77

Having a vector x and I have to add an element (newElem) .

Is there any difference between - 

x(end+1) = newElem;

and 

x = [x newElem];

?

Erfan
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3 Answers3

94

x(end+1) = newElem is a bit more robust.

x = [x newElem] will only work if x is a row-vector, if it is a column vector x = [x; newElem] should be used. x(end+1) = newElem, however, works for both row- and column-vectors.

In general though, growing vectors should be avoided. If you do this a lot, it might bring your code down to a crawl. Think about it: growing an array involves allocating new space, copying everything over, adding the new element, and cleaning up the old mess...Quite a waste of time if you knew the correct size beforehand :)

Rody Oldenhuis
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ThijsW
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    Also for the second method, `x` must be initialized first! – Dan Apr 24 '13 at 09:22
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    @RodyOldenhuis, no problem! I did the same, probably at the same time. @Dan, that's true, but as the question mentioned "having a vector `x` (of size `n`)", I kind of assumed `n` to be non-zero and the vector being initialized already :) – ThijsW Apr 24 '13 at 09:24
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    @ThijsW: Still, using `end` rather than some variable `n` (which might be a `global` for all you know!) is the more universal, robust-no-cost way to go – Rody Oldenhuis Apr 24 '13 at 09:37
  • @Dan x must be initialised for both methods. – Robino Sep 17 '17 at 12:35
  • @Robino I don't think so, I don't have MATLAB to check but in octave you can certainly do `x(end+1)=...` without `x` being initialised and I'm almost certain you can do it in MATLAB as well – Dan Sep 17 '17 at 14:41
  • @Dan `x(end+1)=123` gives _Undefined function or variable 'x'._ – Robino Sep 18 '17 at 07:07
28

Just to add to @ThijsW's answer, there is a significant speed advantage to the first method over the concatenation method:

big = 1e5;
tic;
x = rand(big,1);
toc

x = zeros(big,1);
tic;
for ii = 1:big
    x(ii) = rand;
end
toc

x = []; 
tic; 
for ii = 1:big
    x(end+1) = rand; 
end; 
toc 

x = []; 
tic; 
for ii = 1:big
    x = [x rand]; 
end; 
toc

   Elapsed time is 0.004611 seconds.
   Elapsed time is 0.016448 seconds.
   Elapsed time is 0.034107 seconds.
   Elapsed time is 12.341434 seconds.

I got these times running in 2012b however when I ran the same code on the same computer in matlab 2010a I get

Elapsed time is 0.003044 seconds.
Elapsed time is 0.009947 seconds.
Elapsed time is 12.013875 seconds.
Elapsed time is 12.165593 seconds.

So I guess the speed advantage only applies to more recent versions of Matlab

Dan
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  • +1, Edited to add the obvious as well. I'll test again on a "real" CPU (I'm on this crappy unreliable no-good APU thing now...) – Rody Oldenhuis Apr 24 '13 at 09:28
  • @Dan, same for me, I get 0.028 for the 3rd option and 8.909 for the last – ThijsW Apr 24 '13 at 09:31
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    I also think the JIT optimisation for the `x(end+1)` case is a pretty recent addition (R2012a or so...). I vagualey remember reading something like that in some changenotes at smoe point. I also get very different results on my APU/Matlab R2010, but I'm not sure if that's due to the Matlab version or the APU... – Rody Oldenhuis Apr 24 '13 at 09:33
  • @RodyOldenhuis and ThiijsW see my recent comparison between older and newer matlab – Dan Apr 24 '13 at 09:33
  • @Dan: Ah :) OK, NOW it's all better :) – Rody Oldenhuis Apr 24 '13 at 09:35
4

As mentioned before, the use of x(end+1) = newElem has the advantage that it allows you to concatenate your vector with a scalar, regardless of whether your vector is transposed or not. Therefore it is more robust for adding scalars.

However, what should not be forgotten is that x = [x newElem] will also work when you try to add multiple elements at once. Furthermore, this generalizes a bit more naturally to the case where you want to concatenate matrices. M = [M M1 M2 M3]

All in all, if you want a solution that allows you to concatenate your existing vector x with newElem that may or may not be a scalar, this should do the trick:

 x(end+(1:numel(newElem)))=newElem
Dennis Jaheruddin
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    I think your last example should be: x(end+1:end+length(newElem)) = newElem – Digna Jan 22 '14 at 15:00
  • @Digna Thanks for finding the bug, I have updated the answer to fix the problem. – Dennis Jaheruddin Jan 22 '14 at 15:07
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    With my Matlab2011b, there was also a drastic (~50x) speed improvement on vector concatenation with this method vs. the a=[a b] method. – JaBe Apr 08 '15 at 17:17
  • @Jabe the [a b] method is concatenation. I suppose you are saying that extending the array is quicker than concatenation? – Robino Sep 17 '17 at 12:34