double('y')
+>>> z = double('z')
+>>> a = add(z, mul(div(mul(y, x), y), div(z, x)))
+>>> e = gof.Env([x, y, z], [a])
+>>> e
+[add(z, mul(div(mul(y, x), y), div(z, x)))]
+>>> simplify = gof.TopoOptimizer([local_simplify])
+>>> simplify.optimize(e)
+>>> e
+[add(z, mul(x, div(z, x)))]
 
+TODO: test this.
 
 
 The optimization database (optdb)