def test_rk4_solver(self):
theta = -1.2
eqn = SimpleEquation(theta)
u_exact = lambda t: eqn.solution(t)[0]
ti = 0
tf = 5*math.pi/3
u0 = u_exact(ti)
rk = RKSolver(ti, tf)
rk.equation = eqn
rk.set_initial_condition(u0)
n = 4
err = np.zeros((n,))
dt = np.zeros((n,))
n_steps = 100
for i in range(n):
n_steps *= (i+1)
dt[i] = 1./n_steps
rk.n_steps = n_steps
rk.solve()
err[i] = abs(rk.state() - u_exact(tf))
conv_rate = np.polyfit(np.log(dt), np.log(err), 1)[0]
self.assertAlmostEqual(conv_rate, 4.0, 1)
def test_rk4_gradient_computation(self):
theta = -1.2
eqn = SimpleEquation(theta)
ti = 0
tf = 5*math.pi/3
(u0, du0_dp) = eqn.solution(ti)
rk = RKSolver(ti, tf)
rk.equation = eqn
rk.set_initial_condition(u0, du0_dp)
rk.set_output_gradient_flag(True)
n = 4
err_soln = np.zeros((n,))
err_grad = np.zeros((n,))
dt = np.zeros((n,))
n_steps = 100
for i in range(n):
n_steps *= (i+1)
dt[i] = 1./n_steps
rk.n_steps = n_steps
rk.solve()
err_soln[i] = abs(rk.state()[0] - eqn.solution(tf)[0])
err_grad[i] = abs(rk.state()[1] - eqn.solution(tf)[1])
conv_rate = np.polyfit(np.log(dt), np.log(err_soln), 1)[0]
self.assertAlmostEqual(conv_rate, 4.0, 1)
conv_rate = np.polyfit(np.log(dt), np.log(err_grad), 1)[0]
self.assertAlmostEqual(conv_rate, 4.0, 1)
def test_interface(self):
rk = RKSolver(0, 1)
rk.initial_time = 0.5
rk.final_time = 5
rk.n_steps = 10
self.assertEqual(rk.initial_time,0.5)
self.assertEqual(rk.final_time,5)
self.assertEqual(rk.n_steps,10)
eqn = Seir()
rk.equation = eqn
self.assertEqual(rk.equation, eqn)
rk.output_frequency = 20
self.assertEqual(rk.output_frequency, 20)