%
%  code21: homework hint (djm - 29 oct 2001)
%

%  matrix with alge-mult =2, geom-mult = 1

J = [1 1 ; 0 1];  eigJ = 1;
w_J = [1 ; 0];  w_perp = [0 ; 1];

%  random perturbation

a = rand(2,2)

%  epsilon domain

de = 0.01;  emax = 0.2;  

%  eigenplots

figure(1); clf;
subplot(2,1,1);  hold on
title('\bf eigenvalues')
xlabel('\epsilon')
ylabel('\lambda(\epsilon)-\lambda(0); real=r imag=k')
axis([-emax emax -0.5 0.5])

subplot(2,1,2);  hold on
title('\bf eigenvector projection orthogonal to w1')
xlabel('\epsilon')
ylabel('|w(\epsilon)\cdot w(0)^{\perp}|')
axis([-emax emax 0 0.5])

%  loop for epsilon perturbed matrix

for epsilon = -emax:de:emax
  J1 = J + epsilon*a;

  [W,D] = eig(J1);

  c1 = abs(W(:,1)'*w_perp);
  c2 = abs(W(:,2)'*w_perp);

  subplot(2,1,1)
  plot(epsilon,real(D(1,1)-eigJ),'rx');
  plot(epsilon,real(D(2,2)-eigJ),'ro');
  plot(epsilon,imag(D(1,1)-eigJ),'kx');
  plot(epsilon,imag(D(2,2)-eigJ),'ko');

  subplot(2,1,2)
  plot(epsilon,c1,'rx');
  plot(epsilon,c2,'ro');
end