sum of kronecker products(four loops)

Hello! I would like to know if the following code:

function result = kron_test(var1,var2,var3,var4)
result = zeros(N^2,N^2);
for e=1:N
    for f=1:N
        for g=1:N
            for h=1:N
                result = result + kron(var1(:,:,e,g),var2(:,:,f,h))*var3(e,f)*var4(g,h);
            end
        end
    end
end

end

and the following:

function result = kron_test(var1,var2,var3,var4)
Var1 = reshape(var1,N^2,N^2);
Var2 = reshape(var2,N^2,N^2);
tmp = num2cell( reshape( Var2*kron(var4,var3).'*Var1.', N, N, [] ), [1,2] );
result = cell2mat(reshape(tmp,N,N));
end

are the same. I need to use this code for N > 30.

Thank you.

[Walter Roberson]

At least for the N = 3 and N = 4 cases, it checks out.

Answer 1

[Matt J]

For me, the following test for N=20 gives a very low percent error, so I would bet that the two are equivalent.

N=20;
[var1,var2]=deal( rand(N,N,N,N));
[var3,var4]=deal( rand(N,N) );

d=norm(kron_test0(var1,var2,var3,var4)-kron_test(var1,var2,var3,var4),'inf')
d0=norm(kron_test(var1,var2,var3,var4),'inf');

percentError = d/d0*100 % 9.7209e-13