1  #region License Information


2  /* HeuristicLab


3  * Copyright (C) 20022015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)


4  *


5  * This file is part of HeuristicLab.


6  *


7  * HeuristicLab is free software: you can redistribute it and/or modify


8  * it under the terms of the GNU General Public License as published by


9  * the Free Software Foundation, either version 3 of the License, or


10  * (at your option) any later version.


11  *


12  * HeuristicLab is distributed in the hope that it will be useful,


13  * but WITHOUT ANY WARRANTY; without even the implied warranty of


14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the


15  * GNU General Public License for more details.


16  *


17  * You should have received a copy of the GNU General Public License


18  * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.


19  */


20  #endregion


21 


22  using System;


23  using System.Collections.Generic;


24  using System.Diagnostics.Contracts;


25  using System.Linq;


26 


27  namespace HeuristicLab.Common {


28  public static class EnumerableStatisticExtensions {


29  /// <summary>


30  /// Calculates the median element of the enumeration.


31  /// </summary>


32  /// <param name="values"></param>


33  /// <returns></returns>


34  public static double Median(this IEnumerable<double> values) {


35  // iterate only once


36  double[] valuesArr = values.ToArray();


37  int n = valuesArr.Length;


38  if (n == 0) throw new InvalidOperationException("Enumeration contains no elements.");


39 


40  Array.Sort(valuesArr);


41 


42  // return the middle element (if n is uneven) or the average of the two middle elements if n is even.


43  if (n % 2 == 1) {


44  return valuesArr[n / 2];


45  } else {


46  return (valuesArr[(n / 2)  1] + valuesArr[n / 2]) / 2.0;


47  }


48  }


49 


50  /// <summary>


51  /// Calculates the alphaquantile element of the enumeration.


52  /// </summary>


53  /// <param name="values"></param>


54  /// <returns></returns>


55  public static double Quantile(this IEnumerable<double> values, double alpha) {


56  Contract.Assert(alpha > 0 && alpha < 1);


57  // iterate only once


58  double[] valuesArr = values.ToArray();


59  int n = valuesArr.Length;


60  if (n == 0) throw new InvalidOperationException("Enumeration contains no elements.");


61 


62  Array.Sort(valuesArr);


63  // starts at 0


64 


65  // return the element at Math.Ceiling (if n*alpha is fractional) or the average of two elements if n*alpha is integer.


66  var pos = n * alpha;


67  Contract.Assert(pos >= 0);


68  Contract.Assert(pos < n);


69  bool isInteger = Math.Round(pos).IsAlmost(pos);


70  if (isInteger) {


71  return 0.5 * (valuesArr[(int)pos  1] + valuesArr[(int)pos]);


72  } else {


73  return valuesArr[(int)Math.Ceiling(pos)  1];


74  }


75  }


76 


77  /// <summary>


78  /// Calculates the range (max  min) of the enumeration.


79  /// </summary>


80  /// <param name="values"></param>


81  /// <returns></returns>


82  public static double Range(this IEnumerable<double> values) {


83  double min = double.PositiveInfinity;


84  double max = double.NegativeInfinity;


85  int i = 0;


86  foreach (var e in values) {


87  if (min > e) min = e;


88  if (max < e) max = e;


89  i++;


90  }


91  if (i < 1) throw new ArgumentException("The enumerable must contain at least two elements", "values");


92  return max  min;


93  }


94 


95 


96  /// <summary>


97  /// Calculates the standard deviation of values.


98  /// </summary>


99  /// <param name="values"></param>


100  /// <returns></returns>


101  public static double StandardDeviation(this IEnumerable<double> values) {


102  return Math.Sqrt(Variance(values));


103  }


104 


105  /// <summary>


106  /// Calculates the variance of values. (sum (x  x_mean)² / n)


107  /// </summary>


108  /// <param name="values"></param>


109  /// <returns></returns>


110  public static double Variance(this IEnumerable<double> values) {


111  int m_n = 0;


112  double m_oldM = 0.0;


113  double m_newM = 0.0;


114  double m_oldS = 0.0;


115  double m_newS = 0.0;


116  foreach (double x in values) {


117  m_n++;


118  if (m_n == 1) {


119  m_oldM = m_newM = x;


120  m_oldS = 0.0;


121  } else {


122  m_newM = m_oldM + (x  m_oldM) / m_n;


123  m_newS = m_oldS + (x  m_oldM) * (x  m_newM);


124 


125  // set up for next iteration


126  m_oldM = m_newM;


127  m_oldS = m_newS;


128  }


129  }


130  return ((m_n > 1) ? m_newS / (m_n  1) : 0.0);


131  }


132 


133  /// <summary>


134  /// Calculates the pth percentile of the values.


135  /// </summary


136  public static double Percentile(this IEnumerable<double> values, double p) {


137  // iterate only once


138  double[] valuesArr = values.ToArray();


139  int n = valuesArr.Length;


140  if (n == 0) throw new InvalidOperationException("Enumeration contains no elements.");


141  if (n == 1) return values.ElementAt(0);


142 


143  if (p.IsAlmost(0.0)) return valuesArr[0];


144  if (p.IsAlmost(1.0)) return valuesArr[n  1];


145 


146  double t = p * (n  1);


147  int index = (int)Math.Floor(t);


148  double percentage = t  index;


149  return valuesArr[index] * (1  percentage) + valuesArr[index + 1] * percentage;


150  }


151 


152  public static IEnumerable<double> LimitToRange(this IEnumerable<double> values, double min, double max) {


153  if (min > max) throw new ArgumentException(string.Format("Minimum {0} is larger than maximum {1}.", min, max));


154  foreach (var x in values) {


155  if (double.IsNaN(x)) yield return (max + min) / 2.0;


156  else if (x < min) yield return min;


157  else if (x > max) yield return max;


158  else yield return x;


159  }


160  }


161  }


162  }

