update cases with r

Author: HumphreyYang

lectures/ak2.md

@@ -760,26 +760,26 @@ fig, axs = plt.subplots(3, 3, figsize=(14, 10))
 # quantities
 for i, name in enumerate(['K', 'Y', 'Cy', 'Co']):
     ax = axs[i//3, i%3]
-    ax.plot(range(T+1), quant_seq1[:T+1, i], label=name+', 1/3')
-    ax.plot(range(T+1), quant_seq2[:T+1, i], label=name+', 0.2')
+    ax.plot(range(T+1), quant_seq1[:T+1, i], label=f'{name}, 1/3')
+    ax.plot(range(T+1), quant_seq2[:T+1, i], label=f'{name}, 0.2')
     ax.hlines(init_ss[i], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')
 
 # prices
 for i, name in enumerate(['W', 'r']):
     ax = axs[(i+4)//3, (i+4)%3]
-    ax.plot(range(T+1), price_seq1[:T+1, i], label=name+', 1/3')
-    ax.plot(range(T+1), price_seq2[:T+1, i], label=name+', 0.2')
+    ax.plot(range(T+1), price_seq1[:T+1, i], label=f'{name}, 1/3')
+    ax.plot(range(T+1), price_seq2[:T+1, i], label=f'{name}, 0.2')
     ax.hlines(init_ss[i+4], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')
 
 # policies
 for i, name in enumerate(['τ', 'D', 'G']):
     ax = axs[(i+6)//3, (i+6)%3]
-    ax.plot(range(T+1), policy_seq1[:T+1, i], label=name+', 1/3')
-    ax.plot(range(T+1), policy_seq2[:T+1, i], label=name+', 0.2')
+    ax.plot(range(T+1), policy_seq1[:T+1, i], label=f'{name}, 1/3')
+    ax.plot(range(T+1), policy_seq2[:T+1, i], label=f'{name}, 0.2')
     ax.hlines(init_ss[i+6], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')
@@ -1179,26 +1179,26 @@ fig, axs = plt.subplots(3, 3, figsize=(14, 10))
 # quantities
 for i, name in enumerate(['K', 'Y', 'Cy', 'Co']):
     ax = axs[i//3, i%3]
-    ax.plot(range(T+1), quant_seq3[:T+1, i], label=name+', $\delta$s=0')
-    ax.plot(range(T+1), quant_seq4[:T+1, i], label=name+', $\delta$s=0.005')
+    ax.plot(range(T+1), quant_seq3[:T+1, i], label=rf'{name}, $\delta$s=0')
+    ax.plot(range(T+1), quant_seq4[:T+1, i], label=rf'{name}, $\delta$s=0.005')
     ax.hlines(init_ss[i], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')
 
 # prices
 for i, name in enumerate(['W', 'r']):
     ax = axs[(i+4)//3, (i+4)%3]
-    ax.plot(range(T+1), price_seq3[:T+1, i], label=name+', $\delta$s=0')
-    ax.plot(range(T+1), price_seq4[:T+1, i], label=name+', $\delta$s=0.005')
+    ax.plot(range(T+1), price_seq3[:T+1, i], label=rf'{name}, $\delta$s=0')
+    ax.plot(range(T+1), price_seq4[:T+1, i], label=rf'{name}, $\delta$s=0.005')
     ax.hlines(init_ss[i+4], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')
 
 # policies
 for i, name in enumerate(['τ', 'D', 'G']):
     ax = axs[(i+6)//3, (i+6)%3]
-    ax.plot(range(T+1), policy_seq3[:T+1, i], label=name+', $\delta$s=0')
-    ax.plot(range(T+1), policy_seq4[:T+1, i], label=name+', $\delta$s=0.005')
+    ax.plot(range(T+1), policy_seq3[:T+1, i], label=rf'{name}, $\delta$s=0')
+    ax.plot(range(T+1), policy_seq4[:T+1, i], label=rf'{name}, $\delta$s=0.005')
     ax.hlines(init_ss[i+6], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')
@@ -1244,26 +1244,26 @@ fig, axs = plt.subplots(3, 3, figsize=(14, 10))
 # quantities
 for i, name in enumerate(['K', 'Y', 'Cy', 'Co']):
     ax = axs[i//3, i%3]
-    ax.plot(range(T+1), quant_seq3[:T+1, i], label=name+', tax cut')
-    ax.plot(range(T+1), quant_seq5[:T+1, i], label=name+', transfer')
+    ax.plot(range(T+1), quant_seq3[:T+1, i], label=f'{name}, tax cut')
+    ax.plot(range(T+1), quant_seq5[:T+1, i], label=f'{name}, transfer')
     ax.hlines(init_ss[i], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')
 
 # prices
 for i, name in enumerate(['W', 'r']):
     ax = axs[(i+4)//3, (i+4)%3]
-    ax.plot(range(T+1), price_seq3[:T+1, i], label=name+', tax cut')
-    ax.plot(range(T+1), price_seq5[:T+1, i], label=name+', transfer')
+    ax.plot(range(T+1), price_seq3[:T+1, i], label=f'{name}, tax cut')
+    ax.plot(range(T+1), price_seq5[:T+1, i], label=f'{name}, transfer')
     ax.hlines(init_ss[i+4], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')
 
 # policies
 for i, name in enumerate(['τ', 'D', 'G']):
     ax = axs[(i+6)//3, (i+6)%3]
-    ax.plot(range(T+1), policy_seq3[:T+1, i], label=name+', tax cut')
-    ax.plot(range(T+1), policy_seq5[:T+1, i], label=name+', transfer')
+    ax.plot(range(T+1), policy_seq3[:T+1, i], label=f'{name}, tax cut')
+    ax.plot(range(T+1), policy_seq5[:T+1, i], label=f'{name}, transfer')
     ax.hlines(init_ss[i+6], 0, T+1, color='r', linestyle='--')
     ax.legend()
     ax.set_xlabel('t')

lectures/finite_markov.md

@@ -1242,11 +1242,11 @@ The following code snippet provides a hint as to how you can go about this
 
 ```{code-cell} python3
 import re
-re.findall('\w', 'x +++ y ****** z')  # \w matches alphanumerics
+re.findall(r'\w', 'x +++ y ****** z')  # \w matches alphanumerics
 ```
 
 ```{code-cell} python3
-re.findall('\w', 'a ^^ b &&& $$ c')
+re.findall(r'\w', 'a ^^ b &&& $$ c')
 ```
 
 When you solve for the ranking, you will find that the highest ranked node is in fact `g`, while the lowest is `a`.

lectures/likelihood_bayes.md

@@ -314,7 +314,7 @@ for t in range(T):
 fig, ax1 = plt.subplots()
 
 for i in range(2):
-    ax1.plot(range(T+1), π_seq_f[i, :], label=f"$\pi_0$={π_seq_f[i, 0]}")
+    ax1.plot(range(T+1), π_seq_f[i, :], label=fr"$\pi_0$={π_seq_f[i, 0]}")
 
 ax1.set_ylabel("$\pi_t$")
 ax1.set_xlabel("t")
@@ -348,7 +348,7 @@ for t in range(T):
 fig, ax1 = plt.subplots()
 
 for i in range(2):
-    ax1.plot(range(T+1), π_seq_g[i, :], label=f"$\pi_0$={π_seq_g[i, 0]}")
+    ax1.plot(range(T+1), π_seq_g[i, :], label=fr"$\pi_0$={π_seq_g[i, 0]}")
 
 ax1.set_ylabel("$\pi_t$")
 ax1.set_xlabel("t")

lectures/linear_models.md

@@ -738,7 +738,7 @@ y = y.flatten()
 ygrid = np.linspace(ymin, ymax, 150)
 
 ax.hist(y, bins=50, density=True, alpha=0.4)
-ax.plot(ygrid, f_y.pdf(ygrid), 'k-', lw=2, alpha=0.8, label=r'true density')
+ax.plot(ygrid, f_y.pdf(ygrid), 'k-', lw=2, alpha=0.8, label='true density')
 ax.set_xlim(ymin, ymax)
 ax.set_xlabel('$y_t$', fontsize=12)
 ax.set_ylabel('relative frequency', fontsize=12)
@@ -802,7 +802,7 @@ for t in range(T):
     μ_x, μ_y, Σ_x, Σ_y = next(m)
     population_means.append(float(μ_y))
 
-ax.plot(population_means, color='g', lw=2, alpha=0.8, label='$G\mu_t$')
+ax.plot(population_means, color='g', lw=2, alpha=0.8, label=r'$G\mu_t$')
 ax.set_ylim(ymin, ymax)
 ax.set_xlabel('time', fontsize=12)
 ax.set_ylabel('$y_t$', fontsize=12)

lectures/lln_clt.md

@@ -265,7 +265,7 @@ for ax in axes:
     axlabel = '$\\bar{X}_n$ for $X_i \sim$' + name
     ax.plot(list(range(n)), sample_mean, 'g-', lw=3, alpha=0.6, label=axlabel)
     m = distribution.mean()
-    ax.plot(list(range(n)), [m] * n, 'k--', lw=1.5, label='$\mu$')
+    ax.plot(list(range(n)), [m] * n, 'k--', lw=1.5, label=r'$\mu$')
     ax.vlines(list(range(n)), m, data, lw=0.2)
     ax.legend(**legend_args, fontsize=12)
 
@@ -408,7 +408,7 @@ xmin, xmax = -3 * s, 3 * s
 ax.set_xlim(xmin, xmax)
 ax.hist(Y, bins=60, alpha=0.5, density=True)
 xgrid = np.linspace(xmin, xmax, 200)
-ax.plot(xgrid, norm.pdf(xgrid, scale=s), 'k-', lw=2, label='$N(0, \sigma^2)$')
+ax.plot(xgrid, norm.pdf(xgrid, scale=s), 'k-', lw=2, label=r'$N(0, \sigma^2)$')
 ax.legend()
 
 plt.show()

lectures/mix_model.md

@@ -455,7 +455,7 @@ def plot_π_seq(α, π1=0.2, π2=0.8, T=200):
     # plot
     fig, ax1 = plt.subplots()
     for i in range(2):
-        ax1.plot(range(T+1), π_seq_mixed[i, :], label=f"$\pi_0$={π_seq_mixed[i, 0]}")
+        ax1.plot(range(T+1), π_seq_mixed[i, :], label=fr"$\pi_0$={π_seq_mixed[i, 0]}")
 
     ax1.plot(np.nan, np.nan,  '--', color='b', label='Log likelihood ratio process')
     ax1.set_ylabel("$\pi_t$")

lectures/multivariate_normal.md

@@ -773,7 +773,7 @@ for i in range(1, n+1):
 μθ_hat_higher = μθ_hat_arr + 1.96 * σθ_hat_arr
 
 plt.hlines(θ, 1, n+1, ls='--', label='true $θ$')
-plt.plot(range(1, n+1), μθ_hat_arr, color='b', label='$\hat{μ}_{θ}$')
+plt.plot(range(1, n+1), μθ_hat_arr, color='b', label=r'$\hat{μ}_{θ}$')
 plt.plot(range(1, n+1), μθ_hat_lower, color='b', ls='--')
 plt.plot(range(1, n+1), μθ_hat_higher, color='b', ls='--')
 plt.fill_between(range(1, n+1), μθ_hat_lower, μθ_hat_higher,
@@ -2277,7 +2277,7 @@ coordinate axis versus $y$ on the ordinate axis.
 
 ```{code-cell} python3
 plt.scatter(range(N), Λ @ f, label='$Ey|f$')
-plt.scatter(range(N), y_hat, label='$\hat{y}$')
+plt.scatter(range(N), y_hat, label=r'$\hat{y}$')
 plt.hlines(f[0], 0, N//2-1, ls='--', label='$f_{1}$')
 plt.hlines(f[1], N//2, N-1, ls='-.', label='$f_{2}$')
 

lectures/util_rand_resp.md

@@ -281,11 +281,11 @@ y2 = (pow(x2, 0.5) - 0.4)**2
 x3 = np.arange(0.4**0.5, 1, 0.001)
 y3 = pow(x3**2 - 0.4, 0.5)
 plt.figure(figsize=(12, 10))
-plt.plot(x1, y1, 'r-', label='Truth Border of: $U_i(Pr(A|r_i),\phi_i)=-Pr(A|r_i)+f(\phi_i)$')
+plt.plot(x1, y1, 'r-', label=r'Truth Border of: $U_i(Pr(A|r_i),\phi_i)=-Pr(A|r_i)+f(\phi_i)$')
 plt.fill_between(x1, 0, y1, facecolor='red', alpha=0.05)
-plt.plot(x2, y2, 'b-', label='Truth Border of: $U_i(Pr(A|r_i),\phi_i)=-Pr(A|r_i)^{2}+f(\phi_i)$')
+plt.plot(x2, y2, 'b-', label=r'Truth Border of: $U_i(Pr(A|r_i),\phi_i)=-Pr(A|r_i)^{2}+f(\phi_i)$')
 plt.fill_between(x2, 0, y2, facecolor='blue', alpha=0.05)
-plt.plot(x3, y3, 'y-', label='Truth Border of: $U_i(Pr(A|r_i),\phi_i)=-\sqrt{Pr(A|r_i)}+f(\phi_i)$')
+plt.plot(x3, y3, 'y-', label=r'Truth Border of: $U_i(Pr(A|r_i),\phi_i)=-\sqrt{Pr(A|r_i)}+f(\phi_i)$')
 plt.fill_between(x3, 0, y3, facecolor='green', alpha=0.05)
 plt.plot(x1, x1, ':', linewidth=2)
 plt.xlim([0, 1])
@@ -318,7 +318,7 @@ y1 = x1 - 0.4
 z1 = x1
 z2 = 0
 plt.figure(figsize=(12, 10))
-plt.plot(x1, y1,'r-',label='Truth Border of: $U_i(Pr(A|r_i),\phi_i)=-Pr(A|r_i)+f(\phi_i)$')
+plt.plot(x1, y1,'r-',label=r'Truth Border of: $U_i(Pr(A|r_i),\phi_i)=-Pr(A|r_i)+f(\phi_i)$')
 plt.plot(x1, x1, ':', linewidth=2)
 plt.fill_between(x1, y1, z1, facecolor='blue', alpha=0.05, label='truth telling')
 plt.fill_between(x1, z2, y1, facecolor='green', alpha=0.05, label='lying')

lectures/wald_friedman.md

@@ -597,7 +597,7 @@ ax.plot(wf.π_grid, cost_L1, label='choose f1')
 ax.plot(wf.π_grid, cost_L0, label='choose f0')
 ax.plot(wf.π_grid,
         np.amin(np.column_stack([h_star, cost_L0, cost_L1]),axis=1),
-        lw=15, alpha=0.1, color='b', label='$J(\pi)$')
+        lw=15, alpha=0.1, color='b', label=r'$J(\pi)$')
 
 ax.annotate(r"$\beta$", xy=(β + 0.01, 0.5), fontsize=14)
 ax.annotate(r"$\alpha$", xy=(α + 0.01, 0.5), fontsize=14)

lectures/wealth_dynamics.md

@@ -477,7 +477,7 @@ gini_vals = []
 for μ_r in μ_r_vals:
     wdy = WealthDynamics(μ_r=μ_r)
     gv, (f_vals, l_vals) = generate_lorenz_and_gini(wdy)
-    ax.plot(f_vals, l_vals, label=f'$\psi^*$ at $\mu_r = {μ_r:0.2}$')
+    ax.plot(f_vals, l_vals, label=fr'$\psi^*$ at $\mu_r = {μ_r:0.2}$')
     gini_vals.append(gv)
 
 ax.plot(f_vals, f_vals, label='equality')
@@ -522,7 +522,7 @@ gini_vals = []
 for σ_r in σ_r_vals:
     wdy = WealthDynamics(σ_r=σ_r)
     gv, (f_vals, l_vals) = generate_lorenz_and_gini(wdy)
-    ax.plot(f_vals, l_vals, label=f'$\psi^*$ at $\sigma_r = {σ_r:0.2}$')
+    ax.plot(f_vals, l_vals, label=fr'$\psi^*$ at $\sigma_r = {σ_r:0.2}$')
     gini_vals.append(gv)
 
 ax.plot(f_vals, f_vals, label='equality')