"How do I generate doubly-stochastic matrices uniform randomly? A doubly-stochastic matrix is an n×n matrix P such that sum _(i=1)^(n) p_ij=sum _(j=1)^(n) p_ij=1 where p_ij>=0. Can someone please suggest an algorithm for generating these matrices uniform randomly?"

piopiopioirp 2022-11-17 Answered
How do I generate doubly-stochastic matrices uniform randomly?
A doubly-stochastic matrix is an n×n matrix P such that
i = 1 n p i j = j = 1 n p i j = 1
where p i j 0. Can someone please suggest an algorithm for generating these matrices uniform randomly?
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Answers (1)

mangoslush27fig
Answered 2022-11-18 Author has 15 answers
What we want is to generate a bistochastic matrix in step with the Haar degree, that is the particular distribution that is invariant to multiplication by way of bistochastic matrices from both facets.
the same old set of rules is to take a few iid matrix (every entry is chosen iid from some distribution over non-bad numbers) and then again and again make it row-stochastic and column-stochastic - this is like projecting the matrix to the linear subspace of stochastic matrices. The procedure converges quite fast, and we get a few random bistochastic matrix, even though now not in step with the wanted distribution.
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