LeastSquaresMethod.hs

import Control.Applicative ((<$>))
import Text.Printf (printf)

type Solution = Maybe [Double]

gauss :: [[Double]] -> Solution
gauss [[a, b]] = return [b / a]
gauss (h@(x : xs) : t) = do
	let minor = transform h t
	if any isNull minor
	then Nothing
	else do
		solutions <- gauss minor
		return $ (xs ^*^ (solutions ++ [-1.0])) / (negate x) : solutions

isNull :: [Double] -> Bool
isNull [x] = True
isNull (x:xs) = if x == 0 then isNull xs else False

transform :: [Double] -> [[Double]] -> [[Double]]
transform row = map $ elliminate row
  where
	elliminate :: [Double] -> [Double] -> [Double]
	elliminate (x : xs) (y : ys) =
		let factor = negate (y / x) in
		zipWith (+) (map (* factor) xs) ys

transpose :: Eq a => [[a]] -> [[a]]
transpose xs
  | all (== []) xs = []
  | otherwise = let (col, rest) = multiHead xs in col : transpose rest

multiHead :: [[a]] -> ([a], [[a]])
multiHead = let splitHead (x:xs) = (x, xs) in unzip . map splitHead

(^*^) :: Num a => [a] -> [a] -> a
(^*^) xs ys = sum $ zipWith (*) xs ys

makeSystem :: [[Double]] -> [[Double]]
makeSystem vs =
    let makeEq n = let e = vs !! n in map (^*^ e) vs in
    let l = length vs - 1 in
    map makeEq [0 .. l-1]

readNumList :: String -> [Double]
readNumList = map read . words

printSolution :: [Double] -> IO ()
printSolution = putStrLn . unwords . map (printf "%.8f")

main :: IO ()
main = do
	[n, m] <- readNumList <$> getLine
	inp <- map readNumList <$> (sequence $ replicate (floor n) getLine)
	case gauss . makeSystem $ transpose inp of
		Just solutions -> printSolution solutions
		Nothing -> putStrLn "NO"