ionotrace 0.1.0

High-performance ionospheric ray tracing engine — Hamilton's equations for HF radio propagation through a magnetized, collisional plasma
Documentation 
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use crate::params::ModelParams;
use crate::hamiltonian::hamltn;

pub const NN: usize = 8;

pub struct IntegratorState {
    pub y: [f64; NN],
    pub dydt: [f64; NN],
    pub yu: [[f64; NN]; 6],
    pub fv: [[f64; NN]; 6],
    pub xv: [f64; 6],
    pub t: f64,
    pub step: f64,
    pub mm: usize,
    pub ll: usize,
    pub mode: usize,
    pub alpha: f64,
    pub epm: f64,
    pub e1max: f64,
    pub e1min: f64,
    pub e2max: f64,
    pub e2min: f64,
    pub fact: f64,
}

impl IntegratorState {
    pub fn new(y0: &[f64; NN], t0: f64, step: f64, mode: usize,
           e1max: f64, e1min: f64, e2max: f64, e2min: f64, fact: f64) -> Self {
        let mut s = Self {
            y: *y0,
            dydt: [0.0; NN],
            yu: [[0.0; NN]; 6],
            fv: [[0.0; NN]; 6],
            xv: [0.0; 6],
            t: t0,
            step,
            mm: 1,
            ll: 1,
            mode,
            alpha: t0,
            epm: 0.0,
            e1max,
            e1min: if e1min <= 0.0 { e1max / 55.0 } else { e1min },
            e2max,
            e2min,
            fact: if fact <= 0.0 { 0.5 } else { fact },
        };
        if mode == 1 { s.mm = 4; }
        s.xv[s.mm] = t0;
        for i in 0..NN {
            s.yu[s.mm][i] = y0[i];
        }
        s
    }
}

pub fn rk4_step(
    s: &mut IntegratorState,
    freq_mhz: f64, ray_mode: f64, p: &ModelParams,
) {
    let bet = [0.5, 0.5, 1.0, 0.0];
    let mut dely = [[0.0f64; NN]; 4];
    let mm = s.mm;

    for k in 0..4 {
        for i in 0..NN {
            dely[k][i] = s.step * s.fv[mm][i];
            s.y[i] = s.yu[mm][i] + bet[k] * dely[k][i];
        }
        s.t = bet[k] * s.step + s.xv[mm];
        let (d, _, _, _, _) = hamltn(&s.y, freq_mhz, ray_mode, p, false);
        s.dydt = d;
        for i in 0..NN {
            s.fv[mm][i] = d[i];
        }
    }

    for i in 0..NN {
        let delta = (dely[0][i] + 2.0 * dely[1][i] + 2.0 * dely[2][i] + dely[3][i]) / 6.0;
        s.yu[mm + 1][i] = s.yu[mm][i] + delta;
    }
    s.mm += 1;
    s.xv[s.mm] = s.xv[s.mm - 1] + s.step;
    for i in 0..NN { s.y[i] = s.yu[s.mm][i]; }
    s.t = s.xv[s.mm];

    let (d, _, _, _, _) = hamltn(&s.y, freq_mhz, ray_mode, p, false);
    s.dydt = d;

    if s.mode == 1 {
        exit_routine(s);
        return;
    }

    for i in 0..NN { s.fv[s.mm][i] = d[i]; }

    if s.mm <= 3 {
        rk4_step(s, freq_mhz, ray_mode, p);
        return;
    }

    am_step(s, freq_mhz, ray_mode, p);
}

pub fn am_step(
    s: &mut IntegratorState,
    freq_mhz: f64, ray_mode: f64, p: &ModelParams,
) {
    let mut dely1 = [0.0f64; NN];

    // Predictor (Adams-Bashforth)
    for i in 0..NN {
        let delta = s.step * (55.0 * s.fv[4][i] - 59.0 * s.fv[3][i]
            + 37.0 * s.fv[2][i] - 9.0 * s.fv[1][i]) / 24.0;
        s.y[i] = s.yu[4][i] + delta;
        dely1[i] = s.y[i];
    }

    s.t = s.xv[4] + s.step;
    let (d, _, _, _, _) = hamltn(&s.y, freq_mhz, ray_mode, p, false);
    s.dydt = d;
    s.xv[5] = s.t;

    // Corrector (Adams-Moulton)
    for i in 0..NN {
        let delta = s.step * (9.0 * d[i] + 19.0 * s.fv[4][i]
            - 5.0 * s.fv[3][i] + s.fv[2][i]) / 24.0;
        s.yu[5][i] = s.yu[4][i] + delta;
        s.y[i] = s.yu[5][i];
    }

    let (d2, _, _, _, _) = hamltn(&s.y, freq_mhz, ray_mode, p, false);
    s.dydt = d2;

    if s.mode <= 2 {
        exit_routine(s);
        return;
    }

    // Error analysis (mode 3)
    let mut sse = 0.0f64;
    for i in 0..NN {
        let mut epsil = 8.0 * (s.y[i] - dely1[i]).abs();
        if s.y[i].abs() > 1.0e-8 {
            epsil /= s.y[i].abs();
        }
        if sse < epsil { sse = epsil; }
    }

    if s.e1max <= sse {
        if s.step.abs() <= s.e2min {
            exit_routine(s);
            return;
        }
        s.ll = 1;
        s.mm = 1;
        s.step *= s.fact;
        // Reinit from current y
        for i in 0..NN {
            s.yu[1][i] = s.y[i];
            s.fv[1][i] = s.dydt[i];
        }
        s.xv[1] = s.t;
        rk4_step(s, freq_mhz, ray_mode, p);
        return;
    }

    if s.ll <= 1 || sse >= s.e1min || s.e2max <= s.step.abs() {
        exit_routine(s);
        return;
    }

    // Double step
    s.ll = 2;
    s.mm = 3;
    s.xv[2] = s.xv[3];
    s.xv[3] = s.xv[5];
    for i in 0..NN {
        s.fv[2][i] = s.fv[3][i];
        s.fv[3][i] = s.dydt[i];
        s.yu[2][i] = s.yu[3][i];
        s.yu[3][i] = s.yu[5][i];
    }
    s.step *= 2.0;
    rk4_step(s, freq_mhz, ray_mode, p);
}

fn exit_routine(s: &mut IntegratorState) {
    s.ll = 2;
    s.mm = 4;

    for k in 1..4 {
        s.xv[k] = s.xv[k + 1];
        for i in 0..NN {
            s.fv[k][i] = s.fv[k + 1][i];
            s.yu[k][i] = s.yu[k + 1][i];
        }
    }
    s.xv[4] = s.xv[5];
    for i in 0..NN {
        s.fv[4][i] = s.dydt[i];
        s.yu[4][i] = s.yu[5][i];
    }

    if s.mode <= 2 { return; }
    let e = (s.xv[4] - s.alpha).abs();
    s.epm = s.epm.max(e);
}