Implementation of Gauss-Seidel method for solving of system of linear algebraic equations.

Slae.GaussSeidel.hs

-- file Slae.GaussSeidel xdCrafts 27.09.2012
module 
	Slae.GaussSeidel (
		solveWithAccuracy,
		solveWithAccuracy1
	)
where

-- http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method
-- function that represents Xi(k+1)
-- k1 - number of iteration
-- i - nuber of variable X
-- c - array of coefficients
-- f - array of free coefficients
x :: (Floating floating) => Int -> Int -> [[floating]] -> [floating] -> floating
x 0 _ _ _ = 0
x k1 i c f = 
	(1 / getC i i) * (getF i - sum getK1List - sum getKList)
	where
		getC m n = c !! m !! n
		getF m = f !! m
		getK1List = [getC i j * x k1 j c f | j <- [0 .. i - 1]]
		getKList = [getC i j * x (k1 - 1) j c f | let n = length f - 1, j <- [i + 1 .. n]]

-- http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method
-- function that represents solution of system of linear algebraic equations.
-- k - number of iteration
-- c - array of coefficients
-- f - array of free coefficients
solve :: (Floating floating) => Int -> [[floating]] -> [floating] -> [floating]
solve k c f = 
	[x k i c f | let n = length f - 1, i <- [0..n]]

-- function that calculates absolute differences between two vectors of values
(|-|) :: (Floating floating) => [floating] -> [floating] -> [floating]
[] |-| _ = []
_ |-| [] = []
(x:xs) |-| (y:ys) = abs (y - x) : (xs |-| ys)


-- http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method
-- function that represents solution of system of linear algebraic equations.
-- e - accuracy
-- k - initial iteration number of iteration
-- c - array of coefficients
-- f - array of free coefficients
solveWithAccuracy :: (Floating floating, Ord floating) => floating -> Int -> [[floating]] -> [floating] -> [floating]
solveWithAccuracy e k c f
	| accuracy < e = solutionK1
	| otherwise = solveWithAccuracy e (k + 1) c f
	where 
		accuracy = maximum (solutionK |-| solutionK1)
		solutionK = solve k c f
		solutionK1 = solve (k + 1) c f

-- http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method
-- function that represents solution of system of linear algebraic equations.
-- e - accuracy
-- c - array of coefficients
-- f - array of free coefficients
solveWithAccuracy1 :: (Floating floating, Ord floating) => floating -> [[floating]] -> [floating] -> [floating]
solveWithAccuracy1 e c f = solveWithAccuracy e 1 c f