def combinations(n, k):
"""Returns the number of ways of choosing k items from n.
"""
return exp(lgam(n+1) - lgam(k+1) - lgam(n-k+1))
def brillouin_d(counts):
"""Brilloun index of alpha diversity: Pielou 1975, by way of SDR-IV."""
nz = counts[counts.nonzero()]
n = nz.sum()
return (lgam(n+1) - array(map(lgam, nz+1)).sum())/n
def brillouin_d(counts):
"""Brilloun index of alpha diversity: Pielou 1975, by way of SDR-IV."""
nz = counts[counts.nonzero()]
n = nz.sum()
return (lgam(n + 1) - array(map(lgam, nz + 1)).sum()) / n