# sum of matrix omitting one dimension

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Rafael Schwarzenegger on 2 Nov 2017
Commented: Stephen23 on 2 Nov 2017
Hi, I would like to ask how I could sum over a n dimensional matrix except one dimension, so the output is a vector. The ndims are not known in forehand. The summation is giving always a vector. (In my case a marginal pdf in statistics). Something like sum(K(:) except i-th dimension)
The best in a cyclus ( ndims not known).
For example having matrix K, the sums would be [6 22], [12 16], [10 18]
K(:,:,1) =
0 1
2 3
K(:,:,2) =
4 5
6 7
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Cedric on 2 Nov 2017
There may be a mistake in your example. Isn't the first 12 supposed to be 22?
Rafael Schwarzenegger on 2 Nov 2017
Yeah 22, thank you.
I have as an input a m^n matrix and as and output n vectors of the length m.

Stephen23 on 2 Nov 2017
Edited: Stephen23 on 2 Nov 2017
Here is one very simple way:
>> d = 3; % dimension
>> v = 1:ndims(K);
>> v([1,d]) = v([d,1]);
>> s = sum(reshape(permute(K,v),size(K,d),[]),2)
s =
6
22
It works by swapping the first and the desired dimension, then reshaping so that all trailing dimensions are reduced to one. The sum is then trivially along each row.
Note that the method I show here also has the significant advantage that it does not create any variables with copies of the data from the input array: this will be important for scaling to larger input arrays. Also note that slow and complex arrayfun or cellfun are not required for this task!
Rafael Schwarzenegger on 2 Nov 2017
Oh yeah, that is correct. (I thought first, it is the total dimension.) Thank you very much!
Stephen23 on 2 Nov 2017
@Rafael Schwarzenegger: the dimensions of the input array are automatically measured using ndims(K).

Cedric on 2 Nov 2017
Here is one way, but there is probably a simpler approach:
buffer = arrayfun(@(k) permute(KL, circshift(1:ndims(KL), k-1)), 1:ndims(KL), 'UniformOutput', false) ;
s = cellfun(@(M) sum(reshape(M, [], size(M,2))), buffer, 'UniformOutput', false) ;
where s is a cell array of sum vectors.
EDIT : I won't have time, but maybe you can see how dimensions work with SHIFTDIM and understand how to have the outputs ordered as needed:
buffer = arrayfun(@(k) shiftdim(KL, k-1), 1:ndims(KL), 'UniformOutput', false) ;
s = cellfun(@(M) sum(reshape(M, [], size(M,2))), buffer, 'UniformOutput', false) ;
PS : you'll have to test whether it really does what you need. The approach is based on the fact that MATLAB reads memory column first
Cedric on 2 Nov 2017
As mentioned by Stephen, arrayfun and cellfun are not necessary. They are hidden loops and I used them for conciseness. You can build a FOR loop if you prefer, and again, as Stephen mentions it would have the advantage not to require storing copies of your data (if you are dealing with large arrays).
Rafael Schwarzenegger on 2 Nov 2017
@Cedric Wannaz: Thank you anyway.