// Estimatin of Roots by Exner Enterprises, C.2000
// Author: Nicholas Exner
// http://www.uiuc.edu/ph/www/exner
// Free to redistribute/publish/modify pending that
// the above comments are retained.

import java.applet.*;
import java.awt.*;
import java.awt.event.*;
import java.net.URL;
import java.util.*;

public class Integration2 extends java.applet.Applet {
	Panel controlA, controlB;
	String S_formula;

	TextField inputA, inputB, inputC, inputD;

  	TextArea ta;
      StringBuffer buf;
      Choice d;
	GraphFunction graph;

   public void init(){
	ta= new TextArea("Ready...",15,40);;
      buf= new StringBuffer();
	graph = new GraphFunction();

	// Layout Stuff
	controlA = new Panel();
	controlB = new Panel();
	controlA.setLayout(new GridLayout(5,2));	
	controlB.setLayout(new GridLayout(2,1));
	this.setLayout(new BorderLayout());
	controlA.setBackground(new Color(205,205,205));
	setBackground(new Color(205,205,205));	

	inputA = new TextField(3);
	inputB = new TextField(3);
	inputC = new TextField(10);
	inputD = new TextField(3);

	d = new Choice();
	d.addItem("All Methods");
      d.addItem("Rectangular");
      d.addItem("Trapezoidal");
	d.addItem("Simpson's");
	d.addItem("Romberg");

	controlA.add(new Label("Left Endpoint: "));
	controlA.add(inputA);
	controlA.add(new Label("Right Endpoint: "));
	controlA.add(inputB);
	controlA.add(new Label("Formula: "));
	controlA.add(inputC);
	controlA.add(new Label("# of Partitions:"));
	controlA.add(inputD);
	controlA.add(d);
	controlA.add(new Button("Calculate"));

	inputA.setText("0");
	inputB.setText("1");
	inputC.setText("y=x^3");
	inputD.setText("10");
	controlB.add(controlA);
	controlB.add(ta);
	add("West",graph);
	add("Center",controlB);
	repaint();
   }

  public void paint(Graphics g) {
	// Paint Nothing
   }

   public void processButton() {
		buf = new StringBuffer();	//Clean off buffer
		buf.append("Method name\t\t\tEstimated Integral\n");
		double aa = 0.0,bb = 0.0, dd=0.0;
		String spacedString="";
	try {
		aa = Double.valueOf(inputA.getText()).doubleValue();
		bb = Double.valueOf(inputB.getText()).doubleValue();
		dd = Double.valueOf(inputD.getText()).doubleValue();
		spacedString = inputC.getText();
        } catch (NumberFormatException e) { }

		S_formula = "";
		for (int i=0;i < spacedString.length();i++) {
			if (spacedString.charAt(i) != ' ')
				S_formula += spacedString.charAt(i);

		}
///////////
graph.reset();
for (int i=0;i<40;i++) {
	double step = Math.abs(bb-aa)/40;
	graph.addValue(aa+step*i,f(aa+step*i));
	System.out.println("1: "+f(1));
	System.out.println("-1: "+f(-1));
	System.out.println("-4: "+f(-4));

}
graph.findBounds();
graph.rescale();
///////////
		String key = d.getSelectedItem();
		if (key.equals("All Methods")) {
			rectangular(aa,bb,dd);
			trapezoidal(aa,bb,dd);
			simpsons(aa,bb,dd);
			romberg(aa,bb);
		}
			
		if (key.equals("Rectangular")) {
			rectangular(aa,bb,dd);
		}
		if (key.equals("Trapezoidal")) {
			trapezoidal(aa,bb,dd);
		}
		if (key.equals("Simpson's")) {
			simpsons(aa,bb,dd);
		}
		if (key.equals("Romberg")) {
			romberg(aa,bb);
		}		System.out.println("Button Pressed");
	     	ta.setText(buf.toString());
   } //End Processbutton

   public boolean action (Event evt, Object arg) {
	if (evt.target instanceof Button) {
		processButton();
	}
	return true;
   }

   public void rectangular(double a,double b, double n) {
	double sum1 = 0.0,
		 sum2=0.0, 
		 e=(b-a)/n,
		 x=a;

	for(int i=0;i<n;i++) {
		sum1 += f(x)*e;
    		x += e;
		sum2 += f(x) * e;
	}
	buf.append("Rectangular (Left Endpoint)\t\t"+sum1+"\n");
	buf.append("Rectangular (Right Endpoint)\t\t"+sum2+"\n");
   } // End Rectangular

   public void trapezoidal(double a,double b, double n) {
	double sum = 0.0,
		 e=(b-a)/n, 
		 x=a;

	for(int i=0;i<n;i++) {
		sum += e * (f(x) +  f(x+e))/2;
		x += e;
	}
	buf.append("Trapezoidal\t\t\t"+sum+"\n");
   } // End trapezoidal


   public void simpsons(double a,double b, double n) {
	if (n%2==1){
		buf.append("Simpson's: partition # not even.\n");
		return;
	}
	double sum = 0.0, x=a, e=((b-a)/n);

	for(int i=0;i<n;i+=2){
		sum = sum +e* (f(x)+4*f(x+e)+f(x+2*e))/3;
		x +=2*e;
	}
	buf.append("Simpson's\t\t\t"+sum+"\n");
   } // End trapezoidal


	public void romberg(double start, double end) {
		    double h;
		    int intervals = 8;
                double[][] tee = new double[intervals][intervals];
                h = end - start;
                tee[0][0] = h*(f(end) + f(start))*(0.5);
                //fill up the 0 column
                for(int i = 1; i<intervals ; i++)
                {
                    double sum = 0;
                    for(int j=1; j<=Math.pow(2,i-1) ; j++)
                    {
                        sum += f(start + (j-(0.5))*(h/Math.pow(2,i-1)) );
                    }
                    tee[i][0] = (0.5)*(tee[i-1][0]) + (h/Math.pow(2,i))*sum;
                    //System.out.println("stored "+tee[i][0]+" as the "+i+",0 array elt");
                }

                //fill up the rest o' the columns
                for(int j=1; j<intervals ; j++)
                {
                    for(int k = 1 ; k<=j ; k++)
                    {
                        tee[j][k] = (Math.pow(4,k)*tee[j][k-1] - tee[j-1][k-1])/(Math.pow(4,k) - 1);
                        //System.out.println("stored "+tee[j][k]+" as the "+j+","+k+" array elt");

                    }
                }
                	buf.append("Romberg\t\t\t\t"+tee[intervals-1][intervals-1]);
	} //End Romberg

 
public double f(double x) {
	String s = S_formula,
		 tempNum = "",
		 tempNum2= "";
	double total=0.0;
	boolean addStat = true;

	for (int i=0; i < s.length();i++) {

		if (isNum(s,i)){
			tempNum+=s.charAt(i);
		}	
		if (s.charAt(i) == 'x'){
			double totalTemp;
			// Get coefficient
			double temp=1;
			if (!tempNum.equals("")){
				temp = Double.valueOf(tempNum).doubleValue();
				tempNum="";
			}
			i++;
			if (i<s.length() && s.charAt(i)== '^'){
				tempNum2="";
				i++;
				while (i<s.length() && isNum(s,i)) {
					tempNum2+=s.charAt(i);
					i++;
				}
				double temp3=1;
				if (!tempNum2.equals("")){
				 	temp3= Double.valueOf(tempNum2).doubleValue();
				}
				totalTemp = Math.pow(x,temp3);
			} else {
				totalTemp = x;
			} // End ^
			if (addStat)
				total+=totalTemp*temp;
			else
				total-=totalTemp*temp;
		} // End x
		if (i < s.length() && s.charAt(i) == '+'){
			if (!tempNum.equals("")){
				double temp = Double.valueOf(tempNum).doubleValue();
				if (addStat)
					total+= temp;
				else
					total-= temp;
			}
			tempNum="";
			addStat=true;
		}
		if (i < s.length() && s.charAt(i) == '-'){
			if (!tempNum.equals("")){
				double temp = Double.valueOf(tempNum).doubleValue();
				if (addStat)
					total+= temp;
				else
					total-= temp;
			}	
			tempNum="";	
			addStat=false;	
		}
	} //End String search

	// Process last numbers
	if (!tempNum.equals("")){
		double temp = Double.valueOf(tempNum).doubleValue();
		if (addStat)
			total+= temp;
		else
			total-= temp;
	}
	return total;
}

	public static boolean isNum(String s,int i) {	
		if (s.charAt(i) >= '0' && (s.charAt(i)<= '9')) {
			return true;
		} else
			if (s.charAt(i) == '.')
				return true;
			else
				return false;
	}
} // End class Integration
/////////////////////////////////////////

class GraphFunction extends Canvas {
	Dimension size;
	int width=225,
	    height=225,
	    max=40,
	    index=0,
	    leftInterval=0,
	    rightInterval=0;

	double leftPt  = 0.0,
		 rightPt = 0.0,
		 upPt    = 0.0,
		 downPt  = 0.0;
	double x[] = new double [max];
	double y[] = new double [max];
	boolean showGraph;

	public GraphFunction() {
		size = new Dimension (width,height);
		reset();
	}
	public void paint(Graphics g) {
		g.setColor(Color.blue);
		g.drawLine(0,height/2,width,height/2);
		// X grid lines
		int unit=20;
		for (int i=0;i<width;i+=unit)
			g.drawLine(i,(height/2)+3,i,(height/2)-3);
		g.drawString(""+leftPt,5,height/2+15);
		g.drawString(""+rightPt,width-20,height/2+15);

		if (showGraph) {
			for (int i=1;i< max;i++){
//				g.drawOval((int)Math.round(x[i]),(int)Math.round(y[i]),3,3);
				g.setColor(Color.red);
				g.drawLine((int)Math.round(x[i]),(int)Math.round(y[i]),
				(int)Math.round(x[i-1]),(int)Math.round(y[i-1]));
			}
		}
	}
  	public Dimension getMinimumSize() {
		return size;
	}
	public Dimension getPreferredSize(){
		return size;
	}
	public void findBounds() {
		leftPt=x[0];
		rightPt=x[0];
		upPt = y[0];
		downPt = y[0];
		for (int i=0;i< max;i++) {
			if (x[i] < leftPt)
				leftPt=x[i];
			if (x[i] > rightPt)
				rightPt=x[i];
			if (y[i] < upPt)
				upPt=y[i];
			if (y[i] > downPt)
				downPt=y[i];
		}
	} // End findBounds()
	public void rescale() {
		double scaleFactor, scaleFactorY;
		scaleFactor = width/Math.abs(rightPt-leftPt);
		scaleFactorY = -height/Math.abs(downPt - upPt);

		for (int i=0;i< max;i++) {
			x[i]=x[i]-leftPt;
			x[i]=x[i]*scaleFactor; //+width/2;
			y[i]=y[i]*scaleFactorY +height/2;
		}
		System.out.println("scaleX= "+scaleFactor+" scaleY= "+scaleFactorY);

		showGraph=true;
		repaint();
	}

	public void addValue(double x1, double y1) {
		if (index < max) {
			x[index]=x1;
			y[index]=y1;
			index++;
		}
	} // End addValue()

	public void reset() {
		for (int i=0;i< max;i++) {
			x[i]=0;
			y[i]=0;
		}
		leftInterval=0;
		rightInterval=0;
		index=0;
		showGraph=false;
	}
}