# Prod giving a different answer than repeated multiplication

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Divij Gupta on 23 Jun 2021
Edited: Walter Roberson on 23 Jun 2021
X(:,:,1) = [0.0000 + 0.0000i 0.0000 + 0.0000i 1.0000 + 0.0000i 0.0000 + 0.0000i;0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 1.0000 + 0.0000i;1.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i;0.0000 + 0.0000i 1.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i];
X(:,:,2) = [0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 1.0000i 0.0000 + 0.0000i;0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 1.0000i;0.0000 + 1.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i;0.0000 + 0.0000i 0.0000 + 1.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i];
X(:,:,3) = [0.0000 + 0.0000i 1.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i;1.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i;0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.0000 + 0.0000i;0.0000 + 0.0000i 0.0000 + 0.0000i -1.0000 + 0.0000i 0.0000 + 0.0000i];
X(:,:,4) = [0.0000 + 0.0000i 0.0000 - 1.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i;0.0000 + 1.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i;0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 1.0000i;0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 1.0000i 0.0000 + 0.0000i];
I have the given 3D array. For some reason prod(X(:,:,1:4),3) gives 0 as the output. That does not match with the output for X(:,:,1)*...X(:,:,4). I do not want to use a loop, I want to use a vectorised method. However, prod is giving me issues. Am I doing something wrong? Is there another method?
Divij Gupta on 23 Jun 2021
By 0 as the output I mean the 4x4 zero matrix

KSSV on 23 Jun 2021
prod gives you element by element multiplication.
Check:
A = rand(2,2,3) ;
X = prod(A,3) ;
Y = A(:,:,1).*A(:,:,2).*A(:,:,3) ; % element by element mulltiplication
Z = A(:,:,1)*A(:,:,2)*A(:,:,3) ;
isequal(X,Y)
ans = logical
1
isequal(X,Z)
ans = logical
0
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Walter Roberson on 23 Jun 2021
You cannot vectorize matrix multiplication.
You can make the process a little more compact by using fold() https://www.mathworks.com/help/symbolic/fold.html . However that requires the Symbolic Toolbox
The elements you would implicitly loop over would be created by using num2cell(A,3)