def test_awc():
ref_cell = FIAT.ufc_simplex(2)
ref_element = FIAT.ArnoldWinther(ref_cell, 3)
ref_el_finat = finat.ArnoldWinther(ref_cell, 3)
ref_pts = ref_cell.make_points(2, 0, 3)
ref_vals = ref_element.tabulate(0, ref_pts)[0, 0]
phys_cell = FIAT.ufc_simplex(2)
pvs = np.array(((0.0, 0.0), (1.0, 0.1), (0.0, 2.0)))
phys_cell.vertices = pvs * 0.5
phys_element = FIAT.ArnoldWinther(phys_cell, 3)
phys_pts = phys_cell.make_points(2, 0, 3)
phys_vals = phys_element.tabulate(0, phys_pts)[0, 0]
# Piola map the reference elements
J, b = FIAT.reference_element.make_affine_mapping(ref_cell.vertices,
phys_cell.vertices)
detJ = np.linalg.det(J)
ref_vals_piola = np.zeros(ref_vals.shape)
for i in range(ref_vals.shape[0]):
for k in range(ref_vals.shape[3]):
ref_vals_piola[i, :, :, k] = \
J @ ref_vals[i, :, :, k] @ J.T / detJ**2
# Zany map the results
mppng = MyMapping(ref_cell, phys_cell)
Mgem = ref_el_finat.basis_transformation(mppng)
M = evaluate([Mgem])[0].arr
ref_vals_zany = np.zeros((24, 2, 2, len(phys_pts)))
for k in range(ref_vals_zany.shape[3]):
for ell1 in range(2):
for ell2 in range(2):
ref_vals_zany[:, ell1, ell2, k] = \
M @ ref_vals_piola[:, ell1, ell2, k]
assert np.allclose(ref_vals_zany[:21], phys_vals[:21])
def __init__(self, cell, degree):
if Citations is not None:
Citations().register("Arnold2002")
super(ArnoldWinther, self).__init__(FIAT.ArnoldWinther(cell, degree))
