def compute_lt_price(self, error_tol=1e-7, max_iter=600, verbose=0):
"""
Compute the equilibrium price function associated with Lucas
tree lt
Parameters
----------
error_tol, max_iter, verbose
Arguments to be passed directly to
`quantecon.compute_fixed_point`. See that docstring for more
information
Returns
-------
price : array_like(float)
The prices at the grid points in the attribute `grid` of the
object
"""
# == simplify notation == #
grid, grid_size = self.grid, self.grid_size
lucas_operator, gamma = self.lucas_operator, self.gamma
# == Create storage array for compute_fixed_point. Reduces memory
# allocation and speeds code up == #
Tf = np.empty(grid_size)
# == Initial guess, just a vector of ones == #
f_init = np.ones(grid_size)
f = compute_fixed_point(lucas_operator,
f_init,
error_tol,
max_iter,
verbose,
Tf=Tf)
price = f * grid**gamma
return price
Authors: John Stachurski and Thomas Sargent
LastModified: 11/08/2013
"""
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
import numpy as np
from matplotlib import cm
from quantecon.compute_fp import compute_fixed_point
import quantecon as qe
# === solve for the value function === #
wp = qe.career.workerProblem()
v_init = np.ones((wp.N, wp.N))*100
v = compute_fixed_point(qe.career.bellman, wp, v_init)
# === plot value function === #
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(111, projection='3d')
tg, eg = np.meshgrid(wp.theta, wp.epsilon)
ax.plot_surface(tg,
eg,
v.T,
rstride=2, cstride=2,
cmap=cm.jet,
alpha=0.5,
linewidth=0.25)
ax.set_zlim(150, 200)
ax.set_xlabel('theta', fontsize=14)
ax.set_ylabel('epsilon', fontsize=14)
Authors: John Stachurski and Thomas Sargent
"""
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
from matplotlib import cm
from scipy.interpolate import LinearNDInterpolator
import numpy as np
from quantecon import odu_vfi
from quantecon.compute_fp import compute_fixed_point
sp = odu_vfi.searchProblem(w_grid_size=100, pi_grid_size=100)
v_init = np.zeros(len(sp.grid_points)) + sp.c / (1 - sp.beta)
v = compute_fixed_point(odu_vfi.bellman, sp, v_init)
policy = odu_vfi.get_greedy(sp, v)
# Make functions from these arrays by interpolation
vf = LinearNDInterpolator(sp.grid_points, v)
pf = LinearNDInterpolator(sp.grid_points, policy)
pi_plot_grid_size, w_plot_grid_size = 100, 100
pi_plot_grid = np.linspace(0.001, 0.99, pi_plot_grid_size)
w_plot_grid = np.linspace(0, sp.w_max, w_plot_grid_size)
#plot_choice = 'value_function'
plot_choice = 'policy_function'
if plot_choice == 'value_function':
Z = np.empty((w_plot_grid_size, pi_plot_grid_size))
Filename: odu_vfi_plots.py
Authors: John Stachurski and Thomas Sargent
"""
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
from matplotlib import cm
from scipy.interpolate import LinearNDInterpolator
import numpy as np
from quantecon import odu_vfi
from quantecon.compute_fp import compute_fixed_point
sp = odu_vfi.searchProblem(w_grid_size=100, pi_grid_size=100)
v_init = np.zeros(len(sp.grid_points)) + sp.c / (1 - sp.beta)
v = compute_fixed_point(odu_vfi.bellman, sp, v_init)
policy = odu_vfi.get_greedy(sp, v)
# Make functions from these arrays by interpolation
vf = LinearNDInterpolator(sp.grid_points, v)
pf = LinearNDInterpolator(sp.grid_points, policy)
pi_plot_grid_size, w_plot_grid_size = 100, 100
pi_plot_grid = np.linspace(0.001, 0.99, pi_plot_grid_size)
w_plot_grid = np.linspace(0, sp.w_max, w_plot_grid_size)
#plot_choice = 'value_function'
plot_choice = 'policy_function'
if plot_choice == 'value_function':
Z = np.empty((w_plot_grid_size, pi_plot_grid_size))
""" Origin: QE by John Stachurski and Thomas J. Sargent Filename: jv_test.py Authors: John Stachurski and Thomas Sargent LastModified: 11/08/2013 Tests jv.py with a particular parameterization. """ import matplotlib.pyplot as plt from jv import workerProblem, bellman_operator from quantecon.compute_fp import compute_fixed_point import quantecon.jv as jv # === solve for optimal policy === # wp = jv.workerProblem(grid_size=25) v_init = wp.x_grid * 0.5 V = compute_fixed_point(jv.bellman_operator, wp, v_init, max_iter=40) s_policy, phi_policy = jv.bellman_operator(wp, V, return_policies=True) # === plot policies === # fig, ax = plt.subplots() ax.set_xlim(0, max(wp.x_grid)) ax.set_ylim(-0.1, 1.1) ax.plot(wp.x_grid, phi_policy, 'b-', label='phi') ax.plot(wp.x_grid, s_policy, 'g-', label='s') ax.legend() plt.show()
Authors: John Stachurski and Thomas Sargent
LastModified: 11/08/2013
"""
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
import numpy as np
from matplotlib import cm
from quantecon.compute_fp import compute_fixed_point
import quantecon as qe
# === solve for the value function === #
wp = qe.career.workerProblem()
v_init = np.ones((wp.N, wp.N)) * 100
v = compute_fixed_point(qe.career.bellman, wp, v_init)
# === plot value function === #
fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, projection='3d')
tg, eg = np.meshgrid(wp.theta, wp.epsilon)
ax.plot_surface(tg,
eg,
v.T,
rstride=2,
cstride=2,
cmap=cm.jet,
alpha=0.5,
linewidth=0.25)
ax.set_zlim(150, 200)
ax.set_xlabel('theta', fontsize=14)
