def test_pde_spatial_args(backend):
"""test PDE with spatial dependence"""
field = ScalarField(grids.UnitGrid([2]))
eq = PDE({"a": "x"})
rhs = eq.make_pde_rhs(field, backend=backend)
np.testing.assert_allclose(rhs(field.data, 0.0), np.array([0.5, 1.5]))
# test combination of spatial dependence and differential oeprators
eq = PDE({"a": "dot(gradient(x), gradient(a))"})
rhs = eq.make_pde_rhs(field, backend=backend)
np.testing.assert_allclose(rhs(field.data, 0.0), np.array([0.0, 0.0]))
# test invalid spatial dependence
eq = PDE({"a": "x + y"})
with pytest.raises(RuntimeError):
rhs = eq.make_pde_rhs(field, backend=backend)
rhs(field.data, 0.0)
def test_pde_spatial_args():
""" test ScalarFieldExpression without extra dependence """
eq = PDE({"a": "x"})
field = ScalarField(grids.UnitGrid([2]))
rhs = eq.evolution_rate(field)
assert rhs == field.copy(data=[0.5, 1.5])
rhs = eq.make_pde_rhs(field, backend="numba")
np.testing.assert_allclose(rhs(field.data, 0.0), np.array([0.5, 1.5]))
eq = PDE({"a": "x + y"})
with pytest.raises(RuntimeError):
eq.evolution_rate(field)
def test_pde_integral(backend):
"""test PDE with integral"""
grid = grids.UnitGrid([16])
field = ScalarField.random_uniform(grid)
eq = PDE({"c": "-integral(c)"})
# test rhs
rhs = eq.make_pde_rhs(field, backend=backend)
np.testing.assert_allclose(rhs(field.data, 0), -field.integral)
# test evolution
for method in ["scipy", "explicit"]:
res = eq.solve(field, t_range=1000, method=method, tracker=None)
assert res.integral == pytest.approx(0, abs=1e-2)
np.testing.assert_allclose(res.data, field.data - field.magnitude, atol=1e-3)
