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] = size(C);
S = zeros(m-r,n-r);
for i=1:m-r+1
    for j=1:n-r+1
        S(i,j) = sum(diag(C(i:i+r-1,j:j+r-1)));
    end
end

The code calculates a table of scores, S, for a dynamic programming algorithm, from another score table, C.
The diagonal summing is to generate scores for individual pieces of the data used to generate C, for all possible pieces (of size r).

Thanks in advance for any answers! Sorry if this one should be obvious...

Note
The built-in conv2 turned out to be faster than convnfft, because my eye(r) is quite small ( 5 <= r <= 20 ). convnfft.m states that r should be > 20 for any benefit to manifest.

Answer 1

If I understand correctly, you're trying to calculate the diagonal sum of every subarray of C, where you have removed the last row and column of C (if you should not remove the row/col, you need to loop to m-r+1, and you need to pass the entire array C to the function in my solution below).

You can do this operation via a convolution, like so:

S = conv2(C(1:end-1,1:end-1),eye(r),'valid');

If C and r are large, you may want to have a look at CONVNFFT from the Matlab File Exchange to speed up calculations.