#include <math.h>
#include "CMyVektor.h"
#include "CMyMatrix.h"

using namespace std;

// f( [x,y] ) = sin(x * y) + sin(x) + cos(y)
double ff(CMyVektor X) {
	double x = X[0];
	double y = X[1];

	return (sin(x * y) + sin(x) + cos(y));
}

// g( [x,y,z] ) = -(2x^2 - 2xy + y^2 + z^2 - 2x - 4z)
double gg(CMyVektor X) {
	double x = X[0];
	double y = X[1];
	double z = X[2];

	return -(2 * pow(x, 2) - 2 * x * y + pow(y, 2) + pow(z, 2) - 2 * x - 4 * z);
}

CMyVektor f(CMyVektor x) {
	CMyVektor result(3); // da f: R^4 -> R^3
	result[0] = x[0] * x[1] * exp(x[2]);
	result[1] = x[1] * x[2] * x[3];
	result[2] = x[3];
	return result;
}

int main() {

	cout << "Aufgabe_2 :\n" << jacobi(CMyVektor{ {1, 2, 0, 3} },
		[](CMyVektor x) -> CMyVektor { return { {x[0] * x[1] * exp(x[2]), x[1] * x[2] * x[3], x[3]} }; })
		<< endl;

	newtonverfahren({ {1, 1} },
        [](CMyVektor x) -> CMyVektor { return { {pow(x[0], 3) * pow(x[1], 3) - 2 * x[1], x[0] - 2} }; });
    return 0;
}