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

//! # References:
//!
//! [Wikipedia](https://en.wikipedia.org/wiki/Golden-section_search)

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

const GOLDEN_RATIO: f64 = 1.61803398874989484820;
const G1: f64 = -1.0 + GOLDEN_RATIO;
const G2: f64 = 1.0 - G1;

/// Golden-section search
///
/// The golden-section search is a technique for finding an extremum (minimum or maximum) of a
/// function inside a specified interval.
///
/// The method operates by successively narrowing the range of values on the specified interval,
/// which makes it relatively slow, but very robust. The technique derives its name from the fact
/// that the algorithm maintains the function values for four points whose three interval widths
/// are in the ratio 2-φ:2φ-3:2-φ where φ is the golden ratio. These ratios are maintained for each
/// iteration and are maximally efficient.
///
/// The `min_bound` and `max_bound` arguments define values that bracket the expected minimum. The
/// `init_estimate` argument is the initial estimate of the minimum that is required to be larger
/// than `min_bound` and smaller than `max_bound`.
///
/// # References:
///
/// [Wikipedia](https://en.wikipedia.org/wiki/Golden-section_search)
#[derive(Clone, Serialize, Deserialize)]
pub struct GoldenSectionSearch<F> {
g1: F,
g2: F,
min_bound: F,
max_bound: F,
init_estimate: F,
tolerance: F,

x0: F,
x1: F,
x2: F,
x3: F,
f1: F,
f2: F,
}

impl<F> GoldenSectionSearch<F>
where
F: ArgminFloat,
{
/// Constructor
pub fn new(min_bound: F, max_bound: F) -> Self {
GoldenSectionSearch {
g1: F::from(G1).unwrap(),
g2: F::from(G2).unwrap(),
min_bound,
max_bound,
init_estimate: F::zero(),
tolerance: F::from(0.01).unwrap(),
x0: min_bound,
x1: F::zero(),
x2: F::zero(),
x3: max_bound,
f1: F::zero(),
f2: F::zero(),
}
}

/// Set tolerance
pub fn tolerance(mut self, tol: F) -> Self {
self.tolerance = tol;
self
}
}

impl<O, F> Solver<O> for GoldenSectionSearch<F>
where
O: ArgminOp<Output = F, Param = F, Float = F>,
F: ArgminFloat,
{
const NAME: &'static str = "Golden-section search";

fn init(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<Option<ArgminIterData<O>>, Error> {
let init_estimate = state.param;
if init_estimate < self.min_bound || init_estimate > self.max_bound {
Err(ArgminError::InvalidParameter {
text: "Initial estimate must be ∈ [min_bound, max_bound].".to_string(),
}
.into())
} else {
let ie_min = init_estimate - self.min_bound;
let max_ie = self.max_bound - init_estimate;
let (x1, x2) = if max_ie.abs() > ie_min.abs() {
(init_estimate, init_estimate + self.g2 * max_ie)
} else {
(init_estimate - self.g2 * ie_min, init_estimate)
};
self.x1 = x1;
self.x2 = x2;
self.f1 = op.apply(&self.x1)?;
self.f2 = op.apply(&self.x2)?;
if self.f1 < self.f2 {
Ok(Some(ArgminIterData::new().param(self.x1).cost(self.f1)))
} else {
Ok(Some(ArgminIterData::new().param(self.x2).cost(self.f2)))
}
}
}

fn next_iter(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<ArgminIterData<O>, Error> {
if self.tolerance * (self.x1.abs() + self.x2.abs()) >= (self.x3 - self.x0).abs() {
return Ok(ArgminIterData::new()
.param(state.param)
.cost(state.cost)
.termination_reason(TerminationReason::TargetToleranceReached));
}

if self.f2 < self.f1 {
self.x0 = self.x1;
self.x1 = self.x2;
self.x2 = self.g1 * self.x1 + self.g2 * self.x3;
self.f1 = self.f2;
self.f2 = op.apply(&self.x2)?;
} else {
self.x3 = self.x2;
self.x2 = self.x1;
self.x1 = self.g1 * self.x2 + self.g2 * self.x0;
self.f2 = self.f1;
self.f1 = op.apply(&self.x1)?;
}
if self.f1 < self.f2 {
Ok(ArgminIterData::new().param(self.x1).cost(self.f1))
} else {
Ok(ArgminIterData::new().param(self.x2).cost(self.f2))
}
}
}

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

test_trait_impl!(golden_section_search, GoldenSectionSearch<f64>);
}
```