Fix action interpolate simplification (#447)

* add comment

* fix with test

Author: leo-collins

test/test_interpolate.py

@@ -35,7 +35,7 @@
 )
 from ufl.algorithms.expand_indices import expand_indices
 from ufl.core.interpolate import Interpolate
-from ufl.form import FormSum
+from ufl.form import Form, FormSum
 from ufl.pullback import identity_pullback
 from ufl.sobolevspace import H1
 
@@ -110,7 +110,7 @@ def test_action_adjoint(V1, V2):
     Iu = Interpolate(u, vstar)
 
     v1 = TrialFunction(V1)
-    Iv = Interpolate(v1, vstar)
+    Iv = Interpolate(v1, vstar)  # V1 -> V2
 
     assert Iv.argument_slots() == (vstar, v1)
     assert Iv.arguments() == (vstar, v1)
@@ -126,6 +126,18 @@ def test_action_adjoint(V1, V2):
     # -- Adjoint -- #
     adjoint(Iv) == Adjoint(Iv)
 
+    # action of one-form on interpolation operator
+    one_form = Argument(V2, 0) * dx
+    action_one_form = action(one_form, Iv)  # adjoint interpolation V2^* -> V1^*
+    assert isinstance(action_one_form, Interpolate)
+    assert action_one_form.arguments() == (Argument(V1, 0),)
+    assert action_one_form.ufl_function_space() == V1.dual()
+
+    # zero-form case
+    action_zero_form = action(one_form, Iu)  # a number
+    assert isinstance(action_zero_form, Form)
+    assert action_zero_form.arguments() == ()
+
 
 def test_differentiation(V1, V2):
     u = Coefficient(V1)
@@ -180,6 +192,12 @@ def test_differentiation(V1, V2):
     # Need to expand indices to be able to match equal (different MultiIndex used for both).
     assert expand_indices(dFdIu) == expand_indices(dFdw)
 
+    # Derivative of form I(u, V2) wrt coefficient u
+    J = Iu * dx
+    dJdu = expand_derivatives(derivative(J, u))
+    assert isinstance(dJdu, Interpolate)
+    assert dJdu.arguments() == (Argument(V1, 0),)
+
 
 def test_extract_base_form_operators(V1, V2):
     u = Coefficient(V1)

ufl/action.py

@@ -51,6 +51,9 @@ class Action(BaseForm):
 
     def __new__(cls, *args, **kw):
         """Create a new Action."""
+        from ufl.algorithms.analysis import extract_arguments
+        from ufl.algorithms.replace import replace
+
         left, right = args
 
         # Check trivial case
@@ -98,6 +101,12 @@ def __new__(cls, *args, **kw):
             and len(left.arguments()) == 1
         ):
             v, operand = right.argument_slots()
+            # If the operand has an argument, replace it with number 0
+            operand_args = extract_arguments(operand)
+            if operand_args:
+                (old_arg,) = operand_args
+                new_arg = type(old_arg)(old_arg.ufl_function_space(), 0, old_arg.part())
+                operand = replace(operand, {old_arg: new_arg})
             if v == right.arguments()[0]:
                 return right._ufl_expr_reconstruct_(operand, v=left)