Multiplying all 2D square matricies in a 3D matrix

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Connor LeClaire 2021-10-21

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评论： Paul 2021-10-21

Consider a 3D matrix 'T' made from a concatenation of N square matrices of size m. Is there a easy way to multiply them all together (m1 x m2 x m3 x m4 ... x mN) into a single 2D matrix 'total' of size m? Similar to something like;

total = prod(T(:,:,:));
%This returns a 3D matrix of each 2D matrix of size (1,m)

In a for loop it may look like:

total = eye(m);
for i = 1;N
    total = total*T(:,:,i);   
end

Is it also possible to stop the multiplication at somepoint along the 3D matrix at point 1 < h < N;

total = prod(T(:,:,1:h))

I should also mention in my specific application the matrices are symbolic with both variables and numbers.

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James Tursa 2021-10-21

编辑：James Tursa 2021-10-21

Just use the for-loop. If for some reason you were really pressed for speed you could write a mex routine that could avoid all the intermediate data copies. But even this might only save you 10% - 20% execution time.

Paul 2021-10-21

Can mex routines work with symbolic variables?

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Answer 1

Paul 2021-10-21

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编辑：Paul 2021-10-21

在 MATLAB Online 中打开

Easier than putting that loop in a function?

function mprod = matprod(T,h)
% should do some input checking to verify that 1 <= h <= size(T,3)
mprod = T(:,:,1);
for ii = 2:h
    mprod = mprod*T(:,:,ii);
end
end