Multiplication of two matrices of different rank

I am curious that whether there is a clean way to do the multiplication of two matrices(tensor, strictly speaking) of different ranks?

For example, let say A=100*100*200, B=200*3. Therefore the product would be 100*100*3.

The built-in function 'A*B' seems to refuse to accept the parameters with different ranks, namely, it only accept A B with same rank(both 2-d matrix or both 3-d matrix). However, I can come up with a tentative way that is to reshape A(100*100*200) to another matrix (10000*200) and do the multiplication and reshape it back to (100*100*3) from the result (multiply((10000*200),(200*3))= 10000*3). But I am still curious about some clean or 'orthodoxical' way

Answer 1

[Bruno Luong]

RESHAPE is a cleanest and fastest way to do tensor-extension of mtimes on multi-dimension arrays.

szA = size(A);
szB = size(B);
n = szB(1);
if n ~= 1 || szA(end)==1
    szA(end) = [];
end
szB(1) = [];
AB = reshape(A,[prod(szA),n])*reshape(B,[n,prod(szB)]);
AB = reshape(AB,[szA,szB]);

[Bruno Luong]

Just edit to handle empty array(s), thanks Steph. ;-)

[Stephen23]

+1 probably the neatest solution.

Answer 2

[Stephen23]

" I can come up with a tentative way that is to reshape ... and do the multiplication and reshape it back"

That seems like about the cleanest way using basic MATLAB commands. You could even stick that in its own function, something like this:

function D = tensortimes(A,B)
Sa = size(A);
Sb = size(B);
D = reshape(mtimes(reshape(A,[],Sa(end)),reshape(B,Sb(1),[])),[Sa(1:end-1),Sb(2:end)]);
end

Special cases will need to be handled as well.

[Bruno Luong]

Sa(end) will not match Sb(1) if the intended matching tensor(s) size is 1 and intended ndims(A)>2.

[Stephen23]

@Bruno Luong: no doubt empty arrays will also need to be handled. I leave that as an exercise for the reader.

[Bruno Luong]

Good point