/*
Write a program (with one class and that too having only the
"main" method) to find the eigen values and eigen vectors of a 2X2 
matrix. You may assume that the input matrix is non-singular
and has integer elements.
*/

import javabook.*;
import java.math.*;

public class MyClass {
	static int p,q,r,s;
	static int a,b,c;
    public static void main(String[] args) {
       
       
	MainWindow mainWindow = new MainWindow();
    
    InputBox inputBox = new InputBox(mainWindow);
	OutputBox ob = new OutputBox(mainWindow);
	
	// Input the Matrix in row-major form
	p=inputBox.getInteger("Enter an integer : a11");	
	q=inputBox.getInteger("Enter an integer : a12");
	r=inputBox.getInteger("Enter an integer : a21");	
	s=inputBox.getInteger("Enter an integer : a21");		
	
	// Display the matrix taken as input from user
	ob.print("Input Matrix [2 X 2] is : \n");
	ob.print(p);ob.print("\t");ob.printLine(q);
	ob.print(r);ob.print("\t");ob.printLine(s);

/*
The eigen value equation is  M.V = e.V, where V=(V1,V2) is the eigen 
vector and e is the eigen value of 2X2 matrix M. A 2x2 matrix will have up to two 
eigen values and two eigen vectors.

To solve theequation we transform it to (M-eI).V = 0 where I stands
for identity matrix. Expanding it we get two equations:

                  M11.V1 - e.V1 + M12.V2 = 0
                                                        (1)
and               M21.V1 + M22.V2 - e.V2 = 0

Simplifying these equations leads to the equation

                  e^2 - e.(M11 + M22) + (M11.M22 - M12.M21) = 0.
Substituting the values of M11,M12,M21,M22, we get
                  e^2 - e.(p+s) + (p*s - q*r) = 0
Since this is a quadratic eqn. of the form : a(x^2) + bx + c =0, we get 2
values of eigen values, lets store them in y1, y2
			
*/
	a=1;
	b=-(p+s);
	c=(p*s)-(q*r);

    double midterm= Math.sqrt( (b*b)-(4*a*c)  );
	double y1= (midterm-b)/(2*a);
	double y2= -(midterm+b)/(2*a);

// Display the eigen values
	ob.print("\n First Eigen Value = ");
	ob.printLine(y1);
	ob.print("\n Second Eigen Value = ");
	ob.printLine(y2);
	

//  Substitute the values of eigen values in eqn. 1 to get eigen vectors

	double j2=1.0/( 1+ (((s-y1-q)/(p-y1-r))*((s-y1-q)/(p-y1-r)) ));
	j2=Math.sqrt(j2);
	double i2=j2*(s-y1-q)/(p-y1-r);

	ob.print("\n For first eigen value Unit Eigen vector first component is : ");
	ob.printLine(i2);
	ob.print("\n For first eigen value Unit Eigen vector second component is : ");
	ob.printLine(j2);


	j2=1.0/( 1+(((s-y2-q)/(p-y2-r))*((s-y2-q)/(p-y2-r)) ));
	j2=Math.sqrt(j2);
	i2=j2*(s-y2-q)/(p-y2-r);


	ob.print("\n For second eigen value Unit Eigen vector first component is : ");
	ob.printLine(i2);
	ob.print("\n For second eigen value Unit Eigen vector second component is : ");
	ob.printLine(j2);

	ob.waitUntilClose();

    }
}