/*
 * This file is part of ELKI:
 * Environment for Developing KDD-Applications Supported by Index-Structures
 *
 * Copyright (C) 2022
 * ELKI Development Team
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Affero General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program 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 Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program. If not, see <http://www.gnu.org/licenses/>.
 */
package elki.distance;

import elki.data.NumberVector;
import elki.data.spatial.SpatialComparable;
import elki.data.type.SimpleTypeInformation;
import elki.utilities.Alias;
import elki.utilities.Priority;
import elki.utilities.documentation.Reference;
import elki.utilities.optionhandling.Parameterizer;

/**
 * Canberra distance function, a variation of Manhattan distance.
 * <p>
 * Canberra distance is defined as:
 * \[ \text{Canberra}(\vec{x},\vec{y}) :=
 * \sum\nolimits_i \tfrac{|x_i-y_i|}{|x_i|+|y_i|} \]
 * <p>
 * Reference:<br>
 * G. N. Lance, W. T. Williams<br>
 * Computer Programs for Hierarchical Polythetic Classification ("Similarity
 * Analyses")<br>
 * In: Computer Journal, Volume 9, Issue 1
 * 
 * @author Erich Schubert
 * @since 0.5.0
 */
@Priority(Priority.RECOMMENDED)
@Reference(authors = "G. N. Lance, W. T. Williams", //
    title = "Computer Programs for Hierarchical Polythetic Classification (Similarity Analyses)", //
    booktitle = "Computer Journal, Volume 9, Issue 1", //
    url = "https://doi.org/10.1093/comjnl/9.1.60", //
    bibkey = "doi:10.1093/comjnl/9.1.60")
@Alias({ "canberra" })
public class CanberraDistance implements SpatialPrimitiveDistance<NumberVector>, NumberVectorDistance<NumberVector> {
  /**
   * Static instance. Use this!
   */
  public static final CanberraDistance STATIC = new CanberraDistance();

  /**
   * Constructor.
   */
  protected CanberraDistance() {
    super();
  }

  @Override
  public double distance(NumberVector v1, NumberVector v2) {
    final int dim1 = v1.getDimensionality(), dim2 = v2.getDimensionality();
    final int mindim = (dim1 < dim2) ? dim1 : dim2;
    double agg = 0.;
    for(int d = 0; d < mindim; d++) {
      final double xd = v1.doubleValue(d), yd = v2.doubleValue(d);
      final double div = Math.abs(xd) + Math.abs(yd);
      if(div > 0) {
        agg += Math.abs(xd - yd) / div;
      }
    }
    for(int d = mindim; d < dim1; d++) {
      if(v1.doubleValue(d) != 0) {
        agg += 1;
      }
    }
    for(int d = mindim; d < dim2; d++) {
      if(v2.doubleValue(d) != 0) {
        agg += 1;
      }
    }
    return agg;
  }

  @Override
  public double minDist(SpatialComparable mbr1, SpatialComparable mbr2) {
    final int dim1 = mbr1.getDimensionality(), dim2 = mbr2.getDimensionality();
    final int mindim = (dim1 < dim2) ? dim1 : dim2;
    double agg = 0.;
    for(int d = 0; d < mindim; d++) {
      final double diff;
      if(mbr1.getMax(d) < mbr2.getMin(d)) {
        diff = mbr2.getMin(d) - mbr1.getMax(d);
      }
      else if(mbr1.getMin(d) > mbr2.getMax(d)) {
        diff = mbr1.getMin(d) - mbr2.getMax(d);
      }
      else { // The mbrs intersect!
        continue;
      }
      final double a1 = Math.max(-mbr1.getMin(d), mbr1.getMax(d));
      final double a2 = Math.max(-mbr2.getMin(d), mbr2.getMax(d));
      final double div = a1 + a2;
      // Cannot be 0, because then diff = 0 and we continued above.
      agg += diff / div;
    }
    for(int d = mindim; d < dim1; d++) {
      if(mbr1.getMin(d) > 0. || mbr1.getMax(d) < 0.) {
        agg += 1;
      }
    }
    for(int d = mindim; d < dim2; d++) {
      if(mbr2.getMin(d) > 0. || mbr2.getMax(d) < 0.) {
        agg += 1;
      }
    }
    return agg;
  }

  @Override
  public boolean isMetric() {
    // As this is also referred to as "canberra metric", it is probably a metric
    // But *maybe* only for positive numbers only?
    return true;
  }

  @Override
  public SimpleTypeInformation<? super NumberVector> getInputTypeRestriction() {
    return NumberVector.VARIABLE_LENGTH;
  }

  @Override
  public boolean equals(Object obj) {
    return obj == this || (obj != null && this.getClass().equals(obj.getClass()));
  }

  @Override
  public int hashCode() {
    return getClass().hashCode();
  }

  /**
   * Parameterization class.
   * 
   * @author Erich Schubert
   */
  public static class Par implements Parameterizer {
    @Override
    public CanberraDistance make() {
      return CanberraDistance.STATIC;
    }
  }
}
