double getRiddersRoot(const std::function<double(double)>& f, const double& a, const double& b, const double epsilon)
	{
			double xl=a;
			double xr=b;
		while(std::abs(xl-xr)>epsilon)
		{
			double xn=(xl+xr)/2.;
			double xnn=xn+(xn-xl)*(std::abs(f(xl))/f(xl))*f(xn)/(sqrt(f(xn)*f(xn) -f(xl)*f(xr)));
			double xnnn=0.; //why did I have to initialize the xnnn here, instead of being able to separately declare it inside the ifs?
			if(f(xn)*f(xnn)<0)
			{
			xnnn=xn;
			}
			else if(f(xl)*f(xnn)<0)
			{
			xnnn=xl;
			}
			else
			{
			xnnn=xr;
			}

			if(xnn>xnnn)
			{
			xr=xnn;
			 xl=xnnn;
			}
			else
			{
			xr=xnnn;xl=xnn;
			}

		}

		return xr;
	}