Minor Fixes to Calvo Machine Learning Lecture

lectures/calvo_machine_learn.md

@@ -414,7 +414,7 @@ First, because we'll want to compare the results we obtain here with those obtai
 We hide the cell that copies the class, but readers can find details of the class in this quantecon lecture {doc}`calvo`.
 
 ```{code-cell} ipython3
-:tags: [hide-output]
+:tags: [hide-input]
 
 class ChangLQ:
     """
@@ -558,14 +558,20 @@ def compute_θ(μ, α=1):
     θ = jnp.append(θ, μbar)
 
     return θ
+
+@jit
+def compute_hs(u0, u1, u2, α):
+    h0 = u0
+    h1 = -u1 * α
+    h2 = -0.5 * u2 * α**2
+
+    return h0, h1, h2
 
 @jit
 def compute_V(μ, β, c, α=1, u0=1, u1=0.5, u2=3):
     θ = compute_θ(μ, α)
 
-    h0 = u0
-    h1 = -u1 * α
-    h2 = -0.5 * u2 * α**2
+    h0, h1, h2 = compute_hs(u0, u1, u2, α)
 
     T = len(μ) - 1
     t = np.arange(T)
@@ -890,9 +896,7 @@ With the more structured approach, we can update our gradient descent exercise w
 def compute_J(μ, β, c, α=1, u0=1, u1=0.5, u2=3):
     T = len(μ) - 1
 
-    h0 = u0
-    h1 = -u1 * α
-    h2 = -0.5 * u2 * α**2
+    h0, h1, h2 = compute_hs(u0, u1, u2, α)
     λ = α / (1 + α)
 
     _, B = construct_B(α, T+1)
@@ -944,9 +948,7 @@ We can also derive a closed-form solution for $\vec \mu$
 
 ```{code-cell} ipython3
 def compute_μ(β, c, T, α=1, u0=1, u1=0.5, u2=3):    
-    h0 = u0
-    h1 = -u1 * α
-    h2 = -0.5 * u2 * α**2
+    h0, h1, h2 = compute_hs(u0, u1, u2, α)
 
     _, B = construct_B(α, T+1)
 
@@ -981,9 +983,7 @@ We can check the gradient of the analytical solution against the `JAX` computed
 def compute_grad(μ, β, c, α=1, u0=1, u1=0.5, u2=3):    
     T = len(μ) - 1
 
-    h0 = u0
-    h1 = -u1 * α
-    h2 = -0.5 * u2 * α**2
+    h0, h1, h2 = compute_hs(u0, u1, u2, α)
 
     _, B = construct_B(α, T+1)