def test_lorenz(self):
"""Test the Lorenz model ODE convenience function."""
rv = Constant(np.array([1.0, 1.0, 1.0]))
lg1 = ivp_examples.lorenz(self.tspan, rv)
lg2 = ivp_examples.lorenz(
self.tspan,
rv,
params=(
10.0,
28.0,
8.0 / 3.0,
),
)
self.assertIsInstance(lg1, ivp.IVP)
self.assertIsInstance(lg2, ivp.IVP)
def test_lorenz_jacobian(self):
rv = Constant(np.array([1.0, 1.0, 1.0]))
lg1 = ivp_examples.lorenz(self.tspan, rv)
random_direction = 1 + 0.1 * np.random.rand(lg1.dimension)
random_point = 1 + np.random.rand(lg1.dimension)
fd_approx = (0.5 * 1.0 / self.dt *
(lg1(0.1, random_point + self.dt * random_direction) -
lg1(0.1, random_point - self.dt * random_direction)))
self.assertAllClose(
lg1.jacobian(0.1, random_point) @ random_direction,
fd_approx,
rtol=self.rtol,
)
def test_lorenz_rhs(self):
rv = Constant(np.ones(3))
lg1 = ivp_examples.lorenz(self.tspan, rv)
self.assertEqual(lg1.rhs(0.1, rv).shape, rv.shape)