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
1 2 3 4 5 6 7 
Arguments
x 
for 
decreasing 
logical. Should the sort be increasing or decreasing?
For the 
... 
arguments to be passed to or from methods or (for the
default methods and objects without a class) to 
na.last 
for controlling the treatment of 
partial 

method 
character string specifying the algorithm used. Not available for partial sorting. Can be abbreviated. 
index.return 
logical indicating if the ordering index vector should
be returned as well. Supported by 
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 or is.numeric(x)
is true).
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 sort order for factors is the order of their levels (which is
particularly appropriate for ordered factors).
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 Quicksort if possible) if there
are more than 10.) Names are discarded for partial sorting.
Method "shell"
uses Shellsort (an O(n^{4/3}) variant from
Sedgewick (1986)). If x
has names a stable modification is
used, so ties are not reordered. (This only matters if names are
present.)
Method "quick"
uses Singleton (1969)'s implementation of
Hoare's Quicksort method 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 50% faster on vectors of
length a million and twice as fast at a billion) but has poor
performance in the rare worst case. (Peto's modification using a
pseudorandom midpoint is used to make the worst case rarer.) This is
not a stable sort, and ties may be reordered.
Method "radix"
relies on simple hashing to scale time linearly
with the input size, i.e., its asymptotic time complexity is O(n). The
specific variant and its implementation originated from the data.table
package and are due to Matt Dowle and Arun Srinivasan. For small
inputs (< 200), the implementation uses an insertion sort (O(n^2))
that operates inplace to avoid the allocation overhead of the radix
sort. For integer vectors of range less than 100,000, it switches to a
simpler and faster linear time counting sort. In all cases, the sort
is stable; the order of ties is preserved. It is the default method
for integer vectors and factors.
The "radix"
method generally outperforms the other methods,
especially for character vectors and small integers. Compared to quick
sort, it is slightly faster for (large) integers and double vectors
(but unlike quick sort, radix is stable and supports all
na.last
options). The implementation is order of magnitudes
faster than shell sort for character vectors, in part thanks to clever
use of the internal CHARSXP
table.
However, there are some caveats with the radix sort:

If
x
is acharacter
vector, all elements must share the same encoding. Only UTF8 (including ASCII) and Latin1 encodings are supported. Collation always follows the "C" locale. 
There is a small loss of precision when comparing double values. This may be configurable in the future.

Long vectors (with more than 2^32 elements) and
complex
vectors are not supported yet.
Value
For sort
, the result depends on the S3 method which is
dispatched. If x
does not have a class sort.int
is used
and it description 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 requires a xtfrm
method).
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. For method ==
"radix"
, index.return
is supported for all na.last
modes. The other methods only support index.return
when na.last
is NA
, so the index vector
refers to element numbers after removal of NA
s: see
order
if you want the original element numbers.
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.
Knuth, D. E. (1998) The Art of Computer Programming, Volume 3: Sorting and Searching. 2nd ed. AddisonWesley.
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42  require(stats)
x < swiss$Education[1:25]
x; sort(x); sort(x, partial = c(10, 15))
## illustrate 'stable' sorting (of ties):
sort(c(10:3, 2:12), method = "shell", 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 = "quick", 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 seq_len(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 = "shell") == sort(x, method = "quick"))
}
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"))
system.time(x3 < sort(x, method = "radix"))
stopifnot(identical(x1, x2))
stopifnot(all.equal(x1, x3)) # imprecision in radix sort
## End(Not run)

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