Vectorizing sums of different diagonals in a matrix

Question

I want to vectorize the following MATLAB code. I think it must be simple but I\'m finding it confusing nevertheless.

r = some constant less than m or n
[m,n         


        

Answer 1

Based on the idea of JS, and as Jonas pointed out in the comments, this can be done in two lines using IM2COL with some array manipulation:

B = im2col(C, [r r], 'sliding');
S = reshape( sum(B(1:r+1:end,:)), size(C)-r+1 );

Basically B contains the elements of all sliding blocks of size r-by-r over the matrix C. Then we take the elements on the diagonal of each of these blocks B(1:r+1:end,:), compute their sum, and reshape the result to the expected size.

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Comparing this to the convolution-based solution by Jonas, this does not perform any matrix multiplication, only indexing...