feat: Engine diagnostics (#92)

Adds a `Diagnostics` component that shows the following diagnostics from the last realization:

- Confirmation of success or a short description of what failed.
- The value of the loss function at each step.
- The spectrum of the Hessian at each step.

The loss and spectrum plots are shown on switchable panels.

Also includes some refactoring/renaming of existing code.

Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Reviewed-on: #92
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>

app-proto/examples/irisawa-hexlet.rs

@@ -1,25 +1,23 @@
-use dyna3::engine::{Q, examples::realize_irisawa_hexlet};
+#[path = "common/print.rs"]
+mod print;
+
+use dyna3::engine::{ConfigNeighborhood, examples::realize_irisawa_hexlet};
 
 fn main() {
     const SCALED_TOL: f64 = 1.0e-12;
-    let (config, _, success, history) = realize_irisawa_hexlet(SCALED_TOL);
-    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    if success {
-        println!("Target accuracy achieved!");
-    } else {
-        println!("Failed to reach target accuracy");
-    }
-    println!("Steps: {}", history.scaled_loss.len() - 1);
-    println!("Loss: {}", history.scaled_loss.last().unwrap());
-    if success {
+    let realization = realize_irisawa_hexlet(SCALED_TOL);
+    print::title("Irisawa hexlet");
+    print::realization_diagnostics(&realization);
+    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+        // print the diameters of the chain spheres
         println!("\nChain diameters:");
         println!("  {} sun (given)", 1.0 / config[(3, 3)]);
         for k in 4..9 {
             println!("  {} sun", 1.0 / config[(3, k)]);
         }
+        
+        // print the completed Gram matrix
+        print::gram_matrix(&config);
     }
-    println!("\nStep │ Loss\n─────┼────────────────────────────────");
-    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
-        println!("{:<4} │ {}", step, scaled_loss);
-    }
+    print::loss_history(&realization.history);
 }