public class Main{

    private static final double eps = 0.0000001;
    private static final double h = 0.00001;

    public static double liczfunckje(double x,double y)
    {
        return (y*y*y) + (x*x) - (9*x*y) - (3*x) + 2;
    }
    public static double dx(double x,double y)
    {
        return (1/h)*(liczfunckje(x+h,y)-liczfunckje(x, y));
    }
    public static double dy(double x,double y)
    {
        return (1/h)*(liczfunckje(x,y+h)-liczfunckje(x, y));
    }
    public static double dx2(double x,double y)
    {
        return (1/Math.pow(h,2))*(liczfunckje(x+h, y)-(2*liczfunckje(x, y))+liczfunckje(x-h, y));
    }
    public static double dxy(double x,double y)
    {
        return (1/h)*(((1/h)*(liczfunckje(x+h, y+h)-liczfunckje(x+h, y)))-((1/h)*(liczfunckje(x, y+h)-liczfunckje(x, y))));
    }
    public static double dyx(double x,double y)
    {
        return (1/h)*(((1/h)*(liczfunckje(x+h, y+h)-liczfunckje(x+h, y)))-((1/h)*(liczfunckje(x, y+h)-liczfunckje(x, y))));
    }
    public static double dy2(double x,double y)
    {
        return (1/Math.pow(h,2))*(liczfunckje(x, y+h)-(2*liczfunckje(x, y))+liczfunckje(x, y-h));
    }


//-----------------------------------------------------------------------------------------------------------------------------------------

    //gradient f(xk)
    public static double[] tab1(double x,double y)
    {
        double a,b;
        double [] tab = new double [2];
        tab[0]=dx(x, y);
        tab[1]=dy(x, y);
        return tab;
    }


    //gradient do kwadratu - nie pamietam jak sie nayzwa --- macierz hessego przypomnialem sobie :)))
    public static double[] tab2(double x,double y){
        double c,d,e,f;
        double [] tab2 = new double[4];

        tab2[0]=dx2(x, y);
        tab2[1]=dxy(x, y);
        tab2[2]=dyx(x, y);
        tab2[3]=dy2(x, y);
        return tab2;
    }



    //-----------------------
    public static void main(String[] args) {

        double x=3;
        double y=7;
        double a,b,c,d,e,f,falka;


//a,b wartosci z gradientu a pzoostale z hessego -- > przypisanie do zmiennych
// do falki podstawiam wartosci do wzoru Ak i przypisuje do zmiennej falka
        a=tab1(x, y)[0];
        b=tab1(x, y)[1];
        c=tab2(x, y)[0];
        d=tab2(x, y)[1];
        e=tab2(x, y)[2];
        f=tab2(x, y)[3];
        falka=(Math.pow(a, 2)+Math.pow(b,2))/(a*(a*c+b*e)+b*(a*d+b*f));
        System.out.println(falka);

        double x1 = x;
        double y1 = y;

        while((Math.abs(dx(x1, y1))>eps && Math.abs(dy(x1, y1))>eps) || (Math.abs(x1-x)>eps && Math.abs(y1-y)>eps))
        {
            x=x1;
            y=y1;
        a=tab1(x, y)[0];
        b=tab1(x, y)[1];
        c=tab2(x, y)[0];
        d=tab2(x, y)[1];
        e=tab2(x, y)[2];
        f=tab2(x, y)[3];
            falka=(Math.pow(a, 2)+Math.pow(b,2))/(a*(a*c+b*e)+b*(a*d+b*f));

            x1=x-falka*dx(x, y);
            y1=y-falka*dy(x, y);

            System.out.printf("x: %.8f y: %.8f", x,y);
            System.out.println(" ");
        }
    }
}