gleastsq

Functions

least_squares

pub fn least_squares(
  x: List(Float),
  y: List(Float),
  func: fn(Float, List(Float)) -> Float,
  initial_params: List(Float),
  max_iterations iterations: Option(Int),
  epsilon epsilon: Option(Float),
  tolerance tolerance: Option(Float),
  lambda_reg lambda_reg: Option(Float),
) -> Result(List(Float), FitErrors)

The least_squares function performs a basic least squares optimization algorithm. It is used to find the best-fit parameters for a given model function to a set of data points. This function takes as input the data points, the model function, and several optional parameters to control the optimization process.

Parameters

x (List(Float)) A list of x-values of the data points.
y (List(Float)) A list of y-values of the data points.
func (fn(Float, List(Float)) -> Float) The model function that takes an x-value and a list of parameters, and returns the corresponding y-value.
initial_params (List(Float)) A list of initial guesses for the parameters of the model function.
iterations (Option(Int)) The maximum number of iterations to perform. Default is 100.
epsilon (Option(Float)) A small value to change x when calculating the derivatives for the function. Default is 0.0001.
tolerance (Option(Float)) The convergence tolerance. Default is 0.0001.
lambda_reg (Option(Float)) The regularization parameter. Default is 0.0001.

levenberg_marquardt

</>

pub fn levenberg_marquardt(
  x: List(Float),
  y: List(Float),
  func: fn(Float, List(Float)) -> Float,
  initial_params: List(Float),
  max_iterations iterations: Option(Int),
  epsilon epsilon: Option(Float),
  tolerance tolerance: Option(Float),
  damping damping: Option(Float),
  damping_increase damping_increase: Option(Float),
  damping_decrease damping_decrease: Option(Float),
) -> Result(List(Float), FitErrors)

The levenberg_marquardt function performs the Levenberg-Marquardt optimization algorithm. It is used to solve non-linear least squares problems. This function takes as input the data points, the model function, and several optional parameters to control the optimization process.

Parameters

x (List(Float)) A list of x-values of the data points.
y (List(Float)) A list of y-values of the data points.
func (fn(Float, List(Float)) -> Float) The model function that takes an x-value and a list of parameters, and returns the corresponding y-value.
initial_params (List(Float)) A list of initial guesses for the parameters of the model function.
iterations (Option(Int)) The maximum number of iterations to perform. Default is 100.
epsilon (Option(Float)) A small value to change x when calculating the derivatives for the function. Default is 0.0001.
tolerance (Option(Float)) The convergence tolerance. Default is 0.0001.
damping (Option(Float)) The initial value of the damping parameter. Default is 0.0001.
damping_increase (Option(Float)) The factor by which the damping parameter is increased when a step fails. Default is 10.0.
damping_decrease (Option(Float)): The factor by which the damping parameter is decreased when a step succeeds. Default is 0.1.