api: fix corner case for staggered FD

devito/finite_differences/derivative.py

@@ -201,7 +201,7 @@ def _process_x0(cls, dims, **kwargs):
             # Only given a value
             _x0 = kwargs.get('x0')
             assert len(dims) == 1 or _x0 is None
-            if _x0 is not None:
+            if _x0 is not None and _x0 is not dims[0]:
                 x0 = frozendict({dims[0]: _x0})
             else:
                 x0 = frozendict({})
@@ -360,6 +360,10 @@ def _eval_at(self, func):
         # do not overwrite it
         if self.x0 or self.side is not None or func.function is self.expr.function:
             return self
+        # For basic equation of the form f = Derivative(g, ...) we can just
+        # compare staggering
+        if self.expr.staggered == func.staggered:
+            return self
 
         x0 = func.indices_ref._getters
         if self.expr.is_Add:

tests/test_derivatives.py

@@ -713,6 +713,16 @@ def test_deriv_spec(self):
         assert dxy0.x0 == {y: y+y.spacing/2}
         assert dxy02.x0 == {x: x+x.spacing/2}
 
+    def test_deriv_stagg_plain(self):
+        grid = Grid((11, 11))
+        x, y = grid.dimensions
+        f1 = Function(name="f1", grid=grid, space_order=2, staggered=NODE)
+        f2 = Function(name="f2", grid=grid, space_order=2, staggered=NODE)
+
+        eq0 = Eq(f1, f2.laplace).evaluate
+        assert eq0.rhs == f2.laplace.evaluate
+        assert eq0.rhs != 0
+
 
 class TestTwoStageEvaluation: