-------------------------------------------------------------------------------- -- | -- Module : LevMar.Intermediate.Fitting -- Copyright : (c) 2009 Roel van Dijk & Bas van Dijk -- License : BSD-style (see the file LICENSE) -- -- Maintainer : vandijk.roel@gmail.com, v.dijk.bas@gmail.com -- Stability : Experimental -- -- This module provides the Levenberg-Marquardt algorithm specialised -- for curve-fitting. -- -- For additional documentation see the documentation of the levmar C -- library which this library is based on: -- <http://www.ics.forth.gr/~lourakis/levmar/> -- -------------------------------------------------------------------------------- module LevMar.Intermediate.Fitting ( -- * Model & Jacobian. Model , SimpleModel , Jacobian , SimpleJacobian -- * Levenberg-Marquardt algorithm. , LMA_I.LevMarable , levmar , LMA_I.LinearConstraints -- * Minimization options. , LMA_I.Options(..) , LMA_I.defaultOpts -- * Output , LMA_I.Info(..) , LMA_I.StopReason(..) , LMA_I.CovarMatrix , LMA_I.LevMarError(..) ) where import qualified LevMar.Intermediate as LMA_I -------------------------------------------------------------------------------- -- Model & Jacobian. -------------------------------------------------------------------------------- {- | A functional relation describing measurements represented as a function from a list of parameters and an x-value to an expected measurement. * Ensure that the length of the parameters list equals the lenght of the initial parameters list in 'levmar'. For example, the quadratic function @f(x) = a*x^2 + b*x + c@ can be written as: @ quad :: 'Num' r => 'Model' r r quad [a, b, c] x = a*x^2 + b*x + c @ -} type Model r a = [r] -> a -> r -- | This type synonym expresses that usually the @a@ in @'Model' r a@ -- equals the type of the parameters. type SimpleModel r = Model r r {- | The jacobian of the 'Model' function. Expressed as a function from a list of parameters and an x-value to the partial derivatives of the parameters. See: <http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant> * Ensure that the length of the parameters list equals the lenght of the initial parameters list in 'levmar'. * Ensure that the length of the output parameter derivatives list equals the length of the input parameters list. For example, the jacobian of the above @quad@ model can be written as: @ quadJacob :: 'Num' r => 'Jacobian' N3 r r quadJacob [_, _, _] x = [ x^2 -- with respect to a , x -- with respect to b , 1 -- with respect to c ] @ Notice you don't have to differentiate for @x@. -} type Jacobian r a = [r] -> a -> [r] -- | This type synonym expresses that usually the @a@ in @'Jacobian' r a@ -- equals the type of the parameters. type SimpleJacobian r = Jacobian r r -------------------------------------------------------------------------------- -- Levenberg-Marquardt algorithm. -------------------------------------------------------------------------------- -- | The Levenberg-Marquardt algorithm specialised for curve-fitting. levmar :: LMA_I.LevMarable r => Model r a -- ^ Model -> Maybe (Jacobian r a) -- ^ Optional jacobian -> [r] -- ^ Initial parameters -> [(a, r)] -- ^ Samples -> Integer -- ^ Maximum iterations -> LMA_I.Options r -- ^ Minimization options -> Maybe [r] -- ^ Optional lower bounds -> Maybe [r] -- ^ Optional upper bounds -> Maybe (LMA_I.LinearConstraints r) -- ^ Optional linear constraints -> Maybe [r] -- ^ Optional weights -> Either LMA_I.LevMarError ([r], LMA_I.Info r, LMA_I.CovarMatrix r) levmar model mJac params samples = LMA_I.levmar (convertModel model) (fmap convertJacob mJac) params ys where (xs, ys) = unzip samples convertModel mdl = \ps -> map (mdl ps) xs convertJacob jac = \ps -> map (jac ps) xs -- The End ---------------------------------------------------------------------