def test_solve_ode_model_with_dae_solver(self):
# Create model
model = pybamm.BaseModel()
var = pybamm.Variable("var")
model.rhs = {var: 0.1 * var}
model.initial_conditions = {var: 1}
disc = get_discretisation_for_testing()
disc.process_model(model)
# Solve
solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
t_eval = np.linspace(0, 1, 100)
solution = solver.solve(model, t_eval)
np.testing.assert_array_equal(solution.t, t_eval)
np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t))
def test_model_step_nonsmooth_events(self):
# Create model
model = pybamm.BaseModel()
model.timescale = pybamm.Scalar(1)
var1 = pybamm.Variable("var1")
var2 = pybamm.Variable("var2")
a = 0.6
discontinuities = (np.arange(3) + 1) * a
model.rhs = {var1: pybamm.Modulo(pybamm.t * model.timescale, a)}
model.algebraic = {var2: 2 * var1 - var2}
model.initial_conditions = {var1: 0, var2: 0}
model.events = [
pybamm.Event("var1 = 0.55", pybamm.min(var1 - 0.55)),
pybamm.Event("var2 = 1.2", pybamm.min(var2 - 1.2)),
]
for discontinuity in discontinuities:
model.events.append(
pybamm.Event("nonsmooth rate", pybamm.Scalar(discontinuity)))
disc = get_discretisation_for_testing()
disc.process_model(model)
# Solve
step_solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
dt = 0.05
time = 0
end_time = 3
step_solution = None
while time < end_time:
step_solution = step_solver.step(step_solution,
model,
dt=dt,
npts=10)
time += dt
np.testing.assert_array_less(step_solution.y[0, :-1], 0.55)
np.testing.assert_array_less(step_solution.y[-1, :-1], 1.2)
np.testing.assert_equal(step_solution.t_event[0], step_solution.t[-1])
np.testing.assert_array_equal(step_solution.y_event[:, 0],
step_solution.y[:, -1])
var1_soln = (step_solution.t %
a)**2 / 2 + a**2 / 2 * (step_solution.t // a)
var2_soln = 2 * var1_soln
np.testing.assert_array_almost_equal(step_solution.y[0],
var1_soln,
decimal=5)
np.testing.assert_array_almost_equal(step_solution.y[-1],
var2_soln,
decimal=5)
def test_discretisation(self):
param = pybamm.standard_parameters_lithium_ion
model_n = pybamm.interface.lithium_ion.ButlerVolmer(param, "Negative")
j_n = model_n.get_coupled_variables(
self.variables)["Negative electrode interfacial current density"]
model_p = pybamm.interface.lithium_ion.ButlerVolmer(param, "Positive")
j_p = model_p.get_coupled_variables(
self.variables)["Positive electrode interfacial current density"]
j = pybamm.Concatenation(j_n,
pybamm.PrimaryBroadcast(0,
["separator"]), j_p)
# Process parameters and discretise
parameter_values = pybamm.lithium_ion.BaseModel(
).default_parameter_values
disc = get_discretisation_for_testing()
mesh = disc.mesh
disc.set_variable_slices([
self.c_e_n,
self.c_e_p,
self.delta_phi_s_n,
self.delta_phi_s_p,
self.c_s_n_surf,
self.c_s_p_surf,
])
j_n = disc.process_symbol(parameter_values.process_symbol(j_n))
j_p = disc.process_symbol(parameter_values.process_symbol(j_p))
j = disc.process_symbol(parameter_values.process_symbol(j))
# test butler-volmer in each electrode
submesh = np.concatenate([
mesh["negative electrode"][0].nodes,
mesh["positive electrode"][0].nodes
])
y = np.concatenate([submesh**2, submesh**3, submesh**4])
self.assertEqual(
j_n.evaluate(None, y).shape,
(mesh["negative electrode"][0].npts, 1))
self.assertEqual(
j_p.evaluate(None, y).shape,
(mesh["positive electrode"][0].npts, 1))
# test concatenated butler-volmer
whole_cell = ["negative electrode", "separator", "positive electrode"]
whole_cell_mesh = disc.mesh.combine_submeshes(*whole_cell)
self.assertEqual(
j.evaluate(None, y).shape, (whole_cell_mesh[0].npts, 1))
def test_model_solver_ode_python(self):
model = pybamm.BaseModel()
model.convert_to_format = "python"
whole_cell = ["negative electrode", "separator", "positive electrode"]
var = pybamm.Variable("var", domain=whole_cell)
model.rhs = {var: 0.1 * var}
model.initial_conditions = {var: 1}
disc = get_discretisation_for_testing()
disc.process_model(model)
# Solve
solver = pybamm.ScikitsOdeSolver(rtol=1e-9, atol=1e-9)
t_eval = np.linspace(0, 1, 100)
solution = solver.solve(model, t_eval)
np.testing.assert_array_equal(solution.t, t_eval)
np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t))
def test_process_with_no_check(self):
# create model
whole_cell = ["negative electrode", "separator", "positive electrode"]
c = pybamm.Variable("c", domain=whole_cell)
N = pybamm.grad(c)
model = pybamm.BaseModel()
model.rhs = {c: pybamm.div(N)}
model.initial_conditions = {c: pybamm.Scalar(3)}
model.boundary_conditions = {
c: {"left": (0, "Neumann"), "right": (0, "Neumann")}
}
model.variables = {"c": c, "N": N}
# create discretisation
disc = get_discretisation_for_testing()
disc.process_model(model, check_model=False)
def test_save(self):
model = pybamm.BaseModel()
# create both 1D and 2D variables
c = pybamm.Variable("c")
d = pybamm.Variable("d", domain="negative electrode")
model.rhs = {c: -c, d: 1}
model.initial_conditions = {c: 1, d: 2}
model.variables = {"c": c, "d": d, "2c": 2 * c}
disc = get_discretisation_for_testing()
disc.process_model(model)
solution = pybamm.ScipySolver().solve(model, np.linspace(0, 1))
# test save data
with self.assertRaises(ValueError):
solution.save_data("test.pickle")
# set variables first then save
solution.update(["c", "d"])
solution.save_data("test.pickle")
data_load = pybamm.load("test.pickle")
np.testing.assert_array_equal(solution.data["c"], data_load["c"])
np.testing.assert_array_equal(solution.data["d"], data_load["d"])
# to matlab
solution.save_data("test.mat", to_format="matlab")
data_load = loadmat("test.mat")
np.testing.assert_array_equal(solution.data["c"], data_load["c"].flatten())
np.testing.assert_array_equal(solution.data["d"], data_load["d"])
# to csv
with self.assertRaisesRegex(
ValueError, "only 0D variables can be saved to csv"
):
solution.save_data("test.csv", to_format="csv")
# only save "c" and "2c"
solution.save_data("test.csv", ["c", "2c"], to_format="csv")
# read csv
df = pd.read_csv("test.csv")
np.testing.assert_array_almost_equal(df["c"], solution.data["c"])
np.testing.assert_array_almost_equal(df["2c"], solution.data["2c"])
# test save whole solution
solution.save("test.pickle")
solution_load = pybamm.load("test.pickle")
self.assertEqual(solution.model.name, solution_load.model.name)
np.testing.assert_array_equal(solution["c"].entries, solution_load["c"].entries)
np.testing.assert_array_equal(solution["d"].entries, solution_load["d"].entries)
def test_secondary_broadcast_2D(self):
# secondary broadcast in 2D --> Matrix multiplication
disc = get_discretisation_for_testing()
mesh = disc.mesh
var = pybamm.Variable("var", domain=["negative particle"])
broad = pybamm.SecondaryBroadcast(var, "negative electrode")
disc.set_variable_slices([var])
broad_disc = disc.process_symbol(broad)
self.assertIsInstance(broad_disc, pybamm.MatrixMultiplication)
self.assertIsInstance(broad_disc.children[0], pybamm.Matrix)
self.assertIsInstance(broad_disc.children[1], pybamm.StateVector)
self.assertEqual(
broad_disc.shape,
(mesh["negative particle"][0].npts *
mesh["negative electrode"][0].npts, 1),
)
def test_check_tab_bcs_error(self):
a = pybamm.Variable("a", domain=["current collector"])
b = pybamm.Variable("b", domain=["negative electrode"])
bcs = {
"negative tab": (0, "Dirichlet"),
"positive tab": (0, "Neumann")
}
disc = get_discretisation_for_testing()
# for 0D bcs keys should be unchanged
new_bcs = disc.check_tab_conditions(a, bcs)
self.assertListEqual(list(bcs.keys()), list(new_bcs.keys()))
# error if domain not "current collector"
with self.assertRaisesRegex(pybamm.ModelError, "Boundary conditions"):
disc.check_tab_conditions(b, bcs)
def test_model_solver_dae_inputs_events(self):
# Create model
for form in ["python", "casadi"]:
model = pybamm.BaseModel()
model.convert_to_format = form
whole_cell = [
"negative electrode", "separator", "positive electrode"
]
var1 = pybamm.Variable("var1", domain=whole_cell)
var2 = pybamm.Variable("var2", domain=whole_cell)
model.rhs = {var1: pybamm.InputParameter("rate 1") * var1}
model.algebraic = {
var2: pybamm.InputParameter("rate 2") * var1 - var2
}
model.initial_conditions = {var1: 1, var2: 2}
model.events = [
pybamm.Event("var1 = 1.5", pybamm.min(var1 - 1.5)),
pybamm.Event("var2 = 2.5", pybamm.min(var2 - 2.5)),
]
disc = get_discretisation_for_testing()
disc.process_model(model)
# Solve
if form == "python":
solver = pybamm.ScikitsDaeSolver(rtol=1e-8,
atol=1e-8,
root_method="lm")
else:
solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
t_eval = np.linspace(0, 5, 100)
solution = solver.solve(model,
t_eval,
inputs={
"rate 1": 0.1,
"rate 2": 2
})
np.testing.assert_array_less(solution.y[0, :-1], 1.5)
np.testing.assert_array_less(solution.y[-1, :-1], 2.5)
np.testing.assert_array_equal(solution.y_event[:, 0],
solution.y[:, -1])
np.testing.assert_equal(solution.t_event[0], solution.t[-1])
np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t))
np.testing.assert_allclose(solution.y[-1],
2 * np.exp(0.1 * solution.t))
def test_process_complex_expression(self):
var1 = pybamm.Variable("var1")
var2 = pybamm.Variable("var2")
scal1 = pybamm.Scalar(1)
scal2 = pybamm.Scalar(2)
scal3 = pybamm.Scalar(3)
scal4 = pybamm.Scalar(4)
expression = (scal1 * (scal3 + var2)) / ((var1 - scal4) + scal2)
# create discretisation
disc = get_discretisation_for_testing()
disc.y_slices = {var1.id: [slice(53)], var2.id: [slice(53, 106)]}
exp_disc = disc.process_symbol(expression)
self.assertIsInstance(exp_disc, pybamm.Division)
# left side
self.assertIsInstance(exp_disc.children[0], pybamm.Multiplication)
self.assertIsInstance(exp_disc.children[0].children[0], pybamm.Scalar)
self.assertIsInstance(exp_disc.children[0].children[1], pybamm.Addition)
self.assertTrue(
isinstance(exp_disc.children[0].children[1].children[0], pybamm.Scalar)
)
self.assertTrue(
isinstance(exp_disc.children[0].children[1].children[1], pybamm.StateVector)
)
self.assertEqual(
exp_disc.children[0].children[1].children[1].y_slices[0],
disc.y_slices[var2.id][0],
)
# right side
self.assertIsInstance(exp_disc.children[1], pybamm.Addition)
self.assertTrue(
isinstance(exp_disc.children[1].children[0], pybamm.Subtraction)
)
self.assertTrue(
isinstance(exp_disc.children[1].children[0].children[0], pybamm.StateVector)
)
self.assertEqual(
exp_disc.children[1].children[0].children[0].y_slices[0],
disc.y_slices[var1.id][0],
)
self.assertTrue(
isinstance(exp_disc.children[1].children[0].children[1], pybamm.Scalar)
)
self.assertIsInstance(exp_disc.children[1].children[1], pybamm.Scalar)
def test_simplify_concatenation_state_vectors(self):
disc = get_discretisation_for_testing()
mesh = disc.mesh
a = pybamm.Variable("a", domain=["negative electrode"])
b = pybamm.Variable("b", domain=["separator"])
c = pybamm.Variable("c", domain=["positive electrode"])
conc = pybamm.Concatenation(a, b, c)
disc.set_variable_slices([a, b, c])
conc_disc = disc.process_symbol(conc)
conc_simp = conc_disc.simplify()
y = mesh.combine_submeshes(*conc.domain)[0].nodes ** 2
self.assertIsInstance(conc_simp, pybamm.StateVector)
self.assertEqual(len(conc_simp.y_slices), 1)
self.assertEqual(conc_simp.y_slices[0].start, 0)
self.assertEqual(conc_simp.y_slices[0].stop, len(y))
np.testing.assert_array_equal(conc_disc.evaluate(y=y), conc_simp.evaluate(y=y))
def test_solve_with_symbolic_input_1D_vector_input(self):
var = pybamm.Variable("var", "negative electrode")
model = pybamm.BaseModel()
param = pybamm.InputParameter("param", "negative electrode")
model.rhs = {var: -param * var}
model.initial_conditions = {var: 2}
model.variables = {"var": var}
# create discretisation
disc = get_discretisation_for_testing()
disc.process_model(model)
# Solve - scalar input
solver = pybamm.CasadiSolver()
solution = solver.solve(model, np.linspace(0, 1))
n = disc.mesh["negative electrode"].npts
solver = pybamm.CasadiSolver()
t_eval = np.linspace(0, 1)
solution = solver.solve(model, t_eval)
p = np.linspace(0, 1, n)[:, np.newaxis]
np.testing.assert_array_almost_equal(
solution["var"].value({"param": 3 * np.ones(n)}),
np.repeat(2 * np.exp(-3 * t_eval), 40)[:, np.newaxis],
decimal=4,
)
np.testing.assert_array_almost_equal(
solution["var"].value({"param": 2 * p}),
2 * np.exp(-2 * p * t_eval).T.reshape(-1, 1),
decimal=4,
)
np.testing.assert_array_almost_equal(
solution["var"].sensitivity({"param": 3 * np.ones(n)}),
np.kron(-2 * t_eval * np.exp(-3 * t_eval), np.eye(40)).T,
decimal=4,
)
sens = solution["var"].sensitivity({"param": p}).full()
for idx, t in enumerate(t_eval):
np.testing.assert_array_almost_equal(
sens[40 * idx:40 * (idx + 1), :],
-2 * t * np.exp(-p * t) * np.eye(40),
decimal=4,
)
def test_concatenated_parameters(self):
# create
s_param = pybamm.standard_parameters_lead_acid.s_plus_S
self.assertIsInstance(s_param, pybamm.Concatenation)
self.assertEqual(
s_param.domain,
["negative electrode", "separator", "positive electrode"])
# process parameters and discretise
parameter_values = pybamm.ParameterValues(
chemistry=pybamm.parameter_sets.Sulzer2019)
disc = get_discretisation_for_testing()
processed_s = disc.process_symbol(
parameter_values.process_symbol(s_param))
# test output
combined_submeshes = disc.mesh.combine_submeshes(
"negative electrode", "separator", "positive electrode")
self.assertEqual(processed_s.shape, (combined_submeshes.npts, 1))
def test_concatenation_of_scalars(self):
whole_cell = ["negative electrode", "separator", "positive electrode"]
a = pybamm.PrimaryBroadcast(5, ["negative electrode"])
b = pybamm.PrimaryBroadcast(4, ["separator"])
# create discretisation
disc = get_discretisation_for_testing()
mesh = disc.mesh
variables = [pybamm.Variable("var", domain=whole_cell)]
disc.set_variable_slices(variables)
eqn = pybamm.Concatenation(a, b)
eqn_disc = disc.process_symbol(eqn)
expected_vector = np.concatenate([
5 * np.ones_like(mesh["negative electrode"][0].nodes),
4 * np.ones_like(mesh["separator"][0].nodes),
])[:, np.newaxis]
np.testing.assert_allclose(eqn_disc.evaluate(), expected_vector)
def test_model_solver_dae_bad_ics_python(self):
model = pybamm.BaseModel()
model.convert_to_format = "python"
whole_cell = ["negative electrode", "separator", "positive electrode"]
var1 = pybamm.Variable("var1", domain=whole_cell)
var2 = pybamm.Variable("var2", domain=whole_cell)
model.rhs = {var1: 0.1 * var1}
model.algebraic = {var2: 2 * var1 - var2}
model.initial_conditions = {var1: 1, var2: 3}
disc = get_discretisation_for_testing()
disc.process_model(model)
# Solve
solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8, root_method="lm")
t_eval = np.linspace(0, 1, 100)
solution = solver.solve(model, t_eval)
np.testing.assert_array_equal(solution.t, t_eval)
np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t))
np.testing.assert_allclose(solution.y[-1], 2 * np.exp(0.1 * solution.t))
def test_solve_with_symbolic_input_1D_scalar_input(self):
var = pybamm.Variable("var", "negative electrode")
model = pybamm.BaseModel()
param = pybamm.InputParameter("param")
model.algebraic = {var: var + param}
model.initial_conditions = {var: 2}
model.variables = {"var": var}
# create discretisation
disc = tests.get_discretisation_for_testing()
disc.process_model(model)
# Solve - scalar input
solver = pybamm.CasadiAlgebraicSolver()
solution = solver.solve(model, [0])
np.testing.assert_array_equal(solution["var"].value({"param": 7}), -7)
np.testing.assert_array_equal(solution["var"].value({"param": 3}), -3)
np.testing.assert_array_equal(
solution["var"].sensitivity({"param": 3}), -1)
def test_processed_variable_2D(self):
t = pybamm.t
var = pybamm.Variable("var",
domain=["negative electrode", "separator"])
x = pybamm.SpatialVariable("x",
domain=["negative electrode", "separator"])
eqn = t * var + x
# On nodes
disc = tests.get_discretisation_for_testing()
disc.set_variable_slices([var])
x_sol = disc.process_symbol(x).entries[:, 0]
var_sol = disc.process_symbol(var)
eqn_sol = disc.process_symbol(eqn)
t_sol = np.linspace(0, 1)
y_sol = np.ones_like(x_sol)[:, np.newaxis] * np.linspace(0, 5)
processed_var = pybamm.ProcessedVariable(var_sol,
t_sol,
y_sol,
mesh=disc.mesh)
np.testing.assert_array_equal(processed_var.entries[1:-1], y_sol)
np.testing.assert_array_equal(processed_var(t_sol, x_sol), y_sol)
processed_eqn = pybamm.ProcessedVariable(eqn_sol,
t_sol,
y_sol,
mesh=disc.mesh)
np.testing.assert_array_equal(processed_eqn(t_sol, x_sol),
t_sol * y_sol + x_sol[:, np.newaxis])
# Test extrapolation
np.testing.assert_array_equal(processed_var.entries[0],
2 * y_sol[0] - y_sol[1])
np.testing.assert_array_equal(processed_var.entries[1],
2 * y_sol[-1] - y_sol[-2])
# On edges
x_s_edge = pybamm.Matrix(disc.mesh["separator"][0].edges,
domain="separator")
processed_x_s_edge = pybamm.ProcessedVariable(x_s_edge, t_sol, y_sol,
disc.mesh)
np.testing.assert_array_equal(x_s_edge.entries[:, 0],
processed_x_s_edge.entries[1:-1, 0])
def test_broadcast(self):
whole_cell = ["negative electrode", "separator", "positive electrode"]
a = pybamm.InputParameter("a")
var = pybamm.Variable("var")
# create discretisation
disc = get_discretisation_for_testing()
mesh = disc.mesh
combined_submesh = mesh.combine_submeshes(*whole_cell)
# scalar
broad = disc.process_symbol(pybamm.FullBroadcast(a, whole_cell, {}))
np.testing.assert_array_equal(
broad.evaluate(inputs={"a": 7}),
7 * np.ones_like(combined_submesh[0].nodes[:, np.newaxis]),
)
self.assertEqual(broad.domain, whole_cell)
broad_disc = disc.process_symbol(broad)
self.assertIsInstance(broad_disc, pybamm.Multiplication)
self.assertIsInstance(broad_disc.children[0], pybamm.InputParameter)
self.assertIsInstance(broad_disc.children[1], pybamm.Vector)
# process Broadcast variable
disc.y_slices = {var.id: [slice(1)]}
broad1 = pybamm.FullBroadcast(var, ["negative electrode"], None)
broad1_disc = disc.process_symbol(broad1)
self.assertIsInstance(broad1_disc, pybamm.Multiplication)
self.assertIsInstance(broad1_disc.children[0], pybamm.StateVector)
self.assertIsInstance(broad1_disc.children[1], pybamm.Vector)
# broadcast to edges
broad_to_edges = pybamm.FullBroadcastToEdges(a, ["negative electrode"],
None)
broad_to_edges_disc = disc.process_symbol(broad_to_edges)
np.testing.assert_array_equal(
broad_to_edges_disc.evaluate(inputs={"a": 7}),
7 *
np.ones_like(mesh["negative electrode"][0].edges[:, np.newaxis]),
)
def test_discretise_spatial_operator(self):
# create discretisation
whole_cell = ["negative electrode", "separator", "positive electrode"]
var = pybamm.Variable("var", domain=whole_cell)
disc = get_discretisation_for_testing()
mesh = disc.mesh
variables = [var]
disc.set_variable_slices(variables)
# Simple expressions
for eqn in [pybamm.grad(var), pybamm.div(var)]:
eqn_disc = disc.process_symbol(eqn)
self.assertIsInstance(eqn_disc, pybamm.MatrixMultiplication)
self.assertIsInstance(eqn_disc.children[0], pybamm.Matrix)
self.assertIsInstance(eqn_disc.children[1], pybamm.StateVector)
combined_submesh = mesh.combine_submeshes(*whole_cell)
y = combined_submesh[0].nodes**2
var_disc = disc.process_symbol(var)
# grad and var are identity operators here (for testing purposes)
np.testing.assert_array_equal(eqn_disc.evaluate(None, y),
var_disc.evaluate(None, y))
# More complex expressions
for eqn in [var * pybamm.grad(var), var * pybamm.div(var)]:
eqn_disc = disc.process_symbol(eqn)
self.assertIsInstance(eqn_disc, pybamm.Multiplication)
self.assertIsInstance(eqn_disc.children[0], pybamm.StateVector)
self.assertIsInstance(eqn_disc.children[1],
pybamm.MatrixMultiplication)
self.assertIsInstance(eqn_disc.children[1].children[0],
pybamm.Matrix)
self.assertIsInstance(eqn_disc.children[1].children[1],
pybamm.StateVector)
y = combined_submesh[0].nodes**2
var_disc = disc.process_symbol(var)
# grad and var are identity operators here (for testing purposes)
np.testing.assert_array_equal(eqn_disc.evaluate(None, y),
var_disc.evaluate(None, y)**2)
def test_model_solver_ode_events(self):
# Create model
model = pybamm.BaseModel()
whole_cell = ["negative electrode", "separator", "positive electrode"]
var = pybamm.Variable("var", domain=whole_cell)
model.rhs = {var: 0.1 * var}
model.initial_conditions = {var: 1}
model.events = {
"2 * var = 2.5": pybamm.min(2 * var - 2.5),
"var = 1.5": pybamm.min(var - 1.5),
}
disc = get_discretisation_for_testing()
disc.process_model(model)
# Solve
solver = pybamm.ScikitsOdeSolver(rtol=1e-9, atol=1e-9)
t_eval = np.linspace(0, 10, 100)
solution = solver.solve(model, t_eval)
np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t))
np.testing.assert_array_less(solution.y[0], 1.5)
np.testing.assert_array_less(solution.y[0], 1.25)
def test_exceptions(self):
c_n = pybamm.Variable("c", domain=["negative electrode"])
N_n = pybamm.grad(c_n)
c_s = pybamm.Variable("c", domain=["separator"])
N_s = pybamm.grad(c_s)
model = pybamm.BaseModel()
model.rhs = {c_n: pybamm.div(N_n), c_s: pybamm.div(N_s)}
model.initial_conditions = {
c_n: pybamm.Scalar(3),
c_s: pybamm.Scalar(1)
}
model.boundary_conditions = {
c_n: {
"left": (0, "Neumann"),
"right": (0, "Neumann")
},
c_s: {
"left": (0, "Neumann"),
"right": (0, "Neumann")
},
}
disc = get_discretisation_for_testing()
# check raises error if different sized key and output var
model.variables = {c_n.name: c_s}
with self.assertRaisesRegex(pybamm.ModelError, "variable and its eqn"):
disc.process_model(model)
# check doesn't raise if concatenation
model.variables = {c_n.name: pybamm.Concatenation(c_n, c_s)}
disc.process_model(model, inplace=False)
# check doesn't raise if broadcast
model.variables = {
c_n.name:
pybamm.PrimaryBroadcast(pybamm.InputParameter("a"),
["negative electrode"])
}
disc.process_model(model)
def test_model_step_dae_python(self):
model = pybamm.BaseModel()
model.convert_to_format = "python"
whole_cell = ["negative electrode", "separator", "positive electrode"]
var1 = pybamm.Variable("var1", domain=whole_cell)
var2 = pybamm.Variable("var2", domain=whole_cell)
model.rhs = {var1: 0.1 * var1}
model.algebraic = {var2: 2 * var1 - var2}
model.initial_conditions = {var1: 1, var2: 2}
model.use_jacobian = False
disc = get_discretisation_for_testing()
disc.process_model(model)
solver = pybamm.ScikitsDaeSolver(rtol=1e-8,
atol=1e-8,
root_method="lm")
# Step once
dt = 1
step_sol = solver.step(None, model, dt)
np.testing.assert_array_equal(step_sol.t, [0, dt])
np.testing.assert_allclose(step_sol.y[0], np.exp(0.1 * step_sol.t))
np.testing.assert_allclose(step_sol.y[-1],
2 * np.exp(0.1 * step_sol.t))
# Step again (return 5 points)
step_sol_2 = solver.step(step_sol, model, dt, npts=5)
np.testing.assert_array_equal(
step_sol_2.t,
np.concatenate([np.array([0]),
np.linspace(dt, 2 * dt, 5)]))
np.testing.assert_allclose(step_sol_2.y[0], np.exp(0.1 * step_sol_2.t))
np.testing.assert_allclose(step_sol_2.y[-1],
2 * np.exp(0.1 * step_sol_2.t))
# Check steps give same solution as solve
t_eval = step_sol.t
solution = solver.solve(model, t_eval)
np.testing.assert_allclose(solution.y[0], step_sol.y[0, :])
np.testing.assert_allclose(solution.y[-1], step_sol.y[-1, :])
def test_processed_var_1D_fixed_t_interpolation(self):
var = pybamm.Variable("var", domain=["negative electrode", "separator"])
x = pybamm.SpatialVariable("x", domain=["negative electrode", "separator"])
eqn = var + x
disc = tests.get_discretisation_for_testing()
disc.set_variable_slices([var])
x_sol = disc.process_symbol(x).entries[:, 0]
eqn_sol = disc.process_symbol(eqn)
t_sol = np.array([1])
y_sol = x_sol[:, np.newaxis]
processed_var = pybamm.ProcessedVariable(
eqn_sol, pybamm.Solution(t_sol, y_sol), warn=False
)
# vector
np.testing.assert_array_almost_equal(
processed_var(x=x_sol), 2 * x_sol[:, np.newaxis]
)
# scalar
np.testing.assert_array_almost_equal(processed_var(x=0.5), 1)
def test_discretisation_main_reaction(self):
# With intercalation
param = pybamm.standard_parameters_lead_acid
model_n = pybamm.interface.BaseInterface(param, "Negative", "lead-acid main")
j0_n = model_n._get_exchange_current_density(self.variables)
model_p = pybamm.interface.BaseInterface(param, "Positive", "lead-acid main")
j0_p = model_p._get_exchange_current_density(self.variables)
# Process parameters and discretise
parameter_values = pybamm.lead_acid.BaseModel().default_parameter_values
disc = get_discretisation_for_testing()
mesh = disc.mesh
disc.set_variable_slices([self.c_e])
j0_n = disc.process_symbol(parameter_values.process_symbol(j0_n))
j0_p = disc.process_symbol(parameter_values.process_symbol(j0_p))
# Test
whole_cell = ["negative electrode", "separator", "positive electrode"]
submesh = mesh.combine_submeshes(*whole_cell)
y = submesh.nodes ** 2
# should evaluate to vectors with the right shape
self.assertEqual(j0_n.evaluate(y=y).shape, (mesh["negative electrode"].npts, 1))
self.assertEqual(j0_p.evaluate(y=y).shape, (mesh["positive electrode"].npts, 1))
def test_domain_concatenation_simplify(self):
# create discretisation
disc = get_discretisation_for_testing()
mesh = disc.mesh
a_dom = ["negative electrode"]
b_dom = ["positive electrode"]
a = 2 * pybamm.Vector(np.ones_like(mesh[a_dom[0]].nodes), domain=a_dom)
b = pybamm.Vector(np.ones_like(mesh[b_dom[0]].nodes), domain=b_dom)
conc = pybamm.DomainConcatenation([a, b], mesh)
conc_simp = conc.simplify()
# should be simplified to a vector
self.assertIsInstance(conc_simp, pybamm.Vector)
np.testing.assert_array_equal(
conc_simp.evaluate(),
np.concatenate([
np.full((mesh[a_dom[0]].npts, 1), 2),
np.full((mesh[b_dom[0]].npts, 1), 1),
]),
)
def test_model_solver(self):
# Create model
model = pybamm.BaseModel()
whole_cell = ["negative electrode", "separator", "positive electrode"]
var1 = pybamm.Variable("var1", domain=whole_cell)
var2 = pybamm.Variable("var2", domain=whole_cell)
model.algebraic = {var1: var1 - 3, var2: 2 * var1 - var2}
model.initial_conditions = {var1: pybamm.Scalar(1), var2: pybamm.Scalar(4)}
model.variables = {"var1": var1, "var2": var2}
disc = get_discretisation_for_testing()
disc.process_model(model)
sol = np.concatenate((np.ones(100) * 3, np.ones(100) * 6))[:, np.newaxis]
# Solve
solver = pybamm.AlgebraicSolver()
solution = solver.solve(model)
np.testing.assert_array_equal(
model.variables["var1"].evaluate(t=None, y=solution.y), sol[:100]
)
np.testing.assert_array_equal(
model.variables["var2"].evaluate(t=None, y=solution.y), sol[100:]
)
# Test time
self.assertGreater(
solution.total_time, solution.solve_time + solution.set_up_time
)
# Test without jacobian
model.use_jacobian = False
solution_no_jac = solver.solve(model)
np.testing.assert_array_equal(
model.variables["var1"].evaluate(t=None, y=solution_no_jac.y), sol[:100]
)
np.testing.assert_array_equal(
model.variables["var2"].evaluate(t=None, y=solution_no_jac.y), sol[100:]
)
def test_model_solver_dae_with_jacobian_python(self):
model = pybamm.BaseModel()
model.convert_to_format = "python"
whole_cell = ["negative electrode", "separator", "positive electrode"]
var1 = pybamm.Variable("var1", domain=whole_cell)
var2 = pybamm.Variable("var2", domain=whole_cell)
model.rhs = {var1: 0.1 * var1}
model.algebraic = {var2: 2 * var1 - var2}
model.initial_conditions = {var1: 1.0, var2: 2.0}
model.initial_conditions_ydot = {var1: 0.1, var2: 0.2}
disc = get_discretisation_for_testing()
disc.process_model(model)
# Add user-supplied Jacobian to model
mesh = get_mesh_for_testing()
combined_submesh = mesh.combine_submeshes("negative electrode",
"separator",
"positive electrode")
N = combined_submesh.npts
def jacobian(t, y):
return np.block([
[0.1 * np.eye(N), np.zeros((N, N))],
[2.0 * np.eye(N), -1.0 * np.eye(N)],
])
model.jacobian = jacobian
# Solve
solver = pybamm.ScikitsDaeSolver(rtol=1e-8,
atol=1e-8,
root_method="lm")
t_eval = np.linspace(0, 1, 100)
solution = solver.solve(model, t_eval)
np.testing.assert_array_equal(solution.t, t_eval)
np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t))
np.testing.assert_allclose(solution.y[-1],
2 * np.exp(0.1 * solution.t))
def test_model_solver_dae_no_nonsmooth_python(self):
model = pybamm.BaseModel()
model.convert_to_format = "python"
whole_cell = ["negative electrode", "separator", "positive electrode"]
var1 = pybamm.Variable("var1", domain=whole_cell)
var2 = pybamm.Variable("var2", domain=whole_cell)
discontinuity = 5.6
def nonsmooth_rate(t):
return 0.1 * int(t < discontinuity) + 0.1
def nonsmooth_mult(t):
return int(t < discontinuity) + 1.0
# put in an extra heaviside with no time dependence, this should be ignored by
# the solver i.e. no extra discontinuities added
model.rhs = {var1: 0.1 * var1}
model.algebraic = {var2: 2 * var1 - var2}
model.initial_conditions = {var1: 1, var2: 2}
disc = get_discretisation_for_testing()
disc.process_model(model)
# Solve
solver = pybamm.ScikitsDaeSolver(rtol=1e-9,
atol=1e-9,
root_method="lm")
# create two time series, one without a time point on the discontinuity,
# and one with
t_eval = np.linspace(0, 5, 10)
solution = solver.solve(model, t_eval)
# test solution, discontinuity should not be triggered
np.testing.assert_array_equal(solution.t, t_eval)
np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t))
np.testing.assert_allclose(solution.y[-1],
2 * np.exp(0.1 * solution.t))
def test_model_solver_ode_jacobian_python(self):
model = pybamm.BaseModel()
model.convert_to_format = "python"
whole_cell = ["negative electrode", "separator", "positive electrode"]
var1 = pybamm.Variable("var1", domain=whole_cell)
var2 = pybamm.Variable("var2", domain=whole_cell)
model.rhs = {var1: var1, var2: 1 - var1}
model.initial_conditions = {var1: 1.0, var2: -1.0}
model.variables = {"var1": var1, "var2": var2}
disc = get_discretisation_for_testing()
disc.process_model(model)
# Add user-supplied Jacobian to model
mesh = get_mesh_for_testing()
combined_submesh = mesh.combine_submeshes("negative electrode",
"separator",
"positive electrode")
N = combined_submesh.npts
# Solve
solver = pybamm.ScikitsOdeSolver(rtol=1e-9, atol=1e-9)
t_eval = np.linspace(0, 1, 100)
solution = solver.solve(model, t_eval)
np.testing.assert_array_equal(solution.t, t_eval)
T, Y = solution.t, solution.y
np.testing.assert_array_almost_equal(
model.variables["var1"].evaluate(T, Y),
np.ones((N, T.size)) * np.exp(T[np.newaxis, :]),
)
np.testing.assert_array_almost_equal(
model.variables["var2"].evaluate(T, Y),
np.ones(
(N, T.size)) * (T[np.newaxis, :] - np.exp(T[np.newaxis, :])),
)
def test_process_model_concatenation(self):
# concatenation of variables as the key
cn = pybamm.Variable("c", domain=["negative electrode"])
cs = pybamm.Variable("c", domain=["separator"])
cp = pybamm.Variable("c", domain=["positive electrode"])
c = pybamm.Concatenation(cn, cs, cp)
N = pybamm.grad(c)
model = pybamm.BaseModel()
model.rhs = {c: pybamm.div(N)}
model.initial_conditions = {c: pybamm.Scalar(3)}
model.boundary_conditions = {
c: {
"left": (0, "Neumann"),
"right": (0, "Neumann")
}
}
model.check_well_posedness()
# create discretisation
disc = get_discretisation_for_testing()
mesh = disc.mesh
combined_submesh = mesh.combine_submeshes("negative electrode",
"separator",
"positive electrode")
disc.process_model(model)
y0 = model.concatenated_initial_conditions.evaluate()
np.testing.assert_array_equal(
y0, 3 * np.ones_like(combined_submesh[0].nodes[:, np.newaxis]))
# grad and div are identity operators here
np.testing.assert_array_equal(
y0, model.concatenated_rhs.evaluate(None, y0))
model.check_well_posedness()