def compute_ergodic(self):
r'''
Computes the ergodic distribution over the unemployment and employment
states
Returns
---------
pibar(1d-array) : the ergodic distribution of P
'''
return quantecon.mc_compute_stationary(self.P)
graph_mat = np.zeros((14,14),dtype=float)
for line in f:
tmp = (re.findall('\w', line))
graph_mat[idxdict[tmp[0]],idxdict[tmp[1]]] = 1
return graph_mat
gmat = graph_from_file(filepath)
#normalize graph by number of links to form Markov matrix
n = gmat.shape[0]
gmat = gmat/np.reshape(np.repeat(gmat.sum(axis=1).T,n,axis=0),(n,n))
#solve for stationary distribution
pstat = qe.mc_compute_stationary(gmat)
# Ex 3
def approx_markov(rho, sigma_u, m=3, n=7):
sigma_y = np.sqrt((sigma_u**2)/(1.-rho**2))
x_arr = np.linspace(start=-m*sigma_y,stop=m*sigma_y,num=n)
F = stats.norm(scale=sigma_u**2).cdf
s = x_arr[1]-x_arr[0]
P_arr = np.empty((n,n),dtype=float)
for i in range(0,n):
for j in range(0,n):
if j==0:
P_arr[i][j] = F(x_arr[0]-rho*x_arr[i]+s/2)
elif j==n-1:
P = ((0.971, 0.029, 0.000),
(0.145, 0.778, 0.077),
(0.000, 0.508, 0.492))
P = np.array(P)
psi = (0.0, 0.2, 0.8) # Initial condition
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
ax.set_zlim(0, 1)
ax.set_xticks((0.25, 0.5, 0.75))
ax.set_yticks((0.25, 0.5, 0.75))
ax.set_zticks((0.25, 0.5, 0.75))
x_vals, y_vals, z_vals = [], [], []
for t in range(20):
x_vals.append(psi[0])
y_vals.append(psi[1])
z_vals.append(psi[2])
psi = np.dot(psi, P)
ax.scatter(x_vals, y_vals, z_vals, c='r', s=60)
psi_star = mc_compute_stationary(P)[0]
ax.scatter(psi_star[0], psi_star[1], psi_star[2], c='k', s=60)
plt.show()
