package symjava.examples;

import symjava.relational.Eq;
import symjava.symbolic.Symbol;
import static symjava.symbolic.Symbol.*;


public class Example2 {

	/**
	 * Example from Wikipedia
	 * (http://en.wikipedia.org/wiki/Gauss-Newton_algorithm)
	 * 
	 * Use Gauss-Newton algorithm to fit a given model y=a*x/(b-x)
	 *
	 */
	public static void example1() {
		//Model y=a*x/(b-x), Unknown parameters: a, b
		Symbol[] freeVars = {x};
		Symbol[] params = {a, b};
		Eq eq = new Eq(y, a*x/(b+x), freeVars, params); 
		
		//Data for (x,y)
		double[][] data = {
			{0.038,0.050},
			{0.194,0.127},
			{0.425,0.094},
			{0.626,0.2122},
			{1.253,0.2729},
			{2.500,0.2665},
			{3.740,0.3317}
		};
		
		double[] initialGuess = {0.9, 0.2};
		
		//Here we go ...
		GaussNewton.solve(eq, initialGuess, data, 100, 1e-4);
		
		//symjava.examples.GaussNewton.solve(eq(y,a*x/(b+x)),[0.9,0.2],[[0.038,0.05],[0.194,0.127],[0.425,0.094],[0.626,0.2122],[1.253,0.2729],[2.5,0.2665],[3.74,0.3317]],100,0.0001)
		

	}
	
	/**
	 * Example from Apache Commons Math 
	 * (http://commons.apache.org/proper/commons-math/userguide/optimization.html)
	 * 
	 * "We are looking to find the best parameters [a, b, c] for the quadratic function 
	 * 
	 * f(x) = a x2 + b x + c. 
	 * 
	 * The data set below was generated using [a = 8, b = 10, c = 16]. A random number 
	 * between zero and one was added to each y value calculated. "
	 * 
	 */	
	public static void example2() {
		Symbol[] freeVars = {x};
		Symbol[] params = {a, b, c};
		Eq eq = new Eq(y, a*x*x + b*x + c, freeVars, params);
		
		double[][] data = {
				{1 , 34.234064369},
				{2 , 68.2681162306108},
				{3 , 118.615899084602},
				{4 , 184.138197238557},
				{5 , 266.599877916276},
				{6 , 364.147735251579},
				{7 , 478.019226091914},
				{8 , 608.140949270688},
				{9 , 754.598868667148},
				{10, 916.128818085883},
		};
		
		double[] initialGuess = {1, 1, 1};
		
		GaussNewton.solve(eq, initialGuess, data, 100, 1e-4);
		//a=7.99883 b=10.00184 c=16.32401 
	}
	
	public static void main(String[] args) {
		example1();
		example2();
	}
}