#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 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]
  public abstract class ExpectedImprovementBase : InfillCriterionBase {

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

    #region ParameterProperties
    public IFixedValueParameter<DoubleValue> ExploitationWeightParameter => Parameters[ExploitationWeightParameterName] as IFixedValueParameter<DoubleValue>;
    #endregion

    #region Properties
    protected double ExploitationWeight => ExploitationWeightParameter.Value.Value;
    [Storable]
    protected double BestFitness;
    #endregion

    #region Constructors, Serialization and Cloning 
    [StorableConstructor]
    protected ExpectedImprovementBase(bool deserializing) : base(deserializing) { }
    [StorableHook(HookType.AfterDeserialization)]
    private void AfterDeserialization() {
      RegisterEventhandlers();
    }
    protected ExpectedImprovementBase(ExpectedImprovementBase original, Cloner cloner) : base(original, cloner) {
      BestFitness = original.BestFitness;
      RegisterEventhandlers();
    }
    protected ExpectedImprovementBase() {
      Parameters.Add(new FixedValueParameter<DoubleValue>(ExploitationWeightParameterName, "A value between 0 and 1 indicating the focus on exploration (0) or exploitation (1). 0.5 equates to the original EI by Jones et al.", new DoubleValue(0.5)));
      RegisterEventhandlers();
    }
    #endregion

    public override void Initialize() {
      var solution = RegressionSolution as IConfidenceRegressionSolution;
      if (solution == null) throw new ArgumentException("can not calculate EI without a regression solution providing confidence values");
      BestFitness = FindBestFitness(solution);
    }

    protected abstract double FindBestFitness(IConfidenceRegressionSolution solution);

    public override double Evaluate(RealVector vector) {
      var model = RegressionSolution.Model as IConfidenceRegressionModel;
      var yhat = model.GetEstimation(vector);
      var s = Math.Sqrt(model.GetVariance(vector));
      return Evaluate(vector, yhat, s);
    }

    protected abstract double Evaluate(RealVector vector, double estimatedFitness, double estimatedStandardDeviation);

    #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
    public static double GetEstimatedImprovement(double bestFitness, double estimatedFitness, double modelUncertainty, double weight, bool maximization) {
      if (Math.Abs(modelUncertainty) < double.Epsilon) return 0;
      var diff = maximization ? (estimatedFitness - bestFitness) : (bestFitness - estimatedFitness);
      var val = diff / modelUncertainty;
      var res = weight * diff * StandardNormalDistribution(val) + (1 - weight) * modelUncertainty * 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
  }
}