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Reputation: 2299

Summing across various dimensions a multi-dimensional Matlab array

Consider an N-D array in Matlab composed of (nbins)^(N-2) sub-matrices of size nbins x nbins.

For example,

clear
rng default
N=5;
nbins=3;
A=randn(nbins,nbins,nbins,nbins,nbins);

Let M be an integer less or equal than N. I want to write a generic code that gives me an M-D array, B, obtained by summing A along the dimensions M+1,M+2,...,N.

For example, continuing above,

M=4;
%B is nbins x nbins x nbins x nbins with 
B=A(:,:,:,:,1)+A(:,:,:,:,2)+A(:,:,:,:,3); 

M=3;
%B is nbins x nbins x nbins with 
B_temp=A(:,:,:,:,1)+A(:,:,:,:,2)+A(:,:,:,:,3);
B=B_temp(:,:,:,1)+B_temp(:,:,:,2)+B_temp(:,:,:,3);

M=2
%B is nbins x nbins  with 
B_temp1=A(:,:,:,:,1)+A(:,:,:,:,2)+A(:,:,:,:,3);
B_temp2=B_temp(:,:,:,1)+B_temp(:,:,:,2)+B_temp(:,:,:,3);
B= B_temp2(:,:,1)+B_temp2(:,:,2)+B_temp2(:,:,3);

Upvotes: 1

Views: 104

Answers (2)

Cris Luengo
Cris Luengo

Reputation: 60799

Since R2018b, the function sum can sum along multiple dimensions simultaneously. Thus, you can sum over the dimensions M+1 through N by

B = sum(A,M+1:N);

For older versions of MATLAB, you could sum over each dimension in turn:

B = A
for ii=M+1:N
   B = sum(B,ii);
end

However, Luis’ answer will be more performant in the pre-R2018b case because it avoids the intermediate storage, and does just one pass over the array (at least if all dimensions to be summed over are contiguous, for non-contiguous dimensions you should time these two approaches to see which is faster).

Upvotes: 2

Luis Mendo
Luis Mendo

Reputation: 112769

Since you want to sum along several contiguous dimensions, it's very easy to collapse those dimensions into one using reshape, and then sum over that dimension. This approach applies sum over one dimension only, and thus works even in versions before R2018b, which don't support summing over multiple dimensions at once.

sz = size(A);
B = sum(reshape(A, [sz(1:M) prod(sz(M+1:end))]), M+1);

(If the dimensions to sum over were not contiguous, permute would be needed before reshape to make them contiguous, and the code might be slightly slower.)

Upvotes: 2

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