Class activity

Weighted sums

In a previous assignment, you have computed weighted sums and means. If \(x_1,...,x_n\) is a set of observations and \(w_1,...,w_n\) a set of weights, then \(\sum \limits_{i=1}^n w_i x_i\) is the weighted sum.

In R, sum(w * x) calculates the weighted sum, for vectors w (containing \(w_1,...,w_n\)) and x (containing \(x_1,...,x_n\)).

1. In R, the crossprod function, when applied to vectors, computes the inner product (aka dot product) of the two vectors. Use the crossprod function to compute a weighted sum, and compare the speed with sum(w * x).

2. In question 1, does the relative speed change as we change the length of x?

Concatenating strings

The code below generates 10 random strings, of length 50 characters each, and combines them together:

random_string <- function() {
  paste(sample(letters, 50, replace = TRUE), collapse = "")
}
strings <- replicate(10, random_string())

collapse <- function(xs) {
  out <- ""
  for (x in xs) {
    out <- paste0(out, x)
  }
  out
}

collapse(strings)

3. Write faster code to combine the strings, using the paste function and avoiding a for loop. Compare the speed of your code to the collapse function above.

C++ and Rcpp

When we can’t optimize our code any further in R, we sometimes turn to C++ (a different programming language, which is often faster). In a subsequent lecture, we will discuss how to re-write R code in C++ for performance increases. For now, we will get Rcpp (the package used to integrate C++ code into R) set up.

The installation instructions can be found here and here.

Follow the installation instructions, then run the following code in R to make sure everything was installed correctly:

Rcpp::cppFunction('int add(int x, int y, int z) {
  int sum = x + y + z;
  return sum;
}')

add(1, 2, 3)