Recursive cumulative function

Question

I need to write a cumulative summation function in R but I've been hitting a brick wall. The function has the following structure:

a*x1
a*x2 + a^2*x1
a*x3 + a^2*x2 + a^3*x1
a*x4 + a^2*x3 + a^3*x2 + a^4*x1

And so on. cumsum doesn't seem to work for this type of function. Is there any way this could be implemented in R?

I am looking for something like 1) .5*1=.5 (2) .5*2+.25*1=1.25 (3) .5*3+.25*2+.125*1 = 2.125, and so on. — user1536464, Jul 19 '12 at 01:29
You should add that to the question instead of having it as a comment. — Dason, Jul 19 '12 at 01:34

score 10 · Accepted Answer · answered Jul 19 '12 at 01:31

Since your recursion is

u[n+1] = a * ( x[n+1] + u[n] )

i.e.,

u[n+1]/a = x[n+1] + a * u[n]/a,

you can use filter:

x <- 1:5
a <- 2
a*filter(1:5, a, method="recursive")

# Compare with the expected values
a*x[1]
a*x[2] + a^2*x[1]
a*x[3] + a^2*x[2] + a^3*x[1]
a*x[4] + a^2*x[3] + a^3*x[2] + a^4*x[1]

Recursive cumulative function

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