# Summing within an array to change the size

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Matthew Vincent on 27 Aug 2012
I have an array that has dimensions of 111x46x2. I want to sum the values in the first 3x3 block to become the first value of the next matrix repeating this until the last column is summed together. The dimensions of the new matrix should be 37x16x2.
I could make the dimensions of the original matrix 111x48x2 if that makes the calculations easier and more efficient. The 9x9 blocks will have values only in certain locations such as [ 0 0 #; # 0 0; 0 # 0]; and the last column will have values in each row.
Walter Roberson on 29 Aug 2012

Sean de Wolski on 27 Aug 2012
Edited: Sean de Wolski on 27 Aug 2012
If you have the Image Processing Toolbox:
x = rand(111,46,2);
y = blockproc(x,[3 3],@(s)sum(sum(s.data,1),2));
Or if you don't:
z = convn(x,ones(3),'valid');
z = z(1:3:end,1:3:end,:); %may need to crop differently depending on last edges
Matthew Vincent on 27 Aug 2012
I think that the convn function will work for me. Have other things I need to incorporate before I can test it and be sure. Thanks

Matt Fig on 27 Aug 2012
Here is one way to do it:
A = magic(6);
cellfun(@(x) sum(x(:)),mat2cell(A,2*ones(1,3),2*ones(1,3)))
Matt Fig on 27 Aug 2012
MAT2CELL is slow for large inputs, indeed. What are you MathWorkers doing with your time?! ;-)

Jan on 28 Aug 2012
Edited: Jan on 28 Aug 2012
You can use the fast FEX: BlockMean. Either modify the code or multiply the results accordingly.
A Matlab version:
x = rand(111, 46, 2);
S = size(X);
M = S(1) - mod(S(1), 3);
N = S(2) - mod(S(2), 3);
% Cut and reshape input such that the 1st and 3rd dimension have the lengths V
% and W:
XM = reshape(X(1:M, 1:N, :), 3, M / 3, 3, N / 3, []);
Y = squeeze(sum(sum(XM, 1), 3));
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Jan on 29 Aug 2012
Difference between Andrei's and my solution:
• RESHAPE instead of SQUEEZE (which calls RESHAPE internally)
• Andrei appends zeros, I remove the not matching lines on the bottom.