# How can speed up the blow codes?

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Amir Torabi on 2 Dec 2019
Edited: Fabio Freschi on 3 Dec 2019
The blow code is part of my project. the performance of this code is alittle low. it is about 0,5s but in higher Nx values, the effiency decreases. Also, etas is a (Nx*Ny,ngrain=70) matrix. it does not contain zero values. I'd be appreciate if any suggest can improve the efficiency of below code.
Nx=512;
for igrain=1:70+0
ncount=0;
for i=1:Nx
for j=1:Nx
ii =(i-1)*Nx+j;
eta2(i,j) =eta2(i,j)+etas(ii,igrain)^2;
if(etas(ii,igrain) >= 0.5)
ncount=ncount+1;
end
ncount=ncount/(512*512);
end
end

#### 1 Comment

Nicolas B. on 2 Dec 2019
are eta2 and etas pre-defined tables? Or are the size of these variables change?

Fabio Freschi on 2 Dec 2019
Edited: Fabio Freschi on 2 Dec 2019
I don't understand what ncount is doing, it looks like a counter but I don't understand why you are repeatedly dividing by 512*512. I made my try, but some insight could help. However the calculation of eta2 can be drastically simplified using vectorization. Here I compare your solution (with some fixes) with the vectorized version (with a '0' added o the variables' names)
Nx = 512;
ngrain = 70;
eta2 = zeros(Nx,Nx);
etas = rand(Nx*Nx,ngrain);
ncountTot = zeros(ngrain,1);
% original code (with some fixes)
tic
for igrain=1:ngrain
ncount=0;
for i=1:Nx
for j=1:Nx
ii =(i-1)*Nx+j;
eta2(i,j) =eta2(i,j)+etas(ii,igrain)^2;
if(etas(ii,igrain) >= 0.5)
ncount=ncount+1;
end
end
ncountTot(igrain)=ncount/(Nx*Nx);
end
end
toc
% vectorized code
tic
etas0 = reshape(etas,Nx,Nx,ngrain);
eta20 = sum(etas0.^2,3)';
ncountTot0 = squeeze(sum(etas0 >= 0.5,[1 2])/(Nx*Nx));
toc
% check
norm(eta2-eta20)/norm(eta2)
norm(ncountTot-ncountTot0)

Amir Torabi on 3 Dec 2019
Thanks Fabio. it works great. could you ask you have your advice in the improvment of running time of following code?
term3=0;
ngrian=70;
glist = round(rand(70,1));
etas = rand(512*512,70);
den = zeros(70,70);
en = en = rand(1,70)*10;
for jgr=1:ngrain
if(glist(jgr)== 1)
den(igrain,jgr)=en(jgr)-en(igrain);
term3=term3-8/pi*(etas(:,igrain).*etas(:,jgr)).^0.5*den(igrain,jgr);
end
end
%end
Fabio Freschi on 3 Dec 2019