Lab 05 - Rcpp and C++

Learning goals

• Use the different data types in Rcpp.
• Learn some fundamentals about C++ optimization.
• Practice your GitHub skills.

Lab description

For this lab, we will create a function for propensity score matching. The goal is simple: write out a C++ function with Rcpp and measure how faster it is compared to the following R implementation:

ps_matchR <- function(x) {
  
  match_expected <- as.matrix(dist(x))
  diag(match_expected) <- .Machine$integer.max
  indices <- apply(match_expected, 1, which.min)
  
  list(
    match_id = as.integer(unname(indices)),
    match_x  = x[indices]
  )
  
}

Question 1: Create a simple function

Use the following pseudo-code template to get started:

#include <Rcpp.h>

using namespace Rcpp;

// [[Rcpp::export]]
[output must be list] ps_match1(const NumericVector & x) {

    ...prepare the output (save space)...
    ...it should be an integer vector indicating the id of the match...
    ...and a numeric vector with the value of `x` for the match...

    for (...loop over i...) {

        for (...loop over j and check if it is the optimum...) {
            if (...the closests so far...) {
                ...update the optimum...
            }
        }
        
    }

    return [a list like the R function]

}

Question 2: Things can be done faster

In the previous question, we have a double loop running twice over the full set of observations. We need you to write the C++ so that the computational complexity goes below n^2. (hint: Distance is symmetric)