rank and order in R

i am having trouble understanding the difference between the R function rank and the R function order. they seem to produce the same output:

> rank(c(10,30,20,50,40))
[1] 1 3 2 5 4
> order(c(10,30,20,50,40))
[1] 1 3 2 5 4

Could somebody shed some light on this for me? Thanks

Solution 1:

set.seed(1)
x <- sample(1:50, 30)    
x
# [1] 14 19 28 43 10 41 42 29 27  3  9  7 44 15 48 18 25 33 13 34 47 39 49  4 30 46  1 40 20  8
rank(x)
# [1]  9 12 16 25  7 23 24 17 15  2  6  4 26 10 29 11 14 19  8 20 28 21 30  3 18 27  1 22 13  5
order(x)
# [1] 27 10 24 12 30 11  5 19  1 14 16  2 29 17  9  3  8 25 18 20 22 28  6  7  4 13 26 21 15 23

rank returns a vector with the "rank" of each value. the number in the first position is the 9th lowest. order returns the indices that would put the initial vector x in order.

The 27th value of x is the lowest, so 27 is the first element of order(x) - and if you look at rank(x), the 27th element is 1.

x[order(x)]
# [1]  1  3  4  7  8  9 10 13 14 15 18 19 20 25 27 28 29 30 33 34 39 40 41 42 43 44 46 47 48 49

Solution 2:

As it turned out this was a special case and made things confusing. I explain below for anyone interested:

rank returns the order of each element in an ascending list

order returns the index each element would have in an ascending list