def test_functions(self):
y = pybamm.StateVector(slice(0, 8))
u = pybamm.StateVector(slice(0, 2), slice(4, 6))
v = pybamm.StateVector(slice(2, 4), slice(6, 8))
y0 = np.arange(1, 9)
const = pybamm.Scalar(1)
func = pybamm.sin(u)
jacobian = np.array(
[
[np.cos(1), 0, 0, 0, 0, 0, 0, 0],
[0, np.cos(2), 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, np.cos(5), 0, 0, 0],
[0, 0, 0, 0, 0, np.cos(6), 0, 0],
]
)
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
func = pybamm.cos(v)
jacobian = np.array(
[
[0, 0, -np.sin(3), 0, 0, 0, 0, 0],
[0, 0, 0, -np.sin(4), 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, -np.sin(7), 0],
[0, 0, 0, 0, 0, 0, 0, -np.sin(8)],
]
)
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
func = pybamm.sin(3 * u * v)
jacobian = np.array(
[
[9 * np.cos(9), 0, 3 * np.cos(9), 0, 0, 0, 0, 0],
[0, 12 * np.cos(24), 0, 6 * np.cos(24), 0, 0, 0, 0],
[0, 0, 0, 0, 21 * np.cos(105), 0, 15 * np.cos(105), 0],
[0, 0, 0, 0, 0, 24 * np.cos(144), 0, 18 * np.cos(144)],
]
)
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
# when child evaluates to number
func = pybamm.sin(const)
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(0, dfunc_dy)
# several children
func = pybamm.Function(test_multi_var_function, 2 * y, 3 * y)
jacobian = np.diag(5 * np.ones(8))
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
def test_cos(self):
a = pybamm.InputParameter("a")
fun = pybamm.cos(a)
self.assertIsInstance(fun, pybamm.Cos)
self.assertEqual(fun.children[0].id, a.id)
self.assertEqual(fun.evaluate(inputs={"a": 3}), np.cos(3))
h = 0.0000001
self.assertAlmostEqual(
fun.diff(a).evaluate(inputs={"a": 3}),
(
pybamm.cos(pybamm.Scalar(3 + h)).evaluate()
- fun.evaluate(inputs={"a": 3})
)
/ h,
places=5,
)
# test simplify
y = pybamm.StateVector(slice(0, 1))
fun = pybamm.cos(y)
self.assertEqual(fun.id, fun.simplify().id)
def get_error(n):
# create mesh and discretisation
mesh = get_mesh_for_testing(n)
disc = pybamm.Discretisation(mesh, spatial_methods)
combined_submesh = mesh.combine_submeshes(*whole_cell)
x = combined_submesh.nodes
x_edge = pybamm.standard_spatial_vars.x_edge
# Define flux and bcs
N = x_edge**2 * pybamm.cos(x_edge)
div_eqn = pybamm.div(N)
# Define exact solutions
# N = x**2 * cos(x) --> dNdx = x*(2cos(x) - xsin(x))
div_exact = x * (2 * np.cos(x) - x * np.sin(x))
# Discretise and evaluate
div_eqn_disc = disc.process_symbol(div_eqn)
div_approx = div_eqn_disc.evaluate()
# Return difference between approx and exact
return div_approx[:, 0] - div_exact