Is there a way to do these matrix vector multiplications without loops?

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Shafer
Shafer 2020-7-20
评论： Matt J 2020-7-20
The following brute-force method shows what I want, but is very slow. I would like to find the most efficient way to do this, with vectorized commands or whatever works, using existing Matlab functions (i.e. without loading an user-contributed mex-based package like mmx):
m = 100;
n = 200;
A = rand(m,n,4,4);
v = rand(m,n,4);
u = zeros(size(v));
tic
for i = 1:m
for j = 1:n
u(i,j,:) = squeeze(A(i,j,:,:))*squeeze(v(i,j,:));
end
end
toc

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采纳的回答

Matt J
Matt J 2020-7-20
编辑：Matt J 2020-7-20
First, you would choose a different ordering. Instead of
A = rand(m,n,4,4);
v = rand(m,n,4);
you would have
A = rand(4,4,m,n);
v = rand(4,m,n);
which will permit faster data access.
As for the multiplication, if you have the Parallel Computing Toolbox, you can do this directly with pagefun
Agpu=gpuArray(reshape(A,4,4,[]));
vgpu=gpuArray(reshape(v,4,1,[]));
u=reshape(pagefun(@mtimes,Agpu,vgpu), size(v) );
If you do not have the Parallel Computing Toolbox, you can instead do,
u = sum( A.*reshape(v,1,4,m,n) ,2);
  2 个评论
Shafer
Shafer 2020-7-20
编辑：Shafer 2020-7-20
Thank you for the fast answer, the final line is what I was looking for!
Matt J
Matt J 2020-7-20
You're welcome, but please Accept-click the answer to show that your question is resolved.

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