Note 2 : the way to set up fair comparison

[LinaMiao]

m = 120; n = 512; k = 20; % m rows, n cols, k nonzeros.
p = randperm(n); x0 = zeros(n,1); x0(p(1:k)) = sign(randn(k,1));
A = randn(m,n); [Q,R] = qr(A',0); A = Q';
b = A*x0 + 0.005 * randn(m,1);
opts = spgSetParms('optTol',1e-4);
opts.iterations = 20;
[x,r,g,info] = spgl1(A, b, 0, 1e-3, [], opts); % Find BP sol'n.

sigma = info.rNorm2(end);
[x,r,g,info] = spgl1(A, b, 0, sigma, [], opts); % Find BP sol'n.

% run the above code, it is unfair for the later one, simga is larger, the way of updating tau is not as aggressively as it should be.