#region License Information
/* HeuristicLab
* Copyright (C) 2002-2013 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.Analysis.AlgorithmBehavior.Analyzers {
/*
* Calculate Convex Hull using Linear Programming as described in
* J.B. Rosen et. al., 1989, Efficient computation of convex hull in Rd
* and
* P.M. Pardalos et. al., 1995,
* Linear programming approaches to the convex hull problem in Rm
*
*/
public static class LPHull {
public static List Calculate(double[][] inputs) {
List C = new List();
List E = new List();
//Phase 1
double[][] A = SortA(inputs);
//Phase 2
C.Add(A[0]);
for (int i = 1; i < A.Length; i++) {
C.Add(A[i]);
if (!EXT(C, A[i], C.Count - 1)) {
C.Remove(A[i]);
}
}
//Phase 3
for (int i = 0; i < C.Count; i++) {
if (EXT(C, C[i], i)) {
E.Add(C[i]);
}
}
return E;
}
//sort A decreasing by distance to center of polytope
public static double[][] SortA(double[][] A) {
int length = A[0].Length;
double[] maxs = new double[length];
double[] mins = new double[length];
double[][] sortedA = new double[A.Length][];
for (int i = 0; i < maxs.Length; i++) {
maxs[i] = double.MinValue;
mins[i] = double.MaxValue;
}
for (int i = 0; i < A.Length; i++) {
for (int j = 0; j < A[i].Length; j++) {
if (A[i][j] > maxs[j]) maxs[j] = A[i][j];
if (A[i][j] < mins[j]) mins[j] = A[i][j];
}
}
double[] d = new double[length];
double[] r = new double[length];
//calculate center
for (int i = 0; i < length; i++) {
d[i] = (maxs[i] + mins[i]) / 2.0;
}
//calculate length of sides of rectangle
for (int i = 0; i < length; i++) {
r[i] = maxs[i] - mins[i];
}
VertexComparer comparer = new VertexComparer();
comparer.d = d;
comparer.r = r;
sortedA = A.OrderByDescending(x => x, comparer).ToArray();
return sortedA;
}
///
/// Checks if alpha is an extreme point (lies on convex hull) of A.
/// Returns true if alpha is an extreme point, else false.
///
public static bool EXT(List A, double[] alpha, int aIdx = -1) {
alglib.minbleicstate state;
int N = alpha.Length;
int K = A.Count;
double[] init = new double[K];
double[] lowerBound = new double[K];
double[] upperBound = new double[K];
double[] x;
alglib.minbleicreport rep;
double[,] c = new double[N + 1, K + 1];
int[] ct = new int[N + 1]; //init with 0, means equal
for (int i = 0; i < K; i++) {
init[i] = 0.0;
lowerBound[i] = 0.0;
upperBound[i] = double.MaxValue;
}
init[aIdx] = 1.0;
//last column gets b
for (int i = 0; i < N; i++) {
c[i, K] = alpha[i];
}
//sum(x) == 1 constraint
for (int i = 0; i < K + 1; i++) {
c[N, i] = 1.0;
}
//other constraints
for (int i = 0; i < K; i++) {
for (int j = 0; j < N; j++) {
c[j, i] = A[i][j];
}
}
alglib.minbleiccreate(init, out state);
alglib.minbleicsetbc(state, lowerBound, upperBound);
alglib.minbleicsetlc(state, c, ct);
alglib.minbleicsetcond(state, 0.0, 0.0, 0.0, 0);
alglib.minbleicoptimize(state, Func, null, aIdx);
alglib.minbleicresults(state, out x, out rep);
if (rep.terminationtype < 0) throw new ArgumentException("minbleic terminated with error");
if (rep.terminationtype == 5) Console.WriteLine("max number of iterations reached in minbleic");
return x[aIdx] >= 1.0;
}
private static void Func(double[] x, ref double func, double[] grad, object obj) {
int aIdx = (int)obj;
func = x[aIdx];
for (int i = 0; i < grad.Length; i++) {
grad[i] = 0;
}
grad[aIdx] = 1;
}
}
}