Avoiding unnecessary for loops
显示 更早的评论
How do I do this without the loops in a few lines?
S = zeros(100,100);
sig = 0.05;
for i = 1:100
for j = 1:100
S(i,j) = exp(-norm(D(i,:)-D(j,:),'fro')/sig);
end
end
2 个评论
Deepayan Bhadra
2018-3-7
Jos (10584)
2018-3-7
Note that S will be symmetric with zeros on the diagonal, as norm(x) = norm(-x), so you can let j run from i+1 to 100 to save time.
Since norm is not vectorized it is hard to get rid of the for-loops at all.
采纳的回答
These are a few lines already. The mos expensive is the exp call, so you save the most time with using the symmetry (as mentioned by Jos already):
S = zeros(100,100);
sig = 0.05;
for i = 1:100
for j = i+1:100
S(i,j) = exp(-norm(D(i,:) - D(j,:)) / sig);
S(j,i) = S(i,j);
end
end
You can try if it is faster to replace norm by:
for i = 1:100
v = D(i, :);
for j = i+1:100
w = v - D(j, :);
S(i,j) = exp(-sqrt(w * w.') / sig);
S(j,i) = S(i,j);
end
end
Operating on columns is faster than on rows:
DT = D.';
for i = 1:100
v = DT(:, i);
for j = i+1:100
w = v - DT(:, j);
S(i,j) = exp(-sqrt(w.' * w) / sig);
S(j,i) = S(i,j);
end
end
Please post the timings you get.
4 个评论
Deepayan Bhadra
2018-3-8
编辑：Deepayan Bhadra
2018-3-8
If you ask for the optimizing of code, provide the real dimensions of the problem, because this is essential. If you have 10'000 vectors, creating the temporary arrays by repmat can fill your RAM and let the code run incredibly slow.
The long time needed for the processing is not caused by the loops, if you avoid repeated calculations. Therefore the advice of your instructor to vectorize is important, but not necessarily the best method.
Nevertheless, if the goal is, that you find a vectorized loop-free way by your own, please post, what you have tried so far and ask a specific question. The forum should not solve your homework.
Deepayan Bhadra
2018-3-8
In pdist you find exactly the same loops as in the suggested code, but S = exp(-Z/sig) does not use the symmetry of the input, such that almost the double number of expensive exp() calls are performed. Therefore I assume, that this "loop free" code is not less "nightmarishly time-consuming". I'm interested in the timings you get, especially for the larger matrices with 10'000 vectors.
I did not draw any conclusions about intentions of anybody. I'm convinced, that the forum should not solve homework. That's all. But discussions about homework are very useful for the forum and the students.
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