def test_tet(order):
celltype = basix.CellType.tetrahedron
g = sympy_rt(celltype, order)
x = sympy.Symbol("x")
y = sympy.Symbol("y")
z = sympy.Symbol("z")
rt = basix.create_element(basix.ElementFamily.RT,
basix.CellType.tetrahedron, order)
pts = basix.create_lattice(celltype, 5, basix.LatticeType.equispaced, True)
nderiv = 1
wtab = rt.tabulate(nderiv, pts)
for kx in range(nderiv + 1):
for ky in range(nderiv + 1 - kx):
for kz in range(nderiv + 1 - kx - ky):
wsym = numpy.zeros_like(wtab[0])
for i, gi in enumerate(g):
for j, gij in enumerate(gi):
wd = sympy.diff(gij, x, kx, y, ky, z, kz)
for k, p in enumerate(pts):
wsym[k, i, j] = wd.subs([(x, p[0]), (y, p[1]),
(z, p[2])])
assert (numpy.isclose(wtab[basix.index(kx, ky, kz)],
wsym).all())
def test_tensor_product_factorisation(cell_type, degree, element_type,
element_args):
element = basix.create_element(element_type, cell_type, degree,
*element_args)
tdim = len(basix.topology(cell_type)) - 1
# These elements should have a factorisation
if cell_type in [basix.CellType.quadrilateral,
basix.CellType.hexahedron] and element_type in [
basix.ElementFamily.P
] and basix.LagrangeVariant.equispaced in element_args:
assert element.has_tensor_product_factorisation
if not element.has_tensor_product_factorisation:
with pytest.raises(RuntimeError):
element.get_tensor_product_representation()
pytest.skip()
factors = element.get_tensor_product_representation()
lattice = basix.create_lattice(cell_type, 1, basix.LatticeType.equispaced,
True)
tab1 = element.tabulate(1, lattice)
for i, point in enumerate(lattice):
for ds in product(range(2), repeat=tdim):
if sum(ds) > 1:
continue
deriv = basix.index(*ds)
values1 = tab1[deriv, i, :, :]
values2 = np.empty((element.dim, 1))
for fs, perm in factors:
evals = [
e.tabulate(d, [p])[d, 0, :, 0]
for e, p, d in zip(fs, point, ds)
]
tab2 = tensor_product(*evals)
for a, b in enumerate(perm):
if b != -1:
values2[b, 0] = tab2[a]
assert np.allclose(values1, values2)
def test_tri(order):
celltype = basix.CellType.triangle
g = sympy_nedelec(celltype, order)
x = sympy.Symbol("x")
y = sympy.Symbol("y")
nedelec = basix.create_element(basix.ElementFamily.N1E, basix.CellType.triangle, order)
pts = basix.create_lattice(celltype, 6, basix.LatticeType.equispaced, True)
nderiv = 3
wtab = nedelec.tabulate(nderiv, pts)
for kx in range(nderiv + 1):
for ky in range(nderiv + 1 - kx):
wsym = numpy.zeros_like(wtab[0])
for i, gi in enumerate(g):
for j, gij in enumerate(gi):
wd = sympy.diff(gij, x, kx, y, ky)
for k, p in enumerate(pts):
wsym[k, i, j] = wd.subs([(x, p[0]), (y, p[1])])
assert(numpy.isclose(wtab[basix.index(kx, ky)], wsym).all())
def test_tri(degree):
celltype = basix.CellType.triangle
g = sympy_lagrange(celltype, degree)
x = sympy.Symbol("x")
y = sympy.Symbol("y")
lagrange = basix.create_element(basix.ElementFamily.P,
basix.CellType.triangle, degree,
basix.LagrangeVariant.equispaced)
pts = basix.create_lattice(celltype, 6, basix.LatticeType.equispaced, True)
nderiv = 3
wtab = lagrange.tabulate(nderiv, pts)
for kx in range(nderiv):
for ky in range(0, nderiv - kx):
wsym = numpy.zeros_like(wtab[0])
for i in range(len(g)):
wd = sympy.diff(g[i], x, kx, y, ky)
for j, p in enumerate(pts):
wsym[j, i] = wd.subs([(x, p[0]), (y, p[1])])
assert numpy.allclose(wtab[basix.index(kx, ky)], wsym)
def test_tet(degree):
celltype = basix.CellType.tetrahedron
g = sympy_lagrange(celltype, degree)
x = sympy.Symbol("x")
y = sympy.Symbol("y")
z = sympy.Symbol("z")
lagrange = basix.create_element(basix.ElementFamily.P,
basix.CellType.tetrahedron, degree,
basix.LagrangeVariant.equispaced)
pts = basix.create_lattice(celltype, 6, basix.LatticeType.equispaced, True)
nderiv = 1
wtab = lagrange.tabulate(nderiv, pts)
for k in range(nderiv + 1):
for q in range(k + 1):
for kx in range(q + 1):
ky = q - kx
kz = k - q
wsym = numpy.zeros_like(wtab[0])
for i in range(len(g)):
wd = sympy.diff(g[i], x, kx, y, ky, z, kz)
for j, p in enumerate(pts):
wsym[j, i] = wd.subs([(x, p[0]), (y, p[1]), (z, p[2])])
assert numpy.allclose(wtab[basix.index(kx, ky, kz)], wsym)
def basix_index(*args):
"""Get the Basix index of a derivative."""
return basix.index(*args)
def basix_index(*args):
return basix.index(*args)