Vectorisation of a simple for loop

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.

Answer 1

[Thorsten]

 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);

[David Schranz]

Thank you very much for your solution. I would have never figured that out.

Answer 2

[Teja Muppirala]

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.

( https://en.wikibooks.org/wiki/Control_Systems/Digital_State_Space ).

[David Schranz]

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.

Answer 3

[KSSV]

It is very much possible:

https://in.mathworks.com/matlabcentral/answers/81775-recursive-vector-operation-without-for-loops

[Stephen23]

@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]

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.