MATLAB: How to create N+1 dimensional array by taking exterior product of 1st dimension of two N dimensional arrays

exterior productn-d array

I would like to efficiently create an N+1 dimensional array C, whose first 2 dimensions are the exterior product of the 1st dimension of the N dimensional arrays A and B. The exterior product of m by 1 column vectors x and y is the m by m matrix x*y'.
As an example, given the 2 by 3 by 5 arrays A and B, I would like to create the 2 by 2 by 3 by 5 array C such that C(i,j,k,l) = A(i,k,l)*B(j,k,l).
For efficiency pruposes, I would like to do this without for loops, to the extent possible (I know how to do this with slow, ugly, brute force for loops). Given that I will apply this to YALMIP sdpvar arrays, implicit expansion can't be used. The following (non-exhaustive list) can be used in any combination:
reshape
repmat
vec'ing (i.e., A(:))
.*
kron
bsxfun (if needed)
Thanks.

Best Answer

Solution without expansion as requested
sizeA = size(A);
reshapeB = reshape(B,[1 size(B)]);
reshapeA = reshape(A,[sizeA(1) 1 sizeA(2:end)]);
rA = ones(size(size(A))); rA(2)=size(B,1);
rB = ones(size(size(B))); rB(1)=size(A,1);
C = repmat(reshapeA,rA) .* repmat(reshapeB,rB) ;
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