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HCS_Toolbox_ver01/demo_hnorm.m

+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%  
+%% Example of compuation of homogeneous norm and homogeneous projection
+%%   
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+tol=1e-6; % compuational tolerance
+
+P=[1 -1; -1 2]; % the shape matrix of the wighted Euclidean norm
+if norm(P-P')>tol disp('Error: shape matrix P must be symmetric'); return; end;
+if min(real(eig(P)))<tol disp('Error: shape matrix P must be positive definite'); return; end;
+Gd=[2 0; 1 1]; % a dilation in R^2
+
+%monotonicy check
+if min(real(eig(P*Gd+Gd'*P)))<tol disp('Error: dilation must be monotone'); return; end;
+
+x=[1;-1];          % vector x in R^2
+nx=hnorm(x,Gd,P);   % homogeneous projection of the vector x in R^2
+
+disp(['Hom. norm  = ', num2str(nx)]);
+
+z=hproj(x,Gd,P);   % homogeneous projection of the vector x on the unit sphere x'*P*x=1
+
+disp(['Hom. projection = [', num2str(z(1)),';',num2str(z(2)),']']);
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