def __init__(self, nr_steps):
print("Generating random data for particle filter stresses A...")
self.nr_steps = nr_steps
# prepare random variable components:
a_t, b_t = pb.RVComp(1, 'a_t'), pb.RVComp(1, 'b_t') # state in t
a_tp, b_tp = pb.RVComp(1,
'a_{t-1}'), pb.RVComp(1,
'b_{t-1}') # state in t-1
# arguments to Kalman filter part of the marginalized particle filter
self.kalman_args = {}
# prepare callback functions
sigma_sq = np.array([0.0001])
def f(cond): # log(b_{t-1}) - 1/2 \sigma^2
return np.log(cond) - sigma_sq / 2.
def g(cond): # \sigma^2
return sigma_sq
# p(a_t | a_{t-1} b_t) density:
p_at_atpbt = pb.LinGaussCPdf(1., 0., 1., 0., [a_t], [a_tp, b_t])
self.kalman_args['A'] = np.array([[1.]]) # process model
# p(b_t | b_{t-1}) density:
self.p_bt_btp = pb.GaussCPdf(1,
1,
f,
g,
rv=[b_t],
cond_rv=[b_tp],
base_class=pb.LogNormPdf)
# p(x_t | x_{t-1}) density:
self.p_xt_xtp = pb.ProdCPdf((p_at_atpbt, self.p_bt_btp), [a_t, b_t],
[a_tp, b_tp])
# prepare p(y_t | x_t) density:
self.p_yt_xt = pb.LinGaussCPdf(1., 0., 1., 0.)
self.kalman_args['C'] = np.array([[1.]]) # observation model
# Initial [a_t, b_t] from .. to:
self.init_range = np.array([[-18., 0.3], [-14., 0.7]])
init_mean = (self.init_range[0] + self.init_range[1]) / 2.
x_t = np.zeros((nr_steps, 2))
x_t[0] = init_mean.copy()
y_t = np.empty((nr_steps, 1))
for i in range(nr_steps):
# set b_t:
x_t[i, 1] = i / 100. + init_mean[1]
# simulate random process:
x_t[i, 0:1] = p_at_atpbt.sample(
x_t[i]) # this is effectively [a_{t-1}, b_t]
y_t[i] = self.p_yt_xt.sample(x_t[i])
# DEBUG: print "simulated x_{0} = {1}".format(i, x_t[i])
# DEBUG: print "simulated y_{0} = {1}".format(i, y_t[i])
self.x_t = x_t
self.y_t = y_t
def setUp(self):
def f(x):
return -x
self.f = f
def g(x):
return np.diag(-x)
self.g = g
self.cgauss = pb.GaussCPdf(2, 2, f, g)
self.gauss = pb.GaussPdf(np.array([1., 2.]),
np.array([[1., 0.], [0., 2.]]))
self.cond = np.array([-1., -2.
]) # condition that makes cgauss behave as gauss
def test_different_base_class(self):
condlognorm = pb.GaussCPdf(1,
1,
self.f,
self.g,
base_class=pb.LogNormPdf)
lognorm = pb.LogNormPdf(np.array([1.]), np.array([[1.]]))
cond = np.array([-1.]) # makes condlognorm behave as lognorm
self.assertEqual(condlognorm.mean(cond), lognorm.mean())
self.assertEqual(condlognorm.variance(cond), lognorm.variance())
for x in np.array([[-0.4], [2.4], [4.5], [12.5]]):
self.assertEqual(condlognorm.eval_log(x, cond),
lognorm.eval_log(x))
for i in range(30):
# only test that samples are positive
self.assertTrue(np.all(condlognorm.sample(cond) >= 0))