+
+// W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
+// with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments
+void Compute_Omega(double* X, double* Y, double* M, int* pn, int* pd, double* W)
+{
+ int n=*pn, d=*pd;
+ //int dim = d+d*d+d*d*d
+ //double* W = (double*)calloc(dim*dim,sizeof(double));
+ double* g = (double*)malloc(dim * sizeof(double));
+ for (int i=0; i<n; i++)
+ {
+ // Fill gi:
+ for (int j=0; j<d; j++)
+ g[j] = Y[i] * X[mi(i,j,n,d)] - M[i]
+ for (int j=d; j<d+(d*d); j++)
+ {
+ int idx1 = (j-d) % d; //num row
+ int idx2 = ((j-d) - idx1) / d; //num col
+ g[j] = 0.0;
+ if (idx1 == idx2)
+ g[j] -= Y[i];
+ g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)];
+ }
+ for (int j=d+d*d; j<dim; j++)
+ {
+ int idx1 = (j-d-d*d) % d; //num row
+ int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
+ int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
+ g[j] = 0.0;
+ double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
+ if (idx1 == idx2)
+ g[j] -= Y[i] * X[mi(i,idx3,n,d)];
+ if (idx1 == idx3)
+ g[j] -= Y[i] * X[mi(i,idx2,n,d)];
+ if (idx2 == idx3)
+ g[j] -= Y[i] * X[mi(i,idx1,n,d)];
+ g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)];
+ }
+ // Add 1/n t(gi) %*% gi to W
+ for (int j=0; j<dim; j++)
+ {
+ for (int k=0; k<dim; k++)
+ W[j*dim+k] += g[j] * g[k] / n;
+ }
+ }
+ free(g);
+}