t = linspace(0, 2*pi);
r = 1;
x = r*cos(t);
y = r*sin(t);
figure('name', 'Linear Transform', 'NumberTitle', 'off');
plot(x, y, '.');
limit = 2*[-r r -r r];
axis(limit);
axis image;

% Roatation matrix
theta = pi/3;
A = [cos(theta) -sin(theta); sin(theta) cos(theta)];
% Mirror matrix
theta = pi/3;
A = [cos(2*theta) sin(2*theta); sin(2*theta) -cos(2*theta)];
% Random matrix
A = rand(2);

[eig_vec, eig_value] = eig(A);
eig_vec1 = eig_vec(:, 1);
eig_vec2 = eig_vec(:, 2);
fprintf('The linear transform is represented by matrix A:\n');
disp(A);
if isreal(eig_value),
	fprintf('The first eigen vector is:\n');
	fprintf('%g\n', eig_vec1);
	fprintf('The second eigen vector is:\n');
	fprintf('%g\n', eig_vec2);
	fprintf('The first eigen value is: %g\n', eig_value(1,1));
	fprintf('The second eigen value is: %g\n', eig_value(2,2));
else
	fprintf('The eigen vectors are complex.\n');
	fprintf('The first eigen value is: %g + j*%g\n', ...
		real(eig_value(1,1)), imag(eig_value(1,1))),
	fprintf('The second eigen value is: %g + j*%g\n', ...
		real(eig_value(2,2)), imag(eig_value(2,2))),
end

arrow_x = 1+[-1 0 nan -0.15 0 -0.15];
arrow_y = [0 0 nan 0.15 0 -0.15];
arrow = arrow_x + j*arrow_y;
inputH = line(real(arrow), imag(arrow), ...
	'linewidth', 2, 'erase', 'xor', 'color', 'c', 'clip', 'off');
tmp = A*[arrow_x; arrow_y];
tmp = tmp(1,:)'+j*tmp(2,:)';
outputH = line(real(tmp), imag(tmp), ...
	'linewidth', 2, 'erase', 'xor', 'color', 'm', 'clip', 'off');

% Plot the arrows for eigen vectors
if isreal(eig_value),
	eig_arrow1 = arrow*exp(j*angle(eig_vec1(1)+j*eig_vec1(2)));
	eig_arrow2 = arrow*exp(j*angle(eig_vec2(1)+j*eig_vec2(2)));
	line(real(eig_arrow1), imag(eig_arrow1), 'color', 'g');
	line(real(eig_arrow2), imag(eig_arrow2), 'color', 'g');
	text(eig_vec1(1)/2, eig_vec1(2)/2, '1', 'horizon', 'center');
	text(eig_vec2(1)/2, eig_vec2(2)/2, '2', 'horizon', 'center');
end

xlabel('Click anywhere to drag the input vector.');
title('green: eigenvectors, cyan: input vector, magenta: output vector.');

AxisH = gca; FigH = gcf;
% The following is for animation

% action when button is first pushed down
action1 = ['curr_info=get(AxisH, ''currentPoint'');', ...
	'pointer=curr_info(1,1)+j*curr_info(1,2);', ...
	'input_arrow = arrow*exp(j*angle(pointer));', ...
	'input_arrow = arrow*pointer;', ...
	'set(inputH, ''xdata'', real(input_arrow), ''ydata'', imag(input_arrow));', ...
	'tmp=A*curr_info(1,1:2)'';', ...
	'tmp = tmp(1)+j*tmp(2);', ...
	'output_arrow = arrow*exp(j*angle(tmp));', ...
	'output_arrow = arrow*tmp;', ...
	'set(outputH, ''xdata'', real(output_arrow), ''ydata'', imag(output_arrow));'];

% actions after the mouse is pushed down
action2 = action1;

% action when button is released
action3 = action1;

% temporary storage for the recall in the down_action
set(AxisH,'UserData',action2);

% set action when the mouse is pushed down
down_action=[ ...
    'set(FigH,''WindowButtonMotionFcn'',get(AxisH,''UserData''));' ...
    action1];
set(FigH,'WindowButtonDownFcn',down_action);

% set action when the mouse is released
up_action=[ ...
    'set(FigH,''WindowButtonMotionFcn'','' '');', action3];
set(FigH,'WindowButtonUpFcn',up_action);