#include <iostream>
#include <cmath>
#include <iomanip>
#include <vector>

using namespace std;

double f(double x, double y) {

	return pow(y, 2) - 2*x*y - 6*y + 2*x*x + 12;
}

double fdx(double x, double y) {

	return - 2*y + 4*x;
}

double fdy(double x, double y) {

	return 2 * y - 2 * x - 6;
}

void quadratica(double xi, double yi, int numIt) {

	vector<vector<double>> H = { { 0.5, 0.5 },{ 0.5, 1 } }; //matriz hessiana inversa maxima salva vidas
	double xn, yn;

	for (int i = 0; i < numIt; i++) {

		xn = xi - H[0][0] * fdx(xi, yi) + H[0][1] * fdx(xi, yi);
		yn = yi - H[1][0] * fdy(xi, yi) + H[1][1] * fdy(xi, yi);

		if(f(xn,yn) < f(xi,yi)) {
			xi = xn;
			yi = yn;
		}

		cout << "x = " << xn << endl;
		cout << "y = " << yn << endl;
		cout << "f(x,y) = " << f(xn, yn) << endl;

	}

}

int main()
{
	const int OUT_PREC = 5;
	cout << fixed << setprecision(OUT_PREC);

	quadratica(1, 1, 2);

	system("pause");
    return 0;
}