def test_compare_explicit():
"""test explicit solvers"""
grid = UnitGrid([16, 16])
field = ScalarField.random_uniform(grid, -1, 1)
eq = DiffusionPDE()
c1 = Controller(ExplicitSolver(eq), t_range=0.1, tracker=None)
s1 = c1.run(field, dt=2e-3)
c2 = Controller(ExplicitSolver(eq, scheme="runge-kutta"), t_range=0.1, tracker=None)
with np.errstate(under="ignore"):
s2 = c2.run(field, dt=2e-3)
np.testing.assert_allclose(s1.data, s2.data, rtol=1e-2, atol=1e-2)
def test_storage_persistence(compression, tmp_path):
""" test writing to persistent trackers """
dim = 5
grid = UnitGrid([dim])
field = ScalarField(grid)
path = tmp_path / f"test_storage_persistence_{compression}.hdf5"
# write some data
for write_mode in ["append", "truncate_once", "truncate"]:
storage = FileStorage(path,
info={"a": 1},
write_mode=write_mode,
compression=compression)
# first batch
storage.start_writing(field, info={"b": 2})
storage.append(field.copy(data=np.arange(dim)), 0)
storage.append(field.copy(data=np.arange(dim, 2 * dim)))
storage.end_writing()
# read first batch
np.testing.assert_array_equal(storage.times, np.arange(2))
np.testing.assert_array_equal(np.ravel(storage.data), np.arange(10))
assert {"a": 1, "b": 2}.items() <= storage.info.items()
# second batch
storage.start_writing(field, info={"c": 3})
storage.append(field.copy(data=np.arange(2 * dim, 3 * dim)), 2)
storage.end_writing()
storage.close()
# read the data
storage = FileStorage(path)
if write_mode == "truncate":
np.testing.assert_array_equal(storage.times, np.array([2]))
np.testing.assert_array_equal(np.ravel(storage.data),
np.arange(10, 15))
assert storage.shape == (1, 5)
info = {"c": 3}
assert info.items() <= storage.info.items()
else:
np.testing.assert_array_equal(storage.times, np.arange(0, 3))
np.testing.assert_array_equal(np.ravel(storage.data),
np.arange(0, 15))
assert storage.shape == (3, 5)
info = {"a": 1, "b": 2, "c": 3}
assert info.items() <= storage.info.items()
def test_collections():
"""test field collections"""
grid = UnitGrid([3, 4])
sf = ScalarField.random_uniform(grid, label="sf")
vf = VectorField.random_uniform(grid, label="vf")
tf = Tensor2Field.random_uniform(grid, label="tf")
fields = FieldCollection([sf, vf, tf])
assert fields.data.shape == (7, 3, 4)
assert isinstance(str(fields), str)
fields.data[:] = 0
np.testing.assert_allclose(sf.data, 0)
np.testing.assert_allclose(vf.data, 0)
np.testing.assert_allclose(tf.data, 0)
assert fields[0] is fields["sf"]
assert fields[1] is fields["vf"]
assert fields[2] is fields["tf"]
with pytest.raises(KeyError):
fields["42"]
sf.data = 1
vf.data = 1
tf.data = 1
np.testing.assert_allclose(fields.data, 1)
assert all(np.allclose(i, 12) for i in fields.integrals)
assert all(np.allclose(i, 1) for i in fields.averages)
assert np.allclose(fields.magnitudes, np.sqrt([1, 2, 4]))
assert sf.data.shape == (3, 4)
assert vf.data.shape == (2, 3, 4)
assert tf.data.shape == (2, 2, 3, 4)
c2 = FieldBase.from_state(fields.attributes, data=fields.data)
assert c2 == fields
assert c2.grid is grid
attrs = FieldCollection.unserialize_attributes(
fields.attributes_serialized)
c2 = FieldCollection.from_state(attrs, data=fields.data)
assert c2 == fields
assert c2.grid is not grid
fields["sf"] = 2.0
np.testing.assert_allclose(sf.data, 2)
with pytest.raises(KeyError):
fields["42"] = 0
fields.plot(subplot_args=[{}, {"scale": 1}, {"colorbar": False}])
def main():
"""main routine testing the performance"""
print("Reports calls-per-second (larger is better)\n")
# Cartesian grid with different shapes and boundary conditions
for size in [32, 512]:
grid = UnitGrid([size, size], periodic=False)
print(grid)
field = ScalarField.random_normal(grid)
bc_value = np.ones(size)
result = field.laplace(bc={"value": 1}).data
for bc in ["scalar", "array", "function", "time-dependent", "linked"]:
if bc == "scalar":
bcs = {"value": 1}
elif bc == "array":
bcs = {"value": bc_value}
elif bc == "function":
bcs = grid.get_boundary_conditions(
{"virtual_point": "2 - value"})
elif bc == "time-dependent":
bcs = grid.get_boundary_conditions({"value_expression": "t"})
elif bc == "linked":
bcs = grid.get_boundary_conditions({"value": bc_value})
for ax, upper in grid._iter_boundaries():
bcs[ax][upper].link_value(bc_value)
else:
raise RuntimeError
# create the operator with these conditions
laplace = grid.make_operator("laplace", bc=bcs)
if bc == "time-dependent":
args = numba_dict({"t": 1})
# call once to pre-compile and test result
np.testing.assert_allclose(laplace(field.data, args=args),
result)
# estimate the speed
speed = estimate_computation_speed(laplace,
field.data,
args=args)
else:
# call once to pre-compile and test result
np.testing.assert_allclose(laplace(field.data), result)
# estimate the speed
speed = estimate_computation_speed(laplace, field.data)
print(f"{bc:>14s}:{int(speed):>9d}")
print()
def test_from_scalar_expressions():
""" test creating field collections from scalar expressions """
grid = UnitGrid([3])
expressions = ["x**2", "1"]
fc = FieldCollection.from_scalar_expressions(grid,
expressions=expressions,
label="c",
labels=["a", "b"])
assert fc.label == "c"
assert fc[0].label == "a"
assert fc[1].label == "b"
assert fc[0].grid is grid
assert fc[1].grid is grid
np.testing.assert_allclose(fc[0].data, (np.arange(3) + 0.5)**2)
np.testing.assert_allclose(fc[1].data, 1)
def test_collection_plotting():
""" test simple plotting of various fields on various grids """
grid = UnitGrid([5])
s1 = ScalarField(grid, label="s1")
s2 = ScalarField(grid)
fc = FieldCollection([s1, s2])
# test setting different figure sizes
fc.plot(figsize="default")
fc.plot(figsize="auto")
fc.plot(figsize=(3, 3))
# test different arrangements
fc.plot(arrangement="horizontal")
fc.plot(arrangement="vertical")
def test_evaluate_func_vector():
"""test the evaluate function with vector fields"""
grid = UnitGrid([3])
field = ScalarField.from_expression(grid, "x")
vec = VectorField.from_expression(grid, ["x"])
res = evaluate("inner(v, v)", {"v": vec})
assert isinstance(res, ScalarField)
np.testing.assert_almost_equal(res.data, grid.axes_coords[0] ** 2)
res = evaluate("outer(v, v)", {"v": vec})
assert isinstance(res, Tensor2Field)
np.testing.assert_almost_equal(res.data, [[grid.axes_coords[0] ** 2]])
assert isinstance(evaluate("gradient(a)", {"a": field}), VectorField)
def test_diffusion_time_dependent_bcs(backend):
"""test PDE with time-dependent BCs"""
field = ScalarField(UnitGrid([3]))
eq = DiffusionPDE(bc={"value_expression": "Heaviside(t - 1.5)"})
storage = MemoryStorage()
eq.solve(field,
t_range=10,
dt=1e-2,
backend=backend,
tracker=storage.tracker(1))
np.testing.assert_allclose(storage[1].data, 0)
np.testing.assert_allclose(storage[-1].data, 1, rtol=1e-3)
def test_boundaries():
"""test setting boundaries for multiple systems"""
b = ["periodic", "value", {"type": "derivative", "value": 1}]
for bx, by in itertools.product(b, b):
g = UnitGrid([2, 2], periodic=[b == "periodic" for b in (bx, by)])
bcs = Boundaries.from_data(g, [bx, by])
bc_x = get_boundary_axis(g, 0, bx)
bc_y = get_boundary_axis(g, 1, by)
assert bcs.grid.num_axes == 2
assert bcs[0] == bc_x
assert bcs[1] == bc_y
assert bcs == Boundaries.from_data(g, [bc_x, bc_y])
if bx == by:
assert bcs == Boundaries.from_data(g, bx)
bc2 = bcs.copy()
assert bcs == bc2
assert bcs is not bc2
b1 = Boundaries.from_data(UnitGrid([2, 2]), "natural")
b2 = Boundaries.from_data(UnitGrid([3, 3]), "natural")
assert b1 != b2
def test_unit_rect_grid(periodic):
"""test whether the rectangular grid behaves like a unit grid in special cases"""
dim = random.randrange(1, 4)
shape = np.random.randint(2, 10, size=dim)
g1 = UnitGrid(shape, periodic=periodic)
g2 = CartesianGrid(np.c_[np.zeros(dim), shape], shape, periodic=periodic)
volume = np.prod(shape)
for g in [g1, g2]:
assert g.volume == pytest.approx(volume)
assert g.integrate(1) == pytest.approx(volume)
assert g.make_integrator()(np.ones(shape)) == pytest.approx(volume)
assert g1.dim == g2.dim == dim
np.testing.assert_array_equal(g1.shape, g2.shape)
assert g1.typical_discretization == pytest.approx(g2.typical_discretization)
for _ in range(10):
p1, p2 = np.random.normal(scale=10, size=(2, dim))
assert g1.distance_real(p1, p2) == pytest.approx(g2.distance_real(p1, p2))
p0 = np.random.normal(scale=10, size=dim)
np.testing.assert_allclose(
g1.polar_coordinates_real(p0), g2.polar_coordinates_real(p0)
)
def test_individual_boundaries():
"""test setting individual boundaries"""
g = UnitGrid([2])
for data in [
"value",
{
"value": 1
},
{
"type": "value",
"value": 1
},
"derivative",
{
"derivative": 1
},
{
"type": "derivative",
"value": 1
},
{
"mixed": 1
},
{
"type": "mixed",
"value": 1
},
"extrapolate",
]:
bc = BCBase.from_data(g, 0, upper=True, data=data, rank=0)
assert isinstance(str(bc), str)
assert isinstance(repr(bc), str)
assert "field" in bc.get_mathematical_representation("field")
assert bc.rank == 0
assert bc.homogeneous
bc.check_value_rank(0)
with pytest.raises(RuntimeError):
bc.check_value_rank(1)
for bc_copy in [
BCBase.from_data(g, 0, upper=True, data=bc, rank=0),
bc.copy()
]:
assert bc == bc_copy
assert bc._cache_hash() == bc_copy._cache_hash()
assert bc.extract_component() == bc
def test_solvers_simple_example(scheme, adaptive):
"""test explicit solvers"""
grid = UnitGrid([4])
field = ScalarField(grid, 1)
eq = PDE({"c": "c"})
dt = 1e-3 if scheme == "euler" else 1e-2
solver = ExplicitSolver(eq, scheme=scheme, adaptive=adaptive)
controller = Controller(solver, t_range=10.0, tracker=None)
res = controller.run(field, dt=dt)
np.testing.assert_allclose(res.data, np.exp(10), rtol=0.1)
if adaptive:
assert solver.info["steps"] != pytest.approx(10 / dt, abs=1)
else:
assert solver.info["steps"] == pytest.approx(10 / dt, abs=1)
def test_outer_product():
""" test outer product of vector fields """
vf = VectorField(UnitGrid([1, 1]), [[[1]], [[2]]])
outer = vf.make_outer_prod_operator()
tf = vf.outer_product(vf)
res = np.array([1, 2, 2, 4]).reshape(2, 2, 1, 1)
np.testing.assert_equal(tf.data, res)
np.testing.assert_equal(outer(vf.data, vf.data), res)
tf.data = 0
res = np.array([1, 2, 2, 4]).reshape(2, 2, 1, 1)
vf.outer_product(vf, out=tf)
np.testing.assert_equal(tf.data, res)
outer(vf.data, vf.data, out=tf.data)
np.testing.assert_equal(tf.data, res)
def test_pde_consistency_test():
""" test whether the consistency of a pde implementation is checked """
class TestPDE(pdes.PDEBase):
def evolution_rate(self, field, t=0):
return 2 * field
def _make_pde_rhs_numba(self, state):
def impl(state_data, t):
return 3 * state_data
return impl
eq = TestPDE()
state = ScalarField.random_uniform(UnitGrid([4]))
with pytest.raises(AssertionError):
eq.solve(state, t_range=5, tracker=None)
def test_compare_solvers(solver_class):
""" compare several solvers """
field = ScalarField.random_uniform(UnitGrid([8, 8]), -1, 1)
eq = DiffusionPDE()
# ground truth
c1 = Controller(ExplicitSolver(eq, scheme="runge-kutta"),
t_range=0.1,
tracker=None)
s1 = c1.run(field, dt=5e-3)
c2 = Controller(solver_class(eq), t_range=0.1, tracker=None)
with np.errstate(under="ignore"):
s2 = c2.run(field, dt=5e-3)
np.testing.assert_allclose(s1.data, s2.data, rtol=1e-2, atol=1e-2)
def test_plot_tracker(tmp_path):
""" test whether the plot tracker creates files without errors """
output_file = tmp_path / "img.png"
def get_title(state, t):
return f"{state.integral:g} at {t:g}"
grid = UnitGrid([4, 4])
state = ScalarField.random_uniform(grid)
pde = DiffusionPDE()
tracker = trackers.PlotTracker(
output_file=output_file, title=get_title, interval=0.1, show=False
)
pde.solve(state, t_range=0.5, dt=0.005, tracker=tracker, backend="numpy")
assert output_file.stat().st_size > 0
def test_data_tracker(tmp_path):
""" test the DataTracker """
field = ScalarField(UnitGrid([4, 4]))
eq = DiffusionPDE()
path = tmp_path / "test_data_tracker.pickle"
data1 = trackers.DataTracker(lambda f: f.average, filename=path)
data2 = trackers.DataTracker(lambda f: {"avg": f.average, "int": f.integral})
eq.solve(field, 10, tracker=[data1, data2])
with path.open("br") as fp:
time, data = pickle.load(fp)
np.testing.assert_allclose(time, np.arange(11))
assert isinstance(data, list)
assert len(data) == 11
assert path.stat().st_size > 0
def test_boundary_specifications():
"""test different ways of specifying boundary conditions"""
g = UnitGrid([2])
bc1 = Boundaries.from_data(g, [{
"type": "derivative",
"value": 0
}, {
"type": "value",
"value": 0
}])
assert bc1 == Boundaries.from_data(g, [{
"type": "derivative"
}, {
"type": "value"
}])
assert bc1 == Boundaries.from_data(g, [{"derivative": 0}, {"value": 0}])
assert bc1 == Boundaries.from_data(g, ["neumann", "dirichlet"])
def test_smoothing_collection():
""" test smoothing of a FieldCollection """
grid = UnitGrid([3, 4], periodic=[True, False])
sf = ScalarField.random_uniform(grid)
vf = VectorField.random_uniform(grid)
tf = Tensor2Field.random_uniform(grid)
fields = FieldCollection([sf, vf, tf])
sgm = 0.5 + np.random.random()
out = fields.smooth(sigma=sgm)
for i in range(3):
np.testing.assert_allclose(out[i].data, fields[i].smooth(sgm).data)
out.data = 0
fields.smooth(sigma=sgm, out=out)
for i in range(3):
np.testing.assert_allclose(out[i].data, fields[i].smooth(sgm).data)
def test_solvers_complex(backend):
"""test solvers with a complex PDE"""
r = FieldCollection.scalar_random_uniform(2, UnitGrid([3]), labels=["a", "b"])
c = r["a"] + 1j * r["b"]
assert c.is_complex
# assume c = a + i * b
eq_c = PDE({"c": "-I * laplace(c)"})
eq_r = PDE({"a": "laplace(b)", "b": "-laplace(a)"})
res_r = eq_r.solve(r, t_range=1e-2, dt=1e-3, backend="numpy", tracker=None)
exp_c = res_r[0].data + 1j * res_r[1].data
for solver_class in [ExplicitSolver, ImplicitSolver, ScipySolver]:
solver = solver_class(eq_c, backend=backend)
controller = Controller(solver, t_range=1e-2, tracker=None)
res_c = controller.run(c, dt=1e-3)
np.testing.assert_allclose(res_c.data, exp_c, rtol=1e-3, atol=1e-3)
def test_virtual_points_linked_data(upper):
""" test the calculation of virtual points with linked_data """
g = UnitGrid([2, 2])
point = (1, 1) if upper else (0, 0)
data = np.zeros(g.shape)
# test constant boundary conditions
bc_data = np.array([1, 1])
bc = BCBase.from_data(g, 0, upper, {"type": "value", "value": bc_data})
assert not bc.value_is_linked
bc.link_value(bc_data)
assert bc.value_is_linked
bc_data[:] = 3
assert bc.get_virtual_point(data, point) == pytest.approx(6)
ev = bc.make_virtual_point_evaluator()
assert ev(data, point) == pytest.approx(6)
# test derivative boundary conditions (wrt to outwards derivative)
bc = BCBase.from_data(g, 0, upper, {
"type": "derivative",
"value": bc_data
})
assert not bc.value_is_linked
bc.link_value(bc_data)
assert bc.value_is_linked
bc_data[:] = 4
assert bc.get_virtual_point(data, point) == pytest.approx(4)
ev = bc.make_virtual_point_evaluator()
assert ev(data, point) == pytest.approx(4)
# test derivative boundary conditions (wrt to outwards derivative)
bc = BCBase.from_data(g, 0, upper, {
"type": "mixed",
"value": bc_data,
"const": 3
})
assert not bc.value_is_linked
bc.link_value(bc_data)
assert bc.value_is_linked
bc_data[:] = 4
assert bc.get_virtual_point(data, point) == pytest.approx(1)
ev = bc.make_virtual_point_evaluator()
assert ev(data, point) == pytest.approx(1)
def test_stochastic_solvers(backend):
""" test simple version of the stochastic solver """
field = ScalarField.random_uniform(UnitGrid([16]), -1, 1)
eq = DiffusionPDE()
seq = DiffusionPDE(noise=1e-6)
solver1 = ExplicitSolver(eq, backend=backend)
c1 = Controller(solver1, t_range=1, tracker=None)
s1 = c1.run(field, dt=1e-3)
solver2 = ExplicitSolver(seq, backend=backend)
c2 = Controller(solver2, t_range=1, tracker=None)
s2 = c2.run(field, dt=1e-3)
np.testing.assert_allclose(s1.data, s2.data, rtol=1e-4, atol=1e-4)
assert not solver1.info["stochastic"]
assert solver2.info["stochastic"]
def test_material_conservation_tracker():
""" test the MaterialConservationTracker """
state = ScalarField.random_uniform(UnitGrid([8, 8]), 0, 1)
solver = ExplicitSolver(CahnHilliardPDE())
controller = Controller(solver,
t_range=1,
tracker=["material_conservation"])
controller.run(state, dt=1e-3)
assert controller.info["t_final"] >= 1
solver = ExplicitSolver(AllenCahnPDE())
controller = Controller(solver,
t_range=1,
tracker=["material_conservation"])
controller.run(state, dt=1e-3)
assert controller.info["t_final"] <= 1
def test_from_expressions():
""" test initializing vector fields with expressions """
grid = UnitGrid([4, 4])
vf = VectorField.from_expression(grid, ["x**2", "x * y"])
xs = grid.cell_coords[..., 0]
ys = grid.cell_coords[..., 1]
np.testing.assert_allclose(vf.data[0], xs**2)
np.testing.assert_allclose(vf.data[1], xs * ys)
# corner case
vf = VectorField.from_expression(grid, ["1", "x * y"])
with pytest.raises(ValueError):
VectorField.from_expression(grid, "xy")
with pytest.raises(ValueError):
VectorField.from_expression(grid, ["xy"])
with pytest.raises(ValueError):
VectorField.from_expression(grid, ["x"] * 3)
def test_wave_consistency(dim):
"""test some methods of the wave model"""
eq = WavePDE()
assert isinstance(str(eq), str)
assert isinstance(repr(eq), str)
# compare numba to numpy implementation
grid = UnitGrid([4] * dim)
state = eq.get_initial_condition(ScalarField.random_uniform(grid))
field = eq.evolution_rate(state)
assert field.grid == grid
rhs = eq._make_pde_rhs_numba(state)
np.testing.assert_allclose(field.data, rhs(state.data, 0))
# compare to generic implementation
assert isinstance(eq.expressions, dict)
eq2 = PDE(eq.expressions)
np.testing.assert_allclose(field.data, eq2.evolution_rate(state).data)
def test_emulsion_tracker(tmp_path):
"""test using the emulsions tracker"""
path = tmp_path / "test_emulsion_tracker.hdf5"
d = SphericalDroplet([4, 4], 3)
c = d.get_phase_field(UnitGrid([8, 8]))
pde = CahnHilliardPDE()
e1 = EmulsionTimeCourse()
tracker = e1.tracker(filename=path)
pde.solve(c, t_range=1, dt=1e-3, backend="numpy", tracker=tracker)
e2 = EmulsionTimeCourse.from_file(path, progress=False)
assert e1 == e2
assert len(e1) == 2
assert len(e1[0]) == 1 # found a single droplet
assert path.stat().st_size > 0 # wrote some result
def test_pde_consistency(pde_class, dim):
""" test some methods of generic PDE models """
eq = pde_class()
assert isinstance(str(eq), str)
assert isinstance(repr(eq), str)
# compare numba to numpy implementation
grid = UnitGrid([4] * dim)
state = ScalarField.random_uniform(grid)
field = eq.evolution_rate(state)
assert field.grid == grid
rhs = eq._make_pde_rhs_numba(state)
np.testing.assert_allclose(field.data, rhs(state.data, 0))
# compare to generic implementation
assert isinstance(eq.expression, str)
eq2 = pdes.PDE({"c": eq.expression})
np.testing.assert_allclose(field.data, eq2.evolution_rate(state).data)
def test_field_labels():
""" test the FieldCollection.labels property """
grid = UnitGrid([5])
s1 = ScalarField(grid, label="s1")
s2 = ScalarField(grid)
fc = FieldCollection([s1, s2])
assert fc.labels == ["s1", None]
assert len(fc.labels) == 2
assert fc.labels[0] == "s1"
assert fc.labels.index("s1") == 0
assert fc.labels.index(None) == 1
with pytest.raises(ValueError):
fc.labels.index("a")
fc.labels = ["a", "b"]
assert fc.labels == ["a", "b"]
fc.labels[0] = "c"
assert fc.labels == ["c", "b"]
assert str(fc.labels) == str(["c", "b"])
assert repr(fc.labels) == repr(["c", "b"])
assert fc.labels[0:1] == ["c"]
assert fc.labels[:] == ["c", "b"]
fc.labels[0:1] = "d"
assert fc.labels == ["d", "b"]
fc.labels[:] = "a"
assert fc.labels == ["a", "a"]
labels = fc.labels[:]
labels[0] = "e"
assert fc.labels == ["a", "a"]
fc = FieldCollection([s1, s2], labels=[None, "b"])
assert fc.labels == [None, "b"]
fc = FieldCollection([s1, s2], labels=["a", "b"])
assert fc.labels == ["a", "b"]
with pytest.raises(TypeError):
fc.labels = [1, "b"]
with pytest.raises(TypeError):
fc.labels[0] = 1
def test_appending(tmp_path):
"""test the appending data"""
path = tmp_path / "test_appending.hdf5"
c = ScalarField(UnitGrid([2]), data=1)
storage = FileStorage(path)
storage.start_writing(c)
assert len(storage) == 0
storage.append(c, 0)
assert storage._file_state == "writing"
assert len(storage) == 1
storage.close()
storage2 = FileStorage(path, write_mode="append")
storage2.start_writing(c)
storage2.append(c, 1)
storage2.close()
assert len(storage2) == 2
def test_from_expressions():
"""test initializing tensor fields with expressions"""
grid = UnitGrid([4, 4])
tf = Tensor2Field.from_expression(grid, [[1, 1], ["x**2", "x * y"]])
xs = grid.cell_coords[..., 0]
ys = grid.cell_coords[..., 1]
np.testing.assert_allclose(tf.data[0, 1], 1)
np.testing.assert_allclose(tf.data[0, 1], 1)
np.testing.assert_allclose(tf.data[1, 0], xs**2)
np.testing.assert_allclose(tf.data[1, 1], xs * ys)
# corner case
with pytest.raises(ValueError):
Tensor2Field.from_expression(grid, "xy")
with pytest.raises(ValueError):
Tensor2Field.from_expression(grid, ["xy"])
with pytest.raises(ValueError):
Tensor2Field.from_expression(grid, ["x"] * 3)
with pytest.raises(ValueError):
Tensor2Field.from_expression(grid, [["x"], [1, 1]])