Merge branch 'main' into two_country

Author: HumphreyYang

.github/workflows/collab.yml

@@ -10,6 +10,12 @@ jobs:
       - uses: actions/checkout@v4
         with:
           ref: ${{ github.event.pull_request.head.sha }}
+      # Install build software
+      - name: Install Build Software & LaTeX (kalman_2)
+        shell: bash -l {0}
+        run: |
+          pip install jupyter-book==1.0.3 quantecon-book-theme==0.8.2 sphinx-tojupyter==0.3.0 sphinxext-rediraffe==0.2.7 sphinxcontrib-youtube==1.3.0 sphinx-togglebutton==0.3.2 arviz sphinx-proof sphinx-exercise sphinx-reredirects
+          apt-get install dvipng texlive texlive-latex-extra texlive-fonts-recommended cm-super    
       - name: Check nvidia drivers
         shell: bash -l {0}
         run: |
@@ -28,11 +34,6 @@ jobs:
           branch: main
           name: build-cache
           path: _build
-      # Install build software
-      - name: Install Build Software
-        shell: bash -l {0}
-        run: |
-          pip install jupyter-book==1.0.3 quantecon-book-theme==0.8.2 sphinx-tojupyter==0.3.0 sphinxext-rediraffe==0.2.7 sphinxcontrib-youtube==1.3.0 sphinx-togglebutton==0.3.2 arviz sphinx-proof sphinx-exercise sphinx-reredirects
       # Build of HTML (Execution Testing)
       - name: Build HTML
         shell: bash -l {0}

lectures/back_prop.md

@@ -4,9 +4,9 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.11.5
+    jupytext_version: 1.16.7
 kernelspec:
-  display_name: Python 3
+  display_name: Python 3 (ipykernel)
   language: python
   name: python3
 ---
@@ -22,6 +22,12 @@ kernelspec:
 !pip install --upgrade jax
 ```
 
+```{code-cell} ipython3
+import jax
+## to check that gpu is activated in environment
+print(f"JAX backend: {jax.devices()[0].platform}")
+```
+
 In addition to what's included in base Anaconda, we need to install the following packages
 
 ```{code-cell} ipython3
@@ -604,15 +610,4 @@ Image(fig.to_image(format="png"))
 # notebook locally
 ```
 
-```{code-cell} ipython3
-## to check that gpu is activated in environment
-
-from jax.lib import xla_bridge
-print(xla_bridge.get_backend().platform)
-```
 
-```{note}
-**Cloud Environment:** This lecture site is built in a server environment that doesn't have access to a `gpu`
-If you run this lecture locally this lets you know where your code is being executed, either
-via the `cpu` or the `gpu`
-```

lectures/kalman.md

@@ -3,8 +3,10 @@ jupytext:
   text_representation:
     extension: .md
     format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.16.7
 kernelspec:
-  display_name: Python 3
+  display_name: Python 3 (ipykernel)
   language: python
   name: python3
 ---
@@ -29,10 +31,9 @@ kernelspec:
 
 In addition to what's in Anaconda, this lecture will need the following libraries:
 
-```{code-cell} ipython
----
-tags: [hide-output]
----
+```{code-cell} ipython3
+:tags: [hide-output]
+
 !pip install quantecon
 ```
 
@@ -54,9 +55,8 @@ Required knowledge: Familiarity with matrix manipulations, multivariate normal d
 
 We'll need the following imports:
 
-```{code-cell} ipython
+```{code-cell} ipython3
 import matplotlib.pyplot as plt
-plt.rcParams["figure.figsize"] = (11, 5)  #set default figure size
 from scipy import linalg
 import numpy as np
 import matplotlib.cm as cm
@@ -122,10 +122,9 @@ $2 \times 2$ covariance matrix.  In our simulations, we will suppose that
 
 This density $p(x)$ is shown below as a contour map, with the center of the red ellipse being equal to $\hat x$.
 
-```{code-cell} python3
----
-tags: [output_scroll]
----
+```{code-cell} ipython3
+:tags: [output_scroll]
+
 # Set up the Gaussian prior density p
 Σ = [[0.4, 0.3], [0.3, 0.45]]
 Σ = np.matrix(Σ)
@@ -186,7 +185,7 @@ def bivariate_normal(x, y, σ_x=1.0, σ_y=1.0, μ_x=0.0, μ_y=0.0, σ_xy=0.0):
 
 def gen_gaussian_plot_vals(μ, C):
     "Z values for plotting the bivariate Gaussian N(μ, C)"
-    m_x, m_y = float(μ[0]), float(μ[1])
+    m_x, m_y = float(μ[0,0]), float(μ[1,0])
     s_x, s_y = np.sqrt(C[0, 0]), np.sqrt(C[1, 1])
     s_xy = C[0, 1]
     return bivariate_normal(X, Y, s_x, s_y, m_x, m_y, s_xy)
@@ -213,15 +212,15 @@ The good news is that the missile has been located by our sensors, which report
 The next figure shows the original prior $p(x)$ and the new reported
 location $y$
 
-```{code-cell} python3
+```{code-cell} ipython3
 fig, ax = plt.subplots(figsize=(10, 8))
 ax.grid()
 
 Z = gen_gaussian_plot_vals(x_hat, Σ)
 ax.contourf(X, Y, Z, 6, alpha=0.6, cmap=cm.jet)
 cs = ax.contour(X, Y, Z, 6, colors="black")
 ax.clabel(cs, inline=1, fontsize=10)
-ax.text(float(y[0]), float(y[1]), "$y$", fontsize=20, color="black")
+ax.text(float(y[0].item()), float(y[1].item()), "$y$", fontsize=20, color="black")
 
 plt.show()
 ```
@@ -284,7 +283,7 @@ This new density $p(x \,|\, y) = N(\hat x^F, \Sigma^F)$ is shown in the next fig
 
 The original density is left in as contour lines for comparison
 
-```{code-cell} python3
+```{code-cell} ipython3
 fig, ax = plt.subplots(figsize=(10, 8))
 ax.grid()
 
@@ -298,7 +297,7 @@ new_Z = gen_gaussian_plot_vals(x_hat_F, Σ_F)
 cs2 = ax.contour(X, Y, new_Z, 6, colors="black")
 ax.clabel(cs2, inline=1, fontsize=10)
 ax.contourf(X, Y, new_Z, 6, alpha=0.6, cmap=cm.jet)
-ax.text(float(y[0]), float(y[1]), "$y$", fontsize=20, color="black")
+ax.text(float(y[0].item()), float(y[1].item()), "$y$", fontsize=20, color="black")
 
 plt.show()
 ```
@@ -391,7 +390,7 @@ A
 Q = 0.3 * \Sigma
 $$
 
-```{code-cell} python3
+```{code-cell} ipython3
 fig, ax = plt.subplots(figsize=(10, 8))
 ax.grid()
 
@@ -415,7 +414,7 @@ new_Z = gen_gaussian_plot_vals(new_x_hat, new_Σ)
 cs3 = ax.contour(X, Y, new_Z, 6, colors="black")
 ax.clabel(cs3, inline=1, fontsize=10)
 ax.contourf(X, Y, new_Z, 6, alpha=0.6, cmap=cm.jet)
-ax.text(float(y[0]), float(y[1]), "$y$", fontsize=20, color="black")
+ax.text(float(y[0].item()), float(y[1].item()), "$y$", fontsize=20, color="black")
 
 plt.show()
 ```
@@ -577,7 +576,7 @@ Your figure should -- modulo randomness -- look something like this
 :class: dropdown
 ```
 
-```{code-cell} python3
+```{code-cell} ipython3
 # Parameters
 θ = 10  # Constant value of state x_t
 A, C, G, H = 1, 0, 1, 1
@@ -598,7 +597,7 @@ xgrid = np.linspace(θ - 5, θ + 2, 200)
 
 for i in range(N):
     # Record the current predicted mean and variance
-    m, v = [float(z) for z in (kalman.x_hat, kalman.Sigma)]
+    m, v = [float(z) for z in (kalman.x_hat.item(), kalman.Sigma.item())]
     # Plot, update filter
     ax.plot(xgrid, norm.pdf(xgrid, loc=m, scale=np.sqrt(v)), label=f'$t={i}$')
     kalman.update(y[i])
@@ -641,7 +640,7 @@ Your figure should show error erratically declining something like this
 :class: dropdown
 ```
 
-```{code-cell} python3
+```{code-cell} ipython3
 ϵ = 0.1
 θ = 10  # Constant value of state x_t
 A, C, G, H = 1, 0, 1, 1
@@ -657,7 +656,7 @@ y = y.flatten()
 
 for t in range(T):
     # Record the current predicted mean and variance and plot their densities
-    m, v = [float(temp) for temp in (kalman.x_hat, kalman.Sigma)]
+    m, v = [float(temp) for temp in (kalman.x_hat.item(), kalman.Sigma.item())]
 
     f = lambda x: norm.pdf(x, loc=m, scale=np.sqrt(v))
     integral, error = quad(f, θ - ϵ, θ + ϵ)
@@ -745,7 +744,7 @@ Observe how, after an initial learning period, the Kalman filter performs quite
 :class: dropdown
 ```
 
-```{code-cell} python3
+```{code-cell} ipython3
 # Define A, C, G, H
 G = np.identity(2)
 H = np.sqrt(0.5) * np.identity(2)

lectures/kalman_2.md

@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.14.4
+    jupytext_version: 1.16.7
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
@@ -237,7 +237,7 @@ for t in range(1, T):
     x_hat, Σ = kalman.x_hat, kalman.Sigma
     Σ_t[:, :, t-1] = Σ
     x_hat_t[:, t-1] = x_hat.reshape(-1)
-    y_hat_t[t-1] = worker.G @ x_hat
+    [y_hat_t[t-1]] = worker.G @ x_hat
 
 x_hat_t = np.concatenate((x[:, 1][:, np.newaxis], 
                     x_hat_t), axis=1)
@@ -253,7 +253,6 @@ We also plot $E [u_0 | y^{t-1}]$, which is  the firm inference about  a worker's
 We can  watch as the  firm's inference  $E [u_0 | y^{t-1}]$ of the worker's work ethic converges toward the hidden   $u_0$, which is not directly observed by the firm.
 
 ```{code-cell} ipython3
-
 fig, ax = plt.subplots(1, 2)
 
 ax[0].plot(y_hat_t, label=r'$E[y_t| y^{t-1}]$')
@@ -273,6 +272,7 @@ ax[1].legend()
 fig.tight_layout()
 plt.show()
 ```
+
 ## Some Computational Experiments
 
 Let's look at  $\Sigma_0$ and $\Sigma_T$ in order to see how much the firm learns about the hidden state during the horizon we have set.
@@ -290,7 +290,6 @@ Evidently,  entries in the conditional covariance matrix become smaller over tim
 It is enlightening to  portray how  conditional covariance matrices $\Sigma_t$ evolve by plotting confidence ellipsoides around $E [x_t |y^{t-1}] $ at various $t$'s.
 
 ```{code-cell} ipython3
-
 # Create a grid of points for contour plotting
 h_range = np.linspace(x_hat_t[0, :].min()-0.5*Σ_t[0, 0, 1], 
                       x_hat_t[0, :].max()+0.5*Σ_t[0, 0, 1], 100)
@@ -338,7 +337,6 @@ For example, let's say $h_0 = 0$ and $u_0 = 4$.
 Here is one way to do this.
 
 ```{code-cell} ipython3
-
 # For example, we might want h_0 = 0 and u_0 = 4
 mu_0 = np.array([0.0, 4.0])
 
@@ -361,7 +359,6 @@ print('u_0 =', u_0)
 Another way to accomplish the same goal is to use the following code.
 
 ```{code-cell} ipython3
-
 # If we want to set the initial 
 # h_0 = hhat_0 = 0 and u_0 = uhhat_0 = 4.0:
 worker = create_worker(hhat_0=0.0, uhat_0=4.0)
@@ -398,8 +395,8 @@ for t in range(1, T):
     kalman.update(y[t])
     x_hat, Σ = kalman.x_hat, kalman.Sigma
     Σ_t.append(Σ)
-    y_hat_t[t-1] = worker.G @ x_hat
-    u_hat_t[t-1] = x_hat[1]
+    [y_hat_t[t-1]] = worker.G @ x_hat
+    [u_hat_t[t-1]] = x_hat[1]
 
 
 # Generate plots for y_hat_t and u_hat_t
@@ -426,10 +423,9 @@ plt.show()
 More generally, we can change some or all of the parameters defining a worker in our `create_worker`
 namedtuple.
 
-Here is an example. 
+Here is an example.
 
 ```{code-cell} ipython3
-
 # We can set these parameters when creating a worker -- just like classes!
 hard_working_worker =  create_worker(α=.4, β=.8, 
                         hhat_0=7.0, uhat_0=100, σ_h=2.5, σ_u=3.2)
@@ -475,8 +471,8 @@ def simulate_workers(worker, T, ax, mu_0=None, Sigma_0=None,
         kalman.update(y[i])
         x_hat, Σ = kalman.x_hat, kalman.Sigma
         Σ_t.append(Σ)
-        y_hat_t[i] = worker.G @ x_hat
-        u_hat_t[i] = x_hat[1]
+        [y_hat_t[i]] = worker.G @ x_hat
+        [u_hat_t[i]] = x_hat[1]
 
     if diff == True:
         title = ('Difference between inferred and true work ethic over time' 
@@ -503,7 +499,6 @@ def simulate_workers(worker, T, ax, mu_0=None, Sigma_0=None,
 ```
 
 ```{code-cell} ipython3
-
 num_workers = 3
 T = 50
 fig, ax = plt.subplots(figsize=(7, 7))
@@ -516,7 +511,6 @@ plt.show()
 ```
 
 ```{code-cell} ipython3
-
 # We can also generate plots of u_t:
 
 T = 50
@@ -539,7 +533,6 @@ plt.show()
 ```
 
 ```{code-cell} ipython3
-
 # We can also use exact u_0=1 and h_0=2 for all workers
 
 T = 50
@@ -568,7 +561,6 @@ plt.show()
 ```
 
 ```{code-cell} ipython3
-
 # We can generate a plot for only one of the workers:
 
 T = 50