def create_grids(self):
""" construct grids for states and shocks """
par = self.par
par.a_grid = equilogspace(0,par.a_max,par.Na)
par.e_grid, par.e_trans, par.e_ergodic = markov_rouwenhorst(par.rho,par.sigma_e,par.Ne)
def matrix(l, n, v_a):
#parameter
Na = 1000
Ne = 11 # number of states
sol_shape = (Ne, Na)
a = np.zeros(sol_shape)
r = 0.03
w = 1.000
a_grid = equilogspace(0, 200, Na)
rho = 0.97 # AR(1) parameter
sigma_e = 0.25 # std. of persistent shock
sigma = 2
beta = 0.96
e_grid, e_trans, e_ergodic, e_trans_cumsum, e_ergodic_cumsum = markov_rouwenhorst(
rho, sigma_e, Ne)
#calculation
#step 3
A = np.kron(e_trans, np.identity(n))
B = (beta * A) @ v_a
C = np.power(B, (-sigma))
a_extend = np.tile(a_grid, 11)
m_endo = C + a_extend #samme opbygning som vektoren v_a
#step 4
values = []
m = (1 + r) * a_grid[np.newaxis, :] + w * e_grid[:, np.newaxis]
new_m_endo = np.array_split(m_endo, Ne)
for k in range(Ne):
linear_interp.interp_1d_vec(new_m_endo[k], a_grid, m[k], a[k])
for i_a in range(Na):
a[k, i_a] = np.fmax(a[k, i_a], 0)
values.append(m[k] - a[k])
#print(f'new_m_endo[0]:{new_m_endo[0]}')
#print(new_m_endo[0])
c = np.concatenate(values)
u = np.power(c, (1 - sigma)) / (1 - sigma)
u[u == -np.inf] = -1000000000000000000000000000
print(f'c:{c}')
print(f'u:{u}')
#Create Q^
lis = []
Q = np.zeros(Ne * Na)
#calculate
for e in range(Ne):
q = np.zeros((Na, Na)) #create each Q_i
for k in range(Na):
opt = a[e, k]
if opt >= np.max(a_grid):
q[k, Na - 1] = 1 #If opt equals the end point
elif opt <= np.min(a_grid):
q[k, 0] = 1 #If opt equals the start point
else:
a_high = np.min(np.nonzero(opt <= a_grid)) #create points
a_low = np.max(np.nonzero(opt >= a_grid))
q[k, a_low] = (a_grid[a_low + 1] - opt) / (a_grid[a_low + 1] -
a_grid[a_low])
q[k,
a_high] = (opt - a_grid[a_high - 1]) / (a_grid[a_high] -
a_grid[a_high - 1])
lis.append(q)
Q = block_diag(*lis) #make block matrix from Q's
omega = Q @ A
new_v_a = np.linalg.inv(np.identity(11000) - beta * omega) @ u
return new_v_a