Efficient submatrix product computation
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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
, 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.
1 个评论
Chunru
2022-9-20
Have you tested that your above code works?
采纳的回答
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
b1
% 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
b2
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