% PCA_example-2--sent

close all;
clear all;
format compact;
format short;
warning off;


zakr = 3; % zakres osi wykresow rozrzutu

x0 = randn(500,1);
%E = [x0 x0];
E = [x0+randn(500,1)*0.1 x0+randn(500,1)*0.1];
X = centralize(E);

X
[m,n] = size(X);
[m n]

mean(X)
X'*X/m
vx = sort(diag(X'*X),'descend')
vx = vx/sum(vx)
figure(1); bar(vx); axis([0 length(vx)+1 0 1])

fig_scatter(2,X(:,end),X(:,end-1),zakr);

C = X'*X/m
[K,L] = eigs(C,n,'sm')
%Y = X*K;
% K
% K*diag([1;0])
Y = X*(K*diag([1;0]))
Y
vy = sort(diag(L),'descend') % sortowanie nadmiarowe (eigs)
vy = vy/sum(vy)
figure(11); bar(vy); axis([0 length(vy)+1 0 1])

%fig_scatter(3,Y(:,1),Y(:,2),zakr);
fig_scatter(12,Y(:,1),Y(:,2),zakr);

tilefigs;


close all;

Z = Y*K';

fig_scatter(1,X(:,1),X(:,2),zakr);
fig_scatter(2,Y(:,1),Y(:,2),zakr);
fig_scatter(3,Z(:,1),Z(:,2),zakr);

tilefigs;