/*	Simple Least Squares Applet
	20-July-1997
	This is the fourth in a series of simple statistics applets.
	Written in 1997 by Bryan Lewis
	Department of Mathematics and Computer Science
	Kent State University
	This software is free. Please feel free to use 
	it and modify it.
	
	Needs the following objects:
	lsq.class	the applet
	editor.class 	data editor object
	Matrix.class	linear algebra routines
	ExampleData.class	generates random examples
	specialFucntions.class	F-distribution and others
	
	History:
	11.August, 1997: Added quadratic, cubic models (requested)
	21.December, 1997: Fixed string output of p-value
	24.December, 1997: Incorporated data editor object
	24.December, 1997: Added "nice" output monoString code	
	1.June, 1998: Added fourth degree polynomial fitting
*/

import java.awt.*;
import java.lang.*;
import java.applet.*;

public class lsqFrame extends editor {	

  Panel controlPanel = new Panel();
  Button compute = new Button("Compute");
  Button example = new Button("Example data");
  Button plotData = new Button("Plot data");
  public Choice model = new Choice();
  Plot plot1 = new Plot();
  String newln;
  double zero=0.00001;	// precision for output display
  
  public lsqFrame(String title) {
    super(title);
    // Set line termination character
    newln = System.getProperty("line.separator");
    // Set up the applet
    setBackground(Color.lightGray);
    
    plot1.resize(200,175);
    topPanel.add("East",plot1);	
    plot1.repaint();
    
    controlPanel.add(compute);
    controlPanel.add(example);
    controlPanel.add(plotData);
    model.addItem("Linear");
    model.addItem("Quadratic");
    model.addItem("Cubic");
    model.addItem("Quartic");
    controlPanel.add(model);
    add("South",controlPanel);
    resize(475,450);
    show();
  }
  
  public boolean action(Event e, Object arg) {
    
    if (e.target == compute) {
      // calculate the result
      result.setText("Calculating...");
      Matrix D = new Matrix(data.getText());
      plot1.P = D;
      plot1.repaint();
      result.setText(compute(D));
    }   		   		
    else if (e.target == example) {
      // display some example data
      ExampleData ed = new ExampleData();
      data.setText(ed.example);
    }
    else if (e.target == plotData) {
      // plot the data
      plot1.M = new Matrix("0;0");
      plot1.P = new Matrix(data.getText());
      plot1.repaint();
    }
    return super.action(e, arg);
    
  }	
  
  String compute(Matrix D){
    // perform the least squares calculations
    int i, j, k;
    String result;
    // create a model matrix (normal equations)
    j = model.getSelectedIndex() + 2;
    Matrix A = new Matrix(D.rows, j, 1);
    for(k=1; k<A.columns; k++){
      for(i=0; i<A.rows; i++){
	A.element[i][k] = Math.pow(D.element[i][0],k);
      }
    }
    
    // form QR decomposition of A
    Matrix Q = A.Q();
    Matrix R = Matrix.multiply(Q.transpose(), A);
    Matrix b = Matrix.multiply(Q.transpose(), D.sub(0, D.rows-1, 1, 1));
    // truncate the non-square portion...
    b = new Matrix(b.sub(0, R.columns-1, 0, 0));
    R = new Matrix(R.sub(0, R.columns-1, 0, R.columns-1));
    Matrix x = Matrix.divide(b,R);
    // x now contains the model fit
    plot1.P = new Matrix(data.getText());
    plot1.M = x;
    plot1.repaint();
    // now calculate some statistics...
    b = D.sub(0, D.rows-1, 1, 1);
    double ymean = b.average();
    double yest = 0;
    double numeratorSum = 0;
    double denominatorSum = 0;
    for(i=0; i<D.rows; i++){
      yest = 0;
      for(j=0; j<x.rows; j++){
	yest = yest + x.element[j][0]*Math.pow(D.element[i][0],j);
      }
      numeratorSum = numeratorSum + Math.pow((yest - ymean),2);
      denominatorSum = denominatorSum + Math.pow((b.element[i][0] - ymean),2);
    }
    // "r-squared"
    double r2 = numeratorSum/denominatorSum;
    // calculate the residual norm...
    Matrix Ax = Matrix.multiply(A,x);
    Matrix r = Matrix.subtract(Ax,b);
    double ssr = Math.pow(r.norm(),2);
    double F = (numeratorSum/(A.columns-1))/(ssr/(b.rows-2));
    specialFunctions sf = new specialFunctions();
    double p = 	sf.fDist((double)(A.columns-1),(double)(b.rows-2), F);
    // build a report
    result ="Simple Least Squares Data Fitting" + newln +
      "July 21, 1997     by Bryan Lewis      Kent State University" +
      newln + newln + "y = " + x.element[0][0];
    if(x.element[1][0]>=0){result = result  + " +";}
    result = result + " " + x.element[1][0] + "x";
    for(j=2; j<x.rows; j++){
      if(x.element[j][0]>=0){result = result  + " +";}
      result = result  + " " + x.element[j][0] +"x^" + j;
    }
    result = result + "." + newln +
      "Residual 2-norm = " + monoString(ssr) +  newln;
    if(x.rows == 2){
      result = result + "Generalized correlation coefficient (r^2) = " + monoString(r2) +  newln  +
	newln + "                Analysis of Variance" + newln +
	monoString("Source")  + monoString("Sum squares") + monoString("Deg. Freedom") +
	monoString("Mean square")+monoString("F ratio")+monoString("P(X>F)")+ newln +
	
	monoString("Regression") + monoString(numeratorSum) + 
	monoString(A.columns-1) + monoString(numeratorSum/(A.columns-1)) +
	monoString(F) + p + newln +
	
	monoString("Residual") + monoString(ssr) + monoString(b.rows-2) +
	monoString(ssr/(b.rows-2)) + newln ;
    }
    return result;
  }
  
  String monoString(String s) {
    // convert a generic string s to a fixed length one	
    String sAdd = new String(s + "                                      ");
    return sAdd.substring(0,14);
  }
  String monoString(double s) {
    // convert a generic double s to a "nice" fixed length string	
    Double sD = new Double(s);
    String sAdd = new String();
    if(s>zero){
      sAdd = new String(sD.toString()); }
    else{ sAdd = "<0.00001"; }
    if(sAdd.length()>10){
      sAdd = sAdd.substring(0,10); }
    sAdd = sAdd + "                                      ";
    return sAdd.substring(0,14);
  }
  String monoString(int s) {
    // convert a generic integer s to a fixed length string	
    Integer sD = new Integer(s);
    String sAdd = new String(sD.toString());
    sAdd = sAdd + "                                      ";
    return sAdd.substring(0,14);
  }
  
}