gleastsq

A least squares curve fitting library for Gleam. This library uses the Nx library from Elixir under the hood to perform matrix operations.

Which method should I use?

The library provides three functions for curve fitting: least_squares, gauss_newton and levenberg_marquardt.

Least Squares

The least_squares function is just an alias for the levenberg_marquardt function.

Gauss-Newton

The gauss_newton function is best for least squares problems with good initial guesses and small residuals. It is less computationally intensive and thus can be faster than the Levenberg-Marquardt method but can be unstable with poor initial guesses or large residuals.

Levenberg-Marquardt

The levenberg_marquardt function is robust for nonlinear least squares problems, handling large residuals and poor initial guesses effectively. It is more computationally intensive but provides reliable convergence for a wider range of problems, especially in challenging or ill-conditioned cases.

Installation

gleam add gleastsq

import gleam/io
import gleastsq

fn parabola(x: Float, params: List(Float)) -> Float {
  let assert [a, b, c] = params
  a *. x *. x +. b *. x +. c
}

pub fn main() {
  let x = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0]
  let y = [0.0, 1.0, 4.0, 9.0, 16.0, 25.0]
  let initial_guess = [1.0, 1.0, 1.0]

  let assert Ok(result) =
    gleastsq.least_squares(x, y, parabola, initial_guess, opts: [])

  io.debug(result) // [1.0, 0.0, 0.0] (within numerical error)
}

Further documentation can be found at https://hexdocs.pm/gleastsq.