#include <cmath>
#include <iostream>

using namespace std;




void dyskretyzacja(int n, int min, int max, double *x, double *y) {

	double skok = (max - min) / (1.0 * n );


	for (int i = 0; i <= n; i++) {
		x[i] = min + skok * i;
		y[i] = (sin(2 * x[i]) * sin(sqrt(2) * x[i]));
	}

}

void znajdzGiR(double **g, double *r, double *x,double *y,  int n, int m) {
	//for (int i = 0; i < n; i++) {
	//	std::cout << "x[" << i << "]: " << x[i] << std::endl;
	//}
	//for (int i = 0; i < n; i++) {
	//	std::cout << "y[" << i << "]: " << y[i] << std::endl;
	//}



	//wypelnianie G
	for (int k = 0; k <= m; k++) {
		for (int j = 0; j <= m; j++) {
			double sum = 0;
			for (int i = 0; i <= n; i++) {
				sum += pow(x[i], j + k);
			}

			g[k][j] = sum;

		}
	}

//	std::cout << "G:" << std::endl;
	for (int k = 0; k <= m; k++) {
		for (int j = 0; j <= m; j++) {
		//	std::cout << g[k][j] << " ";
		}
	//	std::cout << std::endl;
	}

	//wypelnianie R
	for (int k = 0; k <= m; k++) {
		double sum = 0;
		for (int i = 0; i <= n; i++) {
			sum += y[i] * pow(x[i], k);
		}
		r[k] = sum;
	}
}


void zrobTrojkatna(int m, double **g, double *r) {

	for (int x = 0; x <= m; x++) {


		for (int y = x + 1; y <= m; y++) {
			double wspolczynnik = 1 * (g[y][x] / g[x][x]);

		//	std::cout << wspolczynnik << std::endl;

			for (int z = x; z <= m; z++) {
				g[y][z] = g[y][z] - wspolczynnik * g[x][z];
			}
			r[y] = r[y] - wspolczynnik * r[x];

		}
	}


	//std::cout << "Trojk:" << std::endl;
	for (int k = 0; k <= m; k++) {
		for (int j = 0; j <= m; j++) {
		//	std::cout << g[k][j] << " ";
		}
	//	std::cout << std::endl;
	}

}

void rozwiazTrojkatna(double *aj, double **g, double *r, int m) {


	aj[m] = r[m] / g[m][m];
	for (int i = m - 1; i >= 0; i--){
		double suma = 0;
		for (int j = i + 1; j <= m; j++){
			suma += g[i][j] * aj[j];
		}
		aj[i] = (r[i] - suma) / g[i][i];
	}

}

void rozwiaz(int m,double **g, double *r, double &fx0, double *aj, double x0) {

	zrobTrojkatna(m,g,r);
	rozwiazTrojkatna(aj,g,r,m);

	double sum = 0;
	for (int i = 0; i <= m; i++) {
		sum += aj[i] * pow(x0, i); \
	}
	fx0 = sum;

}

void obliczBlad(double &S, int n,int m, double *aj,double *x, double *y) {
	double summm = 0;
	for (int i = 0; i <= n; i++){
		double sum = 0;
		for (int j = 0; j <= m; j++){
			sum += aj[j] * pow(x[i], j);
		}
		summm += pow(sum - y[i], 2);
	}
	S = sqrt(summm / (n + 1));

}

double Q(double x, double *a, int m)
{
	double res = 0.0;
	for (int i = 0; i <= m; i++)
	{
		res += a[i] * pow(x, i);
	}
	return res;
}


int main()
{
	using namespace std;
	int n = 49;
	int m = 5;
	int min = -2;
	int max = 2;
	double x0 = 1.5;
	double fx0 = 0;

	double S = 0;
	double* x = new double[n + 1];
	double* y = new double[n + 1];

	double** g	= new double*[m + 1];
	double* r = new double[m + 1];

	for (int i = 0; i <= m; i++) {
		g[i] = new double[m + 1];
	}

	double *aj = new double[m + 1];


	dyskretyzacja(n, min, max, x, y);
	znajdzGiR(g, r, x, y, n, m);
	rozwiaz(m, g, r, fx0, aj, x0);
	obliczBlad(S, n, m, aj, x, y);

	for (int i = 0; i <= m; i++) {
		std::cout << "wsp[" << i << "]: " << aj[i] << std::endl;
	}
cout << "BLAD: " << S << endl;

	//
	//
	//for (int i = 0; i < 50; i++)
//		cout << x[i] << endl;
//	cout << endl << endl;
//	for (int i = 0; i < 50; i++)
//		cout <<Q(x[i], aj, m) << endl;

	for (;;);


	return 0;
}