Efficient matrix multiplication with weights

5 次查看（过去 30 天）
Pierre-Louis Giscard
评论： Matt J 2022-1-20
Let A and B be two matrices, say square NxN matrices. Ordinary matrix multiplication A*B implements (A*B)_{ij} = Sum_k A_{ik} B_{kj}. Is there an efficient way in Matlab to implement a weighted version of this product, where we have a matrix of weights W and we want to do :
Weighted(A*B)_{ij} = Sum_k A_{ik} B_{kj} W_{i-j,k}
(let's say here that A and B are triangular so that only i>=j need be considered).
How can I efficiently express Weighted(A*B), avoiding, if possible, for loops and the like ? I would like to keep everything vectorialized / use only matrix products and elements wise products etc.
  3 个评论
显示 1更早的评论
Matt J
Matt J 2022-1-20
Also, are A and B Toeplitz as well as triangular?
Pierre-Louis Giscard
Pierre-Louis Giscard 2022-1-20
Actually the fastest option is the best so you are right if the for loops are faster I would use them. In general A and B are not Toeplitz. In applications A and B are rather large (say 1000x1000) so memory usage could also be an issue.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Matt J
Matt J 2022-1-20
编辑：Matt J 2022-1-20
A more memory efficient solution is as follows. It has a loop, but is still highly vectorized.
Wt=W.';
At=A.';
T=toeplitz(1:N,[1,zeros(1,N-1)]);
result=zeros(N);
for i=1:N
result(T==i)=sum( At(:,1:end+1-i).*Wt(:,i).*B(:,i:end) ,1);
end
  2 个评论
Pierre-Louis Giscard
Pierre-Louis Giscard 2022-1-20
编辑：Pierre-Louis Giscard 2022-1-20
Thank you for your codes ! I think this second proposition will be more suited to my applications as I am worried about the memory usage. I will try to see how fast this is but it seems it will be much faster than with all the nested for loops of the naive approach.
Matt J
Matt J 2022-1-20
You're welcome. If it works as you need it to, though, please Accept-click the answer.

请先登录，再进行评论。

更多回答（1 个）

Matt J
Matt J 2022-1-20
编辑：Matt J 2022-1-20
Using sepblockfun() from,
https://www.mathworks.com/matlabcentral/fileexchange/48089-separable-block-wise-operations
T=toeplitz(1:N);
WW=W.';
WW=reshape(WW(:,T), N^2,N);
BB=repmat(B,N^2,1);
AA=repmat( reshape(A.',[],1) ,1,N^2);
result=sepblockfun(AA.*WW.*BB, [N,1] , 'sum' ); %
  1 个评论
Matt J
Matt J 2022-1-20
For N=1000, you would need a lot of RAM for this to work. You might be able to mitigate RAM requiements by using single floats inputs. The result could still be obtained in doubles with,
result=sepblockfun(AA.*WW.*BB, [N,1] , @(x,d)sum(x,d,'double') ); %

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Creating and Concatenating Matrices 的更多信息

标签

产品


版本

R2021b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by