How to vectorize this code?
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Hi all,
I need to vectorize the following code in order to make it faster:
ar=[ 115 139 168;
133 160 193;
155 187 226];
at=[ 803 667 552;
3212 2667 2208;
5621 4667 3864];
afr(:,:,1)=[0 17 3;
4 3208 29;
6 127 12];
afr(:,:,2)= [0 0 0;
0 14 2;
0 3 2];
afr(:,:,3)=[0 0 0;
0 4 1;
0 1 0];
here my code with nested loop:
[Sar Iar]=sort(reshape(ar,1,prod(size(ar))));
[Sat Iat]=sort(reshape(at,1,prod(size(at))));
Output=zeros(prod(size(ar)),prod(size(at)));
for i=1:length(afr(1,1,:))
for j=1:length(afr(1,:,1))
for k=1:length(afr(:,1,1))
Output(find(Sat==at(k,i)),find(Sar==ar(j,i)))=afr(k,j,i)
end
end
end
afr(:,:,i) is linked to the i_th column of ar and at. I need to create the a matrix of the following size [prod(size(at)),prod(size(ar))] where the elements of afr are sorted according to ar along the column and to at along the row. Here the result with the aforementioned data:
Ris=[0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0;
0 17 0 3 0 0 0 0 0;
0 0 0 0 0 0 0 4 1;
0 0 0 0 14 0 2 0 0;
4 3208 0 29 0 0 0 0 0;
0 0 0 0 0 0 0 1 0;
0 0 0 0 3 0 2 0 0;
6 127 0 12 0 0 0 0 0];
how can I make it faster?
Thanks
2 comentarios
Geoff Hayes
el 27 de Abr. de 2014
Hi pietro,
Why does the code need to be faster as it runs pretty quick as is. Are you anticipating larger matrices? Note that you could put the find(Sar==ar(j,i)) outside of the k (second inner) loop since ar does not depend on k,just i and j.
Geoff
Respuesta aceptada
Jan
el 27 de Abr. de 2014
Editada: Jan
el 3 de Mayo de 2014
Some standard methods, which improve the code and make it more Matlabish. But the acceleration will not be high:
[Sar, Iar] = sort(ar(:));
[Sat, Iat] = sort(at(:));
Output = zeros(numel(ar), numel(at));
[s1, s2, s3] = size(afr);
for i = 1:s1
for j = 1:s2
v = (Sar==ar(j,i));
for k = 1:s3
Output(Sat==at(k,i), v) = afr(k,j,i);
end
end
end
With your tiny test data set I get for 1000 iterations under Matlab 2009a:
Original: Elapsed time is 0.193134 seconds.
Improved: Elapsed time is 0.079364 seconds.
The main ideas are the logical indexing (avoid the find()) and moving repeated calculations out of the loop (Sar==ar(j,i) does not depend on the inner loop).
length(afr(1,1,:)) creates a temporary vector at first. But this is a waste of time, because size replies the dimensions directly.
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