Rewriting a vector addition and multiplication.

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:

   D = sum(A.^2,2)(:,ones(1,N2)) + sum(B.^2,2)(ones(1,N1),:) - 2.*(A*B');

or perhaps something like this is even better:

D = sum[(A.^2,2)(:,ones(1,N2)) + (B.^2,2)(ones(1,N1),:) - . . .];

I know that above expression is wrong because one needs to store sum in a temporary variable before indexing. However, it is just for illustration purpose that I want to write down this expression in one single step.

I will appreciate any advise.

Answer 1

[Thorsten]

Repmat is your friend here:

D = repmat(sum(A.^2, 2), [1, N2]) + repmat(sum(B.^2, 2)', [N1, 1]) - 2*A*B';

or as a one-liner all together:

D = repmat(sum(A.^2, 2), [1, size(B, 1)]) + repmat(sum(B.^2, 2)', [size(A, 1), 1]) - 2*A*B';

[Thorsten]

I'm pretty sure that it is not possible in Matlab you compute something and then index into the result, like

(A.^2,2)(:,ones(1,N2))

But I agree that this would be quite nice to have.

Answer 2

[James Tursa]

D = bsxfun(@plus,sum(A.^2, 2),sum(B.^2, 2)') - 2.*(A*B');