Merge branch 'main' into ci-warnings-action

Author: mmcky

.github/workflows/cache.yml

@@ -8,7 +8,7 @@ jobs:
   cache:
     runs-on: "runs-on=${{ github.run_id }}/family=g4dn.2xlarge/image=quantecon_ubuntu2404/disk=large"
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v5
         with:
           ref: ${{ github.event.pull_request.head.sha }}
       - name: Setup Anaconda

.github/workflows/ci.yml

@@ -9,7 +9,7 @@ jobs:
       issues: write
       pull-requests: write
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v5
         with:
           ref: ${{ github.event.pull_request.head.sha }}
       - name: Setup Anaconda

.github/workflows/collab.yml

@@ -7,7 +7,7 @@ jobs:
       image: docker://us-docker.pkg.dev/colab-images/public/runtime:latest
       options: --gpus all
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v5
         with:
           ref: ${{ github.event.pull_request.head.sha }}
       # Install build software

.github/workflows/linkcheck.yml

@@ -13,7 +13,7 @@ jobs:
     steps:
       # Checkout the live site (html)
       - name: Checkout
-        uses: actions/checkout@v4
+        uses: actions/checkout@v5
         with:
           ref: gh-pages
       - name: Link Checker

.github/workflows/publish.yml

@@ -9,7 +9,7 @@ jobs:
     runs-on: "runs-on=${{ github.run_id }}/family=g4dn.2xlarge/image=quantecon_ubuntu2404/disk=large"
     steps:
       - name: Checkout
-        uses: actions/checkout@v4
+        uses: actions/checkout@v5
       - name: Setup Anaconda
         uses: conda-incubator/setup-miniconda@v3
         with:

lectures/career.md

@@ -206,8 +206,8 @@ class CareerWorkerProblem:
 
         self.F_probs = BetaBinomial(grid_size - 1, F_a, F_b).pdf()
         self.G_probs = BetaBinomial(grid_size - 1, G_a, G_b).pdf()
-        self.F_mean = np.sum(self.θ * self.F_probs)
-        self.G_mean = np.sum(self.ϵ * self.G_probs)
+        self.F_mean = self.θ @ self.F_probs
+        self.G_mean = self.ϵ @ self.G_probs
 
         # Store these parameters for str and repr methods
         self._F_a, self._F_b = F_a, F_b

lectures/kalman.md

@@ -783,8 +783,10 @@ e2 = np.empty(T-1)
 
 for t in range(1, T):
     kn.update(y[:,t])
-    e1[t-1] = np.sum((x[:, t] - kn.x_hat.flatten())**2)
-    e2[t-1] = np.sum((x[:, t] - A @ x[:, t-1])**2)
+    diff1 = x[:, t] - kn.x_hat.flatten()
+    diff2 = x[:, t] - A @ x[:, t-1]
+    e1[t-1] = diff1 @ diff1
+    e2[t-1] = diff2 @ diff2
 
 fig, ax = plt.subplots(figsize=(9,6))
 ax.plot(range(1, T), e1, 'k-', lw=2, alpha=0.6,

lectures/lagrangian_lqdp.md

@@ -206,29 +206,29 @@ It is useful to proceed with the following steps:
 * arrange the resulting equation and the second equation of {eq}`lag-lqdp-eq2`  into the form
 
 $$
-L\ \begin{pmatrix}x_{t+1}\cr \mu_{t+1}\cr\end{pmatrix}\ = \ N\ \begin{pmatrix}x_t\cr \mu_t\cr\end{pmatrix}\
+L\ \begin{bmatrix}x_{t+1}\cr \mu_{t+1}\cr\end{bmatrix}\ = \ N\ \begin{bmatrix}x_t\cr \mu_t\cr\end{bmatrix}\
 ,\ t \geq 0,
 $$ (eq:systosolve)
 
 where
 
 $$
-L = \ \begin{pmatrix}I & BQ^{-1} B^\prime \cr 0 & A^\prime\cr\end{pmatrix}, \quad N = \
-\begin{pmatrix}A & 0\cr -R & I\cr\end{pmatrix}.
+L = \ \begin{bmatrix}I & BQ^{-1} B^\prime \cr 0 & A^\prime\cr\end{bmatrix}, \quad N = \
+\begin{bmatrix}A & 0\cr -R & I\cr\end{bmatrix}.
 $$
 
 When $L$ is of full rank (i.e., when $A$ is of full rank), we can write
 system {eq}`eq:systosolve` as
 
 $$
-\begin{pmatrix}x_{t+1}\cr \mu_{t+1}\cr\end{pmatrix}\ = M\ \begin{pmatrix}x_t\cr\mu_t\cr\end{pmatrix}
+\begin{bmatrix}x_{t+1}\cr \mu_{t+1}\cr\end{bmatrix}\ = M\ \begin{bmatrix}x_t\cr\mu_t\cr\end{bmatrix}
 $$ (eq4orig)
 
 where
 
 $$
-M\equiv L^{-1} N = \begin{pmatrix}A+B Q^{-1} B^\prime A^{\prime-1}R &
--B Q^{-1} B^\prime A^{\prime-1}\cr -A^{\prime -1} R & A^{\prime -1}\cr\end{pmatrix}.
+M\equiv L^{-1} N = \begin{bmatrix}A+B Q^{-1} B^\prime A^{\prime-1}R &
+-B Q^{-1} B^\prime A^{\prime-1}\cr -A^{\prime -1} R & A^{\prime -1}\cr\end{bmatrix}.
 $$ (Mdefn)
 
 +++
@@ -262,7 +262,7 @@ To proceed, we study properties of the $(2n \times 2n)$ matrix $M$ defined in {e
 It helps to introduce a $(2n \times 2n)$ matrix
 
 $$
-J = \begin{pmatrix}0 & -I_n\cr I_n & 0\cr\end{pmatrix}.
+J = \begin{bmatrix}0 & -I_n\cr I_n & 0\cr\end{bmatrix}.
 $$
 
 The rank of $J$ is $2n$.
@@ -308,12 +308,12 @@ $$
 y_{t+1} = M y_t
 $$ (eq658)
 
-where $y_t = \begin{pmatrix}x_t\cr \mu_t\cr\end{pmatrix}$. 
+where $y_t = \begin{bmatrix}x_t\cr \mu_t\cr\end{bmatrix}$. 
 
 Consider a **triangularization** of $M$
 
 $$
-V^{-1} M V= \begin{pmatrix}W_{11} & W_{12} \cr 0 & W_{22}\cr\end{pmatrix}
+V^{-1} M V= \begin{bmatrix}W_{11} & W_{12} \cr 0 & W_{22}\cr\end{bmatrix}
 $$ (eqn:triangledecomp)
 
 where 
@@ -353,9 +353,9 @@ and where $W^t_{ii}$ is $W_{ii}$ raised to the $t$th  power.
 Write equation {eq}`eq6510` as
 
 $$
-\begin{pmatrix}y^\ast_{1t}\cr y^\ast_{2t}\cr\end{pmatrix}\ =\ \left[\begin{matrix} W^t_{11} &
-W_{12, t}\cr 0 & W^t_{22}\cr\end{matrix}\right]\quad \begin{pmatrix}y^\ast_{10}\cr
-y^\ast_{20}\cr\end{pmatrix}
+\begin{bmatrix}y^\ast_{1t}\cr y^\ast_{2t}\cr\end{bmatrix}\ =\ \left[\begin{matrix} W^t_{11} &
+W_{12, t}\cr 0 & W^t_{22}\cr\end{matrix}\right]\quad \begin{bmatrix}y^\ast_{10}\cr
+y^\ast_{20}\cr\end{bmatrix}
 $$
 
 where $y^\ast_t = V^{-1} y_t$, and in particular where
@@ -394,7 +394,7 @@ But notice that because $(V^{21}\ V^{22})$ is the second row block of
 the inverse of $V,$ it follows that
 
 $$
-(V^{21} \ V^{22})\quad \begin{pmatrix}V_{11}\cr V_{21}\cr\end{pmatrix} = 0
+(V^{21} \ V^{22})\quad \begin{bmatrix}V_{11}\cr V_{21}\cr\end{bmatrix} = 0
 $$
 
 which implies

lectures/lake_model.md

@@ -155,10 +155,10 @@ $$
 X_{t+1} = A X_t
 \quad \text{where} \quad
 A :=
-\begin{pmatrix}
+\begin{bmatrix}
     (1-d)(1-\lambda) + b & (1-d)\alpha + b  \\
     (1-d)\lambda & (1-d)(1-\alpha)
-\end{pmatrix}
+\end{bmatrix}
 $$
 
 This law tells us how total employment and unemployment evolve over time.
@@ -170,16 +170,16 @@ Now let's derive the law of motion for rates.
 To get these we can divide both sides of $X_{t+1} = A X_t$ by  $N_{t+1}$ to get
 
 $$
-\begin{pmatrix}
+\begin{bmatrix}
     U_{t+1}/N_{t+1} \\
     E_{t+1}/N_{t+1}
-\end{pmatrix} =
+\end{bmatrix} =
 \frac1{1+g} A
-\begin{pmatrix}
+\begin{bmatrix}
     U_{t}/N_{t}
     \\
     E_{t}/N_{t}
-\end{pmatrix}
+\end{bmatrix}
 $$
 
 Letting
@@ -699,7 +699,7 @@ def _update_bellman(α, β, γ, c, σ, w_vec, p_vec, V, V_new, U):
         V_new[w_idx] = u(w, σ) + β * ((1 - α) * V[w_idx] + α * U)
 
     U_new = u(c, σ) + β * (1 - γ) * U + \
-                    β * γ * np.sum(np.maximum(U, V) * p_vec)
+                    β * γ * (np.maximum(U, V) @ p_vec)
 
     return U_new
 
@@ -836,8 +836,8 @@ def compute_steady_state_quantities(c, τ):
     u, e = x
 
     # Compute steady state welfare
-    w = np.sum(V * p_vec * (w_vec - τ > w_bar)) / np.sum(p_vec * (w_vec -
-            τ > w_bar))
+    mask = (w_vec - τ > w_bar)
+    w = ((V * p_vec * mask) @ np.ones_like(p_vec)) / ((p_vec * mask) @ np.ones_like(p_vec))
     welfare = e * w + u * U
 
     return e, u, welfare

lectures/linear_algebra.md

@@ -246,15 +246,25 @@ Continuing on from the previous example, the inner product and norm can be compu
 follows
 
 ```{code-cell} python3
-np.sum(x * y)          # Inner product of x and y
+np.sum(x * y)          # Inner product of x and y, method 1
 ```
 
+```{code-cell} python3
+x @ y                  # Inner product of x and y, method 2 (preferred)
+```
+
+The `@` operator is preferred because it uses optimized BLAS libraries that implement fused multiply-add operations, providing better performance and numerical accuracy compared to the separate multiply and sum operations.
+
 ```{code-cell} python3
 np.sqrt(np.sum(x**2))  # Norm of x, take one
 ```
 
 ```{code-cell} python3
-np.linalg.norm(x)      # Norm of x, take two
+np.sqrt(x @ x)         # Norm of x, take two (preferred)
+```
+
+```{code-cell} python3
+np.linalg.norm(x)      # Norm of x, take three
 ```
 
 ### Span