%%%%%%%%%%%%%%%%%%%%% Eigenvalue plot procedure %%%%%%%%%%%%%%%%%%%%%
%
% EIGPLOT
% Usage: EIGPLOT(A)
% Input:  A - square matrix 
%
%      the  eigenvalues of the matrix A are plotted against  
%      the background of the unit circle and the x and y axes

function y=eigplot(A)             

   t=0:(2*pi)/100:2*pi;           % find polar co-ordinates for
   cx= cos(t); cy=sin(t);         % 101 points on the unit circle

   lam=eig(A);                    % vector of eigenvalues
   lamx=real(lam);                % find polar coordinates of eigenvalues
   lamy=imag(lam);

   mlam=1.1*max([abs(lam)' 1]);   % this guarantees that unit circle and all
                                  % eigenvalues will be visible

   xx=[-mlam mlam];               % coordinates of endpoints of x-axis
   xy=[0 0];
   yx=[0 0];                      % coordinates of endpoints of y-axis
   yy=[-mlam mlam];

   plot(xx,xy,'-r',yx,yy,'-r',cx,cy,'-r',lamx,lamy,'*k')
   axis('equal');
   axis([-mlam,mlam,-mlam,mlam]);
                                  % plot everything in the order
                                  % x-axis, y-axis, circle
                                  % and then eigenvalues
                                  % observe that eigen values are 
                                  % yellow stars
 
   title('Eigenvalue Plot')