def test_stochastic_adaptive_solver(caplog):
"""test using an adaptive, stochastic solver"""
field = ScalarField.random_uniform(UnitGrid([16]), -1, 1)
eq = DiffusionPDE(noise=1e-6)
with caplog.at_level(logging.WARNING):
solver = ExplicitSolver(eq, backend="numpy", adaptive=True)
c = Controller(solver, t_range=1, tracker=None)
c.run(field, dt=1e-2)
assert "fixed" in caplog.text
def test_no_dt():
""" test scipy solver without timestep """
grid = UnitGrid([16])
field = ScalarField.random_uniform(grid, -1, 1)
eq = DiffusionPDE()
c1 = Controller(ScipySolver(eq), t_range=1, tracker=None)
s1 = c1.run(field, dt=1e-3)
c2 = Controller(ScipySolver(eq), t_range=1, tracker=None)
s2 = c2.run(field)
np.testing.assert_allclose(s1.data, s2.data, rtol=1e-3, atol=1e-3)
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_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_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_solvers_simple_ode(scheme, adaptive):
"""test explicit solvers with a simple ODE"""
grid = UnitGrid([1])
field = ScalarField(grid, 1)
eq = PDE({"y": "2*sin(t) - y"})
dt = 1e-3 if scheme == "euler" else 1e-2
storage = MemoryStorage()
solver = ExplicitSolver(eq, scheme=scheme, adaptive=adaptive)
controller = Controller(solver, t_range=20.0, tracker=storage.tracker(1))
controller.run(field, dt=dt)
ts = np.ravel(storage.times)
expect = 2 * np.exp(-ts) - np.cos(ts) + np.sin(ts)
np.testing.assert_allclose(np.ravel(storage.data), expect, atol=0.05)
if adaptive:
assert solver.info["steps"] < 20 / dt
else:
assert solver.info["steps"] == pytest.approx(20 / dt, abs=1)
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_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)