# Manipulation of matrix addition and multiplication.

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hello_world on 16 Aug 2016
Commented: the cyclist on 18 Aug 2016
Hello Friends,
I have the following:
A = [1 2 3; 4 5 6; 7 8 9];
B = [10 11 12; 13 14 15];
[N1, D1] = size(A);
[N2, D2] = size(B);
A_sq = sum(A.^2, 2);
B_sq = sum(B.^2, 2)';
D = A_sq(:,ones(1,N2)) + B_sq(ones(1,N1),:) - 2.*(A*B');
where D is N1 x D1 matrix.
I want to write expression for D in one single step, i.e., something like this (this is for illustration purpose, but it should compute the same Euclidean distance as the code above):
D = sum(X - C).^2;
James Tursa on 16 Aug 2016
How is this different from this earlier post which was already answered?

Matt J on 16 Aug 2016
Edited: Matt J on 16 Aug 2016
Bp=permute(B,[3,2,1]);
D=reshape( sum(bsxfun(@minus, A, Bp).^2,2)) , N1,N2);
the cyclist on 18 Aug 2016
I repmat'ed his matrices to make them pretty huge, and found nearly identical timing for the reshape algorithm and the permute algorithm.
Interestingly, my original solution (in the comments)
D = bsxfun(@plus,sum(A.^2, 2),sum(B'.^2, 1)) - 2.*(A*B');
absolutely crushed both of these in timing.
So, as always, best to try to solve the problem (multiple ways if possible!), and then do optimization.