Recursive manipulation of vector elements

Question

I have a vector a and want to multiply each element recursively with b, without using a loop.

a <- rep(0, 10)
a[1] <- 1
b <         


        

Answer 1

For general recursive series of the form:

y[i] = x[i] + f[1]*y[i-1] + ... + f[p]*y[i-p]

you can use the filter function. In your case, you have x[i] = 0, f[1] = 2 and f[i] = 0 for i > 1. This translates into:

filter(rep(0,10), 2, method="recursive", init=1/2)
# Time Series:
# Start = 1 
# End = 10 
# Frequency = 1 
#  [1]   1   2   4   8  16  32  64 128 256 512

After you learn how to use it, which is not always obvious the first time, filter is very powerful and efficient. But maybe it is overkill for your geometric case here.