How can I perform matrix operation efficiently?
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I have an array X(n,m) where m<<n and n can be very large. First, I want to create a 3-d array of dimension (m,m,n) such that each mxm matrix in the nth location is the outer product of the n-th m-dimensional row in the original X- array.
Then I want to form a weighted sum all the mxm arrays where the weights are the elements of another n-dimensional array, Y(n).
result=zeros(m);
for i=1:n
result = result + Y(i) * X(i,:)' * X(i,:);
end
I could do this in the loop, but I think it would be slow when n is very large, compared to if there were a way to do all this with some matrix operation functions in MATLAB.
댓글 수: 3
dpb
2014년 6월 4일
Needs to preallocate the full 3D array, however, and store into it; otherwise it'll be the classic case of reallocation and memory thrashing as he adds planes.
That said, I'd think it likely to be reasonably-decent performing. The alternatives seem to be accumarray and the like which are basically loops themselves...
Dan Gianotti
2014년 7월 22일
Hah! This is exactly the question I was about to ask (presumably implementing some version of the EM algorithm?)!
Did you determine if Roger's loop or James's vectorized version was faster?
채택된 답변
Roger Stafford
2014년 6월 5일
If m is much smaller than n and assuming Y is a column vector, try this:
R = zeros(m);
TX = X';
for ix = 1:m
R(:,ix) = TX*(X(:,ix).*Y); % <-- R is 'result'
end
추가 답변 (1개)
James Tursa
2014년 6월 4일
편집: James Tursa
2014년 6월 4일
This is vectorized, but it creates potentially large intermediate arrays, so I don't know if it will be any faster than your simple loop. Strictly from a memory use perspective, the simple loop is better.
XT = X';
XTc = reshape(XT,m,1,n);
XTr = reshape(XT,1,m,n);
XTX = bsxfun(@times,XTc,XTr);
Yn = reshape(Y,1,1,n);
YXTX = bsxfun(@times,Yn,XTX);
result = sum(YXTX,3);
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