Portability | uses ffi |
---|---|

Stability | provisional |

Maintainer | Alberto Ruiz (aruiz at um dot es) |

Safe Haskell | None |

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)]

- nlFitting :: FittingMethod -> Double -> Double -> Int -> (Vector Double -> Vector Double) -> (Vector Double -> Matrix Double) -> Vector Double -> (Vector Double, Matrix Double)
- data FittingMethod
- 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

:: 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 |

Nonlinear multidimensional least-squares fitting.

data FittingMethod Source

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. |

# Utilities

:: 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 |

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.

:: 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 |

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.