gleastsq

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

Levenberg-Marquardt vs Leasts Squares for curve fitting

The library provides two functions for curve fitting: least_squares and levenberg_marquardt.

Least Squares

The least_squares function is generally simpler and faster but may not converge for some functions, specially for non-linear functions. It is generally recommended for simpler models where the relationship between the parameters and the function is linear.

Levenberg-Marquardt

The levenberg_marquardt function is more robust but may be slower due to the extra calculations. It is generally recommended for non-linear functions where the relationship between the parameters and the function is non-linear.

Installation

gleam add gleastsq

import gleam/option.{None}
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.