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{-# LANGUAGE FlexibleInstances, ScopedTypeVariables #-}
module Math.LinProg.LP (
compile
) where
import Data.List
import Math.LinProg.Types
import Math.LinProg.Compile
import Control.Lens
import Control.Monad.State
import Control.Monad.Free
import Data.Maybe
instance (Show t, Num t, Ord t) => Show (CompilerS t String) where
show s = unlines $ catMaybes [
Just "Minimize"
,Just (showEq $ varTerms (s ^. objective))
,if hasST then Just "Subject to" else Nothing
,if hasEqs then Just (intercalate "\n" $ map (\(a, b) -> showEq a ++ " = " ++ show (negate b)) $ s ^. equals) else Nothing
,if hasUnbounded then Just (intercalate "\n" $ map (\(a, b) -> showEq a ++ " <= " ++ show (negate b)) unbounded) else Nothing
,if hasBounded then Just "Bounds" else Nothing
,if hasBounded then Just (intercalate "\n" $ map (\(l, v, u) -> show l ++ " <= " ++ v ++ " <= " ++ show u) bounded) else Nothing
]
where
getVars eq = zip vs ws
where
vs = vars eq
ws = map (`getVar` eq) vs
showEq = unwords . map (\(a, b) -> render b ++ " " ++ a) . getVars
(bounded, unbounded) = findBounds $ s ^. leqs
hasBounded = not (null bounded)
hasUnbounded = not (null unbounded)
hasEqs = not (null (s^.equals))
hasST = hasUnbounded || hasEqs
render x = (if x >= 0 then "+" else "") ++ show x
findBounds :: (Eq v, Num t, Ord t, Eq t) => [Equation t v] -> ([(t, v, t)], [Equation t v])
findBounds eqs = (mapMaybe bound singleTerms, eqs \\ filter (isBounded . head . vars . fst) singleTermEqs)
where
singleTermEqs = filter (\(ts, _) -> length (vars ts) == 1) eqs
singleTerms = nub $ concatMap (vars . fst) singleTermEqs
upperBound x = mapMaybe (\(a, c) -> let w = getVar x a in if w == 1 then Just (negate c) else Nothing) singleTermEqs
lowerBound x = mapMaybe (\(a, c) -> let w = getVar x a in if w == -1 then Just c else Nothing) singleTermEqs
bound v = bound' (lowerBound v) (upperBound v) where
bound' [] _ = Nothing
bound' _ [] = Nothing
bound' ls us | l <= u = Just (l, v, u)
| otherwise = Nothing where
l = maximum ls
u = minimum us
isBounded v = isJust (bound v)
|
