Cache split cells (#128)

* Cache split cells

FIAT/macro.py

@@ -304,6 +304,13 @@ class AlfeldSplit(PowellSabinSplit):
     """Splits a simplicial complex by connecting cell vertices to their
     barycenter.
     """
+    def __new__(cls, ref_el):
+        try:
+            return ref_el._split_cache[cls]
+        except KeyError:
+            self = super().__new__(cls)
+            return ref_el._split_cache.setdefault(cls, self)
+
     def __init__(self, ref_el):
         sd = ref_el.get_spatial_dimension()
         super().__init__(ref_el, dimension=sd)
@@ -313,6 +320,13 @@ class WorseyFarinSplit(PowellSabinSplit):
     """Splits a simplicial complex by connecting cell and facet vertices to their
     barycenter. This reduces to Powell-Sabin on the triangle, and Alfeld on the interval.
     """
+    def __new__(cls, ref_el):
+        try:
+            return ref_el._split_cache[cls]
+        except KeyError:
+            self = super().__new__(cls)
+            return ref_el._split_cache.setdefault(cls, self)
+
     def __init__(self, ref_el):
         sd = ref_el.get_spatial_dimension()
         super().__init__(ref_el, dimension=sd-1)

FIAT/reference_element.py

@@ -181,6 +181,9 @@ def __init__(self, shape, vertices, topology):
                     d01_entities = tuple(e for d, e in neighbors if d == dim1)
                     self.connectivity[(dim0, dim1)].append(d01_entities)
 
+        # Dictionary with derived cells
+        self._split_cache = {}
+
     def _key(self):
         """Hashable object key data (excluding type)."""
         # Default: only type matters

test/FIAT/unit/test_macro.py

@@ -16,6 +16,15 @@ def cell(request):
     return ufc_simplex(dim)
 
 
+def test_split_cache(cell):
+    A = AlfeldSplit(cell)
+    B = AlfeldSplit(cell)
+    assert B is A
+    fe = Lagrange(cell, 1, variant="alfeld")
+    C = fe.ref_complex
+    assert C is A
+
+
 @pytest.mark.parametrize("split", (AlfeldSplit, IsoSplit))
 def test_split_entity_transform(split, cell):
     split_cell = split(cell)