#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2016 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.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Encodings.RealVectorEncoding;
using HeuristicLab.Parameters;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
using HeuristicLab.Problems.DataAnalysis;

// ReSharper disable once CheckNamespace
namespace HeuristicLab.Algorithms.EGO {

  [StorableClass]
  [Item("ExpectedImprovementMeassure", "Extension of the Expected Improvement to a weighted version by ANDRAS SÓBESTER , STEPHEN J. LEARY and ANDY J. KEANE   in \n On the Design of Optimization Strategies Based on Global Response Surface Approximation Models")]
  public class ExpectedImprovement : InfillCriterionBase {

    #region ParameterNames
    private const string ExploitationWeightParameterName = "ExploitationWeight";
    #endregion

    #region ParameterProperties
    public IFixedValueParameter<DoubleValue> ExploitationWeightParameter
    {
      get { return Parameters[ExploitationWeightParameterName] as IFixedValueParameter<DoubleValue>; }
    }
    #endregion

    #region Properties
    private double ExploitationWeight
    {
      get { return ExploitationWeightParameter.Value.Value; }
    }

    #endregion

    #region HL-Constructors, Serialization and Cloning 
    [StorableConstructor]
    private ExpectedImprovement(bool deserializing) : base(deserializing) { }
    [StorableHook(HookType.AfterDeserialization)]
    private void AfterDeserialization() {
      RegisterEventhandlers();
    }
    private ExpectedImprovement(ExpectedImprovement original, Cloner cloner) : base(original, cloner) {
      RegisterEventhandlers();
    }
    public ExpectedImprovement() {
      Parameters.Add(new FixedValueParameter<DoubleValue>(ExploitationWeightParameterName, "A value between 0 and 1 indicating the focus on exploration (0) or exploitation (1)", new DoubleValue(0.5)));
      RegisterEventhandlers();
    }
    public override IDeepCloneable Clone(Cloner cloner) {
      return new ExpectedImprovement(this, cloner);
    }
    #endregion

    public override double Evaluate(IRegressionSolution solution, RealVector vector, bool maximization) {
      if (maximization) throw new NotImplementedException("Expected Improvement for maximization not yet implemented");
      var model = solution.Model as IConfidenceRegressionModel;
      if (model == null) throw new ArgumentException("can not calculate EI without confidence measure");
      var yhat = model.GetEstimation(vector);
      var min = solution.ProblemData.TargetVariableTrainingValues.Min();
      var s = Math.Sqrt(model.GetVariance(vector));
      return GetEstimatedImprovement(min, yhat, s, ExploitationWeight);
    }

    public override bool Maximization(bool expensiveProblemMaximization) {
      return true;
    }

    #region Eventhandling
    private void RegisterEventhandlers() {
      DeregisterEventhandlers();
      ExploitationWeightParameter.Value.ValueChanged += OnExploitationWeightChanged;
    }
    private void DeregisterEventhandlers() {
      ExploitationWeightParameter.Value.ValueChanged -= OnExploitationWeightChanged;
    }
    private void OnExploitationWeightChanged(object sender, EventArgs e) {
      ExploitationWeightParameter.Value.ValueChanged -= OnExploitationWeightChanged;
      ExploitationWeightParameter.Value.Value = Math.Max(0, Math.Min(ExploitationWeight, 1));
      ExploitationWeightParameter.Value.ValueChanged += OnExploitationWeightChanged;
    }
    #endregion

    #region Helpers
    private static double GetEstimatedImprovement(double ymin, double yhat, double s, double w) {
      if (Math.Abs(s) < double.Epsilon) return 0;
      var val = (ymin - yhat) / s;
      var res = w * (ymin - yhat) * StandardNormalDistribution(val) + (1 - w) * s * StandardNormalDensity(val);
      return double.IsInfinity(res) || double.IsNaN(res) ? 0 : res;
    }

    private static double StandardNormalDensity(double x) {
      if (Math.Abs(x) > 10) return 0;
      return Math.Exp(-0.5 * x * x) / Math.Sqrt(2 * Math.PI);
    }

    //taken from https://www.johndcook.com/blog/2009/01/19/stand-alone-error-function-erf/
    private static double StandardNormalDistribution(double x) {
      if (x > 10) return 1;
      if (x < -10) return 0;
      const double a1 = 0.254829592;
      const double a2 = -0.284496736;
      const double a3 = 1.421413741;
      const double a4 = -1.453152027;
      const double a5 = 1.061405429;
      const double p = 0.3275911;
      var sign = x < 0 ? -1 : 1;
      x = Math.Abs(x) / Math.Sqrt(2.0);
      var t = 1.0 / (1.0 + p * x);
      var y = 1.0 - ((((a5 * t + a4) * t + a3) * t + a2) * t + a1) * t * Math.Exp(-x * x);
      return 0.5 * (1.0 + sign * y);
    }
    #endregion
  }
}