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_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_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_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_hdiv():
S = UFCTriangle()
T = UFCInterval()
RT1 = RaviartThomas(S, 1)
P1_DG = DiscontinuousLagrange(T, 1)
elt = Hdiv(TensorProductElement(RT1, P1_DG))
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_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 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_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 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_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_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])