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package com.thesamet.spatial

import scala.language.implicitConversions
import scala.math.Numeric.Implicits._

/** Metric is a trait whose instances each represent a way to measure distances between
  * instances of a type.
  *
  * `A` represents the type of the points and `R` represents the metric value.
  */
trait Metric[A, R] {
  /** Returns the distance between two points. */
  def distance(x: A, y: A): R

  /** Returns the distance between x and a hyperplane that passes through y and perpendicular to
    * that dimension.
    */
  def planarDistance(dimension: Int)(x: A, y: A): R
}

object Metric {
  implicit def metricFromTuple2[A](implicit n: Numeric[A]): Metric[(A, A), A] = new Metric[(A, A), A] {
    def distance(x: (A, A), y: (A, A)): A = {
      val dx = x._1 - y._1
      val dy = x._2 - y._2
      dx * dx + dy * dy
    }
    def planarDistance(d: Int)(x: (A, A), y: (A, A)): A = {
      val dd = x.productElement(d).asInstanceOf[A] - y.productElement(d).asInstanceOf[A]
      dd * dd
    }
  }

  implicit def metricFromSeq[A](implicit n: Numeric[A]): Metric[Seq[A], A] = new Metric[Seq[A], A] {
    /** Returns the distance between two points. */
    override def distance(x: Seq[A], y: Seq[A]): A = x.zip(y).map{z=>
      val d = z._1 - z._2
      d * d
    }.sum

    /** Returns the distance between x and a hyperplane that passes through y and perpendicular to
      * that dimension.
      */
    override def planarDistance(dimension: Int)(x: Seq[A], y: Seq[A]): A = {
      val dd = x(dimension) - y(dimension)
      dd * dd
    }
  }
}