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// Copyright 2018 Stefan Kroboth // // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or // http://apache.org/licenses/LICENSE-2.0> or the MIT license <LICENSE-MIT or // http://opensource.org/licenses/MIT>, at your option. This file may not be // 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}; /// 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 /// /// ``` /// # extern crate argmin; /// # extern crate ndarray; /// use argmin::prelude::*; /// use argmin::solver::newton::Newton; /// # use argmin::testfunctions::{rosenbrock_2d, rosenbrock_2d_derivative, rosenbrock_2d_hessian}; /// use ndarray::{Array, Array1, Array2}; /// /// # use serde::{Deserialize, Serialize}; /// # /// # #[derive(Clone, Default, Serialize, Deserialize)] /// # struct MyProblem {} /// # /// # impl ArgminOp for MyProblem { /// # type Param= Array1<f64>; /// # type Output = f64; /// # type Hessian = Array2<f64>; /// # /// # fn apply(&self, p: &Self::Param) -> Result<Self::Output, Error> { /// # Ok(rosenbrock_2d(&p.to_vec(), 1.0, 100.0)) /// # } /// # /// # fn gradient(&self, p: &Self::Param) -> Result<Self::Param, Error> { /// # Ok(Array1::from_vec(rosenbrock_2d_derivative(&p.to_vec(), 1.0, 100.0))) /// # } /// # /// # fn hessian(&self, p: &Self::Param) -> Result<Self::Hessian, Error> { /// # let h = rosenbrock_2d_hessian(&p.to_vec(), 1.0, 100.0); /// # Ok(Array::from_shape_vec((2, 2), h)?) /// # } /// # } /// # /// # fn run() -> Result<(), Error> { /// // Define cost function /// let cost = MyProblem {}; /// /// // Define initial parameter vector /// let init_param: Array1<f64> = Array1::from_vec(vec![-1.2, 1.0]); /// /// // Set up solver /// let mut solver = Newton::new(cost, init_param); /// /// // Set maximum number of iterations /// solver.set_max_iters(7); /// /// // Attach a logger /// solver.add_logger(ArgminSlogLogger::term()); /// /// // Run solver /// solver.run()?; /// /// // Wait a second (lets the logger flush everything before printing again) /// std::thread::sleep(std::time::Duration::from_secs(1)); /// /// // Print result /// println!("{:?}", solver.result()); /// # Ok(()) /// # } /// # /// # fn main() { /// # if let Err(ref e) = run() { /// # println!("{} {}", e.as_fail(), e.backtrace()); /// # std::process::exit(1); /// # } /// # } /// ``` /// /// # References: /// /// [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization. /// Springer. ISBN 0-387-30303-0. #[derive(ArgminSolver, Serialize, Deserialize)] pub struct Newton<O> where O: ArgminOp, O::Param: ArgminScaledSub<O::Param, f64, O::Param>, O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>, { /// gamma gamma: f64, /// Base stuff base: ArgminBase<O>, } impl<O> Newton<O> where O: ArgminOp, O::Param: ArgminScaledSub<O::Param, f64, O::Param>, O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>, { /// Constructor pub fn new(cost_function: O, init_param: O::Param) -> Self { Newton { gamma: 1.0, base: ArgminBase::new(cost_function, init_param), } } /// set gamma pub fn set_gamma(&mut self, gamma: f64) -> Result<&mut Self, Error> { if gamma <= 0.0 || gamma > 1.0 { return Err(ArgminError::InvalidParameter { text: "Newton: gamma must be in (0, 1].".to_string(), } .into()); } self.gamma = gamma; Ok(self) } } impl<O> ArgminIter for Newton<O> where O: ArgminOp, O::Param: ArgminScaledSub<O::Param, f64, O::Param>, O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>, { type Param = O::Param; type Output = O::Output; type Hessian = O::Hessian; fn next_iter(&mut self) -> Result<ArgminIterData<Self::Param>, Error> { let param = self.cur_param(); let grad = self.gradient(¶m)?; let hessian = self.hessian(¶m)?; let new_param = param.scaled_sub(&self.gamma, &hessian.inv()?.dot(&grad)); let out = ArgminIterData::new(new_param, 0.0); Ok(out) } } #[cfg(test)] mod tests { use super::*; use crate::send_sync_test; // Only works with ndarray feature because of the required inverse of a matrix #[cfg(feature = "ndarrayl")] type Operator = NoOperator<ndarray::Array1<f64>, f64, ndarray::Array2<f64>>; // Only works with ndarray feature because of the required inverse of a matrix #[cfg(feature = "ndarrayl")] send_sync_test!(newton_method, Newton<Operator>); }