Vectorization time-varying recursive linear function
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Bruno Luong
el 27 de Ag. de 2020
Comentada: David Goodmanson
el 29 de Ag. de 2020
I try to vectorize this simple recursive relation (all quantities are scalars)
x_{0} = 0;
x_{n} = x_{n-1}*a_{n} + b_{n} for n=1,2,...,N
In MATLAB code it can be carried out by for loop
% test inputs
b=rand(1,10);
a=0.9+zeros(size(b));
xk=0;
x=zeros(size(b));
for k=1:length(x)
xk = a(k)*xk+b(k);
x(k) = xk;
end
For a(:) constant this can be vectorized by IIR filter
ac = unique(a);
if length(ac)==1
x = filter(1, [1 -ac], b);
end
I would though it could have some time-varying IIR filter that I can use to vectorize the case where a is time-dependent.
But I couldn't find anywhere such stock function. anyone have an idea?
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Respuesta aceptada
David Goodmanson
el 28 de Ag. de 2020
Editada: David Goodmanson
el 28 de Ag. de 2020
Hi Bruno,
a = rand(1,50);
b = rand(1,50);
% method 1
xk = 0;
x = zeros(1,50);
for k = 1:50
xk = a(k)*xk + b(k);
x(k) = xk;
end
% method 2
cpa = cumprod([1 a(2:end)])
x1 = filter(1,[1 -1],b./cpa).*cpa;
max(abs(x1-x))
ans = 4.4409e-16
2 comentarios
David Goodmanson
el 29 de Ag. de 2020
Hi Bruno,
Also, if one of the a's is nonzero but very small, there are probably going to be numerical accuracy issues. It's unfortunate that Matlab apparently does not have a built-in function for this type of iteration.
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