Sum of sparse vectors: bug or feature?

I recently stumbled upon the following behavior in MATLAB R2022a:

>> a = sparse(1,2,1)
a =
   (1,2)        1

>> b = sparse(2,1,18)
b =
   (2,1)       18

>> a+b
ans =
   (2,1)       18
   (1,2)        1
   (2,2)       19

The presence of the (2,2) element with value 19 is quite puzzling. Intuitively, I would have expected to get either a zero (no element) or an error indicating that the vectors’ sizes are not compatible. I couldn’t find an explanation for this behavior in the documentation.

So, is this a bug or a feature?

>Solution :

This is due to implicit broadcasting and expected behaviour, also for full() arrays. Compare:

bsxfun(@plus, [0 1], [0; 18])

ans =

     0     1
    18    19

(I’m running R2007b, so need bsxfun() instead of implicit broadcasting).

What happens with unequal-sized vectors is that they are "extended" into the appropriate size for addition, see this blog post on an in-depth explanation. In our toy example a is broadcast to [0, 1; 0, 1] and b to [0, 0; 18, 18], resulting in what you see as answer when each element is added to its equivalent index in the other matrix.