Multiplication of two arrays with dimension=5 in a vectorize way

Question

I have a three dimensional domain in MATLAB. For each point in the domain I have defined three arrays of size (NX,NY,NZ) at each point of the domain:

A1; % size(A1) = [NX NY NZ]
A2; % size(A2) = [NX NY NZ]
A3; % size(A3) = [NX NY NZ]

For each element, I am trying to construct an array which holds the value of A1, A2, and A3. Would the following be a good candidate for having a 1×3 vector at each point?

B = [A1(:) A2(:) A3(:)];
B = reshape(B, [size(A1) 1 3]);

If the 1×3 array is named C, I am trying to find C'*C at each point.

C = [A1(i,j,k) A2(i,j,k) A3(i,j,k)]; % size(C) = [1 3]
D = C'*C; % size(D) = [3 3]

My ultimate goal is to find the array D with size 3×3 for all the points in the domain in a vectorize fashion? In fact, the output which consists of array D for each point will have the size [NX NY NZ 3 3]. Could someone help me?

Answer 1

Basically we concatenate A1, A2 and A3 along the 4th and 5th dimensions separately that leaves singleton dimensions in the 5th and 4th dimensions respectively, which are then used by bsxfun [Apply element-by-element binary operation to two arrays with singleton expansion enable] to expand as 3x3 matrices along the 4th-5th dimensions for matrix multiplication result from each triplet of [A1(i,j,k),A2(i,j,k),A3(i,j,k)].

D = bsxfun(@times,cat(4,A1,A2,A3),cat(5,A1,A2,A3));