npm install levenbergmarquardt.js@1.0.3<script src="https://cdn.jsdelivr.net/gh/pterodactylus/levenbergmarquardt.js@latest/js/lm.min.js"></script>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.
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} = MultiFunctionSolver.solve(equations, initialGuess);
console.log('Solution:', solution);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} = MultiFunctionSolver.solve(nonlinearEquations, initialGuessNonlinear);
console.log('Nonlinear Solution:', solution);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} = MultiFunctionSolver.solve(fittingFunction, initialGuessFitting);
console.log('Fitting Parameters:', solution);