Randomise the upper triangle of a matrix
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How can I randomise the elements only in the upper triangle of a square matrix? I want to randomise only the upper triangle elements 10,000 times, each time the upper triangle is different. Please suggest a solution.
Many thanks
Kyle
采纳的回答
Roger Stafford
2014-8-21
If you are going to do this randomization 10000 times, you would want it to be as efficient as possible. Here is a possible way. Let the matrix be of size n x n. (Note that I am assuming by the upper triangular part of a matrix you mean the part above the main diagonal but not including the diagonal.)
Do this just once and save f and n2:
f = find(triu(ones(n),1)==1);
n2 = length(f);
Then each of the 10000 times if your n x n matrix is M, do this:
M(f) = rand(n2,1); % Or use randn or any other random number function
You accomplish the randomization in one line and with only n*(n-1)/2 calls on the random number function.
4 个评论
Patrik Ek
2014-8-21
I guess this should be most effective in respect of both time and memory overhead. +1
Sean de Wolski
2014-8-21
You could skip the find with:
n2 = nnz(triu(ones(numel(M))))
Roger Stafford
2014-8-21
Kyle needs 'f' to address the location in M to be randomized. Also the n2 value here is too large. It would be n^2*(n^2-1)/2.
Sean de Wolski
2014-8-21
Ahh, I see what you're saying.
更多回答（2 个）
Guillaume
2014-8-21
a(logical(triu(ones(size(a))))) = rand(1, sum(sum(triu(ones(size(a))))));
The sum(sum expression is just to find how many random numbers to generate.
Try the triu function that extracts the upper triangular part of a matrix.
b = ones(10);
a = randn(10);
aUpper = triu(a);
b(aUpper ~= 0) = aUpper(aUpper~=0); % To replace the upper elements in b.
Another solution is:
b = ones(10);
bL = tril(b);
a = randn(10);
aU = triu(a);
c = bL+aU;
I think I would do it as in the first example, but if you want you can try both and select the one you want. Of course you will need to create some kind of loop and do some stuff to save the matrices (or may use them and discard them, or whatever you need). However, from here you should be able to handle it by yourself.
Good luck!
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