sum of kronecker products

Hi! I am trying to write in a more efficient way the following code, possibly without the for cycles.

Thank you in advance. var1, var2 are N x N x N arrays. var3 is a N X N array.

function sum = kronecker_sum(var1,var2,var3)

N = size(var1,1);
sum = zeros(N^2,N^2);
for i = 1:N
    for j = 1:N
        sum = sum + kron(var1(:,:,i),var2(:,:,j))*var3(i,j);
    end
end

end

[Jan]

What are the usual sizes for the inputs?

[Mazdack Ameri]

N > 30

Answer 1

[Matt J]

This solution is not completely free of loops (because of num2cell and cell2mat), but you can see below that it is still much faster:

N=35;

[var1,var2]=deal(rand(N,N,N));
var3=rand(N);

%%%% Original Method
tic;
accum = zeros(N^2,N^2);
for i = 1:N
    for j = 1:N
        accum = accum + kron(var1(:,:,i),var2(:,:,j))*var3(i,j);
    end
end

result0=accum;
toc;

Elapsed time is 2.844959 seconds.

%%%% Proposed Alternative
tic;
Var1=reshape(var1,N^2,N);
Var2=reshape(var2,N^2,N);

tmp = num2cell( reshape( Var2*var3.'*Var1.', N,N,[]),  [1,2]);

result=cell2mat( reshape(tmp,N,N) );
toc

Elapsed time is 0.058188 seconds.

Discrepancy = norm(result-result0,'fro')  %check agreement

Discrepancy = 1.8576e-10

[Mazdack Ameri]

It works Matt J, thank you so much!