n=100;
k=10;

% An example such that two covariates have the same correlation with response,
% to test tie breaker in LAR. In the reference paper, this situation is 
% excluded from the proof of correctness(by jittering the response). In
% practice the code should run fine.

% random response
Y=rand(n,1); 
Y=Y-mean(Y); Y=Y/std(Y);

% pick vectors from the space orthogonal to Y and with mean 0
% from them construct covariates with prescribed correlation to Y
nA=null([Y'; ones(1,n)]);
x1=nA(:,1);
x2=nA(:,2);
lambda=3;
x1=lambda*x1+Y; % correlation with Y is 1/sqrt(1+lambda.^2*var(x1_old)/var(Y))
x2=lambda*x2+Y; 
xs=rand(n,k);
X=[x1 x2 xs];
X=X-repmat(mean(X,1),n,1);
X=X./repmat(std(X,0,1),n,1);

% run it through LARS, if x1 and x2 are added first then they should appear together
beta=lars(X,Y,[],true);