Module newton_rootfinder::solver

Solver configuration

The solver is defined in the RootFinder struct.

To create a new solver, it is required to give the 4 following:

• The parameters through the SolverParameters struct
• The iteratives configuration through a reference to a slice of Iteratives
• The residuals configuration through a reference to a slice of ResidualsConfig
• The initial guess to use by the solver

Features

1. Simulation log available for debugging, check the set_debug() method
2. Damping, check the set_damping() method

Examples

use newton_rootfinder as nrf;
use nrf::model::Model;
use nrf::iteratives;
use nrf::residuals;
use nrf::solver::ResolutionMethod;

/// Equation : x**2 - 2 = 0
fn square2(x: &nalgebra::DVector<f64>) -> nalgebra::DVector<f64> {
    let mut y = x * x;
    y[0] -= 2.0;
    y
}

fn main() {
  let problem_size = 1;
  let init_guess = nalgebra::DVector::from_vec(vec![1.0]);
  let vec_iter_params = iteratives::default_vec_iteratives_fd(problem_size);
  let iter_params = iteratives::Iteratives::new(&vec_iter_params);
  let stopping_residuals = vec![residuals::NormalizationMethod::Abs; problem_size];
  let update_methods = vec![residuals::NormalizationMethod::Abs; problem_size];
  let res_config = residuals::ResidualsConfig::new(&stopping_residuals, &update_methods);
  let damping = false;
  let mut rf = nrf::solver::default_with_guess(init_guess, &iter_params, &res_config, ResolutionMethod::NewtonRaphson, damping);
  let mut user_model =
      nrf::model::UserModelFromFunction::new(problem_size, square2);

  rf.solve(&mut user_model).unwrap();

  println!("{}", user_model.get_iteratives()[0]);
  // print 1.4142135623747443
}

Structs

JacobianMatrix

RootFinder

Solver for rootfinding

SolverParameters

A minimal struct holding the resolution parameters

Enums

QuasiNewtonMethod

Quasi-Newton methods are less computationnaly expensive than the Newton-Raphson method.

ResolutionMethod

Choice of the iterative algorithm for the resolution

UpdateQuasiNewtonMethod

This quasi-Newton methods either work on the jacobian or its inverse

Functions

approximate_inv_jacobian

approximate_jacobian

broyden_first_method_udpate_inv_jac

Broyden first method update formula

broyden_first_method_udpate_jac

Broyden first method update formula

broyden_second_method_udpate_inv_jac

Broyden Second method update formula

broyden_second_method_udpate_jac

Broyden second method update formula

compute_jacobian_from_finite_difference

Evaluate a jacobian per forward finite difference when perturbation step eps is provided

default_with_guess

Default function to create a solver with default parameters

evaluate_jacobian_from_analytical_function

evaluate_jacobian_from_finite_difference

greenstadt_second_method_udpate_jac

Greenstadt second method update formula

quasi_method_update_inv_jac

Generic function for quasi method update. This implements Spedicato’s formula. To be used when no formula simplification can be done before implementation

quasi_method_update_jac

Generic function for quasi method update. This implements Spedicato’s formula. To be used when no formula simplification can be done before implementation