Calculate only diagonal elements of multidimensional array product

Question

Michael Werther 2019-11-28

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https://ww2.mathworks.cn/matlabcentral/answers/493659-calculate-only-diagonal-elements-of-multidimensional-array-product

评论： Michael Werther 2019-12-13

采纳的回答： Matt J

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

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Michael Werther 2019-11-28

编辑：Michael Werther 2019-11-28

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 2019-12-2

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

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Answer 1

Matt J 2019-12-2

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编辑：Matt J 2019-12-2

在 MATLAB Online 中打开

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)

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Michael Werther 2019-12-13

Dear Matt,

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

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Answer 2

Matt J 2019-12-2

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编辑：Matt J 2019-12-2

在 MATLAB Online 中打开

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);

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