Is there a way to vectorise this vector/matrix product?

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Daniel Pollard
Daniel Pollard 2021-5-7
回答： Bruno Luong 2021-5-7
I have a piece of code inside a for loop, which looks like
for k = 1:size(G, 1)
G(k) = real(W(:,k)' * R * W(:,k))
end
G is preallocated (which is how I know the length of it). W and R are 2D matrices (so W(:,k) is a vector). This loop is a real bottleneck in my code, that one line taking 90% of the total time that it takes to run a script which itself calls other functions and files. It's not possible to use a parfor loop as I'm already using one in a wrapper function.
Is there a way to vectorise that loop, in order to reduce the number of times the calculation is done? I'm sure it can be done, but it's not at all obvious to me.

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采纳的回答

Matt J
Matt J 2021-5-7
编辑：Matt J 2021-5-7
G=real( sum((R*W).*conj(W),1) );
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Matt J
Matt J 2021-5-7
Ran in:
Here is a test of a agreement with random data:
N=5;
W=complex(rand(N),rand(N));
R=complex(rand(N),rand(N));
%%% Original method
G=nan(N,1);
for k = 1:size(G, 1)
G(k) = real(W(:,k)' * R * W(:,k));
end
Gbase=G;
%%% Proposed alternative
G=real( sum((R*W).*conj(W),1) ).';
Discrepancy=norm(G-Gbase,'fro')
Discrepancy = 1.9860e-15
Daniel Pollard
Daniel Pollard 2021-5-7
You're right, and I just came back to your answer to say that. Thank you!

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更多回答（1 个）

Bruno Luong
Bruno Luong 2021-5-7
G = real(dot(W,R*W,1)).';

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