import java.applet.Applet;
import java.awt.*;
import java.awt.event.*;
import java.applet.*;
import java.awt.geom.*;
import java.math.*;

/**This class is only implemented for the exponents e=1 and e=2.**/

public class IntervalEnergyEstimator {


    /**1 means eliminate.*/

    public static int eliminate(Interval e2,double E,IntervalBoxConfiguration X) {
	Interval e1=energyLowerBound(E,X);
	if(e1.l>e2.r) return(1);
	return(0);
    }



    /**Here is the main energy estimate.  The second number tells which index
       makes the biggest contribution to the error term.**/

     public static Interval energyLowerBound(double E,IntervalBoxConfiguration X) {
	Interval e1=vertexEnergy(E,X);
	Interval e2=errorTerm(E,X);
	Interval t=Interval.minus(e1,e2);
	return(t);
    }

    /**This routine computes the energy at the 128 vertices of a dyadic box and
       then takes the min.**/

    public static Interval vertexEnergy(double E,IntervalBoxConfiguration X) {
	double min=10000000;
	Interval test=new Interval(0.0);
	IntervalComplex[] Z=new IntervalComplex[4];
	for(int n=0;n<128;++n) {
	    Z=X.getConfiguration(n);
	    test=IntervalEnergy.energy(E,Z);
	    if(min>test.l) min=test.l;
	}
	return(new Interval(min));
    }



    /**Here is the error term.  This follows the notation in the paper.**/

    public static Interval errorTerm(double E, IntervalBoxConfiguration X) {
	Interval total=new Interval(0.0);
	Interval test=new Interval(0,0);

	for(int i=0;i<4;++i) {
	    test=errorTermSingleIndex(E,X,i);
	    total=Interval.plus(total,test);
	}
	return(total);
    }



    /**For an individual index **/

    public static Interval errorTermSingleIndex(double E, IntervalBoxConfiguration X,int i) {
	Interval total=new Interval(0.0);
	Interval d=X.B[i].delta();

	    for(int j=0;j<5;++j) {
		if(j!=i) {
		    total=Interval.plus(total,Interval.times(Interval.times(d,d),epsilon(E,X.B[i],X.B[j])));
		}
	    }
	return(total);
    }





    /**epsilon from the paper**/

    public static Interval epsilon(double E,IntervalBox B1,IntervalBox B2) {
	Interval R=IntervalSeparation.psiMin(B1,B2);
	if(R.l<=0) return(new Interval(Math.pow(2,50)));
	Interval l1=lambda1(E,B1,B2,R);
	Interval l2=lambda2(E,B1,B2,R);
	l1=Interval.max(new Interval(0.0),l1);
	Interval l3=Interval.plus(l1,l2);
	return(l3);
    }



    /**lambda 1 from the paper**/

    public static Interval lambda1(double e,IntervalBox B1,IntervalBox B2,Interval R) {

	Interval E0=new Interval(e);
	Interval ONE=new Interval(1.0);
	Interval E1=Interval.plus(E0,ONE);
	Interval E2=Interval.plus(E1,ONE);

                         Interval R0=new Interval();
	      if(e<1.5) R0=new Interval(R);  //R
	      if(e>1.5) R0=Interval.times(R,R);   //R^2

                        Interval R2=new Interval();
                         if(e<1.5) R2=Interval.times(Interval.times(R,R),R);   //R^3
                         if(e>1.5) R2=Interval.times(Interval.times(R,R),Interval.times(R,R));   //R^4


	if(B1.type==0) {
	    Interval t1=Interval.divide(Interval.times(E0,E1),Interval.times(new Interval(4.0),R2));
	    Interval t2=Interval.divide(Interval.times(E0,E2),Interval.times(new Interval(16.0),R0));
	    Interval t=Interval.minus(t1,t2);
	    return(t);
	}

	if(B1.type<1.5) {
	    Interval t1=Interval.divide(Interval.times(E0,E1),Interval.times(new Interval(8.0),R2));
	    Interval t2=Interval.divide(Interval.times(E0,E2),Interval.times(new Interval(32.0),R0));
	    Interval t=Interval.minus(t1,t2);
	    return(t);
	}
	return(new Interval(0.0));
    }


    /**lambda2 from the paper. **/


    public static Interval lambda2(double e,IntervalBox B1,IntervalBox B2,Interval R) {

	Interval E=new Interval(e);

	if(B1.type==1) {
	    Interval R1=new Interval();
                      if(e<1.5) R1=Interval.times(R,R); //R^2
	    if(e>1.5) R1=Interval.times(Interval.times(R,R),R);   //R^3

	    Interval t=Interval.divide(E,Interval.times(new Interval(8.0),R1));
	    return(t);
	}

	if(B1.type==0) {  
	    Interval R1=new Interval();
	    if(e<1.5) R1=Interval.times(R,R); //R^2
	    if(e>1.5) R1=Interval.times(Interval.times(R,R),R);   //R^3

	    Interval ONE=new Interval(1.0);
	    Interval t0=Interval.divide(E,Interval.times(new Interval(7.98),R1));
	    Interval x1=B1.xAbsMax();
	    Interval y1=B1.yAbsMax();
	    Interval t1=Interval.sqrt(Interval.plus(ONE,Interval.times(x1,x1)));
	    Interval t2=Interval.sqrt(Interval.plus(ONE,Interval.times(y1,y1)));
	    Interval t=Interval.times(t0,Interval.plus(t1,t2));
	    return(t);
	}
	return(new Interval(0.0));
    }



}