#region License Information
/* HeuristicLab
* Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL)
*
* This file is part of HeuristicLab.
*
* HeuristicLab is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* HeuristicLab is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with HeuristicLab. If not, see .
*/
#endregion
using System;
using System.Collections.Generic;
using System.Linq;
namespace HeuristicLab.Common {
public class EmpiricalCumulativeDistributionFunction {
private static readonly AbscissaComparer abscissaComparer = new AbscissaComparer();
private static readonly OrdinateComparer ordinateComparer = new OrdinateComparer();
private List> ecdf;
public IEnumerable> SupportingPoints {
get { return ecdf; }
}
public EmpiricalCumulativeDistributionFunction(IList sample) {
ecdf = new List>();
var len = sample.Count;
var cumulative = 0;
var localcumulative = 0;
var prev = double.NaN;
foreach (var p in sample.OrderBy(x => x)) {
if (double.IsNaN(p) || double.IsInfinity(p)) continue;
if (!double.IsNaN(prev) && prev < p) {
cumulative += localcumulative;
localcumulative = 0;
ecdf.Add(Point2D.Create(prev, cumulative / (double)len));
}
prev = p;
localcumulative++;
}
if (!double.IsNaN(prev)) {
cumulative += localcumulative;
ecdf.Add(Point2D.Create(prev, cumulative / (double)len));
}
}
public EmpiricalCumulativeDistributionFunction(IEnumerable> ecdf) {
this.ecdf = new List>();
var prev = Point2D.Empty;
foreach (var point in ecdf) {
if (point.Y < 0 || point.Y > 1 || double.IsNaN(point.X) || double.IsInfinity(point.X)
|| point.IsEmpty || (!prev.IsEmpty && (point.X <= prev.X || point.Y <= prev.Y)))
throw new ArgumentException("Invalid supporting points of a cumulative distribution function. Must be strictly monotonically increasing in both X and Y with X in R and Y in [0;1].", "ecdf");
this.ecdf.Add(point);
prev = point;
}
}
public double Evaluate(double x) {
if (ecdf.Count == 0) return double.NaN;
if (x < ecdf[0].X) return 0;
var last = ecdf[ecdf.Count - 1];
if (x >= last.X) return last.Y;
var index = ecdf.BinarySearch(Point2D.Create(x, 0), abscissaComparer);
if (index >= 0) return ecdf[index].Y;
return ecdf[~index - 1].Y;
}
public double InterpolateLinear(double x) {
if (ecdf.Count == 0) return double.NaN;
if (x < ecdf[0].X) return 0;
var last = ecdf[ecdf.Count - 1];
if (x >= last.X) return last.Y;
var index = ecdf.BinarySearch(Point2D.Create(x, 0), abscissaComparer);
if (index >= 0) return ecdf[index].Y;
var prev = ecdf[~index - 1];
var next = ecdf[~index];
return prev.Y + (next.Y - prev.Y) * ((x - prev.X) / (next.X - prev.X));
}
public double InterpolateNearest(double x) {
if (ecdf.Count == 0) return double.NaN;
if (x < ecdf[0].X) return 0;
var last = ecdf[ecdf.Count - 1];
if (x >= last.X) return last.Y;
var index = ecdf.BinarySearch(Point2D.Create(x, 0), abscissaComparer);
if (index >= 0) return ecdf[index].Y;
var prev = ecdf[~index - 1];
var next = ecdf[~index];
if (x - prev.X < next.X - x) return prev.Y;
return next.Y;
}
public double Inverse(double y) {
if (ecdf.Count == 0) return double.NaN;
if (y < 0 || y > 1) throw new ArgumentException("parameter must be in interval [0;1]", "y");
if (ecdf[ecdf.Count - 1].Y < y) return double.PositiveInfinity;
var index = ecdf.BinarySearch(Point2D.Create(0, y), ordinateComparer);
if (index >= 0) return ecdf[index].X;
return ecdf[Math.Max(~index - 1, 0)].X;
}
private class AbscissaComparer : Comparer> {
public override int Compare(Point2D x, Point2D y) {
return x.X.CompareTo(y.X);
}
}
private class OrdinateComparer : Comparer> {
public override int Compare(Point2D x, Point2D y) {
return x.Y.CompareTo(y.Y);
}
}
}
}