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

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i have 3 dimensional domain in matlab. each point in domain have defined 3 arrays of size (nx,ny,nz) @ each point of domain:

a1; % size(a1) = [nx ny nz] a2; % size(a2) = [nx ny nz] a3; % size(a3) = [nx ny nz]

for each element, trying construct array holds value of a1, a2, , a3. following candidate having 1×3 vector @ each point?

b = [a1(:) a2(:) a3(:)]; b = reshape(b, [size(a1) 1 3]);

if 1×3 array named c, trying find c'*c @ 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 find array d size 3×3 points in domain in vectorize fashion? in fact, output consists of array d each point have size [nx ny nz 3 3]. me?

basically concatenate a1, a2 , a3 along 4th , 5th dimensions separately leaves singleton dimensions in 5th , 4th dimensions respectively, used bsxfun [apply element-by-element binary operation 2 arrays singleton expansion enable] expand 3x3 matrices along 4th-5th dimensions matrix multiplication result 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));

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