# Vectorisation of a simple for loop

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David Schranz 2016 年 9 月 28 日
コメント済み: David Schranz 2016 年 9 月 29 日
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.

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### 採用された回答

Thorsten 2016 年 9 月 28 日
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);
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David Schranz 2016 年 9 月 29 日
Thank you very much for your solution. I would have never figured that out.

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### その他の回答 (2 件)

Teja Muppirala 2016 年 9 月 28 日
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.
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David Schranz 2016 年 9 月 29 日
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.

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KSSV 2016 年 9 月 28 日
It is very much possible:
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KSSV 2016 年 9 月 28 日
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.

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