# MATLAB: How to efficiently multiply each element of a matrix with every other element of two other matrices, i.e. in least time possible

vectorized elementwise multiplication of matrices

I have 3 different matrices, Say [A] [B] and [C]. Each matrix A, B and C is of size 8×3 i.e. 24 elemnts each.
Final desired output is a column vector which has total of 24x24x24= 13824 elements, in the following order:
A(1,1)*B(1,1)*C(1,1)
A(1,1)*B(1,1)*C(8,1)
A(1,1)*B(2,1)*C(1,1)
A(1,1)*B(2,1)*C(8,1)
A(8,1)*B(8,1)*C(8,1)
A(1,1)*B(1,1)*C(1,2)
A(1,1)*B(1,1)*C(8,2)
A(8,3)*B(8,3)*C(8,3)
Currently I am using 6 nested loops (3 loops which run over the 3 columns of each matrix A B and C, and 3 loops for every row of matrices A, B and C)
counterNp=1;
for a1=1:3
for a2=1:3
for a3=1:3
for b1=1:8
for b2=1:8
for b3=1:8
V(counterNp)= A(b1,a1)*B(b2,a2)*C(b3,a3);
counterNp=counterNp+1;
end
end
end
end
end
end
I get the desired output this way, but the problem is it's computationally very expensive for the actual calculations that I am doing (the above example is a simplified version), it takes my code 17 hours to run this calculation.
I am wondering if someone can help me with vectorizing this code.
I was thinking of using bsxfun(@times,A,B'). and then repeat this multiple times, are there better ways?
Thanks

[m,n] = size(A);AA = reshape(A,1,1,m,1,1,n);BB = reshape(B,1,m,1,1,n,1);CC = reshape(C,m,1,1,n,1,1);V = AA.*BB.*CC;V = V(:);