Fast computation of diagonal elements
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I have two matrices, A of size m-by-n and B of size m-by-m. I need to quickly compute the digonal elements of (A'*B*A). Here m is of order 100 while n is of order 10000.
How would I do it ? Doing diag(A'*B*A) will be slow.
Neither B nor A is diagonal. they are full matrices.
采纳的回答
diagonal = sum(A.*(B*A),1);
2 个评论
Azzi Abdelmalek
2013-11-5
or
sum((A'*B).*A',2)
Matt J
2013-11-5
It works. But you'll have overhead from the transpositions.
更多回答（2 个）
Sean de Wolski
2013-11-5
m = 100;
n = 10000;
A = rand(m,n);
B = rand(m);
timeit(@()diag(A'*B*A)) % R2013b
ans = 0.8128
So it takes slightly less than a second on my Win7x64 laptop. How many times do you need to do this computation?
2 个评论
Saurabh
2013-11-5
Sean de Wolski
2013-11-5
编辑：Sean de Wolski
2013-11-5
I.e. less than three minutes total? I would just do the above 200x and go get a cup of coffee while MATLAB is crunchin'
Azzi Abdelmalek
2013-11-5
编辑：Azzi Abdelmalek
2013-11-5
This will reduce the time
S=A'*B;
d1=arrayfun(@(x) S(x,:)*A(:,x),1:n);
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