# R Language Speeding tough-to-vectorize for loops with Rcpp

## Example

Consider the following tough-to-vectorize for loop, which creates a vector of length `len` where the first element is specified (`first`) and each element `x_i` is equal to `cos(x_{i-1} + 1)`:

``````repeatedCosPlusOne <- function(first, len) {
x <- numeric(len)
x <- first
for (i in 2:len) {
x[i] <- cos(x[i-1] + 1)
}
return(x)
}
``````

This code involves a for loop with a fast operation (`cos(x[i-1]+1)`), which often benefit from vectorization. However, it is not trivial to vectorize this operation with base R, since R does not have a "cumulative cosine of x+1" function.

One possible approach to speeding this function would be to implement it in C++, using the Rcpp package:

``````library(Rcpp)
cppFunction("NumericVector repeatedCosPlusOneRcpp(double first, int len) {
NumericVector x(len);
x = first;
for (int i=1; i < len; ++i) {
x[i] = cos(x[i-1]+1);
}
return x;
}")
``````

This often provides significant speedups for large computations while yielding the exact same results:

``````all.equal(repeatedCosPlusOne(1, 1e6), repeatedCosPlusOneRcpp(1, 1e6))
#  TRUE
system.time(repeatedCosPlusOne(1, 1e6))
#    user  system elapsed
#   1.274   0.015   1.310
system.time(repeatedCosPlusOneRcpp(1, 1e6))
#    user  system elapsed
#   0.028   0.001   0.030
``````

In this case, the Rcpp code generates a vector of length 1 million in 0.03 seconds instead of 1.31 seconds with the base R approach. PDF - Download R Language for free