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```// Copyright 2018-2020 argmin developers
//
// copied, modified, or distributed except according to those terms.

//! # References:
//!
//! [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
//! Springer. ISBN 0-387-30303-0.

use crate::prelude::*;
use serde::{Deserialize, Serialize};
use std::default::Default;

/// Gauss-Newton method with linesearch
///
/// [Example](https://github.com/argmin-rs/argmin/blob/master/examples/gaussnewton_linesearch.rs)
///
/// # References:
///
/// [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
/// Springer. ISBN 0-387-30303-0.
#[derive(Clone, Serialize, Deserialize)]
pub struct GaussNewtonLS<L, F> {
/// linesearch
linesearch: L,
/// Tolerance for the stopping criterion based on cost difference
tol: F,
}

impl<L, F: ArgminFloat> GaussNewtonLS<L, F> {
/// Constructor
pub fn new(linesearch: L) -> Self {
GaussNewtonLS {
linesearch,
tol: F::epsilon().sqrt(),
}
}

/// Set tolerance for the stopping criterion based on cost difference
pub fn with_tol(mut self, tol: F) -> Result<Self, Error> {
if tol <= F::from_f64(0.0).unwrap() {
return Err(ArgminError::InvalidParameter {
text: "Gauss-Newton-Linesearch: tol must be positive.".to_string(),
}
.into());
}
self.tol = tol;
Ok(self)
}
}

impl<O, L, F> Solver<O> for GaussNewtonLS<L, F>
where
O: ArgminOp<Float = F>,
O::Param: Default
+ std::fmt::Debug
+ ArgminScaledSub<O::Param, O::Float, O::Param>
+ ArgminSub<O::Param, O::Param>
+ ArgminMul<O::Float, O::Param>,
O::Output: ArgminNorm<O::Float>,
O::Jacobian: ArgminTranspose
+ ArgminInv<O::Jacobian>
+ ArgminDot<O::Jacobian, O::Jacobian>
+ ArgminDot<O::Output, O::Param>
+ ArgminDot<O::Param, O::Param>,
O::Hessian: Default,
L: Clone + ArgminLineSearch<O::Param, O::Float> + Solver<OpWrapper<LineSearchOP<O>>>,
F: ArgminFloat,
{
const NAME: &'static str = "Gauss-Newton method with Linesearch";

fn next_iter(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<ArgminIterData<O>, Error> {
let param = state.get_param();
let residuals = op.apply(&param)?;
let jacobian = op.jacobian(&param)?;
let jacobian_t = jacobian.clone().t();

self.linesearch
.set_search_direction(p.mul(&(F::from_f64(-1.0).unwrap())));

// create operator for linesearch
let line_op = OpWrapper::new(LineSearchOP {
op: op.take_op().unwrap(),
});

// perform linesearch
let ArgminResult {
operator: mut line_op,
state:
IterState {
param: next_param,
cost: next_cost,
..
},
} = Executor::new(line_op, self.linesearch.clone(), param)
.cost(residuals.norm())
.ctrlc(false)
.run()?;

// Here we cannot use `consume_op` because the operator we need is hidden inside a
// `LineSearchOP` hidden inside a `OpWrapper`. Therefore we have to split this in two
// separate tasks: first getting the operator, then dealing with the function counts.
op.op = Some(line_op.take_op().unwrap().op);
op.consume_func_counts(line_op);

Ok(ArgminIterData::new().param(next_param).cost(next_cost))
}

fn terminate(&mut self, state: &IterState<O>) -> TerminationReason {
if (state.get_prev_cost() - state.get_cost()).abs() < self.tol {
return TerminationReason::NoChangeInCost;
}
TerminationReason::NotTerminated
}
}

#[doc(hidden)]
#[derive(Clone, Default, Serialize, Deserialize)]
pub struct LineSearchOP<O> {
pub op: O,
}

impl<O> ArgminOp for LineSearchOP<O>
where
O: ArgminOp,
O::Jacobian: ArgminTranspose + ArgminDot<O::Output, O::Param>,
O::Output: ArgminNorm<O::Float>,
{
type Param = O::Param;
type Output = O::Float;
type Hessian = O::Hessian;
type Jacobian = O::Jacobian;
type Float = O::Float;

fn apply(&self, p: &Self::Param) -> Result<Self::Output, Error> {
Ok(self.op.apply(p)?.norm())
}

fn gradient(&self, p: &Self::Param) -> Result<Self::Param, Error> {
Ok(self.op.jacobian(p)?.t().dot(&self.op.apply(p)?))
}

fn hessian(&self, p: &Self::Param) -> Result<Self::Hessian, Error> {
self.op.hessian(p)
}

fn jacobian(&self, p: &Self::Param) -> Result<Self::Jacobian, Error> {
self.op.jacobian(p)
}
}

#[cfg(test)]
mod tests {
use super::*;
use crate::solver::linesearch::MoreThuenteLineSearch;
use crate::test_trait_impl;

test_trait_impl!(
gauss_newton_linesearch_method,
GaussNewtonLS<MoreThuenteLineSearch<Vec<f64>, f64>, f64>
);

#[test]
fn test_tolerance() {
let tol1: f64 = 1e-4;

let linesearch: MoreThuenteLineSearch<Vec<f64>, f64> = MoreThuenteLineSearch::new();
let GaussNewtonLS { tol: t1, .. } = GaussNewtonLS::new(linesearch).with_tol(tol1).unwrap();

assert!((t1 - tol1).abs() < std::f64::EPSILON);
}
}
```