#include <iostream>
#include <math.h>
#include <fstream>
#include <string>

using namespace std;

// y = cos^2(x) * sin(sqrt(5)*x)
// metoda potęgowa

double y(double x) {
	return (cos(x)*cos(x))*sin((sqrt(5)*x));
}

void dyskretyzuj(double a, double b, double n, double *X, double *Y) {
	for (int i = 0; i <= n; i++){
		X[i] = a + i * (b - a) / n;
		Y[i] = y(X[i]);
	}
}

void macierzGR(double **G, double *R, double *X, double *Y, double m, double n){
	double pom = 0;

	for (int k = 0; k <= m; k++){
		for (int j = 0; j <= m; j++){
			pom = 0;
			for (int i = 0; i <= n; i++){
				pom += pow(X[i], j + k);
			}
			G[k][j] = pom;
		}
	}

	for (int k = 0; k <= m; k++){
		pom = 0;
		for (int i = 0; i <= n; i++){
			pom += Y[i] * pow(X[i], k);
		}
		R[k] = pom;
	}
}

void rozwiaz(double **G, double *R, double *A, int m){
	for (int k = 1; k < m; k++){
		for (int i = k + 1; i < m; i++){
			for (int j = k + 1; j < m; j++){
				if (G[k][k] == 0){
					for (int l = 0; l < m; l++){
						G[k][l] += G[k + 1][l];
					}
					R[k] += R[k + 1];
				}
				else{
					G[i][j] -= ((G[i][k] * G[k][j]) / G[k][k]);
				}
			}
			R[i] -= ((G[i][k] * R[k]) / G[k][k]);
		}
	}

	for (int i = 1; i <= m; i++){
		for (int j = 0; j < i; j++){
			G[i][j] = 0;
		}
	}

	double suma = 0;

	A[m] = R[m] / G[m][m];

	for (int i = m - 1; i >= 0; i--){
		for (int j = i + 1; j < m; j++){
			suma += G[i][j] * A[j];
		}
		A[i] = ((R[i] - suma) / G[i][i]);
		suma = 0;
	}
}

double delta(double *X, double *Y, double *A, int m, int n){
	double suma = 0;
	for (int i = 0; i <= n; i++){
		double suma2 = 0;
		for (int j = 0; j <= m; j++){
			suma2 += A[j] * pow(X[i], j);
		}
		suma2 -= Y[i];
		suma += pow(suma2, 2);
	}
	suma /= (double)(n + 1);
	return sqrt(suma);
}

double Q(double *A, double x, int m){
	double suma = 0;
	for (int j = 0; j < m; j++){
		suma += A[j] * pow(x, j);
	}

	return suma;
}

void zapisz(double a, double b, int n, int m, double *X, double *Y, double **G, double *R, double *A, double blad, string s){
	ofstream plik(s);

	plik << "n = " << n << "\tm = " << m << "\t <a, b> = " << a << " " << b << endl;
	
	plik << "\nX\tY\tQ\n";
	for (int i = 0; i <= n; i++){
		plik << X[i] << "\t" << Y[i] << "\t" << Q(A, X[i], m) << endl;
	}

	plik << "\nA\n";
	for (int i = 0; i <= m; i++){
		plik << A[i] << endl;
	}

	plik << "\nBlad = " << blad << endl;

	plik.close();
}

int main() {

	double a = -2;
	double b = 2;
	int n = 49;
	int m = 1;

	for (m; m < 20; m++){
		double *X = new double[n + 1];
		double *Y = new double[n + 1];

		double **G = new double*[m + 1];
		double *R = new double[m + 1];

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

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

		dyskretyzuj(a, b, n, X, Y);

		macierzGR(G, R, X, Y, m, n);

		rozwiaz(G, R, A, m);
		
		string str = "wynik" + to_string(m) + ".txt";

		zapisz(a, b, n, m, X, Y, G, R, A, delta(X, Y, A, m, n), str);
	}

	system("pause");

	return 0;
}