R: Sorting or Ordering Vectors

sort {base} | R Documentation

## Sorting or Ordering Vectors

### Description

Sort (or order) a vector or factor (partially) into ascending or descending order. For ordering along more than one variable, e.g., for sorting data frames, see `order`.

### Usage

    sort(x, decreasing = FALSE, ...)

    ## Default S3 method:
    sort(x, decreasing = FALSE, na.last = NA, ...)

    sort.int(x, partial = NULL, na.last = NA, decreasing = FALSE,
             method = c("shell", "quick"), index.return = FALSE)

### Arguments

`x` | for `sort` an R object with a class or a numeric, complex, character or logical vector. For `sort.int`, a numeric, complex, character or logical vector, or a factor.
`decreasing` | logical. Should the sort be increasing or decreasing? Not available for partial sorting.
`...` | arguments to be passed to or from methods or (for the default methods and objects without a class) to `sort.int`.
`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.
`partial` | `NULL` or an integer vector of indices for partial sorting.
`method` | character string specifying the algorithm used. Not available for partial sorting.
`index.return` | logical indicating if the ordering index vector should be returned as well; this is only available for a few cases, the default `na.last = NA` and full sorting of non-factors.

### Details

`sort` is a generic function for which methods can be written, and `sort.int` is the internal method which is compatible with S if only the first three arguments are used.

The default `sort` method makes use of `order` for classed objects, which in turn makes use of the generic function `xtfrm` (and can be slow unless a `xtfrm` method has been defined unless `is.numeric(x)` is true).

If `partial` is not `NULL`, it is taken to contain indices of elements of the result which are to be placed in their correct positions in the sorted array by partial sorting. For each of the result values in a specified position, any values smaller than that one are guaranteed to have a smaller index in the sorted array and any values which are greater are guaranteed to have a bigger index in the sorted array. (This is included for efficiency, and many of the options are not available for partial sorting. It is only substantially more efficient if `partial` has a handful of elements, and a full sort is done (a quick sort if possible) if there are more than 10.) Names are discarded for partial sorting.

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

The sort order for character vectors will depend on the collating sequence of the locale in use: see `Comparison`. The sort order for factors is the order of their levels (which is particularly appropriate for ordered factors).

Method `"shell"` uses Shellsort (an O(n^{4/3}) variant from Sedgewick (1996)). If `x` has names a stable sort is used, so ties are not reordered. (This only matters if names are present.)

Method `"quick"` uses Singleton's Quicksort implementation and is only available when `x` is numeric (double or integer) and `partial` is `NULL`. (For other types of `x` Shellsort is used, silently.) It is normally somewhat faster than Shellsort (perhaps twice as fast on vectors of length a million) but has poor performance in the rare worst case. (Peto's modification using a pseudo-random midpoint is used to make the worst case rarer.) This is not a stable sort, and ties may be reordered.

### Value

For `sort`, the result depends on the S3 method which is dispatched. If `x` does not have a class the rest of this section applies. For classed objects which do not have a specific method the default method will be used and is equivalent to `x[order(x, ...)]`: this depends on the class having a suitable method for `[` (and also that `order` will work, which is not the case for a class based on a list).

For `sort.int` the value is the sorted vector unless `index.return` is true, when the result is a list with components named `x` and `ix` containing the sorted numbers and the ordering index vector. In the latter case, if `method == "quick"` ties may be reversed in the ordering, unlike `sort.list`, as quicksort is not stable. NB: the index vector refers to element numbers after removal of `NA`s.

All attributes are removed from the return value (see Becker et al, 1988, p.146) except names, which are sorted. (If `partial` is specified even the names are removed.) Note that this means that the returned value has no class, except for factors and ordered factors (which are treated specially and whose result is transformed back to the original class).

### References

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

Sedgewick, R. (1986) A new upper bound for Shell sort. J. Algorithms 7, 159–173.

Singleton, R. C. (1969) An efficient algorithm for sorting with minimal storage: Algorithm 347. Communications of the ACM 12, 185–187.

### See Also

‘Comparison’ for how character strings are collated.

`order` for sorting on or reordering multiple variables.

`is.unsorted`. `rank`.

### Examples

    require(stats)

    x <- swiss$Education[1:25]
    x; sort(x); sort(x, partial = c(10, 15))
    median.default # shows you another example for 'partial'

    ## illustrate 'stable' sorting (of ties):
    sort(c(10:3,2:12), method = "sh", index.return=TRUE) # is stable
    ## $x : 2  3  3  4  4  5  5  6  6  7  7  8  8  9  9 10 10 11 12
    ## $ix: 9  8 10  7 11  6 12  5 13  4 14  3 15  2 16  1 17 18 19
    sort(c(10:3,2:12), method = "qu", index.return=TRUE) # is not
    ## $x : 2  3  3  4  4  5  5  6  6  7  7  8  8  9  9 10 10 11 12
    ## $ix: 9 10  8  7 11  6 12  5 13  4 14  3 15 16  2 17  1 18 19
    ##        ^^^^^

    x <- c(1:3, 3:5, 10)
    is.unsorted(x)                # FALSE: is sorted
    is.unsorted(x, strictly=TRUE) # TRUE : is not (and cannot be)
                                  # sorted strictly
    ## Not run:
    ## Small speed comparison simulation:
    N <- 2000
    Sim <- 20
    rep <- 1000 # << adjust to your CPU
    c1 <- c2 <- numeric(Sim)
    for(is in 1:Sim){
      x <- rnorm(N)
      c1[is] <- system.time(for(i in 1:rep) sort(x, method = "shell"))[1]
      c2[is] <- system.time(for(i in 1:rep) sort(x, method = "quick"))[1]
      stopifnot(sort(x, method = "s") == sort(x, method = "q"))
    }
    rbind(ShellSort = c1, QuickSort = c2)
    cat("Speedup factor of quick sort():\n")
    summary({qq <- c1 / c2; qq[is.finite(qq)]})

    ## A larger test
    x <- rnorm(1e7)
    system.time(x1 <- sort(x, method = "shell"))
    system.time(x2 <- sort(x, method = "quick"))
    stopifnot(identical(x1, x2))

    ## End(Not run)

[Package base version 2.15.1 Index]