Vectorisation of a simple for loop

1 Ansicht (letzte 30 Tage)
David Schranz
David Schranz am 28 Sep. 2016
Kommentiert: David Schranz am 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.

Akzeptierte Antwort

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

Melden Sie sich an, um zu kommentieren.

Weitere Antworten (2)

Teja Muppirala
Teja Muppirala am 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 Kommentar
David Schranz
David Schranz am 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.

Melden Sie sich an, um zu kommentieren.


KSSV
KSSV am 28 Sep. 2016
It is very much possible:
https://in.mathworks.com/matlabcentral/answers/81775-recursive-vector-operation-without-for-loops
  2 Kommentare
Stephen23
Stephen23 am 28 Sep. 2016
Bearbeitet: Stephen23 am 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
KSSV am 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.

Melden Sie sich an, um zu kommentieren.

Kategorien

Mehr zu Matrices and Arrays finden Sie in Help Center und File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by