%Example NN1 from COMPlib
%formulated as PMI

K=sdpvar(1,2);
lambda=sdpvar(1);

q0 = K(2);
q1 = (-13-5*K(1)+K(2));
q2 = K(1);
q3 = 1;

%the Hermite matrix
H = [q0*q1 q0*q3 0; q0*q3 q2*q3 0; 0 0 q1*q2 - q0*q3];

F = set(H>=lambda*eye(3,3));

%setting initial guess
setsdpvar(K,[3 60]);
setsdpvar(lambda,1);

kk=reshape(K,2,1);
mu=1e-3;
obj = -lambda+mu*kk'*kk;
options=sdpsettings('usex0',1,'penbmi.p0',0.01);
solvesdp(F,obj,options);

double(K)
H=double(H);
eig(H)