# Vectorization question (trying to avoid for loops)

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Jonathan E. on 22 Jan 2016
Commented: Star Strider on 26 Jan 2016
Dear all, I know that this must be quite a common question and I am sorry if the answer has already been posted somewhere, but after a good look all over this website and several other websites I still am not sure whether there is a way for me to avoid 'for' loops in my case. So here is part of my code which I am trying to vectorize:
G=zeros(t_max+1,9); %each column represents the proportion of people using something numbered 1 to 9. So: sum(G,2)=1
P=zeros(t_max+1,4); %each column represents the proportion of people using either item 1, 2, 3 or 4. So: sum(P,2)=1
SS=[1 1 2 1 1 2 3 3 4]; %each number corresponds to each column of P (item 1 to 4)
I=[a b c d e f g h i]; %with a to i, 9 preallocated numbers (basically initial proportion values)
G(1,:)=[I];
for t=1:t_max
%G(t+1,:) is updated but not shown here
for ii=1:4 %columns of P
for jj=1:9 %columns of G
if SS(jj)==ii
P(t+1,ii)=P(t+1,ii)+G(t+1,jj);
end
clear jj;
end
clear ii;
end
end
Basically in plain english (well I will try my best explaining it), at each time step 't' I am updating the proportion in 'P' which is a sum of specific proportions in 'G' (I have not shown this but G(t+1,:) is calculated before the loop). Each proportion of P is updated depending on which column of P the numbers in 'SS' are specifying to. So if SS(:,6) specifies 2, we know that the proportion in the sixth column of G will be added to second column of P (cumulative sums). (I think that might be even less understandable so if you have any question just ask me).
Sorry for the really long post and hopefully someone will be able to tell me if I really need all these 'for' loops or if I can simplify it using vectorization.
Thank you!
Regards
Jonathan
Jonathan E. on 25 Jan 2016
I was trying to remove any unnecessary variables in the computation but I did not know how for loops work so was not sure whether it was really useful or not. Now I know so thanks. I will just add the clear argument after the loop. Thanks for your help!

Kirby Fears on 22 Jan 2016
Edited: Kirby Fears on 22 Jan 2016
I deleted the clear lines and switched the ( t_max+1) tendency to simply be t_max. I added t_max and I values up top so it runs on my machine. Here is the code with those changes:
t_max = 5; % needed a t_max value
G = zeros(t_max,9);
P = zeros(t_max,4);
SS = [1 1 2 1 1 2 3 3 4];
I = 1:9; % needed real I values
G(1,:) = I;
for t = 1:t_max,
for ii = 1:4,
for jj = 1:9,
if SS(jj)==ii,
P(t,ii) = P(t,ii) + G(t,jj);
end
end
end
end
Then I simplified your nested loops to a single loop.
for s = 1:numel(SS),
P(:,SS(s)) = P(:,SS(s)) + G(:,s);
end
This gives the same result as the nested loops, though G and P are mostly full of zeros still. Let us know if this is what you needed.
##### 2 CommentsShowHide 1 older comment
Star Strider on 26 Jan 2016
The sincerest expression of appreciation here on MATLAB Answers is to Accept the Answer that most closely solves your problem.

Jonathan E. on 25 Jan 2016
Well actually if I may take a bit more of your time, I am also wondering how to simplify this one (I am really trying to figure it out but am a bit stuck to be honest). I have the same G matrix of sum 1 (to simplify it here I have considered it as an array). For example:
G=[0.2 0.1 0.05 0.05 0.1 0.3 0.1 0.05 0.05]
I have a 9x9 W matrix (not shown here) which represents the probability for each 1 to 9 individuals to meet one each other.
I was wondering whether these for loops could be simplified:
E=zeros(1,9);
for ii=1:9
for jj=1:9
E(ii)=E(ii)+G(1,ii)*G(1,jj)*W(SS(ii),SS(jj));
end
end
Sorry if that seems obvious again...
Jonathan
##### 2 CommentsShowHide 1 older comment
Kirby Fears on 26 Jan 2016
Here is a simplification assuming W(ii,jj) was the proper indexing.
G = [0.2 0.1 0.05 0.05 0.1 0.3 0.1 0.05 0.05];
W = rand(numel(G));
E = zeros(size(G));
for ii = 1:numel(E),
E(ii) = E(ii) + sum(G(ii)*G.*W(ii,:));
end
Here is the same thing with matrix multiplication instead.
G = [0.2 0.1 0.05 0.05 0.1 0.3 0.1 0.05 0.05];
W = rand(numel(G));
E = G.*(G*W');