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A general-purpose Scala utility library
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/*
  ---------------------------------------------------------------------------
  This software is released under a BSD license, adapted from
  http://opensource.org/licenses/bsd-license.php

  Copyright (c) 2009-2010, Brian M. Clapper
  All rights reserved.

  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are
  met:

   * Redistributions of source code must retain the above copyright notice,
    this list of conditions and the following disclaimer.

   * Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.

   * Neither the names "clapper.org", "Grizzled Scala Library", nor the
    names of its contributors may be used to endorse or promote products
    derived from this software without specific prior written permission.

  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
  IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
  THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
  LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  ---------------------------------------------------------------------------
*/

package grizzled.math

import scala.math

/** Miscellaneous statistics-related functions.
  *
  * Note: You must import `scala.math.Numeric` (or just `Numeric._`) for these
  * functions to work. For example:
  *
  * {{{
  * import Numeric._
  * import grizzled.math.stats._
  *
  * val l = List[Double]( ... )
  * println(median(l))
  * }}}
  */
object stats {
  // See http://scala-programming-language.1934581.n4.nabble.com/How-to-use-scala-math-Numeric-td2013703.html

  /** Calculates the geometric mean of the values of the passed-in
    * numbers, namely, the n-th root of (x1 * x2 * ... * xn). Note that
    * all numbers used in the calculation of a geometric mean must be
    * positive.
    *
    * For a discussion of when a geometric mean is more suitable than an
    * arithmetic mean, see
    * [[http://www.math.toronto.edu/mathnet/questionCorner/geomean.html]].
    *
    * @param items the numbers on which to operate
    *
    * @return the geometric mean
    */
  def geometricMean[T](items: T*)(implicit n: Numeric[T]): Double = {
    val itemList = items.toList
    val len = itemList.length
    require (len > 0)
    require (! itemList.exists(n.toDouble(_) <= 0))

    len match {
      case 1 =>
        n.toDouble(itemList(0))

      case _ =>
        val recip = 1.0 / len.toDouble
        (1.0 /: itemList) ((a, b) => a * math.pow(n.toDouble(b), recip))
    }
  }

  /** Calculates the harmonic mean of the values of the passed-in
    * numbers, namely: `n / (1/x^1^ + 1/x^2^ + ... + 1/x^n^).`
    *
    * @param items the numbers on which to operate
    *
    * @return the harmonic mean
    */
  def harmonicMean[T](items: T*)(implicit n: Numeric[T]): Double = {
    val itemList = items.toList
    val len = itemList.length
    require (len > 0)

    len match {
      case 1 => n.toDouble(itemList(0))
      case _ => len / ((0.0 /: itemList) ((a, b) => a + (1.0 / n.toDouble(b))))
    }
  }

  /** Calculates the arithmetic mean of the values of the passed-in
    * numbers.
    *
    * @param items the numbers on which to operate
    *
    * @return the arithmetic mean
    */
  def arithmeticMean[T](items: T*)(implicit n: Numeric[T]): Double = {
    val itemList = items.toList
    val len = itemList.length
    require (len > 0)

    len match {
      case 1 => n.toDouble(itemList(0))
      case _ => ((0.0 /: itemList) ((a, b) => a + n.toDouble(b))) / len
    }
  }

  /** Synonym for `arithmeticMean`.
    *
    * @see arithmeticMean
    */
  def mean[T](items: T*)(implicit n: Numeric[T]): Double =
    arithmeticMean(items.toList: _*)
  

  /** Calculates the median of the values of the passed-in numbers.
    *
    * @param items the numbers on which to operate
    *
    * @return the median
    */
  def median[T](items: T*)(implicit n: Numeric[T]): Double = {
    val itemList = items.toList
    val len = itemList.length
    require (len > 0)

    if (len == 1)
      n.toDouble(itemList(0))

    else {
      val sorted = itemList sortWith (n.compare(_, _) < 0)
      val midpoint = sorted.length / 2
      len % 2 match {
        case 0 => mean(n.toDouble(sorted(midpoint)),
                       n.toDouble(sorted(midpoint - 1)))
        case 1 => n.toDouble(sorted(midpoint))
      }
    }
  }

  /** Calculates the mode (most common value(s)) of the values of the
    * passed-in numbers. If there are multiple common values, they're all
    * returned.
    *
    * @param items the numbers on which to operate
    *
    * @return list of modal values
    */
  def mode[T](items: T*)(implicit n: Numeric[T]): List[T] = {
    val itemList = items.toList
    val len = itemList.length
    require (len > 0)

    if (len == 1)
      itemList take 1

    else {
      import scala.collection.mutable.{Map => MutableMap}

      val m = MutableMap.empty[T, Int]

      // Count the occurrences of each value.
      itemList.foreach(t => m += t -> (m.getOrElse(t, 0) + 1))

      // Find the maximum count.
      val max = (0 /: m.values) (scala.math.max(_, _))

      // Extract the keys with values that match
      m filter ( tup => tup._2 == max ) map ( tup => tup._1 ) toList
    }
  }

  /** Calculate the population variance of the finite population defined
    * by the `items` arguments. The population variance is defined as:
    *
    * {{{
    * 1 
    * - *  SUM(i=1, N) { (x[i] - mean)^2^ }
    * N 
    * }}}
    *
    * See:
    *
    * - [[http://en.wikipedia.org/wiki/Variance#Population_variance_and_sample_variance]]
    * - [[http://www.quickmba.com/stats/standard-deviation/]]
    *
    * @param items  the numbers on which to operate
    *
    * @return the variance
    */
  def populationVariance[T](items: T*)(implicit n: Numeric[T]): Double =
    calculateVariance(items.length, items.toList)

  /** Calculate the unbiased sample variance of the finite sample defined
    * by the `items` arguments. The sample variance is defined as:
    *
    * {{{
    *   1 
    * ----- *   SUM(i=1, N) { (x[i] - sampleMean)^2^  }
    * N - 1
    * }}}
    *
    * See:
    *
    * - [[http://en.wikipedia.org/wiki/Variance#Population_variance_and_sample_variance]]
    * - [[http://www.quickmba.com/stats/standard-deviation/]]
    *
    * @param items  the numbers on which to operate
    *
    * @return the variance
    */
  def sampleVariance[T](items: T*)(implicit n: Numeric[T]): Double =
    calculateVariance(items.length - 1, items.toList)

  /** Calculate the population standard deviation of the specified values.
    * The population standard deviation is merely the square root of the
    * population variance. Thus, this function is just shorthand for:
    *
    * {{{
    * java.lang.Math.sqrt(populationVariance(items))
    * }}}
    *
    * @param items the numbers on which to operate
    *
    * @return the standard deviation
    */
  def populationStandardDeviation[T](items: T*)
  (implicit n: Numeric[T]): Double =
    java.lang.Math.sqrt(populationVariance(items.toList: _*))

  /** Shorter synonym for `populationStandardDeviation`.
    *
    * @see populationStandardDeviation
    */
  def popStdDev[T](items: T*)(implicit n: Numeric[T]): Double =
    java.lang.Math.sqrt(populationVariance(items.toList: _*))

  /** Calculate the sample standard deviation of the specified values.
    * The sample standard deviation is merely the square root of the
    * sample variance. Thus, this function is just shorthand for:
    *
    * {{{
    * java.lang.Math.sqrt(sampleVariance(items))
    * }}}
    *
    * @param items the numbers on which to operate
    *
    * @return the standard deviation
    */
  def sampleStandardDeviation[T](items: T*)(implicit n: Numeric[T]): Double =
    java.lang.Math.sqrt(sampleVariance(items.toList: _*))

  /** Shorter synonym for `sampleStandardDeviation`.
    *
    * @see populationStandardDeviation
    */
  def sampleStdDev[T](items: T*)(implicit n: Numeric[T]): Double =
    java.lang.Math.sqrt(sampleVariance(items.toList: _*))


  /** Calculate the range of a data set. This function does a single
    * linear pass over the data set.
    *
    * @param items the numbers on which to operate
    *
    * @return the range
    */
  def range[T](items: T*)(implicit n: Numeric[T]): T = {
    // Fold left, generating a (min, max) tuple along the way.

    val (min, max) =
      ((n.fromInt(Int.MaxValue), n.fromInt(0)) /: items)((tuple, i) =>
        (n.min(tuple._1, i), n.max(tuple._1, i))
    )

    n.minus(max, min)
  }

  private def calculateVariance[T](denominator: Int, items: List[T])
                                  (implicit n: Numeric[T]): Double = {

    def sumOfSquares(dList: List[Double]): Double =
      (0.0 /: dList) ((sum, d) => sum + (d * d))

    val itemList = items.toList
    val len = itemList.length
    require (len > 1)

    val mn = mean(itemList: _*)
    val deviations = itemList map (n.toDouble(_) - mn)
    sumOfSquares(deviations) / denominator.toDouble
  }
}