{- | Module : Numeric.GSL.Fitting Copyright : (c) Alberto Ruiz 2010 License : GPL Maintainer : Alberto Ruiz (aruiz at um dot es) Stability : provisional Portability : uses ffi Nonlinear Least-Squares Fitting The example program in the GSL manual (see examples/fitting.hs): @dat = [ ([0.0],([6.0133918608118675],0.1)), ([1.0],([5.5153769909966535],0.1)), ([2.0],([5.261094606015287],0.1)), ... ([39.0],([1.0619821710802808],0.1))] expModel [a,lambda,b] [t] = [a * exp (-lambda * t) + b] expModelDer [a,lambda,b] [t] = [[exp (-lambda * t), -t * a * exp(-lambda*t) , 1]] (sol,path) = fitModelScaled 1E-4 1E-4 20 (expModel, expModelDer) dat [1,0,0] \> path (6><5) [ 1.0, 76.45780563978782, 1.6465931240727802, 1.8147715267618197e-2, 0.6465931240727797 , 2.0, 37.683816318260355, 2.858760367632973, 8.092094813253975e-2, 1.4479636296208662 , 3.0, 9.5807893736187, 4.948995119561291, 0.11942927999921617, 1.0945766509238248 , 4.0, 5.630494933603935, 5.021755718065913, 0.10287787128056883, 1.0338835440862608 , 5.0, 5.443976278682909, 5.045204331329302, 0.10405523433131504, 1.019416067207375 , 6.0, 5.4439736648994685, 5.045357818922331, 0.10404905846029407, 1.0192487112786812 ] \> sol [(5.045357818922331,6.027976702418132e-2), (0.10404905846029407,3.157045047172834e-3), (1.0192487112786812,3.782067731353722e-2)]@ -} ----------------------------------------------------------------------------- module Numeric.GSL.Fitting ( -- * Levenberg-Marquardt nlFitting, FittingMethod(..), -- * Utilities fitModelScaled, fitModel ) where import Data.Packed.Internal import Numeric.LinearAlgebra import Foreign import Foreign.C.Types(CInt) import Numeric.GSL.Internal ------------------------------------------------------------------------- data FittingMethod = LevenbergMarquardtScaled -- ^ Interface to gsl_multifit_fdfsolver_lmsder. This is a robust and efficient version of the Levenberg-Marquardt algorithm as implemented in the scaled lmder routine in minpack. Minpack was written by Jorge J. More, Burton S. Garbow and Kenneth E. Hillstrom. | LevenbergMarquardt -- ^ This is an unscaled version of the lmder algorithm. The elements of the diagonal scaling matrix D are set to 1. This algorithm may be useful in circumstances where the scaled version of lmder converges too slowly, or the function is already scaled appropriately. deriving (Enum,Eq,Show,Bounded) -- | Nonlinear multidimensional least-squares fitting. nlFitting :: FittingMethod -> Double -- ^ absolute tolerance -> Double -- ^ relative tolerance -> Int -- ^ maximum number of iterations allowed -> (Vector Double -> Vector Double) -- ^ function to be minimized -> (Vector Double -> Matrix Double) -- ^ Jacobian -> Vector Double -- ^ starting point -> (Vector Double, Matrix Double) -- ^ solution vector and optimization path nlFitting method epsabs epsrel maxit fun jac xinit = nlFitGen (fi (fromEnum method)) fun jac xinit epsabs epsrel maxit nlFitGen m f jac xiv epsabs epsrel maxit = unsafePerformIO $ do let p = dim xiv n = dim (f xiv) fp <- mkVecVecfun (aux_vTov (checkdim1 n p . f)) jp <- mkVecMatfun (aux_vTom (checkdim2 n p . jac)) rawpath <- createMatrix RowMajor maxit (2+p) app2 (c_nlfit m fp jp epsabs epsrel (fi maxit) (fi n)) vec xiv mat rawpath "c_nlfit" let it = round (rawpath @@> (maxit-1,0)) path = takeRows it rawpath [sol] = toRows $ dropRows (it-1) path freeHaskellFunPtr fp freeHaskellFunPtr jp return (subVector 2 p sol, path) foreign import ccall "nlfit" c_nlfit:: CInt -> FunPtr TVV -> FunPtr TVM -> Double -> Double -> CInt -> CInt -> TVM ------------------------------------------------------- checkdim1 n _p v | dim v == n = v | otherwise = error $ "Error: "++ show n ++ " components expected in the result of the function supplied to nlFitting" checkdim2 n p m | rows m == n && cols m == p = m | otherwise = error $ "Error: "++ show n ++ "x" ++ show p ++ " Jacobian expected in nlFitting" ------------------------------------------------------------ err (model,deriv) dat vsol = zip sol errs where sol = toList vsol c = max 1 (chi/sqrt (fromIntegral dof)) dof = length dat - (rows cov) chi = norm2 (fromList $ cost (resMs model) dat sol) js = fromLists $ jacobian (resDs deriv) dat sol cov = inv $ trans js <> js errs = toList $ scalar c * sqrt (takeDiag cov) -- | Higher level interface to 'nlFitting' 'LevenbergMarquardtScaled'. The optimization function and -- Jacobian are automatically built from a model f vs x = y and its derivatives, and a list of -- instances (x, (y,sigma)) to be fitted. fitModelScaled :: Double -- ^ absolute tolerance -> Double -- ^ relative tolerance -> Int -- ^ maximum number of iterations allowed -> ([Double] -> x -> [Double], [Double] -> x -> [[Double]]) -- ^ (model, derivatives) -> [(x, ([Double], Double))] -- ^ instances -> [Double] -- ^ starting point -> ([(Double, Double)], Matrix Double) -- ^ (solution, error) and optimization path fitModelScaled epsabs epsrel maxit (model,deriv) dt xin = (err (model,deriv) dt sol, path) where (sol,path) = nlFitting LevenbergMarquardtScaled epsabs epsrel maxit (fromList . cost (resMs model) dt . toList) (fromLists . jacobian (resDs deriv) dt . toList) (fromList xin) -- | Higher level interface to 'nlFitting' 'LevenbergMarquardt'. The optimization function and -- Jacobian are automatically built from a model f vs x = y and its derivatives, and a list of -- instances (x,y) to be fitted. fitModel :: Double -- ^ absolute tolerance -> Double -- ^ relative tolerance -> Int -- ^ maximum number of iterations allowed -> ([Double] -> x -> [Double], [Double] -> x -> [[Double]]) -- ^ (model, derivatives) -> [(x, [Double])] -- ^ instances -> [Double] -- ^ starting point -> ([Double], Matrix Double) -- ^ solution and optimization path fitModel epsabs epsrel maxit (model,deriv) dt xin = (toList sol, path) where (sol,path) = nlFitting LevenbergMarquardt epsabs epsrel maxit (fromList . cost (resM model) dt . toList) (fromLists . jacobian (resD deriv) dt . toList) (fromList xin) cost model ds vs = concatMap (model vs) ds jacobian modelDer ds vs = concatMap (modelDer vs) ds -- | Model-to-residual for association pairs with sigma, to be used with 'fitModel'. resMs :: ([Double] -> x -> [Double]) -> [Double] -> (x, ([Double], Double)) -> [Double] resMs m v = \(x,(ys,s)) -> zipWith (g s) (m v x) ys where g s a b = (a-b)/s -- | Associated derivative for 'resMs'. resDs :: ([Double] -> x -> [[Double]]) -> [Double] -> (x, ([Double], Double)) -> [[Double]] resDs m v = \(x,(_,s)) -> map (map (/s)) (m v x) -- | Model-to-residual for association pairs, to be used with 'fitModel'. It is equivalent -- to 'resMs' with all sigmas = 1. resM :: ([Double] -> x -> [Double]) -> [Double] -> (x, [Double]) -> [Double] resM m v = \(x,ys) -> zipWith g (m v x) ys where g a b = a-b -- | Associated derivative for 'resM'. resD :: ([Double] -> x -> [[Double]]) -> [Double] -> (x, [Double]) -> [[Double]] resD m v = \(x,_) -> m v x