#include <iostream>
#include <string>
#include <fstream>
#include <math.h>
using namespace std;

#define PI (3.141592653589793)
#define TIME_SELECTION 0.5

// Name: Daniel Summerhays
// Date: Sun Mar 28 18:12:43 EST 2004

//double func(double theta)
//{
//	return sqrt(2g/L * cos(theta));
//}

int main(int argc, char * argv[])
{
	string filename = "output.dat";
	double error, trueSoln;
	
	ofstream fout(filename.c_str());
	// numeric parameters
	double a = 0.;
	double b = TIME_SELECTION+1;
	int n;

	double h, t;

	// variables
	double theta, y; // y = theta'
	double preciseValue;
	
	// problem constants
	double c = 0.;
	double m = 1.;
	double gL = 6./11.;
	double gamma = 1.;
	double omega = sqrt(gL);

	theta = 1.;
	y = 0.;

	h = .000001;
	n = (int)((b-a)/h);

	for(int i = 1; i <= n+1; i++)
	{
		theta = theta + h*y;
  		y = y + h*(-c/m*y - gL*sin(theta) + gamma*cos(omega*t));
		t = a + i*h;
		if(t == TIME_SELECTION)
			preciseValue = theta;
	}


	for(h = TIME_SELECTION; h >= TIME_SELECTION/((double)(2<<5)); h /= 2){

	//double h = .1;
	n = (int)((b-a)/h);
	
	
	theta = 1.;
	y = 0.;

	
	t = a;
//	fout << "[[" << t << "," << theta << "]" << endl;
	cout << "[[" << t << "," << theta << "]" << endl;
//	fout << "[[" << t << "," << theta << "]";
//	cout << "[[" << t << "," << theta << "]";

	for(int i = 1; i <= n+1; i++)
	{
		theta = theta + h*y;
  		y = y + h*(-c/m*y - gL*sin(theta) + gamma*cos(omega*t));
		
		t = a + i*h;

		cout << ",[" << t << "," << theta << "]" << endl;


		if(t == TIME_SELECTION){
			//trueSoln = cos(sqrt(gL)*t);
			error = fabs(theta - preciseValue);
			cout << endl << "error/n: " << error/(double)n << endl;
			fout << h << " " << error/(double)n << endl;
			break;
		}

		//if(t == TIME_SELECTION){
		//	trueSoln = cos(sqrt(gL)*t);
		//	error = theta - trueSoln;
		//	cout << endl << "error/n: " << error/(double)n << endl;
		//	fout << h << " " << error/(double)n << endl;
		//	break;
		//}

	}
//	cout << "]";
//	fout << "]";
	}
	
	return 0;
}