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

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

Answer 1

[Matt J]

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);

[Shafer]

Thank you for the fast answer, the final line is what I was looking for!

[Matt J]

You're welcome, but please Accept-click the answer to show that your question is resolved.