[kalman_2] Refactor simulate_workers for PEP8 compliance and code clarity (#481)

Author: suda-yuga

lectures/kalman_2.md

@@ -447,9 +447,9 @@ def simulate_workers(worker, T, ax, mu_0=None, Sigma_0=None,
     A, C, G, R = worker.A, worker.C, worker.G, worker.R
     xhat_0, Σ_0 = worker.xhat_0, worker.Σ_0
     
-    if isinstance(mu_0, type(None)):
+    if mu_0 is None:
         mu_0 = xhat_0
-    if isinstance(Sigma_0, type(None)):
+    if Sigma_0 is None:
         Sigma_0 = worker.Σ_0
         
     ss = LinearStateSpace(A, C, G, np.sqrt(R), 
@@ -471,12 +471,12 @@ 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).item()
+        u_hat_t[i] = x_hat[1].item()
 
-    if diff == True:
+    if diff :
         title = ('Difference between inferred and true work ethic over time' 
-                 if title == None else title)
+                 if title is None else title)
         
         ax.plot(u_hat_t - u_0, alpha=.5)
         ax.axhline(y=0, color='grey', linestyle='dashed')
@@ -485,10 +485,10 @@ def simulate_workers(worker, T, ax, mu_0=None, Sigma_0=None,
         ax.set_title(title)
         
     else:
-        label_line = (r'$E[u_t|y^{t-1}]$' if name == None 
+        label_line = (r'$E[u_t|y^{t-1}]$' if name is None 
                       else name)
         title = ('Inferred work ethic over time' 
-                if title == None else title)
+                if title is None else title)
         
         u_hat_plot = ax.plot(u_hat_t, label=label_line)
         ax.axhline(y=u_0, color=u_hat_plot[0].get_color(),