R: find nearest index

Question

I have two vectors with a few thousand points, but generalized here:

A <- c(10, 20, 30, 40, 50)
b <- c(13, 17, 20)

How can I get the indicies of A that are nearest to b? The expected outcome would be c(1, 2, 2).

I know that findInterval can only find the first occurrence, and not the nearest, and I'm aware that which.min(abs(b[2] - A)) is getting warmer, but I can't figure out how to vectorize it to work with long vectors of both A and b.

Emelia

Answer 1

You can just put your code in a sapply. I think this has the same speed as a for loop so isn't technically vectorized though:

sapply(b,function(x)which.min(abs(x - A)))

Prefect

Do note that which.min() only returns the first match. There might be other elements that are equally close. – Prefect

Answer 2

FindInterval gets you very close. You just have to pick between the offset it returns and the next one:

#returns the nearest occurence of x in vec
nearest.vec <- function(x, vec)
{
    smallCandidate <- findInterval(x, vec, all.inside=TRUE)
    largeCandidate <- smallCandidate + 1
    #nudge is TRUE if large candidate is nearer, FALSE otherwise
    nudge <- 2 * x > vec[smallCandidate] + vec[largeCandidate]
    return(smallCandidate + nudge)
}

nearest.vec(b,A)

returns (1,2,2), and should comparable to FindInterval in performance.

Cautionary

Really useful, thank you. I'm surprised that there isn't something to do this in base. Which probably means that there is and I'm not aware of it...! – Wes

Answer 3

Here's a solution that uses R's often overlooked outer function. Not sure if it'll perform better, but it does avoid sapply.

A <- c(10, 20, 30, 40, 50)
b <- c(13, 17, 20)

dist <- abs(outer(A, b, '-'))
result <- apply(dist, 2, which.min)

# [1] 1 2 2

Evangelize