def test_continuous_initial_condition_1d_pde():
diff_eq = DiffusionEquation(1)
mesh = Mesh([(0., 20.)], [.1])
bcs = [(DirichletBoundaryCondition(lambda x, t: np.zeros((len(x), 1)),
is_static=True),
DirichletBoundaryCondition(lambda x, t: np.full((len(x), 1), 1.5),
is_static=True))]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
initial_condition = ContinuousInitialCondition(
cp, lambda x: np.exp(-np.square(np.array(x) - 10.) / (2 * 5**2)))
assert np.isclose(initial_condition.y_0(np.full((1, 1), 10.)), 1.)
assert np.isclose(
initial_condition.y_0(np.full((1, 1),
np.sqrt(50) + 10.)), np.e**-1)
assert np.allclose(initial_condition.y_0(np.full((5, 1), 10.)),
np.ones((5, 1)))
y_0_vertices = initial_condition.discrete_y_0(True)
assert y_0_vertices.shape == (201, 1)
assert y_0_vertices[0, 0] == 0.
assert y_0_vertices[-1, 0] == 1.5
assert y_0_vertices[100, 0] == 1.
assert np.all(0. < y_0_vertices[1:100, 0]) \
and np.all(y_0_vertices[1:100, 0] < 1.)
assert np.all(0. < y_0_vertices[101:-1, 0]) \
and np.all(y_0_vertices[101:-1, 0] < 1.)
y_0_cell_centers = initial_condition.discrete_y_0(False)
assert y_0_cell_centers.shape == (200, 1)
assert np.all(0. < y_0_cell_centers) and np.all(y_0_cell_centers < 1.)
def test_continuous_initial_condition_ode():
diff_eq = LotkaVolterraEquation()
cp = ConstrainedProblem(diff_eq)
initial_condition = ContinuousInitialCondition(
cp, lambda _: np.array([10., 100.]))
assert np.all(initial_condition.y_0(None) == [10., 100.])
assert np.all(initial_condition.discrete_y_0() == [10., 100.])