How to generate a random logical symmetric matrix?
(binary symmetric matrix)
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a = triu(rand(5));
out = a + tril(a',-1)>.5
a = rand(5)
b = a+a'
out = b >= mean(b(:))
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I like the 2nd variant. The "mean" in out = b >= mean(b(:)) is crucial. out = b >= 0.5 gives a highly-biased out.
Hi Derek! Thanks.
a = rand(5)
out = (a+a')/2>.5
I like variant 3 even better. Concise but not obscure. Excellent!
I don't see why the mean() version would work without bias. Suppose that all of the random numbers generated were less than 1/4, so even after adding transpose each total was less than 1/2. Clearly the output for such a matrix should be complete logical 0s. But unless all of the values generated were identical, at least one of the sums is going to be greater than the mean, so if one compares to mean(b(:)) one would get logical 1 in that position. (And if all of the values _are_ identical then they would all be equal to the mean to within roundoff and so the returned result would either be all 0 or all 1 depending which way the mean() rounded.)
It seems to me, then, that for variant 2, instead of comparing to mean(b(:)), one should be comparing to 1
a = rand(5);
b = a + a';
out = b >= 1;
Which can then be made more concise as
a = rand(5);
out = (a+a') >= 1;
Note: the uniform distributions all generate (2^b - 2) different possible numbers, with b=53 for all the generators except one legacy generator that has b=24 . The possible numbers are spaced 2^(-b) apart. The generators cannot generate exactly 0 or exactly 1. If you do a quick counting test, you will see that 0.5 exactly is the first number of the second half of the count, so instead of comparing for > 0.5, you should be comparing for >= 0.5 .
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