% PCA_example-1--sent

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


%%%

zakr = 7; % zakres osi wykresow rozrzutu

X = load(' ... sciezka do pliku ... \PCA_example-1.dat','-ascii');
%X = centralize(X);

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

mean(X)
cov(X,1)
X'*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(:,1),X(:,2),zakr);

C = X'*X/m
[K,L] = eigs(C,n,'sm')
% K*L*inv(K)
K'*K
K*L*K'
[C K*L*K']
Y = X*K;
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(12,Y(:,1),Y(:,2),zakr);

tilefigs;

% figure(1);
% hold on
% draw_big_arrow2 (0,0,K(1,1),K(2,1),'r',2,0.4)
% draw_big_arrow2 (0,0,K(1,2),K(2,2),'b',2,0.4)
% hold off
% figure(2);
% hold on
% draw_big_arrow2 (0,0,1,0,'r',2,0.4)
% draw_big_arrow2 (0,0,0,1,'b',2,0.4)
% hold off
figure(2);
hold on
draw_big_arrow2 (0,0,3*K(1,1),3*K(2,1),'r',2,0.4)
draw_big_arrow2 (0,0,3*K(1,2),3*K(2,2),'b',2,0.4)
hold off
figure(12);
hold on
draw_big_arrow2 (0,0,3*1,3*0,'r',2,0.4)
draw_big_arrow2 (0,0,3*0,3*1,'b',2,0.4)
hold off

X'*X/m
Y'*Y/m
L
trace(X'*X/m)
trace(L)