/core/src/main/scala/scalaz/MetricSpace.scala
http://github.com/scalaz/scalaz · Scala · 94 lines · 57 code · 19 blank · 18 comment · 14 complexity · 29c4c56b109db3b5a8d1e15a734ca2f2 MD5 · raw file
- package scalaz
- ////
- /**
- * Useful metric spaces include the manhattan distance between two points,
- * the Levenshtein edit distance between two strings, the number of
- * edges in the shortest path between two nodes in an undirected graph
- * and the Hamming distance between two binary strings. Any euclidean
- * space also has a metric. However, in this module we use int-valued
- * metrics and that's not compatible with the metrics of euclidean
- * spaces which are real-values.
- *
- * @see [[scalaz.BKTree]]
- */
- ////
- @deprecated("Redundant to spire's `MetricSpace`", "7.0.1")
- trait MetricSpace[F] { self =>
- ////
- def distance(a: F, b: F): Int
- def contramap[B](f: B => F): MetricSpace[B] = new MetricSpace[B] {
- def distance(a: B, b: B): Int = self.distance(f(a), f(b))
- }
- // derived functions
- trait MetricSpaceLaw {
- import std.boolean.conditional
- def nonNegativity(a1: F, a2: F): Boolean = distance(a1, a1) >= 0
- def identity(a1: F): Boolean = distance(a1, a1) == 0
- def equality(a1: F, a2: F)(implicit F: Equal[F]): Boolean = conditional(F.equal(a1, a2), distance(a1, a2) == 0)
- def symmetry(a1: F, a2: F): Boolean = distance(a1, a2) == distance(a2, a1)
- def triangleInequality(a1: F, a2: F, a3: F): Boolean = (distance(a1, a2) + distance(a2, a3)) >= distance(a1, a3)
- }
- def metricSpaceLaw = new MetricSpaceLaw {}
- ////
- val metricSpaceSyntax = new scalaz.syntax.MetricSpaceSyntax[F] { def F = MetricSpace.this }
- }
- object MetricSpace {
- @inline def apply[F](implicit F: MetricSpace[F]): MetricSpace[F] = F
- ////
- val metricSpaceInstance = new Contravariant[MetricSpace] {
- def contramap[A, B](r: MetricSpace[A])(f: B => A): MetricSpace[B] = r contramap f
- }
- def metricSpace[A](f: (A, A) => Int): MetricSpace[A] = new MetricSpace[A] {
- def distance(a1: A, a2: A): Int = f(a1, a2)
- }
- def levenshtein[F[_], A](implicit l: Length[F], i: Index[F], e: Equal[A]): MetricSpace[F[A]] = new MetricSpace[F[A]] {
- def distance(a1: F[A], a2: F[A]): Int = levenshteinDistance(a1, a2)
- }
- def levenshteinDistance[F[_], A](value: F[A], w: F[A])(implicit l: Length[F], ind: Index[F], equ: Equal[A]): Int = {
- import Memo._
- def levenshteinMatrix(w: F[A])(implicit l: Length[F], ind: Index[F], equ: Equal[A]): (Int, Int) => Int = {
- val m = mutableHashMapMemo[(Int, Int), Int]
- def get(i: Int, j: Int): Int = if (i == 0) j
- else if (j == 0) i
- else {
- lazy val t: A = ind.index(value, (i - 1)).get
- lazy val u: A = ind.index(w, (j - 1)).get
- lazy val e: Boolean = equ.equal(t, u)
- val g: ((Int, Int)) => Int = m {
- case (a, b) => get(a, b)
- }
- val a: Int = g((i - 1, j)) + 1
- val b: Int = g((i - 1, j - 1)) + (if (e) 0 else 1)
- def c: Int = g((i, j - 1)) + 1
- if (a < b) a else if (b <= c) b else c
- }
- get
- }
- val k = levenshteinMatrix(w)
- k(l.length(value), l.length(w))
- }
- implicit def LevenshteinString: MetricSpace[String] = {
- import std.list._, std.anyVal._
- levenshtein[List, Char].contramap((s: String) => s.toList)
- }
- ////
- }