MATLAB: Create a vector whose elements depend on its previous elements without a loop

loopsvector

Hi,
As loops take considerable time, I'm trying without loops.
I want to create a vector whose elements depend on its previous elements, for example:
a(i) = 3*a(i-1) + 2
a(1) = 5
where a(i) is the i-th value of vector A.
Can it be done?

Best Answer

Doing this will a loop shouldn't be slow as long as you preallocate the array beforehand:
a = zeros(1, 100);  %preallocation
a(1) = 5;
for i = 2:numel(a)
    a(i) = 3 * a(i-1) + 2;
end
It can indeed be done without a loop, with the filter function, the most difficult is to figure out the inputs. The more about section is the most helpful.
a = filter(1, [1 -3], [5, 2*ones(1, 99)]);  % 1*y(n) = 1*x(n) - (-3)*y(n-1), with x = [5, 2, 2, ...] and y(0) = 0
Frankly, the loop is clearer so you should prefer it.
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