eignmovie.m

This program visualizes eigenvectors for 2x2 matrices.

function eignmovie(A,n,loops)
% This program visualizes eigenvectors for 2x2 matrices. 
% A is a 2x2 matrix. n is optional and determines the number of frames.
% The 3rd optional parameter determines the number of loops shown.
% It is based on an idea by Gilbert Strang, compare CMJ vol.26 no4,
% September 1995, p.316 (article by S. Schonefeld).
%
% Typical examples use the matrices:
% A=[13 9;3 7]/8; (fairly generic)
% A=[cos(pi/4) -sin(pi/4);sin(pi/4) cos(pi/4)];
%                 (nonreal eigenvalues)
% A=[2 -2; -1 1]; (one zero eigenvalue)
% A=[2-sqrt(3) -3; 1 2+sqrt(3)]/2; (double e.value)
%
% All rights reserved: Matthias Kawski, October 1995
%                      http://math.asu.edu/~kawski/
% Last update: Aug. 2004, removed "movie" command -- changed to real-time
% calculation and live display. No more flickering. No need to DoubleBuffer.  

if nargin == 0
   A=[13 9;3 7]/8;
   end;
if nargin < 2 
   n = 72;
   end;
if nargin < 3 
   loops = 3;
   end;
phi=2*pi/n;
z=zeros(1,n+1);
x=cos(phi*[0:n]);
y=sin(phi*[0:n]);
[V,D]=eig(A);
V1=V(:,1)';
V2=V(:,2)';
v=A(1,:)*[x;y];
w=A(2,:)*[x;y];
m=1.2*max([1,max(abs(v)),max(abs(w))]);
myfig=figure
set(myfig,'Renderer','painters')
set(myfig,'DoubleBuffer','on')
hold on
plot(x,y,'c-',v,w,'g-');
text(-0.8*m,0.9*m,num2str(D));
text( 0.2*m,0.9*m,num2str(V));
axis([-m,m,-m,m]);
axis equal
figure(myfig);
%% axis('off');
for j=1:loops
    for i=1:n+1
        p=plot([0;x(i)],[0;y(i)],'b-',[0;v(i)],[0;w(i)],'r-');
        pause(2/n)
        delete(p)
    end;
end;
disp('Hit enter to close the plot window')
pause
close(myfig)