[Feat] Provide derivatives for pow (#246)

* [Feat] Provide manual derivatives for __pow__

* [Feat] Also applied changes to rpow

* [Test] Another pow test added.

Author: fjosw

pyerrors/obs.py

@@ -856,15 +856,12 @@ def __rtruediv__(self, y):
 
     def __pow__(self, y):
         if isinstance(y, Obs):
-            return derived_observable(lambda x: x[0] ** x[1], [self, y])
+            return derived_observable(lambda x, **kwargs: x[0] ** x[1], [self, y], man_grad=[y.value * self.value ** (y.value - 1), self.value ** y.value * np.log(self.value)])
         else:
-            return derived_observable(lambda x: x[0] ** y, [self])
+            return derived_observable(lambda x, **kwargs: x[0] ** y, [self], man_grad=[y * self.value ** (y - 1)])
 
     def __rpow__(self, y):
-        if isinstance(y, Obs):
-            return derived_observable(lambda x: x[0] ** x[1], [y, self])
-        else:
-            return derived_observable(lambda x: y ** x[0], [self])
+        return derived_observable(lambda x, **kwargs: y ** x[0], [self], man_grad=[y ** self.value * np.log(y)])
 
     def __abs__(self):
         return derived_observable(lambda x: anp.abs(x[0]), [self])

tests/obs_test.py

@@ -461,6 +461,18 @@ def test_cobs_overloading():
     obs / cobs
 
 
+def test_pow():
+    data = [1, 2.341, pe.pseudo_Obs(4.8, 0.48, "test_obs"), pe.cov_Obs(1.1, 0.3 ** 2, "test_cov_obs")]
+
+    for d in data:
+        assert d * d == d ** 2
+        assert d * d * d == d ** 3
+
+        for d2 in data:
+            assert np.log(d ** d2) == d2 * np.log(d)
+            assert (d ** d2) ** (1 / d2) == d
+
+
 def test_reweighting():
     my_obs = pe.Obs([np.random.rand(1000)], ['t'])
     assert not my_obs.reweighted