Vectorizing Calculation of the Autocorreltion function of a Matrix (Per Column)

Hello.

I have a matrix

A = [1 2 3; 4 5 6; 7 8 9];

I want to calculate the Autocorrelation function of each of its columns.

Simple way to do so:

for ii = 1:size(A, 2)
autocorrelationFunction(:, ii) = conv2(A(:, ii), A(end:-1:1, ii));
end

Could anyone think of a vectorized way of doing so?

Thanks.

Answer 1

[Royi Avital]

It can be done using Toeplitz matrix.

Answer 2

[Daniel Shub]

Wow, it is like a vectorization party in here today. Why do you want to vectorize your code? In recent years MATLAB has substantially sped up loops. If you are not using r2011a, you could speed up your loop by initializing autorcorrelationFunction to the correct size (r2011a has supposedly cut down on the cost of not pre-allocating arrays). You might be able to get a speed increase out of vectorization, but it may not be as big as you expect.

[Royi Avital]

I know all / most the acceleration methods when dealing with loops.

I'm looking for something which removes the loop completely.

Thank you.