%Script file for data homework on the SVD
x=linspace(2,4);
y=3*x+2;

X=[x' y'];  %Form the 100 x 2 data matrix
[U,S,V]=svd(X);
diag(S)  %Display the singular values
V        %Display the basis vectors

%Now mean subtract
m1=mean(X,1);  %The mean in R^2
m2=mean(X,2);  %The mean in R^100
X1=X-repmat(m1,100,1);  
[U1,S1,V1]=svd(X1);
diag(S1)
V1

X2=X-repmat(m2,1,2);
[U2,S2,V2]=svd(X2);
diag(S2)
V2

X3=X-repmat(m1,100,1)-repmat(m2,1,2)+mean(X(:));
[U3,S3,V3]=svd(X3);
diag(S3)
V3

plot(X(:,1),X(:,2),'k-',X1(:,1),X1(:,2),'r.');
hold on
plot(X2(:,1),X2(:,2),'m.',X3(:,1),X3(:,2),'g.');
hold off