Fix Python warnings in lecture HTML output: handle empty arrays and suppress JAX fork warnings

lectures/back_prop.md

@@ -32,9 +32,11 @@ In addition to what's included in base Anaconda, we need to install the followin
 
 ```{code-cell} ipython3
 :tags: [hide-output]
-
-!pip install kaleido
-!conda install -y -c plotly plotly plotly-orca retrying
+import warnings
+with warnings.catch_warnings():
+    warnings.filterwarnings("ignore", message=".*os.fork.*")
+    !pip install kaleido
+    !conda install -y -c plotly plotly plotly-orca retrying
 ```
 
 ```{note}

lectures/status.md

@@ -23,14 +23,20 @@ These lectures are built on `linux` instances through `github actions`.
 These lectures are using the following python version
 
 ```{code-cell} ipython
-!python --version
+import warnings
+with warnings.catch_warnings():
+    warnings.filterwarnings("ignore", message=".*os.fork.*")
+    !python --version
 ```
 
 and the following package versions
 
 ```{code-cell} ipython
 :tags: [hide-output]
-!conda list
+import warnings
+with warnings.catch_warnings():
+    warnings.filterwarnings("ignore", message=".*os.fork.*")
+    !conda list
 ```
 
 You can check the backend used by JAX using:
@@ -44,5 +50,8 @@ print(f"JAX backend: {jax.devices()[0].platform}")
 and this lecture series also has access to the following GPU
 
 ```{code-cell} ipython
-!nvidia-smi
+import warnings
+with warnings.catch_warnings():
+    warnings.filterwarnings("ignore", message=".*os.fork.*")
+    !nvidia-smi
 ```

lectures/two_auctions.md

@@ -403,6 +403,11 @@ def evaluate_largest(v_hat, array, order=1):
     array_conditional=array_residual[:,index].copy()
 
     array_conditional=np.sort(array_conditional, axis=0)
+
+    # Handle empty array case to avoid "Mean of empty slice" warning
+    if array_conditional.shape[1] == 0:
+        return np.nan
+
     return array_conditional[-order,:].mean()
 ```
 
@@ -561,6 +566,10 @@ class bid_price_solution:
 
         array_conditional=np.sort(array_conditional, axis=0)
 
+        # Handle empty array case to avoid "Mean of empty slice" warning
+        if array_conditional.shape[1] == 0:
+            return np.nan
+
         return array_conditional[-order,:].mean()
 
     def compute_optimal_bid_FPSB(self):