catlog/simulate/ode/
lotka_volterra.rs

1//! Lotka-Volterra differential equations.
2
3use nalgebra::{DMatrix, DVector};
4
5#[cfg(test)]
6use super::ODEProblem;
7use super::ODESystem;
8
9/** A Lotka-Volterra dynamical system.
10
11A system of ODEs that is affine in its *logarithmic* derivative. These are
12sometimes called the "generalized Lotka-Volterra equations." For more, see
13[Wikipedia](https://en.wikipedia.org/wiki/Generalized_Lotka%E2%80%93Volterra_equation).
14*/
15#[derive(Clone, Debug, PartialEq)]
16pub struct LotkaVolterraSystem {
17    interaction_coeffs: DMatrix<f32>,
18    growth_rates: DVector<f32>,
19}
20
21impl LotkaVolterraSystem {
22    /// Create a new Lokta-Volterra system.
23    pub fn new(A: DMatrix<f32>, b: DVector<f32>) -> Self {
24        Self {
25            interaction_coeffs: A,
26            growth_rates: b,
27        }
28    }
29}
30
31impl ODESystem for LotkaVolterraSystem {
32    fn vector_field(&self, dx: &mut DVector<f32>, x: &DVector<f32>, _t: f32) {
33        let A = &self.interaction_coeffs;
34        let b = &self.growth_rates;
35        *dx = (A * x + b).component_mul(x);
36    }
37}
38
39#[cfg(test)]
40pub(crate) fn create_predator_prey() -> ODEProblem<LotkaVolterraSystem> {
41    let A = DMatrix::from_row_slice(2, 2, &[0.0, -1.0, 1.0, 0.0]);
42    let b = DVector::from_column_slice(&[2.0, -1.0]);
43    let sys = LotkaVolterraSystem::new(A, b);
44
45    let x0 = DVector::from_column_slice(&[1.0, 1.0]);
46    ODEProblem::new(sys, x0).end_time(10.0)
47}
48
49#[cfg(test)]
50mod tests {
51    use expect_test::expect;
52
53    use super::super::textplot_ode_result;
54    use super::*;
55
56    #[test]
57    fn predator_prey() {
58        let problem = create_predator_prey();
59        let result = problem.solve_rk4(0.1).unwrap();
60        let expected = expect![["
61                ⡁⠀⠀⠀⠀⠀⠀⠀⢠⠊⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 3.5
62                ⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
63                ⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
64                ⡁⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
65                ⠄⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
66                ⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
67                ⡁⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
68                ⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
69                ⠂⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
70                ⡁⠀⠀⠀⡎⡜⢣⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢹⠸⡀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
71                ⠄⠀⠀⡸⠀⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡜⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
72                ⠂⠀⢠⠃⢸⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠇⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀
73                ⡁⠀⡎⠀⡎⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡸⠀⡸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠃⠀
74                ⠄⢰⠁⢰⠁⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⠇⢀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⡎⠀⠀
75                ⢂⠇⢀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⡜⠀⡜⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢰⠁⡰⠁
76                ⡝⡠⠊⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢰⣁⠜⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢀⢇⡰⠁⠀
77                ⠍⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀
78                ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀
79                ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀
80                ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀
81                ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 0.4
82                0.0                                           10.0
83            "]];
84        expected.assert_eq(&textplot_ode_result(&problem, &result));
85    }
86}
catlog/simulate/ode/lotka_volterra.rs

catlog/simulate/ode/
lotka_volterra.rs
