Python, numpy : 3 dimensions broadcast

Question

I am a newby in broadcasting with numpy. I define three numpy arrays as follows:

from numpy import *
a=array([10,20]).reshape(2,1)
b=array([100,200,300]).reshape(1,3)
c=arange(1,11).reshape(1,1,10)

a+b is a (2,1) vs (1,3) sum so it is supposed to be broadcastable (2vs1 in dim 1, 1vs3 in dim 2, broadcast rule is fulfiled). Indeed it is:

>>> a+b
array([[110, 210, 310],
       [120, 220, 320]])

a+c is a (2,1) vs (1,1,10) sum so it is supposed to be broadcastable (2vs1 in dim 1, 1vs1 in dim 2 and 1vs10 in dim 3, broadcast rule is fulfiled). Indeed it is:

>>> a+c
array([[[11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
        [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]]])

b+c is a (1,3) vs (1,1,10) sum so it is supposed to be broadcastable (1vs1 in dim 1, 3vs1 in dim 2, 1vs10 in dim 3. But it seems it is not:

>>> b+c
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: shape mismatch: objects cannot be broadcast to a single shape

The explanation is certainely obvious ... but please help me !

eumiro · Accepted Answer · 2012-04-17 09:34:04Z

1

b[:,:,None] + c

returns a (1, 3, 10) array. You have to define the missing axis (the third one).

You can also use

b[:,:,newaxis] + c

since you imported * from numpy, which is generally not a good idea.

import numpy as np is better. This way you will always know where the methods come from (if you import more packages):

import numpy as np
a = np.array([10,20]).reshape(2,1)
b = np.array([100,200,300]).reshape(1,3)
c = np.arange(1,11).reshape(1,1,10)

print a + b
print a + c
print b[:,:,np.newaxis] + c

answered Apr 17, 2012 at 9:34

eumiro

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Moi Jaiunvelo Over a year ago

Thank you very much ! I know about from numpy import *, I used it for clarity but you are right this should be avoided everywhere.

Bi Rico · Accepted Answer · 2012-04-17 14:37:17Z

1

a+c is a (2,1) vs (1,1,10) sum so it is supposed to be broadcastable (2vs1 in dim 1, 1vs1 in dim 2 and 1vs10 in dim 3, broadcast rule is fulfiled). Indeed it is:
>>> a+c array([[[11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
                [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]]])

Not quite, notice that a + c is (1, 2, 10) not (2, 1, 10).

>>> from numpy import array, arange, newaxis
>>> a=array([10,20]).reshape(2,1)
>>> b=array([100,200,300]).reshape(1,3)
>>> c=arange(1,11).reshape(1,1,10)
>>> (a + c).shape
(1, 2, 10).shape

When broadcasting arrays with different dimensions, the one with fewer dimensions get padded with 1s at the beginning, more info here, so b + c is like trying to add a (1, 1, 3) with a (1, 1, 10). @eumiro's suggestion, b[:,:,np.newaxis] + c, is probably the easiest way of reshaping b to be (1,3,1) so you get what you expect.

answered Apr 17, 2012 at 14:37

Bi Rico

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Moi Jaiunvelo Over a year ago

Thank you Bago, indeed i did not notice that (a+c) was a (1,2,10). And indeed (as suggested by eumiro), to obtain a (2,1,10) I need to write a[:,:,np.newaxis]+c.

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