K = speye(100,100);
q1 = randn(100,1);
u1 = K'*q1;

population = [-1,1,0];
q2 = randsample(population,100, true)';
u2 = K'*q2;
isSubgradient = @(u,K,q)((sum(abs(K*u))== sum((K'*q).*u)) & (max(abs(q))<=1));

if isSubgradient(u1,K,q1)
    disp(['The first example is a singular vector']);
else
    disp(['The first example is not a singular vector']);
end
if isSubgradient(u2,K,q2)
    disp(['The second example is a singular vector']);
else
    disp(['The second example is not a singular vector']);
end