object ForTranslations extends App {

  /**
   * Adapted from Scala Language Specification section 6.19
   */

  type Vec = Vector[Double]
  type Matrix = Vector[Vec]

  def transpose(xss: Matrix) = {
    for (i <- Vector.range(0, xss(0).length)) yield
      for (xs <- xss) yield xs(i)
  }

  def scalarProduct(xs: Vec, ys: Vec) = {
    var acc = 0.0
    for ((x, y) <- xs zip ys) acc = acc + x * y
    acc
  }

  /* 0 0 */
  def Multiply0(xss: Matrix, yss: Matrix): Matrix = {
    for (xs <- xss) yield
      for (yst <- transpose(yss)) yield
        scalarProduct(xs, yst)
  }

  /* 0 1 */
  def Multiply1(xss: Matrix, yss: Matrix): Matrix = {
    xss map(xs =>
      for (yst <- transpose(yss)) yield
        scalarProduct(xs, yst)
      )
  }

  /* 1 0 */
  def Multiply2(xss: Matrix, yss: Matrix): Matrix = {
    for (xs <- xss) yield
      transpose(yss) map (yst =>
        scalarProduct(xs, yst)
      )
  }

  /* 1 1 */
  def Multiply3(xss: Matrix, yss: Matrix): Matrix = {
    xss map(xs =>
      transpose(yss) map (yst =>
        scalarProduct(xs, yst)
      )
    )
  }

  val m0: Matrix = Vector(Vector(1.0, 0.0), Vector(0.0, 1.0))
  val m1: Matrix = Vector(Vector(4.0, 5.0), Vector(6.0, 7.0))

  val res0 = Multiply0(m0, m1)
  val res1 = Multiply1(m0, m1)
  val res2 = Multiply2(m0, m1)
  val res3 = Multiply3(m0, m1)
  println(res0 == res1 && res0 == res2 && res0 == res3)

}