Fastest way to multiply matrices within an array without for loop?

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Megan Ross
Megan Ross 2021-8-6
编辑： Matt J 2021-8-6
Hi everyone,
I have a 3d matrix, which is made up of an array of 2x2 matrices. I need to perform matrix multiplication of all the 2x2 sub-matrices within this 3d structure. I currently have a solution implemented with for loops, but I was wondering if there was an optimized way to do this (possibly with vectorization, using some in-built matlab function, using cell arrays, restructuring the way the data is stored itself, etc). I added an illustration of the concept below, as well as my current implementation using for loops.
Visual Illustration
Overall Matrix Dimension: 2x2xn (I used n=5 for both the visual and code example)
I'm trying to vectorize the matrix product of M1, M2, M3 ... Mn
Code Example
% Length of 3rd dimension
n = 5;
% Initialize random matrix
A = randn(2,2,n);
product = eye(2);
% Calculate product of matrix across 3rd dimension
tic
for i = 1:n
product = product * A(:,:,i);
end
toc
Thank you!

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回答（1 个）

Matt J
Matt J 2021-8-6
编辑：Matt J 2021-8-6
Ran in:
(possibly with vectorization, using some in-built matlab function, using cell arrays
If your matrices start off in cell array form, it would indeed be faster to keep them that way:
% Number of matrices
n = 1e5;
% Random matrix data
A(:,:,1:n) = {randn(2,2)};
product = eye(2);
%Cell form
tic;
for i = 1:n
product = product * A{i};
end
toc;
Elapsed time is 0.033400 seconds.
%Matrix form
tic
A=cell2mat(A);
for i = 1:n
product = product * A(:,:,i);
end
toc
Elapsed time is 0.127890 seconds.

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