//Evan Warner
	//This class stores an instance of a Gauss-Jacobi quadrature routine for a given alpha, beta, a, and b
   //The format of the calculated integral is fint(f(x)*(x-a)^alpha*(x-b)^beta,x,a,b)
	
    public class GaussQuad
   {
      private static ComplexFunction f;
      private static double alpha, beta;
      private static Complex a, b; 
       public GaussQuad(ComplexFunction f1, double alpha1, double beta1, Complex a1, Complex b1)
      {
         f=f1;
         alpha=alpha1;
         beta=beta1;
         a=a1;
         b=b1;
      }
      
      //Accepts points/weights in range [-1,1]; tranforms to other values using formula
   	//fint((x-a)^alpha*(x-b)^beta*f(x),x,a,b)=-c^(alpha+beta+1)*fint((1-x)^alpha*(1+x)^beta*f(c*x+m),x,-1,1)
   	//where m=(a+b)/2 and c=b-m=m-a.
       public Complex integrate(int N)
      {
         GaussJacobiWeights gjw = new GaussJacobiWeights(alpha,beta,N);
         double[] points = gjw.getPoints();
         double[] weights = gjw.getWeights();
         Complex m= b.add(a).divide(2);
         Complex c= b.subtract(m);
         Complex sum = new Complex(0,0);
         for(int i=0;i<weights.length;i++)
            sum=sum.add(f.value((c.multiply(points[i])).add(m)).multiply(weights[i]));
         sum=sum.multiply(c.power(alpha+beta+1));
         return sum;
      }
   }