ass4_q3

# Eli Simhayev - 2017
# Question 3

n = 5;
maxIter = 50;

# ===== Task C =====

# calculate the coefficient of xᵢ - g.
function calc_g(i,H,g,x)
    sum = 0;
    for j=1:n
        if j != i
            sum += H[i,j]*x[j];
        end
    end

    return sum - g[i];
end

function projected_CD(H,g,a,b,x_CD)
    for i=1:n
        g_coe = -calc_g(i,H,g,x_CD); # g coefficient
        h_coe = H[i,i];              # h coefficient
        g_div_h = g_coe/h_coe;

        if g_div_h < a[i]
            x_CD[i] = a[i];
        elseif g_div_h > b[i]
            x_CD[i] = b[i];
        else
            x_CD[i] = g_div_h;
        end
    end

    return x_CD;
end


# ===== Task D =====
H = [5 -1 -1 -1 -1;
     -1 5 -1 -1 -1;
     -1 -1 5 -1 -1;
     -1 -1 -1 5 -1;
     -1 -1 -1 -1 5];

g = [18; 6; -12; -6; 18];
a = zeros(n); b = 5*ones(n);

x_CD = zeros(n); # guess
for i=1:maxIter
    x_CD = projected_CD(H,g,a,b,x_CD);
end

println("x_CD = ", x_CD); # x_CD = [5.0,3.66667,0.666667,1.66667,5.0]