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%%%%%%%%%%%%%% Create to ICs with unit variance %%%%%%%%%%%%%
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%s1=wavread('lucas1',1000);
%s2=wavread('lucas2',1000);
s1=20*(rand(1,1000)-0.5)-60;
s2=20*(rand(1,1000)-0.5)+40;
s=[s1 s2];
covs=cov(s');
s1=s1./sqrt(covs(1,1));
s2=s2./sqrt(covs(1,1));
sample_size=length(s1);
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%%%%%%%%%%%%%%%%%%%% display jpdf & mpdf %%%%%%%%%%%%%%%%%%%%
figure('name','source')
%%%%%%%%%%%%%%%%%%% joint pdf %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(2,2,1)
scatter (s1,s2,'.')
axis([min(s1(:))-1 max(s1(:))+1 min(s2(:))-1 max(s2(:))+1]);
title('joint pdf');
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%%%%%%%%%%%%%%% 1st IC mpdf %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(2,2,3)
[n1,s11]=hist(s1,sample_size);
n1=n1/sample_size;
%%%%%%%%%%%%%%%%%% Gaussian pdf %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
rv=linspace(min(s11(:))-1, max(s11(:))+1,1000);
ms1=mean(s1');
gauss=gaussmf(rv,1,ms1);
gauss=gauss.*max(n1(:));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
plot(s11,n1,rv,gauss,'m.','LineWidth',1.5)
axis([min(s11(:))-1 max(s11(:))+1 0 max(n1(:))+0.001]);
title('marginal pdf IC1');
%%%%%%%%%%%%%%% 2nd IC mpdf %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(2,2,2)
[n2,s22]=hist(s2,sample_size);
n2=n2/sample_size;
%%%%%%%%%%%%%%%%%% Gaussian pdf %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%rv : random variables
rv=linspace(min(s22(:))-1, max(s22(:))+1,1000);
ms2=mean(s2');
gauss=gaussmf(rv,1,ms2);
gauss=gauss.*max(n2(:));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
plot(n2,s22,gauss,rv,'m-','LineWidth',1.5)
axis([0 max(n2(:))+0.001 min(s22(:))-1 max(s22(:))+1]);
title('marginal pdf IC2');
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subplot(2,2,4)
plot(s1,'color','red')
hold on
plot(s2,'color','green')
hold off
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