Find minimum of unimodal function with golden cut

function [x,fx] = plot_minimum(f,a,b,epsilon,use_ginput)
X = linspace(a,b,500);
hold('off')
plot(X, f(X), 'b-')
hold('on')
axis("manual")
if use_ginput
    a_vector = ginput(1);
    plot(a_vector(1),a_vector(2), 'xk')
    b_vector = ginput(1);
    plot(b_vector(1),b_vector(2), 'xk')
    a = a_vector(1);
    b = b_vector(1);
else
   a = -4;
   b = 2;
end
fprintf('a = %.2f\nb = %.2f\n', a,b)
if a > b
    disp('Digga, der erste Punkt muss LINKS sein!!!')
end
[x,fx] = find_minimum(f,a,b,epsilon);
plot(x,fx,'or')
hold('off')
end

function [x,fx] = find_minimum(f,a,b,epsilon)
    c = (3-sqrt(5))/2;
    xa = a + c*(b-a);
    xb = b - c*(b-a);
    not_first_time = false;
    while abs(a-b) >= epsilon
        if f(xa) < f(xb)
            b = xb;
            xb = xa;
            xa = a + c*(b-a);
        elseif f(xa) > f(xb)
            a = xa;
            xa = xb;
            xb = b - c*(b-a);
        end
    fprintf('a = %f\nx_a = %f\nx_b = %f\nb = %f\n--------\n',a,xa,xb,b)

    hold('on')
    if not_first_time
        delete(a_plot)
        delete(xa_plot)
        delete(xb_plot)
        delete(b_plot)
    end
    a_plot = plot(a,f(a),'mo');
    xa_plot = plot(xa,f(xa), 'mo');
    xb_plot = plot(xb,f(xb), 'mo');
    b_plot = plot(b,f(b), 'mo');
    not_first_time = true;


    pause(1.5)

    end
x = xa;
fx = f(xa);
end

f=@(x) 10+x.^2-10*cos(2*pi*x); a=-10; b=10; epsilon=1e-5; plot_minimum(f,a,b,epsilon,true)