Problem with Karhunen-Loève expansion in matlab

[confused_engineer]

TL;DR

I want to perform the KL expansion in Matlab, but I cannot calculate the zero-mean uncorrelated random variables

I have copied the code of the accepted answer to this post in the official Matlab forums, since I am interested in performing the KL expansion myself.

[CODE lang="matlab" title="Calculation of random variables"]clc

clear all

y=[1,2,4;2,3,10];

y=y' %Reasons for transposing will become clear when you will read the second point given below.

[V,D]=eig(cov(y))

KLT = V' * y';[/CODE]

As far as I understand, the vector defined in the last line, KLT are the uncorrelated random variables. The eigenvectors are certainly orthnormal since

[CODE title="orthonormal eigenvectors"]V(:,2)'* V(:,1) %Eigenvectors
[/CODE]
returns zero and

[CODE title="orthonormal eigenvectors2"]V(:,2)'* V(:,2)
[/CODE]
returns one.

Also,
[CODE title="orthogonal RV"]
cov(KLT')[/CODE]

returns orthogonal results and

[CODE title="variance"]var(KLT')

[/CODE]
are the eigenvalues. However, if I writethe means aren't zero, as the theory says.

Can someone please tell me what am I doing wrong?

Best regards.
Confused Engineer.

 

[Arjan82]

However, if I writethe means aren't zero, as the theory says.

If you write... what? Exactly?

 

[confused_engineer]

Summary:: I want to perform the KL expansion in Matlab, but I cannot calculate the zero-mean uncorrelated random variables

I have copied the code of the accepted answer to this post in the official Matlab forums, since I am interested in performing the KL expansion myself.

[CODE lang="matlab" title="Calculation of random variables"]clc

clear all

y=[1,2,4;2,3,10];

y=y' %Reasons for transposing will become clear when you will read the second point given below.

[V,D]=eig(cov(y))

KLT = V' * y';[/CODE]

As far as I understand, the vector defined in the last line, KLT are the uncorrelated random variables. The eigenvectors are certainly orthnormal since

[CODE title="orthonormal eigenvectors"]V(:,2)'* V(:,1) %Eigenvectors
[/CODE]
returns zero and

[CODE title="orthonormal eigenvectors2"]V(:,2)'* V(:,2)
[/CODE]
returns one.

Also,
[CODE title="orthogonal RV"]
cov(KLT')[/CODE]

returns orthogonal results and

[CODE title="variance"]var(KLT')

[/CODE]
are the eigenvalues. However, if I writethe means aren't zero, as the theory says.

Can someone please tell me what am I doing wrong?

Best regards.
Confused Engineer.

If you write... what? Exactly?

Sorry, if I write mean(KLT')