Numeric.GSL.Minimization
 Portability uses ffi Stability provisional Maintainer Alberto Ruiz (aruiz at um dot es)
Description

Minimization of a multidimensional function Minimization of a multidimensional function using some of the algorithms described in:

Synopsis
 minimizeConjugateGradient :: Double -> Double -> Double -> Int -> ([Double] -> Double) -> ([Double] -> [Double]) -> [Double] -> ([Double], Matrix Double) minimizeNMSimplex :: ([Double] -> Double) -> [Double] -> [Double] -> Double -> Int -> ([Double], Matrix Double)
Documentation
 :: Double initial step size -> Double minimization parameter -> Double desired precision of the solution (gradient test) -> Int maximum number of iterations allowed -> [Double] -> Double function to minimize -> [Double] -> [Double] gradient -> [Double] starting point -> ([Double], Matrix Double) solution vector, and the optimization trajectory followed by the algorithm The Fletcher-Reeves conjugate gradient algorithm gsl_multimin_fminimizer_conjugate_fr. This is the example in the GSL manual: ```minimize = minimizeConjugateGradient 1E-2 1E-4 1E-3 30 f [x,y] = 10*(x-1)^2 + 20*(y-2)^2 + 30 df [x,y] = [20*(x-1), 40*(y-2)] main = do let (s,p) = minimize f df [5,7] print s print p > main [1.0,2.0] 0. 687.848 4.996 6.991 1. 683.555 4.989 6.972 2. 675.013 4.974 6.935 3. 658.108 4.944 6.861 4. 625.013 4.885 6.712 5. 561.684 4.766 6.415 6. 446.467 4.528 5.821 7. 261.794 4.053 4.632 8. 75.498 3.102 2.255 9. 67.037 2.852 1.630 10. 45.316 2.191 1.762 11. 30.186 0.869 2.026 12. 30. 1. 2.```The path to the solution can be graphically shown by means of: `GSL.Plot.mplot \$ drop 2 (toColumns p)`
 :: [Double] -> Double function to minimize -> [Double] starting point -> [Double] sizes of the initial search box -> Double desired precision of the solution -> Int maximum number of iterations allowed -> ([Double], Matrix Double) solution vector, and the optimization trajectory followed by the algorithm The method of Nelder and Mead, implemented by gsl_multimin_fminimizer_nmsimplex. The gradient of the function is not required. This is the example in the GSL manual: ```minimize f xi = minimizeNMSimplex f xi (replicate (length xi) 1) 1e-2 100 f [x,y] = 10*(x-1)^2 + 20*(y-2)^2 + 30 main = do let (s,p) = minimize f [5,7] print s print p > main [0.9920430849306285,1.9969168063253164] 0. 512.500 1.082 6.500 5. 1. 290.625 1.372 5.250 4. 2. 290.625 1.372 5.250 4. 3. 252.500 1.372 5.500 1. 4. 101.406 1.823 2.625 3.500 5. 101.406 1.823 2.625 3.500 6. 60. 1.823 0. 3. 7. 42.275 1.303 2.094 1.875 8. 42.275 1.303 2.094 1.875 9. 35.684 1.026 0.258 1.906 10. 35.664 0.804 0.588 2.445 11. 30.680 0.467 1.258 2.025 12. 30.680 0.356 1.258 2.025 13. 30.539 0.285 1.093 1.849 14. 30.137 0.168 0.883 2.004 15. 30.137 0.123 0.883 2.004 16. 30.090 0.100 0.958 2.060 17. 30.005 6.051e-2 1.022 2.004 18. 30.005 4.249e-2 1.022 2.004 19. 30.005 4.249e-2 1.022 2.004 20. 30.005 2.742e-2 1.022 2.004 21. 30.005 2.119e-2 1.022 2.004 22. 30.001 1.530e-2 0.992 1.997 23. 30.001 1.259e-2 0.992 1.997 24. 30.001 7.663e-3 0.992 1.997```The path to the solution can be graphically shown by means of: `GSL.Plot.mplot \$ drop 3 (toColumns p)`