def test_ddp_to_sa_and_to_product():
n, m = 3, 2
R = np.array([[0, 1], [1, 0], [-np.inf, 1]])
Q = np.empty((n, m, n))
Q[:] = 1 / n
Q[0, 0, 0] = 0
Q[0, 0, 1] = 2 / n
beta = 0.95
sparse_R = np.array([0, 1, 1, 0, 1])
_Q = np.full((5, 3), 1 / 3)
_Q[0, 0] = 0
_Q[0, 1] = 2 / n
sparse_Q = sparse.coo_matrix(_Q)
ddp = DiscreteDP(R, Q, beta)
ddp_sa = ddp.to_sa_pair_form()
ddp_sa2 = ddp_sa.to_sa_pair_form()
ddp_sa3 = ddp.to_sa_pair_form(sparse=False)
ddp2 = ddp_sa.to_product_form()
ddp3 = ddp_sa2.to_product_form()
ddp4 = ddp.to_product_form()
# make sure conversion worked
for ddp_s in [ddp_sa, ddp_sa2, ddp_sa3]:
assert_allclose(ddp_s.R, sparse_R)
# allcose doesn't work on sparse
np.max(np.abs((sparse_Q - ddp_s.Q))) < 1e-15
assert_allclose(ddp_s.beta, beta)
# these two will have probability 0 in state 2, action 0 b/c
# of the infeasiability in R
funky_Q = np.empty((n, m, n))
funky_Q[:] = 1 / n
funky_Q[0, 0, 0] = 0
funky_Q[0, 0, 1] = 2 / n
funky_Q[2, 0, :] = 0
for ddp_f in [ddp2, ddp3]:
assert_allclose(ddp_f.R, ddp.R)
assert_allclose(ddp_f.Q, funky_Q)
assert_allclose(ddp_f.beta, ddp.beta)
# this one is just the original one.
assert_allclose(ddp4.R, ddp.R)
assert_allclose(ddp4.Q, ddp.Q)
assert_allclose(ddp4.beta, ddp.beta)
for method in ["pi", "vi", "mpi"]:
sol1 = ddp.solve(method=method)
for ddp_other in [ddp_sa, ddp_sa2, ddp_sa3, ddp2, ddp3, ddp4]:
sol2 = ddp_other.solve(method=method)
for k in ["v", "sigma", "num_iter"]:
assert_allclose(sol1[k], sol2[k])
def test_ddp_to_sa_and_to_product():
n, m = 3, 2
R = np.array([[0, 1], [1, 0], [-np.inf, 1]])
Q = np.empty((n, m, n))
Q[:] = 1/n
Q[0, 0, 0] = 0
Q[0, 0, 1] = 2/n
beta = 0.95
sparse_R = np.array([0, 1, 1, 0, 1])
_Q = np.full((5, 3), 1/3)
_Q[0, 0] = 0
_Q[0, 1] = 2/n
sparse_Q = sparse.coo_matrix(_Q)
ddp = DiscreteDP(R, Q, beta)
ddp_sa = ddp.to_sa_pair_form()
ddp_sa2 = ddp_sa.to_sa_pair_form()
ddp_sa3 = ddp.to_sa_pair_form(sparse=False)
ddp2 = ddp_sa.to_product_form()
ddp3 = ddp_sa2.to_product_form()
ddp4 = ddp.to_product_form()
# make sure conversion worked
for ddp_s in [ddp_sa, ddp_sa2, ddp_sa3]:
assert_allclose(ddp_s.R, sparse_R)
# allcose doesn't work on sparse
np.max(np.abs((sparse_Q - ddp_s.Q))) < 1e-15
assert_allclose(ddp_s.beta, beta)
# these two will have probability 0 in state 2, action 0 b/c
# of the infeasiability in R
funky_Q = np.empty((n, m, n))
funky_Q[:] = 1/n
funky_Q[0, 0, 0] = 0
funky_Q[0, 0, 1] = 2/n
funky_Q[2, 0, :] = 0
for ddp_f in [ddp2, ddp3]:
assert_allclose(ddp_f.R, ddp.R)
assert_allclose(ddp_f.Q, funky_Q)
assert_allclose(ddp_f.beta, ddp.beta)
# this one is just the original one.
assert_allclose(ddp4.R, ddp.R)
assert_allclose(ddp4.Q, ddp.Q)
assert_allclose(ddp4.beta, ddp.beta)
for method in ["pi", "vi", "mpi"]:
sol1 = ddp.solve(method=method)
for ddp_other in [ddp_sa, ddp_sa2, ddp_sa3, ddp2, ddp3, ddp4]:
sol2 = ddp_other.solve(method=method)
for k in ["v", "sigma", "num_iter"]:
assert_allclose(sol1[k], sol2[k])
def voter_dpp(self, etah, etal, tauy, pipar, prg, prb, Pm, pol_br, etam,
beta, delta):
R = self.rewardv(etam, beta)
Q = self.populate_Q(etah, etal, tauy, pipar, prg, prb, Pm, pol_br)
dpp = DiscreteDP(R=R,
Q=Q,
beta=delta,
s_indices=self.state_indices,
a_indices=self.action_indices)
results = dpp.solve(method='policy_iteration')
sol = DPPsol(results, R, Q)
return (sol)
def prices_to_capital_stock(am, r):
w = r_to_w(r)
am.set_prices(r, w)
aiyagari_ddp = DiscreteDP(am.R, am.Q, β)
# Compute the optimal policy
results = aiyagari_ddp.solve(method='policy_iteration')
# Compute the stationary distribution
stationary_probs = results.mc.stationary_distributions[0]
# Extract the marginal distribution for assets
asset_probs = asset_marginal(stationary_probs, am.a_size, am.z_size)
# Return K
return np.sum(asset_probs * am.a_vals)
def prices_to_capital_stock(am, r):
"""
Map prices to the induced level of capital stock.
Parameters:
----------
am : Household
An instance of an aiyagari_household.Household
r : float
The interest rate
"""
w = r_to_w(r)
am.set_prices(r, w)
aiyagari_ddp = DiscreteDP(am.R, am.Q, beta)
# Compute the optimal policy
results = aiyagari_ddp.solve(method='policy_iteration')
# Compute the stationary distribution
stationary_probs = results.mc.stationary_distributions[0]
# Extract the marginal distribution for assets
asset_probs = asset_marginal(stationary_probs, am.a_size, am.z_size)
# Return K
return np.sum(asset_probs * am.a_vals)
def prices_to_capital_stock(am, r):
"""
Map prices to the induced level of capital stock.
Parameters:
----------
am : Household
An instance of an aiyagari_household.Household
r : float
The interest rate
"""
w = r_to_w(r)
am.set_prices(r, w)
aiyagari_ddp = DiscreteDP(am.R, am.Q, beta)
# Compute the optimal policy
results = aiyagari_ddp.solve(method='policy_iteration')
# Compute the stationary distribution
stationary_probs = results.mc.stationary_distributions[0]
# Extract the marginal distribution for assets
asset_probs = asset_marginal(stationary_probs, am.a_size, am.z_size)
# Return K
return np.sum(asset_probs * am.a_vals)
import matplotlib.pyplot as plt
from aiyagari_household import Household
from quantecon.markov import DiscreteDP
# Example prices
r = 0.03
w = 0.956
# Create an instance of Household
am = Household(a_max=20, r=r, w=w)
# Use the instance to build a discrete dynamic program
am_ddp = DiscreteDP(am.R, am.Q, am.beta)
# Solve using policy function iteration
results = am_ddp.solve(method='policy_iteration')
# Simplify names
z_size, a_size = am.z_size, am.a_size
z_vals, a_vals = am.z_vals, am.a_vals
n = a_size * z_size
# Get all optimal actions across the set of a indices with z fixed in each row
a_star = np.empty((z_size, a_size))
for s_i in range(n):
a_i = s_i // z_size
z_i = s_i % z_size
a_star[z_i, a_i] = a_vals[results.sigma[s_i]]
fig, ax = plt.subplots(figsize=(9, 9))
ax.plot(a_vals, a_vals, 'k--')# 45 degrees
ax.plot(k_vals, r_vals, lw=2, alpha=0.6, color='b', label='supply of capital')
ax.plot(k_vals,
rd(k_vals),
lw=2,
alpha=0.6,
color='r',
label='demand of capital')
ax.set_xlabel('capital stock')
ax.set_ylabel('r')
ax.legend(loc='upper right')
plt.show()
# Report the endogenous distribution of wealth.
#STEP 1: Stationary distribution of wealth.
am_ddp = DiscreteDP(am.R, am.Q, am.β)
results = am_ddp.solve(method='policy_iteration')
# Compute the stationary distribution
stationary_probs = results.mc.stationary_distributions[0]
# Extract the marginal distribution for assets
asset_probs = asset_marginal(stationary_probs, am.a_size, am.z_size)
#PLOT
plt.hist(asset_probs,
bins=None,
range=None,
density=False,
weights=None,
cumulative=False,
bottom=None,
histtype='bar',
align='mid',