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

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.

Answer 1

[Matt J]

G=real( sum((R*W).*conj(W),1) );

[Daniel Pollard]

This looked like it should work but it doesn't produce the same results - all my final output numbers are higher. Unfortunately I can't post the full code here, so I'll keep trying myself. Thanks anyway!

[Matt J]

If W is complex-valued, it might be because I was missing a conj() operation. See my edited answer.

[Matt J]

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]

You're right, and I just came back to your answer to say that. Thank you!

Answer 2

[Bruno Luong]

G = real(dot(W,R*W,1)).';