/*
 * Code for fitLine
 * 	with self-test main routine
 *
 * @author Chee Yap
 * Basic Algorithms, Fall 2005
 */


import java.math.*;
import java.util.Random;

public class fitLine {

   // scalar product of two vectors:
   static double scalar (double[] X, double[] Y)
   {
     double s = 0;
     for (int i=0; i< X.length; i++) 
	s += X[i]* Y[i];
     return s;
   }

   // computes a 2x2 matrix based on 2 input basis vectors (phi0, phi1):

   static double[][] matrix (double[] phi0, double[] phi1)
   {
     double[][] m = new double[2][2];
     m[0][0] = scalar(phi0, phi0);
     m[0][1] = m[1][0] = scalar(phi0, phi1);
     m[1][1] = scalar(phi1, phi1);
     return m;
   }
     
   // computes determinant of a 2x2 matrix:

   static double det (double[][] m)
   {
     return (( m[0][0]*m[1][1] ) - ( m[0][1]* m[1][0] ));
   }

   /**
    * fitLine computes the least squares best fit line (a+bX) for a function
    * where the (discrete) function is given by lX and lY
    * @param lX is a vector of some length n
    * @param lY is a vector of the same length n
    * @returns [a,b] representing the the least-squares line (a+bX)
    */

    public static double[] fitLine(double[] lX, double [] lY) {

	int n = lX.length;

	double[] l1 = new double[n];
	for (int i=0; i<n; i++)
		l1[i] = 1;

	double[][] m = matrix(l1, lX);

        double d = det(m);

        double c0 = scalar(l1, lY);
        double c1 = scalar(lX, lY);

	double[] r = new double[2];
	r[0] = ((   m[1][1] * c0 ) - ( m[0][1] * c1 ))/d;
	r[1] = (( - m[1][0] * c0 ) + ( m[0][0] * c1 ))/d;

	return r;
    } // fitLine

    public static void main (String [] args){
	// Test: y= ax + b
	double a = 1.234;
	double b = 5.678;
	int n = 10;			// number of points
	double inc = 10.5;		// increment 
	Random rnd = new Random ();	// Random number generator

	double[] lX = new double[n];	// X array
	double[] lY = new double[n];	// Y array
	lX[0] = 0.0;
	for (int i=0; i<n-1; i++) {
		lY[i] = a * lX[i] + b + rnd.nextDouble();
		lX[i+1] = lX[i] + inc;
	}
	lY[n-1] = a * lX[n-1] + b;

	double [] results = new double [2];		
	System.out.println("         a = " + a);
	System.out.println("         b = " + b);
	System.out.println("--------------------------------------");
	results=fitLine(lX,lY);
	System.out.println("After fitting:");
	System.out.println(" slope a = "+results[1]
			+", y-intercept b = "+results[0]);
    } //main

}//class