/*     RegressionExampleSix

       Example of the use of the class Regression demonstrating
       the use of the non-linear regression method, Regression.simplexPlot
       in fitting data to the shifted rectangular hyperbola function,
        y = Ao.x/(theta = x) + alpha
       with  Ao, theta and alpha unknown
       The weighted regression uses both x and y experimental errors

       Michael Thomas Flanagan
       http://www.ee.ucl.ac.uk/~mflanaga/java/Regression.html
       March 2012

   Copyright (c) 2012 - 2014

*   PERMISSION TO COPY:
*   Permission to use, copy and modify this software and its documentation for 
*   NON-COMMERCIAL purposes is granted, without fee, provided that an acknowledgement 
*   to the author, Dr Michael Thomas Flanagan at www.ee.ucl.ac.uk/~mflanaga, 
*   appears in all copies and associated documentation or publications. 
*   
*   Public listing of the source codes on the internet is not permitted. 
*   
*   Redistribution of the source codes or of the flanagan.jar file is not permitted. 
*   
*   Redistribution in binary form of all or parts of these classes is not permitted. 
*   
*   Dr Michael Thomas Flanagan makes no representations about the suitability 
*   or fitness of the software for any or for a particular purpose. 
*   Dr Michael Thomas Flanagan shall not be liable for any damages suffered 
*   as a result of using, modifying or distributing this software or its derivatives.
*
***************************************************************************************/

import flanagan.analysis.*;

public class RegressionExampleSix{
    
    public static void main(String[] args){
        
        // x and y data
        double[] x = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0};
        double[] y = {0.11, 0.51, 0.83, 1.15, 1.24, 1.38, 1.36, 1.49, 1.67, 1.66, 1.70};
        
        // x and y measurement errors
        double[] xErrors = {0.005, 0.024, 0.037, 0.059, 0.083, 0.106, 0.119, 0.142, 0.157, 0.177, 0.203};
        double[] yErrors = {0.051, 0.048, 0.049, 0.052, 0.051, 0.049, 0.053, 0.048, 0.049, 0.051, 0.050};
        
        // Number of data points
        int nPoints = 11;

       // Create instance of class to evaluate the rectangulat hyperbola regression function
        RectHypFunc func = new RectHypFunc(); 
        func.setXerrors(xErrors);
        func.setYerrors(yErrors);
        
        // Create instance of Regression
        Regression reg = new Regression(x, y, xErrors, yErrors);
        
        // Initial estimates for the Nelder-Mead simplex regression
        double[] start = new double[3];
        start[0] = 2.0;         // initial estimate of A0
        start[1] = 3.5;         // initial estimate of theta
        start[2] = 0.1;         // initial estimate of alpha
        
        // Initial step sizes
        double[] step = new double[3];
        step[0] = 0.4;         
        step[1] = 0.7;         
        step[2] = 0.05;   
          
        // Call simplex non-linear regression method with plotting option
        // using default tolerance anddefault maximum iterations
        reg.simplexPlot(func, start, step);
        
    }
}

class RectHypFunc implements RegressionFunction3{
    private double[] xErrors = null;
    private double[] yErrors = null;
    
    public double[] function(double[] p, double[] x, int ii){
        double[] y = new double[2];
        double hold = p[1] + x[0];
        
        // Calculated y value
        y[0] = p[0]*x[0]/hold + p[2];
        
        // Calculated the square of the weight
        y[1] = p[0]*p[1]/(hold*hold);   // dy/dx    
        y[1] = this.yErrors[ii]*this.yErrors[ii] + y[1]*y[1]*this.xErrors[ii]*this.xErrors[ii]; // w*w
        
        return y;
    }

    public void setXerrors(double[] xErrors){
        this.xErrors = xErrors;
    }
    
    public void setYerrors(double[] yErrors){
        this.yErrors = yErrors;
    }

}