Update tensor_prod.md

docs/src/tensor_prod.md

@@ -48,34 +48,35 @@ Now let's train various surrogate models and evaluate their performance on the t
 
 ```
 # Train different surrogate models
-function train_surrogates(x_train, y_train)
-    loba = LobachevskySurrogate(x_train, y_train)
-    krig = Kriging(x_train, y_train)
+function train_surrogates(x_train, y_train, lb, ub, alpha=2.0, n=6)
+    loba = LobachevskySurrogate(x_train, y_train, lb, ub, alpha=alpha, n=n)
+    krig = Kriging(x_train, y_train, lb, ub)
     return loba, krig
 end
 
 # Evaluate and compare surrogate model performances
 function evaluate_surrogates(loba, krig, x_test)
-    loba_pred = loba(x_test)
-    krig_pred = krig(x_test)
+    loba_pred = loba.(x_test)
+    krig_pred = krig.(x_test)
     return loba_pred, krig_pred
 end
 
 # Plot surrogate predictions against the true function
-function plot_surrogate_predictions(loba_pred, krig_pred, y_test, a, lb, ub)
-    xs = range(lb, ub, length=1000)
-    
-    plot(xs, tensor_product_function.(Ref(xs), a), label="True function", legend=:top)
-    plot!(xs, loba_pred, label="Lobachevsky")
-    plot!(xs, krig_pred, label="Kriging")
+function plot_surrogate_predictions(loba_pred, krig_pred, x_test, y_test, a, lb, ub)
+    xs = collect(x_test)  # Convert x_test to an array
+    plot(xs, tensor_product_function.(xs, a), label="True Function", legend=:top)
+    plot!(collect(x_test), loba_pred, seriestype=:scatter, label="Lobachevsky")
+    plot!(collect(x_test), krig_pred, seriestype=:scatter, label="Kriging")
+    plot!(collect(x_test), fill(y_test, length(x_test)), seriestype=:scatter, label="Sampled points")  # Use fill to create an array of the same length as x_test
 end
 
 # Train surrogates and evaluate their performance
-loba, krig = train_surrogates(x_train, y_train)
+lb, ub = minimum(x_train), maximum(x_train)
+loba, krig = train_surrogates(x_train, y_train, lb, ub)
 loba_pred, krig_pred = evaluate_surrogates(loba, krig, x_test)
 
-# Plot surrogate predictions against the true function
-plot_surrogate_predictions(loba_pred, krig_pred, y_test, a, lb, ub)
+# Plotting Results
+plot_surrogate_predictions(loba_pred, krig_pred, x_test, y_test, 2.0, lb, ub)
 ```
 
 # Reporting the best Surrogate Model