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Demos for MATLAB/Example_3_c_hom_norm/hnorm_sigmoid.m

+function nx=hnorm_sigmoid(x,Gd,alpha,beta,gamma,hn_fun)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% The function nx=hnorm_sigmoid(x, Gd, alpha, beta, gamma, hn_fun) 
+%% computes (for a given vector x) a canonical homogeneous norm 
+%% using universal approximator
+%% 
+%% The (n x n) matrix Gd is a generator of linear dilation
+%%
+%% alpha, beta, gamma are parameter of universal approximator
+%%
+%% hn_fun a function which computes an explicit homogeneous norm 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+nz=hn_fun(x); pi_z=expm(-log(nz)*Gd)*x;
+nx=0;
+for i=1:size(alpha,2)
+nx=nx+gamma(1,i)/(1+exp(alpha(1,i)+beta(:,i)'*pi_z));
+end;
+nx=nx*nz;
+