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# Copyright (c) 2020 Chris Richardson
# FEniCS Project
# SPDX-License-Identifier: MIT
import basix
import pytest
import numpy as np
@pytest.mark.parametrize("order", [1, 2, 3])
def test_quad(order):
Lpts, Lwts = basix.make_quadrature("default", basix.CellType.interval, 2*order + 1)
Qwts = []
Qpts = []
for p, u in zip(Lpts, Lwts):
for q, v in zip(Lpts, Lwts):
Qpts.append([p[0], q[0]])
Qwts.append(u * v)
basis = basix.tabulate_polynomial_set(basix.CellType.quadrilateral,
order, 0, Qpts)[0]
ndofs = basis.shape[1]
mat = np.zeros((ndofs, ndofs))
for i in range(ndofs):
for j in range(ndofs):
mat[i, j] = sum(basis[:, i] * basis[:, j] * Qwts)
np.set_printoptions(suppress=True)
print(mat, np.eye(mat.shape[0]))
assert(np.isclose(mat * 4.0, np.eye(mat.shape[0])).all())
@pytest.mark.parametrize("order", [1, 2, 3, 4])
def test_pyramid(order):
Lpts, Lwts = basix.make_quadrature("default", basix.CellType.interval, 4*order + 2)
Qwts = []
Qpts = []
for p, u in zip(Lpts, Lwts):
for q, v in zip(Lpts, Lwts):
for r, w in zip(Lpts, Lwts):
sc = (1.0 - r[0])
Qpts.append([p[0] * sc, q[0] * sc, r[0]])
Qwts.append(u * v * sc * sc * w)
basis = basix.tabulate_polynomial_set(basix.CellType.pyramid,
order, 0, Qpts)[0]
ndofs = basis.shape[1]
mat = np.zeros((ndofs, ndofs))
for i in range(ndofs):
for j in range(ndofs):
mat[i, j] = sum(basis[:, i] * basis[:, j] * Qwts)
np.set_printoptions(suppress=True, linewidth=220)
print(mat)
assert(np.isclose(mat * 8.0, np.eye(mat.shape[0])).all())
@pytest.mark.parametrize("order", [1, 2, 3])
def test_hex(order):
Lpts, Lwts = basix.make_quadrature("default", basix.CellType.interval, 2*order + 1)
Qwts = []
Qpts = []
for p, u in zip(Lpts, Lwts):
for q, v in zip(Lpts, Lwts):
for r, w in zip(Lpts, Lwts):
Qpts.append([p[0], q[0], r[0]])
Qwts.append(u * v * w)
basis = basix.tabulate_polynomial_set(basix.CellType.hexahedron,
order, 0, Qpts)[0]
ndofs = basis.shape[1]
mat = np.zeros((ndofs, ndofs))
for i in range(ndofs):
for j in range(ndofs):
mat[i, j] = sum(basis[:, i] * basis[:, j] * Qwts)
np.set_printoptions(suppress=True)
print(mat)
assert(np.isclose(mat * 8.0, np.eye(mat.shape[0])).all())
@pytest.mark.parametrize("order", [1, 2, 3])
def test_prism(order):
Tpts, Twts = basix.make_quadrature("default", basix.CellType.triangle, 2*order + 1)
Lpts, Lwts = basix.make_quadrature("default", basix.CellType.interval, 2*order + 1)
Qwts = []
Qpts = []
for p, u in zip(Tpts, Twts):
for q, v in zip(Lpts, Lwts):
Qpts.append([p[0], p[1], q[0]])
Qwts.append(u * v)
basis = basix.tabulate_polynomial_set(basix.CellType.prism,
order, 0, Qpts)[0]
ndofs = basis.shape[1]
mat = np.zeros((ndofs, ndofs))
for i in range(ndofs):
for j in range(ndofs):
mat[i, j] = sum(basis[:, i] * basis[:, j] * Qwts)
np.set_printoptions(suppress=True)
print(mat)
assert(np.isclose(mat * 8.0, np.eye(mat.shape[0])).all())
@pytest.mark.parametrize("cell_type", [basix.CellType.interval,
basix.CellType.triangle,
basix.CellType.tetrahedron])
@pytest.mark.parametrize("order", [0, 1, 2, 3, 4])
def test_cell(cell_type, order):
Qpts, Qwts = basix.make_quadrature("default", cell_type, 2*order + 1)
basis = basix.tabulate_polynomial_set(cell_type, order, 0, Qpts)[0]
ndofs = basis.shape[1]
mat = np.zeros((ndofs, ndofs))
for i in range(ndofs):
for j in range(ndofs):
mat[i, j] = sum(basis[:, i] * basis[:, j] * Qwts)
np.set_printoptions(suppress=True)
print(mat)
pts = basix.create_lattice(cell_type, 1, basix.LatticeType.equispaced, True)
fac = 2 ** pts.shape[0] / 2
assert(np.isclose(mat * fac, np.eye(mat.shape[0])).all())
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