/*     Example of the use of the class Regression demonstrating
       the use of the non-linear regression method, Regression.simplexPlot
       in fitting data to the function, y = a + b.exp(-c.x) + g^z
       with b fixed and a,c and g unknown

       Michael Thomas Flanagan
       http://www.ee.ucl.ac.uk/~mflanaga/java/Regression.html
       April 2007

   Copyright (c) 2007 - 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.Regression;
import flanagan.analysis.RegressionFunction;

// Class to evaluate the function y = a + b.exp(-c.x) + f^z
class FunctTwo implements RegressionFunction{

         private double b = 0.0D;

         public double function(double[ ] p, double[ ] x){
                  double y = p[0] + b*Math.exp(-p[1]*x[0]) + Math.pow(p[2], x[1]);
                  return y;
         }

         public void setB(double b){
            this.b = b;
         }
}

// Class to demonstrate non-linear regression method, Regression.simplex.
public class RegressionExampleTwo{

         public static void main(String[] arg){

                  // x1 data array
                  double[] xArray = {0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.5,7.0,7.5};
                  // x2 data array
                  double[] zArray = {0.0,0.13,0.26,0.39,0.52,0.65,0.78,0.91,1.04,1.17,1.3,1.43,1.56,1.69,1.82,1.95};
                  // observed y data array
                  double[] yArray = {12.1379,10.1886,8.9674,7.7824,7.9645,7.3671,6.8216,7.2602,7.1105,7.2873,7.9745,8.5188,9.1492,9.3891,10.4923,11.8675};
                  // estimates of the standard deviations of y
                  double[] sdArray = {0.25,0.22,0.27,0.23,0.21,0.26,0.28,0.24,0.25,0.23,0.27,0.22,0.23,0.26,0.28,0.24};

                  // combine x and z data into common array
                  int arrayLen = xArray.length;
                  double[][] doubleArray = new double[2][arrayLen];
                  for(int i=0; i<arrayLen; i++){
                            doubleArray[0][i]=xArray[i];
                            doubleArray[1][i]=zArray[i];
                  }

                  // Create instances of the class holding the function, y = a + b.exp(-c.x1) + f^x2, evaluation method
                  FunctTwo f2 = new FunctTwo();

                  // assign value to constant b in the function
                  f2.setB(8.0D);

                  // initial estimates of a, c and g in y = a + b.exp(-c.x) + g^z)
                  double[] start = new double[3];
                  start[0] = 6.0D;      // initial estimate of b
                  start[1] = 0.1D;      // initial estimate of c
                  start[2] = 1.0D;      // initial estimate of g

                  // initial step sizes for a, c and g in y = a + b.exp(-c.x) + f^z)
                  double[] step = new double[3];
                  step[0] = 0.6D;      // initial step size for b
                  step[1] = 0.05D;     // initial step size for c
                  step[2] = 0.1D;      // initial step size for g

                  // create an instance of Regression
                  Regression reg2 = new Regression(doubleArray, yArray, sdArray);

                  // call non-linear regression using default tolerance and maximum iterations and plot display option
                  reg2.simplexPlot(f2, start, step);
         }
}