%
%           This script illustrates difference between 
%           normal and highly non-normal matrices
%           with respect to small perturbations
%
            d = [ones(20,1) ; 2*ones(60,1) ; 3*ones(40,1)];
            n = length(d);
            b = randn(n,1);
            [Q,R] = qr(randn(n)); 
%
%            change value of tau here to vary non-normality
%            larger tau gives higher non-normality
%
%           tau =  0;
%           tau = .05;
%           tau = .5;
            tau = input(' input tau between 0 and 1 ')
            gamma = input(' input gamma between 0 and .1 ')

            R = R*tau;
            for j = 1:n, R(j,j) = d(j); end

            A = Q*R*Q';
            [Xa,Sa] = eig(A);

%
%           generate a random matrix
%
            B = randn(n);
%
%           perturb the matrices
%
	    Bp = B + gamma*randn(n);
            [Xb,Sb] = eig(B);
            [Xbp,Sbp] = eig(Bp);

	    Ap = A + gamma*randn(n);
            [Xap,Sap] = eig(Ap);

            sA = diag(Sa); 
            sB = diag(Sb); 
            sAp = diag(Sap); 
            sBp = diag(Sbp); 

            figure(1)
            plot(real(sA),imag(sA),'o','linewidth',1.5)
            hold on
            plot(real(d),imag(d),'r*','linewidth',1.5)
            disp('strike key')
            pause
            plot(real(sAp),imag(sAp),'go','linewidth',1.5)
            hold off

            XaCond = cond(Xa)
            
            figure(2)
            plot(real(sB),imag(sB),'o','linewidth',1.5)
            hold on
            disp('strike key')
            pause
            plot(real(sBp),imag(sBp),'go','linewidth',1.5)
            hold off

            XbCond = cond(Xb)