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 HeuristicLab.Data;


24 


25  namespace HeuristicLab.Problems.QuadraticAssignment.Views {


26  public static class MultidimensionalScaling {


27 


28  /// <summary>


29  /// Performs the KruskalShepard algorithm and applies a gradient descent method


30  /// to fit the coordinates such that the difference between the fit distances


31  /// and the actual distances is minimal.


32  /// </summary>


33  /// <param name="distances">A symmetric NxN matrix that specifies the distances between each element i and j. Diagonal elements are ignored.</param>


34  /// <param name="stress">Returns the stress between the fit distances and the actual distances.</param>


35  /// <returns>A Nx2 matrix where the first column represents the x and the second column the y coordinates.</returns>


36  public static DoubleMatrix MetricByDistance(DoubleMatrix distances, out double stress) {


37  if (distances == null) throw new ArgumentNullException("distances");


38  if (distances.Rows != distances.Columns) throw new ArgumentException("Distance matrix must be a square matrix.", "distances");


39  stress = 0.0;


40 


41  int dimension = distances.Rows;


42  if (dimension == 1) return new DoubleMatrix(new double[,] { { 0, 0 } });


43  else if (dimension == 2) return new DoubleMatrix(new double[,] { { 0, distances[0, 1] } });


44 


45  DoubleMatrix coordinates = new DoubleMatrix(dimension, 2);


46  double rad = (2 * Math.PI) / coordinates.Rows;


47  for (int i = 0; i < dimension; i++) {


48  coordinates[i, 0] = 10 * Math.Cos(rad * i);


49  coordinates[i, 1] = 10 * Math.Sin(rad * i);


50  }


51 


52  double epsg = 1e7;


53  double epsf = 0;


54  double epsx = 0;


55  int maxits = 0;


56  alglib.mincgstate state = null;


57  alglib.mincgreport rep;


58 


59  for (int iterations = 0; iterations < 10; iterations++) {


60  for (int i = 0; i < dimension; i++) {


61  double[] c = new double[] { coordinates[i, 0], coordinates[i, 1] };


62 


63  if (iterations == 0 && i == 0) {


64  alglib.mincgcreate(c, out state);


65  alglib.mincgsetcond(state, epsg, epsf, epsx, maxits);


66  } else {


67  alglib.mincgrestartfrom(state, c);


68  }


69  alglib.mincgoptimize(state, StressGradient, null, new Info(coordinates, distances, i));


70  alglib.mincgresults(state, out c, out rep);


71 


72  coordinates[i, 0] = c[0];


73  coordinates[i, 1] = c[1];


74  }


75  }


76  stress = CalculateNormalizedStress(dimension, distances, coordinates);


77  return coordinates;


78  }


79 


80  private static void StressGradient(double[] x, ref double func, double[] grad, object obj) {


81  func = 0; grad[0] = 0; grad[1] = 0;


82  Info info = (obj as Info);


83  for (int i = 0; i < info.Coordinates.Rows; i++) {


84  double c = info.Distances[info.Row, i];


85  if (i != info.Row) {


86  double a = info.Coordinates[i, 0];


87  double b = info.Coordinates[i, 1];


88  func += Stress(x, c, a, b);


89  grad[0] += ((2 * x[0]  2 * a) * Math.Sqrt(x[1] * x[1]  2 * b * x[1] + x[0] * x[0]  2 * a * x[0] + b * b + a * a)  2 * c * x[0] + 2 * a * c) / Math.Sqrt(x[1] * x[1]  2 * b * x[1] + x[0] * x[0]  2 * a * x[0] + b * b + a * a);


90  grad[1] += ((2 * x[1]  2 * b) * Math.Sqrt(x[1] * x[1]  2 * b * x[1] + x[0] * x[0]  2 * a * x[0] + b * b + a * a)  2 * c * x[1] + 2 * b * c) / Math.Sqrt(x[1] * x[1]  2 * b * x[1] + x[0] * x[0]  2 * a * x[0] + b * b + a * a);


91  }


92  }


93  }


94 


95  private static double Stress(double[] x, double distance, double xCoord, double yCoord) {


96  return Stress(x[0], x[1], distance, xCoord, yCoord);


97  }


98 


99  private static double Stress(double x, double y, double distance, double otherX, double otherY) {


100  double d = Math.Sqrt((x  otherX) * (x  otherX)


101  + (y  otherY) * (y  otherY));


102  return (d  distance) * (d  distance);


103  }


104 


105  public static double CalculateNormalizedStress(int dimension, DoubleMatrix distances, DoubleMatrix coordinates) {


106  double stress = 0;


107  for (int i = 0; i < dimension  1; i++) {


108  for (int j = i + 1; j < dimension; j++) {


109  if (distances[i, j] != 0) {


110  stress += Stress(coordinates[i, 0], coordinates[i, 1], distances[i, j], coordinates[j, 0], coordinates[j, 1])


111  / (distances[i, j] * distances[i, j]);


112  }


113  }


114  }


115  return stress;


116  }


117 


118  private class Info {


119  public DoubleMatrix Coordinates { get; set; }


120  public DoubleMatrix Distances { get; set; }


121  public int Row { get; set; }


122 


123  public Info(DoubleMatrix c, DoubleMatrix d, int r) {


124  Coordinates = c;


125  Distances = d;


126  Row = r;


127  }


128  }


129  }


130  } 
