#region License Information /* HeuristicLab * Copyright (C) 2002-2019 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; using HeuristicLab.Common; using HEAL.Attic; namespace HeuristicLab.Problems.DataAnalysis { [StorableType("849e42d3-8934-419d-9aff-64ad81c06b67")] public class Interval : IEquatable { [Storable] public double LowerBound { get; private set; } [Storable] public double UpperBound { get; private set; } [StorableConstructor] protected Interval(StorableConstructorFlag _) { } public Interval(double lowerBound, double upperBound) { if (lowerBound > upperBound) throw new ArgumentException("LowerBound must be smaller than UpperBound."); this.LowerBound = lowerBound; this.UpperBound = upperBound; } public bool Contains(double value) { return LowerBound <= value && value <= UpperBound; } public override string ToString() { return "Interval: [" + LowerBound + ", " + UpperBound + "]"; } public bool IsInfiniteOrUndefined { get { return double.IsInfinity(LowerBound) || double.IsInfinity(UpperBound) || double.IsNaN(LowerBound) || double.IsNaN(UpperBound); } } public static Interval GetInterval(IEnumerable values) { if (values == null) throw new ArgumentNullException("values"); if (!values.Any()) throw new ArgumentException($"No values are present."); var min = double.MaxValue; var max = double.MinValue; foreach (var value in values) { //If an value is NaN return an interval [NaN, NaN] if (double.IsNaN(value)) return new Interval(double.NaN, double.NaN); if (value < min) min = value; if (value > max) max = value; } return new Interval(min, max); } #region Equals, GetHashCode, == , != public bool Equals(Interval other) { if (other == null) return false; return (UpperBound.IsAlmost(other.UpperBound) || (double.IsNaN(UpperBound) && double.IsNaN(other.UpperBound))) && (LowerBound.IsAlmost(other.LowerBound) || (double.IsNaN(LowerBound) && double.IsNaN(other.LowerBound))); } public override bool Equals(object obj) { return Equals(obj as Interval); } public override int GetHashCode() { return LowerBound.GetHashCode() ^ UpperBound.GetHashCode(); } public static bool operator ==(Interval interval1, Interval interval2) { if (ReferenceEquals(interval1, null)) return ReferenceEquals(interval2, null); return interval1.Equals(interval2); } public static bool operator !=(Interval interval1, Interval interval2) { return !(interval1 == interval2); } #endregion #region operations // [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2] public static Interval Add(Interval a, Interval b) { return new Interval(a.LowerBound + b.LowerBound, a.UpperBound + b.UpperBound); } // [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1] public static Interval Subtract(Interval a, Interval b) { return new Interval(a.LowerBound - b.UpperBound, a.UpperBound - b.LowerBound); } // [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)] public static Interval Multiply(Interval a, Interval b) { double v1 = a.LowerBound * b.LowerBound; double v2 = a.LowerBound * b.UpperBound; double v3 = a.UpperBound * b.LowerBound; double v4 = a.UpperBound * b.UpperBound; double min = Math.Min(Math.Min(v1, v2), Math.Min(v3, v4)); double max = Math.Max(Math.Max(v1, v2), Math.Max(v3, v4)); return new Interval(min, max); } //mkommend: Division by intervals containing 0 is implemented as defined in //http://en.wikipedia.org/wiki/Interval_arithmetic public static Interval Divide(Interval a, Interval b) { if (b.Contains(0.0)) { if (b.LowerBound.IsAlmost(0.0)) return Interval.Multiply(a, new Interval(1.0 / b.UpperBound, double.PositiveInfinity)); else if (b.UpperBound.IsAlmost(0.0)) return Interval.Multiply(a, new Interval(double.NegativeInfinity, 1.0 / b.LowerBound)); else return new Interval(double.NegativeInfinity, double.PositiveInfinity); } return Interval.Multiply(a, new Interval(1.0 / b.UpperBound, 1.0 / b.LowerBound)); } public static Interval Sine(Interval a) { if (Math.Abs(a.UpperBound - a.LowerBound) >= Math.PI * 2) return new Interval(-1, 1); //divide the interval by PI/2 so that the optima lie at x element of N (0,1,2,3,4,...) double Pihalf = Math.PI / 2; Interval scaled = Interval.Divide(a, new Interval(Pihalf, Pihalf)); //move to positive scale if (scaled.LowerBound < 0) { int periodsToMove = Math.Abs((int)scaled.LowerBound / 4) + 1; scaled = Interval.Add(scaled, new Interval(periodsToMove * 4, periodsToMove * 4)); } double scaledLowerBound = scaled.LowerBound % 4.0; double scaledUpperBound = scaled.UpperBound % 4.0; if (scaledUpperBound < scaledLowerBound) scaledUpperBound += 4.0; List sinValues = new List(); sinValues.Add(Math.Sin(scaledLowerBound * Pihalf)); sinValues.Add(Math.Sin(scaledUpperBound * Pihalf)); int startValue = (int)Math.Ceiling(scaledLowerBound); while (startValue < scaledUpperBound) { sinValues.Add(Math.Sin(startValue * Pihalf)); startValue += 1; } return new Interval(sinValues.Min(), sinValues.Max()); } public static Interval Cosine(Interval a) { return Interval.Sine(Interval.Subtract(a, new Interval(Math.PI / 2, Math.PI / 2))); } public static Interval Tangens(Interval a) { return Interval.Divide(Interval.Sine(a), Interval.Cosine(a)); } public static Interval Logarithm(Interval a) { return new Interval(Math.Log(a.LowerBound), Math.Log(a.UpperBound)); } public static Interval Exponential(Interval a) { return new Interval(Math.Exp(a.LowerBound), Math.Exp(a.UpperBound)); } public static Interval Power(Interval a, Interval b) { if (a.Contains(0.0) && b.LowerBound < 0) return new Interval(double.NaN, double.NaN); int bLower = (int)Math.Round(b.LowerBound); int bUpper = (int)Math.Round(b.UpperBound); List powerValues = new List(); powerValues.Add(Math.Pow(a.UpperBound, bUpper)); powerValues.Add(Math.Pow(a.UpperBound, bUpper - 1)); powerValues.Add(Math.Pow(a.UpperBound, bLower)); powerValues.Add(Math.Pow(a.UpperBound, bLower + 1)); powerValues.Add(Math.Pow(a.LowerBound, bUpper)); powerValues.Add(Math.Pow(a.LowerBound, bUpper - 1)); powerValues.Add(Math.Pow(a.LowerBound, bLower)); powerValues.Add(Math.Pow(a.LowerBound, bLower + 1)); return new Interval(powerValues.Min(), powerValues.Max()); } public static Interval Square(Interval a) { if (a.UpperBound <= 0) return new Interval(a.UpperBound * a.UpperBound, a.LowerBound * a.LowerBound); // interval is negative else if (a.LowerBound >= 0) return new Interval(a.LowerBound * a.LowerBound, a.UpperBound * a.UpperBound); // interval is positive else return new Interval(0, Math.Max(a.LowerBound*a.LowerBound, a.UpperBound*a.UpperBound)); // interval goes over zero } public static Interval Cube(Interval a) { return new Interval(Math.Pow(a.LowerBound, 3), Math.Pow(a.UpperBound, 3)); } public static Interval Root(Interval a, Interval b) { int lower = (int)Math.Round(b.LowerBound); int higher = (int)Math.Round(b.UpperBound); return new Interval(Math.Pow(a.LowerBound, 1.0 / higher), Math.Pow(a.UpperBound, 1.0 / lower)); } public static Interval SquareRoot(Interval a) { if (a.LowerBound < 0) return new Interval(double.NaN, double.NaN); return new Interval(Math.Sqrt(a.LowerBound), Math.Sqrt(a.UpperBound)); } public static Interval CubicRoot(Interval a) { if (a.LowerBound < 0) return new Interval(double.NaN, double.NaN); return new Interval(Math.Pow(a.LowerBound, 1.0/3), Math.Pow(a.UpperBound, 1.0/3)); } #endregion } }