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conditional_laws_new.py
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conditional_laws_new.py
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import numpy as np
from scipy.linalg import solve_toeplitz, toeplitz
def simul_alpha2(model, noise_H, noise_K):
'''
Simulate alpha in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
# return params['alpha']()
past, present = constants['past'](), constants['present']()
# print(params['T13']())
T = np.concatenate((params['T13']()[:past], data['T2']()))
RP = data['RP']()
cov_top = noise_H.get_toeplitz(present, params['H']())
M = np.tril(toeplitz(cov_top))
cov_top = cov_top / (1-params['H']()**2)
u = np.array([np.dot(M,np.ones(len(T))), np.dot(M,T)])
b = solve_toeplitz(cov_top, u.T)
P1 = np.dot(u,b)
omega = np.linalg.inv(1/params['sigma_p']()**2 *P1 + np.identity(2))
c = solve_toeplitz(cov_top, RP)
mu = 1/params['sigma_p']()**2 *np.dot(np.dot(omega, u), c)
a = np.random.multivariate_normal(mean = mu, cov = omega)
return a
def simul_beta2(model, noise_H, noise_K):
'''
Simulate beta in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
# return params['beta']()
past, future = constants['past'](), constants['future']()
T = np.concatenate((params['T13']()[:past], data['T2'](), params['T13']()[past:]))
cov_top = noise_K.get_toeplitz(future, params['K']())
M = np.tril(toeplitz(cov_top))
cov_top = cov_top / (1-params['K']()**2)
S = data['S']()
V = data['V']()
C = data['C']()
v = np.array([np.dot(M, np.ones((future))), np.dot(M,S), np.dot(M,V), np.dot(M,C)])
b = solve_toeplitz(cov_top, v.T)
P1 = np.dot(v, b)
omega = np.linalg.inv(1/params['sigma_T']()**2 * P1 + np.identity(4))
mu = (1/params['sigma_T']()**2)*omega.dot(T.dot(b))
a = np.random.multivariate_normal(mean = mu, cov = omega)
return a
def simul_s_p2(model, noise_H, noise_K):
'''
Simulate sigma_p in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
# return params['sigma_p']()
past, present = constants['past'](), constants['present']()
T = np.concatenate((params['T13']()[:past], data['T2']()))
cov_top = noise_H.get_toeplitz(present, params['H']())
M = np.tril(toeplitz(cov_top))
cov_top = cov_top / (1-params['H']()**2)
u = np.array([np.dot(M,np.ones(len(T))), np.dot(M,T)])
P1 = np.dot(params['alpha'](), u)
b = solve_toeplitz(cov_top, data['RP']() - P1)
P2 = np.dot((data['RP']() - P1).T,b)
q = 2 + present/2
r = 0.1 + 1/2 * P2
return np.sqrt(1/np.random.gamma(shape = q, scale = 1/r))
def simul_s_T2(model, noise_H, noise_K):
'''
Simulate sigma_T in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
# return params['sigma_T']()
past, future = constants['past'](), constants['future']()
T = np.concatenate((params['T13']()[:past], data['T2'](), params['T13']()[past:]))
cov_top = noise_K.get_toeplitz(future, params['K']())
M = np.tril(toeplitz(cov_top))
cov_top = cov_top / (1-params['K']()**2)
S = data['S']()
V = data['V']()
C = data['C']()
v = np.array([np.dot(M, np.ones((future))), np.dot(M,S), np.dot(M,V), np.dot(M,C)])
P1 = np.dot(params['beta'](), v)
b = solve_toeplitz(cov_top, T - P1)
P2 = np.dot((T - P1).T,b)
q = 2 + future/2
r = 0.1 + 1/2 * P2
return np.sqrt(1/np.random.gamma(shape = q, scale = 1/r))
def simul_T2(model, noise_H, noise_K):
'''
Simulate T13 in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
# return params['T13'](), data['T2']()
past, present, future = constants['past'](), constants['present'](), constants['future']()
cov_top_H = noise_K.get_toeplitz(present, params['H']())
cov_top_K = noise_K.get_toeplitz(future, params['K']())
M_H = np.tril(toeplitz(cov_top_H))
M_K = np.tril(toeplitz(cov_top_K))
cov_top_H = cov_top_H / (1-params['H']()**2)
cov_top_K = cov_top_K / (1-params['K']()**2)
S = data['S']()
V = data['V']()
C = data['C']()
v = np.array([np.dot(M_K, np.ones((future))), np.dot(M_K,S), np.dot(M_K,V), np.dot(M_K,C)])
inv_covK = np.linalg.inv(toeplitz(cov_top_K))
inv_covH = np.linalg.inv(toeplitz(cov_top_H))
P1 = np.pad(np.dot(M_H.T, np.dot(inv_covH, M_H)), pad_width = (0,future-present), mode='constant')
omega = np.linalg.inv((params['alpha']()[1]/params['sigma_p']())**2*P1 + 1/params['sigma_T']()**2 * inv_covK)
a = solve_toeplitz(cov_top_K, np.dot(params['beta'](),v))
b = np.pad(np.dot(M_H.T, solve_toeplitz(cov_top_H, data['RP']() - params['alpha']()[0]*np.dot(M_H, np.ones(present)))), pad_width=(0,future-present), mode='constant')
mu = 1/params['sigma_T']()**2*np.dot(omega, a) + params['alpha']()[1]/params['sigma_p']()**2*np.dot(omega, b)
# T = mu + np.dot(np.linalg.cholesky(omega), np.random.randn(len(mu)))
# print(params['alpha']()[1]/params['sigma_p']()**2*np.dot(omega, b))
M1 = omega[past:present, past:present]
M1_inv = np.linalg.inv(M1)
M2 = np.concatenate((omega[:past, past:present], omega[present:future, past:present]), axis = 0)
M3 = np.concatenate((np.concatenate((omega[:past,:past],omega[:past, present:future]), axis = 1), np.concatenate((omega[present:future,:past], omega[present:future,present:future]), axis = 1)), axis = 0)
M3_inv = np.linalg.inv(M3)
# Bloc 1-3
new_mean13 = np.concatenate((mu[:past], mu[present:future])) + np.dot(M2,np.dot(M1_inv, data['T2']() - mu[past:present]))
new_cov13 = M3 - np.dot(M2, np.dot(M1_inv, M2.T))
T13 = new_mean13 + np.dot(np.linalg.cholesky(new_cov13), np.random.randn(len(new_mean13)))
# Bloc 2
new_mean2 = mu[past:present] + np.dot(M2.T,np.dot(M3_inv, T13 - np.concatenate((mu[:past], mu[present:future]))))
new_cov2 = M1 - np.dot(M2.T, np.dot(M3_inv, M2))
T2 = new_mean2 + np.dot(np.linalg.cholesky(new_cov2), np.random.randn(len(new_mean2)))
return T13, T2
def simul_H2(model, noise_H, noise_K):
'''
Simulate H in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
H = model.params['H']()
return H
if noise_H.n_params == 0:
return H
step_H = constants['step_H']()
n_iteration = constants['n_iteration']()
# Simulation of H
acc = 0
for k in range(n_iteration):
new_H = noise_H.draw_MH(H, step_H)
log_p1 = noise_H.log_p2(params, data, constants, 'H', new_H)
log_p2 = noise_H.log_p2(params, data, constants, 'H', H)
log_q1 = noise_H.log_q(H, new_H, step_H)
log_q2 = noise_H.log_q(new_H, H, step_H)
alpha = log_p1 + log_q1 - log_p2 - log_q2
a = np.random.uniform()
if np.log(a) <= alpha: # Accept
H = new_H
acc += 1
return H
def simul_K2(model, noise_H, noise_K):
'''
Simulate K in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
K = model.params['K']()
return K
if noise_K.n_params == 0:
return K
step_K = constants['step_K']()
n_iteration = constants['n_iteration']()
# Simulation of K
acc = 0
for k in range(n_iteration):
new_K = noise_K.draw_MH(K, step_K)
log_p1 = noise_K.log_p2(params, data, constants, 'K', new_K)
log_p2 = noise_K.log_p2(params, data, constants, 'K', K)
log_q1 = noise_K.log_q(K, new_K, step_K)
log_q2 = noise_K.log_q(new_K, K, step_K)
alpha = log_p1 + log_q1 - log_p2 - log_q2
a = np.random.uniform()
if np.log(a) <= alpha: # Accept
K = K = new_K
acc += 1
return K