/**
 * Copyright (C) 2009-2015 Typesafe Inc. <http://www.typesafe.com>
 */
package akka.cluster.metrics

import scala.concurrent.duration.FiniteDuration

/**
 * The exponentially weighted moving average (EWMA) approach captures short-term
 * movements in volatility for a conditional volatility forecasting model. By virtue
 * of its alpha, or decay factor, this provides a statistical streaming data model
 * that is exponentially biased towards newer entries.
 *
 * http://en.wikipedia.org/wiki/Moving_average#Exponential_moving_average
 *
 * An EWMA only needs the most recent forecast value to be kept, as opposed to a standard
 * moving average model.
 *
 * @param alpha decay factor, sets how quickly the exponential weighting decays for past data compared to new data,
 *   see http://en.wikipedia.org/wiki/Moving_average#Exponential_moving_average
 *
 * @param value the current exponentially weighted moving average, e.g. Y(n - 1), or,
 *             the sampled value resulting from the previous smoothing iteration.
 *             This value is always used as the previous EWMA to calculate the new EWMA.
 *
 */
@SerialVersionUID(1L)
final case class EWMA(value: Double, alpha: Double) {

  require(0.0 <= alpha && alpha <= 1.0, "alpha must be between 0.0 and 1.0")

  /**
   * Calculates the exponentially weighted moving average for a given monitored data set.
   *
   * @param xn the new data point
   * @return a new EWMA with the updated value
   */
  def :+(xn: Double): EWMA = {
    val newValue = (alpha * xn) + (1 - alpha) * value
    if (newValue == value) this // no change
    else copy(value = newValue)
  }

}

object EWMA {

  /**
   * math.log(2)
   */
  private val LogOf2 = 0.69315

  /**
   * Calculate the alpha (decay factor) used in [[akka.cluster.EWMA]]
   * from specified half-life and interval between observations.
   * Half-life is the interval over which the weights decrease by a factor of two.
   * The relevance of each data sample is halved for every passing half-life duration,
   * i.e. after 4 times the half-life, a data sample’s relevance is reduced to 6% of
   * its original relevance. The initial relevance of a data sample is given by
   * 1 – 0.5 ^ (collect-interval / half-life).
   */
  def alpha(halfLife: FiniteDuration, collectInterval: FiniteDuration): Double = {
    val halfLifeMillis = halfLife.toMillis
    require(halfLife.toMillis > 0, "halfLife must be > 0 s")
    val decayRate = LogOf2 / halfLifeMillis
    1 - math.exp(-decayRate * collectInterval.toMillis)
  }
}
