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Dear all:

I am trying to calculate a diagonal of a matrix (denoted A), which is formed by multiplying two large-dimensional matrices (denoted as B*C).

A naive way to do it is: first, calculating explicitly A = B*C, then get diagonal out from A. However, the first step takes forever to run due to the high-dimension of B and C. But the only thing I need is the diagonal of A.

Another straightforward way in my mind is: I could create a loop by calculating each element of the diagonal of A one by one. It will surely save a lot of time, but I am not sure if this is the most efficient way.

I am wondering if anyone knows a faster/smarter way to calculate it.

Thank you very much in advance!

Best,

Long

the cyclist
on 26 Mar 2020

Here is one way:

% Make up some inputs

N = 4;

B = rand(N);

C = rand(N);

% Calculate the diagonal

A_diag = 0;

for nr = 1:N

A_diag = A_diag + B(:,nr).*C(nr,:)';

end

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