GoldenSectionSearch

--module Gold (search, example) where

f :: Double -> Double
f x = (x - 1.0) * (x - 1.0)

golden_ratio :: Double
golden_ratio = ( 1 + sqrt(5) ) / 2

data Interval = Interval {lb :: Double, ub :: Double} deriving Show
data PointValue2 = PointValue2 {x1 :: Double, f1 ::Double, x2 :: Double, f2 :: Double} deriving Show

idp :: Double -> Double -> Double
idp lb ub = (ub - lb) / (golden_ratio + 1.0) + lb

idp2 :: Double -> Double  -> Double
idp2 lb ub = (ub - lb) / golden_ratio + lb

sub :: PointValue2 -> Interval -> Int -> Interval
sub pv val k
 | k <= 0 = val
 | f1 pv < f2 pv = let new_x1 = (idp (lb val) (x2 pv)) in sub (PointValue2 new_x1 (f $ new_x1) (x1 pv) (f1 pv)) (Interval (lb val) (x2 pv)) $ k - 1 
 | otherwise = let new_x2 = (idp2 (x1 pv) (ub val)) in sub (PointValue2 (x2 pv) (f2 pv) new_x2 (f new_x2)) (Interval (x1 pv) (ub val)) $ k - 1 

search :: Double -> Double -> Int -> Double
search _lb _ub _k = ((lb newval) + (ub newval)) / 2.0
 where  
    _x1 = idp _lb _ub
    _x2 = idp2 _lb _ub
    _f1 = f _x1
    _f2 = f _x2
    pv = PointValue2 _x1 _f1 _x2 _f2
    val = Interval _lb _ub
    newval = sub pv val _k

--search :: PointValue2 -> Interval -> Int -> Double
--search pv val k = ((lb newval) + (ub newval)) / 2.0
--  where newval = sub pv val k

example = putStrLn $ unlines $ map show [sub pv val x|x<-[1..30] ]
  where 
    _lb = -10.0
    _ub = 10.0
    _x1 = idp _lb _ub
    _x2 = idp2 _lb _ub
    _f1 = f _x1
    _f2 = f _x2
    pv = PointValue2 _x1 _f1 _x2 _f2
    val = Interval _lb _ub

main = example