source: tools/pytools/combinatorics.py @ 2018

"""
  Combinatorial function using NumPy
  OMN, 2001
"""  
        
import Numeric

def factorial(n):
  v = Numeric.arange(n)+1
  return Numeric.multiply.reduce(v)

def binom (n,k):
  """ Compute the binomial coefficient n!/(k! (n-k)!)
  """
  
  if k > n or n < 0 or k < 0:
    raise Exception
  elif k==n or n==0 or k==0:
    return(1)
  else:
    v = Numeric.arange(k) + n-k+1 #[n-k+1, ..., n-1, n]
    nom = Numeric.multiply.reduce(v)
    denom = factorial(k)
    
    return nom/denom 

def bitvector(i, n):
    """Compute binary representation of positive integer i in a word of size n
    """
    
    b=[0]*n
    k=0
    while i > 0:
        d = i%2
        b[k] = d
        i = i/2
        k = k+1
        if k > n: break
    return b