Adjoint(FormProduct)

Author: pbrubeck

test/test_form.py

@@ -5,10 +5,12 @@
     Argument,
     Coefficient,
     Cofunction,
+    Adjoint,
     Form,
     FormProduct,
     FormSum,
     FunctionSpace,
+    Matrix,
     Mesh,
     SpatialCoordinate,
     TestFunction,
@@ -240,6 +242,16 @@ def test_form_product_constructor_and_arguments(domain):
     assert tuple(argument.number() for argument in nested.arguments()) == (0, 1, 2)
 
 
+def test_form_product_of_one_factor_simplifies(domain):
+    element = LagrangeElement(triangle, 1)
+    V = FunctionSpace(domain, element)
+    v = TestFunction(V)
+    f = Coefficient(V)
+    L = f * v * dx
+
+    assert FormProduct(L) is L
+
+
 def test_form_product_rejects_invalid_inputs(domain):
     element = LagrangeElement(triangle, 1)
     V = FunctionSpace(domain, element)
@@ -248,7 +260,9 @@ def test_form_product_rejects_invalid_inputs(domain):
     L = f * v * dx
 
     with pytest.raises(ValueError):
-        FormProduct(L)
+        FormProduct()
+    with pytest.raises(TypeError):
+        FormProduct(1)
     with pytest.raises(TypeError):
         FormProduct(L, 1)
 
@@ -266,6 +280,38 @@ def test_form_product_is_explicit_not_mul_overload(domain):
         Lf * Lg
 
 
+def test_adjoint_form_product_reverses_adjoint_factors(domain):
+    element = LagrangeElement(triangle, 1)
+    V = FunctionSpace(domain, element)
+    A = Matrix(V, V)
+    B = Matrix(V, V)
+    C = Matrix(V, V)
+
+    product = FormProduct(A, B, C)
+    adjoint_product = Adjoint(product)
+
+    assert isinstance(adjoint_product, FormProduct)
+    assert tuple(factor.form() for factor in adjoint_product.factors()) == (C, B, A)
+    assert adjoint_product.factors() == (Adjoint(C), Adjoint(B), Adjoint(A))
+
+
+def test_adjoint_form_product_leaves_rank_zero_and_one_factors_unadjointed(domain):
+    element = LagrangeElement(triangle, 1)
+    V = FunctionSpace(domain, element)
+    v = TestFunction(V)
+    f = Coefficient(V)
+    functional = f * dx
+    linear = f * v * dx
+    A = Matrix(V, V)
+
+    product = FormProduct(functional, linear, A)
+    adjoint_product = Adjoint(product)
+
+    assert isinstance(adjoint_product, FormProduct)
+    assert adjoint_product.factors() == (Adjoint(A), linear, functional)
+    assert Adjoint(FormProduct(functional, linear)).factors() == (linear, functional)
+
+
 def test_form_product_replace(domain):
     element = LagrangeElement(triangle, 1)
     V = FunctionSpace(domain, element)

ufl/adjoint.py

@@ -12,7 +12,7 @@
 
 from ufl.argument import Coargument
 from ufl.core.ufl_type import ufl_type
-from ufl.form import BaseForm, FormSum, ZeroBaseForm
+from ufl.form import BaseForm, FormProduct, FormSum, ZeroBaseForm
 
 # --- The Adjoint class represents the adjoint of a numerical object that
 #     needs to be computed at assembly time ---
@@ -50,6 +50,14 @@ def __new__(cls, *args, **kw):
         elif isinstance(form, FormSum):
             # Adjoint distributes over sums
             return FormSum(*((Adjoint(c), w) for c, w in zip(form.components(), form.weights())))
+        elif isinstance(form, FormProduct):
+            # Reverse product order and take the adjoint of rank-2 factors.
+            return FormProduct(
+                *(
+                    factor if len(factor.arguments()) < 2 else Adjoint(factor)
+                    for factor in reversed(form.factors())
+                )
+            )
         elif isinstance(form, Coargument):
             # The adjoint of a coargument `c: V* -> V*` is the identity
             # matrix mapping from V to V (i.e. V x V* -> R).

ufl/form.py

@@ -717,6 +717,15 @@ class FormProduct(BaseForm):
     )
     _ufl_required_methods_ = "_analyze_form_arguments"  # type: ignore
 
+    def __new__(cls, *factors):
+        """Create a new FormProduct."""
+        if len(factors) == 1:
+            (factor,) = factors
+            if isinstance(factor, BaseForm):
+                return factor
+            raise TypeError(f"Expected a UFL BaseForm instance, got {type(factor)}.")
+        return super().__new__(cls)
+
     def __init__(self, *factors):
         """Initialise."""
         BaseForm.__init__(self)