def test_EM_algorithm_in_linear_case(self):
n_sample = 100
is_f_linear = True
is_g_linear = True
state_dim = 1
output_dim = 1
A = np.ones((1, 1))
b = rand(1)
C = np.ones((1, 1))
d = rand(1)
Q = np.array([[0.1]])
R = np.array([[0.1]])
ssm = StateSpaceModel(is_f_linear=is_f_linear,
is_g_linear=is_g_linear,
state_dim=state_dim,
output_dim=output_dim,
A=A,
b=b,
C=C,
d=d,
Q=Q,
R=R)
ssm.draw_sample(T=n_sample)
ssm.plot_states_in_1D()
ssm.A[0, 0] = 0.5
ssm.b[0] = 0.5
ssm.C[0, 0] = 0.5
ssm.d[0] = 0.5
use_smoothed_values = False
log_likelihood = ssm.learn_f_and_g_with_EM_algorithm(
use_smoothed_values=use_smoothed_values)
plt.figure(10)
plt.title(
'f and g linear. log-likelihood evolution during EM algorithm')
plt.plot(log_likelihood)
plt.show()
ssm.plot_estimmated_states_in_1D(
use_smoothed_values=use_smoothed_values)
def test_EM_algorithm_in_non_linear_case(self):
n_sample = 5000
is_f_linear = False
is_g_linear = True
state_dim = 1
output_dim = 1
A = 0.5 * np.ones((1, 1))
b = 0.25 * np.ones(1)
C = np.ones((1, 1))
d = np.zeros(1)
Q = np.array([[0.01]])
R = np.array([[0.01]])
f_rbf_parameters = {
'n_rbf': 2,
'centers': np.array([[-0.2], [0.2]]),
'width': np.array([[[0.02]], [[0.02]]])
}
f_rbf_coeffs = np.array([[0.2], [-0.2]])
ssm = StateSpaceModel(is_f_linear=is_f_linear,
is_g_linear=is_g_linear,
f_rbf_parameters=f_rbf_parameters,
f_rbf_coeffs=f_rbf_coeffs,
state_dim=state_dim,
output_dim=output_dim,
A=A,
b=b,
C=C,
d=d,
Q=Q,
R=R)
#on va definir une f_analytical quelconque
#ssm.f_analytical=np.cos
def f_Not_RBF_scalar(x):
value = 0
value = np.cos(10 * x)
return (value)
f_Not_RBF = np.vectorize(f_Not_RBF_scalar)
ssm.f_analytical = f_Not_RBF
ssm.draw_sample(T=n_sample)
ssm.plot_states_in_1D()
ssm.A[0, 0] += 0.1 * random()
ssm.b[0] += 0.1 * random()
ssm.C[0, 0] += 0.1 * random()
ssm.d[0] += 0.1 * random()
#et si on commence a apprendre avec plus de I qu'il n'y en a réellement
f_rbf_parameters_Bis = {
'n_rbf': 4,
'centers': np.array([[-0.2], [0.2], [0.3], [0.7]]),
'width': np.array([[[0.02]], [[0.02]], [[0.02]], [[0.02]]])
}
ssm.f_rbf_parameters = f_rbf_parameters_Bis
ssm.f_rbf_coeffs = np.array([[-0.2], [0.2], [0.3], [0.7]])
#ssm.f_rbf_coeffs = np.array([[0.], [0.]])
use_smoothed_values = False
log_likelihood = ssm.learn_f_and_g_with_EM_algorithm(
use_smoothed_values=use_smoothed_values)
plt.figure(1)
plt.title(
'f non-linear, g linear. log-likelihood evolution during EM algorithm'
)
plt.plot(log_likelihood)
plt.xlabel('Number of Iteration')
plt.ylabel('likelihood')
plt.show()
#pour que compute_f me renvoit ce qui a ete appris
ssm.f_analytical = None
ssm.plot_estimmated_states_in_1D(
use_smoothed_values=use_smoothed_values)
print(ssm.f_rbf_coeffs)