% EVD_in_PCA--sent

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


% EVD (macierzy Grama) w PCA

x1 = randn(4,1)
x2 = randn(4,1)
x3 = randn(4,1)

X = [x1 x2 x3];
X = centralize(X)
[m,n] = size(X);
var(X,1)
eig(X'*X / m)'
sum(var(X,1))
sum(eig(X'*X / m)')

X = [x1 x2 x3/10];
X = centralize(X)
[m,n] = size(X);
var(X,1)
eig(X'*X / m)'
sum(var(X,1))
sum(eig(X'*X / m)')

X = [x1 x2 x3/1e6];
X = centralize(X)
[m,n] = size(X);
var(X,1)
eig(X'*X / m)'
sum(var(X,1))
sum(eig(X'*X / m)')

X = [x1 x2 x1+x2];
X = centralize(X)
[m,n] = size(X);
var(X,1)
eig(X'*X / m)'
sum(var(X,1))
sum(eig(X'*X / m)')

X = [x1 x2 (x1+x2)/2];
X = centralize(X)
[m,n] = size(X);
var(X,1)
eig(X'*X / m)'
sum(var(X,1))
sum(eig(X'*X / m)')

X = [x1 x2 (2*x1-x2)/3];
X = centralize(X)
[m,n] = size(X);
var(X,1)
eig(X'*X / m)'
sum(var(X,1))
sum(eig(X'*X / m)')