Successive Over Relaxation (SOR) Algorithm

sor.lua

-- SOR Algorithm implemented through Lua

function Normalize(m)
	local n = 0
	for i,v in ipairs(m) do
	n = n + v^2
	end
	return math.sqrt(n)
end


local A = {
{-4,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,-11},
{1,-4,1,0,0,1,0,0,0,0,0,0,0,0,0,0,-3},
{0,1,-4,1,0,0,1,0,0,0,0,0,0,0,0,0,-3},
{0,0,1,-4,0,0,0,1,0,0,0,0,0,0,0,0,-11},
{1,0,0,0,-4,1,0,0,1,0,0,0,0,0,0,0,-8},
{0,1,0,0,1,-4,1,0,0,1,0,0,0,0,0,0,0},
{0,0,1,0,0,1,-4,1,0,0,1,0,0,0,0,0,0},
{0,0,0,1,0,0,1,-4,0,0,0,1,0,0,0,0,-8},
{0,0,0,0,1,0,0,0,-4,1,0,0,1,0,0,0,-8},
{0,0,0,0,0,1,0,0,1,-4,1,0,0,1,0,0,0},
{0,0,0,0,0,0,1,0,0,1,-4,1,0,0,1,0,0},
{0,0,0,0,0,0,0,1,0,0,1,-4,0,0,0,1,-8},
{0,0,0,0,0,0,0,0,1,0,0,0,-4,1,0,0,-10},
{0,0,0,0,0,0,0,0,0,1,0,0,1,-4,1,0,-2},
{0,0,0,0,0,0,0,0,0,0,1,0,0,1,-4,1,-2},
{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,-4,-10},
}


local MAXITER = 10000
local N=table.getn(A)
local t = MAXITER
local w = 1.86
local ACCURACY = 1E-6
local x = {}
	for k = 1,N do x[k]=0 end

repeat
t=t-1

local q = Normalize(x)
	for i=1,N do
	local sum=A[i][N+1]
		for j=1,N do
			if (i~=j) then
			sum = sum-A[i][j]*x[j]
			end
		end
	x[i]=(1-w)*x[i]+w*sum/A[i][i]
	end
	local p = Normalize(x)
	local d = math.abs(p-q)
until (d<ACCURACY) or (t==0)

print( 'Num of iter:',MAXITER-t)
for i=1,N do
print('x['..i..']='..x[i])
end