def stoch_value():
#Compute Solution==========================================================
sigma = .5
mu = 4*sigma
K = 7
Gamma, eps = discretenorm.discretenorm(K,mu,sigma)
N = 100
W = np.linspace(0,1,N)
V = np.zeros((N,K))
u = lambda c: np.sqrt(c)
beta = 0.99
X,Y= np.meshgrid(W,W)
Wdiff = Y-X
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
util3 = np.tile(util_grid[:,:,np.newaxis],(1,1,K))
eps_grid = eps[np.newaxis,np.newaxis,:]
eps_util = eps_grid*util3
Gamma_grid = Gamma[np.newaxis,:]
delta = 1
Vprime = V
z = 0
while (delta > 10**-9):
z= z+1
V = Vprime
gamV = Gamma_grid*V
Expval = np.sum(gamV,1)
Exp_grid = np.tile(Expval[np.newaxis,:,np.newaxis],(N,1,K))
arg = eps_util+beta*Exp_grid
arg[index] = -10^10
Vprime = np.amax(arg,1)
psi_ind = np.argmax(arg,1)
psi = W[psi_ind]
delta = np.linalg.norm(Vprime - V)
#============================================================
#Plot 3D
x=np.arange(0,N)
y=np.arange(0,K)
X,Y=np.meshgrid(x,y)
fig1 = plt.figure()
ax1= Axes3D(fig1)
ax1.set_xlabel(r'$W$')
ax1.set_ylabel(r'$\varepsilon$')
ax1.set_zlabel(r'$V$')
ax1.plot_surface(W[X],Y,np.transpose(Vprime), cmap=cm.coolwarm)
plt.savefig('stoch_value.pdf')
plt.clf()
def stoch_value():
#Compute Solution==========================================================
sigma = .5
mu = 4*sigma
K = 7
Gamma, eps = discretenorm.discretenorm(K,mu,sigma)
N = 100
W = np.linspace(0,1,N)
V = np.zeros((N,K))
u = lambda c: np.sqrt(c)
beta = 0.99
X,Y= np.meshgrid(W,W)
Wdiff = Y-X
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
util3 = np.tile(util_grid[:,:,np.newaxis],(1,1,K))
eps_grid = eps[np.newaxis,np.newaxis,:]
eps_util = eps_grid*util3
Gamma_grid = Gamma[np.newaxis,:]
delta = 1
Vprime = V
z = 0
while (delta > 10**-9):
z= z+1
V = Vprime
gamV = Gamma_grid*V
Expval = np.sum(gamV,1)
Exp_grid = np.tile(Expval[np.newaxis,:,np.newaxis],(N,1,K))
arg = eps_util+beta*Exp_grid
arg[index] = -10^10
Vprime = np.amax(arg,1)
psi_ind = np.argmax(arg,1)
psi = W[psi_ind]
delta = np.linalg.norm(Vprime - V)
#============================================================
#Plot 3D
x=np.arange(0,N)
y=np.arange(0,K)
X,Y=np.meshgrid(x,y)
fig1 = plt.figure()
ax1= Axes3D(fig1)
ax1.set_xlabel(r'$W$')
ax1.set_ylabel(r'$\varepsilon$')
ax1.set_zlabel(r'$V$')
ax1.plot_surface(W[X],Y,np.transpose(Vprime), cmap=cm.coolwarm)
plt.savefig('stoch_value.pdf')
plt.clf()
value is 1.
Outputs:
max_vals: The maximum values found along the dimension.
arg_maxes: The locaiton of the max_vals along a dimension.
"""
return np.array([np.max(array, axis=axis), np.argmax(array, axis=axis)])
## --------------------------------Problem 1--------------------------------- ##
sigma = np.sqrt(0.25)
mu = 4 * sigma
nodes = 7
beta = 0.9
tol = 10e-9
eps, gamma = dn.discretenorm(nodes, mu, sigma)
## --------------------------------Problem 2--------------------------------- ##
w = np.array(np.arange(0.01, 1.01, .01))
N = w.size
vtp1 = np.zeros((N,nodes))
# Create probability matrix for epsilon'
E_mat = np.tile(gamma, (N, 1))
# Integrate out epsilon' and get just the E[v(w')] vector.
Evtp1_prime = np.sum(vtp1 * E_mat, axis = 1)
# Flip it so the w' is the third dimension. Then repeat it in w, epsilon dims.
Evtp1_prime = np.reshape(Evtp1_prime, (1,1,N))
Evtp1_mat = np.tile(Evtp1_prime, (N, nodes, 1))
