# adist

##### Approximate String Distances

Compute the approximate string distance between character vectors. The distance is a generalized Levenshtein (edit) distance, giving the minimal possibly weighted number of insertions, deletions and substitutions needed to transform one string into another.

- Keywords
- character

##### Usage

```
adist(x, y = NULL, costs = NULL, counts = FALSE, fixed = TRUE,
partial = !fixed, ignore.case = FALSE, useBytes = FALSE)
```

##### Arguments

- x
a character vector. Long vectors are not supported.

- y
a character vector, or

`NULL`

(default) indicating taking`x`

as`y`

.- costs
a numeric vector or list with names partially matching

`insertions`,`deletions`and`substitutions`giving the respective costs for computing the Levenshtein distance, or`NULL`

(default) indicating using unit cost for all three possible transformations.- counts
a logical indicating whether to optionally return the transformation counts (numbers of insertions, deletions and substitutions) as the

`"counts"`

attribute of the return value.- fixed
a logical. If

`TRUE`

(default), the`x`

elements are used as string literals. Otherwise, they are taken as regular expressions and`partial = TRUE`

is implied (corresponding to the approximate string distance used by`agrep`

with`fixed = FALSE`

.- partial
a logical indicating whether the transformed

`x`

elements must exactly match the complete`y`

elements, or only substrings of these. The latter corresponds to the approximate string distance used by`agrep`

(by default).- ignore.case
a logical. If

`TRUE`

, case is ignored for computing the distances.- useBytes
a logical. If

`TRUE`

distance computations are done byte-by-byte rather than character-by-character.

##### Details

The (generalized) Levenshtein (or edit) distance between two strings
`s` and `t` is the minimal possibly weighted number of
insertions, deletions and substitutions needed to transform `s`
into `t` (so that the transformation exactly matches `t`).
This distance is computed for `partial = FALSE`

, currently using
a dynamic programming algorithm (see, e.g.,
https://en.wikipedia.org/wiki/Levenshtein_distance) with space
and time complexity \(O(mn)\), where \(m\) and \(n\) are the
lengths of `s` and `t`, respectively. Additionally computing
the transformation sequence and counts is \(O(\max(m, n))\).

The generalized Levenshtein distance can also be used for approximate
(fuzzy) string matching, in which case one finds the substring of
`t` with minimal distance to the pattern `s` (which could be
taken as a regular expression, in which case the principle of using
the leftmost and longest match applies), see, e.g.,
https://en.wikipedia.org/wiki/Approximate_string_matching. This
distance is computed for `partial = TRUE`

using `tre` by
Ville Laurikari (http://laurikari.net/tre/) and
corresponds to the distance used by `agrep`

. In this
case, the given cost values are coerced to integer.

Note that the costs for insertions and deletions can be different, in
which case the distance between `s` and `t` can be different
from the distance between `t` and `s`.

##### Value

A matrix with the approximate string distances of the elements of
`x`

and `y`

, with rows and columns corresponding to `x`

and `y`

, respectively.

If `counts`

is `TRUE`

, the transformation counts are
returned as the `"counts"`

attribute of this matrix, as a
3-dimensional array with dimensions corresponding to the elements of
`x`

, the elements of `y`

, and the type of transformation
(insertions, deletions and substitutions), respectively.
Additionally, if `partial = FALSE`

, the transformation sequences
are returned as the `"trafos"`

attribute of the return value, as
character strings with elements `M`, `I`, `D` and
`S` indicating a match, insertion, deletion and substitution,
respectively. If `partial = TRUE`

, the offsets (positions of
the first and last element) of the matched substrings are returned as
the `"offsets"`

attribute of the return value (with both offsets
\(-1\) in case of no match).

##### See Also

`agrep`

for approximate string matching (fuzzy matching)
using the generalized Levenshtein distance.

##### Examples

`library(utils)`

```
## Cf. https://en.wikipedia.org/wiki/Levenshtein_distance
adist("kitten", "sitting")
## To see the transformation counts for the Levenshtein distance:
drop(attr(adist("kitten", "sitting", counts = TRUE), "counts"))
## To see the transformation sequences:
attr(adist(c("kitten", "sitting"), counts = TRUE), "trafos")
## Cf. the examples for agrep:
adist("lasy", "1 lazy 2")
## For a "partial approximate match" (as used for agrep):
adist("lasy", "1 lazy 2", partial = TRUE)
```

*Documentation reproduced from package utils, version 3.4.1, License: Part of R 3.4.1*