1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71


use std::marker::PhantomData;
use ndarray::prelude::*;
use super::traits::{EOM, TimeEvolution};

pub mod markers {
    pub struct EulerMarker {}
    pub struct HeunMarker {}
    pub struct RK4Marker {}
}

pub struct Explicit<F: EOM<D>, D: Dimension, Marker> {
    f: F,
    dt: f64,
    phantom_dim: PhantomData<D>,
    phantom_marker: PhantomData<Marker>,
}

impl<F: EOM<D>, D: Dimension, Marker> Explicit<F, D, Marker> {
    pub fn new(f: F, dt: f64) -> Self {
        Explicit {
            f: f,
            dt: dt,
            phantom_dim: PhantomData,
            phantom_marker: PhantomData,
        }
    }
}

impl<F: EOM<D>, D: Dimension> TimeEvolution<D> for Explicit<F, D, markers::EulerMarker> {
    #[inline(always)]
    fn iterate(&self, x: RcArray<f64, D>) -> RcArray<f64, D> {
        let fx = self.f.rhs(x.clone());
        x + fx * self.dt
    }
}

impl<F: EOM<D>, D: Dimension> TimeEvolution<D> for Explicit<F, D, markers::HeunMarker> {
    #[inline(always)]
    fn iterate(&self, x: RcArray<f64, D>) -> RcArray<f64, D> {
        let k1 = self.dt * self.f.rhs(x.clone());
        let k2 = self.dt * self.f.rhs(x.clone() + k1.clone());
        x + 0.5 * (k1 + k2)
    }
}

impl<F: EOM<D>, D: Dimension> TimeEvolution<D> for Explicit<F, D, markers::RK4Marker> {
    #[inline(always)]
    fn iterate(&self, x: RcArray<f64, D>) -> RcArray<f64, D> {
        let k1 = self.f.rhs(x.clone());
        let l1 = (0.5 * self.dt) * k1.clone() + &x;
        let k2 = self.f.rhs(l1);
        let l2 = (0.5 * self.dt) * k2.clone() + &x;
        let k3 = self.f.rhs(l2);
        let l3 = self.dt * k3.clone() + &x;
        let k4 = self.f.rhs(l3);
        x + (self.dt / 6.0) * (k1 + 2.0 * (k2 + k3) + k4)
    }
}

pub fn euler<F: EOM<D>, D: Dimension>(f: F, dt: f64) -> Explicit<F, D, markers::EulerMarker> {
    Explicit::new(f, dt)
}

pub fn heun<F: EOM<D>, D: Dimension>(f: F, dt: f64) -> Explicit<F, D, markers::HeunMarker> {
    Explicit::new(f, dt)
}

pub fn rk4<F: EOM<D>, D: Dimension>(f: F, dt: f64) -> Explicit<F, D, markers::RK4Marker> {
    Explicit::new(f, dt)
}