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

Answer 1

This is a nice and simple example where Rcpp can shine.

So let us first recast functions 1 and 2 and their compiled counterparts:

library(inline)
library(rbenchmark)
library(compiler)

fun1 <- function(z) {
  for(i in 2:NROW(z)) {
    z[i] <- ifelse(z[i-1]==1, 1, 0)
  }
  z
}
fun1c <- cmpfun(fun1)


fun2 <- function(z) {
  for(i in 2:NROW(z)) {
    z[i] <- if(z[i-1]==1) 1 else 0
  }
  z
}
fun2c <- cmpfun(fun2)

We write a Rcpp variant very easily:

funRcpp <- cxxfunction(signature(zs="numeric"), plugin="Rcpp", body="
  Rcpp::NumericVector z = Rcpp::NumericVector(zs);
  int n = z.size();
  for (int i=1; i

This uses the inline package to compile, load and link the five-liner on the fly.

Now we can define our test-date, which we make a little longer than the original (as just running the original too few times result in unmeasurable times):

R> z <- rep(c(1,1,0,0,0,0), 100)
R> identical(fun1(z),fun2(z),fun1c(z),fun2c(z),funRcpp(z))
[1] TRUE
R> 

All answers are seen as identical.

Finally, we can benchmark:

R> res <- benchmark(fun1(z), fun2(z),
+                  fun1c(z), fun2c(z),
+                  funRcpp(z),
+                  columns=c("test", "replications", "elapsed", 
+                            "relative", "user.self", "sys.self"),
+                  order="relative",
+                  replications=1000)
R> print(res)
        test replications elapsed relative user.self sys.self
5 funRcpp(z)         1000   0.005      1.0      0.01        0
4   fun2c(z)         1000   0.466     93.2      0.46        0
2    fun2(z)         1000   1.918    383.6      1.92        0
3   fun1c(z)         1000  10.865   2173.0     10.86        0
1    fun1(z)         1000  12.480   2496.0     12.47        0

The compiled version wins by a factor of almost 400 against the best R version, and almost 100 against its byte-compiled variant. For function 1, the byte compilation matters much less and both variants trail the C++ by a factor of well over two-thousand.

It took about one minute to write the C++ version. The speed gain suggests it was a minute well spent.

For comparison, here is the result for the original short vector called more often:

R> z <- c(1,1,0,0,0,0)
R> res2 <- benchmark(fun1(z), fun2(z),
+                  fun1c(z), fun2c(z),
+                  funRcpp(z),
+                  columns=c("test", "replications", 
+                            "elapsed", "relative", "user.self", "sys.self"),
+                  order="relative",
+                  replications=10000)
R> print(res2)
        test replications elapsed  relative user.self sys.self
5 funRcpp(z)        10000   0.046  1.000000      0.04        0
4   fun2c(z)        10000   0.132  2.869565      0.13        0
2    fun2(z)        10000   0.271  5.891304      0.27        0
3   fun1c(z)        10000   1.045 22.717391      1.05        0
1    fun1(z)        10000   1.202 26.130435      1.20        0

The qualitative ranking is unchanged: the Rcpp version dominates, function2 is second-best. with the byte-compiled version being about twice as fast that the plain R variant, but still almost three times slower than the C++ version. And the relative difference are lower: relatively speaking, the function call overhead matters less and the actual looping matters more: C++ gets a bigger advantage on the actual loop operations in the longer vectors. That it is an important result as it suggests that more real-life sized data, the compiled version may reap a larger benefit.

Edited to correct two small oversights in the code examples. And edited again with thanks to Josh to catch a setup error relative to fun2c.