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/*
 * File: lm.rs
 * Project: multiple_foci
 * Created Date: 21/09/2020
 * Author: Shun Suzuki
 * -----
 * Last Modified: 08/03/2021
 * Modified By: Shun Suzuki (suzuki@hapis.k.u-tokyo.ac.jp)
 * -----
 * Copyright (c) 2020 Hapis Lab. All rights reserved.
 *
 */

use autd::{
    consts::{DataArray, NUM_TRANS_IN_UNIT},
    geometry::Geometry,
    prelude::Vector3,
    Float, PI,
};

use super::macros::*;
use crate::{
    macros::{MatrixXf, VectorXf},
    Optimizer,
};

const EPS_1: Float = 1e-8;
const EPS_2: Float = 1e-8;
const TAU: Float = 1e-3;
const K_MAX: usize = 5;

/// References
/// * K.Levenberg, “A method for the solution of certain non-linear problems in least squares,” Quarterly of applied mathematics, vol.2, no.2, pp.164–168, 1944.
/// * D.W.Marquardt, “An algorithm for least-squares estimation of non-linear parameters,” Journal of the society for Industrial and AppliedMathematics, vol.11, no.2, pp.431–441, 1963.
/// * K.Madsen, H.Nielsen, and O.Tingleff, “Methods for non-linear least squares problems (2nd ed.),” 2004.
pub struct LM {
    pub eps_1: Float,
    pub eps_2: Float,
    pub tau: Float,
    pub k_max: usize,
}

impl LM {
    pub fn new() -> Self {
        Self::default()
    }
}

impl Default for LM {
    fn default() -> Self {
        Self {
            eps_1: EPS_1,
            eps_2: EPS_2,
            tau: TAU,
            k_max: K_MAX,
        }
    }
}

impl Optimizer for LM {
    #[allow(non_snake_case, clippy::many_single_char_names)]
    fn optimize(
        &self,
        geometry: &Geometry,
        foci: &[Vector3],
        amps: &[Float],
        atten: Float,
        data: &mut [DataArray],
    ) {
        let m = foci.len();
        let n = geometry.num_devices() * NUM_TRANS_IN_UNIT;

        let n_param = n + m;

        let x0 = VectorXf::zeros(n_param);

        let I = MatrixXf::identity(n_param, n_param);

        let BhB = make_BhB(geometry, atten, amps, foci, m);

        let mut x = x0;
        let mut nu = 2.0;

        let T = make_T(&x, n, m);
        let (mut A, mut g) = calc_JtJ_Jtf(&BhB, &T);

        let A_max = A.diagonal().max();
        let mut mu = self.tau * A_max;
        let mut found = g.max() <= self.eps_1;
        let mut Fx = calc_Fx(&BhB, &x, n, m);
        const THIRD: Float = 1. / 3.;
        for _ in 0..self.k_max {
            if found {
                break;
            }

            let h_lm = match (&A + &I.scale(mu)).qr().solve(&g) {
                Some(v) => -v,
                None => {
                    break;
                }
            };
            if h_lm.norm() <= self.eps_2 * (x.norm() + self.eps_2) {
                found = true;
            } else {
                let x_new = &x + &h_lm;
                let Fx_new = calc_Fx(&BhB, &x_new, n, m);
                let L0_Lhlm = 0.5 * h_lm.dot(&(mu * &h_lm - &g));
                let rho = (Fx - Fx_new) / L0_Lhlm;
                Fx = Fx_new;
                if rho > 0.0 {
                    x = x_new;
                    let T = make_T(&x, n, m);
                    let (A_new, g_new) = calc_JtJ_Jtf(&BhB, &T);
                    A = A_new;
                    g = g_new;
                    found = g.max() <= self.eps_1;
                    mu *= THIRD.max(1. - (2. * rho - 1.).powf(3.));
                    nu = 2.;
                } else {
                    mu *= nu;
                    nu *= 2.;
                }
            }
        }

        let duty = 0xFF00;
        for (d, xe) in data.iter_mut().flatten().zip(x.iter()) {
            let phase = (xe % (2.0 * PI)) / (2.0 * PI);
            let phase = (255.0 * (1.0 - phase)) as u16;

            *d = duty | phase;
        }
    }
}