CODEWITHSUNDEEP
matlabvectorizationmatrix-multiplication
Smajjk
Smajjk

Reputation: 394

Vectorization of outer product calculation

I have a matrix A of size KxN. I want to take the outer product between each column of this matrix with itself, creating a new matrix of size KxKxN. I can do this iteratively by doing:

N = 5;
K = 3;

A = rand(K,N);

nA = zeros(K,K,N); 
for n=1:N
    nA(:,:,n) = nA(:,:,n) + A(:,n)*A(:,n)';
end

or faster by writing a mex-file (when N is large). However, I have not yet figured out if I can do this in a vectorized fashion. Any ideas?

Upvotes: 2

Views: 484

Answers (1)

Andras Deak -- Слава Україні
Andras Deak -- Слава Україні

Reputation: 35080

If you reshape your array to size [K,1,N] and [1,K,N] (i.e. inject singleton dimensions in the appropriate positions), you only need to multiply them using array broadcasting.

Newer versions of MATLAB with implicit broadcasting:

nA_bcast = reshape(A,[1,K,N]).*reshape(A,[K,1,N])

Older versions of MATLAB with the help of bsxfun:

nA_bsxfun = bsxfun(@times, reshape(A,[1,K,N]),reshape(A,[K,1,N]))

The three relevant arrays (i.e. nA, nA_bcast and nA_bsxfun) are all the same. Side note: A' will be the adjoint, you probably mean A.' for transpose.

Upvotes: 4

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