function sigma=makeRandomSigma2d(minl,maxl,ratio)
% sigma=makeRandomSigma2d(minl,maxl)
% 
% Generates in sigma a 2x2 covariance matrix. The variances elong the
% principal directions are drawn uniformly from [minl,maxl].
%
% sigma=makeRandomSigma2d(minl,maxl,ratio) draws the first variance at
% random, and then sets the second one to ration*first one.

% random rotation in 2D - more precisely, a random angle
theta=unifrnd(-pi/2,pi/2);
R=[cos(theta) -sin(theta);
   sin(theta) cos(theta)];

% the first eigenvalue drawn within the specified bounds
lambda(1)=unifrnd(minl,maxl);
if (nargin >= 3)
  lambda(2)=lambda(1)*ratio;
else
  lambda(2)=unifrnd(minl,maxl);
end
Lambda=diag(lambda);

sigma=R*Lambda*R';