def test_TFE_2Dx1D_scalar_triangle_hcurl():
S = UFCTriangle()
T = UFCInterval()
P1 = Lagrange(S, 1)
P1_DG = DiscontinuousLagrange(T, 1)
elt = Hcurl(TensorProductElement(P1, P1_DG))
assert elt.value_shape() == (3,)
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tabA = P1.tabulate(1, [(0.1, 0.2)])
tabB = P1_DG.tabulate(1, [(0.3,)])
for da, db in [[(0, 0), (0,)], [(1, 0), (0,)], [(0, 1), (0,)], [(0, 0), (1,)]]:
dc = da + db
assert tab[dc][0][0][0] == 0.0
assert tab[dc][1][0][0] == 0.0
assert tab[dc][2][0][0] == 0.0
assert tab[dc][3][0][0] == 0.0
assert tab[dc][4][0][0] == 0.0
assert tab[dc][5][0][0] == 0.0
assert tab[dc][0][1][0] == 0.0
assert tab[dc][1][1][0] == 0.0
assert tab[dc][2][1][0] == 0.0
assert tab[dc][3][1][0] == 0.0
assert tab[dc][4][1][0] == 0.0
assert tab[dc][5][1][0] == 0.0
assert np.isclose(tab[dc][0][2][0], tabA[da][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][1][2][0], tabA[da][0][0]*tabB[db][1][0])
assert np.isclose(tab[dc][2][2][0], tabA[da][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][3][2][0], tabA[da][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][4][2][0], tabA[da][2][0]*tabB[db][0][0])
assert np.isclose(tab[dc][5][2][0], tabA[da][2][0]*tabB[db][1][0])
def test_TFE_2Dx1D_scalar_quad():
T = UFCInterval()
P1 = Lagrange(T, 1)
P1_DG = DiscontinuousLagrange(T, 1)
elt = TensorProductElement(TensorProductElement(P1, P1_DG), P1)
assert elt.value_shape() == ()
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tA = P1.tabulate(1, [(0.1, )])
tB = P1_DG.tabulate(1, [(0.2, )])
tC = P1.tabulate(1, [(0.3, )])
for da, db, dc in [[(0, ), (0, ), (0, )], [(1, ), (0, ), (0, )],
[(0, ), (1, ), (0, )], [(0, ), (0, ), (1, )]]:
dd = da + db + dc
assert np.isclose(tab[dd][0][0],
tA[da][0][0] * tB[db][0][0] * tC[dc][0][0])
assert np.isclose(tab[dd][1][0],
tA[da][0][0] * tB[db][0][0] * tC[dc][1][0])
assert np.isclose(tab[dd][2][0],
tA[da][0][0] * tB[db][1][0] * tC[dc][0][0])
assert np.isclose(tab[dd][3][0],
tA[da][0][0] * tB[db][1][0] * tC[dc][1][0])
assert np.isclose(tab[dd][4][0],
tA[da][1][0] * tB[db][0][0] * tC[dc][0][0])
assert np.isclose(tab[dd][5][0],
tA[da][1][0] * tB[db][0][0] * tC[dc][1][0])
assert np.isclose(tab[dd][6][0],
tA[da][1][0] * tB[db][1][0] * tC[dc][0][0])
assert np.isclose(tab[dd][7][0],
tA[da][1][0] * tB[db][1][0] * tC[dc][1][0])
def test_TFE_2Dx1D_vector_triangle_hcurl():
S = UFCTriangle()
T = UFCInterval()
Ned1 = Nedelec(S, 1)
P1 = Lagrange(T, 1)
elt = Hcurl(TensorProductElement(Ned1, P1))
assert elt.value_shape() == (3, )
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tabA = Ned1.tabulate(1, [(0.1, 0.2)])
tabB = P1.tabulate(1, [(0.3, )])
for da, db in [[(0, 0), (0, )], [(1, 0), (0, )], [(0, 1), (0, )],
[(0, 0), (1, )]]:
dc = da + db
assert np.isclose(tab[dc][0][0][0], tabA[da][0][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][1][0][0], tabA[da][0][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][2][0][0], tabA[da][1][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][3][0][0], tabA[da][1][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][4][0][0], tabA[da][2][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][5][0][0], tabA[da][2][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][0][1][0], tabA[da][0][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][1][1][0], tabA[da][0][1][0] * tabB[db][1][0])
assert np.isclose(tab[dc][2][1][0], tabA[da][1][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][3][1][0], tabA[da][1][1][0] * tabB[db][1][0])
assert np.isclose(tab[dc][4][1][0], tabA[da][2][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][5][1][0], tabA[da][2][1][0] * tabB[db][1][0])
assert tab[dc][0][2][0] == 0.0
assert tab[dc][1][2][0] == 0.0
assert tab[dc][2][2][0] == 0.0
assert tab[dc][3][2][0] == 0.0
assert tab[dc][4][2][0] == 0.0
assert tab[dc][5][2][0] == 0.0
def test_TFE_2Dx1D_vector_triangle_hcurl_rotate():
S = UFCTriangle()
T = UFCInterval()
RT1 = RaviartThomas(S, 1)
P1 = Lagrange(T, 1)
elt = Hcurl(TensorProductElement(RT1, P1))
assert elt.value_shape() == (3,)
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tabA = RT1.tabulate(1, [(0.1, 0.2)])
tabB = P1.tabulate(1, [(0.3,)])
for da, db in [[(0, 0), (0,)], [(1, 0), (0,)], [(0, 1), (0,)], [(0, 0), (1,)]]:
dc = da + db
assert np.isclose(tab[dc][0][0][0], -tabA[da][0][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][1][0][0], -tabA[da][0][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][2][0][0], -tabA[da][1][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][3][0][0], -tabA[da][1][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][4][0][0], -tabA[da][2][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][5][0][0], -tabA[da][2][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][0][1][0], tabA[da][0][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][1][1][0], tabA[da][0][0][0]*tabB[db][1][0])
assert np.isclose(tab[dc][2][1][0], tabA[da][1][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][3][1][0], tabA[da][1][0][0]*tabB[db][1][0])
assert np.isclose(tab[dc][4][1][0], tabA[da][2][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][5][1][0], tabA[da][2][0][0]*tabB[db][1][0])
assert tab[dc][0][2][0] == 0.0
assert tab[dc][1][2][0] == 0.0
assert tab[dc][2][2][0] == 0.0
assert tab[dc][3][2][0] == 0.0
assert tab[dc][4][2][0] == 0.0
assert tab[dc][5][2][0] == 0.0
def test_TFE_1Dx1D_vector():
T = UFCInterval()
P1_DG = DiscontinuousLagrange(T, 1)
P2 = Lagrange(T, 2)
elt = TensorProductElement(P1_DG, P2)
hdiv_elt = Hdiv(elt)
hcurl_elt = Hcurl(elt)
assert hdiv_elt.value_shape() == (2, )
assert hcurl_elt.value_shape() == (2, )
tabA = P1_DG.tabulate(1, [(0.1, )])
tabB = P2.tabulate(1, [(0.2, )])
hdiv_tab = hdiv_elt.tabulate(1, [(0.1, 0.2)])
for da, db in [[(0, ), (0, )], [(1, ), (0, )], [(0, ), (1, )]]:
dc = da + db
assert hdiv_tab[dc][0][0][0] == 0.0
assert hdiv_tab[dc][1][0][0] == 0.0
assert hdiv_tab[dc][2][0][0] == 0.0
assert hdiv_tab[dc][3][0][0] == 0.0
assert hdiv_tab[dc][4][0][0] == 0.0
assert hdiv_tab[dc][5][0][0] == 0.0
assert np.isclose(hdiv_tab[dc][0][1][0],
tabA[da][0][0] * tabB[db][0][0])
assert np.isclose(hdiv_tab[dc][1][1][0],
tabA[da][0][0] * tabB[db][1][0])
assert np.isclose(hdiv_tab[dc][2][1][0],
tabA[da][0][0] * tabB[db][2][0])
assert np.isclose(hdiv_tab[dc][3][1][0],
tabA[da][1][0] * tabB[db][0][0])
assert np.isclose(hdiv_tab[dc][4][1][0],
tabA[da][1][0] * tabB[db][1][0])
assert np.isclose(hdiv_tab[dc][5][1][0],
tabA[da][1][0] * tabB[db][2][0])
hcurl_tab = hcurl_elt.tabulate(1, [(0.1, 0.2)])
for da, db in [[(0, ), (0, )], [(1, ), (0, )], [(0, ), (1, )]]:
dc = da + db
assert np.isclose(hcurl_tab[dc][0][0][0],
tabA[da][0][0] * tabB[db][0][0])
assert np.isclose(hcurl_tab[dc][1][0][0],
tabA[da][0][0] * tabB[db][1][0])
assert np.isclose(hcurl_tab[dc][2][0][0],
tabA[da][0][0] * tabB[db][2][0])
assert np.isclose(hcurl_tab[dc][3][0][0],
tabA[da][1][0] * tabB[db][0][0])
assert np.isclose(hcurl_tab[dc][4][0][0],
tabA[da][1][0] * tabB[db][1][0])
assert np.isclose(hcurl_tab[dc][5][0][0],
tabA[da][1][0] * tabB[db][2][0])
assert hcurl_tab[dc][0][1][0] == 0.0
assert hcurl_tab[dc][1][1][0] == 0.0
assert hcurl_tab[dc][2][1][0] == 0.0
assert hcurl_tab[dc][3][1][0] == 0.0
assert hcurl_tab[dc][4][1][0] == 0.0
assert hcurl_tab[dc][5][1][0] == 0.0
def __init__(self, ref_el, degree):
element = Lagrange(ref_el, degree)
cell_dim = ref_el.get_dimension()
assert cell_dim == max(element.entity_dofs().keys())
cell_entity_dofs = element.entity_dofs()[cell_dim][0]
if len(cell_entity_dofs) == 0:
raise RuntimeError('Bubble element of degree %d has no dofs' %
degree)
super(Bubble, self).__init__(element, indices=cell_entity_dofs)
def test_TFE_2Dx1D_vector_quad_hdiv():
T = UFCInterval()
P1 = Lagrange(T, 1)
P0 = DiscontinuousLagrange(T, 0)
P1_DG = DiscontinuousLagrange(T, 1)
P1P0 = Hdiv(TensorProductElement(P1, P0))
P0P1 = Hdiv(TensorProductElement(P0, P1))
horiz_elt = EnrichedElement(P1P0, P0P1)
elt = Hdiv(TensorProductElement(horiz_elt, P1_DG))
assert elt.value_shape() == (3, )
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tA = P1.tabulate(1, [(0.1, )])
tB = P0.tabulate(1, [(0.2, )])
tC = P0.tabulate(1, [(0.1, )])
tD = P1.tabulate(1, [(0.2, )])
tE = P1_DG.tabulate(1, [(0.3, )])
for da, db, dc in [[(0, ), (0, ), (0, )], [(1, ), (0, ), (0, )],
[(0, ), (1, ), (0, )], [(0, ), (0, ), (1, )]]:
dd = da + db + dc
assert np.isclose(tab[dd][0][0][0],
-tA[da][0][0] * tB[db][0][0] * tE[dc][0][0])
assert np.isclose(tab[dd][1][0][0],
-tA[da][0][0] * tB[db][0][0] * tE[dc][1][0])
assert np.isclose(tab[dd][2][0][0],
-tA[da][1][0] * tB[db][0][0] * tE[dc][0][0])
assert np.isclose(tab[dd][3][0][0],
-tA[da][1][0] * tB[db][0][0] * tE[dc][1][0])
assert tab[dd][4][0][0] == 0.0
assert tab[dd][5][0][0] == 0.0
assert tab[dd][6][0][0] == 0.0
assert tab[dd][7][0][0] == 0.0
assert tab[dd][0][1][0] == 0.0
assert tab[dd][1][1][0] == 0.0
assert tab[dd][2][1][0] == 0.0
assert tab[dd][3][1][0] == 0.0
assert np.isclose(tab[dd][4][1][0],
tC[da][0][0] * tD[db][0][0] * tE[dc][0][0])
assert np.isclose(tab[dd][5][1][0],
tC[da][0][0] * tD[db][0][0] * tE[dc][1][0])
assert np.isclose(tab[dd][6][1][0],
tC[da][0][0] * tD[db][1][0] * tE[dc][0][0])
assert np.isclose(tab[dd][7][1][0],
tC[da][0][0] * tD[db][1][0] * tE[dc][1][0])
assert tab[dd][0][2][0] == 0.0
assert tab[dd][1][2][0] == 0.0
assert tab[dd][2][2][0] == 0.0
assert tab[dd][3][2][0] == 0.0
assert tab[dd][4][2][0] == 0.0
assert tab[dd][5][2][0] == 0.0
assert tab[dd][6][2][0] == 0.0
assert tab[dd][7][2][0] == 0.0
def __init__(self, ref_el, degree, codim):
element = Lagrange(ref_el, degree)
cell_dim = ref_el.get_dimension()
assert cell_dim == max(element.entity_dofs().keys())
dofs = list(
sorted(chain(*element.entity_dofs()[cell_dim - codim].values())))
if len(dofs) == 0:
raise RuntimeError(
'Bubble element of degree %d and codimension %d has no dofs' %
(degree, codim))
super(CodimBubble, self).__init__(element, indices=dofs)
def _setupElement(self):
"""
Setup the finite element for reference cell.
"""
from FIAT.lagrange import Lagrange
from FIAT.reference_element import default_simplex
return Lagrange(default_simplex(1), self.degree)
def test_TFE_1Dx1D_vector():
T = UFCInterval()
P1_DG = DiscontinuousLagrange(T, 1)
P2 = Lagrange(T, 2)
elt = TensorProductElement(P1_DG, P2)
hdiv_elt = Hdiv(elt)
hcurl_elt = Hcurl(elt)
assert hdiv_elt.value_shape() == (2,)
assert hcurl_elt.value_shape() == (2,)
tabA = P1_DG.tabulate(1, [(0.1,)])
tabB = P2.tabulate(1, [(0.2,)])
hdiv_tab = hdiv_elt.tabulate(1, [(0.1, 0.2)])
for da, db in [[(0,), (0,)], [(1,), (0,)], [(0,), (1,)]]:
dc = da + db
assert hdiv_tab[dc][0][0][0] == 0.0
assert hdiv_tab[dc][1][0][0] == 0.0
assert hdiv_tab[dc][2][0][0] == 0.0
assert hdiv_tab[dc][3][0][0] == 0.0
assert hdiv_tab[dc][4][0][0] == 0.0
assert hdiv_tab[dc][5][0][0] == 0.0
assert np.isclose(hdiv_tab[dc][0][1][0], tabA[da][0][0]*tabB[db][0][0])
assert np.isclose(hdiv_tab[dc][1][1][0], tabA[da][0][0]*tabB[db][1][0])
assert np.isclose(hdiv_tab[dc][2][1][0], tabA[da][0][0]*tabB[db][2][0])
assert np.isclose(hdiv_tab[dc][3][1][0], tabA[da][1][0]*tabB[db][0][0])
assert np.isclose(hdiv_tab[dc][4][1][0], tabA[da][1][0]*tabB[db][1][0])
assert np.isclose(hdiv_tab[dc][5][1][0], tabA[da][1][0]*tabB[db][2][0])
hcurl_tab = hcurl_elt.tabulate(1, [(0.1, 0.2)])
for da, db in [[(0,), (0,)], [(1,), (0,)], [(0,), (1,)]]:
dc = da + db
assert np.isclose(hcurl_tab[dc][0][0][0], tabA[da][0][0]*tabB[db][0][0])
assert np.isclose(hcurl_tab[dc][1][0][0], tabA[da][0][0]*tabB[db][1][0])
assert np.isclose(hcurl_tab[dc][2][0][0], tabA[da][0][0]*tabB[db][2][0])
assert np.isclose(hcurl_tab[dc][3][0][0], tabA[da][1][0]*tabB[db][0][0])
assert np.isclose(hcurl_tab[dc][4][0][0], tabA[da][1][0]*tabB[db][1][0])
assert np.isclose(hcurl_tab[dc][5][0][0], tabA[da][1][0]*tabB[db][2][0])
assert hcurl_tab[dc][0][1][0] == 0.0
assert hcurl_tab[dc][1][1][0] == 0.0
assert hcurl_tab[dc][2][1][0] == 0.0
assert hcurl_tab[dc][3][1][0] == 0.0
assert hcurl_tab[dc][4][1][0] == 0.0
assert hcurl_tab[dc][5][1][0] == 0.0
def __init__(self, ref_el, m):
from FIAT.lagrange import Lagrange
vertices = Lagrange(ref_el, m).dual.get_nodes()
pts = [v.get_point_dict().keys()[0] for v in vertices]
npts = len(pts)
wts = (ref_el.volume() / npts, ) * npts
QuadratureRule.__init__(self, ref_el, pts, wts)
return
def test_TFE_1Dx1D_scalar():
T = UFCInterval()
P1_DG = DiscontinuousLagrange(T, 1)
P2 = Lagrange(T, 2)
elt = TensorProductElement(P1_DG, P2)
assert elt.value_shape() == ()
tab = elt.tabulate(1, [(0.1, 0.2)])
tabA = P1_DG.tabulate(1, [(0.1, )])
tabB = P2.tabulate(1, [(0.2, )])
for da, db in [[(0, ), (0, )], [(1, ), (0, )], [(0, ), (1, )]]:
dc = da + db
assert np.isclose(tab[dc][0][0], tabA[da][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][1][0], tabA[da][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][2][0], tabA[da][0][0] * tabB[db][2][0])
assert np.isclose(tab[dc][3][0], tabA[da][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][4][0], tabA[da][1][0] * tabB[db][1][0])
assert np.isclose(tab[dc][5][0], tabA[da][1][0] * tabB[db][2][0])
def test_TFE_1Dx1D_scalar():
T = UFCInterval()
P1_DG = DiscontinuousLagrange(T, 1)
P2 = Lagrange(T, 2)
elt = TensorProductElement(P1_DG, P2)
assert elt.value_shape() == ()
tab = elt.tabulate(1, [(0.1, 0.2)])
tabA = P1_DG.tabulate(1, [(0.1,)])
tabB = P2.tabulate(1, [(0.2,)])
for da, db in [[(0,), (0,)], [(1,), (0,)], [(0,), (1,)]]:
dc = da + db
assert np.isclose(tab[dc][0][0], tabA[da][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][1][0], tabA[da][0][0]*tabB[db][1][0])
assert np.isclose(tab[dc][2][0], tabA[da][0][0]*tabB[db][2][0])
assert np.isclose(tab[dc][3][0], tabA[da][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][4][0], tabA[da][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][5][0], tabA[da][1][0]*tabB[db][2][0])
def __new__(cls, ref_el, degree):
dim = ref_el.get_spatial_dimension()
if dim == 1:
return Lagrange(ref_el, degree)
elif dim == 0:
raise IndexError("reference element cannot be dimension 0")
else:
self = super().__new__(cls)
return self
def test_TFE_2Dx1D_vector_quad_hdiv():
T = UFCInterval()
P1 = Lagrange(T, 1)
P0 = DiscontinuousLagrange(T, 0)
P1_DG = DiscontinuousLagrange(T, 1)
P1P0 = Hdiv(TensorProductElement(P1, P0))
P0P1 = Hdiv(TensorProductElement(P0, P1))
horiz_elt = EnrichedElement(P1P0, P0P1)
elt = Hdiv(TensorProductElement(horiz_elt, P1_DG))
assert elt.value_shape() == (3,)
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tA = P1.tabulate(1, [(0.1,)])
tB = P0.tabulate(1, [(0.2,)])
tC = P0.tabulate(1, [(0.1,)])
tD = P1.tabulate(1, [(0.2,)])
tE = P1_DG.tabulate(1, [(0.3,)])
for da, db, dc in [[(0,), (0,), (0,)], [(1,), (0,), (0,)], [(0,), (1,), (0,)], [(0,), (0,), (1,)]]:
dd = da + db + dc
assert np.isclose(tab[dd][0][0][0], -tA[da][0][0]*tB[db][0][0]*tE[dc][0][0])
assert np.isclose(tab[dd][1][0][0], -tA[da][0][0]*tB[db][0][0]*tE[dc][1][0])
assert np.isclose(tab[dd][2][0][0], -tA[da][1][0]*tB[db][0][0]*tE[dc][0][0])
assert np.isclose(tab[dd][3][0][0], -tA[da][1][0]*tB[db][0][0]*tE[dc][1][0])
assert tab[dd][4][0][0] == 0.0
assert tab[dd][5][0][0] == 0.0
assert tab[dd][6][0][0] == 0.0
assert tab[dd][7][0][0] == 0.0
assert tab[dd][0][1][0] == 0.0
assert tab[dd][1][1][0] == 0.0
assert tab[dd][2][1][0] == 0.0
assert tab[dd][3][1][0] == 0.0
assert np.isclose(tab[dd][4][1][0], tC[da][0][0]*tD[db][0][0]*tE[dc][0][0])
assert np.isclose(tab[dd][5][1][0], tC[da][0][0]*tD[db][0][0]*tE[dc][1][0])
assert np.isclose(tab[dd][6][1][0], tC[da][0][0]*tD[db][1][0]*tE[dc][0][0])
assert np.isclose(tab[dd][7][1][0], tC[da][0][0]*tD[db][1][0]*tE[dc][1][0])
assert tab[dd][0][2][0] == 0.0
assert tab[dd][1][2][0] == 0.0
assert tab[dd][2][2][0] == 0.0
assert tab[dd][3][2][0] == 0.0
assert tab[dd][4][2][0] == 0.0
assert tab[dd][5][2][0] == 0.0
assert tab[dd][6][2][0] == 0.0
assert tab[dd][7][2][0] == 0.0
def test_TFE_2Dx1D_scalar_triangle_hdiv():
S = UFCTriangle()
T = UFCInterval()
P1_DG = DiscontinuousLagrange(S, 1)
P2 = Lagrange(T, 2)
elt = Hdiv(TensorProductElement(P1_DG, P2))
assert elt.value_shape() == (3, )
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tabA = P1_DG.tabulate(1, [(0.1, 0.2)])
tabB = P2.tabulate(1, [(0.3, )])
for da, db in [[(0, 0), (0, )], [(1, 0), (0, )], [(0, 1), (0, )],
[(0, 0), (1, )]]:
dc = da + db
assert tab[dc][0][0][0] == 0.0
assert tab[dc][1][0][0] == 0.0
assert tab[dc][2][0][0] == 0.0
assert tab[dc][3][0][0] == 0.0
assert tab[dc][4][0][0] == 0.0
assert tab[dc][5][0][0] == 0.0
assert tab[dc][6][0][0] == 0.0
assert tab[dc][7][0][0] == 0.0
assert tab[dc][8][0][0] == 0.0
assert tab[dc][0][1][0] == 0.0
assert tab[dc][1][1][0] == 0.0
assert tab[dc][2][1][0] == 0.0
assert tab[dc][3][1][0] == 0.0
assert tab[dc][4][1][0] == 0.0
assert tab[dc][5][1][0] == 0.0
assert tab[dc][6][1][0] == 0.0
assert tab[dc][7][1][0] == 0.0
assert tab[dc][8][1][0] == 0.0
assert np.isclose(tab[dc][0][2][0], tabA[da][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][1][2][0], tabA[da][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][2][2][0], tabA[da][0][0] * tabB[db][2][0])
assert np.isclose(tab[dc][3][2][0], tabA[da][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][4][2][0], tabA[da][1][0] * tabB[db][1][0])
assert np.isclose(tab[dc][5][2][0], tabA[da][1][0] * tabB[db][2][0])
assert np.isclose(tab[dc][6][2][0], tabA[da][2][0] * tabB[db][0][0])
assert np.isclose(tab[dc][7][2][0], tabA[da][2][0] * tabB[db][1][0])
assert np.isclose(tab[dc][8][2][0], tabA[da][2][0] * tabB[db][2][0])
def test_TFE_2Dx1D_scalar_quad():
T = UFCInterval()
P1 = Lagrange(T, 1)
P1_DG = DiscontinuousLagrange(T, 1)
elt = TensorProductElement(TensorProductElement(P1, P1_DG), P1)
assert elt.value_shape() == ()
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tA = P1.tabulate(1, [(0.1,)])
tB = P1_DG.tabulate(1, [(0.2,)])
tC = P1.tabulate(1, [(0.3,)])
for da, db, dc in [[(0,), (0,), (0,)], [(1,), (0,), (0,)], [(0,), (1,), (0,)], [(0,), (0,), (1,)]]:
dd = da + db + dc
assert np.isclose(tab[dd][0][0], tA[da][0][0]*tB[db][0][0]*tC[dc][0][0])
assert np.isclose(tab[dd][1][0], tA[da][0][0]*tB[db][0][0]*tC[dc][1][0])
assert np.isclose(tab[dd][2][0], tA[da][0][0]*tB[db][1][0]*tC[dc][0][0])
assert np.isclose(tab[dd][3][0], tA[da][0][0]*tB[db][1][0]*tC[dc][1][0])
assert np.isclose(tab[dd][4][0], tA[da][1][0]*tB[db][0][0]*tC[dc][0][0])
assert np.isclose(tab[dd][5][0], tA[da][1][0]*tB[db][0][0]*tC[dc][1][0])
assert np.isclose(tab[dd][6][0], tA[da][1][0]*tB[db][1][0]*tC[dc][0][0])
assert np.isclose(tab[dd][7][0], tA[da][1][0]*tB[db][1][0]*tC[dc][1][0])
def test_basis_derivatives_scaling():
"Regression test for issue #9"
class Interval(ReferenceElement):
def __init__(self, a, b):
verts = ((a,), (b,))
edges = {0: (0, 1)}
topology = {0: {0: (0,), 1: (1,)},
1: edges}
super(Interval, self).__init__(LINE, verts, topology)
random.seed(42)
for i in range(26):
a = 1000.0*(random.random() - 0.5)
b = 1000.0*(random.random() - 0.5)
a, b = min(a, b), max(a, b)
interval = Interval(a, b)
element = Lagrange(interval, 1)
points = [(a,), (0.5*(a+b),), (b,)]
tab = element.get_nodal_basis().tabulate(points, 2)
# first basis function
assert np.isclose(tab[(0,)][0][0], 1.0)
assert np.isclose(tab[(0,)][0][1], 0.5)
assert np.isclose(tab[(0,)][0][2], 0.0)
# second basis function
assert np.isclose(tab[(0,)][1][0], 0.0)
assert np.isclose(tab[(0,)][1][1], 0.5)
assert np.isclose(tab[(0,)][1][2], 1.0)
# first and second derivatives
D = 1.0 / (b - a)
for p in range(len(points)):
assert np.isclose(tab[(1,)][0][p], -D)
assert np.isclose(tab[(1,)][1][p], +D)
assert np.isclose(tab[(2,)][0][p], 0.0)
assert np.isclose(tab[(2,)][1][p], 0.0)
def test_basis_derivatives_scaling():
"Regression test for issue #9"
class Interval(ReferenceElement):
def __init__(self, a, b):
verts = ((a, ), (b, ))
edges = {0: (0, 1)}
topology = {0: {0: (0, ), 1: (1, )}, 1: edges}
super(Interval, self).__init__(LINE, verts, topology)
random.seed(42)
for i in range(26):
a = 1000.0 * (random.random() - 0.5)
b = 1000.0 * (random.random() - 0.5)
a, b = min(a, b), max(a, b)
interval = Interval(a, b)
element = Lagrange(interval, 1)
points = [(a, ), (0.5 * (a + b), ), (b, )]
tab = element.get_nodal_basis().tabulate(points, 2)
# first basis function
assert np.isclose(tab[(0, )][0][0], 1.0)
assert np.isclose(tab[(0, )][0][1], 0.5)
assert np.isclose(tab[(0, )][0][2], 0.0)
# second basis function
assert np.isclose(tab[(0, )][1][0], 0.0)
assert np.isclose(tab[(0, )][1][1], 0.5)
assert np.isclose(tab[(0, )][1][2], 1.0)
# first and second derivatives
D = 1.0 / (b - a)
for p in range(len(points)):
assert np.isclose(tab[(1, )][0][p], -D)
assert np.isclose(tab[(1, )][1][p], +D)
assert np.isclose(tab[(2, )][0][p], 0.0)
assert np.isclose(tab[(2, )][1][p], 0.0)
def test_flattened_against_tpe_quad():
T = UFCInterval()
P1 = Lagrange(T, 1)
tpe_quad = TensorProductElement(P1, P1)
flattened_quad = FlattenedDimensions(tpe_quad)
assert tpe_quad.value_shape() == ()
tpe_tab = tpe_quad.tabulate(1, [(0.1, 0.2)])
flattened_tab = flattened_quad.tabulate(1, [(0.1, 0.2)])
for da, db in [[(0, ), (0, )], [(1, ), (0, )], [(0, ), (1, )]]:
dc = da + db
assert np.isclose(tpe_tab[dc][0][0], flattened_tab[dc][0][0])
assert np.isclose(tpe_tab[dc][1][0], flattened_tab[dc][1][0])
assert np.isclose(tpe_tab[dc][2][0], flattened_tab[dc][2][0])
assert np.isclose(tpe_tab[dc][3][0], flattened_tab[dc][3][0])
def test_flattened_against_tpe_hex():
T = UFCInterval()
P1 = Lagrange(T, 1)
tpe_quad = TensorProductElement(P1, P1)
tpe_hex = TensorProductElement(tpe_quad, P1)
flattened_quad = FlattenedDimensions(tpe_quad)
flattened_hex = FlattenedDimensions(
TensorProductElement(flattened_quad, P1))
assert tpe_quad.value_shape() == ()
tpe_tab = tpe_hex.tabulate(1, [(0.1, 0.2, 0.3)])
flattened_tab = flattened_hex.tabulate(1, [(0.1, 0.2, 0.3)])
for da, db, dc in [[(0, ), (0, ), (0, )], [(1, ), (0, ), (0, )],
[(0, ), (1, ), (0, )], [(0, ), (0, ), (1, )]]:
dd = da + db + dc
assert np.isclose(tpe_tab[dd][0][0], flattened_tab[dd][0][0])
assert np.isclose(tpe_tab[dd][1][0], flattened_tab[dd][1][0])
assert np.isclose(tpe_tab[dd][2][0], flattened_tab[dd][2][0])
assert np.isclose(tpe_tab[dd][3][0], flattened_tab[dd][3][0])
assert np.isclose(tpe_tab[dd][4][0], flattened_tab[dd][4][0])
assert np.isclose(tpe_tab[dd][5][0], flattened_tab[dd][5][0])
assert np.isclose(tpe_tab[dd][6][0], flattened_tab[dd][6][0])
assert np.isclose(tpe_tab[dd][7][0], flattened_tab[dd][7][0])
import os, sys
# Find PETSc/BuildSystem
if 'PETSC_DIR' in os.environ:
configDir = os.path.join(os.environ['PETSC_DIR'], 'config')
bsDir = os.path.join(configDir, 'BuildSystem')
sys.path.insert(0, bsDir)
sys.path.insert(0, configDir)
import PETSc.FEM
from FIAT.reference_element import default_simplex
from FIAT.lagrange import Lagrange
generator = PETSc.FEM.QuadratureGenerator()
generator.setup()
elements = []
if not (len(sys.argv)-2) % 5 == 0:
sys.exit('Incomplete set of arguments')
for n in range((len(sys.argv)-2) / 5):
dim = int(sys.argv[n*5+1])
order = int(sys.argv[n*5+2])
components = int(sys.argv[n*5+3])
numBlocks = int(sys.argv[n*5+4])
operator = sys.argv[n*5+5]
element = Lagrange(default_simplex(dim), order)
element.numComponents = components
elements.append(element)
filename = sys.argv[-1]
generator.quadDegree = max([e.order for e in elements])
generator.run(elements, numBlocks, operator, filename)
# Get coeffs of primal and dual bases w.r.t. expansion set
coeffs_poly = poly_set.get_coeffs()
coeffs_dual = dual_set.to_riesz(poly_set)
assert coeffs_poly.shape == coeffs_dual.shape
# Check nodality
for i in range(coeffs_dual.shape[0]):
for j in range(coeffs_poly.shape[0]):
assert np.isclose(
coeffs_dual[i].flatten().dot(coeffs_poly[j].flatten()),
1.0 if i == j else 0.0)
@pytest.mark.parametrize('elements', [
(Lagrange(I, 2), Bubble(I, 2)),
(Lagrange(T, 3), Bubble(T, 3)),
(Lagrange(S, 4), Bubble(S, 4)),
(Lagrange(I, 1), Lagrange(I, 1)),
(Lagrange(I, 1), Bubble(I, 2), Bubble(I, 2)),
])
def test_illposed_nodal_enriched(elements):
"""Check that nodal enriched element fails on ill-posed
(non-unisolvent) case
"""
with pytest.raises(np.linalg.LinAlgError):
NodalEnrichedElement(*elements)
def test_empty_bubble():
"Check that bubble of too low degree fails"
sys.path.insert(0, bsDir)
sys.path.insert(0, configDir)
if os.path.isdir(os.path.join(fiatDir, 'FIAT')):
sys.path.insert(0, fiatDir)
import PETSc.FEM
from FIAT.reference_element import default_simplex
from FIAT.lagrange import Lagrange
from FIAT.discontinuous_lagrange import DiscontinuousLagrange
generator = PETSc.FEM.QuadratureGenerator()
generator.setup()
elements = []
if not (len(sys.argv) - 2) % 5 == 0:
sys.exit('Incomplete set of arguments')
for n in range((len(sys.argv) - 2) / 5):
dim = int(sys.argv[n * 5 + 1])
order = int(sys.argv[n * 5 + 2])
components = int(sys.argv[n * 5 + 3])
numBlocks = int(sys.argv[n * 5 + 4])
operator = sys.argv[n * 5 + 5]
if order == 0:
element = DiscontinuousLagrange(default_simplex(1), order)
else:
element = Lagrange(default_simplex(1), order)
element.numComponents = components
elements.append(element)
filename = sys.argv[-1]
generator.quadDegree = max([e.order + 1 for e in elements])
generator.runTensorProduct(dim, elements, numBlocks, operator, filename)
import numpy from FIAT.polynomial_set import mis from FIAT.reference_element import default_simplex from FIAT.quadrature import make_quadrature order = 1 quadrature = make_quadrature(default_simplex(1), order) from FIAT.lagrange import Lagrange degree = 1 element = Lagrange(default_simplex(1), degree) vertices = [n.get_point_dict().keys()[0] for n in element.dual.get_nodes()] quadpts = numpy.array(quadrature.get_points(), dtype=numpy.float64) quadwts = numpy.array(quadrature.get_weights(), dtype=numpy.float64) numQuadPts = len(quadpts) evals = element.get_nodal_basis().tabulate(quadrature.get_points(), 1) basis = numpy.array(evals[mis(1, 0)[0]], dtype=numpy.float64).transpose() numBasis = element.get_nodal_basis().get_num_members() basisDeriv = numpy.array([evals[alpha] for alpha in mis(1, 1)], dtype=numpy.float64).transpose() print "order: %d" % order print "degree: %d" % degree print "numQuadPts: %d" % numQuadPts print "basis:" print basis print "basisDeriv:" print basisDeriv
