Documentation‎ > ‎


[X,fX,eig_min,flat,error_flat,norm_H,range]=NCeigOptRand(f,S,d) computes minimizers and the minimum of the polynomial f on D_s and tries to extend dual solution to a flat solution using randomization

f is an NCpoly representing a polynomial
S is a set of nc polynomails defining D_S
d is a starting degree for the hierarchy (even number)
X: from GNS - a matrix where each of its rows represents a square matrix
fX: f(X) where X is from GNS
eig_min: eigenvalues of fX
flat = 1 if program finds flat extension
flat = 0, if program does not find flat extension
flat = -1 if the primal problem is infeasible (f is not in the module M_S,d)
error_flat ... norm of the difference between the flat extension returned by randomization idea and the brute force flat extension (which is no more feasible for constraints)
norm_H ... Frobenious norm of flat extension returned by randomization idea
range ... diference between ranks of original matrix and flat extension used 3 methods for rank computation

possible usage: