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: StudioInfinity/dyna3#92
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>

app-proto/examples/point-on-sphere.rs

@@ -1,4 +1,13 @@
-use dyna3::engine::{Q, point, realize_gram, sphere, ConstraintProblem};
+#[path = "common/print.rs"]
+mod print;
+
+use dyna3::engine::{
+    point,
+    realize_gram,
+    sphere,
+    ConfigNeighborhood,
+    ConstraintProblem
+};
 
 fn main() {
     let mut problem = ConstraintProblem::from_guess(&[
@@ -11,21 +20,14 @@ fn main() {
         }
     }
     problem.frozen.push(3, 0, problem.guess[(3, 0)]);
-    println!();
-    let (config, _, success, history) = realize_gram(
+    let realization = realize_gram(
         &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
     );
-    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    print!("Configuration:{}", 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());
-    println!("\nStep │ Loss\n─────┼────────────────────────────────");
-    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
-        println!("{:<4} │ {}", step, scaled_loss);
+    print::title("Point on a sphere");
+    print::realization_diagnostics(&realization);
+    if let Ok(ConfigNeighborhood{ config, .. }) = realization.result {
+        print::gram_matrix(&config);
+        print::config(&config);
     }
+    print::loss_history(&realization.history);
 }