# order: Ordering Permutation

 order R Documentation

## Ordering Permutation

### Description

`order` returns a permutation which rearranges its first argument into ascending or descending order, breaking ties by further arguments. `sort.list` does the same, using only one argument.
See the examples for how to use these functions to sort data frames, etc.

### Usage

```order(..., na.last = TRUE, decreasing = FALSE,

sort.list(x, partial = NULL, na.last = TRUE, decreasing = FALSE,
method = c("auto", "shell", "quick", "radix"))
```

### Arguments

 `...` a sequence of numeric, complex, character or logical vectors, all of the same length, or a classed R object. `x` an atomic vector for `method`s `"shell"` and `"quick"`. When `x` is a non-atomic R object, the default `"auto"` and `"radix"` methods may work if `order(x,..)` does. `partial` vector of indices for partial sorting. (Non-`NULL` values are not implemented.) `decreasing` logical. Should the sort order be increasing or decreasing? For the `"radix"` method, this can be a vector of length equal to the number of arguments in `...`. For the other methods, it must be length one. `na.last` for controlling the treatment of `NA`s. If `TRUE`, missing values in the data are put last; if `FALSE`, they are put first; if `NA`, they are removed (see ‘Note’.) `method` the method to be used: partial matches are allowed. The default (`"auto"`) implies `"radix"` for numeric vectors, integer vectors, logical vectors and factors with fewer than 2^31 elements. Otherwise, it implies `"shell"`. For details of methods `"shell"`, `"quick"`, and `"radix"`, see the help for `sort`.

### Details

In the case of ties in the first vector, values in the second are used to break the ties. If the values are still tied, values in the later arguments are used to break the tie (see the first example). The sort used is stable (except for `method = "quick"`), so any unresolved ties will be left in their original ordering.

Complex values are sorted first by the real part, then the imaginary part.

Except for method `"radix"`, the sort order for character vectors will depend on the collating sequence of the locale in use: see `Comparison`.

The `"shell"` method is generally the safest bet and is the default method, except for short factors, numeric vectors, integer vectors and logical vectors, where `"radix"` is assumed. Method `"radix"` stably sorts logical, numeric and character vectors in linear time. It outperforms the other methods, although there are drawbacks, especially for character vectors (see `sort`). Method `"quick"` for `sort.list` is only supported for numeric `x` with `na.last = NA`, is not stable, and is slower than `"radix"`.

`partial = NULL` is supported for compatibility with other implementations of S, but no other values are accepted and ordering is always complete.

For a classed R object, the sort order is taken from `xtfrm`: as its help page notes, this can be slow unless a suitable method has been defined or `is.numeric(x)` is true. For factors, this sorts on the internal codes, which is particularly appropriate for ordered factors.

### Value

An integer vector unless any of the inputs has 2^31 or more elements, when it is a double vector.

### Warning

In programmatic use it is unsafe to name the `...` arguments, as the names could match current or future control arguments such as `decreasing`. A sometimes-encountered unsafe practice is to call `do.call('order', df_obj)` where `df_obj` might be a data frame: copy `df_obj` and remove any names, for example using `unname`.

### Note

`sort.list` can get called by mistake as a method for `sort` with a list argument: it gives a suitable error message for list `x`.

There is a historical difference in behaviour for `na.last = NA`: `sort.list` removes the `NA`s and then computes the order amongst the remaining elements: `order` computes the order amongst the non-`NA` elements of the original vector. Thus

```   x[order(x, na.last = NA)]
zz <- x[!is.na(x)]; zz[sort.list(x, na.last = NA)]
```

both sort the non-`NA` values of `x`.

Prior to R 3.3.0 `method = "radix"` was only supported for integers of range less than 100,000.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Knuth, D. E. (1998) The Art of Computer Programming, Volume 3: Sorting and Searching. 2nd ed. Addison-Wesley.

`sort`, `rank`, `xtfrm`.

### Examples

```require(stats)

(ii <- order(x <- c(1,1,3:1,1:4,3), y <- c(9,9:1), z <- c(2,1:9)))
## 6  5  2  1  7  4 10  8  3  9
rbind(x, y, z)[,ii] # shows the reordering (ties via 2nd & 3rd arg)

## Suppose we wanted descending order on y.
## A simple solution for numeric 'y' is
rbind(x, y, z)[, order(x, -y, z)]
## More generally we can make use of xtfrm
cy <- as.character(y)
rbind(x, y, z)[, order(x, -xtfrm(cy), z)]
## The radix sort supports multiple 'decreasing' values:
rbind(x, y, z)[, order(x, cy, z, decreasing = c(FALSE, TRUE, FALSE),

## Sorting data frames:
dd <- transform(data.frame(x, y, z),
z = factor(z, labels = LETTERS[9:1]))
## Either as above {for factor 'z' : using internal coding}:
dd[ order(x, -y, z), ]
## or along 1st column, ties along 2nd, ... *arbitrary* no.{columns}:
dd[ do.call(order, dd), ]

set.seed(1)  # reproducible example:
d4 <- data.frame(x = round(   rnorm(100)), y = round(10*runif(100)),
z = round( 8*rnorm(100)), u = round(50*runif(100)))
(d4s <- d4[ do.call(order, d4), ])
(i <- which(diff(d4s[, 3]) == 0))
#   in 2 places, needed 3 cols to break ties:
d4s[ rbind(i, i+1), ]

## rearrange matched vectors so that the first is in ascending order
x <- c(5:1, 6:8, 12:9)
y <- (x - 5)^2
o <- order(x)
rbind(x[o], y[o])

## tests of na.last
a <- c(4, 3, 2, NA, 1)
b <- c(4, NA, 2, 7, 1)
z <- cbind(a, b)
(o <- order(a, b)); z[o, ]
(o <- order(a, b, na.last = FALSE)); z[o, ]
(o <- order(a, b, na.last = NA)); z[o, ]

##  speed examples on an average laptop for long vectors:
##  factor/small-valued integers:
x <- factor(sample(letters, 1e7, replace = TRUE))
system.time(o <- sort.list(x, method = "quick", na.last = NA)) # 0.1 sec
stopifnot(!is.unsorted(x[o]))
system.time(o <- sort.list(x, method = "radix")) # 0.05 sec, 2X faster
stopifnot(!is.unsorted(x[o]))
##  large-valued integers:
xx <- sample(1:200000, 1e7, replace = TRUE)
system.time(o <- sort.list(xx, method = "quick", na.last = NA)) # 0.3 sec
system.time(o <- sort.list(xx, method = "radix")) # 0.2 sec
##  character vectors:
xx <- sample(state.name, 1e6, replace = TRUE)
system.time(o <- sort.list(xx, method = "shell")) # 2 sec
system.time(o <- sort.list(xx, method = "radix")) # 0.007 sec, 300X faster
##  double vectors:
xx <- rnorm(1e6)
system.time(o <- sort.list(xx, method = "shell")) # 0.4 sec
system.time(o <- sort.list(xx, method = "quick", na.last = NA)) # 0.1 sec
system.time(o <- sort.list(xx, method = "radix")) # 0.05 sec, 2X faster
```