#include <math.h>
#include "CMyVektor.h"
#include "CMyMatrix.h"
#include "C_DGLSolver.h"
#include <iostream>
using namespace std;

CMyVektor DGLSystem(CMyVektor y, double x) {
	CMyVektor result(2);
	result.setElement(1, 2 * y.getElement(2) - x * y.getElement(1));
	result.setElement(2, y.getElement(1) * y.getElement(2) - 2 * pow(x, 3));
	return result;
}

double DGL_dritter_Ordnung(CMyVektor y, double x) {
	return 2 * x * y.getElement(2) * y.getElement(3) + 2 * pow(y.getElement(1), 2) * y.getElement(2);
}

int main() {
	int option;

	cout << "Was soll berechnet werden? \n" <<
		"1 Euler-Verfahren DGL\n" <<
		"2 Heun-Verfahren DGL\n" <<
		"3 Abweichungen DGL 3.O\n" <<
		"0 Beenden\n"
		"> ";
	cin >> option;

	while (0 < option && option < 4) {
		switch (option) {
		case 1: {
			CMyVektor startwerte(vector<double>{0, 1});
			double xStart = 0;				// x0 = 0
			double xEnd = 2;
			C_DGLSolver dglSystemTest(DGLSystem);
			dglSystemTest.euler(startwerte, xStart, xEnd, 100);
			break;
		}
		case 2: {
			CMyVektor startwerte(vector<double>{0, 1});
			double xStart = 0;				// x0 = 0
			double xEnd = 2;
			C_DGLSolver dglSystemTest(DGLSystem);
			dglSystemTest.heun(startwerte, xStart, xEnd, 100);
			break;
		}
		case 3: {
			CMyVektor startwerte(3);
			CMyVektor eulerResult(3);
			CMyVektor heunResult(3);
			CMyVektor allResults(8);
			C_DGLSolver dglSystemTest(DGL_dritter_Ordnung);


			double schritte;
			double xStart;
			double xEnd;
			int j = 1;
			for (int i = 1; i < 5; i++) {
				schritte = pow(10, i);
				xStart = 1;
				xEnd = 2;
				startwerte.setElements(vector<double>{1, -1, 2});
				eulerResult = dglSystemTest.euler(startwerte, xStart, xEnd, schritte);
				allResults.setElement(j, eulerResult.getElement(1) - 0.5);

				startwerte.setElements(vector<double>{1, -1, 2});
				heunResult = dglSystemTest.heun(startwerte, xStart, xEnd, schritte);
				allResults.setElement(++j, heunResult.getElement(1) - 0.5);
				j++;
			}
			cout << endl;
			int k = 1;
			cout << setw(10) << "Verfahren" << setw(10) << "Schritte" << setw(10) << "Δ\n";
			for (int j = 1; j <= 4; j++) {
				double schritte = pow(10, j);
				// E = s+1 , H = E*2
				cout << setw(10) << "Euler" << setw(10) << setprecision(0) << schritte << setw(10) << scientific << setprecision(1) << allResults.getElement(k) << endl;
				cout << setw(10) << "Heun" << setw(10) << setprecision(0) << schritte << setw(10) << scientific << setprecision(1) << allResults.getElement(++k) << endl << endl;
				
				k++;
			}
			break;
		}
		}

		cout << "\nHauptmenü: \n" <<
			"1 Euler-Verfahren DGL\n" <<
			"2 Heun-Verfahren DGL\n" <<
			"3 Euler/Heun Vergleich DGL 3.O\n" <<
			"0 Beenden\n"
			"> ";
		cin >> option;

	};
	cout << endl << endl;
	system("PAUSE");
}