# Kronecker product among multiple arrays

I was wondering whether there is a smart and efficient way in Matlab to compute the kronecker product of several 1D arrays.

What I mean is something like this

A = [a1, a2];
B = [b1, b2];
C = [c1, c2];
K = f(A,B,C) = [a1*b1*c1, a1*b1*c2, a1*b2*c1, ... ]


One possible way it is to use the kron(X,Y) function, but it has to be put inside a loop to obtain the aforementioned result since the kron function accepts only 2 arguments per time.

K = 1;
tot_arrays = [A, B, C];
for i=1:num_arrays
K = kron(K,tot_arrays(:,i));
end


Isn't there a smarter and more efficient way to obtain the same result for the kron multiplication of more than 2 arrays per time?

Thanks

• Have you already seen Fast Kronecker matrix multiplication in the exchange? Sep 18, 2017 at 15:59
• Hi @MauroVanzetto, thanks for the reply. No, I never heard about it. However, after a quick check at the link you provided, it does not seem to be what I'm looking for. Thanks Sep 20, 2017 at 21:55

Faster to write: I don't think there is. Faster to run with larger array lengths: the first thing I would try is the following.

>> a = [1 2];
>> b = [3 4];
>> c = [5 6];
>> a = reshape(a, [length(a) 1 1]);
>> b = reshape(b, [1 length(b) 1]);
>> c = reshape(c, [1 1 length(c)]);
>> P = a.*b.*c;
>> P = reshape(P, [1 length(P)])
P =
15    30    20    40    18    36    24    48

• Thanks for the reply. Which version of Matlab did you use to test this script? I tried it, but it does not seem to work. Sep 20, 2017 at 21:54
• @FancyPants It should work starting from R2016b. There have been some changes to how operators expand singleton dimensions there, which is necessary for a.*b.*c to work. If you have an older version, you have to use bsxfun instead to get the same behavior, but that works only with two arrays at the time. Sep 20, 2017 at 22:00
• @FancyPants If you type edit kron.m you'll see the definition similar to this. You can generalize it from there by removing the sparse stuff. Sep 21, 2017 at 9:28