Calculate only diagonal elements of multidimensional array product

Hi everybody,

I have two arrays and , where M is small and N is large. What would be the fastest way to calculate for all l? I could do

sum(repmat(A.',[1,1,N]).*B,1), but since N is large this doesn't seem the best idea to me. Any help is appreciated.

Thanks

[David Goodmanson]

Hi Michael,

one way is

Ares = reshape(A.',1,M*M);
Bres = reshape(B,M*M,N);
Result = Ares*Bres;

although I have no idea where it stands speedwise.

[Michael Werther]

Dear David,

thank you for your prompt reply. In contrast to my first intention and although it is indeed faster, this is unfortunately not giving the desired result. Probably this was my fault, since I did not pose the question precisely. Actually I need to calculate for all l. I have specified this in the question.

[David Goodmanson]

Hi Michael, your question was pretty clear since it's only a single sum instead of a double one, so my comment is toast.

Answer 1

[Matt J]

Assuming your Matlab version is post-R2016b

reuslt = sum(B.*A.',1)

Otherwise, assuming your Matlab version is post-R2008

result = sum(bsxfun(@times, B,A.'),1)

And even if your Matlab version is really, really, really old, then there is still as a last resort,

At=A.';
C=diag(At(:))*reshape(B,[],N));

result=sum(reshape(C,M,M,N),1)

[Michael Werther]

Dear Matt,

thank your for your reply. This is indeed what I was looking for - never thought it could be that easy!

Answer 2

[Matt J]

Since M is small, a for-loop would probably also be fine,

[j,k]=sub2ind([M,M],1:M.^2);

for i=1:M^2

    B(j(i),k(i),:)=B(j(i),k(i),:).*A(k(i),j(i));

end

result=sum(B,1);