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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. //! Landweber iteration //! //! [Landweber](struct.Landweber.html) //! //! # References //! //! [0] Landweber, L. (1951): An iteration formula for Fredholm integral equations of the first //! kind. Amer. J. Math. 73, 615–624 //! [1] https://en.wikipedia.org/wiki/Landweber_iteration use crate::prelude::*; /// The Landweber iteration is a solver for ill-posed linear inverse problems. /// /// In iteration `k`, the new parameter vector `x_{k+1}` is calculated from the previous parameter /// vector `x_k` and the gradient at `x_k` according to the following update rule: /// /// `x_{k+1} = x_k - omega * \nabla f(x_k)` /// /// # Example /// /// ``` /// # extern crate argmin; /// use argmin::prelude::*; /// use argmin::solver::landweber::Landweber; /// # use argmin::testfunctions::{rosenbrock_2d, rosenbrock_2d_derivative}; /// /// # #[derive(Clone, Default)] /// # struct MyProblem {} /// # /// # impl ArgminOp for MyProblem { /// # type Param = Vec<f64>; /// # type Output = f64; /// # type Hessian = (); /// # /// # fn apply(&self, p: &Vec<f64>) -> Result<f64, Error> { /// # Ok(rosenbrock_2d(p, 1.0, 100.0)) /// # } /// # /// # fn gradient(&self, p: &Vec<f64>) -> Result<Vec<f64>, Error> { /// # Ok(rosenbrock_2d_derivative(p, 1.0, 100.0)) /// # } /// # } /// # /// # fn run() -> Result<(), Error> { /// let operator = MyProblem {}; /// let init_param: Vec<f64> = vec![1.2, 1.2]; /// let omega = 0.001; /// /// let mut solver = Landweber::new(operator, omega, init_param)?; /// solver.set_max_iters(100); /// solver.add_logger(ArgminSlogLogger::term()); /// solver.run()?; /// /// println!("{:?}", solver.result()); /// # Ok(()) /// # } /// # /// # fn main() { /// # if let Err(ref e) = run() { /// # println!("{} {}", e.as_fail(), e.backtrace()); /// # } /// # } /// ``` /// /// # References /// /// [0] Landweber, L. (1951): An iteration formula for Fredholm integral equations of the first /// kind. Amer. J. Math. 73, 615–624 /// [1] https://en.wikipedia.org/wiki/Landweber_iteration #[derive(ArgminSolver)] pub struct Landweber<O> where <O as ArgminOp>::Param: ArgminScaledSub<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param>, O: ArgminOp, { /// omgea omega: f64, /// Base stuff base: ArgminBase<O>, } impl<O> Landweber<O> where <O as ArgminOp>::Param: ArgminScaledSub<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param>, O: ArgminOp, { /// Constructor pub fn new( cost_function: O, omega: f64, init_param: <O as ArgminOp>::Param, ) -> Result<Self, Error> { Ok(Landweber { omega, base: ArgminBase::new(cost_function, init_param), }) } } impl<O> ArgminIter for Landweber<O> where <O as ArgminOp>::Param: ArgminScaledSub<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param>, O: ArgminOp, { type Param = <O as ArgminOp>::Param; type Output = <O as ArgminOp>::Output; type Hessian = <O as ArgminOp>::Hessian; fn next_iter(&mut self) -> Result<ArgminIterData<Self::Param>, Error> { let param = self.cur_param(); let grad = self.gradient(¶m)?; let new_param = param.scaled_sub(&self.omega, &grad); let out = ArgminIterData::new(new_param, 0.0); Ok(out) } }