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Demos for MATLAB/Example_3_c_hom_norm/hsphere.m

+function M=hsphere(r,Gd,Nmax,hn_fun)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% The function M=hsphere(r, Gd, Nmax, hn_fun) returns a randomly generated an 
+%% array of points distributed on a homogeneous sphere of the radius r
+%%                        
+%%  The homogeneous ball of the radius r>0 is the set of point 
+%%
+%%           Sd(r)={z : hz=r, where nz is a homogeneous norm of z}
+%%
+%%
+%% The input parameters are                                   
+%%     r - radius of the homogeneous sphere      
+%%  Nmax - number of points on the shpere  
+%% hn_fun - a function which computes a homogenenous norm 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+tol=1e-6;
+n=size(Gd,1);
+if r<tol disp('Error: radius of homogenenous ball must be strctly positive'); end;
+
+n=size(Gd,1);
+s=log(r);
+M=[];
+for i=1:Nmax
+    x=2*(rand(n,1)-0.5);
+    if norm (x)<tol x=2*(rand(n,1)-0.5); end;
+    M=[M expm(Gd*s)*hproj(x,Gd,hn_fun)];
+end;   
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