module Main where {- | = Example application: trigonometry cheating Find the trigonometric expression of cos(x) through sin(x) using our automatic programming method. -} import qualified Data.Vector as V import Data.List ( foldl' ) import Control.Monad ( foldM ) import Math.Probable.Random -- From `probable` package ( vectorOf , double ) import AI.MEP config = defaultConfig { -- Functions available to genetically produced programs c'ops = V.fromList [ ('*', (*)), ('+', (+)), -- Avoid division by zero ('/', \x y -> if y < 1e-6 then 1 else x / y), ('-', (-)), ('s', \x _ -> sin x) ] -- Chromosome length , c'length = 50 -- Probability to generate a new variable gene , p'var = 0.1 -- Probability to generate a new constant gene , p'const = 0.05 -- Probability to generate a new operator is -- inferred as 1 - 0.1 - 0.5 = 0.85 } -- | Absolute value distance between two scalar values dist :: Double -> Double -> Double dist x y = abs \$ x - y main :: IO () main = do -- A vector of 50 random numbers between 0 and 1 (including 1) let datasetSize = 50 xs <- runRandIO (vectorOf datasetSize double) -- Scale the values to the interval of (-pi, pi] let xs' = V.map ((2*pi *). subtract 0.5) xs -- Target function f to approximate function x = (cos x)^2 -- Pairs (x, f(x)) dataset = map (\x -> (x, function x)) \$ V.toList xs' -- Randomly create a population of chromosomes pop <- runRandIO \$ initialize config let loss = regressionLoss1 dist dataset -- Evaluate the initial population let popEvaluated = evaluatePopulation loss pop norm = fromIntegral datasetSize putStrLn \$ "Average loss in the initial population " ++ show (avgLoss popEvaluated / norm) -- Declare how to produce the new generation let nextGeneration = evolve config loss (mutation3 config) crossover binaryTournament -- Specify the I/O loop, which logs every 5 generation runIO pop i = do newPop <- runRandIO \$ foldM (\xg _ -> nextGeneration xg) pop [1..generations] putStrLn \$ "Population " ++ show (i * generations) ++ ": average loss " ++ show (avgLoss newPop / norm) return newPop where generations = 5 -- The final population final <- foldM runIO popEvaluated [1..20] putStrLn "Interpreted expression:" putStrLn \$ generateCode (best final)