# Vectorisation of a simple for loop

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David Schranz on 28 Sep 2016
Commented: David Schranz on 29 Sep 2016
Will it be possible to write this code vectorised?
x=ones(10,1);
a=zeros(size(x));
b=zeros(size(x));
c=zeros(size(x));
for i = 1:size(x,1)-1
a(i+1) = a(i)+x(i)+b(i);
b(i+1) = b(i)+a(i)+c(i);
c(i+1) = c(i)+b(i)+c(i);
end
Any help would be greatly appreciated.

Thorsten on 28 Sep 2016
A = [1 1 0 0 ; 1 1 1 0 ; 0 1 2 0; 1 0 0 1];
Q = cell2mat(arrayfun(@(i) A^i, 1:9, 'Uni', false));
Q = [zeros(1, 4); reshape(Q(end,:), 4, [])'];
a = Q(:,1); b = Q(:,2); c = Q(:,3);

#### 1 Comment

David Schranz on 29 Sep 2016
Thank you very much for your solution. I would have never figured that out.

Teja Muppirala on 28 Sep 2016
Just wondering, but what is your purpose in vectorizing that code? If it's to make it faster, I don't think you can do much better than what you've already got, especially if you have a recent version of MATLAB.
If it's to make it more readable, or more general (flexibly deal with more variables), so you don't have to keep writing every letter like this
a(i+1)=...
b(i+1)=...
c(i+1)=...
d(i+1)= ...
...
then you could use matrix equations.
x=ones(10,1); % External input
A = [1 1 0; 1 1 1; 0 1 2]; % State matrix
B = [1;0;0]; % Input matrix
v = zeros(length(B),length(x)); % v contains [a,b,c]
for i = 1:size(x,1)-1
v(:,i+1) = A*v(:,i) + B*x(i);
end
For many applications, matrix representation is usually how this type of calculation is expressed.

#### 1 Comment

David Schranz on 29 Sep 2016
Yes, I try to make things faster. And yes it looks like the vectorised version is not faster. Nevertheless your code helped me to understand the solution provided by Thorsten. Also I consider using your code sample to flexibly deal with more variables. Thank you very much for your answer.

KSSV on 28 Sep 2016
It is very much possible:

Stephen Cobeldick on 28 Sep 2016
@Dr. Siva Srinivas Kolukula: the solution presented in that answer, and indeed the filter command itself, is a fundamentally 1D solution, even if applied to an array. The question above has dependencies between the variables a, b, and c. How do you propose to represent these using a 1D filter?
KSSV on 28 Sep 2016
If I am not mistaken, a similar question appeared a week ago which was vectorised using filter...I searched for the question, but could not get it.