Efficient submatrix product computation

Question

Aaron Pim 2022-9-20

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1808520-efficient-submatrix-product-computation

评论： Aaron Pim 2022-9-20

采纳的回答： Karim

在 MATLAB Online 中打开

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 2022-9-20

Have you tested that your above code works?

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Answer 1

Karim 2022-9-20

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1808520-efficient-submatrix-product-computation#answer_1057020

编辑：Karim 2022-9-20

在 MATLAB Online 中打开

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