source: branches/2457_ExpertSystem/HeuristicLab.Analysis.FitnessLandscape/3.3/ProblemCharacteristicAnalysis/CurveAnalysis.cs @ 16096

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2018 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 <http://www.gnu.org/licenses/>.
 */
#endregion

using System;
using System.Collections.Generic;
using System.Linq;

namespace HeuristicLab.Analysis.FitnessLandscape {
  public static class CurveAnalysis<T> {
    public static CurveAnalysisResult GetCharacteristics(List<List<Tuple<T, double>>> trajectories, Func<T, T, double> distFunc) {
      trajectories = trajectories.Where(x => x.Count > 5).ToList();
      var symbols = GetSymbols(trajectories);
      var f1 = trajectories.Select(path => ApproximateDerivative(path, distFunc).ToList()).ToList();
      var f2 = f1.Select(d1 => ApproximateDerivative(d1, distFunc).ToList()).ToList();

      var sharpness = f1.Average(x => x.Average(y => Math.Abs(y.Item2)));
      var bumpiness = 0.0;
      var flatness = 0.0;
      var count = 0;
      for (var p = 0; p < f2.Count; p++) {
        if (f2[p].Count <= 2) continue;
        count++;
        var bump = 0;
        var flat = 0;
        for (var i = 0; i < f2[p].Count - 1; i++) {
          if ((f2[p][i].Item2 > 0 && f2[p][i + 1].Item2 < 0) || (f2[p][i].Item2 < 0 && f2[p][i + 1].Item2 > 0)) {
            bump++;
          } else if (f2[p][i].Item2 == 0) {
            flat++;
          }
        }
        bumpiness += bump / (f2[p].Count - 1.0);
        flatness += flat / (f2[p].Count - 1.0);
      }
      bumpiness /= count;
      flatness /= count;
      var per = new[] { 25, 50, 75 };
      return new CurveAnalysisResult(sharpness, bumpiness, flatness,
        per.Select(p => symbols.Downward.GetPercentileOrDefault(p, 0)).ToArray(),
        per.Select(p => symbols.Neutral.GetPercentileOrDefault(p, 0)).ToArray(),
        per.Select(p => symbols.Upward.GetPercentileOrDefault(p, 0)).ToArray());
    }

    private static Symbols GetSymbols(List<List<Tuple<T, double>>> trajectories) {
      var sym = new Symbols();
      foreach (var t in trajectories) {
        var prev = t[0];
        for (var i = 1; i < t.Count; i++) {
          sym.Add(i / (double)t.Count, t[i].Item2, prev.Item2);
          prev = t[i];
        }
      }
      return sym;
    }

    private static IEnumerable<Tuple<T, double>> ApproximateDerivative(IEnumerable<Tuple<T, double>> data, Func<T, T, double> distFunc) {
      Tuple<T, double> prev = null, prev2 = null;
      foreach (var d in data) {
        if (prev == null) {
          prev = d;
          continue;
        }
        if (prev2 == null) {
          prev2 = prev;
          prev = d;
          continue;
        }
        var dist = distFunc(prev2.Item1, d.Item1);
        yield return Tuple.Create(prev.Item1, (d.Item2 - prev2.Item2) / dist);
        prev2 = prev;
        prev = d;
      }
    }
  }

  public enum CurveAnalysisFeature { Sharpness, Bumpiness, Flatness,
                                     DownQ1, DownQ2, DownQ3,
                                     NeutQ1, NeutQ2, NeutQ3,
                                     UpQ1, UpQ2, UpQ3 }

  public class CurveAnalysisResult {
    private Dictionary<CurveAnalysisFeature, double> results = new Dictionary<CurveAnalysisFeature, double>();

    public double GetValue(CurveAnalysisFeature name) {
      return results[name];
    }

    public static IEnumerable<CurveAnalysisFeature> AllFeatures {
      get { return Enum.GetValues(typeof(CurveAnalysisFeature)).Cast<CurveAnalysisFeature>(); }
    }

    public double[] GetValues() {
      return AllFeatures.Select(x => results[x]).ToArray();
    }

    public CurveAnalysisResult(double sharpness, double bumpiness, double flatness, double[] down, double[] neut, double[] up) {
      foreach (var v in AllFeatures.Zip(new[] { sharpness, bumpiness, flatness }.Concat(down).Concat(neut).Concat(up), (n, v) => Tuple.Create(n, v))) {
        results[v.Item1] = v.Item2;
      }
    }
  }

  public class Symbols {
    public Statistics Downward { get; } = new Statistics();
    public Statistics Neutral { get; } = new Statistics();
    public Statistics Upward { get; } = new Statistics();

    public void Add(double step, double fit, double prev) {
      if (fit < prev) Downward.Add(step);
      else if (fit > prev) Upward.Add(step);
      else Neutral.Add(step);
    }
  }

  public sealed class Statistics {
    private List<double> values = new List<double>();

    public int Count { get { return values.Count; } }

    public double Min { get; private set; }
    public double Max { get; private set; }
    public double Total { get; private set; }
    public double Mean { get; private set; }
    public double StdDev { get { return Math.Sqrt(Variance); } }
    public double Variance { get { return Count > 0 ? variance / Count : 0.0; } }
    
    private double variance;
    private bool sorted = false;
    
    public double GetPercentileOrDefault(int p, double @default = default(double)) {
      if (p < 0 || p > 100) throw new ArgumentOutOfRangeException(nameof(p), p, "Must be in range [0;100]");
      SortIfNecessary();
      if (Count == 0) return @default;
      else if (Count == 1) return values[0];
      if (p == 100) return values[Count - 1];

      var x = p / 100.0 * (Count - 1);
      var inte = (int)x;
      var frac = x - inte;

      return values[inte] + frac * (values[inte + 1] - values[inte]);
    }

    public void Add(double value) {
      sorted = false;
      values.Add(value);

      if (Count == 1) {
        Min = Max = Mean = Total = value;
      } else {
        if (value < Min) Min = value;
        if (value > Max) Max = value;

        Total += value;
        var oldMean = Mean;
        Mean = oldMean + (value - oldMean) / Count;
        variance = variance + (value - oldMean) * (value - Mean);
      }
    }

    public void AddRange(IEnumerable<double> values) {
      foreach (var v in values) Add(v);
    }

    private void SortIfNecessary() {
      if (!sorted) {
        values.Sort();
        sorted = true;
      }
    }
  }
}