Sample uniformly at random from a simplex in Python

Question

I want to uniformly sample from a simplex in python. I found the following in R but nothing so far in python

 runif_in_simplex(n, simplex)

EDIT: Is the following solution correct?

generate N random numbers (N = no of vertices of simplex)
Normalize these N numbers (divide by sum)
Form the linear combination of N numbers and Vertice's coordinates.

Does this answer your question? [Generating N uniform random numbers that sum to M](https://stackoverflow.com/questions/30658932/generating-n-uniform-random-numbers-that-sum-to-m) — Peter O., Dec 05 '20 at 08:27
`Is the following solution correct?` Assuming that your random numbers are floats in [0...1) range, your solution is incorrect — Severin Pappadeux, Dec 05 '20 at 15:42

score 3 · Answer 1 · answered Apr 21 '21 at 19:08

3

Unit exponential variables is what you need (related post).

def runif_in_simplex(n):
  ''' Return uniformly random vector in the n-simplex '''

  k = np.random.exponential(scale=1.0, size=n)
  return k / sum(k)

The procedure that you proposed is not uniformly distributed in the simplex.

Refs

Onn, S., & Weissman, I. (2011). Generating uniform random vectors over a simplex with implications to the volume of a certain polytope and to multivariate extremes. Annals of Operations Research, 189(1), 331-342.

answered Apr 21 '21 at 19:08

Santiago Armstrong

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7

How do you guarantee unicity of the simplex elements? – R.W Feb 10 '22 at 07:00
what do you mean by unicity? – Santiago Armstrong Feb 10 '22 at 22:11
I mean that the decomposition into a simplex is unique for the vertices. – R.W Feb 16 '22 at 08:27
The proposed solution is to generate a uniformly random sample from the "standard simplex". But it works for every simplex by simply scaling the sides – Santiago Armstrong Feb 17 '22 at 13:23

Sample uniformly at random from a simplex in Python

1 Answers1

Refs