Sample uniformly at random from an n-dimensional unit simplex

Question

Sampling uniformly at random from an n-dimensional unit simplex is the fancy way to say that you want n random numbers such that

• they are all non-negative,

Answer 1

Here's a nice concise implementation of the second algorithm from Wikipedia:

SimplexSample[n_] := Rest@# - Most@# &[Sort@Join[{0,1}, RandomReal[{0,1}, n-1]]]

That's adapted from here: http://www.mofeel.net/1164-comp-soft-sys-math-mathematica/14968.aspx (Originally it had Union instead of Sort@Join -- the latter is slightly faster.)

(See comments for some evidence that this is correct!)