R looping over two vectors - r

Question

I have created two vectors in R, using statistical distributions to build the vectors.
The first is a vector of locations on a string of length 1000. That vector has around 10 values and is called mu.
The second vector is a list of numbers, each one representing the number of features at each location mentioned above. This vector is called N.
What I need to do is generate a random distribution for all features (N) at each location (mu)
After some fiddling around, I found that this code works correctly:
for (i in 1:length(mu)){
a <- rnorm(N[i],mu[i],20)
feature.location <- c(feature.location,a)
}
This produces the right output - a list of numbers of length sum(N), and each number is a location figure which correlates with the data in mu.
I found that this only worked when I used concatenate to get the values into a vector.
My question is; why does this code work? How does R know to loop sum(N) times but for each position in mu? What role does concatenate play here?
Thanks in advance.

Answer 1

To try and answer your question directly, c(...) is not "concatenate", it's "combine". That is, it combines it's argument list into a vector. So c(1,2,3) is a vector with 3 elements.
Also, rnorm(n,mu,sigma) is a function that returns a vector of n random numbers sampled from the normal distribution. So at each iteration, i,
a <- rnorm(N[i],mu[i],20)
creates a vector a containing N[i] random numbers sampled from Normal(mu[i],20). Then
feature.location <- c(feature.location,a)
adds the elements of that vector to the vector from the previous iteration. So at the end, you have a vector with sum(N[i]) elements.

Answer 2

I guess you're sampling from a series of locations, each a variable no. of times.
I'm guessing your data looks something like this:
set.seed(1) # make reproducible
N <- ceiling(10*runif(10))
mu <- sample(seq(1000), 10)
> N;mu
[1] 3 4 6 10 3 9 10 7 7 1
[1] 206 177 686 383 767 496 714 985 377 771
Now you want to take a sample from rnorm of length N(i), with mean mu(i) and sd=20 and store all the results in a vector.
The method you're using (growing the vector) is not recommended as it will be re-copied in memory each time an element is added. (See Circle 2, although for small examples like this, it's not so important.)
First, initialize the storage vector:
f.l <- NULL
for (i in 1:length(mu)){
a <- rnorm(n=N[i], mean=mu[i], sd=20)
f.l <- c(f.l, a)
}
Then, each time, a stores your sample of length N[i] and c() combines it with the existing f.l by adding it to the end.
A more efficient approach is
unlist(mapply(rnorm, N, mu, MoreArgs=list(sd=20)))
Which vectorizes the loop. Unlist is used as mapply returns a list of vectors of varying lengths.