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# Copyright (C) 2007-2024 Anders Logg Garth N. Wells, Marie E. Rognes, Lizao Li, Matthew Scroggs
# This test was originally part of FFCx
# Copyright (C) 2007-2017 Anders Logg and Garth N. Wells
#
# This file is part of FFCx.
#
# FFCx is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# FFCx is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with FFCx. If not, see <http://www.gnu.org/licenses/>.
#
# Modified by Marie E. Rognes, 2010
# Modified by Lizao Li, 2016
import random
import numpy as np
import pytest
import basix
import basix.ufl
def random_point(cell):
vertices = basix.geometry(basix.CellType[cell])
w = [random.random() for _ in vertices]
return sum(v * i for v, i in zip(vertices, w)) / sum(w)
@pytest.mark.parametrize(
"family, cell, degree, dim",
[
("Lagrange", "triangle", 1, 3),
("Lagrange", "triangle", 2, 6),
("Lagrange", "triangle", 3, 10),
("DG", "triangle", 1, 3),
("DG", "triangle", 2, 6),
("DG", "triangle", 3, 10),
("Lagrange", "quadrilateral", 1, 4),
("Lagrange", "quadrilateral", 2, 9),
("Lagrange", "quadrilateral", 3, 16),
("Regge", "triangle", 0, 3),
("Regge", "triangle", 1, 9),
("Regge", "triangle", 2, 18),
("Regge", "triangle", 3, 30),
("HHJ", "triangle", 0, 3),
("HHJ", "triangle", 1, 9),
("HHJ", "triangle", 2, 18),
("HHJ", "triangle", 3, 30),
],
)
def test_dimension(family, cell, degree, dim):
e = basix.ufl.element(family, cell, degree)
assert e.dim == dim
@pytest.mark.parametrize(
"family, cell, degree, functions",
[
("Lagrange", "interval", 1, [lambda x: 1 - x[0], lambda x: x[0]]),
(
"Lagrange",
"triangle",
1,
[lambda x: 1 - x[0] - x[1], lambda x: x[0], lambda x: x[1]],
),
(
"Lagrange",
"tetrahedron",
1,
[
lambda x: 1 - x[0] - x[1] - x[2],
lambda x: x[0],
lambda x: x[1],
lambda x: x[2],
],
),
(
"Lagrange",
"quadrilateral",
1,
[
lambda x: (1 - x[0]) * (1 - x[1]),
lambda x: x[0] * (1 - x[1]),
lambda x: (1 - x[0]) * x[1],
lambda x: x[0] * x[1],
],
),
(
"Lagrange",
"hexahedron",
1,
[
lambda x: (1 - x[0]) * (1 - x[1]) * (1 - x[2]),
lambda x: x[0] * (1 - x[1]) * (1 - x[2]),
lambda x: (1 - x[0]) * x[1] * (1 - x[2]),
lambda x: x[0] * x[1] * (1 - x[2]),
lambda x: (1 - x[0]) * (1 - x[1]) * x[2],
lambda x: x[0] * (1 - x[1]) * x[2],
lambda x: (1 - x[0]) * x[1] * x[2],
lambda x: x[0] * x[1] * x[2],
],
),
(
"Brezzi-Douglas-Marini",
"triangle",
1,
[
lambda x: (-x[0], -x[1]),
lambda x: (3**0.5 * x[0], -(3**0.5) * x[1]),
lambda x: (x[0] - 1, x[1]),
lambda x: (3**0.5 * (1 - x[0] - 2 * x[1]), 3**0.5 * x[1]),
lambda x: (-x[0], 1 - x[1]),
lambda x: (-(3**0.5) * x[0], 3**0.5 * (2 * x[0] + x[1] - 1)),
],
),
(
"Raviart-Thomas",
"triangle",
1,
[
lambda x: (-x[0], -x[1]),
lambda x: (x[0] - 1, x[1]),
lambda x: (-x[0], 1 - x[1]),
],
),
(
"Raviart-Thomas",
"tetrahedron",
1,
[
lambda x: (2**0.5 * x[0], 2**0.5 * x[1], 2**0.5 * x[2]),
lambda x: (2**0.5 - 2**0.5 * x[0], -(2**0.5) * x[1], -(2**0.5) * x[2]),
lambda x: (2**0.5 * x[0], 2**0.5 * x[1] - 2**0.5, 2**0.5 * x[2]),
lambda x: (-(2**0.5) * x[0], -(2**0.5) * x[1], 2**0.5 - 2**0.5 * x[2]),
],
),
(
"N1curl",
"triangle",
1,
[
lambda x: (-x[1], x[0]),
lambda x: (x[1], 1 - x[0]),
lambda x: (1.0 - x[1], x[0]),
],
),
(
"N1curl",
"tetrahedron",
1,
[
lambda x: (0.0, -x[2], x[1]),
lambda x: (-x[2], 0.0, x[0]),
lambda x: (-x[1], x[0], 0.0),
lambda x: (x[2], x[2], 1.0 - x[0] - x[1]),
lambda x: (x[1], 1.0 - x[0] - x[2], x[1]),
lambda x: (1.0 - x[1] - x[2], x[0], x[0]),
],
),
],
)
def test_values(family, cell, degree, functions):
# Create element
e = basix.ufl.element(family, cell, degree)
# Get some points and check basis function values at points
points = [random_point(cell) for i in range(5)]
tables = e.tabulate(0, np.array(points, dtype=np.float64))[0]
for x, t in zip(points, tables):
for i, f in enumerate(functions):
assert np.allclose(t[i :: len(functions)], f(x))
def test_hash():
e0 = basix.create_element(basix.ElementFamily.P, basix.CellType.interval, 1)
e1 = basix.create_element(basix.ElementFamily.P, basix.CellType.interval, 1)
e2 = basix.create_element(
basix.ElementFamily.P, basix.CellType.interval, 1, dof_ordering=[0, 1]
)
e3 = basix.create_element(basix.ElementFamily.P, basix.CellType.interval, 2)
e4 = basix.create_element(basix.ElementFamily.P, basix.CellType.triangle, 1)
wcoeffs = np.eye(3)
z = np.zeros((0, 2))
x = [
[np.array([[0.0, 0.0]]), np.array([[1.0, 0.0]]), np.array([[0.0, 1.0]])],
[z, z, z],
[z],
[],
]
z = np.zeros((0, 1, 0, 1))
M = [
[np.array([[[[1.0]]]]), np.array([[[[1.0]]]]), np.array([[[[1.0]]]])],
[z, z, z],
[z],
[],
]
e5 = basix.create_custom_element(
basix.CellType.triangle,
[],
wcoeffs,
x,
M,
0,
basix.MapType.L2Piola,
basix.SobolevSpace.L2,
False,
1,
1,
basix.PolysetType.standard,
)
e6 = basix.create_element(basix.ElementFamily.P, basix.CellType.quadrilateral, 2)
e7 = basix.create_tp_element(basix.ElementFamily.P, basix.CellType.quadrilateral, 2)
assert hash(e0) == hash(e1) == hash(e2)
different_elements = [e2, e3, e4, e5, e6, e7]
for i, d0 in enumerate(different_elements):
for d1 in different_elements[:i]:
assert hash(d0) != hash(d1)
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