api: add priority to fd coefficients for mixed derivatives

devito/finite_differences/differentiable.py

@@ -11,7 +11,7 @@
 from sympy.core.decorators import call_highest_priority
 from sympy.core.evalf import evalf_table
 
-from devito.finite_differences.tools import make_shift_x0
+from devito.finite_differences.tools import make_shift_x0, coeff_priority
 from devito.logger import warning
 from devito.tools import (as_tuple, filter_ordered, flatten, frozendict,
                           infer_dtype, is_integer, split)
@@ -130,11 +130,8 @@ def coefficients(self):
         coefficients = {f.coefficients for f in self._functions}
         # If there is multiple ones, we have to revert to the highest priority
         # i.e we have to remove symbolic
-        if len(coefficients) == 2:
-            return (coefficients - {'symbolic'}).pop()
-        else:
-            assert len(coefficients) == 1
-            return coefficients.pop()
+        key = lambda x: coeff_priority[x]
+        return sorted(coefficients, key=key, reverse=True)[0]
 
     @cached_property
     def _coeff_symbol(self, *args, **kwargs):

devito/finite_differences/tools.py

@@ -248,6 +248,7 @@ def numeric_weights(function, deriv_order, indices, x0):
 
 fd_weights_registry = {'taylor': numeric_weights, 'standard': numeric_weights,
                        'symbolic': symbolic_weights}
+coeff_priority = {'taylor': 1, 'standard': 1, 'symbolic': 0}
 
 
 def generate_indices(expr, dim, order, side=None, matvec=None, x0=None):

tests/test_symbolic_coefficients.py

@@ -510,3 +510,10 @@ def test_compound_nested_subs(self):
 
         # `str` simply because some objects are of type EvalDerivative
         assert str(eq.evaluate.rhs) == str(term0 + term1 + term2)
+
+    def test_priority(self):
+        grid = Grid(shape=(11,))
+        m = Function(name='m', grid=grid, space_order=2, coefficients='symbolic')
+        p = Function(name='p', grid=grid, space_order=2)
+
+        assert (p*m).coefficients == 'taylor'