#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2018 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.Collections.Generic;
using System.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Optimization;
using HeuristicLab.Parameters;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
using HeuristicLab.Problems.DataAnalysis;
using HeuristicLab.Random;
using HeuristicLab.Selection;

namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Regression {
  /// <summary>
  /// eps-Lexicase Selection
  /// </summary>
  [Item("EpsLexicaseSelection", "")]
  [StorableClass]
  public sealed class EpsLexicaseSelection : StochasticSingleObjectiveSelector, ISingleObjectiveSelector {

    [StorableConstructor]
    private EpsLexicaseSelection(bool deserializing) : base(deserializing) { }
    private EpsLexicaseSelection(EpsLexicaseSelection original, Cloner cloner) : base(original, cloner) { }
    public override IDeepCloneable Clone(Cloner cloner) {
      return new EpsLexicaseSelection(this, cloner);
    }

    public EpsLexicaseSelection()
      : base() {
      Parameters.Add(new ScopeTreeLookupParameter<DoubleArray>("Errors", 1));

      var validPolicies = new ItemSet<StringValue>(new string[] { "ϵ_e", "ϵ_y", "ϵ_e,λ", "ϵ_y,λ" }.Select(s => new StringValue(s).AsReadOnly()));
      Parameters.Add(new ConstrainedValueParameter<StringValue>("Policy", "The selection policy (see La Cava, Spector, Danai: eps-Lexicase Selection for Regression, GECCO 2016)", validPolicies));
      Parameters.Add(new ValueParameter<DoubleValue>("ϵ", "The ϵ value for ϵ_e and ϵ_y policies", new DoubleValue(1.0)));
      Parameters.Add(new LookupParameter<DoubleValue>("AvgConsideredTestCases", "The average number of considered test cases for selection."));
    }

    [StorableHook(HookType.AfterDeserialization)]
    private void AfterDeserialization() {
      // remove
      if (!Parameters.ContainsKey("AvgConsideredTestCases")) {
        Parameters.Add(new LookupParameter<DoubleValue>("AvgConsideredTestCases", "The average number of considered test cases for selection."));
      }
    }

    protected override IScope[] Select(List<IScope> scopes) {
      // NOT efficiently implemented, used only for exploration of diversity for a paper

      int parentCount = NumberOfSelectedSubScopesParameter.ActualValue.Value;
      bool copy = CopySelectedParameter.Value.Value;
      if (!copy) throw new ArgumentException("copy is false in eps-lexicase selection.");
      IRandom random = RandomParameter.ActualValue;
      bool maximization = MaximizationParameter.ActualValue.Value;
      IScope[] selected = new IScope[parentCount];

      int nScopes = scopes.Count();
      var errors = (ItemArray<DoubleArray>)((IScopeTreeLookupParameter)Parameters["Errors"]).ActualValue;
      if (errors == null || !errors.Any())
        throw new ArgumentException("Have not found errors of models. Have you used an analyzer that calculates the errors and stores them in the scope?");

      var e = errors.Select(e_m => e_m.ToArray()).ToArray();
      errors = null; // don't use errors


      // see La Cava, Spector, Danai: eps-Lexicase Selection for Regression, GECCO 2016
      var ts = Enumerable.Range(0, e.First().Length).ToArray();

      double eps = ((DoubleValue)Parameters["ϵ"].ActualValue).Value;
      var selectionPolicy = ((StringValue)Parameters["Policy"].ActualValue).Value;

      var selectedScopes = new IScope[parentCount];
      var nCasesList = new List<double>(parentCount);
      var lambda_e = ts.Select(t=> MAD(e.Select(e_m => e_m[t]).ToArray())).ToArray();  

      for (int i = 0; i < parentCount; i++) {
        int nCases;
        var selectedIdx = SelectIdx(random, e, selectionPolicy, ts, eps, lambda_e, out nCases);
        nCasesList.Add(nCases);
        selectedScopes[i] = (IScope)(scopes[selectedIdx]).Clone();
      }
      Parameters["AvgConsideredTestCases"].ActualValue = new DoubleValue(nCasesList.Median());
      return selectedScopes;
    }

    public static int SelectIdx(IRandom random, double[][] errors, string selectionPolicy, int[] ts, double eps, double[] lambda_e, out int nCases) {
      ts.ShuffleInPlace(random);

      var activeModelIdxs = new SortedSet<int>(Enumerable.Range(0, errors.Length));
      nCases = 0;

      foreach (var t in ts) {
        if (activeModelIdxs.Count <= 1) break;
        nCases++;

        switch (selectionPolicy) {
          case "ϵ_e": {
              var bestError = errors.Select(err_m => err_m[t]).Min(); // as noted in corrected version of GECCO 2016 paper
              activeModelIdxs.RemoveWhere(modelIdx => errors[modelIdx][t] > bestError * (1 + eps));
              break;
            }
          case "ϵ_y": {
              activeModelIdxs.RemoveWhere(modelIdx => errors[modelIdx][t] > eps);
              break;
            }
          // Note in a corrected version of the GECCO Paper La Cava changed equations (2) and (5)
          //    Equations 2 and 5 have been corrected to
          //    indicate that the pass conditions for individuals in -lexicase
          //    selection are defined relative to the best error in the population
          //    on that training case, not in the selection pool.

          // a more recent and detailed description of the algorithm is given in https://arxiv.org/pdf/1709.05394.pdf
          // which indicates that semi-dynamic eps-lexicase performs best (Algorithm 4.2)
          // -> we also implement semi-dynamic eps-lexicase which calculates lambda over the whole population

          // I have not found a way to get reasonable convergence using MAD for lambda.
          // If lambda_e[t] is zero this means that all models are effectively the same => select randomly.
          // It seems that linear scaling (or the replacement of NaN outputs with the average of y) 
          // has the effect that MAD is zero (especially in the beginning), which means there is not selection pressure at the beginning.
          //  Semi-dynamic -Lexicase Selection
          case "ϵ_e,λ": {
              var bestError = activeModelIdxs.Select(modelIdx => errors[modelIdx][t]).Min(); // See   https://arxiv.org/pdf/1709.05394.pdf Alg 4.2
              activeModelIdxs.RemoveWhere(modelIdx => errors[modelIdx][t] > bestError + lambda_e[t]); // in the gecco paper the acceptance criterion is err < lambda_et this is later correct to err <= lambda_et
              break;
            }
          case "ϵ_y,λ": {
              activeModelIdxs.RemoveWhere(modelIdx => errors[modelIdx][t] > lambda_e[t]); // in the gecco paper the acceptance criterion is err < lambda_et this is later correct to err <= lambda_et
              break;
            }
          default: throw new ArgumentException("unknown policy " + selectionPolicy);
        }
      }

      if (!activeModelIdxs.Any())
        throw new ArgumentException("nothing left in the pool");
      else
        return activeModelIdxs.SampleRandom(random, 1).First();
    }

    private static double MAD(double[] x) {
      var median_x = x.Median();
      return x.Select(xi => Math.Abs(xi - median_x)).Median();
    }
    private static double StdDev(double[] x) {
      return x.StandardDeviation();
    }
  }
}