Vectorization for Two Nested for-loops

Hello all,

I'm trying to vectorize some operation between two 2D matrices, A and B. Basically, the process is multiplying every row verctor from matrix B by every vector from matrix A and store the value in matrix C. The correct non-vectorized code looks as follows:

A = [2 3 4; 5 2 1; 1 4 3];

B = [3 4 4; 4 2 1; 4 4 1];

C = zeros(3,3); % Initializing C

for ii=1:size(A,1)

for jj=1:size(B,1)

AA = A(ii,:);

BB = transpose(B(jj,:));

C(jj,ii) = sum(BB*AA, 'all')

end

end

C

The resultant C should looks as:

C =

99 88 88

63 56 56

81 72 72

Can I get help here?

Thanks!

Answer 1

[Tomoaki Takagi]

Try:

A = [2 3 4; 5 2 1; 1 4 3];
B = [3 4 4; 4 2 1; 4 4 1];
C = repmat(A,3).*repelem(B,3,3);
C = reshape(sum(C,2),3,3)'

Answer 2

[Stephen23]

Without creating multiple copies of data in memory:

A = [2 3 4; 5 2 1; 1 4 3];
B = [3 4 4; 4 2 1; 4 4 1];
C = sum(permute(A,[3,1,2,4]).*permute(B,[1,3,4,2]),3:4)

C = 3x3

99 88 88 63 56 56 81 72 72

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The same basic approach, more verbose but possibly more efficient:

As = size(A);
Bs = size(B);
C = sum(reshape(A,[1,As]).*reshape(B,[Bs(1),1,1,Bs(2)]),3:4)

C = 3x3

99 88 88 63 56 56 81 72 72

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