Is there a better way to broadcast arrays?

Question

I want to broadcast an array b to the shape it would take if it were in an arithmetic operation with another array a.

For example, if a.shape = (3,3) and b was a scalar, I want to get an array whose shape is (3,3) and is filled with the scalar.

One way to do this is like this:

>>> import numpy as np
>>> a = np.arange(9).reshape((3,3))
>>> b = 1 + a*0
>>> b
array([[1, 1, 1],
       [1, 1, 1],
       [1, 1, 1]])

Although this works practically, I can't help but feel it looks a bit weird, and wouldn't be obvious to someone else looking at the code what I was trying to do.

Is there any more elegant way to do this? I've looked at the documentation for np.broadcast, but it's orders of magnitude slower.

In [1]: a = np.arange(10000).reshape((100,100))

In [2]: %timeit 1 + a*0
10000 loops, best of 3: 31.9 us per loop

In [3]: %timeit bc = np.broadcast(a,1);np.fromiter((v for u, v in bc),float).reshape(bc.shape)
100 loops, best of 3: 5.2 ms per loop

In [4]: 5.2e-3/32e-6
Out[4]: 162.5

Barnstorm

Answer 1

If you just want to fill an array with a scalar, fill is probably the best choice. But it sounds like you want something more generalized. Rather than using broadcast you can use broadcast_arrays to get the result that (I think) you want.

>>> a = numpy.arange(9).reshape(3, 3)
>>> numpy.broadcast_arrays(a, 1)[1]
array([[1, 1, 1],
       [1, 1, 1],
       [1, 1, 1]])

This generalizes to any two broadcastable shapes:

>>> numpy.broadcast_arrays(a, [1, 2, 3])[1]
array([[1, 2, 3],
       [1, 2, 3],
       [1, 2, 3]])

It's not quite as fast as your ufunc-based method, but it's still on the same order of magnitude:

>>> %timeit 1 + a * 0
10000 loops, best of 3: 23.2 us per loop
>>> %timeit numpy.broadcast_arrays(a, 1)[1]
10000 loops, best of 3: 52.3 us per loop

But scalars, fill is still the clear front-runner:

>>> %timeit b = numpy.empty_like(a, dtype='i8'); b.fill(1)
100000 loops, best of 3: 6.59 us per loop

Finally, further testing shows that the fastest approach -- in at least some cases -- is to multiply by ones:

>>> %timeit numpy.broadcast_arrays(a, numpy.arange(100))[1]
10000 loops, best of 3: 53.4 us per loop
>>> %timeit (1 + a * 0) * numpy.arange(100)
10000 loops, best of 3: 45.9 us per loop
>>> %timeit b = numpy.ones_like(a, dtype='i8'); b * numpy.arange(100)
10000 loops, best of 3: 28.9 us per loop

Phyllis

Perfect! This is exactly what I was looking for. I'm surprised I didn't see it; it's right next to broadcast in the docs. – Barnstorm

In case you're curious, the reason I'm interested in this is that the function scipy.ndimage.map_coordinates does not automatically broadcast the input coordinates, so I have to do it manually. – Barnstorm

Answer 2

fill sounds like the simplest way:

>>> a = np.arange(9).reshape((3,3))
>>> a
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
>>> a.fill(10)
>>> a
array([[10, 10, 10],
       [10, 10, 10],
       [10, 10, 10]])

EDIT: As @EOL points out, you don't need arange if you want to create a new array, np.empty((100,100)) (or whatever shape) is better for this.

Timings:

In [3]: a = np.arange(10000).reshape((100,100))
In [4]: %timeit 1 + a*0
100000 loops, best of 3: 19.9 us per loop

In [5]: a = np.arange(10000).reshape((100,100))
In [6]: %timeit a.fill(1)
100000 loops, best of 3: 3.73 us per loop

Berkowitz

There is no reason to use arange(): this wastes time for nothing, as an array has to be created and filled with numbers that will only get erased. – Hurst

@EOL, I was just taking the example in the question to create an array. It's irrelevant for this question (I was assuming the the array was already there, waiting to be filled.) – Berkowitz

Yeah, arange is irrelevant to the timing going on here. I hope the downvoter removes the down vote; it's completely inappropriate IMO. – Mitten

Timing is not the issue I have. My point is that a in this answer is the b in the original question (it is the final result). In the question b does not exist: it has to be created. Creating it is part of the answer, and this should not involve arange(). – Hurst

@EOL it feels a bit odd to be downvoted considering I was the first one to mention fill() and I've also provided timings, but losing 2 points isn't a big deal... I barely copied a = np.arange(9).reshape((3,3)) from the question because I didn't want to make assumptions regarding where it came from in the wider context of the OP. I tend only to downvote when the answer is clearly wrong, misleading or of very low quality, but I guess we all have different criteria for voting. – Berkowitz

@Bruno: fill() is my favorite solution (it's fast and to the point), and you were indeed the first to mention it. However, I consider that writing a = arange(…); a.fill(…) is misleading: it can be taken as an example by newcomers, and using this code is bad practice (it does more work than necessary). However, since you edited your post, I removed my downvote. :) – Hurst

Answer 3

The fastest and cleanest solution I know is:

b_arr = numpy.empty(a.shape)  # Empty array
b_arr.fill(b)  # Filling with one value

Hurst

Answer 4

If you just need to broadcast a scalar to some arbitrary shape, you can do something like this:

a = b*np.ones(shape=(3,3))

Edit: np.tile is more general. You can use it to duplicate any scalar/vector in any number of dimensions:

b = 1
N = 100
a = np.tile(b, reps=(N, N))

Hypesthesia

b*np.ones() involves multiplications whereas we only need to copy values. fill() is both more appropriate and faster. – Hurst