Newton based methods for rootfinding

This crate allows you to use Newton's method for rootfinding.

It aims to implement several Newton based methods (Broyden, ...), whether the jacobian function is provided or not.

It also aims to work on a complex model, limiting the number of model calls to a minimum.

A minimal solver is also provided for basic usages and benchmarking purposes.

Minimal solver

A minimal solver is provided for basic usages in the solver module.

This minimal solver works only on basic 1D functions.

The speed of the advanced solver will be benchmarked against this one to estimate the overhead.

Examples

```rust extern crate newtonrootfinder as nrf; use nrf::solverminimal::{solver1d, solver1d_fd};

fn square2(x: f64) -> f64 { x.powi(2)-2.0 } fn dsquare(x: f64) -> f64 { 2.0*x }

fn main() { let maxiter = 50; let tolerance = 1e-6; let finitediff_dx = 1e-8;

let x1 = solver1d(1.0, square2, dsquare, max_iter, tolerance);
let x2 = solver1d_fd(1.0, square2, max_iter, tolerance, finite_diff_dx);

println!("{}", x1);                         // 1.4142135623746899
println!("{}", x2);                         // 1.4142135623746772
println!("{}", std::f64::consts::SQRT_2);   // 1.4142135623730951

} ```

Advanced solver

An advanced solver is available for n-dimension problems.

To get improved interactions with the user problem (usually a function), the user is required to implement the Model trait in order to use the solver. This ensures a reduced number of calls to the function and a better debugging experience if needed.

It is defined in the solver_advanced module. Don't hesitate to check in this module documentation for examples.

The focus of this crate is the development of this solver.

Key features

1. Works whether the jacobian is provided or not (evaluating it with finite-differentiation).
2. In-detail parametrization of iterative variables, residuals and stopping criteria.
3. Debugging informations available through a .txt log file.
4. The advanced solver is designed to interact with a complex model computing other outputs and having memory effects. The requirements of this model are defined by the Model trait. The struct UserModelWithFunc is provided to easily adapt a given function to the required trait.
5. Real world use cases and an extensive function database are included in the crate for integration testing and benchmarking. (work in progress)

Current limitations

1. The inputs and outputs of the model are assumed to be nalgebra vectors.
2. The test base is still in construction
3. The documentation is not exhaustive
4. Other resolution methods (Broyden, ...) are not available

Comparison with other rust crates

Note: Crates may have evolved since this comparison was established.

N-dimensional :

| crate | version | Advanced
Parametrization | Simulation
Log | Other iterative
algorithms | |-----------------------|--------:|:-----------------------------:|:-------------------:|-------------------------------:| | newton_rootfinder | 0.3.0 | ✔️ | ✔️ | ❌ (not yet) | | peroxide | 0.21.7 | ❌ | ❌ | ❌ |

If you are looking for one dimensional crates, several options are available. As a reminder, the focus of newton_rootfinder is NOT the development of the 1D solver.

One dimension :

| crate | version | Newton-Raphson | Other Iterative methods | Analytical methods | |-----------------------|--------:|---------------:|------------------------:|--------------------:| | newton_rootfinder | 0.3.0 | ✔️ | ❌ | ❌ | | newton-raphson | 0.1.0 | ✔️ | ❌ | ❌ | | nrfind | 1.0.3 | ✔️ | ❌ | ❌ | | rootfind | 0.7.0 | ✔️ | ✔️ | ❌ | | roots | 0.6.0 | ✔️ | ✔️ | ✔️ | | peroxide | 0.21.7 | ✔️ | ❌ | ❌ |