Vectorize a product calculation which depends on previous elements?

Question

I'm trying to speed up/vectorize some calculations in a time series. Can I vectorize a calculation in a for loop which can depend on results from an earlier iteration? For example:

z <- c(1,1,0,0,0,0) zi <- 2:6 for  (i in zi) {z[i] <- ifelse (z[i-1]== 1, 1, 0) } 

uses the z[i] values updated in earlier steps:

> z [1] 1 1 1 1 1 1 

In my effort at vectorizing this

z <- c(1,1,0,0,0,0) z[zi] <- ifelse( z[zi-1] == 1, 1, 0) 

the element-by-element operations don't use results updated in the operation:

> z [1] 1 1 1 0 0 0 

So this vectorized operation operates in 'parallel' rather than iterative fashion. Is there a way I can write/vectorize this to get the results of the for loop?

Answer 1

ifelse is vectorized and there's a bit of a penalty if you're using it on one element at a time in a for-loop. In your example, you can get a pretty good speedup by using if instead of ifelse.

fun1 <- function(z) {   for(i in 2:NROW(z)) {     z[i] <- ifelse(z[i-1]==1, 1, 0)   }   z }  fun2 <- function(z) {   for(i in 2:NROW(z)) {     z[i] <- if(z[i-1]==1) 1 else 0   }   z }  z <- c(1,1,0,0,0,0) identical(fun1(z),fun2(z)) # [1] TRUE system.time(replicate(10000, fun1(z))) #   user  system elapsed  #   1.13    0.00    1.32 system.time(replicate(10000, fun2(z))) #   user  system elapsed  #   0.27    0.00    0.26  

You can get some additional speed gains out of fun2 by compiling it.

library(compiler) cfun2 <- cmpfun(fun2) system.time(replicate(10000, cfun2(z))) #   user  system elapsed  #   0.11    0.00    0.11 

So there's a 10x speedup without vectorization. As others have said (and some have illustrated) there are ways to vectorize your example, but that may not translate to your actual problem. Hopefully this is general enough to be applicable.

The filter function may be useful to you as well if you can figure out how to express your problem in terms of a autoregressive or moving average process.