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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 crate::solver::trustregion::reduction_ratio;
use serde::{Deserialize, Serialize};
use std::fmt::Debug;

/// The trust region method approximates the cost function within a certain region around the
/// current point in parameter space. Depending on the quality of this approximation, the region is
/// either expanded or contracted.
///
/// The calculation of the actual step length and direction is done by one of the following
/// methods:
///
/// * [Cauchy point](../cauchypoint/struct.CauchyPoint.html)
/// * [Dogleg method](../dogleg/struct.Dogleg.html)
/// * [Steihaug method](../steihaug/struct.Steihaug.html)
///
/// This subproblem can be set via set_subproblem(...). If this is not provided, it will default
/// to the Steihaug method.
///
/// [Example](https://github.com/argmin-rs/argmin/blob/master/examples/trustregion_nd.rs)
///
/// # References:
///
/// [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
/// Springer. ISBN 0-387-30303-0.
#[derive(Clone, Serialize, Deserialize)]
pub struct TrustRegion<R, F> {
/// eta \in [0, 1/4)
eta: F,
/// subproblem
subproblem: R,
/// f(xk)
fxk: F,
/// mk(0)
mk0: F,
}

impl<R, F: ArgminFloat> TrustRegion<R, F> {
/// Constructor
pub fn new(subproblem: R) -> Self {
TrustRegion {
eta: F::from_f64(0.125).unwrap(),
subproblem,
fxk: F::nan(),
mk0: F::nan(),
}
}

self
}

self
}

/// Set eta
pub fn eta(mut self, eta: F) -> Result<Self, Error> {
if eta >= F::from_f64(0.25).unwrap() || eta < F::from_f64(0.0).unwrap() {
return Err(ArgminError::InvalidParameter {
text: "TrustRegion: eta must be in [0, 1/4).".to_string(),
}
.into());
}
self.eta = eta;
Ok(self)
}
}

impl<O, R, F> Solver<O> for TrustRegion<R, F>
where
O: ArgminOp<Output = F, Float = F>,
O::Param: Default
+ Clone
+ Debug
+ Serialize
+ ArgminMul<F, O::Param>
+ ArgminWeightedDot<O::Param, F, O::Hessian>
+ ArgminNorm<F>
+ ArgminDot<O::Param, F>
+ ArgminSub<O::Param, O::Param>
+ ArgminZeroLike
+ ArgminMul<F, O::Param>,
O::Hessian: Default + Clone + Debug + Serialize + ArgminDot<O::Param, O::Param>,
R: ArgminTrustRegion<F> + Solver<OpWrapper<O>>,
F: ArgminFloat,
{
const NAME: &'static str = "Trust region";

fn init(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<Option<ArgminIterData<O>>, Error> {
let param = state.get_param();
let hessian = op.hessian(&param)?;
self.fxk = op.apply(&param)?;
self.mk0 = self.fxk;
Ok(Some(
ArgminIterData::new()
.param(param)
.cost(self.fxk)
.hessian(hessian),
))
}

fn next_iter(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<ArgminIterData<O>, Error> {
let param = state.get_param();
let hessian = state
.get_hessian()
.unwrap_or_else(|| op.hessian(&param).unwrap());

let ArgminResult {
operator: sub_op,
state: IterState { param: pk, .. },
} = Executor::new(
OpWrapper::new_from_wrapper(op),
self.subproblem.clone(),
param.clone(),
)
.hessian(hessian.clone())
.ctrlc(false)
.run()?;

// Operator must be consumed again, otherwise the operator, which moved into the subproblem
// executor as well as the function evaluation counts are lost.
op.consume_op(sub_op);

let fxkpk = op.apply(&new_param)?;
let mkpk =
self.fxk + pk.dot(&grad) + F::from_f64(0.5).unwrap() * pk.weighted_dot(&hessian, &pk);

let rho = reduction_ratio(self.fxk, fxkpk, self.mk0, mkpk);

let pk_norm = pk.norm();

self.radius = if rho < F::from_f64(0.25).unwrap() {
F::from_f64(0.25).unwrap() * pk_norm
} else if rho > F::from_f64(0.75).unwrap()
&& (pk_norm - self.radius).abs() <= F::from_f64(10.0).unwrap() * F::epsilon()
{
} else {
};

Ok(if rho > self.eta {
self.fxk = fxkpk;
self.mk0 = fxkpk;
let hessian = op.hessian(&new_param)?;
ArgminIterData::new()
.param(new_param)
.cost(fxkpk)
.hessian(hessian)
} else {
ArgminIterData::new().param(param).cost(self.fxk)
}
}

fn terminate(&mut self, _state: &IterState<O>) -> TerminationReason {
// todo
TerminationReason::NotTerminated
}
}

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

type Operator = MinimalNoOperator;

test_trait_impl!(trustregion, TrustRegion<Steihaug<Operator, f64>, f64>);
}