def multinomial(Tot, vec):
#Computes the special multinomial function \binom{d}{\alpha} defined in the paper
if np.sum(vec)!=Tot:
raise(AssertionError("The multinomial is not well defined"))
else:
if len(vec)==1: return 1
else:
return(binom(Tot,vec[0])*multinomial(Tot-vec[0],np.delete(vec,[0])))
def bernstein(n, k):
"""Bernstein polynomial."""
from scipy.special._ufuncs import binom
coeff = binom(n, k)
def _bpoly(x):
return coeff * x**k * (1 - x)**(n - k)
return _bpoly
def P(n, k):
return binom(2 ** k, n) * 0.25 ** n * 0.75 ** (2 ** k - n)