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|
# Copyright (c) 2021 Matthew Scroggs
# FEniCS Project
# SPDX-License-Identifier: MIT
import numpy as np
import pytest
import basix
from .utils import parametrize_over_elements
def run_test(lower_element, higher_element, power, value_size):
l_points = lower_element.points
l_eval = np.concatenate(
[l_points[:, 0] ** power if i == 0 else 0 * l_points[:, 0] for i in range(value_size)]
)
l_coeffs = lower_element.interpolation_matrix @ l_eval
i_m = basix.compute_interpolation_operator(lower_element, higher_element)
h_coeffs = i_m @ l_coeffs
h_points = higher_element.points
h_eval = np.concatenate(
[h_points[:, 0] ** power if i == 0 else 0 * h_points[:, 0] for i in range(value_size)]
)
h_coeffs2 = higher_element.interpolation_matrix @ h_eval
assert np.allclose(h_coeffs, h_coeffs2)
@pytest.mark.parametrize(
"cell_type",
[
basix.CellType.interval,
basix.CellType.triangle,
basix.CellType.tetrahedron,
basix.CellType.quadrilateral,
basix.CellType.hexahedron,
basix.CellType.prism,
],
)
@pytest.mark.parametrize("orders", [(1, 2), (2, 4), (4, 5)])
def test_different_order_interpolation_lagrange(cell_type, orders):
lower_element = basix.create_element(
basix.ElementFamily.P, cell_type, orders[0], basix.LagrangeVariant.gll_warped
)
higher_element = basix.create_element(
basix.ElementFamily.P, cell_type, orders[1], basix.LagrangeVariant.gll_warped
)
run_test(lower_element, higher_element, orders[0], lower_element.value_size)
@pytest.mark.parametrize(
"variant1",
[
basix.LagrangeVariant.equispaced,
basix.LagrangeVariant.gll_warped,
basix.LagrangeVariant.gll_isaac,
],
)
@pytest.mark.parametrize(
"variant2",
[
basix.LagrangeVariant.equispaced,
basix.LagrangeVariant.gll_warped,
basix.LagrangeVariant.gll_isaac,
],
)
@pytest.mark.parametrize(
"cell_type",
[
basix.CellType.interval,
basix.CellType.triangle,
basix.CellType.tetrahedron,
basix.CellType.quadrilateral,
basix.CellType.hexahedron,
basix.CellType.prism,
],
)
@pytest.mark.parametrize("order", [1, 4])
def test_different_variant_interpolation(cell_type, order, variant1, variant2):
lower_element = basix.create_element(basix.ElementFamily.P, cell_type, order, variant1)
higher_element = basix.create_element(basix.ElementFamily.P, cell_type, order, variant2)
run_test(lower_element, higher_element, order, lower_element.value_size)
@pytest.mark.parametrize(
"family, args",
[
[basix.ElementFamily.RT, (basix.LagrangeVariant.legendre,)],
[basix.ElementFamily.N1E, (basix.LagrangeVariant.legendre,)],
[basix.ElementFamily.BDM, (basix.LagrangeVariant.legendre, basix.DPCVariant.legendre)],
[basix.ElementFamily.N2E, (basix.LagrangeVariant.legendre, basix.DPCVariant.legendre)],
],
)
@pytest.mark.parametrize(
"cell_type",
[
basix.CellType.triangle,
basix.CellType.tetrahedron,
basix.CellType.quadrilateral,
basix.CellType.hexahedron,
],
)
@pytest.mark.parametrize("orders", [(1, 2), (2, 4), (4, 5)])
def test_different_order_interpolation_vector(family, args, cell_type, orders):
lower_element = basix.create_element(family, cell_type, orders[0], *args)
higher_element = basix.create_element(family, cell_type, orders[1], *args)
run_test(lower_element, higher_element, orders[0] - 1, lower_element.value_size)
@pytest.mark.parametrize("family, args", [[basix.ElementFamily.Regge, tuple()]])
@pytest.mark.parametrize("cell_type", [basix.CellType.triangle, basix.CellType.tetrahedron])
@pytest.mark.parametrize("orders", [(1, 2), (2, 4), (4, 5)])
def test_different_order_interpolation_matrix(family, args, cell_type, orders):
lower_element = basix.create_element(family, cell_type, orders[0], *args)
higher_element = basix.create_element(family, cell_type, orders[1], *args)
run_test(lower_element, higher_element, orders[0] - 1, lower_element.value_size)
@pytest.mark.parametrize(
"family1, args1",
[
[basix.ElementFamily.RT, (basix.LagrangeVariant.legendre,)],
[basix.ElementFamily.N1E, (basix.LagrangeVariant.legendre,)],
[basix.ElementFamily.BDM, (basix.LagrangeVariant.legendre, basix.DPCVariant.legendre)],
[basix.ElementFamily.N2E, (basix.LagrangeVariant.legendre, basix.DPCVariant.legendre)],
],
)
@pytest.mark.parametrize(
"family2, args2",
[
[basix.ElementFamily.RT, (basix.LagrangeVariant.legendre,)],
[basix.ElementFamily.N1E, (basix.LagrangeVariant.legendre,)],
[basix.ElementFamily.BDM, (basix.LagrangeVariant.legendre, basix.DPCVariant.legendre)],
[basix.ElementFamily.N2E, (basix.LagrangeVariant.legendre, basix.DPCVariant.legendre)],
],
)
@pytest.mark.parametrize(
"cell_type",
[
basix.CellType.triangle,
basix.CellType.tetrahedron,
basix.CellType.quadrilateral,
basix.CellType.hexahedron,
],
)
@pytest.mark.parametrize("order", [1, 4])
def test_different_element_interpolation(family1, args1, family2, args2, cell_type, order):
lower_element = basix.create_element(family1, cell_type, order, *args1)
higher_element = basix.create_element(family2, cell_type, order, *args2)
run_test(lower_element, higher_element, order - 1, lower_element.value_size)
@pytest.mark.parametrize(
"cell_type",
[
basix.CellType.triangle,
basix.CellType.tetrahedron,
basix.CellType.quadrilateral,
basix.CellType.hexahedron,
],
)
@pytest.mark.parametrize("order", [1, 4])
def test_blocked_interpolation(cell_type, order):
"""Test interpolation of Nedelec's components into a Lagrange space."""
nedelec = basix.create_element(
basix.ElementFamily.N2E,
cell_type,
order,
basix.LagrangeVariant.legendre,
basix.DPCVariant.legendre,
)
lagrange = basix.create_element(
basix.ElementFamily.P, cell_type, order, basix.LagrangeVariant.gll_isaac
)
n_points = nedelec.points
if nedelec.value_size == 2:
n_eval = np.concatenate([n_points[:, 0] ** order, n_points[:, 1] ** order])
else:
n_eval = np.concatenate(
[n_points[:, 0] ** order, 0 * n_points[:, 0], n_points[:, 1] ** order]
)
n_coeffs = nedelec.interpolation_matrix @ n_eval
l_points = lagrange.points
if nedelec.value_size == 2:
values = [l_points[:, 0] ** order, l_points[:, 1] ** order]
else:
values = [l_points[:, 0] ** order, 0 * l_points[:, 0], l_points[:, 1] ** order]
l_coeffs = np.empty(lagrange.dim * nedelec.value_size)
for i, v in enumerate(values):
l_coeffs[i :: nedelec.value_size] = v
# Test interpolation from Nedelec to blocked Lagrange
i_m = basix.compute_interpolation_operator(nedelec, lagrange)
assert np.allclose(l_coeffs, i_m @ n_coeffs)
# Test interpolation from blocked Lagrange to Nedelec
i_m = basix.compute_interpolation_operator(lagrange, nedelec)
assert np.allclose(n_coeffs, i_m @ l_coeffs)
@parametrize_over_elements(5)
def test_degree_bounds(cell_type, degree, element_type, element_args):
generator = np.random.default_rng(13)
element = basix.create_element(element_type, cell_type, degree, *element_args)
points = basix.create_lattice(cell_type, 10, basix.LatticeType.equispaced, True)
tab = element.tabulate(0, points)[0]
# Test that this element's basis functions are contained in Lagrange
# space with degree element.embedded_superdegree
coeffs = generator.random(element.dim)
values = np.array([tab[:, :, i] @ coeffs for i in range(element.value_size)])
if element.polyset_type == basix.PolysetType.standard:
p_family = basix.ElementFamily.P
elif element.polyset_type == basix.PolysetType.macroedge:
p_family = basix.ElementFamily.iso
if element.embedded_superdegree >= 0:
# The element being tested should be a subset of this Lagrange space
lagrange = basix.create_element(
p_family,
cell_type,
element.embedded_superdegree,
basix.LagrangeVariant.equispaced,
discontinuous=True,
)
lagrange_coeffs = basix.compute_interpolation_operator(element, lagrange) @ coeffs
lagrange_tab = lagrange.tabulate(0, points)[0]
lagrange_values = np.array(
[
lagrange_tab[:, :, 0] @ lagrange_coeffs[i :: element.value_size]
for i in range(element.value_size)
]
)
assert np.allclose(values, lagrange_values)
if element.embedded_superdegree >= 1:
# The element being tested should be NOT a subset of this
# Lagrange space
lagrange = basix.create_element(
p_family,
cell_type,
element.embedded_superdegree - 1,
basix.LagrangeVariant.equispaced,
discontinuous=True,
)
lagrange_coeffs = basix.compute_interpolation_operator(element, lagrange) @ coeffs
lagrange_tab = lagrange.tabulate(0, points)[0]
lagrange_values = np.array(
[
lagrange_tab[:, :, 0] @ lagrange_coeffs[i :: element.value_size]
for i in range(element.value_size)
]
)
assert not np.allclose(values, lagrange_values)
# Test that the basis functions of Lagrange space with degree
# element.embedded_subdegree are contained in this space
if element.embedded_subdegree >= 0:
# This Lagrange space should be a subset to the element being
# tested
lagrange = basix.create_element(
p_family,
cell_type,
element.embedded_subdegree,
basix.LagrangeVariant.equispaced,
discontinuous=True,
)
lagrange_coeffs = generator.random(lagrange.dim * element.value_size)
lagrange_tab = lagrange.tabulate(0, points)[0]
lagrange_values = np.array(
[
lagrange_tab[:, :, 0] @ lagrange_coeffs[i :: element.value_size]
for i in range(element.value_size)
]
)
coeffs = basix.compute_interpolation_operator(lagrange, element) @ lagrange_coeffs
values = np.array([tab[:, :, i] @ coeffs for i in range(element.value_size)])
assert np.allclose(values, lagrange_values)
if element.polyset_type == basix.PolysetType.macroedge:
if cell_type == basix.CellType.triangle and element.embedded_subdegree + 1 > 2:
pytest.xfail("Cannot run test with macro polyset on a triangle with degree > 2")
if cell_type == basix.CellType.tetrahedron and element.embedded_subdegree + 1 > 1:
pytest.xfail("Cannot run test with macro polyset on a tetrahedron with degree > 1")
if element.embedded_subdegree >= -1:
# This Lagrange space should NOT be a subset to the element
# being tested
lagrange = basix.create_element(
p_family,
cell_type,
element.embedded_subdegree + 1,
basix.LagrangeVariant.equispaced,
discontinuous=True,
)
lagrange_coeffs = generator.random(lagrange.dim * element.value_size)
lagrange_tab = lagrange.tabulate(0, points)[0]
lagrange_values = np.array(
[
lagrange_tab[:, :, 0] @ lagrange_coeffs[i :: element.value_size]
for i in range(element.value_size)
]
)
coeffs = basix.compute_interpolation_operator(lagrange, element) @ lagrange_coeffs
values = np.array([tab[:, :, i] @ coeffs for i in range(element.value_size)])
assert not np.allclose(values, lagrange_values)
|
