Corrected grad of abs() in complex case.

theano/scalar/basic.py

@@ -1114,11 +1114,9 @@ class Abs(UnaryScalarOp):
         return numpy.abs(x)
     def grad(self, (x, ), (gz, )):
         if x.type in grad_types:
-          return gz * sgn(x),
+            return gz * x / abs(x), # formula works for complex and real
         else:
-          return None,
-        #backport
-        #return gz * sgn(x) if x.type in grad_types else None,
+            return None,
     def c_code(self, node, name, (x, ), (z, ), sub):
         type = node.inputs[0].type
         if type in int_types:

theano/tensor/tests/test_complex.py

@@ -64,3 +64,12 @@ class TestRealImag(unittest.TestCase):
         mval = numpy.asarray(rng.randn(2,5))
         utt.verify_grad(f, [mval])
 
+
+    def test_abs_grad(self):
+        def f(m):
+            c = complex(m[0], m[1])
+            return .5 * abs(c)
+
+        rng = numpy.random.RandomState(9333)
+        mval = numpy.asarray(rng.randn(2,5))
+        utt.verify_grad(f, [mval])