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// Copyright 2018-2020 argmin developers // // 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. //! argmin is a numerical optimization toolbox/framework written entirely in Rust. //! This crate is looking for contributors! //! //! [Documentation of most recent release](https://docs.rs/argmin/latest/argmin/) //! //! [Documentation of master](https://argmin-rs.github.io/argmin/argmin/) //! //! # Design goals //! //! argmin aims at offering a wide range of optimization algorithms with a consistent interface, //! written purely in Rust. It comes with additional features such as checkpointing and observers //! which for instance allow one to log the progress of an optimization to screen or file. //! //! In addition it provides a framework for implementing iterative optimization algorithms in a //! convenient manner. Essentially, a single iteration of the algorithm needs to be implemented and //! everything else, such as handling termination, parameter vectors, gradients and Hessians, is //! taken care of by the library. //! //! This library makes heavy use of generics in order to be as type-agnostic as possible. It //! supports `nalgebra` and `ndarray` types via feature gates, but custom types can easily be made //! compatible with argmin by implementing the respective traits. //! //! Future plans include functionality for easy performance evaluation of optimization algorithms, //! parallel computation of cost functions/gradients/Hessians as well as GPU support //! And of course more optimization algorithms! //! //! # Contributing //! //! This crate is looking for contributors! //! Potential projects can be found in the //! [Github issues](https://github.com/argmin-rs/argmin/issues), but even if you have an idea that //! is not already mentioned there or if you found a bug, feel free to open a new issue. //! Besides adding optimization methods and new features, other contributions are also highly //! welcome, for instance improving performance, documentation, writing examples (with real world //! problems), developing tests, adding observers, implementing a C interface or //! [Python wrappers](https://github.com/argmin-rs/pyargmin). //! //! # 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) //! - [L-BFGS](solver/quasinewton/lbfgs/struct.LBFGS.html) //! - [DFP](solver/quasinewton/dfp/struct.DFP.html) //! - [SR1](solver/quasinewton/sr1/struct.SR1.html) //! - [SR1-TrustRegion](solver/quasinewton/sr1_trustregion/struct.SR1TrustRegion.html) //! - [Gauss-Newton method](solver/gaussnewton/gaussnewton/struct.GaussNewton.html) //! - [Gauss-Newton method with linesearch](solver/gaussnewton/gaussnewton_linesearch/struct.GaussNewtonLS.html) //! - [Golden-section search](solver/goldensectionsearch/struct.GoldenSectionSearch.html) //! - [Landweber iteration](solver/landweber/struct.Landweber.html) //! - [Brent's method](solver/brent/struct.Brent.html) //! - [Nelder-Mead method](solver/neldermead/struct.NelderMead.html) //! - [Simulated Annealing](solver/simulatedannealing/struct.SimulatedAnnealing.html) //! - [Particle Swarm Optimization](solver/particleswarm/struct.ParticleSwarm.html) //! //! # Usage //! //! Add this to your `Cargo.toml`: //! //! ```toml //! [dependencies] //! argmin = "0.4.7" //! ``` //! //! ## Optional features (recommended) //! //! There are additional features which can be activated in `Cargo.toml`: //! //! ```toml //! [dependencies] //! argmin = { version = "0.4.7", features = ["ctrlc", "ndarrayl", "nalgebral"] } //! ``` //! //! 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`, `ndarray-linalg` and `ndarray-rand`. //! - `nalgebral`: Support for `nalgebra`. //! //! Using the `ndarrayl` feature on Windows might require to explicitly choose the `ndarray-linalg` //! BLAS backend in the `Cargo.toml`: //! //! ```toml //! ndarray-linalg = { version = "*", features = ["intel-mkl-static"] } //! ``` //! //! ## Running the tests and building the examples //! //! Running the tests requires the `ndarrayl` and feature to be enabled: //! //! ```bash //! cargo test --features "ndarrayl" //! ``` //! //! The examples require all features to be enabled: //! //! ```bash //! cargo test --features --all-features //! ``` //! //! # 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, `Hessian` is the type of the Hessian and `Jacobian` is the type of the //! Jacobian. //! 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`. //! - `hessian(&self, p: &Self::Param) -> Result<Self::Hessian, Error>`: Computes the Hessian //! at `p`. //! - `jacobian(&self, p: &Self::Param) -> Result<Self::Jacobian, Error>`: Computes the Jacobian //! at `p`. //! //! 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::*; //! //! /// First, create a struct for your problem //! struct Rosenbrock { //! a: f64, //! b: f64, //! } //! //! /// Implement `ArgminOp` for `Rosenbrock` //! impl ArgminOp for Rosenbrock { //! /// Type of the parameter vector //! type Param = Vec<f64>; //! /// Type of the return value computed by the cost function //! type Output = f64; //! /// Type of the Hessian. Can be `()` if not needed. //! type Hessian = Vec<Vec<f64>>; //! /// Type of the Jacobian. Can be `()` if not needed. //! type Jacobian = (); //! /// Floating point precision //! type Float = f64; //! //! /// Apply the cost function to a parameter `p` //! fn apply(&self, p: &Self::Param) -> Result<Self::Output, Error> { //! Ok(rosenbrock_2d(p, self.a, self.b)) //! } //! //! /// Compute the gradient at parameter `p`. //! fn gradient(&self, p: &Self::Param) -> Result<Self::Param, Error> { //! Ok(rosenbrock_2d_derivative(p, self.a, self.b)) //! } //! //! /// Compute the Hessian at parameter `p`. //! fn hessian(&self, p: &Self::Param) -> Result<Self::Hessian, Error> { //! let t = rosenbrock_2d_hessian(p, self.a, self.b); //! Ok(vec![vec![t[0], t[1]], vec![t[2], t[3]]]) //! } //! } //! ``` //! //! It is optional to implement any of these methods, as there are default implementations which //! will return an `Err` when called. What needs to be implemented is defined by the requirements //! of the solver that is to be used. //! //! # Running a solver //! //! The following example shows how to use the previously shown definition of a problem in a //! Steepest Descent (Gradient Descent) solver. //! //! ```rust //! # #![allow(unused_imports)] //! # extern crate argmin; //! # extern crate argmin_testfunctions; //! use argmin::prelude::*; //! use argmin::solver::gradientdescent::SteepestDescent; //! use argmin::solver::linesearch::MoreThuenteLineSearch; //! # use argmin_testfunctions::{rosenbrock_2d, rosenbrock_2d_derivative}; //! # use instant; //! # //! # struct Rosenbrock { //! # a: f64, //! # b: f64, //! # } //! # //! # impl ArgminOp for Rosenbrock { //! # type Param = Vec<f64>; //! # type Output = f64; //! # type Hessian = (); //! # type Jacobian = (); //! # type Float = f64; //! # //! # fn apply(&self, p: &Self::Param) -> Result<Self::Output, Error> { //! # Ok(rosenbrock_2d(p, self.a, self.b)) //! # } //! # //! # fn gradient(&self, p: &Self::Param) -> Result<Self::Param, Error> { //! # Ok(rosenbrock_2d_derivative(p, self.a, self.b)) //! # } //! # } //! # //! # fn run() -> Result<(), Error> { //! //! // Define cost function (must implement `ArgminOperator`) //! let cost = Rosenbrock { a: 1.0, b: 100.0 }; //! //! // Define initial parameter vector //! let init_param: Vec<f64> = vec![-1.2, 1.0]; //! //! // Set up line search //! let linesearch = MoreThuenteLineSearch::new(); //! //! // Set up solver //! let solver = SteepestDescent::new(linesearch); //! //! // Run solver //! let res = Executor::new(cost, solver, init_param) //! // Add an observer which will log all iterations to the terminal //! .add_observer(ArgminSlogLogger::term(), ObserverMode::Always) //! // Set maximum iterations to 10 //! .max_iters(10) //! // run the solver on the defined problem //! .run()?; //! # //! # // Wait a second (lets the logger flush everything first) //! # std::thread::sleep(instant::Duration::from_secs(1)); //! //! // print result //! println!("{}", res); //! # Ok(()) //! # } //! # //! # fn main() { //! # if let Err(ref e) = run() { //! # println!("{}", e); //! # std::process::exit(1); //! # } //! # } //! ``` //! //! # Observing iterations //! //! Argmin offers an interface to observe the state of the iteration at initialization as well as //! after every iteration. This includes the parameter vector, gradient, Hessian, iteration number, //! cost values and many more as well as solver-specific metrics. This interface can be used to //! implement loggers, send the information to a storage or to plot metrics. //! Observers need to implment the `Observe` trait. //! Argmin ships with a logger based on the `slog` crate. `ArgminSlogLogger::term` logs to the //! terminal and `ArgminSlogLogger::file` logs to a file in JSON format. Both loggers also come //! with a `*_noblock` version which does not block the execution of logging, but may drop some //! messages if the buffer is full. //! Parameter vectors can be written to disc using `WriteToFile`. //! For each observer it can be defined how often it will observe the progress of the solver. This //! is indicated via the enum `ObserverMode` which can be either `Always`, `Never`, `NewBest` //! (whenever a new best solution is found) or `Every(i)` which means every `i`th iteration. //! //! ```rust //! # #![allow(unused_imports)] //! # extern crate argmin; //! # extern crate argmin_testfunctions; //! # use argmin::prelude::*; //! # use argmin::solver::gradientdescent::SteepestDescent; //! # use argmin::solver::linesearch::MoreThuenteLineSearch; //! # use argmin_testfunctions::{rosenbrock_2d, rosenbrock_2d_derivative}; //! # //! # struct Rosenbrock { //! # a: f64, //! # b: f64, //! # } //! # //! # impl ArgminOp for Rosenbrock { //! # type Param = Vec<f64>; //! # type Output = f64; //! # type Hessian = (); //! # type Jacobian = (); //! # type Float = f64; //! # //! # fn apply(&self, p: &Self::Param) -> Result<Self::Output, Error> { //! # Ok(rosenbrock_2d(p, self.a, self.b)) //! # } //! # //! # fn gradient(&self, p: &Self::Param) -> Result<Self::Param, Error> { //! # Ok(rosenbrock_2d_derivative(p, self.a, self.b)) //! # } //! # } //! # //! # fn run() -> Result<(), Error> { //! # //! # // Define cost function (must implement `ArgminOperator`) //! # let problem = Rosenbrock { a: 1.0, b: 100.0 }; //! # //! # // Define initial parameter vector //! # let init_param: Vec<f64> = vec![-1.2, 1.0]; //! # //! # // Set up line search //! # let linesearch = MoreThuenteLineSearch::new(); //! # //! # // Set up solver //! # let solver = SteepestDescent::new(linesearch); //! # //! let res = Executor::new(problem, solver, init_param) //! // Add an observer which will log all iterations to the terminal (without blocking) //! .add_observer(ArgminSlogLogger::term_noblock(), ObserverMode::Always) //! // Log to file whenever a new best solution is found //! .add_observer(ArgminSlogLogger::file("solver.log", false)?, ObserverMode::NewBest) //! // Write parameter vector to `params/param.arg` every 20th iteration //! .add_observer(WriteToFile::new("params", "param"), ObserverMode::Every(20)) //! # .max_iters(2) //! // run the solver on the defined problem //! .run()?; //! # Ok(()) //! # } //! # //! # fn main() { //! # if let Err(ref e) = run() { //! # println!("{}", e); //! # std::process::exit(1); //! # } //! # } //! ``` //! //! # Checkpoints //! //! The probability of crashes increases with runtime, therefore one may want to save checkpoints //! in order to be able to resume the optimization after a crash. //! The `CheckpointMode` defines how often checkpoints are saved and is either `Never` (default), //! `Always` (every iteration) or `Every(u64)` (every Nth iteration). It is set via the setter //! method `checkpoint_mode` of `Executor`. //! In addition, the directory where the checkpoints and a prefix for every file can be set via //! `checkpoint_dir` and `checkpoint_name`, respectively. //! //! The following example shows how the `from_checkpoint` method can be used to resume from a //! checkpoint. In case this fails (for instance because the file does not exist, which could mean //! that this is the first run and there is nothing to resume from), it will resort to creating a //! new `Executor`, thus starting from scratch. //! //! ```rust //! # extern crate argmin; //! # extern crate argmin_testfunctions; //! # use argmin::prelude::*; //! # use argmin::solver::landweber::*; //! # use argmin_testfunctions::{rosenbrock_2d, rosenbrock_2d_derivative}; //! # use argmin::core::Error; //! # use instant; //! # //! # #[derive(Default)] //! # struct Rosenbrock {} //! # //! # impl ArgminOp for Rosenbrock { //! # type Param = Vec<f64>; //! # type Output = f64; //! # type Hessian = (); //! # type Jacobian = (); //! # type Float = f64; //! # //! # 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> { //! # // define inital parameter vector //! # let init_param: Vec<f64> = vec![1.2, 1.2]; //! # //! # let iters = 35; //! # let solver = Landweber::new(0.001); //! # //! let res = Executor::from_checkpoint(".checkpoints/optim.arg", Rosenbrock {}) //! .unwrap_or(Executor::new(Rosenbrock {}, solver, init_param)) //! .max_iters(iters) //! .checkpoint_dir(".checkpoints") //! .checkpoint_name("optim") //! .checkpoint_mode(CheckpointMode::Every(20)) //! .run()?; //! # //! # // Wait a second (lets the logger flush everything before printing to screen again) //! # std::thread::sleep(instant::Duration::from_secs(1)); //! # println!("{}", res); //! # Ok(()) //! # } //! # //! # fn main() { //! # if let Err(ref e) = run() { //! # println!("{}", e); //! # } //! # } //! ``` //! //! # 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 specific to the solver. Then, the `Solver` trait needs to be implemented for the //! struct. This requires setting the associated constant `NAME` which gives your solver a name. //! The `next_iter` method defines the computations performed in a single iteration of the solver. //! Via the parameters `op` and `state` one has access to the operator (cost function, gradient //! computation, Hessian, ...) and to the current state of the optimization (parameter vectors, //! cost function values, iteration number, ...), respectively. //! //! ```rust //! use argmin::prelude::*; //! use serde::{Deserialize, Serialize}; //! //! // Define a struct which holds any parameters/data which are needed during the execution of the //! // solver. Note that this does not include parameter vectors, gradients, Hessians, cost //! // function values and so on, as those will be handled by the `Executor`. //! #[derive(Serialize, Deserialize)] //! pub struct Landweber<F> { //! /// omega //! omega: F, //! } //! //! impl<F> Landweber<F> { //! /// Constructor //! pub fn new(omega: F) -> Self { //! Landweber { omega } //! } //! } //! //! impl<O, F> Solver<O> for Landweber<F> //! where //! // `O` always needs to implement `ArgminOp` //! O: ArgminOp<Float = F>, //! // `O::Param` needs to implement `ArgminScaledSub` because of the update formula //! O::Param: ArgminScaledSub<O::Param, O::Float, O::Param>, //! F: ArgminFloat, //! { //! // This gives the solver a name which will be used for logging //! const NAME: &'static str = "Landweber"; //! //! // Defines the computations performed in a single iteration. //! fn next_iter( //! &mut self, //! // This gives access to the operator supplied to the `Executor`. `O` implements //! // `ArgminOp` and `OpWrapper` takes care of counting the calls to the respective //! // functions. //! op: &mut OpWrapper<O>, //! // Current state of the optimization. This gives access to the parameter vector, //! // gradient, Hessian and cost function value of the current, previous and best //! // iteration as well as current iteration number, and many more. //! state: &IterState<O>, //! ) -> Result<ArgminIterData<O>, Error> { //! // First we obtain the current parameter vector from the `state` struct (`x_k`). //! let xk = state.get_param(); //! // Then we compute the gradient at `x_k` (`\nabla f(x_k)`) //! let grad = op.gradient(&xk)?; //! // Now subtract `\nabla f(x_k)` scaled by `omega` from `x_k` to compute `x_{k+1}` //! let xkp1 = xk.scaled_sub(&self.omega, &grad); //! // Return new paramter vector which will then be used by the `Executor` to update //! // `state`. //! Ok(ArgminIterData::new().param(xkp1)) //! } //! } //! ``` //! //! //! # License //! //! Licensed under either of //! //! * Apache License, Version 2.0, //! ([LICENSE-APACHE](https://github.com/argmin-rs/argmin/blob/master/LICENSE-APACHE) or //! http://www.apache.org/licenses/LICENSE-2.0) //! * MIT License ([LICENSE-MIT](https://github.com/argmin-rs/argmin/blob/master/LICENSE-MIT) or //! http://opensource.org/licenses/MIT) //! //! at your option. //! //! ## Contribution //! //! Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion //! in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, //! without any additional terms or conditions. #![warn(missing_docs)] #![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 rand; /// Core functionality #[macro_use] pub mod core; /// Definition of all relevant traits and types pub mod prelude; /// Solvers pub mod solver; /// Macros #[macro_use] mod macros; #[cfg(test)] mod tests;