Added some benchmarking and small performance improvements

src/lib.rs

@@ -18,7 +18,7 @@ pub mod prelude {
 mod tests {
     use crate::prelude::*;
     use approx::assert_relative_eq;
-    use nalgebra::{Vector2, Vector6};
+    use nalgebra::{Vector1, Vector2, Vector6};
     use std::f64::consts::PI;
 
     #[test]
@@ -54,6 +54,32 @@ mod tests {
         let _interpolated_answer = solution.interpolate(4.4);
     }
 
+    #[test]
+    fn test_correctness() {
+        // Define the system (parameters, derivative, and initial state)
+        type Params = ();
+        let params = ();
+
+        fn derivative(_t: f64, y: Vector1<f64>, _p: &Params) -> Vector1<f64> {
+            Vector1::new(5.0 * y[0] - 3.0)
+        }
+
+        let y0 = Vector1::new(1.0);
+
+        // Set up the problem (ODE, Integrator, Controller, and Callbacks)
+        let ode = ODE::new(&derivative, 2.0, 3.0, y0, params);
+        let dp45 = DormandPrince45::new(1e-8_f64, 1e-8_f64);
+        let controller = PIController::default();
+
+        // Solve the problem
+        let mut problem = Problem::new(ode, dp45, controller);
+        let solution = problem.solve();
+        for (time, state) in solution.times.iter().zip(solution.states.iter()) {
+            let exact = 0.4 * (5.0 * (time - 2.0)).exp() + 0.6;
+            assert_relative_eq!(state[0], exact, max_relative = 1e-7);
+        }
+    }
+
     #[test]
     fn test_orbit() {
         // Calculate one period