function [x, i] = SecantMethod(f, x0, x1, tol, max_iter)
    % solves f(x) = 0 by doing max_iter steps of the secant method;
    % the secant method requires two initial values, x0 and x1
    % which should ideally be chosen close to the root;
    % y = feval(f, x)  evaluates a function using its name or its handle
    % and using the input arguments;
    for i = 1 : max_iter
        % function values: f(x0) and f(x1)
        f0 = feval(f, x0);
        f1 = feval(f, x1);

        % the root of function f is approximated using the formula 
        xi = x1 - f1 * (x1 - x0) / (f1 - f0);

        % calculate f(xi)
        fxi = feval(f, xi);
        % xi is the solution
        if abs(fxi) < eps
            x = xi;
            return;
        endif

        % calculate eps
        epsilon = abs((xi - x1) / xi);
        % stop if the secant method reached its convergence limit
        if epsilon < tol
            x = xi;
            return;
        endif

        % update the last two computed values
        x0 = x1;
        x1 = xi;
    endfor

    disp('Maximum number of iterations reached');
endfunction