newton_rootfinder: Newton based methods for rootfinding

This crate allows you to use Newton's method for rootfinding. It aims to implement several Newton based method (Broyden, ...), whereas the jacobian function is provided or not. It also aims to work on a complex model, limiting the number of model calls at a minimum. A minimal solver is also provided for basic usages and benchmarking purposes.

Key selling-points

  1. Minimal solver available for basic 1D function. The speed of the industrial solver will be benchmarked vs this one to estimate the overhead cost.
  2. Advanced solver for n-dimension including advanced stopping and update criteria, step limitation and more. It is designed to work with the jacobian provided or not, evaluating it thanks to finite-differentiation.
  3. Model interaction: the advanced solver is designed to interact with a complex model computing others outputs and having memory effects. A definition of such a model is given through the Model trait. The struct UserModelWithFunc is provided to easily adapt model defined with a function to the required trait.
  4. Extended tests examples: the crate aims at having an import functions bases for integration testing and benchmarks, which is not available in plug and play form.

Current limitations

  1. The inputs and outputs of the model are assuming to be vector from the nalgebra crate.
  2. Only the finite-difference version is currently available.
  3. Benchmarking vs the minimal-solver is not in place.

Examples

```rust extern crate newton_rootfinder as nrf; use nrf::model::Model;

extern crate nalgebra;

/// Equation : x**2 - 2 = 0 fn square2(x: &nalgebra::DVector) -> nalgebra::DVector { let mut y = x * x; y[0] -= 2.0; y }

fn main() { let problemsize = 1; let initguess = nalgebra::DVector::fromvec(vec![1.0]); let rf = nrf::solver::RootFinderFD::defaultwithguess(initguess); let mut usermodel = nrf::modelwithfunc::UserModelWithFunc::new(problemsize, square2);

rf.solve(&mut user_model);

println!("{}", usermodel.getiteratives()[0]); // print 1.4142135623747443 } ```

Comparision with other rust libraries

Crates may have evolved since this comparision was established

| crate | version | 1-dimension | n-dimension | Jacobian not required | Other algorithms¹ | |-----------------------|--------:|:------------:|:-----------:|----------------------:|------------------:| | newton_rootfinder | 0.1.0 | ✔️ | ✔️ | ✔️ | ❌ (not yet) | | newton-raphson | 0.1.0 | ✔️ | ❌ | ❌ | ❌ | | nrfind | 1.0.3 | ✔️ | ❌ | ❌ | ❌ | | rootfind | 0.7.0 | ✔️ | ❌ | ❌ | ✔️ | | roots | 0.6.0 | ✔️ | ❌ | ❌ | ✔️ | | peroxide | 0.21.7 | ✔️ | ✔️ | ❌ | ❌ |

  1. Other algorithms than the Newton-Raphson method.