def test_Poisson(self):
shape = 10, 100
a = 1e-2 * torch.ones((shape[0], 1))
dt = 1e-2
dist = Poisson(dt * 0.1)
init = Normal(a, 1.)
sde = AffineEulerMaruyama((f_sde, g_sde), (a, 0.15),
init,
dist,
dt=dt,
num_steps=10)
# ===== Initialize ===== #
x = sde.i_sample(shape)
# ===== Propagate ===== #
num = 1000
samps = [x]
for t in range(num):
samps.append(sde.propagate(samps[-1]))
samps = torch.stack(samps)
self.assertEqual(samps.size(), torch.Size([num + 1, *shape]))
# ===== Sample path ===== #
path = sde.sample_path(num + 1, shape)
self.assertEqual(samps.shape, path.shape)
def test_SDE(self):
shape = 1000, 100
a = 1e-2 * torch.ones((shape[0], 1))
dt = 0.1
init = norm = DistributionWrapper(Normal, loc=a, scale=math.sqrt(dt))
sde = AffineEulerMaruyama((f_sde, g_sde), (a, 0.15), init, norm, dt=dt, num_steps=10)
# ===== Initialize ===== #
x = sde.i_sample(shape)
self.assert_timeseries_sampling(100, sde, x, shape)
def test_ParameterInDistribution(self):
shape = 10, 100
a = 1e-2 * torch.ones((shape[0], 1))
dt = 1e-2
dist = DistributionWrapper(Normal, loc=0.0, scale=Prior(Exponential, rate=10.0))
init = DistributionWrapper(Normal, loc=a, scale=1.0)
sde = AffineEulerMaruyama((f_sde, g_sde), (a, 0.15), init, dist, dt=dt, num_steps=10)
sde.sample_params(shape)
# ===== Initialize ===== #
x = sde.i_sample(shape)
self.assert_timeseries_sampling(100, sde, x, shape)
def test_SDE(self):
def f(x, a, s):
return -a * x
def g(x, a, s):
return s
em = AffineEulerMaruyama((f, g), (0.02, 0.15), Normal(0., 1.), Normal(0., 1.), dt=1e-2, num_steps=10)
model = LinearGaussianObservations(em, scale=1e-3)
x, y = model.sample_path(500)
with self.assertRaises(NotImplementedError):
SISR(model, 200)
for filt in [SISR(model, 500, proposal=Bootstrap()), UKF(model)]:
filt = filt.initialize().longfilter(y)
means = filt.filtermeans
if isinstance(filt, UKF):
means = means[:, 0]
self.assertLess(torch.std(x - means), 5e-2)
def test_SDE(self):
def f(x, a, s):
return -a * x
def g(x, a, s):
return s
dt = 1e-2
norm = DistributionWrapper(Normal, loc=0.0, scale=sqrt(dt))
em = AffineEulerMaruyama((f, g), (0.02, 0.15), norm, norm, dt=1e-2, num_steps=10)
model = LinearGaussianObservations(em, scale=1e-3)
x, y = model.sample_path(500)
for filt in [SISR(model, 500, proposal=prop.Bootstrap()), UKF(model)]:
result = filt.longfilter(y)
means = result.filter_means
if isinstance(filt, UKF):
means = means[:, 0]
self.assertLess(torch.std(x - means), 5e-2)