numeric_algs/integration/
dormand_prince.rs

1use super::{Integrator, StepSize};
2use crate::traits::{State, StateDerivative};
3use std::mem;
4
5pub struct DPIntegrator<S: State> {
6    default_step: f64,
7    original_default_step: f64,
8    max_err: f64,
9    min_step: f64,
10    max_step: f64,
11    last_derivative: Option<S::Derivative>,
12}
13
14impl<S: State> DPIntegrator<S> {
15    pub fn new(default_step: f64, min_step: f64, max_step: f64, max_err: f64) -> Self {
16        DPIntegrator {
17            default_step: default_step,
18            original_default_step: default_step,
19            min_step: min_step,
20            max_step: max_step,
21            max_err: max_err,
22            last_derivative: None,
23        }
24    }
25
26    pub fn reset_default_step(&mut self) {
27        self.default_step = self.original_default_step;
28    }
29
30    pub fn reset(&mut self) {
31        self.last_derivative = None;
32        self.reset_default_step();
33    }
34}
35
36impl<S: State> Integrator<S> for DPIntegrator<S> {
37    fn propagate_in_place<D>(&mut self, start: &mut S, diff_eq: D, step_size: StepSize)
38    where
39        D: Fn(&S) -> S::Derivative,
40    {
41        let h = match step_size {
42            StepSize::UseDefault => self.default_step,
43            StepSize::Step(x) => x,
44        };
45
46        let k1 = if let Some(last_derivative) = mem::replace(&mut self.last_derivative, None) {
47            last_derivative
48        } else {
49            diff_eq(start)
50        };
51        let k2 = diff_eq(&start.shift(&(k1.clone() / 5.0), h));
52        let k3 = diff_eq(&start.shift(&(k1.clone() * 3.0 / 40.0 + k2.clone() * 9.0 / 40.0), h));
53        let k4 = diff_eq(&start.shift(
54            &(k1.clone() * 44.0 / 45.0 - k2.clone() * 56.0 / 15.0 + k3.clone() * 32.0 / 9.0),
55            h,
56        ));
57        let k5 = diff_eq(&start.shift(
58            &(k1.clone() * 19372.0 / 6561.0 - k2.clone() * 25360.0 / 2187.0
59                + k3.clone() * 64448.0 / 6561.0
60                - k4.clone() * 212.0 / 729.0),
61            h,
62        ));
63        let k6 = diff_eq(&start.shift(
64            &(k1.clone() * 9017.0 / 3168.0 - k2.clone() * 355.0 / 33.0
65                + k3.clone() * 46732.0 / 5247.0
66                + k4.clone() * 49.0 / 176.0
67                - k5.clone() * 5103.0 / 18656.0),
68            h,
69        ));
70
71        let new_state = start.shift(
72            &(k1.clone() * 35.0 / 384.0 + k3.clone() * 500.0 / 1113.0 + k4.clone() * 125.0 / 192.0
73                - k5.clone() * 2187.0 / 6784.0
74                + k6.clone() * 11.0 / 84.0),
75            h,
76        );
77
78        let k7 = diff_eq(&new_state);
79
80        let error = ((k1 * 71.0 / 57600.0 - k3 * 71.0 / 16695.0 + k4 * 71.0 / 1920.0
81            - k5 * 17253.0 / 339200.0
82            + k6 * 22.0 / 525.0
83            - k7.clone() / 40.0)
84            * h)
85            .abs();
86
87        if error != 0.0 {
88            self.default_step = h * (self.max_err / error).powf(0.25);
89        } else {
90            self.default_step = self.max_step;
91        }
92
93        if self.default_step < self.min_step {
94            self.default_step = self.min_step;
95        }
96        if self.default_step > self.max_step {
97            self.default_step = self.max_step;
98        }
99
100        // If the step adjustment makes it much smaller, repeat the calculation to avoid larger
101        // errors
102        if self.default_step < 0.8 * h && step_size == StepSize::UseDefault {
103            self.propagate_in_place(start, diff_eq, step_size);
104            return;
105        }
106
107        *start = new_state;
108
109        //for optimization
110        self.last_derivative = Some(k7);
111    }
112}
numeric_algs/integration/dormand_prince.rs

numeric_algs/integration/
dormand_prince.rs
