readme.md

Getting Started

Install via npm:

npm config set registry https://registry.npmjs.org/
npm i levenbergmarquardt.js

Or import via ES6 CDN:

<script type="module">
  import LevenbergMarquardtSolver from "https://cdn.jsdelivr.net/gh/pterodactylus/levenbergmarquardt.js@latest/js/lm.min.js"
  //Your code here....
</script>

Levenberg Marquardt Solver Examples

This README provides examples of how to use a non-linear least squares multi-function solver. Each example outlines different scenarios and mathematical problems being solved.

Example 1: System of Linear Equations

Solving a system of linear equations can be fundamental yet crucial. Here, we address the system:

$$ \begin{align*} x + 2y &= 5 \\ 3x + 4y &= 11 \end{align*} $$

Here's how you could set up the solver:

const equations = (vars) => [
  vars[0] + 2 * vars[1] - 5,
  3 * vars[0] + 4 * vars[1] - 11
];

const initialGuess = [0, 0];
const {solution, status, iterationData} = LevenbergMarquardtSolver.solve(equations, initialGuess);
console.log('Solution:', solution);

Example 2: Nonlinear System

For nonlinear systems, which are more complex and prevalent in real-world applications, consider the following example where we solve the equations:

$$ \begin{align*} x^2 + y^2 &= 4 \\ e^x + y &= 1 \end{align*} $$

Here's the setup:

const nonlinearEquations = (vars) => [
  vars[0]**2 + vars[1]**2 - 4,
  Math.exp(vars[0]) + vars[1] - 1
];

const initialGuessNonlinear = [1, 1];
const {solution, status, iterationData} = LevenbergMarquardtSolver.solve(nonlinearEquations, initialGuessNonlinear);
console.log('Nonlinear Solution:', solution);

Example 3: Fitting Data

Data fitting is a common problem in statistics and machine learning. Here, we fit a quadratic curve (y = ax^2 + bx + c) to a set of data points.

const xData = [0, 1, 2, 3, 4];
const yData = [1, 2.1, 3.9, 8, 15.9];

const fittingFunction = (params) => xData.map((x, idx) => params[0] * x**2 + params[1] * x + params[2] - yData[idx]);

const initialGuessFitting = [1, 1, 1];
const {solution, status, iterationData} = LevenbergMarquardtSolver.solve(fittingFunction, initialGuessFitting);
console.log('Fitting Parameters:', solution);