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### NCopt

 description: [X,fX,eig_val,eig_vec,A,fA]=NCopt(f,AW) computes minimizers and the minimum of the polynomial f.arguments: f is an NCpoly representing a polynomial.AW: true/false whether AWbd is called. output: X: from GNS - a matrix where each of its rows represents a square matrixfX: f(X) where X is from GNSeig_val: eigenvalues of fXeig_vec: corresponding eigenvectorsA: from AWbdfA: f(A) where A is from AWbd - actually on each block of Apossible usage: NCopt(f), NCopt(f,AW) see also: example: >> f = (1 - y + x*y + y*x)'*(1 - y + x*y + y*x) + (-2 + y^2)^2 + (-x + x^2)^2;>> [X,fX,eig_val,eig_vec]=NCopt(f)*** Minimum eigenvalue for f is 0.000000. ***X = Columns 1 through 8      0.1492    0.1176    0.3287    0.0611    0.1176    0.9387   -0.0007   -0.2507      1.4113   -0.0868    0.0193   -0.0090   -0.0868   -1.3218    0.0909   -0.4394    Columns 9 through 16      0.3287   -0.0007    0.7765    0.0740    0.0611   -0.2507    0.0740   -0.6993      0.0193    0.0909   -1.3201   -0.4347   -0.0090   -0.4394   -0.4347    0.9773fX = 0.0108   -0.0222    0.0066   -0.1102    -0.0222    0.2500    0.1858   -0.2756     0.0066    0.1858    0.2098   -0.4285    -0.1102   -0.2756   -0.4285    3.8200eig_val = 0.0000         0         0         0               0    0.0427         0         0               0         0    0.3507         0               0         0         0    3.8971eig_vec = 0.9304    0.3562   -0.0825    0.0278          0.2804   -0.5590    0.7761    0.0806         -0.2353    0.7468    0.6105    0.1191          0.0207    0.0543    0.1344   -0.9892