clear;clc
format short
%%  Read or Input any square Matrix
A = [10 2 0 1; 5 10 1 0; 0 1 4 1; 0 0 -1 6]% coefficients matrix
C = [10; 2; 8; 3];% constants vector
n = length(C);
X = zeros(n,1);
beta=zeros(n,1);
Error_eval = ones(n,1);

%% Verificar se a matrix A satisfaz o critério de Sassenfeld
for i=1:n
    for j=1:i-1
        beta(i)=beta(i)+abs(A(i,j))/abs(A(i,i))*beta(j);
    end
    for j=i+1:n
            beta(i)=beta(i)+abs(A(i,j))/abs(A(i,i));
    end
    Check = max(beta(:));
    if Check > 1
        error('A matrix não satisfaz o Critério de Sassenfeld')
    end
end

%% Start the Iterative method

iteration = 0;
while max(Error_eval) > 0.0001
    iteration = iteration + 1;
    Z = X;  % save current values to calculate error later
    for i = 1:n
        j = 1:n; % define an array of the coefficients' elements
        j(i) = [];  % eliminate the unknow's coefficient from the remaining coefficients
        Xtemp = X;  % copy the unknows to a new variable
        Xtemp(i) = [];  % eliminate the unknown under question from the set of values
        X(i) = (C(i) - sum(A(i,j) * Xtemp)) / A(i,i);
    end
    Xsolution(:,iteration) = X;
    Error_eval = sqrt((X - Z).^2);
end

%% Display Results
GaussSeidel = [1:iteration;Xsolution]'
%MaTrIx = [A X C]