# L-11 MCS 471 Fri 16 Sep 2022 : runsor.jl
# Interactive running of successive over-relaxation on a test system.

import Random # to fix the seed of the random numbers
include("sor.jl")

"""
Returns a special matrix.
"""
function special_matrix()
    mat = [  3.0, -1.0,  0.0,  0.0,  0.0,  0.5,
            -1.0,  3.0, -1.0,  0.0,  0.5,  0.0,
             0.0, -1.0,  3.0, -1.0,  0.0,  0.0,
             0.0,  0.0, -1.0,  3.0, -1.0,  0.0,
             0.0,  0.5,  0.0, -1.0,  3.0, -1.0,
             0.5,  0.0,  0.0,  0.0, -1.0,  3.0]
    mat = reshape(mat, (6, 6))
    mat = permutedims(mat)
    return mat
end

"""
Runs the successive over-relaxation on a special matrix.
"""
function main()
    mat = special_matrix()
    dim = 6
    sol = ones(dim, 1)
    rhs = mat*sol
    Random.seed!(123)
    noise = 1.0e-4*rand(dim, 1)
    wrk = sol + noise
    println("The matrix :")
    show(stdout, "text/plain", mat); println("");
    println("The right hand side :")
    show(stdout, "text/plain", rhs); println("");
    sol, numit, nrmdx, fail = sor(mat, rhs, wrk)
    println("The solution after ", numit, " iterations :")
    for i=1:dim
        strsol = @sprintf("%.16e", sol[i])
        println(i, " : $strsol")
    end
    print("Estimated forward error : ", nrmdx)
    if fail
        println(" failed.")
    else
        println(" succeeded.")
    end
end

main()