global iteartions = 0;

function ftmin = f(x)
    global iteartions;
    iteartions += 1;
     %ftmin = (cos((3*x.^5 - 10*x + 10^(1./3) - 2 - 10*sqrt(2))./ 10) + atan((10*x.^5 - 10*sqrt(5)*x.^4 + 10*x.^3 + 3*x.^2 - 3*sqrt(5)*x + 1)./(2*x.^2 - 2*sqrt(5)*x + 2)));
     %ftmin = -ftmin;
     ftmin = (sin(x + 0.77)).^4;
end

function a = gold_search(a, b, iter)
    fa = NaN;
    fb = NaN;
    tau = (sqrt(5) - 1) / 2;
    l = b - a;
    x1 = b - tau * l;
    x2 = a + tau * l;
    f1 = f(x1);
    f2 = f(x2);
    i = 0;
    while 1
        if (i >= iter)
            break
        else
            i += 1;
            if (f1 <= f2)
                b = x2; fb = f2;
                l = b - a;

                x2 = x1;
                f2 = f1;

                x1 = b - tau*l;
                f1 = f(x1);
            else
                a = x1; fa = f1;
                l = b - a;

                x1 = x2;
                f1 = f2;

                x2 = a + tau*l;
                f2 = f(x2);
            end
        end
    end
end

function [x,y] = newton(a, b, epsilon, iter)
    h = 1e-5;
    x = gold_search(a, b, iter);
    %x = (a+b)/2;
    y = f(x);
    f2 =  (f(x - h) - 2*f(x) + f(x + h)) / (h.^2);
    while 1
      plot(x, f(x), 'k');
      fa = f(x - h);
      fb = f(x + h);
      f1 = (fb - fa) / (2*h);
      %printf('f1: %.16f', f1);
      if abs(f1) < epsilon
        printf('x = %d\n', x);
        break
      end
      fm = f(x);
      f2 = (fa - 2*fm + fb) / (h^2);
      x = x - f1/f2;
      y = f(x);
      if x < a || x > b
            printf('Error: x = %d\n', x);
            break
        end
    end
end

a = -1.0;
b = 0.0;

iteartions = 0;
hold on
[x_min, y_min] = newton(a, b, 1e-6, 1);
printf('x_min: %.16f, y_min: %.16f\n', x_min, y_min)
err4 = x_min + 0.77;
printf('err4: %.10f \n', err4)
iteartions
plot(a:0.05:b, f(a:0.05:b))
plot(x_min, y_min, 'ro')
hold off


iteartions = 0;
disp('')
disp('fminbnd');
[x_min, y_min, _, _ ] = fminbnd(@f, a, b, optimset('TolX',1e-6));
printf('x_min: %.16f, y_min: %.16f\n', x_min, y_min)
x_min
y_min
iteartions