def test_lotkavolterra(self):
"""Test the LV ODE convenience function."""
rv = Constant(np.ones(2))
lg1 = ivp_examples.lotkavolterra(self.tspan, rv)
lg2 = ivp_examples.lotkavolterra(self.tspan, rv, params=(1.0, 1.0, 1.0, 1.0))
self.assertIsInstance(lg1, ivp.IVP)
self.assertIsInstance(lg2, ivp.IVP)
def test_lotkavolterra_jacobian(self):
rv = Constant(np.ones(2))
lg1 = ivp_examples.lotkavolterra(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_lotkavolterra_rhs(self):
rv = Constant(np.ones(2))
lg1 = ivp_examples.lotkavolterra(self.tspan, rv)
self.assertEqual(lg1.rhs(0.1, rv).shape, rv.shape)