Euclidean distance of two vectors

Question

How do I find the Euclidean distance of two vectors:

x1 <- rnorm(30)
x2 <- rnorm(30)

Answer 1

As defined on Wikipedia, this should do it.

euc.dist <- function(x1, x2) sqrt(sum((x1 - x2) ^ 2))

There's also the rdist function in the fields package that may be useful. See here.

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EDIT: Changed ** operator to ^. Thanks, Gavin.

Answer 2

If you want to use less code, you can also use the norm in the stats package (the 'F' stands for Forbenius, which is the Euclidean norm):

norm(matrix(x1-x2), 'F')

While this may look a bit neater, it's not faster. Indeed, a quick test on very large vectors shows little difference, though so12311's method is slightly faster. We first define:

set.seed(1234)
x1 <- rnorm(300000000)
x2 <- rnorm(300000000)

Then testing for time yields the following:

> system.time(a<-sqrt(sum((x1-x2)^2)))
user  system elapsed 
1.02    0.12    1.18 
> system.time(b<-norm(matrix(x1-x2), 'F'))
user  system elapsed 
0.97    0.33    1.31 

Answer 3

try using this:

sqrt(sum((x1-x2)^2))

Answer 4

Use the dist() function, but you need to form a matrix from the two inputs for the first argument to dist():

dist(rbind(x1, x2))

For the input in the OP's question we get:

> dist(rbind(x1, x2))
        x1
x2 7.94821

a single value that is the Euclidean distance between x1 and x2.