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# Copyright (C) 2011-2022 Garth N. Wells, Jørgen S. Dokken
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
"""Unit tests for the Function class"""
import importlib
from mpi4py import MPI
import cffi
import numpy as np
import pytest
import ufl
from basix.ufl import element, mixed_element
from dolfinx import default_real_type, la
from dolfinx.fem import Function, functionspace
from dolfinx.geometry import bb_tree, compute_colliding_cells, compute_collisions_points
from dolfinx.mesh import create_mesh, create_unit_cube
@pytest.fixture
def mesh():
return create_unit_cube(MPI.COMM_WORLD, 3, 3, 3)
@pytest.fixture
def V(mesh):
return functionspace(mesh, ("Lagrange", 1))
@pytest.fixture
def W(mesh):
gdim = mesh.geometry.dim
return functionspace(mesh, ("Lagrange", 1, (gdim,)))
@pytest.fixture
def Q(mesh):
gdim = mesh.geometry.dim
return functionspace(mesh, ("Lagrange", 1, (gdim, gdim)))
def test_name_argument(W):
u = Function(W)
v = Function(W, name="v")
assert u.name == "f"
assert v.name == "v"
assert str(v) == "v"
def test_copy(V):
u = Function(V)
u.interpolate(lambda x: x[0] + 2 * x[1])
v = u.copy()
assert np.allclose(u.x.array, v.x.array)
u.x.array[:] = 1
assert not np.allclose(u.x.array, v.x.array)
def test_eval(V, W, Q, mesh):
u1 = Function(V)
u2 = Function(W)
u3 = Function(Q)
def e2(x):
values = np.empty((3, x.shape[1]))
values[0] = x[0] + x[1] + x[2]
values[1] = x[0] - x[1] - x[2]
values[2] = x[0] + x[1] + x[2]
return values
def e3(x):
values = np.empty((9, x.shape[1]))
values[0] = x[0] + x[1] + x[2]
values[1] = x[0] - x[1] - x[2]
values[2] = x[0] + x[1] + x[2]
values[3] = x[0]
values[4] = x[1]
values[5] = x[2]
values[6] = -x[0]
values[7] = -x[1]
values[8] = -x[2]
return values
u1.interpolate(lambda x: x[0] + x[1] + x[2])
u2.interpolate(e2)
u3.interpolate(e3)
x0 = (mesh.geometry.x[0] + mesh.geometry.x[1]) / 2.0
tree = bb_tree(mesh, mesh.geometry.dim)
cell_candidates = compute_collisions_points(tree, x0)
cell = compute_colliding_cells(mesh, cell_candidates, x0).array
assert len(cell) > 0
first_cell = cell[0]
assert np.allclose(u3.eval(x0, first_cell)[:3], u2.eval(x0, first_cell), rtol=1e-15, atol=1e-15)
@pytest.mark.skip_in_parallel
def test_eval_manifold():
# Simple two-triangle surface in 3d
vertices = np.array(
[(0.0, 0.0, 1.0), (1.0, 1.0, 1.0), (1.0, 0.0, 0.0), (0.0, 1.0, 0.0)],
dtype=default_real_type,
)
cells = [(0, 1, 2), (0, 1, 3)]
domain = ufl.Mesh(element("Lagrange", "triangle", 1, shape=(2,), dtype=default_real_type))
mesh = create_mesh(MPI.COMM_WORLD, cells, vertices, domain)
Q = functionspace(mesh, ("Lagrange", 1))
u = Function(Q)
u.interpolate(lambda x: x[0] + x[1])
assert np.isclose(u.eval([0.75, 0.25, 0.5], 0)[0], 1.0)
def test_interpolation_mismatch_rank0(W):
u = Function(W)
with pytest.raises(RuntimeError):
u.interpolate(lambda x: np.ones(x.shape[1]))
def test_interpolation_mismatch_rank1(W):
u = Function(W)
with pytest.raises(RuntimeError):
u.interpolate(lambda x: np.ones((2, x.shape[1])))
def test_mixed_element_interpolation():
mesh = create_unit_cube(MPI.COMM_WORLD, 3, 3, 3)
el = element("Lagrange", mesh.basix_cell(), 1, dtype=default_real_type)
V = functionspace(mesh, mixed_element([el, el]))
u = Function(V)
with pytest.raises(RuntimeError):
u.interpolate(lambda x: np.ones(2, x.shape[1]))
def test_interpolation_rank0(V):
class MyExpression:
def __init__(self):
self.t = 0.0
def eval(self, x):
return np.full(x.shape[1], self.t)
f = MyExpression()
f.t = 1.0
w = Function(V)
w.interpolate(f.eval)
assert (w.x.array[:] == 1.0).all() # /NOSONAR
num_vertices = V.mesh.topology.index_map(0).size_global
assert np.isclose(la.norm(w.x, la.Norm.l1) - num_vertices, 0)
f.t = 2.0
w.interpolate(f.eval)
assert (w.x.array[:] == 2.0).all() # /NOSONAR
def test_interpolation_rank1(W):
def f(x):
values = np.empty((3, x.shape[1]))
values[0] = 1.0
values[1] = 2.0
values[2] = 3.0
return values
w = Function(W)
w.interpolate(f)
x = w.x.array
assert x.max() == 3.0 # /NOSONAR
assert x.min() == 1.0 # /NOSONAR
num_vertices = W.mesh.topology.index_map(0).size_global
assert round(la.norm(w.x, la.Norm.l1) - 6 * num_vertices, 7) == 0
@pytest.mark.parametrize("dtype,cdtype", [(np.float32, "float"), (np.float64, "double")])
def test_cffi_expression(dtype, cdtype):
mesh = create_unit_cube(MPI.COMM_WORLD, 3, 3, 3, dtype=dtype)
V = functionspace(mesh, ("Lagrange", 1))
code_h = f"void eval({cdtype}* values, int num_points, int value_size, const {cdtype}* x);"
code_c = """
void eval(xtype* values, int num_points, int value_size, const xtype* x)
{
/* x0 + x1 */
for (int i = 0; i < num_points; ++i)
values[i] = x[i] + x[i + num_points];
}
"""
code_c = code_c.replace("xtype", cdtype)
# Build the kernel
module = "_expr_eval" + cdtype + str(MPI.COMM_WORLD.rank)
ffi = cffi.FFI()
ffi.set_source(module, code_c)
ffi.cdef(code_h)
ffi.compile()
# Import the compiled kernel
kernel_mod = importlib.import_module(module)
ffi, lib = kernel_mod.ffi, kernel_mod.lib
# Get pointer to the compiled function
eval_ptr = ffi.cast("uintptr_t", ffi.addressof(lib, "eval"))
# Handle C func address by hand
f1 = Function(V, dtype=dtype)
f1.interpolate(int(eval_ptr))
f2 = Function(V, dtype=dtype)
f2.interpolate(lambda x: x[0] + x[1])
f1.x.array[:] -= f2.x.array
assert la.norm(f1.x) < 1.0e-12
def test_interpolation_function(mesh):
V = functionspace(mesh, ("Lagrange", 1))
u = Function(V)
u.x.array[:] = 1
Vh = functionspace(mesh, ("Lagrange", 1))
uh = Function(Vh)
uh.interpolate(u)
assert np.allclose(uh.x.array, 1)
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