Blockwise matrix addition without using more than 2 dimensions and cycles

Dear All,

I am looking for a solution of blockwise matrix addition. To give a simple example, let us have

A = [1,2,3,4,5,6,7,8; 9,10,11,12,13,14,15,16];

I would like to get the result:

B = [1+5,2+6,3+7,4+8; 9+13,10+14,11+15,12+16];

The evident solution which comes to mind would be:

sum(reshape(A,2,4,2), 3);

However, I am using a third-party tool with special variables for which 3D arrays are not implemented. My next idea was to use:

B = zeros(2,4);
for i = 1:4
    B(:,i) = sum(A(:, i:4:end), 2);
end

If possible I am looking for functions that can solve this without using a cycle as in my application the number of columns will reach hundreds and thousands. I thank for in advance for anyone's help.

Answer 1

[the cyclist]

This is awkward, but it does what you want. I think there is probably a better way.

% Inputs
A = [1,2,3,4,5,6,7,8; 9,10,11,12,13,14,15,16];
groupSize = 4;

% Output
B = movsum(A,[0,groupSize],2) - movsum(A,[0,groupSize-1],2) + A;
B = B(:,1:groupSize)

B = 2×4

6 8 10 12 22 24 26 28

[Bence Cseppento]

Thanks for your effort, it does look good but I'll have to test it for some other cases.

In the mean time I managed to solve my problem by managing a conversion between types and using the original 3D version, but I did not know about the movsum() function before so you have given me food for thought, thank you!

Answer 2

[the cyclist]

A = [1,2,3,4,5,6,7,8; 9,10,11,12,13,14,15,16];
B = A(:,1:end/2) + A(:,(end/2)+1:end)

B = 2×4

6 8 10 12 22 24 26 28

[Bence Cseppento]

Thank you, I was a bit over-complicating it because of the context of my problem which I have not shared. However, I am still looking for a more general solution, e.g. I want to get a 2x20 matrix from a 2x2000 matrix, by summing the (:,1:20), (:,21:40) ... (:,1981:2000) submatrices without the use of a cycle.