/**
 * This is a little code to do an Euler integration.
 */

#include<vector>
#include<iostream>

using std::vector;

const double k=0.3;

/**
 * This just does a single mass on a spring.  Assume that the vector has
 * position at [0] and velocity at [1].
 */
void springMass(double t,vector<double> x,vector<double> &dx) {
	dx[0]=x[1];
	dx[1]=-k*x[0];
}

template<class Func>
void eulerStep(double t,vector<double> &x,double dt,Func &f) {
	vector<double> dx(x.size());
	f(t,x,dx);

	for(vector<double>::iterator i1=dx.begin(),i2=x.begin(); i1!=dx.end(); ++i1,++i2) {
		*i2+=dt*(*i1);
	}
}

int main(void) {
	double dt=0.001;
	vector<double> x(2);
	x[0]=1.0;
	x[1]=0.0;
	for(int i=0; i*dt<100.0; ++i) {
		eulerStep(i*dt,x,dt,springMass);
		if(i%(int)(1.0/dt)==0) std::cout << x[0] << " " << x[1] << " " <<
			(0.5*x[1]*x[1]+0.5*k*x[0]*x[0]) << "\n";
	}
}