%%%%%%%% GAUSS-SEIDEL METHOD %%%%%%%%%%

%%%% HAVE TO CHECK MAX ERROR MANUALLY - CODE WILL PRINT MORE ITERATIONS %%%%


% Define the matrix A and vector b
A = [8, 0, 6; -1, 12, 0; -7, -0.5, 15];
b = [25; 7; -14];

% Initial guess
x0 = [0; 1; 1];

% Maximum allowed component-wise error percentage
max_error_percentage = 5;

% Initialize variables
x = x0;
n = length(b);
tolerance = max_error_percentage / 100;

% Display the header for the iteration table
fprintf('Iteration\t x1\t\t x2\t\t x3\t\t Max Error (%%)\n');
fprintf('-----------------------------------------------------------------------\n');

% Iteration counter
k = 1;

while true
    % Store the old values of x
    x_old = x;
    
    % Update each component of x
    for i = 1:n
        sigma = 0;
        for j = 1:n
            if j ~= i
                sigma = sigma + A(i, j) * x(j);
            end
        end
        x(i) = (b(i) - sigma) / A(i, i);
    end
    
    % Calculate the component-wise error
    error = abs((x - x_old) ./ x);
    max_error = max(error) * 100;  % Convert to percentage
    
    % Print the current iteration, the values of x, and the max error percentage
    fprintf('%d\t\t %.6f\t %.6f\t %.6f\t %.2f%%\n', k, x(1), x(2), x(3), max_error);
    
    % Check if the maximum component-wise error is below the tolerance
    if max_error < tolerance
        break;
    end
    
    k = k + 1;
end

% Summary table
fprintf('\nSummary Table:\n');
fprintf('Iteration\t x1\t\t x2\t\t x3\t\t Max Error (%%)\n');
fprintf('-----------------------------------------------------------------------\n');
fprintf('%d\t\t %.6f\t %.6f\t %.6f\t %.2f%%\n', k, x(1), x(2), x(3), max_error);