-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Pure Haskell implementation of the Levenberg-Marquardt algorithm
--   
--   The Levenberg-Marquardt algorithm is a minimization algorithm for
--   functions expressed as a sum of squared errors
--   
--   This can be used for curve-fitting, multidimensional function
--   optimization, or neural networks training
--   
--   Go to <a>https://github.com/ktklam9/HaskellLM</a> for example usage
--   (in tests)
@package HaskellLM
@version 0.1.0


-- | The Levenberg-Marquardt algorithm is a minimization algorithm for
--   functions expressed as a sum of squared errors
--   
--   This can be used for curve-fitting, multidimensional function
--   optimization, or neural networks training
module Math.LevenbergMarquardt

-- | Type that represents the function that can calculate the residues
type Function = Vector Double -> Vector Double

-- | Type that represents the function that can calculate the jacobian
--   matrix of the residue with respect to each parameter
type Jacobian = Vector Double -> Matrix Double

-- | Evolves the parameter x for f(x) = sum-square(e(x)) so that f(x) will
--   be minimized, where:
--   
--   f = real-valued error function, e(x) = {e1(x),e2(x),..,eN(x)}, where
--   e1(x) = the residue at the vector x
--   
--   NOTE: eN(x) is usually represented as (sample - hypothesis(x))
--   
--   e.g.: In training neural networks, hypothesis(x) would be the
--   network's output for a training set, and sample would be the expected
--   output for that training set
--   
--   NOTE: The dampening constant(lambda) should be set to 0.01 and the
--   dampening update value (beta) should be set to be 10
lmMinimize :: Function -> Jacobian -> Vector Double -> Double -> Double -> Double -> Int -> (Vector Double, Matrix Double)