Permutations with repetitions

bin_perm_rep.py

import numpy as np

def bin_perm_rep(ndim,a=0,b=1):
    """bin_perm_rep(ndim) -> ndim permutations with repetitions of (a,b).

    Returns an array with all the possible permutations with repetitions of
    (0,1) in ndim dimensions.  The array is shaped as (2**ndim,ndim), and is
    ordered with the last index changing fastest.  For examble, for ndim=3:

    Examples:
    
    >>> bin_perm_rep(3)
    array([[0, 0, 0],
           [0, 0, 1],
           [0, 1, 0],
           [0, 1, 1],
           [1, 0, 0],
           [1, 0, 1],
           [1, 1, 0],
           [1, 1, 1]])
    """
    
    # Create the lefttmost column as 0,0,...,1,1,...
    nperms = 2**ndim
    perms = np.empty((nperms,ndim),type(a))
    perms.fill(a)
    half_point = nperms/2
    perms[half_point:,0] = b
    # Fill the rest of the table by sampling the pervious column every 2 items
    for j in range(1,ndim):
        half_col = perms[::2,j-1]
        perms[:half_point,j] = half_col
        perms[half_point:,j] = half_col

    return perms