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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. //! A pure Rust optimization framework //! //! This crate offers a (work in progress) numerical optimization toolbox/framework written entirely //! in Rust. It is at the moment quite unstable and potentially very buggy. Please use with care and //! report any bugs you encounter. This crate is looking for contributors! //! //! # Design goals //! //! This crate's intention is to be useful to users as well as developers of optimization //! algorithms, meaning that it should be both easy to apply and easy to implement algorithms. In //! particular, as a developer of optimization algorithms you should not need to worry about //! usability features (such as logging, dealing with different types, setters and getters for //! certain common parameters, counting cost function and gradient evaluations, termination, and so //! on). Instead you can focus on implementing your algorithm and let `argmin-codegen` do the rest. //! //! - Easy framework for the implementation of optimization algorithms: Define a struct to hold your //! data, implement a single iteration of your method and let argmin generate the rest with //! `#[derive(ArgminSolver)]`. This lead to similar interfaces for different solvers, making it //! easy for users. //! - Pure Rust implementations of a wide range of optimization methods: This avoids the need to //! compile and interface C/C++/Fortran code. //! - Type-agnostic: Many problems require data structures that go beyond simple vectors to //! represent the parameters. In argmin, everything is generic: All that needs to be done is //! implementing certain traits on your data type. For common types, these traits are already //! implemented. //! - Convenient: Automatic and consistent logging of anything that may be important. Log to the //! terminal, to a file or implement your own loggers. Future plans include sending metrics to //! databases and connecting to big data piplines. //! - Algorithm evaluation: Methods to assess the performance of an algorithm for different //! parameter settings, problem classes, ... //! //! Since this crate is in a very early stage, so far most points are only partially implemented or //! remain future plans. //! //! # Algorithms //! //! - [Line searches](solver/linesearch/index.html) //! - [Backtracking line search](solver/linesearch/backtracking/struct.BacktrackingLineSearch.html) //! - [More-Thuente line search](solver/linesearch/morethuente/struct.MoreThuenteLineSearch.html) //! - [Hager-Zhang line search](solver/linesearch/hagerzhang/struct.HagerZhangLineSearch.html) //! - [Trust region method](solver/trustregion/trustregion_method/struct.TrustRegion.html) //! - [Cauchy point method](solver/trustregion/cauchypoint/struct.CauchyPoint.html) //! - [Dogleg method](solver/trustregion/dogleg/struct.Dogleg.html) //! - [Steihaug method](solver/trustregion/steihaug/struct.Steihaug.html) //! - [Steepest descent](solver/gradientdescent/steepestdescent/struct.SteepestDescent.html) //! - [Conjugate gradient method](solver/conjugategradient/cg/struct.ConjugateGradient.html) //! - [Nonlinear conjugate gradient method](solver/conjugategradient/nonlinear_cg/struct.NonlinearConjugateGradient.html) //! - [Newton methods](solver/newton/index.html) //! - [Newton's method](solver/newton/newton_method/struct.Newton.html) //! - [Newton-CG](solver/newton/newton_cg/struct.NewtonCG.html) //! - [Quasi-Newton methods](solver/quasinewton/index.html) //! - [BFGS](solver/quasinewton/bfgs/struct.BFGS.html) //! - [Landweber iteration](solver/landweber/struct.Landweber.html) //! - [Simulated Annealing](solver/simulatedannealing/struct.SimulatedAnnealing.html) //! //! # Usage //! //! Add this to your `Cargo.toml`: //! //! ```toml //! [dependencies] //! argmin = "0.1.7" //! ``` //! //! ## Optional features //! //! There are additional features which can be activated in `Cargo.toml`: //! //! ```toml //! [dependencies] //! argmin = { version = "0.1.7", features = ["ctrlc", "ndarrayl"] } //! ``` //! //! These may become default features in the future. Without these features compilation to //! `wasm32-unknown-unkown` seems to be possible. //! //! - `ctrlc`: Uses the `ctrlc` crate to properly stop the optimization (and return the current best //! result) after pressing Ctrl+C. //! - `ndarrayl`: Support for `ndarray` and `ndarray-linalg`. //! //! # Defining a problem //! //! A problem can be defined by implementing the `ArgminOp` trait which comes with the //! associated types `Param`, `Output` and `Hessian`. `Param` is the type of your //! parameter vector (i.e. the input to your cost function), `Output` is the type returned //! by the cost function and `Hessian` is the type of the Hessian. //! The trait provides the following methods: //! //! - `apply(&self, p: &Self::Param) -> Result<Self::Output, Error>`: Applys the cost //! function to parameters `p` of type `Self::Param` and returns the cost function value. //! - `gradient(&self, p: &Self::Param) -> Result<Self::Param, Error>`: Computes the //! gradient at `p`. Optional. By default returns an `Err` if not implemented. //! - `hessian(&self, p: &Self::Param) -> Result<Self::Hessian, Error>`: Computes the Hessian //! at `p`. Optional. By default returns an `Err` if not implemented. The type of `Hessian` can //! be set to `()` if this method is not implemented. //! //! //! The following code snippet shows an example of how to use the Rosenbrock test functions from //! `argmin-testfunctions` in argmin: //! //! ```rust //! # extern crate argmin; //! # extern crate argmin_testfunctions; //! # extern crate ndarray; //! # use argmin::testfunctions::{rosenbrock_2d, rosenbrock_2d_derivative, rosenbrock_2d_hessian}; //! # use argmin::prelude::*; //! // [Imports omited] //! //! /// First, create a struct for your problem //! #[derive(Clone, Default)] //! struct Rosenbrock { //! a: f64, //! b: f64, //! } //! //! /// Implement `ArgminOp` for `Rosenbrock` //! impl ArgminOp for Rosenbrock { //! /// Type of the parameter vector //! type Param = ndarray::Array1<f64>; //! /// Type of the return value computed by the cost function //! type Output = f64; //! /// Type of the Hessian. If no Hessian is available or needed for the used solver, this can //! /// be set to `()` //! type Hessian = ndarray::Array2<f64>; //! //! /// Apply the cost function to a parameter `p` //! fn apply(&self, p: &Self::Param) -> Result<Self::Output, Error> { //! Ok(rosenbrock_2d(&p.to_vec(), self.a, self.b)) //! } //! //! /// Compute the gradient at parameter `p`. This is optional: If not implemented, this //! /// method will return an `Err` when called. //! fn gradient(&self, p: &Self::Param) -> Result<Self::Param, Error> { //! Ok(ndarray::Array1::from_vec(rosenbrock_2d_derivative(&p.to_vec(), self.a, self.b))) //! } //! //! /// Compute the Hessian at parameter `p`. This is optional: If not implemented, this method //! /// will return an `Err` when called. //! fn hessian(&self, p: &Self::Param) -> Result<Self::Hessian, Error> { //! let h = rosenbrock_2d_hessian(&p.to_vec(), self.a, self.b); //! Ok(ndarray::Array::from_shape_vec((2, 2), h).unwrap()) //! } //! } //! ``` //! //! # Running a solver //! //! The following example shows how to use the previously shown definition of a problem in a //! Steepest Descent (Gradient Descent) solver. //! //! ``` //! extern crate argmin; //! extern crate ndarray; //! use argmin::testfunctions::{rosenbrock_2d, rosenbrock_2d_derivative, rosenbrock_2d_hessian}; //! use argmin::prelude::*; //! use argmin::solver::gradientdescent::SteepestDescent; //! //! #[derive(Clone, Default)] //! struct Rosenbrock { //! a: f64, //! b: f64, //! } //! //! impl ArgminOp for Rosenbrock { //! type Param = ndarray::Array1<f64>; //! type Output = f64; //! type Hessian = (); //! //! fn apply(&self, p: &Self::Param) -> Result<Self::Output, Error> { //! Ok(rosenbrock_2d(&p.to_vec(), self.a, self.b)) //! } //! //! fn gradient(&self, p: &Self::Param) -> Result<Self::Param, Error> { //! Ok(ndarray::Array1::from_vec(rosenbrock_2d_derivative(&p.to_vec(), self.a, self.b))) //! } //! } //! //! fn run() -> Result<(), Error> { //! // Define cost function //! let cost = Rosenbrock { a: 1.0, b: 100.0 }; //! //! // Define inital parameter vector //! let init_param = ndarray::Array1::from_vec(vec![-1.2, 1.0]); //! //! // Create solver //! let mut solver = SteepestDescent::new(cost, init_param)?; //! //! // Set the maximum number of iterations to 1000 //! solver.set_max_iters(1000); //! //! // Attach a terminal logger (slog) to the solver //! solver.add_logger(ArgminSlogLogger::term()); //! //! // Run the solver //! solver.run()?; //! //! // Print the result //! println!("{:?}", solver.result()); //! Ok(()) //! } //! //! fn main() { //! if let Err(ref e) = run() { //! println!("{} {}", e.as_fail(), e.backtrace()); //! std::process::exit(1); //! } //! } //! ``` //! //! Executing `solver.run()?` performs the actual optimization. In addition, there is //! `solver.run_fast()?`, which only executes the optimization algorithm and avoids all convenience //! functionality such as logging. //! //! # Logging //! //! Information such as the current iteration number, cost function value, and other metrics can be //! logged using any object which implements `argmin_core::ArgminLogger`. So far loggers based on //! the `slog` crate have been implemented: `ArgminSlogLogger::term` logs to the terminal and //! `ArgminSlogLogger::file` logs to a file in JSON format. Both loggers come with a `*_noblock` //! version which does not block the execution for logging, but may drop log entries when the //! buffer fills up. //! //! ``` //! # extern crate argmin; //! # extern crate ndarray; //! # use argmin::testfunctions::{rosenbrock_2d, rosenbrock_2d_derivative, rosenbrock_2d_hessian}; //! # use argmin::prelude::*; //! # use argmin::solver::gradientdescent::SteepestDescent; //! # #[derive(Clone, Default)] //! # struct Rosenbrock { //! # a: f64, //! # b: f64, //! # } //! # impl ArgminOp for Rosenbrock { //! # type Param = ndarray::Array1<f64>; //! # type Output = f64; //! # type Hessian = (); //! # fn apply(&self, p: &Self::Param) -> Result<Self::Output, Error> { //! # Ok(rosenbrock_2d(&p.to_vec(), self.a, self.b)) //! # } //! # fn gradient(&self, p: &Self::Param) -> Result<Self::Param, Error> { //! # Ok(ndarray::Array1::from_vec(rosenbrock_2d_derivative(&p.to_vec(), self.a, self.b))) //! # } //! # } //! # fn run() -> Result<(), Error> { //! # let cost = Rosenbrock { a: 1.0, b: 100.0 }; //! # let init_param = ndarray::Array1::from_vec(vec![-1.2, 1.0]); //! let mut solver = SteepestDescent::new(cost, init_param)?; //! # solver.set_max_iters(10); //! // Log to the terminal //! solver.add_logger(ArgminSlogLogger::term()); //! // Log to the terminal without blocking //! solver.add_logger(ArgminSlogLogger::term_noblock()); //! // Log to the file `log1.log` //! solver.add_logger(ArgminSlogLogger::file("log1.log")?); //! // Log to the file `log2.log` without blocking //! solver.add_logger(ArgminSlogLogger::file_noblock("log2.log")?); //! # solver.run()?; //! # Ok(()) //! # } //! # fn main() { //! # if let Err(ref e) = run() { //! # println!("{} {}", e.as_fail(), e.backtrace()); //! # std::process::exit(1); //! # } //! # } //! ``` //! //! # Implementing an optimization algorithm //! //! In this section we are going to implement the Landweber solver, which essentially is a special //! form of gradient descent. 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)` //! //! In order to implement this using the argmin framework, one first needs to define a struct which //! holds data/parameters needed during the execution of the algorithm. In addition a field with //! the name `base` and type `ArgminBase<'a, T, U, H>` is needed, where `T` is the type of the //! parameter vector, `U` is the type of the return values of the cost function and `H` is the type //! of the Hessian (which can be `()` if not available). //! //! Deriving `ArgminSolver` for the struct using `#[derive(ArgminSolver)]` implements most of the //! API. What remains to be implemented for the struct is a constructor and `ArgminNextIter`. The //! latter is essentially an implementation of a single iteration of the algorithm. //! //! ``` //! // needed for `#[derive(ArgminSolver)]` //! # extern crate argmin_codegen; //! use argmin_codegen::ArgminSolver; //! use argmin::prelude::*; //! use std::default::Default; //! //! // The `Landweber` struct holds the `omega` parameter and has a field `base` which is of type //! // `ArgminBase`. The struct is generic over the ArgminOp `O` which holds type information about //! // the parameter vector which (in this particular case) has to implement //! // `ArgminScaledSub<T, f64>`, which is neede for the update rule. //! // Deriving `ArgminSolver` implements a large portion of the API and provides many convenience //! // functions. It requires that `ArgminIter` is implemented on `Landweber` as well. //! #[derive(ArgminSolver)] //! pub struct Landweber<O> //! where //! <O as ArgminOp>::Param: ArgminScaledSub<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param>, //! O: ArgminOp, //! { //! omega: f64, //! base: ArgminBase<O>, //! } //! //! // For convenience, a constructor can/should be implemented //! impl<O> Landweber<O> //! where //! <O as ArgminOp>::Param: ArgminScaledSub<<O as ArgminOp>::Param, f64, <O as ArgminOp>::Param>, //! O: ArgminOp, //! { //! 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), //! }) //! } //! } //! //! // This implements a single iteration of the optimization algorithm. //! 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> { //! // Obtain current parameter vector //! // The method `cur_param()` has been implemented by deriving `ArgminSolver`. //! let param = self.cur_param(); //! // Compute gradient at current parameter vector `param` //! // The method `gradient()` has been implemented by deriving `ArgminSolver`. //! let grad = self.gradient(¶m)?; //! // Calculate new parameter vector based on update rule //! let new_param = param.scaled_sub(&self.omega, &grad); //! // Return new parameter vector. Since there is no need to compute the cost function //! // value, we return 0.0 instead. //! let out = ArgminIterData::new(new_param, 0.0); //! Ok(out) //! } //! } //! # fn main() { //! # } //! ``` #![warn(missing_docs)] #![feature(custom_attribute)] #![feature(unrestricted_attribute_tokens)] #![allow(unused_attributes)] // Explicitly disallow EQ comparison of floats. (This clippy lint is denied by default; however, // this is just to make sure that it will always stay this way.) #![deny(clippy::float_cmp)] extern crate argmin_core; #[macro_use] extern crate argmin_codegen; extern crate argmin_testfunctions; extern crate rand; /// Definition of all relevant traits and types pub mod prelude; /// Solvers pub mod solver; /// Macros #[macro_use] mod macros; // #[cfg(test)] // use macros::*; use argmin_core::*; /// Testfunctions pub mod testfunctions { //! # Testfunctions //! //! Reexport of `argmin-testfunctions`. pub use argmin_testfunctions::*; }