Calculating diagonal elements of a matrix product without a loop or redundant calculations
23 views (last 30 days)
Show older comments
I have a problem wich invovles calculating the product of the ith row of a matrix, say F, and another matrix, say B, and then multiplying again by the ith row of F as a column (for each row of F). Basically, something like this:
A = [];
for i = 1:length(F)
A(i) = F(i,:)*B*F(i,:)';
end
This code works, but it is not ideal because it uses a loop rather than Matlab's native interpreted language. The following code also achieves the same result:
A = diag(F*B*F');
The problem here is that it is calculating all the elements of F*B*F', and then only selecting the diagonal elements (which is all I ultimately want). So this is also extremely inefficient (especially for larger matrices F and B) because there are many redundant calculations.
Is there a way to get this result without using loops or redundant calculations, for example, using element-wise algebra (i.e. using the ".*" operator)? I tried F*B.*F' but this does not give the same result.
Thanks.
1 Comment
Daniel Shub
on 11 Mar 2012
One can no longer simply say that loops are slow in MATLAB. A lot of improvements have happened in the past 10(?) years. Even the concept of preallocate or die is less rigid (although I would preallocate your A here instead of initializing it to empty).
Accepted Answer
Oleg Komarov
on 11 Mar 2012
% Example inputs
F = rand(10);
B = rand(10);
out1 = sum(F*B.*F,2); % Elementwise
out2 = diag(F*B*F');
isequal(out1,out2)
However I don't see an improvement in the timing, it could actually be the case that diag(F*B*F') doesn't calculate all the cross products.
0 Comments
More Answers (1)
Earl
on 11 Mar 2012
3 Comments
Jan
on 12 Mar 2012
I get this under Win7/Matlab 2009a/64:
tic; out1 = sum(F*B.*F,2); toc;
>> Elapsed time is 0.165536 seconds.
tic; out2 = diag(F*B*F'); toc;
>> Elapsed time is 0.288225 seconds.
Oleg Komarov
on 12 Mar 2012
Average on 100 iterations and size 1000x1000, Win7 R2012a 64bit:
out1 = sum(F*B.*F,2): 0.04818
out2 = diag(F*B*F') : 0.08834
See Also
Categories
Find more on Logical in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!