function showsvd(A);
% SHOWSVD      showsvd(A)
%   Picture a 2x2 matrix A by singular values and corresponding vectors.
%   Try:   >>  showsvd(randn(2))
%          >>  showsvd([2 1; -1 3])
%          >>  showsvd([4 -2; -2 1])

if ~min((size(A)==[2 2])), error('matrix A is not 2 by 2'), end

[U,S,V] = svd(A);

% input space picture
clf, theta = linspace(0,2*pi,100); x = cos(theta); y = sin(theta);
subplot(1,2,1), plot(x,y,'--'), hold on               % draw circle
for j=1:2
    plot([0 V(1,j)],[0 V(2,j)],'r')                   % draw input vectors V ("right singular vectors")
    text(.5*V(1,j),.5*V(2,j),['v_' num2str(j)])
end

% text description
text(1.85,.25,'A'), text(1.7,0,'--->')
text(-.7,2.4,[num2str(A(1,1),'%5.4f') '    ' num2str(A(1,2),'%5.4f')],'Color','r')  
text(-1.0,2.3,'A = ','Color','r')
text(-.7,2.2,[num2str(A(2,1),'%5.4f') '    ' num2str(A(2,2),'%5.4f')],'Color','r')  
text(-1.0,1.75,['\sigma_1 = ' num2str(S(1,1),'%6.4f') ', \sigma_2 = ' num2str(S(2,2),'%6.4f')])
text(-1.5,-1.5,'A v_j = \sigma_j u_j     <==>    A = U \Sigma V^*','Color','r')
axis equal, axis([-2 2.5 -2 3]), hold off

% output space picture
out = A*[x; y];
subplot(1,2,2), plot(out(1,:),out(2,:),'--'), hold on  % draw ellipse
for j=1:2
    sig = S(j,j); ex = sig*U(1,j); ey = sig*U(2,j);
    plot([0 ex],[0 ey],'r')                            % draw output vectors U ("left singular vectors")
    text(.5*ex,.5*ey,['\sigma_' num2str(j) ' u_' num2str(j)])
end
mox = max(abs(out(1,:))); moy = max(abs(out(2,:)));
axis equal, axis([-1.4*mox 1.4*mox -1.1*moy 1.1*moy]), hold off