absorb norm of constant basis function

FIAT/expansions.py

@@ -77,7 +77,7 @@ def dubiner_recurrence(dim, n, order, ref_pts, jacobian, variant=None):
 
     pad_dim = dim + 2
     dX = pad_jacobian(jacobian, pad_dim)
-    phi[0] = sum((ref_pts[i] - ref_pts[i] for i in range(dim)), 1.)
+    phi[0] = sum((ref_pts[i] - ref_pts[i] for i in range(dim)), math.sqrt(0.5)**dim)
     if dphi is not None:
         dphi[0] = (phi[0] - phi[0]) * dX[0]
     if ddphi is not None:
@@ -138,7 +138,7 @@ def dubiner_recurrence(dim, n, order, ref_pts, jacobian, variant=None):
                 n1 = sum(index) - 1
                 alpha = 3*n1*(n1*alpha + len(index)) / (n1+1)**2
 
-            scale = math.sqrt(0.5 * alpha)
+            scale = math.sqrt(alpha)
             icur = idx(*index)
             for result in results:
                 result[icur] *= scale

test/unit/test_fiat.py

@@ -602,7 +602,6 @@ def eval_basis(f, pt):
 
 @pytest.mark.parametrize('cell', [I, T, S])
 def test_make_bubbles(cell):
-    from FIAT.reference_element import make_lattice
     from FIAT.quadrature_schemes import create_quadrature
     from FIAT.expansions import polynomial_dimension
     from FIAT.polynomial_set import make_bubbles, PolynomialSet, ONPolynomialSet
@@ -627,7 +626,7 @@ def test_make_bubbles(cell):
 
     # test linear independence
     m = B.get_num_members()
-    points = make_lattice(cell.get_vertices(), degree, interior=1)
+    points = cell.make_points(sd, 0, degree + 1)
     values = B.tabulate(points)[(0,) * sd]
     assert values.shape == (m, m)
     assert np.linalg.matrix_rank(values.T) == m