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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;

/// Newton's method iteratively finds the stationary points of a function f by using a second order
/// approximation of f at the current point.
///
/// [Example](https://github.com/argmin-rs/argmin/blob/master/examples/newton.rs)
///
/// # References:
///
/// [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
/// Springer. ISBN 0-387-30303-0.
#[derive(Clone, Serialize, Deserialize)]
pub struct Newton<F> {
/// gamma
gamma: F,
}

impl<F: ArgminFloat> Newton<F> {
/// Constructor
pub fn new() -> Self {
Newton {
gamma: F::from_f64(1.0).unwrap(),
}
}

/// set gamma
pub fn set_gamma(mut self, gamma: F) -> Result<Self, Error> {
if gamma <= F::from_f64(0.0).unwrap() || gamma > F::from_f64(1.0).unwrap() {
return Err(ArgminError::InvalidParameter {
text: "Newton: gamma must be in  (0, 1].".to_string(),
}
.into());
}
self.gamma = gamma;
Ok(self)
}
}

impl<F: ArgminFloat> Default for Newton<F> {
fn default() -> Newton<F> {
Newton::new()
}
}

impl<O, F> Solver<O> for Newton<F>
where
O: ArgminOp<Float = F>,
O::Param: ArgminScaledSub<O::Param, O::Float, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
F: ArgminFloat,
{
const NAME: &'static str = "Newton method";

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