Turn non-automated tests into Cargo examples (#24)

Some of the Cargo tests on the main branch are designed to print output for human inspection, not to verify computations automatically. The incoming branch turns these tests into Cargo examples. It also makes two organizational changes in pursuit of this goal:

- It introduces a dyna3 library target, which the examples use as a dependency. In the future, this target could grow into an officially maintained dyna3 library.
- It puts the code for realizing the Irisawa hexlet into a new conditionally compiled `engine::irisawa` module. This code is shared by a test and an example. Compilation is controlled by the `dev` feature, which is turned on by default in development mode.

I've verified that printed output of the examples hasn't changed between the head (848f7d6) and base (e917272) of the incoming branch.

Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: glen/dyna3#24
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>

app-proto/examples/irisawa-hexlet.rs

@@ -0,0 +1,25 @@
+use dyna3::engine::{Q, irisawa::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 {
+        println!("\nChain diameters:");
+        println!("  {} sun (given)", 1.0 / config[(3, 3)]);
+        for k in 4..9 {
+            println!("  {} sun", 1.0 / config[(3, k)]);
+        }
+    }
+    println!("\nStep │ Loss\n─────┼────────────────────────────────");
+    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
+        println!("{:<4} │ {}", step, scaled_loss);
+    }
+}

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

@@ -0,0 +1,38 @@
+use nalgebra::DMatrix;
+
+use dyna3::engine::{Q, point, realize_gram, sphere, PartialMatrix};
+
+fn main() {
+    let gram = {
+        let mut gram_to_be = PartialMatrix::new();
+        for j in 0..2 {
+            for k in j..2 {
+                gram_to_be.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
+            }
+        }
+        gram_to_be
+    };
+    let guess = DMatrix::from_columns(&[
+        point(0.0, 0.0, 2.0),
+        sphere(0.0, 0.0, 0.0, 1.0)
+    ]);
+    let frozen = [(3, 0)];
+    println!();
+    let (config, success, history) = realize_gram(
+        &gram, guess, &frozen,
+        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);
+    }
+}

app-proto/examples/three-spheres.rs

@@ -0,0 +1,40 @@
+use nalgebra::DMatrix;
+
+use dyna3::engine::{Q, realize_gram, sphere, PartialMatrix};
+
+fn main() {
+    let gram = {
+        let mut gram_to_be = PartialMatrix::new();
+        for j in 0..3 {
+            for k in j..3 {
+                gram_to_be.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
+            }
+        }
+        gram_to_be
+    };
+    let guess = {
+        let a: f64 = 0.75_f64.sqrt();
+        DMatrix::from_columns(&[
+            sphere(1.0, 0.0, 0.0, 1.0),
+            sphere(-0.5, a, 0.0, 1.0),
+            sphere(-0.5, -a, 0.0, 1.0)
+        ])
+    };
+    println!();
+    let (config, success, history) = realize_gram(
+        &gram, guess, &[],
+        1.0e-12, 0.5, 0.9, 1.1, 200, 110
+    );
+    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());
+    println!("\nStep │ Loss\n─────┼────────────────────────────────");
+    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
+        println!("{:<4} │ {}", step, scaled_loss);
+    }
+}