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_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)
class TestModelGradOp(utt.InferShapeTester):
rng = np.random.RandomState(43)
def setUp(self):
super(TestModelGradOp, self).setUp()
self.setUpModel()
def setUpModel(self):
# set ode solver
ti = 0
tf = 20
n_steps = tf
self.rk = RKSolver(ti, tf, n_steps)
self.rk.output_frequency = 1
self.rk.set_output_storing_flag(True)
eqn = Seir()
eqn.tau = 5
self.rk.equation = eqn
n_pop = 7E6
u0 = np.array([n_pop - 1, 0, 1, 0])
u0 /= n_pop
du0_dp = np.zeros((eqn.n_components(), eqn.n_parameters()))
self.rk.set_initial_condition(u0, du0_dp)
# set cached_sim object
cached_sim = CachedSEIRSimulation2(self.rk)
cached_sim.set_gradient_flag(True)
# set theano model op object
self.op_class = ModelGradOp(cached_sim)
def test_perform(self):
b = theano.tensor.dscalar('myvar0')
s = theano.tensor.dscalar('myvar1')
g = theano.tensor.dscalar('myvar2')
k = theano.tensor.dscalar('myvar3')
t = theano.tensor.dscalar('myvar4')
dL_df = theano.tensor.matrix()
f = theano.function([b, s, g, k, t, dL_df],
self.op_class((b, s, g, k, t), dL_df))
s_val = 1. / 5.2
g_val = 1. / 2.28
b_val = 2.13 * g_val
k_val = 1.1
t_val = 10
dL_df_val = np.random.rand(1, 21)
out = f(b_val, s_val, g_val, k_val, t_val, dL_df_val)
self.rk.equation.beta = b_val
self.rk.equation.sigma = s_val
self.rk.equation.gamma = g_val
self.rk.equation.kappa = k_val
self.rk.equation.tint = t_val
self.rk.solve()
(_, _, df_dp) = self.rk.get_outputs()
out_act = df_dp[0, :, :] @ dL_df_val.T
out_act = np.reshape(out_act, (self.rk.equation.n_parameters(), ))
assert np.allclose(out_act, out)
class TestModelOp(utt.InferShapeTester):
rng = np.random.RandomState(43)
def setUp(self):
super(TestModelOp, self).setUp()
self.setUpModel()
def setUpModel(self):
# set ode solver
ti = 0
tf = 20
n_steps = tf
self.rk = RKSolver(ti, tf, n_steps)
self.rk.output_frequency = 1
self.rk.set_output_storing_flag(True)
eqn = Seir()
self.rk.equation = eqn
n_pop = 7E6
u0 = np.array([n_pop - 1, 0, 1, 0])
u0 /= n_pop
du0_dp = np.zeros((eqn.n_components(), eqn.n_parameters()))
self.rk.set_initial_condition(u0, du0_dp)
# set cached_sim object
cached_sim = CachedSEIRSimulation(self.rk)
cached_sim.set_gradient_flag(True)
# set theano model op object
self.op_class = ModelOp(cached_sim)
#@unittest.skip("changed output of SEIR eq")
def test_perform(self):
b = theano.tensor.dscalar('myvar0')
s = theano.tensor.dscalar('myvar1')
g = theano.tensor.dscalar('myvar2')
f = theano.function([b, s, g], self.op_class((b, s, g)))
s_val = 1. / 5.2
g_val = 1. / 2.28
b_val = 2.13 * g_val
out = f(b_val, s_val, g_val)
self.rk.equation.beta = b_val
self.rk.equation.sigma = s_val
self.rk.equation.gamma = g_val
self.rk.solve()
(_, out_act, _) = self.rk.get_outputs()
assert np.allclose(out_act, out)
def test_grad(self):
s_val = 1. / 5.2
g_val = 1. / 2.28
b_val = 2.13 * g_val
rng = np.random.RandomState(42)
theano.tensor.verify_grad(self.op_class, [(b_val, s_val, g_val)],
rng=rng)
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