R 中的递归函数应用于向量

Question

i'd like to know the most efficient (think code AND speed, in case i'd be running it on very very large vectors or objects) to compute a recursive function on an vector. (to compute S[i] we just need S[k] up to k<=(i-1) and V[k] with k<=i )

a simple example would be given a num vector v of length N, to return a vector S where S[i] is the sum of the the first i elements of v.

in this particular case, a ( for ) loop is quite ugly...and ( edited ) so not efficient doing something like

myfun <- function(i){sum(length_table[1:i])}
        S <- sapply(v,myfun))

is not good because of many unnecessary calculations ...

any suggestions ?

EDIT: to me there is not much too much difference between iterative and recursive. i didn't know about the cumsum function which solves the problem in this particular case.

ok now let's have a more general case where we have a (num) function f which takes two (num) arguments so f(x,y) is also a num value. we need a num "seed" as well. given a num vector v of length N,

i'd like to construct the vector U defined by

U[1] = f(v[1],seed)
U[2] = f(v[2],U[1])
U[3] = f(v[3],U[2])...

U[N] = f(v[N],U[N-1])

is there a nice efficient way to do that without looping ?

Answer 1

Here are two ways to implement this in R (and while Reduce might seem to be more elegant, my experience is that it is more prone to (my) confusion):

> y <- numeric(); y[1] <- 1; for( i in 2:10 ){ y[i] <- 3+y[i-1]*2}
> y
 [1]    1    5   13   29   61  125  253  509 1021 2045

> Reduce( function(x,y){ y= 3+ x*2}, 1:10, accumulate=TRUE)
 [1]    1    5   13   29   61  125  253  509 1021 2045