Library for solving linear equation system using Successive Over Relaxation method
Successive Over Relaxation (SOR) is a light-weight library for solving linear Equation Systems using a converging iterative process.
It is written in Lua.
Place the file 'SOR.lua' inside your project, call it using require.
local SOR = require ("SOR")
Now assuming you have to solve this linear system of 16x16 (16 equations, 16 unknown variables).
You will have to create a 16x17 matrix representing that system, the 17th column beign the solution vector.
local matrix = {
{-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},
}
To solve this sytem, use SOR.solve().
local x, iterations = SOR.solve(matrix)
-- displays x-vector:
for i,v in ipairs(x) do
print(('x[%d] = %f'):format(i,v))
end
print(('Iterations Made: %d'):format(iterations))
The output will be :
-- x[1] = 5.454459
-- x[2] = 4.594688
-- x[3] = 4.594679
-- x[4] = 5.454531
-- x[5] = 6.223469
-- x[6] = 5.329580
-- x[7] = 5.329561
-- x[8] = 6.223491
-- x[9] = 6.109833
-- x[10] = 5.170488
-- x[11] = 5.170455
-- x[12] = 6.109845
-- x[13] = 5.045460
-- x[14] = 4.071980
-- x[15] = 4.071964
-- x[16] = 5.045457
-- Iterations Made: 78
Consider that, to have this working the input matrix , with the last column left out, must be symmetric and diagonally dominant.
Otherwise, the solver will throw an error.
You can optionnally modify the solver behaviour before using SOR.solve() through these commands.
This work is under MIT-LICENSE
Copyright (c) 2012 Roland Yonaba
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