def test_mc_sample_path():
P = [[0.4, 0.6], [0.2, 0.8]]
Ps = [P, sparse.csr_matrix(P)]
init = 0
sample_size = 10
seed = 42
for P in Ps:
# init: integer
expected = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1]
computed = mc_sample_path(P,
init=init,
sample_size=sample_size,
random_state=seed)
assert_array_equal(computed, expected)
# init: distribution
distribution = (0.5, 0.5)
expected = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1]
computed = mc_sample_path(P,
init=distribution,
sample_size=sample_size,
random_state=seed)
assert_array_equal(computed, expected)
def simulate(self,B_,s_0,T,sHist=None):
'''
Simulates planners policies for T periods
'''
Para,Pi,beta = self.Para,self.Pi,self.beta
Uc = Para.Uc
if sHist == None:
sHist = mc_sample_path(Pi,s_0,T)
cHist,nHist,Bhist,TauHist,muHist = np.zeros((5,T))
RHist = np.zeros(T-1)
#time0
mu,cHist[0],nHist[0],_ = self.time0_allocation(B_,s_0)
TauHist[0] = self.Tau(cHist[0],nHist[0])[s_0]
Bhist[0] = B_
muHist[0] = mu
#time 1 onward
for t in range(1,T):
c,n,x,Xi = self.time1_allocation(mu)
Tau = self.Tau(c,n)
u_c = Uc(c,n)
s = sHist[t]
Eu_c = Pi[sHist[t-1]].dot(u_c)
cHist[t],nHist[t],Bhist[t],TauHist[t] = c[s],n[s],x[s]/u_c[s],Tau[s]
RHist[t-1] = Uc(cHist[t-1],nHist[t-1])/(beta*Eu_c)
muHist[t] = mu
return cHist,nHist,Bhist,TauHist,sHist,muHist,RHist
def simulate(self, B_, s_0, T, sHist=None):
'''
Simulates planners policies for T periods
'''
Para, Pi, beta = self.Para, self.Pi, self.beta
Uc = Para.Uc
if sHist == None:
sHist = mc_sample_path(Pi, s_0, T)
cHist, nHist, Bhist, TauHist, muHist = np.zeros((5, T))
RHist = np.zeros(T - 1)
#time0
mu, cHist[0], nHist[0], _ = self.time0_allocation(B_, s_0)
TauHist[0] = self.Tau(cHist[0], nHist[0])[s_0]
Bhist[0] = B_
muHist[0] = mu
#time 1 onward
for t in range(1, T):
c, n, x, Xi = self.time1_allocation(mu)
Tau = self.Tau(c, n)
u_c = Uc(c, n)
s = sHist[t]
Eu_c = Pi[sHist[t - 1]].dot(u_c)
cHist[t], nHist[t], Bhist[t], TauHist[t] = c[s], n[
s], x[s] / u_c[s], Tau[s]
RHist[t - 1] = Uc(cHist[t - 1], nHist[t - 1]) / (beta * Eu_c)
muHist[t] = mu
return cHist, nHist, Bhist, TauHist, sHist, muHist, RHist
def test_mc_sample_path():
P = [[0.4, 0.6], [0.2, 0.8]]
init = 0
sample_size = 10
seed = 42
# init: integer
expected = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1]
computed = mc_sample_path(P, init=init, sample_size=sample_size,
random_state=seed)
assert_array_equal(computed, expected)
# init: distribution
distribution = (0.5, 0.5)
expected = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1]
computed = mc_sample_path(P, init=distribution, sample_size=sample_size,
random_state=seed)
assert_array_equal(computed, expected)
def test_mc_sample_path_lln():
P = [[0.4, 0.6], [0.2, 0.8]]
stationary_dist = [0.25, 0.75]
init = 0
seed = 4433
sample_size = 10**4
tol = 0.02
frequency_1 = mc_sample_path(P, init=init, sample_size=sample_size,
random_state=seed).mean()
ok_(np.abs(frequency_1 - stationary_dist[1]) < tol)
def test_mc_sample_path_lln():
P = [[0.4, 0.6], [0.2, 0.8]]
stationary_dist = [0.25, 0.75]
init = 0
seed = 4433
sample_size = 10**4
tol = 0.02
frequency_1 = mc_sample_path(P, init=init, sample_size=sample_size,
random_state=seed).mean()
ok_(np.abs(frequency_1 - stationary_dist[1]) < tol)
def simulate(self,B_,s_0,T,sHist=None):
'''
Simulates Ramsey plan for T periods
'''
Para,Pi = self.Para,self.Pi
Uc = Para.Uc
cf,nf,xprimef = self.policies
if sHist == None:
sHist = mc_sample_path(Pi,s_0,T)
cHist,nHist,Bhist,TauHist,muHist = np.zeros((5,T))
RHist = np.zeros(T-1)
#time0
cHist[0],nHist[0],xprime = self.time0_allocation(B_,s_0)
TauHist[0] = self.Tau(cHist[0],nHist[0])[s_0]
Bhist[0] = B_
muHist[0] = 0.
#time 1 onward
for t in range(1,T):
s,x = sHist[t],xprime[sHist[t]]
c,n,xprime = np.empty(self.S),nf[s](x),np.empty(self.S)
for shat in range(self.S):
c[shat] = cf[shat](x)
for sprime in range(self.S):
xprime[sprime] = xprimef[s,sprime](x)
Tau = self.Tau(c,n)[s]
u_c = Uc(c,n)
Eu_c = Pi[sHist[t-1]].dot(u_c)
muHist[t] = self.Vf[s](x,1)
RHist[t-1] = Uc(cHist[t-1],nHist[t-1])/(self.beta*Eu_c)
cHist[t],nHist[t],Bhist[t],TauHist[t] = c[s],n,x/u_c[s],Tau
return cHist,nHist,Bhist,TauHist,sHist,muHist,RHist
def simulate(self, B_, s_0, T, sHist=None):
'''
Simulates Ramsey plan for T periods
'''
Para, Pi = self.Para, self.Pi
Uc = Para.Uc
cf, nf, xprimef = self.policies
if sHist == None:
sHist = mc_sample_path(Pi, s_0, T)
cHist, nHist, Bhist, TauHist, muHist = np.zeros((5, T))
RHist = np.zeros(T - 1)
#time0
cHist[0], nHist[0], xprime = self.time0_allocation(B_, s_0)
TauHist[0] = self.Tau(cHist[0], nHist[0])[s_0]
Bhist[0] = B_
muHist[0] = 0.
#time 1 onward
for t in range(1, T):
s, x = sHist[t], xprime[sHist[t]]
c, n, xprime = np.empty(self.S), nf[s](x), np.empty(self.S)
for shat in range(self.S):
c[shat] = cf[shat](x)
for sprime in range(self.S):
xprime[sprime] = xprimef[s, sprime](x)
Tau = self.Tau(c, n)[s]
u_c = Uc(c, n)
Eu_c = Pi[sHist[t - 1]].dot(u_c)
muHist[t] = self.Vf[s](x, 1)
RHist[t - 1] = Uc(cHist[t - 1], nHist[t - 1]) / (self.beta * Eu_c)
cHist[t], nHist[t], Bhist[t], TauHist[t] = c[s], n, x / u_c[s], Tau
return cHist, nHist, Bhist, TauHist, sHist, muHist, RHist
