An elegant way to make a 2d array with all possible columns

Question

In numpy I would like to make a 2d arrray (r, by 2**r) where the columns are all possible binary columns.

For example, if height of the columns is 5, the columns would be

[0,0,0,0,0],  [0,0,0,0,1], [0,0,0,1,0], [0,0,0,1,1], [0,0,1,0,0], ...

My solution is

 np.array(list(itertools.product([0,1],repeat = c))).T

This seems very ugly. Is there a more elegant way?

Answer 1

You can use some broadcasting here, like so -

(((np.arange(2**r)[:,None] & 2**np.arange(r)[::-1]))>0).astype(int)

For r between 0 and 8, you can also use np.unpackbits -

np.unpackbits(np.arange(2**r,dtype='uint8')[:,None], axis=1)[:,8-r:]

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Runtime tests -

Case #1 (Original r = 5):

In [217]: r = 5

In [218]: from itertools import product

In [219]: %timeit np.array(list(product([0,1], repeat=5)))
10000 loops, best of 3: 33.9 µs per loop

In [220]: %timeit np.unpackbits(np.arange(2**r,dtype='uint8')[:,None], axis=1)[:,8-r:]
100000 loops, best of 3: 10.6 µs per loop

In [221]: %timeit (((np.arange(2**r)[:,None] & 2**np.arange(r)[::-1]))>0).astype(int) 
10000 loops, best of 3: 31.1 µs per loop

Case #2 (Larger r):

In [242]: r = 15

In [243]: %timeit (((np.arange(2**r)[:,None] & 2**np.arange(r)[::-1]))>0).astype(int)
100 loops, best of 3: 6.6 ms per loop

In [244]: %timeit np.array(list(product([0,1], repeat=r)))
10 loops, best of 3: 77.5 ms per loop