Compute the least squares fit of a function to a set of data points.

Parameters:

• x: The X axis of the data points as a list of floats.
• y: The Y axis of the data points as a list of floats.
• func: The function to fit to the data points. The function should take a float and a list of floats (the function coefficients) as arguments and return a float.
• initial_params: The initial guess for the function coefficients.
• max_iterations: The maximum number of iterations to perform. Default is 100.
• epsilon: The epsilon value for the numerical derivative. Default is 0.0001.
• tolerance: The tolerance for the convergence criterion. Default is 0.0001.
• lambda_reg: The regularization parameter. Default is 0.0001.

Examples

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 = list.map(x, fn(x) { x *. x })
  let initial_guess = [1.0, 1.0, 1.0]

  let assert Ok(result) =
    gleastsq.least_squares(
      x,
      y,
      parabola,
      initial_guess,
      max_iterations: None,
      epsilon: None,
      tolerance: None,
      lambda_reg: None,
    )

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