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I am working with largish binary matrices, at the moment up to 100x100.

Lets say I am working with 30x30 binary matrices. Then there are a total of 2^(30x30) binary matrices. I want to select a binary matrix at random, where each of the 2^(30x30) matrices has the same probability of being selected.

My solution attempt was to pick a number between 1 and 2^(30x30) using the function randi(n) with n = 2^(30x30) and then converting the result to the appropriate binary matrix. The problem I ran into was that randi(n) does not take values for n larger than 2^54. Matlab in general does not seem to like very large numbers.

Any suggestions?

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If each matrix of booleans has equal probability, then the elements of the matrix each have equal probability of 0 and 1. You can just fill a matrix of the appropriate size with n² uniform random booleans.

I don't have MATLAB handy, but in Octave you'd do something like unidrnd(2, n, n) - 1.

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Thanks, that seems so obvious now. A fresh perspective often helps... :)
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You can use randint in the range [0 1]:

matrix=randint(30,30,[0 1]);

You can also use rand and threshold the resulting matrix:

matrix=rand(30,30);
matrix=round(matrix);

EDIT: just realized it also works with randi with the following syntax:

matrix=randi([0 1],30,30);
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Thanks. I missed the connection that each individual element has equal probability of being either 1 or 0 as @larsmans pointed out.

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