maths.scala

abstract class InterpolationMethod(val s: Traversable[(Double, Double)]) extends (Double => Double) {
  protected val x_i = s.map(_._1)
  protected val y_i = s.map(_._2)

  def this(f: Double => Double, f2: Int => Double, n: Int) = this(for(i <- 0 to n) yield {
    val x = f2(i)
    (x, f(x))
  })

  def this(f: Double => Double, n: Int) = this(f, _.toDouble, n)
}

class Lagrange(s: Traversable[(Double, Double)]) extends InterpolationMethod(s) {
  val level = s.size

  private def poly(i: Int)(x: Double): Double = {
    val xi = x_i(i)
    x_i.drop(i).map(xj => (xj - x) / (xj - xi)).reduce[Double](_ * _)
  }

  def apply(x: Double) = (for(i <- 0 to x_i.size) yield y_i(i) * poly(i)(x)).sum[Double]
}