// lsfit_lect.java  from lecture notes
//                  compile   javac -cp . lsfit_lect.java
//                  run       java -cp . lsfit_lect > lsfit_lect_java.out
//                  just first order, linear fit

class lsfit_lect
{
  //       fit      x1   x2   x3          y    y = a x1 + b x2 + c x3
  double xd[][] = {{1.0, 2.5, 3.7},  //  32.5
                   {2.0, 2.5, 3.6},  //   7.2
                   {3.0, 2.7, 3.5},  //   6.9
	 	   {2.2, 2.1, 3.1},  //  22.4
		   {1.5, 2.0, 2.6},  //  10.4
		   {1.6, 2.0, 3.1}}; //  11.3
    
  double yd[] = {32.5, 7.2, 6.9, 22.4, 10.4, 11.3}; // Y actual
  double A[][] = new double[3][3];
  double X[] = new double[3];
  double Y[] = new double[3];     // |A| * |X| = |Y|  |X| will be  a, b, c

  lsfit_lect()
  {
    System.out.println("lsfit_lect.java run to make lsfit_lect.out");
    for(int i=0; i<3; i++)
    {
      Y[i] = 0.0; // must start sum with zero
      for(int k=0; k<6; k++) Y[i] += xd[k][i]*yd[k]; // Xi * Yk

      for(int j=0; j<3; j++)
      {
        A[i][j] = 0.0;  // must start sum with zero
        for(int k=0; k<6; k++) // run through observations
        {
          A[i][j] += xd[k][j]*xd[k][i];  // Xj * Xi
        }
      }
    }  // end i
    new simeq(A, Y, X); // pick correct argument list
    System.out.println("a="+X[0]+" b="+X[1]+" c="+X[2]);
    // check
    System.out.println("really bad fit");
    for(int k=0; k<6; k++)  // k is observation
       System.out.println("Y_actual="+yd[k]+" Y_approximate="+
         (X[0]*xd[k][0]+X[1]*xd[k][1]+X[2]*xd[k][2]));
  }
  public static void main (String[] args)
  {
    new lsfit_lect(); // construct and execute
  }
} // end lsfit_lect.java