Relativity transformer

lorenz_transformation.sc

type Plane = (Double, Double)

  type Matrix = (Plane, Plane)

  type TaggedEvents = Map[String, Plane]
  private val sin45 = Math.sqrt(0.5)

  private val matrixMinus45 = ((sin45, sin45), (-sin45, sin45))
  private val matrixPlus45 = ((sin45, -sin45), (sin45, sin45))

  def transform(events: TaggedEvents, from: String): TaggedEvents = {
    val reference = events(from)
    val spacetimeT = multiplyV(matrixMinus45, reference)
    println("ref="+spacetimeT)
    val lambda = Math.sqrt(spacetimeT._2 / spacetimeT._1)
    println("lamda="+lambda)
    println(multiplyM(matrixMinus45,matrixPlus45))
    val lorenzMatrix = ((lambda, 0d), (0d, 1.0 / lambda))
    val ultimateMatrix = multiplyM(multiplyM(matrixMinus45, lorenzMatrix), matrixPlus45)
    events.mapValues {
      plane =>
        multiplyV(matrixPlus45,multiplyV(lorenzMatrix,multiplyV(matrixMinus45, plane)))
    }

  }

   def multiplyM(matrix1: Matrix, matrix2: Matrix): Matrix = {
    ((matrix1._1._1 * matrix2._1._1 + matrix1._1._2 * matrix2._2._1,
      matrix1._1._1 * matrix2._1._2 + matrix1._1._2 * matrix2._2._2),
      (matrix1._2._1 * matrix2._1._1 + matrix1._2._2 * matrix2._2._1,
        matrix1._2._1 * matrix2._1._2 + matrix1._2._2 * matrix2._2._2))
  }

   def multiplyV(matrix: Matrix, plane: Plane): Plane = {
    (
      matrix._1._1 * plane._1 + matrix._1._2 * plane._2,
      matrix._2._1 * plane._1 + matrix._2._2 * plane._2
    )
  }


  println(transform(Map("normal"->(3,4)),"normal"))