gleastsq - v0.5.0

gleastsq

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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 four functions for curve fitting: least_squares, gauss_newton, levenberg_marquardt and trust_region_reflective.

Least Squares

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

Levenberg-Marquardt

Ideal for non-linear least squares problems, particularly when the initial guess is far from the solution. It combines the benefits of the Gauss-Newton method and gradient descent, making it robust and efficient for various scenarios. However, it requires careful tuning of the damping parameter to balance convergence speed and stability.

Trust-Region Reflective

Best suited for large-scale problems or those with constraints, this method ensures that each iteration stays within a predefined “trust region,” preventing large, unstable steps. It is reliable and effective for challenging optimization problems but can be computationally intensive.

Gauss-Newton

Efficient for problems where residuals are small and the initial guess is close to the true solution. It approximates the Hessian matrix, leading to faster convergence for well-behaved problems. However, it may struggle with highly non-linear problems or poor initial guesses, as it lacks the robustness of the Levenberg-Marquardt and trust-region reflective methods.

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.

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