def test_compute_entity_collisions_tree_1d(self):
references = [[set([8, 9, 10, 11, 12, 13, 14, 15]),
set([0, 1, 2, 3, 4, 5, 6, 7])],
[set([14, 15]),
set([0, 1])]]
points = [Point(0.52), Point(0.9)]
for i, point in enumerate(points):
mesh_A = UnitIntervalMesh(16)
mesh_B = UnitIntervalMesh(16)
mesh_B.translate(point)
tree_A = BoundingBoxTree()
tree_A.build(mesh_A)
tree_B = BoundingBoxTree()
tree_B.build(mesh_B)
entities_A, entities_B = tree_A.compute_entity_collisions(tree_B)
if MPI.size(mesh_A.mpi_comm()) == 1:
self.assertEqual(set(entities_A), references[i][0])
self.assertEqual(set(entities_B), references[i][1])
def test_compute_collisions_tree_1d():
references = [[set([8, 9, 10, 11, 12, 13, 14, 15]),
set([0, 1, 2, 3, 4, 5, 6, 7])],
[set([14, 15]),
set([0, 1])]]
points = [Point(0.52), Point(0.9)]
for i, point in enumerate(points):
mesh_A = UnitIntervalMesh(16)
mesh_B = UnitIntervalMesh(16)
mesh_B.translate(point)
tree_A = BoundingBoxTree()
tree_A.build(mesh_A)
tree_B = BoundingBoxTree()
tree_B.build(mesh_B)
entities_A, entities_B = tree_A.compute_collisions(tree_B)
assert set(entities_A) == references[i][0]
assert set(entities_B) == references[i][1]
def test_mesh_point_1d(self):
"Test mesh-point intersection in 1D"
point = Point(0.1)
mesh = UnitIntervalMesh(16)
intersection = intersect(mesh, point)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(intersection.intersected_cells(), [1])
def test_compute_collisions_point_1d(self):
reference = {1: set([4])}
p = Point(0.3)
mesh = UnitIntervalMesh(16)
for dim in range(1, 2):
tree = BoundingBoxTree()
tree.build(mesh, dim)
entities = tree.compute_collisions(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(set(entities), reference[dim])
def test_compute_first_entity_collision_1d():
reference = [4]
p = Point(0.3)
mesh = UnitIntervalMesh(16)
tree = BoundingBoxTree()
tree.build(mesh)
first = tree.compute_first_entity_collision(p)
assert first in reference
tree = mesh.bounding_box_tree()
first = tree.compute_first_entity_collision(p)
assert first in reference
def test_compute_entity_collisions_1d():
reference = set([4])
p = Point(0.3)
mesh = UnitIntervalMesh(16)
tree = BoundingBoxTree()
tree.build(mesh)
entities = tree.compute_entity_collisions(p)
assert set(entities) == reference
tree = mesh.bounding_box_tree()
entities = tree.compute_entity_collisions(p)
assert set(entities) == reference
def test_compute_first_collision_1d():
reference = {1: [4]}
p = Point(0.3)
mesh = UnitIntervalMesh(16)
for dim in range(1, 2):
tree = BoundingBoxTree()
tree.build(mesh, dim)
first = tree.compute_first_collision(p)
assert first in reference[dim]
tree = mesh.bounding_box_tree()
first = tree.compute_first_collision(p)
assert first in reference[mesh.topology().dim()]
def test_compute_first_entity_collision_1d(self):
reference = [4]
p = Point(0.3)
mesh = UnitIntervalMesh(16)
tree = BoundingBoxTree()
tree.build(mesh)
first = tree.compute_first_entity_collision(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertIn(first, reference)
tree = mesh.bounding_box_tree()
first = tree.compute_first_entity_collision(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertIn(first, reference)
def test_compute_first_collision_1d(self):
reference = {1: [4]}
p = Point(0.3)
mesh = UnitIntervalMesh(16)
for dim in range(1, 2):
tree = BoundingBoxTree()
tree.build(mesh, dim)
first = tree.compute_first_collision(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertIn(first, reference[dim])
tree = mesh.bounding_box_tree()
first = tree.compute_first_collision(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertIn(first, reference[mesh.topology().dim()])
def test_compute_entity_collisions_1d(self):
reference = [4]
p = Point(0.3)
mesh = UnitIntervalMesh(16)
tree = BoundingBoxTree()
tree.build(mesh)
entities = tree.compute_entity_collisions(p, mesh)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities), reference)
tree = mesh.bounding_box_tree()
entities = tree.compute_entity_collisions(p, mesh)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities), reference)
def test_compute_closest_entity_1d():
reference = (0, 1.0)
p = Point(-1.0)
mesh = UnitIntervalMesh(16)
tree = BoundingBoxTree()
tree.build(mesh)
entity, distance = tree.compute_closest_entity(p)
assert entity == reference[0]
assert round(distance - reference[1], 7) == 0
tree = mesh.bounding_box_tree()
entity, distance = tree.compute_closest_entity(p)
assert entity == reference[0]
assert round(distance - reference[1], 7) == 0
def test_compute_collisions_1d(self):
reference = {1: [4]}
p = Point(0.3)
mesh = UnitIntervalMesh(16)
for dim in range(1, 2):
tree = BoundingBoxTree()
tree.build(mesh, dim)
entities = tree.compute_collisions(p)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities), reference[dim])
tree = mesh.bounding_box_tree()
entities = tree.compute_collisions(p)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities), reference[mesh.topology().dim()])
def test_compute_entity_collisions_1d(self):
reference = set([4])
p = Point(0.3)
mesh = UnitIntervalMesh(16)
tree = BoundingBoxTree()
tree.build(mesh)
entities = tree.compute_entity_collisions(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(set(entities), reference)
tree = mesh.bounding_box_tree()
entities = tree.compute_entity_collisions(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(set(entities), reference)
def test_compute_closest_entity_1d(self):
reference = (0, 1.0)
p = Point(-1.0)
mesh = UnitIntervalMesh(16)
tree = BoundingBoxTree()
tree.build(mesh)
entity, distance = tree.compute_closest_entity(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(entity, reference[0])
self.assertAlmostEqual(distance, reference[1])
tree = mesh.bounding_box_tree()
entity, distance = tree.compute_closest_entity(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(entity, reference[0])
self.assertAlmostEqual(distance, reference[1])
def test_transport_rectangle(self):
m, n = 10, 100
v = 0.1 * np.ones((m, n))
# Define mesh.
mesh = UnitIntervalMesh(n - 1)
# Define function spaces
V = FunctionSpace(mesh, 'CG', 1)
f0 = Rectangle(degree=1)
f0 = interpolate(f0, V)
# Compute transport
f = transport1d(v, np.zeros_like(v), f0.vector().get_local())
fig, ax = plt.subplots(figsize=(10, 5))
cax = ax.imshow(f, cmap=cm.coolwarm)
fig.colorbar(cax, orientation='vertical')
plt.show()
plt.close(fig)
np.testing.assert_equal(f.shape, (m + 1, n))
def test_block_size_real(mesh):
mesh = UnitIntervalMesh(12)
V = FiniteElement('DG', mesh.ufl_cell(), 0)
R = FiniteElement('R', mesh.ufl_cell(), 0)
X = FunctionSpace(mesh, V * R)
assert X.dofmap().index_map.block_size == 1
def interval():
return UnitIntervalMesh(MPI.comm_world, 10)
def mesh1d():
# Create 1D mesh with degenerate cell
mesh1d = UnitIntervalMesh(MPI.comm_world, 4)
mesh1d.geometry.points[4] = mesh1d.geometry.points[3]
return mesh1d
def initMesh(self, n):
self.mesh = UnitIntervalMesh(n)
def test_structured(tol=1E-15):
'Test with structured non-uniform mesh. Fenicstools vs matrix.'
passed = []
for d in [1, 2, 3]:
if d == 1:
mesh = UnitIntervalMesh(20)
mesh.coordinates()[:] = np.cos(2*pi*mesh.coordinates())
elif d == 2:
mesh = UnitSquareMesh(20, 20)
mesh.coordinates()[:] = np.cos(2*pi*mesh.coordinates())
else:
mesh = UnitCubeMesh(5, 5, 5)
mesh.coordinates()[:, 0] = mesh.coordinates()[:, 0]**3
mesh.coordinates()[:, 1] = mesh.coordinates()[:, 1]**2
mesh.coordinates()[:, 2] = mesh.coordinates()[:, 2]**2
for j in range(d):
WP = build_WP(mesh, 'harmonic', i=j).array()
F_WP = f_build_WP(mesh, i=j).array()
e = np.linalg.norm(WP - F_WP)/WP.shape[0]
passed.append(e < tol)
assert(all(passed))
def structured_mesh_1d():
return UnitIntervalMesh(24)
def test_dolfin():
from dolfin import FiniteElement, FunctionSpace, UnitIntervalMesh, interval
mesh = UnitIntervalMesh(20)
elem = FiniteElement("CG", interval, 1)
W = FunctionSpace(mesh, elem)
writer = csv.DictWriter(csvfile, fieldnames=fieldnames)
writer.writeheader()
for step in range(steps):
if model == 'SmoothSol':
fac = 2**(step)
# Set discretization level
nt = 30 * fac
nx = 5 * fac
ny = 5 * fac
T = [0, 1]
# Mesh for stochastic part
mx = UnitIntervalMesh(nx)
x = SpatialCoordinate(mx)[0]
# Mesh for deterministic part
my = UnitIntervalMesh(ny)
y = SpatialCoordinate(my)[0]
# Set up coefficients as described above
# Diffusion in x direction
ax = as_matrix([[1]])
# Convection in x direction
bx = as_vector([0])
# Convection in y direction
def by(t, x, y):
def meshes_p1():
return UnitIntervalMesh(10), UnitSquareMesh(3, 3), UnitCubeMesh(2, 2, 2)
# 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 DOLFIN. If not, see <http://www.gnu.org/licenses/>.
import pytest
import numpy as np
from dolfin import (UnitIntervalMesh, UnitSquareMesh, UnitCubeMesh, Point, MPI,
FunctionSpace, TestFunction, TrialFunction, assemble,
Constant, PointSource, dx, Cell, VectorFunctionSpace, near,
vertex_to_dof_map, vertices, dot, FiniteElement, Function,
VectorElement, MixedElement)
meshes = [UnitIntervalMesh(10), UnitSquareMesh(10, 10), UnitCubeMesh(4, 4, 4)]
data = [(UnitIntervalMesh(10), Point(0.5)),
(UnitSquareMesh(10, 10), Point(0.5, 0.5)),
(UnitCubeMesh(3, 3, 3), Point(0.5, 0.5, 0.5))]
@pytest.mark.parametrize("mesh, point", data)
def test_pointsource_vector_node(mesh, point):
"""Tests point source when given constructor PointSource(V, point,
mag) with a vector and when placed at a node for 1D, 2D and
3D. Global points given to constructor from rank 0 processor.
"""
rank = MPI.rank(mesh.mpi_comm())
V = FunctionSpace(mesh, "CG", 1)
def mesh_generator(n):
return UnitIntervalMesh(n)
m, n = 40, 200
# Define parameters of artificial velocity field.
c0 = 0.05
v0 = 0.5
tau0 = 0.5
tau1 = 0.5
# Create artificial velocity.
v = velocity(m, n, c0, v0, tau0, tau1)
# Convert to array.
v = funvec2img(v.vector().get_local(), m, n)
# Define mesh.
mesh = UnitIntervalMesh(n - 1)
# Define function spaces
V = FunctionSpace(mesh, 'CG', 1)
class DoubleHat(UserExpression):
def eval(self, value, x):
value[0] = max(0, 0.1 - abs(x[0] - 0.4)) \
+ max(0, 0.1 - abs(x[0] - 0.6))
def value_shape(self):
return ()
class InitialData(UserExpression):
def test_ghost_facet_1d():
mesh = UnitIntervalMesh(MPI.comm_world,
20,
ghost_mode=cpp.mesh.GhostMode.shared_facet)
assert mesh.num_entities_global(0) == 21
assert mesh.num_entities_global(1) == 20
import numpy as np
from dolfin import (
interpolate,
Constant,
Expression,
FunctionSpace,
UnitIntervalMesh,
)
from tests.utils.solves import assert_solves
from tests.utils.types import assemble_with_mixed_types
MESH = UnitIntervalMesh(32)
EXACT_EXPRESSION = "sin(DOLFIN_PI * x[0])"
EXACT = Expression(EXACT_EXPRESSION, degree=4)
DIFFUSIVITY = 1.0 / (np.pi * np.pi)
DIFFUSION_TERM = f"DOLFIN_PI * DOLFIN_PI * {DIFFUSIVITY} * {EXACT_EXPRESSION}"
CONVECTIVITY = [1.0 / np.pi]
CONVECTION_TERM = "-cos(DOLFIN_PI * x[0])"
REACTIVITY = 1.0
REACTION_TERM = EXACT_EXPRESSION
def test_1d_types():
mesh = UnitIntervalMesh(4)
CG = FunctionSpace(mesh, "CG", 1)
DG = FunctionSpace(mesh, "DG", 0)
diffusion = Expression("1. + x[0] * (1. - x[0])", degree=2)
from dolfin import Expression, plot, UnitIntervalMesh
from ufl.algorithms import estimate_total_polynomial_degree as get_degree
class MyExpr(Expression):
def __init__(self, a, **kwargs):
self.a = a
def eval(self, value, x):
value[0] = x[0] + self.a
f = MyExpr(10, degree=10)
assert get_degree(f) == 10
mesh = UnitIntervalMesh(100)
plot(f, mesh=mesh, interactive=True)
def test_diff_then_integrate():
# Define 1D geometry
n = 21
mesh = UnitIntervalMesh(MPI.comm_world, n)
# Shift and scale mesh
x0, x1 = 1.5, 3.14
mesh.coordinates()[:] *= (x1 - x0)
mesh.coordinates()[:] += x0
x = SpatialCoordinate(mesh)[0]
xs = 0.1 + 0.8 * x / x1 # scaled to be within [0.1,0.9]
# Define list of expressions to test, and configure
# accuracies these expressions are known to pass with.
# The reason some functions are less accurately integrated is
# likely that the default choice of quadrature rule is not perfect
F_list = []
def reg(exprs, acc=10):
for expr in exprs:
F_list.append((expr, acc))
# FIXME: 0*dx and 1*dx fails in the ufl-ffc-jit framework somewhere
# reg([Constant(0.0, cell=cell)])
# reg([Constant(1.0, cell=cell)])
monomial_list = [x**q for q in range(2, 6)]
reg(monomial_list)
reg([2.3 * p + 4.5 * q for p in monomial_list for q in monomial_list])
reg([x**x])
reg([x**(x**2)], 8)
reg([x**(x**3)], 6)
reg([x**(x**4)], 2)
# Special functions:
reg([atan(xs)], 8)
reg([sin(x), cos(x), exp(x)], 5)
reg([ln(xs), pow(x, 2.7), pow(2.7, x)], 3)
reg([asin(xs), acos(xs)], 1)
reg([tan(xs)], 7)
try:
import scipy
except ImportError:
scipy = None
if hasattr(math, 'erf') or scipy is not None:
reg([erf(xs)])
else:
print(
"Warning: skipping test of erf, old python version and no scipy.")
# if 0:
# print("Warning: skipping tests of bessel functions, doesn't build on all platforms.")
# elif scipy is None:
# print("Warning: skipping tests of bessel functions, missing scipy.")
# else:
# for nu in (0, 1, 2):
# # Many of these are possibly more accurately integrated,
# # but 4 covers all and is sufficient for this test
# reg([bessel_J(nu, xs), bessel_Y(nu, xs), bessel_I(nu, xs), bessel_K(nu, xs)], 4)
# To handle tensor algebra, make an x dependent input tensor
# xx and square all expressions
def reg2(exprs, acc=10):
for expr in exprs:
F_list.append((inner(expr, expr), acc))
xx = as_matrix([[2 * x**2, 3 * x**3], [11 * x**5, 7 * x**4]])
x3v = as_vector([3 * x**2, 5 * x**3, 7 * x**4])
cc = as_matrix([[2, 3], [4, 5]])
reg2([xx])
reg2([x3v])
reg2([cross(3 * x3v, as_vector([-x3v[1], x3v[0], x3v[2]]))])
reg2([xx.T])
reg2([tr(xx)])
reg2([det(xx)])
reg2([dot(xx, 0.1 * xx)])
reg2([outer(xx, xx.T)])
reg2([dev(xx)])
reg2([sym(xx)])
reg2([skew(xx)])
reg2([elem_mult(7 * xx, cc)])
reg2([elem_div(7 * xx, xx + cc)])
reg2([elem_pow(1e-3 * xx, 1e-3 * cc)])
reg2([elem_pow(1e-3 * cc, 1e-3 * xx)])
reg2([elem_op(lambda z: sin(z) + 2, 0.03 * xx)], 2) # pretty inaccurate...
# FIXME: Add tests for all UFL operators:
# These cause discontinuities and may be harder to test in the
# above fashion:
# 'inv', 'cofac',
# 'eq', 'ne', 'le', 'ge', 'lt', 'gt', 'And', 'Or', 'Not',
# 'conditional', 'sign',
# 'jump', 'avg',
# 'LiftingFunction', 'LiftingOperator',
# FIXME: Test other derivatives: (but algorithms for operator
# derivatives are the same!):
# 'variable', 'diff',
# 'Dx', 'grad', 'div', 'curl', 'rot', 'Dn', 'exterior_derivative',
# Run through all operators defined above and compare integrals
debug = 0
for F, acc in F_list:
# Apply UFL differentiation
f = diff(F, SpatialCoordinate(mesh))[..., 0]
if debug:
print(F)
print(x)
print(f)
# Apply integration with DOLFIN
# (also passes through form compilation and jit)
M = f * dx
f_integral = assemble_scalar(M) # noqa
f_integral = MPI.sum(mesh.mpi_comm(), f_integral)
# Compute integral of f manually from anti-derivative F
# (passes through PyDOLFIN interface and uses UFL evaluation)
F_diff = F((x1, )) - F((x0, ))
# Compare results. Using custom relative delta instead
# of decimal digits here because some numbers are >> 1.
delta = min(abs(f_integral), abs(F_diff)) * 10**-acc
assert f_integral - F_diff <= delta
def test_distance_tetrahedron():
mesh = UnitCubeMesh(MPI.comm_self, 1, 1, 1)
cell = MeshEntity(mesh, mesh.topology.dim, 5)
assert cpp.geometry.squared_distance(cell,
numpy.array([-1.0, -1.0, -1.0
])) == pytest.approx(3.0)
assert cpp.geometry.squared_distance(cell,
numpy.array([-1.0, 0.5, 0.5
])) == pytest.approx(1.0)
assert cpp.geometry.squared_distance(cell,
numpy.array([0.5, 0.5, 0.5
])) == pytest.approx(0.0)
@pytest.mark.parametrize('mesh', [
UnitIntervalMesh(MPI.comm_world, 8),
UnitSquareMesh(MPI.comm_world, 8, 9, CellType.triangle),
UnitSquareMesh(MPI.comm_world, 8, 9, CellType.quadrilateral),
UnitCubeMesh(MPI.comm_world, 8, 9, 5, CellType.tetrahedron)
])
def test_volume_cells(mesh):
num_cells = mesh.num_entities(mesh.topology.dim)
v = cpp.mesh.volume_entities(mesh, range(num_cells), mesh.topology.dim)
v = MPI.sum(mesh.mpi_comm(), v.sum())
assert v == pytest.approx(1.0, rel=1e-9)
def test_volume_quadrilateralR2():
mesh = UnitSquareMesh(MPI.comm_self, 1, 1, CellType.quadrilateral)
assert cpp.mesh.volume_entities(mesh, [0], mesh.topology.dim) == 1.0
