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matlabmultidimensional-arraymultiplication
Theodoros Theodoridis
Theodoros Theodoridis

Reputation: 79

Multidimensional Arrays Multiplication in Matlab

I have the following three arrays in Matlab:

A size: 2xMxN

B size: MxN

C size: 2xN

Is there any way to remove the following loop to speed things up?

D = zeros(2,N);
for i=1:N
    D(:,i) = A(:,:,i) * ( B(:,i) - A(:,:,i)' * C(:,i) );
end

Thanks

Upvotes: 2

Views: 2335

Answers (2)

Paul Fackler
Paul Fackler

Reputation: 1

You may find that the following

D=tprod(A,[1 -3 2],B-tprod(A,[-3 1 2],C,[-3 2]),[-3 2]);

cuts the time taken. I did a few tests and found the time was cut in about half.

tprod is available at http://www.mathworks.com/matlabcentral/fileexchange/16275

tprod requires that A, B and C are full (not sparse).

Upvotes: 0

A. Donda
A. Donda

Reputation: 8467

Yes, it is possible to do without the for loop, but whether this leads to a speed-up depends on the values of M and N.

Your idea of a generalized matrix multiplication is interesting, but it is not exactly to the point here, because through the repeated use of the index i you effectively take a generalized diagonal of a generalized product, which means that most of the multiplication results are not needed.

The trick to implement the computation without a loop is to a) match matrix dimensions through reshape, b) obtain the matrix product through bsxfun(@times, …) and sum, and c) get rid of the resulting singleton dimensions through reshape:

par = B - reshape(sum(bsxfun(@times, A, reshape(C, 2, 1, N)), 1), M, N);
D = reshape(sum(bsxfun(@times, A, reshape(par, 1, M, N)), 2), 2, N);

par is the value of the inner expression in parentheses, D the final result.

As said, the timing depends on the exact values. For M = 100 and N = 1000000 I find a speed-up by about a factor of two, for M = 10000 and N = 10000 the loop-less implementation is actually a bit slower.

Upvotes: 2

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