@spec levenberg_marquardt(
  [float()],
  [float()],
  (float(), [float()] -> float()),
  (float(), [float()] -> [float()]),
  [float()],
  keyword()
) :: {:ok, map()} | {:error, term()}

Levenberg-Marquardt nonlinear least squares optimization.

Fits parameters to minimize the sum of squared residuals between the model predictions and observed data.

Parameters

• x - Independent variable values (list of floats)
• y - Observed dependent variable values (list of floats)
• model_fn - Function (x, params) -> y_predicted where params is a list
• jacobian_fn - Function (x, params) -> [dy/dp1, dy/dp2, ...] partial derivatives
• initial_params - Initial parameter guesses (list of floats)
• opts - Options:
  • :max_iterations - Maximum iterations (default: 100)
  • :tolerance - Convergence tolerance for parameter change (default: 1.0e-8)
  • :lambda - Initial damping factor (default: 0.001)

Returns

{:ok, %{params: [...], iterations: n, final_error: e}} on success, {:error, reason} on failure.

Example

# Fit y = a * x + b
model = fn x, [a, b] -> a * x + b end
jacobian = fn x, [_a, _b] -> [x, 1.0] end

{:ok, result} = Nanodrop.Math.levenberg_marquardt(
  x_data, y_data, model, jacobian, [1.0, 0.0]
)