Crate 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 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_minimal module. Don't hesitate to check in this module documentation for examples.

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.

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 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. Several Newton-based methods will be made available (not yet)
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. Only the finite-difference version is currently available.
3. Benchmarking vs the minimal-solver is not yet in place.

Comparison with other rust crates

Note: Crates may have evolved since this comparison 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.

Modules

model	The rootfinder is operating on a Model
model_with_func	Blanket implementation to easily adapt user function to the Model trait required by the solver
solver	Advanced solver
solver_minimal	Minimal 1d solver
util	Definition of the structure of the resolution parameters