def stochEatCake(beta, N, e_params, W_max=1., plot=False, iid=True):
#step 1
if iid:
e, gamma = discretenorm(*e_params)
else:
e, gamma = tauchenhussey(*e_params)
#step 2
w = np.linspace(0,W_max,N)
#step 3
v = np.zeros((N,K))
p = np.zeros((N,K))
#step 4
actions = np.tile(w, N).reshape((N,N)).T
actions = actions - actions.T
actions[actions<0] = 0
u = np.sqrt(actions)
u_hat = np.repeat(u,K).reshape((N,N,K))*e
delta = 2.
while delta >= 1e-9:
#step 5
if iid:
E = (v*gamma).sum(axis=1)
else:
E = v.dot(gamma.T)
#step 6
if iid:
c = np.swapaxes(np.swapaxes(u_hat, 1, 2)+beta*E, 1, 2)
else:
c = u_hat + beta*E
c[np.triu_indices(N, k=1)] = -1e10
v_new = np.max(c, axis=1)
max_indices = np.argmax(c, axis=1)
p = w[max_indices]
#step 7
delta = math.sqrt(((v_new - v)**2).sum())
v = v_new
#step 8
if plot:
x = np.arange(0,N)
y = np.arange(0,K)
X,Y = np.meshgrid(x,y)
fig1 = plt.figure()
ax1 = Axes3D(fig1)
ax1.plot_surface(w[X], Y, v.T, cmap=cm.coolwarm)
plt.show()
fig2 = plt.figure()
ax2 = Axes3D(fig2)
ax2.plot_surface(w[X], Y, p.T, cmap=cm.coolwarm)
plt.show()
return v, p
def stochEatCake(beta, N, e_params, W_max=1., plot=False, iid=True):
#step 1
if iid:
e, gamma = discretenorm(*e_params)
else:
e, gamma = tauchenhussey(*e_params)
#step 2
w = np.linspace(0, W_max, N)
#step 3
v = np.zeros((N, K))
p = np.zeros((N, K))
#step 4
actions = np.tile(w, N).reshape((N, N)).T
actions = actions - actions.T
actions[actions < 0] = 0
u = np.sqrt(actions)
u_hat = np.repeat(u, K).reshape((N, N, K)) * e
delta = 2.
while delta >= 1e-9:
#step 5
if iid:
E = (v * gamma).sum(axis=1)
else:
E = v.dot(gamma.T)
#step 6
if iid:
c = np.swapaxes(np.swapaxes(u_hat, 1, 2) + beta * E, 1, 2)
else:
c = u_hat + beta * E
c[np.triu_indices(N, k=1)] = -1e10
v_new = np.max(c, axis=1)
max_indices = np.argmax(c, axis=1)
p = w[max_indices]
#step 7
delta = math.sqrt(((v_new - v)**2).sum())
v = v_new
#step 8
if plot:
x = np.arange(0, N)
y = np.arange(0, K)
X, Y = np.meshgrid(x, y)
fig1 = plt.figure()
ax1 = Axes3D(fig1)
ax1.plot_surface(w[X], Y, v.T, cmap=cm.coolwarm)
plt.show()
fig2 = plt.figure()
ax2 = Axes3D(fig2)
ax2.plot_surface(w[X], Y, p.T, cmap=cm.coolwarm)
plt.show()
return v, p
def Problem5Real():
sigma = .5
mu = 4*sigma
K = 7
Gamma, eps = discretenorm(K,mu,sigma)
N = 100
W = sp.linspace(0,1,N)
V = sp.zeros((N,K))
u = lambda c: sp.sqrt(c)
beta = 0.99
X,Y= sp.meshgrid(W,W)
Wdiff = Y-X
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
util3 = sp.tile(util_grid[:,:,sp.newaxis],(1,1,K))
eps_grid = eps[sp.newaxis,sp.newaxis,:]
eps_util = eps_grid*util3
Gamma_grid = Gamma[sp.newaxis,:]
delta = 1
Vprime = V
z = 0
while (delta > 10**-9):
z= z+1
V = Vprime
gamV = Gamma_grid*V
Expval = sp.sum(gamV,1)
Exp_grid = sp.tile(Expval[sp.newaxis,:,sp.newaxis],(N,1,K))
arg = eps_util+beta*Exp_grid
arg[index] = -10^10
Vprime = sp.amax(arg,1)
psi_ind = sp.argmax(arg,1)
psi = W[psi_ind]
delta = sp.linalg.norm(Vprime - V)
return Vprime,psi
def Problem2Real():
sigma = .5
mu = 4*sigma
K = 7
Gamma, eps = discretenorm(K,mu,sigma)
N = 100
W = sp.linspace(0,1,N)
V = sp.zeros((N,K))
u = lambda c: sp.sqrt(c)
beta = 0.99
X,Y= sp.meshgrid(W,W)
Wdiff = Y-X
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
util3 = sp.tile(util_grid[:,:,sp.newaxis],(1,1,K))
eps_grid = eps[sp.newaxis,sp.newaxis,:]
eps_util = eps_grid*util3
Gamma_grid = Gamma[sp.newaxis,:]
delta = 1
Vprime = V
z = 0
while (delta > 10**-9):
z= z+1
V = Vprime
gamV = Gamma_grid*V
Expval = sp.sum(gamV,1)
Exp_grid = sp.tile(Expval[sp.newaxis,:,sp.newaxis],(N,1,K))
arg = eps_util+beta*Exp_grid
arg[index] = -10^10
Vprime = sp.amax(arg,1)
psi_ind = sp.argmax(arg,1)
psi = W[psi_ind]
delta = sp.linalg.norm(Vprime - V)
return Vprime,psi
left = lower
prob = sp.zeros(K)
eps = sp.zeros(K)
for k in range(K):
prob[k] = st.norm.cdf(left+inc,mu,sigma) - st.norm.cdf(left,mu,sigma)
eps[k] = left + .5*inc
left = left + inc
return prob, eps
#Problem 2=====================================================================
sigma = .5
mu = 4*sigma
K = 7
Gamma, eps = discretenorm(K,mu,sigma)
N = 100
W = sp.linspace(0,1,N)
V = sp.zeros((N,K))
u = lambda c: sp.sqrt(c)
beta = 0.99
X,Y= sp.meshgrid(W,W)
Wdiff = Y-X
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
