An accept-reject sampler using RcppArmadillo::sample()

May 8, 2013

(This article was first published on Rcpp Gallery, and kindly contributed to R-bloggers)

The recently added RcppArmadillo::sample() functionality provides the same algorithm used in R’s sample() to Rcpp-level code. Because R’s own sample() is written in C with minimal work done in R, writing a wrapper around RcppArmadillo::sample() to then call in R won’t get you much of a performance boost. However, if you need to repeatedly call sample(), then calling a single function which performs everything in Rcpp-land (including multiple calls to sample()) before returning to R can produce a noticeable speedup over a purely R-based solution.

Accept-Reject Sampler Example

One place where this situation arises is in an accept-reject sampler where the candidate “draw” is the output of a call to sample(). Concretely, let’s suppose we want to sample 20 integers (without replacement) from 1 to 50 such that the sum of the 20 integers is less than 400. Far fewer than 10% of randomly drawn samples will meet this constraint.

Loading required package: RcppArmadillo
Loading required package: Rcpp
Loading required package: rbenchmark

The R code is straightforward enough. It has been written to mirror the logic of the C++ code, although that doesn’t come at the cost of much performance.

r_getInts <- function(samples) {
    thresh <- 400
    results <- matrix(0, 20, samples) ;
    cnt <-  0

    while(cnt < samples) {
        candidate = sample(1:50, 20)

        if (sum(candidate) < thresh) {
            results[, cnt + 1] <- candidate
            cnt <- cnt + 1


Although it is a bit longer, the logic of the C++ code is similar.

#include <RcppArmadilloExtensions/sample.h>
// [[Rcpp::depends(RcppArmadillo)]]

using namespace Rcpp ;

// [[Rcpp::export]]
IntegerMatrix cpp_getInts(int samples
                          ) {
    RNGScope scope;
    int cnt = 0 ;
    IntegerMatrix results(20, samples) ;
    IntegerVector frame = seq_len(50) ;
    IntegerVector candidate(20) ;
    int thresh = 400 ;
    while (cnt < samples) {
        candidate = RcppArmadillo::sample(frame, 
                                          FALSE, NumericVector::create()
                                          ) ;
        double sum = std::accumulate(candidate.begin(), candidate.end(), 0.0) ;
        if (sum < thresh) {
            results(_, cnt) = candidate ;
            cnt++ ;
    return results ;


The Rcpp code tends to be about 7-9 times faster and this boost increases as the constraint becomes more complicated (and necessarily more costly in R).

benchmark(r = {set.seed(1); r_getInts(50)},
          cpp = {set.seed(1); cpp_getInts(50)},
          replications = 10,
          order = 'relative',
          columns = c("test", "replications", "relative", "elapsed")
  test replications relative elapsed
2  cpp           10     1.00   0.036
1    r           10    11.97   0.431

In the Real World …

Where might the structure in this problem arise in practice? One set of instances are those where “space” matters:

  • sampling US cities such that no more than two are in any one state
  • sampling cellphone towers such that no two are closer than X miles apart
  • sampling nodes in a graph/network such that no one has more than K edges

In these situations, R code to check the acceptance condition will likely be less efficient relative to the corresponding C++ code and so even larger speed-ups are realized.

To leave a comment for the author, please follow the link and comment on their blog: Rcpp Gallery. offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.


Mango solutions

RStudio homepage

Zero Inflated Models and Generalized Linear Mixed Models with R

Dommino data lab

Quantide: statistical consulting and training



CRC R books series

Six Sigma Online Training

Contact us if you wish to help support R-bloggers, and place your banner here.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)