/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
   Support by National Science Foundation                           
*/
/* JamaFit: NIST JAMA matrix libe least-squares parabola fit 
    y(x) = b0 + b1 x + b2 xx JAMA libe must be in same directory as 
    program, or modify CLASSPATH to include JAMA                  */
		
import Jama.*;  
import java.io.*;

public class JamaFit {  
	
	public static void main(String[] argv) {
		
    double []   x = {1., 1.05, 1.15, 1.32,  1.51, 1.68, 1.92};
    double []   y = {0.52, 0.73, 1.08, 1.44, 1.39, 1.46, 1.58}; 
    double [] sig = {0.1, 0.1, 0.2, 0.3, 0.2, 0.1, 0.1};
    int Nd = 7;                              // Number of data points
    double sig2, s, sx, sxx, sy, sxxx, sxxxx, sxy, sxxy, rhl;
    double [][] Sx = new double[3][3];            // Create 3x3 array
    double [][] Sy = new double[3][1];            // Create 3x1 array
		
    s = sx = sxx = sy = sxxx = sxxxx = sxy = sxy = sxxy = 0;
		                                      // Generate matrix elements
    for (int i=0; i <= Nd-1; i++)  {         
      sig2   = sig[i]*sig[i];
      s     += 1./sig2;
      sx    += x[i]/sig2;
      sy    += y[i]/sig2;
      rhl    = x[i]*x[i];
      sxx   += rhl/sig2;
      sxxy  += rhl*y[i]/sig2;
      sxy   += x[i]*y[i]/sig2;
      sxxx  += rhl*x[i]/sig2;
      sxxxx += rhl*rhl/sig2;
    }    
		                                                 // Assign arrays
    Sx[0][0] = s; 
    Sx[0][1] = Sx[1][0] = sx;
    Sx[0][2] = Sx[2][0] = Sx[1][1] = sxx;
    Sx[1][2] = Sx[2][1] = sxxx;
    Sx[2][2] = sxxxx;
    Sy[0][0] = sy;
    Sy[1][0] = sxy;
    Sy[2][0] = sxxy;
		                                            // Form Jama Matrices
    Matrix MatSx = new Matrix(Sx); 
    Matrix MatSy = new Matrix(3, 1);
    MatSy.set(0, 0, sy);
    MatSy.set(1, 0, sxy);
    MatSy.set(2, 0, sxxy);
		                                             // Determine inverse
    Matrix B = MatSx.inverse().times(MatSy);  
    Matrix Itest = MatSx.inverse().times(MatSx);      // Test inverse
		                                                    // Jama print
    System.out.print( "B Matrix via inverse" );   
    B.print (16, 14);
    System.out.print( "MatSx.inverse().times(MatSx) " );
    Itest.print (16, 14);
		                                           // Direct solution too
    B = MatSx.solve(MatSy);     
    System.out.print( "B Matrix via direct" );
    B.print (16,14);
		
               //Extract using Jama get & Print parabola coefficients
    System.out.println("FitParabola2 Final Results"); 
    System.out.println("\n");
    System.out.println("y(x) = b0 + b1 x + b2 x^2");
    System.out.println("\n");
    System.out.println("b0 = "+B.get(0,0));
    System.out.println("b1 = "+B.get(1,0));
    System.out.println("b2 = "+B.get(2,0));
    System.out.println("\n");
		                                                      // Test fit
    for (int i=0; i <= Nd-1; i++) {             
        s=B.get(0,0)+B.get(1,0)*x[i]+B.get(2,0)*x[i]*x[i];
        System.out.println
		             ("i, x, y, yfit = "+i+", "+x[i]+", "+y[i]+", "+s);}
 }   }