# 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.