//  -----------------------------------------------------------------
//  -------  Numerische Mathematik                   ----------------
//  -------  Ib 03                                   ----------------
//  -------  Romberg Quadratur                       ----------------
//  -------                                          ----------------
//  -------  2005 Januar 26     Manfred Vogel        ----------------
//  -----------------------------------------------------------------

class Romberg{

	// # of Romberg steps
	static final int n = 12;
	static double[][] r = new double[n][n];

	// Integrationsintervall [a, b]
	static final double a = 1.0;
	static final double b = 2.0;
	
	// definiert die zu integrierende Funktion f
	static double f(double x)
	{
		if( x==0.0) return 0.0;
	    return x*Math.log(x);
//	    return 1.0/Math.sqrt(x*x-4.0) ;
//	    return x*x*Math.exp(-x);
//	    return x*x*Math.cos(x);

//		if( x==0.0) return 1.0;
//	    return Math.sin(x)/x;
//	    return Math.exp(-x*x);
	}


	// implementiert die Romberg Methode
	static double romberg(double a, double b, double eps)
	{
		r[0][0]=(b-a)/2.0 *(f(a)+f(b)) ;
		int k = 0;
		double h = (b-a);
		double sum;
		double err = 100.0;
		while (err > eps  &&  k < (n-1) ) 
		{
            k++;
			h= h/2.0 ;
			sum=0.0;
			for (int i = 1; i <= Math.pow(2,(k-1)); i++) sum += f(a+(2*i-1)*h);
			r[k][0]= (r[k-1][0] + h*2.0*sum)/2.0;
			for (int j = 1; j <= k; j++)  {
			r[k][j]= r[k][j-1] + (r[k][j-1] - r[k-1][j-1])/(Math.pow(4,j)-1.0);
            err= Math.abs( r[k][k] - r[k-1][k-1] ); 
			}
			System.out.println  (k+". Romberg-Approximation :" + r[k][k]);
		}
        if ( k ==  n-1) r[k][k]=-999.999;
		return r[k][k];
	}

	public static void main(String[] args)
	{
		double integral = romberg(a, b, 1e-6);
		
		System.out.println("\n\n");
		System.out.println(" ** Romberg Integration ** " + "\n");
		if ( integral == -999.999) System.out.print  ("    Integral( f(x), x=a..b )    not converged "); 
		else System.out.print  ("    Integral( f(x), x=a..b ) = " + integral);
		System.out.println("\n\n");
	}
}