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
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138

use ndarray::{Dimension, IntoNdProducer, Zip};
use std::fmt::Debug;

use crate::ode::Ode;

use super::{Stepper, ZipMarker};

#[derive(Debug)]
pub struct RungeKutta4<T: Debug> {
    pub(crate) dt: f64,
    pub(crate) dt_2: f64,
    pub(crate) dt_3: f64,
    pub(crate) dt_6: f64,

    pub(crate) temp: T,

    pub(crate) k1: T,
    pub(crate) k2: T,
    pub(crate) k3: T,
    pub(crate) k4: T,
}

impl<T> RungeKutta4<T>
where
    T: Clone + Debug,
{
    pub fn new(state: &T, dt: f64) -> Self {
        let dt_2 = dt / 2.0;
        let dt_3 = dt / 3.0;
        let dt_6 = dt / 6.0;

        let temp = state.clone();
        let k1 = state.clone();
        let k2 = state.clone();
        let k3 = state.clone();
        let k4 = state.clone();

        RungeKutta4 {
            dt: dt,
            dt_2: dt_2,
            dt_3: dt_3,
            dt_6: dt_6,

            temp: temp,
            k1: k1,
            k2: k2,
            k3: k3,
            k4: k4,
        }
    }

    fn timestep(&self) -> f64 {
        self.dt
    }
}

impl Stepper for RungeKutta4<f64> {
    type State = f64;

    fn do_step<Sy>(&mut self, system: &mut Sy, state: &mut Self::State)
    where
        Sy: Ode<State = f64>,
    {
        system.differentiate_into(state, &mut self.k1);
        system.differentiate_into(&(*state + &self.k1 * self.dt_2), &mut self.k2);
        system.differentiate_into(&(*state + &self.k2 * self.dt_2), &mut self.k3);
        system.differentiate_into(&(*state + &self.k3 * self.dt), &mut self.k4);
        self.temp = *state
            + &(self.dt_6 * &self.k1)
            + &(self.dt_3 * &self.k2)
            + &(self.dt_3 * &self.k3)
            + &(self.dt_6 * &self.k4);
        system.update_state(state, &self.temp);
    }

    fn timestep(&self) -> f64 {
        self.timestep()
    }
}

impl<D, P: ZipMarker> Stepper for RungeKutta4<P>
where
    P: Clone + Debug,
    D: Dimension,
    for<'a> &'a P: IntoNdProducer<Dim = D, Item = &'a f64>,
    for<'a> &'a mut P: IntoNdProducer<Dim = D, Item = &'a mut f64>,
{
    type State = P;

    fn do_step<Sy>(&mut self, system: &mut Sy, state: &mut Self::State)
    where
        Sy: Ode<State = P>,
    {
        let dt = self.dt;
        let dt_2 = self.dt_2;
        let dt_3 = self.dt_3;
        let dt_6 = self.dt_6;

        system.differentiate_into(state, &mut self.k1);

        Zip::from(&mut self.temp)
            .and(&*state)
            .and(&self.k1)
            .apply(|next_x, &x, &x_k1| *next_x = x + dt_2 * x_k1);

        system.differentiate_into(&self.temp, &mut self.k2);

        Zip::from(&mut self.temp)
            .and(&*state)
            .and(&self.k2)
            .apply(|next_x, &x, &x_k2| *next_x = x + dt_2 * x_k2);

        system.differentiate_into(&self.temp, &mut self.k3);

        Zip::from(&mut self.temp)
            .and(&*state)
            .and(&self.k3)
            .apply(|next_x, &x, &x_k3| *next_x = x + dt * x_k3);

        system.differentiate_into(&self.temp, &mut self.k4);

        Zip::from(&mut self.temp)
            .and(&*state)
            .and(&self.k1)
            .and(&self.k2)
            .and(&self.k3)
            .and(&self.k4)
            .apply(|next_x, &x, &x_k1, &x_k2, &x_k3, &x_k4| {
                *next_x = x + dt_6 * x_k1 + dt_3 * x_k2 + dt_3 * x_k3 + dt_6 * x_k4
            });

        system.update_state(state, &self.temp);
    }

    fn timestep(&self) -> f64 {
        self.timestep()
    }
}