-- the multidimensional minimization example in the GSL manual import Numeric.GSL import Numeric.LinearAlgebra import Graphics.Plot import Text.Printf(printf) -- the function to be minimized f [x,y] = 10*(x-1)^2 + 20*(y-2)^2 + 30 -- exact gradient df [x,y] = [20*(x-1), 40*(y-2)] -- a minimization algorithm which does not require the gradient minimizeS f xi = minimize NMSimplex2 1E-2 100 (replicate (length xi) 1) f xi -- Numerical estimation of the gradient gradient f v = [partialDerivative k f v | k <- [0 .. length v -1]] partialDerivative n f v = fst (derivCentral 0.01 g (v!!n)) where g x = f (concat [a,x:b]) (a,_:b) = splitAt n v disp' = putStrLn . format " " (printf "%.3f") allMethods :: (Enum a, Bounded a) => [a] allMethods = [minBound .. maxBound] test method = do print method let (s,p) = minimize method 1E-2 30 [1,1] f [5,7] print s disp' p testD method = do print method let (s,p) = minimizeD method 1E-3 30 1E-2 1E-4 f df [5,7] print s disp' p testD' method = do putStrLn \$ show method ++ " with estimated gradient" let (s,p) = minimizeD method 1E-3 30 1E-2 1E-4 f (gradient f) [5,7] print s disp' p main = do mapM_ test [NMSimplex, NMSimplex2] mapM_ testD allMethods testD' ConjugateFR mplot \$ drop 3 . toColumns . snd \$ minimizeS f [5,7]