def test_mass_matrix(self):
# Solve
t_eval = np.linspace(0.0, 1.0, 80)
def fun(y, t):
return jax.numpy.stack([0.1 * y[0], y[1] - 2.0 * y[0]])
mass = jax.numpy.array([[2.0, 0.0], [0.0, 0.0]])
# give some bad initial conditions, solver should calculate correct ones using
# this as a guess
y0 = jax.numpy.array([1.0, 1.5])
t0 = time.perf_counter()
y = pybamm.jax_bdf_integrate(fun, y0, t_eval, mass=mass, rtol=1e-8, atol=1e-8)
t1 = time.perf_counter() - t0
# test accuracy
soln = np.exp(0.05 * t_eval)
np.testing.assert_allclose(y[:, 0], soln, rtol=1e-7, atol=1e-7)
np.testing.assert_allclose(y[:, 1], 2.0 * soln, rtol=1e-7, atol=1e-7)
t0 = time.perf_counter()
y = pybamm.jax_bdf_integrate(fun, y0, t_eval, mass=mass, rtol=1e-8, atol=1e-8)
t2 = time.perf_counter() - t0
# second run should be much quicker
self.assertLess(t2, t1)
# test second run is accurate
np.testing.assert_allclose(y[:, 0], np.exp(0.05 * t_eval), rtol=1e-7, atol=1e-7)
def test_solver_with_inputs(self):
# Create model
model = pybamm.BaseModel()
model.convert_to_format = "jax"
domain = ["negative electrode", "separator", "positive electrode"]
var = pybamm.Variable("var", domain=domain)
model.rhs = {var: -pybamm.InputParameter("rate") * var}
model.initial_conditions = {var: 1}
# create discretisation
mesh = get_mesh_for_testing()
spatial_methods = {"macroscale": pybamm.FiniteVolume()}
disc = pybamm.Discretisation(mesh, spatial_methods)
disc.process_model(model)
# Solve
t_eval = np.linspace(0, 10, 80)
y0 = model.concatenated_initial_conditions.evaluate().reshape(-1)
rhs = pybamm.EvaluatorJax(model.concatenated_rhs)
def fun(y, t, inputs):
return rhs.evaluate(t=t, y=y, inputs=inputs).reshape(-1)
y = pybamm.jax_bdf_integrate(
fun, y0, t_eval, {"rate": 0.1}, rtol=1e-9, atol=1e-9
)
np.testing.assert_allclose(y[:, 0].reshape(-1), np.exp(-0.1 * t_eval))
def solve_bdf(rate):
return jax.numpy.sum(
pybamm.jax_bdf_integrate(fun,
y0,
t_eval, {'rate': rate},
rtol=1e-9,
atol=1e-9))
def test_solver(self):
# Create model
model = pybamm.BaseModel()
model.convert_to_format = "jax"
domain = ["negative electrode", "separator", "positive electrode"]
var = pybamm.Variable("var", domain=domain)
model.rhs = {var: 0.1 * var}
model.initial_conditions = {var: 1}
# No need to set parameters; can use base discretisation (no spatial operators)
# create discretisation
mesh = get_mesh_for_testing()
spatial_methods = {"macroscale": pybamm.FiniteVolume()}
disc = pybamm.Discretisation(mesh, spatial_methods)
disc.process_model(model)
# Solve
t_eval = np.linspace(0.0, 1.0, 80)
y0 = model.concatenated_initial_conditions.evaluate().reshape(-1)
rhs = pybamm.EvaluatorJax(model.concatenated_rhs)
def fun(y, t):
return rhs.evaluate(t=t, y=y).reshape(-1)
t0 = time.perf_counter()
y = pybamm.jax_bdf_integrate(fun, y0, t_eval, rtol=1e-8, atol=1e-8)
t1 = time.perf_counter() - t0
# test accuracy
np.testing.assert_allclose(y[:, 0],
np.exp(0.1 * t_eval),
rtol=1e-6,
atol=1e-6)
t0 = time.perf_counter()
y = pybamm.jax_bdf_integrate(fun, y0, t_eval, rtol=1e-8, atol=1e-8)
t2 = time.perf_counter() - t0
# second run should be much quicker
self.assertLess(t2, t1)
# test second run is accurate
np.testing.assert_allclose(y[:, 0],
np.exp(0.1 * t_eval),
rtol=1e-6,
atol=1e-6)
def solve_model_bdf(inputs):
y = pybamm.jax_bdf_integrate(rhs_dae,
y0,
t_eval,
inputs,
rtol=self.rtol,
atol=self.atol,
mass=mass,
**self.extra_options)
return jnp.transpose(y)
