use crate::beta_functions::{eichhorn_beta_system, linearized_beta, BetaSystem};
use crate::coupling_space::{gravitational_fixed_point, CouplingPoint};

pub fn rk4_step(system: BetaSystem, step: f64, point: CouplingPoint) -> CouplingPoint {
    let k1 = linearized_beta(system, point);
    let k2 = linearized_beta(system, point.add(k1.scale(step / 2.0)));
    let k3 = linearized_beta(system, point.add(k2.scale(step / 2.0)));
    let k4 = linearized_beta(system, point.add(k3.scale(step)));
    let weighted = k1
        .add(k2.scale(2.0))
        .add(k3.scale(2.0))
        .add(k4);
    point.add(weighted.scale(step / 6.0))
}

pub fn demo_portal_coupling() -> f64 {
    let system = eichhorn_beta_system();
    let mut start = gravitational_fixed_point(system.truncation);
    start.portal_coupling = 0.08;
    start.top_yukawa = 0.05;
    start.higgs_quartic = 0.02;
    rk4_step(system, 0.08333333333333333, start).portal_coupling
}