source: branches/FitnessLandscapeAnalysis/HeuristicLab.Analysis.FitnessLandscape/Analysis/InformationAnalysis.cs @ 7403

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

namespace HeuristicLab.Analysis.FitnessLandscape.Analysis {

  public class InformationAnalysis {

    public class Peak {
      public double QualityDelta { get; private set; }
      public double Value { get; private set; }
      public Peak(double qualityDelta, double value) {
        QualityDelta = qualityDelta;
        Value = value;
      }
    }

    public List<double> InformationContent { get; private set; }
    public List<double> PartialInformationContent { get; private set; }
    public List<double> DensityBasinInformation { get; private set; }
    public List<double> QualityDelta { get; private set; }
    public double InformationStability { get; private set; }
    public int Regularity { get; private set; }
    public Peak PeakInformationContent { get; private set; }
    public Peak PeakPartialInformationContent { get; private set; }
    public Peak PeakDensityBasinInformation { get; private set; }

    public InformationAnalysis(IEnumerable<double> qualities, int nQuantiles) {
      InformationContent = new List<double>();
      PartialInformationContent = new List<double>();
      DensityBasinInformation = new List<double>();
      QualityDelta = new List<double>();
      PerformAnalysis(qualities, nQuantiles);
    }

    private void PerformAnalysis(IEnumerable<double> qualities, int nQuantiles) {
      var differences = Differences(qualities).ToList();
      InformationStability = differences.Select(d => Math.Abs(d)).Max();
      Regularity = new HashSet<double>(differences).Count;
      var thresholds = UniqueThresholdCalculator.DetermineThresholds(differences, nQuantiles).ToList();
      foreach (var eps in thresholds) {
        var shapes = Shapes(eps, differences).ToList();
        int[] shape_counts = CountShapes(shapes);
        QualityDelta.Add(eps);
        InformationContent.Add(CalculateInformationContent(shape_counts, shapes.Count));
        PartialInformationContent.Add(CalculatePartialInformationContent(eps, differences));
        DensityBasinInformation.Add(CalculateDensityBasinInformation(shape_counts, shapes.Count));
      }
      PeakDensityBasinInformation = GetPeak(QualityDelta, InformationContent);
      PeakPartialInformationContent = GetPeak(QualityDelta, PartialInformationContent);
      PeakDensityBasinInformation = GetPeak(QualityDelta, DensityBasinInformation);
    }

    public static Peak GetPeak(IEnumerable<double> indexes, IEnumerable<double> values) {
      var max = indexes.Zip(values, (i, v) => new { i, v }).OrderByDescending(p => p.v).First();
      return new Peak(max.i, max.v);
    }

    public enum Shape {
      DecDec = -4,
      EquDec = -3,
      IncDec = -2,
      DecEqu = -1,
      EquEqu = 0,
      IncEqu = 1,
      DecInc = 2,
      EquInc = 3,
      IncInc = 4
    }

    private static IEnumerable<Shape> Shapes(double eps, IEnumerable<double> differences) {
      return Utils.Delta(differences, (x, y) =>
        (Shape)
          ((x >= eps ? 1 : (x <= -eps ? -1 : 0)) +
           (y >= eps ? 3 : (y <= -eps ? -3 : 0))));
    }

    private static double CalculateInformationContent(int[] shape_counts, int total_n_shapes) {
      return
        -Entropy(shape_counts[(int)Shape.EquDec + 4], total_n_shapes, 6)
        - Entropy(shape_counts[(int)Shape.IncDec + 4], total_n_shapes, 6)
        - Entropy(shape_counts[(int)Shape.DecEqu + 4], total_n_shapes, 6)
        - Entropy(shape_counts[(int)Shape.IncEqu + 4], total_n_shapes, 6)
        - Entropy(shape_counts[(int)Shape.DecInc + 4], total_n_shapes, 6)
        - Entropy(shape_counts[(int)Shape.EquInc + 4], total_n_shapes, 6);
    }

    private static double CalculateDensityBasinInformation(int[] shape_counts, int total_n_shapes) {
      return
        -Entropy(shape_counts[(int)Shape.DecDec + 4], total_n_shapes, 3)
        - Entropy(shape_counts[(int)Shape.EquEqu + 4], total_n_shapes, 3)
        - Entropy(shape_counts[(int)Shape.IncInc + 4], total_n_shapes, 3);
    }

    private static double CalculatePartialInformationContent(double eps, List<double> differences) {
      int slope = 0;
      int nPeaks = 0;
      foreach (var d in differences) {
        if (d >= eps) {
          if (slope < 0) nPeaks++;
          slope = +1;
        } else if (d <= -eps) {
          if (slope > 0) nPeaks++;
          slope = -1;
        }
      }
      return 1.0 * nPeaks / differences.Count;
    }

    private static int[] CountShapes(IEnumerable<Shape> shapes) {
      int[] shape_counts = new int[9];
      foreach (var s in shapes) {
        shape_counts[(int)s + 4]++;
      }
      return shape_counts;
    }

    private static double Entropy(int count, int total, int n_cases) {
      if (count == 0)
        return 0;
      double freq = 1.0 * count / total;
      return freq * Math.Log(freq, n_cases);
    }

    private static IEnumerable<double> Differences(IEnumerable<double> values) {
      return Utils.Delta(values, (x, y) => y - x);
    }

  }
}