CODEWITHSUNDEEP
matlabmultidimensional-arraymatrix-multiplication
jonem
jonem

Reputation: 459

Multidimensional Matrix Multiplication

I'm wondering if it is possible to perform a multidimensional matrix multiplication without resorting to a for-loop. Given the N-by-P matrix A and the N-by-M-by-P matrix B, I want to compute the M-dimensional vector y, defined element-wise as

y(j) = sum_(i = 1,...,N) sum_(k = 1,...,P) A(i,k)*B(i,j,k)

Upvotes: 2

Views: 464

Answers (1)

Luis Mendo
Luis Mendo

Reputation: 112679

You can linearize A into a row vector, then reshape and permute the array B as a matrix, so that the desired result is just matrix multiplication:

M = 5;
N = 6;
P = 8;
A = rand(N,P);
B = rand(N,M,P);
result = A(:).'*reshape(permute(B, [1 3 2]), [], M);

Or reshape matrix A so that its dimensions are aligned with those of B, use bsxfun to multiply with singleton-expansion, and sum over the two desired dimensions:

result = sum(sum(bsxfun(@times, reshape(A, N, 1, P), B), 1), 3);

Upvotes: 3

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