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How to convert an integer array to a specific length binary array

I am trying to convert a numpy integer array, let's say A=[3,5,2], into a numpy binary array with least significant bit first format and specific length. That is, the outcome for length 6 should be as follows:

A' = [1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0]

The first 6 values are for the first element of A, the second 6 of those are for the second element of A and the last 6 of those for the last element of A.

My current solution is as follows:

np.multiply( np.delete( np.unpackbits( np.abs(A.astype(int)).view("uint8")).reshape(-1,8)[:,::-1].reshape(-1,64), np.s_[ln::],1).astype("float64").ravel(), np.repeat(np.sign(A), ln))

where ln represents the specific ln (in the example, it was 6)

Is there any faster way to do this?

Thanks in advance.

EDIT: I should have pointed out before. A can also have negative values. For instance, if A=[-11,5] and ln=6, then the returned array should be:

A'=[-1 -1 0 -1 0 0 1 0 1 0 0 0]

Note that ln=6 is just an example. It could be even 60.

Sorry for missing this part of the requirement.

Answer*

Here's a vectorized one -

 ((A[:,None] & (1 << np.arange(ln)))!=0).ravel().view('i1')

Another with `np.unpackbits` -

 np.unpackbits(A.view(np.uint8)[::8]).reshape(-1,8)[:,ln-7:1:-1].ravel()

Sample run -

 In [197]: A
 Out[197]: array([3, 5, 2])
 
 In [198]: ln = 6
 
 In [199]: ((A[:,None] & (1 << np.arange(ln)))!=0).ravel().view('i1')
 Out[199]: array([1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], dtype=int8)
 
 In [200]: np.unpackbits(A.view(np.uint8)[::8]).reshape(-1,8)[:,ln-7:1:-1].ravel()
 Out[200]: array([1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], dtype=uint8)

Timings on a large array -

 In [201]: A = np.random.randint(0,6,1000000)
 
 In [202]: ln = 6
 
 In [203]: %timeit ((A[:,None] & (1 << np.arange(ln)))!=0).ravel().view('i1')
 10 loops, best of 3: 32.1 ms per loop
 
 In [204]: %timeit np.unpackbits(A.view(np.uint8)[::8]).reshape(-1,8)[:,ln-7:1:-1].ravel()
 100 loops, best of 3: 8.14 ms per loop

If you are okay with a `2D` array output with each row holding binary info for each element off the input, it's much better -

 In [205]: %timeit np.unpackbits(A.view(np.uint8)[::8]).reshape(-1,8)[:,ln-7:1:-1]
 1000 loops, best of 3: 1.04 ms per loop

Other posted approaches -

 # @aburak's soln
 In [206]: %timeit np.multiply( np.delete( np.unpackbits( np.abs(A.astype(int)).view("uint8")).reshape(-1,8)[:,::-1].reshape(-1,64), np.s_[ln::],1).astype("float64").ravel(), np.repeat(np.sign(A), ln))
 10 loops, best of 3: 180 ms per loop
 
 # @Jacques Gaudin's soln
 In [208]: %timeit np.array([int(c) for i in A for c in np.binary_repr(i, width=6)[::-1]])
 1 loop, best of 3: 3.34 s per loop
 
 # @Paul Panzer's soln
 In [209]: %timeit np.unpackbits(A[:, None].view(np.uint8)[..., ::-1] if sys.byteorder=='little' else A[:, None].view(np.uint8), axis=-1)[..., :-ln-1:-1].reshape(-1)
 10 loops, best of 3: 35.4 ms per loop


The best thing that worked in favour of the second approach from this post is that we have an `uint8` dtype version of the input, which is simply a view into the input and hence memory efficient -

 In [238]: A
 Out[238]: array([3, 5, 2])
 
 In [239]: A.view(np.uint8)[::8]
 Out[239]: array([3, 5, 2], dtype=uint8)
 
 In [240]: np.shares_memory(A,A.view(np.uint8)[::8])
 Out[240]: True

So, when we use `np.unpackbits`, we are feeding in the same number of elements as the original one.

Also, `A.view(np.uint8)[::8]` seems like a good trick to view an `int` dtype array as an `uint8` one!

----

To solve for generic case, we could extend the earlier listed approaches.

Approach #1 (for ln upto 63) :

 (((np.abs(A)[:,None] & (1 << np.arange(ln)))!=0)*np.sign(A)[:,None]).ravel()


Approach #2 :

 a = np.abs(A)
 m = ((ln-1)//8)+1
 b = a.view(np.uint8).reshape(-1,8)[:,:m]
 U = np.unpackbits(b,axis=1)
 out = U.reshape(-1,m,8)[...,::-1].reshape(len(A),-1)[...,:ln]
 out = (out*np.sign(A)[:,None]).ravel()

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Thanks for the benchmark, I didn't dare publishing the results 😖

Jacques Gaudin
– Jacques Gaudin

2019年04月11日 15:28:53 +00:00
Commented Apr 11, 2019 at 15:28
I tried to extend your solution to the cases where we have ln>6 such as 60. I somehow got lost among the indices. Can you point out the solution for it?

aburak
– aburak

2019年04月11日 15:38:23 +00:00
Commented Apr 11, 2019 at 15:38

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How to convert an integer array to a specific length binary array

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