def compute_omega(T, K, alg, model, X):
if alg == 'gibbs':
rw_matrix = gibbs.transition_kernel(
X, model).T # As defined in the course
elif alg == 'mh_uniform':
rw_matrix = load_mh_uniform_transitionmatrix(T, K, model, X)
elif alg == 'mh_prior':
rw_matrix = load_mh_prior_transitionmatrix(T, K, model, X)
eigvals = np.linalg.eigvals(rw_matrix)
order = np.argsort(eigvals)[::-1]
w = eigvals[order]
omega = w[1]
assert np.abs(np.real(omega) - np.linalg.norm(omega)) < 1e-10
omega = np.real(omega)
# print(f"T: {T}, K: {K}, Omega: {omega:.5f}")
return omega
def compute_pi(T, K, alg):
(_, X), model = loaddatamodel(T, K)
if alg == 'gibbs':
rw_matrix = gibbs2.transition_kernel(
X, model).T # As defined in the course
elif alg == 'mh_uniform':
rw_matrix = load_mh_uniform_transitionmatrix(T, K)
elif alg == 'mh_prior':
rw_matrix = load_mh_prior_transitionmatrix(T, K)
eigvals, eigvecs = np.linalg.eig(rw_matrix)
order = np.argsort(eigvals)[::-1]
pi = eigvecs[:, order[0]]
real = np.real(pi)
assert np.abs(np.linalg.norm(real) - np.linalg.norm(pi)) < 1e-10
pi = np.copy(real)
pi = pi / pi.sum()
w = eigvals[order]
omega = w[1]
assert np.abs(np.real(omega) - np.linalg.norm(omega)) < 1e-10
omega = np.real(omega)
print(f"T: {T}, K: {K}, Omega: {omega:.5f}, Pi: {pi}")
return pi
def load_gibbs_transitionmatrix(T, K, modelversion=2):
Z, X = loaddata(T, K)
model = loadmodel(K, modelversion)
return gibbs1.transition_kernel(
X, model) if modelversion == 1 else gibbs2.transition_kernel(X, model)