Prod giving a different answer than repeated multiplication

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Divij Gupta 2021-6-23

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https://ww2.mathworks.cn/matlabcentral/answers/862975-prod-giving-a-different-answer-than-repeated-multiplication

编辑： Walter Roberson 2021-6-23

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?

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Divij Gupta 2021-6-23

By 0 as the output I mean the 4x4 zero matrix

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Answer 1

KSSV 2021-6-23

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https://ww2.mathworks.cn/matlabcentral/answers/862975-prod-giving-a-different-answer-than-repeated-multiplication#answer_731110

在 MATLAB Online 中打开

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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Divij Gupta 2021-6-23

Thank you so much, that makes sense. What function can I use to vectorise matrix multiplication then?

Walter Roberson 2021-6-23

编辑：Walter Roberson 2021-6-23

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)

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