def test_correct_caching2(self):
# setup equation
eqn = Seir(population=1)
# setup ode solver
ti = 0.
tf = 2.
n_steps = 3
rk = RKSolver(ti, tf, n_steps)
rk.output_frequency = 1
rk.set_output_storing_flag(True)
rk.equation = eqn
u0 = np.array([100., 0., 10., 0.])
du0_dp = np.zeros((eqn.n_components(), eqn.n_parameters()))
rk.set_initial_condition(u0, du0_dp)
rk.set_output_gradient_flag(True)
# setup cached simulation object
cached_sim = CachedSEIRSimulation(rk)
params = np.array([2.3, 0.2, 1. / 3., 1. / 4.])
(f, df) = cached_sim(params)
f1 = np.copy(f)
df1 = np.copy(df)
f *= 0.
df += 0.
(f2, df2) = cached_sim(params)
assert np.allclose(f1, f2)
assert np.allclose(df1, df2)
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_rk4_gradient_computation2(self):
n_pop = 7E6
sigma = 1/5.2
gamma = 1/2.28
beta = 2.13*gamma
eqn = Seir(beta, sigma, gamma)
ti = 0
tf = 218
n_steps = 2*tf
rk = RKSolver(ti, tf, n_steps)
rk.equation = eqn
u0 = np.array([n_pop - 1, 0, 1, 0])
u0 /= n_pop
du0_dp = np.zeros((eqn.n_components(), eqn.n_parameters()))
rk.set_initial_condition(u0, du0_dp)
rk.set_output_gradient_flag(True)
rk.solve()
(u, du_dp) = rk.state()
rk.set_output_gradient_flag(False)
epsi = 0.001
# perturb beta0
eqn.beta = beta + epsi
rk.solve()
u_p1 = rk.state()
eqn.beta = beta - epsi
rk.solve()
u_m1 = rk.state()
diff = np.linalg.norm(du_dp[:,0] - (u_p1 - u_m1)/(2*epsi))/np.linalg.norm(u0)
np.testing.assert_almost_equal(diff, 0, 5)
# reset
eqn.beta = beta
# perturb sigma
eqn.sigma = sigma + epsi
rk.solve()
u_p1 = rk.state()
eqn.sigma = sigma - epsi
rk.solve()
u_m1 = rk.state()
diff = np.linalg.norm(du_dp[:,1] - (u_p1 - u_m1)/(2*epsi))/np.linalg.norm(u0)
np.testing.assert_almost_equal(diff, 0, 5)
# reset
eqn.sigma = sigma
# perturb gamma
eqn.gamma = gamma + epsi
rk.solve()
u_p1 = rk.state()
eqn.gamma = gamma - epsi
rk.solve()
u_m1 = rk.state()
diff = np.linalg.norm(du_dp[:,2] - (u_p1 - u_m1)/(2*epsi))/np.linalg.norm(u0)
np.testing.assert_almost_equal(diff, 0, 5)
# reset
eqn.gamma = gamma
# perturb kappa
kappa = 1
eqn.kappa = kappa + epsi
rk.solve()
u_p1 = rk.state()
eqn.kappa = kappa - epsi
rk.solve()
u_m1 = rk.state()
diff = np.linalg.norm(du_dp[:,3] - (u_p1 - u_m1)/(2*epsi))/np.linalg.norm(u0)
np.testing.assert_almost_equal(diff, 0, 5)
# reset
eqn.kappa = kappa