# How to add matrices dimension by dimension without using a loop?

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Tintin Milou on 17 Feb 2015
Commented: Stephen on 17 Feb 2015
Hi all,
I've got this huge loop that takes a lot of time to be computed:
for i1=1:xN
for j1=1:zN
for i2=1:xN
for j2=1:zN
for j3=1:zN
J(i1,j1,i2,j2,j3) = (ldp(i2,j2,j3) - ld(i1,j1,j2))*pdf_transp(i1,j1,i2,j2,j3);
end
end
end
end
end
xN and zN are 300 and 7 for now, but it easily takes several minutes to compute.
I have tried to use repmat and permute and then do something like this
ld_old = permute(repmat(ld,[1 1 1 xN zN]),[1 2 4 3 5]);
ld_new = permute(repmat(ldp,[1 1 1 xN zN]),[4 5 1 2 3]);
J2 = (ld_new(:)-ld_old(:)).*pdf_transp(:);
That is much faster, but still pretty slow. Is there a more efficient way for this kind of operation?
Thanks!
Stephen on 17 Feb 2015
Instead of using repmat, you might be able to use bsxfun and avoid this whole business. bsxfun can save a lot memory in these kind of situations, which speed things up.

James Tursa on 17 Feb 2015
Don't know if this will be faster than your repmat code, but try this:
J = bsxfun(@minus,reshape(ldp,1,1,i2,j2,j3),reshape(ld,i1,j1,1,j2,1)).*pdf_transp;
Tintin Milou on 17 Feb 2015
By the way, do you expect running the bsxfun on CUDA would improve the performance by quite a bit?