Add haskel and benchmark results

benchmarks/linalg/gauss_haskell.hs

@@ -0,0 +1,68 @@
+--module Gauss where
+import Data.Ratio
+import System.CPUTime
+import System.Environment
+isMatrix xs = null xs || all ((== (length.head $ xs)).length) xs
+
+isSquareMatrix xs = null xs || all ((== (length xs)).length) xs
+
+mult:: Num a => [[a]] -> [[a]] -> [[a]]
+mult uss vss = map ((\xs -> if null xs then [] else foldl1 (zipWith (+)) xs). zipWith (\vs u -> map (u*) vs) vss) uss
+
+--gauss::[[Double]] -> [[Double]] -> [[Double]]
+gauss xs bs = map (map fromRational) $ solveGauss (toR xs) (toR bs)
+    where toR = map $ map toRational
+
+solveGauss:: (Fractional a, Ord a) => [[a]] -> [[a]] -> [[a]]
+solveGauss xs bs | null xs || null bs || length xs /= length bs || (not $ isSquareMatrix xs) || (not $ isMatrix bs) = []
+                 | otherwise = uncurry solveTriangle $ triangle xs bs
+
+solveTriangle::(Fractional a,Eq a) => [[a]] -> [[a]] -> [[a]]
+solveTriangle us _ | not.null.dropWhile ((/= 0).head) $ us = []
+solveTriangle ([c]:as) (b:bs) = go as bs [map (/c) b]
+  where
+  val us vs ws = let u = head us in map (/u) $ zipWith (-) vs (head $ mult [tail us] ws)
+  go [] _ zs          = zs
+  go _ [] zs          = zs
+  go (x:xs) (y:ys) zs = go xs ys $ (val x y zs):zs
+
+triangle::(Num a, Ord a) => [[a]] -> [[a]] -> ([[a]],[[a]])
+triangle xs bs = triang ([],[]) (xs,bs)
+    where
+    triang ts (_,[]) = ts
+    triang ts ([],_) = ts
+    triang (os,ps) zs = triang (us:os,cs:ps).unzip $ [(fun tus vs, fun cs es) | (v:vs,es) <- zip uss css,let fun = zipWith (\x y -> v*x - u*y)]
+        where ((us@(u:tus)):uss,cs:css) = bubble zs
+
+bubble::(Num a, Ord a) => ([[a]],[[a]]) -> ([[a]],[[a]])
+bubble (xs,bs) = (go xs, go bs)
+    where
+    idmax = snd.maximum.flip zip [0..].map (abs.head) $ xs
+    go ys = let (us,vs) = splitAt idmax ys in vs ++ us
+
+-- Custom zipWith for two lists
+myZipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
+myZipWith _ [] _ = []
+myZipWith _ _ [] = []
+myZipWith f (x:xs) (y:ys) = f x y : myZipWith f xs ys
+
+-- Custom unzip for a list of pairs
+myUnzip :: [(a, b)] -> ([a], [b])
+myUnzip [] = ([], [])
+myUnzip ((x, y):xs) = (x : fst rest, y : snd rest)
+    where rest = myUnzip xs
+
+parseInt :: String -> Integer
+parseInt str = read str
+
+main = do
+    env <- getEnv "N"
+    let n = parseInt env
+    start <- getCPUTime
+    let matrixA = [[1 % (i + j - 1) | j <- [1..n]] | i <- [1..n] ]
+    let b = [[sum [1 % k | k <- [i..n+i-1]]] | i <- [1..n]]
+    let res = gauss matrixA b
+    print $ res
+    end <- getCPUTime
+    let diff = fromIntegral (end - start) / (10 ^ 12) :: Double
+    putStrLn $ "Total time: " ++ show diff ++ " seconds"