# Efficient submatrix product computation

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Aaron Pim le 20 Sep 2022
Commenté : Aaron Pim le 20 Sep 2022
I am considering the discrete Smoluchowski equations and I need efficiently compute a matrix product.
For , and a given I want to compute the product
I can easily do this by the following for loop
b = 0
for j = 1:ceil((i-1)/2)
b = b + K(j,i-j)*y(j)*y(i-j);
end
However, I want to know if there is a more efficient way of computing this product in a single line or less.
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Chunru le 20 Sep 2022
Have you tested that your above code works?

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### Réponse acceptée

Karim le 20 Sep 2022
Modifié(e) : Karim le 20 Sep 2022
Do note that a for loop can be very efficient. I'm not sure the single line methods will always be faster.
Below you can find one (of many) methods to reduce the number of lines in the code. I used the sub2ind command to get the data directy out of the matrix K.
% initialize data
N = 1000;
y = rand(N,1);
K = rand(N,N);
i = randi(N,1);
% test loop...
tic
b1 = 0;
for j = 1:ceil((i-1)/2)
b1 = b1 + K(j,i-j)*y(j)*y(i-j);
end
toc
Elapsed time is 0.006585 seconds.
b1
b1 = 60.1868
% test single line
tic
% first setup indices
j = (1:ceil((i-1)/2))';
% now compute the sum
b2 = sum( K(sub2ind(size(K),j,i-j)) .* y(j) .* y(i-j) );
toc
Elapsed time is 0.006417 seconds.
b2
b2 = 60.1868
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Aaron Pim le 20 Sep 2022
This is perfect, thank you.

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