hmatrix-0.9.3.0: Linear algebra and numerical computationSource codeContentsIndex
Numeric.GSL.Fitting
Portabilityuses ffi
Stabilityprovisional
MaintainerAlberto Ruiz (aruiz at um dot es)
Contents
Levenberg-Marquardt
Utilities
Description

Nonlinear Least-Squares Fitting

http://www.gnu.org/software/gsl/manual/html_node/Nonlinear-Least_002dSquares-Fitting.html

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)]
Synopsis
nlFitting :: FittingMethod -> Double -> Double -> Int -> (Vector Double -> Vector Double) -> (Vector Double -> Matrix Double) -> Vector Double -> (Vector Double, Matrix Double)
data FittingMethod
= LevenbergMarquardtScaled
| LevenbergMarquardt
fitModelScaled :: Double -> Double -> Int -> ([Double] -> x -> [Double], [Double] -> x -> [[Double]]) -> [(x, ([Double], Double))] -> [Double] -> ([(Double, Double)], Matrix Double)
fitModel :: Double -> Double -> Int -> ([Double] -> x -> [Double], [Double] -> x -> [[Double]]) -> [(x, [Double])] -> [Double] -> ([Double], Matrix Double)
Levenberg-Marquardt
nlFittingSource
:: FittingMethod
-> Doubleabsolute tolerance
-> Doublerelative tolerance
-> Intmaximum number of iterations allowed
-> Vector Double -> Vector Doublefunction to be minimized
-> Vector Double -> Matrix DoubleJacobian
-> Vector Doublestarting point
-> (Vector Double, Matrix Double)solution vector and optimization path
Nonlinear multidimensional least-squares fitting.
data FittingMethod Source
Constructors
LevenbergMarquardtScaledInterface 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.
LevenbergMarquardtThis 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.
show/hide Instances
Utilities
fitModelScaledSource
:: Doubleabsolute tolerance
-> Doublerelative tolerance
-> Intmaximum 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
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.
fitModelSource
:: Doubleabsolute tolerance
-> Doublerelative tolerance
-> Intmaximum 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
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.
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