auto sync from book-dp1

Author: quantecon-services

code/jl/expo_curve.py

@@ -1,41 +1,18 @@
-# ---
-# jupyter:
-#   jupytext:
-#     text_representation:
-#       extension: .py
-#       format_name: light
-#       format_version: '1.5'
-#       jupytext_version: 1.14.6
-#   kernelspec:
-#     display_name: Python 3
-#     language: python
-#     name: python3
-# ---
-
 import numpy as np
 import matplotlib.pyplot as plt
 import matplotlib
+from scipy.linalg import expm, eigvals
 
 matplotlib.rc("text", usetex=True) # allow tex rendering
-fontsize=16
-from scipy.linalg import expm, eigvals
 
-# %matplotlib inline
+fontsize = 16
 
-# +
 A = ((-2, -0.4, 0),
      (-1.4, -1, 2.2),
      (0, -2, -0.6))
 
 A = np.array(A)
-# -
-
 ev = eigvals(A)
-
-np.imag(ev)
-
-np.max(np.real(ev))
-
 h = 0.01
 s0 = 0.01 * np.array((1, 1, 1))
 
@@ -48,7 +25,6 @@
     y.append(b)
     z.append(c)
 
-# +
 ax = plt.figure().add_subplot(projection='3d')
 
 ax.plot(x, y, z, label='$t \mapsto \mathrm{e}^{t A} u_0$')
@@ -67,8 +43,3 @@
 
 plt.savefig("../figures/expo_curve_1.pdf")
 plt.show()
-# -
-
-
-
-

code/jl/markov_js_with_sep.jl

@@ -117,7 +117,7 @@ function plot_w_stars(; α_vals=LinRange(0.0, 1.0, 10),
     ax.plot(α_vals, w_star_vec, lw=2, alpha=0.6, label="reservation wage")
     ax.legend(frameon=false, fontsize=fontsize)
     ax.set_xlabel(L"\alpha", fontsize=fontsize)
-    ax.set_xlabel(L"w", fontsize=fontsize)
+    ax.set_ylabel(L"w", fontsize=fontsize)
     plt.show()
     if savefig
         fig.savefig(figname)

code/jl/stoch_dom_finite.jl

@@ -6,7 +6,7 @@ PyPlot.matplotlib[:rc]("text", usetex=true) # allow tex rendering
 p, q = 0.75, 0.25
 fig, axes = plt.subplots(1, 2, figsize=(10, 5.2))
 ax = axes[1]
-ax.bar(1:2, (p, 1-p), label=L"\phi")
+ax.bar(1:2, (p, 1-p), label=L"\varphi")
 
 ax = axes[2]
 ax.bar(1:2, (q, 1-q), label=L"\psi")

code/py/american_option.py

@@ -7,6 +7,7 @@
 from quantecon import compute_fixed_point
 
 import numpy as np
+import matplotlib.pyplot as plt
 from collections import namedtuple
 from numba import njit, prange
 
@@ -36,7 +37,7 @@ def create_american_option_model(
     z_vals, Q = mc.state_values + μ, mc.P
     w_vals, φ, β = np.array([-s, s]), np.array([0.5, 0.5]), 1 / (1 + r)
     return Model(t_vals=t_vals, z_vals=z_vals, w_vals=w_vals, Q=Q,
-                φ=φ, T=T, β=β, K=K)
+                 φ=φ, T=T, β=β, K=K)
 
 
 @njit(parallel=True)
@@ -72,12 +73,8 @@ def compute_cvf(model):
 
 # Plots
 
-
-import matplotlib.pyplot as plt
-
-
 def plot_contours(savefig=False,
-                  figname="./figures/american_option_1.pdf"):
+                  figname="../figures_py/american_option_1.png"):
 
     model = create_american_option_model()
     t_vals, z_vals, w_vals, Q, φ, T, β, K = model
@@ -110,7 +107,7 @@ def plot_contours(savefig=False,
 
 def plot_strike(savefig=False,
                 fontsize=9,
-                figname="./figures/american_option_2.pdf"):
+                figname="../figures_py/american_option_2.png"):
     model = create_american_option_model()
     t_vals, z_vals, w_vals, Q, φ, T, β, K = model
     h_star = compute_cvf(model)

code/py/ar1_spec_rad.py

@@ -9,6 +9,7 @@
 """
 
 import numpy as np
+import matplotlib.pyplot as plt
 
 from quantecon.markov import tauchen
 
@@ -69,12 +70,9 @@ def compute_mc_spec_rad(n, ρ, σ, μ, m, b):
 # Plots
 
 
-import matplotlib.pyplot as plt
-
-
 def plot_beta_sim(T=80,
                   savefig=True,
-                  figname="./figures/ar1_spec_rad.png"):
+                  figname="../figures_py/ar1_spec_rad.png"):
     β_vals = np.zeros(T)
     Z = 1
     for t in range(T):
@@ -92,5 +90,3 @@ def plot_beta_sim(T=80,
     if savefig:
         fig.savefig(figname)
     plt.show()
-
-plot_beta_sim()

code/py/bellman_envelope.py

@@ -0,0 +1,56 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+xmin = -0.5
+xmax = 2.0
+
+xgrid = np.linspace(xmin, xmax, 1000)
+
+a1, b1 = 0.15, 0.5    # first T_σ
+a2, b2 = 0.5, 0.4     # second T_σ
+a3, b3 = 0.75, 0.2    # third T_σ
+
+v1 = b1/(1-a1)
+v2 = b2/(1-a2)
+v3 = b3/(1-a3)
+
+T1 = a1 * xgrid + b1
+T2 = a2 * xgrid + b2
+T3 = a3 * xgrid + b3
+T =  np.maximum.reduce([T1, T2, T3])
+
+fig, ax = plt.subplots(figsize=(6, 5))
+for spine in ["left", "bottom"]:
+    ax.spines[spine].set_position("zero")
+
+for spine in ["right", "top"]:
+    ax.spines[spine].set_color("none")
+
+ax.plot(xgrid, T1, "k-", lw=1)
+ax.plot(xgrid, T2, "k-", lw=1)
+ax.plot(xgrid, T3, "k-", lw=1)
+
+ax.plot(xgrid, T, lw=6, alpha=0.3, color="blue",
+        label=r"$T = \bigvee_{\sigma \in \Sigma} T_\sigma$")
+
+
+ax.text(2.1, 0.6, r"$T_{\sigma'}$")
+ax.text(2.1, 1.4, r"$T_{\sigma''}$")
+ax.text(2.1, 1.9, r"$T_{\sigma'''}$")
+
+ax.legend(frameon=False, loc="upper center")
+
+
+ax.set_xlim(xmin, xmax+0.5)
+ax.set_ylim(-0.2, 2.5)
+ax.text(2.4, -0.15, r"$v$")
+
+ax.set_xticks([])
+ax.set_yticks([])
+
+plt.show()
+
+file_name = "../figures_py/bellman_envelope.png"
+fig.savefig(file_name)
+

code/py/binom_stoch_dom.py

@@ -0,0 +1,25 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import binom
+
+
+n, m, p = 10, 18, 0.5
+
+phi = binom(n, p)
+psi = binom(m, p)
+
+x = np.arange(0, m+1)
+
+fig, ax = plt.subplots(figsize=(9, 5.2))
+lb = r"$\phi = B({}, {})$".format(n, p)
+ax.plot(x, np.concatenate((phi.pmf(np.arange(0, n+1)),
+                           np.zeros(m-n))), "-o", alpha=0.6, label=lb)
+lb = r"$\psi = B({}, {})$".format(m, p)
+ax.plot(x, psi.pmf(x), "-o", alpha=0.6, label=lb)
+
+ax.legend(fontsize=16, frameon=False)
+
+plt.show()
+
+file_name = "../figures_py/binom_stoch_dom.png"
+fig.savefig(file_name)

code/py/concave_map_fp.py

@@ -0,0 +1,42 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+x0 = 0.25
+xmin, xmax = 0, 3
+fs = 18
+
+x_grid = np.linspace(xmin, xmax, 1200)
+
+def g(x):
+    return 1 + 0.5 * x**0.5
+
+xstar = 1.64
+
+fig, ax = plt.subplots(figsize=(10, 5.5))
+
+# Plot the functions
+lb = r"$g$"
+ax.plot(x_grid, g(x_grid), lw=2, alpha=0.6, label=lb)
+ax.plot(x_grid, x_grid, "k--", lw=1, alpha=0.7, label=r"$45$")
+
+# Show and annotate the fixed point
+fps = (xstar,)
+ax.plot(fps, fps, "go", ms=10, alpha=0.6)
+ax.set_xlabel(r"$x$", fontsize=fs)
+ax.annotate(r"$x^*$",
+            xy=(xstar, xstar),
+            xycoords="data",
+            xytext=(-20, 20),
+            textcoords="offset points",
+            fontsize=fs)
+
+ax.legend(loc="upper left", frameon=False, fontsize=fs)
+ax.set_xticks((0, 1, 2, 3))
+ax.set_yticks((0, 1, 2, 3))
+ax.set_ylim(0, 3)
+ax.set_xlim(0, 3)
+
+plt.show()
+
+file_name = "../figures_py/concave_map_fp.png"
+fig.savefig(file_name)