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?

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

Answer 1

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.